LMFDB - Embedded newform 637.2.bl.a.53.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			53.24
Character	$\chi$	$=$	637.53
Dual form			637.2.bl.a.625.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73040 + 1.17977i) q^{2} +(-0.623413 - 0.578442i) q^{3} +(0.871761 + 2.22121i) q^{4} +(3.60339 - 1.11150i) q^{5} +(-0.396327 - 1.73642i) q^{6} +(-2.15272 - 1.53811i) q^{7} +(-0.179960 + 0.788456i) q^{8} +(-0.170143 - 2.27039i) q^{9} +O(q^{10})$	\(q+(1.73040 + 1.17977i) q^{2} +(-0.623413 - 0.578442i) q^{3} +(0.871761 + 2.22121i) q^{4} +(3.60339 - 1.11150i) q^{5} +(-0.396327 - 1.73642i) q^{6} +(-2.15272 - 1.53811i) q^{7} +(-0.179960 + 0.788456i) q^{8} +(-0.170143 - 2.27039i) q^{9} +(7.54663 + 2.32783i) q^{10} +(-0.324474 + 4.32981i) q^{11} +(0.741375 - 1.88899i) q^{12} +(0.900969 - 0.433884i) q^{13} +(-1.91046 - 5.20127i) q^{14} +(-2.88933 - 1.39143i) q^{15} +(2.25675 - 2.09396i) q^{16} +(4.97454 - 0.749792i) q^{17} +(2.38413 - 4.12943i) q^{18} +(-0.0277917 - 0.0481367i) q^{19} +(5.61016 + 7.03492i) q^{20} +(0.452326 + 2.20410i) q^{21} +(-5.66965 + 7.10952i) q^{22} +(-5.21097 - 0.785427i) q^{23} +(0.568266 - 0.387437i) q^{24} +(7.61778 - 5.19371i) q^{25} +(2.07092 + 0.312141i) q^{26} +(-2.79794 + 3.50850i) q^{27} +(1.53981 - 6.12251i) q^{28} +(0.928954 + 1.16487i) q^{29} +(-3.35815 - 5.81649i) q^{30} +(-4.14033 + 7.17127i) q^{31} +(7.97488 - 1.20202i) q^{32} +(2.70683 - 2.51157i) q^{33} +(9.49256 + 4.57137i) q^{34} +(-9.46670 - 3.14966i) q^{35} +(4.89470 - 2.35716i) q^{36} +(-2.30100 + 5.86286i) q^{37} +(0.00869927 - 0.116084i) q^{38} +(-0.812652 - 0.250670i) q^{39} +(0.227902 + 3.04114i) q^{40} +(-0.0523555 + 0.229384i) q^{41} +(-1.81763 + 4.34763i) q^{42} +(-1.73287 - 7.59219i) q^{43} +(-9.90028 + 3.05383i) q^{44} +(-3.13663 - 7.99200i) q^{45} +(-8.09046 - 7.50685i) q^{46} +(5.90380 + 4.02514i) q^{47} -2.61812 q^{48} +(2.26843 + 6.62225i) q^{49} +19.3092 q^{50} +(-3.53490 - 2.41006i) q^{51} +(1.74918 + 1.62300i) q^{52} +(-0.819254 - 2.08742i) q^{53} +(-8.98078 + 2.77020i) q^{54} +(3.64337 + 15.9626i) q^{55} +(1.60014 - 1.42053i) q^{56} +(-0.0105186 + 0.0460849i) q^{57} +(0.233186 + 3.11165i) q^{58} +(-2.02006 - 0.623105i) q^{59} +(0.571850 - 7.63081i) q^{60} +(-5.27791 + 13.4479i) q^{61} +(-15.6249 + 7.52455i) q^{62} +(-3.12585 + 5.14923i) q^{63} +(9.67049 + 4.65706i) q^{64} +(2.76428 - 2.56488i) q^{65} +(7.64698 - 1.15260i) q^{66} +(1.79800 - 3.11423i) q^{67} +(6.00206 + 10.3959i) q^{68} +(2.79426 + 3.50389i) q^{69} +(-12.6653 - 16.6187i) q^{70} +(-5.70107 + 7.14891i) q^{71} +(1.82073 + 0.274430i) q^{72} +(-10.9284 + 7.45084i) q^{73} +(-10.8985 + 7.43047i) q^{74} +(-7.75328 - 1.16862i) q^{75} +(0.0826939 - 0.103695i) q^{76} +(7.35823 - 8.82180i) q^{77} +(-1.11048 - 1.39250i) q^{78} +(-5.44503 - 9.43107i) q^{79} +(5.80452 - 10.0537i) q^{80} +(-2.98026 + 0.449202i) q^{81} +(-0.361217 + 0.335160i) q^{82} +(13.0849 + 6.30138i) q^{83} +(-4.50146 + 2.92616i) q^{84} +(17.0918 - 8.23098i) q^{85} +(5.95848 - 15.1819i) q^{86} +(0.0946894 - 1.26354i) q^{87} +(-3.35547 - 1.03503i) q^{88} +(-1.04224 - 13.9077i) q^{89} +(4.00108 - 17.5299i) q^{90} +(-2.60690 - 0.451759i) q^{91} +(-2.79812 - 12.2594i) q^{92} +(6.72930 - 2.07571i) q^{93} +(5.46722 + 13.9302i) q^{94} +(-0.153648 - 0.142565i) q^{95} +(-5.66694 - 3.86366i) q^{96} -15.3829 q^{97} +(-3.88744 + 14.1354i) q^{98} +9.88559 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

Coefficient data

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

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

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

$2$	1.73040	+	1.17977i	1.22358	+	0.834223i	0.990403	−	0.138211i	$-0.0441352\pi$
$2$	1.73040	+	1.17977i	1.22358	+	0.834223i	0.233178	+	0.972434i	$0.425088\pi$
$3$	−0.623413	−	0.578442i	−0.359927	−	0.333964i	0.479394	−	0.877600i	$-0.340857\pi$
$3$	−0.623413	−	0.578442i	−0.359927	−	0.333964i	−0.839321	+	0.543636i	$0.817047\pi$
$4$	0.871761	+	2.22121i	0.435880	+	1.11061i
$5$	3.60339	−	1.11150i	1.61148	−	0.497077i	0.647283	−	0.762250i	$-0.275905\pi$
$5$	3.60339	−	1.11150i	1.61148	−	0.497077i	0.964201	+	0.265173i	$0.0854291\pi$
$6$	−0.396327	−	1.73642i	−0.161800	−	0.708891i
$7$	−2.15272	−	1.53811i	−0.813653	−	0.581351i
$7$	−2.15272	−	1.53811i	−0.813653	−	0.581351i
$8$	−0.179960	+	0.788456i	−0.0636255	+	0.278761i
$9$	−0.170143	−	2.27039i	−0.0567142	−	0.756798i
$10$	7.54663	+	2.32783i	2.38645	+	0.736123i
$11$	−0.324474	+	4.32981i	−0.0978327	+	1.30549i	0.704968	+	0.709239i	$0.250961\pi$
$11$	−0.324474	+	4.32981i	−0.0978327	+	1.30549i	−0.802801	+	0.596248i	$0.796658\pi$
$12$	0.741375	−	1.88899i	0.214017	−	0.545305i
$13$	0.900969	−	0.433884i	0.249884	−	0.120338i
$13$	0.900969	−	0.433884i	0.249884	−	0.120338i
$14$	−1.91046	−	5.20127i	−0.510593	−	1.39010i
$15$	−2.88933	−	1.39143i	−0.746023	−	0.359266i
$16$	2.25675	−	2.09396i	0.564188	−	0.523490i
$17$	4.97454	−	0.749792i	1.20650	−	0.181851i	0.485158	−	0.874426i	$-0.338762\pi$
$17$	4.97454	−	0.749792i	1.20650	−	0.181851i	0.721346	+	0.692575i	$0.243524\pi$
$18$	2.38413	−	4.12943i	0.561944	−	0.973316i
$19$	−0.0277917	−	0.0481367i	−0.00637586	−	0.0110433i	0.862820	−	0.505511i	$-0.168696\pi$
$19$	−0.0277917	−	0.0481367i	−0.00637586	−	0.0110433i	−0.869196	+	0.494468i	$0.835363\pi$
$20$	5.61016	+	7.03492i	1.25447	+	1.57306i
$21$	0.452326	+	2.20410i	0.0987056	+	0.480975i
$22$	−5.66965	+	7.10952i	−1.20877	+	1.51575i
$23$	−5.21097	−	0.785427i	−1.08656	−	0.163773i	−0.418749	−	0.908102i	$-0.637531\pi$
$23$	−5.21097	−	0.785427i	−1.08656	−	0.163773i	−0.667813	+	0.744329i	$0.732769\pi$
$24$	0.568266	−	0.387437i	0.115997	−	0.0790853i
$25$	7.61778	−	5.19371i	1.52356	−	1.03874i
$26$	2.07092	+	0.312141i	0.406142	+	0.0612160i
$27$	−2.79794	+	3.50850i	−0.538463	+	0.675211i
$28$	1.53981	−	6.12251i	0.290997	−	1.15705i
$29$	0.928954	+	1.16487i	0.172502	+	0.216311i	0.860566	−	0.509340i	$-0.170110\pi$
$29$	0.928954	+	1.16487i	0.172502	+	0.216311i	−0.688063	+	0.725651i	$0.741539\pi$
$30$	−3.35815	−	5.81649i	−0.613111	−	1.06194i
$31$	−4.14033	+	7.17127i	−0.743626	+	1.28800i	0.207208	+	0.978297i	$0.433562\pi$
$31$	−4.14033	+	7.17127i	−0.743626	+	1.28800i	−0.950834	+	0.309701i	$0.899771\pi$
$32$	7.97488	−	1.20202i	1.40977	−	0.212489i
$33$	2.70683	−	2.51157i	0.471198	−	0.437208i
$34$	9.49256	+	4.57137i	1.62796	+	0.783984i
$35$	−9.46670	−	3.14966i	−1.60016	−	0.532390i
$36$	4.89470	−	2.35716i	0.815783	−	0.392861i
$37$	−2.30100	+	5.86286i	−0.378283	+	0.963849i	0.607272	+	0.794494i	$0.292264\pi$
$37$	−2.30100	+	5.86286i	−0.378283	+	0.963849i	−0.985555	+	0.169355i	$0.945832\pi$
$38$	0.00869927	−	0.116084i	0.00141121	−	0.0188313i
$39$	−0.812652	−	0.250670i	−0.130128	−	0.0401393i
$40$	0.227902	+	3.04114i	0.0360344	+	0.480846i
$41$	−0.0523555	+	0.229384i	−0.00817655	+	0.0358238i	−0.978852	−	0.204571i	$-0.934420\pi$
$41$	−0.0523555	+	0.229384i	−0.00817655	+	0.0358238i	0.970675	+	0.240395i	$0.0772771\pi$
$42$	−1.81763	+	4.34763i	−0.280466	+	0.670854i
$43$	−1.73287	−	7.59219i	−0.264260	−	1.15780i	−0.916579	−	0.399854i	$-0.869061\pi$
$43$	−1.73287	−	7.59219i	−0.264260	−	1.15780i	0.652319	−	0.757945i	$-0.273796\pi$
$44$	−9.90028	+	3.05383i	−1.49252	+	0.460383i
$45$	−3.13663	−	7.99200i	−0.467581	−	1.19138i
$46$	−8.09046	−	7.50685i	−1.19287	−	1.10683i
$47$	5.90380	+	4.02514i	0.861157	+	0.587127i	0.911359	−	0.411612i	$-0.135034\pi$
$47$	5.90380	+	4.02514i	0.861157	+	0.587127i	−0.0502019	+	0.998739i	$0.515986\pi$
$48$	−2.61812			−0.377893
$49$	2.26843	+	6.62225i	0.324061	+	0.946036i
$50$	19.3092			2.73074
$51$	−3.53490	−	2.41006i	−0.494986	−	0.337476i
$52$	1.74918	+	1.62300i	0.242567	+	0.225069i
$53$	−0.819254	−	2.08742i	−0.112533	−	0.286730i	0.863501	−	0.504347i	$-0.168267\pi$
$53$	−0.819254	−	2.08742i	−0.112533	−	0.286730i	−0.976034	+	0.217617i	$0.930172\pi$
$54$	−8.98078	+	2.77020i	−1.22213	+	0.376977i
$55$	3.64337	+	15.9626i	0.491272	+	2.15240i
$56$	1.60014	−	1.42053i	0.213827	−	0.189826i
$57$	−0.0105186	+	0.0460849i	−0.00139322	+	0.00610409i
$58$	0.233186	+	3.11165i	0.0306188	+	0.408580i
$59$	−2.02006	−	0.623105i	−0.262989	−	0.0811214i	0.160457	−	0.987043i	$-0.448703\pi$
$59$	−2.02006	−	0.623105i	−0.262989	−	0.0811214i	−0.423446	+	0.905922i	$0.639180\pi$
$60$	0.571850	−	7.63081i	0.0738256	−	0.985134i
$61$	−5.27791	+	13.4479i	−0.675767	+	1.72183i	0.0161692	+	0.999869i	$0.494853\pi$
$61$	−5.27791	+	13.4479i	−0.675767	+	1.72183i	−0.691937	+	0.721958i	$0.743242\pi$
$62$	−15.6249	+	7.52455i	−1.98436	+	0.955619i
$63$	−3.12585	+	5.14923i	−0.393820	+	0.648742i
$64$	9.67049	+	4.65706i	1.20881	+	0.582133i
$65$	2.76428	−	2.56488i	0.342867	−	0.318134i
$66$	7.64698	−	1.15260i	0.941278	−	0.141875i
$67$	1.79800	−	3.11423i	0.219661	−	0.380464i	−0.735043	−	0.678020i	$-0.762838\pi$
$67$	1.79800	−	3.11423i	0.219661	−	0.380464i	0.954704	+	0.297556i	$0.0961716\pi$
$68$	6.00206	+	10.3959i	0.727856	+	1.26068i
$69$	2.79426	+	3.50389i	0.336389	+	0.421819i
$70$	−12.6653	−	16.6187i	−1.51380	−	1.98632i
$71$	−5.70107	+	7.14891i	−0.676592	+	0.848420i	−0.995035	−	0.0995220i	$-0.968269\pi$
$71$	−5.70107	+	7.14891i	−0.676592	+	0.848420i	0.318443	+	0.947942i	$0.396840\pi$
$72$	1.82073	+	0.274430i	0.214575	+	0.0323419i
$73$	−10.9284	+	7.45084i	−1.27907	+	0.872055i	−0.996199	−	0.0871032i	$-0.972239\pi$
