LMFDB - Embedded newform 205.2.y.a.112.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [205,2,Mod(7,205)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("205.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(205, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([10, 39])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 205 = 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	205.y (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.63693324144$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$19$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			112.13
Character	$\chi$	$=$	205.112
Dual form			205.2.y.a.108.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.494362 + 0.359175i) q^{2} +(0.785792 + 1.89707i) q^{3} +(-0.502647 - 1.54699i) q^{4} +(2.00288 + 0.994219i) q^{5} +(-0.292915 + 1.22008i) q^{6} +(1.46658 - 2.39324i) q^{7} +(0.684809 - 2.10763i) q^{8} +(-0.860084 + 0.860084i) q^{9} +(0.633050 + 1.21089i) q^{10} +(-2.08662 + 2.44312i) q^{11} +(2.53977 - 2.16917i) q^{12} +(-1.26164 + 5.25511i) q^{13} +(1.58461 - 0.656368i) q^{14} +(-0.312255 + 4.58085i) q^{15} +(-1.53634 + 1.11622i) q^{16} +(-4.54370 - 3.88069i) q^{17} +(-0.734114 + 0.116272i) q^{18} +(-1.96330 + 3.20382i) q^{19} +(0.531303 - 3.59817i) q^{20} +(5.69256 + 0.901613i) q^{21} +(-1.90906 + 0.458324i) q^{22} +(-1.34561 - 8.49582i) q^{23} +(4.53643 - 0.357025i) q^{24} +(3.02306 + 3.98260i) q^{25} +(-2.51121 + 2.14478i) q^{26} +(3.38372 + 1.40158i) q^{27} +(-4.43948 - 1.06582i) q^{28} +(0.346789 - 4.40638i) q^{29} +(-1.79970 + 2.15245i) q^{30} +(-1.19616 - 0.388657i) q^{31} -5.59261 q^{32} +(-6.27442 - 2.03868i) q^{33} +(-0.852388 - 3.55045i) q^{34} +(5.31678 - 3.33527i) q^{35} +(1.76286 + 0.898220i) q^{36} +(3.26934 - 6.41643i) q^{37} +(-2.12131 + 0.878677i) q^{38} +(-10.9607 + 1.73600i) q^{39} +(3.46703 - 3.54047i) q^{40} +(2.59870 + 5.85207i) q^{41} +(2.49035 + 2.49035i) q^{42} +(-0.0532016 + 0.0732258i) q^{43} +(4.82831 + 1.99995i) q^{44} +(-2.57776 + 0.867533i) q^{45} +(2.38627 - 4.68332i) q^{46} +(-3.47815 + 2.13141i) q^{47} +(-3.32479 - 2.03743i) q^{48} +(-0.398796 - 0.782682i) q^{49} +(0.0640344 + 3.05466i) q^{50} +(3.79153 - 11.6691i) q^{51} +(8.76375 - 0.689722i) q^{52} +(0.908993 + 1.06429i) q^{53} +(1.16937 + 1.90824i) q^{54} +(-6.60825 + 2.81872i) q^{55} +(-4.03972 - 4.72991i) q^{56} +(-7.62061 - 1.20699i) q^{57} +(1.75410 - 2.05379i) q^{58} +(1.43568 - 1.97604i) q^{59} +(7.24347 - 1.81950i) q^{60} +(0.231902 - 1.46417i) q^{61} +(-0.451742 - 0.621769i) q^{62} +(0.797004 + 3.31976i) q^{63} +(0.307907 + 0.223708i) q^{64} +(-7.75164 + 9.27101i) q^{65} +(-2.36959 - 3.26146i) q^{66} +(-8.65274 - 0.680986i) q^{67} +(-3.71950 + 8.97966i) q^{68} +(15.0598 - 9.22865i) q^{69} +(3.82636 + 0.260825i) q^{70} +(-11.0438 - 9.43233i) q^{71} +(1.22374 + 2.40173i) q^{72} +11.6454i q^{73} +(3.92086 - 1.99778i) q^{74} +(-5.17978 + 8.86445i) q^{75} +(5.94311 + 1.42681i) q^{76} +(2.78677 + 8.57680i) q^{77} +(-6.04209 - 3.07860i) q^{78} +(-0.503369 + 1.21524i) q^{79} +(-4.18687 + 0.708190i) q^{80} +11.1695i q^{81} +(-0.817220 + 3.82643i) q^{82} +(-3.16779 + 3.16779i) q^{83} +(-1.46656 - 9.25951i) q^{84} +(-5.24224 - 12.2900i) q^{85} +(-0.0526018 + 0.0170914i) q^{86} +(8.63171 - 2.80461i) q^{87} +(3.72025 + 6.07089i) q^{88} +(2.35666 - 0.565784i) q^{89} +(-1.58594 - 0.496990i) q^{90} +(10.7264 + 10.7264i) q^{91} +(-12.4666 + 6.35203i) q^{92} +(-0.202626 - 2.57461i) q^{93} +(-2.48502 - 0.195575i) q^{94} +(-7.11755 + 4.46491i) q^{95} +(-4.39462 - 10.6096i) q^{96} +(0.237170 - 