LMFDB - Embedded newform 77.2.n.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(17,77)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 27]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("77.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.n (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	77.17
Dual form			77.2.n.a.68.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0202070 - 0.0181945i) q^{2} +(-0.500742 - 1.12469i) q^{3} +(-0.208980 - 1.98831i) q^{4} +(-0.240558 - 1.13174i) q^{5} +(-0.0103446 + 0.0318373i) q^{6} +(-0.296416 + 2.62909i) q^{7} +(-0.0639186 + 0.0879764i) q^{8} +(0.993218 - 1.10308i) q^{9} +O(q^{10})$	\(q+(-0.0202070 - 0.0181945i) q^{2} +(-0.500742 - 1.12469i) q^{3} +(-0.208980 - 1.98831i) q^{4} +(-0.240558 - 1.13174i) q^{5} +(-0.0103446 + 0.0318373i) q^{6} +(-0.296416 + 2.62909i) q^{7} +(-0.0639186 + 0.0879764i) q^{8} +(0.993218 - 1.10308i) q^{9} +(-0.0157304 + 0.0272459i) q^{10} +(3.28543 + 0.453819i) q^{11} +(-2.13158 + 1.23067i) q^{12} +(1.77250 + 5.45520i) q^{13} +(0.0538247 - 0.0477330i) q^{14} +(-1.15239 + 0.837261i) q^{15} +(-3.90825 + 0.830725i) q^{16} +(-4.17932 - 4.64160i) q^{17} +(-0.0401399 + 0.00421888i) q^{18} +(-0.247610 + 2.35585i) q^{19} +(-2.19997 + 0.714814i) q^{20} +(3.10533 - 0.983123i) q^{21} +(-0.0581318 - 0.0689470i) q^{22} +(2.75747 + 4.77608i) q^{23} +(0.130953 + 0.0278348i) q^{24} +(3.34477 - 1.48919i) q^{25} +(0.0634375 - 0.142483i) q^{26} +(-5.25056 - 1.70601i) q^{27} +(5.28940 + 0.0399401i) q^{28} +(-2.64421 - 3.63944i) q^{29} +(0.0385199 + 0.00404861i) q^{30} +(-0.414010 + 1.94777i) q^{31} +(0.282440 + 0.163067i) q^{32} +(-1.13475 - 3.92232i) q^{33} +0.169834i q^{34} +(3.04675 - 0.296985i) q^{35} +(-2.40083 - 1.74430i) q^{36} +(2.53463 + 1.12849i) q^{37} +(0.0478669 - 0.0430995i) q^{38} +(5.24781 - 4.72515i) q^{39} +(0.114942 + 0.0511756i) q^{40} +(-1.14068 - 0.828752i) q^{41} +(-0.0806369 - 0.0366339i) q^{42} +1.93454i q^{43} +(0.215744 - 6.62729i) q^{44} +(-1.48732 - 0.858707i) q^{45} +(0.0311781 - 0.146681i) q^{46} +(4.63547 + 0.487208i) q^{47} +(2.89133 + 3.97957i) q^{48} +(-6.82427 - 1.55861i) q^{49} +(-0.0946827 - 0.0307643i) q^{50} +(-3.12758 + 7.02467i) q^{51} +(10.4762 - 4.66430i) q^{52} +(-8.74313 - 1.85841i) q^{53} +(0.0750582 + 0.130005i) q^{54} +(-0.276733 - 3.82741i) q^{55} +(-0.212352 - 0.194126i) q^{56} +(2.77358 - 0.901189i) q^{57} +(-0.0127862 + 0.121652i) q^{58} +(-8.79313 + 0.924195i) q^{59} +(1.90556 + 2.11634i) q^{60} +(-1.94887 + 0.414244i) q^{61} +(0.0438045 - 0.0318258i) q^{62} +(2.60569 + 2.93823i) q^{63} +(2.46665 + 7.59158i) q^{64} +(5.74746 - 3.31830i) q^{65} +(-0.0484347 + 0.0999046i) q^{66} +(-5.00725 + 8.67281i) q^{67} +(-8.35555 + 9.27978i) q^{68} +(3.99081 - 5.49288i) q^{69} +(-0.0669693 - 0.0494329i) q^{70} +(0.143110 - 0.440446i) q^{71} +(0.0335599 + 0.157887i) q^{72} +(0.0315641 + 0.300313i) q^{73} +(-0.0306850 - 0.0689197i) q^{74} +(-3.34973 - 3.01611i) q^{75} +4.73590 q^{76} +(-2.16699 + 8.50319i) q^{77} -0.192014 q^{78} +(-4.78548 - 4.30886i) q^{79} +(1.88032 + 4.22328i) q^{80} +(0.244985 + 2.33087i) q^{81} +(0.00797101 + 0.0375007i) q^{82} +(-1.25976 + 3.87715i) q^{83} +(-2.60370 - 5.96891i) q^{84} +(-4.24771 + 5.84647i) q^{85} +(0.0351979 - 0.0390913i) q^{86} +(-2.76916 + 4.79632i) q^{87} +(-0.249925 + 0.260033i) q^{88} +(12.9864 - 7.49768i) q^{89} +(0.0144307 + 0.0444130i) q^{90} +(-14.8676 + 3.04306i) q^{91} +(8.92007 - 6.48081i) q^{92} +(2.39794 - 0.509697i) q^{93} +(-0.0848046 - 0.0941850i) q^{94} +(2.72577 - 0.286490i) q^{95} +(0.0419693 - 0.399311i) q^{96} +(4.66426 - 1.51551i) q^{97} +(0.109540 + 0.155659i) q^{98} +(3.76374 - 3.17335i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9}+O(q^{10}) $ 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9	$ 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} - q^{11} - 12 q^{12} - 8 q^{14} - 27 q^{16} + 15 q^{17} + 20 q^{18} - 15 q^{19} - 76 q^{22} + 10 q^{23} + 75 q^{24} + q^{25} + 27 q^{26} - 40 q^{28} - 40 q^{29} + 25 q^{30} + 9 q^{31} + 42 q^{33} + 5 q^{35} - 38 q^{36} - q^{37} + 33 q^{38} - 45 q^{39} + 75 q^{40} + 64 q^{42} + 30 q^{44} - 84 q^{45} - 20 q^{46} + 3 q^{47} + 59 q^{49} + 30 q^{50} + 55 q^{51} - 15 q^{52} - 3 q^{53} - 8 q^{56} + 60 q^{57} + 46 q^{58} - 3 q^{59} - 15 q^{60} - 30 q^{61} - 40 q^{63} + 12 q^{64} - 93 q^{66} + 44 q^{67} - 75 q^{68} - 27 q^{70} + 20 q^{71} - 60 q^{72} - 60 q^{73} + 45 q^{74} - 57 q^{75} + 92 q^{78} - 70 q^{79} - 75 q^{80} - 29 q^{81} - 129 q^{82} - 125 q^{84} + 10 q^{85} - 62 q^{86} + 19 q^{88} + 6 q^{89} - 12 q^{91} + 30 q^{92} - 92 q^{93} + 105 q^{94} + 30 q^{95} + 75 q^{96} - 12 q^{99}+O(q^{100}) $ 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9 - q^11 - 12 * q^12 - 8 * q^14 - 27 * q^16 + 15 * q^17 + 20 * q^18 - 15 * q^19 - 76 * q^22 + 10 * q^23 + 75 * q^24 + q^25 + 27 * q^26 - 40 * q^28 - 40 * q^29 + 25 * q^30 + 9 * q^31 + 42 * q^33 + 5 * q^35 - 38 * q^36 - q^37 + 33 * q^38 - 45 * q^39 + 75 * q^40 + 64 * q^42 + 30 * q^44 - 84 * q^45 - 20 * q^46 + 3 * q^47 + 59 * q^49 + 30 * q^50 + 55 * q^51 - 15 * q^52 - 3 * q^53 - 8 * q^56 + 60 * q^57 + 46 * q^58 - 3 * q^59 - 15 * q^60 - 30 * q^61 - 40 * q^63 + 12 * q^64 - 93 * q^66 + 44 * q^67 - 75 * q^68 - 27 * q^70 + 20 * q^71 - 60 * q^72 - 60 * q^73 + 45 * q^74 - 57 * q^75 + 92 * q^78 - 70 * q^79 - 75 * q^80 - 29 * q^81 - 129 * q^82 - 125 * q^84 + 10 * q^85 - 62 * q^86 + 19 * q^88 + 6 * q^89 - 12 * q^91 + 30 * q^92 - 92 * q^93 + 105 * q^94 + 30 * q^95 + 75 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0202070	−	0.0181945i	−0.0142885	−	0.0128654i	0.661955	−	0.749543i	$-0.269727\pi$
$2$	−0.0202070	−	0.0181945i	−0.0142885	−	0.0128654i	−0.676244	+	0.736678i	$0.736393\pi$
$3$	−0.500742	−	1.12469i	−0.289104	−	0.649337i	0.709354	−	0.704852i	$-0.248987\pi$
$3$	−0.500742	−	1.12469i	−0.289104	−	0.649337i	−0.998458	+	0.0555148i	$0.982320\pi$
$4$	−0.208980	−	1.98831i	−0.104490	−	0.994154i
$5$	−0.240558	−	1.13174i	−0.107581	−	0.506129i	−0.998635	−	0.0522314i	$-0.983367\pi$
$5$	−0.240558	−	1.13174i	−0.107581	−	0.506129i	0.891054	−	0.453897i	$-0.149967\pi$
$6$	−0.0103446	+	0.0318373i	−0.00422315	+	0.0129975i
$7$	−0.296416	+	2.62909i	−0.112035	+	0.993704i
$7$	−0.296416	+	2.62909i	−0.112035	+	0.993704i
$8$	−0.0639186	+	0.0879764i	−0.0225986	+	0.0311044i
$9$	0.993218	−	1.10308i	0.331073	−	0.367693i
$10$	−0.0157304	+	0.0272459i	−0.00497440	+	0.00861591i
$11$	3.28543	+	0.453819i	0.990594	+	0.136832i
$11$	3.28543	+	0.453819i	0.990594	+	0.136832i
$12$	−2.13158	+	1.23067i	−0.615333	+	0.355263i
$13$	1.77250	+	5.45520i	0.491603	+	1.51300i	0.822184	+	0.569222i	$0.192755\pi$
$13$	1.77250	+	5.45520i	0.491603	+	1.51300i	−0.330581	+	0.943778i	$0.607245\pi$
$14$	0.0538247	−	0.0477330i	0.0143853	−	0.0127572i
$15$	−1.15239	+	0.837261i	−0.297546	+	0.216180i
$16$	−3.90825	+	0.830725i	−0.977063	+	0.207681i
$17$	−4.17932	−	4.64160i	−1.01363	−	1.12575i	−0.992032	−	0.125988i	$-0.959790\pi$
$17$	−4.17932	−	4.64160i	−1.01363	−	1.12575i	−0.0216020	−	0.999767i	$-0.506877\pi$
$18$	−0.0401399	+	0.00421888i	−0.00946107	+	0.000994399i
$19$	−0.247610	+	2.35585i	−0.0568055	+	0.540469i	0.928701	+	0.370830i	$0.120927\pi$
$19$	−0.247610	+	2.35585i	−0.0568055	+	0.540469i	−0.985506	+	0.169639i	$0.945740\pi$
$20$	−2.19997	+	0.714814i	−0.491929	+	0.159837i
$21$	3.10533	−	0.983123i	0.677639	−	0.214535i
$22$	−0.0581318	−	0.0689470i	−0.0123937	−	0.0146996i
$23$	2.75747	+	4.77608i	0.574973	+	0.995882i	0.996045	+	0.0888549i	$0.0283207\pi$
$23$	2.75747	+	4.77608i	0.574973	+	0.995882i	−0.421072	+	0.907027i	$0.638346\pi$
$24$	0.130953	+	0.0278348i	0.0267306	+	0.00568176i
$25$	3.34477	−	1.48919i	0.668953	−	0.297837i
$26$	0.0634375	−	0.142483i	0.0124411	−	0.0279432i
$27$	−5.25056	−	1.70601i	−1.01047	−	0.328322i
$28$	5.28940	+	0.0399401i	0.999602	+	0.00754798i
$29$	−2.64421	−	3.63944i	−0.491017	−	0.675827i	0.489558	−	0.871971i	$-0.337158\pi$
$29$	−2.64421	−	3.63944i	−0.491017	−	0.675827i	−0.980575	+	0.196144i	$0.937158\pi$
$30$	0.0385199	+	0.00404861i	0.00703275	+	0.000739171i
$31$	−0.414010	+	1.94777i	−0.0743585	+	0.349829i	−0.999560	−	0.0296459i	$-0.990562\pi$
$31$	−0.414010	+	1.94777i	−0.0743585	+	0.349829i	0.925202	+	0.379475i	$0.123895\pi$
$32$	0.282440	+	0.163067i	0.0499289	+	0.0288264i
$33$	−1.13475	−	3.92232i	−0.197535	−	0.682788i
$34$			0.169834i			0.0291262i
$35$	3.04675	−	0.296985i	0.514995	−	0.0501996i
$36$	−2.40083	−	1.74430i	−0.400138	−	0.290717i
$37$	2.53463	+	1.12849i	0.416690	+	0.185522i	0.604363	−	0.796709i	$-0.293428\pi$
$37$	2.53463	+	1.12849i	0.416690	+	0.185522i	−0.187673	+	0.982232i	$0.560094\pi$
$38$	0.0478669	−	0.0430995i	0.00776504	−	0.00699167i
$39$	5.24781	−	4.72515i	0.840323	−	0.756630i
$40$	0.114942	+	0.0511756i	0.0181740	+	0.00809158i
$41$	−1.14068	−	0.828752i	−0.178144	−	0.129429i	0.495140	−	0.868813i	$-0.335117\pi$
$41$	−1.14068	−	0.828752i	−0.178144	−	0.129429i	−0.673284	+	0.739384i	$0.735117\pi$
$42$	−0.0806369	−	0.0366339i	−0.0124425	−	0.00565274i
$43$			1.93454i			0.295014i	0.989061	+	0.147507i	$0.0471250\pi$
$43$			1.93454i			0.295014i	−0.989061	+	0.147507i	$0.952875\pi$
$44$	0.215744	−	6.62729i	0.0325246	−	0.999101i
$45$	−1.48732	−	0.858707i	−0.221717	−	0.128008i
$46$	0.0311781	−	0.146681i	0.00459695	−	0.0216270i
$47$	4.63547	+	0.487208i	0.676153	+	0.0710665i	0.436380	−	0.899762i	$-0.356260\pi$
$47$	4.63547	+	0.487208i	0.676153	+	0.0710665i	0.239773	+	0.970829i	$0.422927\pi$
$48$	2.89133	+	3.97957i	0.417328	+	0.574402i
$49$	−6.82427	−	1.55861i	−0.974896	−	0.222659i
$50$	−0.0946827	−	0.0307643i	−0.0133902	−	0.00435073i
$51$	−3.12758	+	7.02467i	−0.437949	+	0.983650i
$52$	10.4762	−	4.66430i	1.45279	−	0.646822i
$53$	−8.74313	−	1.85841i	−1.20096	−	0.255272i	−0.436358	−	0.899773i	$-0.643732\pi$
$53$	−8.74313	−	1.85841i	−1.20096	−	0.255272i	−0.764604	+	0.644501i	$0.777065\pi$
$54$	0.0750582	+	0.130005i	0.0102141	+	0.0176914i
$55$	−0.276733	−	3.82741i	−0.0373147	−	0.516089i
$56$	−0.212352	−	0.194126i	−0.0283767	−	0.0259411i
$57$	2.77358	−	0.901189i	0.367369	−	0.119365i
$58$	−0.0127862	+	0.121652i	−0.00167891	+	0.0159737i
$59$	−8.79313	+	0.924195i	−1.14477	+	0.120320i	−0.657865	−	0.753136i	$-0.728540\pi$
$59$	−8.79313	+	0.924195i	−1.14477	+	0.120320i	−0.486903	+	0.873456i	$0.661873\pi$
