LMFDB - Embedded newform 77.2.n.a.19.5

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			19.5
Character	$\chi$	$=$	77.19
Dual form			77.2.n.a.73.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39661 - 0.146790i) q^{2} +(0.151995 + 0.136856i) q^{3} +(-0.0273118 + 0.00580530i) q^{4} +(0.618266 + 1.38865i) q^{5} +(0.232367 + 0.168824i) q^{6} +(-1.57500 - 2.12588i) q^{7} +(-2.70844 + 0.880026i) q^{8} +(-0.309213 - 2.94196i) q^{9} +O(q^{10})$	\(q+(1.39661 - 0.146790i) q^{2} +(0.151995 + 0.136856i) q^{3} +(-0.0273118 + 0.00580530i) q^{4} +(0.618266 + 1.38865i) q^{5} +(0.232367 + 0.168824i) q^{6} +(-1.57500 - 2.12588i) q^{7} +(-2.70844 + 0.880026i) q^{8} +(-0.309213 - 2.94196i) q^{9} +(1.06732 + 1.84865i) q^{10} +(3.19157 - 0.902154i) q^{11} +(-0.00494574 - 0.00285542i) q^{12} +(-5.09949 + 3.70500i) q^{13} +(-2.51173 - 2.73784i) q^{14} +(-0.0960725 + 0.295681i) q^{15} +(-3.60245 + 1.60392i) q^{16} +(-0.286530 + 2.72615i) q^{17} +(-0.863702 - 4.06340i) q^{18} +(6.45371 + 1.37178i) q^{19} +(-0.0249475 - 0.0343372i) q^{20} +(0.0515495 - 0.538671i) q^{21} +(4.32496 - 1.72845i) q^{22} +(0.513095 - 0.888707i) q^{23} +(-0.532106 - 0.236909i) q^{24} +(1.79956 - 1.99862i) q^{25} +(-6.57817 + 5.92301i) q^{26} +(0.716285 - 0.985882i) q^{27} +(0.0553574 + 0.0489183i) q^{28} +(-3.40669 - 1.10690i) q^{29} +(-0.0907732 + 0.427054i) q^{30} +(0.225952 - 0.507496i) q^{31} +(0.136779 - 0.0789694i) q^{32} +(0.608567 + 0.299665i) q^{33} +3.84944i q^{34} +(1.97833 - 3.50148i) q^{35} +(0.0255241 + 0.0785552i) q^{36} +(2.91149 + 3.23353i) q^{37} +(9.21471 + 0.968505i) q^{38} +(-1.28215 - 0.134759i) q^{39} +(-2.89658 - 3.21698i) q^{40} +(-2.25325 - 6.93478i) q^{41} +(-0.00707689 - 0.759883i) q^{42} +9.51832i q^{43} +(-0.0819302 + 0.0431675i) q^{44} +(3.89418 - 2.24830i) q^{45} +(0.586143 - 1.31650i) q^{46} +(1.52622 - 7.18031i) q^{47} +(-0.767059 - 0.249233i) q^{48} +(-2.03875 + 6.69653i) q^{49} +(2.21992 - 3.05545i) q^{50} +(-0.416642 + 0.375146i) q^{51} +(0.117768 - 0.130794i) q^{52} +(2.74441 + 1.22189i) q^{53} +(0.855656 - 1.48204i) q^{54} +(3.22601 + 3.87420i) q^{55} +(6.13663 + 4.37179i) q^{56} +(0.793192 + 1.09174i) q^{57} +(-4.92031 - 1.04585i) q^{58} +(0.150088 + 0.706109i) q^{59} +(0.000907396 - 0.00863330i) q^{60} +(-7.18503 + 3.19898i) q^{61} +(0.241072 - 0.741943i) q^{62} +(-5.76726 + 5.29094i) q^{63} +(6.55995 - 4.76608i) q^{64} +(-8.29778 - 4.79073i) q^{65} +(0.893921 + 0.329184i) q^{66} +(-2.16696 - 3.75328i) q^{67} +(-0.00800047 - 0.0761194i) q^{68} +(0.199613 - 0.0648582i) q^{69} +(2.24899 - 5.18062i) q^{70} +(-3.87422 - 2.81478i) q^{71} +(3.42649 + 7.69602i) q^{72} +(-9.53478 + 2.02668i) q^{73} +(4.54087 + 4.08862i) q^{74} +(0.547047 - 0.0574970i) q^{75} -0.184226 q^{76} +(-6.94459 - 5.36401i) q^{77} -1.81045 q^{78} +(2.74362 - 0.288366i) q^{79} +(-4.45455 - 4.01089i) q^{80} +(-8.43678 + 1.79329i) q^{81} +(-4.16487 - 9.35446i) q^{82} +(-5.85520 - 4.25406i) q^{83} +(0.00171924 + 0.0150113i) q^{84} +(-3.96281 + 1.28760i) q^{85} +(1.39719 + 13.2934i) q^{86} +(-0.366312 - 0.634471i) q^{87} +(-7.85026 + 5.25210i) q^{88} +(0.985593 + 0.569032i) q^{89} +(5.10863 - 3.71164i) q^{90} +(15.9081 + 5.00555i) q^{91} +(-0.00885434 + 0.0272509i) q^{92} +(0.103798 - 0.0462136i) q^{93} +(1.07754 - 10.2522i) q^{94} +(2.08519 + 9.81006i) q^{95} +(0.0315971 + 0.00671618i) q^{96} +(4.71690 + 6.49225i) q^{97} +(-1.86437 + 9.65173i) q^{98} +(-3.64098 - 9.11052i) 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 $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	1.39661	−	0.146790i	0.987555	−	0.103796i	0.403043	−	0.915181i	$-0.367953\pi$
$2$	1.39661	−	0.146790i	0.987555	−	0.103796i	0.584512	+	0.811385i	$0.301286\pi$
$3$	0.151995	+	0.136856i	0.0877541	+	0.0790141i	0.711840	−	0.702341i	$-0.247862\pi$
$3$	0.151995	+	0.136856i	0.0877541	+	0.0790141i	−0.624086	+	0.781355i	$0.714529\pi$
$4$	−0.0273118	+	0.00580530i	−0.0136559	+	0.00290265i
$5$	0.618266	+	1.38865i	0.276497	+	0.621022i	0.997404	−	0.0720095i	$-0.0229412\pi$
$5$	0.618266	+	1.38865i	0.276497	+	0.621022i	−0.720907	+	0.693032i	$0.756275\pi$
$6$	0.232367	+	0.168824i	0.0948634	+	0.0689223i
$7$	−1.57500	−	2.12588i	−0.595294	−	0.803508i
$7$	−1.57500	−	2.12588i	−0.595294	−	0.803508i
$8$	−2.70844	+	0.880026i	−0.957579	+	0.311136i
$9$	−0.309213	−	2.94196i	−0.103071	−	0.980654i
$10$	1.06732	+	1.84865i	0.337516	+	0.584595i
$11$	3.19157	−	0.902154i	0.962295	−	0.272010i
$11$	3.19157	−	0.902154i	0.962295	−	0.272010i
$12$	−0.00494574	−	0.00285542i	−0.00142771	−	0.000824289i
$13$	−5.09949	+	3.70500i	−1.41435	+	1.02758i	−0.421672	+	0.906748i	$0.638557\pi$
$13$	−5.09949	+	3.70500i	−1.41435	+	1.02758i	−0.992673	+	0.120834i	$0.961443\pi$
$14$	−2.51173	−	2.73784i	−0.671287	−	0.731719i
$15$	−0.0960725	+	0.295681i	−0.0248058	+	0.0763444i
$16$	−3.60245	+	1.60392i	−0.900613	+	0.400979i
$17$	−0.286530	+	2.72615i	−0.0694937	+	0.661188i	0.903220	+	0.429178i	$0.141197\pi$
$17$	−0.286530	+	2.72615i	−0.0694937	+	0.661188i	−0.972713	+	0.232010i	$0.925470\pi$
$18$	−0.863702	−	4.06340i	−0.203576	−	0.957752i
$19$	6.45371	+	1.37178i	1.48058	+	0.314708i	0.876185	−	0.481975i	$-0.160080\pi$
$19$	6.45371	+	1.37178i	1.48058	+	0.314708i	0.604398	+	0.796683i	$0.293414\pi$
$20$	−0.0249475	−	0.0343372i	−0.00557842	−	0.00767804i
$21$	0.0515495	−	0.538671i	0.0112490	−	0.117548i
$22$	4.32496	−	1.72845i	0.922085	−	0.368507i
$23$	0.513095	−	0.888707i	0.106988	−	0.185308i	−0.807561	−	0.589784i	$-0.799213\pi$
$23$	0.513095	−	0.888707i	0.106988	−	0.185308i	0.914549	+	0.404476i	$0.132546\pi$
$24$	−0.532106	−	0.236909i	−0.108616	−	0.0483588i
$25$	1.79956	−	1.99862i	0.359912	−	0.399723i
$26$	−6.57817	+	5.92301i	−1.29008	+	1.16160i
$27$	0.716285	−	0.985882i	0.137849	−	0.189733i
$28$	0.0553574	+	0.0489183i	0.0104616	+	0.00924469i
$29$	−3.40669	−	1.10690i	−0.632607	−	0.205546i	−0.0248772	−	0.999691i	$-0.507919\pi$
$29$	−3.40669	−	1.10690i	−0.632607	−	0.205546i	−0.607729	+	0.794144i	$0.707919\pi$
$30$	−0.0907732	+	0.427054i	−0.0165728	+	0.0779691i
$31$	0.225952	−	0.507496i	0.0405821	−	0.0911489i	−0.892117	−	0.451805i	$-0.850780\pi$
$31$	0.225952	−	0.507496i	0.0405821	−	0.0911489i	0.932699	+	0.360656i	$0.117447\pi$
$32$	0.136779	−	0.0789694i	0.0241793	−	0.0139599i
$33$	0.608567	+	0.299665i	0.105938	+	0.0521649i
$34$			3.84944i			0.660173i
$35$	1.97833	−	3.50148i	0.334399	−	0.591858i
$36$	0.0255241	+	0.0785552i	0.00425402	+	0.0130925i
$37$	2.91149	+	3.23353i	0.478645	+	0.531590i	0.933309	−	0.359073i	$-0.116907\pi$
$37$	2.91149	+	3.23353i	0.478645	+	0.531590i	−0.454664	+	0.890663i	$0.650241\pi$
$38$	9.21471	+	0.968505i	1.49482	+	0.157112i
$39$	−1.28215	−	0.134759i	−0.205308	−	0.0215787i
$40$	−2.89658	−	3.21698i	−0.457990	−	0.508650i
$41$	−2.25325	−	6.93478i	−0.351898	−	1.08303i	−0.957786	−	0.287481i	$-0.907182\pi$
$41$	−2.25325	−	6.93478i	−0.351898	−	1.08303i	0.605888	−	0.795550i	$-0.292818\pi$
$42$	−0.00707689	−	0.759883i	−0.00109199	−	0.117252i
$43$			9.51832i			1.45153i	0.687943	+	0.725765i	$0.258514\pi$
$43$			9.51832i			1.45153i	−0.687943	+	0.725765i	$0.741486\pi$
$44$	−0.0819302	+	0.0431675i	−0.0123514	+	0.00650774i
$45$	3.89418	−	2.24830i	0.580509	−	0.335157i
$46$	0.586143	−	1.31650i	0.0864220	−	0.194107i
$47$	1.52622	−	7.18031i	0.222622	−	1.04736i	−0.714845	−	0.699283i	$-0.753503\pi$
$47$	1.52622	−	7.18031i	0.222622	−	1.04736i	0.937467	−	0.348073i	$-0.113164\pi$
$48$	−0.767059	−	0.249233i	−0.110716	−	0.0359736i
$49$	−2.03875	+	6.69653i	−0.291250	+	0.956647i
$50$	2.21992	−	3.05545i	0.313944	−	0.432106i
$51$	−0.416642	+	0.375146i	−0.0583416	+	0.0525310i
$52$	0.117768	−	0.130794i	0.0163314	−	0.0181379i
$53$	2.74441	+	1.22189i	0.376974	+	0.167840i	0.586472	−	0.809969i	$-0.300516\pi$
$53$	2.74441	+	1.22189i	0.376974	+	0.167840i	−0.209498	+	0.977809i	$0.567183\pi$
$54$	0.855656	−	1.48204i	0.116440	−	0.201680i
$55$	3.22601	+	3.87420i	0.434996	+	0.522397i
$56$	6.13663	+	4.37179i	0.820041	+	0.584205i
$57$	0.793192	+	1.09174i	0.105061	+	0.144604i
$58$	−4.92031	−	1.04585i	−0.646069	−	0.137326i
$59$	0.150088	+	0.706109i	0.0195398	+	0.0919275i	0.986837	−	0.161718i	$-0.0517036\pi$
$59$	0.150088	+	0.706109i	0.0195398	+	0.0919275i	−0.967297	+	0.253646i	$0.918370\pi$
$60$	0.000907396	−	0.00863330i	0.000117144	−	0.00111455i
$61$	−7.18503	+	3.19898i	−0.919949	+	0.409588i	−0.811392	−	0.584503i	$-0.801290\pi$
$61$	−7.18503	+	3.19898i	−0.919949	+	0.409588i	−0.108557	+	0.994090i	$0.534623\pi$
$62$	0.241072	−	0.741943i	0.0306162	−	0.0942269i
$63$	−5.76726	+	5.29094i	−0.726606	+	0.666596i
$64$	6.55995	−	4.76608i	0.819994	−	0.595761i
$65$	−8.29778	−	4.79073i	−1.02921	−	0.594217i
$66$	0.893921	+	0.329184i	0.110034	+	0.0405198i
$67$	−2.16696	−	3.75328i	−0.264736	−	0.458536i	0.702758	−	0.711429i	$-0.251952\pi$
$67$	−2.16696	−	3.75328i	−0.264736	−	0.458536i	−0.967494	+	0.252892i	$0.918618\pi$
$68$	−0.00800047	−	0.0761194i	−0.000970200	−	0.00923083i
$69$	0.199613	−	0.0648582i	0.0240306	−	0.00780801i
$70$	2.24899	−	5.18062i	0.268805	−	0.619202i
$71$	−3.87422	−	2.81478i	−0.459785	−	0.334053i	0.333662	−	0.942693i	$-0.391716\pi$
$71$	−3.87422	−	2.81478i	−0.459785	−	0.334053i	−0.793447	+	0.608639i	$0.791716\pi$
$72$	3.42649	+	7.69602i	0.403816	+	0.906985i
$73$	−9.53478	+	2.02668i	−1.11596	+	0.237205i	−0.728746	−	0.684784i	$-0.759897\pi$
$73$	−9.53478	+	2.02668i	−1.11596	+	0.237205i	−0.387216	+	0.921989i	$0.626563\pi$
$74$	4.54087	+	4.08862i	0.527866	+	0.475293i
$75$	0.547047	−	0.0574970i	0.0631676	−	0.00663918i
$76$	−0.184226			−0.0211322
$77$	−6.94459	−	5.36401i	−0.791410	−	0.611286i
$78$	−1.81045			−0.204993
$79$	2.74362	−	0.288366i	0.308682	−	0.0324437i	0.0510787	−	0.998695i	$-0.483734\pi$