3.01353i) q^{97} +(0.0839701 - 0.530166i) q^{98} +(-0.306618 - 3.89596i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q - 16 q^{2} - 16 q^{3} - 68 q^{4} - 16 q^{5} - 32 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{9} - 12 q^{10} - 32 q^{11} + 20 q^{12} - 4 q^{13} - 16 q^{14} + 16 q^{15} - 76 q^{16} - 16 q^{17} + 28 q^{18} - 40 q^{20}+ \cdots - 72 q^{99}+O(q^{100}) $ 304 * q - 16 * q^2 - 16 * q^3 - 68 * q^4 - 16 * q^5 - 32 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^9 - 12 * q^10 - 32 * q^11 + 20 * q^12 - 4 * q^13 - 16 * q^14 + 16 * q^15 - 76 * q^16 - 16 * q^17 + 28 * q^18 - 40 * q^20 - 40 * q^21 - 40 * q^22 - 20 * q^23 + 40 * q^24 - 20 * q^25 - 24 * q^26 - 76 * q^27 - 4 * q^28 + 76 * q^29 - 8 * q^30 - 40 * q^31 + 48 * q^32 - 120 * q^33 + 16 * q^34 - 80 * q^35 - 24 * q^36 + 24 * q^37 - 20 * q^38 - 16 * q^39 + 56 * q^40 - 32 * q^41 + 176 * q^42 + 20 * q^43 + 16 * q^44 - 32 * q^46 + 40 * q^47 + 76 * q^48 - 8 * q^49 - 8 * q^50 - 24 * q^51 - 80 * q^52 - 16 * q^53 + 40 * q^54 + 48 * q^55 + 24 * q^56 + 12 * q^57 + 20 * q^58 - 40 * q^59 + 120 * q^60 + 4 * q^61 - 20 * q^62 + 108 * q^63 - 68 * q^64 - 92 * q^65 - 40 * q^66 + 8 * q^67 + 76 * q^68 + 32 * q^69 + 48 * q^70 - 40 * q^71 - 220 * q^72 + 144 * q^74 + 44 * q^75 - 48 * q^76 + 72 * q^77 - 212 * q^78 + 232 * q^80 - 72 * q^82 - 112 * q^83 - 256 * q^84 + 116 * q^85 - 40 * q^86 - 20 * q^87 + 92 * q^88 - 80 * q^89 + 212 * q^90 - 72 * q^91 + 20 * q^92 + 96 * q^93 - 40 * q^94 - 36 * q^95 - 8 * q^96 - 136 * q^97 - 12 * q^98 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/205\mathbb{Z}\right)^\times$.

$n$	$6$	$42$
$\chi(n)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.494362	+	0.359175i	0.349567	+	0.253975i	0.748687	−	0.662923i	$-0.230684\pi$
$2$	0.494362	+	0.359175i	0.349567	+	0.253975i	−0.399120	+	0.916899i	$0.630684\pi$
$3$	0.785792	+	1.89707i	0.453677	+	1.09527i	0.970913	+	0.239431i	$0.0769609\pi$
$3$	0.785792	+	1.89707i	0.453677	+	1.09527i	−0.517236	+	0.855843i	$0.673039\pi$
$4$	−0.502647	−	1.54699i	−0.251323	−	0.773494i
$5$	2.00288	+	0.994219i	0.895715	+	0.444628i
$5$	2.00288	+	0.994219i	0.895715	+	0.444628i
$6$	−0.292915	+	1.22008i	−0.119582	+	0.498094i
$7$	1.46658	−	2.39324i	0.554314	−	0.904558i	−0.445642	−	0.895211i	$-0.647025\pi$
$7$	1.46658	−	2.39324i	0.554314	−	0.904558i	0.999956	−	0.00934702i	$-0.00297529\pi$
$8$	0.684809	−	2.10763i	0.242117	−	0.745159i
$9$	−0.860084	+	0.860084i	−0.286695	+	0.286695i
$10$	0.633050	+	1.21089i	0.200188	+	0.382917i
$11$	−2.08662	+	2.44312i	−0.629140	+	0.736628i	−0.979823	−	0.199866i	$-0.935949\pi$
$11$	−2.08662	+	2.44312i	−0.629140	+	0.736628i	0.350683	+	0.936494i	$0.385949\pi$
$12$	2.53977	−	2.16917i	0.733168	−	0.626184i
$13$	−1.26164	+	5.25511i	−0.349916	+	1.45751i	0.468799	+	0.883305i	$0.344687\pi$
$13$	−1.26164	+	5.25511i	−0.349916	+	1.45751i	−0.818715	+	0.574200i	$0.805313\pi$
$14$	1.58461	−	0.656368i	0.423505	−	0.175422i
$15$	−0.312255	+	4.58085i	−0.0806238	+	1.18277i
$16$	−1.53634	+	1.11622i	−0.384085	+	0.279054i
$17$	−4.54370	−	3.88069i	−1.10201	−	0.941205i	−0.103438	−	0.994636i	$-0.532984\pi$
$17$	−4.54370	−	3.88069i	−1.10201	−	0.941205i	−0.998572	+	0.0534311i	$0.982984\pi$
$18$	−0.734114	+	0.116272i	−0.173032	+	0.0274056i
$19$	−1.96330	+	3.20382i	−0.450412	+	0.735006i	−0.994580	−	0.103970i	$-0.966845\pi$
$19$	−1.96330	+	3.20382i	−0.450412	+	0.735006i	0.544168	+	0.838976i	$0.316845\pi$
$20$	0.531303	−	3.59817i	0.118803	−	0.804576i
$21$	5.69256	+	0.901613i	1.24222	+	0.196748i
$22$	−1.90906	+	0.458324i	−0.407012	+	0.0977149i
