LMFDB - Embedded newform 637.2.bl.a.625.24

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			625.24
Character	$\chi$	$=$	637.625
Dual form			637.2.bl.a.53.24

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{16}{21}\right)$

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	0.233178	−	0.972434i	$-0.425088\pi$
$2$	1.73040	−	1.17977i	1.22358	−	0.834223i	0.990403	+	0.138211i	$0.0441352\pi$
$3$	−0.623413	+	0.578442i	−0.359927	+	0.333964i	−0.839321	−	0.543636i	$-0.817047\pi$
$3$	−0.623413	+	0.578442i	−0.359927	+	0.333964i	0.479394	+	0.877600i	$0.340857\pi$
$4$	0.871761	−	2.22121i	0.435880	−	1.11061i
$5$	3.60339	+	1.11150i	1.61148	+	0.497077i	0.964201	−	0.265173i	$-0.0854291\pi$
$5$	3.60339	+	1.11150i	1.61148	+	0.497077i	0.647283	+	0.762250i	$0.275905\pi$
$6$	−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	−0.802801	−	0.596248i	$-0.796658\pi$
$11$	−0.324474	−	4.32981i	−0.0978327	−	1.30549i	0.704968	−	0.709239i	$-0.250961\pi$
$12$	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	0.721346	−	0.692575i	$-0.243524\pi$
$17$	4.97454	+	0.749792i	1.20650	+	0.181851i	0.485158	+	0.874426i	$0.338762\pi$
$18$	2.38413	+	4.12943i	0.561944	+	0.973316i
$19$	−0.0277917	+	0.0481367i	−0.00637586	+	0.0110433i	−0.869196	−	0.494468i	$-0.835363\pi$
$19$	−0.0277917	+	0.0481367i	−0.00637586	+	0.0110433i	0.862820	+	0.505511i	$0.168696\pi$
$20$	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	−0.667813	−	0.744329i	$-0.732769\pi$
$23$	−5.21097	+	0.785427i	−1.08656	+	0.163773i	−0.418749	+	0.908102i	$0.637531\pi$
$24$	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	−0.688063	−	0.725651i	$-0.741539\pi$
$29$	0.928954	−	1.16487i	0.172502	−	0.216311i	0.860566	+	0.509340i	$0.170110\pi$
$30$	−3.35815	+	5.81649i	−0.613111	+	1.06194i
$31$	−4.14033	−	7.17127i	−0.743626	−	1.28800i	−0.950834	−	0.309701i	$-0.899771\pi$
$31$	−4.14033	−	7.17127i	−0.743626	−	1.28800i	0.207208	−	0.978297i	$-0.433562\pi$
$32$	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	−0.985555	−	0.169355i	$-0.945832\pi$
$37$	−2.30100	−	5.86286i	−0.378283	−	0.963849i	0.607272	−	0.794494i	$-0.292264\pi$
$38$	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	0.970675	−	0.240395i	$-0.0772771\pi$
$41$	−0.0523555	−	0.229384i	−0.00817655	−	0.0358238i	−0.978852	+	0.204571i	$0.934420\pi$
$42$	−1.81763	−	4.34763i	−0.280466	−	0.670854i
$43$	−1.73287	+	7.59219i	−0.264260	+	1.15780i	0.652319	+	0.757945i	$0.273796\pi$
$43$	−1.73287	+	7.59219i	−0.264260	+	1.15780i	−0.916579	+	0.399854i	$0.869061\pi$
$44$	−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	−0.0502019	−	0.998739i	$-0.515986\pi$
$47$	5.90380	−	4.02514i	0.861157	−	0.587127i	0.911359	+	0.411612i	$0.135034\pi$
$48$	−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	−0.976034	−	0.217617i	$-0.930172\pi$
$53$	−0.819254	+	2.08742i	−0.112533	+	0.286730i	0.863501	+	0.504347i	$0.168267\pi$
$54$	−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	−0.423446	−	0.905922i	$-0.639180\pi$
$59$	−2.02006	+	0.623105i	−0.262989	+	0.0811214i	0.160457	+	0.987043i	$0.448703\pi$
$60$	0.571850	+	7.63081i	0.0738256	+	0.985134i
$61$	−5.27791	−	13.4479i	−0.675767	−	1.72183i	−0.691937	−	0.721958i	$-0.743242\pi$
$61$	−5.27791	−	13.4479i	−0.675767	−	1.72183i	0.0161692	−	0.999869i	$-0.494853\pi$
$62$	−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	0.954704	−	0.297556i	$-0.0961716\pi$
$67$	1.79800	+	3.11423i	0.219661	+	0.380464i	−0.735043	+	0.678020i	$0.762838\pi$
$68$	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	0.318443	−	0.947942i	$-0.396840\pi$
$71$	−5.70107	−	7.14891i	−0.676592	−	0.848420i	−0.995035	+	0.0995220i	$0.968269\pi$
$72$	1.82073	−	0.274430i	0.214575	−	0.0323419i
$73$	−10.9284	−	7.45084i	−1.27907	−	0.872055i	−0.282870	−	0.959158i	$-0.591287\pi$
$73$	−10.9284	−	7.45084i	−1.27907	−	0.872055i	−0.996199	+	0.0871032i	$0.972239\pi$