$79$	2.74362	−	0.288366i	0.308682	−	0.0324437i	0.257603	+	0.966251i	$0.417067\pi$
$80$	−4.45455	−	4.01089i	−0.498034	−	0.448432i
$81$	−8.43678	+	1.79329i	−0.937420	+	0.199255i
$82$	−4.16487	−	9.35446i	−0.459933	−	1.03303i
$83$	−5.85520	−	4.25406i	−0.642692	−	0.466943i	0.218082	−	0.975930i	$-0.430020\pi$
$83$	−5.85520	−	4.25406i	−0.642692	−	0.466943i	−0.860774	+	0.508987i	$0.830020\pi$
$84$	0.00171924	+	0.0150113i	0.000187585	+	0.00163787i
$85$	−3.96281	+	1.28760i	−0.429828	+	0.139659i
$86$	1.39719	+	13.2934i	0.150663	+	1.43347i
$87$	−0.366312	−	0.634471i	−0.0392727	−	0.0680224i
$88$	−7.85026	+	5.25210i	−0.836841	+	0.559875i
$89$	0.985593	+	0.569032i	0.104473	+	0.0603173i	0.551326	−	0.834290i	$-0.314122\pi$
$89$	0.985593	+	0.569032i	0.104473	+	0.0603173i	−0.446853	+	0.894607i	$0.647455\pi$
$90$	5.10863	−	3.71164i	0.538497	−	0.391241i
$91$	15.9081	+	5.00555i	1.66762	+	0.524724i
$92$	−0.00885434	+	0.0272509i	−0.000923129	+	0.00284110i
$93$	0.103798	−	0.0462136i	0.0107633	−	0.00479213i
$94$	1.07754	−	10.2522i	0.111140	−	1.05743i
$95$	2.08519	+	9.81006i	0.213936	+	1.00649i
$96$	0.0315971	+	0.00671618i	0.00322487	+	0.000685467i
$97$	4.71690	+	6.49225i	0.478928	+	0.659188i	0.978299	−	0.207200i	$-0.0664352\pi$
$97$	4.71690	+	6.49225i	0.478928	+	0.659188i	−0.499370	+	0.866389i	$0.666435\pi$
$98$	−1.86437	+	9.65173i	−0.188329	+	0.974972i
$99$	−3.64098	−	9.11052i	−0.365932	−	0.915642i
$100$	−0.0375467	+	0.0650328i	−0.00375467	+	0.00650328i
$101$	−6.30645	−	2.80781i	−0.627516	−	0.279388i	0.0682373	−	0.997669i	$-0.478263\pi$
$101$	−6.30645	−	2.80781i	−0.627516	−	0.279388i	−0.695753	+	0.718281i	$0.744929\pi$
$102$	−0.526821	+	0.585094i	−0.0521630	+	0.0579329i
$103$	1.65195	−	1.48743i	0.162772	−	0.146560i	−0.583720	−	0.811955i	$-0.698403\pi$
$103$	1.65195	−	1.48743i	0.162772	−	0.146560i	0.746492	+	0.665395i	$0.231737\pi$
$104$	10.5512	−	14.5225i	1.03463	−	1.42404i
$105$	0.779896	−	0.261458i	0.0761101	−	0.0255157i
$106$	4.01224	+	1.30366i	0.389704	+	0.126622i
$107$	3.37955	−	15.8995i	0.326713	−	1.53706i	−0.441731	−	0.897147i	$-0.645636\pi$
$107$	3.37955	−	15.8995i	0.326713	−	1.53706i	0.768444	−	0.639917i	$-0.221031\pi$
$108$	−0.0138397	+	0.0310844i	−0.00133172	+	0.00299110i
$109$	1.53706	−	0.887424i	0.147224	−	0.0849998i	−0.424579	−	0.905391i	$-0.639578\pi$
$109$	1.53706	−	0.887424i	0.147224	−	0.0849998i	0.571802	+	0.820391i	$0.306244\pi$
$110$	5.07419	+	4.93721i	0.483805	+	0.470745i
$111$			0.889935i			0.0844689i
$112$	9.08360	+	5.13223i	0.858319	+	0.484950i
$113$	3.45199	+	10.6241i	0.324736	+	0.999433i	0.971560	+	0.236794i	$0.0760967\pi$
$113$	3.45199	+	10.6241i	0.324736	+	0.999433i	−0.646824	+	0.762639i	$0.723903\pi$
$114$	1.26804	+	1.40830i	0.118763	+	0.131899i
$115$	1.55133	+	0.163051i	0.144662	+	0.0152046i
$116$	0.0994687	+	0.0104546i	0.00923544	+	0.000970684i
$117$	12.4768	+	13.8569i	1.15348	+	1.28107i
$118$	0.313265	+	0.964130i	0.0288384	+	0.0887553i
$119$	6.24676	−	3.68456i	0.572639	−	0.337763i
$120$		−	0.885380i		−	0.0808238i
$121$	9.37224	−	5.75857i	0.852021	−	0.523507i
$122$	−9.56513	+	5.52243i	−0.865986	+	0.499978i
$123$	0.606589	−	1.36242i	0.0546943	−	0.122845i
$124$	−0.00322498	+	0.0151723i	−0.000289612	+	0.00136252i
$125$	11.1163	+	3.61191i	0.994274	+	0.323059i
$126$	−7.27797	+	8.23598i	−0.648374	+	0.733719i
$127$	−2.28795	+	3.14910i	−0.203023	+	0.279437i	−0.898372	−	0.439235i	$-0.855250\pi$
$127$	−2.28795	+	3.14910i	−0.203023	+	0.279437i	0.695349	+	0.718672i	$0.255250\pi$
$128$	8.22737	−	7.40795i	0.727203	−	0.654777i
$129$	−1.30264	+	1.44673i	−0.114691	+	0.127378i
$130$	−12.2920	−	5.47277i	−1.07808	−	0.479993i
$131$	7.02508	−	12.1678i	0.613784	−	1.06311i	−0.376812	−	0.926290i	$-0.622980\pi$
$131$	7.02508	−	12.1678i	0.613784	−	1.06311i	0.990596	−	0.136816i	$-0.0436869\pi$
$132$	−0.0183607	−	0.00465146i	−0.00159809	−	0.000404858i
$133$	−7.24835	−	15.8804i	−0.628512	−	1.37700i
$134$	−3.57735	−	4.92380i	−0.309036	−	0.425351i
$135$	1.81190	+	0.385131i	0.155943	+	0.0331468i
$136$	−1.62303	−	7.63577i	−0.139174	−	0.654762i
$137$	−1.08887	+	10.3599i	−0.0930286	+	0.885108i	0.844115	+	0.536163i	$0.180127\pi$
$137$	−1.08887	+	10.3599i	−0.0930286	+	0.885108i	−0.937143	+	0.348945i	$0.886540\pi$
$138$	0.269262	−	0.119883i	0.0229211	−	0.0102051i
$139$	−0.656279	+	2.01982i	−0.0556649	+	0.171319i	−0.975024	−	0.222102i	$-0.928708\pi$
$139$	−0.656279	+	2.01982i	−0.0556649	+	0.171319i	0.919359	+	0.393420i	$0.128708\pi$
$140$	−0.0337047	+	0.107117i	−0.00284857	+	0.00905300i
$141$	1.21465	−	0.882494i	0.102292	−	0.0743194i
$142$	−5.82397	−	3.36247i	−0.488737	−	0.282172i
$143$	−12.9329	+	16.4253i	−1.08150	+	1.37355i
$144$	5.83258	+	10.1023i	0.486049	+	0.841861i
$145$	−0.569145	−	5.41505i	−0.0472649	−	0.449696i
$146$	−13.0189	+	4.23010i	−1.07745	+	0.350086i
$147$	−1.22634	+	0.738819i	−0.101147	+	0.0609368i
$148$	−0.0982895	−	0.0714115i	−0.00807935	−	0.00586999i
$149$	2.03156	+	4.56296i	0.166432	+	0.373813i	0.977437	−	0.211227i	$-0.0677458\pi$
$149$	2.03156	+	4.56296i	0.166432	+	0.373813i	−0.811005	+	0.585039i	$0.801079\pi$
$150$	0.755574	−	0.160602i	0.0616923	−	0.0131131i
$151$	1.66543	+	1.49956i	0.135531	+	0.122032i	0.734108	−	0.679033i	$-0.237601\pi$
$151$	1.66543	+	1.49956i	0.135531	+	0.122032i	−0.598578	+	0.801065i	$0.704267\pi$
$152$	−18.6867	+	1.96405i	−1.51569	+	0.159306i
$153$	8.10883			0.655560
$154$	−10.4863	−	6.47205i	−0.845010	−	0.521533i
$155$	0.844431			0.0678264
$156$	0.0358001	−	0.00376274i	0.00286630	−	0.000301260i
$157$	−3.55792	−	3.20357i	−0.283953	−	0.255672i	0.514829	−	0.857293i	$-0.327855\pi$
$157$	−3.55792	−	3.20357i	−0.283953	−	0.255672i	−0.798782	+	0.601620i	$0.794522\pi$
$158$	3.78945	−	0.805473i	0.301473	−	0.0640800i
$159$	0.249912	+	0.561311i	0.0198193	+	0.0445149i
$160$	0.194227	+	0.141114i	0.0153550	+	0.0111560i
$161$	−2.69741	+	0.308933i	−0.212586	+	0.0243473i
$162$	−11.5197	+	3.74297i	−0.905072	+	0.294076i
$163$	−0.0671055	−	0.638466i	−0.00525611	−	0.0500085i	0.991579	−	0.129500i	$-0.0413371\pi$
$163$	−0.0671055	−	0.638466i	−0.00525611	−	0.0500085i	−0.996836	+	0.0794911i	$0.974670\pi$
$164$	0.101799	+	0.176321i	0.00794914	+	0.0137683i
$165$	−0.0398725	+	1.03036i	−0.00310407	+	0.0802132i
$166$	−8.80191	−	5.08179i	−0.683161	−	0.394423i
$167$	−11.5322	+	8.37861i	−0.892386	+	0.648356i	−0.936499	−	0.350670i	$-0.885954\pi$
$167$	−11.5322	+	8.37861i	−0.892386	+	0.648356i	0.0441131	+	0.999027i	$0.485954\pi$
$168$	0.334426	+	1.50433i	0.0258015	+	0.116061i
$169$	8.26060	−	25.4235i	0.635431	−	1.95565i
$170$	−5.34552	+	2.37998i	−0.409982	+	0.182536i
$171$	2.04015	−	19.4107i	0.156014	−	1.48438i
$172$	−0.0552567	−	0.259962i	−0.00421328	−	0.0198219i
$173$	15.0807	+	3.20550i	1.14656	+	0.243710i	0.741741	−	0.670686i	$-0.234000\pi$
$173$	15.0807	+	3.20550i	1.14656	+	0.243710i	0.404822	+	0.914396i	$0.367334\pi$
$174$	−0.604730	−	0.832340i	−0.0458445	−	0.0630995i
$175$	−7.08313	−	0.677838i	−0.535434	−	0.0512397i
$176$	−10.0505	+	8.36898i	−0.757585	+	0.630835i
$177$	−0.0738230	+	0.127865i	−0.00554887	+	0.00961093i
$178$	1.46002	+	0.650043i	0.109433	+	0.0487228i
$179$	−3.01017	+	3.34313i	−0.224991	+	0.249877i	−0.845062	−	0.534668i	$-0.820437\pi$
$179$	−3.01017	+	3.34313i	−0.224991	+	0.249877i	0.620072	+	0.784545i	$0.287103\pi$
$180$	−0.0933048	+	0.0840120i	−0.00695453	+	0.00626189i
$181$	3.65652	−	5.03277i	0.271787	−	0.374083i	−0.651205	−	0.758902i	$-0.725736\pi$
$181$	3.65652	−	5.03277i	0.271787	−	0.374083i	0.922992	+	0.384819i	$0.125736\pi$
$182$	22.9522	+	4.65567i	1.70133	+	0.345102i
$183$	−1.52989	−	0.497090i	−0.113092	−	0.0367460i
$184$	−0.607603	+	2.85855i	−0.0447931	+	0.210735i
$185$	−2.69017	+	6.04221i	−0.197785	+	0.444232i
$186$	0.138181	−	0.0797791i	0.0101319	−	0.00584968i
$187$	1.54493	+	8.95919i	0.112976	+	0.655161i
$188$			0.204967i			0.0149488i
$189$	−3.22402	+	0.0300257i	−0.234513	+	0.00218405i
$190$	4.35223	+	13.3948i	0.315744	+	0.971759i
$191$	6.26495	+	6.95793i	0.453316	+	0.503458i	0.925869	−	0.377844i	$-0.123334\pi$
$191$	6.26495	+	6.95793i	0.453316	+	0.503458i	−0.472554	+	0.881302i	$0.656668\pi$
$192$	1.64935	+	0.173353i	0.119031	+	0.0125107i
$193$	1.08415	+	0.113948i	0.0780386	+	0.00820218i	0.143467	−	0.989655i	$-0.454175\pi$
$193$	1.08415	+	0.113948i	0.0780386	+	0.00820218i	−0.0654287	+	0.997857i	$0.520841\pi$
$194$	7.54068	+	8.37478i	0.541390	+	0.601274i
$195$	−0.605576	−	1.86377i	−0.0433662	−	0.133467i
$196$	0.0168066	−	0.194730i	0.00120047	−	0.0139093i
$197$		−	10.2948i		−	0.733475i	−0.930325	−	0.366737i	$-0.880475\pi$
$197$		−	10.2948i		−	0.733475i	0.930325	−	0.366737i	$-0.119525\pi$
$198$	−6.42237	−	12.1894i	−0.456418	−	0.866265i
$199$	−2.09410	+	1.20903i	−0.148447	+	0.0857058i	−0.572384	−	0.819986i	$-0.693981\pi$
$199$	−2.09410	+	1.20903i	−0.148447	+	0.0857058i	0.423937	+	0.905692i	$0.360648\pi$
$200$	−3.11518	+	6.99680i	−0.220276	+	0.494748i
$201$	0.184295	−	0.867041i	0.0129992	−	0.0611563i
$202$	−9.21984	−	2.99571i	−0.648706	−	0.210777i
$203$	3.01240	+	8.98559i	0.211429	+	0.630665i
$204$	0.00920141	−	0.0126646i	0.000644227	−	0.000886703i
$205$	8.23687	−	7.41651i	0.575288	−	0.517991i
$206$	2.08880	−	2.31985i	0.145534	−	0.161632i
$207$	−2.77320	−	1.23471i	−0.192751	−	0.0858181i
$208$	12.4282	−	21.5262i	0.861740	−	1.49258i
$209$	21.8350	−	1.44411i	1.51036	−	0.0998914i
$210$	1.05083	−	0.479637i	0.0725145	−	0.0330981i
$211$	15.5886	+	21.4559i	1.07317	+	1.47709i	0.866829	+	0.498605i	$0.166154\pi$
$211$	15.5886	+	21.4559i	1.07317	+	1.47709i	0.206336	+	0.978481i	$0.433846\pi$
$212$	−0.0820482	−	0.0174399i	−0.00563509	−	0.00119778i
$213$	−0.203638	−	0.958044i	−0.0139531	−	0.0656441i
$214$	2.38603	−	22.7016i	0.163106	−	1.55185i
$215$	−13.2176	+	5.88485i	−0.901432	+	0.401344i
$216$	−1.07241	+	3.30055i	−0.0729686	+	0.224574i
