LMFDB - Embedded newform 418.2.v.a.29.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(13,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([9, 25]))

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

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

chi := DirichletCharacter("418.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.v (of order $90$, degree $24$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$10$ over $\Q(\zeta_{90})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			29.4
Character	$\chi$	$=$	418.29
Dual form			418.2.v.a.173.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.438371 + 0.898794i) q^{2} +(-0.913816 + 0.369206i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(0.341675 - 0.0979736i) q^{5} +(0.0687508 - 0.983182i) q^{6} +(-0.672800 + 3.16528i) q^{7} +(0.978148 - 0.207912i) q^{8} +(-1.45927 + 1.40920i) q^{9} +O(q^{10})$	\(q+(-0.438371 + 0.898794i) q^{2} +(-0.913816 + 0.369206i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(0.341675 - 0.0979736i) q^{5} +(0.0687508 - 0.983182i) q^{6} +(-0.672800 + 3.16528i) q^{7} +(0.978148 - 0.207912i) q^{8} +(-1.45927 + 1.40920i) q^{9} +(-0.0617222 + 0.350044i) q^{10} +(3.31380 - 0.136859i) q^{11} +(0.853540 + 0.492791i) q^{12} +(-1.06129 - 4.25658i) q^{13} +(-2.54999 - 1.99227i) q^{14} +(-0.276055 + 0.215678i) q^{15} +(-0.241922 + 0.970296i) q^{16} +(-2.72139 + 2.81808i) q^{17} +(-0.626880 - 1.92934i) q^{18} +(-3.90610 + 1.93453i) q^{19} +(-0.287560 - 0.208925i) q^{20} +(-0.553822 - 3.14088i) q^{21} +(-1.32967 + 3.03842i) q^{22} +(-4.84646 + 1.76397i) q^{23} +(-0.817085 + 0.551131i) q^{24} +(-4.13310 + 2.58265i) q^{25} +(4.29103 + 0.912086i) q^{26} +(2.01584 - 4.52765i) q^{27} +(2.90849 - 1.41856i) q^{28} +(-5.69461 + 0.800325i) q^{29} +(-0.0728355 - 0.342664i) q^{30} +(2.58375 + 5.80319i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-2.97768 + 1.34854i) q^{33} +(-1.33990 - 3.68134i) q^{34} +(0.0802348 + 1.14741i) q^{35} +(2.00888 + 0.282330i) q^{36} +(-2.69884 + 0.876907i) q^{37} +(-0.0264252 - 4.35882i) q^{38} +(2.54138 + 3.49790i) q^{39} +(0.313838 - 0.166871i) q^{40} +(-0.454082 - 1.12389i) q^{41} +(3.06579 + 0.879100i) q^{42} +(3.93241 - 10.8042i) q^{43} +(-2.14803 - 2.52705i) q^{44} +(-0.360532 + 0.624459i) q^{45} +(0.539105 - 5.12924i) q^{46} +(-6.91348 - 3.67596i) q^{47} +(-0.137167 - 0.975991i) q^{48} +(-3.17149 - 1.41204i) q^{49} +(-0.509436 - 4.84696i) q^{50} +(1.44640 - 3.57996i) q^{51} +(-2.70084 + 3.45692i) q^{52} +(0.0928281 - 0.323730i) q^{53} +(3.18574 + 3.79661i) q^{54} +(1.11883 - 0.371426i) q^{55} +3.23599i q^{56} +(2.85521 - 3.20996i) q^{57} +(1.77702 - 5.46912i) q^{58} +(6.19026 + 11.6422i) q^{59} +(0.339913 + 0.0847499i) q^{60} +(6.85493 + 4.62371i) q^{61} +(-6.34851 - 0.221695i) q^{62} +(-3.47872 - 5.56711i) q^{63} +(0.913545 - 0.406737i) q^{64} +(-0.779647 - 1.35039i) q^{65} +(0.0932690 - 3.26748i) q^{66} +(12.6985 + 2.23909i) q^{67} +(3.89613 + 0.409500i) q^{68} +(3.77750 - 3.40128i) q^{69} +(-1.06646 - 0.430877i) q^{70} +(2.04094 + 7.11762i) q^{71} +(-1.13439 + 1.68181i) q^{72} +(-7.68286 + 12.2951i) q^{73} +(0.394936 - 2.81012i) q^{74} +(2.82336 - 3.88603i) q^{75} +(3.92926 + 1.88703i) q^{76} +(-1.79633 + 10.5812i) q^{77} +(-4.25796 + 0.750793i) q^{78} +(13.7054 - 0.958376i) q^{79} +(0.0124048 + 0.355227i) q^{80} +(0.0419215 - 1.20048i) q^{81} +(1.20920 + 0.0845557i) q^{82} +(-1.48766 + 0.156360i) q^{83} +(-2.13408 + 2.37014i) q^{84} +(-0.653732 + 1.22949i) q^{85} +(7.98691 + 8.27069i) q^{86} +(4.90834 - 2.83383i) q^{87} +(3.21293 - 0.822846i) q^{88} +(1.34985 - 1.60868i) q^{89} +(-0.403213 - 0.597788i) q^{90} +(14.1873 - 0.495431i) q^{91} +(4.37380 + 2.73305i) q^{92} +(-4.50364 - 4.34911i) q^{93} +(6.33460 - 4.60236i) q^{94} +(-1.14508 + 1.04367i) q^{95} +(0.937345 + 0.304562i) q^{96} +(-3.54404 - 1.72854i) q^{97} +(2.65942 - 2.23152i) q^{98} +(-4.64287 + 4.86953i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9}+O(q^{10}) $ 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9	$ 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9} - 3 q^{11} - 6 q^{13} - 18 q^{14} + 21 q^{15} + 21 q^{17} - 60 q^{18} + 45 q^{19} + 12 q^{20} + 48 q^{21} - 12 q^{22} + 12 q^{24} - 18 q^{25} - 96 q^{26} - 9 q^{27} - 6 q^{28} + 18 q^{29} + 9 q^{31} + 87 q^{33} - 24 q^{34} - 36 q^{35} - 12 q^{36} - 36 q^{38} + 60 q^{41} - 6 q^{42} - 12 q^{43} + 18 q^{44} + 48 q^{45} + 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} - 21 q^{50} - 75 q^{51} + 3 q^{52} - 39 q^{53} + 27 q^{54} - 126 q^{55} - 90 q^{57} - 24 q^{58} + 69 q^{59} - 42 q^{60} + 66 q^{61} - 45 q^{62} - 9 q^{63} + 30 q^{64} - 12 q^{66} - 9 q^{67} + 12 q^{68} - 54 q^{69} + 9 q^{70} + 48 q^{71} + 6 q^{72} - 12 q^{74} + 72 q^{77} - 36 q^{79} - 27 q^{81} + 45 q^{82} + 36 q^{83} + 36 q^{84} - 210 q^{85} + 3 q^{86} + 216 q^{87} + 3 q^{88} + 18 q^{89} - 96 q^{90} - 108 q^{91} - 30 q^{92} + 147 q^{93} - 18 q^{94} + 66 q^{95} - 9 q^{97} - 12 q^{98} - 42 q^{99}+O(q^{100}) $ 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9 - 3 * q^11 - 6 * q^13 - 18 * q^14 + 21 * q^15 + 21 * q^17 - 60 * q^18 + 45 * q^19 + 12 * q^20 + 48 * q^21 - 12 * q^22 + 12 * q^24 - 18 * q^25 - 96 * q^26 - 9 * q^27 - 6 * q^28 + 18 * q^29 + 9 * q^31 + 87 * q^33 - 24 * q^34 - 36 * q^35 - 12 * q^36 - 36 * q^38 + 60 * q^41 - 6 * q^42 - 12 * q^43 + 18 * q^44 + 48 * q^45 + 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 - 21 * q^50 - 75 * q^51 + 3 * q^52 - 39 * q^53 + 27 * q^54 - 126 * q^55 - 90 * q^57 - 24 * q^58 + 69 * q^59 - 42 * q^60 + 66 * q^61 - 45 * q^62 - 9 * q^63 + 30 * q^64 - 12 * q^66 - 9 * q^67 + 12 * q^68 - 54 * q^69 + 9 * q^70 + 48 * q^71 + 6 * q^72 - 12 * q^74 + 72 * q^77 - 36 * q^79 - 27 * q^81 + 45 * q^82 + 36 * q^83 + 36 * q^84 - 210 * q^85 + 3 * q^86 + 216 * q^87 + 3 * q^88 + 18 * q^89 - 96 * q^90 - 108 * q^91 - 30 * q^92 + 147 * q^93 - 18 * q^94 + 66 * q^95 - 9 * q^97 - 12 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.438371	+	0.898794i	−0.309975	+	0.635543i
$2$	−0.438371	+	0.898794i	−0.309975	+	0.635543i
$3$	−0.913816	+	0.369206i	−0.527592	+	0.213161i	−0.622921	−	0.782285i	$-0.714054\pi$
$3$	−0.913816	+	0.369206i	−0.527592	+	0.213161i	0.0953288	+	0.995446i	$0.469610\pi$
$4$	−0.615661	−	0.788011i	−0.307831	−	0.394005i
$5$	0.341675	−	0.0979736i	0.152802	−	0.0438151i	−0.198365	−	0.980128i	$-0.563563\pi$
$5$	0.341675	−	0.0979736i	0.152802	−	0.0438151i	0.351166	+	0.936313i	$0.385785\pi$
$6$	0.0687508	−	0.983182i	0.0280674	−	0.401382i
$7$	−0.672800	+	3.16528i	−0.254295	+	1.19636i	0.646773	+	0.762683i	$0.276118\pi$
$7$	−0.672800	+	3.16528i	−0.254295	+	1.19636i	−0.901067	+	0.433679i	$0.857215\pi$
$8$	0.978148	−	0.207912i	0.345827	−	0.0735079i
$9$	−1.45927	+	1.40920i	−0.486424	+	0.469734i
$10$	−0.0617222	+	0.350044i	−0.0195183	+	0.110694i
$11$	3.31380	−	0.136859i	0.999148	−	0.0412646i
$11$	3.31380	−	0.136859i	0.999148	−	0.0412646i
$12$	0.853540	+	0.492791i	0.246396	+	0.142257i
$13$	−1.06129	−	4.25658i	−0.294348	−	1.18056i	−0.917265	−	0.398277i	$-0.869608\pi$
$13$	−1.06129	−	4.25658i	−0.294348	−	1.18056i	0.622918	−	0.782287i	$-0.285947\pi$
$14$	−2.54999	−	1.99227i	−0.681515	−	0.532458i
$15$	−0.276055	+	0.215678i	−0.0712772	+	0.0556879i
$16$	−0.241922	+	0.970296i	−0.0604805	+	0.242574i
$17$	−2.72139	+	2.81808i	−0.660034	+	0.683485i	−0.962995	−	0.269518i	$-0.913136\pi$
$17$	−2.72139	+	2.81808i	−0.660034	+	0.683485i	0.302961	+	0.953003i	$0.402025\pi$
$18$	−0.626880	−	1.92934i	−0.147757	−	0.454749i
$19$	−3.90610	+	1.93453i	−0.896120	+	0.443812i
$19$	−3.90610	+	1.93453i	−0.896120	+	0.443812i
$20$	−0.287560	−	0.208925i	−0.0643004	−	0.0467170i
$21$	−0.553822	−	3.14088i	−0.120854	−	0.685397i
$22$	−1.32967	+	3.03842i	−0.283486	+	0.647793i
$23$	−4.84646	+	1.76397i	−1.01056	+	0.367812i	−0.793646	−	0.608379i	$-0.791820\pi$
$23$	−4.84646	+	1.76397i	−1.01056	+	0.367812i	−0.216910	+	0.976192i	$0.569598\pi$
$24$	−0.817085	+	0.551131i	−0.166787	+	0.112499i
$25$	−4.13310	+	2.58265i	−0.826620	+	0.516529i
$26$	4.29103	+	0.912086i	0.841540	+	0.178875i
$27$	2.01584	−	4.52765i	0.387948	−	0.871346i
$28$	2.90849	−	1.41856i	0.549653	−	0.268084i
$29$	−5.69461	+	0.800325i	−1.05746	+	0.148617i	−0.646406	−	0.762993i	$-0.723729\pi$
$29$	−5.69461	+	0.800325i	−1.05746	+	0.148617i	−0.411056	+	0.911610i	$0.634840\pi$
$30$	−0.0728355	−	0.342664i	−0.0132979	−	0.0625616i
$31$	2.58375	+	5.80319i	0.464055	+	1.04228i	0.982345	+	0.187079i	$0.0599020\pi$
$31$	2.58375	+	5.80319i	0.464055	+	1.04228i	−0.518290	+	0.855205i	$0.673431\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	−2.97768	+	1.34854i	−0.518347	+	0.234750i
$34$	−1.33990	−	3.68134i	−0.229790	−	0.631344i
$35$	0.0802348	+	1.14741i	0.0135622	+	0.193948i
$36$	2.00888	+	0.282330i	0.334814	+	0.0470550i
$37$	−2.69884	+	0.876907i	−0.443687	+	0.144163i	−0.522336	−	0.852740i	$-0.674939\pi$
$37$	−2.69884	+	0.876907i	−0.443687	+	0.144163i	0.0786490	+	0.996902i	$0.474939\pi$
$38$	−0.0264252	−	4.35882i	−0.00428673	−	0.707094i
$39$	2.54138	+	3.49790i	0.406946	+	0.560113i
$40$	0.313838	−	0.166871i	0.0496222	−	0.0263846i
$41$	−0.454082	−	1.12389i	−0.0709156	−	0.175522i	0.887563	−	0.460686i	$-0.152397\pi$
$41$	−0.454082	−	1.12389i	−0.0709156	−	0.175522i	−0.958479	+	0.285164i	$0.907952\pi$
$42$	3.06579	+	0.879100i	0.473061	+	0.135648i
$43$	3.93241	−	10.8042i	0.599688	−	1.64763i	−0.152210	−	0.988348i	$-0.548639\pi$
$43$	3.93241	−	10.8042i	0.599688	−	1.64763i	0.751898	−	0.659280i	$-0.229139\pi$
$44$	−2.14803	−	2.52705i	−0.323827	−	0.380967i
$45$	−0.360532	+	0.624459i	−0.0537449	+	0.0930889i
$46$	0.539105	−	5.12924i	0.0794866	−	0.756265i
$47$	−6.91348	−	3.67596i	−1.00843	−	0.536194i	−0.118824	−	0.992915i	$-0.537912\pi$
$47$	−6.91348	−	3.67596i	−1.00843	−	0.536194i	−0.889610	+	0.456721i	$0.849024\pi$
$48$	−0.137167	−	0.975991i	−0.0197983	−	0.140872i
$49$	−3.17149	−	1.41204i	−0.453070	−	0.201720i
$50$	−0.509436	−	4.84696i	−0.0720452	−	0.685464i
$51$	1.44640	−	3.57996i	0.202536	−	0.501295i
$52$	−2.70084	+	3.45692i	−0.374539	+	0.479388i