$74$	−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	0.378184	+	0.925730i	$0.376549\pi$
$79$	−5.44503	+	9.43107i	−0.612614	+	1.06108i	−0.990798	+	0.135348i	$0.956785\pi$
$80$	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	0.456109	−	0.889924i	$-0.349243\pi$
$83$	13.0849	−	6.30138i	1.43626	−	0.691666i	0.980150	+	0.198258i	$0.0635284\pi$
$84$	−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	0.616391	+	0.787440i	$0.288594\pi$
$89$	−1.04224	+	13.9077i	−0.110477	+	1.47422i	−0.726868	+	0.686777i	$0.759025\pi$
$90$	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	−0.801009	−	0.598652i	$-0.795703\pi$
$101$	−2.65207	+	2.46076i	−0.263891	+	0.244855i	0.537118	+	0.843507i	$0.319513\pi$
$102$	−3.27350	+	8.34075i	−0.324125	+	0.825857i
$103$	10.0146	+	3.08909i	0.986766	+	0.304377i	0.745810	−	0.666159i	$-0.232063\pi$
$103$	10.0146	+	3.08909i	0.986766	+	0.304377i	0.240956	+	0.970536i	$0.422539\pi$
$104$	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	0.0488188	+	0.998808i	$0.484454\pi$
$107$	−1.53423	+	20.4728i	−0.148319	+	1.97918i	−0.197138	+	0.980376i	$0.563165\pi$
$108$	−10.2322	+	3.15623i	−0.984598	+	0.303708i
$109$	−0.321894	−	4.29538i	−0.0308319	−	0.411423i	−0.991171	−	0.132589i	$-0.957671\pi$
$109$	−0.321894	−	4.29538i	−0.0308319	−	0.411423i	0.960339	−	0.278834i	$-0.0899479\pi$
$110$	−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	−0.315333	−	0.948981i	$-0.602116\pi$
$113$	2.44498	−	1.17744i	0.230004	−	0.110764i	0.545337	+	0.838217i	$0.316402\pi$
$114$	−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	−0.248792	−	0.968557i	$-0.580034\pi$
$127$	8.46157	−	10.6105i	0.750843	−	0.941527i	0.999635	+	0.0270302i	$0.00860502\pi$
$128$	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	0.894655	−	0.446757i	$-0.147421\pi$
$131$	5.90596	+	5.47993i	0.516006	+	0.478783i	−0.378650	+	0.925540i	$0.623612\pi$
$132$	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	−0.653828	−	0.756643i	$-0.726838\pi$
$137$	−8.98704	+	2.77213i	−0.767814	+	0.236839i	−0.113986	+	0.993482i	$0.536362\pi$
$138$	0.701415	−	9.35973i	0.0597084	−	0.796753i
$139$	−0.521300	−	2.28396i	−0.0442161	−	0.193723i	0.947996	−	0.318282i	$-0.103106\pi$
$139$	−0.521300	−	2.28396i	−0.0442161	−	0.193723i	−0.992212	+	0.124558i	$0.960249\pi$
$140$	−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	−0.998532	−	0.0541611i	$-0.982752\pi$
$149$	−16.0262	+	10.9265i	−1.31292	+	0.895134i	−0.314388	+	0.949295i	$0.601799\pi$
$150$	−12.0376	+	11.1693i	−0.982867	+	0.911967i
$151$	−0.441405	+	1.12468i	−0.0359210	+	0.0915252i	−0.947709	−	0.319137i	$-0.896607\pi$
$151$	−0.441405	+	1.12468i	−0.0359210	+	0.0915252i	0.911788	+	0.410662i	$0.134702\pi$
$152$	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	−0.255941	−	0.966692i	$-0.582385\pi$
$157$	0.966650	−	0.298172i	0.0771470	−	0.0237967i	0.333088	+	0.942896i	$0.391909\pi$
$158$	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	0.168150	−	0.985761i	$-0.446221\pi$
$163$	−10.2429	−	9.50407i	−0.802290	−	0.744416i	−0.970439	+	0.241345i	$0.922411\pi$
$164$	−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	−0.781524	−	0.623876i	$-0.785557\pi$
$167$	0.00795730	−	0.00997814i	0.000615755	−	0.000772132i	0.782139	+	0.623104i	$0.214129\pi$
$168$	−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	0.674871	−	0.737936i	$-0.264199\pi$
$173$	20.2196	−	3.04762i	1.53727	−	0.231706i	0.862399	+	0.506229i	$0.168961\pi$
$174$	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	0.649307	−	0.760526i	$-0.275059\pi$
$179$	13.9892	+	2.10853i	1.04560	+	0.157599i	0.396291	+	0.918125i	$0.370297\pi$
$180$	15.0175	+	13.9342i	1.11934	+	1.03860i
$181$	15.8350	−	7.62574i	1.17701	−	0.566817i	0.259970	−	0.965617i	$-0.416287\pi$
$181$	15.8350	−	7.62574i	1.17701	−	0.566817i	0.917038	+	0.398800i	$0.130573\pi$