$217$	−1.43475	+	0.318959i	−0.0973972	+	0.0216523i
$218$	2.01642	−	1.46501i	0.136569	−	0.0992233i
$219$	−1.72660	−	0.996853i	−0.116673	−	0.0673611i
$220$	−0.110599	−	0.0870833i	−0.00745659	−	0.00587115i
$221$	−8.63922	−	14.9636i	−0.581137	−	1.00656i
$222$	0.130634	+	1.24290i	0.00876756	+	0.0834177i
$223$	−10.8917	+	3.53893i	−0.729363	+	0.236985i	−0.650078	−	0.759867i	$-0.725264\pi$
$223$	−10.8917	+	3.53893i	−0.729363	+	0.236985i	−0.0792853	+	0.996852i	$0.525264\pi$
$224$	−0.383307	−	0.166399i	−0.0256107	−	0.0111180i
$225$	−6.43630	−	4.67625i	−0.429087	−	0.311750i
$226$	6.38061	+	14.3311i	0.424432	+	0.953289i
$227$	18.8558	−	4.00793i	1.25150	−	0.266015i	0.465951	−	0.884810i	$-0.345712\pi$
$227$	18.8558	−	4.00793i	1.25150	−	0.266015i	0.785553	+	0.618795i	$0.212379\pi$
$228$	−0.0280013	−	0.0252125i	−0.00185443	−	0.00166974i
$229$	−22.8684	+	2.40356i	−1.51118	+	0.158832i	−0.823557	−	0.567233i	$-0.808014\pi$
$229$	−22.8684	+	2.40356i	−1.51118	+	0.158832i	−0.687626	+	0.726065i	$0.741347\pi$
$230$	2.19054			0.144440
$231$	−0.321441	−	1.76571i	−0.0211493	−	0.116175i
$232$	10.2009			0.669724
$233$	−8.75121	+	0.919789i	−0.573311	+	0.0602574i	−0.386748	−	0.922186i	$-0.626402\pi$
$233$	−8.75121	+	0.919789i	−0.573311	+	0.0602574i	−0.186563	+	0.982443i	$0.559735\pi$
$234$	19.4593	+	17.5213i	1.27210	+	1.14540i
$235$	10.9145	−	2.31996i	0.711986	−	0.151337i
$236$	−0.00819834	−	0.0184138i	−0.000533667	−	0.00119863i
$237$	0.456480	+	0.331652i	0.0296516	+	0.0215431i
$238$	8.18345	−	6.06286i	0.530454	−	0.392997i
$239$	−9.19679	+	2.98822i	−0.594891	+	0.193292i	−0.590961	−	0.806700i	$-0.701251\pi$
$239$	−9.19679	+	2.98822i	−0.594891	+	0.193292i	−0.00393051	+	0.999992i	$0.501251\pi$
$240$	−0.128150	−	1.21927i	−0.00827206	−	0.0787034i
$241$	12.5688	+	21.7698i	0.809628	+	1.40232i	0.913122	+	0.407687i	$0.133665\pi$
$241$	12.5688	+	21.7698i	0.809628	+	1.40232i	−0.103494	+	0.994630i	$0.533002\pi$
$242$	12.2441	−	9.41826i	0.787080	−	0.605429i
$243$	−4.69383	−	2.70998i	−0.301109	−	0.173845i
$244$	0.177665	−	0.129081i	0.0113738	−	0.00826357i
$245$	−10.5596	+	1.30913i	−0.674629	+	0.0836370i
$246$	0.647181	−	1.99182i	0.0412627	−	0.126994i
$247$	−37.9931	+	16.9156i	−2.41744	+	1.07631i
$248$	−0.165368	+	1.57337i	−0.0105008	+	0.0999089i
$249$	−0.307764	−	1.44792i	−0.0195038	−	0.0917579i
$250$	16.0554	+	3.41268i	1.01543	+	0.215837i
$251$	−12.7273	−	17.5176i	−0.803337	−	1.10570i	−0.992317	−	0.123718i	$-0.960518\pi$
$251$	−12.7273	−	17.5176i	−0.803337	−	1.10570i	0.188980	−	0.981981i	$-0.439482\pi$
$252$	0.126799	−	0.177986i	0.00798756	−	0.0112120i
$253$	0.835829	−	3.29926i	0.0525481	−	0.207423i
$254$	−2.73313	+	4.73392i	−0.171492	+	0.297033i
$255$	−0.778542	−	0.346629i	−0.0487542	−	0.0217068i
$256$	−0.448315	+	0.497904i	−0.0280197	+	0.0311190i
$257$	−11.7064	+	10.5405i	−0.730226	+	0.657499i	−0.947916	−	0.318519i	$-0.896814\pi$
$257$	−11.7064	+	10.5405i	−0.730226	+	0.657499i	0.217690	+	0.976018i	$0.430148\pi$
$258$	−1.60692	+	2.21174i	−0.100043	+	0.137697i
$259$	2.28852	−	11.2823i	0.142202	−	0.701048i
$260$	0.254439	+	0.0826722i	0.0157796	+	0.00512711i
$261$	−2.20307	+	10.3646i	−0.136367	+	0.641554i
$262$	8.02522	−	18.0249i	0.495800	−	1.11358i
$263$	17.0102	−	9.82083i	1.04889	−	0.605579i	0.126554	−	0.991960i	$-0.459608\pi$
$263$	17.0102	−	9.82083i	1.04889	−	0.605579i	0.922339	+	0.386381i	$0.126275\pi$
$264$	−1.91198	−	0.276069i	−0.117674	−	0.0169909i
$265$			4.56648i			0.280516i
$266$	−12.4542	−	21.1148i	−0.763618	−	1.29463i
$267$	0.0719289	+	0.221375i	0.00440198	+	0.0135479i
$268$	0.0809724	+	0.0899290i	0.00494618	+	0.00549329i
$269$	28.5221	+	2.99779i	1.73902	+	0.182779i	0.920247	−	0.391337i	$-0.127987\pi$
$269$	28.5221	+	2.99779i	1.73902	+	0.182779i	0.818774	+	0.574115i	$0.194654\pi$
$270$	2.58706	+	0.271910i	0.157443	+	0.0165479i
$271$	−3.62388	−	4.02473i	−0.220135	−	0.244485i	0.622954	−	0.782258i	$-0.285932\pi$
$271$	−3.62388	−	4.02473i	−0.220135	−	0.244485i	−0.843089	+	0.537773i	$0.819266\pi$
$272$	−3.34030	−	10.2804i	−0.202536	−	0.623341i
$273$	1.73290	+	2.93794i	0.104880	+	0.177812i
$274$			14.6286i			0.883749i
$275$	3.94037	−	8.00221i	0.237613	−	0.482551i
$276$	−0.00507527	+	0.00293021i	−0.000305495	+	0.000176378i
$277$	1.03470	−	2.32398i	0.0621693	−	0.139635i	−0.879789	−	0.475364i	$-0.842316\pi$
$277$	1.03470	−	2.32398i	0.0621693	−	0.139635i	0.941958	+	0.335730i	$0.108983\pi$
$278$	−0.620079	+	2.91724i	−0.0371899	+	0.174965i
$279$	−1.56290	−	0.507817i	−0.0935684	−	0.0304022i
$280$	−2.27681	+	11.2245i	−0.136065	+	0.670795i
$281$	12.3913	−	17.0551i	0.739200	−	1.01742i	−0.259464	−	0.965753i	$-0.583546\pi$
$281$	12.3913	−	17.0551i	0.739200	−	1.01742i	0.998664	−	0.0516692i	$-0.0164541\pi$
$282$	1.56685	−	1.41080i	0.0933049	−	0.0840121i
$283$	−4.77114	+	5.29889i	−0.283615	+	0.314986i	−0.868072	−	0.496438i	$-0.834641\pi$
$283$	−4.77114	+	5.29889i	−0.283615	+	0.314986i	0.584457	+	0.811425i	$0.301308\pi$
$284$	0.122153	+	0.0543858i	0.00724842	+	0.00322720i
$285$	−1.02563	+	1.77645i	−0.0607532	+	0.105228i
$286$	−15.6512	+	24.8382i	−0.925476	+	1.46871i
$287$	−11.1937	+	15.7124i	−0.660741	+	0.927475i
$288$	−0.274619	−	0.377980i	−0.0161821	−	0.0222727i
$289$	9.27872	+	1.97225i	0.545807	+	0.116015i
$290$	−1.58975	−	7.47920i	−0.0933535	−	0.439193i
$291$	−0.171564	+	1.63233i	−0.0100573	+	0.0956886i
$292$	0.248647	−	0.110705i	0.0145509	−	0.00647849i
$293$	−1.96372	+	6.04371i	−0.114722	+	0.353077i	−0.991889	−	0.127108i	$-0.959431\pi$
$293$	−1.96372	+	6.04371i	−0.114722	+	0.353077i	0.877167	+	0.480185i	$0.159431\pi$
$294$	−1.60428	+	1.21186i	−0.0935633	+	0.0706771i
$295$	−0.887742	+	0.644982i	−0.0516863	+	0.0375523i
$296$	−10.7312	−	6.19565i	−0.623738	−	0.360115i
$297$	1.39666	−	3.79271i	0.0810422	−	0.220075i
$298$	3.50711	+	6.07449i	0.203161	+	0.351886i
$299$	0.676133	+	6.43297i	0.0391018	+	0.372029i
$300$	−0.0146070	+	0.00474612i	−0.000843338	+	0.000274017i
$301$	20.2348	−	14.9913i	1.16632	−	0.864087i
$302$	2.54608	+	1.84984i	0.146510	+	0.106446i
$303$	−0.574279	−	1.28985i	−0.0329915	−	0.0741000i
$304$	−25.4494	+	5.40944i	−1.45962	+	0.310253i
$305$	−8.88452	−	7.99966i	−0.508726	−	0.458059i
$306$	11.3249	−	1.19030i	0.647402	−	0.0680447i
$307$	−20.5417			−1.17238			−0.586189	−	0.810174i	$-0.699372\pi$
$307$	−20.5417			−1.17238			−0.586189	+	0.810174i	$0.699372\pi$
$308$	0.220809	+	0.106185i	0.0125818	+	0.00605047i
$309$	0.454652			0.0258642
$310$	1.17934	−	0.123954i	0.0669823	−	0.00704012i
$311$	−12.0350	−	10.8364i	−0.682444	−	0.614475i	0.253203	−	0.967413i	$-0.418516\pi$
$311$	−12.0350	−	10.8364i	−0.682444	−	0.614475i	−0.935647	+	0.352938i	$0.885183\pi$
$312$	3.59122	−	0.763337i	0.203313	−	0.0432154i
$313$	−11.1745	−	25.0984i	−0.631623	−	1.41865i	−0.891506	−	0.453008i	$-0.850351\pi$
$313$	−11.1745	−	25.0984i	−0.631623	−	1.41865i	0.259883	−	0.965640i	$-0.416316\pi$
$314$	−5.43929	−	3.95188i	−0.306957	−	0.223017i
$315$	−10.9130	−	4.73748i	−0.614875	−	0.266927i
$316$	−0.0732592	+	0.0238033i	−0.00412115	+	0.00133904i
$317$	2.11287	+	20.1026i	0.118671	+	1.12908i	0.878097	+	0.478483i	$0.158813\pi$
$317$	2.11287	+	20.1026i	0.118671	+	1.12908i	−0.759426	+	0.650594i	$0.774520\pi$
$318$	0.431425	+	0.747250i	0.0241931	+	0.0419037i
$319$	−11.8713	−	0.459392i	−0.664664	−	0.0257210i
$320$	10.6742	+	6.16276i	0.596707	+	0.344509i
$321$	2.68962	−	1.95413i	0.150120	−	0.109069i
$322$	−3.72189	+	0.827414i	−0.207413	+	0.0461100i
$323$	−5.58885	+	17.2007i	−0.310972	+	0.957074i
$324$	0.220013	−	0.0979561i	0.0122229	−	0.00544200i
$325$	−1.77198	+	16.8593i	−0.0982920	+	0.935186i
$326$	−0.187441	−	0.881841i	−0.0103814	−	0.0488406i
$327$	0.355075	+	0.0754735i	0.0196357	+	0.00417369i
$328$	12.2056	+	16.7995i	0.673941	+	0.927600i
$329$	−17.6683	+	8.06442i	−0.974085	+	0.444606i
$330$	0.0955597	+	1.44486i	0.00526039	+	0.0795372i
$331$	−0.0955258	+	0.165455i	−0.00525057	+	0.00909426i	−0.868639	−	0.495446i	$-0.835005\pi$
$331$	−0.0955258	+	0.165455i	−0.00525057	+	0.00909426i	0.863388	+	0.504540i	$0.168338\pi$
$332$	0.184612	+	0.0821946i	0.0101319	+	0.00451102i
$333$	8.61267	−	9.56534i	0.471971	−	0.524177i
$334$	−14.8761	+	13.3945i	−0.813983	+	0.732914i
$335$	3.87223	−	5.32967i	0.211563	−	0.291191i
$336$	0.678279	+	2.02322i	0.0370032	+	0.110376i
$337$	−4.30418	−	1.39851i	−0.234464	−	0.0761819i	0.189428	−	0.981895i	$-0.439337\pi$
$337$	−4.30418	−	1.39851i	−0.234464	−	0.0761819i	−0.423892	+	0.905713i	$0.639337\pi$
$338$	7.80495	−	36.7194i	0.424533	−	1.99727i
$339$	−0.929297	+	2.08724i	−0.0504725	+	0.113363i
$340$	0.100757	−	0.0581719i	0.00546430	−	0.00315481i
$341$	0.263301	−	1.82355i	0.0142586	−	0.0987509i
$342$		−	27.4088i		−	1.48210i
$343$	17.4471	−	6.21288i	0.942053	−	0.335464i
$344$	−8.37637	−	25.7798i	−0.451624	−	1.38995i
$345$	0.213479	+	0.237093i	0.0114933	+	0.0127646i
$346$	21.5324	+	2.26315i	1.15759	+	0.121668i
$347$	−15.9378	−	1.67513i	−0.855586	−	0.0899257i	−0.333429	−	0.942775i	$-0.608206\pi$
$347$	−15.9378	−	1.67513i	−0.855586	−	0.0899257i	−0.522157	+	0.852849i	$0.674872\pi$
$348$	0.0136879	+	0.0152020i	0.000733750	+	0.000814911i
$349$	8.81872	+	27.1412i	0.472055	+	1.45284i	0.849888	+	0.526963i	$0.176669\pi$
$349$	8.81872	+	27.1412i	0.472055	+	1.45284i	−0.377833	+	0.925874i	$0.623331\pi$
$350$	−9.99190	+	0.0930559i	−0.534090	+	0.00497405i
$351$			7.68133i			0.409999i
$352$	0.365297	−	0.375432i	0.0194704	−	0.0200106i
$353$	18.1201	−	10.4617i	0.964438	−	0.556818i	0.0669018	−	0.997760i	$-0.478689\pi$
$353$	18.1201	−	10.4617i	0.964438	−	0.556818i	0.897536	+	0.440941i	$0.145355\pi$
$354$	−0.0843329	+	0.189415i	−0.00448224	+	0.0100673i
$355$	1.51345	−	7.12021i	0.0803255	−	0.377902i
$356$	−0.0302217	−	0.00981963i	−0.00160175	−	0.000520439i
