LMFDB - Embedded newform 950.2.r.a.11.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(11,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([24, 20]))

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

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

chi := DirichletCharacter("950.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.r (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$25$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			11.8
Character	$\chi$	$=$	950.11
Dual form			950.2.r.a.691.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104528 + 0.994522i) q^{2} +(-0.955473 - 1.06116i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(0.663784 - 2.13527i) q^{5} +(0.955473 - 1.06116i) q^{6} -1.22437 q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.100453 - 0.955746i) q^{9} +O(q^{10})$	\(q+(0.104528 + 0.994522i) q^{2} +(-0.955473 - 1.06116i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(0.663784 - 2.13527i) q^{5} +(0.955473 - 1.06116i) q^{6} -1.22437 q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.100453 - 0.955746i) q^{9} +(2.19296 + 0.436951i) q^{10} +(-2.40985 + 1.75086i) q^{11} +(1.15522 + 0.839317i) q^{12} +(0.313204 - 2.97993i) q^{13} +(-0.127982 - 1.21767i) q^{14} +(-2.90009 + 1.33581i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.501156 + 0.106524i) q^{17} +0.961011 q^{18} +(0.00483604 + 4.35890i) q^{19} +(-0.205331 + 2.22662i) q^{20} +(1.16986 + 1.29926i) q^{21} +(-1.99317 - 2.21364i) q^{22} +(-0.282530 - 0.125791i) q^{23} +(-0.713966 + 1.23663i) q^{24} +(-4.11878 - 2.83472i) q^{25} +2.99635 q^{26} +(-4.57584 + 3.32454i) q^{27} +(1.19762 - 0.254562i) q^{28} +(-7.28487 + 1.54845i) q^{29} +(-1.63164 - 2.74458i) q^{30} +(-0.0174028 - 0.0535604i) q^{31} +(0.500000 + 0.866025i) q^{32} +(4.16049 + 0.884340i) q^{33} +(-0.0535554 + 0.509546i) q^{34} +(-0.812720 + 2.61437i) q^{35} +(0.100453 + 0.955746i) q^{36} +(1.46749 + 1.06620i) q^{37} +(-4.33451 + 0.460438i) q^{38} +(-3.46144 + 2.51489i) q^{39} +(-2.23589 + 0.0285395i) q^{40} +(-2.49741 + 1.11192i) q^{41} +(-1.16986 + 1.29926i) q^{42} +(-0.211978 + 0.367157i) q^{43} +(1.99317 - 2.21364i) q^{44} +(-1.97410 - 0.848904i) q^{45} +(0.0955690 - 0.294131i) q^{46} +(-4.74042 + 1.00761i) q^{47} +(-1.30448 - 0.580792i) q^{48} -5.50091 q^{49} +(2.38866 - 4.39253i) q^{50} +(-0.365802 - 0.633588i) q^{51} +(0.313204 + 2.97993i) q^{52} +(7.41240 - 1.57555i) q^{53} +(-3.78464 - 4.20327i) q^{54} +(2.13894 + 6.30788i) q^{55} +(0.378352 + 1.16445i) q^{56} +(4.62087 - 4.16994i) q^{57} +(-2.30144 - 7.08311i) q^{58} +(-5.14164 + 2.28921i) q^{59} +(2.55899 - 1.90959i) q^{60} +(-6.84452 - 3.04738i) q^{61} +(0.0514479 - 0.0229061i) q^{62} +(-0.122992 + 1.17019i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-6.15507 - 2.64681i) q^{65} +(-0.444605 + 4.23014i) q^{66} +(-3.30250 + 3.66780i) q^{67} -0.512352 q^{68} +(0.136466 + 0.419999i) q^{69} +(-2.68500 - 0.534991i) q^{70} +(6.32289 + 7.02228i) q^{71} +(-0.940010 + 0.199805i) q^{72} +(0.0646682 + 0.615276i) q^{73} +(-0.906960 + 1.57090i) q^{74} +(0.927292 + 7.07919i) q^{75} +(-0.910996 - 4.26264i) q^{76} +(2.95056 - 2.14371i) q^{77} +(-2.86293 - 3.17961i) q^{78} +(-7.87946 - 8.75103i) q^{79} +(-0.262097 - 2.22065i) q^{80} +(5.07994 + 1.07977i) q^{81} +(-1.36688 - 2.36751i) q^{82} +(-4.64032 - 14.2814i) q^{83} +(-1.41442 - 1.02764i) q^{84} +(0.560117 - 0.999397i) q^{85} +(-0.387303 - 0.172438i) q^{86} +(8.60365 + 6.25091i) q^{87} +(2.40985 + 1.75086i) q^{88} +(-15.1633 - 6.75114i) q^{89} +(0.637904 - 2.05202i) q^{90} +(-0.383478 + 3.64855i) q^{91} +(0.302510 + 0.0643004i) q^{92} +(-0.0402082 + 0.0696427i) q^{93} +(-1.49760 - 4.60913i) q^{94} +(9.31064 + 2.88304i) q^{95} +(0.441255 - 1.35804i) q^{96} +(-6.39262 - 7.09973i) q^{97} +(-0.575002 - 5.47078i) q^{98} +(1.43130 + 2.47909i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 25 q^{2} + 25 q^{4} + q^{5} - 36 q^{7} + 50 q^{8} + 37 q^{9}+O(q^{10}) $ 200 * q - 25 * q^2 + 25 * q^4 + q^5 - 36 * q^7 + 50 * q^8 + 37 * q^9	\( 200 q - 25 q^{2} + 25 q^{4} + q^{5} - 36 q^{7} + 50 q^{8} + 37 q^{9} + 4 q^{10} - 2 q^{11} + 8 q^{13} + 7 q^{14} + 10 q^{15} + 25 q^{16} - 13 q^{17} - 216 q^{18} - 36 q^{19} - 2 q^{20} + 4 q^{22} - 13 q^{23} + 33 q^{25} - 64 q^{26} - 2 q^{28} + 12 q^{29} - 20 q^{30} + 12 q^{31} + 100 q^{32} - 12 q^{33} + 8 q^{34} - 22 q^{35} + 37 q^{36} + 8 q^{37} + 18 q^{38} + 28 q^{39} - q^{40} + 2 q^{41} + 70 q^{43} - 4 q^{44} + 60 q^{45} + 24 q^{46} - 22 q^{47} + 156 q^{49} + 26 q^{50} - 42 q^{51} + 8 q^{52} - 18 q^{53} - 10 q^{55} - 4 q^{56} + 74 q^{57} + 24 q^{58} + 50 q^{59} + 12 q^{61} - 4 q^{62} - 45 q^{63} - 50 q^{64} + 120 q^{65} + 2 q^{66} - 18 q^{67} - 84 q^{68} + 4 q^{69} - 13 q^{70} + 19 q^{71} - 17 q^{72} - 24 q^{73} + 4 q^{74} - 136 q^{75} - 6 q^{76} - 12 q^{77} - 26 q^{78} - 8 q^{79} + q^{80} - 63 q^{81} + 28 q^{82} + 16 q^{83} - 20 q^{84} - 5 q^{85} + 20 q^{86} - 64 q^{87} + 2 q^{88} + 16 q^{89} - 65 q^{90} + 72 q^{91} + 12 q^{92} - 8 q^{93} - 44 q^{94} - 73 q^{95} - 11 q^{97} - 27 q^{98} + 16 q^{99}+O(q^{100}) \) 200 * q - 25 * q^2 + 25 * q^4 + q^5 - 36 * q^7 + 50 * q^8 + 37 * q^9 + 4 * q^10 - 2 * q^11 + 8 * q^13 + 7 * q^14 + 10 * q^15 + 25 * q^16 - 13 * q^17 - 216 * q^18 - 36 * q^19 - 2 * q^20 + 4 * q^22 - 13 * q^23 + 33 * q^25 - 64 * q^26 - 2 * q^28 + 12 * q^29 - 20 * q^30 + 12 * q^31 + 100 * q^32 - 12 * q^33 + 8 * q^34 - 22 * q^35 + 37 * q^36 + 8 * q^37 + 18 * q^38 + 28 * q^39 - q^40 + 2 * q^41 + 70 * q^43 - 4 * q^44 + 60 * q^45 + 24 * q^46 - 22 * q^47 + 156 * q^49 + 26 * q^50 - 42 * q^51 + 8 * q^52 - 18 * q^53 - 10 * q^55 - 4 * q^56 + 74 * q^57 + 24 * q^58 + 50 * q^59 + 12 * q^61 - 4 * q^62 - 45 * q^63 - 50 * q^64 + 120 * q^65 + 2 * q^66 - 18 * q^67 - 84 * q^68 + 4 * q^69 - 13 * q^70 + 19 * q^71 - 17 * q^72 - 24 * q^73 + 4 * q^74 - 136 * q^75 - 6 * q^76 - 12 * q^77 - 26 * q^78 - 8 * q^79 + q^80 - 63 * q^81 + 28 * q^82 + 16 * q^83 - 20 * q^84 - 5 * q^85 + 20 * q^86 - 64 * q^87 + 2 * q^88 + 16 * q^89 - 65 * q^90 + 72 * q^91 + 12 * q^92 - 8 * q^93 - 44 * q^94 - 73 * q^95 - 11 * q^97 - 27 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.104528	+	0.994522i	0.0739128	+	0.703233i
$2$	0.104528	+	0.994522i	0.0739128	+	0.703233i
$3$	−0.955473	−	1.06116i	−0.551643	−	0.612661i	0.401250	−	0.915968i	$-0.368576\pi$
$3$	−0.955473	−	1.06116i	−0.551643	−	0.612661i	−0.952893	+	0.303307i	$0.901909\pi$
$4$	−0.978148	+	0.207912i	−0.489074	+	0.103956i
$5$	0.663784	−	2.13527i	0.296853	−	0.954923i
$5$	0.663784	−	2.13527i	0.296853	−	0.954923i
$6$	0.955473	−	1.06116i	0.390070	−	0.433217i
$7$	−1.22437			−0.462770			−0.231385	−	0.972862i	$-0.574326\pi$
$7$	−1.22437			−0.462770			−0.231385	+	0.972862i	$0.574326\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	0.100453	−	0.955746i	0.0334843	−	0.318582i
$10$	2.19296	+	0.436951i	0.693475	+	0.138176i
$11$	−2.40985	+	1.75086i	−0.726598	+	0.527904i	−0.888485	−	0.458905i	$-0.848242\pi$
$11$	−2.40985	+	1.75086i	−0.726598	+	0.527904i	0.161888	+	0.986809i	$0.448242\pi$
$12$	1.15522	+	0.839317i	0.333484	+	0.242290i
$13$	0.313204	−	2.97993i	0.0868671	−	0.826485i	−0.861168	−	0.508320i	$-0.830267\pi$
$13$	0.313204	−	2.97993i	0.0868671	−	0.826485i	0.948035	−	0.318165i	$-0.103067\pi$
$14$	−0.127982	−	1.21767i	−0.0342046	−	0.325435i
$15$	−2.90009	+	1.33581i	−0.748801	+	0.344906i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	0.501156	+	0.106524i	0.121548	+	0.0258359i	0.268284	−	0.963340i	$-0.413543\pi$
$17$	0.501156	+	0.106524i	0.121548	+	0.0258359i	−0.146736	+	0.989176i	$0.546877\pi$
$18$	0.961011			0.226512
$19$	0.00483604	+	4.35890i	0.00110946	+	0.999999i
$19$	0.00483604	+	4.35890i	0.00110946	+	0.999999i
$20$	−0.205331	+	2.22662i	−0.0459133	+	0.497888i
$21$	1.16986	+	1.29926i	0.255283	+	0.283521i
$22$	−1.99317	−	2.21364i	−0.424944	−	0.471949i
$23$	−0.282530	−	0.125791i	−0.0589116	−	0.0262291i	0.377069	−	0.926185i	$-0.376932\pi$
$23$	−0.282530	−	0.125791i	−0.0589116	−	0.0262291i	−0.435981	+	0.899956i	$0.643599\pi$
$24$	−0.713966	+	1.23663i	−0.145738	+	0.252425i
$25$	−4.11878	−	2.83472i	−0.823756	−	0.566944i
$26$	2.99635			0.587632
$27$	−4.57584	+	3.32454i	−0.880621	+	0.639809i
$28$	1.19762	−	0.254562i	0.226329	−	0.0481076i
$29$	−7.28487	+	1.54845i	−1.35277	+	0.287539i	−0.826575	−	0.562827i	$-0.809714\pi$
$29$	−7.28487	+	1.54845i	−1.35277	+	0.287539i	−0.526192	+	0.850366i	$0.676381\pi$
$30$	−1.63164	−	2.74458i	−0.297895	−	0.501089i
$31$	−0.0174028	−	0.0535604i	−0.00312564	−	0.00961973i	0.949482	−	0.313823i	$-0.101610\pi$
$31$	−0.0174028	−	0.0535604i	−0.00312564	−	0.00961973i	−0.952607	+	0.304203i	$0.901610\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	4.16049	+	0.884340i	0.724248	+	0.153944i
$34$	−0.0535554	+	0.509546i	−0.00918468	+	0.0873864i
$35$	−0.812720	+	2.61437i	−0.137375	+	0.441909i
$36$	0.100453	+	0.955746i	0.0167422	+	0.159291i
$37$	1.46749	+	1.06620i	0.241254	+	0.175281i	0.701842	−	0.712333i	$-0.252361\pi$
$37$	1.46749	+	1.06620i	0.241254	+	0.175281i	−0.460588	+	0.887614i	$0.652361\pi$
$38$	−4.33451	+	0.460438i	−0.703151	+	0.0746930i
$39$	−3.46144	+	2.51489i	−0.554275	+	0.402704i
$40$	−2.23589	+	0.0285395i	−0.353525	+	0.00451250i
$41$	−2.49741	+	1.11192i	−0.390031	+	0.173653i	−0.592376	−	0.805661i	$-0.701810\pi$
$41$	−2.49741	+	1.11192i	−0.390031	+	0.173653i	0.202346	+	0.979314i	$0.435143\pi$
$42$	−1.16986	+	1.29926i	−0.180513	+	0.200480i
$43$	−0.211978	+	0.367157i	−0.0323263	+	0.0559909i	−0.881736	−	0.471743i	$-0.843625\pi$
$43$	−0.211978	+	0.367157i	−0.0323263	+	0.0559909i	0.849410	+	0.527734i	$0.176958\pi$
$44$	1.99317	−	2.21364i	0.300481	−	0.333718i
$45$	−1.97410	−	0.848904i	−0.294281	−	0.126547i
$46$	0.0955690	−	0.294131i	0.0140909	−	0.0433673i
$47$	−4.74042	+	1.00761i	−0.691462	+	0.146975i	−0.540222	−	0.841522i	$-0.681660\pi$
$47$	−4.74042	+	1.00761i	−0.691462	+	0.146975i	−0.151239	+	0.988497i	$0.548326\pi$
$48$	−1.30448	−	0.580792i	−0.188286	−	0.0838301i
$49$	−5.50091			−0.785844
