LMFDB - Embedded newform 429.2.bb.b.64.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(25,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 5]))

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

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

chi := DirichletCharacter("429.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bb (of order $10$, degree $4$, 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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.4
Character	$\chi$	$=$	429.64
Dual form			429.2.bb.b.181.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54582 - 0.502269i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.519265 + 0.377268i) q^{4} +(-1.17463 + 0.381659i) q^{5} +(-1.54582 + 0.502269i) q^{6} +(0.262950 - 0.361920i) q^{7} +(1.29754 + 1.78591i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-1.54582 - 0.502269i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.519265 + 0.377268i) q^{4} +(-1.17463 + 0.381659i) q^{5} +(-1.54582 + 0.502269i) q^{6} +(0.262950 - 0.361920i) q^{7} +(1.29754 + 1.78591i) q^{8} +(0.309017 - 0.951057i) q^{9} +2.00746 q^{10} +(-3.04399 - 1.31687i) q^{11} +0.641847 q^{12} +(0.726018 - 3.53170i) q^{13} +(-0.588256 + 0.427393i) q^{14} +(-0.725959 + 0.999197i) q^{15} +(-1.50545 - 4.63329i) q^{16} +(0.944039 + 2.90545i) q^{17} +(-0.955372 + 1.31496i) q^{18} +(-4.20662 - 5.78992i) q^{19} +(-0.753930 - 0.244967i) q^{20} -0.447358i q^{21} +(4.04404 + 3.56455i) q^{22} -6.54722 q^{23} +(2.09947 + 0.682158i) q^{24} +(-2.81100 + 2.04231i) q^{25} +(-2.89616 + 5.09473i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.273082 - 0.0887296i) q^{28} +(-2.77921 - 2.01922i) q^{29} +(1.62407 - 1.17996i) q^{30} +(6.68042 + 2.17060i) q^{31} +3.50337i q^{32} +(-3.23667 + 0.723839i) q^{33} -4.96548i q^{34} +(-0.170738 + 0.525478i) q^{35} +(0.519265 - 0.377268i) q^{36} +(-1.24674 + 1.71599i) q^{37} +(3.59460 + 11.0631i) q^{38} +(-1.48852 - 3.28395i) q^{39} +(-2.20574 - 1.60256i) q^{40} +(-2.32491 - 3.19996i) q^{41} +(-0.224694 + 0.691537i) q^{42} -6.93097 q^{43} +(-1.08382 - 1.83220i) q^{44} +1.23507i q^{45} +(10.1209 + 3.28846i) q^{46} +(-4.09662 - 5.63851i) q^{47} +(-3.94131 - 2.86353i) q^{48} +(2.10128 + 6.46706i) q^{49} +(5.37111 - 1.74518i) q^{50} +(2.47153 + 1.79567i) q^{51} +(1.70939 - 1.55998i) q^{52} +(-0.790898 + 2.43413i) q^{53} +1.62538i q^{54} +(4.07814 + 0.385066i) q^{55} +0.987547 q^{56} +(-6.80646 - 2.21155i) q^{57} +(3.28199 + 4.51727i) q^{58} +(-5.07623 + 6.98682i) q^{59} +(-0.753930 + 0.244967i) q^{60} +(-4.43757 - 13.6574i) q^{61} +(-9.23653 - 6.71073i) q^{62} +(-0.262950 - 0.361920i) q^{63} +(-1.25126 + 3.85098i) q^{64} +(0.495106 + 4.42552i) q^{65} +(5.36689 + 0.506752i) q^{66} -8.02093i q^{67} +(-0.605928 + 1.86486i) q^{68} +(-5.29681 + 3.84836i) q^{69} +(0.527863 - 0.726541i) q^{70} +(0.507879 - 0.165020i) q^{71} +(2.09947 - 0.682158i) q^{72} +(9.10476 - 12.5316i) q^{73} +(2.78913 - 2.02642i) q^{74} +(-1.07371 + 3.30453i) q^{75} -4.59353i q^{76} +(-1.27702 + 0.755408i) q^{77} +(0.651566 + 5.82404i) q^{78} +(-1.88672 + 5.80673i) q^{79} +(3.53667 + 4.86781i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(1.98666 + 6.11431i) q^{82} +(0.522697 - 0.169835i) q^{83} +(0.168774 - 0.232297i) q^{84} +(-2.21779 - 3.05252i) q^{85} +(10.7141 + 3.48121i) q^{86} -3.43530 q^{87} +(-1.59788 - 7.14499i) q^{88} +0.360786i q^{89} +(0.620339 - 1.90921i) q^{90} +(-1.08729 - 1.19142i) q^{91} +(-3.39974 - 2.47006i) q^{92} +(6.68042 - 2.17060i) q^{93} +(3.50060 + 10.7737i) q^{94} +(7.15099 + 5.19549i) q^{95} +(2.05923 + 2.83428i) q^{96} +(11.6351 + 3.78047i) q^{97} -11.0523i q^{98} +(-2.19306 + 2.48807i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9}+O(q^{10}) $ 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9	$ 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9} + 60 q^{12} - 3 q^{13} - 42 q^{14} - 16 q^{16} - 6 q^{17} - 40 q^{22} + 12 q^{23} + 4 q^{25} - 24 q^{26} + 14 q^{27} - 22 q^{29} - 10 q^{30} - 10 q^{35} + 20 q^{36} - 26 q^{38} + 3 q^{39} - 18 q^{42} + 6 q^{48} - 14 q^{49} - 24 q^{51} + 39 q^{52} + 10 q^{53} - 64 q^{55} - 20 q^{56} + 2 q^{61} - 8 q^{62} + 24 q^{64} - 58 q^{65} + 30 q^{66} + 18 q^{68} - 2 q^{69} - 86 q^{74} - 14 q^{75} + 52 q^{77} + 14 q^{78} - 24 q^{79} - 14 q^{81} + 62 q^{82} - 28 q^{87} - 46 q^{88} - 10 q^{90} - 19 q^{91} + 58 q^{92} + 86 q^{94} + 156 q^{95}+O(q^{100}) $ 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9 + 60 * q^12 - 3 * q^13 - 42 * q^14 - 16 * q^16 - 6 * q^17 - 40 * q^22 + 12 * q^23 + 4 * q^25 - 24 * q^26 + 14 * q^27 - 22 * q^29 - 10 * q^30 - 10 * q^35 + 20 * q^36 - 26 * q^38 + 3 * q^39 - 18 * q^42 + 6 * q^48 - 14 * q^49 - 24 * q^51 + 39 * q^52 + 10 * q^53 - 64 * q^55 - 20 * q^56 + 2 * q^61 - 8 * q^62 + 24 * q^64 - 58 * q^65 + 30 * q^66 + 18 * q^68 - 2 * q^69 - 86 * q^74 - 14 * q^75 + 52 * q^77 + 14 * q^78 - 24 * q^79 - 14 * q^81 + 62 * q^82 - 28 * q^87 - 46 * q^88 - 10 * q^90 - 19 * q^91 + 58 * q^92 + 86 * q^94 + 156 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.54582	−	0.502269i	−1.09306	−	0.355158i	−0.293634	−	0.955918i	$-0.594865\pi$
$2$	−1.54582	−	0.502269i	−1.09306	−	0.355158i	−0.799429	+	0.600760i	$0.794865\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	0.519265	+	0.377268i	0.259632	+	0.188634i
$5$	−1.17463	+	0.381659i	−0.525309	+	0.170683i	−0.559653	−	0.828727i	$-0.689066\pi$
$5$	−1.17463	+	0.381659i	−0.525309	+	0.170683i	0.0343445	+	0.999410i	$0.489066\pi$
$6$	−1.54582	+	0.502269i	−0.631080	+	0.205050i
$7$	0.262950	−	0.361920i	0.0993859	−	0.136793i	−0.756428	−	0.654077i	$-0.773057\pi$
$7$	0.262950	−	0.361920i	0.0993859	−	0.136793i	0.855814	+	0.517284i	$0.173057\pi$
$8$	1.29754	+	1.78591i	0.458750	+	0.631416i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	2.00746			0.634815
$11$	−3.04399	−	1.31687i	−0.917796	−	0.397052i
$11$	−3.04399	−	1.31687i	−0.917796	−	0.397052i
$12$	0.641847			0.185285
$13$	0.726018	−	3.53170i	0.201361	−	0.979517i
$13$	0.726018	−	3.53170i	0.201361	−	0.979517i
$14$	−0.588256	+	0.427393i	−0.157218	+	0.114226i
$15$	−0.725959	+	0.999197i	−0.187442	+	0.257991i
$16$	−1.50545	−	4.63329i	−0.376362	−	1.15832i
$17$	0.944039	+	2.90545i	0.228963	+	0.704676i	0.997865	+	0.0653093i	$0.0208034\pi$
$17$	0.944039	+	2.90545i	0.228963	+	0.704676i	−0.768902	+	0.639367i	$0.779197\pi$
$18$	−0.955372	+	1.31496i	−0.225183	+	0.309938i
$19$	−4.20662	−	5.78992i	−0.965066	−	1.32830i	−0.944500	−	0.328510i	$-0.893453\pi$
$19$	−4.20662	−	5.78992i	−0.965066	−	1.32830i	−0.0205653	−	0.999789i	$-0.506547\pi$
$20$	−0.753930	−	0.244967i	−0.168584	−	0.0547762i
$21$		−	0.447358i		−	0.0976215i
$22$	4.04404	+	3.56455i	0.862193	+	0.759965i
$23$	−6.54722			−1.36519			−0.682595	−	0.730797i	$-0.739149\pi$
$23$	−6.54722			−1.36519			−0.682595	+	0.730797i	$0.739149\pi$
$24$	2.09947	+	0.682158i	0.428552	+	0.139245i
$25$	−2.81100	+	2.04231i	−0.562201	+	0.408463i
$26$	−2.89616	+	5.09473i	−0.567983	+	0.999159i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	0.273082	−	0.0887296i	0.0516076	−	0.0167683i
$29$	−2.77921	−	2.01922i	−0.516087	−	0.374959i	0.299041	−	0.954240i	$-0.403333\pi$
$29$	−2.77921	−	2.01922i	−0.516087	−	0.374959i	−0.815128	+	0.579281i	$0.803333\pi$
$30$	1.62407	−	1.17996i	0.296513	−	0.215429i
$31$	6.68042	+	2.17060i	1.19984	+	0.389851i	0.839701	−	0.543048i	$-0.182730\pi$
$31$	6.68042	+	2.17060i	1.19984	+	0.389851i	0.360137	+	0.932899i	$0.382730\pi$
$32$			3.50337i			0.619314i
$33$	−3.23667	+	0.723839i	−0.563433	+	0.126004i
$34$		−	4.96548i		−	0.851573i
$35$	−0.170738	+	0.525478i	−0.0288600	+	0.0888220i
$36$	0.519265	−	0.377268i	0.0865441	−	0.0628780i
$37$	−1.24674	+	1.71599i	−0.204963	+	0.282107i	−0.899107	−	0.437729i	$-0.855783\pi$
$37$	−1.24674	+	1.71599i	−0.204963	+	0.282107i	0.694144	+	0.719836i	$0.255783\pi$
$38$	3.59460	+	11.0631i	0.583122	+	1.79466i
$39$	−1.48852	−	3.28395i	−0.238354	−	0.525852i
$40$	−2.20574	−	1.60256i	−0.348757	−	0.253387i
$41$	−2.32491	−	3.19996i	−0.363090	−	0.499750i	0.587917	−	0.808922i	$-0.299948\pi$
$41$	−2.32491	−	3.19996i	−0.363090	−	0.499750i	−0.951006	+	0.309171i	$0.899948\pi$
$42$	−0.224694	+	0.691537i	−0.0346710	+	0.106706i
$43$	−6.93097			−1.05696			−0.528481	−	0.848945i	$-0.677238\pi$
$43$	−6.93097			−1.05696			−0.528481	+	0.848945i	$0.677238\pi$
$44$	−1.08382	−	1.83220i	−0.163392	−	0.276215i
$45$			1.23507i			0.184114i
$46$	10.1209	+	3.28846i	1.49224	+	0.484858i
$47$	−4.09662	−	5.63851i	−0.597553	−	0.822461i	0.397929	−	0.917416i	$-0.369729\pi$
$47$	−4.09662	−	5.63851i	−0.597553	−	0.822461i	−0.995482	+	0.0949554i	$0.969729\pi$
$48$	−3.94131	−	2.86353i	−0.568879	−	0.413315i
$49$	2.10128	+	6.46706i	0.300182	+	0.923866i
$50$	5.37111	−	1.74518i	0.759589	−	0.246805i
$51$	2.47153	+	1.79567i	0.346083	+	0.251444i
$52$	1.70939	−	1.55998i	0.237050	−	0.216331i
$53$	−0.790898	+	2.43413i	−0.108638	+	0.334354i	−0.990567	−	0.137028i	$-0.956245\pi$
$53$	−0.790898	+	2.43413i	−0.108638	+	0.334354i	0.881929	+	0.471382i	$0.156245\pi$
$54$			1.62538i			0.221186i
$55$	4.07814	+	0.385066i	0.549896	+	0.0519223i
$56$	0.987547			0.131967
$57$	−6.80646	−	2.21155i	−0.901538	−	0.292927i
$58$	3.28199	+	4.51727i	0.430946	+	0.593146i
$59$	−5.07623	+	6.98682i	−0.660868	+	0.909607i	−0.999510	−	0.0313084i	$-0.990033\pi$