$357$	1.45373	+	0.294877i	0.0769395	+	0.0156065i
$358$	−3.71331	+	5.11093i	−0.196254	+	0.270121i
$359$	−3.52511	+	3.17402i	−0.186048	+	0.167519i	−0.756892	−	0.653540i	$-0.773283\pi$
$359$	−3.52511	+	3.17402i	−0.186048	+	0.167519i	0.570843	+	0.821059i	$0.306616\pi$
$360$	−8.56858	+	9.51638i	−0.451604	+	0.501557i
$361$	22.4112	+	9.97813i	1.17954	+	0.525165i
$362$	4.36799	−	7.56558i	0.229577	−	0.397638i
$363$	2.21263	+	0.407380i	0.116133	+	0.0213819i
$364$	−0.463537	−	0.0443593i	−0.0242960	−	0.00232506i
$365$	−8.70938	−	11.9874i	−0.455870	−	0.627451i
$366$	−2.20963	−	0.469671i	−0.115499	−	0.0245501i
$367$	−0.152321	−	0.716612i	−0.00795107	−	0.0374068i	0.973993	−	0.226577i	$-0.0727535\pi$
$367$	−0.152321	−	0.716612i	−0.00795107	−	0.0374068i	−0.981944	+	0.189170i	$0.939420\pi$
$368$	−0.422991	+	4.02449i	−0.0220499	+	0.209791i
$369$	−19.7051	+	8.77329i	−1.02581	+	0.456719i
$370$	−2.87019	+	8.83353i	−0.149214	+	0.459233i
$371$	−1.72485	−	7.75877i	−0.0895498	−	0.402815i
$372$	−0.00256661	+	0.00186475i	−0.000133073	+	9.66829e-5i
$373$	−4.67716	−	2.70036i	−0.242174	−	0.139819i	0.374001	−	0.927428i	$-0.377986\pi$
$373$	−4.67716	−	2.70036i	−0.242174	−	0.139819i	−0.616176	+	0.787609i	$0.711319\pi$
$374$	3.47279	+	12.2858i	0.179573	+	0.635281i
$375$	1.19531	+	2.07033i	0.0617254	+	0.106911i
$376$	2.18518	+	20.7906i	0.112692	+	1.07219i
$377$	21.4735	−	6.97715i	1.10594	−	0.359342i
$378$	−4.49830	+	0.515188i	−0.231368	+	0.0264984i
$379$	20.7759	+	15.0946i	1.06719	+	0.775358i	0.975405	−	0.220421i	$-0.0707432\pi$
$379$	20.7759	+	15.0946i	1.06719	+	0.775358i	0.0917835	+	0.995779i	$0.470743\pi$
$380$	−0.113901	−	0.255825i	−0.00584298	−	0.0131235i
$381$	−0.778731	+	0.165524i	−0.0398956	+	0.00848007i
$382$	9.77107	+	8.79791i	0.499931	+	0.450140i
$383$	37.4436	−	3.93548i	1.91328	−	0.201094i	0.928063	−	0.372423i	$-0.121473\pi$
$383$	37.4436	−	3.93548i	1.91328	−	0.201094i	0.985214	+	0.171329i	$0.0548062\pi$
$384$	2.26434			0.115552
$385$	3.15512	−	12.9600i	0.160800	−	0.660502i
$386$	1.53086			0.0779187
$387$	28.0025	−	2.94319i	1.42345	−	0.149611i
$388$	−0.166516	−	0.149932i	−0.00845359	−	0.00761165i
$389$	−23.1500	+	4.92069i	−1.17375	+	0.249489i	−0.753208	−	0.657783i	$-0.771494\pi$
$389$	−23.1500	+	4.92069i	−1.17375	+	0.249489i	−0.420545	+	0.907272i	$0.638161\pi$
$390$	−1.11934	−	2.51407i	−0.0566799	−	0.127305i
$391$	2.27573	+	1.65342i	0.115089	+	0.0836168i
$392$	−0.371278	−	19.9313i	−0.0187524	−	1.00668i
$393$	2.73302	−	0.888011i	0.137862	−	0.0447942i
$394$	−1.51117	−	14.3779i	−0.0761319	−	0.724347i
$395$	2.09673	+	3.63164i	0.105498	+	0.182728i
$396$	0.152331	+	0.227688i	0.00765492	+	0.0114417i
$397$	16.2965	+	9.40879i	0.817898	+	0.472214i	0.849691	−	0.527281i	$-0.176788\pi$
$397$	16.2965	+	9.40879i	0.817898	+	0.472214i	−0.0317930	+	0.999494i	$0.510122\pi$
$398$	−2.74718	+	1.99594i	−0.137704	+	0.100047i
$399$	1.07162	−	3.40572i	0.0536483	−	0.170499i
$400$	−3.27723	+	10.0863i	−0.163861	+	0.504313i
$401$	14.1435	−	6.29711i	0.706295	−	0.314463i	−0.0219699	−	0.999759i	$-0.506994\pi$
$401$	14.1435	−	6.29711i	0.706295	−	0.314463i	0.728265	+	0.685296i	$0.240327\pi$
$402$	0.130116	−	1.23797i	0.00648961	−	0.0617445i
$403$	0.728032	+	3.42512i	0.0362659	+	0.170618i
$404$	0.188541	+	0.0400756i	0.00938025	+	0.00199383i
$405$	−7.70643	−	10.6070i	−0.382935	−	0.527065i
$406$	5.52615	+	12.1072i	0.274258	+	0.600871i
$407$	12.2094	+	7.69344i	0.605195	+	0.381350i
$408$	0.798313	−	1.38272i	0.0395224	−	0.0684548i
$409$	−18.7463	−	8.34640i	−0.926946	−	0.412703i	−0.112968	−	0.993599i	$-0.536036\pi$
$409$	−18.7463	−	8.34640i	−0.926946	−	0.412703i	−0.813978	+	0.580896i	$0.802702\pi$
$410$	10.4151	−	11.5671i	0.514363	−	0.571258i
$411$	−1.58333	+	1.42563i	−0.0780997	+	0.0703213i
$412$	−0.0364828	+	0.0502143i	−0.00179738	+	0.00247388i
$413$	1.26472	−	1.43119i	0.0622326	−	0.0704243i
$414$	−4.05433	−	1.31733i	−0.199260	−	0.0647433i
$415$	2.28731	−	10.7610i	0.112280	−	0.528235i
$416$	−0.404922	+	0.909470i	−0.0198529	+	0.0445904i
$417$	−0.376176	+	0.217185i	−0.0184214	+	0.0106356i
$418$	30.2831	−	5.22203i	1.48120	−	0.255418i
$419$			11.3707i			0.555494i	0.960654	+	0.277747i	$0.0895877\pi$
$419$			11.3707i			0.555494i	−0.960654	+	0.277747i	$0.910412\pi$
$420$	−0.0197825	+	0.0116684i	−0.000965288	+	0.000569361i
$421$	−4.55177	−	14.0089i	−0.221839	−	0.682752i	−0.998597	−	0.0529520i	$-0.983137\pi$
$421$	−4.55177	−	14.0089i	−0.221839	−	0.682752i	0.776758	−	0.629800i	$-0.216863\pi$
$422$	24.9208	+	27.6774i	1.21313	+	1.34731i
$423$	−21.5961	−	2.26984i	−1.05004	−	0.110364i
$424$	−8.50838	−	0.894266i	−0.413203	−	0.0434294i
$425$	4.93290	+	5.47854i	0.239281	+	0.265748i
$426$	−0.425036	−	1.30813i	−0.0205930	−	0.0633789i
$427$	18.1171	+	10.2361i	0.876747	+	0.495361i
$428$			0.453863i			0.0219383i
$429$	−4.21364	+	0.726602i	−0.203436	+	0.0350807i
$430$	−17.5960	+	10.1591i	−0.848556	+	0.489914i
$431$	4.84010	−	10.8710i	0.233139	−	0.523640i	−0.758653	−	0.651494i	$-0.774142\pi$
$431$	4.84010	−	10.8710i	0.233139	−	0.523640i	0.991793	+	0.127855i	$0.0408091\pi$
$432$	−0.999112	+	4.70045i	−0.0480698	+	0.226151i
$433$	−29.8361	−	9.69435i	−1.43383	−	0.465881i	−0.513864	−	0.857871i	$-0.671787\pi$
$433$	−29.8361	−	9.69435i	−1.43383	−	0.465881i	−0.919969	+	0.391991i	$0.871787\pi$
$434$	−1.95697	+	0.656070i	−0.0939377	+	0.0314924i
$435$	0.654578	−	0.900950i	0.0313846	−	0.0431972i
$436$	−0.0368282	+	0.0331602i	−0.00176375	+	0.00158809i
$437$	4.53048	−	5.03161i	0.216722	−	0.240694i
$438$	−2.55772	−	1.13877i	−0.122213	−	0.0544126i
$439$	−12.3534	+	21.3966i	−0.589593	+	1.02121i	0.404692	+	0.914453i	$0.367379\pi$
$439$	−12.3534	+	21.3966i	−0.589593	+	1.02121i	−0.994286	+	0.106753i	$0.965955\pi$
$440$	−12.1469	−	7.65406i	−0.579079	−	0.364893i
$441$	20.3313	+	3.92728i	0.968159	+	0.187013i
$442$	−14.2622	−	19.6302i	−0.678382	−	0.933713i
$443$	−32.6374	−	6.93728i	−1.55065	−	0.329600i	−0.648563	−	0.761161i	$-0.724630\pi$
$443$	−32.6374	−	6.93728i	−1.55065	−	0.329600i	−0.902084	+	0.431560i	$0.857963\pi$
$444$	−0.00516634	−	0.0243057i	−0.000245184	−	0.00115350i
$445$	−0.180827	+	1.72045i	−0.00857203	+	0.0815574i
$446$	−14.6920	+	6.54132i	−0.695688	+	0.309740i
$447$	−0.315685	+	0.971578i	−0.0149314	+	0.0459541i
$448$	−20.4641	−	6.43911i	−0.966836	−	0.304219i
$449$	−18.9658	+	13.7795i	−0.895053	+	0.650294i	−0.937190	−	0.348818i	$-0.886583\pi$
$449$	−18.9658	+	13.7795i	−0.895053	+	0.650294i	0.0421379	+	0.999112i	$0.486583\pi$
$450$	−9.67546	−	5.58613i	−0.456105	−	0.263333i
$451$	−13.4476	−	20.1001i	−0.633225	−	0.946475i
$452$	−0.155956	−	0.270124i	−0.00733556	−	0.0127056i
$453$	0.0479117	+	0.455849i	0.00225109	+	0.0214177i
$454$	25.7460	−	8.36537i	1.20832	−	0.392606i
$455$	2.88448	+	25.1855i	0.135227	+	1.18071i
$456$	−3.10907	−	2.25887i	−0.145596	−	0.105781i
$457$	0.613358	+	1.37762i	0.0286917	+	0.0644426i	0.927323	−	0.374262i	$-0.122104\pi$
$457$	0.613358	+	1.37762i	0.0286917	+	0.0644426i	−0.898631	+	0.438705i	$0.855437\pi$
$458$	−31.5854	+	6.71369i	−1.47589	+	0.313710i
$459$	2.48242	+	2.23518i	0.115870	+	0.104329i
$460$	−0.0433162	+	0.00455271i	−0.00201963	+	0.000212271i
$461$	15.7812			0.735004			0.367502	−	0.930023i	$-0.380213\pi$
$461$	15.7812			0.735004			0.367502	+	0.930023i	$0.380213\pi$
$462$	−0.708118	−	2.41884i	−0.0329446	−	0.112534i
$463$	−8.99614			−0.418086			−0.209043	−	0.977906i	$-0.567035\pi$
$463$	−8.99614			−0.418086			−0.209043	+	0.977906i	$0.567035\pi$
$464$	14.0478	−	1.47649i	0.652154	−	0.0685441i
$465$	0.128349	+	0.115566i	0.00595204	+	0.00535924i
$466$	−12.0870	+	2.56918i	−0.559922	+	0.119015i
$467$	−13.4404	−	30.1877i	−0.621950	−	1.39692i	−0.899802	−	0.436298i	$-0.856289\pi$
$467$	−13.4404	−	30.1877i	−0.621950	−	1.39692i	0.277852	−	0.960624i	$-0.410377\pi$
$468$	−0.421207	−	0.306025i	−0.0194703	−	0.0141460i
$469$	−4.56608	+	10.5181i	−0.210842	+	0.485682i
$470$	14.9028	−	4.84223i	0.687417	−	0.223355i
$471$	−0.102356	−	0.973849i	−0.00471630	−	0.0448726i
$472$	−1.02790	−	1.78037i	−0.0473129	−	0.0819483i
$473$	8.58699	+	30.3784i	0.394830	+	1.39680i
$474$	0.686210	+	0.396183i	0.0315187	+	0.0181973i
$475$	14.3555	−	10.4299i	0.658676	−	0.478556i
$476$	−0.149220	+	0.136896i	−0.00683950	+	0.00627462i
$477$	2.74615	−	8.45178i	0.125738	−	0.386980i
$478$	−12.4057	+	5.52339i	−0.567425	+	0.252634i
$479$	2.92875	−	27.8652i	0.133818	−	1.27319i	−0.697171	−	0.716905i	$-0.745558\pi$
$479$	2.92875	−	27.8652i	0.133818	−	1.27319i	0.830989	−	0.556289i	$-0.187775\pi$
$480$	0.0102090	+	0.0480297i	0.000465976	+	0.00219225i
$481$	−26.8273	−	5.70233i	−1.22322	−	0.260004i
$482$	20.7494	+	28.5591i	0.945108	+	1.30083i
$483$	−0.452271	−	0.322202i	−0.0205791	−	0.0146607i
$484$	−0.222542	+	0.211686i	−0.0101156	+	0.00962207i
$485$	−6.09916	+	10.5641i	−0.276949	+	0.479689i
$486$	−6.95326	−	3.09579i	−0.315406	−	0.140428i
$487$	−11.4648	+	12.7329i	−0.519519	+	0.576984i	−0.944622	−	0.328161i	$-0.893571\pi$
$487$	−11.4648	+	12.7329i	−0.519519	+	0.576984i	0.425103	+	0.905145i	$0.360238\pi$
$488$	16.6450	−	14.9873i	0.753486	−	0.678442i
$489$	0.0771786	−	0.106227i	0.00349014	−	0.00480376i
$490$	−14.5555	+	3.37839i	−0.657552	+	0.152620i
$491$	−26.5774	−	8.63553i	−1.19942	−	0.389716i	−0.359874	−	0.933001i	$-0.617180\pi$
$491$	−26.5774	−	8.63553i	−1.19942	−	0.389716i	−0.839549	+	0.543285i	$0.817180\pi$
$492$	−0.00865776	+	0.0407316i	−0.000390322	+	0.00183632i
$493$	3.99370	−	8.96999i	0.179867	−	0.403988i
$494$	−50.5787	+	29.2016i	−2.27564	+	1.31384i
$495$	10.4002	−	10.6888i	0.467455	−	0.480424i
$496$			2.19064i			0.0983625i
$497$	0.117992	+	12.6694i	0.00529266	+	0.568301i
$498$	−0.642367	−	1.97700i	−0.0287852	−	0.0885916i
$499$	8.94217	+	9.93129i	0.400307	+	0.444586i	0.909273	−	0.416201i	$-0.136639\pi$