$182$	−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	0.219684	−	0.975571i	$-0.429497\pi$
$191$	−2.05041	−	0.632468i	−0.148363	−	0.0457638i	−0.368047	+	0.929807i	$0.619973\pi$
$192$	−3.33486	+	8.49709i	−0.240673	+	0.613225i
$193$	−3.04832	+	2.82843i	−0.219423	+	0.203595i	−0.782223	−	0.622998i	$-0.785914\pi$
$193$	−3.04832	+	2.82843i	−0.219423	+	0.203595i	0.562800	+	0.826593i	$0.309724\pi$
$194$	−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	−0.834879	−	0.550433i	$-0.814463\pi$
$199$	−4.91444	+	4.55994i	−0.348376	+	0.323245i	0.486504	+	0.873679i	$0.338272\pi$
$200$	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	−0.690035	−	0.723776i	$-0.742405\pi$
$211$	−8.05305	+	3.87814i	−0.554395	+	0.266982i	0.135641	+	0.990758i	$0.456691\pi$
$212$	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	0.981724	−	0.190310i	$-0.0609494\pi$
$223$	8.62736	+	10.8184i	0.577731	+	0.724452i	−0.403993	+	0.914762i	$0.632378\pi$
$224$	−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	−0.999257	−	0.0385536i	$-0.987725\pi$
$227$	−8.03071	−	13.9096i	−0.533017	−	0.923212i	0.466240	−	0.884658i	$-0.345608\pi$
$228$	−0.111534	−	0.0168110i	−0.00738652	−	0.00111334i
$229$	7.12490	+	6.61094i	0.470827	+	0.436863i	0.879558	−	0.475791i	$-0.157838\pi$
$229$	7.12490	+	6.61094i	0.470827	+	0.436863i	−0.408732	+	0.912655i	$0.634029\pi$
$230$	−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	0.815228	−	0.579141i	$-0.196612\pi$
$233$	−2.69098	−	6.85652i	−0.176292	−	0.449185i	−0.991520	+	0.129955i	$0.958517\pi$
$234$	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	−0.633248	−	0.773949i	$-0.718279\pi$
$239$	4.22191	−	18.4974i	0.273093	−	1.19650i	0.906341	−	0.422548i	$-0.138864\pi$
$240$	−9.43411	−	2.91004i	−0.608969	−	0.187842i
$241$	3.53990	−	9.01952i	0.228025	−	0.580998i	−0.770372	−	0.637595i	$-0.779930\pi$
$241$	3.53990	−	9.01952i	0.228025	−	0.580998i	0.998397	+	0.0565963i	$0.0180248\pi$
$242$	−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	−0.592305	−	0.805714i	$-0.701782\pi$
$251$	4.60919	−	20.1942i	0.290929	−	1.27464i	0.883235	−	0.468931i	$-0.155361\pi$
$252$	−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	0.976248	−	0.216657i	$-0.0695154\pi$
$257$	1.81543	+	4.62563i	0.113243	+	0.288539i	−0.863005	+	0.505196i	$0.831420\pi$
$258$	−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	0.607916	−	0.794001i	$-0.292006\pi$
$263$	−6.22204	−	10.7769i	−0.383668	−	0.664532i	−0.991583	+	0.129470i	$0.958672\pi$
$264$	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	0.158125	−	0.987419i	$-0.449455\pi$
$269$	−11.5345	−	7.86406i	−0.703268	−	0.479480i	−0.861393	+	0.507939i	$0.830408\pi$
$270$	−29.2822	−	19.9642i	−1.78206	−	1.21498i
$271$	−5.87593	+	0.885654i	−0.356937	+	0.0537996i	−0.325063	−	0.945692i	$-0.605386\pi$
$271$	−5.87593	+	0.885654i	−0.356937	+	0.0537996i	−0.0318740	+	0.999492i	$0.510148\pi$
$272$	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	0.273593	−	0.961845i	$-0.411788\pi$
$277$	4.18617	+	0.630964i	0.251523	+	0.0379109i	−0.0220707	+	0.999756i	$0.507026\pi$
$278$	−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	−0.199187	−	0.979962i	$-0.563830\pi$
$281$	−18.2641	−	8.79551i	−1.08954	−	0.524696i	−0.890356	+	0.455266i	$0.849544\pi$
$282$	4.64951	+	11.8468i	0.276874	+	0.705464i
$283$	2.21951	+	29.6173i	0.131936	+	1.76056i	0.534496	+	0.845171i	$0.320501\pi$
$283$	2.21951	+	29.6173i	0.131936	+	1.76056i	−0.402560	+	0.915393i	$0.631880\pi$
$284$	−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	0.473507	−	0.880790i	$-0.342988\pi$
$307$	1.40354	+	0.675907i	0.0801040	+	0.0385761i	−0.393403	+	0.919366i	$0.628702\pi$
$308$	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	−0.0700548	−	0.997543i	$-0.522317\pi$
$311$	−7.60127	−	1.14571i	−0.431028	−	0.0649671i	−0.360973	+	0.932576i	$0.617556\pi$
