LMFDB - Embedded newform 429.2.bi.a.5.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(5,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 8, 15]))

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

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

chi := DirichletCharacter("429.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bi (of order $20$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			5.8
Character	$\chi$	$=$	429.5
Dual form			429.2.bi.a.86.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.942586 + 1.84993i) q^{2} +(-1.52624 - 0.818902i) q^{3} +(-1.35820 - 1.86940i) q^{4} +(-2.61854 + 1.33421i) q^{5} +(2.95352 - 2.05155i) q^{6} +(-3.28014 - 0.519524i) q^{7} +(0.637161 - 0.100916i) q^{8} +(1.65880 + 2.49968i) q^{9} +O(q^{10})$	\(q+(-0.942586 + 1.84993i) q^{2} +(-1.52624 - 0.818902i) q^{3} +(-1.35820 - 1.86940i) q^{4} +(-2.61854 + 1.33421i) q^{5} +(2.95352 - 2.05155i) q^{6} +(-3.28014 - 0.519524i) q^{7} +(0.637161 - 0.100916i) q^{8} +(1.65880 + 2.49968i) q^{9} -6.10173i q^{10} +(1.08198 + 3.13517i) q^{11} +(0.542079 + 3.96539i) q^{12} +(-3.60016 - 0.197042i) q^{13} +(4.05290 - 5.57834i) q^{14} +(5.08910 + 0.108002i) q^{15} +(1.01421 - 3.12141i) q^{16} +(0.844836 - 2.60014i) q^{17} +(-6.18779 + 0.712502i) q^{18} +(7.55903 - 1.19723i) q^{19} +(6.05069 + 3.08298i) q^{20} +(4.58084 + 3.47903i) q^{21} +(-6.81971 - 0.953577i) q^{22} +1.41869 q^{23} +(-1.05510 - 0.367750i) q^{24} +(2.13770 - 2.94229i) q^{25} +(3.75798 - 6.47432i) q^{26} +(-0.484733 - 5.17349i) q^{27} +(3.48389 + 6.83753i) q^{28} +(-1.54550 - 2.12719i) q^{29} +(-4.99671 + 9.31268i) q^{30} +(-3.06267 - 1.56051i) q^{31} +(5.73072 + 5.73072i) q^{32} +(0.916034 - 5.67106i) q^{33} +(4.01374 + 4.01374i) q^{34} +(9.28234 - 3.01602i) q^{35} +(2.41992 - 6.49603i) q^{36} +(5.07895 + 0.804426i) q^{37} +(-4.91024 + 15.1122i) q^{38} +(5.33335 + 3.24891i) q^{39} +(-1.53379 + 1.11436i) q^{40} +(-0.927946 - 5.85882i) q^{41} +(-10.7538 + 5.19494i) q^{42} +4.98368i q^{43} +(4.39135 - 6.28086i) q^{44} +(-7.67873 - 4.33231i) q^{45} +(-1.33724 + 2.62448i) q^{46} +(-4.54047 + 0.719139i) q^{47} +(-4.10404 + 3.93347i) q^{48} +(3.83204 + 1.24510i) q^{49} +(3.42807 + 6.72797i) q^{50} +(-3.41868 + 3.27659i) q^{51} +(4.52139 + 6.99778i) q^{52} +(-4.61943 + 1.50094i) q^{53} +(10.0275 + 3.97974i) q^{54} +(-7.01621 - 6.76598i) q^{55} -2.14241 q^{56} +(-12.5173 - 4.36284i) q^{57} +(5.39193 - 0.853997i) q^{58} +(-2.16828 + 13.6900i) q^{59} +(-6.71013 - 9.66027i) q^{60} +(4.23812 - 13.0436i) q^{61} +(5.77366 - 4.19481i) q^{62} +(-4.14246 - 9.06108i) q^{63} +(-9.76031 + 3.17132i) q^{64} +(9.69007 - 4.28742i) q^{65} +(9.62762 + 7.04006i) q^{66} +(5.62946 - 5.62946i) q^{67} +(-6.00816 + 1.95217i) q^{68} +(-2.16526 - 1.16177i) q^{69} +(-3.16999 + 20.0145i) q^{70} +(-5.65782 + 2.88280i) q^{71} +(1.30918 + 1.42530i) q^{72} +(-1.46250 - 0.231638i) q^{73} +(-6.27548 + 8.63745i) q^{74} +(-5.67209 + 2.74007i) q^{75} +(-12.5048 - 12.5048i) q^{76} +(-1.92027 - 10.8459i) q^{77} +(-11.0374 + 6.80393i) q^{78} +(-0.462800 - 1.42435i) q^{79} +(1.50888 + 9.52669i) q^{80} +(-3.49677 + 8.29293i) q^{81} +(11.7131 + 3.80581i) q^{82} +(5.20267 - 2.65089i) q^{83} +(0.282014 - 13.2887i) q^{84} +(1.25690 + 7.93575i) q^{85} +(-9.21946 - 4.69755i) q^{86} +(0.616832 + 4.51221i) q^{87} +(1.00579 + 1.88842i) q^{88} +(1.80567 - 1.80567i) q^{89} +(15.2523 - 10.1215i) q^{90} +(11.7067 + 2.51669i) q^{91} +(-1.92687 - 2.65211i) q^{92} +(3.39646 + 4.88973i) q^{93} +(2.94942 - 9.07739i) q^{94} +(-18.1963 + 13.2204i) q^{95} +(-4.05354 - 13.4393i) q^{96} +(-1.24109 - 0.632366i) q^{97} +(-5.91538 + 5.91538i) q^{98} +(-6.04212 + 7.90524i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) $ 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9	$ 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9} - 20 q^{13} - 30 q^{15} + 32 q^{16} + 2 q^{18} - 4 q^{19} - 12 q^{21} - 24 q^{22} - 78 q^{24} - 36 q^{27} - 84 q^{28} - 28 q^{31} - 44 q^{33} - 24 q^{34} - 12 q^{37} + 54 q^{39} + 88 q^{40} - 56 q^{42} + 8 q^{45} - 92 q^{46} + 40 q^{48} - 44 q^{52} - 176 q^{54} - 72 q^{55} - 6 q^{57} - 4 q^{58} + 12 q^{60} - 48 q^{61} - 46 q^{63} + 204 q^{66} - 64 q^{67} + 56 q^{70} - 66 q^{72} - 12 q^{73} - 104 q^{76} - 92 q^{78} + 104 q^{79} + 124 q^{81} + 16 q^{84} - 12 q^{85} - 24 q^{87} - 84 q^{91} - 124 q^{93} + 328 q^{94} - 152 q^{96} + 52 q^{97} - 142 q^{99}+O(q^{100}) $ 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9 - 20 * q^13 - 30 * q^15 + 32 * q^16 + 2 * q^18 - 4 * q^19 - 12 * q^21 - 24 * q^22 - 78 * q^24 - 36 * q^27 - 84 * q^28 - 28 * q^31 - 44 * q^33 - 24 * q^34 - 12 * q^37 + 54 * q^39 + 88 * q^40 - 56 * q^42 + 8 * q^45 - 92 * q^46 + 40 * q^48 - 44 * q^52 - 176 * q^54 - 72 * q^55 - 6 * q^57 - 4 * q^58 + 12 * q^60 - 48 * q^61 - 46 * q^63 + 204 * q^66 - 64 * q^67 + 56 * q^70 - 66 * q^72 - 12 * q^73 - 104 * q^76 - 92 * q^78 + 104 * q^79 + 124 * q^81 + 16 * q^84 - 12 * q^85 - 24 * q^87 - 84 * q^91 - 124 * q^93 + 328 * q^94 - 152 * q^96 + 52 * q^97 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{5}\right)$	$-1$

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 $

$2$	−0.942586	+	1.84993i	−0.666509	+	1.30810i	0.271818	+	0.962349i	$0.412375\pi$
$2$	−0.942586	+	1.84993i	−0.666509	+	1.30810i	−0.938327	+	0.345749i	$0.887625\pi$
$3$	−1.52624	−	0.818902i	−0.881173	−	0.472793i
$3$	−1.52624	−	0.818902i	−0.881173	−	0.472793i
$4$	−1.35820	−	1.86940i	−0.679101	−	0.934702i
$5$	−2.61854	+	1.33421i	−1.17105	+	0.596678i	−0.927724	−	0.373267i	$-0.878237\pi$
$5$	−2.61854	+	1.33421i	−1.17105	+	0.596678i	−0.243323	+	0.969945i	$0.578237\pi$
$6$	2.95352	−	2.05155i	1.20577	−	0.837540i
$7$	−3.28014	−	0.519524i	−1.23978	−	0.196361i	−0.498101	−	0.867119i	$-0.665969\pi$
$7$	−3.28014	−	0.519524i	−1.23978	−	0.196361i	−0.741677	+	0.670758i	$0.765969\pi$
$8$	0.637161	−	0.100916i	0.225270	−	0.0356793i
$9$	1.65880	+	2.49968i	0.552933	+	0.833226i
$10$		−	6.10173i		−	1.92954i
$11$	1.08198	+	3.13517i	0.326230	+	0.945290i
$11$	1.08198	+	3.13517i	0.326230	+	0.945290i
$12$	0.542079	+	3.96539i	0.156485	+	1.14471i
$13$	−3.60016	−	0.197042i	−0.998506	−	0.0546495i
$13$	−3.60016	−	0.197042i	−0.998506	−	0.0546495i
$14$	4.05290	−	5.57834i	1.08318	−	1.49087i
$15$	5.08910	+	0.108002i	1.31400	+	0.0278860i
$16$	1.01421	−	3.12141i	0.253552	−	0.780351i
$17$	0.844836	−	2.60014i	0.204903	−	0.630626i	−0.794815	−	0.606852i	$-0.792432\pi$
$17$	0.844836	−	2.60014i	0.204903	−	0.630626i	0.999717	−	0.0237736i	$-0.00756808\pi$
$18$	−6.18779	+	0.712502i	−1.45848	+	0.167938i
$19$	7.55903	−	1.19723i	1.73416	−	0.274664i	0.792169	−	0.610302i	$-0.208952\pi$
$19$	7.55903	−	1.19723i	1.73416	−	0.274664i	0.941991	+	0.335638i	$0.108952\pi$
$20$	6.05069	+	3.08298i	1.35297	+	0.689375i
$21$	4.58084	+	3.47903i	0.999621	+	0.759187i
$22$	−6.81971	−	0.953577i	−1.45397	−	0.203303i
$23$	1.41869			0.295818			0.147909	−	0.989001i	$-0.452746\pi$
$23$	1.41869			0.295818			0.147909	+	0.989001i	$0.452746\pi$
$24$	−1.05510	−	0.367750i	−0.215371	−	0.0750666i
$25$	2.13770	−	2.94229i	0.427540	−	0.588459i
$26$	3.75798	−	6.47432i	0.737000	−	1.26972i
$27$	−0.484733	−	5.17349i	−0.0932868	−	0.995639i
$28$	3.48389	+	6.83753i	0.658394	+	1.29217i
$29$	−1.54550	−	2.12719i	−0.286992	−	0.395010i	0.641042	−	0.767505i	$-0.278502\pi$
$29$	−1.54550	−	2.12719i	−0.286992	−	0.395010i	−0.928034	+	0.372495i	$0.878502\pi$
$30$	−4.99671	+	9.31268i	−0.912271	+	1.70026i
$31$	−3.06267	−	1.56051i	−0.550071	−	0.280275i	0.156785	−	0.987633i	$-0.449887\pi$
$31$	−3.06267	−	1.56051i	−0.550071	−	0.280275i	−0.706856	+	0.707357i	$0.749887\pi$
$32$	5.73072	+	5.73072i	1.01306	+	1.01306i
$33$	0.916034	−	5.67106i	0.159461	−	0.987204i
$34$	4.01374	+	4.01374i	0.688351	+	0.688351i
$35$	9.28234	−	3.01602i	1.56900	−	0.509800i
$36$	2.41992	−	6.49603i	0.403320	−	1.08267i
$37$	5.07895	+	0.804426i	0.834974	+	0.132247i	0.559259	−	0.828993i	$-0.311086\pi$
$37$	5.07895	+	0.804426i	0.834974	+	0.132247i	0.275714	+	0.961240i	$0.411086\pi$
$38$	−4.91024	+	15.1122i	−0.796546	+	2.45152i
$39$	5.33335	+	3.24891i	0.854019	+	0.520242i
$40$	−1.53379	+	1.11436i	−0.242513	+	0.176196i
$41$	−0.927946	−	5.85882i	−0.144921	−	0.914994i	−0.947803	−	0.318856i	$-0.896701\pi$
$41$	−0.927946	−	5.85882i	−0.144921	−	0.914994i	0.802882	−	0.596138i	$-0.203299\pi$
$42$	−10.7538	+	5.19494i	−1.65935	+	0.801597i
$43$			4.98368i			0.760004i	0.924986	+	0.380002i	$0.124077\pi$
$43$			4.98368i			0.760004i	−0.924986	+	0.380002i	$0.875923\pi$
$44$	4.39135	−	6.28086i	0.662021	−	0.946875i
$45$	−7.67873	−	4.33231i	−1.14468	−	0.645823i
$46$	−1.33724	+	2.62448i	−0.197165	+	0.386959i
$47$	−4.54047	+	0.719139i	−0.662295	+	0.104897i	−0.478528	−	0.878073i	$-0.658829\pi$
$47$	−4.54047	+	0.719139i	−0.662295	+	0.104897i	−0.183767	+	0.982970i	$0.558829\pi$
$48$	−4.10404	+	3.93347i	−0.592368	+	0.567748i
$49$	3.83204	+	1.24510i	0.547434	+	0.177872i
$50$	3.42807	+	6.72797i	0.484802	+	0.951478i
$51$	−3.41868	+	3.27659i	−0.478711	+	0.458814i
$52$	4.52139	+	6.99778i	0.627005	+	0.970417i
$53$	−4.61943	+	1.50094i	−0.634527	+	0.206170i	−0.608580	−	0.793493i	$-0.708260\pi$
$53$	−4.61943	+	1.50094i	−0.634527	+	0.206170i	−0.0259477	+	0.999663i	$0.508260\pi$
$54$	10.0275	+	3.97974i	1.36457	+	0.541574i
$55$	−7.01621	−	6.76598i	−0.946065	−	0.912324i
$56$	−2.14241			−0.286291
$57$	−12.5173	−	4.36284i	−1.65795	−	0.577872i
$58$	5.39193	−	0.853997i	0.707995	−	0.112135i
$59$	−2.16828	+	13.6900i	−0.282285	+	1.78228i	0.284766	+	0.958597i	$0.408084\pi$
$59$	−2.16828	+	13.6900i	−0.282285	+	1.78228i	−0.567051	+	0.823683i	$0.691916\pi$
$60$	−6.71013	−	9.66027i	−0.866273	−	1.24714i