$53$	0.0928281	−	0.323730i	0.0127509	−	0.0444677i	−0.954629	−	0.297797i	$-0.903748\pi$
$53$	0.0928281	−	0.323730i	0.0127509	−	0.0444677i	0.967380	+	0.253330i	$0.0815258\pi$
$54$	3.18574	+	3.79661i	0.433524	+	0.516654i
$55$	1.11883	−	0.371426i	0.150863	−	0.0500831i
$56$			3.23599i			0.432427i
$57$	2.85521	−	3.20996i	0.378182	−	0.425170i
$58$	1.77702	−	5.46912i	0.233335	−	0.718131i
$59$	6.19026	+	11.6422i	0.805903	+	1.51568i	0.856022	+	0.516939i	$0.172929\pi$
$59$	6.19026	+	11.6422i	0.805903	+	1.51568i	−0.0501195	+	0.998743i	$0.515960\pi$
$60$	0.339913	+	0.0847499i	0.0438826	+	0.0109412i
$61$	6.85493	+	4.62371i	0.877684	+	0.592005i	0.913267	−	0.407362i	$-0.133551\pi$
$61$	6.85493	+	4.62371i	0.877684	+	0.592005i	−0.0355833	+	0.999367i	$0.511329\pi$
$62$	−6.34851	−	0.221695i	−0.806262	−	0.0281553i
$63$	−3.47872	−	5.56711i	−0.438277	−	0.701390i
$64$	0.913545	−	0.406737i	0.114193	−	0.0508421i
$65$	−0.779647	−	1.35039i	−0.0967034	−	0.167495i
$66$	0.0932690	−	3.26748i	0.0114806	−	0.402199i
$67$	12.6985	+	2.23909i	1.55137	+	0.273549i	0.882674	−	0.469985i	$-0.155741\pi$
$67$	12.6985	+	2.23909i	1.55137	+	0.273549i	0.668698	+	0.743534i	$0.266852\pi$
$68$	3.89613	+	0.409500i	0.472476	+	0.0496592i
$69$	3.77750	−	3.40128i	0.454758	−	0.409466i
$70$	−1.06646	−	0.430877i	−0.127466	−	0.0514997i
$71$	2.04094	+	7.11762i	0.242215	+	0.844706i	0.984613	+	0.174747i	$0.0559106\pi$
$71$	2.04094	+	7.11762i	0.242215	+	0.844706i	−0.742398	+	0.669959i	$0.766312\pi$
$72$	−1.13439	+	1.68181i	−0.133690	+	0.198203i
$73$	−7.68286	+	12.2951i	−0.899210	+	1.43904i	−0.000741757		1.00000i	$0.500236\pi$
$73$	−7.68286	+	12.2951i	−0.899210	+	1.43904i	−0.898469	+	0.439038i	$0.855319\pi$
$74$	0.394936	−	2.81012i	0.0459104	−	0.326669i
$75$	2.82336	−	3.88603i	0.326014	−	0.448720i
$76$	3.92926	+	1.88703i	0.450718	+	0.216457i
$77$	−1.79633	+	10.5812i	−0.204711	+	1.20584i
$78$	−4.25796	+	0.750793i	−0.482119	+	0.0850106i
$79$	13.7054	−	0.958376i	1.54198	−	0.107826i	0.726726	−	0.686928i	$-0.241041\pi$
$79$	13.7054	−	0.958376i	1.54198	−	0.107826i	0.815255	+	0.579102i	$0.196597\pi$
$80$	0.0124048	+	0.355227i	0.00138690	+	0.0397156i
$81$	0.0419215	−	1.20048i	0.00465795	−	0.133386i
$82$	1.20920	+	0.0845557i	0.133534	+	0.00933762i
$83$	−1.48766	+	0.156360i	−0.163292	+	0.0171627i	−0.185822	−	0.982583i	$-0.559495\pi$
$83$	−1.48766	+	0.156360i	−0.163292	+	0.0171627i	0.0225295	+	0.999746i	$0.492828\pi$
$84$	−2.13408	+	2.37014i	−0.232847	+	0.258603i
$85$	−0.653732	+	1.22949i	−0.0709072	+	0.133357i
$86$	7.98691	+	8.27069i	0.861251	+	0.891851i
$87$	4.90834	−	2.83383i	0.526229	−	0.303819i
$88$	3.21293	−	0.822846i	0.342500	−	0.0877157i
$89$	1.34985	−	1.60868i	0.143083	−	0.170520i	−0.689743	−	0.724054i	$-0.742277\pi$
$89$	1.34985	−	1.60868i	0.143083	−	0.170520i	0.832827	+	0.553534i	$0.186721\pi$
$90$	−0.403213	−	0.597788i	−0.0425024	−	0.0630124i
$91$	14.1873	−	0.495431i	1.48723	−	0.0519353i
$92$	4.37380	+	2.73305i	0.456000	+	0.284941i
$93$	−4.50364	−	4.34911i	−0.467006	−	0.450982i
$94$	6.33460	−	4.60236i	0.653364	−	0.474697i
$95$	−1.14508	+	1.04367i	−0.117483	+	0.107079i
$96$	0.937345	+	0.304562i	0.0956674	+	0.0310842i
$97$	−3.54404	−	1.72854i	−0.359842	−	0.175507i	0.249577	−	0.968355i	$-0.419708\pi$
$97$	−3.54404	−	1.72854i	−0.359842	−	0.175507i	−0.609419	+	0.792848i	$0.708597\pi$
$98$	2.65942	−	2.23152i	0.268642	−	0.225418i
$99$	−4.64287	+	4.86953i	−0.466626	+	0.489406i
$100$	4.57974	+	1.66689i	0.457974	+	0.166689i
$101$	−14.4328	+	3.59851i	−1.43612	+	0.358065i	−0.880768	−	0.473548i	$-0.842973\pi$
$101$	−14.4328	+	3.59851i	−1.43612	+	0.358065i	−0.555354	+	0.831614i	$0.687417\pi$
$102$	2.58359	+	2.86937i	0.255813	+	0.284110i
$103$	8.61324	+	7.75540i	0.848688	+	0.764162i	0.973662	−	0.227998i	$-0.0732180\pi$
$103$	8.61324	+	7.75540i	0.848688	+	0.764162i	−0.124974	+	0.992160i	$0.539885\pi$
$104$	−1.92309	−	3.94291i	−0.188574	−	0.386634i
$105$	−0.496951	−	1.01890i	−0.0484974	−	0.0994345i
$106$	0.250274	+	0.225347i	0.0243087	+	0.0218877i
$107$	−11.0992	−	12.3269i	−1.07300	−	1.19169i	−0.980611	−	0.195964i	$-0.937216\pi$
$107$	−11.0992	−	12.3269i	−1.07300	−	1.19169i	−0.0923889	−	0.995723i	$-0.529450\pi$
$108$	−4.80891	+	1.19900i	−0.462738	+	0.115373i
$109$	−6.80611	−	2.47722i	−0.651907	−	0.237275i	−0.00516843	−	0.999987i	$-0.501645\pi$
$109$	−6.80611	−	2.47722i	−0.651907	−	0.237275i	−0.646738	+	0.762712i	$0.723867\pi$
$110$	−0.156628	+	1.16842i	−0.0149339	+	0.111405i
$111$	2.14249	−	1.79776i	0.203356	−	0.170636i
$112$	−2.90849	−	1.41856i	−0.274826	−	0.134042i
$113$	8.98924	+	2.92078i	0.845637	+	0.274764i	0.699617	−	0.714518i	$-0.253354\pi$
$113$	8.98924	+	2.92078i	0.845637	+	0.274764i	0.146019	+	0.989282i	$0.453354\pi$
$114$	1.63345	+	3.97340i	0.152987	+	0.372143i
$115$	−1.48309	+	1.07753i	−0.138299	+	0.100480i
$116$	4.13662	+	3.99468i	0.384075	+	0.370897i
$117$	7.54709	+	4.71595i	0.697729	+	0.435989i
$118$	−13.1775	+	0.460170i	−1.21309	+	0.0423621i
$119$	−7.08906	−	10.5100i	−0.649853	−	0.963446i
$120$	−0.225181	+	0.268360i	−0.0205561	+	0.0244978i
$121$	10.9625	−	0.907047i	0.996594	−	0.0824588i
$122$	−7.16076	+	4.13427i	−0.648305	+	0.374299i
$123$	0.829894	+	0.859381i	0.0748291	+	0.0774878i
$124$	2.98226	−	5.60882i	0.267815	−	0.503687i
$125$	−2.34834	+	2.60809i	−0.210042	+	0.233275i
$126$	6.52865	−	0.686189i	0.581619	−	0.0611306i
$127$	12.7575	+	0.892088i	1.13204	+	0.0791600i	0.623461	−	0.781854i	$-0.285726\pi$
$127$	12.7575	+	0.892088i	1.13204	+	0.0791600i	0.508580	+	0.861014i	$0.330170\pi$
$128$	−0.0348995	+	0.999391i	−0.00308471	+	0.0883345i
$129$	0.395476	+	11.3249i	0.0348197	+	0.997106i
$130$	1.55550	−	0.108771i	0.136426	−	0.00953984i
$131$	−14.4776	+	2.55279i	−1.26491	+	0.223038i	−0.765561	−	0.643363i	$-0.777539\pi$
$131$	−14.4776	+	2.55279i	−1.26491	+	0.223038i	−0.499349	+	0.866401i	$0.666428\pi$
$132$	2.89590	+	1.51620i	0.252056	+	0.131968i
$133$	−3.49530	−	13.6654i	−0.303081	−	1.18494i
$134$	−7.57915	+	10.4318i	−0.654739	+	0.901171i
$135$	0.245171	−	1.74448i	0.0211010	−	0.150141i
$136$	−2.07601	+	3.32231i	−0.178016	+	0.284886i
$137$	3.29786	−	4.88928i	0.281755	−	0.417719i	−0.661420	−	0.750016i	$-0.730046\pi$
$137$	3.29786	−	4.88928i	0.281755	−	0.417719i	0.943175	+	0.332297i	$0.107824\pi$
$138$	1.40110	+	4.88622i	0.119270	+	0.415943i
$139$	14.9328	+	6.03324i	1.26658	+	0.511733i	0.906901	−	0.421343i	$-0.138441\pi$
$139$	14.9328	+	6.03324i	1.26658	+	0.511733i	0.359681	+	0.933075i	$0.382885\pi$
$140$	0.854775	−	0.769643i	0.0722417	−	0.0650467i
$141$	7.67483	+	0.806657i	0.646337	+	0.0679328i
$142$	−7.29196	−	1.28577i	−0.611928	−	0.107899i
$143$	−4.09944	−	13.9602i	−0.342812	−	1.16741i
$144$	−1.01431	−	1.75684i	−0.0845261	−	0.146404i
$145$	−1.86729	+	0.831372i	−0.155070	+	0.0690417i
$146$	−7.68286	−	12.2951i	−0.635838	−	1.01755i
$147$	3.41950	+	0.119411i	0.282035	+	0.00984889i
$148$	2.35259	+	1.58684i	0.193381	+	0.130437i
$149$	8.08190	+	2.01504i	0.662095	+	0.165079i	0.558454	−	0.829536i	$-0.311395\pi$
$149$	8.08190	+	2.01504i	0.662095	+	0.165079i	0.103642	+	0.994615i	$0.466950\pi$
$150$	2.25506	+	4.24115i	0.184125	+	0.346288i
$151$	1.80720	−	5.56199i	0.147068	−	0.452629i	−0.850203	−	0.526455i	$-0.823521\pi$
$151$	1.80720	−	5.56199i	0.147068	−	0.452629i	0.997271	+	0.0738261i	$0.0235210\pi$
$152$	−3.41853	+	2.70438i	−0.277279	+	0.219354i
$153$		−	7.94734i		−	0.642504i
$154$	−8.72283	−	6.25301i	−0.702906	−	0.503882i
$155$	1.45136	+	1.72966i	0.116576	+	0.138930i
$156$	1.19176	−	4.15616i	0.0954170	−	0.332759i
$157$	7.11378	−	9.10522i	0.567741	−	0.726676i	−0.415376	−	0.909650i	$-0.636350\pi$
$157$	7.11378	−	9.10522i	0.567741	−	0.726676i	0.983118	+	0.182974i	$0.0585724\pi$
$158$	−5.14668	+	12.7385i	−0.409448	+	1.01342i
$159$	0.0346952	+	0.330103i	0.00275151	+	0.0261788i
$160$	−0.324714	−	0.144572i	−0.0256709	−	0.0114294i
$161$	−2.32274	−	16.5272i	−0.183058	−	1.30252i
$162$	1.06060	+	0.563932i	0.0833288	+	0.0443067i
$163$	−0.999218	+	9.50693i	−0.0782648	+	0.744640i	0.883067	+	0.469247i	$0.155475\pi$
$163$	−0.999218	+	9.50693i	−0.0782648	+	0.744640i	−0.961332	+	0.275393i	$0.911192\pi$
$164$	−0.606078	+	1.04976i	−0.0473267	+	0.0819723i
$165$	−0.885275	+	0.752495i	−0.0689186	+	0.0585817i
$166$	0.511614	−	1.40565i	0.0397089	−	0.109099i
$167$	−15.5630	−	4.46262i	−1.20430	−	0.345328i	−0.387294	−	0.921956i	$-0.626590\pi$
$167$	−15.5630	−	4.46262i	−1.20430	−	0.345328i	−0.817007	+	0.576628i	$0.804368\pi$
$168$	−1.19475	−	2.95710i	−0.0921767	−	0.228145i
$169$	−5.51386	+	2.93177i	−0.424143	+	0.225521i
$170$	−0.818482	−	1.12654i	−0.0627747	−	0.0864020i
$171$	2.97391	−	8.32749i	0.227421	−	0.636819i
$172$	−10.9349	+	3.55296i	−0.833776	+	0.270910i
$173$	7.62032	+	1.07097i	0.579362	+	0.0814240i	0.422766	−	0.906239i	$-0.361059\pi$
$173$	7.62032	+	1.07097i	0.579362	+	0.0814240i	0.156596	+	0.987663i	$0.449948\pi$
$174$	0.395356	+	5.65386i	0.0299719	+	0.428618i
$175$	−5.39404	−	14.8200i	−0.407751	−	1.12029i
$176$	−0.668887	+	3.24848i	−0.0504193	+	0.244863i
$177$	−9.95512	−	8.35333i	−0.748272	−	0.627875i
$178$	0.854142	+	1.91843i	0.0640206	+	0.143793i
$179$	4.04291	+	19.0204i	0.302182	+	1.42165i	0.823027	+	0.568002i	$0.192283\pi$
$179$	4.04291	+	19.0204i	0.302182	+	1.42165i	−0.520846	+	0.853651i	$0.674383\pi$
$180$	0.714046	−	0.100353i	0.0532218	−	0.00747984i
$181$	8.03040	−	3.91669i	0.596895	−	0.291125i	−0.115051	−	0.993360i	$-0.536703\pi$
$181$	8.03040	−	3.91669i	0.596895	−	0.291125i	0.711946	+	0.702234i	$0.247814\pi$
$182$	−5.77401	+	12.9686i	−0.427998	+	0.961299i
$183$	−7.97125	−	1.69434i	−0.589251	−	0.125249i
$184$	−4.37380	+	2.73305i	−0.322441	+	0.201483i
$185$	−0.836213	+	0.564033i	−0.0614796	+	0.0414685i
$186$	5.88322	−	2.14132i	0.431379	−	0.157009i
$187$	−8.63246	+	9.71101i	−0.631268	+	0.710139i
$188$	1.35966	+	7.71104i	0.0991637	+	0.562385i
$189$	12.9750	+	9.42689i	0.943792	+	0.685705i
$190$	−0.436078	−	1.48671i	−0.0316364	−	0.107857i
$191$	3.89712	+	11.9941i	0.281986	+	0.867862i	0.987286	+	0.158954i	$0.0508121\pi$