$60$	1.90556	+	2.11634i	0.246007	+	0.273218i
$61$	−1.94887	+	0.414244i	−0.249527	+	0.0530385i	−0.330977	−	0.943639i	$-0.607378\pi$
$61$	−1.94887	+	0.414244i	−0.249527	+	0.0530385i	0.0814501	+	0.996677i	$0.474045\pi$
$62$	0.0438045	−	0.0318258i	0.00556318	−	0.00404189i
$63$	2.60569	+	2.93823i	0.328287	+	0.370183i
$64$	2.46665	+	7.59158i	0.308332	+	0.948948i
$65$	5.74746	−	3.31830i	0.712885	−	0.411584i
$66$	−0.0484347	+	0.0999046i	−0.00596190	+	0.0122974i
$67$	−5.00725	+	8.67281i	−0.611733	+	1.05955i	0.379215	+	0.925309i	$0.376194\pi$
$67$	−5.00725	+	8.67281i	−0.611733	+	1.05955i	−0.990948	+	0.134244i	$0.957139\pi$
$68$	−8.35555	+	9.27978i	−1.01326	+	1.12534i
$69$	3.99081	−	5.49288i	0.480437	−	0.661265i
$70$	−0.0669693	−	0.0494329i	−0.00800436	−	0.00590836i
$71$	0.143110	−	0.440446i	0.0169840	−	0.0522713i	−0.942205	−	0.335036i	$-0.891252\pi$
$71$	0.143110	−	0.440446i	0.0169840	−	0.0522713i	0.959189	+	0.282765i	$0.0912515\pi$
$72$	0.0335599	+	0.157887i	0.00395508	+	0.0186072i
$73$	0.0315641	+	0.300313i	0.00369430	+	0.0351489i	0.996214	−	0.0869377i	$-0.0277081\pi$
$73$	0.0315641	+	0.300313i	0.00369430	+	0.0351489i	−0.992519	+	0.122087i	$0.961041\pi$
$74$	−0.0306850	−	0.0689197i	−0.00356706	−	0.00801175i
$75$	−3.34973	−	3.01611i	−0.386793	−	0.348270i
$76$	4.73590			0.543245
$77$	−2.16699	+	8.50319i	−0.246951	+	0.969028i
$78$	−0.192014			−0.0217414
$79$	−4.78548	−	4.30886i	−0.538408	−	0.484785i	0.354480	−	0.935064i	$-0.384658\pi$
$79$	−4.78548	−	4.30886i	−0.538408	−	0.484785i	−0.892888	+	0.450279i	$0.851325\pi$
$80$	1.88032	+	4.22328i	0.210227	+	0.472177i
$81$	0.244985	+	2.33087i	0.0272205	+	0.258986i
$82$	0.00797101	+	0.0375007i	0.000880251	+	0.00414126i
$83$	−1.25976	+	3.87715i	−0.138277	+	0.425572i	−0.996085	−	0.0883972i	$-0.971826\pi$
$83$	−1.25976	+	3.87715i	−0.138277	+	0.425572i	0.857809	+	0.513969i	$0.171826\pi$
$84$	−2.60370	−	5.96891i	−0.284087	−	0.651261i
$85$	−4.24771	+	5.84647i	−0.460729	+	0.634139i
$86$	0.0351979	−	0.0390913i	0.00379549	−	0.00421532i
$87$	−2.76916	+	4.79632i	−0.296885	+	0.514219i
$88$	−0.249925	+	0.260033i	−0.0266421	+	0.0277196i
$89$	12.9864	−	7.49768i	1.37655	−	0.794752i	0.384809	−	0.922996i	$-0.374267\pi$
$89$	12.9864	−	7.49768i	1.37655	−	0.794752i	0.991743	+	0.128244i	$0.0409340\pi$
$90$	0.0144307	+	0.0444130i	0.00152112	+	0.00468154i
$91$	−14.8676	+	3.04306i	−1.55855	+	0.319000i
$92$	8.92007	−	6.48081i	0.929982	−	0.675671i
$93$	2.39794	−	0.509697i	0.248654	−	0.0528531i
$94$	−0.0848046	−	0.0941850i	−0.00874693	−	0.00971444i
$95$	2.72577	−	0.286490i	0.279658	−	0.0293932i
$96$	0.0419693	−	0.399311i	0.00428347	−	0.0407545i
$97$	4.66426	−	1.51551i	0.473584	−	0.153877i	−0.0624937	−	0.998045i	$-0.519905\pi$
$97$	4.66426	−	1.51551i	0.473584	−	0.153877i	0.536078	+	0.844169i	$0.319905\pi$
$98$	0.109540	+	0.155659i	0.0110652	+	0.0157239i
$99$	3.76374	−	3.17335i	0.378271	−	0.318934i
$100$	−3.65995	−	6.33922i	−0.365995	−	0.633922i
$101$	12.9267	+	2.74765i	1.28625	+	0.273401i	0.799779	−	0.600295i	$-0.204950\pi$
$101$	12.9267	+	2.74765i	1.28625	+	0.273401i	0.486473	+	0.873696i	$0.338283\pi$
$102$	0.191009	−	0.0850428i	0.0189127	−	0.00842050i
$103$	3.34431	−	7.51145i	0.329525	−	0.740125i	−0.670473	−	0.741933i	$-0.733909\pi$
$103$	3.34431	−	7.51145i	0.329525	−	0.740125i	0.999998	+	0.00180848i	$0.000575659\pi$
$104$	−0.593224	−	0.192750i	−0.0581704	−	0.0189007i
$105$	−1.85965	−	3.27792i	−0.181483	−	0.319893i
$106$	0.142860	+	0.196630i	0.0138758	+	0.0190984i
$107$	−12.0042	−	1.26170i	−1.16049	−	0.121973i	−0.495353	−	0.868692i	$-0.664961\pi$
$107$	−12.0042	−	1.26170i	−1.16049	−	0.121973i	−0.665139	+	0.746719i	$0.731628\pi$
$108$	−2.29482	+	10.7963i	−0.220819	+	1.03887i
$109$	−12.5095	−	7.22235i	−1.19819	−	0.691776i	−0.238040	−	0.971255i	$-0.576505\pi$
$109$	−12.5095	−	7.22235i	−1.19819	−	0.691776i	−0.960152	+	0.279479i	$0.909838\pi$
$110$	−0.0640459	+	0.0823757i	−0.00610654	+	0.00785421i
$111$		−	3.41574i		−	0.324208i
$112$	−1.02558	−	10.5214i	−0.0969085	−	0.994179i
$113$	0.0554138	+	0.0402604i	0.00521289	+	0.00378738i	0.590389	−	0.807119i	$-0.298974\pi$
$113$	0.0554138	+	0.0402604i	0.00521289	+	0.00378738i	−0.585176	+	0.810906i	$0.698974\pi$
$114$	−0.0724424	−	0.0322534i	−0.00678485	−	0.00302081i
$115$	4.74194	−	4.26966i	0.442188	−	0.398148i
$116$	−6.68374	+	6.01807i	−0.620570	+	0.558763i
$117$	7.77800	+	3.46299i	0.719076	+	0.320153i
$118$	0.194498	+	0.141311i	0.0179050	+	0.0130088i
$119$	13.4420	−	9.61198i	1.23223	−	0.881128i
$120$		−	0.154900i		−	0.0141404i
$121$	10.5881	+	2.98198i	0.962554	+	0.271089i
$122$	0.0469177	+	0.0270880i	0.00424773	+	0.00245243i
$123$	−0.360899	+	1.69790i	−0.0325412	+	0.153094i
$124$	3.95928	+	0.416137i	0.355554	+	0.0373702i
$125$	−5.89038	−	8.10741i	−0.526852	−	0.725149i
$126$	0.000806311	−	0.106782i	7.18319e−5	−	0.00951292i
$127$	−1.40575	−	0.456755i	−0.124740	−	0.0405304i	0.245982	−	0.969274i	$-0.420890\pi$
$127$	−1.40575	−	0.456755i	−0.124740	−	0.0405304i	−0.370722	+	0.928744i	$0.620890\pi$
$128$	0.353582	−	0.794159i	0.0312526	−	0.0701944i
$129$	2.17575	−	0.968705i	0.191564	−	0.0852897i
$130$	−0.176514	−	0.0375192i	−0.0154813	−	0.00329065i
$131$	0.174669	+	0.302535i	0.0152609	+	0.0264326i	0.873555	−	0.486725i	$-0.161809\pi$
$131$	0.174669	+	0.302535i	0.0152609	+	0.0264326i	−0.858294	+	0.513158i	$0.828475\pi$
$132$	−7.56164	+	3.07592i	−0.658157	+	0.267724i
$133$	−6.12035	−	1.34930i	−0.530702	−	0.116999i
$134$	0.258979	−	0.0841474i	0.0223724	−	0.00726923i
$135$	−0.667691	+	6.35265i	−0.0574657	+	0.546749i
$136$	0.675488	−	0.0709966i	0.0579226	−	0.00608791i
$137$	6.58243	+	7.31052i	0.562375	+	0.624580i	0.955531	−	0.294891i	$-0.0952835\pi$
$137$	6.58243	+	7.31052i	0.562375	+	0.624580i	−0.393156	+	0.919472i	$0.628617\pi$
$138$	−0.180582	+	0.0383840i	−0.0153722	+	0.00326746i
$139$	10.7944	−	7.84259i	0.915569	−	0.665200i	−0.0268479	−	0.999640i	$-0.508547\pi$
$139$	10.7944	−	7.84259i	0.915569	−	0.665200i	0.942417	+	0.334439i	$0.108547\pi$
$140$	−1.22721	−	5.99582i	−0.103718	−	0.506739i
$141$	−1.77322	−	5.45741i	−0.149332	−	0.459597i
$142$	−0.0109055	+	0.00629630i	−0.000915170	+	0.000528374i
$143$	3.34776	+	18.7271i	0.279953	+	1.56604i
$144$	−2.96539	+	5.13620i	−0.247116	+	0.428017i
$145$	−3.48280	+	3.86805i	−0.289231	+	0.321224i
$146$	0.00482622	−	0.00664272i	0.000399420	−	0.000549755i
$147$	1.66425	+	8.45562i	0.137265	+	0.697408i
$148$	1.71410	−	5.27545i	0.140898	−	0.433640i
$149$	1.60137	+	7.53384i	0.131189	+	0.617197i	0.993786	+	0.111305i	$0.0355031\pi$
$149$	1.60137	+	7.53384i	0.131189	+	0.617197i	−0.862597	+	0.505891i	$0.831164\pi$
$150$	0.0128115	+	0.121893i	0.00104605	+	0.00995254i
$151$	−1.04302	−	2.34267i	−0.0848800	−	0.190644i	0.866119	−	0.499838i	$-0.166607\pi$
$151$	−1.04302	−	2.34267i	−0.0848800	−	0.190644i	−0.950999	+	0.309195i	$0.899941\pi$
$152$	−0.191432	−	0.172366i	−0.0155272	−	0.0139808i
$153$	−9.27103			−0.749519
$154$	0.198499	−	0.132397i	0.0159955	−	0.0106688i
$155$	2.30395			0.185058
$156$	−10.4917	−	9.44681i	−0.840012	−	0.756350i
$157$	−3.99394	−	8.97055i	−0.318751	−	0.715927i	0.681117	−	0.732175i	$-0.261495\pi$
$157$	−3.99394	−	8.97055i	−0.318751	−	0.715927i	−0.999868	+	0.0162476i	$0.994828\pi$
$158$	0.0183027	+	0.174139i	0.00145609	+	0.0138537i
$159$	2.28793	+	10.7639i	0.181445	+	0.853630i
$160$	0.116606	−	0.358875i	0.00921849	−	0.0283716i
$161$	−13.3741	+	5.83395i	−1.05403	+	0.459779i
$162$	0.0374586	−	0.0515574i	0.00294303	−	0.00405073i
$163$	12.8433	−	14.2640i	1.00597	−	1.11724i	0.0128739	−	0.999917i	$-0.495902\pi$
$163$	12.8433	−	14.2640i	1.00597	−	1.11724i	0.993094	−	0.117323i	$-0.0374313\pi$
$164$	−1.40944	+	2.44121i	−0.110058	+	0.190627i
$165$	−4.16606	+	2.22779i	−0.324328	+	0.173433i
$166$	0.0959987	−	0.0554249i	0.00745095	−	0.00430181i
$167$	−0.972816	−	2.99402i	−0.0752788	−	0.231684i	0.906336	−	0.422558i	$-0.138868\pi$
$167$	−0.972816	−	2.99402i	−0.0752788	−	0.231684i	−0.981615	+	0.190874i	$0.938868\pi$
$168$	−0.111997	+	0.336036i	−0.00864074	+	0.0259257i
$169$	−16.1002	+	11.6975i	−1.23848	+	0.899805i
$170$	0.192207	−	0.0408549i	0.0147416	−	0.00313343i
$171$	2.35276	+	2.61300i	0.179920	+	0.199821i
$172$	3.84646	−	0.404279i	0.293290	−	0.0308260i
$173$	−1.07724	+	10.2493i	−0.0819011	+	0.779237i	0.874075	+	0.485792i	$0.161469\pi$
$173$	−1.07724	+	10.2493i	−0.0819011	+	0.779237i	−0.955976	+	0.293446i	$0.905198\pi$
$174$	0.143223	−	0.0465360i	0.0108577	−	0.00352788i
$175$	2.92377	+	9.23512i	0.221016	+	0.698110i
$176$	−13.2173	+	0.955649i	−0.996290	+	0.0720348i
$177$	5.44252	+	9.42672i	0.409085	+	0.708556i
$178$	−0.398832	−	0.0847744i	−0.0298937	−	0.00635411i
$179$	−7.90044	+	3.51750i	−0.590506	+	0.262910i	−0.680161	−	0.733063i	$-0.738090\pi$
$179$	−7.90044	+	3.51750i	−0.590506	+	0.262910i	0.0896550	+	0.995973i	$0.471424\pi$
$180$	−1.39655	+	3.13671i	−0.104093	+	0.233797i
$181$	23.0894	+	7.50219i	1.71622	+	0.557633i	0.991349	−	0.131252i	$-0.0418998\pi$
$181$	23.0894	+	7.50219i	1.71622	+	0.557633i	0.724870	+	0.688886i	$0.241900\pi$
$182$	0.355797	+	0.209018i	0.0263735	+	0.0154934i
$183$	1.44177	+	1.98443i	0.106579	+	0.146693i
$184$	−0.596437	−	0.0626880i	−0.0439699	−	0.00462142i
$185$	0.667428	−	3.14000i	0.0490703	−	0.230858i
$186$	−0.0577288	−	0.0333298i	−0.00423288	−	0.00244386i
$187$	−11.6244	−	17.1463i	−0.850061	−	1.25386i
$188$		−	9.31856i		−	0.679626i
$189$	6.04162	−	13.2985i	0.439463	−	0.967326i
$190$	−0.0602922	−	0.0438048i	−0.00437405	−	0.00317794i
$191$	7.22678	+	3.21757i	0.522912	+	0.232815i	0.651179	−	0.758924i	$-0.274275\pi$
$191$	7.22678	+	3.21757i	0.522912	+	0.232815i	−0.128267	+	0.991740i	$0.540941\pi$
$192$	7.30298	−	6.57563i	0.527047	−	0.474556i
$193$	−6.24950	+	5.62708i	−0.449849	+	0.405046i	−0.862671	−	0.505766i	$-0.831210\pi$
$193$	−6.24950	+	5.62708i	−0.449849	+	0.405046i	0.412822	+	0.910812i	$0.364543\pi$
$194$	−0.121825	−	0.0542399i	−0.00874651	−	0.00389420i
$195$	−6.61004	−	4.80247i	−0.473355	−	0.343912i
$196$	−1.67287	+	13.8945i	−0.119491	+	0.992463i
$197$			12.7308i			0.907029i	0.891249	+	0.453515i	$0.149830\pi$
$197$			12.7308i			0.907029i	−0.891249	+	0.453515i	$0.850170\pi$
$198$	−0.133792	−	0.00435543i	−0.00950815	−	0.000309527i
$199$	−9.72371	−	5.61399i	−0.689295	−	0.397965i	0.114053	−	0.993475i	$-0.463617\pi$