$312$	0.343887	+	0.595630i	0.0194688	+	0.0337209i
$313$	−2.39985	+	4.15667i	−0.135648	+	0.234949i	−0.925845	−	0.377904i	$-0.876645\pi$
$313$	−2.39985	+	4.15667i	−0.135648	+	0.234949i	0.790197	+	0.612853i	$0.209978\pi$
$314$	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	−0.507272	−	0.861786i	$-0.669346\pi$
$317$	−13.1395	+	1.98047i	−0.737991	+	0.111234i	−0.230719	+	0.973020i	$0.574108\pi$
$318$	−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	0.988395	−	0.151905i	$-0.0485407\pi$
$331$	2.92056	+	7.44147i	0.160529	+	0.409020i	−0.827866	+	0.560925i	$0.810446\pi$
$332$	−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	−0.589320	−	0.807899i	$-0.700604\pi$
$337$	5.36359	−	23.4994i	0.292173	−	1.28010i	0.881494	−	0.472196i	$-0.156538\pi$
$338$	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	0.698761	+	0.715356i	$0.253735\pi$
$347$	−5.58899	+	14.2405i	−0.300033	+	0.764471i	−0.998793	+	0.0491149i	$0.984360\pi$
$348$	2.88914	+	0.891181i	0.154874	+	0.0477723i
$349$	−0.323591	+	1.41775i	−0.0173214	+	0.0758902i	−0.982850	−	0.184407i	$-0.940963\pi$
$349$	−0.323591	+	1.41775i	−0.0173214	+	0.0758902i	0.965528	+	0.260297i	$0.0838206\pi$
$350$	−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	−0.134149	−	0.990961i	$-0.542830\pi$
$353$	5.88527	−	1.81536i	0.313241	−	0.0966221i	0.447390	+	0.894339i	$0.352354\pi$
$354$	−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	0.989307	−	0.145846i	$-0.0465903\pi$
$359$	17.3898	+	16.1354i	0.917800	+	0.851594i	−0.0715069	+	0.997440i	$0.522781\pi$
$360$	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	0.950985	+	0.309238i	$0.100074\pi$
$367$	30.3887	+	20.7187i	1.58628	+	1.08151i	0.635295	+	0.772270i	$0.280879\pi$
$368$	−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	−0.856827	−	0.515604i	$-0.827568\pi$
$373$	0.349815	−	0.605898i	0.0181128	−	0.0313722i	0.874940	+	0.484232i	$0.160901\pi$
$374$	−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	0.750961	−	0.660347i	$-0.229591\pi$
$379$	13.6839	+	6.58984i	0.702897	+	0.338497i	−0.0480636	+	0.998844i	$0.515305\pi$
$380$	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	0.984334	+	0.176311i	$0.0564165\pi$
$383$	−0.299106	+	3.99129i	−0.0152836	+	0.203946i	−0.999618	+	0.0276344i	$0.991203\pi$
$384$	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	−0.350353	+	0.936618i	$0.613939\pi$
$389$	−25.8478	+	23.9832i	−1.31053	+	1.21600i	−0.960181	+	0.279380i	$0.909871\pi$
$390$	−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	0.544859	−	0.838528i	$-0.316583\pi$
$397$	10.4144	+	3.21241i	0.522683	+	0.161226i	−0.0221758	+	0.999754i	$0.507059\pi$
$398$	−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	0.864001	+	0.503490i	$0.167951\pi$
$401$	−1.30946	+	17.4735i	−0.0653911	+	0.872584i	−0.929392	+	0.369094i	$0.879668\pi$
$402$	−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	0.362726	−	0.931896i	$-0.381846\pi$
$409$	8.79038	+	1.32494i	0.434657	+	0.0655139i	0.0719303	+	0.997410i	$0.477084\pi$
$410$	−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	0.694178	−	0.719803i	$-0.255768\pi$
$419$	−3.31702	−	4.15941i	−0.162047	−	0.203201i	−0.856225	+	0.516602i	$0.827197\pi$
$420$	−12.9681	−	15.5475i	−0.632777	−	0.758638i
$421$	5.62453	−	7.05294i	0.274123	−	0.343739i	−0.625645	−	0.780108i	$-0.715164\pi$
$421$	5.62453	−	7.05294i	0.274123	−	0.343739i	0.899768	+	0.436369i	$0.143736\pi$
$422$	−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	0.338408	−	0.941000i	$-0.390112\pi$
$431$	23.8351	−	7.35216i	1.14810	−	0.354141i	0.809689	+	0.586859i	$0.199636\pi$
$432$	1.03241	−	13.7766i	0.0496719	−	0.662826i
$433$	−1.35285	−	5.92724i	−0.0650140	−	0.284845i	0.931962	−	0.362556i	$-0.118096\pi$
$433$	−1.35285	−	5.92724i	−0.0650140	−	0.284845i	−0.996976	+	0.0777113i	$0.975239\pi$