$59$	−5.07623	+	6.98682i	−0.660868	+	0.909607i	0.338642	+	0.940915i	$0.390033\pi$
$60$	−0.753930	+	0.244967i	−0.0973319	+	0.0316251i
$61$	−4.43757	−	13.6574i	−0.568172	−	1.74866i	−0.658332	−	0.752728i	$-0.728738\pi$
$61$	−4.43757	−	13.6574i	−0.568172	−	1.74866i	0.0901594	−	0.995927i	$-0.471262\pi$
$62$	−9.23653	−	6.71073i	−1.17304	−	0.852264i
$63$	−0.262950	−	0.361920i	−0.0331286	−	0.0455977i
$64$	−1.25126	+	3.85098i	−0.156408	+	0.481373i
$65$	0.495106	+	4.42552i	0.0614103	+	0.548918i
$66$	5.36689	+	0.506752i	0.660619	+	0.0623769i
$67$		−	8.02093i		−	0.979913i	−0.871747	−	0.489956i	$-0.837013\pi$
$67$		−	8.02093i		−	0.979913i	0.871747	−	0.489956i	$-0.162987\pi$
$68$	−0.605928	+	1.86486i	−0.0734796	+	0.226147i
$69$	−5.29681	+	3.84836i	−0.637661	+	0.463288i
$70$	0.527863	−	0.726541i	0.0630916	−	0.0868382i
$71$	0.507879	−	0.165020i	0.0602741	−	0.0195842i	−0.278725	−	0.960371i	$-0.589912\pi$
$71$	0.507879	−	0.165020i	0.0602741	−	0.0195842i	0.338999	+	0.940787i	$0.389912\pi$
$72$	2.09947	−	0.682158i	0.247425	−	0.0803931i
$73$	9.10476	−	12.5316i	1.06563	−	1.46672i	0.191209	−	0.981549i	$-0.438759\pi$
$73$	9.10476	−	12.5316i	1.06563	−	1.46672i	0.874422	−	0.485166i	$-0.161241\pi$
$74$	2.78913	−	2.02642i	0.324229	−	0.235566i
$75$	−1.07371	+	3.30453i	−0.123981	+	0.381574i
$76$		−	4.59353i		−	0.526914i
$77$	−1.27702	+	0.755408i	−0.145530	+	0.0860867i
$78$	0.651566	+	5.82404i	0.0737754	+	0.659443i
$79$	−1.88672	+	5.80673i	−0.212273	+	0.653308i	0.787063	+	0.616872i	$0.211600\pi$
$79$	−1.88672	+	5.80673i	−0.212273	+	0.653308i	−0.999336	+	0.0364356i	$0.988400\pi$
$80$	3.53667	+	4.86781i	0.395412	+	0.544238i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	1.98666	+	6.11431i	0.219390	+	0.675212i
$83$	0.522697	−	0.169835i	0.0573735	−	0.0186418i	−0.280190	−	0.959945i	$-0.590397\pi$
$83$	0.522697	−	0.169835i	0.0573735	−	0.0186418i	0.337563	+	0.941303i	$0.390397\pi$
$84$	0.168774	−	0.232297i	0.0184147	−	0.0253457i
$85$	−2.21779	−	3.05252i	−0.240553	−	0.331092i
$86$	10.7141	+	3.48121i	1.15533	+	0.375388i
$87$	−3.43530			−0.368303
$88$	−1.59788	−	7.14499i	−0.170335	−	0.761658i
$89$			0.360786i			0.0382432i	0.999817	+	0.0191216i	$0.00608697\pi$
$89$			0.360786i			0.0382432i	−0.999817	+	0.0191216i	$0.993913\pi$
$90$	0.620339	−	1.90921i	0.0653895	−	0.201248i
$91$	−1.08729	−	1.19142i	−0.113979	−	0.124895i
$92$	−3.39974	−	2.47006i	−0.354447	−	0.257521i
$93$	6.68042	−	2.17060i	0.692727	−	0.225081i
$94$	3.50060	+	10.7737i	0.361060	+	1.11123i
$95$	7.15099	+	5.19549i	0.733676	+	0.533047i
$96$	2.05923	+	2.83428i	0.210169	+	0.289273i
$97$	11.6351	+	3.78047i	1.18136	+	0.383848i	0.832873	−	0.553464i	$-0.186694\pi$
$97$	11.6351	+	3.78047i	1.18136	+	0.383848i	0.348491	+	0.937312i	$0.386694\pi$
$98$		−	11.0523i		−	1.11646i
$99$	−2.19306	+	2.48807i	−0.220411	+	0.250060i
$100$	−2.23015			−0.223015
$101$	5.92821	−	18.2452i	0.589879	−	1.81546i	0.0111547	−	0.999938i	$-0.496449\pi$
$101$	5.92821	−	18.2452i	0.589879	−	1.81546i	0.578724	−	0.815523i	$-0.303551\pi$
$102$	−2.91864	−	4.01716i	−0.288988	−	0.397758i
$103$	6.27255	+	4.55728i	0.618053	+	0.449042i	0.852241	−	0.523150i	$-0.175243\pi$
$103$	6.27255	+	4.55728i	0.618053	+	0.449042i	−0.234188	+	0.972191i	$0.575243\pi$
$104$	7.24935	−	3.28592i	0.710857	−	0.322211i
$105$	0.170738	+	0.525478i	0.0166623	+	0.0512814i
$106$	2.44518	−	3.36550i	0.237497	−	0.326886i
$107$	14.7557	−	10.7206i	1.42648	−	1.03640i	0.435824	−	0.900032i	$-0.356457\pi$
$107$	14.7557	−	10.7206i	1.42648	−	1.03640i	0.990658	−	0.136369i	$-0.0435431\pi$
$108$	0.198342	−	0.610432i	0.0190854	−	0.0587389i
$109$			18.8397i			1.80452i	0.431194	+	0.902259i	$0.358093\pi$
$109$			18.8397i			1.80452i	−0.431194	+	0.902259i	$0.641907\pi$
$110$	−6.11068	−	2.64357i	−0.582631	−	0.252054i
$111$			2.12108i			0.201324i
$112$	−2.07274	−	0.673473i	−0.195855	−	0.0636372i
$113$	9.97818	−	7.24957i	0.938668	−	0.681982i	−0.00943147	−	0.999956i	$-0.503002\pi$
$113$	9.97818	−	7.24957i	0.938668	−	0.681982i	0.948100	+	0.317973i	$0.103002\pi$
$114$	9.41080	+	6.83734i	0.881402	+	0.640376i
$115$	7.69053	−	2.49881i	0.717146	−	0.233015i
$116$	−0.681362	−	2.09702i	−0.0632629	−	0.194703i
$117$	−3.13449	−	1.78184i	−0.289784	−	0.164731i
$118$	11.3562	−	8.25077i	1.04542	−	0.759545i
$119$	1.29978	+	0.422323i	0.119150	+	0.0387143i
$120$	−2.72644			−0.248889
$121$	7.53170	+	8.01707i	0.684700	+	0.728825i
$122$			23.3408i			2.11318i
$123$	−3.76178	−	1.22228i	−0.339188	−	0.110209i
$124$	2.65001	+	3.64742i	0.237978	+	0.327548i
$125$	6.15220	−	8.46778i	0.550270	−	0.757381i
$126$	0.224694	+	0.691537i	0.0200173	+	0.0616070i
$127$	1.29268	+	3.97846i	0.114707	+	0.353031i	0.991886	−	0.127132i	$-0.0405773\pi$
$127$	1.29268	+	3.97846i	0.114707	+	0.353031i	−0.877179	+	0.480164i	$0.840577\pi$
$128$	7.98691	−	10.9930i	0.705950	−	0.971657i
$129$	−5.60727	+	4.07392i	−0.493692	+	0.358689i
$130$	1.45745	−	7.08975i	0.127827	−	0.621812i
$131$	11.0780			0.967892			0.483946	−	0.875098i	$-0.339203\pi$
$131$	11.0780			0.967892			0.483946	+	0.875098i	$0.339203\pi$
$132$	−1.95377	−	0.845229i	−0.170054	−	0.0735678i
$133$	−3.20162			−0.277616
$134$	−4.02866	+	12.3989i	−0.348023	+	1.07111i
$135$	0.725959	+	0.999197i	0.0624806	+	0.0859971i
$136$	−3.96396	+	5.45592i	−0.339906	+	0.467841i
$137$	7.66681	−	2.49110i	0.655019	−	0.212829i	0.0373933	−	0.999301i	$-0.488095\pi$
$137$	7.66681	−	2.49110i	0.655019	−	0.212829i	0.617626	+	0.786472i	$0.288095\pi$
$138$	10.1209	−	3.28846i	0.861544	−	0.279933i
$139$	−9.86896	−	7.17022i	−0.837074	−	0.608170i	0.0844778	−	0.996425i	$-0.473078\pi$
$139$	−9.86896	−	7.17022i	−0.837074	−	0.608170i	−0.921552	+	0.388256i	$0.873078\pi$
$140$	−0.286904	+	0.208448i	−0.0242479	+	0.0176171i
$141$	−6.62846	−	2.15372i	−0.558217	−	0.181376i
$142$	−0.867975			−0.0728389
$143$	−6.86078	+	9.79437i	−0.573727	+	0.819046i
$144$	−4.87173			−0.405977
$145$	4.03519	+	1.31111i	0.335104	+	0.108882i
$146$	−20.3686	+	14.7987i	−1.68572	+	1.22475i
$147$	5.50121	+	3.99686i	0.453732	+	0.329656i
$148$	−1.29477	+	0.420698i	−0.106430	+	0.0345811i
$149$	−13.0245	+	4.23191i	−1.06701	+	0.346692i	−0.789321	−	0.613980i	$-0.789567\pi$
$149$	−13.0245	+	4.23191i	−1.06701	+	0.346692i	−0.277686	+	0.960672i	$0.589567\pi$
$150$	3.31953	−	4.56894i	0.271038	−	0.373052i
$151$	−3.33311	−	4.58764i	−0.271245	−	0.373337i	0.651565	−	0.758593i	$-0.274113\pi$
$151$	−3.33311	−	4.58764i	−0.271245	−	0.373337i	−0.922809	+	0.385257i	$0.874113\pi$
$152$	4.88202	−	15.0253i	0.395984	−	1.21871i
$153$	3.05497			0.246980
$154$	2.35347	−	0.526321i	0.189648	−	0.0424122i
$155$	−8.67542			−0.696827
$156$	0.465992	−	2.26681i	0.0373092	−	0.181490i
$157$	−11.8390	+	8.60157i	−0.944858	+	0.686480i	−0.949585	−	0.313509i	$-0.898495\pi$
$157$	−11.8390	+	8.60157i	−0.944858	+	0.686480i	0.00472701	+	0.999989i	$0.498495\pi$
$158$	5.83307	−	8.02854i	0.464054	−	0.638716i
$159$	0.790898	+	2.43413i	0.0627223	+	0.193039i
$160$	−1.33709	−	4.11515i	−0.105706	−	0.325331i
$161$	−1.72159	+	2.36957i	−0.135681	+	0.186748i
$162$	0.955372	+	1.31496i	0.0750611	+	0.103313i
$163$	−10.6436	−	3.45830i	−0.833668	−	0.270875i	−0.139078	−	0.990281i	$-0.544414\pi$
$163$	−10.6436	−	3.45830i	−0.833668	−	0.270875i	−0.694590	+	0.719406i	$0.744414\pi$
$164$		−	2.53874i		−	0.198242i
$165$	3.52562	−	2.08555i	0.274469	−	0.162360i
$166$	−0.893301			−0.0693336
$167$	−9.83604	−	3.19592i	−0.761135	−	0.247308i	−0.0973696	−	0.995248i	$-0.531043\pi$
$167$	−9.83604	−	3.19592i	−0.761135	−	0.247308i	−0.663766	+	0.747940i	$0.731043\pi$
$168$	0.798942	−	0.580466i	0.0616397	−	0.0447839i
$169$	−11.9458	−	5.12815i	−0.918907	−	0.394473i
$170$	1.89512	+	5.83258i	0.145349	+	0.447339i
$171$	−6.80646	+	2.21155i	−0.520503	+	0.169122i
$172$	−3.59901	−	2.61483i	−0.274422	−	0.199379i
$173$	7.40599	−	5.38077i	0.563067	−	0.409092i	−0.269513	−	0.962997i	$-0.586863\pi$
$173$	7.40599	−	5.38077i	0.563067	−	0.409092i	0.832580	+	0.553904i	$0.186863\pi$
$174$	5.31037	+	1.72544i	0.402578	+	0.130806i
$175$			1.55439i			0.117500i
$176$	−1.51888	+	16.0861i	−0.114490	+	1.21254i
$177$			8.63619i			0.649136i
$178$	0.181212	−	0.557712i	0.0135824	−	0.0418023i
$179$	−3.62396	+	2.63296i	−0.270867	+	0.196797i	−0.714924	−	0.699202i	$-0.753539\pi$
$179$	−3.62396	+	2.63296i	−0.270867	+	0.196797i	0.444057	+	0.895999i	$0.353539\pi$
$180$	−0.465954	+	0.641331i	−0.0347302	+	0.0478020i
$181$	6.31114	+	19.4237i	0.469103	+	1.44375i	0.853748	+	0.520687i	$0.174324\pi$
$181$	6.31114	+	19.4237i	0.469103	+	1.44375i	−0.384644	+	0.923065i	$0.625676\pi$
$182$	1.08234	+	2.38784i	0.0802284	+	0.176998i
$183$	−11.6177	−	8.44076i	−0.858806	−	0.623959i
$184$	−8.49529	−	11.6928i	−0.626281	−	0.862002i
$185$	0.809529	−	2.49147i	0.0595177	−	0.183177i
$186$	−11.4170			−0.837133
$187$	0.952466	−	10.0873i	0.0696512	−	0.737659i
$188$		−	4.47340i		−	0.326256i
$189$	−0.425463	−	0.138241i	−0.0309479	−	0.0100556i
$190$	−8.44463	−	11.6230i	−0.612638	−	0.843224i
$191$	−3.28385	−	2.38586i	−0.237611	−	0.172635i	0.462607	−	0.886563i	$-0.346914\pi$
$191$	−3.28385	−	2.38586i	−0.237611	−	0.172635i	−0.700218	+	0.713929i	$0.746914\pi$
$192$	1.25126	+	3.85098i	0.0903020	+	0.277921i
$193$	6.58839	−	2.14070i	0.474243	−	0.154091i	−0.0621370	−	0.998068i	$-0.519792\pi$
$193$	6.58839	−	2.14070i	0.474243	−	0.154091i	0.536380	+	0.843977i	$0.319792\pi$
$194$	−16.0870	−	11.6879i	−1.15498	−	0.839141i