$50$	2.38866	−	4.39253i	0.337808	−	0.621197i
$51$	−0.365802	−	0.633588i	−0.0512225	−	0.0887201i
$52$	0.313204	+	2.97993i	0.0434335	+	0.413242i
$53$	7.41240	−	1.57555i	1.01817	−	0.216419i	0.331552	−	0.943437i	$-0.392428\pi$
$53$	7.41240	−	1.57555i	1.01817	−	0.216419i	0.686619	+	0.727018i	$0.259094\pi$
$54$	−3.78464	−	4.20327i	−0.515024	−	0.571992i
$55$	2.13894	+	6.30788i	0.288415	+	0.850555i
$56$	0.378352	+	1.16445i	0.0505594	+	0.155606i
$57$	4.62087	−	4.16994i	0.612049	−	0.552322i
$58$	−2.30144	−	7.08311i	−0.302194	−	0.930057i
$59$	−5.14164	+	2.28921i	−0.669385	+	0.298029i	−0.713149	−	0.701013i	$-0.752732\pi$
$59$	−5.14164	+	2.28921i	−0.669385	+	0.298029i	0.0437640	+	0.999042i	$0.486065\pi$
$60$	2.55899	−	1.90959i	0.330364	−	0.246527i
$61$	−6.84452	−	3.04738i	−0.876351	−	0.390177i	−0.0812789	−	0.996691i	$-0.525900\pi$
$61$	−6.84452	−	3.04738i	−0.876351	−	0.390177i	−0.795072	+	0.606515i	$0.792567\pi$
$62$	0.0514479	−	0.0229061i	0.00653389	−	0.00290907i
$63$	−0.122992	+	1.17019i	−0.0154955	+	0.147430i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−6.15507	−	2.64681i	−0.763443	−	0.328296i
$66$	−0.444605	+	4.23014i	−0.0547271	+	0.520694i
$67$	−3.30250	+	3.66780i	−0.403465	+	0.448093i	−0.910300	−	0.413950i	$-0.864149\pi$
$67$	−3.30250	+	3.66780i	−0.403465	+	0.448093i	0.506835	+	0.862043i	$0.330815\pi$
$68$	−0.512352			−0.0621319
$69$	0.136466	+	0.419999i	0.0164286	+	0.0505620i
$70$	−2.68500	−	0.534991i	−0.320919	−	0.0639437i
$71$	6.32289	+	7.02228i	0.750389	+	0.833391i	0.990523	−	0.137349i	$-0.0438581\pi$
$71$	6.32289	+	7.02228i	0.750389	+	0.833391i	−0.240134	+	0.970740i	$0.577191\pi$
$72$	−0.940010	+	0.199805i	−0.110781	+	0.0235473i
$73$	0.0646682	+	0.615276i	0.00756884	+	0.0720127i	0.997654	−	0.0684536i	$-0.0218065\pi$
$73$	0.0646682	+	0.615276i	0.00756884	+	0.0720127i	−0.990085	+	0.140466i	$0.955140\pi$
$74$	−0.906960	+	1.57090i	−0.105432	+	0.182613i
$75$	0.927292	+	7.07919i	0.107074	+	0.817434i
$76$	−0.910996	−	4.26264i	−0.104498	−	0.488958i
$77$	2.95056	−	2.14371i	0.336247	−	0.244298i
$78$	−2.86293	−	3.17961i	−0.324163	−	0.360019i
$79$	−7.87946	−	8.75103i	−0.886509	−	0.984568i	0.113451	−	0.993544i	$-0.463809\pi$
$79$	−7.87946	−	8.75103i	−0.886509	−	0.984568i	−0.999960	+	0.00897603i	$0.997143\pi$
$80$	−0.262097	−	2.22065i	−0.0293033	−	0.248277i
$81$	5.07994	+	1.07977i	0.564437	+	0.119975i
$82$	−1.36688	−	2.36751i	−0.150947	−	0.261447i
$83$	−4.64032	−	14.2814i	−0.509341	−	1.56759i	−0.793349	−	0.608768i	$-0.791664\pi$
$83$	−4.64032	−	14.2814i	−0.509341	−	1.56759i	0.284008	−	0.958822i	$-0.408336\pi$
$84$	−1.41442	−	1.02764i	−0.154326	−	0.112124i
$85$	0.560117	−	0.999397i	0.0607533	−	0.108400i
$86$	−0.387303	−	0.172438i	−0.0417640	−	0.0185945i
$87$	8.60365	+	6.25091i	0.922408	+	0.670168i
$88$	2.40985	+	1.75086i	0.256891	+	0.186642i
$89$	−15.1633	−	6.75114i	−1.60731	−	0.715619i	−0.610245	−	0.792213i	$-0.708929\pi$
$89$	−15.1633	−	6.75114i	−1.60731	−	0.715619i	−0.997062	+	0.0765931i	$0.975596\pi$
$90$	0.637904	−	2.05202i	0.0672409	−	0.216302i
$91$	−0.383478	+	3.64855i	−0.0401994	+	0.382472i
$92$	0.302510	+	0.0643004i	0.0315388	+	0.00670378i
$93$	−0.0402082	+	0.0696427i	−0.00416940	+	0.00722161i
$94$	−1.49760	−	4.60913i	−0.154465	−	0.475395i
$95$	9.31064	+	2.88304i	0.955252	+	0.295794i
$96$	0.441255	−	1.35804i	0.0450354	−	0.138605i
$97$	−6.39262	−	7.09973i	−0.649072	−	0.720868i	0.325350	−	0.945594i	$-0.394518\pi$
$97$	−6.39262	−	7.09973i	−0.649072	−	0.720868i	−0.974422	+	0.224726i	$0.927851\pi$
$98$	−0.575002	−	5.47078i	−0.0580839	−	0.552632i
$99$	1.43130	+	2.47909i	0.143851	+	0.249157i
$100$	4.61815	+	1.91643i	0.461815	+	0.191643i
$101$	2.57371	+	4.45780i	0.256094	+	0.443568i	0.965192	−	0.261542i	$-0.0842309\pi$
$101$	2.57371	+	4.45780i	0.256094	+	0.443568i	−0.709098	+	0.705110i	$0.750898\pi$
$102$	0.591880	−	0.430026i	0.0586049	−	0.0425789i
$103$	3.15958	−	9.72417i	0.311322	−	0.958151i	−0.665920	−	0.746023i	$-0.731961\pi$
$103$	3.15958	−	9.72417i	0.311322	−	0.958151i	0.977242	−	0.212128i	$-0.0680393\pi$
$104$	−2.93087	+	0.622976i	−0.287396	+	0.0610878i
$105$	3.55080	−	1.63554i	0.346522	−	0.159612i
$106$	2.34173	+	7.20710i	0.227449	+	0.700016i
$107$	16.3035			1.57611			0.788057	−	0.615602i	$-0.211087\pi$
$107$	16.3035			1.57611			0.788057	+	0.615602i	$0.211087\pi$
$108$	3.78464	−	4.20327i	0.364177	−	0.404460i
$109$	11.8241	−	5.26444i	1.13255	−	0.504242i	0.247102	−	0.968989i	$-0.420522\pi$
$109$	11.8241	−	5.26444i	1.13255	−	0.504242i	0.885443	+	0.464748i	$0.153855\pi$
$110$	−6.04975	+	2.78658i	−0.576821	+	0.265690i
$111$	−0.270745	−	2.57596i	−0.0256980	−	0.244500i
$112$	−1.11852	+	0.497998i	−0.105690	+	0.0470563i
$113$	1.49272	+	1.08452i	0.140423	+	0.102023i	0.655779	−	0.754953i	$-0.272340\pi$
$113$	1.49272	+	1.08452i	0.140423	+	0.102023i	−0.515356	+	0.856976i	$0.672340\pi$
$114$	4.63011	+	4.15968i	0.433649	+	0.389589i
$115$	−0.456136	+	0.519781i	−0.0425349	+	0.0484699i
$116$	6.80374	−	3.02922i	0.631711	−	0.281256i
$117$	−2.81660	−	0.598686i	−0.260395	−	0.0553486i
$118$	−2.81411	−	4.87419i	−0.259060	−	0.448706i
$119$	−0.613602	−	0.130425i	−0.0562488	−	0.0119561i
$120$	2.16661	+	2.34536i	0.197784	+	0.214101i
$121$	−0.657312	+	2.02300i	−0.0597556	+	0.183909i
$122$	2.31524	−	7.12556i	0.209612	−	0.645118i
$123$	3.56614	+	1.58775i	0.321548	+	0.143162i
$124$	0.0281583	+	0.0487717i	0.00252869	+	0.00437983i
$125$	−8.78688	+	6.91308i	−0.785923	+	0.618325i
$126$	−1.17664			−0.104823
$127$	−1.45052	−	0.645813i	−0.128713	−	0.0573067i	0.341370	−	0.939929i	$-0.389109\pi$
$127$	−1.45052	−	0.645813i	−0.128713	−	0.0573067i	−0.470083	+	0.882622i	$0.655776\pi$
$128$	−0.669131	−	0.743145i	−0.0591433	−	0.0656853i
$129$	0.592151	−	0.125866i	0.0521360	−	0.0110819i
$130$	1.98893	−	6.39802i	0.174441	−	0.561144i
$131$	−2.63518	−	0.560126i	−0.230237	−	0.0489384i	0.0913482	−	0.995819i	$-0.470882\pi$
$131$	−2.63518	−	0.560126i	−0.230237	−	0.0489384i	−0.321585	+	0.946881i	$0.604216\pi$
$132$	−4.25344			−0.370214
$133$	−0.00592112	−	5.33692i	−0.000513426	−	0.462769i
$134$	−3.99291	−	2.90102i	−0.344935	−	0.250610i
$135$	4.06144	+	11.9775i	0.349553	+	1.03086i
$136$	−0.0535554	−	0.509546i	−0.00459234	−	0.0436932i
$137$	0.0242210	−	0.230447i	0.00206934	−	0.0196884i	−0.993439	−	0.114368i	$-0.963516\pi$
$137$	0.0242210	−	0.230447i	0.00206934	−	0.0196884i	0.995508	+	0.0946791i	$0.0301825\pi$
$138$	−0.403434	+	0.179620i	−0.0343426	+	0.0152903i
$139$	2.54379	+	1.13257i	0.215762	+	0.0960633i	0.511771	−	0.859122i	$-0.328989\pi$
$139$	2.54379	+	1.13257i	0.215762	+	0.0960633i	−0.296010	+	0.955185i	$0.595656\pi$
$140$	0.251401	−	2.72622i	0.0212473	−	0.230407i
$141$	5.59858	+	4.06760i	0.471485	+	0.342554i
$142$	−6.32289	+	7.02228i	−0.530605	+	0.589296i
$143$	4.46267	+	7.72957i	0.373187	+	0.646379i
$144$	−0.296969	−	0.913975i	−0.0247474	−	0.0761646i
$145$	−1.52922	+	16.5830i	−0.126995	+	1.37714i
$146$	−0.605146	+	0.128628i	−0.0500823	+	0.0106453i
$147$	5.25597	+	5.83735i	0.433505	+	0.481456i
$148$	−1.65710	−	0.737788i	−0.136213	−	0.0606458i
$149$	−4.59550	+	7.95964i	−0.376478	+	0.652079i	−0.990547	−	0.137173i	$-0.956198\pi$
$149$	−4.59550	+	7.95964i	−0.376478	+	0.652079i	0.614069	+	0.789252i	$0.289532\pi$
$150$	−6.94348	+	1.66219i	−0.566932	+	0.135717i
$151$	11.5284			0.938170			0.469085	−	0.883153i	$-0.344584\pi$
$151$	11.5284			0.938170			0.469085	+	0.883153i	$0.344584\pi$
$152$	4.14406	−	1.35157i	0.336128	−	0.109627i
$153$	0.152153	−	0.468278i	0.0123008	−	0.0378580i
$154$	2.44038	+	2.71032i	0.196651	+	0.218404i
$155$	−0.125918	+	0.00160725i	−0.0101140	+	0.000129098i
$156$	2.86293	−	3.17961i	0.229218	−	0.254572i
$157$	4.64225	−	8.04061i	0.370492	−	0.641711i	−0.619149	−	0.785273i	$-0.712522\pi$
$157$	4.64225	−	8.04061i	0.370492	−	0.641711i	0.989641	+	0.143563i	$0.0458558\pi$
$158$	7.87946	−	8.75103i	0.626856	−	0.696194i
$159$	−8.75426	−	6.36034i	−0.694258	−	0.504408i
$160$	2.18109	−	0.492783i	0.172431	−	0.0389579i
$161$	0.345923	+	0.154015i	0.0272625	+	0.0121381i
$162$	−0.542861	+	5.16498i	−0.0426512	+	0.405799i
$163$	9.73797	+	7.07505i	0.762737	+	0.554161i	0.899749	−	0.436409i	$-0.143750\pi$
$163$	9.73797	+	7.07505i	0.762737	+	0.554161i	−0.137012	+	0.990569i	$0.543750\pi$
$164$	2.21166	−	1.60686i	0.172702	−	0.125475i
$165$	4.64997	−	8.29677i	0.362000	−	0.645903i
$166$	13.7181	−	6.10771i	1.06473	−	0.474050i
$167$	2.94694	−	3.27291i	0.228041	−	0.253266i	−0.618255	−	0.785977i	$-0.712160\pi$
$167$	2.94694	−	3.27291i	0.228041	−	0.253266i	0.846297	+	0.532712i	$0.178827\pi$
$168$	0.874161	−	1.51409i	0.0674430	−	0.116815i
$169$	3.93401	+	0.836200i	0.302616	+	0.0643231i
$170$	1.05247	+	0.452584i	0.0807208	+	0.0347116i
$171$	4.16648	+	0.433242i	0.318619	+	0.0331308i
$172$	0.131010	−	0.403206i	0.00998939	−	0.0307442i
$173$	1.64827	+	15.6822i	0.125315	+	1.19230i	0.858699	+	0.512481i	$0.171273\pi$
$173$	1.64827	+	15.6822i	0.125315	+	1.19230i	−0.733383	+	0.679815i	$0.762060\pi$
$174$	−5.31735	+	9.20991i	−0.403107	+	0.698202i
$175$	5.04293	+	3.47076i	0.381209	+	0.262364i
$176$	−1.48937	+	2.57966i	−0.112265	+	0.194450i
$177$	7.34192	+	3.26883i	0.551852	+	0.245700i
$178$	5.12916	−	15.7859i	0.384447	−	1.18321i
$179$	−2.86979	+	8.83230i	−0.214498	+	0.660157i	0.784691	+	0.619887i	$0.212822\pi$
$179$	−2.86979	+	8.83230i	−0.214498	+	0.660157i	−0.999189	+	0.0402698i	$0.987178\pi$
$180$	2.10746	+	0.419915i	0.157081	+	0.0312986i
$181$	−3.77742	+	4.19525i	−0.280774	+	0.311831i	−0.866992	−	0.498323i	$-0.833949\pi$
$181$	−3.77742	+	4.19525i	−0.280774	+	0.311831i	0.586218	+	0.810153i	$0.300616\pi$
$182$	−3.66865			−0.271938
$183$	3.30600	+	10.1748i	0.244386	+	0.752144i
$184$	−0.0323273	+	0.307574i	−0.00238320	+	0.0226746i
$185$	3.25072	−	2.42577i	0.238997	−	0.178346i
$186$	−0.0734640	−	0.0327083i	−0.00538664	−	0.00239829i
$187$	−1.39422	+	0.620747i	−0.101956	+	0.0453935i
$188$	4.42734	−	1.97118i	0.322897	−	0.143763i
$189$	5.60254	−	4.07048i	0.407525	−	0.296084i
$190$	−1.89402	+	9.56100i	−0.137407	+	0.693628i