$61$	4.23812	−	13.0436i	0.542636	−	1.67006i	−0.183911	−	0.982943i	$-0.558876\pi$
$61$	4.23812	−	13.0436i	0.542636	−	1.67006i	0.726546	−	0.687118i	$-0.241124\pi$
$62$	5.77366	−	4.19481i	0.733255	−	0.532741i
$63$	−4.14246	−	9.06108i	−0.521901	−	1.14159i
$64$	−9.76031	+	3.17132i	−1.22004	+	0.396415i
$65$	9.69007	−	4.28742i	1.20190	−	0.531789i
$66$	9.62762	+	7.04006i	1.18508	+	0.866571i
$67$	5.62946	−	5.62946i	0.687748	−	0.687748i	−0.273986	−	0.961734i	$-0.588342\pi$
$67$	5.62946	−	5.62946i	0.687748	−	0.687748i	0.961734	+	0.273986i	$0.0883421\pi$
$68$	−6.00816	+	1.95217i	−0.728597	+	0.236735i
$69$	−2.16526	−	1.16177i	−0.260667	−	0.139861i
$70$	−3.16999	+	20.0145i	−0.378886	+	2.39219i
$71$	−5.65782	+	2.88280i	−0.671459	+	0.342126i	−0.756259	−	0.654272i	$-0.772975\pi$
$71$	−5.65782	+	2.88280i	−0.671459	+	0.342126i	0.0847996	+	0.996398i	$0.472975\pi$
$72$	1.30918	+	1.42530i	0.154288	+	0.167973i
$73$	−1.46250	−	0.231638i	−0.171173	−	0.0271111i	0.0702595	−	0.997529i	$-0.477617\pi$
$73$	−1.46250	−	0.231638i	−0.171173	−	0.0271111i	−0.241433	+	0.970418i	$0.577617\pi$
$74$	−6.27548	+	8.63745i	−0.729509	+	1.00408i
$75$	−5.67209	+	2.74007i	−0.654957	+	0.316396i
$76$	−12.5048	−	12.5048i	−1.43440	−	1.43440i
$77$	−1.92027	−	10.8459i	−0.218835	−	1.23601i
$78$	−11.0374	+	6.80393i	−1.24974	+	0.770394i
$79$	−0.462800	−	1.42435i	−0.0520691	−	0.160252i	0.921641	−	0.388044i	$-0.126849\pi$
$79$	−0.462800	−	1.42435i	−0.0520691	−	0.160252i	−0.973710	+	0.227792i	$0.926849\pi$
$80$	1.50888	+	9.52669i	0.168698	+	1.06512i
$81$	−3.49677	+	8.29293i	−0.388530	+	0.921436i
$82$	11.7131	+	3.80581i	1.29349	+	0.420281i
$83$	5.20267	−	2.65089i	0.571067	−	0.290973i	−0.144514	−	0.989503i	$-0.546162\pi$
$83$	5.20267	−	2.65089i	0.571067	−	0.290973i	0.715581	+	0.698530i	$0.246162\pi$
$84$	0.282014	−	13.2887i	0.0307703	−	1.44991i
$85$	1.25690	+	7.93575i	0.136330	+	0.860753i
$86$	−9.21946	−	4.69755i	−0.994160	−	0.506550i
$87$	0.616832	+	4.51221i	0.0661314	+	0.483760i
$88$	1.00579	+	1.88842i	0.107217	+	0.201306i
$89$	1.80567	−	1.80567i	0.191401	−	0.191401i	−0.604900	−	0.796301i	$-0.706787\pi$
$89$	1.80567	−	1.80567i	0.191401	−	0.191401i	0.796301	+	0.604900i	$0.206787\pi$
$90$	15.2523	−	10.1215i	1.60774	−	1.06690i
$91$	11.7067	+	2.51669i	1.22719	+	0.263821i
$92$	−1.92687	−	2.65211i	−0.200890	−	0.276502i
$93$	3.39646	+	4.88973i	0.352196	+	0.507041i
$94$	2.94942	−	9.07739i	0.304210	−	0.936262i
$95$	−18.1963	+	13.2204i	−1.86690	+	1.35638i
$96$	−4.05354	−	13.4393i	−0.413713	−	1.37165i
$97$	−1.24109	−	0.632366i	−0.126013	−	0.0642070i	0.389847	−	0.920880i	$-0.372528\pi$
$97$	−1.24109	−	0.632366i	−0.126013	−	0.0642070i	−0.515861	+	0.856672i	$0.672528\pi$
$98$	−5.91538	+	5.91538i	−0.597544	+	0.597544i
$99$	−6.04212	+	7.90524i	−0.607256	+	0.794506i
$100$	−8.40377			−0.840377
$101$	−5.58308	−	17.1830i	−0.555537	−	1.70977i	−0.694520	−	0.719474i	$-0.744383\pi$
$101$	−5.58308	−	17.1830i	−0.555537	−	1.70977i	0.138982	−	0.990295i	$-0.455617\pi$
$102$	−2.83906	−	9.41278i	−0.281109	−	0.932004i
$103$	−3.38132	−	4.65399i	−0.333171	−	0.458571i	0.609260	−	0.792971i	$-0.291467\pi$
$103$	−3.38132	−	4.65399i	−0.333171	−	0.458571i	−0.942431	+	0.334399i	$0.891467\pi$
$104$	−2.31377	+	0.237768i	−0.226884	+	0.0233151i
$105$	−16.6369	−	2.99817i	−1.62359	−	0.292591i
$106$	1.57757	−	9.96039i	0.153227	−	0.967438i
$107$	10.8159	−	14.8869i	1.04562	−	1.43917i	0.153066	−	0.988216i	$-0.451085\pi$
$107$	10.8159	−	14.8869i	1.04562	−	1.43917i	0.892549	−	0.450950i	$-0.148915\pi$
$108$	−9.01298	+	7.93280i	−0.867275	+	0.763334i
$109$	11.6070	−	11.6070i	1.11175	−	1.11175i	0.118837	−	0.992914i	$-0.462083\pi$
$109$	11.6070	−	11.6070i	1.11175	−	1.11175i	0.992914	−	0.118837i	$-0.0379165\pi$
$110$	19.1300	−	6.60197i	1.82397	−	0.629473i
$111$	−7.09293	−	5.38690i	−0.673231	−	0.511302i
$112$	−4.94839	+	9.71175i	−0.467578	+	0.917674i
$113$	5.32481	−	7.32898i	0.500916	−	0.689452i	−0.481438	−	0.876480i	$-0.659885\pi$
$113$	5.32481	−	7.32898i	0.500916	−	0.689452i	0.982355	+	0.187028i	$0.0598855\pi$
$114$	19.8696	−	19.0437i	1.86096	−	1.78361i
$115$	−3.71491	+	1.89284i	−0.346417	+	0.176508i
$116$	−1.87749	+	5.77832i	−0.174320	+	0.536503i
$117$	−5.47941	−	9.32610i	−0.506572	−	0.862198i
$118$	−23.2817	−	16.9151i	−2.14325	−	1.55716i
$119$	−4.12202	+	8.08991i	−0.377865	+	0.741601i
$120$	3.25348	−	0.444759i	0.297000	−	0.0406008i
$121$	−8.65862	+	6.78442i	−0.787147	+	0.616765i
$122$	20.1349	+	20.1349i	1.82293	+	1.82293i
$123$	−3.38153	+	9.70185i	−0.304902	+	0.874786i
$124$	1.24250	+	7.84485i	0.111580	+	0.704488i
$125$	0.626680	−	3.95670i	0.0560520	−	0.353898i
$126$	20.6670	+	0.877593i	1.84116	+	0.0781822i
$127$	4.13868	+	1.34474i	0.367248	+	0.119326i	0.486827	−	0.873499i	$-0.338154\pi$
$127$	4.13868	+	1.34474i	0.367248	+	0.119326i	−0.119579	+	0.992825i	$0.538154\pi$
$128$	0.797588	−	5.03577i	0.0704975	−	0.445104i
$129$	4.08114	−	7.60628i	0.359325	−	0.669695i
$130$	−1.20229	+	21.9672i	−0.105448	+	1.92665i
$131$		−	7.74621i		−	0.676789i	−0.941004	−	0.338395i	$-0.890116\pi$
$131$		−	7.74621i		−	0.676789i	0.941004	−	0.338395i	$-0.109884\pi$
$132$	−11.8457	+	5.99000i	−1.03103	+	0.521362i
$133$	−25.4167			−2.20391
$134$	5.10786	+	15.7204i	0.441252	+	1.35803i
$135$	8.17183	+	12.9003i	0.703319	+	1.11028i
$136$	0.275900	−	1.74196i	0.0236582	−	0.149372i
$137$	−2.90530	−	5.70196i	−0.248216	−	0.487152i	0.732959	−	0.680273i	$-0.238139\pi$
$137$	−2.90530	−	5.70196i	−0.248216	−	0.487152i	−0.981175	+	0.193122i	$0.938139\pi$
$138$	4.19014	−	2.91052i	0.356689	−	0.247760i
$139$	−1.22605	+	0.890776i	−0.103992	+	0.0755546i	−0.638566	−	0.769567i	$-0.720472\pi$
$139$	−1.22605	+	0.890776i	−0.103992	+	0.0755546i	0.534574	+	0.845122i	$0.320472\pi$
$140$	−18.2454	−	13.2561i	−1.54202	−	1.12034i
$141$	7.51873	+	2.62062i	0.633191	+	0.220696i
$142$		−	13.1839i		−	1.10636i
$143$	−3.27756	−	11.5003i	−0.274083	−	0.961706i
$144$	9.48487	−	2.64260i	0.790406	−	0.220217i
$145$	6.88508	+	3.50812i	0.571775	+	0.291334i
$146$	1.80705	−	2.48719i	0.149552	−	0.205841i
$147$	−4.82898	−	5.03839i	−0.398288	−	0.415559i
$148$	−5.39443	−	10.5872i	−0.443420	−	0.870260i
$149$	−12.1377	+	6.18446i	−0.994358	+	0.506651i	−0.873920	−	0.486070i	$-0.838430\pi$
$149$	−12.1377	+	6.18446i	−0.994358	+	0.506651i	−0.120438	+	0.992721i	$0.538430\pi$
$150$	0.277495	−	13.0757i	0.0226574	−	1.06763i
$151$	3.79870	+	23.9840i	0.309133	+	1.95179i	0.306736	+	0.951795i	$0.400763\pi$
$151$	3.79870	+	23.9840i	0.309133	+	1.95179i	0.00239715	+	0.999997i	$0.499237\pi$
$152$	4.69550	−	1.52566i	0.380855	−	0.123747i
$153$	7.90092	−	2.20129i	0.638751	−	0.177964i
$154$	21.8742	+	6.67087i	1.76268	+	0.537554i
$155$	10.1018			0.811394
$156$	−1.17023	−	14.3828i	−0.0936932	−	1.15155i
$157$	−0.747905	−	0.543385i	−0.0596893	−	0.0433668i	0.557541	−	0.830150i	$-0.311745\pi$
$157$	−0.747905	−	0.543385i	−0.0596893	−	0.0433668i	−0.617230	+	0.786783i	$0.711745\pi$
$158$	3.07118	+	0.486427i	0.244330	+	0.0386981i
$159$	8.27947	+	1.49206i	0.656605	+	0.118328i
$160$	−22.6521	−	7.36012i	−1.79081	−	0.581868i
$161$	−4.65352	−	0.737045i	−0.366749	−	0.0580873i
$162$	−12.0453	−	14.2856i	−0.946370	−	1.12238i
$163$	−0.249633	+	0.489932i	−0.0195527	+	0.0383744i	−0.900576	−	0.434698i	$-0.856855\pi$
$163$	−0.249633	+	0.489932i	−0.0195527	+	0.0383744i	0.881024	+	0.473072i	$0.156855\pi$
$164$	−9.69216	+	9.69216i	−0.756831	+	0.756831i
$165$	5.16772	+	16.0721i	0.402307	+	1.25121i
$166$			12.1233i			0.940948i
$167$	−1.18525	−	0.603916i	−0.0917176	−	0.0467324i	0.407530	−	0.913192i	$-0.366390\pi$
$167$	−1.18525	−	0.603916i	−0.0917176	−	0.0467324i	−0.499248	+	0.866459i	$0.666390\pi$
$168$	3.26982	+	1.75442i	0.252272	+	0.135357i
$169$	12.9223	+	1.41876i	0.994027	+	0.109136i
$170$	−15.8653	−	5.15496i	−1.21682	−	0.395367i
$171$	15.5316	+	16.9092i	1.18773	+	1.29308i
$172$	9.31651	−	6.76884i	0.710377	−	0.516119i
$173$	10.1967	+	7.40834i	0.775242	+	0.563246i	0.903547	−	0.428489i	$-0.140954\pi$
$173$	10.1967	+	7.40834i	0.775242	+	0.563246i	−0.128306	+	0.991735i	$0.540954\pi$
$174$	−8.92870	−	3.11206i	−0.676883	−	0.235924i
$175$	−8.54056	+	8.54056i	−0.645606	+	0.645606i
$176$	10.8835	−	0.197600i	0.820375	−	0.0148946i
$177$	14.5200	−	19.1185i	1.09139	−	1.43704i
$178$	1.63837	+	5.04237i	0.122801	+	0.377942i
$179$	−11.8977	−	8.64417i	−0.889274	−	0.646095i	0.0464145	−	0.998922i	$-0.485220\pi$
$179$	−11.8977	−	8.64417i	−0.889274	−	0.646095i	−0.935689	+	0.352827i	$0.885220\pi$
$180$	2.33043	+	20.2388i	0.173700	+	1.50851i
$181$	21.3244	+	6.92871i	1.58503	+	0.515007i	0.963346	−	0.268263i	$-0.0864496\pi$
$181$	21.3244	+	6.92871i	1.58503	+	0.515007i	0.621682	+	0.783270i	$0.286450\pi$
$182$	−15.6903	+	19.2843i	−1.16304	+	1.42945i
$183$	−17.1498	+	16.4370i	−1.26775	+	1.21506i
$184$	0.903936	−	0.143169i	0.0666390	−	0.0105546i
$185$	−14.3727	+	4.66997i	−1.05670	+	0.343343i
$186$	−12.2471	+	1.67421i	−0.898002	+	0.122759i
$187$	9.06598	−	0.164601i	0.662970	−	0.0120368i
$188$	7.51123	+	7.51123i	0.547812	+	0.547812i
$189$	−1.09776	+	17.2216i	−0.0798503	+	1.25269i
$190$	−7.30518	−	46.1231i	−0.529974	−	3.34612i
$191$	7.88631	+	10.8546i	0.570633	+	0.785409i	0.992630	−	0.121188i	$-0.0386705\pi$
$191$	7.88631	+	10.8546i	0.570633	+	0.785409i	−0.421996	+	0.906598i	$0.638670\pi$
$192$	17.4935	+	3.15255i	1.26249	+	0.227516i
$193$	−8.81329	+	4.49060i	−0.634395	+	0.323240i	−0.741445	−	0.671013i	$-0.765859\pi$
$193$	−8.81329	+	4.49060i	−0.634395	+	0.323240i	0.107051	+	0.994254i	$0.465859\pi$
$194$	2.33967	−	1.69987i	0.167978	−	0.122043i
$195$	−18.3003	−	1.39159i	−1.31051	−	0.0996538i
$196$	−2.87708	−	8.85473i	−0.205505	−	0.632481i