$73$	−10.9284	+	7.45084i	−1.27907	+	0.872055i	−0.282870	+	0.959158i	$0.591287\pi$
$74$	−10.8985	+	7.43047i	−1.26692	+	0.863774i
$75$	−7.75328	−	1.16862i	−0.895272	−	0.134941i
$76$	0.0826939	−	0.103695i	0.00948564	−	0.0118946i
$77$	7.35823	−	8.82180i	0.838548	−	1.00534i
$78$	−1.11048	−	1.39250i	−0.125738	−	0.157670i
$79$	−5.44503	−	9.43107i	−0.612614	−	1.06108i	−0.990798	−	0.135348i	$-0.956785\pi$
$79$	−5.44503	−	9.43107i	−0.612614	−	1.06108i	0.378184	−	0.925730i	$-0.376549\pi$
$80$	5.80452	−	10.0537i	0.648965	−	1.12404i
$81$	−2.98026	+	0.449202i	−0.331140	+	0.0499114i
$82$	−0.361217	+	0.335160i	−0.0398897	+	0.0370123i
$83$	13.0849	+	6.30138i	1.43626	+	0.691666i	0.980150	−	0.198258i	$-0.0635284\pi$
$83$	13.0849	+	6.30138i	1.43626	+	0.691666i	0.456109	+	0.889924i	$0.349243\pi$
$84$	−4.50146	+	2.92616i	−0.491149	+	0.319270i
$85$	17.0918	−	8.23098i	1.85387	−	0.892776i
$86$	5.95848	−	15.1819i	0.642519	−	1.63711i
$87$	0.0946894	−	1.26354i	0.0101518	−	0.135466i
$88$	−3.35547	−	1.03503i	−0.357695	−	0.110334i
$89$	−1.04224	−	13.9077i	−0.110477	−	1.47422i	−0.726868	−	0.686777i	$-0.759025\pi$
$89$	−1.04224	−	13.9077i	−0.110477	−	1.47422i	0.616391	−	0.787440i	$-0.288594\pi$
$90$	4.00108	−	17.5299i	0.421751	−	1.84781i
$91$	−2.60690	−	0.451759i	−0.273277	−	0.0473572i
$92$	−2.79812	−	12.2594i	−0.291724	−	1.27813i
$93$	6.72930	−	2.07571i	0.697796	−	0.215242i
$94$	5.46722	+	13.9302i	0.563900	+	1.43679i
$95$	−0.153648	−	0.142565i	−0.0157640	−	0.0146268i
$96$	−5.66694	−	3.86366i	−0.578380	−	0.394333i
$97$	−15.3829			−1.56190			−0.780950	−	0.624594i	$-0.785265\pi$
$97$	−15.3829			−1.56190			−0.780950	+	0.624594i	$0.785265\pi$
$98$	−3.88744	+	14.1354i	−0.392690	+	1.42789i
$99$	9.88559			0.993539
$100$	18.1772	+	12.3930i	1.81772	+	1.23930i
$101$	−2.65207	−	2.46076i	−0.263891	−	0.244855i	0.537118	−	0.843507i	$-0.319513\pi$
$101$	−2.65207	−	2.46076i	−0.263891	−	0.244855i	−0.801009	+	0.598652i	$0.795703\pi$
$102$	−3.27350	−	8.34075i	−0.324125	−	0.825857i
$103$	10.0146	−	3.08909i	0.986766	−	0.304377i	0.240956	−	0.970536i	$-0.422539\pi$
$103$	10.0146	−	3.08909i	0.986766	−	0.304377i	0.745810	+	0.666159i	$0.232063\pi$
$104$	0.179960	+	0.788456i	0.0176465	+	0.0773145i
$105$	4.07976	+	7.43948i	0.398144	+	0.726019i
$106$	1.04504	−	4.57862i	0.101503	−	0.444715i
$107$	−1.53423	−	20.4728i	−0.148319	−	1.97918i	−0.197138	−	0.980376i	$-0.563165\pi$
$107$	−1.53423	−	20.4728i	−0.148319	−	1.97918i	0.0488188	−	0.998808i	$-0.484454\pi$
$108$	−10.2322	−	3.15623i	−0.984598	−	0.303708i
$109$	−0.321894	+	4.29538i	−0.0308319	+	0.411423i	0.960339	+	0.278834i	$0.0899479\pi$
$109$	−0.321894	+	4.29538i	−0.0308319	+	0.411423i	−0.991171	+	0.132589i	$0.957671\pi$
$110$	−12.5277	+	31.9201i	−1.19447	+	3.04347i
$111$	4.82580	−	2.32398i	0.458045	−	0.220583i
$112$	−8.07890	+	1.03658i	−0.763385	+	0.0979475i
$113$	2.44498	+	1.17744i	0.230004	+	0.110764i	0.545337	−	0.838217i	$-0.316402\pi$
$113$	2.44498	+	1.17744i	0.230004	+	0.110764i	−0.315333	+	0.948981i	$0.602116\pi$
$114$	−0.0725710	+	0.0673360i	−0.00679689	+	0.00630660i
$115$	−19.6501	+	2.96178i	−1.83239	+	0.276188i
$116$	−1.77760	+	3.07889i	−0.165046	+	0.285868i
$117$	−1.13838	−	1.97173i	−0.105243	−	0.182287i
$118$	−2.76040	−	3.46143i	−0.254115	−	0.318650i
$119$	−11.8621	−	6.03731i	−1.08739	−	0.553439i
$120$	1.61705	−	2.02771i	0.147615	−	0.185104i
$121$	−7.76483	−	1.17036i	−0.705894	−	0.106396i
$122$	−24.9984	+	17.0436i	−2.26324	+	1.54305i
$123$	0.165325	−	0.112716i	0.0149068	−	0.0101633i
$124$	−19.5383	−	2.94492i	−1.75459	−	0.264462i
$125$	9.92135	−	12.4410i	0.887393	−	1.11276i
$126$	−11.4839	+	5.22246i	−1.02307	+	0.465254i
$127$	8.46157	+	10.6105i	0.750843	+	0.941527i	0.999635	−	0.0270302i	$-0.00860502\pi$
$127$	8.46157	+	10.6105i	0.750843	+	0.941527i	−0.248792	+	0.968557i	$0.580034\pi$
$128$	3.17463	+	5.49863i	0.280601	+	0.486015i
$129$	−3.31135	+	5.73543i	−0.291548	+	0.504977i
$130$	7.80928	−	1.17706i	0.684919	−	0.103235i
$131$	5.90596	−	5.47993i	0.516006	−	0.478783i	−0.378650	−	0.925540i	$-0.623612\pi$
$131$	5.90596	−	5.47993i	0.516006	−	0.478783i	0.894655	+	0.446757i	$0.147421\pi$
$132$	7.93843	+	3.82294i	0.690951	+	0.332745i
$133$	−0.0142117	+	0.146372i	−0.00123231	+	0.0126920i
$134$	6.78534	−	3.26765i	0.586164	−	0.282282i
$135$	−6.18235	+	15.7524i	−0.532092	+	1.35575i
$136$	−0.304041	+	4.05714i	−0.0260713	+	0.347897i
$137$	−8.98704	−	2.77213i	−0.767814	−	0.236839i	−0.113986	−	0.993482i	$-0.536362\pi$
$137$	−8.98704	−	2.77213i	−0.767814	−	0.236839i	−0.653828	+	0.756643i	$0.726838\pi$
$138$	0.701415	+	9.35973i	0.0597084	+	0.796753i
$139$	−0.521300	+	2.28396i	−0.0442161	+	0.193723i	−0.992212	−	0.124558i	$-0.960249\pi$
$139$	−0.521300	+	2.28396i	−0.0442161	+	0.193723i	0.947996	+	0.318282i	$0.103106\pi$
$140$	−1.25663	−	23.7733i	−0.106205	−	2.00921i
$141$	−1.35219	−	5.92433i	−0.113875	−	0.498919i
$142$	−18.2992	+	5.64456i	−1.53564	+	0.473681i
$143$	1.58629	+	4.04181i	0.132652	+	0.337993i
$144$	−5.13809	−	4.76745i	−0.428174	−	0.397287i
$145$	4.64213	+	3.16495i	0.385508	+	0.262835i
$146$	−27.7008			−2.29253
$147$	2.41642	−	5.44055i	0.199303	−	0.448729i
$148$	−15.0286			−1.23534
$149$	−16.0262	−	10.9265i	−1.31292	−	0.895134i	−0.314388	−	0.949295i	$-0.601799\pi$
$149$	−16.0262	−	10.9265i	−1.31292	−	0.895134i	−0.998532	+	0.0541611i	$0.982752\pi$
$150$	−12.0376	−	11.1693i	−0.982867	−	0.911967i
$151$	−0.441405	−	1.12468i	−0.0359210	−	0.0915252i	0.911788	−	0.410662i	$-0.134702\pi$
$151$	−0.441405	−	1.12468i	−0.0359210	−	0.0915252i	−0.947709	+	0.319137i	$0.896607\pi$
$152$	0.0429551	−	0.0132499i	0.00348411	−	0.00107471i
$153$	−2.54871	−	11.1666i	−0.206051	−	0.902767i
$154$	23.1404	−	6.58426i	1.86471	−	0.530575i
$155$	−6.94838	+	30.4428i	−0.558107	+	2.44523i
$156$	−0.151647	−	2.02360i	−0.0121415	−	0.162017i
$157$	0.966650	+	0.298172i	0.0771470	+	0.0237967i	0.333088	−	0.942896i	$-0.391909\pi$
$157$	0.966650	+	0.298172i	0.0771470	+	0.0237967i	−0.255941	+	0.966692i	$0.582385\pi$
$158$	1.70439	−	22.7434i	0.135594	−	1.80937i
$159$	−0.696722	+	1.77522i	−0.0552536	+	0.140784i
$160$	27.4006	−	13.1954i	2.16620	−	1.04319i
$161$	10.0097	+	9.70586i	0.788875	+	0.764929i
$162$	−5.68701	−	2.73872i	−0.446814	−	0.215174i
$163$	−10.2429	+	9.50407i	−0.802290	+	0.744416i	−0.970439	−	0.241345i	$-0.922411\pi$
$163$	−10.2429	+	9.50407i	−0.802290	+	0.744416i	0.168150	+	0.985761i	$0.446221\pi$
$164$	−0.555152	+	0.0836757i	−0.0433501	+	0.00653398i
$165$	6.96214	−	12.0588i	0.542002	−	0.938775i
$166$	15.2081	+	26.3411i	1.18037	+	2.04447i
$167$	0.00795730	+	0.00997814i	0.000615755	+	0.000772132i	0.782139	−	0.623104i	$-0.214129\pi$
$167$	0.00795730	+	0.00997814i	0.000615755	+	0.000772132i	−0.781524	+	0.623876i	$0.785557\pi$
$168$	−1.81924	−	0.0400115i	−0.140357	−	0.00308695i
$169$	0.623490	−	0.781831i	0.0479608	−	0.0601409i
$170$	39.2864	+	5.92148i	3.01313	+	0.454156i
$171$	−0.104561	+	0.0712883i	−0.00799596	+	0.00545155i
$172$	15.3532	−	10.4676i	1.17067	−	0.798150i
$173$	20.2196	+	3.04762i	1.53727	+	0.231706i	0.862399	−	0.506229i	$-0.168961\pi$
$173$	20.2196	+	3.04762i	1.53727	+	0.231706i	0.674871	+	0.737936i	$0.264199\pi$
$174$	1.65454	−	2.07473i	0.125430	−	0.157285i
$175$	−24.3875	−	0.536366i	−1.84352	−	0.0405455i
$176$	8.33419	+	10.4507i	0.628213	+	0.787755i
$177$	0.898899	+	1.55694i	0.0675654	+	0.117027i
$178$	14.6044	−	25.2956i	1.09465	−	1.89599i
$179$	13.9892	−	2.10853i	1.04560	−	0.157599i	0.396291	−	0.918125i	$-0.370297\pi$
$179$	13.9892	−	2.10853i	1.04560	−	0.157599i	0.649307	+	0.760526i	$0.275059\pi$
$180$	15.0175	−	13.9342i	1.11934	−	1.03860i
$181$	15.8350	+	7.62574i	1.17701	+	0.566817i	0.917038	−	0.398800i	$-0.130573\pi$
$181$	15.8350	+	7.62574i	1.17701	+	0.566817i	0.259970	+	0.965617i	$0.416287\pi$
$182$	−3.97802	−	3.85726i	−0.294870	−	0.285919i
$183$	11.0692	−	5.33062i	0.818255	−	0.394051i
$184$	1.55704	−	3.96728i	0.114787	−	0.292472i
$185$	−1.77485	+	23.6837i	−0.130490	+	1.74126i
$186$	14.0933	+	4.34720i	1.03337	+	0.318752i
$187$	1.63234	+	21.7821i	0.119369	+	1.59287i
$188$	−3.79399	+	16.6225i	−0.276705	+	1.21232i
$189$	11.4196	−	3.24929i	0.830657	−	0.236351i
$190$	−0.0976799	−	0.427964i	−0.00708645	−	0.0310478i
$191$	−2.05041	+	0.632468i	−0.148363	+	0.0457638i	−0.368047	−	0.929807i	$-0.619973\pi$
$191$	−2.05041	+	0.632468i	−0.148363	+	0.0457638i	0.219684	+	0.975571i	$0.429497\pi$
$192$	−3.33486	−	8.49709i	−0.240673	−	0.613225i
$193$	−3.04832	−	2.82843i	−0.219423	−	0.203595i	0.562800	−	0.826593i	$-0.309724\pi$
$193$	−3.04832	−	2.82843i	−0.219423	−	0.203595i	−0.782223	+	0.622998i	$0.785914\pi$
$194$	−26.6187	−	18.1483i	−1.91111	−	1.30297i
$195$	−3.20692			−0.229652
$196$	−12.7319	+	10.8117i	−0.909421	+	0.772263i
$197$	10.9559			0.780576			0.390288	−	0.920693i	$-0.372375\pi$
$197$	10.9559			0.780576			0.390288	+	0.920693i	$0.372375\pi$
$198$	17.1061	+	11.6627i	1.21567	+	0.828833i
$199$	−4.91444	−	4.55994i	−0.348376	−	0.323245i	0.486504	−	0.873679i	$-0.338272\pi$
$199$	−4.91444	−	4.55994i	−0.348376	−	0.323245i	−0.834879	+	0.550433i	$0.814463\pi$
$200$	2.72412	+	6.94094i	0.192624	+	0.490799i
$201$	−2.92230	+	0.901410i	−0.206123	+	0.0635805i
$202$	−1.68602	−	7.38695i	−0.118628	−	0.519744i
$203$	−0.208078	−	3.93648i	−0.0146042	−	0.276287i
$204$	2.27165	−	9.95276i	0.159047	−	0.696833i
$205$	0.0663031	+	0.884753i	0.00463081	+	0.0617939i