$199$	−9.72371	−	5.61399i	−0.689295	−	0.397965i	−0.803348	+	0.595510i	$0.796950\pi$
$200$	−0.0827795	+	0.389447i	−0.00585340	+	0.0275381i
$201$	12.2615	+	1.28874i	0.864862	+	0.0909006i
$202$	−0.211217	−	0.290716i	−0.0148612	−	0.0204547i
$203$	10.3522	−	5.87308i	0.726583	−	0.412209i
$204$	14.6208	+	4.75059i	1.02366	+	0.332608i
$205$	−0.663530	+	1.49031i	−0.0463429	+	0.104088i
$206$	−0.204246	+	0.0909360i	−0.0142305	+	0.00633581i
$207$	8.00717	+	1.70198i	0.556537	+	0.118296i
$208$	−11.4591	−	19.8478i	−0.794549	−	1.37620i
$209$	−1.88263	+	7.62760i	−0.130224	+	0.527612i
$210$	−0.0220621	+	0.100072i	−0.00152243	+	0.00690566i
$211$	7.24960	−	2.35554i	0.499083	−	0.162162i	−0.0486487	−	0.998816i	$-0.515491\pi$
$211$	7.24960	−	2.35554i	0.499083	−	0.162162i	0.547732	+	0.836654i	$0.315491\pi$
$212$	−1.86796	+	17.7724i	−0.128292	+	1.22061i
$213$	−0.567024	+	0.0595966i	−0.0388519	+	0.00408349i
$214$	0.219614	+	0.243906i	0.0150125	+	0.0166731i
$215$	2.18939	−	0.465369i	0.149315	−	0.0317379i
$216$	0.485697	−	0.352880i	0.0330475	−	0.0240104i
$217$	−4.99814	−	1.66582i	−0.339296	−	0.113083i
$218$	0.121372	+	0.373546i	0.00822038	+	0.0252997i
$219$	0.321952	−	0.185879i	0.0217555	−	0.0125605i
$220$	−7.55225	+	1.35008i	−0.509173	+	0.0910226i
$221$	17.9130	−	31.0263i	1.20496	−	2.08705i
$222$	−0.0621477	+	0.0690220i	−0.00417108	+	0.00463245i
$223$	0.561518	−	0.772864i	0.0376020	−	0.0517548i	−0.789802	−	0.613362i	$-0.789817\pi$
$223$	0.561518	−	0.772864i	0.0376020	−	0.0517548i	0.827404	+	0.561607i	$0.189817\pi$
$224$	−0.512438	+	0.694226i	−0.0342387	+	0.0463850i
$225$	1.67939	−	5.16863i	0.111959	−	0.344575i
$226$	−0.000387229	−	0.00182177i	−2.57581e−5	−	0.000121182i
$227$	−2.17145	−	20.6600i	−0.144124	−	1.37125i	−0.792472	−	0.609908i	$-0.791206\pi$
$227$	−2.17145	−	20.6600i	−0.144124	−	1.37125i	0.648347	−	0.761345i	$-0.275460\pi$
$228$	−2.37146	−	5.32639i	−0.157054	−	0.352749i
$229$	−12.5845	−	11.3311i	−0.831606	−	0.748781i	0.138785	−	0.990323i	$-0.455680\pi$
$229$	−12.5845	−	11.3311i	−0.831606	−	0.748781i	−0.970391	+	0.241541i	$0.922347\pi$
$230$	−0.173505			−0.0114406
$231$	10.6485	−	1.82072i	0.700621	−	0.119795i
$232$	0.489199			0.0321175
$233$	−21.6131	−	19.4605i	−1.41592	−	1.27490i	−0.911412	−	0.411494i	$-0.865007\pi$
$233$	−21.6131	−	19.4605i	−1.41592	−	1.27490i	−0.504509	−	0.863407i	$-0.668326\pi$
$234$	−0.0941629	−	0.211493i	−0.00615562	−	0.0138257i
$235$	−0.563710	−	5.36334i	−0.0367724	−	0.349866i
$236$	3.67517	+	17.2903i	0.239233	+	1.12550i
$237$	−2.44982	+	7.53979i	−0.159133	+	0.489762i
$238$	−0.446509	−	0.0503415i	−0.0289428	−	0.00326315i
$239$	14.8275	−	20.4082i	0.959108	−	1.32010i	0.0117475	−	0.999931i	$-0.496261\pi$
$239$	14.8275	−	20.4082i	0.959108	−	1.32010i	0.947361	−	0.320168i	$-0.103739\pi$
$240$	3.80830	−	4.22955i	0.245825	−	0.273016i
$241$	0.112069	−	0.194110i	0.00721901	−	0.0125037i	−0.862393	−	0.506239i	$-0.831035\pi$
$241$	0.112069	−	0.194110i	0.00721901	−	0.0125037i	0.869612	+	0.493735i	$0.164369\pi$
$242$	−0.159698	−	0.252902i	−0.0102658	−	0.0162572i
$243$	−11.8445	+	6.83845i	−0.759828	+	0.438687i
$244$	1.23092	+	3.78838i	0.0788015	+	0.242526i
$245$	−0.122306	+	8.09823i	−0.00781385	+	0.517377i
$246$	0.0381850	−	0.0277431i	0.00243459	−	0.00176883i
$247$	−13.2905	+	2.82498i	−0.845654	+	0.179749i
$248$	−0.144894	−	0.160922i	−0.00920081	−	0.0102185i
$249$	4.99139	−	0.524616i	0.316316	−	0.0332462i
$250$	−0.0284832	+	0.270999i	−0.00180143	+	0.0171395i
$251$	−22.4666	+	7.29984i	−1.41808	+	0.460762i	−0.914991	−	0.403474i	$-0.867803\pi$
$251$	−22.4666	+	7.29984i	−1.41808	+	0.460762i	−0.503087	+	0.864236i	$0.667803\pi$
$252$	5.29758	−	5.79496i	0.333716	−	0.365048i
$253$	6.89201	+	16.9429i	0.433297	+	1.06519i
$254$	0.0200955	+	0.0348065i	0.00126091	+	0.00218395i
$255$	8.70245	+	1.84976i	0.544968	+	0.115837i
$256$	14.5627	−	6.48374i	0.910170	−	0.405234i
$257$	4.57413	−	10.2737i	0.285326	−	0.640854i	−0.712844	−	0.701323i	$-0.752593\pi$
$257$	4.57413	−	10.2737i	0.285326	−	0.640854i	0.998170	+	0.0604694i	$0.0192597\pi$
$258$	−0.0615905	−	0.0200120i	−0.00383446	−	0.00124589i
$259$	−3.71821	+	6.32927i	−0.231038	+	0.393282i
$260$	−7.79890	−	10.7343i	−0.483667	−	0.665711i
$261$	−6.64086	−	0.697983i	−0.411059	−	0.0432040i
$262$	0.00197493	−	0.00929134i	0.000122012	−	0.000574021i
$263$	17.0926	+	9.86840i	1.05397	+	0.608512i	0.923759	−	0.382974i	$-0.125100\pi$
$263$	17.0926	+	9.86840i	1.05397	+	0.608512i	0.130214	+	0.991486i	$0.458433\pi$
$264$	0.417603	+	0.150878i	0.0257017	+	0.00928590i
$265$			10.3420i			0.635304i
$266$	0.0991242	+	0.138622i	0.00607770	+	0.00849946i
$267$	−14.9353	−	10.8512i	−0.914028	−	0.664081i
$268$	18.2906	+	8.14352i	1.11728	+	0.497445i
$269$	−7.83983	+	7.05901i	−0.478003	+	0.430396i	−0.872583	−	0.488466i	$-0.837557\pi$
$269$	−7.83983	+	7.05901i	−0.478003	+	0.430396i	0.394580	+	0.918861i	$0.370890\pi$
$270$	0.129075	−	0.116220i	0.00785527	−	0.00707292i
$271$	19.6872	+	8.76529i	1.19591	+	0.532454i	0.905458	−	0.424436i	$-0.139528\pi$
$271$	19.6872	+	8.76529i	1.19591	+	0.532454i	0.290452	+	0.956889i	$0.406194\pi$
$272$	20.1897	+	14.6687i	1.22418	+	0.889420i
$273$	10.8673	+	15.1976i	0.657721	+	0.919801i
$274$		−	0.267488i		−	0.0161595i
$275$	11.6648	−	3.37470i	0.703415	−	0.203502i
$276$	−11.7555	−	6.78706i	−0.707600	−	0.408533i
$277$	−0.159955	+	0.752531i	−0.00961078	+	0.0452152i	−0.982692	−	0.185249i	$-0.940691\pi$
$277$	−0.159955	+	0.752531i	−0.00961078	+	0.0452152i	0.973081	+	0.230464i	$0.0740243\pi$
$278$	−0.360815	−	0.0379232i	−0.0216402	−	0.00227448i
$279$	1.73734	+	2.39124i	0.104012	+	0.143160i
$280$	−0.168616	+	0.287025i	−0.0100768	+	0.0171530i
$281$	−15.7142	−	5.10587i	−0.937433	−	0.304590i	−0.199834	−	0.979830i	$-0.564040\pi$
$281$	−15.7142	−	5.10587i	−0.937433	−	0.304590i	−0.737599	+	0.675239i	$0.764040\pi$
$282$	−0.0634633	+	0.142541i	−0.00377918	+	0.00848819i
$283$	−7.74389	+	3.44780i	−0.460326	+	0.204950i	−0.623779	−	0.781601i	$-0.714404\pi$
$283$	−7.74389	+	3.44780i	−0.460326	+	0.204950i	0.163453	+	0.986551i	$0.447737\pi$
$284$	−0.905649	−	0.192502i	−0.0537404	−	0.0114229i
$285$	−1.68712	−	2.92217i	−0.0999362	−	0.173095i
$286$	0.273081	−	0.439329i	0.0161476	−	0.0259781i
$287$	2.51698	−	2.75330i	0.148573	−	0.162522i
$288$	0.460401	−	0.149593i	0.0271294	−	0.00881486i
$289$	−2.30080	+	21.8906i	−0.135341	+	1.28768i
$290$	0.140754	−	0.0147939i	0.00826537	−	0.000868725i
$291$	−4.04007	−	4.48695i	−0.236833	−	0.263030i
$292$	0.590518	−	0.125518i	0.0345574	−	0.00734541i
$293$	−14.4285	+	10.4829i	−0.842921	+	0.612418i	−0.923185	−	0.384356i	$-0.874424\pi$
$293$	−14.4285	+	10.4829i	−0.842921	+	0.612418i	0.0802640	+	0.996774i	$0.474424\pi$
$294$	0.120216	−	0.201143i	0.00701115	−	0.0117309i
$295$	3.16121	+	9.72919i	0.184053	+	0.566455i
$296$	−0.261290	+	0.150856i	−0.0151872	+	0.00876833i
$297$	−16.4761	−	7.98778i	−0.956042	−	0.463498i
$298$	0.104716	−	0.181373i	0.00606601	−	0.0105066i
$299$	−21.1669	+	23.5082i	−1.22411	+	1.35951i
$300$	−5.29693	+	7.29060i	−0.305819	+	0.420923i
$301$	−5.08609	−	0.573429i	−0.293157	−	0.0330519i
$302$	−0.0215472	+	0.0663156i	−0.00123990	+	0.00381603i
$303$	−3.38269	−	15.9143i	−0.194330	−	0.914252i
$304$	−0.989340	−	9.41294i	−0.0567425	−	0.539869i
$305$	0.937632	+	2.10596i	0.0536886	+	0.120587i
$306$	0.187340	+	0.168682i	0.0107095	+	0.00964289i
$307$	−20.4524			−1.16728			−0.583641	−	0.812012i	$-0.698372\pi$
$307$	−20.4524			−1.16728			−0.583641	+	0.812012i	$0.698372\pi$
$308$	17.3598	+	2.53165i	0.989167	+	0.144254i
$309$	−10.1227			−0.575858
$310$	−0.0465560	−	0.0419193i	−0.00264421	−	0.00238085i
$311$	−11.6827	−	26.2397i	−0.662464	−	1.48792i	−0.861411	−	0.507909i	$-0.830419\pi$
$311$	−11.6827	−	26.2397i	−0.662464	−	1.48792i	0.198947	−	0.980010i	$-0.436248\pi$
$312$	0.0802690	+	0.763709i	0.00454434	+	0.0432365i
$313$	−4.18985	−	19.7117i	−0.236824	−	1.11417i	−0.922420	−	0.386188i	$-0.873792\pi$
$313$	−4.18985	−	19.7117i	−0.236824	−	1.11417i	0.685596	−	0.727983i	$-0.259542\pi$
$314$	−0.0825087	+	0.253936i	−0.00465624	+	0.0143304i
$315$	2.69849	−	3.65578i	0.152043	−	0.205980i
$316$	−7.56728	+	10.4155i	−0.425693	+	0.585916i
$317$	0.131487	−	0.146031i	0.00738504	−	0.00820192i	−0.739441	−	0.673221i	$-0.764910\pi$
$317$	0.131487	−	0.146031i	0.00738504	−	0.00820192i	0.746826	+	0.665019i	$0.231577\pi$
$318$	0.149611	−	0.259133i	0.00838975	−	0.0145315i
$319$	−7.03571	−	13.1571i	−0.393924	−	0.736657i
$320$	7.99830	−	4.61782i	0.447119	−	0.258144i
$321$	4.59201	+	14.1328i	0.256301	+	0.788814i
$322$	0.376397	+	0.125449i	0.0209758	+	0.00699099i
$323$	11.9698	−	8.69653i	0.666015	−	0.483888i
$324$	4.58330	−	0.974210i	0.254628	−	0.0541228i
$325$	14.0524	+	15.6068i	0.779487	+	0.865708i
$326$	−0.519051	+	0.0545545i	−0.0287476	+	0.00302149i
$327$	−1.85885	+	17.6858i	−0.102795	+	0.978025i
$328$	0.145821	−	0.0473802i	0.00805163	−	0.00261613i
$329$	−2.65494	+	12.0427i	−0.146372	+	0.663934i
$330$	0.124717	+	0.0307825i	0.00686546	+	0.00169452i
$331$	4.26919	+	7.39446i	0.234656	+	0.406436i	0.959173	−	0.282821i	$-0.0912703\pi$
$331$	4.26919	+	7.39446i	0.234656	+	0.406436i	−0.724517	+	0.689257i	$0.757937\pi$
$332$	7.97223	+	1.69455i	0.437533	+	0.0930005i
$333$	3.76225	−	1.67506i	0.206170	−	0.0917928i
$334$	−0.0348169	+	0.0782001i	−0.00190510	+	0.00427892i
$335$	11.0199	+	3.58058i	0.602081	+	0.195628i
$336$	−11.3197	+	6.42197i	−0.617541	+	0.350347i
$337$	9.57144	+	13.1740i	0.521390	+	0.717631i	0.985788	−	0.167995i	$-0.0537293\pi$
$337$	9.57144	+	13.1740i	0.521390	+	0.717631i	−0.464398	+	0.885627i	$0.653729\pi$
$338$	0.538166	+	0.0565636i	0.0292724	+	0.00307665i
$339$	0.0175323	−	0.0824831i	0.000952226	−	0.00447987i
$340$	12.5123	+	7.22396i	0.678573	+	0.391774i
$341$	−2.24413	+	6.21136i	−0.121527	+	0.336364i
$342$		−	0.0956082i		−	0.00516990i
$343$	6.12057	−	17.4797i	0.330480	−	0.943813i
$344$	−0.170194	−	0.123653i	−0.00917623	−	0.00666692i
$345$	−7.17652	−	3.19519i	−0.386371	−	0.172023i
$346$	0.208248	−	0.187507i	0.0111955	−	0.0100805i
$347$	7.11851	−	6.40953i	0.382141	−	0.344082i	−0.455565	−	0.890203i	$-0.650563\pi$
$347$	7.11851	−	6.40953i	0.382141	−	0.344082i	0.837706	+	0.546121i	$0.183896\pi$
$348$	10.1153	+	4.50360i	0.542235	+	0.241419i
$349$	9.30391	+	6.75969i	0.498027	+	0.361838i	0.808263	−	0.588822i	$-0.200408\pi$