$434$	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	−0.926601	−	0.376045i	$-0.877284\pi$
$439$	−19.1730	+	13.0719i	−0.915076	+	0.623888i	0.0115251	+	0.999934i	$0.496331\pi$
$440$	−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	−0.887812	−	0.460206i	$-0.847776\pi$
$443$	−16.4965	+	11.2471i	−0.783773	+	0.534367i	0.104039	+	0.994573i	$0.466823\pi$
$444$	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	0.961756	+	0.273909i	$0.0883166\pi$
$449$	4.53645	+	19.8755i	0.214088	+	0.937982i	−0.747668	+	0.664073i	$0.768826\pi$
$450$	−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	−0.982522	−	0.186146i	$-0.940400\pi$
$457$	−26.5418	−	24.6272i	−1.24157	−	1.15201i	−0.259049	−	0.965864i	$-0.583409\pi$
$458$	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	−0.477359	−	0.878708i	$-0.658406\pi$
$461$	10.4250	−	13.0725i	0.485541	−	0.608849i	0.962900	+	0.269860i	$0.0869773\pi$
$462$	−18.2346	+	9.28068i	−0.848352	+	0.431776i
$463$	3.95161	+	4.95516i	0.183647	+	0.230286i	0.865130	−	0.501548i	$-0.167236\pi$
$463$	3.95161	+	4.95516i	0.183647	+	0.230286i	−0.681483	+	0.731834i	$0.738665\pi$
$464$	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	−0.223319	−	0.974745i	$-0.571689\pi$
$467$	−3.22869	+	0.486647i	−0.149406	+	0.0225193i	0.0739133	+	0.997265i	$0.476451\pi$
$468$	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	0.999868	+	0.0162752i	$0.00518078\pi$
$479$	0.297506	+	3.96994i	0.0135934	+	0.181391i	−0.986274	+	0.165116i	$0.947200\pi$
$480$	−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	−0.931136	−	0.364672i	$-0.881181\pi$
$487$	−14.0589	+	13.0447i	−0.637068	+	0.591113i	0.294068	+	0.955784i	$0.404991\pi$
$488$	−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	0.435851	+	0.900019i	$0.356448\pi$
$499$	−2.88774	+	38.5341i	−0.129273	+	1.72503i	−0.565123	+	0.825006i	$0.691171\pi$
$500$	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	0.0868697	−	0.996220i	$-0.472314\pi$
$503$	−14.3053	−	6.88909i	−0.637844	−	0.307169i	−0.724714	+	0.689050i	$0.758028\pi$
$504$	−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	−0.999998	−	0.00176515i	$-0.999438\pi$
$509$	−11.2460	+	19.4787i	−0.498471	+	0.863376i	0.501528	+	0.865141i	$0.332771\pi$
$510$	−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	0.929244	−	0.369466i	$-0.120460\pi$
$521$	3.30181	+	5.71890i	0.144655	+	0.250549i	−0.784589	+	0.620016i	$0.787126\pi$
$522$	7.02500	+	1.05885i	0.307476	+	0.0463445i
$523$	5.36709	+	4.97993i	0.234686	+	0.217757i	0.788745	−	0.614720i	$-0.210731\pi$
$523$	5.36709	+	4.97993i	0.234686	+	0.217757i	−0.554059	+	0.832478i	$0.686922\pi$
$524$	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	−0.994983	−	0.100045i	$-0.968101\pi$
$541$	−29.4316	+	20.0661i	−1.26536	+	0.862709i	−0.270379	+	0.962754i	$0.587149\pi$
$542$	−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	0.885958	+	0.463765i	$0.153502\pi$
$547$	6.75815	+	29.6094i	0.288957	+	1.26601i	−0.597001	+	0.802241i	$0.703641\pi$
$548$	−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	−0.945700	−	0.325041i	$-0.894622\pi$
$557$	−17.8032	−	30.8360i	−0.754344	−	1.30656i	0.191356	−	0.981521i	$-0.438711\pi$
$558$	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	0.749325	−	0.662203i	$-0.230378\pi$
$563$	9.64898	+	6.57857i	0.406656	+	0.277253i	−0.342668	+	0.939456i	$0.611331\pi$
$564$	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	−0.196532	−	0.980497i	$-0.562968\pi$
$569$	17.9110	−	31.0228i	0.750870	−	1.30054i	0.947402	−	0.320047i	$-0.103699\pi$
$570$	−0.186657	−	0.323300i	−0.00781822	−	0.0135416i
$571$	−17.2763	−	2.60399i	−0.722991	−	0.108973i	−0.222770	−	0.974871i	$-0.571510\pi$
$571$	−17.2763	−	2.60399i	−0.722991	−	0.108973i	−0.500221	+	0.865898i	$0.666748\pi$
$572$	−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	−0.937757	−	0.347292i	$-0.887101\pi$