$206$	20.9737	+	6.46953i	1.46131	+	0.450753i
$207$	−0.896623	+	11.9646i	−0.0623196	+	0.831597i
$208$	1.12473	−	2.86576i	0.0779859	−	0.198705i
$209$	0.217440	−	0.104714i	0.0150407	−	0.00724320i
$210$	−1.71724	+	17.6865i	−0.118501	+	1.22048i
$211$	−8.05305	−	3.87814i	−0.554395	−	0.266982i	0.135641	−	0.990758i	$-0.456691\pi$
$211$	−8.05305	−	3.87814i	−0.554395	−	0.266982i	−0.690035	+	0.723776i	$0.742405\pi$
$212$	3.92242	−	3.63947i	0.269393	−	0.249960i
$213$	7.68935	−	1.15898i	0.526866	−	0.0794122i
$214$	21.4984	−	37.2363i	1.46960	−	2.54542i
$215$	−14.6829	−	25.4315i	−1.00137	−	1.73442i
$216$	−2.26278	−	2.83744i	−0.153963	−	0.193063i
$217$	19.9432	−	9.06946i	1.35383	−	0.615675i
$218$	−5.62456	+	7.05298i	−0.380944	+	0.477688i
$219$	11.1228	+	1.67649i	0.751607	+	0.113287i
$220$	−32.2802	+	22.0083i	−2.17633	+	1.48380i
$221$	4.15659	−	2.83391i	0.279602	−	0.190630i
$222$	11.0924	+	1.67190i	0.744470	+	0.112211i
$223$	8.62736	−	10.8184i	0.577731	−	0.724452i	−0.403993	−	0.914762i	$-0.632378\pi$
$223$	8.62736	−	10.8184i	0.577731	−	0.724452i	0.981724	+	0.190310i	$0.0609494\pi$
$224$	−19.0166	−	9.67864i	−1.27060	−	0.646681i
$225$	−13.0879	−	16.4117i	−0.872526	−	1.09411i
$226$	2.84169	+	4.92195i	0.189026	+	0.327403i
$227$	−8.03071	+	13.9096i	−0.533017	+	0.923212i	0.466240	+	0.884658i	$0.345608\pi$
$227$	−8.03071	+	13.9096i	−0.533017	+	0.923212i	−0.999257	+	0.0385536i	$0.987725\pi$
$228$	−0.111534	+	0.0168110i	−0.00738652	+	0.00111334i
$229$	7.12490	−	6.61094i	0.470827	−	0.436863i	−0.408732	−	0.912655i	$-0.634029\pi$
$229$	7.12490	−	6.61094i	0.470827	−	0.436863i	0.879558	+	0.475791i	$0.157838\pi$
$230$	−37.4969	−	18.0576i	−2.47247	−	1.19068i
$231$	−9.69012	+	1.24331i	−0.637563	+	0.0818037i
$232$	−1.08562	+	0.522809i	−0.0712748	+	0.0343241i
$233$	−2.69098	+	6.85652i	−0.176292	+	0.449185i	−0.991520	−	0.129955i	$-0.958517\pi$
$233$	−2.69098	+	6.85652i	−0.176292	+	0.449185i	0.815228	+	0.579141i	$0.196612\pi$
$234$	0.356332	−	4.75492i	0.0232942	−	0.310839i
$235$	25.7476	+	7.94208i	1.67959	+	0.518084i
$236$	−0.376959	−	5.03017i	−0.0245380	−	0.327436i
$237$	−2.06083	+	9.02908i	−0.133865	+	0.586502i
$238$	−13.4036	−	24.4415i	−0.868823	−	1.58431i
$239$	4.22191	+	18.4974i	0.273093	+	1.19650i	0.906341	+	0.422548i	$0.138864\pi$
$239$	4.22191	+	18.4974i	0.273093	+	1.19650i	−0.633248	+	0.773949i	$0.718279\pi$
$240$	−9.43411	+	2.91004i	−0.608969	+	0.187842i
$241$	3.53990	+	9.01952i	0.228025	+	0.580998i	0.998397	−	0.0565963i	$-0.0180248\pi$
$241$	3.53990	+	9.01952i	0.228025	+	0.580998i	−0.770372	+	0.637595i	$0.779930\pi$
$242$	−12.0555	−	11.1859i	−0.774960	−	0.719058i
$243$	13.2411	+	9.02763i	0.849417	+	0.579123i
$244$	−34.4717			−2.20682
$245$	15.5346	+	21.3412i	0.992472	+	1.36344i
$246$	0.419058			0.0267182
$247$	−0.0459252	−	0.0313113i	−0.00292215	−	0.00199229i
$248$	−4.90914	−	4.55501i	−0.311731	−	0.289244i
$249$	−4.51233	−	11.4972i	−0.285958	−	0.728608i
$250$	31.8454	−	9.82302i	2.01408	−	0.621262i
$251$	4.60919	+	20.1942i	0.290929	+	1.27464i	0.883235	+	0.468931i	$0.155361\pi$
$251$	4.60919	+	20.1942i	0.290929	+	1.27464i	−0.592305	+	0.805714i	$0.701782\pi$
$252$	−14.1625	−	2.45427i	−0.892154	−	0.154605i
$253$	5.09158	−	22.3077i	0.320105	−	1.40247i
$254$	2.12402	+	28.3431i	0.133273	+	1.77840i
$255$	−15.4164	−	4.75533i	−0.965413	−	0.297790i
$256$	0.610508	−	8.14666i	0.0381567	−	0.509166i
$257$	1.81543	−	4.62563i	0.113243	−	0.288539i	−0.863005	−	0.505196i	$-0.831420\pi$
$257$	1.81543	−	4.62563i	0.113243	−	0.288539i	0.976248	+	0.216657i	$0.0695154\pi$
$258$	−12.4965	+	6.01798i	−0.777996	+	0.374663i
$259$	13.9712	−	9.08192i	0.868125	−	0.564323i
$260$	8.10692	+	3.90409i	0.502770	+	0.242121i
$261$	2.48666	−	2.30729i	0.153921	−	0.142817i
$262$	16.6847	−	2.51482i	1.03079	−	0.155366i
$263$	−6.22204	+	10.7769i	−0.383668	+	0.664532i	−0.991583	−	0.129470i	$-0.958672\pi$
$263$	−6.22204	+	10.7769i	−0.383668	+	0.664532i	0.607916	+	0.794001i	$0.292006\pi$
$264$	1.49314	+	2.58620i	0.0918965	+	0.159169i
$265$	−5.27226	−	6.61120i	−0.323872	−	0.406123i
$266$	−0.197277	+	0.236516i	−0.0120958	+	0.0145017i
$267$	−7.39508	+	9.27313i	−0.452571	+	0.567507i
$268$	8.48478	+	1.27888i	0.518291	+	0.0781197i
$269$	−11.5345	+	7.86406i	−0.703268	+	0.479480i	−0.861393	−	0.507939i	$-0.830408\pi$
$269$	−11.5345	+	7.86406i	−0.703268	+	0.479480i	0.158125	+	0.987419i	$0.449455\pi$
$270$	−29.2822	+	19.9642i	−1.78206	+	1.21498i
$271$	−5.87593	−	0.885654i	−0.356937	−	0.0537996i	−0.0318740	−	0.999492i	$-0.510148\pi$
$271$	−5.87593	−	0.885654i	−0.356937	−	0.0537996i	−0.325063	+	0.945692i	$0.605386\pi$
$272$	9.65628	−	12.1086i	0.585498	−	0.734191i
$273$	1.36386	+	1.78957i	0.0825443	+	0.108310i
$274$	−12.2807	−	15.3995i	−0.741906	−	0.930321i
$275$	20.0160	+	34.6688i	1.20701	+	2.09060i
$276$	−5.34695	+	9.26119i	−0.321849	+	0.557458i
$277$	4.18617	−	0.630964i	0.251523	−	0.0379109i	−0.0220707	−	0.999756i	$-0.507026\pi$
$277$	4.18617	−	0.630964i	0.251523	−	0.0379109i	0.273593	+	0.961845i	$0.411788\pi$
$278$	−3.59661	+	3.33717i	−0.215710	+	0.200150i
$279$	16.9861	+	8.18006i	1.01693	+	0.489727i
$280$	4.18700	−	6.89726i	0.250221	−	0.412190i
$281$	−18.2641	+	8.79551i	−1.08954	+	0.524696i	−0.890356	−	0.455266i	$-0.849544\pi$
$281$	−18.2641	+	8.79551i	−1.08954	+	0.524696i	−0.199187	+	0.979962i	$0.563830\pi$
$282$	4.64951	−	11.8468i	0.276874	−	0.705464i
$283$	2.21951	−	29.6173i	0.131936	−	1.76056i	−0.402560	−	0.915393i	$-0.631880\pi$
$283$	2.21951	−	29.6173i	0.131936	−	1.76056i	0.534496	−	0.845171i	$-0.320501\pi$
$284$	−20.8492	−	6.43113i	−1.23717	−	0.381617i
$285$	0.0133208	+	0.177753i	0.000789053	+	0.0105292i
$286$	−2.02347	+	8.86542i	−0.119651	+	0.524223i
$287$	0.465525	−	0.413272i	0.0274791	−	0.0243947i
$288$	−4.08593	−	17.9016i	−0.240766	−	1.05486i
$289$	7.93916	−	2.44891i	0.467010	−	0.144053i
$290$	4.29885	+	10.9533i	0.252437	+	0.643200i
$291$	9.58991	+	8.89813i	0.562170	+	0.521618i
$292$	−26.0768	−	17.7789i	−1.52603	−	1.04043i
$293$	20.1850			1.17922			0.589611	−	0.807687i	$-0.299281\pi$
$293$	20.1850			1.17922			0.589611	+	0.807687i	$0.299281\pi$
$294$	10.6000	−	6.56353i	0.618204	−	0.382793i
$295$	−7.97163			−0.464126
$296$	−4.20852	−	2.86932i	−0.244615	−	0.166776i
$297$	−14.2833	−	13.2529i	−0.828800	−	0.769014i
$298$	−14.8411	−	37.8145i	−0.859722	−	2.19054i
$299$	−5.03571	+	1.55331i	−0.291222	+	0.0898302i
$300$	−4.16326	−	18.2404i	−0.240366	−	1.05311i
$301$	−7.94725	+	19.0092i	−0.458072	+	1.09567i
$302$	0.563056	−	2.46691i	0.0324002	−	0.141955i
$303$	0.229925	+	3.06814i	0.0132089	+	0.176260i
$304$	−0.163515	−	0.0504378i	−0.00937824	−	0.00289280i
$305$	−4.07105	+	54.3244i	−0.233108	+	3.11061i
$306$	8.76374	−	22.3296i	0.500989	−	1.27650i
$307$	1.40354	−	0.675907i	0.0801040	−	0.0385761i	−0.393403	−	0.919366i	$-0.628702\pi$
$307$	1.40354	−	0.675907i	0.0801040	−	0.0385761i	0.473507	+	0.880790i	$0.342988\pi$
$308$	26.0097	+	8.65368i	1.48204	+	0.493089i
$309$	−8.03008	−	3.86708i	−0.456815	−	0.219991i
$310$	−47.9390	+	44.4809i	−2.72275	+	2.52635i
$311$	−7.60127	+	1.14571i	−0.431028	+	0.0649671i	−0.360973	−	0.932576i	$-0.617556\pi$
$311$	−7.60127	+	1.14571i	−0.431028	+	0.0649671i	−0.0700548	+	0.997543i	$0.522317\pi$
$312$	0.343887	−	0.595630i	0.0194688	−	0.0337209i
$313$	−2.39985	−	4.15667i	−0.135648	−	0.234949i	0.790197	−	0.612853i	$-0.209978\pi$
$313$	−2.39985	−	4.15667i	−0.135648	−	0.234949i	−0.925845	+	0.377904i	$0.876645\pi$
$314$	1.32092	+	1.65638i	0.0745439	+	0.0934750i
$315$	−5.54029	+	22.0290i	−0.312160	+	1.24120i
$316$	16.2016	−	20.3162i	0.911413	−	1.14288i
$317$	−13.1395	−	1.98047i	−0.737991	−	0.111234i	−0.230719	−	0.973020i	$-0.574108\pi$
$317$	−13.1395	−	1.98047i	−0.737991	−	0.111234i	−0.507272	+	0.861786i	$0.669346\pi$
$318$	−3.29996	+	2.24987i	−0.185052	+	0.126167i
$319$	−5.34509	+	3.64422i	−0.299268	+	0.204037i
$320$	40.0228	+	6.03247i	2.23734	+	0.337225i
$321$	−10.8859	+	13.6505i	−0.607591	+	0.761896i
$322$	5.87015	+	28.6042i	0.327131	+	1.59405i
$323$	−0.174344	−	0.218620i	−0.00970074	−	0.0121643i
$324$	−3.59585	−	6.22819i	−0.199769	−	0.346011i
$325$	4.60991	−	7.98460i	0.255712	−	0.442906i
$326$	−28.9371	+	4.36156i	−1.60268	+	0.241564i
$327$	2.68530	−	2.49160i	0.148498	−	0.137786i
$328$	−0.171438	−	0.0825600i	−0.00946606	−	0.00455861i
$329$	−6.51812	−	17.7457i	−0.359356	−	0.978353i
$330$	26.2739	−	12.6528i	1.44633	−	0.696516i
$331$	2.92056	−	7.44147i	0.160529	−	0.409020i	−0.827866	−	0.560925i	$-0.810446\pi$
$331$	2.92056	−	7.44147i	0.160529	−	0.409020i	0.988395	+	0.151905i	$0.0485407\pi$
$332$	−2.58974	+	34.5577i	−0.142131	+	1.89660i
$333$	13.7025	+	4.22666i	0.750893	+	0.231620i
$334$	0.00199744	+	0.0266540i	0.000109295	+	0.00145844i
$335$	3.01743	−	13.2202i	0.164860	−	0.722299i
$336$	5.63609	+	4.02696i	0.307474	+	0.219689i
$337$	5.36359	+	23.4994i	0.292173	+	1.28010i	0.881494	+	0.472196i	$0.156538\pi$
$337$	5.36359	+	23.4994i	0.292173	+	1.28010i	−0.589320	+	0.807899i	$0.700604\pi$
$338$	2.00127	−	0.617310i	0.108855	−	0.0335773i
$339$	−0.843148	−	2.14831i	−0.0457935	−	0.116680i
$340$	33.1827	+	30.7891i	1.79959	+	1.66977i
$341$	−29.7068	−	20.2538i	−1.60871	−	1.09680i
$342$	−0.265036			−0.0143315
$343$	5.30246	−	17.7450i	0.286306	−	0.958138i
$344$	6.29796			0.339563
$345$	13.9634	+	9.52006i	0.751762	+	0.512543i
$346$	31.3927	+	29.1281i	1.68768	+	1.56594i