$195$	3.00180	+	3.28930i	0.214964	+	0.235552i
$196$	−1.34870	+	4.15086i	−0.0963355	+	0.296490i
$197$			10.9699i			0.781572i	0.920482	+	0.390786i	$0.127797\pi$
$197$			10.9699i			0.781572i	−0.920482	+	0.390786i	$0.872203\pi$
$198$	4.63977	−	2.74461i	0.329734	−	0.195051i
$199$	−2.27497			−0.161268			−0.0806341	−	0.996744i	$-0.525695\pi$
$199$	−2.27497			−0.161268			−0.0806341	+	0.996744i	$0.525695\pi$
$200$	−7.29479	−	2.37022i	−0.515819	−	0.167600i
$201$	−4.71458	−	6.48907i	−0.332541	−	0.457704i
$202$	−18.3279	+	25.2263i	−1.28955	+	1.77491i
$203$	−1.46159	+	0.474900i	−0.102584	+	0.0333314i
$204$	0.605928	+	1.86486i	0.0424235	+	0.130566i
$205$	3.95219	+	2.87144i	0.276033	+	0.200550i
$206$	−7.40729	−	10.1953i	−0.516090	−	0.710337i
$207$	−2.02320	+	6.22678i	−0.140622	+	0.432791i
$208$	−17.4564	+	1.95293i	−1.21038	+	0.135412i
$209$	5.18032	+	23.1640i	0.358331	+	1.60229i
$210$		−	0.898053i		−	0.0619716i
$211$	4.38761	−	13.5037i	0.302055	−	0.929630i	−0.678704	−	0.734411i	$-0.737458\pi$
$211$	4.38761	−	13.5037i	0.302055	−	0.929630i	0.980760	−	0.195219i	$-0.0625417\pi$
$212$	−1.32901	+	0.965580i	−0.0912766	+	0.0663163i
$213$	0.313886	−	0.432027i	0.0215071	−	0.0296020i
$214$	−28.1943	+	9.16087i	−1.92732	+	0.626224i
$215$	8.14129	−	2.64527i	0.555231	−	0.180406i
$216$	1.29754	−	1.78591i	0.0882865	−	0.121516i
$217$	2.54220	−	1.84702i	0.172576	−	0.125384i
$218$	9.46261	−	29.1229i	0.640889	−	1.97245i
$219$		−	15.4899i		−	1.04671i
$220$	1.97236	+	1.73850i	0.132977	+	0.117210i
$221$	10.9466	−	1.22465i	0.736346	−	0.0823789i
$222$	1.06535	−	3.27881i	0.0715017	−	0.220060i
$223$	−6.45719	−	8.88756i	−0.432405	−	0.595155i	0.536098	−	0.844156i	$-0.319898\pi$
$223$	−6.45719	−	8.88756i	−0.432405	−	0.595155i	−0.968503	+	0.249001i	$0.919898\pi$
$224$	1.26794	+	0.921212i	0.0847177	+	0.0615510i
$225$	1.07371	+	3.30453i	0.0715805	+	0.220302i
$226$	−19.0657	+	6.19484i	−1.26823	+	0.412074i
$227$	9.67528	−	13.3169i	0.642171	−	0.883873i	−0.356558	−	0.934273i	$-0.616050\pi$
$227$	9.67528	−	13.3169i	0.642171	−	0.883873i	0.998729	+	0.0504005i	$0.0160498\pi$
$228$	−2.70001	−	3.71624i	−0.178812	−	0.246114i
$229$	11.8453	+	3.84877i	0.782759	+	0.254334i	0.673018	−	0.739626i	$-0.264998\pi$
$229$	11.8453	+	3.84877i	0.782759	+	0.254334i	0.109742	+	0.993960i	$0.464998\pi$
$230$	−13.1433			−0.866643
$231$	−0.589113	+	1.36175i	−0.0387608	+	0.0895967i
$232$		−	7.58346i		−	0.497878i
$233$	−2.32015	+	7.14070i	−0.151998	+	0.467803i	−0.997844	−	0.0656244i	$-0.979096\pi$
$233$	−2.32015	+	7.14070i	−0.151998	+	0.467803i	0.845846	+	0.533427i	$0.179096\pi$
$234$	3.95041	+	4.32877i	0.258247	+	0.282980i
$235$	6.96398	+	5.05963i	0.454280	+	0.330054i
$236$	−5.27181	+	1.71291i	−0.343166	+	0.111501i
$237$	1.88672	+	5.80673i	0.122556	+	0.377187i
$238$	−1.79711	−	1.30568i	−0.116489	−	0.0846344i
$239$	−2.93113	−	4.03436i	−0.189599	−	0.260961i	0.703626	−	0.710571i	$-0.251563\pi$
$239$	−2.93113	−	4.03436i	−0.189599	−	0.260961i	−0.893225	+	0.449610i	$0.851563\pi$
$240$	5.72246	+	1.85934i	0.369383	+	0.120020i
$241$			29.4604i			1.89771i	0.315712	+	0.948855i	$0.397757\pi$
$241$			29.4604i			1.89771i	−0.315712	+	0.948855i	$0.602243\pi$
$242$	−7.61596	−	16.1759i	−0.489572	−	1.03983i
$243$	−1.00000			−0.0641500
$244$	2.84824	−	8.76598i	0.182340	−	0.561184i
$245$	−4.93643	−	6.79441i	−0.315377	−	0.434079i
$246$	5.20114	+	3.77885i	0.331613	+	0.240931i
$247$	−23.5023	+	10.6529i	−1.49542	+	0.677831i
$248$	4.79162	+	14.7471i	0.304268	+	0.936441i
$249$	0.323045	−	0.444633i	0.0204721	−	0.0281775i
$250$	−13.7633	+	9.99964i	−0.870469	+	0.632433i
$251$	2.93546	−	9.03443i	0.185285	−	0.570248i	−0.814668	−	0.579927i	$-0.803081\pi$
$251$	2.93546	−	9.03443i	0.185285	−	0.570248i	0.999953	+	0.00967901i	$0.00308097\pi$
$252$		−	0.287135i		−	0.0180878i
$253$	19.9296	+	8.62184i	1.25297	+	0.542051i
$254$		−	6.79927i		−	0.426624i
$255$	−3.58845	−	1.16596i	−0.224718	−	0.0730152i
$256$	−11.3161	+	8.22166i	−0.707259	+	0.513854i
$257$	−23.0040	−	16.7134i	−1.43495	−	1.04255i	−0.989068	−	0.147460i	$-0.952890\pi$
$257$	−23.0040	−	16.7134i	−1.43495	−	1.04255i	−0.445882	−	0.895092i	$-0.647110\pi$
$258$	10.7141	−	3.48121i	0.667028	−	0.216731i
$259$	0.293220	+	0.902439i	0.0182198	+	0.0560749i
$260$	−1.41251	+	2.48480i	−0.0876004	+	0.154101i
$261$	−2.77921	+	2.01922i	−0.172029	+	0.124986i
$262$	−17.1247	−	5.56415i	−1.05797	−	0.343754i
$263$	15.2513			0.940435			0.470217	−	0.882551i	$-0.344176\pi$
$263$	15.2513			0.940435			0.470217	+	0.882551i	$0.344176\pi$
$264$	−5.49243	−	4.84121i	−0.338036	−	0.297956i
$265$		−	3.16105i		−	0.194182i
$266$	4.94915	+	1.60807i	0.303452	+	0.0985974i
$267$	0.212065	+	0.291882i	0.0129782	+	0.0178629i
$268$	3.02604	−	4.16499i	0.184845	−	0.254417i
$269$	6.15134	+	18.9319i	0.375054	+	1.15430i	0.943442	+	0.331537i	$0.107567\pi$
$269$	6.15134	+	18.9319i	0.375054	+	1.15430i	−0.568388	+	0.822761i	$0.692433\pi$
$270$	−0.620339	−	1.90921i	−0.0377527	−	0.116191i
$271$	−3.76951	+	5.18829i	−0.228982	+	0.315166i	−0.908012	−	0.418944i	$-0.862400\pi$
$271$	−3.76951	+	5.18829i	−0.228982	+	0.315166i	0.679031	+	0.734110i	$0.262400\pi$
$272$	12.0406	−	8.74801i	0.730069	−	0.530426i
$273$	−1.57993	−	0.324790i	−0.0956219	−	0.0196572i
$274$	−13.1027			−0.791565
$275$	11.2461	−	2.51504i	0.678166	−	0.151663i
$276$	−4.20231			−0.252949
$277$	0.802466	−	2.46974i	0.0482155	−	0.148392i	−0.924050	−	0.382271i	$-0.875142\pi$
$277$	0.802466	−	2.46974i	0.0482155	−	0.148392i	0.972266	+	0.233879i	$0.0751420\pi$
$278$	11.6543	+	16.0408i	0.698978	+	0.962061i
$279$	4.12873	−	5.68270i	0.247180	−	0.340215i
$280$	−1.16000	+	0.376906i	−0.0693232	+	0.0225245i
$281$	−13.9760	+	4.54108i	−0.833739	+	0.270898i	−0.694619	−	0.719377i	$-0.744427\pi$
$281$	−13.9760	+	4.54108i	−0.833739	+	0.270898i	−0.139119	+	0.990276i	$0.544427\pi$
$282$	9.16470	+	6.65854i	0.545750	+	0.396510i
$283$	15.2807	−	11.1020i	0.908341	−	0.659948i	−0.0322540	−	0.999480i	$-0.510269\pi$
$283$	15.2807	−	11.1020i	0.908341	−	0.659948i	0.940595	+	0.339532i	$0.110269\pi$
$284$	0.325980	+	0.105917i	0.0193434	+	0.00628504i
$285$	8.83910			0.523583
$286$	15.5250	−	11.6944i	0.918011	−	0.691506i
$287$	−1.76947			−0.104448
$288$	3.33190	+	1.08260i	0.196334	+	0.0637928i
$289$	6.20284	−	4.50663i	0.364873	−	0.265096i
$290$	−5.57916	−	4.05350i	−0.327620	−	0.238030i
$291$	11.6351	−	3.78047i	0.682061	−	0.221615i
$292$	9.45556	−	3.07230i	0.553345	−	0.179793i
$293$	−10.9772	+	15.1089i	−0.641297	+	0.882669i	−0.998684	−	0.0512870i	$-0.983668\pi$
$293$	−10.9772	+	15.1089i	−0.641297	+	0.882669i	0.357387	+	0.933956i	$0.383668\pi$
$294$	−6.49641	−	8.94154i	−0.378878	−	0.521481i
$295$	3.29608	−	10.1443i	0.191905	−	0.590624i
$296$	−4.68230			−0.272153
$297$	−0.311775	+	3.30194i	−0.0180910	+	0.191598i
$298$	22.2591			1.28944
$299$	−4.75340	+	23.1228i	−0.274896	+	1.33723i
$300$	−1.80423	+	1.31085i	−0.104167	+	0.0756821i
$301$	−1.82250	+	2.50846i	−0.105047	+	0.144585i
$302$	2.84818	+	8.76580i	0.163894	+	0.504415i
$303$	−5.92821	−	18.2452i	−0.340567	−	1.04816i
$304$	−20.4935	+	28.2069i	−1.17538	+	1.61778i
$305$	10.4250	+	14.3487i	0.596932	+	0.821606i
$306$	−4.72245	−	1.53442i	−0.269965	−	0.0877168i
$307$		−	6.86567i		−	0.391845i	−0.980619	−	0.195922i	$-0.937230\pi$
$307$		−	6.86567i		−	0.391845i	0.980619	−	0.195922i	$-0.0627700\pi$
$308$	−0.948103	−	0.0895217i	−0.0540232	−	0.00510097i
$309$	7.75330			0.441070
$310$	13.4107	+	4.35739i	0.761675	+	0.247483i
$311$	−4.97391	+	3.61376i	−0.282045	+	0.204917i	−0.719809	−	0.694172i	$-0.755771\pi$
$311$	−4.97391	+	3.61376i	−0.282045	+	0.204917i	0.437764	+	0.899090i	$0.355771\pi$
$312$	3.93343	−	6.91943i	0.222686	−	0.391735i
$313$	−8.17521	−	25.1607i	−0.462090	−	1.42217i	−0.862605	−	0.505878i	$-0.831169\pi$
$313$	−8.17521	−	25.1607i	−0.462090	−	1.42217i	0.400515	−	0.916290i	$-0.368831\pi$
$314$	22.6214	−	7.35013i	1.27660	−	0.414792i
$315$	0.446998	+	0.324763i	0.0251855	+	0.0182983i
$316$	−3.17040	+	2.30343i	−0.178349	+	0.129578i
$317$	−11.0838	−	3.60135i	−0.622529	−	0.202272i	−0.0192659	−	0.999814i	$-0.506133\pi$
$317$	−11.0838	−	3.60135i	−0.622529	−	0.202272i	−0.603263	+	0.797543i	$0.706133\pi$
$318$		−	4.15999i		−	0.233281i
$319$	5.80084	+	9.80634i	0.324785	+	0.549050i
$320$		−	5.00102i		−	0.279566i
$321$	5.63616	−	17.3463i	0.314580	−	0.968177i
$322$	3.85144	−	2.79824i	0.214633	−	0.155940i
$323$	12.8511	−	17.6881i	0.715056	−	0.984190i
$324$	−0.198342	−	0.610432i	−0.0110190	−	0.0339129i
$325$	5.17200	+	11.4104i	0.286891	+	0.632933i
$326$	14.7161	+	10.6919i	0.815048	+	0.592167i
$327$	11.0737	+	15.2417i	0.612378	+	0.842866i
$328$	2.69819	−	8.30417i	0.148982	−	0.458521i
$329$	−3.11790			−0.171895
$330$	−6.49750	+	1.45308i	−0.357675	+	0.0799893i
$331$			3.21166i			0.176529i	0.996097	+	0.0882643i	$0.0281320\pi$
$331$			3.21166i			0.176529i	−0.996097	+	0.0882643i	$0.971868\pi$
$332$	0.335492	+	0.109008i	0.0184125	+	0.00598258i
$333$	1.24674	+	1.71599i	0.0683208	+	0.0940356i
$334$	13.5996	+	9.88067i	0.744136	+	0.540646i
$335$	3.06126	+	9.42159i	0.167255	+	0.514757i
$336$	−2.07274	+	0.673473i	−0.113077	+	0.0367410i
$337$	−11.1649	−	8.11180i	−0.608193	−	0.441878i	0.240585	−	0.970628i	$-0.422661\pi$
$337$	−11.1649	−	8.11180i	−0.608193	−	0.441878i	−0.848778	+	0.528750i	$0.822661\pi$
$338$	15.8904	+	13.9272i	0.864323	+	0.757541i