$191$	−14.4004	−	10.4625i	−1.04198	−	0.757040i	−0.0713063	−	0.997454i	$-0.522717\pi$
$191$	−14.4004	−	10.4625i	−1.04198	−	0.757040i	−0.970670	+	0.240414i	$0.922717\pi$
$192$	1.39673	+	0.296884i	0.100800	+	0.0214257i
$193$	−0.767746	+	1.32977i	−0.0552636	+	0.0957193i	−0.892334	−	0.451376i	$-0.850933\pi$
$193$	−0.767746	+	1.32977i	−0.0552636	+	0.0957193i	0.837070	+	0.547096i	$0.184267\pi$
$194$	6.39262	−	7.09973i	0.458963	−	0.509731i
$195$	3.07232	+	9.06047i	0.220013	+	0.648834i
$196$	5.38070	−	1.14370i	0.384336	−	0.0816931i
$197$	7.73512	−	23.8063i	0.551105	−	1.69613i	−0.154910	−	0.987929i	$-0.549509\pi$
$197$	7.73512	−	23.8063i	0.551105	−	1.69613i	0.706015	−	0.708197i	$-0.250491\pi$
$198$	−2.31589	+	1.68259i	−0.164583	+	0.119577i
$199$	2.58383	+	4.47533i	0.183163	+	0.317248i	0.942956	−	0.332917i	$-0.108033\pi$
$199$	2.58383	+	4.47533i	0.183163	+	0.317248i	−0.759793	+	0.650165i	$0.774700\pi$
$200$	−1.42321	+	4.79317i	−0.100636	+	0.338928i
$201$	7.04757			0.497098
$202$	−4.16436	+	3.02558i	−0.293003	+	0.212879i
$203$	8.91940	−	1.89588i	0.626019	−	0.133065i
$204$	0.489539	+	0.543688i	0.0342746	+	0.0380658i
$205$	0.716510	+	6.07074i	0.0500432	+	0.423999i
$206$	10.0012	+	2.12581i	0.696815	+	0.148112i
$207$	−0.148605	+	0.257391i	−0.0103288	+	0.0178899i
$208$	−0.925922	−	2.84970i	−0.0642012	−	0.197591i
$209$	−7.64347	−	10.4958i	−0.528710	−	0.726011i
$210$	1.99774	+	3.36039i	0.137857	+	0.231889i
$211$	−1.54738	−	14.7224i	−0.106526	−	1.01353i	−0.908987	−	0.416824i	$-0.863143\pi$
$211$	−1.54738	−	14.7224i	−0.106526	−	1.01353i	0.802461	−	0.596705i	$-0.203524\pi$
$212$	−6.92284	+	3.08225i	−0.475463	+	0.211690i
$213$	1.41041	−	13.4192i	0.0966400	−	0.919468i
$214$	1.70418	+	16.2141i	0.116495	+	1.10838i
$215$	0.643272	+	0.696344i	0.0438708	+	0.0474902i
$216$	4.57584	+	3.32454i	0.311347	+	0.226207i
$217$	0.0213075	+	0.0655779i	0.00144645	+	0.00445172i
$218$	6.47156	+	11.2091i	0.438309	+	0.759174i
$219$	0.591118	−	0.656503i	0.0399441	−	0.0443624i
$220$	−3.40368	−	5.72533i	−0.229476	−	0.386002i
$221$	0.474399	−	1.46005i	0.0319115	−	0.0982135i
$222$	2.53355	−	0.538523i	0.170041	−	0.0361433i
$223$	−0.240211	−	2.28546i	−0.0160857	−	0.153045i	0.983531	−	0.180741i	$-0.0578497\pi$
$223$	−0.240211	−	2.28546i	−0.0160857	−	0.153045i	−0.999616	+	0.0276959i	$0.991183\pi$
$224$	−0.612187	−	1.06034i	−0.0409034	−	0.0708468i
$225$	−3.12302	+	3.65175i	−0.208201	+	0.243450i
$226$	−0.922551	+	1.59791i	−0.0613672	+	0.106291i
$227$	6.34168	−	4.60750i	0.420912	−	0.305811i	−0.357092	−	0.934069i	$-0.616232\pi$
$227$	6.34168	−	4.60750i	0.420912	−	0.305811i	0.778005	+	0.628258i	$0.216232\pi$
$228$	−3.65291	+	5.03955i	−0.241920	+	0.333752i
$229$	4.40665	−	13.5623i	0.291199	−	0.896220i	−0.693272	−	0.720676i	$-0.743832\pi$
$229$	4.40665	−	13.5623i	0.291199	−	0.896220i	0.984472	−	0.175544i	$-0.0561684\pi$
$230$	−0.564613	−	0.399306i	−0.0372295	−	0.0263294i
$231$	−5.09399	−	1.08276i	−0.335160	−	0.0712405i
$232$	3.72381	+	6.44983i	0.244480	+	0.423452i
$233$	−24.2970	−	5.16449i	−1.59175	−	0.338337i	−0.675006	−	0.737812i	$-0.735859\pi$
$233$	−24.2970	−	5.16449i	−1.59175	−	0.338337i	−0.916744	+	0.399475i	$0.869192\pi$
$234$	0.300992	−	2.86375i	0.0196765	−	0.187209i
$235$	−0.995098	+	10.7909i	−0.0649131	+	0.703922i
$236$	4.55333	−	3.30819i	0.296397	−	0.215345i
$237$	−1.75763	+	16.7227i	−0.114170	+	1.08626i
$238$	0.0655718	−	0.623874i	0.00425039	−	0.0404398i
$239$	−15.5276	+	11.2814i	−1.00439	+	0.729735i	−0.963026	−	0.269409i	$-0.913172\pi$
$239$	−15.5276	+	11.2814i	−1.00439	+	0.729735i	−0.0413679	+	0.999144i	$0.513172\pi$
$240$	−2.10604	+	2.39990i	−0.135945	+	0.154913i
$241$	−0.0578006	+	0.549936i	−0.00372326	+	0.0354245i	−0.996226	−	0.0867996i	$-0.972336\pi$
$241$	−0.0578006	+	0.549936i	−0.00372326	+	0.0354245i	0.992503	+	0.122224i	$0.0390027\pi$
$242$	−2.08062	−	0.442250i	−0.133748	−	0.0284289i
$243$	4.77615	+	8.27254i	0.306390	+	0.530683i
$244$	7.32854	+	1.55773i	0.469162	+	0.0997234i
$245$	−3.65142	+	11.7459i	−0.233280	+	0.750421i
$246$	−1.20629	+	3.71257i	−0.0769100	+	0.236705i
$247$	12.9907	+	1.35081i	0.826581	+	0.0859501i
$248$	−0.0455612	+	0.0331021i	−0.00289314	+	0.00210199i
$249$	−10.7212	+	18.5696i	−0.679427	+	1.17680i
$250$	−7.79369	−	8.01613i	−0.492916	−	0.506985i
$251$	−0.891763	−	1.54458i	−0.0562876	−	0.0974929i	0.836509	−	0.547954i	$-0.184593\pi$
$251$	−0.891763	−	1.54458i	−0.0562876	−	0.0974929i	−0.892796	+	0.450461i	$0.851260\pi$
$252$	−0.122992	−	1.17019i	−0.00774776	−	0.0737151i
$253$	0.901098	−	0.191534i	0.0566515	−	0.0120417i
$254$	0.490655	−	1.51008i	0.0307864	−	0.0947508i
$255$	−1.59570	+	0.360522i	−0.0999264	+	0.0225768i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	−0.0269474	−	0.0466742i	−0.00168093	−	0.00291146i	0.865184	−	0.501455i	$-0.167202\pi$
$257$	−0.0269474	−	0.0466742i	−0.00168093	−	0.00291146i	−0.866865	+	0.498544i	$0.833868\pi$
$258$	0.187073	+	0.575751i	0.0116466	+	0.0358447i
$259$	−1.79676	−	1.30542i	−0.111645	−	0.0811149i
$260$	6.57087	+	1.30926i	0.407508	+	0.0811967i
$261$	0.748135	+	7.11803i	0.0463084	+	0.440595i
$262$	0.281606	−	2.67930i	0.0173976	−	0.165528i
$263$	−20.7937	+	9.25796i	−1.28220	+	0.570870i	−0.930859	−	0.365379i	$-0.880939\pi$
$263$	−20.7937	+	9.25796i	−1.28220	+	0.570870i	−0.351336	+	0.936249i	$0.614273\pi$
$264$	−0.444605	−	4.23014i	−0.0273636	−	0.260347i
$265$	1.55599	−	16.8733i	0.0955839	−	1.03652i
$266$	5.30706	−	0.563748i	0.325397	−	0.0345656i
$267$	7.32409	+	22.5412i	0.448227	+	1.37950i
$268$	2.46776	−	4.27428i	0.150742	−	0.261093i
$269$	6.15112	+	1.30746i	0.375040	+	0.0797173i	0.391575	−	0.920146i	$-0.371930\pi$
$269$	6.15112	+	1.30746i	0.375040	+	0.0797173i	−0.0165352	+	0.999863i	$0.505264\pi$
$270$	−11.4873	+	5.29117i	−0.699095	+	0.322011i
$271$	−6.31401	−	7.01242i	−0.383549	−	0.425974i	0.520195	−	0.854047i	$-0.325859\pi$
$271$	−6.31401	−	7.01242i	−0.383549	−	0.425974i	−0.903744	+	0.428073i	$0.859193\pi$
$272$	0.501156	−	0.106524i	0.0303871	−	0.00645897i
$273$	4.23810	−	3.07916i	0.256502	−	0.186359i
$274$	0.231717			0.0139985
$275$	14.8888	−	0.380154i	0.897831	−	0.0229241i
$276$	−0.220807	−	0.382448i	−0.0132910	−	0.0230207i
$277$	11.3498	−	8.24609i	0.681942	−	0.495460i	−0.192059	−	0.981383i	$-0.561517\pi$
$277$	11.3498	−	8.24609i	0.681942	−	0.495460i	0.874001	+	0.485923i	$0.161517\pi$
$278$	−0.860466	+	2.64824i	−0.0516073	+	0.158831i
$279$	−0.0529383	+	0.0112524i	−0.00316933	+	0.000673662i
$280$	2.73756	−	0.0349431i	0.163600	−	0.00208825i
$281$	−1.97142	+	2.18948i	−0.117605	+	0.130613i	−0.799072	−	0.601235i	$-0.794675\pi$
$281$	−1.97142	+	2.18948i	−0.117605	+	0.130613i	0.681467	+	0.731849i	$0.261342\pi$
$282$	−3.46011	+	5.99309i	−0.206047	+	0.356883i
$283$	−4.90868	−	1.04337i	−0.291791	−	0.0620221i	0.0596905	−	0.998217i	$-0.480989\pi$
$283$	−4.90868	−	1.04337i	−0.291791	−	0.0620221i	−0.351481	+	0.936195i	$0.614322\pi$
$284$	−7.64473	−	5.55422i	−0.453631	−	0.329582i
$285$	−5.83670	−	12.6347i	−0.345736	−	0.748418i
$286$	−7.22075	+	5.24618i	−0.426972	+	0.310213i
$287$	3.05777	−	1.36141i	0.180494	−	0.0803613i
$288$	0.877927	−	0.390878i	0.0517323	−	0.0230327i
$289$	−15.2905	−	6.80775i	−0.899439	−	0.400456i
$290$	−16.6520	+	0.212552i	−0.977841	+	0.0124815i
$291$	−1.42597	+	13.5672i	−0.0835918	+	0.795323i
$292$	−0.191178	−	0.588386i	−0.0111879	−	0.0344327i
$293$	−5.62169			−0.328423			−0.164211	−	0.986425i	$-0.552508\pi$
$293$	−5.62169			−0.328423			−0.164211	+	0.986425i	$0.552508\pi$
$294$	−5.25597	+	5.83735i	−0.306534	+	0.340441i
$295$	1.47514	+	12.4984i	0.0858861	+	0.727682i
$296$	0.560532	−	1.72514i	0.0325803	−	0.100272i
$297$	5.20629	−	16.0233i	0.302100	−	0.929767i
$298$	−8.39640	−	3.73832i	−0.486390	−	0.216555i
$299$	−0.463337	+	0.802523i	−0.0267955	+	0.0464111i
$300$	−2.37887	−	6.73169i	−0.137344	−	0.388654i
$301$	0.259540	−	0.449537i	0.0149597	−	0.0259109i
$302$	1.20505	+	11.4653i	0.0693427	+	0.659752i
$303$	2.27133	−	6.99043i	0.130484	−	0.401590i
$304$	1.77734	+	3.98008i	0.101937	+	0.228273i
$305$	−11.0503	+	12.5921i	−0.632736	+	0.721023i
$306$	0.481617	+	0.102371i	0.0275322	+	0.00585215i
$307$	12.5946	−	21.8145i	0.718812	−	1.24502i	−0.242658	−	0.970112i	$-0.578019\pi$
$307$	12.5946	−	21.8145i	0.718812	−	1.24502i	0.961471	−	0.274908i	$-0.0886473\pi$
$308$	−2.44038	+	2.71032i	−0.139054	+	0.154435i
$309$	−13.3378	+	5.93837i	−0.758761	+	0.337822i
$310$	−0.0147604	−	0.125060i	−0.000838336	−	0.00710293i
$311$	−14.8661	+	10.8008i	−0.842977	+	0.612459i	−0.923201	−	0.384318i	$-0.874437\pi$
$311$	−14.8661	+	10.8008i	−0.842977	+	0.612459i	0.0802236	+	0.996777i	$0.474437\pi$
$312$	3.46144	+	2.51489i	0.195966	+	0.142377i
$313$	2.77055	−	26.3600i	0.156601	−	1.48996i	−0.580547	−	0.814226i	$-0.697161\pi$
$313$	2.77055	−	26.3600i	0.156601	−	1.48996i	0.737148	−	0.675731i	$-0.236172\pi$
$314$	8.48181	+	3.77635i	0.478656	+	0.213112i
$315$	2.41704	+	1.03937i	0.136185	+	0.0585621i
$316$	9.52672	+	6.92156i	0.535920	+	0.389368i
$317$	21.6006	−	23.9899i	1.21321	−	1.34741i	0.292938	−	0.956131i	$-0.405367\pi$
$317$	21.6006	−	23.9899i	1.21321	−	1.34741i	0.920273	−	0.391276i	$-0.127966\pi$
$318$	5.41043	−	9.37114i	0.303402	−	0.525507i
$319$	14.8443	−	16.4863i	0.831124	−	0.923056i
$320$	0.718069	+	2.11763i	0.0401413	+	0.118379i
$321$	−15.5775	−	17.3006i	−0.869452	−	0.965624i
$322$	−0.117012	+	0.360126i	−0.00652083	+	0.0200691i
$323$	−0.461904	+	2.18500i	−0.0257010	+	0.121577i
$324$	−5.19343			−0.288524
$325$	−9.73730	+	11.3859i	−0.540128	+	0.631573i
$326$	−6.01840	+	10.4242i	−0.333328	+	0.577342i
$327$	−16.8840	−	7.51726i	−0.933690	−	0.415705i
$328$	1.82924	+	2.03158i	0.101003	+	0.112175i
$329$	5.80405	−	1.23369i	0.319987	−	0.0680154i
$330$	8.73738	+	3.75725i	0.480977	+	0.206830i
$331$	4.31229	+	13.2719i	0.237025	+	0.729488i	0.996846	+	0.0793560i	$0.0252864\pi$
$331$	4.31229	+	13.2719i	0.237025	+	0.729488i	−0.759821	+	0.650132i	$0.774714\pi$
$332$	7.50819	+	13.0046i	0.412065	+	0.713718i
$333$	1.16643	−	1.29545i	0.0639197	−	0.0709901i
$334$	3.56302	+	2.58869i	0.194960	+	0.141647i