$23$	−1.34561	−	8.49582i	−0.280578	−	1.77150i	−0.577296	−	0.816535i	$-0.695892\pi$
$23$	−1.34561	−	8.49582i	−0.280578	−	1.77150i	0.296718	−	0.954965i	$-0.404108\pi$
$24$	4.53643	−	0.357025i	0.925995	−	0.0728774i
$25$	3.02306	+	3.98260i	0.604612	+	0.796520i
$26$	−2.51121	+	2.14478i	−0.492489	+	0.420626i
$27$	3.38372	+	1.40158i	0.651198	+	0.269735i
$28$	−4.43948	−	1.06582i	−0.838982	−	0.201422i
$29$	0.346789	−	4.40638i	0.0643972	−	0.818244i	−0.876902	−	0.480670i	$-0.840394\pi$
$29$	0.346789	−	4.40638i	0.0643972	−	0.818244i	0.941299	−	0.337574i	$-0.109606\pi$
$30$	−1.79970	+	2.15245i	−0.328578	+	0.392981i
$31$	−1.19616	−	0.388657i	−0.214837	−	0.0698048i	0.199621	−	0.979873i	$-0.436029\pi$
$31$	−1.19616	−	0.388657i	−0.214837	−	0.0698048i	−0.414458	+	0.910068i	$0.636029\pi$
$32$	−5.59261			−0.988642
$33$	−6.27442	−	2.03868i	−1.09224	−	0.354889i
$34$	−0.852388	−	3.55045i	−0.146183	−	0.608897i
$35$	5.31678	−	3.33527i	0.898699	−	0.563763i
$36$	1.76286	+	0.898220i	0.293809	+	0.149703i
$37$	3.26934	−	6.41643i	0.537475	−	1.05486i	−0.449394	−	0.893334i	$-0.648360\pi$
$37$	3.26934	−	6.41643i	0.537475	−	1.05486i	0.986869	−	0.161521i	$-0.0516400\pi$
$38$	−2.12131	+	0.878677i	−0.344123	+	0.142540i
$39$	−10.9607	+	1.73600i	−1.75512	+	0.277983i
$40$	3.46703	−	3.54047i	0.548186	−	0.559798i
$41$	2.59870	+	5.85207i	0.405849	+	0.913940i
$41$	2.59870	+	5.85207i	0.405849	+	0.913940i
$42$	2.49035	+	2.49035i	0.384269	+	0.384269i
$43$	−0.0532016	+	0.0732258i	−0.00811317	+	0.0111668i	−0.813054	−	0.582188i	$-0.802197\pi$
$43$	−0.0532016	+	0.0732258i	−0.00811317	+	0.0111668i	0.804941	+	0.593355i	$0.202197\pi$
$44$	4.82831	+	1.99995i	0.727895	+	0.301504i
$45$	−2.57776	+	0.867533i	−0.384269	+	0.129324i
$46$	2.38627	−	4.68332i	0.351837	−	0.690518i
$47$	−3.47815	+	2.13141i	−0.507340	+	0.310899i	−0.752509	−	0.658582i	$-0.771157\pi$
$47$	−3.47815	+	2.13141i	−0.507340	+	0.310899i	0.245169	+	0.969480i	$0.421157\pi$
$48$	−3.32479	−	2.03743i	−0.479891	−	0.294078i
$49$	−0.398796	−	0.782682i	−0.0569709	−	0.111812i
$50$	0.0640344	+	3.05466i	0.00905583	+	0.431994i
$51$	3.79153	−	11.6691i	0.530920	−	1.63400i
$52$	8.76375	−	0.689722i	1.21531	−	0.0956472i
$53$	0.908993	+	1.06429i	0.124860	+	0.146192i	0.819314	−	0.573344i	$-0.194354\pi$
$53$	0.908993	+	1.06429i	0.124860	+	0.146192i	−0.694455	+	0.719537i	$0.744354\pi$
$54$	1.16937	+	1.90824i	0.159131	+	0.259679i
$55$	−6.60825	+	2.81872i	−0.891056	+	0.380076i
$56$	−4.03972	−	4.72991i	−0.539831	−	0.632060i
$57$	−7.62061	−	1.20699i	−1.00937	−	0.159869i
$58$	1.75410	−	2.05379i	0.230325	−	0.269676i
$59$	1.43568	−	1.97604i	0.186910	−	0.257259i	−0.705271	−	0.708938i	$-0.749175\pi$
$59$	1.43568	−	1.97604i	0.186910	−	0.257259i	0.892181	+	0.451679i	$0.149175\pi$
$60$	7.24347	−	1.81950i	0.935129	−	0.234896i
$61$	0.231902	−	1.46417i	0.0296920	−	0.187468i	−0.968384	−	0.249462i	$-0.919746\pi$
$61$	0.231902	−	1.46417i	0.0296920	−	0.187468i	0.998076	+	0.0619945i	$0.0197461\pi$
$62$	−0.451742	−	0.621769i	−0.0573713	−	0.0789648i
$63$	0.797004	+	3.31976i	0.100413	+	0.418251i
$64$	0.307907	+	0.223708i	0.0384884	+	0.0279635i
$65$	−7.75164	+	9.27101i	−0.961473	+	1.14993i
$66$	−2.36959	−	3.26146i	−0.291677	−	0.401458i
$67$	−8.65274	−	0.680986i	−1.05710	−	0.0831956i	−0.462026	−	0.886866i	$-0.652877\pi$
$67$	−8.65274	−	0.680986i	−1.05710	−	0.0831956i	−0.595074	+	0.803671i	$0.702877\pi$
$68$	−3.71950	+	8.97966i	−0.451055	+	1.08894i
$69$	15.0598	−	9.22865i	1.81299	−	1.11100i
$70$	3.82636	+	0.260825i	0.457338	+	0.0311745i
$71$	−11.0438	−	9.43233i	−1.31066	−	1.11941i	−0.984743	−	0.174014i	$-0.944326\pi$