$191$	3.89712	+	11.9941i	0.281986	+	0.867862i	−0.705300	+	0.708908i	$0.749188\pi$
$192$	−0.684643	+	0.708969i	−0.0494099	+	0.0511654i
$193$	−4.34558	+	17.4292i	−0.312802	+	1.25458i	0.583857	+	0.811856i	$0.301543\pi$
$193$	−4.34558	+	17.4292i	−0.312802	+	1.25458i	−0.896659	+	0.442722i	$0.854013\pi$
$194$	3.10721	−	2.42761i	0.223084	−	0.174293i
$195$	1.21103	+	0.946157i	0.0867234	+	0.0677557i
$196$	0.839864	+	3.36851i	0.0599903	+	0.240608i
$197$	−20.1389	−	11.6272i	−1.43484	−	0.828403i	−0.437352	−	0.899290i	$-0.644084\pi$
$197$	−20.1389	−	11.6272i	−1.43484	−	0.828403i	−0.997484	+	0.0708868i	$0.977417\pi$
$198$	−2.34140	−	6.30765i	−0.166396	−	0.448265i
$199$	2.80996	−	15.9361i	0.199193	−	1.12968i	−0.707128	−	0.707086i	$-0.750009\pi$
$199$	2.80996	−	15.9361i	0.199193	−	1.12968i	0.906320	−	0.422591i	$-0.138879\pi$
$200$	−3.50582	+	3.38553i	−0.247899	+	0.239393i
$201$	−12.4308	+	2.64225i	−0.876802	+	0.186370i
$202$	3.09262	−	14.5496i	0.217596	−	1.02371i
$203$	1.29808	−	18.5635i	0.0911076	−	1.30290i
$204$	−3.71154	+	1.06427i	−0.259860	+	0.0745136i
$205$	−0.265260	−	0.339517i	−0.0185266	−	0.0237129i
$206$	−10.7463	+	4.34179i	−0.748730	+	0.302507i
$207$	4.58651	−	9.40374i	0.318785	−	0.653605i
$208$	4.38689			0.304176
$209$	−12.6793	+	6.94523i	−0.877043	+	0.480412i
$210$	1.13363			0.0782279
$211$	−1.65083	+	3.38471i	−0.113648	+	0.233013i	−0.948035	−	0.318166i	$-0.896933\pi$
$211$	−1.65083	+	3.38471i	−0.113648	+	0.233013i	0.834387	+	0.551179i	$0.185822\pi$
$212$	−0.312253	+	0.126159i	−0.0214457	+	0.00866461i
$213$	−4.49291	−	5.75067i	−0.307849	−	0.394029i
$214$	15.9449	−	4.57213i	1.08997	−	0.312545i
$215$	0.285078	−	4.07680i	0.0194421	−	0.278036i
$216$	1.03044	−	4.84782i	0.0701123	−	0.329853i
$217$	−20.1070	+	4.27388i	−1.36495	+	0.290130i
$218$	5.21011	−	5.03135i	0.352873	−	0.340766i
$219$	2.48128	−	14.0721i	0.167670	−	0.950901i
$220$	−0.981510	−	0.652979i	−0.0661734	−	0.0440239i
$221$	14.8836	+	8.59304i	1.00118	+	0.578030i
$222$	0.676612	+	2.71374i	0.0454112	+	0.182134i
$223$	−15.9420	−	12.4552i	−1.06755	−	0.834065i	−0.0808721	−	0.996724i	$-0.525771\pi$
$223$	−15.9420	−	12.4552i	−1.06755	−	0.834065i	−0.986682	+	0.162660i	$0.947993\pi$
$224$	2.54999	−	1.99227i	0.170379	−	0.133114i
$225$	2.39184	−	9.59316i	0.159456	−	0.639544i
$226$	−6.56581	+	6.79909i	−0.436751	+	0.452269i
$227$	4.46891	+	13.7539i	0.296612	+	0.912878i	0.982675	+	0.185336i	$0.0593373\pi$
$227$	4.46891	+	13.7539i	0.296612	+	0.912878i	−0.686063	+	0.727542i	$0.740663\pi$
$228$	−4.28733	−	0.273691i	−0.283935	−	0.0181257i
$229$	12.8878	+	9.36351i	0.851647	+	0.618758i	0.925600	−	0.378504i	$-0.123561\pi$
$229$	12.8878	+	9.36351i	0.851647	+	0.618758i	−0.0739525	+	0.997262i	$0.523561\pi$
$230$	−0.318332	−	1.80535i	−0.0209902	−	0.119041i
$231$	−2.26511	−	10.3325i	−0.149034	−	0.679826i
$232$	−5.40377	+	1.96681i	−0.354775	+	0.129128i
$233$	11.8372	−	7.98430i	0.775481	−	0.523069i	−0.106523	−	0.994310i	$-0.533972\pi$
$233$	11.8372	−	7.98430i	0.775481	−	0.523069i	0.882004	+	0.471242i	$0.156194\pi$
$234$	−7.54709	+	4.71595i	−0.493369	+	0.308291i
$235$	−2.72231	−	0.578644i	−0.177584	−	0.0377466i
$236$	5.36306	−	12.0456i	0.349105	−	0.784104i
$237$	−12.1704	+	5.93590i	−0.790552	+	0.385578i
$238$	12.5539	−	1.76434i	0.813750	−	0.114365i
$239$	−0.0913288	−	0.429668i	−0.00590757	−	0.0277929i	0.975095	−	0.221787i	$-0.0711890\pi$
$239$	−0.0913288	−	0.429668i	−0.00590757	−	0.0277929i	−0.981003	+	0.193994i	$0.937856\pi$
$240$	−0.142488	−	0.320033i	−0.00919754	−	0.0206580i
$241$	−14.4965	−	12.1640i	−0.933798	−	0.783550i	0.0426970	−	0.999088i	$-0.486405\pi$
$241$	−14.4965	−	12.1640i	−0.933798	−	0.783550i	−0.976495	+	0.215538i	$0.930849\pi$
$242$	−3.99041	+	10.2507i	−0.256513	+	0.658939i
$243$	5.49020	+	15.0842i	0.352196	+	0.967652i
$244$	−0.576784	−	8.24840i	−0.0369248	−	0.528049i
$245$	−1.22196	−	0.171736i	−0.0780683	−	0.0109718i
$246$	−1.13621	+	0.369176i	−0.0724420	+	0.0235378i
$247$	12.3800	+	14.5735i	0.787719	+	0.927292i
$248$	3.73384	+	5.13918i	0.237099	+	0.326339i
$249$	1.30172	−	0.692138i	0.0824933	−	0.0438625i
$250$	−1.31469	−	3.25398i	−0.0831486	−	0.205800i
$251$	6.76294	+	1.93924i	0.426873	+	0.122404i	0.482194	−	0.876065i	$-0.339840\pi$
$251$	6.76294	+	1.93924i	0.426873	+	0.122404i	−0.0553203	+	0.998469i	$0.517618\pi$
$252$	−2.24523	+	6.16872i	−0.141436	+	0.388593i
$253$	−15.8188	+	6.50871i	−0.994518	+	0.409199i
$254$	−6.39431	+	11.0753i	−0.401214	+	0.694924i
$255$	0.143456	−	1.36489i	0.00898356	−	0.0854728i
$256$	−0.882948	−	0.469472i	−0.0551842	−	0.0293420i
$257$	−0.717054	−	5.10211i	−0.0447286	−	0.318261i	−0.999763	−	0.0217659i	$-0.993071\pi$
$257$	−0.717054	−	5.10211i	−0.0447286	−	0.318261i	0.955034	−	0.296495i	$-0.0958177\pi$
$258$	−10.3522	−	4.60908i	−0.644497	−	0.286949i
$259$	−0.959872	−	9.13257i	−0.0596435	−	0.567470i
$260$	−0.584122	+	1.44575i	−0.0362257	+	0.0896618i
$261$	7.18216	−	9.19275i	0.444565	−	0.569017i
$262$	4.05212	−	14.1314i	0.250341	−	0.873042i
$263$	19.6993	+	23.4768i	1.21471	+	1.44764i	0.858174	+	0.513359i	$0.171599\pi$
$263$	19.6993	+	23.4768i	1.21471	+	1.44764i	0.356539	+	0.934280i	$0.383957\pi$
$264$	−2.63223	+	1.93816i	−0.162003	+	0.119286i
$265$		−	0.119705i		−	0.00735342i
$266$	13.8146	+	2.84897i	0.847030	+	0.174682i
$267$	−0.639576	+	1.96841i	−0.0391414	+	0.120465i
$268$	−6.05357	−	11.3851i	−0.369780	−	0.695456i
$269$	−12.9374	−	3.22565i	−0.788805	−	0.196671i	−0.173368	−	0.984857i	$-0.555465\pi$
$269$	−12.9374	−	3.22565i	−0.788805	−	0.196671i	−0.615437	+	0.788186i	$0.711021\pi$
$270$	1.46045	+	0.985089i	0.0888804	+	0.0599506i
$271$	−18.8383	−	0.657846i	−1.14434	−	0.0399613i	−0.543558	−	0.839372i	$-0.682923\pi$
$271$	−18.8383	−	0.657846i	−1.14434	−	0.0399613i	−0.600785	+	0.799411i	$0.705145\pi$
$272$	−2.07601	−	3.32231i	−0.125877	−	0.201445i
$273$	−12.7817	+	5.69076i	−0.773582	+	0.344421i
$274$	2.94877	+	5.10742i	0.178142	+	0.308550i
$275$	−13.3428	+	9.12402i	−0.804601	+	0.550199i
$276$	−5.00591	−	0.882677i	−0.301320	−	0.0531309i
$277$	−29.9198	−	3.14470i	−1.79771	−	0.188947i	−0.854121	−	0.520074i	$-0.825904\pi$
$277$	−29.9198	−	3.14470i	−1.79771	−	0.188947i	−0.943586	+	0.331127i	$0.892571\pi$
$278$	−11.9687	+	10.7767i	−0.717837	+	0.646344i
$279$	−11.9483	−	4.82741i	−0.715323	−	0.289009i
$280$	0.317042	+	1.10566i	0.0189469	+	0.0660756i
$281$	0.765057	−	1.13424i	0.0456395	−	0.0676633i	−0.805527	−	0.592559i	$-0.798118\pi$
$281$	0.765057	−	1.13424i	0.0456395	−	0.0676633i	0.851167	+	0.524895i	$0.175896\pi$
$282$	−4.08944	+	6.54448i	−0.243523	+	0.389718i
$283$	−0.596766	+	4.24621i	−0.0354740	+	0.252411i	−0.999930	−	0.0118328i	$-0.996233\pi$
$283$	−0.596766	+	4.24621i	−0.0354740	+	0.252411i	0.964456	+	0.264244i	$0.0851223\pi$
$284$	4.35223	−	5.99033i	0.258257	−	0.355461i
$285$	0.661063	−	1.37650i	0.0391580	−	0.0815367i
$286$	14.3444	+	2.43521i	0.848204	+	0.143997i
$287$	3.86293	−	0.681139i	0.228022	−	0.0402064i
$288$	2.02369	−	0.141510i	0.119247	−	0.00833855i
$289$	0.0576696	+	1.65144i	0.00339233	+	0.0971436i
$290$	0.0713348	−	2.04276i	0.00418892	−	0.119955i
$291$	3.87678	+	0.271091i	0.227261	+	0.0158916i
$292$	14.4187	−	1.51547i	0.843793	−	0.0886862i
$293$	−5.93287	+	6.58912i	−0.346602	+	0.384940i	−0.891089	−	0.453829i	$-0.850058\pi$
$293$	−5.93287	+	6.58912i	−0.346602	+	0.384940i	0.544487	+	0.838769i	$0.316724\pi$
$294$	−1.60633	+	3.02108i	−0.0936833	+	0.176193i
$295$	3.25568	+	3.37136i	0.189553	+	0.196288i
$296$	−2.45755	+	1.41887i	−0.142842	+	0.0824699i
$297$	6.06044	−	15.2796i	0.351662	−	0.886613i
$298$	−5.35398	+	6.38063i	−0.310148	+	0.369620i
$299$	12.6519	+	18.7573i	0.731681	+	1.08476i
$300$	−4.80047	+	0.167636i	−0.277155	+	0.00967847i
$301$	31.5526	+	19.7163i	1.81866	+	1.13643i
$302$	4.20686	+	4.06252i	0.242078	+	0.233772i
$303$	11.8604	−	8.61707i	0.681361	−	0.495038i
$304$	−0.932097	−	4.25807i	−0.0534594	−	0.244217i
$305$	2.79516	+	0.908202i	0.160050	+	0.0520035i
$306$	7.14302	+	3.48388i	0.408339	+	0.199160i
$307$	1.84299	−	1.54646i	0.105185	−	0.0882609i	−0.588678	−	0.808367i	$-0.700352\pi$
$307$	1.84299	−	1.54646i	0.105185	−	0.0882609i	0.693864	+	0.720106i	$0.255907\pi$
$308$	9.44401	−	5.09889i	0.538122	−	0.290536i
$309$	−10.7343	−	3.90695i	−0.610651	−	0.222259i
$310$	−2.19085	+	0.546239i	−0.124432	+	0.0310243i
$311$	4.70108	+	5.22108i	0.266574	+	0.296060i	0.861539	−	0.507691i	$-0.169501\pi$
$311$	4.70108	+	5.22108i	0.266574	+	0.296060i	−0.594965	+	0.803751i	$0.702834\pi$
$312$	3.21310	+	2.89308i	0.181906	+	0.163789i
$313$	−0.622636	−	1.27659i	−0.0351934	−	0.0721572i	0.880473	−	0.474096i	$-0.157225\pi$
$313$	−0.622636	−	1.27659i	−0.0351934	−	0.0721572i	−0.915666	+	0.401939i	$0.868336\pi$
$314$	5.06524	+	10.3853i	0.285848	+	0.586076i
$315$	−1.73402	−	1.56132i	−0.0977009	−	0.0879703i
$316$	−9.19311	−	10.2100i	−0.517153	−	0.574357i
$317$	−10.5494	+	2.63025i	−0.592512	+	0.147730i	−0.526625	−	0.850097i	$-0.676543\pi$
$317$	−10.5494	+	2.63025i	−0.592512	+	0.147730i	−0.0658861	+	0.997827i	$0.520987\pi$
$318$	−0.311904	−	0.113524i	−0.0174907	−	0.00636609i
$319$	−18.7613	+	3.43148i	−1.05043	+	0.192126i
$320$	0.272286	−	0.228475i	0.0152212	−	0.0127721i
$321$	14.6938	+	7.16664i	0.820128	+	0.400003i
$322$	15.8727	+	5.15737i	0.884553	+	0.287409i
$323$	5.17834	−	16.2723i	0.288131	−	0.905416i
$324$	−0.971797	+	0.706052i	−0.0539887	+	0.0392251i
$325$	15.3796	+	14.8520i	0.853109	+	0.823838i
$326$	−8.10674	−	5.06565i	−0.448991	−	0.280561i
$327$	7.13413	−	0.249129i	0.394519	−	0.0137769i
$328$	−0.677829	−	1.00492i	−0.0374268	−	0.0554876i
$329$	16.2868	−	19.4099i	0.897921	−	1.07010i
$330$	−0.288259	−	1.12555i	−0.0158681	−	0.0619596i
$331$	30.3083	−	17.4985i	1.66589	−	0.961803i	0.696076	−	0.717969i	$-0.254928\pi$
$331$	30.3083	−	17.4985i	1.66589	−	0.961803i	0.969817	−	0.243835i	$-0.0784055\pi$
$332$	1.03911	+	1.07603i	0.0570286	+	0.0590548i
$333$	2.70261	−	5.08286i	0.148102	−	0.278539i
$334$	10.8333	−	12.0316i	0.592774	−	0.658343i
$335$	4.55814	−	0.479080i	0.249038	−	0.0261749i
$336$	3.18157	+	0.222477i	0.173569	+	0.0121371i