$347$	−5.58899	−	14.2405i	−0.300033	−	0.764471i	−0.998793	−	0.0491149i	$-0.984360\pi$
$347$	−5.58899	−	14.2405i	−0.300033	−	0.764471i	0.698761	−	0.715356i	$-0.253735\pi$
$348$	2.88914	−	0.891181i	0.154874	−	0.0477723i
$349$	−0.323591	−	1.41775i	−0.0173214	−	0.0758902i	0.965528	−	0.260297i	$-0.0838206\pi$
$349$	−0.323591	−	1.41775i	−0.0173214	−	0.0758902i	−0.982850	+	0.184407i	$0.940963\pi$
$350$	−41.5674	−	29.6997i	−2.22187	−	1.58752i
$351$	−0.998571	+	4.37503i	−0.0532998	+	0.233522i
$352$	2.61687	+	34.9198i	0.139480	+	1.86123i
$353$	5.88527	+	1.81536i	0.313241	+	0.0966221i	0.447390	−	0.894339i	$-0.352354\pi$
$353$	5.88527	+	1.81536i	0.313241	+	0.0966221i	−0.134149	+	0.990961i	$0.542830\pi$
$354$	−0.281370	+	3.75463i	−0.0149547	+	0.199556i
$355$	−12.5972	+	32.0970i	−0.668588	+	1.70353i
$356$	29.9834	−	14.4393i	1.58912	−	0.765279i
$357$	3.90273	+	10.6253i	0.206555	+	0.562348i
$358$	26.6945	+	12.8554i	1.41085	+	0.679428i
$359$	17.3898	−	16.1354i	0.917800	−	0.851594i	−0.0715069	−	0.997440i	$-0.522781\pi$
$359$	17.3898	−	16.1354i	0.917800	−	0.851594i	0.989307	+	0.145846i	$0.0465903\pi$
$360$	6.86581	−	1.03485i	0.361860	−	0.0545416i
$361$	9.49846	−	16.4518i	0.499919	−	0.865885i
$362$	18.4044	+	31.8773i	0.967312	+	1.67543i
$363$	4.16371	+	5.22112i	0.218538	+	0.274038i
$364$	−1.26914	−	6.18429i	−0.0665210	−	0.324145i
$365$	−31.0976	+	38.9951i	−1.62772	+	2.04110i
$366$	25.4430	+	3.83492i	1.32993	+	0.200454i
$367$	30.3887	−	20.7187i	1.58628	−	1.08151i	0.635295	−	0.772270i	$-0.280879\pi$
$367$	30.3887	−	20.7187i	1.58628	−	1.08151i	0.950985	−	0.309238i	$-0.100074\pi$
$368$	−13.4045	+	9.13905i	−0.698759	+	0.476406i
$369$	0.529701	+	0.0798396i	0.0275751	+	0.00415628i
$370$	−31.0125	+	38.8885i	−1.61227	+	2.02172i
$371$	−1.44706	+	5.75375i	−0.0751279	+	0.298720i
$372$	10.4769	+	13.1377i	0.543204	+	0.681156i
$373$	0.349815	+	0.605898i	0.0181128	+	0.0313722i	0.874940	−	0.484232i	$-0.160901\pi$
$373$	0.349815	+	0.605898i	0.0181128	+	0.0313722i	−0.856827	+	0.515604i	$0.827568\pi$
$374$	−22.8733	+	39.6177i	−1.18275	+	2.04858i
$375$	−13.3815	+	2.01693i	−0.691017	+	0.104154i
$376$	−4.23609	+	3.93052i	−0.218460	+	0.202701i
$377$	1.34238	+	0.646455i	0.0691360	+	0.0332941i
$378$	23.5940	+	7.84996i	1.21355	+	0.403758i
$379$	13.6839	−	6.58984i	0.702897	−	0.338497i	−0.0480636	−	0.998844i	$-0.515305\pi$
$379$	13.6839	−	6.58984i	0.702897	−	0.338497i	0.750961	+	0.660347i	$0.229591\pi$
$380$	0.182722	−	0.465567i	0.00937342	−	0.0238831i
$381$	0.862497	−	11.5092i	0.0441871	−	0.589636i
$382$	−4.29421	−	1.32459i	−0.219711	−	0.0677718i
$383$	−0.299106	−	3.99129i	−0.0152836	−	0.203946i	−0.999618	−	0.0276344i	$-0.991203\pi$
$383$	−0.299106	−	3.99129i	−0.0152836	−	0.203946i	0.984334	−	0.176311i	$-0.0564165\pi$
$384$	1.20153	−	5.26426i	0.0613154	−	0.268640i
$385$	16.7091	−	39.9670i	0.851577	−	2.03691i
$386$	−1.93793	−	8.49064i	−0.0986382	−	0.432162i
$387$	−16.9424	+	5.22605i	−0.861233	+	0.265655i
$388$	−13.4102	−	34.1687i	−0.680801	−	1.73465i
$389$	−25.8478	−	23.9832i	−1.31053	−	1.21600i	−0.960181	−	0.279380i	$-0.909871\pi$
$389$	−25.8478	−	23.9832i	−1.31053	−	1.21600i	−0.350353	−	0.936618i	$-0.613939\pi$
$390$	−5.54927	−	3.78343i	−0.280998	−	0.191581i
$391$	−26.5111			−1.34072
$392$	−5.62958	+	0.596816i	−0.284337	+	0.0301438i
$393$	−6.85167			−0.345621
$394$	18.9581	+	12.9254i	0.955098	+	0.651175i
$395$	−30.1032	−	27.9317i	−1.51465	−	1.40539i
$396$	8.61787	+	21.9580i	0.433064	+	1.10343i
$397$	10.4144	−	3.21241i	0.522683	−	0.161226i	−0.0221758	−	0.999754i	$-0.507059\pi$
$397$	10.4144	−	3.21241i	0.522683	−	0.161226i	0.544859	+	0.838528i	$0.316583\pi$
$398$	−3.12430	−	13.6884i	−0.156607	−	0.686140i
$399$	0.0935273	−	0.0830293i	0.00468222	−	0.00415666i
$400$	6.31601	−	27.6722i	0.315800	−	1.38361i
$401$	−1.30946	−	17.4735i	−0.0653911	−	0.872584i	−0.929392	−	0.369094i	$-0.879668\pi$
$401$	−1.30946	−	17.4735i	−0.0653911	−	0.872584i	0.864001	−	0.503490i	$-0.167951\pi$
$402$	−6.12021	−	1.88784i	−0.305249	−	0.0941567i
$403$	−0.618815	+	8.25751i	−0.0308254	+	0.411336i
$404$	3.15390	−	8.03600i	0.156912	−	0.399806i
$405$	−10.2398	+	4.93120i	−0.508817	+	0.245034i
$406$	4.28408	−	7.05719i	0.212615	−	0.350242i
$407$	−24.6385	−	11.8653i	−1.22128	−	0.588139i
$408$	2.53637	−	2.35340i	0.125569	−	0.116511i
$409$	8.79038	−	1.32494i	0.434657	−	0.0655139i	0.0719303	−	0.997410i	$-0.477084\pi$
$409$	8.79038	−	1.32494i	0.434657	−	0.0655139i	0.362726	+	0.931896i	$0.381846\pi$
$410$	−0.929074	+	1.60920i	−0.0458837	+	0.0794729i
$411$	3.99911	+	6.92667i	0.197262	+	0.341667i
$412$	15.5918	+	19.5515i	0.768155	+	0.963236i
$413$	3.39022	+	4.44845i	0.166822	+	0.218894i
$414$	−15.6670	+	19.6458i	−0.769991	+	0.965538i
$415$	54.1541	+	8.16241i	2.65832	+	0.400677i
$416$	6.66359	−	4.54316i	0.326709	−	0.222747i
$417$	1.64613	−	1.12231i	0.0806111	−	0.0549597i
$418$	0.499798	+	0.0753324i	0.0244459	+	0.00368463i
$419$	−3.31702	+	4.15941i	−0.162047	+	0.203201i	−0.856225	−	0.516602i	$-0.827197\pi$
$419$	−3.31702	+	4.15941i	−0.162047	+	0.203201i	0.694178	+	0.719803i	$0.255768\pi$
$420$	−12.9681	+	15.5475i	−0.632777	+	0.758638i
$421$	5.62453	+	7.05294i	0.274123	+	0.343739i	0.899768	−	0.436369i	$-0.143736\pi$
$421$	5.62453	+	7.05294i	0.274123	+	0.343739i	−0.625645	+	0.780108i	$0.715164\pi$
$422$	−9.35971	−	16.2115i	−0.455624	−	0.789163i
$423$	8.13417	−	14.0888i	0.395497	−	0.685021i
$424$	1.79328	−	0.270293i	0.0870892	−	0.0131266i
$425$	34.0008	−	31.5481i	1.64928	−	1.53031i
$426$	14.6730	+	7.06616i	0.710910	+	0.342356i
$427$	32.0463	−	20.8316i	1.55083	−	1.00811i
$428$	44.1370	−	21.2553i	2.13344	−	1.02741i
$429$	1.34904	−	3.43729i	0.0651322	−	0.165954i
$430$	4.59599	−	61.3293i	0.221638	−	2.95756i
$431$	23.8351	+	7.35216i	1.14810	+	0.354141i	0.809689	−	0.586859i	$-0.199636\pi$
$431$	23.8351	+	7.35216i	1.14810	+	0.354141i	0.338408	+	0.941000i	$0.390112\pi$
$432$	1.03241	+	13.7766i	0.0496719	+	0.662826i
$433$	−1.35285	+	5.92724i	−0.0650140	+	0.284845i	−0.996976	−	0.0777113i	$-0.975239\pi$
$433$	−1.35285	+	5.92724i	−0.0650140	+	0.284845i	0.931962	+	0.362556i	$0.118096\pi$
$434$	45.2097	+	7.83455i	2.17013	+	0.376071i
$435$	−1.06322	−	4.65828i	−0.0509776	−	0.223347i
$436$	−9.82155	+	3.02955i	−0.470367	+	0.145089i
$437$	0.107014	+	0.272667i	0.00511917	+	0.0130434i
$438$	17.2690	+	16.0233i	0.825146	+	0.765623i
$439$	−19.1730	−	13.0719i	−0.915076	−	0.623888i	0.0115251	−	0.999934i	$-0.496331\pi$
$439$	−19.1730	−	13.0719i	−0.915076	−	0.623888i	−0.926601	+	0.376045i	$0.877284\pi$
$440$	−13.2415			−0.631264
$441$	14.6492	−	6.27696i	0.697580	−	0.298903i
$442$	10.5359			0.501144
$443$	−16.4965	−	11.2471i	−0.783773	−	0.534367i	0.104039	−	0.994573i	$-0.466823\pi$
$443$	−16.4965	−	11.2471i	−0.783773	−	0.534367i	−0.887812	+	0.460206i	$0.847776\pi$
$444$	9.36900	+	8.69316i	0.444633	+	0.412559i
$445$	−19.2140	−	48.9565i	−0.910832	−	2.32076i
$446$	27.6920	−	8.54186i	1.31126	−	0.404469i
$447$	3.67060	+	16.0820i	0.173614	+	0.760651i
$448$	−13.6548	−	24.8997i	−0.645129	−	1.17640i
$449$	4.53645	−	19.8755i	0.214088	−	0.937982i	−0.747668	−	0.664073i	$-0.768826\pi$
$449$	4.53645	−	19.8755i	0.214088	−	0.937982i	0.961756	−	0.273909i	$-0.0883166\pi$
$450$	−3.28532	−	43.8396i	−0.154871	−	2.06662i
$451$	−0.976203	−	0.301119i	−0.0459676	−	0.0141791i
$452$	−0.483904	+	6.45725i	−0.0227609	+	0.303723i
$453$	−0.375386	+	0.956467i	−0.0176372	+	0.0449387i
$454$	−30.3065	+	14.5948i	−1.42235	+	0.684969i
$455$	−9.89579	+	1.26970i	−0.463922	+	0.0595244i
$456$	−0.0344430	−	0.0165869i	−0.00161294	−	0.000776752i
$457$	−26.5418	+	24.6272i	−1.24157	+	1.15201i	−0.259049	+	0.965864i	$0.583409\pi$
$457$	−26.5418	+	24.6272i	−1.24157	+	1.15201i	−0.982522	+	0.186146i	$0.940400\pi$
$458$	20.1283	−	3.03386i	0.940536	−	0.141763i
$459$	−11.2878	+	19.5511i	−0.526870	+	0.912565i
$460$	−23.7090	−	41.0651i	−1.10544	−	1.91467i
$461$	10.4250	+	13.0725i	0.485541	+	0.608849i	0.962900	−	0.269860i	$-0.0869773\pi$
$461$	10.4250	+	13.0725i	0.485541	+	0.608849i	−0.477359	+	0.878708i	$0.658406\pi$
$462$	−18.2346	−	9.28068i	−0.848352	−	0.431776i
$463$	3.95161	−	4.95516i	0.183647	−	0.230286i	−0.681483	−	0.731834i	$-0.738665\pi$
$463$	3.95161	−	4.95516i	0.183647	−	0.230286i	0.865130	+	0.501548i	$0.167236\pi$
$464$	4.53561	+	0.683634i	0.210561	+	0.0317369i
$465$	21.9411	−	14.9592i	1.01750	−	0.693717i
$466$	−12.7456	+	8.68980i	−0.590429	+	0.402547i
$467$	−3.22869	−	0.486647i	−0.149406	−	0.0225193i	0.0739133	−	0.997265i	$-0.476451\pi$
$467$	−3.22869	−	0.486647i	−0.149406	−	0.0225193i	−0.223319	+	0.974745i	$0.571689\pi$
$468$	3.38724	−	4.24746i	0.156575	−	0.196339i
$469$	−8.66063	+	3.93855i	−0.399911	+	0.181865i
$470$	35.1839	+	44.1193i	1.62291	+	2.03507i
$471$	−0.430146	−	0.745035i	−0.0198201	−	0.0343294i
$472$	0.854821	−	1.48059i	0.0393463	−	0.0681498i
$473$	33.4350	−	5.03952i	1.53734	−	0.231717i
$474$	−14.2183	+	13.1927i	−0.653069	+	0.605959i
$475$	−0.461719	−	0.222352i	−0.0211851	−	0.0102022i
$476$	3.06924	−	31.6113i	0.140678	−	1.44890i
$477$	−4.59989	+	2.21519i	−0.210614	+	0.101427i
$478$	−14.5171	+	36.9888i	−0.663994	+	1.69183i
$479$	0.297506	−	3.96994i	0.0135934	−	0.181391i	−0.986274	−	0.165116i	$-0.947200\pi$
$479$	0.297506	−	3.96994i	0.0135934	−	0.181391i	0.999868	−	0.0162752i	$-0.00518078\pi$
$480$	−24.7146	−	7.62345i	−1.12806	−	0.347962i