$71$	−11.0438	−	9.43233i	−1.31066	−	1.11941i	−0.325919	−	0.945398i	$-0.605674\pi$
$72$	1.22374	+	2.40173i	0.144219	+	0.283046i
$73$			11.6454i			1.36299i	0.731821	+	0.681497i	$0.238671\pi$
$73$			11.6454i			1.36299i	−0.731821	+	0.681497i	$0.761329\pi$
$74$	3.92086	−	1.99778i	0.455791	−	0.232237i
$75$	−5.17978	+	8.86445i	−0.598109	+	1.02358i
$76$	5.94311	+	1.42681i	0.681722	+	0.163667i
$77$	2.78677	+	8.57680i	0.317582	+	0.977417i
$78$	−6.04209	−	3.07860i	−0.684131	−	0.348582i
$79$	−0.503369	+	1.21524i	−0.0566335	+	0.136725i	−0.949664	−	0.313272i	$-0.898575\pi$
$79$	−0.503369	+	1.21524i	−0.0566335	+	0.136725i	0.893030	+	0.449997i	$0.148575\pi$
$80$	−4.18687	+	0.708190i	−0.468106	+	0.0791781i
$81$			11.1695i			1.24106i
$82$	−0.817220	+	3.82643i	−0.0902469	+	0.422559i
$83$	−3.16779	+	3.16779i	−0.347710	+	0.347710i	−0.859256	−	0.511546i	$-0.829073\pi$
$83$	−3.16779	+	3.16779i	−0.347710	+	0.347710i	0.511546	+	0.859256i	$0.329073\pi$
$84$	−1.46656	−	9.25951i	−0.160015	−	1.01030i
$85$	−5.24224	−	12.2900i	−0.568600	−	1.33304i
$86$	−0.0526018	+	0.0170914i	−0.00567220	+	0.00184301i
$87$	8.63171	−	2.80461i	0.925416	−	0.300686i
$88$	3.72025	+	6.07089i	0.396580	+	0.647159i
$89$	2.35666	−	0.565784i	0.249805	−	0.0599730i	−0.106609	−	0.994301i	$-0.533999\pi$
$89$	2.35666	−	0.565784i	0.249805	−	0.0599730i	0.356414	+	0.934328i	$0.383999\pi$
$90$	−1.58594	−	0.496990i	−0.167173	−	0.0523874i
$91$	10.7264	+	10.7264i	1.12443	+	1.12443i
$92$	−12.4666	+	6.35203i	−1.29973	+	0.662245i
$93$	−0.202626	−	2.57461i	−0.0210113	−	0.266974i
$94$	−2.48502	−	0.195575i	−0.256310	−	0.0201720i
$95$	−7.11755	+	4.46491i	−0.730245	+	0.458090i
$96$	−4.39462	−	10.6096i	−0.448525	−	1.08283i
$97$	0.237170	−	3.01353i	0.0240809	−	0.305977i	−0.973068	−	0.230518i	$-0.925958\pi$
$97$	0.237170	−	3.01353i	0.0240809	−	0.305977i	0.997149	−	0.0754589i	$-0.0240422\pi$
$98$	0.0839701	−	0.530166i	0.00848226	−	0.0535549i
$99$	−0.306618	−	3.89596i	−0.0308163	−	0.391558i
$100$	4.64150	−	6.67848i	0.464150	−	0.667848i
$101$	11.9149	+	7.30148i	1.18558	+	0.726525i	0.968350	−	0.249596i	$-0.0802977\pi$
$101$	11.9149	+	7.30148i	1.18558	+	0.726525i	0.217231	+	0.976120i	$0.430298\pi$
$102$	6.06565	−	4.40695i	0.600589	−	0.436354i
$103$	14.6261	−	10.6265i	1.44115	−	1.04706i	0.453349	−	0.891333i	$-0.350229\pi$
$103$	14.6261	−	10.6265i	1.44115	−	1.04706i	0.987801	−	0.155724i	$-0.0497709\pi$
$104$	10.2118	+	6.25781i	1.00135	+	0.613629i
$105$	10.5051	+	7.46547i	1.02519	+	0.728555i
$106$	0.0671039	+	0.852635i	0.00651770	+	0.0828153i
$107$	2.21798	−	14.0038i	0.214420	−	1.35380i	−0.612052	−	0.790818i	$-0.709656\pi$
$107$	2.21798	−	14.0038i	0.214420	−	1.35380i	0.826472	−	0.562978i	$-0.190344\pi$
$108$	0.467416	−	5.93908i	0.0449771	−	0.571488i
$109$	6.27071	+	15.1388i	0.600625	+	1.45004i	0.872939	+	0.487828i	$0.162211\pi$
$109$	6.27071	+	15.1388i	0.600625	+	1.45004i	−0.272315	+	0.962208i	$0.587789\pi$
$110$	−4.27928	−	0.980051i	−0.408014	−	0.0934442i
$111$	14.7414	+	1.16018i	1.39920	+	0.110119i
$112$	0.418209	+	5.31384i	0.0395170	+	0.502111i
$113$	6.11650	−	3.11651i	0.575392	−	0.293177i	−0.141978	−	0.989870i	$-0.545346\pi$
$113$	6.11650	−	3.11651i	0.575392	−	0.293177i	0.717369	+	0.696693i	$0.245346\pi$
$114$	−3.33382	−	3.33382i	−0.312241	−	0.312241i
$115$	5.75161	−	18.3539i	0.536341	−	1.71151i
$116$	−6.99092	+	1.67837i	−0.649091	+	0.155833i
$117$	−3.43472	−	5.60495i	−0.317540	−	0.518178i
$118$	1.41949	−	0.461221i	0.130675	−	0.0424588i
$119$	−15.9511	+	5.18282i	−1.46223	+	0.475108i
$120$	9.44089	+	3.79513i	0.861831	+	0.346446i
$121$	0.105934	+	0.668842i	0.00963037	+	0.0608038i