$577$	−1.49494	−	19.9486i	−0.0622351	−	0.830470i	0.875522	−	0.483178i	$-0.160518\pi$
$578$	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	0.250608	−	0.968089i	$-0.419369\pi$
$593$	−2.13500	−	0.658559i	−0.0876738	−	0.0270438i	−0.338282	+	0.941045i	$0.609846\pi$
$594$	−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	0.971296	+	0.237873i	$0.0764500\pi$
$599$	1.13321	+	15.1216i	0.0463016	+	0.617852i	−0.924995	+	0.379980i	$0.875931\pi$
$600$	2.31669	+	5.90282i	0.0945783	+	0.240982i
$601$	14.8006	+	7.12759i	0.603729	+	0.290740i	0.710671	−	0.703525i	$-0.248392\pi$
$601$	14.8006	+	7.12759i	0.603729	+	0.290740i	−0.106942	+	0.994265i	$0.534106\pi$
$602$	−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	−0.803355	−	0.595501i	$-0.796954\pi$
$607$	2.80968	−	4.86651i	0.114041	−	0.197526i	0.917396	+	0.397975i	$0.130287\pi$
$608$	−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	0.924369	−	0.381499i	$-0.124592\pi$
$613$	22.4551	+	15.3096i	0.906952	+	0.618350i	−0.0174171	+	0.999848i	$0.505544\pi$
$614$	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	−0.888996	−	0.457915i	$-0.848597\pi$
$617$	−6.07927	+	7.62317i	−0.244742	+	0.306897i	0.644254	+	0.764812i	$0.277168\pi$
$618$	−9.33302	+	16.1653i	−0.375429	+	0.650262i
$619$	−3.87274	−	6.70778i	−0.155658	−	0.269608i	0.777640	−	0.628710i	$-0.216417\pi$
$619$	−3.87274	−	6.70778i	−0.155658	−	0.269608i	−0.933299	+	0.359101i	$0.883083\pi$
$620$	−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	0.800917	+	0.598775i	$0.204346\pi$
$631$	−4.53368	+	19.8634i	−0.180483	+	0.790748i	−0.981400	+	0.191973i	$0.938512\pi$
$632$	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	−0.931233	−	0.364424i	$-0.881266\pi$
$641$	−0.0182246	+	0.0464354i	−0.000719827	+	0.00183409i	0.930513	+	0.366258i	$0.119361\pi$
$642$	−34.9414	−	10.7780i	−1.37903	−	0.425374i
$643$	−1.93995	+	8.49949i	−0.0765043	+	0.335187i	−0.998667	−	0.0516148i	$-0.983563\pi$
$643$	−1.93995	+	8.49949i	−0.0765043	+	0.335187i	0.922163	+	0.386802i	$0.126420\pi$
$644$	−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	0.147050	−	0.989129i	$-0.453022\pi$
$647$	21.0038	−	6.47881i	0.825744	−	0.254708i	0.678694	+	0.734421i	$0.262546\pi$
$648$	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	0.898097	+	0.439797i	$0.144950\pi$
$653$	35.8720	+	33.2843i	1.40378	+	1.30252i	0.505682	+	0.862720i	$0.331241\pi$
$654$	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	0.519695	−	0.854352i	$-0.326046\pi$
$659$	−11.0098	−	13.8058i	−0.428880	−	0.537799i	−0.948575	+	0.316553i	$0.897474\pi$
$660$	32.8544	−	4.95201i	1.27886	−	0.192757i
$661$	26.2514	+	17.8979i	1.02106	+	0.696148i	0.953446	−	0.301564i	$-0.0975086\pi$
$661$	26.2514	+	17.8979i	1.02106	+	0.696148i	0.0676152	+	0.997711i	$0.478461\pi$
$662$	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	−0.137939	−	0.990441i	$-0.544048\pi$
$673$	−25.8981	−	12.4719i	−0.998300	−	0.480756i	−0.860361	+	0.509685i	$0.829762\pi$
$674$	−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	0.932849	+	0.360266i	$0.117314\pi$
$677$	−1.12600	+	15.0255i	−0.0432758	+	0.577475i	−0.976125	+	0.217209i	$0.930305\pi$
$678$	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	0.145309	−	0.989386i	$-0.453582\pi$
$683$	29.8659	−	27.7115i	1.14279	−	1.06035i	0.997479	−	0.0709657i	$-0.0226081\pi$
$684$	−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	0.457464	−	0.889228i	$-0.348758\pi$
$691$	8.79342	+	2.71241i	0.334517	+	0.103185i	−0.122946	+	0.992413i	$0.539234\pi$
$692$	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	−0.604960	−	0.796256i	$-0.706811\pi$
$701$	−9.52112	+	4.58513i	−0.359608	+	0.173178i	0.245352	+	0.969434i	$0.421097\pi$
$702$	−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	0.423666	−	0.905818i	$-0.360743\pi$
$709$	29.1701	−	4.39668i	1.09551	−	0.165121i	0.671839	+	0.740697i	$0.265505\pi$