$481$	0.470668	+	6.28062i	0.0214606	+	0.286372i
$482$	−4.51550	+	19.7837i	−0.205675	+	0.901122i
$483$	−0.625892	−	11.8408i	−0.0284791	−	0.538775i
$484$	−4.16946	−	18.2676i	−0.189521	−	0.830345i
$485$	−55.4306	+	17.0981i	−2.51698	+	0.776384i
$486$	12.2619	+	31.2429i	0.556213	+	1.41721i
$487$	−14.0589	−	13.0447i	−0.637068	−	0.591113i	0.294068	−	0.955784i	$-0.404991\pi$
$487$	−14.0589	−	13.0447i	−0.637068	−	0.591113i	−0.931136	+	0.364672i	$0.881181\pi$
$488$	−9.65327	−	6.58149i	−0.436983	−	0.297930i
$489$	11.8831			0.537374
$490$	1.70353	+	55.2562i	0.0769576	+	2.49622i
$491$	−36.8111			−1.66126			−0.830631	−	0.556823i	$-0.812020\pi$
$491$	−36.8111			−1.66126			−0.830631	+	0.556823i	$0.812020\pi$
$492$	0.394490	+	0.268959i	0.0177850	+	0.0121256i
$493$	5.49453	+	5.09818i	0.247461	+	0.229611i
$494$	−0.0425291	−	0.108362i	−0.00191347	−	0.00487545i
$495$	35.6216	−	10.9878i	1.60107	−	0.493865i
$496$	5.67264	+	24.8535i	0.254709	+	1.11595i
$497$	23.2686	−	6.62075i	1.04374	−	0.296981i
$498$	5.75593	−	25.2184i	0.257930	−	1.13006i
$499$	−2.88774	−	38.5341i	−0.129273	−	1.72503i	−0.565123	−	0.825006i	$-0.691171\pi$
$499$	−2.88774	−	38.5341i	−0.129273	−	1.72503i	0.435851	−	0.900019i	$-0.356448\pi$
$500$	36.2831	+	11.1918i	1.62263	+	0.500515i
$501$	0.000811097	−	0.0108233i	3.62371e−5	−	0.000483551i
$502$	−15.8487	+	40.3819i	−0.707363	+	1.80233i
$503$	−14.3053	+	6.88909i	−0.637844	+	0.307169i	−0.724714	−	0.689050i	$-0.758028\pi$
$503$	−14.3053	+	6.88909i	−0.637844	+	0.307169i	0.0868697	+	0.996220i	$0.472314\pi$
$504$	−3.49741	−	3.39125i	−0.155787	−	0.151058i
$505$	−12.2916	−	5.91931i	−0.546968	−	0.263406i
$506$	35.1284	−	32.5944i	1.56165	−	1.44900i
$507$	−0.840936	+	0.126751i	−0.0373473	+	0.00562920i
$508$	−16.1916	+	28.0447i	−0.718387	+	1.24428i
$509$	−11.2460	−	19.4787i	−0.498471	−	0.863376i	0.501528	−	0.865141i	$-0.332771\pi$
$509$	−11.2460	−	19.4787i	−0.498471	−	0.863376i	−0.999998	+	0.00176515i	$0.999438\pi$
$510$	−21.0664	−	26.4165i	−0.932837	−	1.16974i
$511$	34.9860	+	0.769465i	1.54769	+	0.0340391i
$512$	18.5850	−	23.3049i	0.821349	−	1.02994i
$513$	0.246647	+	0.0371760i	0.0108897	+	0.00164136i
$514$	8.59860	−	5.86243i	0.379268	−	0.258581i
$515$	32.6529	−	22.2624i	1.43886	−	0.980997i
$516$	−15.6263	−	2.35529i	−0.687910	−	0.103686i
$517$	−19.3437	+	24.2563i	−0.850736	+	1.06679i
$518$	34.8903	+	0.767361i	1.53299	+	0.0337159i
$519$	−10.8423	−	13.5958i	−0.475924	−	0.596790i
$520$	1.52483	+	2.64109i	0.0668683	+	0.115819i
$521$	3.30181	−	5.71890i	0.144655	−	0.250549i	−0.784589	−	0.620016i	$-0.787126\pi$
$521$	3.30181	−	5.71890i	0.144655	−	0.250549i	0.929244	+	0.369466i	$0.120460\pi$
$522$	7.02500	−	1.05885i	0.307476	−	0.0463445i
$523$	5.36709	−	4.97993i	0.234686	−	0.217757i	−0.554059	−	0.832478i	$-0.686922\pi$
$523$	5.36709	−	4.97993i	0.234686	−	0.217757i	0.788745	+	0.614720i	$0.210731\pi$
$524$	17.3206	+	8.34118i	0.756656	+	0.364386i
$525$	14.8932	+	14.4411i	0.649992	+	0.630262i
$526$	−23.4809	+	11.3078i	−1.02382	+	0.493044i
$527$	−15.2193	+	38.7782i	−0.662964	+	1.68920i
$528$	0.849514	−	11.3360i	0.0369703	−	0.493335i
$529$	4.55915	+	1.40631i	0.198224	+	0.0611439i
$530$	−1.32344	−	17.6601i	−0.0574866	−	0.767106i
$531$	−1.07100	+	4.69234i	−0.0464773	+	0.203630i
$532$	−0.337511	+	0.0960339i	−0.0146330	+	0.00416360i
$533$	0.0523555	+	0.229384i	0.00226777	+	0.00993574i
$534$	−23.7366	+	7.32178i	−1.02718	+	0.316845i
$535$	−28.2839	−	72.0662i	−1.22282	−	3.11570i
$536$	2.13187	+	1.97808i	0.0920825	+	0.0854401i
$537$	−9.94067	−	6.77744i	−0.428972	−	0.292468i
$538$	−29.2371			−1.26050
$539$	−29.4091	+	7.67311i	−1.26674	+	0.330504i
$540$	−40.3789			−1.73763
$541$	−29.4316	−	20.0661i	−1.26536	−	0.862709i	−0.270379	−	0.962754i	$-0.587149\pi$
$541$	−29.4316	−	20.0661i	−1.26536	−	0.862709i	−0.994983	+	0.100045i	$0.968101\pi$
$542$	−9.12287	−	8.46478i	−0.391861	−	0.363594i
$543$	−5.46070	−	13.9136i	−0.234341	−	0.597091i
$544$	38.7702	−	11.9590i	1.66226	−	0.512738i
$545$	3.61439	+	15.8357i	0.154824	+	0.678327i
$546$	0.248740	+	4.70572i	0.0106451	+	0.201386i
$547$	6.75815	−	29.6094i	0.288957	−	1.26601i	−0.597001	−	0.802241i	$-0.703641\pi$
$547$	6.75815	−	29.6094i	0.288957	−	1.26601i	0.885958	−	0.463765i	$-0.153502\pi$
$548$	−1.67705	−	22.3787i	−0.0716402	−	0.955972i
$549$	31.4300	+	9.69489i	1.34140	+	0.413768i
$550$	−6.26535	+	83.6053i	−0.267155	+	3.56494i
$551$	0.0302558	−	0.0770905i	0.00128894	−	0.00328417i
$552$	−3.26552	+	1.57259i	−0.138990	+	0.0669339i
$553$	−2.78439	+	28.6775i	−0.118404	+	1.21949i
$554$	7.98816	+	3.84690i	0.339384	+	0.163439i
$555$	14.8061	−	13.7381i	0.628485	−	0.583149i
$556$	−5.52761	+	0.833153i	−0.234423	+	0.0353336i
$557$	−17.8032	+	30.8360i	−0.754344	+	1.30656i	0.191356	+	0.981521i	$0.438711\pi$
$557$	−17.8032	+	30.8360i	−0.754344	+	1.30656i	−0.945700	+	0.325041i	$0.894622\pi$
$558$	19.7422	+	34.1944i	0.835753	+	1.44757i
$559$	−4.85539	−	6.08847i	−0.205361	−	0.257515i
$560$	−27.9593	+	12.7149i	−1.18149	+	0.537302i
$561$	11.5821	−	14.5235i	0.488996	−	0.613181i
$562$	−41.9809	−	6.32760i	−1.77086	−	0.266914i
$563$	9.64898	−	6.57857i	0.406656	−	0.277253i	−0.342668	−	0.939456i	$-0.611331\pi$
$563$	9.64898	−	6.57857i	0.406656	−	0.277253i	0.749325	+	0.662203i	$0.230378\pi$
$564$	11.9804	−	8.16810i	0.504466	−	0.343939i
$565$	10.1189	+	1.52518i	0.425706	+	0.0641648i
$566$	38.7822	−	48.6314i	1.63014	−	2.04413i
$567$	7.10660	+	3.61697i	0.298449	+	0.151898i
$568$	−4.61064	−	5.78156i	−0.193458	−	0.242589i
$569$	17.9110	+	31.0228i	0.750870	+	1.30054i	0.947402	+	0.320047i	$0.103699\pi$
$569$	17.9110	+	31.0228i	0.750870	+	1.30054i	−0.196532	+	0.980497i	$0.562968\pi$
$570$	−0.186657	+	0.323300i	−0.00781822	+	0.0135416i
$571$	−17.2763	+	2.60399i	−0.722991	+	0.108973i	−0.500221	−	0.865898i	$-0.666748\pi$
$571$	−17.2763	+	2.60399i	−0.722991	+	0.108973i	−0.222770	+	0.974871i	$0.571510\pi$
$572$	−7.59484	+	7.04698i	−0.317556	+	0.294649i
$573$	1.64410	+	0.791756i	0.0686832	+	0.0330761i
$574$	1.29311	−	0.165915i	0.0539735	−	0.00692517i
$575$	−43.7753	+	21.0811i	−1.82556	+	0.879141i
$576$	8.92801	−	22.7482i	0.372000	−	0.947842i
$577$	−1.49494	+	19.9486i	−0.0622351	+	0.830470i	0.875522	+	0.483178i	$0.160518\pi$
$577$	−1.49494	+	19.9486i	−0.0622351	+	0.830470i	−0.937757	+	0.347292i	$0.887101\pi$
$578$	16.6271	+	5.12878i	0.691597	+	0.213329i
$579$	0.264279	+	3.52656i	0.0109831	+	0.146559i
$580$	−2.98320	+	13.0702i	−0.123870	+	0.542712i
$581$	−18.4760	−	33.6912i	−0.766515	−	1.39775i
$582$	6.09667	+	26.7113i	0.252715	+	1.10722i
$583$	9.30398	−	2.86990i	0.385331	−	0.118859i
$584$	−3.90799	−	9.95740i	−0.161714	−	0.412040i
$585$	−6.29360	−	5.83961i	−0.260208	−	0.241438i
$586$	34.9283	+	23.8137i	1.44287	+	0.983735i
$587$	−21.8460			−0.901682			−0.450841	−	0.892604i	$-0.648876\pi$
$587$	−21.8460			−0.901682			−0.450841	+	0.892604i	$0.648876\pi$
$588$	14.1912	+	0.624529i	0.585233	+	0.0257551i
$589$	0.460268			0.0189650
$590$	−13.7941	−	9.40469i	−0.567896	−	0.387185i
$591$	−6.83005	−	6.33736i	−0.280951	−	0.260684i
$592$	7.08380	+	18.0492i	0.291143	+	0.741819i
$593$	−2.13500	+	0.658559i	−0.0876738	+	0.0270438i	−0.338282	−	0.941045i	$-0.609846\pi$
$593$	−2.13500	+	0.658559i	−0.0876738	+	0.0270438i	0.250608	+	0.968089i	$0.419369\pi$
$594$	−9.08042	−	39.7839i	−0.372574	−	1.63235i
$595$	−49.4541	−	8.57009i	−2.02742	−	0.351339i
$596$	10.2990	−	45.1229i	0.421864	−	1.84831i
$597$	0.426065	+	5.68544i	0.0174377	+	0.232690i
$598$	−10.5464	−	3.25312i	−0.431273	−	0.133030i
$599$	1.13321	−	15.1216i	0.0463016	−	0.617852i	−0.924995	−	0.379980i	$-0.875931\pi$
$599$	1.13321	−	15.1216i	0.0463016	−	0.617852i	0.971296	−	0.237873i	$-0.0764500\pi$
$600$	2.31669	−	5.90282i	0.0945783	−	0.240982i
$601$	14.8006	−	7.12759i	0.603729	−	0.290740i	−0.106942	−	0.994265i	$-0.534106\pi$
$601$	14.8006	−	7.12759i	0.603729	−	0.290740i	0.710671	+	0.703525i	$0.248392\pi$
$602$	−36.1785	+	23.5177i	−1.47452	+	0.958511i
$603$	−7.37645	−	3.55231i	−0.300392	−	0.144661i
$604$	2.11335	−	1.96090i	0.0859911	−	0.0797881i
$605$	−29.2805	+	4.41333i	−1.19042	+	0.179427i
$606$	−3.22184	+	5.58038i	−0.130878	+	0.226688i
$607$	2.80968	+	4.86651i	0.114041	+	0.197526i	0.917396	−	0.397975i	$-0.130287\pi$
$607$	2.80968	+	4.86651i	0.114041	+	0.197526i	−0.803355	+	0.595501i	$0.796954\pi$
$608$	−0.279497	−	0.350478i	−0.0113351	−	0.0142138i
$609$	−2.14731	+	2.57441i	−0.0870133	+	0.104320i
$610$	−71.1348	+	89.2003i	−2.88017	+	3.61161i
$611$	7.06558	+	1.06496i	0.285843	+	0.0430839i
$612$	22.5815	−	15.3958i	0.912804	−	0.622339i
$613$	22.4551	−	15.3096i	0.906952	−	0.618350i	−0.0174171	−	0.999848i	$-0.505544\pi$
$613$	22.4551	−	15.3096i	0.906952	−	0.618350i	0.924369	+	0.381499i	$0.124592\pi$
$614$	3.22610	+	0.486256i	0.130195	+	0.0196237i
$615$	0.470445	−	0.589919i	0.0189702	−	0.0237878i
$616$	5.63142	+	7.38922i	0.226896	+	0.297720i
$617$	−6.07927	−	7.62317i	−0.244742	−	0.306897i	0.644254	−	0.764812i	$-0.277168\pi$
$617$	−6.07927	−	7.62317i	−0.244742	−	0.306897i	−0.888996	+	0.457915i	$0.848597\pi$
$618$	−9.33302	−	16.1653i	−0.375429	−	0.650262i
$619$	−3.87274	+	6.70778i	−0.155658	+	0.269608i	−0.933299	−	0.359101i	$-0.883083\pi$
$619$	−3.87274	+	6.70778i	−0.155658	+	0.269608i	0.777640	+	0.628710i	$0.216417\pi$
$620$	−73.6772	+	11.1051i	−2.95895	+	0.445990i
$621$	17.3356	−	16.0851i	0.695655	−	0.645473i