$349$	9.30391	+	6.75969i	0.498027	+	0.361838i	−0.310236	+	0.950660i	$0.600408\pi$
$350$	0.108948	−	0.239811i	0.00582350	−	0.0128184i
$351$		−	31.6667i		−	1.69025i
$352$	0.853935	+	0.663922i	0.0455149	+	0.0353872i
$353$	10.7699	+	6.21799i	0.573223	+	0.330950i	0.758436	−	0.651748i	$-0.225964\pi$
$353$	10.7699	+	6.21799i	0.573223	+	0.330950i	−0.185213	+	0.982698i	$0.559297\pi$
$354$	0.0615372	−	0.289510i	0.00327067	−	0.0153873i
$355$	−0.532896	−	0.0560096i	−0.0282832	−	0.00297268i
$356$	−17.6216	−	24.2540i	−0.933942	−	1.28546i
$357$	−17.5414	−	10.3049i	−0.928392	−	0.545395i
$358$	0.223643	+	0.0726661i	0.0118199	+	0.00384053i
$359$	−7.17350	+	16.1119i	−0.378603	+	0.850355i	0.619271	+	0.785177i	$0.287428\pi$
$359$	−7.17350	+	16.1119i	−0.378603	+	0.850355i	−0.997874	+	0.0651781i	$0.979238\pi$
$360$	0.170614	−	0.0759621i	0.00899213	−	0.00400355i
$361$	13.0961	+	2.78366i	0.689268	+	0.146508i
$362$	−0.330069	−	0.571696i	−0.0173480	−	0.0300477i
$363$	−1.94812	−	13.4015i	−0.102250	−	0.703395i
$364$	9.15758	+	28.9255i	0.479987	+	1.51611i
$365$	0.332282	−	0.107965i	0.0173924	−	0.00565114i
$366$	0.00697175	−	0.0663318i	0.000364419	−	0.00346722i
$367$	−5.46328	+	0.574214i	−0.285181	+	0.0299737i	−0.246039	−	0.969260i	$-0.579129\pi$
$367$	−5.46328	+	0.574214i	−0.285181	+	0.0299737i	−0.0391419	+	0.999234i	$0.512462\pi$
$368$	−14.7445	−	16.3754i	−0.768611	−	0.853629i
$369$	−2.04712	+	0.435129i	−0.106569	+	0.0226519i
$370$	−0.0706175	+	0.0513066i	−0.00367123	+	0.00266730i
$371$	7.47755	−	22.4357i	0.388215	−	1.16480i
$372$	−1.51455	−	4.66132i	−0.0785260	−	0.241678i
$373$	19.8839	−	11.4800i	1.02955	−	0.594411i	0.112694	−	0.993630i	$-0.464052\pi$
$373$	19.8839	−	11.4800i	1.02955	−	0.594411i	0.916856	+	0.399219i	$0.130719\pi$
$374$	−0.0770737	+	0.557976i	−0.00398538	+	0.0288523i
$375$	−6.16873	+	10.6845i	−0.318552	+	0.551748i
$376$	−0.339156	+	0.376671i	−0.0174906	+	0.0194253i
$377$	15.1670	−	20.8756i	0.781140	−	1.07515i
$378$	−0.364043	+	0.158800i	−0.0187244	+	0.00816777i
$379$	−4.73263	+	14.5655i	−0.243099	+	0.748181i	0.752845	+	0.658198i	$0.228681\pi$
$379$	−4.73263	+	14.5655i	−0.243099	+	0.748181i	−0.995943	+	0.0899826i	$0.971319\pi$
$380$	−1.13926	−	5.35979i	−0.0584428	−	0.274952i
$381$	0.190211	+	1.80974i	0.00974481	+	0.0927157i
$382$	−0.0874897	−	0.196505i	−0.00447636	−	0.0100541i
$383$	−16.7011	−	15.0378i	−0.853389	−	0.768395i	0.121145	−	0.992635i	$-0.461343\pi$
$383$	−16.7011	−	15.0378i	−0.853389	−	0.768395i	−0.974534	+	0.224240i	$0.928010\pi$
$384$	−1.07023			−0.0546151
$385$	10.1447	+	0.406950i	0.517020	+	0.0207401i
$386$	0.228666			0.0116388
$387$	2.13395	+	1.92142i	0.108475	+	0.0976712i
$388$	−3.98804	−	8.95728i	−0.202462	−	0.454737i
$389$	1.52757	+	14.5339i	0.0774509	+	0.736897i	0.962479	+	0.271358i	$0.0874727\pi$
$389$	1.52757	+	14.5339i	0.0774509	+	0.736897i	−0.885028	+	0.465539i	$0.845861\pi$
$390$	0.0461907	+	0.217310i	0.00233895	+	0.0110039i
$391$	10.6443	−	32.7599i	0.538307	−	1.65674i
$392$	0.573319	−	0.500751i	0.0289570	−	0.0252917i
$393$	0.252793	−	0.347939i	0.0127517	−	0.0175512i
$394$	0.231630	−	0.257251i	0.0116693	−	0.0129601i
$395$	−3.72532	+	6.45244i	−0.187441	+	0.324657i
$396$	−7.09615	−	6.82032i	−0.356595	−	0.342734i
$397$	4.23284	−	2.44383i	0.212440	−	0.122652i	−0.390005	−	0.920813i	$-0.627527\pi$
$397$	4.23284	−	2.44383i	0.212440	−	0.122652i	0.602445	+	0.798160i	$0.294193\pi$
$398$	0.0943436	+	0.290360i	0.00472902	+	0.0145544i
$399$	1.54718	+	7.55912i	0.0774558	+	0.378429i
$400$	−11.8351	+	8.59869i	−0.591754	+	0.429934i
$401$	−21.9112	+	4.65738i	−1.09420	+	0.232578i	−0.719446	−	0.694548i	$-0.755604\pi$
$401$	−21.9112	+	4.65738i	−1.09420	+	0.232578i	−0.374749	+	0.927126i	$0.622271\pi$
$402$	−0.224321	−	0.249134i	−0.0111881	−	0.0124257i
$403$	−11.3593	+	1.19391i	−0.565846	+	0.0594728i
$404$	2.76176	−	26.2764i	0.137403	−	1.30730i
$405$	2.57900	−	0.837969i	0.128152	−	0.0416390i
$406$	−0.316045	−	0.0696757i	−0.0156851	−	0.00345795i
$407$	7.81521	+	4.85783i	0.387386	+	0.240794i
$408$	−0.418094	−	0.724160i	−0.0206987	−	0.0358513i
$409$	37.2799	+	7.92409i	1.84337	+	0.391821i	0.991302	−	0.131605i	$-0.0420129\pi$
$409$	37.2799	+	7.92409i	1.84337	+	0.391821i	0.852071	+	0.523426i	$0.175346\pi$
$410$	0.0405234	−	0.0180422i	0.00200131	−	0.000891041i
$411$	4.92594	−	11.0638i	0.242979	−	0.545739i
$412$	−15.6340	−	5.07978i	−0.770230	−	0.250263i
$413$	0.176632	−	23.3919i	0.00869149	−	1.15104i
$414$	−0.130835	−	0.180078i	−0.00643017	−	0.00885036i
$415$	4.69096	+	0.493040i	0.230270	+	0.0242024i
$416$	−0.388937	+	1.82980i	−0.0190692	+	0.0897135i
$417$	−14.2257	−	8.21319i	−0.696634	−	0.402202i
$418$	0.176823	−	0.119878i	0.00864868	−	0.00586341i
$419$			14.3200i			0.699577i	0.936829	+	0.349788i	$0.113747\pi$
$419$			14.3200i			0.699577i	−0.936829	+	0.349788i	$0.886253\pi$
$420$	−6.12889	+	4.38258i	−0.299059	+	0.213848i
$421$	16.4125	+	11.9244i	0.799899	+	0.581160i	0.910884	−	0.412662i	$-0.135401\pi$
$421$	16.4125	+	11.9244i	0.799899	+	0.581160i	−0.110986	+	0.993822i	$0.535401\pi$
$422$	−0.189351	−	0.0843043i	−0.00921744	−	0.00410387i
$423$	5.14146	−	4.62939i	0.249986	−	0.225089i
$424$	0.722345	−	0.650403i	0.0350802	−	0.0315863i
$425$	−20.8911	−	9.30130i	−1.01336	−	0.451179i
$426$	0.0125422	+	0.00911244i	0.000607672	+	0.000441499i
$427$	−0.511411	−	5.24654i	−0.0247489	−	0.253898i
$428$			24.1318i			1.16645i
$429$	19.3857	−	13.1426i	0.935950	−	0.634531i
$430$	−0.0527082	−	0.0304311i	−0.00254182	−	0.00146752i
$431$	−6.82615	+	32.1145i	−0.328804	+	1.54690i	0.434386	+	0.900727i	$0.356965\pi$
$431$	−6.82615	+	32.1145i	−0.328804	+	1.54690i	−0.763190	+	0.646174i	$0.776368\pi$
$432$	21.9377	+	2.30575i	1.05548	+	0.110935i
$433$	13.5409	+	18.6374i	0.650734	+	0.895658i	0.999131	−	0.0416890i	$-0.0132739\pi$
$433$	13.5409	+	18.6374i	0.650734	+	0.895658i	−0.348397	+	0.937347i	$0.613274\pi$
$434$	0.0706888	+	0.124600i	0.00339317	+	0.00598099i
$435$	6.09432	+	1.98016i	0.292200	+	0.0949416i
$436$	−11.7460	+	26.3820i	−0.562533	+	1.26347i
$437$	−11.9345	+	5.31358i	−0.570905	+	0.254183i
$438$	−0.00988765	−	0.00210169i	−0.000472450	−	0.000100422i
$439$	9.60913	+	16.6435i	0.458619	+	0.794351i	0.998888	−	0.0471410i	$-0.0150110\pi$
$439$	9.60913	+	16.6435i	0.458619	+	0.794351i	−0.540269	+	0.841492i	$0.681678\pi$
$440$	0.354411	+	0.220297i	0.0168959	+	0.0105022i
$441$	−8.49726	+	5.97968i	−0.404632	+	0.284747i
$442$	−0.926476	+	0.301030i	−0.0440679	+	0.0143185i
$443$	2.05938	−	19.5937i	0.0978440	−	0.930924i	−0.829952	−	0.557835i	$-0.811632\pi$
$443$	2.05938	−	19.5937i	0.0978440	−	0.930924i	0.927796	−	0.373088i	$-0.121701\pi$
$444$	−6.79155	+	0.713820i	−0.322313	+	0.0338764i
$445$	−11.6094	−	12.8935i	−0.550338	−	0.611212i
$446$	−0.0254085	+	0.00540074i	−0.00120313	+	0.000255732i
$447$	7.67133	−	5.57355i	0.362841	−	0.263620i
$448$	−20.6901	+	4.23480i	−0.977517	+	0.200075i
$449$	−3.04025	−	9.35693i	−0.143478	−	0.441581i	0.853334	−	0.521365i	$-0.174577\pi$
$449$	−3.04025	−	9.35693i	−0.143478	−	0.441581i	−0.996812	+	0.0797839i	$0.974577\pi$
$450$	−0.127976	+	0.0738870i	−0.00603285	+	0.00348307i
$451$	−3.37152	−	3.24047i	−0.158759	−	0.152588i
$452$	0.0684698	−	0.118593i	0.00322055	−	0.00557816i
$453$	−2.11248	+	2.34614i	−0.0992529	+	0.110232i
$454$	−0.332020	+	0.456986i	−0.0155825	+	0.0214474i
$455$	7.02048	+	16.0942i	0.329125	+	0.754509i
$456$	−0.0979997	+	0.301612i	−0.00458926	+	0.0141243i
$457$	−2.35873	−	11.0970i	−0.110337	−	0.519094i	−0.998253	−	0.0590882i	$-0.981181\pi$
$457$	−2.35873	−	11.0970i	−0.110337	−	0.519094i	0.887916	−	0.460006i	$-0.152153\pi$
$458$	0.0481311	+	0.457936i	0.00224902	+	0.0213980i
$459$	14.0251	+	31.5010i	0.654638	+	1.47034i
$460$	−9.48038	−	8.53617i	−0.442025	−	0.398001i
$461$	23.3735			1.08861			0.544307	−	0.838886i	$-0.316793\pi$
$461$	23.3735			1.08861			0.544307	+	0.838886i	$0.316793\pi$
$462$	−0.248302	−	0.156953i	−0.0115520	−	0.00730210i
$463$	−13.4430			−0.624750			−0.312375	−	0.949959i	$-0.601125\pi$
$463$	−13.4430			−0.624750			−0.312375	+	0.949959i	$0.601125\pi$
$464$	13.3576	+	12.0272i	0.620111	+	0.558350i
$465$	−1.15369	−	2.59122i	−0.0535009	−	0.120165i
$466$	0.0826622	+	0.786478i	0.00382925	+	0.0364329i
$467$	7.00620	+	32.9616i	0.324208	+	1.52528i	0.774601	+	0.632450i	$0.217951\pi$
$467$	7.00620	+	32.9616i	0.324208	+	1.52528i	−0.450393	+	0.892831i	$0.648716\pi$
$468$	5.26004	−	16.1887i	0.243146	−	0.748325i
$469$	−21.3174	−	15.7353i	−0.984347	−	0.726589i
$470$	−0.0861923	+	0.118634i	−0.00397576	+	0.00547216i
$471$	−8.08910	+	8.98386i	−0.372726	+	0.413954i
$472$	0.480737	−	0.832661i	0.0221277	−	0.0383263i
$473$	−0.877930	+	6.35579i	−0.0403673	+	0.292240i
$474$	0.186686	−	0.107783i	0.00857478	−	0.00495065i
$475$	2.68010	+	8.24849i	0.122971	+	0.378467i
$476$	−21.9207	−	24.7182i	−1.00473	−	1.13296i
$477$	−10.7338	+	7.79857i	−0.491467	+	0.357072i
$478$	−0.670936	+	0.142612i	−0.0306879	+	0.00652292i
$479$	14.0790	+	15.6363i	0.643286	+	0.714441i	0.973301	−	0.229535i	$-0.0737204\pi$
$479$	14.0790	+	15.6363i	0.643286	+	0.714441i	−0.330015	+	0.943976i	$0.607054\pi$
$480$	−0.462011	+	0.0485594i	−0.0210878	+	0.00221642i
$481$	−1.66350	+	15.8271i	−0.0758491	+	0.721656i
$482$	−0.00579631	+	0.00188334i	−0.000264015	+	8.57836e-5i
$483$	13.2583	+	12.1204i	0.603276	+	0.551497i
$484$	3.71640	−	21.6756i	0.168927	−	0.985253i
$485$	−2.83719	−	4.91415i	−0.128830	−	0.223140i
$486$	0.363765	+	0.0773207i	0.0165007	+	0.00350734i
$487$	−13.0471	+	5.80894i	−0.591220	+	0.263228i	−0.680464	−	0.732782i	$-0.738222\pi$
$487$	−13.0471	+	5.80894i	−0.591220	+	0.263228i	0.0892436	+	0.996010i	$0.471555\pi$
$488$	0.0881251	−	0.197932i	0.00398923	−	0.00895997i
$489$	−22.4737	−	7.30214i	−1.01629	−	0.330214i
$490$	0.149815	−	0.161416i	0.00676793	−	0.00729202i
$491$	−1.58042	−	2.17527i	−0.0713235	−	0.0981684i	0.771865	−	0.635787i	$-0.219324\pi$
$491$	−1.58042	−	2.17527i	−0.0713235	−	0.0981684i	−0.843188	+	0.537618i	$0.819324\pi$
$492$	3.45136	+	0.362753i	0.155599	+	0.0163542i
$493$	−5.84185	+	27.4837i	−0.263104	+	1.23781i
$494$	0.319961	+	0.184729i	0.0143957	+	0.00831136i
$495$	−4.49680	−	3.49620i	−0.202116	−	0.157142i
$496$		−	7.95629i		−	0.357248i
$497$	1.11555	+	0.506804i	0.0500394	+	0.0227333i
$498$	−0.110406	−	0.0802148i	−0.00494742	−	0.00359451i