$339$	3.81133	−	11.7301i	0.207003	−	0.637089i
$340$		−	2.42177i		−	0.131339i
$341$	−17.4767	−	15.4045i	−0.946416	−	0.834202i
$342$	11.6324			0.629007
$343$	5.87133	+	1.90771i	0.317022	+	0.103007i
$344$	−8.99322	−	12.3781i	−0.484882	−	0.667382i
$345$	4.75301	−	6.54196i	0.255894	−	0.352207i
$346$	−14.1510	+	4.59792i	−0.760760	+	0.247186i
$347$	1.29272	+	3.97859i	0.0693970	+	0.213582i	0.979740	−	0.200272i	$-0.0641825\pi$
$347$	1.29272	+	3.97859i	0.0693970	+	0.213582i	−0.910343	+	0.413854i	$0.864182\pi$
$348$	−1.78383	−	1.29603i	−0.0956233	−	0.0694744i
$349$	−2.43455	−	3.35088i	−0.130319	−	0.179368i	0.738871	−	0.673847i	$-0.235359\pi$
$349$	−2.43455	−	3.35088i	−0.130319	−	0.179368i	−0.869190	+	0.494478i	$0.835359\pi$
$350$	0.780719	−	2.40281i	0.0417312	−	0.128435i
$351$	−3.58320	+	0.400871i	−0.191257	+	0.0213969i
$352$	4.61348	−	10.6642i	0.245899	−	0.568404i
$353$			5.83975i			0.310818i	0.987850	+	0.155409i	$0.0496696\pi$
$353$			5.83975i			0.310818i	−0.987850	+	0.155409i	$0.950330\pi$
$354$	4.33769	−	13.3500i	0.230546	−	0.709546i
$355$	−0.533586	+	0.387673i	−0.0283198	+	0.0205755i
$356$	−0.136113	+	0.187344i	−0.00721398	+	0.00992919i
$357$	1.29978	−	0.422323i	0.0687915	−	0.0223517i
$358$	6.92446	−	2.24989i	0.365969	−	0.118911i
$359$	8.04999	−	11.0799i	0.424862	−	0.584773i	−0.541902	−	0.840442i	$-0.682296\pi$
$359$	8.04999	−	11.0799i	0.424862	−	0.584773i	0.966764	+	0.255669i	$0.0822957\pi$
$360$	−2.20574	+	1.60256i	−0.116252	+	0.0844624i
$361$	−9.95618	+	30.6420i	−0.524009	+	1.61273i
$362$		−	33.1955i		−	1.74472i
$363$	10.8056	+	2.05893i	0.567147	+	0.108066i
$364$	−0.115104	−	1.02886i	−0.00603310	−	0.0539270i
$365$	−5.91188	+	18.1949i	−0.309442	+	0.952364i
$366$	13.7194	+	18.8831i	0.717125	+	0.987037i
$367$	1.44306	+	1.04844i	0.0753269	+	0.0547282i	0.624811	−	0.780776i	$-0.285176\pi$
$367$	1.44306	+	1.04844i	0.0753269	+	0.0547282i	−0.549484	+	0.835504i	$0.685176\pi$
$368$	9.85649	+	30.3351i	0.513805	+	1.58133i
$369$	−3.76178	+	1.22228i	−0.195830	+	0.0636292i
$370$	−2.50278	+	3.44478i	−0.130113	+	0.179086i
$371$	0.672995	+	0.926299i	0.0349402	+	0.0480910i
$372$	4.28780	+	1.39319i	0.222312	+	0.0722336i
$373$	13.5618			0.702202			0.351101	−	0.936338i	$-0.385807\pi$
$373$	13.5618			0.702202			0.351101	+	0.936338i	$0.385807\pi$
$374$	−6.53890	+	15.1149i	−0.338118	+	0.781571i
$375$		−	10.4668i		−	0.540501i
$376$	4.75435	−	14.6324i	0.245187	−	0.754608i
$377$	−9.14903	+	8.34936i	−0.471199	+	0.430014i
$378$	0.588256	+	0.427393i	0.0302566	+	0.0219827i
$379$	2.22742	−	0.723733i	0.114415	−	0.0371756i	−0.251250	−	0.967922i	$-0.580842\pi$
$379$	2.22742	−	0.723733i	0.114415	−	0.0371756i	0.365665	+	0.930747i	$0.380842\pi$
$380$	1.75316	+	5.39568i	0.0899353	+	0.276792i
$381$	3.38428	+	2.45882i	0.173382	+	0.125969i
$382$	3.87792	+	5.33749i	0.198411	+	0.273090i
$383$	17.8264	+	5.79215i	0.910887	+	0.295965i	0.726723	−	0.686930i	$-0.241042\pi$
$383$	17.8264	+	5.79215i	0.910887	+	0.295965i	0.184164	+	0.982896i	$0.441042\pi$
$384$		−	13.5881i		−	0.693417i
$385$	1.21171	−	1.37471i	0.0617546	−	0.0700616i
$386$	−11.2597			−0.573103
$387$	−2.14179	+	6.59174i	−0.108873	+	0.335077i
$388$	4.61544	+	6.35261i	0.234314	+	0.322505i
$389$	−16.0304	−	11.6468i	−0.812773	−	0.590514i	0.101861	−	0.994799i	$-0.467520\pi$
$389$	−16.0304	−	11.6468i	−0.812773	−	0.590514i	−0.914633	+	0.404285i	$0.867520\pi$
$390$	−2.98815	−	6.59239i	−0.151311	−	0.333819i
$391$	−6.18083	−	19.0226i	−0.312578	−	0.962016i
$392$	−8.82312	+	12.1440i	−0.445635	+	0.613363i
$393$	8.96232	−	6.51150i	0.452089	−	0.328462i
$394$	5.50983	−	16.9575i	0.277581	−	0.854308i
$395$		−	7.54081i		−	0.379420i
$396$	−2.07745	+	0.464594i	−0.104396	+	0.0233467i
$397$			9.26404i			0.464949i	0.972603	+	0.232474i	$0.0746822\pi$
$397$			9.26404i			0.464949i	−0.972603	+	0.232474i	$0.925318\pi$
$398$	3.51670	+	1.14265i	0.176276	+	0.0572756i
$399$	−2.59017	+	1.88187i	−0.129671	+	0.0942112i
$400$	13.6944	+	9.94959i	0.684722	+	0.497479i
$401$	28.8467	−	9.37285i	1.44053	−	0.468058i	0.518471	−	0.855096i	$-0.326502\pi$
$401$	28.8467	−	9.37285i	1.44053	−	0.468058i	0.922064	+	0.387037i	$0.126502\pi$
$402$	4.02866	+	12.3989i	0.200931	+	0.618403i
$403$	12.5160	−	22.0173i	0.623467	−	1.09676i
$404$	9.96162	−	7.23754i	0.495609	−	0.360081i
$405$	1.17463	+	0.381659i	0.0583676	+	0.0189648i
$406$	2.49789			0.123968
$407$	6.05479	−	3.58165i	0.300125	−	0.177536i
$408$			6.74389i			0.333872i
$409$	32.2912	+	10.4921i	1.59670	+	0.518799i	0.966288	−	0.257463i	$-0.0828865\pi$
$409$	32.2912	+	10.4921i	1.59670	+	0.518799i	0.630411	+	0.776262i	$0.282886\pi$
$410$	−4.66716	−	6.42380i	−0.230495	−	0.317249i
$411$	4.73835	−	6.52177i	0.233725	−	0.321695i
$412$	1.53780	+	4.73287i	0.0757620	+	0.233172i
$413$	1.19388	+	3.67438i	0.0587469	+	0.180804i
$414$	6.25503	−	8.60931i	0.307418	−	0.423125i
$415$	−0.549155	+	0.398984i	−0.0269570	+	0.0195854i
$416$	12.3728	+	2.54351i	0.606628	+	0.124706i
$417$	−12.1987			−0.597373
$418$	3.62669	−	38.4094i	0.177387	−	1.87867i
$419$	−16.5255			−0.807323			−0.403661	−	0.914908i	$-0.632263\pi$
$419$	−16.5255			−0.807323			−0.403661	+	0.914908i	$0.632263\pi$
$420$	−0.109588	+	0.337276i	−0.00534733	+	0.0164574i
$421$	4.20292	+	5.78482i	0.204838	+	0.281935i	0.899060	−	0.437826i	$-0.144251\pi$
$421$	4.20292	+	5.78482i	0.204838	+	0.281935i	−0.694222	+	0.719761i	$0.744251\pi$
$422$	−13.5649	+	18.6705i	−0.660331	+	0.908867i
$423$	−6.62846	+	2.15372i	−0.322287	+	0.104717i
$424$	−5.37338	+	1.74592i	−0.260954	+	0.0847892i
$425$	−8.58754	−	6.23921i	−0.416557	−	0.302646i
$426$	−0.702207	+	0.510183i	−0.0340220	+	0.0247184i
$427$	−6.10976	−	1.98518i	−0.295672	−	0.0960697i
$428$	11.7066			0.565861
$429$	0.206499	+	11.9565i	0.00996986	+	0.577264i
$430$	−13.9136			−0.670975
$431$	−27.5431	−	8.94931i	−1.32671	−	0.431073i	−0.441914	−	0.897058i	$-0.645700\pi$
$431$	−27.5431	−	8.94931i	−1.32671	−	0.431073i	−0.884793	+	0.465984i	$0.845700\pi$
$432$	−3.94131	+	2.86353i	−0.189626	+	0.137772i
$433$	3.79559	+	2.75766i	0.182404	+	0.132524i	0.675241	−	0.737598i	$-0.264040\pi$
$433$	3.79559	+	2.75766i	0.182404	+	0.132524i	−0.492836	+	0.870122i	$0.664040\pi$
$434$	−4.85750	+	1.57830i	−0.233167	+	0.0757607i
$435$	4.03519	−	1.31111i	0.193473	−	0.0628631i
$436$	−7.10763	+	9.78281i	−0.340394	+	0.468512i
$437$	27.5417	+	37.9079i	1.31750	+	1.81338i
$438$	−7.78011	+	23.9447i	−0.371748	+	1.14412i
$439$	−31.9534			−1.52505			−0.762527	−	0.646956i	$-0.776042\pi$
$439$	−31.9534			−1.52505			−0.762527	+	0.646956i	$0.776042\pi$
$440$	4.60386	+	7.78284i	0.219481	+	0.371032i
$441$	6.79987			0.323803
$442$	−17.5366	−	3.60503i	−0.834130	−	0.171474i
$443$	−3.39873	+	2.46932i	−0.161479	+	0.117321i	−0.665590	−	0.746318i	$-0.731820\pi$
$443$	−3.39873	+	2.46932i	−0.161479	+	0.117321i	0.504111	+	0.863639i	$0.331820\pi$
$444$	−0.800215	+	1.10140i	−0.0379765	+	0.0522702i
$445$	−0.137697	−	0.423789i	−0.00652748	−	0.0200895i
$446$	5.51774	+	16.9818i	0.261272	+	0.804114i
$447$	−8.04957	+	11.0793i	−0.380732	+	0.524032i
$448$	1.06473	+	1.46547i	0.0503037	+	0.0692372i
$449$	−31.3213	−	10.1769i	−1.47814	−	0.480278i	−0.544587	−	0.838704i	$-0.683314\pi$
$449$	−31.3213	−	10.1769i	−1.47814	−	0.480278i	−0.933558	+	0.358426i	$0.883314\pi$
$450$		−	5.64751i		−	0.266226i
$451$	2.86305	+	12.8022i	0.134816	+	0.602834i
$452$	7.91635			0.372354
$453$	−5.39309	−	1.75232i	−0.253389	−	0.0823312i
$454$	−21.6449	+	15.7260i	−1.01585	+	0.738056i
$455$	1.73187	+	0.984503i	0.0811914	+	0.0461542i
$456$	−4.88202	−	15.0253i	−0.228622	−	0.703625i
$457$	12.4777	−	4.05424i	0.583680	−	0.189649i	−0.00226822	−	0.999997i	$-0.500722\pi$
$457$	12.4777	−	4.05424i	0.583680	−	0.189649i	0.585949	+	0.810348i	$0.300722\pi$
$458$	−16.3776	−	11.8990i	−0.765277	−	0.556006i
$459$	2.47153	−	1.79567i	0.115361	−	0.0838146i
$460$	4.93614	+	1.60385i	0.230149	+	0.0747799i
$461$		−	19.7339i		−	0.919101i	−0.888152	−	0.459550i	$-0.848011\pi$
$461$		−	19.7339i		−	0.919101i	0.888152	−	0.459550i	$-0.151989\pi$
$462$	1.59463	−	1.80914i	0.0741889	−	0.0841686i
$463$		−	32.0400i		−	1.48903i	−0.667608	−	0.744513i	$-0.732682\pi$
$463$		−	32.0400i		−	1.48903i	0.667608	−	0.744513i	$-0.267318\pi$
$464$	−5.17166	+	15.9167i	−0.240088	+	0.738915i
$465$	−7.01856	+	5.09928i	−0.325478	+	0.236474i
$466$	7.17310	−	9.87292i	0.332287	−	0.457354i
$467$	−11.4963	−	35.3820i	−0.531986	−	1.63728i	−0.750073	−	0.661355i	$-0.769982\pi$
$467$	−11.4963	−	35.3820i	−0.531986	−	1.63728i	0.218087	−	0.975929i	$-0.430018\pi$
$468$	−0.955401	−	2.10779i	−0.0441634	−	0.0974326i
$469$	−2.90294	−	2.10911i	−0.134045	−	0.0973895i
$470$	−8.22380	−	11.3191i	−0.379335	−	0.522110i
$471$	−4.52211	+	13.9176i	−0.208368	+	0.641290i
$472$	−19.0645			−0.877514
$473$	21.0978	+	9.12719i	0.970076	+	0.419669i
$474$		−	9.92382i		−	0.455816i
$475$	23.6497	+	7.68424i	1.08512	+	0.352577i
$476$	0.515600	+	0.709662i	0.0236325	+	0.0325273i
$477$	2.07060	+	1.50438i	0.0948062	+	0.0688807i
$478$	2.50468	+	7.70862i	0.114562	+	0.352584i
$479$	−9.32478	+	3.02981i	−0.426060	+	0.138435i	−0.514195	−	0.857673i	$-0.671909\pi$
$479$	−9.32478	+	3.02981i	−0.426060	+	0.138435i	0.0881350	+	0.996109i	$0.471909\pi$
$480$	−3.50055	−	2.54330i	−0.159778	−	0.116085i
$481$	5.15520	+	5.64894i	0.235057	+	0.257570i
$482$	14.7970	−	45.5406i	0.673986	−	2.07432i
$483$			2.92895i			0.133272i