$197$	−14.1279	−	14.1279i	−1.00657	−	1.00657i	−0.999978	−	0.00659021i	$-0.997902\pi$
$197$	−14.1279	−	14.1279i	−1.00657	−	1.00657i	−0.00659021	−	0.999978i	$-0.502098\pi$
$198$	−8.92891	−	18.6289i	−0.634550	−	1.32390i
$199$			9.94489i			0.704975i	0.935817	+	0.352487i	$0.114664\pi$
$199$			9.94489i			0.704975i	−0.935817	+	0.352487i	$0.885336\pi$
$200$	1.06513	−	2.09044i	0.0753164	−	0.147817i
$201$	−13.2019	+	3.98192i	−0.931188	+	0.280863i
$202$	37.0498	+	5.86811i	2.60682	+	0.412879i
$203$	3.96433	+	7.78043i	0.278241	+	0.546079i
$204$	10.7685	+	1.94062i	0.753947	+	0.135871i
$205$	10.2468	+	14.1035i	0.715666	+	0.985030i
$206$	11.7967	−	1.86842i	0.821918	−	0.130179i
$207$	2.35333	+	3.54628i	0.163568	+	0.246483i
$208$	−4.26636	+	11.0377i	−0.295818	+	0.765329i
$209$	11.9323	+	22.4035i	0.825373	+	1.54968i
$210$	21.2281	−	27.9510i	1.46488	−	1.92880i
$211$	−2.31763	−	7.13294i	−0.159553	−	0.491052i	0.839041	−	0.544068i	$-0.183117\pi$
$211$	−2.31763	−	7.13294i	−0.159553	−	0.491052i	−0.998594	+	0.0530158i	$0.983117\pi$
$212$	9.07998	+	6.59699i	0.623616	+	0.453083i
$213$	10.9959	+	0.233357i	0.753427	+	0.0159894i
$214$	17.3447	+	34.0409i	1.18566	+	2.32699i
$215$	−6.64929	−	13.0500i	−0.453478	−	0.890000i
$216$	−0.830943	−	3.24743i	−0.0565385	−	0.220960i
$217$	9.23527	+	6.70982i	0.626931	+	0.455492i
$218$	10.5316	+	32.4128i	0.713287	+	2.19527i
$219$	2.04244	+	1.55118i	0.138015	+	0.104819i
$220$	−3.11892	+	22.3057i	−0.210278	+	1.50385i
$221$	−3.55388	+	9.19445i	−0.239060	+	0.618486i
$222$	16.6511	−	8.04380i	1.11755	−	0.539865i
$223$	−3.62840	+	0.574683i	−0.242976	+	0.0384836i	−0.276735	−	0.960946i	$-0.589252\pi$
$223$	−3.62840	+	0.574683i	−0.242976	+	0.0384836i	0.0337586	+	0.999430i	$0.489252\pi$
$224$	−15.8203	−	21.7748i	−1.05704	−	1.45489i
$225$	10.9008	+	0.462886i	0.726720	+	0.0308591i
$226$	8.53900	+	16.7587i	0.568006	+	1.11477i
$227$	25.7319	+	4.07553i	1.70788	+	0.270502i	0.932548	−	0.361047i	$-0.117580\pi$
$227$	25.7319	+	4.07553i	1.70788	+	0.270502i	0.775336	+	0.631549i	$0.217580\pi$
$228$	8.84508	+	29.3255i	0.585780	+	1.94213i
$229$	2.35429	−	4.62055i	0.155576	−	0.305335i	−0.800042	−	0.599944i	$-0.795190\pi$
$229$	2.35429	−	4.62055i	0.155576	−	0.305335i	0.955618	+	0.294609i	$0.0951895\pi$
$230$		−	8.65648i		−	0.570791i
$231$	−5.95097	+	18.1260i	−0.391545	+	1.19260i
$232$	−1.19940	−	1.19940i	−0.0787444	−	0.0787444i
$233$	1.68424	+	5.18356i	0.110338	+	0.339586i	0.990946	−	0.134259i	$-0.0428655\pi$
$233$	1.68424	+	5.18356i	0.110338	+	0.339586i	−0.880608	+	0.473846i	$0.842865\pi$
$234$	22.4174	−	1.34587i	1.46547	−	0.0879824i
$235$	10.9299	−	7.94104i	0.712988	−	0.518016i
$236$	28.5370	−	14.5403i	1.85760	−	0.946495i
$237$	−0.460062	+	2.55289i	−0.0298842	+	0.165828i
$238$	−11.0804	−	15.2509i	−0.718236	−	0.988568i
$239$	−2.42020	−	15.2805i	−0.156550	−	0.988416i	−0.933428	−	0.358765i	$-0.883198\pi$
$239$	−2.42020	−	15.2805i	−0.156550	−	0.988416i	0.776878	−	0.629651i	$-0.216802\pi$
$240$	5.49852	−	15.7756i	0.354928	−	1.01831i
$241$	−13.9633	−	13.9633i	−0.899458	−	0.899458i	0.0959297	−	0.995388i	$-0.469418\pi$
$241$	−13.9633	−	13.9633i	−0.899458	−	0.899458i	−0.995388	+	0.0959297i	$0.969418\pi$
$242$	−4.38919	−	22.4127i	−0.282148	−	1.44075i
$243$	12.1280	−	9.79346i	0.778011	−	0.628251i
$244$	−30.1399	+	9.79306i	−1.92951	+	0.626937i
$245$	−11.6956	+	1.85240i	−0.747203	+	0.118345i
$246$	−14.7603	−	15.4004i	−0.941085	−	0.981895i
$247$	−27.4496	+	2.82079i	−1.74658	+	0.179482i
$248$	−2.10889	−	0.685221i	−0.133915	−	0.0435116i
$249$	−10.1113	−	0.214584i	−0.640779	−	0.0135987i
$250$	6.72892	+	4.88885i	0.425575	+	0.309198i
$251$	−5.60274	−	17.2435i	−0.353642	−	1.08840i	−0.956793	−	0.290771i	$-0.906088\pi$
$251$	−5.60274	−	17.2435i	−0.353642	−	1.08840i	0.603151	−	0.797627i	$-0.293912\pi$
$252$	−11.3125	+	20.0507i	−0.712622	+	1.26308i
$253$	1.53500	+	4.44785i	0.0965049	+	0.279634i
$254$	−6.38873	+	6.38873i	−0.400865	+	0.400865i
$255$	4.58028	−	13.1411i	0.286828	−	0.822929i
$256$	−8.04120	−	5.84228i	−0.502575	−	0.365142i
$257$	−5.29350	+	3.84595i	−0.330199	+	0.239904i	−0.740515	−	0.672040i	$-0.765418\pi$
$257$	−5.29350	+	3.84595i	−0.330199	+	0.239904i	0.410316	+	0.911943i	$0.365418\pi$
$258$	10.2242	+	14.7194i	0.636534	+	0.916390i
$259$	−16.2418	−	5.27727i	−1.00921	−	0.327913i
$260$	−21.1760	−	12.2915i	−1.31328	−	0.762284i
$261$	2.75363	−	7.39183i	0.170445	−	0.457543i
$262$	14.3299	+	7.30147i	0.885307	+	0.451086i
$263$		−	18.4605i		−	1.13832i	−0.822225	−	0.569162i	$-0.807268\pi$
$263$		−	18.4605i		−	1.13832i	0.822225	−	0.569162i	$-0.192732\pi$
$264$	0.0113588	−	3.70582i	0.000699085	−	0.228077i
$265$	10.0936	−	10.0936i	0.620044	−	0.620044i
$266$	23.9574	−	47.0191i	1.46892	−	2.88292i
$267$	−4.23455	+	1.27722i	−0.259150	+	0.0781644i
$268$	−18.1697	−	2.87779i	−1.10989	−	0.175789i
$269$	13.3001	+	4.32147i	0.810923	+	0.263485i	0.684989	−	0.728554i	$-0.259807\pi$
$269$	13.3001	+	4.32147i	0.810923	+	0.263485i	0.125934	+	0.992039i	$0.459807\pi$
$270$	−31.5672	+	2.95771i	−1.92112	+	0.180000i
$271$	−16.5287	−	2.61788i	−1.00404	−	0.159025i	−0.367302	−	0.930102i	$-0.619719\pi$
$271$	−16.5287	−	2.61788i	−1.00404	−	0.159025i	−0.636742	+	0.771077i	$0.719719\pi$
$272$	−7.25925	−	5.27415i	−0.440156	−	0.319792i
$273$	−15.8062	−	13.4277i	−0.956638	−	0.812681i
$274$	13.2867			0.802680
$275$	11.5376	+	3.51855i	0.695741	+	0.212177i
$276$	0.769044	+	5.62567i	0.0462910	+	0.338625i
$277$	0.266086	−	0.0864567i	0.0159876	−	0.00519468i	−0.301012	−	0.953620i	$-0.597325\pi$
$277$	0.266086	−	0.0864567i	0.0159876	−	0.00519468i	0.317000	+	0.948426i	$0.397325\pi$
$278$	−0.492217	−	3.10774i	−0.0295212	−	0.186390i
$279$	−1.17959	−	10.2443i	−0.0706202	−	0.613307i
$280$	5.60998	−	2.85843i	0.335260	−	0.170824i
$281$	−14.5640	−	28.5835i	−0.868816	−	1.70515i	−0.693272	−	0.720676i	$-0.743832\pi$
$281$	−14.5640	−	28.5835i	−0.868816	−	1.70515i	−0.175544	−	0.984472i	$-0.556168\pi$
$282$	−11.9350	+	11.4390i	−0.710720	+	0.681181i
$283$	−0.278671	+	0.383557i	−0.0165653	+	0.0228001i	−0.817219	−	0.576327i	$-0.804486\pi$
$283$	−0.278671	+	0.383557i	−0.0165653	+	0.0228001i	0.800654	+	0.599127i	$0.204486\pi$
$284$	13.0736	+	6.66132i	0.775774	+	0.395277i
$285$	38.5980	−	5.27645i	2.28635	−	0.312550i
$286$	24.3642	+	4.77680i	1.44068	+	0.282458i
$287$			19.6999i			1.16285i
$288$	−4.81883	+	23.8311i	−0.283952	+	1.40426i
$289$	7.70632	+	5.59897i	0.453313	+	0.329351i
$290$	−12.9796	+	9.43020i	−0.762186	+	0.553761i
$291$	1.37635	+	1.98147i	0.0806830	+	0.116156i
$292$	1.55335	+	3.04862i	0.0909028	+	0.178407i
$293$	−0.959257	+	6.05651i	−0.0560404	+	0.353825i	0.943695	+	0.330817i	$0.107324\pi$
$293$	−0.959257	+	6.05651i	−0.0560404	+	0.353825i	−0.999735	+	0.0230081i	$0.992676\pi$
$294$	13.8724	−	4.18416i	0.809055	−	0.244025i
$295$	−12.5876	−	38.7406i	−0.732878	−	2.25557i
$296$	3.31728			0.192813
$297$	15.6953	−	7.11736i	0.910735	−	0.412991i
$298$		−	28.2833i		−	1.63841i
$299$	−5.10753	−	0.279542i	−0.295376	−	0.0161663i
$300$	12.8261	+	6.88186i	0.740517	+	0.397324i
$301$	2.58914	−	16.3472i	0.149236	−	0.942236i
$302$	−47.9493	−	15.5797i	−2.75917	−	0.896510i
$303$	−5.55005	+	30.7973i	−0.318842	+	1.76926i
$304$	3.92936	−	24.8090i	0.225365	−	1.42290i
$305$	6.30524	+	39.8097i	0.361037	+	2.27950i
$306$	−3.37506	+	16.6910i	−0.192939	+	0.954164i
$307$	0.732961	+	0.732961i	0.0418323	+	0.0418323i	0.727714	−	0.685881i	$-0.240583\pi$
$307$	0.732961	+	0.732961i	0.0418323	+	0.0418323i	−0.685881	+	0.727714i	$0.740583\pi$
$308$	−17.6673	+	18.3207i	−1.00669	+	1.04392i
$309$	1.34954	+	9.87206i	0.0767725	+	0.561602i
$310$	−9.52179	+	18.6876i	−0.540801	+	1.06138i
$311$	12.6671	+	9.20318i	0.718285	+	0.521865i	0.885836	−	0.463999i	$-0.153586\pi$
$311$	12.6671	+	9.20318i	0.718285	+	0.521865i	−0.167551	+	0.985863i	$0.553586\pi$
$312$	3.72607	+	1.53186i	0.210947	+	0.0867244i
$313$	5.23895	−	16.1238i	0.296123	−	0.911373i	−0.686719	−	0.726923i	$-0.740950\pi$
$313$	5.23895	−	16.1238i	0.296123	−	0.911373i	0.982842	−	0.184450i	$-0.0590503\pi$
$314$	1.71019	−	0.871385i	0.0965115	−	0.0491751i
$315$	22.9366	+	18.1999i	1.29233	+	1.02545i
$316$	−2.03411	+	2.79972i	−0.114428	+	0.157496i
$317$	8.15664	−	16.0083i	0.458123	−	0.899116i	−0.540218	−	0.841525i	$-0.681658\pi$
$317$	8.15664	−	16.0083i	0.458123	−	0.899116i	0.998340	−	0.0575908i	$-0.0183419\pi$
$318$	−10.5643	+	13.9100i	−0.592418	+	0.780036i
$319$	4.99692	−	7.14699i	0.279774	−	0.400155i
$320$	21.3266	−	21.3266i	1.19219	−	1.19219i
$321$	−28.6985	+	13.8637i	−1.60180	+	0.773795i
$322$	5.74982	−	7.91395i	0.320425	−	0.441027i
$323$	3.27317	−	20.6660i	0.182124	−	1.14989i
$324$	20.2521	−	4.72660i	1.12512	−	0.262589i
$325$	−8.27583	+	10.1715i	−0.459061	+	0.564215i
$326$	−0.671039	−	0.923605i	−0.0371654	−	0.0511538i
$327$	−27.2201	+	8.21005i	−1.50527	+	0.454017i
$328$	−1.18250	−	3.63937i	−0.0652927	−	0.200950i
$329$	15.2670			0.841696
$330$	−34.6032	−	5.58939i	−1.90485	−	0.307686i
$331$	−19.7601	+	19.7601i	−1.08611	+	1.08611i	−0.0901873	+	0.995925i	$0.528747\pi$
$331$	−19.7601	+	19.7601i	−1.08611	+	1.08611i	−0.995925	+	0.0901873i	$0.971253\pi$
$332$	−12.0219	−	6.12544i	−0.659785	−	0.336177i
$333$	6.41415	+	14.0301i	0.351493	+	0.768845i
$334$	2.23441	−	1.62339i	0.122261	−	0.0888280i
$335$	−7.23007	+	22.2519i	−0.395021	+	1.21575i
$336$	15.5054	−	10.7702i	0.845888	−	0.587562i
$337$	−11.0887	−	15.2623i	−0.604040	−	0.831389i	0.392031	−	0.919952i	$-0.371773\pi$
$337$	−11.0887	−	15.2623i	−0.604040	−	0.831389i	−0.996071	+	0.0885628i	$0.971773\pi$
$338$	−14.8050	+	22.5681i	−0.805288	+	1.22754i
$339$	−14.1286	+	6.82526i	−0.767362	+	0.370697i
$340$	13.1280	−	13.1280i	0.711966	−	0.711966i
$341$	1.57870	−	11.2904i	0.0854915	−	0.611412i