$337$	0.643407	−	18.4248i	0.0350486	−	1.00366i	−0.846737	−	0.532011i	$-0.821436\pi$
$337$	0.643407	−	18.4248i	0.0350486	−	1.00366i	0.881786	−	0.471650i	$-0.156341\pi$
$338$	−0.217941	−	6.24103i	−0.0118545	−	0.339467i
$339$	−9.29289	+	0.649822i	−0.504720	+	0.0352935i
$340$	1.37133	−	0.241803i	0.0743708	−	0.0131136i
$341$	9.35624	+	18.8770i	0.506669	+	1.02225i
$342$	6.18102	+	6.32346i	0.334231	+	0.341934i
$343$	−6.71119	+	9.23717i	−0.362370	+	0.498760i
$344$	1.60016	−	11.3857i	0.0862747	−	0.613877i
$345$	0.957442	−	1.53223i	0.0515469	−	0.0824923i
$346$	−4.30310	+	6.37961i	−0.231336	+	0.342970i
$347$	2.35996	+	8.23017i	0.126690	+	0.441819i	0.998878	−	0.0473505i	$-0.0150778\pi$
$347$	2.35996	+	8.23017i	0.126690	+	0.441819i	−0.872189	+	0.489169i	$0.837300\pi$
$348$	−5.25497	−	2.12314i	−0.281696	−	0.113812i
$349$	−11.0468	+	9.94655i	−0.591320	+	0.532427i	−0.909554	−	0.415585i	$-0.863577\pi$
$349$	−11.0468	+	9.94655i	−0.591320	+	0.532427i	0.318234	+	0.948012i	$0.396910\pi$
$350$	15.6847	+	1.64853i	0.838383	+	0.0881177i
$351$	−21.4117	−	3.77546i	−1.14287	−	0.201519i
$352$	−2.62649	−	2.02523i	−0.139992	−	0.107945i
$353$	8.80143	+	15.2445i	0.468453	+	0.811384i	0.999350	−	0.0360521i	$-0.0114782\pi$
$353$	8.80143	+	15.2445i	0.468453	+	0.811384i	−0.530897	+	0.847436i	$0.678145\pi$
$354$	11.8720	−	5.28574i	0.630988	−	0.280934i
$355$	1.39468	+	2.23195i	0.0740218	+	0.118460i
$356$	−2.09871	−	0.0732885i	−0.111231	−	0.00388428i
$357$	10.3584	+	6.98685i	0.548226	+	0.369783i
$358$	−18.8677	−	4.70425i	−0.997191	−	0.248628i
$359$	−6.04997	−	11.3783i	−0.319305	−	0.600526i	0.670672	−	0.741754i	$-0.266006\pi$
$359$	−6.04997	−	11.3783i	−0.319305	−	0.600526i	−0.989977	+	0.141228i	$0.954895\pi$
$360$	−0.222821	+	0.685772i	−0.0117437	+	0.0361433i
$361$	11.5152	−	15.1129i	0.606062	−	0.795417i
$362$			8.93464i			0.469594i
$363$	−9.68286	+	4.87631i	−0.508218	+	0.255940i
$364$	−9.12498	−	10.8747i	−0.478279	−	0.569990i
$365$	−1.42044	+	4.95366i	−0.0743491	+	0.259286i
$366$	5.01723	−	6.42176i	0.262255	−	0.335671i
$367$	−6.40216	+	15.8459i	−0.334190	+	0.827150i	0.662740	+	0.748850i	$0.269394\pi$
$367$	−6.40216	+	15.8459i	−0.334190	+	0.827150i	−0.996930	+	0.0782999i	$0.975051\pi$
$368$	−0.539105	−	5.12924i	−0.0281028	−	0.267380i
$369$	2.24642	+	1.00017i	0.116944	+	0.0520668i
$370$	−0.140378	−	0.998839i	−0.00729788	−	0.0519271i
$371$	0.962240	+	0.511632i	0.0499570	+	0.0265626i
$372$	−0.654431	+	6.22650i	−0.0339307	+	0.322829i
$373$	10.9923	−	19.0393i	0.569162	−	0.985818i	−0.427487	−	0.904022i	$-0.640601\pi$
$373$	10.9923	−	19.0393i	0.569162	−	0.985818i	0.996649	−	0.0817962i	$-0.0260657\pi$
$374$	−4.94397	−	12.0158i	−0.255647	−	0.621324i
$375$	1.18303	−	3.25034i	0.0610912	−	0.167847i
$376$	−7.52667	−	2.15824i	−0.388159	−	0.111303i
$377$	9.45026	+	23.3902i	0.486713	+	1.20466i
$378$	−14.1607	+	7.52938i	−0.728348	+	0.387269i
$379$	14.4919	+	19.9464i	0.744398	+	1.02458i	0.998354	+	0.0573603i	$0.0182684\pi$
$379$	14.4919	+	19.9464i	0.744398	+	1.02458i	−0.253955	+	0.967216i	$0.581732\pi$
$380$	1.52741	+	0.259786i	0.0783544	+	0.0133267i
$381$	−11.9873	+	3.89492i	−0.614130	+	0.199543i
$382$	−12.4886	−	1.75516i	−0.638973	−	0.0898017i
$383$	−1.08738	−	15.5503i	−0.0555626	−	0.794582i	−0.942819	−	0.333305i	$-0.891836\pi$
$383$	−1.08738	−	15.5503i	−0.0555626	−	0.794582i	0.887256	−	0.461277i	$-0.152608\pi$
$384$	−0.337089	−	0.926145i	−0.0172020	−	0.0472621i
$385$	0.422916	+	3.79131i	0.0215538	+	0.193223i
$386$	−13.7603	−	11.5462i	−0.700379	−	0.587687i
$387$	9.48687	+	21.3079i	0.482245	+	1.08314i
$388$	0.819817	+	3.85693i	0.0416199	+	0.195806i
$389$	3.15163	−	0.442933i	0.159794	−	0.0224576i	−0.0588223	−	0.998268i	$-0.518735\pi$
$389$	3.15163	−	0.442933i	0.159794	−	0.0224576i	0.218616	+	0.975811i	$0.429846\pi$
$390$	−1.38128	+	0.673695i	−0.0699438	+	0.0341139i
$391$	8.21810	−	18.4582i	0.415607	−	0.933469i
$392$	−3.39577	−	0.721793i	−0.171512	−	0.0364560i
$393$	12.2873	−	7.67798i	0.619814	−	0.387303i
$394$	19.2788	−	13.0037i	0.971250	−	0.655116i
$395$	4.58890	−	1.67022i	0.230893	−	0.0840380i
$396$	6.69568	+	0.660652i	0.336471	+	0.0331990i
$397$	2.42850	+	13.7727i	0.121883	+	0.691233i	0.983110	+	0.183013i	$0.0585850\pi$
$397$	2.42850	+	13.7727i	0.121883	+	0.691233i	−0.861228	+	0.508220i	$0.830304\pi$
$398$	13.0914	+	9.51148i	0.656214	+	0.476767i
$399$	8.23942	+	11.1972i	0.412487	+	0.560561i
$400$	−1.50604	−	4.63513i	−0.0753022	−	0.231756i
$401$	4.18349	−	4.33213i	0.208913	−	0.216336i	−0.606704	−	0.794928i	$-0.707509\pi$
$401$	4.18349	−	4.33213i	0.208913	−	0.216336i	0.815617	+	0.578592i	$0.196398\pi$
$402$	3.07447	−	12.3310i	0.153341	−	0.615016i
$403$	21.9597	−	17.1568i	1.09389	−	0.854640i
$404$	11.7214	+	9.15777i	0.583162	+	0.455616i
$405$	−0.103291	−	0.414279i	−0.00513259	−	0.0205857i
$406$	16.1157	+	9.30440i	0.799808	+	0.461770i
$407$	−8.82342	+	3.27526i	−0.437360	+	0.162348i
$408$	0.670475	−	3.80246i	0.0331935	−	0.188250i
$409$	−15.8524	+	15.3085i	−0.783850	+	0.756955i	−0.974424	−	0.224717i	$-0.927854\pi$
$409$	−15.8524	+	15.3085i	−0.783850	+	0.756955i	0.190574	+	0.981673i	$0.438965\pi$
$410$	0.421438	−	0.0895795i	0.0208134	−	0.00442402i
$411$	−1.20849	+	5.68549i	−0.0596104	+	0.280445i
$412$	0.808496	−	11.5620i	0.0398317	−	0.569620i
$413$	−41.0155	+	11.7610i	−2.01824	+	0.578721i
$414$	6.44143	+	8.24466i	0.316579	+	0.405203i
$415$	−0.492978	+	0.199176i	−0.0241993	+	0.00977716i
$416$	−1.92309	+	3.94291i	−0.0942871	+	0.193317i
$417$	−15.8733			−0.777320
$418$	−0.684112	−	14.4406i	−0.0334610	−	0.706315i
$419$	−20.7142			−1.01195			−0.505977	−	0.862547i	$-0.668868\pi$
$419$	−20.7142			−1.01195			−0.505977	+	0.862547i	$0.668868\pi$
$420$	−0.496951	+	1.01890i	−0.0242487	+	0.0497172i
$421$	13.7585	−	5.55879i	0.670548	−	0.270919i	−0.0139837	−	0.999902i	$-0.504451\pi$
$421$	13.7585	−	5.55879i	0.670548	−	0.270919i	0.684531	+	0.728983i	$0.260007\pi$
$422$	−2.31848	−	2.96751i	−0.112862	−	0.144456i
$423$	15.2688	−	4.37826i	0.742395	−	0.212878i
$424$	0.0234923	−	0.335956i	0.00114089	−	0.0163155i
$425$	3.96966	−	18.6758i	0.192557	−	0.905909i
$426$	7.13823	−	1.51728i	0.345848	−	0.0735123i
$427$	−19.2473	+	18.5869i	−0.931443	+	0.899484i
$428$	−2.88039	+	16.3355i	−0.139229	+	0.789606i
$429$	8.90033	+	11.2435i	0.429712	+	0.542843i
$430$	3.53923	+	2.04338i	0.170677	+	0.0985404i
$431$	−5.83764	−	23.4135i	−0.281189	−	1.12779i	−0.930213	−	0.367020i	$-0.880378\pi$
$431$	−5.83764	−	23.4135i	−0.281189	−	1.12779i	0.649024	−	0.760768i	$-0.275177\pi$
$432$	3.90548	+	3.05130i	0.187903	+	0.146806i
$433$	13.9297	−	10.8831i	0.669418	−	0.523006i	−0.222656	−	0.974897i	$-0.571473\pi$
$433$	13.9297	−	10.8831i	0.669418	−	0.523006i	0.892073	+	0.451891i	$0.149250\pi$
$434$	4.97301	−	19.9456i	0.238712	−	0.957421i
$435$	1.39942	−	1.44914i	0.0670968	−	0.0694808i
$436$	2.23818	+	6.88841i	0.107189	+	0.329895i
$437$	15.5183	−	16.2658i	0.742340	−	0.778101i
$438$	11.5602	+	8.39895i	0.552366	+	0.401317i
$439$	−0.00650147	−	0.0368717i	−0.000310298	−	0.00175979i	0.984652	−	0.174528i	$-0.0558400\pi$
$439$	−0.00650147	−	0.0368717i	−0.000310298	−	0.00175979i	−0.984963	+	0.172768i	$0.944729\pi$
$440$	1.01716	−	0.595928i	0.0484912	−	0.0284098i
$441$	6.61792	−	2.40873i	0.315139	−	0.114701i
$442$	−14.2479	+	9.61033i	−0.677703	+	0.457117i
$443$	−7.95082	+	4.96822i	−0.377755	+	0.236047i	−0.705486	−	0.708724i	$-0.749271\pi$
$443$	−7.95082	+	4.96822i	−0.377755	+	0.236047i	0.327732	+	0.944771i	$0.393716\pi$
$444$	−2.73570	−	0.581492i	−0.129831	−	0.0275964i
$445$	0.303599	−	0.681896i	0.0143920	−	0.0323249i
$446$	18.1832	−	8.86854i	0.861000	−	0.419938i
$447$	−8.12934	+	1.14250i	−0.384505	+	0.0540386i
$448$	0.672800	+	3.16528i	0.0317868	+	0.149545i
$449$	5.92485	+	13.3074i	0.279611	+	0.628016i	0.997689	−	0.0679461i	$-0.0216446\pi$
$449$	5.92485	+	13.3074i	0.279611	+	0.628016i	−0.718078	+	0.695963i	$0.754978\pi$
$450$	7.57376	+	6.35514i	0.357030	+	0.299584i
$451$	−1.65855	−	3.66221i	−0.0780981	−	0.172447i
$452$	−3.23272	−	8.88183i	−0.152054	−	0.417766i
$453$	0.402070	+	5.74987i	0.0188909	+	0.270152i
$454$	−14.3210	−	2.01268i	−0.672116	−	0.0944597i
$455$	4.79890	−	1.55926i	0.224976	−	0.0730991i
$456$	2.12543	−	3.73345i	0.0995325	−	0.174835i
$457$	4.24745	+	5.84611i	0.198687	+	0.273469i	0.896722	−	0.442594i	$-0.145942\pi$
$457$	4.24745	+	5.84611i	0.198687	+	0.273469i	−0.698035	+	0.716064i	$0.745942\pi$
$458$	−14.0655	+	7.47875i	−0.657237	+	0.349459i
$459$	7.27340	+	18.0023i	0.339493	+	0.840275i
$460$	1.76218	+	0.505298i	0.0821623	+	0.0235596i
$461$	9.90297	−	27.2082i	0.461227	−	1.26721i	−0.463336	−	0.886183i	$-0.653348\pi$
$461$	9.90297	−	27.2082i	0.461227	−	1.26721i	0.924563	−	0.381029i	$-0.124430\pi$
$462$	10.2797	+	2.49358i	0.478256	+	0.116012i
$463$	−14.2800	+	24.7336i	−0.663646	+	1.14947i	0.316004	+	0.948758i	$0.397659\pi$
$463$	−14.2800	+	24.7336i	−0.663646	+	1.14947i	−0.979650	+	0.200711i	$0.935675\pi$
$464$	0.601099	−	5.71907i	0.0279053	−	0.265501i
$465$	−1.96488	−	1.04474i	−0.0911191	−	0.0484489i
$466$	1.98715	+	14.1393i	0.0920529	+	0.654990i
$467$	16.5692	+	7.37710i	0.766733	+	0.341371i	0.752556	−	0.658528i	$-0.228821\pi$
$467$	16.5692	+	7.37710i	0.766733	+	0.341371i	0.0141767	+	0.999900i	$0.495487\pi$
$468$	−0.930237	−	8.85062i	−0.0430002	−	0.409120i
$469$	−15.6309	+	38.6879i	−0.721769	+	1.78644i
$470$	1.71346	−	2.19313i	0.0790361	−	0.101162i
$471$	−3.13899	+	10.9469i	−0.144637	+	0.504409i
$472$	8.47553	+	10.1007i	0.390118	+	0.464924i
$473$	11.5526	−	36.3412i	0.531188	−	1.67097i
$474$		−	13.5408i		−	0.621950i
$475$	11.1481	−	18.0837i	0.511508	−	0.829736i
$476$	−3.91750	+	12.0568i	−0.179558	+	0.552624i
$477$	0.320740	+	0.603224i	0.0146857	+	0.0276197i
$478$	0.426219	+	0.106268i	0.0194948	+	0.00486060i
$479$	−6.11211	−	4.12267i	−0.279270	−	0.188370i	0.411569	−	0.911378i	$-0.364981\pi$
$479$	−6.11211	−	4.12267i	−0.279270	−	0.188370i	−0.690839	+	0.723009i	$0.742759\pi$
$480$	0.350106	+	0.0122260i	0.0159801	+	0.000558037i
$481$	6.59687	+	10.5572i	0.300792	+	0.481367i
$482$	17.2877	−	7.69699i	0.787434	−	0.350588i