$499$	8.94217	+	9.93129i	0.400307	+	0.444586i	−0.508966	+	0.860787i	$0.669972\pi$
$500$	−0.324575	−	0.0341142i	−0.0145154	−	0.00152563i
$501$	−2.89949	−	0.304749i	−0.129540	−	0.0136152i
$502$	−20.3465	−	22.5970i	−0.908108	−	1.00856i
$503$	3.19674	+	9.83855i	0.142535	+	0.438679i	0.996686	−	0.0813470i	$-0.0259222\pi$
$503$	3.19674	+	9.83855i	0.142535	+	0.438679i	−0.854150	+	0.520026i	$0.825922\pi$
$504$	10.9641	−	19.4055i	0.488381	−	0.864392i
$505$		−	10.4934i		−	0.466951i
$506$	0.683032	−	4.73049i	0.0303645	−	0.210296i
$507$	4.73494	−	2.73372i	0.210286	−	0.121409i
$508$	0.0442067	−	0.0992898i	0.00196135	−	0.00440527i
$509$	0.614894	−	2.89285i	0.0272547	−	0.128223i	−0.962417	−	0.271576i	$-0.912455\pi$
$509$	0.614894	−	2.89285i	0.0272547	−	0.128223i	0.989672	+	0.143353i	$0.0457884\pi$
$510$	−1.13820	−	0.369825i	−0.0504005	−	0.0163761i
$511$	19.3258	+	17.0778i	0.854922	+	0.755478i
$512$	−13.5678	+	18.6745i	−0.599617	+	0.825302i
$513$	5.97511	−	5.38001i	0.263807	−	0.237533i
$514$	−14.8021	+	16.4394i	−0.652893	+	0.725111i
$515$	3.08686	+	1.37436i	0.136023	+	0.0605614i
$516$	0.0271788	−	0.0470751i	0.00119648	−	0.00207236i
$517$	−1.60670	−	24.2933i	−0.0706626	−	1.06842i
$518$	1.54005	−	16.0929i	0.0676660	−	0.707083i
$519$	1.85349	+	2.55111i	0.0813591	+	0.111981i
$520$	26.6900	+	5.67314i	1.17044	+	0.248784i
$521$	−3.86268	−	18.1725i	−0.169227	−	0.796150i	−0.978095	−	0.208160i	$-0.933253\pi$
$521$	−3.86268	−	18.1725i	−0.169227	−	0.796150i	0.808868	−	0.587991i	$-0.200081\pi$
$522$	−1.55541	+	14.7988i	−0.0680786	+	0.647725i
$523$	29.0458	−	12.9320i	1.27008	−	0.565478i	0.342649	−	0.939463i	$-0.388676\pi$
$523$	29.0458	−	12.9320i	1.27008	−	0.565478i	0.927435	+	0.373986i	$0.122009\pi$
$524$	−0.121230	+	0.373107i	−0.00529595	+	0.0162993i
$525$	−0.983831	−	1.07240i	−0.0429379	−	0.0468034i
$526$	22.3151	−	16.2128i	0.972983	−	0.706913i
$527$	1.31877	+	0.761391i	0.0574464	+	0.0331667i
$528$	−2.67297	−	0.103438i	−0.116326	−	0.00450156i
$529$	10.9735	+	19.0066i	0.477107	+	0.826374i
$530$	0.670313	+	6.37760i	0.0291165	+	0.277025i
$531$	2.03094	−	0.659891i	0.0881351	−	0.0286368i
$532$	0.290156	+	0.391643i	0.0125799	+	0.0169799i
$533$	37.1838	+	27.0156i	1.61061	+	1.17018i
$534$	0.132953	+	0.298616i	0.00575342	+	0.0129224i
$535$	24.1683	−	5.13713i	1.04489	−	0.222097i
$536$	9.17207	+	8.25857i	0.396173	+	0.356716i
$537$	−0.915058	+	0.0961765i	−0.0394877	+	0.00415032i
$538$	40.2744			1.73635
$539$	−0.465520	+	23.2117i	−0.0200514	+	0.999799i
$540$	−0.0517220			−0.00222576
$541$	−21.1136	+	2.21912i	−0.907742	+	0.0954076i	−0.546880	−	0.837211i	$-0.684184\pi$
$541$	−21.1136	+	2.21912i	−0.907742	+	0.0954076i	−0.360863	+	0.932619i	$0.617518\pi$
$542$	−5.65196	−	5.08905i	−0.242772	−	0.218593i
$543$	1.24454	−	0.264535i	0.0534083	−	0.0113523i
$544$	0.176091	+	0.395507i	0.00754984	+	0.0169572i
$545$	2.18263	+	1.58578i	0.0934937	+	0.0679272i
$546$	2.85145	+	3.84880i	0.122031	+	0.164713i
$547$	22.4334	−	7.28904i	0.959181	−	0.311657i	0.212740	−	0.977109i	$-0.431761\pi$
$547$	22.4334	−	7.28904i	0.959181	−	0.311657i	0.746441	+	0.665452i	$0.231761\pi$
$548$	−0.0304034	−	0.289269i	−0.00129877	−	0.0123570i
$549$	11.6330	+	20.1489i	0.496484	+	0.859935i
$550$	4.32853	−	11.7544i	0.184569	−	0.501209i
$551$	−20.4674	−	11.8168i	−0.871939	−	0.503414i
$552$	−0.483563	+	0.351329i	−0.0205818	+	0.0149536i
$553$	−4.93424	−	5.37844i	−0.209825	−	0.228715i
$554$	1.10394	−	3.39759i	0.0469021	−	0.144350i
$555$	−1.23581	+	0.550217i	−0.0524571	+	0.0233554i
$556$	0.00619850	−	0.0589748i	0.000262875	−	0.00250109i
$557$	−5.22601	−	24.5864i	−0.221433	−	1.04176i	−0.938639	−	0.344900i	$-0.887913\pi$
$557$	−5.22601	−	24.5864i	−0.221433	−	1.04176i	0.717206	−	0.696861i	$-0.245420\pi$
$558$	−2.25731	−	0.479807i	−0.0955596	−	0.0203118i
$559$	−35.2654	−	48.5386i	−1.49157	−	2.05296i
$560$	−1.51078	+	15.7870i	−0.0638419	+	0.667123i
$561$	−0.991303	+	1.57318i	−0.0418528	+	0.0664198i
$562$	14.8023	−	25.6383i	0.624397	−	1.08149i
$563$	14.8918	+	6.63027i	0.627616	+	0.279433i	0.695795	−	0.718240i	$-0.255052\pi$
$563$	14.8918	+	6.63027i	0.627616	+	0.279433i	−0.0681788	+	0.997673i	$0.521719\pi$
$564$	−0.0280511	+	0.0311539i	−0.00118116	+	0.00131182i
$565$	−12.6189	+	11.3621i	−0.530882	+	0.478008i
$566$	−5.88562	+	8.10086i	−0.247391	+	0.340504i
$567$	17.1003	+	15.1112i	0.718143	+	0.634609i
$568$	12.9702	+	4.21427i	0.544217	+	0.176827i
$569$	−7.14099	+	33.5957i	−0.299366	+	1.40841i	0.529191	+	0.848502i	$0.322495\pi$
$569$	−7.14099	+	33.5957i	−0.299366	+	1.40841i	−0.828557	+	0.559904i	$0.810838\pi$
$570$	−1.17165	+	2.63156i	−0.0490749	+	0.110224i
$571$	18.1029	−	10.4517i	0.757584	−	0.437392i	−0.0708434	−	0.997487i	$-0.522569\pi$
$571$	18.1029	−	10.4517i	0.757584	−	0.437392i	0.828428	+	0.560096i	$0.189236\pi$
$572$	0.257867	−	0.523684i	0.0107820	−	0.0218963i
$573$			1.91497i			0.0799988i
$574$	−13.3268	+	23.5873i	−0.556250	+	0.984515i
$575$	−0.852838	−	2.62476i	−0.0355658	−	0.109460i
$576$	−16.0501	−	17.8254i	−0.668753	−	0.742725i
$577$	−21.0480	−	2.21224i	−0.876242	−	0.0920967i	−0.344282	−	0.938866i	$-0.611878\pi$
$577$	−21.0480	−	2.21224i	−0.876242	−	0.0920967i	−0.531960	+	0.846770i	$0.678544\pi$
$578$	13.2483	+	1.39245i	0.551056	+	0.0579184i
$579$	0.149190	+	0.165692i	0.00620011	+	0.00688592i
$580$	0.0469804	+	0.144591i	0.00195075	+	0.00600380i
$581$	0.178324	+	19.1476i	0.00739814	+	0.794377i
$582$			2.30491i			0.0955417i
$583$	9.86131	+	1.42387i	0.408414	+	0.0589706i
$584$	24.0409	−	13.8800i	0.994819	−	0.574359i
$585$	−11.5284	+	25.8931i	−0.476639	+	1.07055i
$586$	−1.85540	+	8.72898i	−0.0766460	+	0.360591i
$587$	14.7646	+	4.79732i	0.609401	+	0.198007i	0.597429	−	0.801922i	$-0.296189\pi$
$587$	14.7646	+	4.79732i	0.609401	+	0.198007i	0.0119725	+	0.999928i	$0.496189\pi$
$588$	0.0292045	−	0.0272978i	0.00120437	−	0.00112574i
$589$	2.15440	−	2.96528i	0.0887705	−	0.122182i
$590$	−1.14516	+	1.03110i	−0.0471453	+	0.0424498i
$591$	1.40891	−	1.56475i	0.0579548	−	0.0643654i
$592$	−15.6748	−	6.97888i	−0.644231	−	0.286830i
$593$	3.79829	−	6.57883i	0.155977	−	0.270160i	−0.777437	−	0.628960i	$-0.783481\pi$
$593$	3.79829	−	6.57883i	0.155977	−	0.270160i	0.933414	+	0.358800i	$0.116814\pi$
$594$	1.39386	−	5.50197i	0.0571907	−	0.225748i
$595$	8.97871	+	6.39651i	0.368091	+	0.262231i
$596$	−0.0819750	−	0.112829i	−0.00335783	−	0.00462165i
$597$	−0.483755	−	0.102825i	−0.0197988	−	0.00420836i
$598$	1.88859	+	8.88513i	0.0772303	+	0.363340i
$599$	3.21334	−	30.5729i	0.131294	−	1.24918i	−0.708281	−	0.705931i	$-0.750529\pi$
$599$	3.21334	−	30.5729i	0.131294	−	1.24918i	0.839575	−	0.543244i	$-0.182804\pi$
$600$	−1.43105	+	0.637143i	−0.0584222	+	0.0260113i
$601$	14.0820	−	43.3399i	0.574416	−	1.76787i	−0.0637412	−	0.997966i	$-0.520303\pi$
$601$	14.0820	−	43.3399i	0.574416	−	1.76787i	0.638158	−	0.769906i	$-0.279697\pi$
$602$	26.0597	−	23.9074i	1.06211	−	0.974393i
$603$	−10.3720	+	7.53567i	−0.422379	+	0.306876i
$604$	−0.0541912	−	0.0312873i	−0.00220501	−	0.00127306i
$605$	13.7912	+	9.45441i	0.560691	+	0.384376i
$606$	−0.991383	−	1.71713i	−0.0402722	−	0.0697535i
$607$	−1.80505	−	17.1739i	−0.0732648	−	0.697068i	−0.968082	−	0.250635i	$-0.919361\pi$
$607$	−1.80505	−	17.1739i	−0.0732648	−	0.697068i	0.894817	−	0.446433i	$-0.147306\pi$
$608$	0.991061	−	0.322015i	0.0401928	−	0.0130594i
$609$	−0.771869	+	1.77803i	−0.0312777	+	0.0720493i
$610$	−13.5825	−	9.86827i	−0.549940	−	0.399555i
$611$	18.8201	+	42.2706i	0.761379	+	1.71009i
$612$	−0.221467	+	0.0470742i	−0.00895226	+	0.00190286i
$613$	−30.2241	−	27.2139i	−1.22074	−	1.09916i	−0.992074	−	0.125656i	$-0.959896\pi$
$613$	−30.2241	−	27.2139i	−1.22074	−	1.09916i	−0.228668	−	0.973504i	$-0.573437\pi$
$614$	−28.6889	+	3.01532i	−1.15779	+	0.121688i
$615$	2.26696			0.0914125
$616$	23.5295	+	8.41669i	0.948031	+	0.339118i
$617$	−9.08065			−0.365573			−0.182787	−	0.983153i	$-0.558512\pi$
$617$	−9.08065			−0.365573			−0.182787	+	0.983153i	$0.558512\pi$
$618$	0.634973	−	0.0667383i	0.0255424	−	0.00268461i
$619$	−0.366785	−	0.330255i	−0.0147423	−	0.0132741i	0.661727	−	0.749745i	$-0.269824\pi$
$619$	−0.366785	−	0.330255i	−0.0147423	−	0.0132741i	−0.676469	+	0.736471i	$0.736491\pi$
$620$	−0.0230629	+	0.00490218i	−0.000926230	+	0.000196876i
$621$	−0.508638	−	1.14242i	−0.0204109	−	0.0458437i
$622$	−18.3990	−	13.3676i	−0.737731	−	0.535993i
$623$	−0.342613	−	2.99148i	−0.0137265	−	0.119851i
$624$	4.83502	−	1.57099i	0.193556	−	0.0628901i
$625$	0.451573	+	4.29643i	0.0180629	+	0.171857i
$626$	−19.2907	−	33.4125i	−0.771013	−	1.33543i
$627$	3.51644	+	2.76877i	0.140433	+	0.110574i
$628$	0.115771	+	0.0668403i	0.00461976	+	0.00266722i
$629$	−9.64932	+	7.01064i	−0.384744	+	0.279533i
$630$	−15.9366	−	5.01452i	−0.634929	−	0.199783i
$631$	−12.8784	+	39.6357i	−0.512682	+	1.57787i	0.274779	+	0.961508i	$0.411395\pi$
$631$	−12.8784	+	39.6357i	−0.512682	+	1.57787i	−0.787461	+	0.616365i	$0.788605\pi$
$632$	−7.17717	+	3.19548i	−0.285493	+	0.127109i
$633$	−0.566994	+	5.39459i	−0.0225360	+	0.214416i
$634$	5.90173	+	27.7655i	0.234388	+	1.10271i
$635$	−5.78756	−	1.23018i	−0.229672	−	0.0488183i
$636$	−0.0100841	−	0.0138796i	−0.000399861	−	0.000550362i
$637$	−14.4140	−	41.7025i	−0.571105	−	1.65231i
$638$	−16.6470	+	1.10099i	−0.659063	+	0.0435887i
$639$	−7.08303	+	12.2682i	−0.280200	+	0.485321i
$640$	15.3737	+	6.84483i	0.607700	+	0.270566i
$641$	−21.3669	+	23.7303i	−0.843941	+	0.937291i	−0.998716	−	0.0506586i	$-0.983868\pi$
$641$	−21.3669	+	23.7303i	−0.843941	+	0.937291i	0.154775	+	0.987950i	$0.450535\pi$
$642$	3.46952	−	3.12397i	0.136931	−	0.123293i
$643$	−12.4241	+	17.1003i	−0.489959	+	0.674370i	−0.980380	−	0.197115i	$-0.936843\pi$
$643$	−12.4241	+	17.1003i	−0.489959	+	0.674370i	0.490422	+	0.871485i	$0.336843\pi$