$710$	−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	0.649710	−	0.760182i	$-0.274890\pi$
$719$	−1.60331	−	1.48766i	−0.0597934	−	0.0554802i	−0.709504	+	0.704702i	$0.751081\pi$
$720$	−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	0.889510	+	0.456916i	$0.151046\pi$
$727$	7.72050	+	33.8257i	0.286338	+	1.25453i	−0.603172	+	0.797611i	$0.706097\pi$
$728$	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	−0.770339	−	0.637634i	$-0.779913\pi$
$733$	−12.4058	+	8.45814i	−0.458219	+	0.312408i	0.312120	+	0.950043i	$0.398961\pi$
$734$	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	−0.393631	−	0.919268i	$-0.628781\pi$
$739$	14.1409	−	36.0305i	0.520182	−	1.32540i	0.913813	−	0.406134i	$-0.133123\pi$
$740$	−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	−0.887365	−	0.461068i	$-0.847466\pi$
$743$	−7.84831	−	34.3857i	−0.287927	−	1.26149i	0.599438	−	0.800421i	$-0.295391\pi$
$744$	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	0.761067	−	0.648673i	$-0.224676\pi$
$751$	4.68843	+	4.35022i	0.171083	+	0.158742i	−0.589984	+	0.807415i	$0.700866\pi$
$752$	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	0.841441	−	0.540349i	$-0.181708\pi$
$757$	3.50529	+	4.39549i	0.127402	+	0.159757i	−0.714039	+	0.700106i	$0.753136\pi$
$758$	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	−0.937386	−	0.348292i	$-0.886762\pi$
$761$	−47.7370	+	7.19520i	−1.73047	+	0.260826i	−0.793080	+	0.609118i	$0.791524\pi$
$762$	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	−0.932770	−	0.360472i	$-0.882616\pi$
$769$	−34.1787	+	16.4596i	−1.23251	+	0.593548i	−0.299744	+	0.954020i	$0.596901\pi$
$770$	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	−0.727305	−	0.686314i	$-0.759228\pi$
$773$	−3.06980	−	40.9637i	−0.110413	−	1.47336i	0.616892	−	0.787048i	$-0.288391\pi$
$774$	−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	−0.812267	−	0.583286i	$-0.801767\pi$
$787$	−8.17233	+	7.58281i	−0.291312	+	0.270298i	0.520955	+	0.853584i	$0.325576\pi$
$788$	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	0.621645	−	0.783299i	$-0.286465\pi$
$797$	11.2029	+	5.39502i	0.396826	+	0.191102i	−0.224819	+	0.974401i	$0.572179\pi$
$798$	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	0.603447	−	0.797403i	$-0.293794\pi$
$809$	2.32177	+	1.58296i	0.0816291	+	0.0556538i	−0.521818	+	0.853057i	$0.674746\pi$
$810$	−23.5366	+	3.54757i	−0.826992	+	0.124649i
$811$	−10.5990	−	13.2908i	−0.372183	−	0.466703i	0.560104	−	0.828422i	$-0.310761\pi$
$811$	−10.5990	−	13.2908i	−0.372183	−	0.466703i	−0.932287	+	0.361720i	$0.882190\pi$
$812$	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	0.825560	+	0.564314i	$0.190859\pi$
$821$	17.3126	+	44.1117i	0.604213	+	1.53951i	−0.221348	+	0.975195i	$0.571046\pi$
$822$	−1.25179	−	16.7040i	−0.0436612	−	0.582618i
$823$	8.32205	−	2.56701i	0.290088	−	0.0894804i	−0.146296	−	0.989241i	$-0.546735\pi$
$823$	8.32205	−	2.56701i	0.290088	−	0.0894804i	0.436384	+	0.899760i	$0.356259\pi$
$824$	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	−0.941151	−	0.337987i	$-0.890254\pi$
$827$	1.53691	−	6.73365i	0.0534437	−	0.234152i	0.994595	+	0.103835i	$0.0331113\pi$
$828$	−27.3575	−	8.43868i	−0.950740	−	0.293264i
$829$	7.67326	−	19.5511i	0.266503	−	0.679039i	−0.733496	−	0.679693i	$-0.762113\pi$
$829$	7.67326	−	19.5511i	0.266503	−	0.679039i	1.00000		0.000653823i	$0.000208118\pi$
$830$	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	−0.914519	−	0.404543i	$-0.867431\pi$
$839$	2.46087	−	10.7818i	0.0849586	−	0.372228i	0.999478	+	0.0323146i	$0.0102878\pi$
$840$	−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	−0.285353	−	0.958423i	$-0.592111\pi$
$853$	20.8105	−	26.0955i	0.712537	−	0.893493i	0.997890	+	0.0649294i	$0.0206822\pi$
$854$	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	0.985988	−	0.166816i	$-0.0533485\pi$