$342$	−45.9206	+	12.7940i	−2.48310	+	0.691823i
$343$	8.79065	+	4.47906i	0.474650	+	0.241846i
$344$	0.502935	+	3.17541i	0.0271164	+	0.171206i
$345$	7.21988	+	0.153222i	0.388705	+	0.00824917i
$346$	−23.3162	+	11.8802i	−1.25349	+	0.638683i
$347$	13.2385	+	4.30143i	0.710678	+	0.230913i	0.641977	−	0.766724i	$-0.278115\pi$
$347$	13.2385	+	4.30143i	0.710678	+	0.230913i	0.0687009	+	0.997637i	$0.478115\pi$
$348$	7.59737	−	7.28160i	0.407262	−	0.390335i
$349$	−4.04580	−	25.5442i	−0.216567	−	1.36735i	−0.821107	−	0.570774i	$-0.806643\pi$
$349$	−4.04580	−	25.5442i	−0.216567	−	1.36735i	0.604541	−	0.796574i	$-0.293357\pi$
$350$	−7.74922	−	23.8497i	−0.414213	−	1.27482i
$351$	0.725722	+	18.7209i	0.0387362	+	0.999249i
$352$	−11.7662	+	24.1673i	−0.627143	+	1.28812i
$353$	−5.75812	−	5.75812i	−0.306474	−	0.306474i	0.537066	−	0.843540i	$-0.319532\pi$
$353$	−5.75812	−	5.75812i	−0.306474	−	0.306474i	−0.843540	+	0.537066i	$0.819532\pi$
$354$	21.6815	+	44.8819i	1.15236	+	2.38544i
$355$	10.9690	−	15.0975i	0.582171	−	0.801290i
$356$	−5.82800	−	0.923064i	−0.308883	−	0.0489223i
$357$	12.9160	−	8.97160i	0.683588	−	0.474827i
$358$	27.2057	−	13.8620i	1.43787	−	0.732629i
$359$	0.609773	−	3.84996i	0.0321826	−	0.203193i	−0.966358	−	0.257201i	$-0.917200\pi$
$359$	0.609773	−	3.84996i	0.0321826	−	0.203193i	0.998540	+	0.0540082i	$0.0171997\pi$
$360$	−5.32979	−	1.98547i	−0.280905	−	0.104643i
$361$	37.6355	−	12.2285i	1.98081	−	0.643605i
$362$	−32.9177	+	32.9177i	−1.73011	+	1.73011i
$363$	18.7709	−	3.26407i	0.985216	−	0.171319i
$364$	−11.1953	−	25.3027i	−0.586794	−	1.32622i
$365$	4.13868	−	1.34474i	0.216628	−	0.0703868i
$366$	−14.2422	−	47.2192i	−0.744449	−	2.46819i
$367$	−10.1979	+	7.40920i	−0.532326	+	0.386757i	−0.821227	−	0.570602i	$-0.806710\pi$
$367$	−10.1979	+	7.40920i	−0.532326	+	0.386757i	0.288901	+	0.957359i	$0.406710\pi$
$368$	1.43885	−	4.42832i	0.0750051	−	0.230842i
$369$	13.1059	−	12.0382i	0.682265	−	0.626682i
$370$	4.90839	−	30.9903i	0.255175	−	1.61111i
$371$	15.9322	−	2.52341i	0.827157	−	0.131009i
$372$	4.52781	−	12.9906i	0.234756	−	0.673530i
$373$	5.82100			0.301400			0.150700	−	0.988580i	$-0.451847\pi$
$373$	5.82100			0.301400			0.150700	+	0.988580i	$0.451847\pi$
$374$	−8.24097	+	16.9266i	−0.426130	+	0.875252i
$375$	−4.19661	+	5.52568i	−0.216712	+	0.285345i
$376$	−2.82043	+	0.916414i	−0.145453	+	0.0472605i
$377$	5.14490	+	7.96278i	0.264976	+	0.410104i
$378$	−30.8241	−	18.2637i	−1.58542	−	0.939381i
$379$	−5.42463	−	10.6464i	−0.278644	−	0.546871i	0.708691	−	0.705519i	$-0.249286\pi$
$379$	−5.42463	−	10.6464i	−0.278644	−	0.546871i	−0.987335	+	0.158649i	$0.949286\pi$
$380$	49.4283	+	16.0602i	2.53562	+	0.823873i
$381$	−5.21539	−	5.44156i	−0.267193	−	0.278779i
$382$	−27.5137	+	4.35775i	−1.40772	+	0.222962i
$383$	10.3074	−	20.2294i	0.526682	−	1.03367i	−0.462450	−	0.886645i	$-0.653030\pi$
$383$	10.3074	−	20.2294i	0.526682	−	1.03367i	0.989132	−	0.147027i	$-0.0469704\pi$
$384$	−5.34111	+	7.03264i	−0.272563	+	0.358883i
$385$	19.4991	+	25.8385i	0.993765	+	1.31685i
$386$		−	20.5367i		−	1.04529i
$387$	−12.4576	+	8.26693i	−0.633255	+	0.420232i
$388$	0.503500	+	3.17897i	0.0255613	+	0.161388i
$389$	−17.6423	+	12.8178i	−0.894498	+	0.649891i	−0.937047	−	0.349204i	$-0.886452\pi$
$389$	−17.6423	+	12.8178i	−0.894498	+	0.649891i	0.0425491	+	0.999094i	$0.486452\pi$
$390$	19.8240	−	32.5426i	1.00383	−	1.64786i
$391$	1.19856	−	3.68880i	0.0606139	−	0.186551i
$392$	2.56728	+	0.406617i	0.129667	+	0.0205372i
$393$	−6.34338	+	11.8226i	−0.319981	+	0.596369i
$394$	39.4523	−	12.8188i	1.98758	−	0.645803i
$395$	3.11225	+	3.11225i	0.156594	+	0.156594i
$396$	22.9845	+	0.558268i	1.15501	+	0.0280540i
$397$	−17.7203	−	17.7203i	−0.889354	−	0.889354i	0.105106	−	0.994461i	$-0.466482\pi$
$397$	−17.7203	−	17.7203i	−0.889354	−	0.889354i	−0.994461	+	0.105106i	$0.966482\pi$
$398$	−18.3974	−	9.37392i	−0.922176	−	0.469872i
$399$	38.7919	+	20.8138i	1.94202	+	1.04199i
$400$	−7.01602	−	9.65673i	−0.350801	−	0.482836i
$401$	1.18122	+	2.31827i	0.0589873	+	0.115769i	0.918618	−	0.395147i	$-0.129306\pi$
$401$	1.18122	+	2.31827i	0.0589873	+	0.115769i	−0.859631	+	0.510916i	$0.829306\pi$
$402$	5.07763	−	28.1758i	0.253249	−	1.40528i
$403$	10.7186	+	6.22156i	0.533933	+	0.309918i
$404$	−24.5389	+	33.7749i	−1.22086	+	1.68037i
$405$	−1.90811	−	26.3808i	−0.0948146	−	1.31087i
$406$	−18.1300			−0.899775
$407$	2.97332	+	16.7938i	0.147382	+	0.832435i
$408$	−1.84759	+	2.43271i	−0.0914691	+	0.120437i
$409$	−4.39093	−	2.23729i	−0.217117	−	0.110627i	0.342050	−	0.939682i	$-0.388879\pi$
$409$	−4.39093	−	2.23729i	−0.217117	−	0.110627i	−0.559167	+	0.829055i	$0.688879\pi$
$410$	−35.7489	+	5.66207i	−1.76551	+	0.279630i
$411$	−0.235178	+	11.0817i	−0.0116005	+	0.546620i
$412$	−4.10767	+	12.6421i	−0.202370	+	0.622832i
$413$	14.2245	−	43.7785i	0.699942	−	2.15420i
$414$	−8.77858	+	1.01082i	−0.431443	+	0.0496792i
$415$	−10.0865	+	13.8829i	−0.495129	+	0.681486i
$416$	−19.5023	−	21.7607i	−0.956180	−	1.06691i
$417$	2.60070	−	0.355523i	0.127357	−	0.0174100i
$418$	−52.6921	+	0.956670i	−2.57725	+	0.0467923i
$419$			27.1830i			1.32798i	0.747743	+	0.663989i	$0.231138\pi$
$419$			27.1830i			1.32798i	−0.747743	+	0.663989i	$0.768862\pi$
$420$	16.9914	+	35.1731i	0.829097	+	1.71627i
$421$	4.54795	−	0.720325i	0.221654	−	0.0351065i	−0.0446198	−	0.999004i	$-0.514208\pi$
$421$	4.54795	−	0.720325i	0.221654	−	0.0351065i	0.266273	+	0.963898i	$0.414208\pi$
$422$	15.3800	+	2.43596i	0.748688	+	0.118580i
$423$	−9.32934	−	10.1568i	−0.453608	−	0.493840i
$424$	−2.79185	+	1.42252i	−0.135584	+	0.0690836i
$425$	−5.84436	−	8.04408i	−0.283493	−	0.390195i
$426$	−10.7963	+	20.1217i	−0.523082	+	0.974899i
$427$	−20.6781	+	40.5830i	−1.00068	+	1.96395i
$428$	−42.5197			−2.05527
$429$	−4.41531	+	20.2362i	−0.213173	+	0.977014i
$430$	30.4091			1.46645
$431$	1.24360	−	2.44070i	0.0599020	−	0.117564i	−0.859114	−	0.511784i	$-0.828985\pi$
$431$	1.24360	−	2.44070i	0.0599020	−	0.117564i	0.919016	+	0.394219i	$0.128985\pi$
$432$	−16.6402	−	3.73394i	−0.800602	−	0.179649i
$433$	6.34526	+	8.73350i	0.304934	+	0.419705i	0.933793	−	0.357814i	$-0.116478\pi$
$433$	6.34526	+	8.73350i	0.304934	+	0.419705i	−0.628859	+	0.777519i	$0.716478\pi$
$434$	−21.1177	+	10.7600i	−1.01368	+	0.516498i
$435$	−7.63545	−	10.9924i	−0.366092	−	0.527047i
$436$	−37.4629	−	5.93353i	−1.79415	−	0.284165i
$437$	10.7239	−	1.69851i	0.512996	−	0.0812506i
$438$	−4.79475	+	2.31625i	−0.229102	+	0.110674i
$439$		−	32.5179i		−	1.55199i	−0.630737	−	0.775997i	$-0.717247\pi$
$439$		−	32.5179i		−	1.55199i	0.630737	−	0.775997i	$-0.282753\pi$
$440$	−5.15325	−	3.60297i	−0.245672	−	0.171765i
$441$	3.24423	+	11.6442i	0.154487	+	0.554487i
$442$	−13.6592	−	15.2410i	−0.649704	−	0.724940i
$443$	−18.8835	+	25.9909i	−0.897182	+	1.23487i	0.0741758	+	0.997245i	$0.476367\pi$
$443$	−18.8835	+	25.9909i	−0.897182	+	1.23487i	−0.971358	+	0.237620i	$0.923633\pi$
$444$	−0.436669	+	20.5760i	−0.0207234	+	0.976496i
$445$	−2.31907	+	7.13738i	−0.109935	+	0.338344i
$446$	2.35696	−	7.25398i	0.111605	−	0.343486i
$447$	23.5895	+	0.500620i	1.11574	+	0.0236785i
$448$	33.6628	−	5.33166i	1.59042	−	0.251897i
$449$	5.32010	+	2.71073i	0.251071	+	0.127927i	0.574997	−	0.818155i	$-0.305003\pi$
$449$	5.32010	+	2.71073i	0.251071	+	0.127927i	−0.323926	+	0.946082i	$0.605003\pi$
$450$	−11.1313	+	19.7294i	−0.524733	+	0.930054i
$451$	17.3644	−	9.24842i	0.817657	−	0.435491i
$452$	−20.9330			−0.984605
$453$	13.8428	−	39.7161i	0.650394	−	1.86602i
$454$	−31.7939	+	43.7606i	−1.49216	+	2.05379i
$455$	−34.0122	+	9.02914i	−1.59452	+	0.423293i
$456$	−8.41580	−	1.51663i	−0.394106	−	0.0710228i
$457$	5.79650	+	11.3763i	0.271149	+	0.532160i	0.985924	−	0.167195i	$-0.0534709\pi$
$457$	5.79650	+	11.3763i	0.271149	+	0.532160i	−0.714775	+	0.699354i	$0.753471\pi$
$458$	6.32857	+	8.71054i	0.295715	+	0.407017i
$459$	−13.8613	−	3.11038i	−0.646991	−	0.145180i
$460$	8.58407	+	4.37380i	0.400234	+	0.203930i
$461$	−10.6079	−	10.6079i	−0.494059	−	0.494059i	0.415523	−	0.909583i	$-0.363598\pi$
$461$	−10.6079	−	10.6079i	−0.494059	−	0.494059i	−0.909583	+	0.415523i	$0.863598\pi$
$462$	−27.9225	−	28.0942i	−1.29907	−	1.30706i
$463$	21.8251	+	21.8251i	1.01430	+	1.01430i	0.999896	+	0.0144006i	$0.00458400\pi$
$463$	21.8251	+	21.8251i	1.01430	+	1.01430i	0.0144006	+	0.999896i	$0.495416\pi$
$464$	−8.20729	+	2.66671i	−0.381014	+	0.123799i
$465$	−15.4177	−	8.27236i	−0.714979	−	0.383621i
$466$	−11.1768	−	1.77023i	−0.517754	−	0.0820041i
$467$	−9.17678	+	28.2432i	−0.424651	+	1.30694i	0.478678	+	0.877991i	$0.341116\pi$
$467$	−9.17678	+	28.2432i	−0.424651	+	1.30694i	−0.903328	+	0.428950i	$0.858884\pi$
$468$	−9.99210	+	22.9099i	−0.461885	+	1.05901i
$469$	−21.3901	+	15.5408i	−0.987702	+	0.717608i
$470$	4.38799	+	27.7047i	0.202403	+	1.27792i
$471$	0.696502	+	1.44179i	0.0320931	+	0.0664344i
$472$			8.94151i			0.411567i
$473$	−15.6247	+	5.39226i	−0.718424	+	0.247936i
$474$	−4.28901	−	3.25740i	−0.197001	−	0.149617i
$475$	12.6363	−	24.8002i	0.579795	−	1.13791i
$476$	20.7218	−	3.28202i	0.949784	−	0.150431i
$477$	−11.4146	−	9.05731i	−0.522638	−	0.414706i
$478$	30.5492	+	9.92603i	1.39729	+	0.454006i
$479$	−12.9291	−	25.3747i	−0.590744	−	1.15940i	−0.972011	−	0.234936i	$-0.924512\pi$
$479$	−12.9291	−	25.3747i	−0.590744	−	1.15940i	0.381267	−	0.924465i	$-0.375488\pi$
$480$	28.5453	+	29.7831i	1.30291	+	1.35941i
$481$	−18.1265	−	3.89683i	−0.826499	−	0.177680i
$482$	38.9929	−	12.6696i	1.77608	−	0.577082i
$483$	6.49881	+	4.93568i	0.295706	+	0.224581i
$484$	24.4430	+	6.97185i	1.11104	+	0.316902i
$485$	4.09355			0.185879
$486$	6.68555	+	31.6671i	0.303263	+	1.43645i