$644$	0.0718777	−	0.0240968i	0.00283238	−	0.000949547i
$645$	−2.81438	−	0.914448i	−0.110816	−	0.0360064i
$646$	−5.28058	+	24.8432i	−0.207762	+	0.977441i
$647$	6.47971	−	14.5537i	0.254744	−	0.572164i	−0.740224	−	0.672360i	$-0.765281\pi$
$647$	6.47971	−	14.5537i	0.254744	−	0.572164i	0.994968	+	0.100197i	$0.0319472\pi$
$648$	21.2724	−	12.2816i	0.835658	−	0.482468i
$649$	1.11603	+	2.11819i	0.0438082	+	0.0831463i
$650$			23.8061i			0.933750i
$651$	−0.261726	−	0.147875i	−0.0102578	−	0.00579567i
$652$	0.00553926	+	0.0170481i	0.000216934	+	0.000667655i
$653$	−31.1194	−	34.5616i	−1.21780	−	1.35250i	−0.917039	−	0.398798i	$-0.869427\pi$
$653$	−31.1194	−	34.5616i	−1.21780	−	1.35250i	−0.300757	−	0.953701i	$-0.597239\pi$
$654$	0.506981	+	0.0532859i	0.0198245	+	0.00208364i
$655$	21.2402	+	2.23243i	0.829922	+	0.0872283i
$656$	19.2400	+	21.3682i	0.751197	+	0.834289i
$657$	8.91070	+	27.4243i	0.347639	+	1.06992i
$658$	−23.4920	+	13.8564i	−0.915814	+	0.540179i
$659$		−	15.0416i		−	0.585939i	−0.956122	−	0.292970i	$-0.905357\pi$
$659$		−	15.0416i		−	0.585939i	0.956122	−	0.292970i	$-0.0946435\pi$
$660$	−0.00489254	−	0.0283724i	−0.000190442	−	0.00110439i
$661$	−2.85554	+	1.64864i	−0.111067	+	0.0641248i	−0.554505	−	0.832181i	$-0.687092\pi$
$661$	−2.85554	+	1.64864i	−0.111067	+	0.0641248i	0.443437	+	0.896305i	$0.353759\pi$
$662$	−0.109125	+	0.245100i	−0.00424128	+	0.00952607i
$663$	0.734748	−	3.45672i	0.0285352	−	0.134248i
$664$	19.6022	+	6.36913i	0.760712	+	0.247170i
$665$	17.5709	−	19.8837i	0.681368	−	0.771057i
$666$	10.6245	−	14.6233i	0.411690	−	0.566643i
$667$	−2.73167	+	2.45960i	−0.105771	+	0.0952363i
$668$	0.266324	−	0.295782i	0.0103044	−	0.0114442i
$669$	−2.13981	−	0.952704i	−0.0827297	−	0.0368336i
$670$	4.62567	−	8.01190i	0.178705	−	0.309527i
$671$	−20.0455	+	16.6918i	−0.773850	+	0.644379i
$672$	−0.0354877	−	0.0777498i	−0.00136897	−	0.00299926i
$673$	−10.2565	−	14.1168i	−0.395358	−	0.544164i	0.564213	−	0.825629i	$-0.309180\pi$
$673$	−10.2565	−	14.1168i	−0.395358	−	0.544164i	−0.959571	+	0.281465i	$0.909180\pi$
$674$	−6.21657	−	1.32137i	−0.239453	−	0.0508974i
$675$	−0.681400	−	3.20573i	−0.0262271	−	0.123389i
$676$	−0.0780206	+	0.742317i	−0.00300079	+	0.0285506i
$677$	−13.1423	+	5.85134i	−0.505101	+	0.224885i	−0.643436	−	0.765500i	$-0.722492\pi$
$677$	−13.1423	+	5.85134i	−0.505101	+	0.224885i	0.138335	+	0.990386i	$0.455825\pi$
$678$	−0.991484	+	3.05147i	−0.0380777	+	0.117191i
$679$	6.37265	−	20.2529i	0.244560	−	0.777234i
$680$	9.59994	−	6.97476i	0.368141	−	0.267470i
$681$	3.41449	+	1.97136i	0.130844	+	0.0755426i
$682$	0.100051	−	2.58545i	0.00383115	−	0.0990019i
$683$	−7.01481	−	12.1500i	−0.268414	−	0.464907i	0.700038	−	0.714105i	$-0.253166\pi$
$683$	−7.01481	−	12.1500i	−0.268414	−	0.464907i	−0.968453	+	0.249198i	$0.919833\pi$
$684$	0.0569650	+	0.541986i	0.00217811	+	0.0207234i
$685$	−15.0595	+	4.89313i	−0.575394	+	0.186957i
$686$	23.4548	−	11.2381i	0.895509	−	0.429071i
$687$	−3.80481	−	2.76435i	−0.145162	−	0.105467i
$688$	−15.2666	−	34.2893i	−0.582033	−	1.30727i
$689$	−18.5222	+	3.93702i	−0.705640	+	0.149988i
$690$	0.332951	+	0.299790i	0.0126752	+	0.0114128i
$691$	−17.7082	+	1.86121i	−0.673652	+	0.0708037i	−0.435177	−	0.900345i	$-0.643314\pi$
$691$	−17.7082	+	1.86121i	−0.673652	+	0.0708037i	−0.238475	+	0.971149i	$0.576648\pi$
$692$	−0.430489			−0.0163648
$693$	−13.6334	+	22.0894i	−0.517889	+	0.839105i
$694$	−22.5049			−0.854273
$695$	−3.21057	+	0.337445i	−0.121784	+	0.0128000i
$696$	1.55049	+	1.39606i	0.0587710	+	0.0529176i
$697$	19.5509	−	4.15567i	0.740542	−	0.157407i
$698$	16.3004	+	36.6113i	0.616980	+	1.38576i
$699$	−1.45602	−	1.05786i	−0.0550715	−	0.0400118i
$700$	0.197388	−	0.0226068i	0.00746057	−	0.000854455i
$701$	42.9916	−	13.9688i	1.62377	−	0.527594i	0.650942	−	0.759128i	$-0.274374\pi$
$701$	42.9916	−	13.9688i	1.62377	−	0.527594i	0.972827	+	0.231534i	$0.0743743\pi$
$702$	1.12754	+	10.7279i	0.0425564	+	0.404897i
$703$	14.3542	+	24.8622i	0.541379	+	0.937696i
$704$	16.6368	−	21.1294i	0.627023	−	0.796343i
$705$	1.97645	+	1.14110i	0.0744374	+	0.0429765i
$706$	23.7712	−	17.2708i	0.894640	−	0.649994i
$707$	3.96358	+	17.8291i	0.149066	+	0.670532i
$708$	0.00127394	−	0.00392079i	4.78777e−5	−	0.000147352i
$709$	5.24705	−	2.33614i	0.197057	−	0.0877354i	−0.305836	−	0.952084i	$-0.598936\pi$
$709$	5.24705	−	2.33614i	0.197057	−	0.0877354i	0.502893	+	0.864349i	$0.332269\pi$
$710$	1.06853	−	10.1663i	0.0401011	−	0.381536i
$711$	−1.69673	−	7.98247i	−0.0636322	−	0.299366i
$712$	−3.17018	−	0.673844i	−0.118808	−	0.0252534i
$713$	−0.335080	−	0.461199i	−0.0125489	−	0.0172720i
$714$	2.07358	+	0.198436i	0.0776019	+	0.00742630i
$715$	−30.8049	−	7.80406i	−1.15204	−	0.291855i
$716$	0.0628052	−	0.108782i	0.00234714	−	0.00406537i
$717$	−1.80682	−	0.804448i	−0.0674769	−	0.0300427i
$718$	−4.45730	+	4.95034i	−0.166345	+	0.184745i
$719$	33.6734	−	30.3197i	1.25581	−	1.13073i	0.269998	−	0.962861i	$-0.412977\pi$
$719$	33.6734	−	30.3197i	1.25581	−	1.13073i	0.985809	−	0.167873i	$-0.0536898\pi$
$720$	−10.4225	+	14.3453i	−0.388424	+	0.534619i
$721$	−5.76392	−	1.16916i	−0.214659	−	0.0435419i
$722$	32.7646	+	10.6458i	1.21937	+	0.396197i
$723$	−1.06895	+	5.02902i	−0.0397547	+	0.187031i
$724$	−0.0706494	+	0.158681i	−0.00262567	+	0.00589734i
$725$	−8.34282	+	4.81673i	−0.309845	+	0.178889i
$726$	3.14999	+	0.244160i	0.116907	+	0.00906164i
$727$		−	11.2267i		−	0.416374i	−0.978089	−	0.208187i	$-0.933244\pi$
$727$		−	11.2267i		−	0.416374i	0.978089	−	0.208187i	$-0.0667562\pi$
$728$	−47.4912	+	0.442292i	−1.76014	+	0.0163924i
$729$	7.65350	+	23.5551i	0.283463	+	0.872409i
$730$	−13.9233	−	15.4634i	−0.515324	−	0.572325i
$731$	−25.9484	−	2.72728i	−0.959735	−	0.100872i
$732$	0.0446697	+	0.00469497i	0.00165104	+	0.000173531i
$733$	8.74772	+	9.71533i	0.323104	+	0.358844i	0.882712	−	0.469914i	$-0.155715\pi$
$733$	8.74772	+	9.71533i	0.323104	+	0.358844i	−0.559608	+	0.828757i	$0.689048\pi$
$734$	−0.317925	−	0.978471i	−0.0117348	−	0.0361160i
$735$	−1.78417	−	1.24617i	−0.0658099	−	0.0459657i
$736$		−	0.162075i		−	0.00597418i
$737$	−10.3020	−	10.0239i	−0.379480	−	0.369236i
$738$	−26.2326	+	15.1454i	−0.965637	+	0.557511i
$739$	0.362924	−	0.815141i	0.0133504	−	0.0299855i	−0.906747	−	0.421675i	$-0.861442\pi$
$739$	0.362924	−	0.815141i	0.0133504	−	0.0299855i	0.920098	+	0.391689i	$0.128109\pi$
$740$	0.0383964	−	0.180641i	0.00141148	−	0.00664049i
$741$	−8.08976	−	2.62852i	−0.297185	−	0.0965611i
$742$	−3.54786	−	10.5828i	−0.130246	−	0.388508i
$743$	4.60807	−	6.34246i	0.169054	−	0.232682i	−0.716081	−	0.698017i	$-0.754066\pi$
$743$	4.60807	−	6.34246i	0.169054	−	0.232682i	0.885135	+	0.465335i	$0.154066\pi$
$744$	−0.240460	+	0.216512i	−0.00881571	+	0.00793770i
$745$	−5.08031	+	5.64225i	−0.186128	+	0.206716i
$746$	−6.92858	−	3.08480i	−0.253673	−	0.112943i
$747$	−10.7048	+	18.5412i	−0.391667	+	0.678387i
$748$	−0.0942055	−	0.235723i	−0.00344449	−	0.00861888i
$749$	−39.1233	+	17.8572i	−1.42953	+	0.652488i
$750$	1.97329	+	2.71599i	0.0720542	+	0.0991741i
$751$	24.2543	+	5.15541i	0.885052	+	0.188124i	0.627944	−	0.778259i	$-0.283897\pi$
$751$	24.2543	+	5.15541i	0.885052	+	0.188124i	0.257109	+	0.966383i	$0.417230\pi$
$752$	6.01847	+	28.3147i	0.219471	+	1.03253i
$753$	0.462919	−	4.40438i	0.0168697	−	0.160505i
$754$	28.9660	−	12.8965i	1.05488	−	0.469662i
$755$	−1.05268	+	3.23982i	−0.0383110	+	0.117909i
$756$	0.0878794	−	0.0195364i	0.00319614	−	0.000710534i
$757$	−28.3258	+	20.5799i	−1.02952	+	0.747989i	−0.968212	−	0.250130i	$-0.919527\pi$
$757$	−28.3258	+	20.5799i	−1.02952	+	0.747989i	−0.0613062	+	0.998119i	$0.519527\pi$
$758$	31.2317	+	18.0316i	1.13439	+	0.654938i
$759$	0.578567	−	0.387081i	0.0210006	−	0.0140502i
$760$	−14.2807	−	24.7350i	−0.518017	−	0.897231i
$761$	0.234007	+	2.22643i	0.00848275	+	0.0807080i	0.997944	−	0.0640884i	$-0.0204140\pi$
$761$	0.234007	+	2.22643i	0.00848275	+	0.0807080i	−0.989461	+	0.144796i	$0.953747\pi$
$762$	−1.06329	+	0.345484i	−0.0385189	+	0.0125156i
$763$	−4.30743	−	1.86992i	−0.155939	−	0.0676958i
$764$	−0.211500	−	0.153664i	−0.00765179	−	0.00555935i
$765$	5.01341	+	11.2603i	0.181260	+	0.407117i
$766$	51.7165	−	10.9927i	1.86859	−	0.397182i
$767$	−3.38150	−	3.04472i	−0.122099	−	0.109938i
$768$	−0.136283	+	0.0143239i	−0.00491768	+	0.000516869i
$769$	−16.6808			−0.601525			−0.300762	−	0.953699i	$-0.597241\pi$
$769$	−16.6808			−0.601525			−0.300762	+	0.953699i	$0.597241\pi$
$770$	2.50408	−	18.5632i	0.0902409	−	0.668973i
$771$	−3.22185			−0.116032
$772$	−0.0302715	+	0.00318166i	−0.00108949	+	0.000114510i
$773$	27.8081	+	25.0385i	1.00019	+	0.900573i	0.995046	−	0.0994139i	$-0.0316968\pi$
$773$	27.8081	+	25.0385i	1.00019	+	0.900573i	0.00514131	+	0.999987i	$0.498363\pi$
$774$	38.6767	−	8.22099i	1.39021	−	0.295497i
$775$	−0.607675	−	1.36486i	−0.0218283	−	0.0490273i
$776$	−18.4888	−	13.4329i	−0.663709	−	0.482213i
$777$	1.89190	−	1.40165i	0.0678715	−	0.0502838i
$778$	−31.6093	+	10.2705i	−1.13325	+	0.368215i
$779$	−5.02882	−	47.8460i	−0.180176	−	1.71426i
$780$	0.0273591	+	0.0473873i	0.000979613	+	0.00169674i
$781$	−14.9042	−	5.48844i	−0.533314	−	0.196392i
$782$	3.42102	+	1.97513i	0.122336	+	0.0706305i
$783$	−3.53144	+	2.56574i	−0.126203	+	0.0916920i
$784$	−3.39616	−	27.3939i	−0.121291	−	0.978354i
$785$	2.24889	−	6.92136i	0.0802662	−	0.247034i
$786$	3.68662	−	1.64139i	0.131497	−	0.0585464i
$787$	−2.93832	+	27.9562i	−0.104740	+	0.996532i	0.808330	+	0.588729i	$0.200372\pi$
$787$	−2.93832	+	27.9562i	−0.104740	+	0.996532i	−0.913070	+	0.407803i	$0.866295\pi$
$788$	0.0597644	+	0.281170i	0.00212902	+	0.0100163i
$789$	3.92950	+	0.835241i	0.139894	+	0.0297354i
$790$	3.46141	+	4.76422i	0.123151	+	0.169503i
$791$	17.1488	−	24.0715i	0.609740	−	0.855884i