$857$	34.8638	+	23.7698i	1.19093	+	0.811959i	0.204938	+	0.978775i	$0.434301\pi$
$858$	6.38960	+	4.35635i	0.218137	+	0.148723i
$859$	−40.0466	+	6.03606i	−1.36637	+	0.205948i	−0.790936	−	0.611898i	$-0.790406\pi$
$859$	−40.0466	+	6.03606i	−1.36637	+	0.205948i	−0.575437	+	0.817846i	$0.695168\pi$
$860$	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	−0.959982	−	0.280061i	$-0.909645\pi$
$863$	−6.97556	+	12.0820i	−0.237451	+	0.411277i	0.722531	+	0.691338i	$0.242979\pi$
$864$	−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	0.578458	−	0.815712i	$-0.303655\pi$
$877$	17.6766	+	5.45249i	0.596895	+	0.184118i	0.0184371	+	0.999830i	$0.494131\pi$
$878$	−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	−0.349197	−	0.937049i	$-0.613546\pi$
$887$	−34.7138	−	10.7078i	−1.16558	−	0.359532i	−0.816379	+	0.577517i	$0.804022\pi$
$888$	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	−0.139515	−	0.990220i	$-0.544554\pi$
$907$	−33.4972	−	22.8380i	−1.11226	−	0.758323i	−0.972740	+	0.231897i	$0.925507\pi$
$908$	−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	−0.0470801	−	0.998891i	$-0.514992\pi$
$911$	28.2886	−	35.4728i	0.937243	−	1.17527i	0.984323	−	0.176374i	$-0.0564370\pi$
$912$	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	−0.929494	−	0.368838i	$-0.879756\pi$
$919$	−15.1272	−	38.5434i	−0.499000	−	1.27143i	0.430494	−	0.902593i	$-0.358339\pi$
$920$	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	−0.999932	−	0.0116279i	$-0.996299\pi$
$929$	−41.2822	+	28.1457i	−1.35442	+	0.923431i	−0.354492	+	0.935059i	$0.615346\pi$
$930$	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	−0.960733	−	0.277475i	$-0.910502\pi$
$937$	0.772900	−	3.38630i	0.0252495	−	0.110625i	0.985982	+	0.166850i	$0.0533595\pi$
$938$	−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	−0.244549	−	0.969637i	$-0.578640\pi$
$941$	3.05565	−	0.942544i	0.0996114	−	0.0307260i	0.344160	+	0.938911i	$0.388164\pi$
$942$	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	0.973069	−	0.230513i	$-0.0740404\pi$
$947$	25.1086	+	23.2973i	0.815918	+	0.757062i	−0.157151	+	0.987575i	$0.550231\pi$
$948$	−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	0.820020	+	0.572335i	$0.193962\pi$
$953$	36.9070	+	46.2799i	1.19553	+	1.49915i	0.375514	+	0.926817i	$0.377466\pi$
$954$	−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	0.550835	−	0.834614i	$-0.314309\pi$
$967$	7.51752	+	3.62025i	0.241747	+	0.116419i	−0.309088	+	0.951034i	$0.600024\pi$
$968$	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	−0.820669	−	0.571404i	$-0.806399\pi$
$971$	2.36814	−	31.6006i	0.0759971	−	1.01411i	0.896666	−	0.442707i	$-0.145982\pi$
$972$	−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	0.0173721	−	0.999849i	$-0.494470\pi$
$977$	31.7485	−	29.4583i	1.01572	−	0.942454i	0.998352	+	0.0573953i	$0.0182795\pi$
$978$	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	0.234821	−	0.972039i	$-0.424550\pi$
$983$	38.3034	−	35.5404i	1.22169	−	1.13356i	0.986869	−	0.161523i	$-0.0516407\pi$
$984$	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	0.924726	+	0.380634i	$0.124294\pi$
$991$	2.11103	+	28.1697i	0.0670590	+	0.894840i	−0.857667	+	0.514206i	$0.828087\pi$
$992$	−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	−0.398198	−	0.917299i	$-0.630364\pi$
$997$	−33.1252	−	4.99281i	−1.04908	−	0.158124i	−0.650886	+	0.759175i	$0.725602\pi$
$998$	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.625.24	yes	324
49.4	even	21	inner	637.2.bl.a.53.24	✓	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.53.24	✓	324	49.4	even	21	inner
637.2.bl.a.625.24	yes	324	1.1	even	1	trivial

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

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Database

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