$622$	−14.5049	−	6.98521i	−0.581595	−	0.280081i
$623$	−19.1480	+	31.5426i	−0.767148	+	1.26373i
$624$	−2.35885	+	1.13596i	−0.0944295	+	0.0454748i
$625$	5.08045	−	12.9448i	0.203218	−	0.517791i
$626$	0.751194	−	10.0240i	0.0300238	−	0.400639i
$627$	−0.196126	−	0.0604968i	−0.00783251	−	0.00241601i
$628$	0.180385	+	2.40707i	0.00719813	+	0.0960524i
$629$	−7.05052	+	30.8903i	−0.281123	+	1.23168i
$630$	−35.5761	+	31.5829i	−1.41739	+	1.25829i
$631$	−4.53368	−	19.8634i	−0.180483	−	0.790748i	−0.981400	−	0.191973i	$-0.938512\pi$
$631$	−4.53368	−	19.8634i	−0.180483	−	0.790748i	0.800917	−	0.598775i	$-0.204346\pi$
$632$	8.41587	−	2.59595i	0.334766	−	0.103261i
$633$	2.77709	+	7.07591i	0.110379	+	0.281242i
$634$	−20.4002	−	18.9287i	−0.810197	−	0.751753i
$635$	42.2838	+	28.8286i	1.67798	+	1.14403i
$636$	−4.55051			−0.180439
$637$	4.91707	+	4.98221i	0.194821	+	0.197402i
$638$	−13.5485			−0.536391
$639$	17.2009	+	11.7273i	0.680455	+	0.463927i
$640$	17.5511	+	16.2851i	0.693770	+	0.643724i
$641$	−0.0182246	−	0.0464354i	−0.000719827	−	0.00183409i	0.930513	−	0.366258i	$-0.119361\pi$
$641$	−0.0182246	−	0.0464354i	−0.000719827	−	0.00183409i	−0.931233	+	0.364424i	$0.881266\pi$
$642$	−34.9414	+	10.7780i	−1.37903	+	0.425374i
$643$	−1.93995	−	8.49949i	−0.0765043	−	0.335187i	0.922163	−	0.386802i	$-0.126420\pi$
$643$	−1.93995	−	8.49949i	−0.0765043	−	0.335187i	−0.998667	+	0.0516148i	$0.983563\pi$
$644$	−12.8327	+	30.6948i	−0.505679	+	1.20955i
$645$	−5.55717	+	24.3475i	−0.218813	+	0.958684i
$646$	−0.0437637	−	0.583986i	−0.00172186	−	0.0229766i
$647$	21.0038	+	6.47881i	0.825744	+	0.254708i	0.678694	−	0.734421i	$-0.262546\pi$
$647$	21.0038	+	6.47881i	0.825744	+	0.254708i	0.147050	+	0.989129i	$0.453022\pi$
$648$	0.182152	−	2.43065i	0.00715559	−	0.0954848i
$649$	3.35338	−	8.54428i	0.131632	−	0.335392i
$650$	17.3970	−	8.37796i	0.682367	−	0.328610i
$651$	−17.6790	−	5.88198i	−0.692895	−	0.230533i
$652$	−30.0399	−	14.4665i	−1.17645	−	0.566551i
$653$	35.8720	−	33.2843i	1.40378	−	1.30252i	0.505682	−	0.862720i	$-0.331241\pi$
$653$	35.8720	−	33.2843i	1.40378	−	1.30252i	0.898097	−	0.439797i	$-0.144950\pi$
$654$	7.58617	−	1.14343i	0.296643	−	0.0447117i
$655$	15.1905	−	26.3107i	0.593543	−	1.02805i
$656$	0.362168	+	0.627294i	0.0141403	+	0.0244917i
$657$	18.7757	+	23.5440i	0.732511	+	0.918540i
$658$	9.65686	−	38.3971i	0.376464	−	1.49688i
$659$	−11.0098	+	13.8058i	−0.428880	+	0.537799i	−0.948575	−	0.316553i	$-0.897474\pi$
$659$	−11.0098	+	13.8058i	−0.428880	+	0.537799i	0.519695	+	0.854352i	$0.326046\pi$
$660$	32.8544	+	4.95201i	1.27886	+	0.192757i
$661$	26.2514	−	17.8979i	1.02106	−	0.696148i	0.0676152	−	0.997711i	$-0.478461\pi$
$661$	26.2514	−	17.8979i	1.02106	−	0.696148i	0.953446	+	0.301564i	$0.0975086\pi$
$662$	13.8330	−	9.43117i	0.537634	−	0.366553i
$663$	−4.23052	−	0.637649i	−0.164300	−	0.0247642i
$664$	−7.32313	+	9.18291i	−0.284192	+	0.356366i
$665$	0.111482	+	0.543230i	0.00432307	+	0.0210656i
$666$	18.7244	+	23.4796i	0.725556	+	0.909818i
$667$	−3.92583	−	6.79974i	−0.152009	−	0.263287i
$668$	−0.0152267	+	0.0263734i	−0.000589138	+	0.00102042i
$669$	−11.6362	+	1.75388i	−0.449882	+	0.0678088i
$670$	20.8182	−	19.3165i	0.804278	−	0.746261i
$671$	−56.5143	−	27.2159i	−2.18171	−	1.05066i
$672$	6.25662	+	17.0338i	0.241354	+	0.657092i
$673$	−25.8981	+	12.4719i	−0.998300	+	0.480756i	−0.860361	−	0.509685i	$-0.829762\pi$
$673$	−25.8981	+	12.4719i	−0.998300	+	0.480756i	−0.137939	+	0.990441i	$0.544048\pi$
$674$	−18.4427	+	46.9913i	−0.710387	+	1.81004i
$675$	−3.09191	+	41.2586i	−0.119008	+	1.58805i
$676$	2.28015	+	0.703332i	0.0876979	+	0.0270512i
$677$	−1.12600	−	15.0255i	−0.0432758	−	0.577475i	−0.976125	−	0.217209i	$-0.930305\pi$
$677$	−1.12600	−	15.0255i	−0.0432758	−	0.577475i	0.932849	−	0.360266i	$-0.117314\pi$
$678$	1.07552	−	4.71216i	0.0413051	−	0.180969i
$679$	33.1152	+	23.6606i	1.27084	+	0.908012i
$680$	3.41393	+	14.9574i	0.130918	+	0.573590i
$681$	13.0523	−	4.02611i	0.500167	−	0.154281i
$682$	−27.5100	−	70.0944i	−1.05341	−	2.68405i
$683$	29.8659	+	27.7115i	1.14279	+	1.06035i	0.997479	+	0.0709657i	$0.0226081\pi$
$683$	29.8659	+	27.7115i	1.14279	+	1.06035i	0.145309	+	0.989386i	$0.453582\pi$
$684$	−0.249498	−	0.170105i	−0.00953980	−	0.00650412i
$685$	−35.4650			−1.35505
$686$	30.1104	−	24.4503i	1.14962	−	0.933516i
$687$	−8.26580			−0.315360
$688$	−19.8084	−	13.5051i	−0.755188	−	0.514879i
$689$	−1.64382	−	1.52524i	−0.0626246	−	0.0581072i
$690$	12.9308	+	32.9471i	0.492267	+	1.25428i
$691$	8.79342	−	2.71241i	0.334517	−	0.103185i	−0.122946	−	0.992413i	$-0.539234\pi$
$691$	8.79342	−	2.71241i	0.334517	−	0.103185i	0.457464	+	0.889228i	$0.348758\pi$
$692$	10.8573	+	47.5688i	0.412732	+	1.80830i
$693$	−21.2809	−	15.2051i	−0.808395	−	0.577595i
$694$	7.12931	−	31.2356i	0.270625	−	1.18569i
$695$	0.660175	+	8.80943i	0.0250419	+	0.334161i
$696$	0.979207	+	0.302045i	0.0371168	+	0.0114490i
$697$	−0.0884541	+	1.18034i	−0.00335044	+	0.0447085i
$698$	1.11267	−	2.83504i	0.0421152	−	0.107308i
$699$	5.64369	−	2.71786i	0.213464	−	0.102799i
$700$	−20.0687	−	54.6373i	−0.758524	−	2.06509i
$701$	−9.52112	−	4.58513i	−0.359608	−	0.173178i	0.245352	−	0.969434i	$-0.421097\pi$
$701$	−9.52112	−	4.58513i	−0.359608	−	0.173178i	−0.604960	+	0.796256i	$0.706811\pi$
$702$	−6.88946	+	6.39248i	−0.260026	+	0.241269i
$703$	0.346167	−	0.0521763i	0.0130560	−	0.00196787i
$704$	−23.3020	+	40.3603i	−0.878228	+	1.52114i
$705$	−11.4573	−	19.8447i	−0.431508	−	0.747395i
$706$	8.04218	+	10.0846i	0.302671	+	0.379538i
$707$	1.92425	+	9.37652i	0.0723688	+	0.352640i
$708$	−2.67466	+	3.35392i	−0.100520	+	0.126048i
$709$	29.1701	+	4.39668i	1.09551	+	0.165121i	0.671839	−	0.740697i	$-0.265505\pi$
$709$	29.1701	+	4.39668i	1.09551	+	0.165121i	0.423666	+	0.905818i	$0.360743\pi$
$710$	−59.6653	+	40.6791i	−2.23920	+	1.52666i
$711$	−20.4858	+	13.9670i	−0.768278	+	0.523803i
$712$	11.1532	+	1.68107i	0.417984	+	0.0630009i
$713$	27.2077	−	34.1173i	1.01894	−	1.27770i
$714$	−5.78205	+	22.9903i	−0.216388	+	0.860391i
$715$	10.2085	+	12.8010i	0.381776	+	0.478732i
$716$	16.8787	+	29.2347i	0.630786	+	1.09255i
$717$	8.06768	−	13.9736i	0.301293	−	0.521855i
$718$	49.1275	−	7.40478i	1.83342	−	0.276344i
$719$	−1.60331	+	1.48766i	−0.0597934	+	0.0554802i	−0.709504	−	0.704702i	$-0.751081\pi$
$719$	−1.60331	+	1.48766i	−0.0597934	+	0.0554802i	0.649710	+	0.760182i	$0.274890\pi$
$720$	−23.8135	−	11.4680i	−0.887477	−	0.427387i
$721$	−26.3100	−	8.75359i	−0.979835	−	0.326001i
$722$	35.8455	−	17.2623i	1.33403	−	0.642436i
$723$	3.01045	−	7.67051i	0.111960	−	0.285269i
$724$	−3.13403	+	41.8207i	−0.116475	+	1.55425i
$725$	13.1266	+	4.04901i	0.487509	+	0.150376i
$726$	1.04517	+	13.9469i	0.0387900	+	0.517617i
$727$	7.72050	−	33.8257i	0.286338	−	1.25453i	−0.603172	−	0.797611i	$-0.706097\pi$
$727$	7.72050	−	33.8257i	0.286338	−	1.25453i	0.889510	−	0.456916i	$-0.151046\pi$
$728$	0.825329	−	1.97413i	0.0305887	−	0.0731660i
$729$	−1.02072	−	4.47208i	−0.0378045	−	0.165632i
$730$	−99.8167	+	30.7894i	−3.69438	+	1.13957i
$731$	−14.3128	−	36.4684i	−0.529378	−	1.34883i
$732$	21.4901	+	19.9399i	0.794297	+	0.736999i
$733$	−12.4058	−	8.45814i	−0.458219	−	0.312408i	0.312120	−	0.950043i	$-0.398961\pi$
$733$	−12.4058	−	8.45814i	−0.458219	−	0.312408i	−0.770339	+	0.637634i	$0.779913\pi$
$734$	77.0281			2.84316
$735$	2.66015	−	22.2903i	0.0981213	−	0.822189i
$736$	−42.5010			−1.56661
$737$	12.9006	+	8.79549i	0.475200	+	0.323986i
$738$	0.822405	+	0.763080i	0.0302731	+	0.0280894i
$739$	14.1409	+	36.0305i	0.520182	+	1.32540i	0.913813	+	0.406134i	$0.133123\pi$
$739$	14.1409	+	36.0305i	0.520182	+	1.32540i	−0.393631	+	0.919268i	$0.628781\pi$
$740$	−54.1538	+	16.7042i	−1.99073	+	0.614060i
$741$	0.0105186	+	0.0460849i	0.000386410	+	0.00169297i
$742$	−9.29211	+	8.24911i	−0.341124	+	0.302834i
$743$	−7.84831	+	34.3857i	−0.287927	+	1.26149i	0.599438	+	0.800421i	$0.295391\pi$
$743$	−7.84831	+	34.3857i	−0.287927	+	1.26149i	−0.887365	+	0.461068i	$0.847466\pi$
$744$	0.425605	+	5.67931i	0.0156034	+	0.208213i
$745$	−69.8935	−	21.5593i	−2.56070	−	0.789871i
$746$	−0.109498	+	1.46115i	−0.00400901	+	0.0534965i
$747$	12.0803	−	30.7801i	0.441995	−	1.12619i
$748$	−46.9597	+	22.6146i	−1.71701	+	0.826871i
$749$	−28.1867	+	46.4321i	−1.02992	+	1.69659i
$750$	−25.5349	−	12.2970i	−0.932403	−	0.449022i
$751$	4.68843	−	4.35022i	0.171083	−	0.158742i	−0.589984	−	0.807415i	$-0.700866\pi$
$751$	4.68843	−	4.35022i	0.171083	−	0.158742i	0.761067	+	0.648673i	$0.224676\pi$
$752$	21.7519	−	3.27857i	0.793210	−	0.119557i
$753$	8.80774	−	15.2554i	0.320972	−	0.555939i
$754$	1.56019	+	2.70232i	0.0568187	+	0.0984129i
$755$	−2.84063	−	3.56204i	−0.103381	−	0.129636i
$756$	17.1726	+	22.5328i	0.624560	+	0.819511i
$757$	3.50529	−	4.39549i	0.127402	−	0.159757i	−0.714039	−	0.700106i	$-0.753136\pi$
$757$	3.50529	−	4.39549i	0.127402	−	0.159757i	0.841441	+	0.540349i	$0.181708\pi$
$758$	31.4533	+	4.74082i	1.14243	+	0.172194i
$759$	−16.0779	+	10.9617i	−0.583589	+	0.397884i
$760$	0.140056	−	0.0954889i	0.00508038	−	0.00346375i
$761$	−47.7370	−	7.19520i	−1.73047	−	0.260826i	−0.793080	−	0.609118i	$-0.791524\pi$
$761$	−47.7370	−	7.19520i	−1.73047	−	0.260826i	−0.937386	+	0.348292i	$0.886762\pi$
$762$	15.0707	−	18.8981i	0.545954	−	0.684605i
$763$	7.29972	−	8.75165i	0.264268	−	0.316831i
$764$	−3.19231	−	4.00303i	−0.115494	−	0.144825i