$792$	17.8789	+	21.4712i	0.635298	+	0.762945i
$793$	24.7878	−	42.9337i	0.880240	−	1.52462i
$794$	24.1410	+	10.7483i	0.856733	+	0.381442i
$795$	−0.624952	+	0.694079i	−0.0221648	+	0.0246165i
$796$	0.0501749	−	0.0451776i	0.00177840	−	0.00160128i
$797$	−14.7943	+	20.3626i	−0.524041	+	0.721281i	−0.986208	−	0.165512i	$-0.947072\pi$
$797$	−14.7943	+	20.3626i	−0.524041	+	0.721281i	0.462166	+	0.886793i	$0.347072\pi$
$798$	0.996719	−	4.91377i	0.0352835	−	0.173946i
$799$	19.1373	+	6.21808i	0.677029	+	0.219980i
$800$	0.0883128	−	0.415479i	0.00312233	−	0.0146894i
$801$	1.36931	−	3.07553i	0.0483823	−	0.108668i
$802$	18.8287	−	10.8708i	0.664865	−	0.383860i
$803$	−28.6026	+	15.0701i	−1.00936	+	0.531814i
$804$			0.0247503i			0.000872876i
$805$	−2.09672	−	3.55475i	−0.0738996	−	0.125289i
$806$	1.51955	+	4.67671i	0.0535240	+	0.164730i
$807$	3.92493	+	4.35908i	0.138164	+	0.153447i
$808$	19.5516	+	2.05496i	0.687824	+	0.0722932i
$809$	32.0934	+	3.37316i	1.12834	+	0.118594i	0.650254	−	0.759717i	$-0.274662\pi$
$809$	32.0934	+	3.37316i	1.12834	+	0.118594i	0.478091	+	0.878310i	$0.341329\pi$
$810$	−12.3199	−	13.6826i	−0.432877	−	0.480759i
$811$	0.126094	+	0.388078i	0.00442776	+	0.0136273i	0.953246	−	0.302195i	$-0.0977195\pi$
$811$	0.126094	+	0.388078i	0.00442776	+	0.0136273i	−0.948818	+	0.315823i	$0.897720\pi$
$812$	−0.134438	−	0.227925i	−0.00471785	−	0.00799859i
$813$		−	1.10769i		−	0.0388484i
$814$	18.1811	+	8.95255i	0.637247	+	0.313787i
$815$	0.845116	−	0.487928i	0.0296031	−	0.0170914i
$816$	0.899231	−	2.01971i	0.0314794	−	0.0707039i
$817$	−13.0570	+	61.4285i	−0.456807	+	2.14911i
$818$	−27.4065	−	8.90493i	−0.958247	−	0.311353i
$819$	9.80716	−	48.3488i	0.342690	−	1.68944i
$820$	−0.181909	+	0.250376i	−0.00635252	+	0.00874350i
$821$	5.37448	−	4.83920i	0.187571	−	0.168889i	−0.569995	−	0.821648i	$-0.693055\pi$
$821$	5.37448	−	4.83920i	0.187571	−	0.168889i	0.757566	+	0.652759i	$0.226388\pi$
$822$	−2.00203	+	2.22347i	−0.0698287	+	0.0775526i
$823$	27.4328	+	12.2139i	0.956249	+	0.425749i	0.824706	−	0.565561i	$-0.191340\pi$
$823$	27.4328	+	12.2139i	0.956249	+	0.425749i	0.131542	+	0.991311i	$0.458007\pi$
$824$	−3.16525	+	5.48237i	−0.110267	+	0.190987i
$825$	1.69407	−	0.677026i	0.0589799	−	0.0235710i
$826$	1.55623	−	2.18447i	0.0541483	−	0.0760074i
$827$	8.17649	+	11.2540i	0.284324	+	0.391339i	0.927160	−	0.374665i	$-0.122242\pi$
$827$	8.17649	+	11.2540i	0.284324	+	0.391339i	−0.642836	+	0.766004i	$0.722242\pi$
$828$	0.0829089	+	0.0176228i	0.00288128	+	0.000612436i
$829$	−5.75497	−	27.0750i	−0.199878	−	0.940354i	−0.957673	−	0.287860i	$-0.907056\pi$
$829$	−5.75497	−	27.0750i	−0.199878	−	0.940354i	0.757794	−	0.652494i	$-0.226277\pi$
$830$	1.61489	−	15.3647i	0.0560537	−	0.533315i
$831$	0.475321	−	0.211627i	0.0164887	−	0.00734125i
$832$	−15.7941	+	48.6092i	−0.547562	+	1.68522i
$833$	−17.6716	−	7.47670i	−0.612284	−	0.259052i
$834$	−0.493492	+	0.358543i	−0.0170882	+	0.0124153i
$835$	−18.7649	−	10.8339i	−0.649386	−	0.374923i
$836$	−0.587970	+	0.166200i	−0.0203354	+	0.00574815i
$837$	−0.338485	−	0.586273i	−0.0116998	−	0.0202646i
$838$	1.66910	+	15.8805i	0.0576582	+	0.548581i
$839$	11.5281	−	3.74570i	0.397994	−	0.129316i	−0.103180	−	0.994663i	$-0.532902\pi$
$839$	11.5281	−	3.74570i	0.397994	−	0.129316i	0.501174	+	0.865347i	$0.332902\pi$
$840$	−1.88221	+	1.39447i	−0.0649426	+	0.0481139i
$841$	−13.0812	−	9.50403i	−0.451075	−	0.327725i
$842$	−8.41343	−	18.8969i	−0.289946	−	0.651229i
$843$	4.21750	−	0.896458i	0.145259	−	0.0308757i
$844$	−0.550311	−	0.495503i	−0.0189425	−	0.0170559i
$845$	40.4116	−	4.24743i	1.39020	−	0.146116i
$846$	−30.4947			−1.04843
$847$	−27.0033	−	10.8545i	−0.927845	−	0.372966i
$848$	−11.8464			−0.406808
$849$	−1.45037	+	0.152441i	−0.0497767	+	0.00523174i
$850$	7.69355	+	6.92730i	0.263887	+	0.237605i
$851$	4.36753	−	0.928348i	0.149717	−	0.0318234i
$852$	0.0111235	+	0.0249837i	0.000381084	+	0.000855928i
$853$	45.6424	+	33.1611i	1.56277	+	1.13542i	0.933696	+	0.358067i	$0.116564\pi$
$853$	45.6424	+	33.1611i	1.56277	+	1.13542i	0.629070	+	0.777349i	$0.283436\pi$
$854$	26.8051	+	11.6365i	0.917252	+	0.398194i
$855$	28.2161	−	9.16795i	0.964969	−	0.313537i
$856$	4.83868	+	46.0370i	0.165383	+	1.57351i
$857$	−10.8680	−	18.8240i	−0.371244	−	0.643014i	0.618513	−	0.785775i	$-0.287735\pi$
$857$	−10.8680	−	18.8240i	−0.371244	−	0.643014i	−0.989757	+	0.142760i	$0.954402\pi$
$858$	−5.77817	+	1.63330i	−0.197263	+	0.0557600i
$859$	47.8041	+	27.5997i	1.63105	+	0.941689i	0.983769	+	0.179441i	$0.0574288\pi$
$859$	47.8041	+	27.5997i	1.63105	+	0.941689i	0.647285	+	0.762248i	$0.275905\pi$
$860$	0.326833	−	0.237458i	0.0111449	−	0.00809725i
$861$	−3.85172	+	0.856276i	−0.131266	+	0.0291818i
$862$	5.16399	−	15.8931i	0.175886	−	0.541322i
$863$	28.0347	−	12.4819i	0.954312	−	0.424887i	0.130310	−	0.991473i	$-0.458403\pi$
$863$	28.0347	−	12.4819i	0.954312	−	0.424887i	0.824003	+	0.566586i	$0.191736\pi$
$864$	0.0201183	−	0.191413i	0.000684437	−	0.00651199i
$865$	4.87257	+	22.9236i	0.165672	+	0.779426i
$866$	−43.0926	−	9.15962i	−1.46435	−	0.311256i
$867$	1.14040	+	1.56962i	0.0387300	+	0.0533072i
$868$	0.0373339	−	0.0170405i	0.00126720	−	0.000578392i
$869$	8.49631	−	3.39551i	0.288218	−	0.115185i
$870$	0.781943	−	1.35436i	0.0265103	−	0.0459173i
$871$	24.9563	+	11.1113i	0.845612	+	0.376491i
$872$	−3.38209	+	3.75619i	−0.114532	+	0.127201i
$873$	17.6414	−	15.8844i	0.597072	−	0.537606i
$874$	5.58874	−	7.69224i	0.189042	−	0.260194i
$875$	−9.82970	−	29.3207i	−0.332305	−	0.991222i
$876$	0.0529435	+	0.0172024i	0.00178880	+	0.000581215i
$877$	0.354828	−	1.66933i	0.0119817	−	0.0563694i	−0.971751	−	0.236010i	$-0.924160\pi$
$877$	0.354828	−	1.66933i	0.0119817	−	0.0563694i	0.983732	+	0.179641i	$0.0574935\pi$
$878$	−14.1121	+	31.6962i	−0.476259	+	1.06969i
$879$	−1.12560	+	0.649863i	−0.0379654	+	0.0219193i
$880$	−17.8354	−	8.78236i	−0.601233	−	0.296053i
$881$		−	5.50028i		−	0.185309i	−0.995698	−	0.0926546i	$-0.970465\pi$
$881$		−	5.50028i		−	0.185309i	0.995698	−	0.0926546i	$-0.0295352\pi$
$882$	28.9715	+	2.50046i	0.975522	+	0.0841948i
$883$	−6.27316	−	19.3068i	−0.211109	−	0.649725i	−0.999407	−	0.0344323i	$-0.989038\pi$
$883$	−6.27316	−	19.3068i	−0.211109	−	0.649725i	0.788299	−	0.615293i	$-0.210962\pi$
$884$	0.322821	+	0.358529i	0.0108576	+	0.0120586i
$885$	−0.223202	−	0.0234595i	−0.00750285	−	0.000788581i
$886$	−46.6001	−	4.89787i	−1.56556	−	0.164547i
$887$	11.0318	+	12.2520i	0.370411	+	0.411383i	0.899317	−	0.437297i	$-0.144064\pi$
$887$	11.0318	+	12.2520i	0.370411	+	0.411383i	−0.528906	+	0.848680i	$0.677398\pi$
$888$	−0.783166	−	2.41034i	−0.0262813	−	0.0808857i
$889$	10.2981	−	0.0959079i	0.345389	−	0.00321665i
$890$			2.42935i			0.0814322i
$891$	−25.3087	+	13.3347i	−0.847875	+	0.446729i
$892$	0.276928	−	0.159884i	0.00927222	−	0.00535332i
$893$	19.6996	−	44.2460i	0.659222	−	1.48064i
$894$	−0.298272	+	1.40326i	−0.00997571	+	0.0469320i
$895$	−6.50352	−	2.11312i	−0.217389	−	0.0706338i
$896$	−28.7065	−	5.82289i	−0.959018	−	0.194529i
$897$	−0.777626	+	1.07031i	−0.0259642	+	0.0357366i
$898$	−24.4652	+	22.0286i	−0.816416	+	0.735104i
$899$	−1.33150	+	1.47878i	−0.0444079	+	0.0493199i
$900$	0.202934	+	0.0903520i	0.00676446	+	0.00301173i
$901$	−4.11741	+	7.13157i	−0.137171	+	0.237587i
$902$	−21.7317	−	26.0981i	−0.723585	−	0.868970i
$903$	5.12725	+	0.490664i	0.170624	+	0.0163283i
$904$	−18.6990	−	25.7370i	−0.621920	−	0.855999i
$905$	9.24945	+	1.96603i	0.307462	+	0.0653531i
$906$	0.133828	+	0.629612i	0.00444615	+	0.0209175i
$907$	−1.27396	+	12.1209i	−0.0423011	+	0.402468i	0.952799	+	0.303600i	$0.0981887\pi$
$907$	−1.27396	+	12.1209i	−0.0423011	+	0.402468i	−0.995101	+	0.0988677i	$0.968478\pi$
$908$	−0.491719	+	0.218927i	−0.0163183	+	0.00726536i
$909$	−6.31045	+	19.4216i	−0.209304	+	0.644173i
$910$	7.72549	+	34.7510i	0.256098	+	1.15199i
$911$	−24.7576	+	17.9875i	−0.820257	+	0.595952i	−0.916786	−	0.399379i	$-0.869226\pi$
$911$	−24.7576	+	17.9875i	−0.820257	+	0.595952i	0.0965292	+	0.995330i	$0.469226\pi$
$912$	−4.60849	−	2.66071i	−0.152602	−	0.0881050i
$913$	−22.5251	−	8.29482i	−0.745472	−	0.274518i
$914$	1.05885	+	1.83398i	0.0350235	+	0.0606625i
$915$	−0.255593	−	2.43181i	−0.00844965	−	0.0803931i
$916$	0.610622	−	0.198403i	0.0201755	−	0.00655542i
$917$	−36.9318	+	4.22978i	−1.21960	+	0.139680i
$918$	3.79509	+	2.75730i	0.125257	+	0.0910043i
$919$	−20.6819	−	46.4524i	−0.682234	−	1.53232i	−0.838673	−	0.544635i	$-0.816668\pi$
$919$	−20.6819	−	46.4524i	−0.682234	−	1.53232i	0.156440	−	0.987688i	$-0.449998\pi$
$920$	−4.34518	+	0.923597i	−0.143256	+	0.0304501i
$921$	−3.12223	−	2.81127i	−0.102881	−	0.0926344i
$922$	22.0403	−	2.31652i	0.725857	−	0.0762907i
$923$	30.1853			0.993562
$924$	0.0190296	+	0.0463587i	0.000626028	+	0.00152509i
$925$	11.7020			0.384759
$926$	−12.5641	+	1.32054i	−0.412883	+	0.0433958i
$927$	−4.88676	−	4.40005i	−0.160502	−	0.144517i
$928$	−0.553375	+	0.117624i	−0.0181654	+	0.00386118i
$929$	−7.01854	−	15.7639i	−0.230271	−	0.517197i	0.761045	−	0.648699i	$-0.224687\pi$
$929$	−7.01854	−	15.7639i	−0.230271	−	0.517197i	−0.991316	+	0.131502i	$0.958020\pi$
$930$	0.196218	+	0.142561i	0.00643424	+	0.00467475i
$931$	−22.3437	+	40.4207i	−0.732284	+	1.32474i
$932$	0.233672	−	0.0759245i	0.00765417	−	0.00248699i
$933$	−0.346228	−	3.29414i	−0.0113350	−	0.107845i
$934$	−23.2024	−	40.1877i	−0.759205	−	1.31498i
$935$	−11.4860	+	7.68452i	−0.375632	+	0.251311i
$936$	−45.9871	−	26.5507i	−1.50314	−	0.867836i
$937$	0.449363	−	0.326481i	0.0146801	−	0.0106657i	−0.580421	−	0.814317i	$-0.697112\pi$
$937$	0.449363	−	0.326481i	0.0146801	−	0.0106657i	0.595101	+	0.803651i	$0.297112\pi$
$938$	−4.83309	+	15.3600i	−0.157806	+	0.501522i
$939$	1.73642	−	5.34414i	0.0566658	−	0.174399i