$335$	5.63961	+	9.48637i	0.308125	+	0.518296i
$336$	1.59717	+	0.711107i	0.0871328	+	0.0387940i
$337$	29.2961	−	13.0435i	1.59586	−	0.710523i	0.599880	−	0.800090i	$-0.295215\pi$
$337$	29.2961	−	13.0435i	1.59586	−	0.710523i	0.995981	+	0.0895666i	$0.0285482\pi$
$338$	−0.420403	+	3.99987i	−0.0228669	+	0.217564i
$339$	−0.275399	−	2.62025i	−0.0149576	−	0.142312i
$340$	−0.340091	+	1.09401i	−0.0184440	+	0.0593311i
$341$	0.135715	+	0.0986026i	0.00734937	+	0.00533963i
$342$	0.00464748	+	4.18895i	0.000251307	+	0.226512i
$343$	15.3058			0.826435
$344$	0.414692	+	0.0881454i	0.0223587	+	0.00475248i
$345$	0.987397	−	0.0126034i	0.0531597	−	0.000678547i
$346$	−15.4240	+	3.27847i	−0.829200	+	0.176252i
$347$	−20.7628	−	23.0594i	−1.11461	−	1.23790i	−0.968603	−	0.248612i	$-0.920026\pi$
$347$	−20.7628	−	23.0594i	−1.11461	−	1.23790i	−0.146003	−	0.989284i	$-0.546641\pi$
$348$	−9.71527	−	4.32552i	−0.520793	−	0.231872i
$349$	31.6070			1.69188			0.845942	−	0.533275i	$-0.179039\pi$
$349$	31.6070			1.69188			0.845942	+	0.533275i	$0.179039\pi$
$350$	−2.92461	+	5.37809i	−0.156327	+	0.287471i
$351$	8.47375	+	14.6770i	0.452295	+	0.783399i
$352$	−2.72121	−	1.21156i	−0.145041	−	0.0645765i
$353$	−3.62978	+	11.1713i	−0.193194	+	0.594589i	0.806799	+	0.590826i	$0.201198\pi$
$353$	−3.62978	+	11.1713i	−0.193194	+	0.594589i	−0.999993	+	0.00376312i	$0.998802\pi$
$354$	−2.48349	+	7.64338i	−0.131996	+	0.406241i
$355$	19.1915	−	8.83981i	1.01858	−	0.469169i
$356$	16.2356	+	3.45098i	0.860485	+	0.182902i
$357$	0.447878	+	0.775748i	0.0237042	+	0.0410570i
$358$	−9.08389	−	1.93084i	−0.480099	−	0.102048i
$359$	−20.3702	+	9.06942i	−1.07510	+	0.478665i	−0.866419	−	0.499318i	$-0.833584\pi$
$359$	−20.3702	+	9.06942i	−1.07510	+	0.478665i	−0.208681	+	0.977984i	$0.566917\pi$
$360$	−0.197325	+	2.13981i	−0.0103999	+	0.112778i
$361$	−19.0000	+	0.0421596i	−0.999998	+	0.00221892i
$362$	−4.56712	−	3.31820i	−0.240042	−	0.174401i
$363$	2.77477	−	1.23541i	0.145638	−	0.0648420i
$364$	−0.383478	−	3.64855i	−0.0200997	−	0.191236i
$365$	1.35671	+	0.270326i	0.0710134	+	0.0141495i
$366$	−9.77351	+	4.35145i	−0.510870	+	0.227454i
$367$	6.90937	−	7.67363i	0.360666	−	0.400560i	−0.535315	−	0.844653i	$-0.679807\pi$
$367$	6.90937	−	7.67363i	0.360666	−	0.400560i	0.895981	+	0.444092i	$0.146474\pi$
$368$	−0.309268			−0.0161217
$369$	0.811841	+	2.49859i	0.0422628	+	0.130071i
$370$	2.75228	+	2.97935i	0.143084	+	0.154889i
$371$	−9.07554	+	1.92907i	−0.471179	+	0.100152i
$372$	0.0248500	−	0.0764805i	0.00128841	−	0.00396533i
$373$	−3.17971	+	2.31019i	−0.164639	+	0.119617i	−0.667054	−	0.745009i	$-0.732445\pi$
$373$	−3.17971	+	2.31019i	−0.164639	+	0.119617i	0.502415	+	0.864627i	$0.332445\pi$
$374$	−0.763082	−	1.32170i	−0.0394581	−	0.0683434i
$375$	15.7315	+	2.71903i	0.812372	+	0.140410i
$376$	2.42316	+	4.19704i	0.124965	+	0.216446i
$377$	2.33262	+	22.1934i	0.120136	+	1.14302i
$378$	4.63381	+	5.14637i	0.238338	+	0.264701i
$379$	10.2568	−	31.5672i	0.526857	−	1.62150i	−0.233757	−	0.972295i	$-0.575102\pi$
$379$	10.2568	−	31.5672i	0.526857	−	1.62150i	0.760614	−	0.649204i	$-0.224898\pi$
$380$	−9.70660	−	0.884246i	−0.497938	−	0.0453609i
$381$	0.700621	+	2.15629i	0.0358939	+	0.110470i
$382$	8.89994	−	15.4151i	0.455361	−	0.788708i
$383$	−31.4245	−	6.67949i	−1.60572	−	0.341306i	−0.684095	−	0.729393i	$-0.739803\pi$
$383$	−31.4245	−	6.67949i	−1.60572	−	0.341306i	−0.921623	+	0.388087i	$0.873136\pi$
$384$	−0.149260	+	1.42011i	−0.00761687	+	0.0724697i
$385$	−2.61886	−	7.72321i	−0.133470	−	0.393611i
$386$	−1.40274	−	0.624541i	−0.0713977	−	0.0317883i
$387$	0.329615	+	0.239479i	0.0167553	+	0.0121734i
$388$	7.72904	+	5.61548i	0.392383	+	0.285083i
$389$	−18.9059	−	8.41745i	−0.958567	−	0.426782i	−0.133019	−	0.991113i	$-0.542467\pi$
$389$	−18.9059	−	8.41745i	−0.958567	−	0.426782i	−0.825548	+	0.564332i	$0.809134\pi$
$390$	−8.68969	+	4.00256i	−0.440020	+	0.202678i
$391$	−0.128192	−	0.0931370i	−0.00648295	−	0.00471014i
$392$	1.69987	+	5.23168i	0.0858566	+	0.264240i
$393$	1.92346	+	3.33154i	0.0970259	+	0.168054i
$394$	24.4844	+	5.20432i	1.23351	+	0.262190i
$395$	−23.9161	+	11.0160i	−1.20335	+	0.554275i
$396$	−1.91545	−	2.12733i	−0.0962552	−	0.106902i
$397$	−2.15617	−	2.39467i	−0.108215	−	0.120185i	0.686604	−	0.727032i	$-0.259101\pi$
$397$	−2.15617	−	2.39467i	−0.108215	−	0.120185i	−0.794819	+	0.606847i	$0.792434\pi$
$398$	−4.18073	+	3.03748i	−0.209561	+	0.152255i
$399$	−5.65767	+	5.10556i	−0.283238	+	0.255598i
$400$	−4.91568	−	0.914386i	−0.245784	−	0.0457193i
$401$	0.895123	−	1.55040i	0.0447003	−	0.0774232i	−0.842810	−	0.538212i	$-0.819100\pi$
$401$	0.895123	−	1.55040i	0.0447003	−	0.0774232i	0.887510	+	0.460789i	$0.152433\pi$
$402$	0.736672	+	7.00897i	0.0367419	+	0.349576i
$403$	−0.165057	+	0.0350839i	−0.00822207	+	0.00174766i
$404$	−3.44430	−	3.82529i	−0.171360	−	0.190315i
$405$	5.67759	−	10.1303i	0.282122	−	0.503379i
$406$	2.81782	+	8.67237i	0.139846	+	0.430402i
$407$	−5.40320			−0.267826
$408$	−0.489539	+	0.543688i	−0.0242358	+	0.0269166i
$409$	4.07281	−	38.7502i	0.201387	−	1.91607i	−0.166215	−	0.986089i	$-0.553155\pi$
$409$	4.07281	−	38.7502i	0.201387	−	1.91607i	0.367603	−	0.929983i	$-0.380179\pi$
$410$	−5.96258	+	1.34715i	−0.294471	+	0.0665310i
$411$	−0.267684	+	0.194484i	−0.0132039	+	0.00959317i
$412$	−1.06876	+	10.1686i	−0.0526541	+	0.500970i
$413$	6.29529	−	2.80284i	0.309771	−	0.137919i
$414$	−0.271515	−	0.120886i	−0.0133442	−	0.00594123i
$415$	−33.5749	+	0.428560i	−1.64813	+	0.0210372i
$416$	2.73730	−	1.21872i	0.134207	−	0.0597529i
$417$	−1.22869	−	3.78151i	−0.0601691	−	0.185181i
$418$	9.63937	−	8.69871i	0.471477	−	0.425468i
$419$	5.97871	+	18.4006i	0.292079	+	0.898928i	0.984187	+	0.177133i	$0.0566823\pi$
$419$	5.97871	+	18.4006i	0.292079	+	0.898928i	−0.692108	+	0.721794i	$0.743318\pi$
$420$	−3.13316	+	2.33805i	−0.152882	+	0.114085i
$421$	19.7976	+	21.9875i	0.964876	+	1.07160i	0.997395	+	0.0721320i	$0.0229803\pi$
$421$	19.7976	+	21.9875i	0.964876	+	1.07160i	−0.0325193	+	0.999471i	$0.510353\pi$
$422$	14.4800	−	3.07781i	0.704873	−	0.149825i
$423$	0.486828	+	4.63186i	0.0236704	+	0.225209i
$424$	−3.78900	−	6.56274i	−0.184010	−	0.318715i
$425$	−1.76219	−	1.85939i	−0.0854786	−	0.0901935i
$426$	13.4931			0.653743
$427$	8.38025	+	3.73113i	0.405549	+	0.180562i
$428$	−15.9472	+	3.38968i	−0.770836	+	0.163846i
$429$	3.93835	−	12.1210i	0.190146	−	0.585208i
$430$	−0.625289	+	0.712536i	−0.0301541	+	0.0343615i
$431$	12.8000	−	14.2158i	0.616552	−	0.684751i	−0.351302	−	0.936262i	$-0.614261\pi$
$431$	12.8000	−	14.2158i	0.616552	−	0.684751i	0.967854	+	0.251512i	$0.0809276\pi$
$432$	−2.82803	+	4.89829i	−0.136063	+	0.235669i
$433$	0.850902	−	0.945023i	0.0408918	−	0.0454149i	−0.722352	−	0.691526i	$-0.756939\pi$
$433$	0.850902	−	0.945023i	0.0408918	−	0.0454149i	0.763244	+	0.646111i	$0.223606\pi$
$434$	−0.0629914	+	0.0280456i	−0.00302368	+	0.00134623i
$435$	19.0584	−	14.2219i	0.913779	−	0.681887i
$436$	−10.4712	+	7.60777i	−0.501480	+	0.364346i
$437$	0.546942	−	1.23213i	0.0261638	−	0.0589407i
$438$	0.714696	+	0.519257i	0.0341495	+	0.0248110i
$439$	−3.19241	−	30.3738i	−0.152366	−	1.44966i	−0.757134	−	0.653260i	$-0.773401\pi$
$439$	−3.19241	−	30.3738i	−0.152366	−	1.44966i	0.604768	−	0.796401i	$-0.293266\pi$
$440$	5.33818	−	3.98350i	0.254488	−	0.189906i
$441$	−0.552583	+	5.25747i	−0.0263135	+	0.250356i
$442$	1.50164	+	0.319183i	0.0714257	+	0.0151820i
$443$	−0.872437	−	1.51111i	−0.0414507	−	0.0717948i	0.844556	−	0.535468i	$-0.179865\pi$
$443$	−0.872437	−	1.51111i	−0.0414507	−	0.0717948i	−0.886006	+	0.463673i	$0.846531\pi$
$444$	0.800401	+	2.46338i	0.0379854	+	0.116907i
$445$	−24.4807	+	27.8965i	−1.16050	+	1.32242i
$446$	2.24783	−	0.477790i	0.106438	−	0.0226240i
$447$	12.8373	−	2.72866i	0.607185	−	0.129061i
$448$	0.990539	−	0.719669i	0.0467986	−	0.0340011i
$449$	5.74838			0.271283			0.135641	−	0.990758i	$-0.456691\pi$
$449$	5.74838			0.271283			0.135641	+	0.990758i	$0.456691\pi$
$450$	−3.95819	−	2.72420i	−0.186591	−	0.128420i
$451$	4.07158	−	7.05219i	0.191723	−	0.332074i
$452$	−1.68558	−	0.750471i	−0.0792832	−	0.0352992i
$453$	−11.0151	−	12.2335i	−0.517534	−	0.574780i
$454$	5.24515	+	5.82533i	0.246167	+	0.273396i
$455$	7.53611	+	3.24068i	0.353298	+	0.151925i
$456$	−5.39377	−	3.10612i	−0.252587	−	0.145458i
$457$	−7.24468			−0.338892			−0.169446	−	0.985539i	$-0.554198\pi$
$457$	−7.24468			−0.338892			−0.169446	+	0.985539i	$0.554198\pi$
$458$	13.9486	+	2.96486i	0.651775	+	0.138539i
$459$	−2.64736	+	1.17868i	−0.123568	+	0.0550160i
$460$	0.338100	−	0.603259i	0.0157640	−	0.0281271i
$461$	−0.284270	−	2.70465i	−0.0132398	−	0.125968i	0.985906	−	0.167303i	$-0.0535057\pi$
$461$	−0.284270	−	2.70465i	−0.0132398	−	0.125968i	−0.999145	+	0.0413347i	$0.986839\pi$
$462$	0.544363	−	5.17927i	0.0253261	−	0.240961i
$463$	−1.65967	−	1.20582i	−0.0771315	−	0.0560393i	0.548551	−	0.836117i	$-0.315180\pi$
$463$	−1.65967	−	1.20582i	−0.0771315	−	0.0560393i	−0.625683	+	0.780078i	$0.715180\pi$
$464$	−6.02525	+	4.37760i	−0.279715	+	0.203225i
$465$	0.122017	+	0.132083i	0.00565838	+	0.00612521i
$466$	2.59647	−	24.7037i	0.120279	−	1.14438i
$467$	5.29749	+	16.3040i	0.245139	+	0.754459i	0.995614	+	0.0935602i	$0.0298248\pi$
$467$	5.29749	+	16.3040i	0.245139	+	0.754459i	−0.750475	+	0.660899i	$0.770175\pi$
$468$	2.87952			0.133106
$469$	4.04350	−	4.49076i	0.186711	−	0.207364i
$470$	−10.8358	+	0.138312i	−0.499820	+	0.00637985i
$471$	−12.9679	+	2.75642i	−0.597530	+	0.127009i
$472$	3.76602	+	4.18259i	0.173345	+	0.192519i
$473$	−0.132004	−	1.25594i	−0.00606956	−	0.0577480i
$474$	−16.8149			−0.772332
$475$	12.3363	−	17.9671i	0.566030	−	0.824385i
$476$	0.627311			0.0287527
$477$	−0.761232	−	7.24264i	−0.0348544	−	0.331618i
$478$	−12.8427	−	14.2633i	−0.587411	−	0.652386i
$479$	−9.96972	+	2.11913i	−0.455528	+	0.0968255i	−0.429961	−	0.902848i	$-0.641473\pi$
$479$	−9.96972	+	2.11913i	−0.455528	+	0.0968255i	−0.0255674	+	0.999673i	$0.508139\pi$
$480$	−2.60690	−	1.84365i	−0.118988	−	0.0841506i
$481$	3.63681	−	4.03909i	0.165824	−	0.184167i
$482$	−0.552965			−0.0251869