$499$	−24.3833	−	10.8561i	−1.09155	−	0.485987i	−0.219600	−	0.975590i	$-0.570475\pi$
$499$	−24.3833	−	10.8561i	−1.09155	−	0.485987i	−0.871946	+	0.489603i	$0.837142\pi$
$500$	−14.8891	+	13.4062i	−0.665859	+	0.599542i
$501$	−2.88020	+	2.59334i	−0.128678	+	0.115862i
$502$	0.586800	+	0.261260i	0.0261901	+	0.0116606i
$503$	−19.3729	−	14.0753i	−0.863796	−	0.627585i	0.0651189	−	0.997878i	$-0.479257\pi$
$503$	−19.3729	−	14.0753i	−0.863796	−	0.627585i	−0.928915	+	0.370293i	$0.879257\pi$
$504$	−0.425048	+	0.0414319i	−0.0189331	+	0.00184552i
$505$		−	15.2906i		−	0.680421i
$506$	0.169000	−	0.467762i	0.00751297	−	0.0207945i
$507$	21.2180	+	12.2502i	0.942325	+	0.544052i
$508$	−0.614397	+	2.89051i	−0.0272594	+	0.128246i
$509$	22.4949	+	2.36431i	0.997069	+	0.104796i	0.588981	−	0.808147i	$-0.299529\pi$
$509$	22.4949	+	2.36431i	0.997069	+	0.104796i	0.408087	+	0.912943i	$0.366196\pi$
$510$	−0.142195	−	0.195715i	−0.00629650	−	0.00866639i
$511$	−0.798906	−	0.00603253i	−0.0353415	−	0.000266863i
$512$	−2.06577	−	0.671211i	−0.0912952	−	0.0296636i
$513$	5.31919	−	11.9471i	0.234848	−	0.527477i
$514$	−0.279354	+	0.124376i	−0.0123218	+	0.00548600i
$515$	−9.30549	−	1.97794i	−0.410049	−	0.0871586i
$516$	−2.38077	−	4.12362i	−0.104808	−	0.181532i
$517$	15.0084	+	3.70435i	0.660069	+	0.162917i
$518$	0.190292	−	0.0602449i	0.00836094	−	0.00264701i
$519$	12.0666	−	3.92068i	0.529666	−	0.172099i
$520$	−0.0754377	+	0.717742i	−0.00330816	+	0.0314751i
$521$	30.2117	−	3.17537i	1.32360	−	0.139116i	0.583773	−	0.811917i	$-0.301576\pi$
$521$	30.2117	−	3.17537i	1.32360	−	0.139116i	0.739823	+	0.672801i	$0.234909\pi$
$522$	0.121493	+	0.134931i	0.00531759	+	0.00590578i
$523$	11.6993	−	2.48677i	0.511575	−	0.108739i	0.0551107	−	0.998480i	$-0.482449\pi$
$523$	11.6993	−	2.48677i	0.511575	−	0.108739i	0.456465	+	0.889742i	$0.349116\pi$
$524$	0.565031	−	0.410519i	0.0246835	−	0.0179336i
$525$	8.92255	−	7.91273i	0.389412	−	0.345340i
$526$	−0.165840	−	0.510402i	−0.00723095	−	0.0222546i
$527$	10.7710	−	6.21866i	0.469194	−	0.270889i
$528$	7.69326	+	14.3868i	0.334806	+	0.626103i
$529$	−3.70732	+	6.42126i	−0.161188	+	0.279185i
$530$	0.188167	−	0.208981i	0.00817346	−	0.00907755i
$531$	−7.71403	+	10.6174i	−0.334760	+	0.460758i
$532$	−1.40380	+	12.4511i	−0.0608624	+	0.539825i
$533$	2.49915	−	7.69159i	0.108250	−	0.333160i
$534$	0.104368	+	0.491011i	0.00451643	+	0.0212481i
$535$	1.45981	+	13.8891i	0.0631130	+	0.600480i
$536$	−0.442947	−	0.994874i	−0.0191324	−	0.0429720i
$537$	7.91216	+	7.12414i	0.341435	+	0.307429i
$538$	0.286855			0.0123672
$539$	−21.7133	−	8.21770i	−0.935260	−	0.353961i
$540$	12.7706			0.549558
$541$	−16.4508	−	14.8123i	−0.707273	−	0.636832i	0.234876	−	0.972025i	$-0.424532\pi$
$541$	−16.4508	−	14.8123i	−0.707273	−	0.636832i	−0.942149	+	0.335194i	$0.891198\pi$
$542$	−0.238339	−	0.535318i	−0.0102375	−	0.0229939i
$543$	−3.12422	−	29.7249i	−0.134073	−	1.27562i
$544$	−0.423516	−	1.99249i	−0.0181581	−	0.0854271i
$545$	−5.16455	+	15.8949i	−0.221225	+	0.680861i
$546$	0.0569162	−	0.504824i	0.00243579	−	0.0216045i
$547$	23.9937	−	33.0245i	1.02590	−	1.41203i	0.117911	−	0.993024i	$-0.462380\pi$
$547$	23.9937	−	33.0245i	1.02590	−	1.41203i	0.907986	−	0.419001i	$-0.137620\pi$
$548$	13.1600	−	14.6156i	0.562167	−	0.624349i
$549$	−1.47870	+	2.56119i	−0.0631095	+	0.109309i
$550$	−0.297112	−	0.144043i	−0.0126689	−	0.00614200i
$551$	9.22869	−	5.32819i	0.393155	−	0.226988i
$552$	0.228157	+	0.702194i	0.00971099	+	0.0298874i
$553$	12.7469	−	11.3043i	0.542053	−	0.480706i
$554$	0.0169241	−	0.0122961i	0.000719037	−	0.000522411i
$555$	−3.86572	+	0.821685i	−0.164091	+	0.0348786i
$556$	−17.8493	−	19.8237i	−0.756979	−	0.840711i
$557$	−12.7913	+	1.34442i	−0.541984	+	0.0569648i	−0.371565	−	0.928407i	$-0.621179\pi$
$557$	−12.7913	+	1.34442i	−0.541984	+	0.0569648i	−0.170419	+	0.985372i	$0.554512\pi$
$558$	0.00840097	−	0.0799299i	0.000355641	−	0.00338370i
$559$	−10.5533	+	3.42897i	−0.446357	+	0.145030i
$560$	−11.6608	+	3.69170i	−0.492757	+	0.156003i
$561$	−13.4634	+	21.6597i	−0.568424	+	0.914473i
$562$	0.224639	+	0.389087i	0.00947584	+	0.0164126i
$563$	−19.5327	−	4.15180i	−0.823204	−	0.174977i	−0.222994	−	0.974820i	$-0.571583\pi$
$563$	−19.5327	−	4.15180i	−0.823204	−	0.174977i	−0.600210	+	0.799843i	$0.704916\pi$
$564$	−10.4805	+	4.66620i	−0.441307	+	0.196482i
$565$	0.0322340	−	0.0723988i	0.00135610	−	0.00304584i
$566$	0.219212	+	0.0712262i	0.00921416	+	0.00299386i
$567$	−6.20070	−	0.0468214i	−0.260405	−	0.00196631i
$568$	0.0296015	+	0.0407430i	0.00124205	+	0.00170954i
$569$	5.97262	+	0.627748i	0.250385	+	0.0263166i	0.228890	−	0.973452i	$-0.426491\pi$
$569$	5.97262	+	0.627748i	0.250385	+	0.0263166i	0.0214957	+	0.999769i	$0.493157\pi$
$570$	−0.0190758	+	0.0897446i	−0.000798998	+	0.00375899i
$571$	1.89375	+	1.09336i	0.0792510	+	0.0457556i	0.539102	−	0.842241i	$-0.318764\pi$
$571$	1.89375	+	1.09336i	0.0792510	+	0.0457556i	−0.459851	+	0.887996i	$0.652097\pi$
$572$	36.5356	−	10.5699i	1.52763	−	0.441952i
$573$		−	9.73903i		−	0.406854i
$574$	−0.100956	+	0.00984073i	−0.00421380	+	0.000410744i
$575$	16.3356	+	11.8685i	0.681241	+	0.494950i
$576$	10.8240	+	4.81917i	0.451002	+	0.200799i
$577$	21.1167	−	19.0135i	0.879098	−	0.791543i	−0.0999886	−	0.994989i	$-0.531881\pi$
$577$	21.1167	−	19.0135i	0.879098	−	0.791543i	0.979086	+	0.203445i	$0.0652140\pi$
$578$	0.444781	−	0.400482i	0.0185004	−	0.0166579i
$579$	9.45808	+	4.21101i	0.393065	+	0.175004i
$580$	8.41870	+	6.11655i	0.349568	+	0.253976i
$581$	−9.81997	−	4.46128i	−0.407401	−	0.185085i
$582$			0.164175i			0.00680527i
$583$	−27.8816	−	10.0735i	−1.15474	−	0.417201i
$584$	−0.0284380	−	0.0164187i	−0.00117677	−	0.000679409i
$585$	2.04813	−	9.63570i	0.0846798	−	0.398387i
$586$	0.482288	+	0.0506905i	0.0199231	+	0.00209401i
$587$	−2.11154	−	2.90629i	−0.0871527	−	0.119955i	0.763214	−	0.646145i	$-0.223620\pi$
$587$	−2.11154	−	2.90629i	−0.0871527	−	0.119955i	−0.850367	+	0.526190i	$0.823620\pi$
$588$	16.4646	−	5.07610i	0.678988	−	0.209335i
$589$	−4.48613	−	1.45763i	−0.184848	−	0.0600606i
$590$	0.113139	−	0.254115i	0.00465786	−	0.0104617i
$591$	14.3181	−	6.37483i	0.588968	−	0.262225i
$592$	−10.8434	−	2.30484i	−0.445662	−	0.0947284i
$593$	−12.2013	−	21.1332i	−0.501047	−	0.867838i	−0.999999	−	0.00120904i	$-0.999615\pi$
$593$	−12.2013	−	21.1332i	−0.501047	−	0.867838i	0.498953	−	0.866629i	$-0.333718\pi$
$594$	0.187600	+	0.461184i	0.00769732	+	0.0189226i
$595$	−14.1118	−	12.9006i	−0.578529	−	0.528874i
$596$	14.6450	−	4.75843i	0.599881	−	0.194913i
$597$	−1.44490	+	13.7473i	−0.0591357	+	0.562638i
$598$	0.855438	−	0.0899102i	0.0349815	−	0.00367670i
$599$	4.00763	+	4.45092i	0.163747	+	0.181860i	0.819434	−	0.573173i	$-0.194288\pi$
$599$	4.00763	+	4.45092i	0.163747	+	0.181860i	−0.655687	+	0.755033i	$0.727621\pi$
$600$	0.479457	−	0.101912i	0.0195737	−	0.00416053i
$601$	22.2250	−	16.1474i	0.906578	−	0.658667i	−0.0335692	−	0.999436i	$-0.510687\pi$
$601$	22.2250	−	16.1474i	0.906578	−	0.658667i	0.940147	+	0.340769i	$0.110687\pi$
$602$	0.0923414	+	0.104126i	0.00376355	+	0.00424386i
$603$	4.59352	+	14.1374i	0.187062	+	0.575719i
$604$	−4.43998	+	2.56342i	−0.180660	+	0.104304i
$605$	0.827764	−	12.7003i	0.0336534	−	0.516340i
$606$	−0.221198	+	0.383127i	−0.00898557	+	0.0155635i
$607$	−8.88085	+	9.86319i	−0.360463	+	0.400334i	−0.895911	−	0.444234i	$-0.853476\pi$
$607$	−8.88085	+	9.86319i	−0.360463	+	0.400334i	0.535448	+	0.844568i	$0.320143\pi$
$608$	−0.454096	+	0.625009i	−0.0184160	+	0.0253475i
$609$	−11.7892	−	8.70208i	−0.477721	−	0.352626i
$610$	0.0193700	−	0.0596148i	0.000784270	−	0.00241373i
$611$	5.55856	+	26.1510i	0.224875	+	1.05796i
$612$	1.93746	+	18.4337i	0.0783171	+	0.745137i
$613$	5.29716	+	11.8976i	0.213950	+	0.480540i	0.988358	−	0.152147i	$-0.0486187\pi$
$613$	5.29716	+	11.8976i	0.213950	+	0.480540i	−0.774408	+	0.632687i	$0.781952\pi$
$614$	0.413283	+	0.372121i	0.0166787	+	0.0150176i
$615$	2.00839			0.0809861
$616$	−0.609569	−	0.734156i	−0.0245602	−	0.0295800i
$617$	−11.0583			−0.445190			−0.222595	−	0.974911i	$-0.571453\pi$
$617$	−11.0583			−0.445190			−0.222595	+	0.974911i	$0.571453\pi$
$618$	0.204549	+	0.184176i	0.00822816	+	0.00740866i
$619$	5.33590	+	11.9846i	0.214468	+	0.481703i	0.988458	−	0.151495i	$-0.0484087\pi$
$619$	5.33590	+	11.9846i	0.214468	+	0.481703i	−0.773990	+	0.633198i	$0.781742\pi$
$620$	−0.481479	−	4.58097i	−0.0193367	−	0.183976i
$621$	−6.33023	−	29.7814i	−0.254023	−	1.19509i
$622$	−0.241346	+	0.742787i	−0.00967710	+	0.0297831i
$623$	15.8627	+	36.3648i	0.635527	+	1.45693i
$624$	−16.5845	+	22.8266i	−0.663910	+	0.913794i
$625$	4.49096	−	4.98772i	0.179638	−	0.199509i
$626$	−0.273980	+	0.474547i	−0.0109504	+	0.0189667i
$627$	9.52136	−	1.70209i	0.380247	−	0.0679751i
$628$	−17.0016	+	9.81585i	−0.678436	+	0.391695i
$629$	−5.35502	−	16.4811i	−0.213519	−	0.657143i
$630$	−0.121043	+	0.0247748i	−0.00482249	+	0.000987052i
$631$	17.6825	−	12.8471i	0.703928	−	0.511434i	−0.177281	−	0.984160i	$-0.556730\pi$
$631$	17.6825	−	12.8471i	0.703928	−	0.511434i	0.881209	+	0.472726i	$0.156730\pi$
$632$	0.684959	−	0.145593i	0.0272462	−	0.00579136i
$633$	−6.27942	−	6.97400i	−0.249584	−	0.277192i
$634$	−0.00531392		0.000558515i	−0.000211043		2.21815e-5i
$635$	−0.178763	+	1.70081i	−0.00709398	+	0.0674947i
$636$	20.9237	−	6.79854i	0.829680	−	0.269579i
$637$	−3.59349	−	39.9904i	−0.142379	−	1.58448i
$638$	−0.0972161	+	0.393877i	−0.00384882	+	0.0155937i
$639$	−0.343708	−	0.595320i	−0.0135969	−	0.0235505i
$640$	−0.983837	−	0.209121i	−0.0388896	−	0.00826623i
$641$	1.21328	−	0.540188i	0.0479218	−	0.0213361i	−0.382636	−	0.923899i	$-0.624984\pi$
$641$	1.21328	−	0.540188i	0.0479218	−	0.0213361i	0.430558	+	0.902563i	$0.358317\pi$
$642$	0.164347	−	0.369130i	0.00648628	−	0.0145684i
$643$	−9.74239	−	3.16549i	−0.384202	−	0.124835i	0.110546	−	0.993871i	$-0.464740\pi$
$643$	−9.74239	−	3.16549i	−0.384202	−	0.124835i	−0.494749	+	0.869036i	$0.664740\pi$
$644$	14.3946	+	25.3727i	0.567227	+	0.999826i
$645$	−1.61971	−	2.22935i	−0.0637762	−	0.0877804i
$646$	−0.400102	−	0.0420524i	−0.0157418	−	0.00165453i
$647$	−6.61724	+	31.1317i	−0.260151	+	1.22391i	0.632999	+	0.774153i	$0.281824\pi$
$647$	−6.61724	+	31.1317i	−0.260151	+	1.22391i	−0.893149	+	0.449760i	$0.851510\pi$
$648$	−0.220721	−	0.127433i	−0.00867074	−	0.00500605i