$484$	0.886362	+	7.00445i	0.0402892	+	0.318384i
$485$	−15.1097			−0.686097
$486$	1.54582	+	0.502269i	0.0701200	+	0.0227834i
$487$	−13.7062	−	18.8649i	−0.621086	−	0.854852i	0.376345	−	0.926479i	$-0.377181\pi$
$487$	−13.7062	−	18.8649i	−0.621086	−	0.854852i	−0.997431	+	0.0716278i	$0.977181\pi$
$488$	18.6331	−	25.6462i	0.843479	−	1.16095i
$489$	−10.6436	+	3.45830i	−0.481318	+	0.156390i
$490$	4.21823	+	12.9824i	0.190560	+	0.586484i
$491$	−3.57053	−	2.59414i	−0.161136	−	0.117072i	0.504295	−	0.863531i	$-0.331752\pi$
$491$	−3.57053	−	2.59414i	−0.161136	−	0.117072i	−0.665431	+	0.746459i	$0.731752\pi$
$492$	−1.49223	−	2.05388i	−0.0672751	−	0.0925963i
$493$	3.24306	−	9.98110i	0.146060	−	0.449526i
$494$	41.6811	−	4.66309i	1.87532	−	0.209802i
$495$	1.62643	−	3.75955i	0.0731028	−	0.168979i
$496$		−	34.2200i		−	1.53652i
$497$	0.0738229	−	0.227203i	0.00331141	−	0.0101915i
$498$	−0.722696	+	0.525069i	−0.0323848	+	0.0235289i
$499$	0.335426	−	0.461675i	0.0150158	−	0.0206674i	−0.801443	−	0.598071i	$-0.795934\pi$
$499$	0.335426	−	0.461675i	0.0150158	−	0.0206674i	0.816459	+	0.577404i	$0.195934\pi$
$500$	6.38924	−	2.07599i	0.285736	−	0.0928412i
$501$	−9.83604	+	3.19592i	−0.439442	+	0.142783i
$502$	−9.07542	+	12.4913i	−0.405056	+	0.557512i
$503$	−17.8273	+	12.9523i	−0.794882	+	0.577516i	−0.909408	−	0.415905i	$-0.863465\pi$
$503$	−17.8273	+	12.9523i	−0.794882	+	0.577516i	0.114526	+	0.993420i	$0.463465\pi$
$504$	0.305169	−	0.939213i	0.0135933	−	0.0418359i
$505$			23.6938i			1.05436i
$506$	−26.4772	−	23.3379i	−1.17706	−	1.03750i
$507$	−12.6786	+	2.87280i	−0.563077	+	0.127586i
$508$	−0.829702	+	2.55356i	−0.0368121	+	0.113296i
$509$	20.5869	+	28.3355i	0.912499	+	1.25595i	0.966306	+	0.257396i	$0.0828646\pi$
$509$	20.5869	+	28.3355i	0.912499	+	1.25595i	−0.0538065	+	0.998551i	$0.517135\pi$
$510$	4.96149	+	3.60473i	0.219699	+	0.159620i
$511$	−2.14135	−	6.59039i	−0.0947276	−	0.291542i
$512$	−4.22395	+	1.37244i	−0.186674	+	0.0606541i
$513$	−4.20662	+	5.78992i	−0.185727	+	0.255631i
$514$	27.1655	+	37.3901i	1.19822	+	1.64921i
$515$	−9.10723	−	2.95912i	−0.401312	−	0.130394i
$516$	−4.44862			−0.195839
$517$	5.04485	+	22.5583i	0.221872	+	0.992111i
$518$		−	1.54229i		−	0.0677643i
$519$	2.82884	−	8.70627i	0.124172	−	0.382163i
$520$	−7.26117	+	6.62651i	−0.318423	+	0.290592i
$521$	20.3779	+	14.8054i	0.892773	+	0.648637i	0.936600	−	0.350402i	$-0.113955\pi$
$521$	20.3779	+	14.8054i	0.892773	+	0.648637i	−0.0438266	+	0.999039i	$0.513955\pi$
$522$	5.31037	−	1.72544i	0.232428	−	0.0755206i
$523$	5.58882	+	17.2006i	0.244382	+	0.752130i	0.995738	+	0.0922325i	$0.0294003\pi$
$523$	5.58882	+	17.2006i	0.244382	+	0.752130i	−0.751356	+	0.659897i	$0.770600\pi$
$524$	5.75243	+	4.17939i	0.251296	+	0.182577i
$525$	0.913645	+	1.25752i	0.0398747	+	0.0548829i
$526$	−23.5758	−	7.66024i	−1.02795	−	0.334003i
$527$			21.4588i			0.934759i
$528$	8.22639	+	13.9067i	0.358008	+	0.605213i
$529$	19.8661			0.863743
$530$	−1.58770	+	4.88643i	−0.0689652	+	0.212253i
$531$	5.07623	+	6.98682i	0.220289	+	0.303202i
$532$	−1.66249	−	1.20787i	−0.0720781	−	0.0523678i
$533$	−12.9892	+	5.88765i	−0.562626	+	0.255022i
$534$	−0.181212	−	0.557712i	−0.00784179	−	0.0241346i
$535$	−13.2408	+	18.2243i	−0.572448	+	0.787907i
$536$	14.3247	−	10.4075i	0.618732	−	0.449535i
$537$	−1.38423	+	4.26022i	−0.0597339	+	0.183842i
$538$		−	32.3550i		−	1.39492i
$539$	2.12003	−	22.4528i	0.0913163	−	0.967109i
$540$			0.792729i			0.0341136i
$541$	6.44811	+	2.09512i	0.277226	+	0.0900762i	0.444330	−	0.895863i	$-0.353442\pi$
$541$	6.44811	+	2.09512i	0.277226	+	0.0900762i	−0.167104	+	0.985939i	$0.553442\pi$
$542$	8.43292	−	6.12687i	0.362225	−	0.263172i
$543$	16.5228	+	12.0045i	0.709060	+	0.515162i
$544$	−10.1789	+	3.30731i	−0.436415	+	0.141800i
$545$	−7.19035	−	22.1296i	−0.308001	−	0.947929i
$546$	2.27917	+	1.29562i	0.0975394	+	0.0554474i
$547$	−14.0472	+	10.2059i	−0.600614	+	0.436372i	−0.846097	−	0.533029i	$-0.821054\pi$
$547$	−14.0472	+	10.2059i	−0.600614	+	0.436372i	0.245483	+	0.969401i	$0.421054\pi$
$548$	4.92091	+	1.59890i	0.210211	+	0.0683017i
$549$	−14.3603			−0.612882
$550$	−18.6477	−	1.76076i	−0.795143	−	0.0750789i
$551$			24.5855i			1.04738i
$552$	−13.7457	−	4.46624i	−0.585055	−	0.190096i
$553$	1.60546	+	2.20972i	0.0682710	+	0.0939670i
$554$	−2.48094	+	3.41472i	−0.105405	+	0.145078i
$555$	−0.809529	−	2.49147i	−0.0343626	−	0.105757i
$556$	−2.41951	−	7.44648i	−0.102610	−	0.315801i
$557$	−9.14541	+	12.5876i	−0.387503	+	0.533353i	−0.957553	−	0.288258i	$-0.906924\pi$
$557$	−9.14541	+	12.5876i	−0.387503	+	0.533353i	0.570049	+	0.821610i	$0.306924\pi$
$558$	−9.23653	+	6.71073i	−0.391013	+	0.284088i
$559$	−5.03200	+	24.4781i	−0.212831	+	1.03531i
$560$	2.69173			0.113746
$561$	−5.15863	−	8.72067i	−0.217797	−	0.368187i
$562$	23.8853			1.00754
$563$	3.77388	−	11.6148i	0.159050	−	0.489506i	−0.839499	−	0.543362i	$-0.817151\pi$
$563$	3.77388	−	11.6148i	0.159050	−	0.489506i	0.998549	+	0.0538559i	$0.0171512\pi$
$564$	−2.62940	−	3.61906i	−0.110718	−	0.152390i
$565$	−8.95376	+	12.3238i	−0.376688	+	0.518466i
$566$	−29.1974	+	9.48682i	−1.22726	+	0.398761i
$567$	−0.425463	+	0.138241i	−0.0178678	+	0.00580558i
$568$	0.953704	+	0.692907i	0.0400166	+	0.0290737i
$569$	−22.1080	+	16.0624i	−0.926817	+	0.673372i	−0.945211	−	0.326459i	$-0.894145\pi$
$569$	−22.1080	+	16.0624i	−0.926817	+	0.673372i	0.0183943	+	0.999831i	$0.494145\pi$
$570$	−13.6637	−	4.43961i	−0.572309	−	0.185955i
$571$	2.87205			0.120192			0.0600958	−	0.998193i	$-0.480859\pi$
$571$	2.87205			0.120192			0.0600958	+	0.998193i	$0.480859\pi$
$572$	−7.25766	+	2.49752i	−0.303458	+	0.104427i
$573$	−4.05906			−0.169570
$574$	2.73528	+	0.888748i	0.114169	+	0.0370956i
$575$	18.4043	−	13.3715i	0.767510	−	0.557629i
$576$	3.27584	+	2.38004i	0.136493	+	0.0991683i
$577$	26.0117	−	8.45172i	1.08288	−	0.351850i	0.287390	−	0.957814i	$-0.407212\pi$
$577$	26.0117	−	8.45172i	1.08288	−	0.351850i	0.795492	+	0.605964i	$0.207212\pi$
$578$	−11.8520	+	3.85096i	−0.492980	+	0.160179i
$579$	4.07185	−	5.60442i	0.169220	−	0.232912i
$580$	1.60069	+	2.20316i	0.0664651	+	0.0914814i
$581$	0.0759769	−	0.233833i	0.00315205	−	0.00970102i
$582$	−19.8846			−0.824244
$583$	5.61293	−	6.36796i	0.232464	−	0.263734i
$584$	34.1942			1.41497
$585$	4.36191	+	0.896686i	0.180343	+	0.0370734i
$586$	24.5576	−	17.8421i	1.01446	−	0.737052i
$587$	13.6000	−	18.7188i	0.561333	−	0.772608i	−0.430162	−	0.902752i	$-0.641544\pi$
$587$	13.6000	−	18.7188i	0.561333	−	0.772608i	0.991495	+	0.130143i	$0.0415437\pi$
$588$	1.34870	+	4.15086i	0.0556193	+	0.171179i
$589$	−15.5344	−	47.8100i	−0.640084	−	1.96998i
$590$	−10.1903	+	14.0258i	−0.419529	+	0.577432i
$591$	6.44794	+	8.87483i	0.265233	+	0.365062i
$592$	9.82756	+	3.19317i	0.403910	+	0.131238i
$593$		−	23.4571i		−	0.963267i	−0.876373	−	0.481634i	$-0.840044\pi$
$593$		−	23.4571i		−	0.963267i	0.876373	−	0.481634i	$-0.159956\pi$
$594$	2.14041	−	4.94762i	0.0878221	−	0.203003i
$595$	−1.68794			−0.0691986
$596$	−8.35972	−	2.71624i	−0.342427	−	0.111261i
$597$	−1.84049	+	1.33719i	−0.0753262	+	0.0547277i
$598$	18.9618	−	33.3563i	0.775405	−	1.36404i
$599$	11.6351	+	35.8092i	0.475397	+	1.46312i	0.845421	+	0.534100i	$0.179349\pi$
$599$	11.6351	+	35.8092i	0.475397	+	1.46312i	−0.370024	+	0.929022i	$0.620651\pi$
$600$	−7.29479	+	2.37022i	−0.297808	+	0.0967638i
$601$	5.36014	+	3.89437i	0.218645	+	0.158855i	0.691716	−	0.722169i	$-0.256855\pi$
$601$	5.36014	+	3.89437i	0.218645	+	0.158855i	−0.473072	+	0.881024i	$0.656855\pi$
$602$	4.07718	−	2.96225i	0.166174	−	0.120732i
$603$	−7.62836	−	2.47860i	−0.310651	−	0.100937i
$604$		−	3.63967i		−	0.148096i
$605$	−11.9067	−	6.54252i	−0.484077	−	0.265991i
$606$			31.1814i			1.26666i
$607$	4.53109	−	13.9453i	0.183911	−	0.566021i	−0.816017	−	0.578028i	$-0.803822\pi$
$607$	4.53109	−	13.9453i	0.183911	−	0.566021i	0.999928	+	0.0120077i	$0.00382227\pi$
$608$	20.2842	−	14.7373i	0.822634	−	0.597678i
$609$	−0.903313	+	1.24330i	−0.0366041	+	0.0503812i
$610$	−8.90825	−	27.4168i	−0.360684	−	1.11007i
$611$	−22.8877	+	10.3744i	−0.925939	+	0.419702i
$612$	1.58634	+	1.15254i	0.0641240	+	0.0465888i
$613$	−12.0046	−	16.5230i	−0.484862	−	0.667356i	0.494568	−	0.869139i	$-0.335326\pi$
$613$	−12.0046	−	16.5230i	−0.484862	−	0.667356i	−0.979430	+	0.201783i	$0.935326\pi$
$614$	−3.44841	+	10.6131i	−0.139167	+	0.428311i
$615$	4.88518			0.196989
$616$	−3.00608	−	1.30047i	−0.121118	−	0.0523975i
$617$		−	9.22092i		−	0.371220i	−0.982623	−	0.185610i	$-0.940574\pi$
$617$		−	9.22092i		−	0.371220i	0.982623	−	0.185610i	$-0.0594261\pi$
$618$	−11.9852	−	3.89424i	−0.482117	−	0.156649i
$619$	−23.3145	−	32.0896i	−0.937087	−	1.28979i	−0.957030	−	0.289989i	$-0.906348\pi$
$619$	−23.3145	−	32.0896i	−0.937087	−	1.28979i	0.0199427	−	0.999801i	$-0.493652\pi$
$620$	−4.50484	−	3.27296i	−0.180919	−	0.131445i
$621$	2.02320	+	6.22678i	0.0811883	+	0.249872i
$622$	9.50387	−	3.08800i	0.381071	−	0.123817i
$623$	0.130576	+	0.0948688i	0.00523141	+	0.00380084i
$624$	−12.9746	+	11.8405i	−0.519399	+	0.474001i
$625$	1.37381	−	4.22814i	0.0549522	−	0.169126i
$626$			43.0002i			1.71863i
$627$	17.8064	+	15.6952i	0.711121	+	0.626805i
$628$	−9.39269			−0.374809
$629$	−6.16269	−	2.00238i	−0.245723	−	0.0798401i
$630$	−0.527863	−	0.726541i	−0.0210305	−	0.0289461i
$631$	−3.49953	+	4.81669i	−0.139314	+	0.191749i	−0.872973	−	0.487769i	$-0.837811\pi$