$483$	−0.167085	−	0.514236i	−0.00760265	−	0.0233985i
$484$	0.222343	−	2.11545i	0.0101065	−	0.0961570i
$485$	−19.4032	+	8.93731i	−0.881053	+	0.405822i
$486$	−7.72797	+	5.61470i	−0.350548	+	0.254688i
$487$	11.0300	+	8.01378i	0.499818	+	0.363139i	0.808947	−	0.587881i	$-0.200038\pi$
$487$	11.0300	+	8.01378i	0.499818	+	0.363139i	−0.309130	+	0.951020i	$0.600038\pi$
$488$	−0.783155	+	7.45122i	−0.0354517	+	0.337301i
$489$	−1.79661	−	17.0936i	−0.0812454	−	0.772998i
$490$	−12.0633	−	2.40363i	−0.544963	−	0.108585i
$491$	−13.0715	+	5.81979i	−0.589907	+	0.262643i	−0.679907	−	0.733298i	$-0.737980\pi$
$491$	−13.0715	+	5.81979i	−0.589907	+	0.262643i	0.0900003	+	0.995942i	$0.471313\pi$
$492$	−3.81832	−	0.811609i	−0.172143	−	0.0365902i
$493$	−3.81581			−0.171855
$494$	0.0144904	+	13.0608i	0.000651956	+	0.587632i
$495$	6.24360	−	1.41064i	0.280629	−	0.0634036i
$496$	−0.0376832	−	0.0418515i	−0.00169203	−	0.00187919i
$497$	−7.74158	−	8.59789i	−0.347257	−	0.385668i
$498$	−19.5886	−	8.72139i	−0.877785	−	0.390815i
$499$	−10.7335	+	18.5910i	−0.480499	+	0.832249i	−0.999750	−	0.0223731i	$-0.992878\pi$
$499$	−10.7335	+	18.5910i	−0.480499	+	0.832249i	0.519251	+	0.854622i	$0.326211\pi$
$500$	7.15756	−	8.58891i	0.320096	−	0.384108i
$501$	−6.28881			−0.280963
$502$	1.44290	−	1.04833i	0.0643999	−	0.0467892i
$503$	−12.2301	+	2.59958i	−0.545312	+	0.115910i	−0.472327	−	0.881424i	$-0.656586\pi$
$503$	−12.2301	+	2.59958i	−0.545312	+	0.115910i	−0.0729848	+	0.997333i	$0.523252\pi$
$504$	1.15092	−	0.244636i	0.0512662	−	0.0108970i
$505$	11.2270	−	2.53656i	0.499596	−	0.112876i
$506$	0.284675	+	0.876141i	0.0126554	+	0.0389492i
$507$	−2.87150	−	4.97358i	−0.127528	−	0.220885i
$508$	1.55309	+	0.330121i	0.0689074	+	0.0146467i
$509$	1.01912	−	9.69628i	0.0451717	−	0.429780i	−0.948442	−	0.316949i	$-0.897341\pi$
$509$	1.01912	−	9.69628i	0.0451717	−	0.429780i	0.993614	−	0.112831i	$-0.0359918\pi$
$510$	−0.525343	−	1.54927i	−0.0232626	−	0.0686029i
$511$	−0.0791780	−	0.753328i	−0.00350263	−	0.0333253i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−14.5135	−	19.9295i	−0.640786	−	0.879911i
$514$	0.0436018	−	0.0316785i	0.00192319	−	0.00139728i
$515$	−18.6665	−	13.2013i	−0.822544	−	0.581719i
$516$	−0.553042	+	0.246230i	−0.0243463	+	0.0108397i
$517$	9.65953	−	10.7280i	0.424826	−	0.471817i
$518$	1.11046	−	1.92337i	0.0487907	−	0.0845080i
$519$	15.0665	−	16.7330i	0.661344	−	0.734497i
$520$	−0.615242	+	6.67173i	−0.0269801	+	0.292575i
$521$	2.51977	−	7.75506i	0.110393	−	0.339755i	−0.880565	−	0.473925i	$-0.842837\pi$
$521$	2.51977	−	7.75506i	0.110393	−	0.339755i	0.990958	+	0.134170i	$0.0428367\pi$
$522$	−7.00084	+	1.48807i	−0.306418	+	0.0651312i
$523$	−31.8416	−	14.1768i	−1.39233	−	0.619907i	−0.432798	−	0.901491i	$-0.642474\pi$
$523$	−31.8416	−	14.1768i	−1.39233	−	0.619907i	−0.959537	+	0.281583i	$0.909140\pi$
$524$	2.69406			0.117690
$525$	−1.13535	−	8.66757i	−0.0495508	−	0.378284i
$526$	−11.3808	−	19.7121i	−0.496225	−	0.859488i
$527$	−0.00301606	−	0.0286959i	−0.000131382	−	0.00125001i
$528$	4.16049	−	0.884340i	0.181062	−	0.0384859i
$529$	−15.3260	−	17.0213i	−0.666348	−	0.740054i
$530$	16.9435	−	0.216272i	0.735980	−	0.00939428i
$531$	1.67141	+	5.14406i	0.0725329	+	0.223233i
$532$	1.11540	+	5.21906i	0.0483587	+	0.226275i
$533$	2.53125	+	7.79039i	0.109641	+	0.337439i
$534$	−21.6522	+	9.64017i	−0.936981	+	0.417171i
$535$	10.8220	−	34.8123i	0.467875	−	1.50507i
$536$	4.50881	+	2.00745i	0.194751	+	0.0867088i
$537$	12.1145	−	5.39372i	0.522779	−	0.232756i
$538$	−0.657331	+	6.25409i	−0.0283396	+	0.269633i
$539$	13.2564	−	9.63132i	0.570993	−	0.414850i
$540$	−6.46294	−	10.8713i	−0.278121	−	0.467826i
$541$	−2.82562	+	26.8840i	−0.121483	+	1.15583i	0.748632	+	0.662986i	$0.230711\pi$
$541$	−2.82562	+	26.8840i	−0.121483	+	1.15583i	−0.870115	+	0.492848i	$0.835956\pi$
$542$	6.31401	−	7.01242i	0.271210	−	0.301209i
$543$	8.06106			0.345933
$544$	0.158326	+	0.487276i	0.00678815	+	0.0208918i
$545$	−3.39235	−	28.7422i	−0.145312	−	1.23118i
$546$	3.50529	+	3.89302i	0.150013	+	0.166606i
$547$	−16.2611	+	3.45641i	−0.695276	+	0.147786i	−0.541976	−	0.840394i	$-0.682324\pi$
$547$	−16.2611	+	3.45641i	−0.695276	+	0.147786i	−0.153300	+	0.988180i	$0.548990\pi$
$548$	0.0242210	+	0.230447i	0.00103467	+	0.00984421i
$549$	−3.60007	+	6.23551i	−0.153647	+	0.266125i
$550$	1.93438	+	14.7675i	0.0824822	+	0.629690i
$551$	−6.78475	−	31.7465i	−0.289040	−	1.35245i
$552$	0.357273	−	0.259574i	0.0152065	−	0.0110482i
$553$	9.64740	+	10.7145i	0.410249	+	0.455628i
$554$	9.38730	+	10.4256i	0.398828	+	0.442943i
$555$	−5.68010	−	1.13177i	−0.241107	−	0.0480410i
$556$	−2.72368	−	0.578936i	−0.115510	−	0.0245524i
$557$	−13.0204	−	22.5520i	−0.551691	−	0.955558i	−0.998153	−	0.0607547i	$-0.980649\pi$
$557$	−13.0204	−	22.5520i	−0.551691	−	0.955558i	0.446461	−	0.894803i	$-0.352684\pi$
$558$	−0.0167243	−	0.0514721i	−0.000707996	−	0.00217899i
$559$	1.02771	+	0.746675i	0.0434675	+	0.0315810i
$560$	0.320904	+	2.71891i	0.0135607	+	0.114895i
$561$	1.99085	+	0.886385i	0.0840539	+	0.0374232i
$562$	−2.38355	−	1.73175i	−0.100544	−	0.0730496i
$563$	29.0049	+	21.0733i	1.22241	+	0.888134i	0.996298	−	0.0859665i	$-0.0273978\pi$
$563$	29.0049	+	21.0733i	1.22241	+	0.888134i	0.226114	+	0.974101i	$0.427398\pi$
$564$	−6.32194	−	2.81471i	−0.266202	−	0.118521i
$565$	3.30660	−	2.46747i	0.139110	−	0.103807i
$566$	0.524560	−	4.99086i	0.0220489	−	0.209781i
$567$	−6.21974	−	1.32205i	−0.261205	−	0.0555207i
$568$	4.72470	−	8.18343i	0.198244	−	0.343369i
$569$	0.782955	+	2.40969i	0.0328232	+	0.101019i	0.966126	−	0.258071i	$-0.0830869\pi$
$569$	0.782955	+	2.40969i	0.0328232	+	0.101019i	−0.933303	+	0.359091i	$0.883087\pi$
$570$	11.9554	−	7.12542i	0.500758	−	0.298451i
$571$	10.0746	−	31.0063i	0.421607	−	1.29757i	−0.484599	−	0.874736i	$-0.661034\pi$
$571$	10.0746	−	31.0063i	0.421607	−	1.29757i	0.906206	−	0.422836i	$-0.138966\pi$
$572$	−5.97222	−	6.63282i	−0.249711	−	0.277332i
$573$	2.65680	+	25.2778i	0.110989	+	1.05599i
$574$	1.67357	+	2.89871i	0.0698535	+	0.120990i
$575$	0.807099	+	1.31900i	0.0336584	+	0.0550060i
$576$	0.480505	+	0.832260i	0.0200211	+	0.0346775i
$577$	−16.9760	+	12.3338i	−0.706722	+	0.513463i	−0.882114	−	0.471035i	$-0.843880\pi$
$577$	−16.9760	+	12.3338i	−0.706722	+	0.513463i	0.175393	+	0.984499i	$0.443880\pi$
$578$	5.17217	−	15.9183i	0.215134	−	0.662114i
$579$	2.14466	−	0.455863i	0.0891292	−	0.0189450i
$580$	−1.95200	−	16.5386i	−0.0810523	−	0.686727i
$581$	5.68148	+	17.4858i	0.235707	+	0.725433i
$582$	−13.6419			−0.565476
$583$	−15.1042	+	16.7749i	−0.625552	+	0.694746i
$584$	0.565179	−	0.251634i	0.0233873	−	0.0104127i
$585$	−3.14797	+	5.61681i	−0.130153	+	0.232226i
$586$	−0.587627	−	5.59090i	−0.0242746	−	0.230958i
$587$	−21.3075	+	9.48671i	−0.879455	+	0.391559i	−0.796246	−	0.604974i	$-0.793184\pi$
$587$	−21.3075	+	9.48671i	−0.879455	+	0.391559i	−0.0832093	+	0.996532i	$0.526517\pi$
$588$	−6.35477	−	4.61701i	−0.262066	−	0.190402i
$589$	0.233380	−	0.0761161i	0.00961625	−	0.00313631i
$590$	−12.2757	+	2.77349i	−0.505382	+	0.114183i
$591$	−32.6529	+	14.5380i	−1.34316	+	0.598015i
$592$	1.77428	+	0.377135i	0.0729225	+	0.0155002i
$593$	−2.58058	−	4.46970i	−0.105972	−	0.183549i	0.808163	−	0.588959i	$-0.200462\pi$
$593$	−2.58058	−	4.46970i	−0.105972	−	0.183549i	−0.914135	+	0.405410i	$0.867129\pi$
$594$	16.4797	+	3.50288i	0.676172	+	0.143725i
$595$	−0.685793	+	1.22363i	−0.0281148	+	0.0501641i
$596$	2.84018	−	8.74116i	0.116338	−	0.358052i
$597$	2.28026	−	7.01792i	0.0933248	−	0.287224i
$598$	−0.846559	−	0.376912i	−0.0346184	−	0.0154131i
$599$	−6.22300	−	10.7786i	−0.254265	−	0.440400i	0.710431	−	0.703767i	$-0.248500\pi$
$599$	−6.22300	−	10.7786i	−0.254265	−	0.440400i	−0.964696	+	0.263367i	$0.915167\pi$
$600$	6.44616	−	3.06950i	0.263163	−	0.125312i
$601$	42.5401			1.73525			0.867623	−	0.497223i	$-0.165647\pi$
$601$	42.5401			1.73525			0.867623	+	0.497223i	$0.165647\pi$
$602$	0.474204	+	0.211129i	0.0193271	+	0.00860498i
$603$	3.17374	+	3.52480i	0.129245	+	0.143541i
$604$	−11.2765	+	2.39689i	−0.458834	+	0.0975282i
$605$	3.88334	+	2.74637i	0.157880	+	0.111656i
$606$	7.18956	+	1.52819i	0.292056	+	0.0620784i
$607$	−39.4762			−1.60229			−0.801145	−	0.598471i	$-0.795775\pi$
$607$	−39.4762			−1.60229			−0.801145	+	0.598471i	$0.795775\pi$
$608$	−3.77250	+	2.18364i	−0.152995	+	0.0885581i
$609$	−10.5341	−	7.65345i	−0.426862	−	0.310134i
$610$	−13.6782	−	9.67350i	−0.553814	−	0.391668i
$611$	1.51789	+	14.4417i	0.0614071	+	0.584250i
$612$	−0.0514673	+	0.489679i	−0.00208044	+	0.0197941i
$613$	−1.25046	+	0.556741i	−0.0505056	+	0.0224866i	−0.431834	−	0.901953i	$-0.642133\pi$
$613$	−1.25046	+	0.556741i	−0.0505056	+	0.0224866i	0.381328	+	0.924440i	$0.375467\pi$
$614$	23.0115	+	10.2454i	0.928668	+	0.413470i
$615$	5.75742	−	6.56076i	0.232161	−	0.264555i
$616$	−2.95056	−	2.14371i	−0.118881	−	0.0863724i
$617$	7.87281	−	8.74364i	0.316947	−	0.352006i	−0.563529	−	0.826097i	$-0.690557\pi$
$617$	7.87281	−	8.74364i	0.316947	−	0.352006i	0.880476	+	0.474091i	$0.157223\pi$
$618$	−7.30002	−	12.6440i	−0.293650	−	0.508616i
$619$	9.10140	+	28.0112i	0.365816	+	1.12587i	0.949468	+	0.313863i	$0.101623\pi$
$619$	9.10140	+	28.0112i	0.365816	+	1.12587i	−0.583652	+	0.812004i	$0.698377\pi$
$620$	0.122832	−	0.0277519i	0.00493305	−	0.00111454i
$621$	1.71101	−	0.363687i	0.0686605	−	0.0145942i
$622$	−12.2956	−	13.6556i	−0.493008	−	0.547541i
$623$	18.5656	+	8.26592i	0.743813	+	0.331167i
$624$	−2.13929	+	3.70536i	−0.0856402	+	0.148333i
$625$	8.92872	+	23.3512i	0.357149	+	0.934047i
$626$	26.5052			1.05936
$627$	−3.83462	+	18.1394i	−0.153140	+	0.724419i
$628$	−2.86907	+	8.83008i	−0.114488	+	0.352359i
$629$	0.621867	+	0.690654i	0.0247955	+	0.0275382i
$630$	−0.781032	+	2.51244i	−0.0311171	+	0.100098i
$631$	−10.4834	+	11.6430i	−0.417338	+	0.463501i	−0.914754	−	0.404011i	$-0.867616\pi$
$631$	−10.4834	+	11.6430i	−0.417338	+	0.463501i	0.497416	+	0.867512i	$0.334282\pi$
$632$	−5.88783	+	10.1980i	−0.234205	+	0.405656i
$633$	−14.1443	+	15.7088i	−0.562185	+	0.624370i