$649$	−29.3086	−	0.954109i	−1.15046	−	0.0374521i
$650$		−	0.571043i		−	0.0223981i
$651$	0.629254	+	6.45548i	0.0246624	+	0.253010i
$652$	−31.0452	−	22.5556i	−1.21582	−	0.883347i
$653$	19.8527	+	8.83900i	0.776897	+	0.345897i	0.756584	−	0.653897i	$-0.226867\pi$
$653$	19.8527	+	8.83900i	0.776897	+	0.345897i	0.0203134	+	0.999794i	$0.493534\pi$
$654$	0.359345	−	0.323556i	0.0140515	−	0.0126520i
$655$	0.300372	−	0.270456i	0.0117365	−	0.0105676i
$656$	5.14652	+	2.29138i	0.200938	+	0.0894634i
$657$	0.362619	+	0.263458i	0.0141471	+	0.0102785i
$658$	0.272759	−	0.195041i	0.0106332	−	0.00760350i
$659$			32.8951i			1.28141i	0.767787	+	0.640705i	$0.221358\pi$
$659$			32.8951i			1.28141i	−0.767787	+	0.640705i	$0.778642\pi$
$660$	5.30015	+	7.81786i	0.206308	+	0.304310i
$661$	2.95425	+	1.70564i	0.114907	+	0.0663417i	0.556352	−	0.830947i	$-0.312201\pi$
$661$	2.95425	+	1.70564i	0.114907	+	0.0663417i	−0.441445	+	0.897288i	$0.645534\pi$
$662$	0.0482707	−	0.227096i	0.00187609	−	0.00882633i
$663$	−43.8646	−	4.61035i	−1.70356	−	0.179051i
$664$	−0.260575	−	0.358651i	−0.0101123	−	0.0139184i
$665$	−0.0547538	+	7.25122i	−0.00212326	+	0.281190i
$666$	−0.106501	−	0.0346042i	−0.00412682	−	0.00134089i
$667$	10.0909	−	22.6646i	0.390722	−	0.877577i
$668$	−5.74974	+	2.55995i	−0.222464	+	0.0990473i
$669$	−1.15040	−	0.244526i	−0.0444772	−	0.00945392i
$670$	−0.157532	−	0.272854i	−0.00608601	−	0.0105413i
$671$	−6.59085	+	0.476538i	−0.254437	+	0.0183966i
$672$	1.03739	+	0.228704i	0.0400180	+	0.00882243i
$673$	−27.6268	+	8.97650i	−1.06494	+	0.346019i	−0.788513	−	0.615018i	$-0.789149\pi$
$673$	−27.6268	+	8.97650i	−1.06494	+	0.346019i	−0.276423	+	0.961036i	$0.589149\pi$
$674$	0.0462831	−	0.440354i	0.00178276	−	0.0169618i
$675$	−20.1025	+	2.11285i	−0.773744	+	0.0813238i
$676$	26.6228	+	29.5676i	1.02395	+	1.13722i
$677$	−18.4482	+	3.92128i	−0.709020	+	0.150707i	−0.548286	−	0.836291i	$-0.684720\pi$
$677$	−18.4482	+	3.92128i	−0.709020	+	0.150707i	−0.160734	+	0.986998i	$0.551386\pi$
$678$	−0.00185501	+	0.00134775i	−7.12414e−5	+	5.17599e-5i
$679$	2.60186	+	12.7120i	0.0998501	+	0.487842i
$680$	−0.242844	−	0.747396i	−0.00931264	−	0.0286613i
$681$	−22.1487	+	12.7875i	−0.848739	+	0.490020i
$682$	0.158360	−	0.0846823i	0.00606391	−	0.00324265i
$683$	7.06832	−	12.2427i	0.270462	−	0.468454i	−0.698518	−	0.715592i	$-0.746157\pi$
$683$	7.06832	−	12.2427i	0.270462	−	0.468454i	0.968980	+	0.247138i	$0.0794903\pi$
$684$	4.70378	−	5.22407i	0.179853	−	0.199747i
$685$	6.69014	−	9.20819i	0.255617	−	0.351827i
$686$	−0.441712	+	0.241851i	−0.0168646	+	0.00923393i
$687$	−6.44236	+	19.8276i	−0.245791	+	0.756468i
$688$	−1.60707	−	7.56066i	−0.0612689	−	0.288248i
$689$	−5.35922	−	50.9896i	−0.204170	−	1.94255i
$690$	0.0868812	+	0.195138i	0.00330751	+	0.00742879i
$691$	37.3080	+	33.5923i	1.41926	+	1.27791i	0.908308	+	0.418303i	$0.137375\pi$
$691$	37.3080	+	33.5923i	1.41926	+	1.27791i	0.510955	+	0.859607i	$0.329292\pi$
$692$	20.6038			0.783240
$693$	7.22740	+	10.8359i	0.274546	+	0.411621i
$694$	−0.260462			−0.00988700
$695$	−11.4724	−	10.3298i	−0.435175	−	0.391833i
$696$	−0.244962	−	0.550195i	−0.00928528	−	0.0208551i
$697$	0.920524	+	8.75820i	0.0348673	+	0.331740i
$698$	−0.0650153	−	0.305873i	−0.00246087	−	0.0115775i
$699$	−11.0644	+	34.0526i	−0.418493	+	1.28799i
$700$	17.7513	−	7.74330i	0.670935	−	0.292669i
$701$	−6.93401	+	9.54384i	−0.261894	+	0.360466i	−0.919632	−	0.392780i	$-0.871513\pi$
$701$	−6.93401	+	9.54384i	−0.261894	+	0.360466i	0.657738	+	0.753246i	$0.271513\pi$
$702$	−0.576160	+	0.639891i	−0.0217458	+	0.0241511i
$703$	−3.28615	+	5.69177i	−0.123939	+	0.214669i
$704$	4.65882	+	26.0610i	0.175586	+	0.982212i
$705$	−5.74980	+	3.31965i	−0.216550	+	0.125025i
$706$	−0.104494	−	0.321600i	−0.00393268	−	0.0121036i
$707$	−11.0555	+	33.1710i	−0.415785	+	1.24752i
$708$	17.6058	−	12.7914i	0.661668	−	0.480730i
$709$	18.2346	−	3.87588i	0.684814	−	0.145562i	0.147650	−	0.989040i	$-0.452829\pi$
$709$	18.2346	−	3.87588i	0.684814	−	0.145562i	0.537164	+	0.843478i	$0.319496\pi$
$710$	0.00974917	+	0.0108275i	0.000365880	+	0.000406351i
$711$	−9.50604	+	0.999125i	−0.356504	+	0.0374701i
$712$	−0.170451	+	1.62173i	−0.00638793	+	0.0607771i
$713$	−10.4443	+	3.39356i	−0.391143	+	0.127090i
$714$	0.166967	+	0.527390i	0.00624860	+	0.0197371i
$715$	20.3888	−	8.29373i	0.762497	−	0.310168i
$716$	8.64491	+	14.9734i	0.323075	+	0.559583i
$717$	−30.3776	−	6.45695i	−1.13447	−	0.241139i
$718$	0.438103	−	0.195056i	0.0163499	−	0.00727943i
$719$	−9.13653	+	20.5210i	−0.340735	+	0.765304i	0.659176	+	0.751989i	$0.270905\pi$
$719$	−9.13653	+	20.5210i	−0.340735	+	0.765304i	−0.999911	+	0.0133152i	$0.995762\pi$
$720$	6.52618	+	2.12049i	0.243217	+	0.0790258i
$721$	18.7570	+	11.0190i	0.698547	+	0.410370i
$722$	−0.213986	−	0.294526i	−0.00796373	−	0.0109611i
$723$	−0.274430	−	0.0288438i	−0.0102062	−	0.00107271i
$724$	10.0915	−	47.4766i	0.375046	−	1.76445i
$725$	−14.2640	−	8.23535i	−0.529753	−	0.305853i
$726$	−0.204467	+	0.306249i	−0.00758850	+	0.0113660i
$727$		−	20.8136i		−	0.771936i	−0.922512	−	0.385968i	$-0.873868\pi$
$727$		−	20.8136i		−	0.771936i	0.922512	−	0.385968i	$-0.126132\pi$
$728$	0.682600	−	1.50251i	0.0252988	−	0.0556867i
$729$	19.3105	+	14.0299i	0.715203	+	0.519625i
$730$	−0.00867880	−	0.00386405i	−0.000321217	−	0.000143015i
$731$	8.97936	−	8.08506i	0.332114	−	0.299037i
$732$	3.64436	−	3.28140i	0.134699	−	0.121284i
$733$	−1.56901	−	0.698570i	−0.0579529	−	0.0258023i	0.377556	−	0.925987i	$-0.376765\pi$
$733$	−1.56901	−	0.698570i	−0.0579529	−	0.0258023i	−0.435508	+	0.900185i	$0.643431\pi$
$734$	0.120844	+	0.0877984i	0.00446044	+	0.00324070i
$735$	9.16920	−	3.91757i	0.338211	−	0.144502i
$736$			1.79861i			0.0662977i
$737$	−20.3869	+	26.2215i	−0.750960	+	0.965883i
$738$	0.0492832	+	0.0284537i	0.00181414	+	0.00104739i
$739$	8.49334	−	39.9580i	0.312433	−	1.46988i	−0.489257	−	0.872140i	$-0.662732\pi$
$739$	8.49334	−	39.9580i	0.312433	−	1.46988i	0.801690	−	0.597740i	$-0.203935\pi$
$740$	−6.38277	−	0.670856i	−0.234635	−	0.0246612i
$741$	9.83233	+	13.5330i	0.361200	+	0.497149i
$742$	−0.559304	+	0.317308i	−0.0205327	+	0.0116487i
$743$	−31.2956	−	10.1686i	−1.14813	−	0.373049i	−0.327689	−	0.944786i	$-0.606270\pi$
$743$	−31.2956	−	10.1686i	−1.14813	−	0.373049i	−0.820437	+	0.571737i	$0.806270\pi$
$744$	−0.108431	+	0.243541i	−0.00397529	+	0.00892864i
$745$	8.14111	−	3.62466i	0.298267	−	0.132797i
$746$	−0.610667	−	0.129801i	−0.0223581	−	0.00475236i
$747$	3.02559	+	5.24047i	0.110700	+	0.191739i
$748$	−31.6629	+	26.6961i	−1.15771	+	0.976108i
$749$	6.87537	−	31.1863i	0.251220	−	1.13952i
$750$	0.319051	−	0.103666i	0.0116501	−	0.00378535i
$751$	−0.164413	+	1.56428i	−0.00599950	+	0.0570814i	−0.997112	−	0.0759447i	$-0.975803\pi$
$751$	−0.164413	+	1.56428i	−0.00599950	+	0.0570814i	0.991113	+	0.133026i	$0.0424694\pi$
$752$	−18.5213	+	1.94667i	−0.675403	+	0.0709877i
$753$	19.4600	+	21.6125i	0.709161	+	0.787603i
$754$	−0.686300	+	0.145878i	−0.0249936	+	0.00531255i
$755$	−2.40038	+	1.74398i	−0.0873587	+	0.0634698i
$756$	−27.7042	−	9.23347i	−1.00759	−	0.335818i
$757$	−1.02317	−	3.14898i	−0.0371876	−	0.114452i	0.930740	−	0.365683i	$-0.119165\pi$
$757$	−1.02317	−	3.14898i	−0.0371876	−	0.114452i	−0.967927	+	0.251231i	$0.919165\pi$
$758$	0.360645	−	0.208218i	0.0130992	−	0.00756283i
$759$	15.6043	−	16.2354i	0.566400	−	0.589306i
$760$	−0.149023	+	0.258115i	−0.00540563	+	0.00936282i
$761$	31.1862	−	34.6358i	1.13050	−	1.25555i	0.167549	−	0.985864i	$-0.446415\pi$
$761$	31.1862	−	34.6358i	1.13050	−	1.25555i	0.962949	−	0.269682i	$-0.0869186\pi$
$762$	0.0290837	−	0.0400302i	0.00105359	−	0.00145014i
$763$	22.6963	−	30.7478i	0.821660	−	1.11314i
$764$	4.88727	−	15.0415i	0.176815	−	0.544182i
$765$	2.23022	+	10.4924i	0.0806339	+	0.379353i
$766$	0.0638758	+	0.607738i	0.00230793	+	0.0219584i
$767$	−20.6275	−	46.3301i	−0.744816	−	1.67288i
$768$	−14.5843	−	13.1318i	−0.526267	−	0.473853i
$769$	−32.6455			−1.17723			−0.588613	−	0.808415i	$-0.700326\pi$
$769$	−32.6455			−1.17723			−0.588613	+	0.808415i	$0.700326\pi$
$770$	−0.197589	−	0.192800i	−0.00712062	−	0.00694804i
$771$	−13.8451			−0.498619
$772$	12.4944	+	11.2500i	0.449683	+	0.404896i
$773$	12.1880	+	27.3748i	0.438373	+	0.984602i	0.988735	+	0.149676i	$0.0478230\pi$
$773$	12.1880	+	27.3748i	0.438373	+	0.984602i	−0.550362	+	0.834926i	$0.685510\pi$
$774$	−0.00816158	−	0.0776523i	−0.000293362	−	0.00279115i
$775$	1.51582	+	7.13136i	0.0544497	+	0.256166i
$776$	−0.164804	+	0.507215i	−0.00591612	+	0.0182079i
$777$	8.98031	+	1.01248i	0.322167	+	0.0363226i
$778$	0.233569	−	0.321480i	0.00837384	−	0.0115256i
$779$	2.23486	−	2.48206i	0.0800720	−	0.0889290i
$780$	−8.16744	+	14.1464i	−0.292441	+	0.506523i
$781$	0.670059	−	1.38211i	0.0239766	−	0.0494557i
$782$	−0.811139	+	0.468312i	−0.0290063	+	0.0167468i
$783$	7.67465	+	23.6201i	0.274270	+	0.844115i
$784$	27.9658	+	0.422362i	0.998777	+	0.0150844i
$785$	−9.19153	+	6.67804i	−0.328060	+	0.238349i
$786$	−0.0114388	+	0.00243138i	−0.000408007	+	8.67246e-5i
$787$	−1.82775	−	2.02992i	−0.0651521	−	0.0723588i	0.709688	−	0.704517i	$-0.248836\pi$
$787$	−1.82775	−	2.02992i	−0.0651521	−	0.0723588i	−0.774840	+	0.632158i	$0.782169\pi$
$788$	25.3127	−	2.66047i	0.901727	−	0.0947753i
$789$	2.53988	−	24.1653i	0.0904219	−	0.860307i
$790$	0.192676	−	0.0626043i	0.00685512	−	0.00222736i
$791$	−0.122274	+	0.133754i	−0.00434757	+	0.00475575i
$792$	0.0386067	+	0.533957i	0.00137183	+	0.0189733i
$793$	−5.71415	−	9.89720i	−0.202915	−	0.351460i
$794$	−0.129997	−	0.0276318i	−0.00461343	−	0.000980616i
$795$	11.6315	−	5.17867i	0.412526	−	0.183669i
$796$	−9.13028	+	20.5069i	−0.323614	+	0.726849i
$797$	39.1366	+	12.7162i	1.38629	+	0.450432i	0.904731	−	0.425982i	$-0.140071\pi$
$797$	39.1366	+	12.7162i	1.38629	+	0.450432i	0.481557	+	0.876415i	$0.340071\pi$
$798$	0.106270	−	0.180897i	0.00376193	−	0.00640370i
$799$	−17.1117	−	23.5522i	−0.605368	−	0.833218i
$800$	1.18753	+	0.124815i	0.0419856	+	0.00441287i
$801$	4.62774	−	21.7718i	0.163513	−	0.769269i
$802$	0.527500	+	0.304552i	0.0186267	+	0.0107541i
$803$	−0.0325858	+	1.00098i	−0.00114993	+	0.0353238i
$804$		−	24.6490i		−	0.869304i
$805$	9.81976	+	13.7326i	0.346101	+	0.484011i
$806$	0.251260	+	0.182551i	0.00885025	+	0.00643008i
$807$	11.8649	+	5.28259i	0.417664	+	0.185956i