$122$	0.640538	−	0.640538i	0.0579916	−	0.0579916i
$123$	−9.05975	+	9.52843i	−0.816890	+	0.859149i
$124$			2.04581i			0.183719i
$125$	2.09525	+	10.9823i	0.187405	+	0.982283i
$126$	−0.798367	+	1.92743i	−0.0711242	+	0.171709i
$127$	1.43753	+	0.732460i	0.127560	+	0.0649953i	0.516606	−	0.856223i	$-0.327195\pi$
$127$	1.43753	+	0.732460i	0.127560	+	0.0649953i	−0.389046	+	0.921218i	$0.627195\pi$
$128$	3.52829	+	10.8590i	0.311860	+	0.959805i
$129$	−0.180720	−	0.0433870i	−0.0159115	−	0.00382001i
$130$	−7.16204	+	1.79904i	−0.628152	+	0.157786i
$131$	−1.01371	+	0.516513i	−0.0885687	+	0.0451280i	−0.497714	−	0.867341i	$-0.665827\pi$
$131$	−1.01371	+	0.516513i	−0.0885687	+	0.0451280i	0.409145	+	0.912469i	$0.365827\pi$
$132$			10.7312i			0.934030i
$133$	4.78816	+	9.39729i	0.415186	+	0.814848i
$134$	−4.03300	−	3.44450i	−0.348398	−	0.297560i
$135$	5.38371	+	6.17137i	0.463356	+	0.531147i
$136$	−11.2906	+	6.91889i	−0.968162	+	0.593290i
$137$	2.66754	−	6.44001i	0.227903	−	0.550207i	−0.768019	−	0.640428i	$-0.778757\pi$
$137$	2.66754	−	6.44001i	0.227903	−	0.550207i	0.995922	+	0.0902205i	$0.0287572\pi$
$138$	10.7597	+	0.846807i	0.915926	+	0.0720850i
$139$	2.65673	+	3.65668i	0.225341	+	0.310155i	0.906685	−	0.421808i	$-0.138604\pi$
$139$	2.65673	+	3.65668i	0.225341	+	0.310155i	−0.681344	+	0.731963i	$0.738604\pi$
$140$	−7.83208	−	6.54853i	−0.661931	−	0.553452i
$141$	−6.77654	−	4.92345i	−0.570688	−	0.414629i
$142$	−2.07180	−	8.62966i	−0.173861	−	0.724185i
$143$	−10.2063	−	14.0478i	−0.853493	−	1.17473i
$144$	0.361342	−	2.28142i	0.0301118	−	0.190118i
$145$	5.07548	−	8.48066i	0.421496	−	0.704280i
$146$	−4.18275	+	5.75706i	−0.346167	+	0.476457i
$147$	1.17143	−	1.37157i	0.0966180	−	0.113125i
$148$	−11.5695	−	1.83242i	−0.951004	−	0.150624i
$149$	4.33976	+	5.08121i	0.355527	+	0.416269i	0.909130	−	0.416512i	$-0.136748\pi$
$149$	4.33976	+	5.08121i	0.355527	+	0.416269i	−0.553603	+	0.832781i	$0.686748\pi$
$150$	−5.74458	+	2.52180i	−0.469043	+	0.205904i
$151$	5.05031	+	8.24135i	0.410988	+	0.670672i	0.989423	−	0.145056i	$-0.0463364\pi$
$151$	5.05031	+	8.24135i	0.410988	+	0.670672i	−0.578435	+	0.815728i	$0.696336\pi$
$152$	5.40796	+	6.33191i	0.438644	+	0.513586i
$153$	7.24568	−	0.570247i	0.585778	−	0.0461018i
$154$	−1.70290	+	5.24099i	−0.137224	+	0.422331i
$155$	−2.00936	−	1.96768i	−0.161396	−	0.158048i
$156$	8.19493	+	16.0835i	0.656120	+	1.28771i
$157$	−1.13345	−	0.694579i	−0.0904592	−	0.0554334i	0.476533	−	0.879156i	$-0.341893\pi$
$157$	−1.13345	−	0.694579i	−0.0904592	−	0.0554334i	−0.566992	+	0.823723i	$0.691893\pi$
$158$	−0.685331	+	0.419972i	−0.0545220	+	0.0334111i
$159$	−1.30476	+	2.56074i	−0.103474	+	0.203080i
$160$	−11.2013	−	5.56027i	−0.885542	−	0.439578i
$161$	−22.3059	−	9.23942i	−1.75795	−	0.728168i
$162$	−4.01182	+	5.52180i	−0.315199	+	0.433834i
$163$	−8.74310	−	8.74310i	−0.684813	−	0.684813i	0.276268	−	0.961081i	$-0.410902\pi$
$163$	−8.74310	−	8.74310i	−0.684813	−	0.684813i	−0.961081	+	0.276268i	$0.910902\pi$
$164$	7.74686	−	6.96168i	0.604928	−	0.543616i
$165$	−10.5400	−	10.3214i	−0.820539	−	0.803518i
$166$	−2.70383	+	0.428244i	−0.209858	+	0.0332382i
$167$	−9.62614	+	3.98728i	−0.744893	+	0.308545i	−0.722656	−	0.691208i	$-0.757079\pi$
$167$	−9.62614	+	3.98728i	−0.744893	+	0.308545i	−0.0222373	+	0.999753i	$0.507079\pi$
$168$	5.79858	−	11.3804i	0.447370	−	0.878013i
$169$	−14.4414	−	7.35824i	−1.11087	−	0.566018i
$170$	1.82269	−	7.95859i	0.139794	−	0.610396i
$171$	−1.06695	−	4.44415i	−0.0815915	−	0.339853i
$172$	0.140021	+	0.0454956i	0.0106765	+	0.00346901i
$173$	4.43967			0.337542			0.168771	−	0.985655i	$-0.446020\pi$