$765$	−21.5956	−	37.4047i	−0.780792	−	1.35237i
$766$	4.19123	−	7.25943i	0.151435	−	0.262294i
$767$	−2.09036	+	0.315072i	−0.0754787	+	0.0113766i
$768$	−5.09297	+	4.72559i	−0.183777	+	0.170520i
$769$	−34.1787	−	16.4596i	−1.23251	−	0.593548i	−0.299744	−	0.954020i	$-0.596901\pi$
$769$	−34.1787	−	16.4596i	−1.23251	−	0.593548i	−0.932770	+	0.360472i	$0.882616\pi$
$770$	76.0655	−	49.4462i	2.74121	−	1.78192i
$771$	−3.80742	+	1.83356i	−0.137121	+	0.0660339i
$772$	3.62513	−	9.23667i	0.130471	−	0.332435i
$773$	−3.06980	+	40.9637i	−0.110413	+	1.47336i	0.616892	+	0.787048i	$0.288391\pi$
$773$	−3.06980	+	40.9637i	−0.110413	+	1.47336i	−0.727305	+	0.686314i	$0.759228\pi$
$774$	−35.4828	−	10.9450i	−1.27540	−	0.393410i
$775$	5.70537	+	76.1328i	0.204943	+	2.73477i
$776$	2.76831	−	12.1288i	0.0993766	−	0.435397i
$777$	−13.9632	−	2.41973i	−0.500926	−	0.0868072i
$778$	−16.4324	−	71.9951i	−0.589130	−	2.58115i
$779$	0.0124968	−	0.00385477i	0.000447746	−	0.000138111i
$780$	−2.79567	−	7.12324i	−0.100101	−	0.255053i
$781$	−29.1036	−	27.0042i	−1.04141	−	0.966286i
$782$	−45.8749	−	31.2770i	−1.64048	−	1.11846i
$783$	−6.68610			−0.238942
$784$	18.9860	+	10.1948i	0.678072	+	0.364099i
$785$	3.81463			0.136150
$786$	−11.8562	−	8.08339i	−0.422895	−	0.288325i
$787$	−8.17233	−	7.58281i	−0.291312	−	0.270298i	0.520955	−	0.853584i	$-0.325576\pi$
$787$	−8.17233	−	7.58281i	−0.291312	−	0.270298i	−0.812267	+	0.583286i	$0.801767\pi$
$788$	9.55093	+	24.3354i	0.340238	+	0.866912i
$789$	10.1127	−	3.11936i	0.360022	−	0.111052i
$790$	−19.1377	−	83.8479i	−0.680890	−	2.98317i
$791$	−3.45232	−	6.29534i	−0.122750	−	0.223837i
$792$	−1.77901	+	7.79435i	−0.0632144	+	0.276960i
$793$	1.07959	+	14.4061i	0.0383374	+	0.511577i
$794$	21.8110	+	6.72781i	0.774044	+	0.238761i
$795$	−0.537407	+	7.17120i	−0.0190599	+	0.254336i
$796$	5.84436	−	14.8912i	0.207148	−	0.527804i
$797$	11.2029	−	5.39502i	0.396826	−	0.191102i	−0.224819	−	0.974401i	$-0.572179\pi$
$797$	11.2029	−	5.39502i	0.396826	−	0.191102i	0.621645	+	0.783299i	$0.286465\pi$
$798$	0.259795	−	0.0333335i	0.00919666	−	0.00117999i
$799$	32.3867	+	15.5966i	1.14576	+	0.551769i
$800$	54.5079	−	50.5760i	1.92715	−	1.78813i
$801$	−31.3987	+	4.73260i	−1.10942	+	0.167218i
$802$	18.3488	−	31.7810i	0.647918	−	1.12223i
$803$	−28.7147	−	49.7354i	−1.01332	−	1.75512i
$804$	−4.54977	−	5.70522i	−0.160458	−	0.201208i
$805$	46.8569	+	23.8482i	1.65149	+	0.840539i
$806$	−10.8128	+	13.5588i	−0.380863	+	0.477588i
$807$	11.7396	+	1.76946i	0.413255	+	0.0622881i
$808$	2.41747	−	1.64820i	0.0850463	−	0.0579836i
$809$	2.32177	−	1.58296i	0.0816291	−	0.0556538i	−0.521818	−	0.853057i	$-0.674746\pi$
$809$	2.32177	−	1.58296i	0.0816291	−	0.0556538i	0.603447	+	0.797403i	$0.293794\pi$
$810$	−23.5366	−	3.54757i	−0.826992	−	0.124649i
$811$	−10.5990	+	13.2908i	−0.372183	+	0.466703i	−0.932287	−	0.361720i	$-0.882190\pi$
$811$	−10.5990	+	13.2908i	−0.372183	+	0.466703i	0.560104	+	0.828422i	$0.310761\pi$
$812$	8.56235	−	3.89385i	0.300480	−	0.136647i
$813$	3.15083	+	3.95101i	0.110504	+	0.138568i
$814$	−28.6362	−	49.5994i	−1.00370	−	1.73846i
$815$	−26.3456	+	45.6318i	−0.922845	+	1.59841i
$816$	−13.0240	+	1.96305i	−0.455930	+	0.0687204i
$817$	−0.317303	+	0.294415i	−0.0111010	+	0.0103003i
$818$	16.7740	+	8.07795i	0.586491	+	0.282439i
$819$	−0.582127	+	5.99555i	−0.0203412	+	0.209501i
$820$	−1.90742	+	0.918567i	−0.0666101	+	0.0320777i
$821$	17.3126	−	44.1117i	0.604213	−	1.53951i	−0.221348	−	0.975195i	$-0.571046\pi$
$821$	17.3126	−	44.1117i	0.604213	−	1.53951i	0.825560	−	0.564314i	$-0.190859\pi$
$822$	−1.25179	+	16.7040i	−0.0436612	+	0.582618i
$823$	8.32205	+	2.56701i	0.290088	+	0.0894804i	0.436384	−	0.899760i	$-0.356259\pi$
$823$	8.32205	+	2.56701i	0.290088	+	0.0894804i	−0.146296	+	0.989241i	$0.546735\pi$
$824$	0.633388	+	8.45197i	0.0220651	+	0.294438i
$825$	7.57564	−	33.1910i	0.263750	−	1.15556i
$826$	0.618307	+	11.6973i	0.0215136	+	0.407001i
$827$	1.53691	+	6.73365i	0.0534437	+	0.234152i	0.994595	−	0.103835i	$-0.0331113\pi$
$827$	1.53691	+	6.73365i	0.0534437	+	0.234152i	−0.941151	+	0.337987i	$0.890254\pi$
$828$	−27.3575	+	8.43868i	−0.950740	+	0.293264i
$829$	7.67326	+	19.5511i	0.266503	+	0.679039i	1.00000		0.000653823i	$-0.000208118\pi$
$829$	7.67326	+	19.5511i	0.266503	+	0.679039i	−0.733496	+	0.679693i	$0.762113\pi$
$830$	84.0787	+	78.0136i	2.91841	+	2.70789i
$831$	−2.97469	−	2.02811i	−0.103191	−	0.0703543i
$832$	10.7334			0.372115
$833$	16.2497	+	31.2418i	0.563019	+	1.08247i
$834$	4.17253			0.144483
$835$	0.0397639	+	0.0271106i	0.00137609	+	0.000938200i
$836$	0.422147	+	0.391695i	0.0146003	+	0.0135471i
$837$	−13.5760	−	34.5911i	−0.469256	−	1.19564i
$838$	−10.6469	+	3.28415i	−0.367792	+	0.113449i
$839$	2.46087	+	10.7818i	0.0849586	+	0.372228i	0.999478	−	0.0323146i	$-0.0102878\pi$
$839$	2.46087	+	10.7818i	0.0849586	+	0.372228i	−0.914519	+	0.404543i	$0.867431\pi$
$840$	−6.59990	+	1.87790i	−0.227718	+	0.0647938i
$841$	5.95914	−	26.1087i	0.205487	−	0.900300i
$842$	1.41187	+	18.8401i	0.0486562	+	0.649272i
$843$	16.4737	+	5.08147i	0.567386	+	0.175015i
$844$	1.59384	−	21.2683i	0.0548623	−	0.732086i
$845$	1.37767	−	3.51025i	0.0473933	−	0.120756i
$846$	30.6969	−	14.7829i	1.05538	−	0.508246i
$847$	14.9154	+	14.4626i	0.512499	+	0.496942i
$848$	−6.21984	−	2.99532i	−0.213590	−	0.102860i
$849$	−18.5156	+	17.1799i	−0.635452	+	0.589613i
$850$	96.0546	−	14.4779i	3.29464	−	0.496588i
$851$	16.5953	−	28.7439i	0.568880	−	0.985329i
$852$	9.27762	+	16.0693i	0.317846	+	0.550526i
$853$	20.8105	+	26.0955i	0.712537	+	0.893493i	0.997890	−	0.0649294i	$-0.0206822\pi$
$853$	20.8105	+	26.0955i	0.712537	+	0.893493i	−0.285353	+	0.958423i	$0.592111\pi$
$854$	80.0294	+	1.76013i	2.73855	+	0.0602304i
$855$	−0.297536	+	0.373098i	−0.0101755	+	0.0127597i
$856$	16.4180	+	2.47462i	0.561157	+	0.0845808i
$857$	34.8638	−	23.7698i	1.19093	−	0.811959i	0.204938	−	0.978775i	$-0.434301\pi$
$857$	34.8638	−	23.7698i	1.19093	−	0.811959i	0.985988	+	0.166816i	$0.0533485\pi$
$858$	6.38960	−	4.35635i	0.218137	−	0.148723i
$859$	−40.0466	−	6.03606i	−1.36637	−	0.205948i	−0.575437	−	0.817846i	$-0.695168\pi$
$859$	−40.0466	−	6.03606i	−1.36637	−	0.205948i	−0.790936	+	0.611898i	$0.790406\pi$
$860$	43.6888	−	54.7840i	1.48978	−	1.86812i
$861$	−0.529269	−	0.0116405i	−0.0180374	−	0.000396706i
$862$	32.5705	+	40.8422i	1.10936	+	1.39109i
$863$	−6.97556	−	12.0820i	−0.237451	−	0.411277i	0.722531	−	0.691338i	$-0.242979\pi$
$863$	−6.97556	−	12.0820i	−0.237451	−	0.411277i	−0.959982	+	0.280061i	$0.909645\pi$
$864$	−18.0959	+	31.3431i	−0.615636	+	1.06631i
$865$	76.2466	−	11.4923i	2.59246	−	0.390751i
$866$	−9.33376	+	8.66046i	−0.317174	+	0.294295i
$867$	−6.36593	−	3.06567i	−0.216198	−	0.104116i
$868$	37.5309	+	36.3916i	1.27388	+	1.23521i
$869$	42.6015	−	20.5158i	1.44516	−	0.695951i
$870$	3.65589	−	9.31506i	0.123946	−	0.315810i
$871$	0.268730	−	3.58595i	0.00910555	−	0.121505i
$872$	−3.32879	−	1.02680i	−0.112727	−	0.0347717i
$873$	2.61729	+	34.9253i	0.0885819	+	1.18204i
$874$	−0.136507	+	0.598076i	−0.00461742	+	0.0202302i
$875$	−40.4935	+	11.5218i	−1.36893	+	0.389509i
$876$	5.97256	+	26.1675i	0.201794	+	0.884118i
$877$	17.6766	−	5.45249i	0.596895	−	0.184118i	0.0184371	−	0.999830i	$-0.494131\pi$
$877$	17.6766	−	5.45249i	0.596895	−	0.184118i	0.578458	+	0.815712i	$0.303655\pi$
$878$	−17.7552	−	45.2394i	−0.599207	−	1.52676i
$879$	−12.5836	−	11.6759i	−0.424435	−	0.393818i
$880$	41.6473	+	28.3946i	1.40393	+	0.957183i
$881$	15.1227			0.509497			0.254749	−	0.967007i	$-0.418007\pi$
$881$	15.1227			0.509497			0.254749	+	0.967007i	$0.418007\pi$
$882$	32.7544	+	6.42098i	1.10290	+	0.216206i
$883$	−14.4291			−0.485578			−0.242789	−	0.970079i	$-0.578062\pi$
$883$	−14.4291			−0.485578			−0.242789	+	0.970079i	$0.578062\pi$
$884$	9.91827	+	6.76216i	0.333587	+	0.227436i
$885$	4.96961	+	4.61113i	0.167052	+	0.155001i
$886$	−15.2766	−	38.9242i	−0.513228	−	1.30768i
$887$	−34.7138	+	10.7078i	−1.16558	+	0.359532i	−0.816379	−	0.577517i	$-0.804022\pi$
$887$	−34.7138	+	10.7078i	−1.16558	+	0.359532i	−0.349197	+	0.937049i	$0.613546\pi$
$888$	0.963908	+	4.22316i	0.0323466	+	0.141720i
$889$	−1.89532	−	35.8562i	−0.0635671	−	1.20258i
$890$	24.5094	−	107.383i	0.821557	−	3.59948i
$891$	−0.977942	−	13.0497i	−0.0327623	−	0.437182i
$892$	31.5509	+	9.73216i	1.05640	+	0.325857i
$893$	0.0296802	−	0.396055i	0.000993210	−	0.0132535i
$894$	−12.6214	+	32.1588i	−0.422122	+	1.07555i
$895$	48.0647	−	23.1467i	1.60663	−	0.773710i
$896$	1.62339	−	16.7200i	0.0542338	−	0.558575i
$897$	4.03782	+	1.94451i	0.134819	+	0.0649254i
$898$	31.2984	−	29.0407i	1.04444	−	0.969099i
$899$	−12.1998	+	1.83882i	−0.406886	+	0.0613281i
$900$	25.0443	−	43.3780i	0.834810	−	1.44593i
$901$	−5.64055	−	9.76972i	−0.187914	−	0.325476i
$902$	−1.33397	−	1.67275i	−0.0444165	−	0.0556965i
$903$	15.9502	−	7.25356i	0.530788	−	0.241384i
$904$	−1.36836	+	1.71586i	−0.0455109	+	0.0570688i
$905$	65.5357	+	9.87792i	2.17848	+	0.328353i
$906$	−1.77798	+	1.21221i	−0.0590694	+	0.0402729i
$907$	−33.4972	+	22.8380i	−1.11226	+	0.758323i	−0.972740	−	0.231897i	$-0.925507\pi$
$907$	−33.4972	+	22.8380i	−1.11226	+	0.758323i	−0.139515	+	0.990220i	$0.544554\pi$
$908$	−37.8970	−	5.71205i	−1.25766	−	0.189561i
$909$	−5.13567	+	6.43993i	−0.170340	+	0.213599i
$910$	−18.6217	−	9.47766i	−0.617302	−	0.314181i