$487$	6.06095	−	0.959960i	0.274648	−	0.0434999i	−0.0175912	−	0.999845i	$-0.505600\pi$
$487$	6.06095	−	0.959960i	0.274648	−	0.0434999i	0.292239	+	0.956345i	$0.405600\pi$
$488$	1.38405	−	8.73856i	0.0626531	−	0.395576i
$489$	0.782204	−	0.543327i	0.0353725	−	0.0245701i
$490$	7.59729	−	23.3820i	0.343210	−	1.05629i
$491$	29.1268	−	21.1618i	1.31447	−	0.955021i	0.314490	−	0.949261i	$-0.398166\pi$
$491$	29.1268	−	21.1618i	1.31447	−	0.955021i	0.999983	−	0.00576014i	$-0.00183352\pi$
$492$	22.7295	−	6.85561i	1.02472	−	0.309075i
$493$	−6.83669	+	2.22138i	−0.307909	+	0.100046i
$494$	20.6554	−	53.4387i	0.929330	−	2.40432i
$495$	5.27428	−	28.7617i	0.237061	−	1.29274i
$496$	−7.97715	+	7.97715i	−0.358185	+	0.358185i
$497$	20.0561	−	6.51663i	0.899641	−	0.292311i
$498$	9.92776	−	18.5030i	0.444874	−	0.829138i
$499$	−5.46353	+	34.4954i	−0.244581	+	1.54423i	0.493639	+	0.869667i	$0.335666\pi$
$499$	−5.46353	+	34.4954i	−0.244581	+	1.54423i	−0.738221	+	0.674559i	$0.764334\pi$
$500$	−8.24783	+	4.20248i	−0.368854	+	0.187941i
$501$	1.31443	+	1.89232i	0.0587243	+	0.0845428i
$502$	37.1803	+	5.88878i	1.65944	+	0.262829i
$503$	−15.2078	+	20.9318i	−0.678084	+	0.933303i	−0.999909	−	0.0134963i	$-0.995704\pi$
$503$	−15.2078	+	20.9318i	−0.678084	+	0.933303i	0.321825	+	0.946799i	$0.395704\pi$
$504$	−3.55382	−	5.35532i	−0.158300	−	0.238545i
$505$	37.5453	+	37.5453i	1.67074	+	1.67074i
$506$	−9.67508	−	1.35283i	−0.430110	−	0.0601408i
$507$	−18.5607	−	12.7475i	−0.824311	−	0.566137i
$508$	−3.10730	−	9.56328i	−0.137864	−	0.424302i
$509$	−2.10409	−	13.2847i	−0.0932621	−	0.588834i	−0.989418	−	0.145094i	$-0.953652\pi$
$509$	−2.10409	−	13.2847i	−0.0932621	−	0.588834i	0.896156	−	0.443740i	$-0.146348\pi$
$510$	19.9928	+	20.8598i	0.885298	+	0.923689i
$511$	4.67688	+	1.51961i	0.206893	+	0.0672236i
$512$	27.4730	−	13.9982i	1.21415	−	0.618639i
$513$	−9.85798	−	38.5262i	−0.435240	−	1.70098i
$514$	−2.12516	−	13.4177i	−0.0937369	−	0.591831i
$515$	15.0635	+	7.67526i	0.663779	+	0.338212i
$516$	−19.7622	+	2.70155i	−0.869983	+	0.118929i
$517$	−7.16734	−	13.4570i	−0.315219	−	0.591840i
$518$	25.0718	−	25.0718i	1.10159	−	1.10159i
$519$	−9.49589	−	19.6570i	−0.416823	−	0.862846i
$520$	5.74146	−	3.70966i	0.251780	−	0.162680i
$521$	4.44336	+	6.11576i	0.194667	+	0.267936i	0.895181	−	0.445702i	$-0.147046\pi$
$521$	4.44336	+	6.11576i	0.194667	+	0.267936i	−0.700514	+	0.713638i	$0.747046\pi$
$522$	11.0788	+	12.0615i	0.484908	+	0.527916i
$523$	2.37786	−	7.31830i	0.103977	−	0.320007i	−0.885512	−	0.464616i	$-0.846192\pi$
$523$	2.37786	−	7.31830i	0.103977	−	0.320007i	0.989489	+	0.144609i	$0.0461924\pi$
$524$	−14.4808	+	10.5209i	−0.632596	+	0.459608i
$525$	20.0288	−	6.04104i	0.874129	−	0.263653i
$526$	34.1507	+	17.4006i	1.48904	+	0.758704i
$527$	−6.64499	+	6.64499i	−0.289460	+	0.289460i
$528$	−16.7726	−	8.61094i	−0.729935	−	0.374743i
$529$	−20.9873			−0.912492
$530$	9.15834	+	28.1865i	0.397813	+	1.22434i
$531$	−37.8172	+	17.2889i	−1.64113	+	0.750274i
$532$	34.5210	+	47.5140i	1.49667	+	2.05999i
$533$	2.18632	+	21.2756i	0.0947002	+	0.921546i
$534$	1.62867	−	9.03751i	0.0704795	−	0.391091i
$535$	−8.45972	+	53.4126i	−0.365746	+	2.30923i
$536$	3.01877	−	4.15498i	0.130391	−	0.179468i
$537$	11.0800	+	22.9361i	0.478135	+	0.989765i
$538$	−20.5309	+	20.5309i	−0.885152	+	0.885152i
$539$	0.242586	+	13.3613i	0.0104489	+	0.575511i
$540$	13.0168	−	32.7976i	0.560154	−	1.41138i
$541$	−3.96252	+	7.77687i	−0.170362	+	0.334354i	−0.960363	−	0.278751i	$-0.910080\pi$
$541$	−3.96252	+	7.77687i	−0.170362	+	0.334354i	0.790002	+	0.613105i	$0.210080\pi$
$542$	20.4226	−	28.1093i	0.877225	−	1.20740i
$543$	−26.8721	−	28.0374i	−1.15319	−	1.20320i
$544$	19.7422	−	10.0591i	0.846439	−	0.431282i
$545$	−14.9072	+	45.8797i	−0.638555	+	1.96527i
$546$	39.7390	−	16.5837i	1.70067	−	0.709716i
$547$	13.3586	+	9.70561i	0.571174	+	0.414982i	0.835531	−	0.549443i	$-0.185160\pi$
$547$	13.3586	+	9.70561i	0.571174	+	0.414982i	−0.264358	+	0.964425i	$0.585160\pi$
$548$	−6.71329	+	13.1756i	−0.286778	+	0.562833i
$549$	39.6349	−	11.0428i	1.69158	−	0.471294i
$550$	−17.3842	+	18.0271i	−0.741266	+	0.768680i
$551$	−14.2292	−	14.2292i	−0.606185	−	0.606185i
$552$	−1.49686	−	0.521724i	−0.0637107	−	0.0222061i
$553$	0.778066	+	4.91252i	0.0330867	+	0.208901i
$554$	−0.0908705	+	0.573734i	−0.00386072	+	0.0243756i
$555$	25.7604	+	4.64234i	1.09347	+	0.197056i
$556$	3.33044	+	1.08213i	0.141242	+	0.0458923i
$557$	1.04796	−	6.61655i	0.0444035	−	0.280352i	−0.955489	−	0.295027i	$-0.904671\pi$
$557$	1.04796	−	6.61655i	0.0444035	−	0.280352i	0.999892	+	0.0146748i	$0.00467130\pi$
$558$	20.0630	+	7.47393i	0.849335	+	0.316397i
$559$	0.981993	−	17.9421i	0.0415339	−	0.758868i
$560$		−	32.0328i		−	1.35363i
$561$	−13.9716	−	7.17293i	−0.589883	−	0.302841i
$562$	66.6053			2.80957
$563$	−2.55434	−	7.86144i	−0.107652	−	0.331320i	0.882691	−	0.469953i	$-0.155729\pi$
$563$	−2.55434	−	7.86144i	−0.107652	−	0.331320i	−0.990344	+	0.138633i	$0.955729\pi$
$564$	−5.31296	−	17.6149i	−0.223716	−	0.741720i
$565$	−4.16482	+	26.2957i	−0.175215	+	1.10627i
$566$	−0.446883	−	0.877058i	−0.0187839	−	0.0368655i
$567$	15.7783	−	25.3853i	0.662625	−	1.06608i
$568$	−3.31402	+	2.40777i	−0.139053	+	0.101028i
$569$	8.42108	+	6.11828i	0.353030	+	0.256491i	0.750139	−	0.661280i	$-0.229986\pi$
$569$	8.42108	+	6.11828i	0.353030	+	0.256491i	−0.397109	+	0.917771i	$0.629986\pi$
$570$	−26.6209	+	76.3770i	−1.11503	+	3.19908i
$571$		−	1.73216i		−	0.0724888i	−0.999343	−	0.0362444i	$-0.988461\pi$
$571$		−	1.73216i		−	0.0724888i	0.999343	−	0.0362444i	$-0.0115395\pi$
$572$	−17.0472	+	21.7468i	−0.712778	+	0.909281i
$573$	−3.14755	−	23.0248i	−0.131491	−	0.961873i
$574$	−36.4434	−	18.5688i	−1.52112	−	0.775047i
$575$	3.03274	−	4.17421i	0.126474	−	0.174077i
$576$	−24.1177	−	19.1370i	−1.00490	−	0.797377i
$577$	−15.6333	−	30.6821i	−0.650822	−	1.27731i	−0.946710	−	0.322088i	$-0.895615\pi$
$577$	−15.6333	−	30.6821i	−0.650822	−	1.27731i	0.295888	−	0.955223i	$-0.404385\pi$
$578$	−17.6216	+	8.97864i	−0.732961	+	0.373462i
$579$	17.1285	+	0.363505i	0.711837	+	0.0151067i
$580$	−2.79322	−	17.6357i	−0.115982	−	0.732284i
$581$	−18.4427	+	5.99240i	−0.765132	+	0.248606i
$582$	−4.96291	+	0.678443i	−0.205719	+	0.0281224i
$583$	−9.70386	−	12.8587i	−0.401893	−	0.532553i
$584$	−0.955225			−0.0395275
$585$	26.7911	+	17.1101i	1.10767	+	0.707414i
$586$	−10.2999	−	7.48335i	−0.425487	−	0.309134i
$587$	16.4499	+	2.60540i	0.678958	+	0.107536i	0.486383	−	0.873746i	$-0.338316\pi$
$587$	16.4499	+	2.60540i	0.678958	+	0.107536i	0.192575	+	0.981282i	$0.438316\pi$
$588$	−2.86005	+	15.8705i	−0.117947	+	0.654487i
$589$	−25.0191	−	8.12919i	−1.03089	−	0.334958i
$590$	83.5323	+	13.2302i	3.43897	+	0.544680i
$591$	9.99314	+	33.1318i	0.411063	+	1.36286i
$592$	7.66204	−	15.0376i	0.314908	−	0.618041i
$593$	−13.3995	+	13.3995i	−0.550251	+	0.550251i	−0.926513	−	0.376263i	$-0.877209\pi$
$593$	−13.3995	+	13.3995i	−0.550251	+	0.550251i	0.376263	+	0.926513i	$0.377209\pi$
$594$	−1.62759	+	35.7440i	−0.0667806	+	1.46659i
$595$		−	26.6834i		−	1.09391i
$596$	28.0467	+	14.2905i	1.14884	+	0.585361i
$597$	8.14389	−	15.1783i	0.333307	−	0.621205i
$598$	5.33142	−	9.18508i	0.218018	−	0.375606i
$599$	−16.9226	−	5.49847i	−0.691437	−	0.224661i	−0.0578411	−	0.998326i	$-0.518422\pi$
$599$	−16.9226	−	5.49847i	−0.691437	−	0.224661i	−0.633596	+	0.773664i	$0.718422\pi$
$600$	−3.33752	+	2.31827i	−0.136254	+	0.0946431i
$601$	−24.1986	+	17.5813i	−0.987081	+	0.717157i	−0.959280	−	0.282457i	$-0.908851\pi$
$601$	−24.1986	+	17.5813i	−0.987081	+	0.717157i	−0.0278013	+	0.999613i	$0.508851\pi$
$602$	27.8007	+	20.1984i	1.13307	+	0.823224i
$603$	23.4100	+	4.73368i	0.953328	+	0.192770i
$604$	39.6764	−	39.6764i	1.61441	−	1.61441i
$605$	13.6211	−	29.3177i	0.553776	−	1.19193i
$606$	−51.7414	−	39.2963i	−2.10185	−	1.59630i
$607$	1.00960	+	3.10724i	0.0409785	+	0.126119i	0.969453	−	0.245277i	$-0.0788791\pi$
$607$	1.00960	+	3.10724i	0.0409785	+	0.126119i	−0.928474	+	0.371396i	$0.878879\pi$
$608$	50.1797	+	36.4577i	2.03505	+	1.47855i
$609$	0.320904	−	15.1212i	0.0130037	−	0.612741i
$610$	−79.5884	−	25.8598i	−3.22244	−	1.04703i
$611$	16.4881	−	1.69436i	0.667038	−	0.0685463i
$612$	−14.8461	−	11.7802i	−0.600119	−	0.476186i
$613$	−32.2765	+	5.11209i	−1.30364	+	0.206476i	−0.769349	−	0.638828i	$-0.779419\pi$
$613$	−32.2765	+	5.11209i	−1.30364	+	0.206476i	−0.534286	+	0.845304i	$0.679419\pi$
$614$	−2.04681	+	0.665048i	−0.0826024	+	0.0268391i
$615$	−4.08965	−	29.9164i	−0.164911	−	1.20634i
$616$	−2.31805	−	6.71682i	−0.0933969	−	0.270628i
$617$	−23.3958	−	23.3958i	−0.941878	−	0.941878i	0.0565231	−	0.998401i	$-0.481999\pi$
$617$	−23.3958	−	23.3958i	−0.941878	−	0.941878i	−0.998401	+	0.0565231i	$0.981999\pi$
$618$	−19.5347	−	6.80872i	−0.785800	−	0.273887i
$619$	−6.03018	−	38.0731i	−0.242374	−	1.53029i	−0.745754	−	0.666221i	$-0.767911\pi$
$619$	−6.03018	−	38.0731i	−0.242374	−	1.53029i	0.503380	−	0.864065i	$-0.332089\pi$
$620$	−13.7202	−	18.8843i	−0.551018	−	0.758411i
$621$	−0.687687	−	7.33960i	−0.0275959	−	0.294528i
$622$	−28.9651	+	14.7584i	−1.16139	+	0.591760i
$623$	−6.86095	+	4.98478i	−0.274878	+	0.199711i
$624$	15.5503	−	13.3525i	0.622510	−	0.534526i
$625$	9.25738	+	28.4913i	0.370295	+	1.13965i
$626$	24.8898	+	24.8898i	0.994796	+	0.994796i
$627$	0.134756	−	43.9644i	0.00538165	−	1.75577i
$628$			2.13616i			0.0852421i
$629$	6.38249	−	12.5263i	0.254487	−	0.499458i
$630$	−55.2882	+	25.2762i	−2.20274	+	1.00703i
$631$	3.47074	+	0.549711i	0.138168	+	0.0218836i	0.225135	−	0.974328i	$-0.427718\pi$
$631$	3.47074	+	0.549711i	0.138168	+	0.0218836i	−0.0869674	+	0.996211i	$0.527718\pi$
$632$	−0.438619	−	0.860837i	−0.0174473	−	0.0342423i
$633$	−2.30392	+	12.7845i	−0.0915726	+	0.508137i