$173$	4.43967			0.337542			0.168771	+	0.985655i	$0.446020\pi$
$174$	5.27454	+	1.71380i	0.399862	+	0.129923i
$175$	13.9649	−	1.39410i	1.05564	−	0.105384i
$176$	0.478710	−	6.08259i	0.0360841	−	0.458492i
$177$	4.87684	+	1.17083i	0.366566	+	0.0880046i
$178$	1.36826	+	0.566752i	0.102555	+	0.0424798i
$179$	−2.97665	+	2.54230i	−0.222485	+	0.190020i	−0.753703	−	0.657215i	$-0.771734\pi$
$179$	−2.97665	+	2.54230i	−0.222485	+	0.190020i	0.531218	+	0.847235i	$0.321734\pi$
$180$	2.63776	+	3.55169i	0.196607	+	0.264728i
$181$	−4.54815	+	0.357947i	−0.338061	+	0.0266060i	−0.246354	−	0.969180i	$-0.579232\pi$
$181$	−4.54815	+	0.357947i	−0.338061	+	0.0266060i	−0.0917076	+	0.995786i	$0.529232\pi$
$182$	1.45007	+	9.15541i	0.107487	+	0.678644i
$183$	2.95986	−	0.710600i	0.218799	−	0.0525290i
$184$	−18.8275	−	2.98198i	−1.38798	−	0.219835i
$185$	12.9274	−	9.60091i	0.950443	−	0.705873i
$186$	0.824564	−	1.34557i	0.0604600	−	0.0986617i
$187$	18.9620	−	3.00328i	1.38664	−	0.219622i
$188$	5.04555	+	4.30931i	0.367985	+	0.314289i
$189$	8.31681	−	6.04252i	0.604959	−	0.439528i
$190$	−5.12234	−	0.349165i	−0.371613	−	0.0253311i
$191$	3.07829	−	1.27507i	0.222737	−	0.0922608i	−0.268524	−	0.963273i	$-0.586536\pi$
$191$	3.07829	−	1.27507i	0.222737	−	0.0922608i	0.491262	+	0.871012i	$0.336536\pi$
$192$	−0.182438	+	0.759909i	−0.0131663	+	0.0548417i
$193$	15.4853	−	13.2257i	1.11466	−	0.952006i	0.115509	−	0.993306i	$-0.463150\pi$
$193$	15.4853	−	13.2257i	1.11466	−	0.952006i	0.999147	+	0.0413001i	$0.0131500\pi$
$194$	1.19963	−	1.40459i	0.0861285	−	0.100844i
$195$	−23.6789	−	7.42032i	−1.69568	−	0.531380i
$196$	−1.01035	+	1.01035i	−0.0721675	+	0.0721675i
$197$	−1.75928	+	5.41450i	−0.125343	+	0.385767i	−0.993963	−	0.109711i	$-0.965007\pi$
$197$	−1.75928	+	5.41450i	−0.125343	+	0.385767i	0.868620	+	0.495479i	$0.165007\pi$
$198$	1.24775	−	2.03614i	0.0886738	−	0.144702i
$199$	−5.70848	+	23.7775i	−0.404664	+	1.68555i	0.282681	+	0.959214i	$0.408776\pi$
$199$	−5.70848	+	23.7775i	−0.404664	+	1.68555i	−0.687345	+	0.726331i	$0.741224\pi$
$200$	10.4641	−	3.64416i	0.739920	−	0.257681i
$201$	−5.50738	−	16.9500i	−0.388460	−	1.19556i
$202$	3.26779	+	7.88913i	0.229921	+	0.555077i
$203$	−10.0369	−	7.29224i	−0.704453	−	0.511815i
$204$	−19.9578			−1.39733
$205$	−0.613354	+	14.3047i	−0.0428385	+	0.999082i
$206$	11.0473			0.769705
$207$	8.46445	+	6.14978i	0.588320	+	0.427439i
$208$	−3.92753	−	9.48190i	−0.272325	−	0.657452i
$209$	−3.73064	−	11.4817i	−0.258054	−	0.794208i
$210$	2.51192	+	7.46383i	0.173339	+	0.515053i
$211$	−0.270212	+	1.12551i	−0.0186022	+	0.0774836i	−0.980899	−	0.194518i	$-0.937686\pi$
$211$	−0.270212	+	1.12551i	−0.0186022	+	0.0774836i	0.962297	+	0.272002i	$0.0876857\pi$
$212$	1.18955	−	1.94117i	0.0816985	−	0.133320i
$213$	9.21563	−	28.3628i	0.631444	−	1.94339i
$214$	6.12630	−	6.12630i	0.418785	−	0.418785i
$215$	−0.179359	+	0.0937684i	−0.0122322	+	0.00639495i
$216$	5.27122	−	6.17181i	0.358661	−	0.419938i
$217$	−2.68441	+	2.29270i	−0.182230	+	0.155639i
$218$	−2.33749	+	9.73635i	−0.158315	+	0.659429i
$219$	−22.0922	+	9.15088i	−1.49285	+	0.618359i
$220$	7.68214	+	8.80606i	0.517929	+	0.593704i
$221$	26.1260	−	18.9816i	1.75742	−	1.27684i
$222$	6.87091	+	5.86831i	0.461145	+	0.393855i
$223$	−6.37875	+	1.01029i	−0.427152	+	0.0676543i	−0.366310	−	0.930493i	$-0.619379\pi$
$223$	−6.37875	+	1.01029i	−0.427152	+	0.0676543i	−0.0608429	+	0.998147i	$0.519379\pi$
$224$	−8.20199	+	13.3844i	−0.548018	+	0.894284i
$225$	−6.02545	−	0.825287i	−0.401697	−	0.0550191i
$226$	4.14314	+	0.656209i	0.275598	+	0.0436504i