$483$	8.22448	+	14.2452i	0.374227	+	0.648180i
$484$	−7.46398	−	8.08016i	−0.339272	−	0.367280i
$485$	−1.38026	−	0.243377i	−0.0626743	−	0.0110512i
$486$	−15.9643	−	1.67792i	−0.724157	−	0.0761120i
$487$	−5.32892	+	4.79818i	−0.241477	+	0.217426i	−0.780979	−	0.624558i	$-0.785279\pi$
$487$	−5.32892	+	4.79818i	−0.241477	+	0.217426i	0.539502	+	0.841984i	$0.318613\pi$
$488$	7.66645	+	3.09745i	0.347044	+	0.140215i
$489$	−2.59691	−	9.05650i	−0.117436	−	0.409549i
$490$	0.690028	−	1.02301i	0.0311723	−	0.0462148i
$491$	16.8942	−	27.0364i	0.762424	−	1.22013i	−0.207859	−	0.978159i	$-0.566649\pi$
$491$	16.8942	−	27.0364i	0.762424	−	1.22013i	0.970283	−	0.241975i	$-0.0777951\pi$
$492$	0.166267	−	1.18305i	0.00749591	−	0.0533362i
$493$	13.2419	−	18.2259i	0.596384	−	0.820852i
$494$	−18.5256	+	4.73843i	−0.833508	+	0.213192i
$495$	−1.10927	+	2.11867i	−0.0498578	+	0.0952273i
$496$	−6.25587	+	1.10308i	−0.280897	+	0.0495297i
$497$	−23.9024	+	1.67142i	−1.07217	+	0.0749733i
$498$	0.0514520	+	1.47339i	0.00230562	+	0.0660243i
$499$	0.732329	−	20.9712i	0.0327835	−	0.938798i	−0.865905	−	0.500209i	$-0.833256\pi$
$499$	0.732329	−	20.9712i	0.0327835	−	0.938798i	0.898688	−	0.438588i	$-0.144521\pi$
$500$	3.50098	+	0.244813i	0.156569	+	0.0109484i
$501$	15.8693	−	1.66794i	0.708990	−	0.0745179i
$502$	−4.70766	+	5.22839i	−0.210113	+	0.233354i
$503$	−6.76470	+	12.7225i	−0.301623	+	0.567270i	−0.986962	−	0.160954i	$-0.948543\pi$
$503$	−6.76470	+	12.7225i	−0.301623	+	0.567270i	0.685339	+	0.728224i	$0.259654\pi$
$504$	−4.56017	−	4.72219i	−0.203126	−	0.210343i
$505$	−4.57878	+	2.64356i	−0.203753	+	0.117637i
$506$	1.08450	−	17.0710i	0.0482120	−	0.758901i
$507$	3.95623	−	4.71485i	0.175702	−	0.209394i
$508$	−7.15130	−	10.6022i	−0.317288	−	0.470398i
$509$	−5.00605	+	0.174815i	−0.221889	+	0.00774855i	−0.145628	−	0.989339i	$-0.546520\pi$
$509$	−5.00605	+	0.174815i	−0.221889	+	0.00774855i	−0.0762609	+	0.997088i	$0.524298\pi$
$510$	1.16387	+	0.727266i	0.0515370	+	0.0322039i
$511$	−33.7485	−	32.5905i	−1.49295	−	1.44172i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	0.884816	+	21.5851i	0.0390656	+	0.953007i
$514$	4.90008	+	1.59213i	0.216133	+	0.0702259i
$515$	3.70275	+	1.80595i	0.163163	+	0.0795798i
$516$	8.68070	−	7.28397i	0.382146	−	0.320659i
$517$	−23.4130	−	11.2352i	−1.02970	−	0.494125i
$518$	8.62908	+	3.14073i	0.379140	+	0.137996i
$519$	−7.35898	+	1.83480i	−0.323023	+	0.0805387i
$520$	−1.04337	−	1.15878i	−0.0457549	−	0.0508159i
$521$	−18.6584	−	16.8001i	−0.817438	−	0.736024i	0.150122	−	0.988667i	$-0.452033\pi$
$521$	−18.6584	−	16.8001i	−0.817438	−	0.736024i	−0.967559	+	0.252643i	$0.918700\pi$
$522$	5.11393	+	10.4851i	0.223831	+	0.458921i
$523$	3.30956	+	6.78561i	0.144717	+	0.296714i	0.958824	−	0.284001i	$-0.0916619\pi$
$523$	3.30956	+	6.78561i	0.144717	+	0.296714i	−0.814107	+	0.580715i	$0.802773\pi$
$524$	10.9249	+	9.83683i	0.477257	+	0.429724i
$525$	10.4008	+	11.5512i	0.453928	+	0.504138i
$526$	−29.7364	+	7.41412i	−1.29657	+	0.323271i
$527$	−23.3852	−	8.51153i	−1.01868	−	0.370768i
$528$	−0.588116	−	3.21547i	−0.0255945	−	0.139935i
$529$	2.75754	−	2.31385i	0.119893	−	0.100602i
$530$	0.107590	+	0.0524753i	0.00467342	+	0.00227938i
$531$	−25.4395	−	8.26578i	−1.10398	−	0.358704i
$532$	−8.61658	+	11.1676i	−0.373576	+	0.484177i
$533$	−4.30203	+	3.12561i	−0.186342	+	0.135385i
$534$	−1.48883	−	1.43774i	−0.0644278	−	0.0622172i
$535$	−5.00003	−	3.12436i	−0.216170	−	0.135078i
$536$	12.8866	−	0.450009i	0.556615	−	0.0194374i
$537$	−10.7169	−	15.8885i	−0.462470	−	0.685639i
$538$	8.57056	−	10.2140i	0.369503	−	0.440357i
$539$	−10.7029	−	4.24517i	−0.461008	−	0.182852i
$540$	−1.52561	+	0.880813i	−0.0656519	+	0.0379041i
$541$	12.4819	+	12.9254i	0.536638	+	0.555705i	0.931831	−	0.362894i	$-0.118211\pi$
$541$	12.4819	+	12.9254i	0.536638	+	0.555705i	−0.395193	+	0.918598i	$0.629322\pi$
$542$	8.84942	−	16.6433i	0.380115	−	0.714892i
$543$	−5.89225	+	6.54401i	−0.252861	+	0.280830i
$544$	3.89613	−	0.409500i	0.167045	−	0.0175572i
$545$	−2.56818	−	0.179584i	−0.110009	−	0.00769255i
$546$	0.488288	−	13.9828i	0.0208968	−	0.598407i
$547$	0.359535	+	10.2957i	0.0153726	+	0.440214i	0.982538	+	0.186064i	$0.0595733\pi$
$547$	0.359535	+	10.2957i	0.0153726	+	0.440214i	−0.967165	+	0.254149i	$0.918204\pi$
$548$	−5.88317	+	0.411391i	−0.251317	+	0.0175738i
$549$	−16.5189	+	2.91274i	−0.705011	+	0.124313i
$550$	−2.35152	−	15.9921i	−0.100269	−	0.681907i
$551$	20.6954	−	14.1425i	0.881655	−	0.602493i
$552$	2.98779	−	4.11234i	0.127169	−	0.175033i
$553$	−6.18748	+	44.0262i	−0.263119	+	1.87219i
$554$	15.9424	−	25.5132i	0.677329	−	1.08395i
$555$	0.555901	−	0.824157i	0.0235967	−	0.0349835i
$556$	−4.43929	−	15.4816i	−0.188268	−	0.656567i
$557$	21.4997	+	8.68643i	0.910970	+	0.368056i	0.781773	−	0.623563i	$-0.214316\pi$
$557$	21.4997	+	8.68643i	0.910970	+	0.368056i	0.129197	+	0.991619i	$0.458760\pi$
$558$	9.57662	−	8.62283i	0.405411	−	0.365033i
$559$	−50.1625	−	5.27229i	−2.12165	−	0.222994i
$560$	−1.13274	−	0.199732i	−0.0478670	−	0.00844024i
$561$	4.30313	−	12.0612i	0.181678	−	0.509226i
$562$	0.684073	+	1.18485i	0.0288559	+	0.0499798i
$563$	5.48021	−	2.43995i	0.230963	−	0.102832i	−0.287992	−	0.957633i	$-0.592988\pi$
$563$	5.48021	−	2.43995i	0.230963	−	0.102832i	0.518955	+	0.854801i	$0.326321\pi$
$564$	−4.08944	−	6.54448i	−0.172197	−	0.275572i
$565$	3.35756	+	0.117248i	0.141253	+	0.00493268i
$566$	−3.55486	−	2.39778i	−0.149422	−	0.100786i
$567$	3.77163	+	0.940373i	0.158394	+	0.0394920i
$568$	3.47618	+	6.53774i	0.145857	+	0.274318i
$569$	0.429735	−	1.32259i	0.0180154	−	0.0554458i	−0.941645	−	0.336609i	$-0.890720\pi$
$569$	0.429735	−	1.32259i	0.0180154	−	0.0554458i	0.959660	+	0.281163i	$0.0907201\pi$
$570$	0.947397	+	1.19758i	0.0396821	+	0.0501610i
$571$			37.6600i			1.57602i	0.615660	+	0.788012i	$0.288889\pi$
$571$			37.6600i			1.57602i	−0.615660	+	0.788012i	$0.711111\pi$
$572$	−8.47694	+	11.8252i	−0.354439	+	0.494435i
$573$	−7.98954	−	9.52156i	−0.333768	−	0.397769i
$574$	−1.08119	+	3.77057i	−0.0451282	+	0.157381i
$575$	15.4752	−	19.8073i	0.645359	−	0.826022i
$576$	−0.759937	+	1.88091i	−0.0316640	+	0.0783712i
$577$	0.380990	+	3.62488i	0.0158608	+	0.150906i	0.999586	−	0.0287744i	$-0.00916043\pi$
$577$	0.380990	+	3.62488i	0.0158608	+	0.150906i	−0.983725	+	0.179680i	$0.942494\pi$
$578$	−1.50959	−	0.672111i	−0.0627905	−	0.0279561i
$579$	−2.46389	−	17.5315i	−0.102396	−	0.728583i
$580$	1.80475	+	0.959603i	0.0749382	+	0.0398453i
$581$	0.505979	−	4.81406i	0.0209915	−	0.199721i
$582$	−1.94313	+	3.36559i	−0.0805452	+	0.139508i
$583$	0.263308	−	1.08548i	0.0109051	−	0.0449560i
$584$	−4.95866	+	13.6238i	−0.205191	+	0.563758i
$585$	3.04069	+	0.871904i	0.125717	+	0.0360488i
$586$	−3.32146	−	8.22090i	−0.137208	−	0.339602i
$587$	−8.92983	+	4.74808i	−0.368574	+	0.195974i	−0.643419	−	0.765514i	$-0.722485\pi$
$587$	−8.92983	+	4.74808i	−0.368574	+	0.195974i	0.274845	+	0.961489i	$0.411373\pi$
$588$	−2.01115	−	2.76812i	−0.0829386	−	0.114155i
$589$	−21.3188	−	17.6695i	−0.878426	−	0.728058i
$590$	−4.45735	+	1.44828i	−0.183506	+	0.0596248i
$591$	22.6961	+	3.18973i	0.933592	+	0.131208i
$592$	−0.197950	−	2.83082i	−0.00813570	−	0.116346i
$593$	11.1073	+	30.5171i	0.456122	+	1.25319i	0.928349	+	0.371709i	$0.121228\pi$
$593$	11.1073	+	30.5171i	0.456122	+	1.25319i	−0.472227	+	0.881477i	$0.656550\pi$
$594$	11.0765	+	12.1452i	0.454474	+	0.498324i
$595$	−3.45185	−	2.89645i	−0.141512	−	0.118743i
$596$	−3.38784	−	7.60921i	−0.138771	−	0.311685i
$597$	3.31590	+	15.6001i	0.135711	+	0.638469i
$598$	−22.4052	+	3.14884i	−0.916216	+	0.128766i
$599$	−28.8456	+	14.0689i	−1.17860	+	0.574841i	−0.920296	−	0.391223i	$-0.872052\pi$
$599$	−28.8456	+	14.0689i	−1.17860	+	0.574841i	−0.258302	+	0.966064i	$0.583163\pi$
$600$	1.95372	−	4.38812i	0.0797601	−	0.179144i
$601$	24.1617	+	5.13572i	0.985575	+	0.209490i	0.672386	−	0.740200i	$-0.265269\pi$
$601$	24.1617	+	5.13572i	0.985575	+	0.209490i	0.313189	+	0.949691i	$0.398603\pi$
$602$	−31.5526	+	19.7163i	−1.28599	+	0.803575i
$603$	−21.6859	+	14.6274i	−0.883120	+	0.595672i
$604$	−5.49553	+	2.00021i	−0.223610	+	0.0813874i
$605$	3.65676	−	1.38395i	0.148668	−	0.0562658i
$606$	2.54572	+	14.4375i	0.103413	+	0.586484i
$607$	−13.3765	−	9.71859i	−0.542935	−	0.394465i	0.282239	−	0.959344i	$-0.408923\pi$
$607$	−13.3765	−	9.71859i	−0.542935	−	0.394465i	−0.825174	+	0.564879i	$0.808923\pi$
$608$	4.23574	+	1.02885i	0.171782	+	0.0417255i
$609$	5.66753	+	17.4429i	0.229660	+	0.706820i
$610$	−2.04160	+	2.11414i	−0.0826621	+	0.0855991i
$611$	−8.30986	+	33.3290i	−0.336181	+	1.34835i
$612$	−6.26259	+	4.89287i	−0.253150	+	0.197783i
$613$	12.4501	+	9.72708i	0.502855	+	0.392873i	0.834910	−	0.550387i	$-0.185520\pi$
$613$	12.4501	+	9.72708i	0.502855	+	0.392873i	−0.332055	+	0.943260i	$0.607742\pi$
$614$	0.582030	+	2.33439i	0.0234888	+	0.0942085i
$615$	0.367751	+	0.212321i	0.0148291	+	0.00856160i
$616$	0.442875	+	10.7234i	0.0178439	+	0.432059i
$617$	−4.06508	+	23.0542i	−0.163654	+	0.928127i	0.786788	+	0.617224i	$0.211743\pi$
$617$	−4.06508	+	23.0542i	−0.163654	+	0.928127i	−0.950442	+	0.310903i	$0.899368\pi$
$618$	8.21713	−	7.93519i	0.330542	−	0.319200i
$619$	−7.13416	+	1.51641i	−0.286746	+	0.0609497i	−0.349039	−	0.937108i	$-0.613492\pi$
$619$	−7.13416	+	1.51641i	−0.286746	+	0.0609497i	0.0622931	+	0.998058i	$0.480159\pi$
$620$	0.469447	−	2.20857i	0.0188534	−	0.0886985i
$621$	−1.78306	+	25.4989i	−0.0715516	+	1.02324i
$622$	−6.75350	+	1.93653i	−0.270791	+	0.0776480i
$623$	4.18375	+	5.35496i	0.167618	+	0.214542i
$624$	−4.00881	+	1.61967i	−0.160481	+	0.0648385i
$625$	10.1355	−	20.7809i	0.405421	−	0.831235i
$626$	1.42034			0.0567682
$627$	9.02230	−	11.0279i	0.360316	−	0.440413i
$628$	−11.5547			−0.461082
$629$	4.87341	−	9.99197i	0.194316	−	0.398406i
$630$	2.16345	−	0.874089i	0.0861938	−	0.0348246i
$631$	17.4156	+	22.2909i	0.693304	+	0.887388i	0.997879	−	0.0651001i	$-0.0207367\pi$
$631$	17.4156	+	22.2909i	0.693304	+	0.887388i	−0.304575	+	0.952488i	$0.598514\pi$
$632$	13.2067	−	3.78695i	0.525333	−	0.150637i
$633$	0.258904	−	3.70250i	0.0102905	−	0.147161i