$634$	21.9259	+	30.1784i	0.870789	+	1.19854i
$635$	−12.6315	+	2.00063i	−0.501264	+	0.0793924i
$636$	−8.45592	−	17.5042i	−0.335299	−	0.694086i
$637$	−13.5506	−	5.23765i	−0.536895	−	0.207523i
$638$	8.51141	+	15.9806i	0.336970	+	0.632678i
$639$	−16.5913	−	9.36072i	−0.656340	−	0.370304i
$640$	4.63028	+	14.2505i	0.183028	+	0.563302i
$641$	−17.2639	−	12.5430i	−0.681884	−	0.495417i	0.192098	−	0.981376i	$-0.438471\pi$
$641$	−17.2639	−	12.5430i	−0.681884	−	0.495417i	−0.873982	+	0.485958i	$0.838471\pi$
$642$	1.40402	−	66.1580i	0.0554121	−	2.61105i
$643$	−6.34257	−	12.4480i	−0.250127	−	0.490901i	0.731468	−	0.681875i	$-0.238835\pi$
$643$	−6.34257	−	12.4480i	−0.250127	−	0.490901i	−0.981595	+	0.190974i	$0.938835\pi$
$644$	4.94258	+	9.70036i	0.194765	+	0.382248i
$645$	−0.538247	+	25.3625i	−0.0211934	+	0.998646i
$646$	35.1454	+	25.5346i	1.38278	+	1.00465i
$647$	−3.57033	−	10.9883i	−0.140364	−	0.431996i	0.856022	−	0.516940i	$-0.172929\pi$
$647$	−3.57033	−	10.9883i	−0.140364	−	0.431996i	−0.996386	+	0.0849439i	$0.972929\pi$
$648$	−1.39111	+	5.63681i	−0.0546480	+	0.221435i
$649$	−45.2664	+	8.01439i	−1.77686	+	0.314592i
$650$	−11.0159	−	24.8972i	−0.432080	−	0.976550i
$651$	−8.60053	−	17.8036i	−0.337081	−	0.697776i
$652$	1.25493	−	0.198762i	0.0491469	−	0.00778410i
$653$	−0.227285	−	0.312832i	−0.00889437	−	0.0122420i	0.804547	−	0.593889i	$-0.202408\pi$
$653$	−0.227285	−	0.312832i	−0.00889437	−	0.0122420i	−0.813441	+	0.581647i	$0.802408\pi$
$654$	10.4692	−	58.0939i	0.409380	−	2.27165i
$655$	10.3351	+	20.2838i	0.403825	+	0.792552i
$656$	−19.2289	−	3.04556i	−0.750762	−	0.118909i
$657$	−1.84698	−	4.04002i	−0.0720576	−	0.157616i
$658$	−14.3905	+	28.2429i	−0.560998	+	1.10102i
$659$		−	17.6209i		−	0.686413i	−0.939260	−	0.343206i	$-0.888487\pi$
$659$		−	17.6209i		−	0.686413i	0.939260	−	0.343206i	$-0.111513\pi$
$660$	23.0264	−	31.4897i	0.896301	−	1.22573i
$661$	24.6229	+	24.6229i	0.957719	+	0.957719i	0.999142	−	0.0414227i	$-0.0131890\pi$
$661$	24.6229	+	24.6229i	0.957719	+	0.957719i	−0.0414227	+	0.999142i	$0.513189\pi$
$662$	−17.9292	−	55.1803i	−0.696837	−	2.14464i
$663$	12.9534	−	11.1226i	0.503069	−	0.431967i
$664$	3.04742	−	2.21408i	0.118263	−	0.0859229i
$665$	66.5546	−	33.9113i	2.58088	−	1.31502i
$666$	−32.0006	−	1.35886i	−1.24000	−	0.0526546i
$667$	−2.19259	−	3.01784i	−0.0848973	−	0.116851i
$668$	0.480848	+	3.03595i	0.0186046	+	0.117465i
$669$	6.00842	+	2.09420i	0.232299	+	0.0809666i
$670$	−34.3494	−	34.3494i	−1.32703	−	1.32703i
$671$	45.4795	−	0.825720i	1.75572	−	0.0318766i
$672$	6.31414	+	46.1888i	0.243573	+	1.78177i
$673$	−22.9411	+	7.45402i	−0.884315	+	0.287331i	−0.715748	−	0.698359i	$-0.753914\pi$
$673$	−22.9411	+	7.45402i	−0.884315	+	0.287331i	−0.168567	+	0.985690i	$0.553914\pi$
$674$	38.6862	−	6.12729i	1.49014	−	0.236014i
$675$	−16.2582	−	9.63316i	−0.625777	−	0.370781i
$676$	−14.8989	−	26.0841i	−0.573035	−	1.00323i
$677$	20.7602	+	6.74538i	0.797877	+	0.259246i	0.679455	−	0.733717i	$-0.262216\pi$
$677$	20.7602	+	6.74538i	0.797877	+	0.259246i	0.118422	+	0.992963i	$0.462216\pi$
$678$	0.691215	−	32.5704i	0.0265459	−	1.25086i
$679$	3.74242	+	2.71903i	0.143621	+	0.104347i
$680$	1.60169	+	4.92951i	0.0614222	+	0.189038i
$681$	−35.9355	−	27.2921i	−1.37705	−	1.04584i
$682$	19.3985	+	13.5627i	0.742805	+	0.519343i
$683$	7.01705	−	7.01705i	0.268500	−	0.268500i	−0.559996	−	0.828496i	$-0.689197\pi$
$683$	7.01705	−	7.01705i	0.268500	−	0.268500i	0.828496	+	0.559996i	$0.189197\pi$
$684$	10.5150	−	52.0009i	0.402051	−	1.98830i
$685$	15.2153	+	11.0545i	0.581345	+	0.422372i
$686$	−16.5719	+	12.0402i	−0.632718	+	0.459696i
$687$	−7.37698	+	5.12413i	−0.281449	+	0.195498i
$688$	15.5561	+	5.05448i	0.593070	+	0.192700i
$689$	16.9264	−	4.49342i	0.644846	−	0.171186i
$690$	−7.08881	+	13.2118i	−0.269866	+	0.502966i
$691$	−27.0271	−	13.7710i	−1.02816	−	0.523873i	−0.143273	−	0.989683i	$-0.545763\pi$
$691$	−27.0271	−	13.7710i	−1.02816	−	0.523873i	−0.884884	+	0.465811i	$0.845763\pi$
$692$		−	29.1238i		−	1.10712i
$693$	23.9260	−	22.7913i	0.908873	−	0.865769i
$694$	−20.4357	+	20.4357i	−0.775730	+	0.775730i
$695$	2.02197	−	3.96834i	0.0766977	−	0.150528i
$696$	0.848378	+	2.81276i	0.0321577	+	0.106617i
$697$	−16.0177	−	2.53695i	−0.606714	−	0.0960940i
$698$	51.0684	+	16.5931i	1.93297	+	0.628060i
$699$	1.67428	−	9.29057i	0.0633269	−	0.351402i
$700$	27.5656	+	4.36595i	1.04188	+	0.165018i
$701$	25.9801	+	18.8756i	0.981254	+	0.712923i	0.957988	−	0.286807i	$-0.0925938\pi$
$701$	25.9801	+	18.8756i	0.981254	+	0.712923i	0.0232653	+	0.999729i	$0.492594\pi$
$702$	−35.3165	−	16.3036i	−1.33293	−	0.615338i
$703$	39.3550			1.48430
$704$	−20.5031	−	27.1690i	−0.772741	−	1.02397i
$705$	−23.1846	+	3.16939i	−0.873181	+	0.119366i
$706$	16.0796	−	5.22459i	0.605165	−	0.196630i
$707$	9.38636	+	59.2631i	0.353010	+	2.22882i
$708$	−55.4613	−	1.17701i	−2.08436	−	0.0442347i
$709$	19.9502	−	10.1651i	0.749246	−	0.381760i	−0.0372898	−	0.999304i	$-0.511872\pi$
$709$	19.9502	−	10.1651i	0.749246	−	0.381760i	0.786536	+	0.617545i	$0.211872\pi$
$710$	17.5901	+	34.5225i	0.660144	+	1.29560i
$711$	2.79273	−	3.51957i	0.104735	−	0.131994i
$712$	0.968282	−	1.33273i	0.0362879	−	0.0499460i
$713$	−4.34499	−	2.21388i	−0.162721	−	0.0829105i
$714$	4.42237	+	32.3502i	0.165503	+	1.21068i
$715$	23.9263	+	25.7411i	0.894793	+	0.962663i
$716$			33.9821i			1.26997i
$717$	−8.81946	+	25.3036i	−0.329369	+	0.944981i
$718$	6.54739	+	4.75695i	0.244346	+	0.177528i
$719$	15.6790	−	11.3915i	0.584728	−	0.424830i	−0.255698	−	0.966757i	$-0.582305\pi$
$719$	15.6790	−	11.3915i	0.584728	−	0.424830i	0.840426	+	0.541927i	$0.182305\pi$
$720$	−21.3107	+	19.5746i	−0.794204	+	0.729502i
$721$	8.67336	+	17.0224i	0.323013	+	0.633948i
$722$	−12.8528	+	81.1494i	−0.478332	+	3.02007i
$723$	9.87677	+	32.7460i	0.367321	+	1.21784i
$724$	−16.0102	−	49.2744i	−0.595016	−	1.83127i
$725$	−9.56265			−0.355148
$726$	−11.6549	+	37.8015i	−0.432553	+	1.40294i
$727$		−	41.9465i		−	1.55571i	−0.628443	−	0.777856i	$-0.716307\pi$
$727$		−	41.9465i		−	1.55571i	0.628443	−	0.777856i	$-0.283693\pi$
$728$	7.71301	+	0.422144i	0.285863	+	0.0156457i
$729$	−26.5301	+	5.01552i	−0.982595	+	0.185760i
$730$	−1.41339	+	8.92379i	−0.0523119	+	0.330284i
$731$	12.9583	+	4.21039i	0.479278	+	0.155727i
$732$	54.0203	+	9.73512i	1.99665	+	0.359820i
$733$	2.72117	−	17.1808i	0.100509	−	0.634587i	−0.885081	−	0.465436i	$-0.845897\pi$
$733$	2.72117	−	17.1808i	0.100509	−	0.634587i	0.985590	−	0.169151i	$-0.0541026\pi$
$734$	−4.09411	−	25.8492i	−0.151116	−	0.954111i
$735$	19.3672	+	6.75033i	0.714369	+	0.248990i
$736$	8.13013	+	8.13013i	0.299681	+	0.299681i
$737$	23.7403	+	11.5583i	0.874486	+	0.425757i
$738$	9.91636	+	35.5920i	0.365026	+	1.31016i
$739$	2.85562	−	5.60446i	0.105046	−	0.206163i	−0.832501	−	0.554024i	$-0.813092\pi$
$739$	2.85562	−	5.60446i	0.105046	−	0.206163i	0.937546	+	0.347860i	$0.113092\pi$
$740$	28.2511	+	20.5256i	1.03853	+	0.754536i
$741$	44.2046	+	18.1734i	1.62390	+	0.667615i
$742$	−10.3493	+	31.8519i	−0.379935	+	1.16932i
$743$	−40.0841	+	20.4239i	−1.47054	+	0.749279i	−0.991694	−	0.128619i	$-0.958946\pi$
$743$	−40.0841	+	20.4239i	−1.47054	+	0.749279i	−0.478849	+	0.877898i	$0.658946\pi$
$744$	2.65754	+	2.77279i	0.0974302	+	0.101655i
$745$	23.5316	−	32.3885i	0.862132	−	1.18662i
$746$	−5.48679	+	10.7684i	−0.200886	+	0.394261i
$747$	15.2566	+	8.60769i	0.558208	+	0.314939i
$748$	−12.6211	−	16.7244i	−0.461474	−	0.611505i
$749$	−43.2119	+	43.2119i	−1.57893	+	1.57893i
$750$	−6.26645	−	12.9719i	−0.228818	−	0.473666i
$751$	−5.63594	+	7.75721i	−0.205658	+	0.283065i	−0.899370	−	0.437188i	$-0.855974\pi$
$751$	−5.63594	+	7.75721i	−0.205658	+	0.283065i	0.693712	+	0.720253i	$0.255974\pi$
$752$	−2.36024	+	14.9020i	−0.0860692	+	0.543420i
$753$	−5.56959	+	30.9057i	−0.202967	+	1.12627i
$754$	−19.5801	+	2.01209i	−0.713065	+	0.0732762i
$755$	−41.9468	−	57.7348i	−1.52660	−	2.10119i
$756$	33.6851	−	21.3383i	1.22512	−	0.776066i
$757$	−5.27648	−	16.2393i	−0.191777	−	0.590228i	−0.999999	−	0.00135086i	$-0.999570\pi$
$757$	−5.27648	−	16.2393i	−0.191777	−	0.590228i	0.808222	−	0.588878i	$-0.200430\pi$
$758$	24.8083			0.901079
$759$	1.29957	−	8.04549i	0.0471715	−	0.292033i
$760$	−10.2598	+	10.2598i	−0.372162	+	0.372162i
$761$	16.8979	+	8.60993i	0.612550	+	0.312110i	0.732601	−	0.680658i	$-0.238306\pi$
$761$	16.8979	+	8.60993i	0.612550	+	0.312110i	−0.120052	+	0.992768i	$0.538306\pi$
$762$	14.9825	−	4.51898i	0.542757	−	0.163705i
$763$	−44.1028	+	32.0426i	−1.59663	+	1.16002i
$764$	9.58038	−	29.4854i	0.346606	−	1.06674i
$765$	−17.7519	+	16.3057i	−0.641820	+	0.589533i
$766$	27.7073	+	38.1358i	1.00111	+	1.37790i
$767$	10.5036	−	48.8588i	0.379264	−	1.76419i
$768$	7.48853	+	15.5017i	0.270219	+	0.559368i
$769$	−5.91618	+	5.91618i	−0.213343	+	0.213343i	−0.805686	−	0.592343i	$-0.798203\pi$
$769$	−5.91618	+	5.91618i	−0.213343	+	0.213343i	0.592343	+	0.805686i	$0.298203\pi$
$770$	−66.1789	+	11.7169i	−2.38492	+	0.422249i
$771$	11.2286	−	1.53498i	0.404388	−	0.0552809i
$772$	20.3650	+	10.3765i	0.732951	+	0.373457i
$773$	2.67965	+	16.9186i	0.0963803	+	0.608521i	0.987846	+	0.155434i	$0.0496775\pi$
$773$	2.67965	+	16.9186i	0.0963803	+	0.608521i	−0.891466	+	0.453088i	$0.850322\pi$
$774$	−3.55088	−	30.8380i	−0.127634	−	1.10845i
$775$	−11.1385	+	5.67537i	−0.400108	+	0.203865i
$776$	−0.854589	−	0.277673i	−0.0306779	−	0.00996787i
$777$	20.4672	+	21.3548i	0.734257	+	0.766098i
$778$	−7.08277	−	44.7189i	−0.253930	−	1.60325i
$779$	−14.0287	−	43.1760i	−0.502632	−	1.54694i
$780$	22.2541	+	36.1007i	0.796823	+	1.29261i
$781$	−15.1598	−	14.6191i	−0.542459	−	0.523112i
$782$	5.69427	+	5.69427i	0.203627	+	0.203627i