$631$	−3.49953	+	4.81669i	−0.139314	+	0.191749i	0.733659	+	0.679518i	$0.237811\pi$
$632$	−12.8184	+	4.16495i	−0.509889	+	0.165673i
$633$	−4.38761	−	13.5037i	−0.174392	−	0.536722i
$634$	15.3248	+	11.1341i	0.608624	+	0.442192i
$635$	−3.03683	−	4.17984i	−0.120513	−	0.165872i
$636$	−0.507635	+	1.56234i	−0.0201291	+	0.0619509i
$637$	24.3653	−	2.72587i	0.965387	−	0.108003i
$638$	−4.04166	−	18.0725i	−0.160011	−	0.715495i
$639$		−	0.534015i		−	0.0211253i
$640$	−5.18604	+	15.9610i	−0.204996	+	0.630914i
$641$	33.8687	−	24.6071i	1.33773	−	0.971921i	0.338211	−	0.941070i	$-0.390178\pi$
$641$	33.8687	−	24.6071i	1.33773	−	0.971921i	0.999524	−	0.0308508i	$-0.00982168\pi$
$642$	−17.4250	+	23.9835i	−0.687711	+	0.946552i
$643$	13.4326	−	4.36452i	0.529730	−	0.172120i	−0.0319265	−	0.999490i	$-0.510164\pi$
$643$	13.4326	−	4.36452i	0.529730	−	0.172120i	0.561657	+	0.827371i	$0.310164\pi$
$644$	−1.78793	+	0.580932i	−0.0704542	+	0.0228919i
$645$	5.03159	−	6.92540i	0.198119	−	0.272687i
$646$	−28.7497	+	20.8879i	−1.13114	+	0.821824i
$647$	−0.969025	+	2.98235i	−0.0380963	+	0.117248i	−0.968296	−	0.249805i	$-0.919633\pi$
$647$	−0.969025	+	2.98235i	−0.0380963	+	0.117248i	0.930200	+	0.367054i	$0.119633\pi$
$648$		−	2.20751i		−	0.0867192i
$649$	24.6527	−	14.5831i	0.967703	−	0.572435i
$650$	−2.26393	−	20.2362i	−0.0887985	−	0.793727i
$651$	0.971035	−	2.98854i	0.0380579	−	0.117130i
$652$	−4.22212	−	5.81125i	−0.165351	−	0.227586i
$653$	−17.6420	−	12.8177i	−0.690387	−	0.501595i	0.186401	−	0.982474i	$-0.440318\pi$
$653$	−17.6420	−	12.8177i	−0.690387	−	0.501595i	−0.876787	+	0.480879i	$0.840318\pi$
$654$	−9.46261	−	29.1229i	−0.370017	−	1.13880i
$655$	−13.0125	+	4.22803i	−0.508442	+	0.165203i
$656$	−11.3263	+	15.5893i	−0.442218	+	0.608661i
$657$	−9.10476	−	12.5316i	−0.355210	−	0.488905i
$658$	4.81972	+	1.56602i	0.187892	+	0.0610499i
$659$	34.8816			1.35880			0.679398	−	0.733770i	$-0.262241\pi$
$659$	34.8816			1.35880			0.679398	+	0.733770i	$0.262241\pi$
$660$	2.61754	+	0.247153i	0.101888	+	0.00962043i
$661$			29.5903i			1.15093i	0.817827	+	0.575464i	$0.195179\pi$
$661$			29.5903i			1.15093i	−0.817827	+	0.575464i	$0.804821\pi$
$662$	1.61311	−	4.96466i	0.0626955	−	0.192957i
$663$	8.13613	−	7.42500i	0.315981	−	0.288363i
$664$	0.981532	+	0.713125i	0.0380908	+	0.0276746i
$665$	3.76071	−	1.22193i	0.145834	−	0.0473843i
$666$	−1.06535	−	3.27881i	−0.0412815	−	0.127051i
$667$	18.1961	+	13.2203i	0.704557	+	0.511891i
$668$	−3.90179	−	5.37035i	−0.150965	−	0.207785i
$669$	−10.4479	−	3.39474i	−0.403941	−	0.131248i
$670$		−	16.1017i		−	0.622063i
$671$	−4.47718	+	47.4167i	−0.172840	+	1.83050i
$672$	1.56726			0.0604583
$673$	−5.92449	+	18.2337i	−0.228372	+	0.702858i	0.769559	+	0.638575i	$0.220476\pi$
$673$	−5.92449	+	18.2337i	−0.228372	+	0.702858i	−0.997932	+	0.0642825i	$0.979524\pi$
$674$	13.1847	+	18.1472i	0.507857	+	0.699005i
$675$	2.81100	+	2.04231i	0.108196	+	0.0786087i
$676$	−4.26834	−	7.16964i	−0.164167	−	0.275755i
$677$	−8.41510	−	25.8990i	−0.323418	−	0.995380i	−0.972149	−	0.234362i	$-0.924700\pi$
$677$	−8.41510	−	25.8990i	−0.323418	−	0.995380i	0.648731	−	0.761018i	$-0.275300\pi$
$678$	−11.7833	+	16.2183i	−0.452534	+	0.622860i
$679$	4.42768	−	3.21690i	0.169919	−	0.123453i
$680$	2.57387	−	7.92154i	0.0987032	−	0.303777i
$681$		−	16.4606i		−	0.630771i
$682$	19.2787	+	32.5907i	0.738219	+	1.24796i
$683$		−	19.4916i		−	0.745827i	−0.927866	−	0.372914i	$-0.878359\pi$
$683$		−	19.4916i		−	0.745827i	0.927866	−	0.372914i	$-0.121641\pi$
$684$	−4.36870	−	1.41948i	−0.167042	−	0.0542751i
$685$	−8.05488	+	5.85221i	−0.307761	+	0.223602i
$686$	−8.11786	−	5.89797i	−0.309941	−	0.225186i
$687$	11.8453	−	3.84877i	0.451926	−	0.146840i
$688$	10.4342	+	32.1132i	0.397800	+	1.22430i
$689$	8.02243	+	4.56044i	0.305630	+	0.173739i
$690$	−10.6331	+	7.72543i	−0.404797	+	0.294102i
$691$	−37.9898	−	12.3436i	−1.44520	−	0.469574i	−0.521686	−	0.853137i	$-0.674697\pi$
$691$	−37.9898	−	12.3436i	−1.44520	−	0.469574i	−0.923515	+	0.383563i	$0.874697\pi$
$692$	5.87566			0.223359
$693$	0.323815	+	1.44795i	0.0123007	+	0.0550031i
$694$		−	6.79950i		−	0.258106i
$695$	14.3289	+	4.65575i	0.543527	+	0.176602i
$696$	−4.45744	−	6.13514i	−0.168959	−	0.232552i
$697$	7.10254	−	9.77580i	0.269028	−	0.370285i
$698$	2.08035	+	6.40267i	0.0787425	+	0.242344i
$699$	2.32015	+	7.14070i	0.0877562	+	0.270086i
$700$	−0.586420	+	0.807138i	−0.0221646	+	0.0305069i
$701$	8.41524	−	6.11403i	0.317839	−	0.230924i	−0.417414	−	0.908717i	$-0.637063\pi$
$701$	8.41524	−	6.11403i	0.317839	−	0.230924i	0.735253	+	0.677793i	$0.237063\pi$
$702$	5.74034	+	1.18005i	0.216655	+	0.0445382i
$703$	15.1800			0.572524
$704$	8.88007	−	10.0746i	0.334680	−	0.379701i
$705$	8.60795			0.324194
$706$	2.93312	−	9.02722i	0.110390	−	0.339744i
$707$	−5.04446	−	6.94311i	−0.189717	−	0.261123i
$708$	−3.25816	+	4.48447i	−0.122449	+	0.168537i
$709$	−8.38422	+	2.72420i	−0.314876	+	0.102309i	−0.462192	−	0.886780i	$-0.652937\pi$
$709$	−8.38422	+	2.72420i	−0.314876	+	0.102309i	0.147315	+	0.989090i	$0.452937\pi$
$710$	1.01955	−	0.331271i	0.0382629	−	0.0124324i
$711$	4.93950	+	3.58875i	0.185246	+	0.134589i
$712$	−0.644332	+	0.468135i	−0.0241474	+	0.0175441i
$713$	−43.7382	−	14.2114i	−1.63801	−	0.532221i
$714$	−2.22135			−0.0831318
$715$	4.32074	−	14.1232i	0.161587	−	0.528178i
$716$	−2.87513			−0.107449
$717$	−4.74267	−	1.54099i	−0.177118	−	0.0575492i
$718$	−18.0089	+	13.0843i	−0.672088	+	0.488300i
$719$	−33.2023	−	24.1229i	−1.23824	−	0.899631i	−0.240756	−	0.970586i	$-0.577395\pi$
$719$	−33.2023	−	24.1229i	−1.23824	−	0.899631i	−0.997480	+	0.0709550i	$0.977395\pi$
$720$	5.72246	−	1.85934i	0.213263	−	0.0692935i
$721$	3.29874	−	1.07183i	0.122852	−	0.0399169i
$722$	30.7810	−	42.3664i	1.14555	−	1.57671i
$723$	17.3164	+	23.8339i	0.644003	+	0.886394i
$724$	−4.05078	+	12.4670i	−0.150546	+	0.463334i
$725$	11.9363			0.443301
$726$	−15.6694	−	8.61005i	−0.581546	−	0.319549i
$727$	−21.4491			−0.795503			−0.397751	−	0.917493i	$-0.630209\pi$
$727$	−21.4491			−0.795503			−0.397751	+	0.917493i	$0.630209\pi$
$728$	0.716977	−	3.48772i	0.0265729	−	0.129263i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	18.2774	−	25.1567i	0.676479	−	0.931093i
$731$	−6.54310	−	20.1376i	−0.242005	−	0.744816i
$732$	−2.84824	−	8.76598i	−0.105274	−	0.324000i
$733$	6.78466	−	9.33828i	0.250597	−	0.344917i	−0.665123	−	0.746734i	$-0.731621\pi$
$733$	6.78466	−	9.33828i	0.250597	−	0.344917i	0.915720	+	0.401816i	$0.131621\pi$
$734$	−1.70411	−	2.34551i	−0.0628999	−	0.0865743i
$735$	−7.98730	−	2.59523i	−0.294616	−	0.0957266i
$736$		−	22.9373i		−	0.845480i
$737$	−10.5625	+	24.4156i	−0.389076	+	0.899360i
$738$	6.42896			0.236653
$739$	−21.2467	−	6.90346i	−0.781572	−	0.253948i	−0.109061	−	0.994035i	$-0.534784\pi$
$739$	−21.2467	−	6.90346i	−0.781572	−	0.253948i	−0.672511	+	0.740087i	$0.734784\pi$
$740$	1.36031	−	0.988325i	0.0500061	−	0.0363315i
$741$	−12.7521	+	22.4327i	−0.468462	+	0.824087i
$742$	−0.575082	−	1.76992i	−0.0211119	−	0.0649758i
$743$	−19.5439	+	6.35019i	−0.716996	+	0.232966i	−0.644720	−	0.764419i	$-0.723026\pi$
$743$	−19.5439	+	6.35019i	−0.716996	+	0.232966i	−0.0722755	+	0.997385i	$0.523026\pi$
$744$	12.5446	+	9.11420i	0.459908	+	0.334143i
$745$	13.6837	−	9.94182i	0.501334	−	0.364240i
$746$	−20.9641	−	6.81166i	−0.767551	−	0.249393i
$747$		−	0.549597i		−	0.0201087i
$748$	4.30021	−	4.87866i	0.157231	−	0.178382i
$749$		−	8.15936i		−	0.298136i
$750$	−5.25712	+	16.1798i	−0.191963	+	0.590801i
$751$	30.9236	−	22.4673i	1.12842	−	0.819844i	0.142954	−	0.989729i	$-0.454340\pi$
$751$	30.9236	−	22.4673i	1.12842	−	0.819844i	0.985464	+	0.169886i	$0.0543399\pi$
$752$	−19.9576	+	27.4693i	−0.727779	+	1.00170i
$753$	−2.93546	−	9.03443i	−0.106974	−	0.329233i
$754$	18.3364	−	8.31138i	0.667773	−	0.302682i
$755$	5.66607	+	4.11664i	0.206210	+	0.149820i
$756$	−0.168774	−	0.232297i	−0.00613824	−	0.00844857i
$757$	−13.4507	+	41.3971i	−0.488876	+	1.50460i	0.337412	+	0.941357i	$0.390448\pi$
$757$	−13.4507	+	41.3971i	−0.488876	+	1.50460i	−0.826288	+	0.563248i	$0.809552\pi$
$758$	−3.80671			−0.138266
$759$	21.1912	−	4.73913i	0.769192	−	0.172020i
$760$			19.5124i			0.707789i
$761$	−24.3453	−	7.91025i	−0.882515	−	0.286746i	−0.167514	−	0.985870i	$-0.553574\pi$
$761$	−24.3453	−	7.91025i	−0.882515	−	0.286746i	−0.715001	+	0.699123i	$0.753574\pi$
$762$	−3.99651	−	5.50073i	−0.144778	−	0.199270i
$763$	6.81848	+	4.95391i	0.246845	+	0.179344i
$764$	−0.805081	−	2.47778i	−0.0291268	−	0.0896431i
$765$	−3.58845	+	1.16596i	−0.129741	+	0.0421553i
$766$	−24.6473	−	17.9073i	−0.890543	−	0.647017i
$767$	20.9899	+	23.0003i	0.757903	+	0.830491i
$768$	−4.32238	+	13.3029i	−0.155970	+	0.480028i
$769$			30.9733i			1.11693i	0.829529	+	0.558464i	$0.188609\pi$
$769$			30.9733i			1.11693i	−0.829529	+	0.558464i	$0.811391\pi$
$770$	−2.56357	+	1.51645i	−0.0923845	+	0.0546491i
$771$	−28.4345			−1.02404
$772$	4.22873	+	1.37400i	0.152196	+	0.0494513i
$773$	−11.7036	−	16.1086i	−0.420948	−	0.579386i	0.544898	−	0.838503i	$-0.316569\pi$
$773$	−11.7036	−	16.1086i	−0.420948	−	0.579386i	−0.965846	+	0.259117i	$0.916569\pi$
$774$	6.62165	−	9.11392i	0.238010	−	0.327593i
$775$	−23.2117	+	7.54194i	−0.833789	+	0.270915i
$776$	8.34542	+	25.6846i	0.299583	+	0.922022i
$777$	0.767661	+	0.557738i	0.0275397	+	0.0200087i
$778$	18.9304	+	26.0554i	0.678686	+	0.934131i