$634$	26.1164	+	18.9747i	1.03721	+	0.753580i
$635$	−2.34182	+	2.66858i	−0.0929323	+	0.105899i
$636$	9.88535	+	4.40124i	0.391979	+	0.174521i
$637$	−1.72290	+	16.3923i	−0.0682640	+	0.649488i
$638$	17.9477	+	13.0397i	0.710554	+	0.516248i
$639$	7.34667	−	5.33767i	0.290630	−	0.211155i
$640$	−2.03098	+	0.935489i	−0.0802813	+	0.0369784i
$641$	−11.6991	+	5.20877i	−0.462086	+	0.205734i	−0.624557	−	0.780979i	$-0.714720\pi$
$641$	−11.6991	+	5.20877i	−0.462086	+	0.205734i	0.162471	+	0.986713i	$0.448054\pi$
$642$	15.5775	−	17.3006i	0.614795	−	0.682799i
$643$	−8.63120	+	14.9497i	−0.340381	+	0.589558i	−0.984504	−	0.175365i	$-0.943890\pi$
$643$	−8.63120	+	14.9497i	−0.340381	+	0.589558i	0.644122	+	0.764923i	$0.277223\pi$
$644$	−0.370385	−	0.0787277i	−0.0145952	−	0.00310231i
$645$	0.124303	−	1.34795i	0.00489443	−	0.0530756i
$646$	−2.22132	−	0.230978i	−0.0873965	−	0.00908772i
$647$	−2.70137	+	8.31397i	−0.106202	+	0.326856i	−0.990011	−	0.140992i	$-0.954971\pi$
$647$	−2.70137	+	8.31397i	−0.106202	+	0.326856i	0.883809	+	0.467848i	$0.154971\pi$
$648$	−0.542861	−	5.16498i	−0.0213256	−	0.202899i
$649$	8.38252	−	14.5189i	0.329043	−	0.569918i
$650$	−12.3413	−	8.49381i	−0.484066	−	0.333155i
$651$	0.0492299	−	0.0852686i	0.00192947	−	0.00334194i
$652$	−10.9962	−	4.89581i	−0.430643	−	0.191735i
$653$	−12.8453	+	39.5337i	−0.502674	+	1.54707i	0.301971	+	0.953317i	$0.402355\pi$
$653$	−12.8453	+	39.5337i	−0.502674	+	1.54707i	−0.804645	+	0.593756i	$0.797645\pi$
$654$	5.71122	−	17.5773i	0.223326	−	0.687328i
$655$	−2.94521	+	5.25504i	−0.115079	+	0.205331i
$656$	−1.82924	+	2.03158i	−0.0714199	+	0.0793199i
$657$	0.594544			0.0231954
$658$	1.83362	+	5.64330i	0.0714819	+	0.219999i
$659$	−4.61112	+	43.8719i	−0.179624	+	1.70900i	0.419010	+	0.907982i	$0.362377\pi$
$659$	−4.61112	+	43.8719i	−0.179624	+	1.70900i	−0.598633	+	0.801023i	$0.704289\pi$
$660$	−2.82336	+	9.08225i	−0.109899	+	0.353526i
$661$	20.9706	+	9.33669i	0.815660	+	0.363155i	0.771786	−	0.635882i	$-0.219363\pi$
$661$	20.9706	+	9.33669i	0.815660	+	0.363155i	0.0438735	+	0.999037i	$0.486030\pi$
$662$	−12.7484	+	5.67596i	−0.495481	+	0.220602i
$663$	−2.00262	+	0.891624i	−0.0777753	+	0.0346278i
$664$	−12.1485	+	8.82640i	−0.471453	+	0.342531i
$665$	−11.3997	−	3.52992i	−0.442062	−	0.136884i
$666$	1.41028	+	1.02462i	0.0546471	+	0.0397034i
$667$	2.25298	+	0.478885i	0.0872356	+	0.0185425i
$668$	−2.20207	+	3.81410i	−0.0852006	+	0.147572i
$669$	−2.19572	+	2.43859i	−0.0848914	+	0.0942815i
$670$	−8.84490	+	6.60031i	−0.341708	+	0.254992i
$671$	21.8298	−	4.64007i	0.842730	−	0.179128i
$672$	−0.540261	+	1.66275i	−0.0208410	+	0.0641421i
$673$	−10.3466	+	7.51724i	−0.398832	+	0.289768i	−0.769065	−	0.639171i	$-0.779278\pi$
$673$	−10.3466	+	7.51724i	−0.398832	+	0.289768i	0.370233	+	0.928939i	$0.379278\pi$
$674$	16.0343	+	27.7722i	0.617618	+	1.06975i
$675$	28.2711	−	0.721839i	1.08815	−	0.0277836i
$676$	−4.02190			−0.154688
$677$	3.20007	−	2.32499i	0.122989	−	0.0893565i	−0.524590	−	0.851355i	$-0.675782\pi$
$677$	3.20007	−	2.32499i	0.122989	−	0.0893565i	0.647579	+	0.761998i	$0.275782\pi$
$678$	2.57711	−	0.547781i	0.0989732	−	0.0210374i
$679$	7.82696	+	8.69272i	0.300371	+	0.333596i
$680$	−1.12357	−	0.223873i	−0.0430869	−	0.00858513i
$681$	−10.9486	−	2.32720i	−0.419552	−	0.0891784i
$682$	−0.0838764	+	0.145278i	−0.00321179	+	0.00556299i
$683$	3.59192	+	11.0548i	0.137441	+	0.423000i	0.995962	−	0.0897791i	$-0.0286161\pi$
$683$	3.59192	+	11.0548i	0.137441	+	0.423000i	−0.858521	+	0.512779i	$0.828616\pi$
$684$	−4.16551	+	0.442486i	−0.159272	+	0.0169189i
$685$	−0.475990	−	0.204686i	−0.0181866	−	0.00782063i
$686$	1.59989	+	15.2219i	0.0610841	+	0.581176i
$687$	−18.6022	+	8.28222i	−0.709717	+	0.315986i
$688$	−0.0443155	+	0.421634i	−0.00168951	+	0.0160746i
$689$	−2.37346	−	22.5819i	−0.0904214	−	0.860303i
$690$	0.115746	+	0.980671i	0.00440636	+	0.0373335i
$691$	−17.3424	−	12.6000i	−0.659738	−	0.479328i	0.206837	−	0.978376i	$-0.433683\pi$
$691$	−17.3424	−	12.6000i	−0.659738	−	0.479328i	−0.866574	+	0.499048i	$0.833683\pi$
$692$	−4.87276	−	14.9968i	−0.185235	−	0.570093i
$693$	−1.75245	−	3.03533i	−0.0665699	−	0.115303i
$694$	20.7628	−	23.0594i	0.788146	−	0.875324i
$695$	4.10687	−	4.67991i	0.155783	−	0.177519i
$696$	3.28630	−	10.1142i	0.124567	−	0.383377i
$697$	−1.37004	+	0.291211i	−0.0518940	+	0.0110304i
$698$	3.30383	+	31.4339i	0.125052	+	1.18979i
$699$	17.7348	+	30.7175i	0.670791	+	1.16184i
$700$	−5.65434	−	2.34643i	−0.213714	−	0.0886867i
$701$	−6.63575	+	11.4935i	−0.250629	+	0.434102i	−0.963699	−	0.266991i	$-0.913971\pi$
$701$	−6.63575	+	11.4935i	−0.250629	+	0.434102i	0.713070	+	0.701092i	$0.247304\pi$
$702$	−13.7108	+	9.96149i	−0.517481	+	0.375972i
$703$	−4.64034	+	6.40180i	−0.175014	+	0.241448i
$704$	0.920481	−	2.83295i	0.0346919	−	0.106771i
$705$	12.4017	−	9.25448i	0.467075	−	0.348544i
$706$	−11.4895	−	2.44217i	−0.432414	−	0.0919124i
$707$	−3.15119	−	5.45802i	−0.118513	−	0.205270i
$708$	−7.86111	−	1.67093i	−0.295438	−	0.0627974i
$709$	−1.65206	+	15.7183i	−0.0620445	+	0.590314i	0.918691	+	0.394976i	$0.129247\pi$
$709$	−1.65206	+	15.7183i	−0.0620445	+	0.590314i	−0.980736	+	0.195338i	$0.937420\pi$
$710$	10.7974	+	18.1624i	0.405221	+	0.681621i
$711$	−9.15528	+	6.65170i	−0.343350	+	0.249458i
$712$	−1.73500	+	16.5074i	−0.0650217	+	0.618640i
$713$	−0.00182057	+	0.0173215i	−6.81808e−5	+	0.000648697i
$714$	−0.724683	+	0.526513i	−0.0271206	+	0.0197042i
$715$	19.4670	−	4.39825i	0.728024	−	0.164485i
$716$	0.970738	−	9.23596i	0.0362782	−	0.345164i
$717$	26.8076	+	5.69812i	1.00115	+	0.212800i
$718$	−11.1490	−	19.3106i	−0.416077	−	0.720667i
$719$	−5.11912	−	1.08810i	−0.190911	−	0.0405794i	0.111464	−	0.993768i	$-0.464446\pi$
$719$	−5.11912	−	1.08810i	−0.190911	−	0.0405794i	−0.302375	+	0.953189i	$0.597779\pi$
$720$	−2.14871	+	0.0274268i	−0.0800777	+	0.00102214i
$721$	−3.86850	+	11.9060i	−0.144070	+	0.443403i
$722$	−2.02796	−	18.8915i	−0.0754730	−	0.703067i
$723$	0.638797	−	0.464113i	0.0237571	−	0.0172605i
$724$	2.82263	−	4.88894i	0.104902	−	0.181696i
$725$	34.3942	+	14.2729i	1.27737	+	0.530080i
$726$	1.51868	+	2.63043i	0.0563635	+	0.0976245i
$727$	2.33502	+	22.2162i	0.0866010	+	0.823954i	0.948479	+	0.316839i	$0.102621\pi$
$727$	2.33502	+	22.2162i	0.0866010	+	0.823954i	−0.861878	+	0.507115i	$0.830712\pi$
$728$	3.58848	−	0.762755i	0.132998	−	0.0282696i
$729$	9.02957	−	27.7902i	0.334429	−	1.02927i
$730$	−0.127031	+	1.37753i	−0.00470163	+	0.0509848i
$731$	−0.145345	+	0.161422i	−0.00537578	+	0.00597041i
$732$	−5.34922	−	9.26512i	−0.197713	−	0.342449i
$733$	−10.5976	−	32.6162i	−0.391433	−	1.20471i	−0.931705	−	0.363216i	$-0.881679\pi$
$733$	−10.5976	−	32.6162i	−0.391433	−	1.20471i	0.540272	−	0.841491i	$-0.318321\pi$
$734$	8.35382	+	6.06941i	0.308345	+	0.224026i
$735$	15.9532	−	7.34819i	0.588441	−	0.271042i
$736$	−0.0323273	−	0.307574i	−0.00119160	−	0.0113373i
$737$	1.53674	−	14.6211i	0.0566064	−	0.538574i
$738$	−2.40004	+	1.06857i	−0.0883468	+	0.0393345i
$739$	0.148626	+	1.41408i	0.00546730	+	0.0520179i	0.996915	−	0.0784838i	$-0.0250079\pi$
$739$	0.148626	+	1.41408i	0.00546730	+	0.0520179i	−0.991448	+	0.130502i	$0.958341\pi$
$740$	−2.67533	+	3.04863i	−0.0983472	+	0.112070i
$741$	−10.9789	−	15.0759i	−0.403319	−	0.553828i
$742$	−2.86715	−	8.82418i	−0.105256	−	0.323946i
$743$	−21.7657	+	37.6993i	−0.798506	+	1.38305i	0.122083	+	0.992520i	$0.461042\pi$
$743$	−21.7657	+	37.6993i	−0.798506	+	1.38305i	−0.920589	+	0.390533i	$0.872291\pi$
$744$	0.0786591	+	0.0167195i	0.00288378	+	0.000612967i
$745$	13.9456	+	15.0961i	0.510927	+	0.553079i
$746$	−2.62991	−	2.92081i	−0.0962877	−	0.106938i
$747$	−14.1155	+	3.00035i	−0.516461	+	0.109777i
$748$	1.23469	−	0.897057i	0.0451449	−	0.0327997i
$749$	−19.9615			−0.729378
$750$	−1.05974	+	15.9296i	−0.0386963	+	0.581665i
$751$	2.24922	+	3.89577i	0.0820753	+	0.142159i	0.904141	−	0.427234i	$-0.140512\pi$
$751$	2.24922	+	3.89577i	0.0820753	+	0.142159i	−0.822066	+	0.569392i	$0.807179\pi$
$752$	−3.92076	+	2.84860i	−0.142975	+	0.103878i
$753$	−0.786990	+	2.42211i	−0.0286795	+	0.0882664i
$754$	−21.8280	+	4.63969i	−0.794929	+	0.168967i
$755$	7.65238	−	24.6163i	0.278499	−	0.895880i
$756$	−4.63381	+	5.14637i	−0.168530	+	0.187172i
$757$	−19.5187	+	33.8073i	−0.709418	+	1.22875i	0.255656	+	0.966768i	$0.417709\pi$
$757$	−19.5187	+	33.8073i	−0.709418	+	1.22875i	−0.965073	+	0.261980i	$0.915625\pi$
$758$	32.4664	+	6.90095i	1.17923	+	0.250654i
$759$	−1.06422	−	0.773203i	−0.0386288	−	0.0280655i
$760$	−0.135214	−	9.74586i	−0.00490472	−	0.353519i
$761$	23.6498	−	17.1826i	0.857304	−	0.622868i	−0.0698459	−	0.997558i	$-0.522251\pi$
$761$	23.6498	−	17.1826i	0.857304	−	0.622868i	0.927150	+	0.374690i	$0.122251\pi$
$762$	−2.07124	+	0.922177i	−0.0750332	+	0.0334070i
$763$	−14.4771	+	6.44564i	−0.524108	+	0.233348i
$764$	16.2610	+	7.23986i	0.588302	+	0.261929i
$765$	−0.898904	−	0.635723i	−0.0324999	−	0.0229846i
$766$	3.35814	−	31.9506i	0.121335	−	1.15442i
$767$	5.21130	+	16.0387i	0.188169	+	0.579125i
$768$	−1.42793			−0.0515261
$769$	−6.75641	+	7.50375i	−0.243642	+	0.270592i	−0.852546	−	0.522652i	$-0.824943\pi$
$769$	−6.75641	+	7.50375i	−0.243642	+	0.270592i	0.608904	+	0.793244i	$0.291610\pi$
$770$	7.40715	−	3.41181i	0.266935	−	0.122953i
$771$	−0.0237813	+	0.0731915i	−0.000856464	+	0.00263593i
$772$	0.474493	−	1.46034i	0.0170774	−	0.0525588i
$773$	20.7413	+	9.23460i	0.746011	+	0.332146i	0.744293	−	0.667853i	$-0.232786\pi$
$773$	20.7413	+	9.23460i	0.746011	+	0.332146i	0.00171803	+	0.999999i	$0.499453\pi$
$774$	−0.203713	+	0.352842i	−0.00732232	+	0.0126826i
$775$	−0.0801502	+	0.269936i	−0.00287908	+	0.00969637i
$776$	−4.77681	+	8.27368i	−0.171478	+	0.297008i
$777$	0.331493	+	3.15394i	0.0118922	+	0.113147i
$778$	6.39513	−	19.6822i	0.229277	−	0.705641i
$779$	−4.85882	−	10.8806i	−0.174085	−	0.389838i
$780$	−4.88896	−	8.22371i	−0.175053	−	0.294456i
$781$	−27.5322	−	5.85216i	−0.985181	−	0.209407i
$782$	0.0792271	−	0.137225i	0.00283315	−	0.00490717i
$783$	28.1865	−	31.3043i	1.00730	−	1.11873i
$784$	−5.02533	+	2.23742i	−0.179476	+	0.0799079i