$634$	2.26048	−	10.6347i	0.0897753	−	0.422359i
$635$	4.44630	−	0.945091i	0.176446	−	0.0375048i
$636$	0.238764	−	0.230572i	0.00946760	−	0.00914276i
$637$	−2.64461	+	14.9983i	−0.104783	+	0.594254i
$638$	5.14021	−	18.3668i	0.203503	−	0.727147i
$639$	−13.0085	−	7.51044i	−0.514607	−	0.297108i
$640$	0.0859897	+	0.344886i	0.00339904	+	0.0136328i
$641$	15.4259	+	12.0520i	0.609287	+	0.476027i	0.872436	−	0.488728i	$-0.162539\pi$
$641$	15.4259	+	12.0520i	0.609287	+	0.476027i	−0.263150	+	0.964755i	$0.584761\pi$
$642$	−12.8827	+	10.0650i	−0.508438	+	0.397236i
$643$	−2.59218	+	10.3967i	−0.102226	+	0.410005i	−0.999505	−	0.0314585i	$-0.989985\pi$
$643$	−2.59218	+	10.3967i	−0.102226	+	0.410005i	0.897279	+	0.441463i	$0.145540\pi$
$644$	−11.5936	+	12.0055i	−0.456850	+	0.473082i
$645$	1.24467	+	3.83070i	0.0490088	+	0.150834i
$646$	12.3554	+	11.7876i	0.486118	+	0.463776i
$647$	−35.6347	−	25.8901i	−1.40095	−	1.01785i	−0.994562	−	0.104143i	$-0.966790\pi$
$647$	−35.6347	−	25.8901i	−1.40095	−	1.01785i	−0.406383	−	0.913703i	$-0.633210\pi$
$648$	−0.208587	−	1.18296i	−0.00819409	−	0.0464710i
$649$	22.1066	+	37.7327i	0.867760	+	1.48114i
$650$	−20.0908	+	7.31247i	−0.788028	+	0.286819i
$651$	16.7962	−	11.3292i	0.658295	−	0.444026i
$652$	8.10674	−	5.06565i	0.317484	−	0.198386i
$653$	−42.7627	−	9.08950i	−1.67344	−	0.355700i	−0.729030	−	0.684482i	$-0.760028\pi$
$653$	−42.7627	−	9.08950i	−1.67344	−	0.355700i	−0.944406	+	0.328782i	$0.893362\pi$
$654$	−2.90348	+	6.52133i	−0.113535	+	0.255004i
$655$	−4.69651	+	2.29064i	−0.183508	+	0.0895028i
$656$	1.20036	−	0.168700i	0.0468662	−	0.00658661i
$657$	−6.11497	−	28.7687i	−0.238568	−	1.12237i
$658$	10.3058	+	23.1472i	0.401762	+	0.902373i
$659$	−3.67090	−	3.08025i	−0.142998	−	0.119989i	0.568483	−	0.822695i	$-0.307531\pi$
$659$	−3.67090	−	3.08025i	−0.142998	−	0.119989i	−0.711481	+	0.702706i	$0.751975\pi$
$660$	1.13800	+	0.234324i	0.0442967	+	0.00912105i
$661$	−11.1061	−	30.5137i	−0.431977	−	1.18685i	−0.944597	−	0.328232i	$-0.893547\pi$
$661$	−11.1061	−	30.5137i	−0.431977	−	1.18685i	0.512620	−	0.858615i	$-0.328675\pi$
$662$	2.44126	+	34.9117i	0.0948824	+	1.35688i
$663$	−16.7735	−	2.35735i	−0.651427	−	0.0915521i
$664$	−1.42265	+	0.462246i	−0.0552094	+	0.0179386i
$665$	−2.53311	−	4.32668i	−0.0982297	−	0.167782i
$666$	3.38370	+	4.65727i	0.131116	+	0.180465i
$667$	26.1869	−	13.9238i	1.01396	−	0.539133i
$668$	6.06495	+	15.0113i	0.234660	+	0.580804i
$669$	19.1666	+	5.49593i	0.741023	+	0.212485i
$670$	−1.56756	+	4.30684i	−0.0605602	+	0.166388i
$671$	23.3487	+	14.3839i	0.901365	+	0.555284i
$672$	−1.59467	+	2.76205i	−0.0615156	+	0.106548i
$673$	2.63232	−	25.0448i	0.101468	−	0.965408i	−0.818789	−	0.574094i	$-0.805354\pi$
$673$	2.63232	−	25.0448i	0.101468	−	0.965408i	0.920258	−	0.391313i	$-0.127979\pi$
$674$	16.2780	+	8.65518i	0.627006	+	0.333385i
$675$	3.36165	+	23.9194i	0.129390	+	0.920658i
$676$	5.70494	+	2.54000i	0.219421	+	0.0976924i
$677$	−4.77487	−	45.4298i	−0.183513	−	1.74601i	−0.568135	−	0.822936i	$-0.692335\pi$
$677$	−4.77487	−	45.4298i	−0.183513	−	1.74601i	0.384622	−	0.923074i	$-0.374332\pi$
$678$	3.48968	−	8.63725i	0.134020	−	0.331712i
$679$	7.85574	−	10.0549i	0.301476	−	0.385871i
$680$	−0.383821	+	1.33854i	−0.0147189	+	0.0513308i
$681$	−9.16178	−	10.9186i	−0.351080	−	0.418401i
$682$	−21.0680	+	0.134199i	−0.806737	+	0.00513874i
$683$			27.2653i			1.04328i	0.853166	+	0.521639i	$0.174679\pi$
$683$			27.2653i			1.04328i	−0.853166	+	0.521639i	$0.825321\pi$
$684$	−8.39307	+	2.78344i	−0.320917	+	0.106427i
$685$	0.647775	−	1.99365i	0.0247502	−	0.0761733i
$686$	−5.36032	−	10.0813i	−0.204658	−	0.384905i
$687$	−15.2341	−	3.79829i	−0.581217	−	0.144914i
$688$	9.53195	+	6.42938i	0.363402	+	0.245118i
$689$	−1.47650	−	0.0515606i	−0.0562502	−	0.00196430i
$690$	0.957442	+	1.53223i	0.0364492	+	0.0583309i
$691$	−5.75247	+	2.56117i	−0.218834	+	0.0974314i	−0.513226	−	0.858254i	$-0.671550\pi$
$691$	−5.75247	+	2.56117i	−0.218834	+	0.0974314i	0.294392	+	0.955685i	$0.404883\pi$
$692$	−3.84760	−	6.66424i	−0.146264	−	0.253337i
$693$	−12.2897	−	17.9722i	−0.466846	−	0.682707i
$694$	−8.43177	−	1.48675i	−0.320066	−	0.0564362i
$695$	5.69325	+	0.598385i	0.215957	+	0.0226980i
$696$	4.21190	−	3.79241i	0.159651	−	0.143751i
$697$	4.40295	+	1.77891i	0.166774	+	0.0673809i
$698$	−4.09732	−	14.2891i	−0.155086	−	0.540849i
$699$	−7.86918	+	11.6665i	−0.297640	+	0.441269i
$700$	−8.35742	+	13.3747i	−0.315881	+	0.505515i
$701$	0.781337	−	5.55950i	0.0295107	−	0.209980i	−0.969931	−	0.243378i	$-0.921744\pi$
$701$	0.781337	−	5.55950i	0.0295107	−	0.209980i	0.999442	+	0.0333989i	$0.0106332\pi$
$702$	12.7796	−	17.5896i	0.482336	−	0.663879i
$703$	8.84554	−	8.64628i	0.333616	−	0.326101i
$704$	2.97164	−	1.47287i	0.111998	−	0.0555109i
$705$	2.70133	−	0.476317i	0.101738	−	0.0179391i
$706$	−17.5600	+	1.22791i	−0.660879	+	0.0462131i
$707$	−1.67986	−	48.1050i	−0.0631778	−	1.80918i
$708$	−0.453536	+	12.9876i	−0.0170449	+	0.488103i
$709$	−0.284541	−	0.0198970i	−0.0106861	−	0.000747248i	0.0644124	−	0.997923i	$-0.479483\pi$
$709$	−0.284541	−	0.0198970i	−0.0106861	−	0.000747248i	−0.0750985	+	0.997176i	$0.523927\pi$
$710$	−2.61745	+	0.275105i	−0.0982312	+	0.0103245i
$711$	−18.6494	+	20.7122i	−0.699407	+	0.776770i
$712$	0.985884	−	1.85418i	0.0369476	−	0.0694883i
$713$	−22.7586	−	23.5673i	−0.852318	−	0.882601i
$714$	−10.8206	+	6.24726i	−0.404950	+	0.233798i
$715$	−2.76841	−	4.36822i	−0.103533	−	0.163362i
$716$	12.4992	−	14.8960i	0.467118	−	0.556690i
$717$	0.242094	+	0.358919i	0.00904115	+	0.0134041i
$718$	12.8789	−	0.449742i	0.480637	−	0.0167842i
$719$	9.46802	+	5.91627i	0.353097	+	0.220640i	0.694857	−	0.719147i	$-0.255467\pi$
$719$	9.46802	+	5.91627i	0.353097	+	0.220640i	−0.341760	+	0.939787i	$0.611023\pi$
$720$	−0.518689	−	0.500893i	−0.0193304	−	0.0186672i
$721$	−30.3430	+	22.0455i	−1.13003	+	0.821015i
$722$	8.53549	+	16.9748i	0.317658	+	0.631738i
$723$	17.7381	+	5.76346i	0.659687	+	0.214345i
$724$	−8.03040	−	3.91669i	−0.298448	−	0.145563i
$725$	21.4694	−	18.0150i	0.797354	−	0.669060i
$726$	−0.138109	−	10.8405i	−0.00512571	−	0.402330i
$727$	−28.5437	−	10.3891i	−1.05863	−	0.385309i	−0.246715	−	0.969088i	$-0.579351\pi$
$727$	−28.5437	−	10.3891i	−1.05863	−	0.385309i	−0.811912	+	0.583779i	$0.801573\pi$
$728$	13.7743	−	3.43431i	0.510508	−	0.127284i
$729$	−8.17492	−	9.07916i	−0.302775	−	0.336265i
$730$	−3.82964	−	3.44822i	−0.141741	−	0.127624i
$731$	19.7455	+	40.4844i	0.730315	+	1.49737i
$732$	3.57243	+	7.32457i	0.132041	+	0.270724i
$733$	−27.3082	−	24.5884i	−1.00865	−	0.908194i	−0.0128670	−	0.999917i	$-0.504096\pi$
$733$	−27.3082	−	24.5884i	−1.00865	−	0.908194i	−0.995785	+	0.0917233i	$0.970762\pi$
$734$	−11.4357	−	12.7006i	−0.422099	−	0.468788i
$735$	1.18005	−	0.294221i	0.0435270	−	0.0108525i
$736$	4.84646	+	1.76397i	0.178643	+	0.0650206i
$737$	42.3868	+	5.68200i	1.56134	+	0.209299i
$738$	−1.88371	+	1.58062i	−0.0693404	+	0.0581835i
$739$	0.217202	+	0.105936i	0.00798990	+	0.00389693i	0.442362	−	0.896837i	$-0.354141\pi$
$739$	0.217202	+	0.105936i	0.00798990	+	0.00389693i	−0.434372	+	0.900734i	$0.643030\pi$
$740$	0.959288	+	0.311691i	0.0352641	+	0.0114580i
$741$	−16.6937	−	8.74678i	−0.613257	−	0.321321i
$742$	−0.881670	+	0.640571i	−0.0323671	+	0.0235161i
$743$	−1.72712	−	1.66786i	−0.0633619	−	0.0611878i	0.662303	−	0.749236i	$-0.269579\pi$
$743$	−1.72712	−	1.66786i	−0.0633619	−	0.0611878i	−0.725665	+	0.688048i	$0.758468\pi$
$744$	−5.30946	−	3.31772i	−0.194654	−	0.121633i
$745$	2.95880	−	0.103324i	0.108402	−	0.00378549i
$746$	12.2937	+	18.2261i	0.450104	+	0.667306i
$747$	1.95056	−	2.32459i	0.0713674	−	0.0850523i
$748$	12.9671	+	0.823780i	0.474122	+	0.0301204i
$749$	46.4856	−	26.8385i	1.69855	−	0.980657i
$750$	2.40278	+	2.48815i	0.0877370	+	0.0908544i
$751$	2.20648	−	4.14978i	0.0805156	−	0.151428i	−0.839438	−	0.543456i	$-0.817115\pi$
$751$	2.20648	−	4.14978i	0.0805156	−	0.151428i	0.919953	+	0.392028i	$0.128227\pi$
$752$	5.23929	−	5.81882i	0.191057	−	0.212191i
$753$	−6.89607	+	0.724806i	−0.251307	+	0.0264134i
$754$	−25.1657	−	1.75976i	−0.916481	−	0.0640866i
$755$	0.0725462	−	2.07745i	0.00264022	−	0.0756061i
$756$	−0.559717	−	16.0282i	−0.0203567	−	0.582940i
$757$	−15.8598	+	1.10903i	−0.576435	+	0.0403083i	−0.354999	−	0.934867i	$-0.615519\pi$
$757$	−15.8598	+	1.10903i	−0.576435	+	0.0403083i	−0.221436	+	0.975175i	$0.571074\pi$
$758$	−24.2805	+	4.28131i	−0.881908	+	0.155504i
$759$	12.0524	−	11.7881i	0.437474	−	0.427883i
$760$	−0.903066	+	1.25894i	−0.0327577	+	0.0456667i
$761$	5.84107	−	8.03955i	0.211739	−	0.291433i	−0.689916	−	0.723889i	$-0.742353\pi$
$761$	5.84107	−	8.03955i	0.211739	−	0.291433i	0.901655	+	0.432456i	$0.142353\pi$
$762$	1.75417	−	12.4816i	0.0635469	−	0.452160i
$763$	12.4202	−	19.8765i	0.449643	−	0.719579i
$764$	7.05217	−	10.4553i	0.255139	−	0.378258i
$765$	−0.778630	−	2.71540i	−0.0281514	−	0.0981756i
$766$	14.4532	+	5.83946i	0.522214	+	0.210988i
$767$	42.9863	−	38.7050i	1.55214	−	1.39756i
$768$	0.980184	+	0.103021i	0.0353693	+	0.00371747i
$769$	11.0956	+	1.95645i	0.400117	+	0.0705515i	0.370086	−	0.928997i	$-0.379328\pi$
$769$	11.0956	+	1.95645i	0.400117	+	0.0705515i	0.0300313	+	0.999549i	$0.490439\pi$
$770$	−3.59300	−	1.28189i	−0.129483	−	0.0461960i
$771$	2.53898	+	4.39765i	0.0914392	+	0.158377i
$772$	16.4098	−	7.30610i	0.590601	−	0.262952i
$773$	−6.21870	−	9.95199i	−0.223671	−	0.357948i	0.717112	−	0.696958i	$-0.245464\pi$
$773$	−6.21870	−	9.95199i	−0.223671	−	0.357948i	−0.940783	+	0.339010i	$0.889908\pi$
$774$	−23.3101	−	0.814008i	−0.837866	−	0.0292589i
$775$	−25.6665	−	17.3122i	−0.921966	−	0.621874i
$776$	−3.82597	−	0.953922i	−0.137344	−	0.0342438i
$777$	4.24894	+	7.99110i	0.152430	+	0.286679i
$778$	−0.983480	+	3.02684i	−0.0352595	+	0.108517i
$779$	3.94789	+	3.51159i	0.141448	+	0.125816i
$780$		−	1.53681i		−	0.0550268i
$781$	7.73739	+	23.3070i	0.276866	+	0.833991i
$782$	12.9875	+	15.4779i	0.464432	+	0.553489i
$783$	−7.85582	+	27.3965i	−0.280744	+	0.979071i
$784$	2.13735	−	2.73568i	0.0763339	−	0.0977030i
$785$	1.53853	−	3.80799i	0.0549124	−	0.135913i