$808$	−1.06798	+	0.961616i	−0.0375715	+	0.0338295i
$809$	34.2222	−	30.8138i	1.20319	−	1.08335i	0.208756	−	0.977968i	$-0.433059\pi$
$809$	34.2222	−	30.8138i	1.20319	−	1.08335i	0.994431	−	0.105387i	$-0.0336081\pi$
$810$	−0.0673604	−	0.0299908i	−0.00236680	−	0.00105377i
$811$	−31.6058	−	22.9629i	−1.10983	−	0.806337i	−0.127192	−	0.991878i	$-0.540596\pi$
$811$	−31.6058	−	22.9629i	−1.10983	−	0.806337i	−0.982637	+	0.185541i	$0.940596\pi$
$812$	−13.8409	−	19.3560i	−0.485720	−	0.679264i
$813$		−	26.5310i		−	0.930484i
$814$	−0.0695364	−	0.240356i	−0.00243725	−	0.00842448i
$815$	−19.2326	−	11.1040i	−0.673690	−	0.388955i
$816$	6.38782	−	30.0523i	0.223618	−	1.05204i
$817$	−4.55748	−	0.479010i	−0.159446	−	0.0167585i
$818$	−0.609142	−	0.838411i	−0.0212981	−	0.0293144i
$819$	−11.4100	+	19.4226i	−0.398699	+	0.678681i
$820$	3.10187	+	1.00786i	0.108322	+	0.0351959i
$821$	−4.77810	+	10.7318i	−0.166757	+	0.374542i	−0.977523	−	0.210828i	$-0.932384\pi$
$821$	−4.77810	+	10.7318i	−0.166757	+	0.374542i	0.810766	+	0.585370i	$0.199051\pi$
$822$	−0.300840	+	0.133942i	−0.0104930	+	0.00467178i
$823$	1.75383	+	0.372788i	0.0611347	+	0.0129946i	0.238377	−	0.971173i	$-0.423384\pi$
$823$	1.75383	+	0.372788i	0.0611347	+	0.0129946i	−0.177243	+	0.984167i	$0.556718\pi$
$824$	0.447067	+	0.774342i	0.0155743	+	0.0269755i
$825$	−9.63653	−	11.4294i	−0.335501	−	0.397920i
$826$	−0.429173	+	0.469467i	−0.0149328	+	0.0163349i
$827$	4.92332	−	1.59968i	0.171201	−	0.0556264i	−0.222163	−	0.975010i	$-0.571312\pi$
$827$	4.92332	−	1.59968i	0.171201	−	0.0556264i	0.393363	+	0.919383i	$0.371312\pi$
$828$	1.71072	−	16.2764i	0.0594516	−	0.565644i
$829$	−25.5374	+	2.68408i	−0.886949	+	0.0932221i	−0.537035	−	0.843560i	$-0.680456\pi$
$829$	−25.5374	+	2.68408i	−0.886949	+	0.0932221i	−0.349914	+	0.936782i	$0.613789\pi$
$830$	−0.0858197	−	0.0953125i	−0.00297885	−	0.00330834i
$831$	0.926456	−	0.196924i	0.0321384	−	0.00683123i
$832$	−37.0414	+	26.9122i	−1.28418	+	0.933011i
$833$	21.2864	+	38.1895i	0.737528	+	1.32319i
$834$	0.138024	+	0.424793i	0.00477936	+	0.0147094i
$835$	−3.15443	+	1.82121i	−0.109163	+	0.0630255i
$836$	15.5595	+	2.14924i	0.538135	+	0.0743330i
$837$	5.49670	−	9.52056i	0.189994	−	0.329079i
$838$	0.260545	−	0.289364i	0.00900037	−	0.00999592i
$839$	−8.11024	+	11.1628i	−0.279996	+	0.385382i	−0.925733	−	0.378179i	$-0.876551\pi$
$839$	−8.11024	+	11.1628i	−0.279996	+	0.385382i	0.645736	+	0.763561i	$0.276551\pi$
$840$	0.407246	+	0.0459149i	0.0140513	+	0.00158421i
$841$	2.70781	−	8.33379i	0.0933728	−	0.287372i
$842$	−0.114690	−	0.539575i	−0.00395248	−	0.0185950i
$843$	2.12629	+	20.2303i	0.0732333	+	0.696768i
$844$	−6.19855	−	13.9222i	−0.213363	−	0.479221i
$845$	17.1115	+	15.4073i	0.588654	+	0.530026i
$846$	−0.188123			−0.00646780
$847$	−10.9784	+	26.9532i	−0.377222	+	0.926123i
$848$	35.7142			1.22643
$849$	7.75538	+	6.98298i	0.266164	+	0.239655i
$850$	0.252914	+	0.568053i	0.00867487	+	0.0194841i
$851$	1.59941	+	15.2174i	0.0548271	+	0.521645i
$852$	0.236993	+	1.11496i	0.00811925	+	0.0381980i
$853$	−15.8472	+	48.7726i	−0.542598	+	1.66994i	0.184037	+	0.982919i	$0.441083\pi$
$853$	−15.8472	+	48.7726i	−0.542598	+	1.66994i	−0.726634	+	0.687024i	$0.758917\pi$
$854$	−0.0851240	+	0.115322i	−0.00291288	+	0.00394623i
$855$	2.39126	−	3.29128i	0.0817793	−	0.112560i
$856$	0.878293	−	0.975443i	0.0300194	−	0.0333400i
$857$	7.34751	−	12.7263i	0.250986	−	0.434721i	−0.712812	−	0.701356i	$-0.752579\pi$
$857$	7.34751	−	12.7263i	0.250986	−	0.434721i	0.963798	+	0.266635i	$0.0859118\pi$
$858$	−0.630850	−	0.0871397i	−0.0215369	−	0.00297490i
$859$	18.2065	−	10.5115i	0.621197	−	0.358649i	−0.156138	−	0.987735i	$-0.549904\pi$
$859$	18.2065	−	10.5115i	0.621197	−	0.358649i	0.777335	+	0.629087i	$0.216571\pi$
$860$	−1.38284	−	4.25593i	−0.0471543	−	0.145126i
$861$	−4.35695	−	1.45212i	−0.148485	−	0.0494882i
$862$	0.722243	−	0.524740i	0.0245997	−	0.0178727i
$863$	53.9023	−	11.4573i	1.83486	−	0.390011i	0.845317	−	0.534266i	$-0.179412\pi$
$863$	53.9023	−	11.4573i	1.83486	−	0.390011i	0.989541	+	0.144255i	$0.0460784\pi$
$864$	−1.20478	−	1.33804i	−0.0409873	−	0.0455210i
$865$	11.8586	−	1.24639i	0.403205	−	0.0423786i
$866$	0.0654775	−	0.622977i	0.00222502	−	0.0211696i
$867$	25.7722	−	8.37388i	0.875269	−	0.284392i
$868$	−2.26766	+	10.2860i	−0.0769694	+	0.349129i
$869$	−13.7669	−	16.3282i	−0.467010	−	0.553896i
$870$	−0.0871200	−	0.150896i	−0.00295364	−	0.00511586i
$871$	−56.1873	−	11.9430i	−1.90383	−	0.404672i
$872$	1.43499	−	0.638897i	0.0485947	−	0.0216358i
$873$	2.96090	−	6.65029i	0.100211	−	0.225078i
$874$	0.337839	+	0.109770i	0.0114276	+	0.00371304i
$875$	23.0612	−	13.0832i	0.779609	−	0.442293i
$876$	−0.436866	−	0.601294i	−0.0147603	−	0.0203158i
$877$	−21.3896	−	2.24814i	−0.722277	−	0.0759143i	−0.263745	−	0.964592i	$-0.584958\pi$
$877$	−21.3896	−	2.24814i	−0.722277	−	0.0759143i	−0.458532	+	0.888678i	$0.651624\pi$
$878$	0.108648	−	0.511149i	0.00366669	−	0.0172504i
$879$	19.0149	+	10.9783i	0.641357	+	0.370288i
$880$	4.26107	+	14.7286i	0.143641	+	0.496501i
$881$			55.5027i			1.86993i	0.354733	+	0.934967i	$0.384572\pi$
$881$			55.5027i			1.86993i	−0.354733	+	0.934967i	$0.615428\pi$
$882$	0.280502	+	0.0337719i	0.00944498	+	0.00113716i
$883$	−6.31201	−	4.58594i	−0.212416	−	0.154329i	0.476490	−	0.879180i	$-0.341909\pi$
$883$	−6.31201	−	4.58594i	−0.212416	−	0.154329i	−0.688906	+	0.724851i	$0.741909\pi$
$884$	−65.4332	−	29.1327i	−2.20076	−	0.979840i
$885$	9.35933	−	8.42718i	0.314610	−	0.283277i
$886$	−0.398111	+	0.358461i	−0.0133748	+	0.0120427i
$887$	−37.4203	−	16.6606i	−1.25645	−	0.559408i	−0.332929	−	0.942952i	$-0.608037\pi$
$887$	−37.4203	−	16.6606i	−1.25645	−	0.559408i	−0.923523	+	0.383544i	$0.874704\pi$
$888$	0.300505	+	0.218329i	0.0100843	+	0.00732666i
$889$	1.61754	−	3.56045i	0.0542505	−	0.119414i
$890$			0.471767i			0.0158137i
$891$	−0.252914	+	7.76910i	−0.00847295	+	0.260275i
$892$	−1.65404	−	0.954959i	−0.0553813	−	0.0319744i
$893$	−2.29557	+	10.7998i	−0.0768185	+	0.361402i
$894$	−0.256423	−	0.0269511i	−0.00857605	−	0.000901380i
$895$	5.88140	+	8.09506i	0.196594	+	0.270588i
$896$	1.98311	+	1.16500i	0.0662511	+	0.0389200i
$897$	37.0384	+	12.0345i	1.23668	+	0.401821i
$898$	−0.108810	+	0.244392i	−0.00363104	+	0.00815545i
$899$	8.18350	−	3.64353i	0.272935	−	0.121519i
$900$	−10.6278	−	2.25901i	−0.354260	−	0.0753002i
$901$	27.9143	+	48.3491i	0.929962	+	1.61074i
$902$	0.00916970	+	0.126823i	0.000305317	+	0.00422275i
$903$	1.90189	+	6.00739i	0.0632909	+	0.199913i
$904$	−0.00708394	+	0.00230171i	−0.000235608	+	7.65538e-5i
$905$	2.93617	−	27.9358i	0.0976017	−	0.928618i
$906$	0.0853738	−	0.00897315i	0.00283635	−	0.000298113i
$907$	6.94735	+	7.71581i	0.230683	+	0.256199i	0.847362	−	0.531015i	$-0.178189\pi$
$907$	6.94735	+	7.71581i	0.230683	+	0.256199i	−0.616680	+	0.787214i	$0.711523\pi$
$908$	−40.6247	+	8.63504i	−1.34818	+	0.286564i
$909$	15.8699	−	11.5301i	0.526370	−	0.382430i
$910$	0.150963	−	0.452950i	0.00500438	−	0.0150152i
$911$	−4.85068	−	14.9289i	−0.160710	−	0.494615i	0.837984	−	0.545694i	$-0.183734\pi$
$911$	−4.85068	−	14.9289i	−0.160710	−	0.494615i	−0.998695	+	0.0510789i	$0.983734\pi$
$912$	−10.0912	+	5.82615i	−0.334153	+	0.192923i
$913$	−5.89838	+	12.1664i	−0.195208	+	0.402649i
$914$	−0.154241	+	0.267153i	−0.00510182	+	0.00883662i
$915$	1.89903	−	2.10908i	0.0627798	−	0.0697241i
$916$	−19.8999	+	27.3898i	−0.657510	+	0.904985i
$917$	−0.847167	+	0.369544i	−0.0279759	+	0.0122034i
$918$	0.289738	−	0.891722i	0.00956278	−	0.0294312i
$919$	9.50099	+	44.6987i	0.313409	+	1.47447i	0.799554	+	0.600595i	$0.205069\pi$
$919$	9.50099	+	44.6987i	0.313409	+	1.47447i	−0.486145	+	0.873878i	$0.661597\pi$
$920$	0.0725314	+	0.690090i	0.00239129	+	0.0227516i
$921$	10.2414	+	23.0025i	0.337465	+	0.757960i
$922$	−0.472310	−	0.425270i	−0.0155547	−	0.0140055i
$923$	2.65638			0.0874358
$924$	−5.84548	−	20.7920i	−0.192302	−	0.684008i
$925$	10.1583			0.334002
$926$	0.271643	+	0.244589i	0.00892675	+	0.00803769i
$927$	−4.96410	−	11.1495i	−0.163042	−	0.366199i
$928$	−0.153358	−	1.45911i	−0.00503423	−	0.0478975i
$929$	−4.28715	−	20.1695i	−0.140657	−	0.661738i	−0.990816	−	0.135213i	$-0.956828\pi$
$929$	−4.28715	−	20.1695i	−0.140657	−	0.661738i	0.850160	−	0.526525i	$-0.176505\pi$
$930$	−0.0238334	+	0.0733516i	−0.000781528	+	0.00240530i
$931$	5.36161	−	15.6910i	0.175720	−	0.514253i
$932$	−34.1768	+	47.0404i	−1.11950	+	1.54086i
$933$	−23.6614	+	26.2787i	−0.774641	+	0.860326i
$934$	0.458145	−	0.793530i	0.0149910	−	0.0259651i
$935$	−16.6088	+	17.2805i	−0.543165	+	0.565132i
$936$	−0.801820	+	0.462931i	−0.0262083	+	0.0151314i
$937$	−13.0474	−	40.1558i	−0.426241	−	1.31183i	−0.901801	−	0.432151i	$-0.857755\pi$
$937$	−13.0474	−	40.1558i	−0.426241	−	1.31183i	0.475561	−	0.879683i	$-0.342245\pi$
$938$	0.144466	+	0.705823i	0.00471698	+	0.0230459i
$939$	−20.0714	+	14.5827i	−0.655006	+	0.475890i
$940$	−10.5462	+	2.24166i	−0.343978	+	0.0731148i
$941$	−35.6036	−	39.5418i	−1.16064	−	1.28902i	−0.950278	−	0.311402i	$-0.899202\pi$
$941$	−35.6036	−	39.5418i	−1.16064	−	1.28902i	−0.210365	−	0.977623i	$-0.567465\pi$
$942$	0.326913	−	0.0343600i	0.0106514	−	0.00111951i
$943$	0.812796	−	7.73324i	0.0264683	−	0.251829i
$944$	33.5980	−	10.9167i	1.09352	−	0.355307i
$945$	−16.5038	−	3.63845i	−0.536869	−	0.118359i
$946$	0.133381	−	0.112458i	0.00433658	−	0.00365633i
$947$	−14.9992	−	25.9793i	−0.487407	−	0.844214i	0.512488	−	0.858695i	$-0.328724\pi$
$947$	−14.9992	−	25.9793i	−0.487407	−	0.844214i	−0.999895	+	0.0144802i	$0.995391\pi$
$948$	15.5034	+	3.29535i	0.503526	+	0.107028i
$949$	−1.58232	+	0.704493i	−0.0513642	+	0.0228688i
$950$	0.0959203	−	0.215441i	0.00311207	−	0.00698981i
$951$	−0.230080	−	0.0747575i	−0.00746085	−	0.00242418i
$952$	−0.0135689	+	1.79697i	−0.000439769	+	0.0582400i
$953$	21.6006	+	29.7307i	0.699713	+	0.963072i	0.999958	+	0.00920971i	$0.00293158\pi$
$953$	21.6006	+	29.7307i	0.699713	+	0.963072i	−0.300245	+	0.953862i	$0.597068\pi$
$954$	0.358789	+	0.0377103i	0.0116162	+	0.00122092i
$955$	1.90298	−	8.95284i	0.0615791	−	0.289707i
$956$	−43.6765	−	25.2166i	−1.41260	−	0.815565i
$957$	−11.2745	+	14.5013i	−0.364454	+	0.468760i
$958$		−	0.572123i		−	0.0184845i
$959$	−21.1712	+	15.1389i	−0.683654	+	0.488859i
$960$	−9.19869	−	6.68324i	−0.296886	−	0.215701i