$785$	−14.0874	−	15.2497i	−0.502803	−	0.544285i
$786$	−3.11223	+	2.26117i	−0.111010	+	0.0806532i
$787$	−16.6122	−	12.0695i	−0.592160	−	0.430230i	0.250927	−	0.968006i	$-0.419265\pi$
$787$	−16.6122	−	12.0695i	−0.592160	−	0.430230i	−0.843088	+	0.537776i	$0.819265\pi$
$788$	−2.61649	+	24.8943i	−0.0932086	+	0.886821i
$789$	29.6920	+	13.2197i	1.05706	+	0.470635i
$790$	−13.4556	−	22.6336i	−0.478728	−	0.805267i
$791$	−1.82765	−	1.32786i	−0.0649836	−	0.0472134i
$792$	1.91545	−	2.12733i	0.0680627	−	0.0755913i
$793$	−11.2247	+	19.4418i	−0.398601	+	0.690397i
$794$	2.15617	−	2.39467i	0.0765197	−	0.0849838i
$795$	−19.3920	+	14.4708i	−0.687763	+	0.513228i
$796$	−3.45784	−	3.84032i	−0.122560	−	0.136117i
$797$	−2.37631	+	7.31353i	−0.0841732	+	0.259058i	−0.984281	−	0.176608i	$-0.943487\pi$
$797$	−2.37631	+	7.31353i	−0.0841732	+	0.259058i	0.900108	+	0.435667i	$0.143487\pi$
$798$	−5.66898	−	5.09300i	−0.200680	−	0.180290i
$799$	−2.48303			−0.0878432
$800$	0.395549	−	4.98433i	0.0139848	−	0.176223i
$801$	−7.97558	+	13.8141i	−0.281803	+	0.488097i
$802$	1.63547	+	0.728159i	0.0577505	+	0.0257122i
$803$	−1.23310	−	1.36950i	−0.0435153	−	0.0483286i
$804$	−6.89357	+	1.46527i	−0.243117	+	0.0516762i
$805$	0.558481	−	0.636407i	0.0196839	−	0.0224304i
$806$	−0.0521449	−	0.160485i	−0.00183673	−	0.00565286i
$807$	−4.48980	−	7.77656i	−0.158048	−	0.273748i
$808$	3.44430	−	3.82529i	0.121170	−	0.134573i
$809$	43.3169	+	31.4716i	1.52294	+	1.10648i	0.960006	+	0.279979i	$0.0903276\pi$
$809$	43.3169	+	31.4716i	1.52294	+	1.10648i	0.562934	+	0.826502i	$0.309672\pi$
$810$	10.6683	+	4.58758i	0.374846	+	0.161191i
$811$	15.0976	+	6.72190i	0.530150	+	0.236038i	0.654313	−	0.756224i	$-0.272958\pi$
$811$	15.0976	+	6.72190i	0.530150	+	0.236038i	−0.124163	+	0.992262i	$0.539625\pi$
$812$	−8.33032	+	3.70890i	−0.292337	+	0.130157i
$813$	−1.40843	+	13.4004i	−0.0493959	+	0.469971i
$814$	−0.564788	−	5.37360i	−0.0197958	−	0.188344i
$815$	21.5711	−	16.0969i	0.755602	−	0.563851i
$816$	−0.591880	−	0.430026i	−0.0207200	−	0.0150539i
$817$	−1.60142	−	0.922215i	−0.0560267	−	0.0322642i
$818$	38.9636			1.36233
$819$	3.44857	+	0.733016i	0.120503	+	0.0256136i
$820$	−1.96303	−	5.78911i	−0.0685520	−	0.202164i
$821$	29.6726	−	6.30710i	1.03558	−	0.220119i	0.341398	−	0.939919i	$-0.389100\pi$
$821$	29.6726	−	6.30710i	1.03558	−	0.220119i	0.694182	+	0.719800i	$0.255766\pi$
$822$	−0.221399	−	0.245888i	−0.00772217	−	0.00857634i
$823$	8.83112	+	3.93187i	0.307834	+	0.137056i	0.554839	−	0.831958i	$-0.312780\pi$
$823$	8.83112	+	3.93187i	0.307834	+	0.137056i	−0.247005	+	0.969014i	$0.579447\pi$
$824$	−10.2246			−0.356191
$825$	−14.6293	−	15.4362i	−0.509327	−	0.537420i
$826$	3.44553	+	5.96783i	0.119885	+	0.207647i
$827$	−25.5907	−	11.3937i	−0.889875	−	0.396198i	−0.0897028	−	0.995969i	$-0.528592\pi$
$827$	−25.5907	−	11.3937i	−0.889875	−	0.396198i	−0.800172	+	0.599771i	$0.795258\pi$
$828$	0.0918429	−	0.282663i	0.00319176	−	0.00982323i
$829$	−5.91878	+	18.2161i	−0.205568	+	0.632673i	0.794122	+	0.607759i	$0.207931\pi$
$829$	−5.91878	+	18.2161i	−0.205568	+	0.632673i	−0.999690	+	0.0249139i	$0.992069\pi$
$830$	−3.93575	−	33.3462i	−0.136612	−	1.15746i
$831$	−19.5948	−	4.16501i	−0.679737	−	0.144483i
$832$	1.49817	+	2.59491i	0.0519398	+	0.0899624i
$833$	−2.75682	−	0.585979i	−0.0955180	−	0.0203030i
$834$	3.63236	−	1.61723i	0.125778	−	0.0560002i
$835$	−5.03243	−	8.46504i	−0.174154	−	0.292945i
$836$	9.65865	+	8.67730i	0.334051	+	0.300111i
$837$	0.257696	+	0.187227i	0.00890729	+	0.00647153i
$838$	−17.6748	+	7.86935i	−0.610567	+	0.271842i
$839$	−4.36758	−	41.5548i	−0.150786	−	1.43463i	−0.764256	−	0.644913i	$-0.776894\pi$
$839$	−4.36758	−	41.5548i	−0.150786	−	1.43463i	0.613471	−	0.789718i	$-0.289773\pi$
$840$	−2.65274	−	2.87160i	−0.0915284	−	0.0990797i
$841$	24.1788	−	10.7651i	0.833753	−	0.371211i
$842$	−19.7976	+	21.9875i	−0.682270	+	0.757738i
$843$	4.20702			0.144897
$844$	4.57452	+	14.0789i	0.157461	+	0.484616i
$845$	4.39685	−	7.84513i	0.151256	−	0.269881i
$846$	−4.55560	+	0.968322i	−0.156625	+	0.0332916i
$847$	0.804795	−	2.47691i	0.0276531	−	0.0851075i
$848$	6.13073	−	4.45423i	0.210530	−	0.152959i
$849$	3.58293	+	6.20581i	0.122966	+	0.212983i
$850$	1.66500	−	1.94689i	0.0571091	−	0.0667779i
$851$	−0.280494	−	0.485829i	−0.00961519	−	0.0166540i
$852$	1.41041	+	13.4192i	0.0483200	+	0.459734i
$853$	4.28512	+	4.75910i	0.146720	+	0.162949i	0.812025	−	0.583623i	$-0.198365\pi$
$853$	4.28512	+	4.75910i	0.146720	+	0.162949i	−0.665305	+	0.746571i	$0.731699\pi$
$854$	−2.83471	+	8.72435i	−0.0970019	+	0.298541i
$855$	3.69074	−	8.60900i	0.126220	−	0.294422i
$856$	−5.03805	−	15.5055i	−0.172197	−	0.529967i
$857$	23.3278	−	40.4049i	0.796862	−	1.38021i	−0.124788	−	0.992183i	$-0.539825\pi$
$857$	23.3278	−	40.4049i	0.796862	−	1.38021i	0.921650	−	0.388022i	$-0.126842\pi$
$858$	12.4663	+	2.64979i	0.425592	+	0.0904623i
$859$	1.01427	−	9.65011i	0.0346064	−	0.329258i	−0.963498	−	0.267715i	$-0.913731\pi$
$859$	1.01427	−	9.65011i	0.0346064	−	0.329258i	0.998104	−	0.0615424i	$-0.0196020\pi$
$860$	−0.773993	−	0.547383i	−0.0263929	−	0.0186656i
$861$	−4.36628	−	1.94399i	−0.148803	−	0.0662512i
$862$	15.4759	+	11.2439i	0.527110	+	0.382968i
$863$	−18.1917	−	13.2171i	−0.619254	−	0.449915i	0.233407	−	0.972379i	$-0.425013\pi$
$863$	−18.1917	−	13.2171i	−0.619254	−	0.449915i	−0.852661	+	0.522465i	$0.825013\pi$
$864$	−5.16706	−	2.30052i	−0.175787	−	0.0782654i
$865$	34.5799	+	6.89010i	1.17575	+	0.234270i
$866$	1.02879	+	0.747459i	0.0349597	+	0.0253997i
$867$	7.38551	+	22.7303i	0.250825	+	0.771960i
$868$	−0.0344763	−	0.0597148i	−0.00117020	−	0.00202685i
$869$	34.3102	+	7.29285i	1.16389	+	0.247393i
$870$	16.1361	+	17.4674i	0.547065	+	0.592200i
$871$	9.89545	+	10.9900i	0.335294	+	0.372382i
$872$	−8.66063	−	9.61861i	−0.293286	−	0.325727i
$873$	−7.42769	+	5.39653i	−0.251389	+	0.182645i
$874$	1.28255	+	0.415153i	0.0433829	+	0.0140428i
$875$	10.7584	−	8.46419i	0.363701	−	0.286142i
$876$	−0.441706	+	0.765057i	−0.0149239	+	0.0258489i
$877$	4.15332	+	39.5162i	0.140248	+	1.33437i	0.807646	+	0.589667i	$0.200741\pi$
$877$	4.15332	+	39.5162i	0.140248	+	1.33437i	−0.667398	+	0.744701i	$0.732592\pi$
$878$	29.8737	−	6.34985i	1.00819	−	0.214297i
$879$	5.37137	+	5.96552i	0.181172	+	0.201212i
$880$	4.51967	+	4.89255i	0.152358	+	0.164928i
$881$	15.9626	+	49.1278i	0.537794	+	1.65516i	0.737534	+	0.675310i	$0.235990\pi$
$881$	15.9626	+	49.1278i	0.537794	+	1.65516i	−0.199740	+	0.979849i	$0.564010\pi$
$882$	−5.28643			−0.178003
$883$	14.4002	−	15.9930i	0.484604	−	0.538208i	−0.450408	−	0.892823i	$-0.648721\pi$
$883$	14.4002	−	15.9930i	0.484604	−	0.538208i	0.935012	+	0.354615i	$0.115388\pi$
$884$	−0.160471	+	1.52678i	−0.00539721	+	0.0513510i
$885$	11.8533	−	13.5072i	0.398444	−	0.454039i
$886$	1.41163	−	1.02561i	0.0474247	−	0.0344561i
$887$	−3.51374	+	33.4310i	−0.117980	+	1.12250i	0.762028	+	0.647544i	$0.224204\pi$
$887$	−3.51374	+	33.4310i	−0.117980	+	1.12250i	−0.880008	+	0.474960i	$0.842463\pi$
$888$	−2.36622	+	1.05351i	−0.0794052	+	0.0353535i
$889$	1.77598	+	0.790716i	0.0595644	+	0.0265198i
$890$	−30.3026	−	21.4306i	−1.01575	−	0.718355i
$891$	−14.1324	+	6.29216i	−0.473454	+	0.210795i
$892$	0.710135	+	2.18557i	0.0237771	+	0.0731783i
$893$	−4.41498	−	20.6581i	−0.147742	−	0.691298i
$894$	4.05558	+	12.4818i	0.135639	+	0.417453i
$895$	16.9545	+	11.9905i	0.566725	+	0.400799i
$896$	0.819266	+	0.909887i	0.0273697	+	0.0303972i
$897$	1.29431	−	0.275114i	0.0432158	−	0.00918580i
$898$	0.600869	+	5.71689i	0.0200513	+	0.190775i
$899$	0.209713	+	0.363233i	0.00699431	+	0.0121145i
$900$	2.29553	−	4.22127i	0.0765176	−	0.140709i
$901$	3.88260			0.129348
$902$	7.43915	+	3.31212i	0.247697	+	0.110282i
$903$	−0.725014	+	0.154107i	−0.0241270	+	0.00512835i
$904$	0.570168	−	1.75480i	0.0189635	−	0.0583637i
$905$	6.45061	+	10.8506i	0.214426	+	0.360685i
$906$	11.0151	−	12.2335i	0.365952	−	0.406431i
$907$	29.6839	−	51.4141i	0.985638	−	1.70718i	0.346574	−	0.938023i	$-0.387345\pi$
$907$	29.6839	−	51.4141i	0.985638	−	1.70718i	0.639064	−	0.769153i	$-0.279322\pi$
$908$	−5.24515	+	5.82533i	−0.174066	+	0.193320i
$909$	4.51907	−	2.01202i	0.149888	−	0.0667344i
$910$	−2.43519	+	7.83357i	−0.0807258	+	0.259680i
$911$	22.8828	−	16.6253i	0.758141	−	0.550821i	−0.140199	−	0.990123i	$-0.544774\pi$
$911$	22.8828	−	16.6253i	0.758141	−	0.550821i	0.898339	+	0.439302i	$0.144774\pi$
$912$	2.52530	−	5.68890i	0.0836212	−	0.188378i
$913$	36.1872	+	26.2916i	1.19762	+	0.870124i
$914$	−0.757276	−	7.20500i	−0.0250485	−	0.238320i
$915$	23.9205	−	0.305329i	0.790787	−	0.0100938i
$916$	−1.49060	+	14.1821i	−0.0492507	+	0.468590i
$917$	3.22645	+	0.685803i	0.106547	+	0.0226472i
$918$	−1.44895	−	2.50965i	−0.0478224	−	0.0828307i
$919$	9.23146	+	28.4115i	0.304518	+	0.937209i	0.979857	+	0.199702i	$0.0639974\pi$
$919$	9.23146	+	28.4115i	0.304518	+	0.937209i	−0.675339	+	0.737508i	$0.736003\pi$
$920$	0.635295	+	0.273190i	0.0209451	+	0.00900681i
$921$	−35.1825	+	7.47827i	−1.15930	+	0.246417i
$922$	2.66012	−	0.565425i	0.0876062	−	0.0186213i
$923$	22.9063	−	16.6424i	0.753969	−	0.547791i
$924$	5.20780			0.171324
$925$	−3.02191	−	8.55135i	−0.0993599	−	0.281167i
$926$	1.02573	−	1.77662i	0.0337077	−	0.0583834i
$927$	−8.97645	−	3.99657i	−0.294825	−	0.131265i
$928$	−4.98343	−	5.53466i	−0.163589	−	0.181684i
$929$	−34.3601	−	38.1608i	−1.12732	−	1.25202i	−0.964133	−	0.265420i	$-0.914489\pi$
$929$	−34.3601	−	38.1608i	−1.12732	−	1.25202i	−0.163187	−	0.986595i	$-0.552177\pi$
$930$	−0.118605	+	0.135155i	−0.00388922	+	0.00443189i
$931$	−0.0266026	−	23.9779i	−0.000871865	−	0.785844i
$932$	24.8398			0.813655
$933$	25.6655	+	5.45538i	0.840252	+	0.178601i
$934$	−15.6609	+	6.97270i	−0.512442	+	0.228154i
$935$	0.400003	+	3.38908i	0.0130815	+	0.110835i
$936$	0.300992	+	2.86375i	0.00983823	+	0.0936045i
$937$	1.55864	−	14.8294i	0.0509184	−	0.484456i	−0.939113	−	0.343609i	$-0.888351\pi$
$937$	1.55864	−	14.8294i	0.0509184	−	0.484456i	0.990031	−	0.140847i	$-0.0449827\pi$
$938$	4.88882	+	3.55193i	0.159626	+	0.115975i