$783$	−10.2559	+	9.02674i	−0.366515	+	0.322589i
$784$	7.77295	−	10.6986i	0.277605	−	0.382091i
$785$	2.68341	+	0.425010i	0.0957750	+	0.0151693i
$786$	−15.8917	−	22.8786i	−0.566838	−	0.816052i
$787$	1.47012	−	0.749066i	0.0524043	−	0.0267013i	−0.427592	−	0.903972i	$-0.640638\pi$
$787$	1.47012	−	0.749066i	0.0524043	−	0.0267013i	0.479996	+	0.877271i	$0.340638\pi$
$788$	−7.22220	+	45.5992i	−0.257280	+	1.62440i
$789$	−15.1174	+	28.1751i	−0.538192	+	1.00306i
$790$	−8.69101	+	2.82388i	−0.309212	+	0.100469i
$791$	−21.2737	+	21.2737i	−0.756407	+	0.756407i
$792$	−3.05204	+	5.64665i	−0.108449	+	0.200645i
$793$	−17.8281	+	46.1240i	−0.633093	+	1.63791i
$794$	49.4841	−	16.0784i	1.75613	−	0.570600i
$795$	−23.6708	+	7.13955i	−0.839518	+	0.253214i
$796$	18.5910	−	13.5072i	0.658941	−	0.478749i
$797$	7.39478	−	22.7588i	0.261936	−	0.806158i	−0.730447	−	0.682970i	$-0.760688\pi$
$797$	7.39478	−	22.7588i	0.261936	−	0.806158i	0.992383	−	0.123188i	$-0.0393118\pi$
$798$	−75.0687	+	52.1435i	−2.65740	+	1.84586i
$799$	−1.96609	+	12.4134i	−0.0695552	+	0.439154i
$800$	29.1120	−	4.61089i	1.02927	−	0.163020i
$801$	7.50885	+	1.51835i	0.265312	+	0.0536482i
$802$	−5.40204			−0.190753
$803$	−0.856181	−	4.83583i	−0.0302140	−	0.170653i
$804$	25.3746	+	19.2714i	0.894893	+	0.679649i
$805$	13.1688	−	4.27880i	0.464139	−	0.150808i
$806$	−21.6127	+	13.9643i	−0.761274	+	0.491873i
$807$	−16.7603	−	17.4871i	−0.589990	−	0.615575i
$808$	−5.29136	−	10.3849i	−0.186150	−	0.365339i
$809$	−17.3643	−	5.64202i	−0.610498	−	0.198363i	−0.0125809	−	0.999921i	$-0.504005\pi$
$809$	−17.3643	−	5.64202i	−0.610498	−	0.198363i	−0.597917	+	0.801558i	$0.704005\pi$
$810$	50.6012	+	21.3363i	1.77794	+	0.749682i
$811$	39.1953	−	6.20793i	1.37633	−	0.217990i	0.575954	−	0.817482i	$-0.304631\pi$
$811$	39.1953	−	6.20793i	1.37633	−	0.217990i	0.800380	+	0.599492i	$0.204631\pi$
$812$	9.16040	−	17.9783i	0.321467	−	0.630915i
$813$	23.0829	+	17.5309i	0.809551	+	0.614834i
$814$	−33.8699	−	10.3291i	−1.18714	−	0.362035i
$815$		−	1.61597i		−	0.0566049i
$816$	6.76032	+	13.9942i	0.236659	+	0.489896i
$817$	5.96662	+	37.6718i	0.208746	+	1.31797i
$818$	8.27765	−	6.01407i	0.289421	−	0.210277i
$819$	13.1281	+	33.4376i	0.458734	+	1.16840i
$820$	12.4479	−	38.3107i	0.434700	−	1.33787i
$821$	−4.55211	−	0.720983i	−0.158870	−	0.0251625i	0.0764929	−	0.997070i	$-0.475628\pi$
$821$	−4.55211	−	0.720983i	−0.158870	−	0.0251625i	−0.235363	+	0.971908i	$0.575628\pi$
$822$	−20.2787	−	10.8805i	−0.707301	−	0.379502i
$823$	40.2474	−	13.0772i	1.40294	−	0.455842i	0.492798	−	0.870144i	$-0.335974\pi$
$823$	40.2474	−	13.0772i	1.40294	−	0.455842i	0.910140	+	0.414302i	$0.135974\pi$
$824$	−2.62411	−	2.62411i	−0.0914152	−	0.0914152i
$825$	−14.7277	−	14.8183i	−0.512753	−	0.515906i
$826$	67.5794	+	67.5794i	2.35139	+	2.35139i
$827$	15.9553	+	8.12962i	0.554819	+	0.282695i	0.708836	−	0.705374i	$-0.249221\pi$
$827$	15.9553	+	8.12962i	0.554819	+	0.282695i	−0.154016	+	0.988068i	$0.549221\pi$
$828$	3.43313	−	9.21588i	0.119309	−	0.320274i
$829$	−1.09988	−	1.51385i	−0.0382002	−	0.0525781i	0.789490	−	0.613764i	$-0.210345\pi$
$829$	−1.09988	−	1.51385i	−0.0382002	−	0.0525781i	−0.827690	+	0.561186i	$0.810345\pi$
$830$	−16.1750	−	31.7453i	−0.561443	−	1.10189i
$831$	−0.476910	−	0.0859452i	−0.0165438	−	0.00298140i
$832$	35.7636	−	9.49407i	1.23988	−	0.329148i
$833$	6.47489	−	8.91192i	0.224342	−	0.308780i
$834$	−1.79369	+	5.14622i	−0.0621104	+	0.178199i
$835$	3.90938			0.135290
$836$	25.6747	−	52.7347i	0.887978	−	1.82387i
$837$	−6.58870	+	16.6011i	−0.227739	+	0.573819i
$838$	−50.2867	−	25.6223i	−1.73712	−	0.885109i
$839$	−37.1095	+	5.87756i	−1.28116	+	0.202916i	−0.759652	−	0.650330i	$-0.774631\pi$
$839$	−37.1095	+	5.87756i	−1.28116	+	0.202916i	−0.521509	+	0.853246i	$0.674631\pi$
$840$	−10.9029	−	0.231384i	−0.376187	−	0.00798350i
$841$	6.82510	−	21.0055i	0.235348	−	0.724327i
$842$	−2.95429	+	9.09236i	−0.101811	+	0.313343i
$843$	−1.17893	+	55.5517i	−0.0406044	+	1.91330i
$844$	−10.1865	+	14.0206i	−0.350635	+	0.482608i
$845$	−35.7306	+	13.5261i	−1.22917	+	0.465311i
$846$	27.5831	−	7.68497i	0.948325	−	0.264215i
$847$	31.9262	−	17.7555i	1.09700	−	0.610086i
$848$			15.9414i			0.547429i
$849$	0.739414	−	0.357196i	0.0253766	−	0.0122589i
$850$	20.3898	−	3.22943i	0.699364	−	0.110768i
$851$	7.20547	+	1.14123i	0.247000	+	0.0391210i
$852$	−14.4984	−	20.8727i	−0.496707	−	0.715088i
$853$	−29.0249	+	14.7889i	−0.993794	+	0.506363i	−0.873734	−	0.486404i	$-0.838308\pi$
$853$	−29.0249	+	14.7889i	−0.993794	+	0.506363i	−0.120059	+	0.992767i	$0.538308\pi$
$854$	−55.5849	−	76.5060i	−1.90208	−	2.61798i
$855$	−63.2305	−	23.5548i	−2.16244	−	0.805558i
$856$	5.38916	−	10.5768i	0.184198	−	0.361508i
$857$	−17.4117			−0.594773			−0.297387	−	0.954757i	$-0.596115\pi$
$857$	−17.4117			−0.594773			−0.297387	+	0.954757i	$0.596115\pi$
$858$	−33.2738	−	27.2424i	−1.13595	−	0.930040i
$859$	−26.2761			−0.896529			−0.448264	−	0.893901i	$-0.647958\pi$
$859$	−26.2761			−0.896529			−0.448264	+	0.893901i	$0.647958\pi$
$860$	−15.3646	+	30.1547i	−0.523928	+	1.02827i
$861$	16.1322	−	30.0667i	0.549786	−	1.02467i
$862$	3.34292	+	4.60113i	0.113860	+	0.156715i
$863$	−15.0592	+	7.67303i	−0.512620	+	0.261193i	−0.691111	−	0.722749i	$-0.742878\pi$
$863$	−15.0592	+	7.67303i	−0.512620	+	0.261193i	0.178491	+	0.983942i	$0.442878\pi$
$864$	26.8700	−	32.4257i	0.914135	−	1.10314i
$865$	−36.5848	−	5.79446i	−1.24392	−	0.197018i
$866$	−22.1373	+	3.50621i	−0.752257	+	0.119146i
$867$	−7.17667	−	14.8561i	−0.243732	−	0.504539i
$868$		−	26.3777i		−	0.895318i
$869$	3.96485	−	2.99209i	0.134498	−	0.101500i
$870$	27.5323	−	3.76374i	0.933432	−	0.127603i
$871$	−21.3762	+	19.1577i	−0.724306	+	0.649135i
$872$	6.22420	−	8.56687i	0.210778	−	0.290111i
$873$	−0.478006	−	4.15129i	−0.0161781	−	0.140500i
$874$	−6.96613	+	21.4395i	−0.235633	+	0.725203i
$875$	−4.11120	+	12.6530i	−0.138984	+	0.427749i
$876$	0.125740	−	5.92495i	0.00424838	−	0.200186i
$877$	2.39448	−	0.379248i	0.0808557	−	0.0128063i	−0.115875	−	0.993264i	$-0.536967\pi$
$877$	2.39448	−	0.379248i	0.0808557	−	0.0128063i	0.196731	+	0.980457i	$0.436967\pi$
$878$	60.1558	+	30.6509i	2.03016	+	1.03442i
$879$	6.42374	−	8.45814i	0.216667	−	0.285286i
$880$	−28.2352	+	15.0383i	−0.951810	+	0.506942i
$881$	31.8891			1.07437			0.537185	−	0.843464i	$-0.319488\pi$
$881$	31.8891			1.07437			0.537185	+	0.843464i	$0.319488\pi$
$882$	−24.5990	−	4.97411i	−0.828291	−	0.167487i
$883$	10.5583	−	14.5322i	0.355313	−	0.489047i	−0.593522	−	0.804818i	$-0.702263\pi$
$883$	10.5583	−	14.5322i	0.355313	−	0.489047i	0.948836	+	0.315771i	$0.102263\pi$
$884$	22.0150	−	5.84427i	0.740445	−	0.196564i
$885$	−12.5131	+	69.4354i	−0.420624	+	2.33405i
$886$	−30.2820	−	59.4318i	−1.01734	−	1.99665i
$887$	−2.29955	−	3.16506i	−0.0772113	−	0.106272i	0.768664	−	0.639652i	$-0.220922\pi$
$887$	−2.29955	−	3.16506i	−0.0772113	−	0.106272i	−0.845876	+	0.533380i	$0.820922\pi$
$888$	−5.06296	−	2.71653i	−0.169902	−	0.0911608i
$889$	−12.8768	−	6.56107i	−0.431875	−	0.220051i
$890$	−11.0177	−	11.0177i	−0.369315	−	0.369315i
$891$	−29.7832	−	1.99015i	−0.997775	−	0.0666726i
$892$	6.00242	+	6.00242i	0.200976	+	0.200976i
$893$	−33.4605	+	10.8720i	−1.11971	+	0.363817i
$894$	−23.1612	+	43.1670i	−0.774627	+	1.44372i
$895$	42.6877	+	6.76107i	1.42689	+	0.225998i
$896$	−5.23241	+	16.1037i	−0.174802	+	0.537987i
$897$	7.56638	+	4.60921i	0.252634	+	0.153897i
$898$	−10.0293	+	7.28672i	−0.334682	+	0.243161i
$899$	1.41384	+	8.92665i	0.0471543	+	0.297721i
$900$	−13.9402	−	21.0067i	−0.464672	−	0.700223i
$901$			13.2792i			0.442394i
$902$	0.741492	+	40.8403i	0.0246890	+	1.35983i
$903$	−17.3384	+	22.8294i	−0.576985	+	0.759716i
$904$	2.65315	−	5.20710i	0.0882424	−	0.173185i
$905$	−65.0831	+	10.3081i	−2.16343	+	0.342654i
$906$	60.4238	+	63.0441i	2.00745	+	2.09450i
$907$	−6.09868	−	1.98158i	−0.202503	−	0.0657974i	0.206009	−	0.978550i	$-0.433952\pi$
$907$	−6.09868	−	1.98158i	−0.202503	−	0.0657974i	−0.408513	+	0.912753i	$0.633952\pi$
$908$	−27.3302	−	53.6386i	−0.906986	−	1.78006i
$909$	33.6906	−	42.4590i	1.11745	−	1.40828i
$910$	15.3562	−	71.4310i	0.509053	−	2.36791i
$911$	11.5829	−	3.76353i	0.383760	−	0.124691i	−0.110782	−	0.993845i	$-0.535336\pi$
$911$	11.5829	−	3.76353i	0.383760	−	0.124691i	0.494542	+	0.869153i	$0.335336\pi$
$912$	−26.3133	+	34.6467i	−0.871321	+	1.14727i
$913$	13.9402	+	13.4430i	0.461354	+	0.444900i
$914$	−26.5090			−0.876840
$915$	22.9770	−	65.9224i	0.759595	−	2.17933i
$916$	−11.8353	+	1.87452i	−0.391048	+	0.0619360i
$917$	−4.02434	+	25.4087i	−0.132895	+	0.839068i
$918$	18.8195	−	22.7107i	0.621135	−	0.749563i
$919$	−6.66871	+	20.5242i	−0.219980	+	0.677030i	0.778782	+	0.627295i	$0.215838\pi$
$919$	−6.66871	+	20.5242i	−0.219980	+	0.677030i	−0.998762	+	0.0497353i	$0.984162\pi$
$920$	−2.17597	+	1.58094i	−0.0717397	+	0.0521220i
$921$	−0.518449	−	1.71890i	−0.0170835	−	0.0566395i
$922$	29.6227	−	9.62501i	0.975573	−	0.316983i
$923$	20.9371	−	9.26373i	0.689153	−	0.304919i
$924$	41.9674	−	13.4940i	1.38063	−	0.443918i
$925$	13.2241	−	13.2241i	0.434807	−	0.434807i
$926$	−60.9469	+	19.8028i	−2.00284	+	0.650761i
$927$	6.02453	−	16.1722i	0.197872	−	0.531166i
$928$	3.33354	−	21.0472i	0.109429	−	0.690907i
$929$	−22.5233	+	11.4762i	−0.738965	+	0.376521i	−0.782599	−	0.622526i	$-0.786106\pi$
$929$	−22.5233	+	11.4762i	−0.738965	+	0.376521i	0.0436340	+	0.999048i	$0.486106\pi$
$930$	29.8358	−	20.7242i	0.978354	−	0.679575i
$931$	30.4572	+	4.82394i	0.998193	+	0.158098i
$932$	7.40263	−	10.1888i	0.242481	−	0.333747i
$933$	−11.7965	−	24.4193i	−0.386200	−	0.799453i
$934$	−43.5981	−	43.5981i	−1.42657	−	1.42657i
$935$	−23.5200	+	12.5270i	−0.769187	+	0.409675i