$911$	28.2886	+	35.4728i	0.937243	+	1.17527i	0.984323	+	0.176374i	$0.0564370\pi$
$911$	28.2886	+	35.4728i	0.937243	+	1.17527i	−0.0470801	+	0.998891i	$0.514992\pi$
$912$	0.0727621	+	0.126028i	0.00240939	+	0.00417319i
$913$	−31.5295	+	54.6107i	−1.04347	+	1.80735i
$914$	−74.9824	+	11.3018i	−2.48020	+	0.373829i
$915$	33.9615	−	31.5116i	1.12273	−	1.04174i
$916$	20.8955	+	10.0627i	0.690407	+	0.332482i
$917$	−21.1426	+	2.71274i	−0.698191	+	0.0895827i
$918$	−42.5982	+	20.5142i	−1.40595	+	0.677070i
$919$	−15.1272	+	38.5434i	−0.499000	+	1.27143i	0.430494	+	0.902593i	$0.358339\pi$
$919$	−15.1272	+	38.5434i	−0.499000	+	1.27143i	−0.929494	+	0.368838i	$0.879756\pi$
$920$	1.20100	−	16.0263i	0.0395959	−	0.528371i
$921$	−1.26596	−	0.390496i	−0.0417147	−	0.0128673i
$922$	2.61688	+	34.9199i	0.0861824	+	1.15002i
$923$	−2.03469	+	8.91455i	−0.0669726	+	0.293426i
$924$	−11.2091	−	20.4399i	−0.368753	−	0.672424i
$925$	12.9215	+	56.6127i	0.424856	+	1.86141i
$926$	12.6838	−	3.91244i	0.416816	−	0.128571i
$927$	−8.71736	−	22.2115i	−0.286316	−	0.729521i
$928$	8.80850	+	8.17309i	0.289153	+	0.268295i
$929$	−41.2822	−	28.1457i	−1.35442	−	0.923431i	−0.354492	−	0.935059i	$-0.615346\pi$
$929$	−41.2822	−	28.1457i	−1.35442	−	0.923431i	−0.999932	+	0.0116279i	$0.996299\pi$
$930$	55.6154			1.82370
$931$	0.255730	−	0.293238i	0.00838120	−	0.00961050i
$932$	−17.5757			−0.575710
$933$	5.40145	+	3.68265i	0.176836	+	0.120564i
$934$	−5.01281	−	4.65121i	−0.164024	−	0.152192i
$935$	30.0927	+	76.6751i	0.984138	+	2.50754i
$936$	1.75949	−	0.542730i	0.0575107	−	0.0177397i
$937$	0.772900	+	3.38630i	0.0252495	+	0.110625i	0.985982	−	0.166850i	$-0.0533595\pi$
$937$	0.772900	+	3.38630i	0.0252495	+	0.110625i	−0.960733	+	0.277475i	$0.910502\pi$
$938$	−19.6330	−	3.40227i	−0.641039	−	0.111088i
$939$	−0.908294	+	3.97950i	−0.0296411	+	0.129866i
$940$	4.80471	+	64.1144i	0.156712	+	2.09118i
$941$	3.05565	+	0.942544i	0.0996114	+	0.0307260i	0.344160	−	0.938911i	$-0.388164\pi$
$941$	3.05565	+	0.942544i	0.0996114	+	0.0307260i	−0.244549	+	0.969637i	$0.578640\pi$
$942$	0.134643	−	1.79669i	0.00438691	−	0.0585392i
$943$	0.452988	−	1.15419i	0.0147513	−	0.0375857i
$944$	−5.86353	+	2.82373i	−0.190842	+	0.0919044i
$945$	37.5378	−	24.4014i	1.22110	−	0.793776i
$946$	63.8016	+	30.7252i	2.07437	+	0.998963i
$947$	25.1086	−	23.2973i	0.815918	−	0.757062i	−0.157151	−	0.987575i	$-0.550231\pi$
$947$	25.1086	−	23.2973i	0.815918	−	0.757062i	0.973069	+	0.230513i	$0.0740404\pi$
$948$	−21.8520	+	3.29367i	−0.709721	+	0.106973i
$949$	−6.61333	+	11.4546i	−0.214678	+	0.371833i
$950$	−0.536636	−	0.929481i	−0.0174108	−	0.0301564i
$951$	7.04577	+	8.83512i	0.228475	+	0.286498i
$952$	6.89485	−	8.26625i	0.223463	−	0.267911i
$953$	36.9070	−	46.2799i	1.19553	−	1.49915i	0.375514	−	0.926817i	$-0.377466\pi$
$953$	36.9070	−	46.2799i	1.19553	−	1.49915i	0.820020	−	0.572335i	$-0.193962\pi$
$954$	−10.5731	−	1.59364i	−0.342316	−	0.0515959i
$955$	−6.68544	+	4.55806i	−0.216336	+	0.147495i
$956$	−37.4061	+	25.5030i	−1.20980	+	0.824827i
$957$	5.44017	+	0.819974i	0.175856	+	0.0265060i
$958$	5.19842	−	6.51861i	0.167953	−	0.210607i
$959$	15.0827	+	19.7907i	0.487047	+	0.639075i
$960$	−21.4613	−	26.9116i	−0.692660	−	0.868569i
$961$	−18.7847	−	32.5361i	−0.605959	−	1.04955i
$962$	−6.59525	+	11.4233i	−0.212639	+	0.368302i
$963$	−46.2204	+	6.96660i	−1.48943	+	0.224496i
$964$	−16.9483	+	15.7257i	−0.545868	+	0.506491i
$965$	−14.1281	−	6.80372i	−0.454799	−	0.219020i
$966$	12.8864	−	21.2278i	0.414612	−	0.682992i
$967$	7.51752	−	3.62025i	0.241747	−	0.116419i	−0.309088	−	0.951034i	$-0.600024\pi$
$967$	7.51752	−	3.62025i	0.241747	−	0.116419i	0.550835	+	0.834614i	$0.314309\pi$
$968$	2.32014	−	5.91161i	0.0745720	−	0.190006i
$969$	−0.0177710	+	0.237138i	−0.000570888	+	0.00761797i
$970$	−116.089	−	35.8088i	−3.72740	−	1.14975i
$971$	2.36814	+	31.6006i	0.0759971	+	1.01411i	0.896666	+	0.442707i	$0.145982\pi$
$971$	2.36814	+	31.6006i	0.0759971	+	1.01411i	−0.820669	+	0.571404i	$0.806399\pi$
$972$	−8.50920	+	37.2812i	−0.272933	+	1.19580i
$973$	4.63520	−	4.11492i	0.148598	−	0.131918i
$974$	−8.93776	−	39.1589i	−0.286384	−	1.25473i
$975$	−7.49251	+	2.31113i	−0.239952	+	0.0740155i
$976$	16.2484	+	41.4003i	0.520100	+	1.32519i
$977$	31.7485	+	29.4583i	1.01572	+	0.942454i	0.998352	−	0.0573953i	$-0.0182795\pi$
$977$	31.7485	+	29.4583i	1.01572	+	0.942454i	0.0173721	+	0.999849i	$0.494470\pi$
$978$	20.5626	+	14.0194i	0.657521	+	0.448290i
$979$	60.5560			1.93538
$980$	−33.8608	+	53.1101i	−1.08164	+	1.69654i
$981$	9.80697			0.313113
$982$	−63.6981	−	43.4286i	−2.03269	−	1.38586i
$983$	38.3034	+	35.5404i	1.22169	+	1.13356i	0.986869	+	0.161523i	$0.0516407\pi$
$983$	38.3034	+	35.5404i	1.22169	+	1.13356i	0.234821	+	0.972039i	$0.424550\pi$
$984$	0.0591202	+	0.150636i	0.00188468	+	0.00480209i
$985$	39.4784	−	12.1775i	1.25789	−	0.388006i
$986$	3.49308	+	15.3042i	0.111242	+	0.487385i
$987$	−6.20139	+	14.8333i	−0.197392	+	0.472148i
$988$	0.0295131	−	0.129305i	0.000938937	−	0.00411375i
$989$	3.06681	+	40.9237i	0.0975189	+	1.30130i
$990$	74.6028	+	23.0119i	2.37103	+	0.731367i
$991$	2.11103	−	28.1697i	0.0670590	−	0.894840i	−0.857667	−	0.514206i	$-0.828087\pi$
$991$	2.11103	−	28.1697i	0.0670590	−	0.894840i	0.924726	−	0.380634i	$-0.124294\pi$
$992$	−24.3987	+	62.1668i	−0.774659	+	1.97380i
$993$	−6.12518	+	2.94973i	−0.194377	+	0.0936069i
$994$	48.0751	+	15.9951i	1.52485	+	0.507333i
$995$	−22.7770	−	10.9688i	−0.722079	−	0.347735i
$996$	21.6041	−	20.0457i	0.684552	−	0.635172i
$997$	−33.1252	+	4.99281i	−1.04908	+	0.158124i	−0.650886	−	0.759175i	$-0.725602\pi$
$997$	−33.1252	+	4.99281i	−1.04908	+	0.158124i	−0.398198	+	0.917299i	$0.630364\pi$
$998$	40.4645	−	70.0865i	1.28088	−	2.21855i
$999$	−14.1318	−	24.4770i	−0.447110	−	0.774417i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.53.24	✓	324
49.37	even	21	inner	637.2.bl.a.625.24	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.53.24	✓	324	1.1	even	1	trivial
637.2.bl.a.625.24	yes	324	49.37	even	21	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73040 + 1.17977i) q^{2} +(-0.623413 - 0.578442i) q^{3} +(0.871761 + 2.22121i) q^{4} +(3.60339 - 1.11150i) q^{5} +(-0.396327 - 1.73642i) q^{6} +(-2.15272 - 1.53811i) q^{7} +(-0.179960 + 0.788456i) q^{8} +(-0.170143 - 2.27039i) q^{9} +O(q^{10})\)	\(q+(1.73040 + 1.17977i) q^{2} +(-0.623413 - 0.578442i) q^{3} +(0.871761 + 2.22121i) q^{4} +(3.60339 - 1.11150i) q^{5} +(-0.396327 - 1.73642i) q^{6} +(-2.15272 - 1.53811i) q^{7} +(-0.179960 + 0.788456i) q^{8} +(-0.170143 - 2.27039i) q^{9} +(7.54663 + 2.32783i) q^{10} +(-0.324474 + 4.32981i) q^{11} +(0.741375 - 1.88899i) q^{12} +(0.900969 - 0.433884i) q^{13} +(-1.91046 - 5.20127i) q^{14} +(-2.88933 - 1.39143i) q^{15} +(2.25675 - 2.09396i) q^{16} +(4.97454 - 0.749792i) q^{17} +(2.38413 - 4.12943i) q^{18} +(-0.0277917 - 0.0481367i) q^{19} +(5.61016 + 7.03492i) q^{20} +(0.452326 + 2.20410i) q^{21} +(-5.66965 + 7.10952i) q^{22} +(-5.21097 - 0.785427i) q^{23} +(0.568266 - 0.387437i) q^{24} +(7.61778 - 5.19371i) q^{25} +(2.07092 + 0.312141i) q^{26} +(-2.79794 + 3.50850i) q^{27} +(1.53981 - 6.12251i) q^{28} +(0.928954 + 1.16487i) q^{29} +(-3.35815 - 5.81649i) q^{30} +(-4.14033 + 7.17127i) q^{31} +(7.97488 - 1.20202i) q^{32} +(2.70683 - 2.51157i) q^{33} +(9.49256 + 4.57137i) q^{34} +(-9.46670 - 3.14966i) q^{35} +(4.89470 - 2.35716i) q^{36} +(-2.30100 + 5.86286i) q^{37} +(0.00869927 - 0.116084i) q^{38} +(-0.812652 - 0.250670i) q^{39} +(0.227902 + 3.04114i) q^{40} +(-0.0523555 + 0.229384i) q^{41} +(-1.81763 + 4.34763i) q^{42} +(-1.73287 - 7.59219i) q^{43} +(-9.90028 + 3.05383i) q^{44} +(-3.13663 - 7.99200i) q^{45} +(-8.09046 - 7.50685i) q^{46} +(5.90380 + 4.02514i) q^{47} -2.61812 q^{48} +(2.26843 + 6.62225i) q^{49} +19.3092 q^{50} +(-3.53490 - 2.41006i) q^{51} +(1.74918 + 1.62300i) q^{52} +(-0.819254 - 2.08742i) q^{53} +(-8.98078 + 2.77020i) q^{54} +(3.64337 + 15.9626i) q^{55} +(1.60014 - 1.42053i) q^{56} +(-0.0105186 + 0.0460849i) q^{57} +(0.233186 + 3.11165i) q^{58} +(-2.02006 - 0.623105i) q^{59} +(0.571850 - 7.63081i) q^{60} +(-5.27791 + 13.4479i) q^{61} +(-15.6249 + 7.52455i) q^{62} +(-3.12585 + 5.14923i) q^{63} +(9.67049 + 4.65706i) q^{64} +(2.76428 - 2.56488i) q^{65} +(7.64698 - 1.15260i) q^{66} +(1.79800 - 3.11423i) q^{67} +(6.00206 + 10.3959i) q^{68} +(2.79426 + 3.50389i) q^{69} +(-12.6653 - 16.6187i) q^{70} +(-5.70107 + 7.14891i) q^{71} +(1.82073 + 0.274430i) q^{72} +(-10.9284 + 7.45084i) q^{73} +(-10.8985 + 7.43047i) q^{74} +(-7.75328 - 1.16862i) q^{75} +(0.0826939 - 0.103695i) q^{76} +(7.35823 - 8.82180i) q^{77} +(-1.11048 - 1.39250i) q^{78} +(-5.44503 - 9.43107i) q^{79} +(5.80452 - 10.0537i) q^{80} +(-2.98026 + 0.449202i) q^{81} +(-0.361217 + 0.335160i) q^{82} +(13.0849 + 6.30138i) q^{83} +(-4.50146 + 2.92616i) q^{84} +(17.0918 - 8.23098i) q^{85} +(5.95848 - 15.1819i) q^{86} +(0.0946894 - 1.26354i) q^{87} +(-3.35547 - 1.03503i) q^{88} +(-1.04224 - 13.9077i) q^{89} +(4.00108 - 17.5299i) q^{90} +(-2.60690 - 0.451759i) q^{91} +(-2.79812 - 12.2594i) q^{92} +(6.72930 - 2.07571i) q^{93} +(5.46722 + 13.9302i) q^{94} +(-0.153648 - 0.142565i) q^{95} +(-5.66694 - 3.86366i) q^{96} -15.3829 q^{97} +(-3.88744 + 14.1354i) q^{98} +9.88559 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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