$779$	−8.74751	+	26.9221i	−0.313412	+	0.964583i
$780$	0.317782	+	2.84050i	0.0113784	+	0.101706i
$781$	−1.76328	−	0.166493i	−0.0630953	−	0.00595758i
$782$			32.5101i			1.16256i
$783$	−1.06157	+	3.26716i	−0.0379373	+	0.116759i
$784$	26.8004	−	19.4716i	0.957157	−	0.695415i
$785$	10.6236	−	14.6221i	0.379172	−	0.521885i
$786$	−17.1247	+	5.56415i	−0.610818	+	0.198467i
$787$	1.67094	−	0.542922i	0.0595627	−	0.0193531i	−0.279084	−	0.960267i	$-0.590031\pi$
$787$	1.67094	−	0.542922i	0.0595627	−	0.0193531i	0.338647	+	0.940914i	$0.390031\pi$
$788$	−4.13859	+	5.69628i	−0.147431	+	0.202921i
$789$	12.3385	−	8.96448i	0.439264	−	0.319144i
$790$	−3.78752	+	11.6568i	−0.134754	+	0.414729i
$791$		−	5.51758i		−	0.196183i
$792$	−7.28906	−	0.688247i	−0.259005	−	0.0244558i
$793$	−51.4557	+	5.75662i	−1.82725	+	0.204424i
$794$	4.65304	−	14.3206i	0.165130	−	0.508218i
$795$	−1.85802	−	2.55734i	−0.0658972	−	0.0906997i
$796$	−1.18131	−	0.858273i	−0.0418705	−	0.0304207i
$797$	3.46894	+	10.6763i	0.122876	+	0.378174i	0.993508	−	0.113761i	$-0.0362898\pi$
$797$	3.46894	+	10.6763i	0.122876	+	0.378174i	−0.870632	+	0.491935i	$0.836290\pi$
$798$	4.94915	−	1.60807i	0.175198	−	0.0569252i
$799$	12.5151	−	17.2255i	0.442751	−	0.609394i
$800$	−7.15497	−	9.84797i	−0.252966	−	0.348178i
$801$	0.343128	+	0.111489i	0.0121238	+	0.00393927i
$802$	−49.2996			−1.74083
$803$	−44.2173	+	26.1563i	−1.56039	+	0.923036i
$804$		−	5.14821i		−	0.181563i
$805$	1.11786	−	3.44042i	0.0393994	−	0.121259i
$806$	−30.4062	+	27.7485i	−1.07101	+	0.977400i
$807$	16.1044	+	11.7005i	0.566903	+	0.411879i
$808$	40.2764	−	13.0866i	1.41692	−	0.460384i
$809$	−2.54918	−	7.84558i	−0.0896245	−	0.275836i	0.896191	−	0.443668i	$-0.146323\pi$
$809$	−2.54918	−	7.84558i	−0.0896245	−	0.275836i	−0.985816	+	0.167833i	$0.946323\pi$
$810$	−1.62407	−	1.17996i	−0.0570640	−	0.0414594i
$811$	−33.3528	−	45.9062i	−1.17118	−	1.61199i	−0.655473	−	0.755218i	$-0.727531\pi$
$811$	−33.3528	−	45.9062i	−1.17118	−	1.61199i	−0.515703	−	0.856768i	$-0.672469\pi$
$812$	−0.938117	−	0.304813i	−0.0329215	−	0.0106968i
$813$			6.41308i			0.224916i
$814$	−11.1586	+	2.49547i	−0.391108	+	0.0874662i
$815$	13.8221			0.484167
$816$	4.59910	−	14.1546i	0.161001	−	0.495509i
$817$	29.1560	+	40.1297i	1.02004	+	1.40396i
$818$	−44.6467	−	32.4378i	−1.56104	−	1.13416i
$819$	−1.46910	+	0.665901i	−0.0513345	+	0.0232685i
$820$	0.968934	+	2.98207i	0.0338366	+	0.104138i
$821$	−5.40402	+	7.43799i	−0.188601	+	0.259588i	−0.892838	−	0.450378i	$-0.851289\pi$
$821$	−5.40402	+	7.43799i	−0.188601	+	0.259588i	0.704237	+	0.709965i	$0.251289\pi$
$822$	−10.6003	+	7.70159i	−0.369729	+	0.268624i
$823$	−6.06093	+	18.6536i	−0.211271	+	0.650224i	0.788127	+	0.615513i	$0.211051\pi$
$823$	−6.06093	+	18.6536i	−0.211271	+	0.650224i	−0.999397	+	0.0347111i	$0.988949\pi$
$824$			17.1155i			0.596246i
$825$	7.61999	−	8.64501i	0.265294	−	0.300981i
$826$		−	6.27959i		−	0.218495i
$827$	30.3961	+	9.87628i	1.05697	+	0.343432i	0.785402	−	0.618986i	$-0.212456\pi$
$827$	30.3961	+	9.87628i	1.05697	+	0.343432i	0.271572	+	0.962418i	$0.412456\pi$
$828$	−3.39974	+	2.47006i	−0.118149	+	0.0858404i
$829$	−5.70258	−	4.14317i	−0.198059	−	0.143898i	0.484336	−	0.874882i	$-0.339061\pi$
$829$	−5.70258	−	4.14317i	−0.198059	−	0.143898i	−0.682395	+	0.730984i	$0.739061\pi$
$830$	1.04929	−	0.340937i	0.0364215	−	0.0118341i
$831$	−0.802466	−	2.46974i	−0.0278372	−	0.0856742i
$832$	12.6921	+	7.21496i	0.440019	+	0.250134i
$833$	−16.8061	+	12.2103i	−0.582295	+	0.423062i
$834$	18.8570	+	6.12703i	0.652966	+	0.212162i
$835$	12.7734			0.442042
$836$	−6.04908	+	13.9826i	−0.209212	+	0.483599i
$837$		−	7.02421i		−	0.242792i
$838$	25.5455	+	8.30023i	0.882454	+	0.286727i
$839$	6.08388	+	8.37375i	0.210039	+	0.289094i	0.901019	−	0.433780i	$-0.142821\pi$
$839$	6.08388	+	8.37375i	0.210039	+	0.289094i	−0.690980	+	0.722874i	$0.742821\pi$
$840$	−0.716918	+	0.986753i	−0.0247360	+	0.0340462i
$841$	−5.31470	−	16.3570i	−0.183265	−	0.564033i
$842$	−3.59144	−	11.0533i	−0.123769	−	0.380922i
$843$	−8.63765	+	11.8887i	−0.297496	+	0.409469i
$844$	7.37283	−	5.35667i	0.253783	−	0.184384i
$845$	15.9890	+	1.46444i	0.550040	+	0.0503782i
$846$	11.3282			0.389471
$847$	4.88200	−	0.617782i	0.167748	−	0.0212272i
$848$	12.4687			0.428177
$849$	5.83669	−	17.9635i	0.200315	−	0.616505i
$850$	10.1411	+	13.9580i	0.347836	+	0.478755i
$851$	8.16267	−	11.2350i	0.279813	−	0.385129i
$852$	0.325980	−	0.105917i	0.0111679	−	0.00362867i
$853$	−3.76108	+	1.22205i	−0.128777	+	0.0418421i	−0.372696	−	0.927953i	$-0.621567\pi$
$853$	−3.76108	+	1.22205i	−0.128777	+	0.0418421i	0.243920	+	0.969795i	$0.421567\pi$
$854$	8.44752	+	6.13748i	0.289068	+	0.210020i
$855$	7.15099	−	5.19549i	0.244559	−	0.177682i
$856$	38.2921	+	12.4419i	1.30880	+	0.425254i
$857$	21.6463			0.739424			0.369712	−	0.929146i	$-0.379456\pi$
$857$	21.6463			0.739424			0.369712	+	0.929146i	$0.379456\pi$
$858$	5.68615	−	18.5863i	0.194122	−	0.634527i
$859$	−6.48972			−0.221426			−0.110713	−	0.993852i	$-0.535313\pi$
$859$	−6.48972			−0.221426			−0.110713	+	0.993852i	$0.535313\pi$
$860$	5.22546	+	1.69785i	0.178187	+	0.0578964i
$861$	−1.43153	+	1.04007i	−0.0487864	+	0.0354454i
$862$	38.0819	+	27.6681i	1.29707	+	0.942380i
$863$	49.1813	−	15.9800i	1.67415	−	0.543964i	0.690387	−	0.723440i	$-0.257440\pi$
$863$	49.1813	−	15.9800i	1.67415	−	0.543964i	0.983762	+	0.179476i	$0.0574401\pi$
$864$	3.33190	−	1.08260i	0.113354	−	0.0368308i
$865$	−6.64565	+	9.14696i	−0.225959	+	0.311006i
$866$	−4.48223	−	6.16926i	−0.152312	−	0.209640i
$867$	2.36927	−	7.29188i	0.0804648	−	0.247645i
$868$	2.01690			0.0684579
$869$	13.3899	−	15.1910i	0.454220	−	0.515320i
$870$	−6.89623			−0.233804
$871$	−28.3275	−	5.82334i	−0.959841	−	0.197316i
$872$	−33.6461	+	24.4453i	−1.13940	+	0.827823i
$873$	7.19088	−	9.89740i	0.243374	−	0.334976i
$874$	−23.5347	−	72.4323i	−0.796072	−	2.45006i
$875$	−1.44694	−	4.45321i	−0.0489154	−	0.150546i
$876$	5.84386	−	8.04338i	0.197446	−	0.271761i
$877$	−28.3979	−	39.0864i	−0.958929	−	1.31985i	−0.947445	−	0.319919i	$-0.896344\pi$
$877$	−28.3979	−	39.0864i	−0.958929	−	1.31985i	−0.0114844	−	0.999934i	$-0.503656\pi$
$878$	49.3944	+	16.0492i	1.66698	+	0.541635i
$879$			18.6756i			0.629912i
$880$	−4.35530	−	19.4749i	−0.146817	−	0.656498i
$881$	10.7969			0.363756			0.181878	−	0.983321i	$-0.441782\pi$
$881$	10.7969			0.363756			0.181878	+	0.983321i	$0.441782\pi$
$882$	−10.5114	−	3.41536i	−0.353937	−	0.115001i
$883$	33.1168	−	24.0608i	1.11447	−	0.809709i	0.131107	−	0.991368i	$-0.458147\pi$
$883$	33.1168	−	24.0608i	1.11447	−	0.809709i	0.983362	+	0.181659i	$0.0581469\pi$
$884$	6.14619	+	3.49387i	0.206719	+	0.117512i
$885$	−3.29608	−	10.1443i	−0.110797	−	0.340997i
$886$	6.49410	−	2.11006i	0.218174	−	0.0708889i
$887$	−23.3136	−	16.9383i	−0.782793	−	0.568732i	0.123023	−	0.992404i	$-0.460741\pi$
$887$	−23.3136	−	16.9383i	−0.782793	−	0.568732i	−0.905816	+	0.423672i	$0.860741\pi$
$888$	−3.78806	+	2.75219i	−0.127119	+	0.0923573i
$889$	1.77980	+	0.578291i	0.0596924	+	0.0193952i
$890$			0.724264i			0.0242774i
$891$	1.68860	+	2.85458i	0.0565702	+	0.0956321i
$892$		−	7.05109i		−	0.236088i
$893$	−15.4136	+	47.4382i	−0.515796	+	1.58746i
$894$	18.0080	−	13.0836i	0.602278	−	0.437580i
$895$	3.25190	−	4.47586i	0.108699	−	0.149612i
$896$	−1.87844	−	5.78125i	−0.0627543	−	0.193138i
$897$	9.74567	+	21.5007i	0.325398	+	0.717888i
$898$	43.3057	+	31.4634i	1.44513	+	1.04995i
$899$	−14.1834	−	19.5218i	−0.473043	−	0.651088i
$900$	−0.689155	+	2.12100i	−0.0229718	+	0.0707001i
$901$	−7.81890			−0.260485
$902$	2.00439	−	21.2280i	0.0667390	−	0.706816i
$903$			3.10062i			0.103182i
$904$	25.8942	+	8.41354i	0.861229	+	0.279830i
$905$	−14.8265	−	20.4069i	−0.492848	−	0.678347i
$906$	7.45663	+	5.41756i	0.247730	+	0.179986i
$907$	5.57286	+	17.1515i	0.185044	+	0.569506i	0.999949	−	0.0100879i	$-0.00321113\pi$
$907$	5.57286	+	17.1515i	0.185044	+	0.569506i	−0.814905	+	0.579594i	$0.803211\pi$
$908$	10.0481	−	3.26482i	0.333457	−	0.108347i
$909$	−15.5203	−	11.2761i	−0.514774	−	0.374006i
$910$	−2.18268	−	2.39173i	−0.0723553	−	0.0792852i
$911$	−5.19457	+	15.9872i	−0.172104	+	0.529681i	−0.999489	−	0.0319534i	$-0.989827\pi$
$911$	−5.19457	+	15.9872i	−0.172104	+	0.529681i	0.827386	+	0.561634i	$0.189827\pi$
$912$			34.8657i			1.15452i
$913$	−1.81473	−	0.171351i	−0.0600589	−	0.00567088i
$914$	−21.3246			−0.705355
$915$	16.8680	+	5.48073i	0.557637	+	0.181187i
$916$	4.69883	+	6.46738i	0.155254	+	0.213688i
$917$	2.91297	−	4.00936i	0.0961948	−	0.132401i
$918$	−4.72245	+	1.53442i	−0.155864	+	0.0506433i
$919$	−1.20454	−	3.70719i	−0.0397340	−	0.122289i	0.929222	−	0.369522i	$-0.120479\pi$
$919$	−1.20454	−	3.70719i	−0.0397340	−	0.122289i	−0.968956	+	0.247233i	$0.920479\pi$
$920$	14.4414	+	10.4923i	0.476120	+	0.345922i
$921$	−4.03554	−	5.55445i	−0.132976	−	0.183025i
$922$	−9.91174	+	30.5052i	−0.326426	+	1.00463i
$923$	−0.214071	−	1.91348i	−0.00704624	−	0.0629830i
$924$	−0.819651	+	0.484856i	−0.0269645	+	0.0159506i
$925$		−	7.36988i		−	0.242320i
$926$	−16.0927	+	49.5282i	−0.528839	+	1.62760i
$927$	6.27255	−	4.55728i	0.206018	−	0.149681i
$928$	7.07406	−	9.73661i	0.232217	−	0.319620i
$929$	−48.9737	+	15.9125i	−1.60678	+	0.522073i	−0.968771	−	0.247959i	$-0.920240\pi$
$929$	−48.9737	+	15.9125i	−1.60678	+	0.522073i	−0.638006	+	0.770032i	$0.720240\pi$