$227$	−11.4749	+	2.75487i	−0.761615	+	0.182847i	−0.595606	−	0.803277i	$-0.703088\pi$
$227$	−11.4749	+	2.75487i	−0.761615	+	0.182847i	−0.166009	+	0.986124i	$0.553088\pi$
$228$	1.96328	+	12.3957i	0.130022	+	0.820924i
$229$	24.1219	−	1.89843i	1.59402	−	0.125452i	0.749879	−	0.661575i	$-0.230112\pi$
$229$	24.1219	−	1.89843i	1.59402	−	0.125452i	0.844140	+	0.536123i	$0.180112\pi$
$230$	9.43566	−	7.00766i	0.622169	−	0.462071i
$231$	−14.0810	+	12.0263i	−0.926459	+	0.791271i
$232$	−9.04951	−	3.74843i	−0.594129	−	0.246096i
$233$	7.10552	+	1.70588i	0.465498	+	0.111756i	0.459408	−	0.888225i	$-0.348062\pi$
$233$	7.10552	+	1.70588i	0.465498	+	0.111756i	0.00608984	+	0.999981i	$0.498062\pi$
$234$	0.315164	−	4.00454i	0.0206029	−	0.261785i
$235$	−9.08541	+	0.810924i	−0.592667	+	0.0528988i
$236$	−3.77856	−	1.22773i	−0.245963	−	0.0799182i
$237$	−2.70094			−0.175445
$238$	−9.74716	−	3.16704i	−0.631814	−	0.205289i
$239$	1.41543	+	5.89568i	0.0915564	+	0.381360i	0.999269	−	0.0382330i	$-0.0121729\pi$
$239$	1.41543	+	5.89568i	0.0915564	+	0.381360i	−0.907712	+	0.419593i	$0.862173\pi$
$240$	−4.63350	−	7.38629i	−0.299091	−	0.476783i
$241$	−22.8424	−	11.6388i	−1.47141	−	0.749719i	−0.479603	−	0.877486i	$-0.659219\pi$
$241$	−22.8424	−	11.6388i	−1.47141	−	0.749719i	−0.991804	+	0.127766i	$0.959219\pi$
$242$	−0.187862	+	0.368699i	−0.0120762	+	0.0237009i
$243$	−11.0382	+	4.57218i	−0.708102	+	0.293305i
$244$	−2.38162	+	0.377211i	−0.152468	+	0.0241485i
$245$	−0.0205844	−	1.96411i	−0.00131509	−	0.125482i
$246$	−7.90118	+	1.45646i	−0.503761	+	0.0928603i
$247$	−14.3594	−	14.3594i	−0.913668	−	0.913668i
$248$	−1.63829	+	2.25491i	−0.104031	+	0.143187i
$249$	−8.49873	−	3.52029i	−0.538585	−	0.223089i
$250$	−2.90874	+	6.18178i	−0.183965	+	0.390970i
$251$	−6.01782	+	11.8106i	−0.379841	+	0.745480i	−0.999215	−	0.0396160i	$-0.987387\pi$
$251$	−6.01782	+	11.8106i	−0.379841	+	0.745480i	0.619374	+	0.785096i	$0.287387\pi$
$252$	4.73502	−	2.90162i	0.298278	−	0.182785i
$253$	23.5641	+	14.4401i	1.48146	+	0.907840i
$254$	0.447581	+	0.878427i	0.0280837	+	0.0551174i
$255$	19.1956	−	19.6023i	1.20208	−	1.22754i
$256$	−1.92080	+	5.91160i	−0.120050	+	0.369475i
$257$	−18.6919	+	1.47109i	−1.16597	+	0.0917639i	−0.646630	−	0.762804i	$-0.723822\pi$
$257$	−18.6919	+	1.47109i	−1.16597	+	0.0917639i	−0.519340	+	0.854567i	$0.673822\pi$
$258$	−0.0737575	−	0.0863590i	−0.00459194	−	0.00537648i
$259$	−10.5613	−	17.2345i	−0.656248	−	1.07090i
$260$	18.2385	+	7.33165i	1.13110	+	0.454690i
$261$	3.49158	+	4.08812i	0.216124	+	0.253048i
$262$	−0.686661	−	0.108756i	−0.0424221	−	0.00671900i
$263$	13.2601	−	15.5256i	0.817655	−	0.957351i	−0.182008	−	0.983297i	$-0.558260\pi$
$263$	13.2601	−	15.5256i	0.817655	−	0.957351i	0.999663	+	0.0259456i	$0.00825967\pi$
$264$	−8.59356	+	11.8280i	−0.528897	+	0.727964i
$265$	0.762464	+	3.03539i	0.0468378	+	0.186463i
$266$	−1.00819	+	6.36545i	−0.0618160	+	0.390291i
$267$	2.92518	+	4.02616i	0.179018	+	0.246397i
$268$	3.29580	+	13.7280i	0.201323	+	0.838570i
$269$	−12.7186	−	9.24057i	−0.775464	−	0.563408i	0.128150	−	0.991755i	$-0.459096\pi$
$269$	−12.7186	−	9.24057i	−0.775464	−	0.563408i	−0.903614	+	0.428347i	$0.859096\pi$
$270$	0.444903	+	4.98459i	0.0270759	+	0.303352i
$271$	6.44162	+	8.86613i	0.391301	+	0.538579i	0.958534	−	0.284978i	$-0.0919863\pi$
$271$	6.44162	+	8.86613i	0.391301	+	0.538579i	−0.567233	+	0.823557i	$0.691986\pi$
$272$	11.3124	+	0.890302i	0.685913	+	0.0539825i
$273$	−11.9200	+	28.7775i	−0.721433	+	1.74169i
$274$	3.63182	−	2.22558i	0.219406	−	0.134452i
$275$	−16.0380	−	0.924487i	−0.967125	−	0.0557487i
$276$	−21.8464	−	18.6586i	−1.31500	−	1.12311i