$939$	−30.6194	+	22.2463i	−0.999227	+	0.725981i
$940$	−1.27021	−	10.7620i	−0.0414296	−	0.351018i
$941$	3.44178	−	32.7464i	0.112199	−	1.06750i	−0.783057	−	0.621949i	$-0.786341\pi$
$941$	3.44178	−	32.7464i	0.112199	−	1.06750i	0.895256	−	0.445552i	$-0.146992\pi$
$942$	−4.09683	−	12.6088i	−0.133482	−	0.410815i
$943$	0.845464			0.0275321
$944$	−3.76602	+	4.18259i	−0.122574	+	0.136132i
$945$	−4.97272	−	14.6649i	−0.161763	−	0.477048i
$946$	1.23526	−	0.262562i	0.0401617	−	0.00853664i
$947$	22.3378	+	24.8086i	0.725880	+	0.806172i	0.987269	−	0.159062i	$-0.0508470\pi$
$947$	22.3378	+	24.8086i	0.725880	+	0.806172i	−0.261388	+	0.965234i	$0.584180\pi$
$948$	−1.75763	−	16.7227i	−0.0570852	−	0.543129i
$949$	1.85374			0.0601749
$950$	19.1581	+	10.3907i	0.621572	+	0.337118i
$951$	−46.0959			−1.49476
$952$	0.0655718	+	0.623874i	0.00212520	+	0.0202199i
$953$	33.2086	+	36.8819i	1.07573	+	1.19472i	0.979934	+	0.199323i	$0.0638742\pi$
$953$	33.2086	+	36.8819i	1.07573	+	1.19472i	0.0957998	+	0.995401i	$0.469459\pi$
$954$	7.12339	−	1.51412i	0.230628	−	0.0490216i
$955$	−31.8991	+	23.8040i	−1.03223	+	0.770278i
$956$	12.8427	−	14.2633i	0.415362	−	0.461307i
$957$	−31.6780			−1.02400
$958$	−3.14964	−	9.69360i	−0.101760	−	0.313186i
$959$	−0.0296555	+	0.282153i	−0.000957626	+	0.00911121i
$960$	1.56105	−	2.78533i	0.0503828	−	0.0898961i
$961$	25.0770	−	18.2195i	0.808934	−	0.587725i
$962$	4.39712	+	3.19469i	0.141769	+	0.103001i
$963$	1.63773	−	15.5820i	0.0527751	−	0.502122i
$964$	−0.0578006	−	0.549936i	−0.00186163	−	0.0177122i
$965$	2.32982	+	2.52203i	0.0749994	+	0.0811870i
$966$	0.493954	−	0.219922i	0.0158927	−	0.00707589i
$967$	25.3891	+	5.39661i	0.816457	+	0.173543i	0.597167	−	0.802117i	$-0.296293\pi$
$967$	25.3891	+	5.39661i	0.816457	+	0.173543i	0.219289	+	0.975660i	$0.429626\pi$
$968$	2.12711			0.0683678
$969$	2.75998	−	1.59756i	0.0886632	−	0.0513209i
$970$	−10.9165	−	18.3627i	−0.350509	−	0.589590i
$971$	−6.00013	−	6.66381i	−0.192553	−	0.213852i	0.639136	−	0.769094i	$-0.279292\pi$
$971$	−6.00013	−	6.66381i	−0.192553	−	0.213852i	−0.831689	+	0.555242i	$0.812626\pi$
$972$	−6.39174	−	7.09874i	−0.205015	−	0.227692i
$973$	−3.11455	−	1.38669i	−0.0998480	−	0.0444552i
$974$	−6.81693	+	11.8073i	−0.218428	+	0.378329i
$975$	21.3859	−	0.546042i	0.684898	−	0.0174874i
$976$	−7.49226			−0.239821
$977$	18.9353	−	13.7573i	0.605792	−	0.440134i	−0.242138	−	0.970242i	$-0.577849\pi$
$977$	18.9353	−	13.7573i	0.605792	−	0.440134i	0.847930	+	0.530108i	$0.177849\pi$
$978$	16.8121	−	3.57353i	0.537593	−	0.114269i
$979$	48.3616	−	10.2796i	1.54564	−	0.328537i
$980$	1.12950	−	12.2484i	0.0360807	−	0.391262i
$981$	−3.84370	−	11.8297i	−0.122720	−	0.377693i
$982$	−7.15425	−	12.3915i	−0.228301	−	0.395429i
$983$	−4.25844	−	0.905159i	−0.135823	−	0.0288701i	0.139498	−	0.990222i	$-0.455451\pi$
$983$	−4.25844	−	0.905159i	−0.135823	−	0.0288701i	−0.275322	+	0.961352i	$0.588784\pi$
$984$	0.408040	−	3.88224i	0.0130078	−	0.123761i
$985$	−45.6984	−	32.3188i	−1.45607	−	1.02976i
$986$	−0.398860	−	3.79490i	−0.0127023	−	0.120854i
$987$	−6.85475	−	4.98027i	−0.218189	−	0.158524i
$988$	−12.9877	+	1.37963i	−0.413194	+	0.0438920i
$989$	0.106075	−	0.0770680i	0.00337299	−	0.00245062i
$990$	2.05555	+	6.06194i	0.0653296	+	0.192661i
$991$	30.3328	−	13.5051i	0.963555	−	0.429002i	0.136200	−	0.990681i	$-0.456511\pi$
$991$	30.3328	−	13.5051i	0.963555	−	0.429002i	0.827355	+	0.561679i	$0.189845\pi$
$992$	0.0376832	−	0.0418515i	0.00119644	−	0.00132879i
$993$	9.96330	−	17.2569i	0.316176	−	0.547633i
$994$	7.74158	−	8.59789i	0.245548	−	0.272709i
$995$	11.2712	−	2.54654i	0.357320	−	0.0807306i
$996$	6.62605	−	20.3929i	0.209955	−	0.646174i
$997$	−42.4898	+	9.03149i	−1.34567	+	0.286030i	−0.823743	−	0.566963i	$-0.808118\pi$
$997$	−42.4898	+	9.03149i	−1.34567	+	0.286030i	−0.521922	+	0.852993i	$0.674785\pi$
$998$	−19.6111	−	8.73145i	−0.620780	−	0.276389i
$999$	−10.2596			−0.324600

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.r.a.11.8	✓	200
19.7	even	3	inner	950.2.r.a.311.18	yes	200
25.16	even	5	inner	950.2.r.a.391.18	yes	200
475.216	even	15	inner	950.2.r.a.691.8	yes	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.r.a.11.8	✓	200	1.1	even	1	trivial
950.2.r.a.311.18	yes	200	19.7	even	3	inner
950.2.r.a.391.18	yes	200	25.16	even	5	inner
950.2.r.a.691.8	yes	200	475.216	even	15	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.r (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.104528 + 0.994522i) q^{2} +(-0.955473 - 1.06116i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(0.663784 - 2.13527i) q^{5} +(0.955473 - 1.06116i) q^{6} -1.22437 q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.100453 - 0.955746i) q^{9} +O(q^{10})\)	\(q+(0.104528 + 0.994522i) q^{2} +(-0.955473 - 1.06116i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(0.663784 - 2.13527i) q^{5} +(0.955473 - 1.06116i) q^{6} -1.22437 q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.100453 - 0.955746i) q^{9} +(2.19296 + 0.436951i) q^{10} +(-2.40985 + 1.75086i) q^{11} +(1.15522 + 0.839317i) q^{12} +(0.313204 - 2.97993i) q^{13} +(-0.127982 - 1.21767i) q^{14} +(-2.90009 + 1.33581i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.501156 + 0.106524i) q^{17} +0.961011 q^{18} +(0.00483604 + 4.35890i) q^{19} +(-0.205331 + 2.22662i) q^{20} +(1.16986 + 1.29926i) q^{21} +(-1.99317 - 2.21364i) q^{22} +(-0.282530 - 0.125791i) q^{23} +(-0.713966 + 1.23663i) q^{24} +(-4.11878 - 2.83472i) q^{25} +2.99635 q^{26} +(-4.57584 + 3.32454i) q^{27} +(1.19762 - 0.254562i) q^{28} +(-7.28487 + 1.54845i) q^{29} +(-1.63164 - 2.74458i) q^{30} +(-0.0174028 - 0.0535604i) q^{31} +(0.500000 + 0.866025i) q^{32} +(4.16049 + 0.884340i) q^{33} +(-0.0535554 + 0.509546i) q^{34} +(-0.812720 + 2.61437i) q^{35} +(0.100453 + 0.955746i) q^{36} +(1.46749 + 1.06620i) q^{37} +(-4.33451 + 0.460438i) q^{38} +(-3.46144 + 2.51489i) q^{39} +(-2.23589 + 0.0285395i) q^{40} +(-2.49741 + 1.11192i) q^{41} +(-1.16986 + 1.29926i) q^{42} +(-0.211978 + 0.367157i) q^{43} +(1.99317 - 2.21364i) q^{44} +(-1.97410 - 0.848904i) q^{45} +(0.0955690 - 0.294131i) q^{46} +(-4.74042 + 1.00761i) q^{47} +(-1.30448 - 0.580792i) q^{48} -5.50091 q^{49} +(2.38866 - 4.39253i) q^{50} +(-0.365802 - 0.633588i) q^{51} +(0.313204 + 2.97993i) q^{52} +(7.41240 - 1.57555i) q^{53} +(-3.78464 - 4.20327i) q^{54} +(2.13894 + 6.30788i) q^{55} +(0.378352 + 1.16445i) q^{56} +(4.62087 - 4.16994i) q^{57} +(-2.30144 - 7.08311i) q^{58} +(-5.14164 + 2.28921i) q^{59} +(2.55899 - 1.90959i) q^{60} +(-6.84452 - 3.04738i) q^{61} +(0.0514479 - 0.0229061i) q^{62} +(-0.122992 + 1.17019i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-6.15507 - 2.64681i) q^{65} +(-0.444605 + 4.23014i) q^{66} +(-3.30250 + 3.66780i) q^{67} -0.512352 q^{68} +(0.136466 + 0.419999i) q^{69} +(-2.68500 - 0.534991i) q^{70} +(6.32289 + 7.02228i) q^{71} +(-0.940010 + 0.199805i) q^{72} +(0.0646682 + 0.615276i) q^{73} +(-0.906960 + 1.57090i) q^{74} +(0.927292 + 7.07919i) q^{75} +(-0.910996 - 4.26264i) q^{76} +(2.95056 - 2.14371i) q^{77} +(-2.86293 - 3.17961i) q^{78} +(-7.87946 - 8.75103i) q^{79} +(-0.262097 - 2.22065i) q^{80} +(5.07994 + 1.07977i) q^{81} +(-1.36688 - 2.36751i) q^{82} +(-4.64032 - 14.2814i) q^{83} +(-1.41442 - 1.02764i) q^{84} +(0.560117 - 0.999397i) q^{85} +(-0.387303 - 0.172438i) q^{86} +(8.60365 + 6.25091i) q^{87} +(2.40985 + 1.75086i) q^{88} +(-15.1633 - 6.75114i) q^{89} +(0.637904 - 2.05202i) q^{90} +(-0.383478 + 3.64855i) q^{91} +(0.302510 + 0.0643004i) q^{92} +(-0.0402082 + 0.0696427i) q^{93} +(-1.49760 - 4.60913i) q^{94} +(9.31064 + 2.88304i) q^{95} +(0.441255 - 1.35804i) q^{96} +(-6.39262 - 7.09973i) q^{97} +(-0.575002 - 5.47078i) q^{98} +(1.43130 + 2.47909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 25 q^{2} + 25 q^{4} + q^{5} - 36 q^{7} + 50 q^{8} + 37 q^{9}+O(q^{10}) \) 200 * q - 25 * q^2 + 25 * q^4 + q^5 - 36 * q^7 + 50 * q^8 + 37 * q^9	\( 200 q - 25 q^{2} + 25 q^{4} + q^{5} - 36 q^{7} + 50 q^{8} + 37 q^{9} + 4 q^{10} - 2 q^{11} + 8 q^{13} + 7 q^{14} + 10 q^{15} + 25 q^{16} - 13 q^{17} - 216 q^{18} - 36 q^{19} - 2 q^{20} + 4 q^{22} - 13 q^{23} + 33 q^{25} - 64 q^{26} - 2 q^{28} + 12 q^{29} - 20 q^{30} + 12 q^{31} + 100 q^{32} - 12 q^{33} + 8 q^{34} - 22 q^{35} + 37 q^{36} + 8 q^{37} + 18 q^{38} + 28 q^{39} - q^{40} + 2 q^{41} + 70 q^{43} - 4 q^{44} + 60 q^{45} + 24 q^{46} - 22 q^{47} + 156 q^{49} + 26 q^{50} - 42 q^{51} + 8 q^{52} - 18 q^{53} - 10 q^{55} - 4 q^{56} + 74 q^{57} + 24 q^{58} + 50 q^{59} + 12 q^{61} - 4 q^{62} - 45 q^{63} - 50 q^{64} + 120 q^{65} + 2 q^{66} - 18 q^{67} - 84 q^{68} + 4 q^{69} - 13 q^{70} + 19 q^{71} - 17 q^{72} - 24 q^{73} + 4 q^{74} - 136 q^{75} - 6 q^{76} - 12 q^{77} - 26 q^{78} - 8 q^{79} + q^{80} - 63 q^{81} + 28 q^{82} + 16 q^{83} - 20 q^{84} - 5 q^{85} + 20 q^{86} - 64 q^{87} + 2 q^{88} + 16 q^{89} - 65 q^{90} + 72 q^{91} + 12 q^{92} - 8 q^{93} - 44 q^{94} - 73 q^{95} - 11 q^{97} - 27 q^{98} + 16 q^{99}+O(q^{100}) \) 200 * q - 25 * q^2 + 25 * q^4 + q^5 - 36 * q^7 + 50 * q^8 + 37 * q^9 + 4 * q^10 - 2 * q^11 + 8 * q^13 + 7 * q^14 + 10 * q^15 + 25 * q^16 - 13 * q^17 - 216 * q^18 - 36 * q^19 - 2 * q^20 + 4 * q^22 - 13 * q^23 + 33 * q^25 - 64 * q^26 - 2 * q^28 + 12 * q^29 - 20 * q^30 + 12 * q^31 + 100 * q^32 - 12 * q^33 + 8 * q^34 - 22 * q^35 + 37 * q^36 + 8 * q^37 + 18 * q^38 + 28 * q^39 - q^40 + 2 * q^41 + 70 * q^43 - 4 * q^44 + 60 * q^45 + 24 * q^46 - 22 * q^47 + 156 * q^49 + 26 * q^50 - 42 * q^51 + 8 * q^52 - 18 * q^53 - 10 * q^55 - 4 * q^56 + 74 * q^57 + 24 * q^58 + 50 * q^59 + 12 * q^61 - 4 * q^62 - 45 * q^63 - 50 * q^64 + 120 * q^65 + 2 * q^66 - 18 * q^67 - 84 * q^68 + 4 * q^69 - 13 * q^70 + 19 * q^71 - 17 * q^72 - 24 * q^73 + 4 * q^74 - 136 * q^75 - 6 * q^76 - 12 * q^77 - 26 * q^78 - 8 * q^79 + q^80 - 63 * q^81 + 28 * q^82 + 16 * q^83 - 20 * q^84 - 5 * q^85 + 20 * q^86 - 64 * q^87 + 2 * q^88 + 16 * q^89 - 65 * q^90 + 72 * q^91 + 12 * q^92 - 8 * q^93 - 44 * q^94 - 73 * q^95 - 11 * q^97 - 27 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more