$936$	−4.43242	−	5.38926i	−0.144878	−	0.176153i
$937$	16.6004	+	51.0907i	0.542310	+	1.66906i	0.727301	+	0.686319i	$0.240774\pi$
$937$	16.6004	+	51.0907i	0.542310	+	1.66906i	−0.184991	+	0.982740i	$0.559226\pi$
$938$	−8.58740	−	54.2187i	−0.280388	−	1.77030i
$939$	−21.1997	+	20.3186i	−0.691827	+	0.663073i
$940$	−29.6900	−	9.64687i	−0.968382	−	0.314646i
$941$	8.29206	−	4.22502i	0.270313	−	0.137732i	−0.313580	−	0.949562i	$-0.601528\pi$
$941$	8.29206	−	4.22502i	0.270313	−	0.137732i	0.583894	+	0.811830i	$0.301528\pi$
$942$	−3.32373	−	0.0705368i	−0.108293	−	0.00229821i
$943$	−1.31647	−	8.31187i	−0.0428702	−	0.270672i
$944$	40.5328	+	20.6525i	1.31923	+	0.672182i
$945$	−20.1028	−	46.5602i	−0.653944	−	1.51460i
$946$	4.75232	−	33.9873i	0.154511	−	1.10502i
$947$	30.4591	−	30.4591i	0.989786	−	0.989786i	−0.0101621	−	0.999948i	$-0.503235\pi$
$947$	30.4591	−	30.4591i	0.989786	−	0.989786i	0.999948	+	0.0101621i	$0.00323475\pi$
$948$	5.39723	−	2.60729i	0.175294	−	0.0846809i
$949$	5.21961	+	1.12211i	0.169436	+	0.0364252i
$950$	33.9678	+	46.7527i	1.10206	+	1.51686i
$951$	−25.5582	+	17.7530i	−0.828781	+	0.575680i
$952$	−1.80998	+	5.57055i	−0.0586619	+	0.180543i
$953$	−32.4764	+	23.5955i	−1.05201	+	0.764332i	−0.972594	−	0.232509i	$-0.925307\pi$
$953$	−32.4764	+	23.5955i	−1.05201	+	0.764332i	−0.0794191	+	0.996841i	$0.525307\pi$
$954$	27.5146	−	12.5789i	0.890819	−	0.407256i
$955$	−35.1329	−	17.9011i	−1.13687	−	0.579267i
$956$	−25.2784	+	25.2784i	−0.817561	+	0.817561i
$957$	−13.4792	+	6.81602i	−0.435720	+	0.220331i
$958$	59.1282			1.91035
$959$	6.56748	+	20.2126i	0.212075	+	0.652700i
$960$	−50.0137	+	15.0850i	−1.61419	+	0.486867i
$961$	−11.2766	−	15.5209i	−0.363761	−	0.500674i
$962$	24.2947	−	29.8597i	0.783292	−	0.962716i
$963$	55.1538	+	2.34202i	1.77731	+	0.0754706i
$964$	−7.13810	+	45.0682i	−0.229903	+	1.45155i
$965$	17.0865	−	23.5176i	0.550035	−	0.757059i
$966$	−15.2563	+	7.37003i	−0.490865	+	0.237127i
$967$	−9.52606	+	9.52606i	−0.306337	+	0.306337i	−0.843487	−	0.537150i	$-0.819501\pi$
$967$	−9.52606	+	9.52606i	−0.306337	+	0.306337i	0.537150	+	0.843487i	$0.319501\pi$
$968$	−4.83227	+	5.19656i	−0.155315	+	0.167024i
$969$	−21.9190	+	28.8608i	−0.704141	+	0.927142i
$970$	−3.85852	+	7.57278i	−0.123890	+	0.243147i
$971$	21.9240	−	30.1759i	0.703576	−	0.968389i	−0.296336	−	0.955084i	$-0.595765\pi$
$971$	21.9240	−	30.1759i	0.703576	−	0.968389i	0.999911	−	0.0133053i	$-0.00423534\pi$
$972$	−34.7802	−	9.37060i	−1.11557	−	0.300562i
$973$	4.48439	−	2.28491i	0.143763	−	0.0732509i
$974$	−3.93711	+	12.1172i	−0.126153	+	0.388259i
$975$	20.9604	−	8.74707i	0.671269	−	0.280130i
$976$	−36.4160	−	26.4578i	−1.16565	−	0.846893i
$977$	−19.1088	+	37.5032i	−0.611346	+	1.19983i	0.353108	+	0.935583i	$0.385125\pi$
$977$	−19.1088	+	37.5032i	−0.611346	+	1.19983i	−0.964454	+	0.264252i	$0.914875\pi$
$978$	0.267822	+	1.95916i	0.00856400	+	0.0626469i
$979$	7.61481	+	3.70739i	0.243370	+	0.118489i
$980$	19.3478	+	19.3478i	0.618044	+	0.618044i
$981$	48.2675	+	9.76007i	1.54106	+	0.311615i
$982$	11.6934	+	73.8294i	0.373152	+	2.35599i
$983$	4.52957	−	28.5986i	0.144471	−	0.912153i	−0.803848	−	0.594834i	$-0.797218\pi$
$983$	4.52957	−	28.5986i	0.144471	−	0.912153i	0.948319	−	0.317318i	$-0.102782\pi$
$984$	−1.17550	+	6.52289i	−0.0374737	+	0.207942i
$985$	55.8439	+	18.1448i	1.77934	+	0.578141i
$986$	2.33478	−	14.7412i	0.0743546	−	0.469457i
$987$	−23.3010	−	12.5022i	−0.741680	−	0.397948i
$988$	42.5553	+	47.4832i	1.35386	+	1.51064i
$989$			7.07031i			0.224823i
$990$	48.2356	+	36.8674i	1.53303	+	1.17172i
$991$	−0.498318			−0.0158296			−0.00791480	−	0.999969i	$-0.502519\pi$
$991$	−0.498318			−0.0158296			−0.00791480	+	0.999969i	$0.502519\pi$
$992$	−8.60846	−	26.4941i	−0.273319	−	0.841189i
$993$	46.3401	−	13.9770i	1.47056	−	0.443547i
$994$	−6.84932	+	43.2449i	−0.217247	+	1.37165i
$995$	−13.2686	−	26.0411i	−0.420643	−	0.825558i
$996$	13.3321	+	19.1936i	0.422443	+	0.608172i
$997$	30.4569	−	22.1283i	0.964581	−	0.700809i	0.0103706	−	0.999946i	$-0.496699\pi$
$997$	30.4569	−	22.1283i	0.964581	−	0.700809i	0.954210	+	0.299137i	$0.0966989\pi$
$998$	−58.6642	−	42.6220i	−1.85698	−	1.34918i
$999$	1.69976	−	26.6658i	0.0537781	−	0.843669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bi.a.5.8	✓	416
3.2	odd	2	inner	429.2.bi.a.5.45	yes	416
11.9	even	5	inner	429.2.bi.a.317.45	yes	416
13.8	odd	4	inner	429.2.bi.a.203.8	yes	416
33.20	odd	10	inner	429.2.bi.a.317.8	yes	416
39.8	even	4	inner	429.2.bi.a.203.45	yes	416
143.86	odd	20	inner	429.2.bi.a.86.45	yes	416
429.86	even	20	inner	429.2.bi.a.86.8	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bi.a.5.8	✓	416	1.1	even	1	trivial
429.2.bi.a.5.45	yes	416	3.2	odd	2	inner
429.2.bi.a.86.8	yes	416	429.86	even	20	inner
429.2.bi.a.86.45	yes	416	143.86	odd	20	inner
429.2.bi.a.203.8	yes	416	13.8	odd	4	inner
429.2.bi.a.203.45	yes	416	39.8	even	4	inner
429.2.bi.a.317.8	yes	416	33.20	odd	10	inner
429.2.bi.a.317.45	yes	416	11.9	even	5	inner

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.942586 + 1.84993i) q^{2} +(-1.52624 - 0.818902i) q^{3} +(-1.35820 - 1.86940i) q^{4} +(-2.61854 + 1.33421i) q^{5} +(2.95352 - 2.05155i) q^{6} +(-3.28014 - 0.519524i) q^{7} +(0.637161 - 0.100916i) q^{8} +(1.65880 + 2.49968i) q^{9} +O(q^{10})\)	\(q+(-0.942586 + 1.84993i) q^{2} +(-1.52624 - 0.818902i) q^{3} +(-1.35820 - 1.86940i) q^{4} +(-2.61854 + 1.33421i) q^{5} +(2.95352 - 2.05155i) q^{6} +(-3.28014 - 0.519524i) q^{7} +(0.637161 - 0.100916i) q^{8} +(1.65880 + 2.49968i) q^{9} -6.10173i q^{10} +(1.08198 + 3.13517i) q^{11} +(0.542079 + 3.96539i) q^{12} +(-3.60016 - 0.197042i) q^{13} +(4.05290 - 5.57834i) q^{14} +(5.08910 + 0.108002i) q^{15} +(1.01421 - 3.12141i) q^{16} +(0.844836 - 2.60014i) q^{17} +(-6.18779 + 0.712502i) q^{18} +(7.55903 - 1.19723i) q^{19} +(6.05069 + 3.08298i) q^{20} +(4.58084 + 3.47903i) q^{21} +(-6.81971 - 0.953577i) q^{22} +1.41869 q^{23} +(-1.05510 - 0.367750i) q^{24} +(2.13770 - 2.94229i) q^{25} +(3.75798 - 6.47432i) q^{26} +(-0.484733 - 5.17349i) q^{27} +(3.48389 + 6.83753i) q^{28} +(-1.54550 - 2.12719i) q^{29} +(-4.99671 + 9.31268i) q^{30} +(-3.06267 - 1.56051i) q^{31} +(5.73072 + 5.73072i) q^{32} +(0.916034 - 5.67106i) q^{33} +(4.01374 + 4.01374i) q^{34} +(9.28234 - 3.01602i) q^{35} +(2.41992 - 6.49603i) q^{36} +(5.07895 + 0.804426i) q^{37} +(-4.91024 + 15.1122i) q^{38} +(5.33335 + 3.24891i) q^{39} +(-1.53379 + 1.11436i) q^{40} +(-0.927946 - 5.85882i) q^{41} +(-10.7538 + 5.19494i) q^{42} +4.98368i q^{43} +(4.39135 - 6.28086i) q^{44} +(-7.67873 - 4.33231i) q^{45} +(-1.33724 + 2.62448i) q^{46} +(-4.54047 + 0.719139i) q^{47} +(-4.10404 + 3.93347i) q^{48} +(3.83204 + 1.24510i) q^{49} +(3.42807 + 6.72797i) q^{50} +(-3.41868 + 3.27659i) q^{51} +(4.52139 + 6.99778i) q^{52} +(-4.61943 + 1.50094i) q^{53} +(10.0275 + 3.97974i) q^{54} +(-7.01621 - 6.76598i) q^{55} -2.14241 q^{56} +(-12.5173 - 4.36284i) q^{57} +(5.39193 - 0.853997i) q^{58} +(-2.16828 + 13.6900i) q^{59} +(-6.71013 - 9.66027i) q^{60} +(4.23812 - 13.0436i) q^{61} +(5.77366 - 4.19481i) q^{62} +(-4.14246 - 9.06108i) q^{63} +(-9.76031 + 3.17132i) q^{64} +(9.69007 - 4.28742i) q^{65} +(9.62762 + 7.04006i) q^{66} +(5.62946 - 5.62946i) q^{67} +(-6.00816 + 1.95217i) q^{68} +(-2.16526 - 1.16177i) q^{69} +(-3.16999 + 20.0145i) q^{70} +(-5.65782 + 2.88280i) q^{71} +(1.30918 + 1.42530i) q^{72} +(-1.46250 - 0.231638i) q^{73} +(-6.27548 + 8.63745i) q^{74} +(-5.67209 + 2.74007i) q^{75} +(-12.5048 - 12.5048i) q^{76} +(-1.92027 - 10.8459i) q^{77} +(-11.0374 + 6.80393i) q^{78} +(-0.462800 - 1.42435i) q^{79} +(1.50888 + 9.52669i) q^{80} +(-3.49677 + 8.29293i) q^{81} +(11.7131 + 3.80581i) q^{82} +(5.20267 - 2.65089i) q^{83} +(0.282014 - 13.2887i) q^{84} +(1.25690 + 7.93575i) q^{85} +(-9.21946 - 4.69755i) q^{86} +(0.616832 + 4.51221i) q^{87} +(1.00579 + 1.88842i) q^{88} +(1.80567 - 1.80567i) q^{89} +(15.2523 - 10.1215i) q^{90} +(11.7067 + 2.51669i) q^{91} +(-1.92687 - 2.65211i) q^{92} +(3.39646 + 4.88973i) q^{93} +(2.94942 - 9.07739i) q^{94} +(-18.1963 + 13.2204i) q^{95} +(-4.05354 - 13.4393i) q^{96} +(-1.24109 - 0.632366i) q^{97} +(-5.91538 + 5.91538i) q^{98} +(-6.04212 + 7.90524i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) \) 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9	\( 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9} - 20 q^{13} - 30 q^{15} + 32 q^{16} + 2 q^{18} - 4 q^{19} - 12 q^{21} - 24 q^{22} - 78 q^{24} - 36 q^{27} - 84 q^{28} - 28 q^{31} - 44 q^{33} - 24 q^{34} - 12 q^{37} + 54 q^{39} + 88 q^{40} - 56 q^{42} + 8 q^{45} - 92 q^{46} + 40 q^{48} - 44 q^{52} - 176 q^{54} - 72 q^{55} - 6 q^{57} - 4 q^{58} + 12 q^{60} - 48 q^{61} - 46 q^{63} + 204 q^{66} - 64 q^{67} + 56 q^{70} - 66 q^{72} - 12 q^{73} - 104 q^{76} - 92 q^{78} + 104 q^{79} + 124 q^{81} + 16 q^{84} - 12 q^{85} - 24 q^{87} - 84 q^{91} - 124 q^{93} + 328 q^{94} - 152 q^{96} + 52 q^{97} - 142 q^{99}+O(q^{100}) \) 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9 - 20 * q^13 - 30 * q^15 + 32 * q^16 + 2 * q^18 - 4 * q^19 - 12 * q^21 - 24 * q^22 - 78 * q^24 - 36 * q^27 - 84 * q^28 - 28 * q^31 - 44 * q^33 - 24 * q^34 - 12 * q^37 + 54 * q^39 + 88 * q^40 - 56 * q^42 + 8 * q^45 - 92 * q^46 + 40 * q^48 - 44 * q^52 - 176 * q^54 - 72 * q^55 - 6 * q^57 - 4 * q^58 + 12 * q^60 - 48 * q^61 - 46 * q^63 + 204 * q^66 - 64 * q^67 + 56 * q^70 - 66 * q^72 - 12 * q^73 - 104 * q^76 - 92 * q^78 + 104 * q^79 + 124 * q^81 + 16 * q^84 - 12 * q^85 - 24 * q^87 - 84 * q^91 - 124 * q^93 + 328 * q^94 - 152 * q^96 + 52 * q^97 - 142 * q^99

Introduction

L-functions

Modular forms

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