$786$	1.51451	+	14.4096i	0.0540207	+	0.513973i
$787$	14.5840	+	6.49324i	0.519865	+	0.231459i	0.649857	−	0.760056i	$-0.274829\pi$
$787$	14.5840	+	6.49324i	0.519865	+	0.231459i	−0.129992	+	0.991515i	$0.541495\pi$
$788$	3.23639	+	23.0281i	0.115291	+	0.820341i
$789$	−26.6693	−	14.1803i	−0.949453	−	0.504833i
$790$	−0.510455	+	4.85665i	−0.0181612	+	0.172792i
$791$	−15.2930	+	26.4883i	−0.543758	+	0.941817i
$792$	−3.52898	+	5.72843i	−0.125397	+	0.203551i
$793$	12.4062	−	34.0857i	0.440556	−	1.21042i
$794$	−13.4434	−	3.85484i	−0.477089	−	0.136803i
$795$	0.0441958	+	0.109388i	0.00156746	+	0.00387961i
$796$	−14.2878	+	7.59694i	−0.506416	+	0.269266i
$797$	−16.6508	−	22.9179i	−0.589802	−	0.811793i	0.404925	−	0.914350i	$-0.367298\pi$
$797$	−16.6508	−	22.9179i	−0.589802	−	0.811793i	−0.994727	+	0.102557i	$0.967298\pi$
$798$	−13.6759	+	2.49701i	−0.484122	+	0.0883932i
$799$	29.1734	−	9.47902i	1.03208	−	0.335344i
$800$	4.82623	+	0.678282i	0.170633	+	0.0239809i
$801$	0.297169	+	4.24971i	0.0104999	+	0.150156i
$802$	2.05977	+	5.65917i	0.0727330	+	0.199832i
$803$	−23.7767	+	41.7951i	−0.839063	+	1.47492i
$804$	9.73529	+	8.16888i	0.343337	+	0.288094i
$805$	−2.41285	−	5.41935i	−0.0850417	−	0.191007i
$806$	5.79392	+	27.2583i	0.204082	+	0.960131i
$807$	13.0133	−	1.82890i	0.458090	−	0.0643804i
$808$	−13.3693	+	6.52064i	−0.470330	+	0.229395i
$809$	12.4097	−	27.8727i	0.436303	−	0.979952i	−0.552880	−	0.833261i	$-0.686471\pi$
$809$	12.4097	−	27.8727i	0.436303	−	0.979952i	0.989182	−	0.146691i	$-0.0468623\pi$
$810$	0.417632	+	0.0887703i	0.0146741	+	0.00311907i
$811$	5.57268	−	3.48220i	0.195683	−	0.122277i	−0.428539	−	0.903523i	$-0.640972\pi$
$811$	5.57268	−	3.48220i	0.195683	−	0.122277i	0.624222	+	0.781247i	$0.285416\pi$
$812$	−15.4274	+	10.4059i	−0.541395	+	0.365176i
$813$	17.4576	−	6.35404i	0.612264	−	0.222846i
$814$	0.924149	−	9.36621i	0.0323914	−	0.328286i
$815$	0.590021	+	3.34617i	0.0206675	+	0.117211i
$816$	3.12371	+	2.26951i	0.109352	+	0.0794486i
$817$	5.54071	+	49.8097i	0.193845	+	1.74262i
$818$	−6.80994	−	20.9588i	−0.238104	−	0.732808i
$819$	−20.0050	+	20.7157i	−0.699030	+	0.723867i
$820$	−0.104233	+	0.418055i	−0.00363997	+	0.0145991i
$821$	2.88553	−	2.25442i	0.100706	−	0.0786798i	−0.564051	−	0.825740i	$-0.690758\pi$
$821$	2.88553	−	2.25442i	0.100706	−	0.0786798i	0.664756	+	0.747060i	$0.268535\pi$
$822$	−4.58032	−	3.57854i	−0.159757	−	0.124816i
$823$	3.96294	+	15.8945i	0.138139	+	0.554047i	0.998979	+	0.0451710i	$0.0143833\pi$
$823$	3.96294	+	15.8945i	0.138139	+	0.554047i	−0.860840	+	0.508876i	$0.830061\pi$
$824$	10.0375	+	5.79513i	0.349671	+	0.201883i
$825$	8.82423	−	13.2639i	0.307220	−	0.461790i
$826$	7.40929	−	42.0202i	0.257802	−	1.46207i
$827$	5.23822	−	5.05849i	0.182151	−	0.175901i	−0.597993	−	0.801502i	$-0.704035\pi$
$827$	5.23822	−	5.05849i	0.182151	−	0.175901i	0.780144	+	0.625600i	$0.215146\pi$
$828$	−10.2340	+	2.17530i	−0.355656	+	0.0755970i
$829$	2.63825	−	12.4120i	0.0916300	−	0.431085i	−0.908289	−	0.418344i	$-0.862611\pi$
$829$	2.63825	−	12.4120i	0.0916300	−	0.431085i	0.999919	−	0.0127417i	$-0.00405592\pi$
$830$	0.0370891	−	0.530399i	0.00128738	−	0.0184104i
$831$	28.5023	−	8.17289i	0.988732	−	0.283514i
$832$	−2.70084	−	3.45692i	−0.0936348	−	0.119847i
$833$	12.6101	−	5.09482i	0.436915	−	0.176525i
$834$	6.95841	−	14.2669i	0.240950	−	0.494021i
$835$	−5.75470			−0.199150
$836$	13.2791	+	5.71548i	0.459266	+	0.197674i
$837$	31.4832			1.08822
$838$	9.08049	−	18.6178i	0.313680	−	0.643140i
$839$	−35.0788	+	14.1727i	−1.21105	+	0.489297i	−0.889212	−	0.457496i	$-0.848746\pi$
$839$	−35.0788	+	14.1727i	−1.21105	+	0.489297i	−0.321842	+	0.946794i	$0.604302\pi$
$840$	−0.697932	−	0.893313i	−0.0240810	−	0.0308222i
$841$	3.91145	−	1.12159i	0.134878	−	0.0386756i
$842$	−1.03512	+	14.8029i	−0.0356725	+	0.510140i
$843$	−0.280352	+	1.31895i	−0.00965585	+	0.0454272i
$844$	3.68354	−	0.782960i	0.126793	−	0.0269506i
$845$	−1.59671	+	1.54192i	−0.0549285	+	0.0530438i
$846$	−2.75825	+	15.6428i	−0.0948306	+	0.537811i
$847$	−4.50454	+	35.3097i	−0.154778	+	1.21326i
$848$	0.291657	+	0.168388i	0.0100155	+	0.00578247i
$849$	−1.02239	−	4.10058i	−0.0350883	−	0.140732i
$850$	15.0455	+	11.7548i	0.516057	+	0.403188i
$851$	11.5330	−	9.01056i	0.395346	−	0.308878i
$852$	−1.76547	+	7.08093i	−0.0604841	+	0.242589i
$853$	30.4910	−	31.5744i	1.04399	−	1.08109i	0.0473777	−	0.998877i	$-0.484914\pi$
$853$	30.4910	−	31.5744i	1.04399	−	1.08109i	0.996615	−	0.0822092i	$-0.0261976\pi$
$854$	−8.26834	−	25.4473i	−0.282937	−	0.870790i
$855$	0.200236	−	3.13666i	0.00684791	−	0.107271i
$856$	−13.4196	−	9.74988i	−0.458671	−	0.333244i
$857$	2.39193	+	13.5653i	0.0817068	+	0.463383i	0.998019	+	0.0629172i	$0.0200404\pi$
$857$	2.39193	+	13.5653i	0.0817068	+	0.463383i	−0.916312	+	0.400465i	$0.868848\pi$
$858$	−14.0073	+	3.07072i	−0.478200	+	0.104833i
$859$	−17.5504	+	6.38782i	−0.598812	+	0.217950i	−0.623601	−	0.781743i	$-0.714331\pi$
$859$	−17.5504	+	6.38782i	−0.598812	+	0.217950i	0.0247889	+	0.999693i	$0.492109\pi$
$860$	−3.38807	+	2.28528i	−0.115532	+	0.0779276i
$861$	−3.27853	+	2.04865i	−0.111732	+	0.0698179i
$862$	23.6030	+	5.01696i	0.803920	+	0.170878i
$863$	−13.6358	+	30.6264i	−0.464167	+	1.04254i	0.518147	+	0.855292i	$0.326622\pi$
$863$	−13.6358	+	30.6264i	−0.464167	+	1.04254i	−0.982314	+	0.187243i	$0.940045\pi$
$864$	−4.45454	+	2.17262i	−0.151546	+	0.0739141i
$865$	2.70860	−	0.380668i	0.0920950	−	0.0129431i
$866$	3.67526	+	17.2907i	0.124890	+	0.587563i
$867$	−0.662421	−	1.48782i	−0.0224970	−	0.0505291i
$868$	15.7470	+	13.2133i	0.534488	+	0.448489i
$869$	45.2859	−	5.05158i	1.53622	−	0.171363i
$870$	0.689012	+	1.89305i	0.0233597	+	0.0641803i
$871$	−3.94588	−	56.4287i	−0.133701	−	1.91201i
$872$	−7.17242	−	1.00802i	−0.242889	−	0.0341358i
$873$	7.60758	−	2.47185i	0.257477	−	0.0836595i
$874$	7.81688	+	21.0782i	0.264410	+	0.712981i
$875$	−6.67537	−	9.18785i	−0.225669	−	0.310606i
$876$	−12.6166	+	6.70835i	−0.426274	+	0.226654i
$877$	−0.171098	−	0.423482i	−0.00577756	−	0.0143000i	0.924268	−	0.381745i	$-0.124677\pi$
$877$	−0.171098	−	0.423482i	−0.00577756	−	0.0143000i	−0.930045	+	0.367445i	$0.880232\pi$
$878$	0.0359901	+	0.0103200i	0.00121461	+	0.000348283i
$879$	2.98881	−	8.21169i	0.100810	−	0.276973i
$880$	0.0897232	+	1.17545i	0.00302457	+	0.0396246i
$881$	−21.5221	+	37.2773i	−0.725097	+	1.25590i	0.233838	+	0.972276i	$0.424872\pi$
$881$	−21.5221	+	37.2773i	−0.725097	+	1.25590i	−0.958934	+	0.283628i	$0.908462\pi$
$882$	−0.736157	+	7.00406i	−0.0247877	+	0.235839i
$883$	−4.05775	−	2.15755i	−0.136554	−	0.0726072i	0.399789	−	0.916607i	$-0.369084\pi$
$883$	−4.05775	−	2.15755i	−0.136554	−	0.0726072i	−0.536343	+	0.844000i	$0.680195\pi$
$884$	−2.39184	−	17.0188i	−0.0804462	−	0.572405i
$885$	−4.21982	−	1.87878i	−0.141848	−	0.0631546i
$886$	−0.980000	−	9.32407i	−0.0329237	−	0.313248i
$887$	11.8679	−	29.3742i	0.398486	−	0.986289i	−0.585918	−	0.810370i	$-0.699266\pi$
$887$	11.8679	−	29.3742i	0.398486	−	0.986289i	0.984405	−	0.175918i	$-0.0562895\pi$
$888$	1.72189	−	2.20392i	0.0577830	−	0.0739588i
$889$	−11.4069	+	39.7807i	−0.382576	+	1.33420i
$890$	0.479794	+	0.571797i	0.0160827	+	0.0191667i
$891$	−0.0253764	−	3.98387i	−0.000850141	−	0.133465i
$892$			20.2307i			0.677373i
$893$	34.1160	+	0.984320i	1.14165	+	0.0329390i
$894$	2.53679	−	7.80744i	0.0848430	−	0.261120i
$895$	3.24486	+	6.10270i	0.108464	+	0.203991i
$896$	−3.13987	−	0.782857i	−0.104896	−	0.0261534i
$897$	−18.4868	−	12.4695i	−0.617258	−	0.416346i
$898$	−14.5579	−	0.508374i	−0.485804	−	0.0169647i
$899$	−19.3579	−	30.9791i	−0.645621	−	1.03321i
$900$	−9.03207	+	4.02134i	−0.301069	+	0.134045i
$901$	0.659676	+	1.14259i	0.0219770	+	0.0380653i
$902$	4.01863	+	0.114710i	0.133806	+	0.00381944i
$903$	−36.1126	−	6.36763i	−1.20175	−	0.211902i
$904$	9.40007	+	0.987987i	0.312642	+	0.0328600i
$905$	2.36005	−	2.12500i	0.0784508	−	0.0706374i
$906$	−5.34420	−	2.15920i	−0.177549	−	0.0717346i
$907$	−6.70698	−	23.3900i	−0.222702	−	0.776653i	−0.990684	−	0.136182i	$-0.956517\pi$
$907$	−6.70698	−	23.3900i	−0.222702	−	0.776653i	0.767982	−	0.640471i	$-0.221261\pi$
$908$	8.08688	−	11.9893i	0.268372	−	0.397879i
$909$	15.9904	−	25.5900i	0.530369	−	0.848767i
$910$	−0.702248	+	4.99676i	−0.0232793	+	0.165641i
$911$	16.2414	−	22.3544i	0.538103	−	0.740635i	−0.450236	−	0.892910i	$-0.648660\pi$
$911$	16.2414	−	22.3544i	0.538103	−	0.740635i	0.988338	+	0.152275i	$0.0486600\pi$
$912$	2.42387	+	3.54696i	0.0802624	+	0.117452i
$913$	−4.90842	+	0.721745i	−0.162445	+	0.0238863i
$914$	−7.11641	+	1.25481i	−0.235390	+	0.0415056i
$915$	−2.88957	+	0.202059i	−0.0955263	+	0.00667985i
$916$	−0.555954	−	15.9204i	−0.0183692	−	0.526026i
$917$	1.66024	−	47.5430i	0.0548259	−	1.57001i
$918$	−19.3688	−	1.35440i	−0.639266	−	0.0447018i
$919$	−26.2627	+	2.76032i	−0.866327	+	0.0910546i	−0.527256	−	0.849706i	$-0.676779\pi$
$919$	−26.2627	+	2.76032i	−0.866327	+	0.0910546i	−0.339070	+	0.940761i	$0.610113\pi$
$920$	−1.22665	+	1.36233i	−0.0404414	+	0.0449148i
$921$	−1.11320	+	2.09362i	−0.0366811	+	0.0689871i
$922$	20.1134	+	20.8280i	0.662399	+	0.685934i
$923$	28.1307	−	16.2413i	0.925933	−	0.534588i
$924$	−6.74755	+	8.14623i	−0.221978	+	0.267991i
$925$	8.88984	−	10.5945i	0.292296	−	0.348345i
$926$	−15.9705	−	23.6773i	−0.524824	−	0.778083i
$927$	−23.4980	+	0.820568i	−0.771775	+	0.0269510i
$928$	4.87676	+	3.04734i	0.160088	+	0.100034i
$929$	33.9465	+	32.7818i	1.11375	+	1.07554i	0.996598	+	0.0824211i	$0.0262653\pi$
$929$	33.9465	+	32.7818i	1.11375	+	1.07554i	0.117152	+	0.993114i	$0.462624\pi$
$930$	1.80036	−	1.30804i	0.0590360	−	0.0428922i
$931$	15.1198	−	0.619789i	0.495531	−	0.0203128i
$932$	−13.5794	−	4.41222i	−0.444809	−	0.144527i
$933$	−6.22358	−	3.03544i	−0.203751	−	0.0993760i
$934$	−13.8940	+	11.6584i	−0.454625	+	0.381475i
$935$	−1.99807	+	4.16376i	−0.0653439	+	0.136169i
$936$	8.36267	+	3.04376i	0.273342	+	0.0994885i
$937$	−4.49583	+	1.12094i	−0.146872	+	0.0366194i	−0.314664	−	0.949203i	$-0.601892\pi$
$937$	−4.49583	+	1.12094i	−0.146872	+	0.0366194i	0.167792	+	0.985822i	$0.446336\pi$