$961$	24.6975	+	10.9960i	0.796694	+	0.354711i
$962$	0.321581	−	0.289553i	0.0103682	−	0.00933556i
$963$	−13.3146	+	11.9885i	−0.429056	+	0.386323i
$964$	−0.409370	−	0.182263i	−0.0131849	−	0.00587030i
$965$	7.87175	+	5.71916i	0.253401	+	0.184106i
$966$	−0.0473875	−	0.486146i	−0.00152467	−	0.0156415i
$967$		−	7.63848i		−	0.245637i	−0.992429	−	0.122818i	$-0.960807\pi$
$967$		−	7.63848i		−	0.245637i	0.992429	−	0.122818i	$-0.0391933\pi$
$968$	−0.939120	+	0.740899i	−0.0301845	+	0.0238134i
$969$	−15.7746	−	9.10748i	−0.506754	−	0.292575i
$970$	−0.0320794	+	0.150922i	−0.00103001	+	0.00484580i
$971$	−20.6910	−	2.17471i	−0.664005	−	0.0697898i	−0.233471	−	0.972364i	$-0.575008\pi$
$971$	−20.6910	−	2.17471i	−0.664005	−	0.0697898i	−0.430535	+	0.902574i	$0.641675\pi$
$972$	16.0722	+	22.1215i	0.515517	+	0.709548i
$973$	17.4193	+	30.7042i	0.558436	+	0.984331i
$974$	0.369334	+	0.120004i	0.0118342	+	0.00384517i
$975$	10.5161	−	23.6195i	0.336784	−	0.756429i
$976$	7.27254	−	3.23794i	0.232788	−	0.103644i
$977$	26.8480	+	5.70672i	0.858943	+	0.182574i	0.616271	−	0.787534i	$-0.288643\pi$
$977$	26.8480	+	5.70672i	0.858943	+	0.182574i	0.242673	+	0.970108i	$0.421976\pi$
$978$	0.321267	+	0.556451i	0.0102730	+	0.0177934i
$979$	46.0684	−	18.7396i	1.47235	−	0.598922i
$980$	16.1273	−	1.44918i	0.515169	−	0.0462924i
$981$	−20.3915	+	6.62559i	−0.651050	+	0.211539i
$982$	−0.00764220	+	0.0727107i	−0.000243872	+	0.00232029i
$983$	54.4782	−	5.72589i	1.73758	−	0.182628i	0.817920	−	0.575332i	$-0.195127\pi$
$983$	54.4782	−	5.72589i	1.73758	−	0.182628i	0.919665	+	0.392704i	$0.128460\pi$
$984$	−0.126307	−	0.140278i	−0.00402651	−	0.00447189i
$985$	14.4079	−	3.06249i	0.459073	−	0.0975791i
$986$	0.618099	−	0.449075i	0.0196843	−	0.0143015i
$987$	14.8737	−	3.04430i	0.473434	−	0.0969011i
$988$	8.39438	+	25.8352i	0.267061	+	0.821929i
$989$	−9.23952	+	5.33444i	−0.293800	+	0.169625i
$990$	0.0272555	+	0.152465i	0.000866235	+	0.00484565i
$991$	−17.5833	+	30.4551i	−0.558551	+	0.967439i	0.439066	+	0.898455i	$0.355309\pi$
$991$	−17.5833	+	30.4551i	−0.558551	+	0.967439i	−0.997618	+	0.0689846i	$0.978024\pi$
$992$	−0.434550	+	0.482616i	−0.0137970	+	0.0153231i
$993$	6.17868	−	8.50422i	0.196074	−	0.269873i
$994$	−0.0133210	−	0.0305379i	−0.000422516	−	0.000968604i
$995$	−4.01444	+	12.3552i	−0.127266	+	0.391685i
$996$	−2.08620	−	9.81478i	−0.0661037	−	0.310993i
$997$	6.06299	+	57.6855i	0.192017	+	1.82692i	0.489284	+	0.872124i	$0.337258\pi$
$997$	6.06299	+	57.6855i	0.192017	+	1.82692i	−0.297267	+	0.954794i	$0.596075\pi$
$998$	0.295192	+	0.663011i	0.00934413	+	0.0209873i
$999$	−11.3830	−	10.2493i	−0.360142	−	0.324274i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.n.a.17.4	✓	48
3.2	odd	2		693.2.cg.a.325.3		48
7.2	even	3		539.2.s.d.215.4		48
7.3	odd	6		539.2.m.a.391.6		48
7.4	even	3		539.2.m.a.391.5		48
7.5	odd	6	inner	77.2.n.a.61.4	yes	48
7.6	odd	2		539.2.s.d.325.4		48
11.2	odd	10	inner	77.2.n.a.24.4	yes	48
11.3	even	5		847.2.i.b.241.12		48
11.4	even	5		847.2.r.a.360.3		48
11.5	even	5		847.2.r.d.766.3		48
11.6	odd	10		847.2.r.a.766.4		48
11.7	odd	10		847.2.r.d.360.4		48
11.8	odd	10		847.2.i.b.241.13		48
11.9	even	5		847.2.r.c.717.3		48
11.10	odd	2		847.2.r.c.94.3		48
21.5	even	6		693.2.cg.a.523.3		48
33.2	even	10		693.2.cg.a.640.3		48
77.2	odd	30		539.2.s.d.68.4		48
77.5	odd	30		847.2.r.d.40.4		48
77.13	even	10		539.2.s.d.178.4		48
77.19	even	30		847.2.i.b.362.12		48
77.24	even	30		539.2.m.a.244.5		48
77.26	odd	30		847.2.r.a.481.4		48
77.40	even	30		847.2.r.d.481.3		48
77.46	odd	30		539.2.m.a.244.6		48
77.47	odd	30		847.2.i.b.362.13		48
77.54	even	6		847.2.r.c.215.3		48
77.61	even	30		847.2.r.a.40.3		48
77.68	even	30	inner	77.2.n.a.68.4	yes	48
77.75	odd	30		847.2.r.c.838.3		48
231.68	odd	30		693.2.cg.a.145.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.n.a.17.4	✓	48	1.1	even	1	trivial
77.2.n.a.24.4	yes	48	11.2	odd	10	inner
77.2.n.a.61.4	yes	48	7.5	odd	6	inner
77.2.n.a.68.4	yes	48	77.68	even	30	inner
539.2.m.a.244.5		48	77.24	even	30
539.2.m.a.244.6		48	77.46	odd	30
539.2.m.a.391.5		48	7.4	even	3
539.2.m.a.391.6		48	7.3	odd	6
539.2.s.d.68.4		48	77.2	odd	30
539.2.s.d.178.4		48	77.13	even	10
539.2.s.d.215.4		48	7.2	even	3
539.2.s.d.325.4		48	7.6	odd	2
693.2.cg.a.145.3		48	231.68	odd	30
693.2.cg.a.325.3		48	3.2	odd	2
693.2.cg.a.523.3		48	21.5	even	6
693.2.cg.a.640.3		48	33.2	even	10
847.2.i.b.241.12		48	11.3	even	5
847.2.i.b.241.13		48	11.8	odd	10
847.2.i.b.362.12		48	77.19	even	30
847.2.i.b.362.13		48	77.47	odd	30
847.2.r.a.40.3		48	77.61	even	30
847.2.r.a.360.3		48	11.4	even	5
847.2.r.a.481.4		48	77.26	odd	30
847.2.r.a.766.4		48	11.6	odd	10
847.2.r.c.94.3		48	11.10	odd	2
847.2.r.c.215.3		48	77.54	even	6
847.2.r.c.717.3		48	11.9	even	5
847.2.r.c.838.3		48	77.75	odd	30
847.2.r.d.40.4		48	77.5	odd	30
847.2.r.d.360.4		48	11.7	odd	10
847.2.r.d.481.3		48	77.40	even	30
847.2.r.d.766.3		48	11.5	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.n (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0202070 - 0.0181945i) q^{2} +(-0.500742 - 1.12469i) q^{3} +(-0.208980 - 1.98831i) q^{4} +(-0.240558 - 1.13174i) q^{5} +(-0.0103446 + 0.0318373i) q^{6} +(-0.296416 + 2.62909i) q^{7} +(-0.0639186 + 0.0879764i) q^{8} +(0.993218 - 1.10308i) q^{9} +O(q^{10})\)	\(q+(-0.0202070 - 0.0181945i) q^{2} +(-0.500742 - 1.12469i) q^{3} +(-0.208980 - 1.98831i) q^{4} +(-0.240558 - 1.13174i) q^{5} +(-0.0103446 + 0.0318373i) q^{6} +(-0.296416 + 2.62909i) q^{7} +(-0.0639186 + 0.0879764i) q^{8} +(0.993218 - 1.10308i) q^{9} +(-0.0157304 + 0.0272459i) q^{10} +(3.28543 + 0.453819i) q^{11} +(-2.13158 + 1.23067i) q^{12} +(1.77250 + 5.45520i) q^{13} +(0.0538247 - 0.0477330i) q^{14} +(-1.15239 + 0.837261i) q^{15} +(-3.90825 + 0.830725i) q^{16} +(-4.17932 - 4.64160i) q^{17} +(-0.0401399 + 0.00421888i) q^{18} +(-0.247610 + 2.35585i) q^{19} +(-2.19997 + 0.714814i) q^{20} +(3.10533 - 0.983123i) q^{21} +(-0.0581318 - 0.0689470i) q^{22} +(2.75747 + 4.77608i) q^{23} +(0.130953 + 0.0278348i) q^{24} +(3.34477 - 1.48919i) q^{25} +(0.0634375 - 0.142483i) q^{26} +(-5.25056 - 1.70601i) q^{27} +(5.28940 + 0.0399401i) q^{28} +(-2.64421 - 3.63944i) q^{29} +(0.0385199 + 0.00404861i) q^{30} +(-0.414010 + 1.94777i) q^{31} +(0.282440 + 0.163067i) q^{32} +(-1.13475 - 3.92232i) q^{33} +0.169834i q^{34} +(3.04675 - 0.296985i) q^{35} +(-2.40083 - 1.74430i) q^{36} +(2.53463 + 1.12849i) q^{37} +(0.0478669 - 0.0430995i) q^{38} +(5.24781 - 4.72515i) q^{39} +(0.114942 + 0.0511756i) q^{40} +(-1.14068 - 0.828752i) q^{41} +(-0.0806369 - 0.0366339i) q^{42} +1.93454i q^{43} +(0.215744 - 6.62729i) q^{44} +(-1.48732 - 0.858707i) q^{45} +(0.0311781 - 0.146681i) q^{46} +(4.63547 + 0.487208i) q^{47} +(2.89133 + 3.97957i) q^{48} +(-6.82427 - 1.55861i) q^{49} +(-0.0946827 - 0.0307643i) q^{50} +(-3.12758 + 7.02467i) q^{51} +(10.4762 - 4.66430i) q^{52} +(-8.74313 - 1.85841i) q^{53} +(0.0750582 + 0.130005i) q^{54} +(-0.276733 - 3.82741i) q^{55} +(-0.212352 - 0.194126i) q^{56} +(2.77358 - 0.901189i) q^{57} +(-0.0127862 + 0.121652i) q^{58} +(-8.79313 + 0.924195i) q^{59} +(1.90556 + 2.11634i) q^{60} +(-1.94887 + 0.414244i) q^{61} +(0.0438045 - 0.0318258i) q^{62} +(2.60569 + 2.93823i) q^{63} +(2.46665 + 7.59158i) q^{64} +(5.74746 - 3.31830i) q^{65} +(-0.0484347 + 0.0999046i) q^{66} +(-5.00725 + 8.67281i) q^{67} +(-8.35555 + 9.27978i) q^{68} +(3.99081 - 5.49288i) q^{69} +(-0.0669693 - 0.0494329i) q^{70} +(0.143110 - 0.440446i) q^{71} +(0.0335599 + 0.157887i) q^{72} +(0.0315641 + 0.300313i) q^{73} +(-0.0306850 - 0.0689197i) q^{74} +(-3.34973 - 3.01611i) q^{75} +4.73590 q^{76} +(-2.16699 + 8.50319i) q^{77} -0.192014 q^{78} +(-4.78548 - 4.30886i) q^{79} +(1.88032 + 4.22328i) q^{80} +(0.244985 + 2.33087i) q^{81} +(0.00797101 + 0.0375007i) q^{82} +(-1.25976 + 3.87715i) q^{83} +(-2.60370 - 5.96891i) q^{84} +(-4.24771 + 5.84647i) q^{85} +(0.0351979 - 0.0390913i) q^{86} +(-2.76916 + 4.79632i) q^{87} +(-0.249925 + 0.260033i) q^{88} +(12.9864 - 7.49768i) q^{89} +(0.0144307 + 0.0444130i) q^{90} +(-14.8676 + 3.04306i) q^{91} +(8.92007 - 6.48081i) q^{92} +(2.39794 - 0.509697i) q^{93} +(-0.0848046 - 0.0941850i) q^{94} +(2.72577 - 0.286490i) q^{95} +(0.0419693 - 0.399311i) q^{96} +(4.66426 - 1.51551i) q^{97} +(0.109540 + 0.155659i) q^{98} +(3.76374 - 3.17335i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9}+O(q^{10}) \) 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9	\( 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} - q^{11} - 12 q^{12} - 8 q^{14} - 27 q^{16} + 15 q^{17} + 20 q^{18} - 15 q^{19} - 76 q^{22} + 10 q^{23} + 75 q^{24} + q^{25} + 27 q^{26} - 40 q^{28} - 40 q^{29} + 25 q^{30} + 9 q^{31} + 42 q^{33} + 5 q^{35} - 38 q^{36} - q^{37} + 33 q^{38} - 45 q^{39} + 75 q^{40} + 64 q^{42} + 30 q^{44} - 84 q^{45} - 20 q^{46} + 3 q^{47} + 59 q^{49} + 30 q^{50} + 55 q^{51} - 15 q^{52} - 3 q^{53} - 8 q^{56} + 60 q^{57} + 46 q^{58} - 3 q^{59} - 15 q^{60} - 30 q^{61} - 40 q^{63} + 12 q^{64} - 93 q^{66} + 44 q^{67} - 75 q^{68} - 27 q^{70} + 20 q^{71} - 60 q^{72} - 60 q^{73} + 45 q^{74} - 57 q^{75} + 92 q^{78} - 70 q^{79} - 75 q^{80} - 29 q^{81} - 129 q^{82} - 125 q^{84} + 10 q^{85} - 62 q^{86} + 19 q^{88} + 6 q^{89} - 12 q^{91} + 30 q^{92} - 92 q^{93} + 105 q^{94} + 30 q^{95} + 75 q^{96} - 12 q^{99}+O(q^{100}) \) 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9 - q^11 - 12 * q^12 - 8 * q^14 - 27 * q^16 + 15 * q^17 + 20 * q^18 - 15 * q^19 - 76 * q^22 + 10 * q^23 + 75 * q^24 + q^25 + 27 * q^26 - 40 * q^28 - 40 * q^29 + 25 * q^30 + 9 * q^31 + 42 * q^33 + 5 * q^35 - 38 * q^36 - q^37 + 33 * q^38 - 45 * q^39 + 75 * q^40 + 64 * q^42 + 30 * q^44 - 84 * q^45 - 20 * q^46 + 3 * q^47 + 59 * q^49 + 30 * q^50 + 55 * q^51 - 15 * q^52 - 3 * q^53 - 8 * q^56 + 60 * q^57 + 46 * q^58 - 3 * q^59 - 15 * q^60 - 30 * q^61 - 40 * q^63 + 12 * q^64 - 93 * q^66 + 44 * q^67 - 75 * q^68 - 27 * q^70 + 20 * q^71 - 60 * q^72 - 60 * q^73 + 45 * q^74 - 57 * q^75 + 92 * q^78 - 70 * q^79 - 75 * q^80 - 29 * q^81 - 129 * q^82 - 125 * q^84 + 10 * q^85 - 62 * q^86 + 19 * q^88 + 6 * q^89 - 12 * q^91 + 30 * q^92 - 92 * q^93 + 105 * q^94 + 30 * q^95 + 75 * q^96 - 12 * q^99

Introduction

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Modular forms

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