$930$	13.4107	−	4.35739i	0.439753	−	0.142885i
$931$	28.6045	−	39.3707i	0.937475	−	1.29032i
$932$	−3.89873	+	2.83259i	−0.127707	+	0.0927847i
$933$	−1.89987	+	5.84718i	−0.0621988	+	0.191428i
$934$			60.4686i			1.97859i
$935$	2.73113	+	12.2124i	0.0893176	+	0.399387i
$936$	−0.884927	−	7.90994i	−0.0289247	−	0.258545i
$937$	6.16055	−	18.9602i	0.201256	−	0.619404i	−0.798590	−	0.601876i	$-0.794420\pi$
$937$	6.16055	−	18.9602i	0.201256	−	0.619404i	0.999846	−	0.0175282i	$-0.00557968\pi$
$938$	3.42809	+	4.71836i	0.111931	+	0.154060i
$939$	−21.4030	−	15.5502i	−0.698460	−	0.507461i
$940$	1.70731	+	5.25457i	0.0556865	+	0.171385i
$941$	46.6268	−	15.1500i	1.51999	−	0.493875i	0.574218	−	0.818702i	$-0.305306\pi$
$941$	46.6268	−	15.1500i	1.51999	−	0.493875i	0.945773	+	0.324827i	$0.105306\pi$
$942$	13.9808	−	19.2429i	0.455518	−	0.626967i
$943$	15.2217	+	20.9509i	0.495686	+	0.682254i
$944$	40.0139	+	13.0013i	1.30234	+	0.423157i
$945$	0.552520			0.0179735
$946$	−28.0291	−	24.7058i	−0.911306	−	0.803254i
$947$			29.1868i			0.948444i	0.880405	+	0.474222i	$0.157271\pi$
$947$			29.1868i			0.948444i	−0.880405	+	0.474222i	$0.842729\pi$
$948$	−1.21098	+	3.72703i	−0.0393309	+	0.121048i
$949$	−37.6477	−	41.2534i	−1.22210	−	1.33914i
$950$	−32.6987	−	23.7570i	−1.06088	−	0.770778i
$951$	−11.0838	+	3.60135i	−0.359417	+	0.116782i
$952$	0.932283	+	2.86927i	0.0302155	+	0.0929936i
$953$	33.8243	+	24.5748i	1.09568	+	0.796055i	0.980349	−	0.197272i	$-0.0632082\pi$
$953$	33.8243	+	24.5748i	1.09568	+	0.796055i	0.115328	+	0.993328i	$0.463208\pi$
$954$	−2.44518	−	3.36550i	−0.0791656	−	0.108962i
$955$	4.76788	+	1.54918i	0.154285	+	0.0501302i
$956$		−	3.20072i		−	0.103519i
$957$	10.4570	+	4.52385i	0.338027	+	0.146235i
$958$	15.9362			0.514877
$959$	1.11441	−	3.42981i	0.0359862	−	0.110754i
$960$	−2.93953	−	4.04591i	−0.0948728	−	0.130581i
$961$	14.8370	+	10.7797i	0.478611	+	0.347731i
$962$	−5.13174	−	11.3216i	−0.165454	−	0.365022i
$963$	−5.63616	−	17.3463i	−0.181623	−	0.558977i
$964$	−11.1145	+	15.2977i	−0.357973	+	0.492707i
$965$	−6.92188	+	5.02904i	−0.222823	+	0.161890i
$966$	1.47112	−	4.52764i	0.0473325	−	0.145675i
$967$			7.41044i			0.238304i	0.992876	+	0.119152i	$0.0380175\pi$
$967$			7.41044i			0.238304i	−0.992876	+	0.119152i	$0.961982\pi$
$968$	−4.54510	+	23.8534i	−0.146085	+	0.766679i
$969$		−	21.8636i		−	0.702361i
$970$	23.3570	+	7.58914i	0.749948	+	0.243673i
$971$	30.5149	−	22.1704i	0.979269	−	0.711481i	0.0217242	−	0.999764i	$-0.493084\pi$
$971$	30.5149	−	22.1704i	0.979269	−	0.711481i	0.957545	+	0.288283i	$0.0930844\pi$
$972$	−0.519265	−	0.377268i	−0.0166554	−	0.0121009i
$973$	−5.19009	+	1.68636i	−0.166387	+	0.0540623i
$974$	11.7121	+	36.0461i	0.375279	+	1.15499i
$975$	10.8911	+	6.19116i	0.348794	+	0.198276i
$976$	−56.5983	+	41.1211i	−1.81167	+	1.31625i
$977$	−11.9032	−	3.86757i	−0.380816	−	0.123734i	0.112353	−	0.993668i	$-0.464161\pi$
$977$	−11.9032	−	3.86757i	−0.380816	−	0.123734i	−0.493168	+	0.869934i	$0.664161\pi$
$978$	18.1901			0.581654
$979$	0.475109	−	1.09823i	0.0151845	−	0.0350995i
$980$		−	5.39045i		−	0.172192i
$981$	17.9176	+	5.82180i	0.572066	+	0.185876i
$982$	4.21645	+	5.80345i	0.134552	+	0.185196i
$983$	−30.0220	+	41.3218i	−0.957554	+	1.31796i	−0.00946510	+	0.999955i	$0.503013\pi$
$983$	−30.0220	+	41.3218i	−0.957554	+	1.31796i	−0.948089	+	0.318005i	$0.896987\pi$
$984$	−2.69819	−	8.30417i	−0.0860151	−	0.264727i
$985$	−4.18676	−	12.8855i	−0.133401	−	0.410567i
$986$	−10.0264	+	13.8001i	−0.319305	+	0.439486i
$987$	−2.52243	+	1.83265i	−0.0802899	+	0.0583340i
$988$	−16.2230	−	3.33498i	−0.516121	−	0.106100i
$989$	45.3786			1.44295
$990$	−4.40249	+	4.99470i	−0.139920	+	0.158742i
$991$	5.29523			0.168208			0.0841042	−	0.996457i	$-0.473197\pi$
$991$	5.29523			0.168208			0.0841042	+	0.996457i	$0.473197\pi$
$992$	−7.60440	+	23.4040i	−0.241440	+	0.743076i
$993$	1.88776	+	2.59829i	0.0599064	+	0.0824541i
$994$	−0.228234	+	0.314138i	−0.00723916	+	0.00996384i
$995$	2.67224	−	0.868262i	0.0847156	−	0.0275258i
$996$	0.335492	−	0.109008i	0.0106305	−	0.00345405i
$997$	16.1406	+	11.7269i	0.511179	+	0.371393i	0.813271	−	0.581885i	$-0.197685\pi$
$997$	16.1406	+	11.7269i	0.511179	+	0.371393i	−0.302091	+	0.953279i	$0.597685\pi$
$998$	−0.750395	+	0.545194i	−0.0237533	+	0.0172578i
$999$	2.01726	+	0.655449i	0.0638234	+	0.0207375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bb.b.64.4	✓	56
11.5	even	5	inner	429.2.bb.b.181.11	yes	56
13.12	even	2	inner	429.2.bb.b.64.11	yes	56
143.38	even	10	inner	429.2.bb.b.181.4	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bb.b.64.4	✓	56	1.1	even	1	trivial
429.2.bb.b.64.11	yes	56	13.12	even	2	inner
429.2.bb.b.181.4	yes	56	143.38	even	10	inner
429.2.bb.b.181.11	yes	56	11.5	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.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54582 - 0.502269i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.519265 + 0.377268i) q^{4} +(-1.17463 + 0.381659i) q^{5} +(-1.54582 + 0.502269i) q^{6} +(0.262950 - 0.361920i) q^{7} +(1.29754 + 1.78591i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-1.54582 - 0.502269i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.519265 + 0.377268i) q^{4} +(-1.17463 + 0.381659i) q^{5} +(-1.54582 + 0.502269i) q^{6} +(0.262950 - 0.361920i) q^{7} +(1.29754 + 1.78591i) q^{8} +(0.309017 - 0.951057i) q^{9} +2.00746 q^{10} +(-3.04399 - 1.31687i) q^{11} +0.641847 q^{12} +(0.726018 - 3.53170i) q^{13} +(-0.588256 + 0.427393i) q^{14} +(-0.725959 + 0.999197i) q^{15} +(-1.50545 - 4.63329i) q^{16} +(0.944039 + 2.90545i) q^{17} +(-0.955372 + 1.31496i) q^{18} +(-4.20662 - 5.78992i) q^{19} +(-0.753930 - 0.244967i) q^{20} -0.447358i q^{21} +(4.04404 + 3.56455i) q^{22} -6.54722 q^{23} +(2.09947 + 0.682158i) q^{24} +(-2.81100 + 2.04231i) q^{25} +(-2.89616 + 5.09473i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.273082 - 0.0887296i) q^{28} +(-2.77921 - 2.01922i) q^{29} +(1.62407 - 1.17996i) q^{30} +(6.68042 + 2.17060i) q^{31} +3.50337i q^{32} +(-3.23667 + 0.723839i) q^{33} -4.96548i q^{34} +(-0.170738 + 0.525478i) q^{35} +(0.519265 - 0.377268i) q^{36} +(-1.24674 + 1.71599i) q^{37} +(3.59460 + 11.0631i) q^{38} +(-1.48852 - 3.28395i) q^{39} +(-2.20574 - 1.60256i) q^{40} +(-2.32491 - 3.19996i) q^{41} +(-0.224694 + 0.691537i) q^{42} -6.93097 q^{43} +(-1.08382 - 1.83220i) q^{44} +1.23507i q^{45} +(10.1209 + 3.28846i) q^{46} +(-4.09662 - 5.63851i) q^{47} +(-3.94131 - 2.86353i) q^{48} +(2.10128 + 6.46706i) q^{49} +(5.37111 - 1.74518i) q^{50} +(2.47153 + 1.79567i) q^{51} +(1.70939 - 1.55998i) q^{52} +(-0.790898 + 2.43413i) q^{53} +1.62538i q^{54} +(4.07814 + 0.385066i) q^{55} +0.987547 q^{56} +(-6.80646 - 2.21155i) q^{57} +(3.28199 + 4.51727i) q^{58} +(-5.07623 + 6.98682i) q^{59} +(-0.753930 + 0.244967i) q^{60} +(-4.43757 - 13.6574i) q^{61} +(-9.23653 - 6.71073i) q^{62} +(-0.262950 - 0.361920i) q^{63} +(-1.25126 + 3.85098i) q^{64} +(0.495106 + 4.42552i) q^{65} +(5.36689 + 0.506752i) q^{66} -8.02093i q^{67} +(-0.605928 + 1.86486i) q^{68} +(-5.29681 + 3.84836i) q^{69} +(0.527863 - 0.726541i) q^{70} +(0.507879 - 0.165020i) q^{71} +(2.09947 - 0.682158i) q^{72} +(9.10476 - 12.5316i) q^{73} +(2.78913 - 2.02642i) q^{74} +(-1.07371 + 3.30453i) q^{75} -4.59353i q^{76} +(-1.27702 + 0.755408i) q^{77} +(0.651566 + 5.82404i) q^{78} +(-1.88672 + 5.80673i) q^{79} +(3.53667 + 4.86781i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(1.98666 + 6.11431i) q^{82} +(0.522697 - 0.169835i) q^{83} +(0.168774 - 0.232297i) q^{84} +(-2.21779 - 3.05252i) q^{85} +(10.7141 + 3.48121i) q^{86} -3.43530 q^{87} +(-1.59788 - 7.14499i) q^{88} +0.360786i q^{89} +(0.620339 - 1.90921i) q^{90} +(-1.08729 - 1.19142i) q^{91} +(-3.39974 - 2.47006i) q^{92} +(6.68042 - 2.17060i) q^{93} +(3.50060 + 10.7737i) q^{94} +(7.15099 + 5.19549i) q^{95} +(2.05923 + 2.83428i) q^{96} +(11.6351 + 3.78047i) q^{97} -11.0523i q^{98} +(-2.19306 + 2.48807i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9}+O(q^{10}) \) 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9	\( 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9} + 60 q^{12} - 3 q^{13} - 42 q^{14} - 16 q^{16} - 6 q^{17} - 40 q^{22} + 12 q^{23} + 4 q^{25} - 24 q^{26} + 14 q^{27} - 22 q^{29} - 10 q^{30} - 10 q^{35} + 20 q^{36} - 26 q^{38} + 3 q^{39} - 18 q^{42} + 6 q^{48} - 14 q^{49} - 24 q^{51} + 39 q^{52} + 10 q^{53} - 64 q^{55} - 20 q^{56} + 2 q^{61} - 8 q^{62} + 24 q^{64} - 58 q^{65} + 30 q^{66} + 18 q^{68} - 2 q^{69} - 86 q^{74} - 14 q^{75} + 52 q^{77} + 14 q^{78} - 24 q^{79} - 14 q^{81} + 62 q^{82} - 28 q^{87} - 46 q^{88} - 10 q^{90} - 19 q^{91} + 58 q^{92} + 86 q^{94} + 156 q^{95}+O(q^{100}) \) 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9 + 60 * q^12 - 3 * q^13 - 42 * q^14 - 16 * q^16 - 6 * q^17 - 40 * q^22 + 12 * q^23 + 4 * q^25 - 24 * q^26 + 14 * q^27 - 22 * q^29 - 10 * q^30 - 10 * q^35 + 20 * q^36 - 26 * q^38 + 3 * q^39 - 18 * q^42 + 6 * q^48 - 14 * q^49 - 24 * q^51 + 39 * q^52 + 10 * q^53 - 64 * q^55 - 20 * q^56 + 2 * q^61 - 8 * q^62 + 24 * q^64 - 58 * q^65 + 30 * q^66 + 18 * q^68 - 2 * q^69 - 86 * q^74 - 14 * q^75 + 52 * q^77 + 14 * q^78 - 24 * q^79 - 14 * q^81 + 62 * q^82 - 28 * q^87 - 46 * q^88 - 10 * q^90 - 19 * q^91 + 58 * q^92 + 86 * q^94 + 156 * q^95

Introduction

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