$938$	−27.9203	−	31.0086i	−0.911630	−	1.01247i
$939$	1.04030	+	0.936690i	0.0339489	+	0.0305677i
$940$	1.22004	+	2.50146i	0.0397934	+	0.0815885i
$941$	1.20615	+	2.47298i	0.0393195	+	0.0806170i	0.917549	−	0.397622i	$-0.130164\pi$
$941$	1.20615	+	2.47298i	0.0393195	+	0.0806170i	−0.878230	+	0.478239i	$0.841275\pi$
$942$	−8.46301	−	7.62013i	−0.275740	−	0.248277i
$943$	4.18319	+	4.64591i	0.136223	+	0.151292i
$944$	−12.7939	+	3.18988i	−0.416406	+	0.103822i
$945$	5.35681	+	1.94972i	0.174257	+	0.0634244i
$946$	27.5989	+	26.3143i	0.897319	+	0.855552i
$947$	−13.3591	+	11.2097i	−0.434114	+	0.364265i	−0.833501	−	0.552517i	$-0.813667\pi$
$947$	−13.3591	+	11.2097i	−0.434114	+	0.364265i	0.399387	+	0.916782i	$0.369223\pi$
$948$	12.1704	+	5.93590i	0.395276	+	0.192789i
$949$	60.4890	+	19.6541i	1.96356	+	0.637998i
$950$	11.3665	+	17.9472i	0.368778	+	0.582283i
$951$	8.66908	−	6.29846i	0.281114	−	0.204241i
$952$	−9.11929	−	8.80639i	−0.295558	−	0.285417i
$953$	13.1457	+	8.21432i	0.425830	+	0.266088i	0.725861	−	0.687841i	$-0.241442\pi$
$953$	13.1457	+	8.21432i	0.425830	+	0.266088i	−0.300031	+	0.953929i	$0.596997\pi$
$954$	−0.682777	+	0.0238431i	−0.0221057	+	0.000771949i
$955$	2.50665	+	3.71626i	0.0811133	+	0.120255i
$956$	−0.282355	+	0.336498i	−0.00913203	+	0.0108831i
$957$	15.8774	−	10.0625i	0.513244	−	0.325275i
$958$	6.38481	−	3.68627i	0.206284	−	0.119098i
$959$	13.2571	+	13.7281i	0.428095	+	0.443305i
$960$	−0.164465	+	0.309314i	−0.00530809	+	0.00998306i
$961$	−6.25821	+	6.95045i	−0.201878	+	0.224208i
$962$	−12.3806	+	1.30126i	−0.399168	+	0.0419542i
$963$	33.5679	+	2.34729i	1.08171	+	0.0756405i
$964$	−0.660430	+	18.9122i	−0.0212710	+	0.609122i
$965$	0.222824	+	6.38086i	0.00717297	+	0.205407i
$966$	−16.4089	+	1.14742i	−0.527948	+	0.0369177i
$967$	49.8780	−	8.79484i	1.60397	−	0.282823i	0.701205	−	0.712960i	$-0.252646\pi$
$967$	49.8780	−	8.79484i	1.60397	−	0.282823i	0.902764	+	0.430137i	$0.141535\pi$
$968$	10.5344	−	3.16647i	0.338588	−	0.101774i
$969$	1.27578	+	16.7818i	0.0409838	+	0.539109i
$970$	0.823811	−	1.13388i	0.0264510	−	0.0364067i
$971$	5.18897	−	36.9215i	0.166522	−	1.18487i	−0.710246	−	0.703953i	$-0.751416\pi$
$971$	5.18897	−	36.9215i	0.166522	−	1.18487i	0.876768	−	0.480913i	$-0.159695\pi$
$972$	8.50641	−	13.6131i	0.272843	−	0.436640i
$973$	−29.1436	+	43.2072i	−0.934302	+	1.38516i
$974$	−1.97653	−	6.89299i	−0.0633322	−	0.220866i
$975$	−19.5376	−	7.89370i	−0.625704	−	0.252801i
$976$	−6.14472	+	5.53273i	−0.196688	+	0.177098i
$977$	21.7065	+	2.28144i	0.694452	+	0.0729898i	0.445176	−	0.895443i	$-0.353141\pi$
$977$	21.7065	+	2.28144i	0.694452	+	0.0729898i	0.249275	+	0.968433i	$0.419808\pi$
$978$	9.27834	+	1.63602i	0.296689	+	0.0523142i
$979$	4.25295	−	5.51559i	0.135925	−	0.176279i
$980$	0.616985	+	1.06865i	0.0197089	+	0.0341368i
$981$	13.4229	−	5.97624i	0.428559	−	0.190807i
$982$	16.8942	+	27.0364i	0.539115	+	0.862765i
$983$	12.5034	+	0.436629i	0.398797	+	0.0139263i	0.233596	−	0.972334i	$-0.424951\pi$
$983$	12.5034	+	0.436629i	0.398797	+	0.0139263i	0.165201	+	0.986260i	$0.447173\pi$
$984$	0.990435	+	0.668057i	0.0315739	+	0.0212969i
$985$	−8.02011	−	1.99964i	−0.255542	−	0.0637138i
$986$	10.5765	+	19.8914i	0.336823	+	0.633472i
$987$	−7.71692	+	23.7502i	−0.245632	+	0.755979i
$988$	3.86223	−	18.7279i	0.122874	−	0.595815i
$989$			59.2988i			1.88559i
$990$	−1.41798	−	1.92577i	−0.0450664	−	0.0612049i
$991$	−20.7518	−	24.7310i	−0.659202	−	0.785606i	0.328069	−	0.944654i	$-0.393602\pi$
$991$	−20.7518	−	24.7310i	−0.659202	−	0.785606i	−0.987271	+	0.159048i	$0.949158\pi$
$992$	1.75095	−	6.10630i	0.0555928	−	0.193875i
$993$	−21.2356	+	27.1804i	−0.673893	+	0.862543i
$994$	8.97585	−	22.2160i	0.284697	−	0.704649i
$995$	−0.601222	−	5.72025i	−0.0190600	−	0.181344i
$996$	−1.34683	−	0.599648i	−0.0426760	−	0.0190006i
$997$	1.41742	+	10.0855i	0.0448901	+	0.319409i	0.999750	+	0.0223535i	$0.00711592\pi$
$997$	1.41742	+	10.0855i	0.0448901	+	0.319409i	−0.954860	+	0.297056i	$0.903995\pi$
$998$	18.5277	+	9.85136i	0.586485	+	0.311839i
$999$	−1.47011	+	13.9871i	−0.0465121	+	0.442533i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.v.a.29.4	✓	240
11.8	odd	10		418.2.v.b.371.7	yes	240
19.2	odd	18		418.2.v.b.249.7	yes	240
209.173	even	90	inner	418.2.v.a.173.4	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.v.a.29.4	✓	240	1.1	even	1	trivial
418.2.v.a.173.4	yes	240	209.173	even	90	inner
418.2.v.b.249.7	yes	240	19.2	odd	18
418.2.v.b.371.7	yes	240	11.8	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.v (of order \(90\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.438371 + 0.898794i) q^{2} +(-0.913816 + 0.369206i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(0.341675 - 0.0979736i) q^{5} +(0.0687508 - 0.983182i) q^{6} +(-0.672800 + 3.16528i) q^{7} +(0.978148 - 0.207912i) q^{8} +(-1.45927 + 1.40920i) q^{9} +O(q^{10})\)	\(q+(-0.438371 + 0.898794i) q^{2} +(-0.913816 + 0.369206i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(0.341675 - 0.0979736i) q^{5} +(0.0687508 - 0.983182i) q^{6} +(-0.672800 + 3.16528i) q^{7} +(0.978148 - 0.207912i) q^{8} +(-1.45927 + 1.40920i) q^{9} +(-0.0617222 + 0.350044i) q^{10} +(3.31380 - 0.136859i) q^{11} +(0.853540 + 0.492791i) q^{12} +(-1.06129 - 4.25658i) q^{13} +(-2.54999 - 1.99227i) q^{14} +(-0.276055 + 0.215678i) q^{15} +(-0.241922 + 0.970296i) q^{16} +(-2.72139 + 2.81808i) q^{17} +(-0.626880 - 1.92934i) q^{18} +(-3.90610 + 1.93453i) q^{19} +(-0.287560 - 0.208925i) q^{20} +(-0.553822 - 3.14088i) q^{21} +(-1.32967 + 3.03842i) q^{22} +(-4.84646 + 1.76397i) q^{23} +(-0.817085 + 0.551131i) q^{24} +(-4.13310 + 2.58265i) q^{25} +(4.29103 + 0.912086i) q^{26} +(2.01584 - 4.52765i) q^{27} +(2.90849 - 1.41856i) q^{28} +(-5.69461 + 0.800325i) q^{29} +(-0.0728355 - 0.342664i) q^{30} +(2.58375 + 5.80319i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-2.97768 + 1.34854i) q^{33} +(-1.33990 - 3.68134i) q^{34} +(0.0802348 + 1.14741i) q^{35} +(2.00888 + 0.282330i) q^{36} +(-2.69884 + 0.876907i) q^{37} +(-0.0264252 - 4.35882i) q^{38} +(2.54138 + 3.49790i) q^{39} +(0.313838 - 0.166871i) q^{40} +(-0.454082 - 1.12389i) q^{41} +(3.06579 + 0.879100i) q^{42} +(3.93241 - 10.8042i) q^{43} +(-2.14803 - 2.52705i) q^{44} +(-0.360532 + 0.624459i) q^{45} +(0.539105 - 5.12924i) q^{46} +(-6.91348 - 3.67596i) q^{47} +(-0.137167 - 0.975991i) q^{48} +(-3.17149 - 1.41204i) q^{49} +(-0.509436 - 4.84696i) q^{50} +(1.44640 - 3.57996i) q^{51} +(-2.70084 + 3.45692i) q^{52} +(0.0928281 - 0.323730i) q^{53} +(3.18574 + 3.79661i) q^{54} +(1.11883 - 0.371426i) q^{55} +3.23599i q^{56} +(2.85521 - 3.20996i) q^{57} +(1.77702 - 5.46912i) q^{58} +(6.19026 + 11.6422i) q^{59} +(0.339913 + 0.0847499i) q^{60} +(6.85493 + 4.62371i) q^{61} +(-6.34851 - 0.221695i) q^{62} +(-3.47872 - 5.56711i) q^{63} +(0.913545 - 0.406737i) q^{64} +(-0.779647 - 1.35039i) q^{65} +(0.0932690 - 3.26748i) q^{66} +(12.6985 + 2.23909i) q^{67} +(3.89613 + 0.409500i) q^{68} +(3.77750 - 3.40128i) q^{69} +(-1.06646 - 0.430877i) q^{70} +(2.04094 + 7.11762i) q^{71} +(-1.13439 + 1.68181i) q^{72} +(-7.68286 + 12.2951i) q^{73} +(0.394936 - 2.81012i) q^{74} +(2.82336 - 3.88603i) q^{75} +(3.92926 + 1.88703i) q^{76} +(-1.79633 + 10.5812i) q^{77} +(-4.25796 + 0.750793i) q^{78} +(13.7054 - 0.958376i) q^{79} +(0.0124048 + 0.355227i) q^{80} +(0.0419215 - 1.20048i) q^{81} +(1.20920 + 0.0845557i) q^{82} +(-1.48766 + 0.156360i) q^{83} +(-2.13408 + 2.37014i) q^{84} +(-0.653732 + 1.22949i) q^{85} +(7.98691 + 8.27069i) q^{86} +(4.90834 - 2.83383i) q^{87} +(3.21293 - 0.822846i) q^{88} +(1.34985 - 1.60868i) q^{89} +(-0.403213 - 0.597788i) q^{90} +(14.1873 - 0.495431i) q^{91} +(4.37380 + 2.73305i) q^{92} +(-4.50364 - 4.34911i) q^{93} +(6.33460 - 4.60236i) q^{94} +(-1.14508 + 1.04367i) q^{95} +(0.937345 + 0.304562i) q^{96} +(-3.54404 - 1.72854i) q^{97} +(2.65942 - 2.23152i) q^{98} +(-4.64287 + 4.86953i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9}+O(q^{10}) \) 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9	\( 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9} - 3 q^{11} - 6 q^{13} - 18 q^{14} + 21 q^{15} + 21 q^{17} - 60 q^{18} + 45 q^{19} + 12 q^{20} + 48 q^{21} - 12 q^{22} + 12 q^{24} - 18 q^{25} - 96 q^{26} - 9 q^{27} - 6 q^{28} + 18 q^{29} + 9 q^{31} + 87 q^{33} - 24 q^{34} - 36 q^{35} - 12 q^{36} - 36 q^{38} + 60 q^{41} - 6 q^{42} - 12 q^{43} + 18 q^{44} + 48 q^{45} + 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} - 21 q^{50} - 75 q^{51} + 3 q^{52} - 39 q^{53} + 27 q^{54} - 126 q^{55} - 90 q^{57} - 24 q^{58} + 69 q^{59} - 42 q^{60} + 66 q^{61} - 45 q^{62} - 9 q^{63} + 30 q^{64} - 12 q^{66} - 9 q^{67} + 12 q^{68} - 54 q^{69} + 9 q^{70} + 48 q^{71} + 6 q^{72} - 12 q^{74} + 72 q^{77} - 36 q^{79} - 27 q^{81} + 45 q^{82} + 36 q^{83} + 36 q^{84} - 210 q^{85} + 3 q^{86} + 216 q^{87} + 3 q^{88} + 18 q^{89} - 96 q^{90} - 108 q^{91} - 30 q^{92} + 147 q^{93} - 18 q^{94} + 66 q^{95} - 9 q^{97} - 12 q^{98} - 42 q^{99}+O(q^{100}) \) 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9 - 3 * q^11 - 6 * q^13 - 18 * q^14 + 21 * q^15 + 21 * q^17 - 60 * q^18 + 45 * q^19 + 12 * q^20 + 48 * q^21 - 12 * q^22 + 12 * q^24 - 18 * q^25 - 96 * q^26 - 9 * q^27 - 6 * q^28 + 18 * q^29 + 9 * q^31 + 87 * q^33 - 24 * q^34 - 36 * q^35 - 12 * q^36 - 36 * q^38 + 60 * q^41 - 6 * q^42 - 12 * q^43 + 18 * q^44 + 48 * q^45 + 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 - 21 * q^50 - 75 * q^51 + 3 * q^52 - 39 * q^53 + 27 * q^54 - 126 * q^55 - 90 * q^57 - 24 * q^58 + 69 * q^59 - 42 * q^60 + 66 * q^61 - 45 * q^62 - 9 * q^63 + 30 * q^64 - 12 * q^66 - 9 * q^67 + 12 * q^68 - 54 * q^69 + 9 * q^70 + 48 * q^71 + 6 * q^72 - 12 * q^74 + 72 * q^77 - 36 * q^79 - 27 * q^81 + 45 * q^82 + 36 * q^83 + 36 * q^84 - 210 * q^85 + 3 * q^86 + 216 * q^87 + 3 * q^88 + 18 * q^89 - 96 * q^90 - 108 * q^91 - 30 * q^92 + 147 * q^93 - 18 * q^94 + 66 * q^95 - 9 * q^97 - 12 * q^98 - 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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