$940$	−0.284627	+	0.126724i	−0.00928352	+	0.00413329i
$941$	−3.27635	+	31.1724i	−0.106806	+	1.01619i	0.801532	+	0.597952i	$0.204019\pi$
$941$	−3.27635	+	31.1724i	−0.106806	+	1.01619i	−0.908338	+	0.418238i	$0.862648\pi$
$942$	−0.285903	−	1.34507i	−0.00931521	−	0.0438246i
$943$	−7.31912	−	1.55573i	−0.238343	−	0.0506615i
$944$	−1.67322	−	2.30299i	−0.0544588	−	0.0749561i
$945$	−2.03500	−	4.45846i	−0.0661984	−	0.145034i
$946$	16.4520	+	41.1664i	0.534899	+	1.33843i
$947$	−28.5500	+	49.4500i	−0.927749	+	1.60691i	−0.140671	+	0.990056i	$0.544926\pi$
$947$	−28.5500	+	49.4500i	−0.927749	+	1.60691i	−0.787079	+	0.616853i	$0.788407\pi$
$948$	−0.0143926	−	0.00640801i	−0.000467451	−	0.000208123i
$949$	41.1137	−	45.6614i	1.33461	−	1.48223i
$950$	18.5181	−	16.6738i	0.600807	−	0.540969i
$951$	−2.43003	+	3.34465i	−0.0787992	+	0.108458i
$952$	−13.6765	+	15.4767i	−0.443257	+	0.501603i
$953$	−0.0567606	−	0.0184426i	−0.00183866	−	0.000597416i	0.308098	−	0.951355i	$-0.400308\pi$
$953$	−0.0567606	−	0.0184426i	−0.00183866	−	0.000597416i	−0.309936	+	0.950757i	$0.600308\pi$
$954$	2.59467	−	12.2070i	0.0840057	−	0.395216i
$955$	−5.78871	+	13.0017i	−0.187318	+	0.420724i
$956$	0.233833	−	0.135004i	0.00756271	−	0.00436633i
$957$	−1.74150	−	1.69449i	−0.0562947	−	0.0547750i
$958$		−	39.3468i		−	1.27124i
$959$	23.7390	−	14.0021i	0.766571	−	0.452150i
$960$	0.779008	+	2.39754i	0.0251424	+	0.0773803i
$961$	20.5366	+	22.8082i	0.662469	+	0.735747i
$962$	−38.3045	−	4.02596i	−1.23499	−	0.129802i
$963$	−47.8208	−	5.02617i	−1.54100	−	0.161966i
$964$	−0.469657	−	0.521607i	−0.0151266	−	0.0167998i
$965$	0.512057	+	1.57595i	0.0164837	+	0.0507316i
$966$	−0.678945	−	0.383603i	−0.0218447	−	0.0123422i
$967$		−	27.4643i		−	0.883194i	−0.897214	−	0.441597i	$-0.854412\pi$
$967$		−	27.4643i		−	0.883194i	0.897214	−	0.441597i	$-0.145588\pi$
$968$	−20.3165	+	23.8446i	−0.652996	+	0.766394i
$969$	−3.20351	+	1.84955i	−0.102911	+	0.0594159i
$970$	−6.96747	+	15.6492i	−0.223712	+	0.502466i
$971$	1.43350	−	6.74411i	0.0460034	−	0.216429i	−0.949142	−	0.314850i	$-0.898046\pi$
$971$	1.43350	−	6.74411i	0.0460034	−	0.216429i	0.995145	+	0.0984210i	$0.0313792\pi$
$972$	0.143929	+	0.0467654i	0.00461653	+	0.00150000i
$973$	5.32754	−	1.78604i	0.170793	−	0.0572579i
$974$	−14.1428	+	19.4659i	−0.453165	+	0.623728i
$975$	−2.57664	+	2.32001i	−0.0825184	+	0.0742999i
$976$	20.7528	−	23.0484i	0.664282	−	0.737760i
$977$	−12.8903	−	5.73912i	−0.412396	−	0.183611i	0.190042	−	0.981776i	$-0.439138\pi$
$977$	−12.8903	−	5.73912i	−0.412396	−	0.183611i	−0.602439	+	0.798165i	$0.705804\pi$
$978$	0.0921956	−	0.159687i	0.00294809	−	0.00510624i
$979$	3.65894	+	0.926950i	0.116940	+	0.0296254i
$980$	0.280802	−	0.0970563i	0.00896989	−	0.00310035i
$981$	−3.08605	−	4.24758i	−0.0985299	−	0.135615i
$982$	−38.3860	−	8.15920i	−1.22495	−	0.260371i
$983$	4.48746	+	21.1119i	0.143128	+	0.673364i	0.989942	+	0.141475i	$0.0451844\pi$
$983$	4.48746	+	21.1119i	0.143128	+	0.673364i	−0.846814	+	0.531889i	$0.821482\pi$
$984$	−0.443945	+	4.22385i	−0.0141524	+	0.134651i
$985$	14.2959	−	6.36493i	0.455504	−	0.202803i
$986$	4.26095	−	13.1138i	0.135696	−	0.417630i
$987$	−3.78915	−	1.19227i	−0.120610	−	0.0379505i
$988$	0.939459	−	0.682557i	0.0298882	−	0.0217150i
$989$	8.45900	+	4.88380i	0.268980	+	0.155296i
$990$	12.9561	−	16.4547i	0.411771	−	0.522965i
$991$	16.2034	+	28.0651i	0.514717	+	0.891516i	0.999854	+	0.0170778i	$0.00543631\pi$
$991$	16.2034	+	28.0651i	0.514717	+	0.891516i	−0.485137	+	0.874438i	$0.661230\pi$
$992$	−0.00917119	−	0.0872581i	−0.000291186	−	0.00277045i
$993$	−0.0371630	+	0.0120750i	−0.00117933	+	0.000383189i
$994$	2.02453	+	17.6770i	0.0642143	+	0.560679i
$995$	−2.97363	−	2.16047i	−0.0942704	−	0.0684914i
$996$	0.0168112	+	0.0377585i	0.000532682	+	0.00119642i
$997$	28.8954	−	6.14191i	0.915127	−	0.194516i	0.273802	−	0.961786i	$-0.411719\pi$
$997$	28.8954	−	6.14191i	0.915127	−	0.194516i	0.641324	+	0.767270i	$0.278385\pi$
$998$	13.9466	+	12.5576i	0.441471	+	0.397502i
$999$	5.27334	−	0.554250i	0.166841	−	0.0175357i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.n.a.19.5	✓	48
3.2	odd	2		693.2.cg.a.19.2		48
7.2	even	3		539.2.m.a.195.3		48
7.3	odd	6	inner	77.2.n.a.52.2	yes	48
7.4	even	3		539.2.s.d.129.2		48
7.5	odd	6		539.2.m.a.195.4		48
7.6	odd	2		539.2.s.d.19.5		48
11.2	odd	10		847.2.i.b.362.18		48
11.3	even	5		847.2.r.d.215.5		48
11.4	even	5		847.2.r.c.40.5		48
11.5	even	5		847.2.r.a.838.2		48
11.6	odd	10		847.2.r.d.838.5		48
11.7	odd	10	inner	77.2.n.a.40.2	yes	48
11.8	odd	10		847.2.r.a.215.2		48
11.9	even	5		847.2.i.b.362.7		48
11.10	odd	2		847.2.r.c.481.2		48
21.17	even	6		693.2.cg.a.514.5		48
33.29	even	10		693.2.cg.a.271.5		48
77.3	odd	30		847.2.r.d.94.5		48
77.10	even	6		847.2.r.c.360.5		48
77.17	even	30		847.2.r.d.717.5		48
77.18	odd	30		539.2.s.d.227.5		48
77.24	even	30		847.2.i.b.241.7		48
77.31	odd	30		847.2.i.b.241.18		48
77.38	odd	30		847.2.r.a.717.2		48
77.40	even	30		539.2.m.a.293.3		48
77.51	odd	30		539.2.m.a.293.4		48
77.52	even	30		847.2.r.a.94.2		48
77.59	odd	30		847.2.r.c.766.2		48
77.62	even	10		539.2.s.d.117.2		48
77.73	even	30	inner	77.2.n.a.73.5	yes	48
231.227	odd	30		693.2.cg.a.73.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.n.a.19.5	✓	48	1.1	even	1	trivial
77.2.n.a.40.2	yes	48	11.7	odd	10	inner
77.2.n.a.52.2	yes	48	7.3	odd	6	inner
77.2.n.a.73.5	yes	48	77.73	even	30	inner
539.2.m.a.195.3		48	7.2	even	3
539.2.m.a.195.4		48	7.5	odd	6
539.2.m.a.293.3		48	77.40	even	30
539.2.m.a.293.4		48	77.51	odd	30
539.2.s.d.19.5		48	7.6	odd	2
539.2.s.d.117.2		48	77.62	even	10
539.2.s.d.129.2		48	7.4	even	3
539.2.s.d.227.5		48	77.18	odd	30
693.2.cg.a.19.2		48	3.2	odd	2
693.2.cg.a.73.2		48	231.227	odd	30
693.2.cg.a.271.5		48	33.29	even	10
693.2.cg.a.514.5		48	21.17	even	6
847.2.i.b.241.7		48	77.24	even	30
847.2.i.b.241.18		48	77.31	odd	30
847.2.i.b.362.7		48	11.9	even	5
847.2.i.b.362.18		48	11.2	odd	10
847.2.r.a.94.2		48	77.52	even	30
847.2.r.a.215.2		48	11.8	odd	10
847.2.r.a.717.2		48	77.38	odd	30
847.2.r.a.838.2		48	11.5	even	5
847.2.r.c.40.5		48	11.4	even	5
847.2.r.c.360.5		48	77.10	even	6
847.2.r.c.481.2		48	11.10	odd	2
847.2.r.c.766.2		48	77.59	odd	30
847.2.r.d.94.5		48	77.3	odd	30
847.2.r.d.215.5		48	11.3	even	5
847.2.r.d.717.5		48	77.17	even	30
847.2.r.d.838.5		48	11.6	odd	10

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)

\(f(q)\)	\(=\)	\(q+(1.39661 - 0.146790i) q^{2} +(0.151995 + 0.136856i) q^{3} +(-0.0273118 + 0.00580530i) q^{4} +(0.618266 + 1.38865i) q^{5} +(0.232367 + 0.168824i) q^{6} +(-1.57500 - 2.12588i) q^{7} +(-2.70844 + 0.880026i) q^{8} +(-0.309213 - 2.94196i) q^{9} +O(q^{10})\)	\(q+(1.39661 - 0.146790i) q^{2} +(0.151995 + 0.136856i) q^{3} +(-0.0273118 + 0.00580530i) q^{4} +(0.618266 + 1.38865i) q^{5} +(0.232367 + 0.168824i) q^{6} +(-1.57500 - 2.12588i) q^{7} +(-2.70844 + 0.880026i) q^{8} +(-0.309213 - 2.94196i) q^{9} +(1.06732 + 1.84865i) q^{10} +(3.19157 - 0.902154i) q^{11} +(-0.00494574 - 0.00285542i) q^{12} +(-5.09949 + 3.70500i) q^{13} +(-2.51173 - 2.73784i) q^{14} +(-0.0960725 + 0.295681i) q^{15} +(-3.60245 + 1.60392i) q^{16} +(-0.286530 + 2.72615i) q^{17} +(-0.863702 - 4.06340i) q^{18} +(6.45371 + 1.37178i) q^{19} +(-0.0249475 - 0.0343372i) q^{20} +(0.0515495 - 0.538671i) q^{21} +(4.32496 - 1.72845i) q^{22} +(0.513095 - 0.888707i) q^{23} +(-0.532106 - 0.236909i) q^{24} +(1.79956 - 1.99862i) q^{25} +(-6.57817 + 5.92301i) q^{26} +(0.716285 - 0.985882i) q^{27} +(0.0553574 + 0.0489183i) q^{28} +(-3.40669 - 1.10690i) q^{29} +(-0.0907732 + 0.427054i) q^{30} +(0.225952 - 0.507496i) q^{31} +(0.136779 - 0.0789694i) q^{32} +(0.608567 + 0.299665i) q^{33} +3.84944i q^{34} +(1.97833 - 3.50148i) q^{35} +(0.0255241 + 0.0785552i) q^{36} +(2.91149 + 3.23353i) q^{37} +(9.21471 + 0.968505i) q^{38} +(-1.28215 - 0.134759i) q^{39} +(-2.89658 - 3.21698i) q^{40} +(-2.25325 - 6.93478i) q^{41} +(-0.00707689 - 0.759883i) q^{42} +9.51832i q^{43} +(-0.0819302 + 0.0431675i) q^{44} +(3.89418 - 2.24830i) q^{45} +(0.586143 - 1.31650i) q^{46} +(1.52622 - 7.18031i) q^{47} +(-0.767059 - 0.249233i) q^{48} +(-2.03875 + 6.69653i) q^{49} +(2.21992 - 3.05545i) q^{50} +(-0.416642 + 0.375146i) q^{51} +(0.117768 - 0.130794i) q^{52} +(2.74441 + 1.22189i) q^{53} +(0.855656 - 1.48204i) q^{54} +(3.22601 + 3.87420i) q^{55} +(6.13663 + 4.37179i) q^{56} +(0.793192 + 1.09174i) q^{57} +(-4.92031 - 1.04585i) q^{58} +(0.150088 + 0.706109i) q^{59} +(0.000907396 - 0.00863330i) q^{60} +(-7.18503 + 3.19898i) q^{61} +(0.241072 - 0.741943i) q^{62} +(-5.76726 + 5.29094i) q^{63} +(6.55995 - 4.76608i) q^{64} +(-8.29778 - 4.79073i) q^{65} +(0.893921 + 0.329184i) q^{66} +(-2.16696 - 3.75328i) q^{67} +(-0.00800047 - 0.0761194i) q^{68} +(0.199613 - 0.0648582i) q^{69} +(2.24899 - 5.18062i) q^{70} +(-3.87422 - 2.81478i) q^{71} +(3.42649 + 7.69602i) q^{72} +(-9.53478 + 2.02668i) q^{73} +(4.54087 + 4.08862i) q^{74} +(0.547047 - 0.0574970i) q^{75} -0.184226 q^{76} +(-6.94459 - 5.36401i) q^{77} -1.81045 q^{78} +(2.74362 - 0.288366i) q^{79} +(-4.45455 - 4.01089i) q^{80} +(-8.43678 + 1.79329i) q^{81} +(-4.16487 - 9.35446i) q^{82} +(-5.85520 - 4.25406i) q^{83} +(0.00171924 + 0.0150113i) q^{84} +(-3.96281 + 1.28760i) q^{85} +(1.39719 + 13.2934i) q^{86} +(-0.366312 - 0.634471i) q^{87} +(-7.85026 + 5.25210i) q^{88} +(0.985593 + 0.569032i) q^{89} +(5.10863 - 3.71164i) q^{90} +(15.9081 + 5.00555i) q^{91} +(-0.00885434 + 0.0272509i) q^{92} +(0.103798 - 0.0462136i) q^{93} +(1.07754 - 10.2522i) q^{94} +(2.08519 + 9.81006i) q^{95} +(0.0315971 + 0.00671618i) q^{96} +(4.71690 + 6.49225i) q^{97} +(-1.86437 + 9.65173i) q^{98} +(-3.64098 - 9.11052i) 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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