$277$	6.47078	+	12.6996i	0.388791	+	0.763046i	0.999587	−	0.0287425i	$-0.00915028\pi$
$277$	6.47078	+	12.6996i	0.388791	+	0.763046i	−0.610796	+	0.791788i	$0.709150\pi$
$278$			2.76195i			0.165651i
$279$	1.36308	−	0.694522i	0.0816053	−	0.0415800i
$280$	−3.38852	−	13.4898i	−0.202503	−	0.806170i
$281$	9.12643	+	2.19106i	0.544437	+	0.130708i	0.496329	−	0.868134i	$-0.334681\pi$
$281$	9.12643	+	2.19106i	0.544437	+	0.130708i	0.0481079	+	0.998842i	$0.484681\pi$
$282$	−1.58169	−	4.86793i	−0.0941881	−	0.289881i
$283$	18.2561	+	9.30196i	1.08521	+	0.552944i	0.902705	−	0.430260i	$-0.141578\pi$
$283$	18.2561	+	9.30196i	1.08521	+	0.552944i	0.182509	+	0.983204i	$0.441578\pi$
$284$	−9.04055	+	21.8258i	−0.536458	+	1.29512i
$285$	−14.0632	−	9.99400i	−0.833030	−	0.591993i
$286$		−	10.6105i		−	0.627414i
$287$	17.8166	+	2.36321i	1.05168	+	0.139496i
$288$	4.81011	−	4.81011i	0.283438	−	0.283438i
$289$	2.92610	+	18.4747i	0.172123	+	1.08674i
$290$	5.55517	−	2.36953i	0.326211	−	0.139144i
$291$	5.90323	−	1.91808i	0.346054	−	0.112440i
$292$	18.0153	−	5.85353i	1.05427	−	0.342552i
$293$	6.70131	+	10.9356i	0.391495	+	0.638862i	0.986291	−	0.165015i	$-0.0527672\pi$
$293$	6.70131	+	10.9356i	0.391495	+	0.638862i	−0.594796	+	0.803877i	$0.702767\pi$
$294$	1.07175	−	0.257303i	0.0625055	−	0.0150062i
$295$	4.84011	−	2.53040i	0.281802	−	0.147326i
$296$	−11.2846	−	11.2846i	−0.655902	−	0.655902i
$297$	−10.4848	+	5.34227i	−0.608389	+	0.309990i
$298$	0.320371	+	4.07069i	0.0185586	+	0.235809i
$299$	46.3441	+	3.64736i	2.68015	+	0.210932i
$300$	16.3168	+	3.55736i	0.942050	+	0.205385i
$301$	0.0972223	+	0.234715i	0.00560380	+	0.0135288i
$302$	−0.463408	+	5.88816i	−0.0266662	+	0.338826i
$303$	−4.48876	+	28.3409i	−0.257873	+	1.62814i
$304$	−0.559854	−	7.11362i	−0.0321098	−	0.407994i
$305$	1.92018	−	2.70200i	0.109949	−	0.154716i
$306$	3.78681	+	2.32056i	0.216477	+	0.132658i
$307$	−5.61563	+	4.07999i	−0.320501	+	0.232857i	−0.736389	−	0.676558i	$-0.763471\pi$
$307$	−5.61563	+	4.07999i	−0.320501	+	0.232857i	0.415888	+	0.909416i	$0.363471\pi$
$308$	11.8674	−	8.62220i	0.676210	−	0.491295i
$309$	31.6522	+	19.3965i	1.80063	+	1.10343i
$310$	−0.286610	−	1.69446i	−0.0162784	−	0.0962388i
$311$	−1.07087	−	13.6067i	−0.0607235	−	0.771565i	−0.949609	−	0.313436i	$-0.898520\pi$
$311$	−1.07087	−	13.6067i	−0.0607235	−	0.771565i	0.888886	−	0.458129i	$-0.151480\pi$
$312$	−3.84714	+	24.2899i	−0.217801	+	1.37514i
$313$	2.14889	−	27.3042i	0.121462	−	1.54332i	−0.570444	−	0.821336i	$-0.693229\pi$
$313$	2.14889	−	27.3042i	0.121462	−	1.54332i	0.691906	−	0.721987i	$-0.256771\pi$
$314$	−0.310859	−	0.750481i	−0.0175428	−	0.0423521i
$315$	−1.70426	+	7.44148i	−0.0960244	+	0.419280i
$316$	2.13298	+	0.167869i	0.119989	+	0.00944337i
$317$	−0.883102	−	11.2209i	−0.0496000	−	0.630227i	−0.970605	−	0.240677i	$-0.922631\pi$
$317$	−0.883102	−	11.2209i	−0.0496000	−	0.630227i	0.921005	−	0.389550i	$-0.127369\pi$
$318$	−1.56478	+	0.797295i	−0.0877484	+	0.0447101i
$319$	10.0417	+	10.0417i	0.562226	+	0.562226i
$320$	0.394287	+	0.754187i	0.0220413	+	0.0421603i
$321$	28.3090	−	6.79639i	1.58005	−	0.379337i
$322$	−7.70864	−	12.5794i	−0.429586	−	0.701020i
$323$	21.3537	−	6.93823i	1.18815	−	0.386053i
$324$	17.2791	−	5.61433i	0.959952	−	0.311907i
$325$	−24.7430	+	10.8619i	−1.37250	+	0.602510i
$326$	−1.18195	−	7.46257i	−0.0654624	−	0.413313i
$327$	−23.7919	+	23.7919i	−1.31570	+	1.31570i
$328$	14.1136	−	1.46954i	0.779293	−	0.0811415i
$329$			11.4499i			0.631254i
$330$	−1.50340	−	8.88821i	−0.0827595	−	0.489280i
$331$	0.00873280	−	0.0210829i	0.000479998	−	0.00115882i	−0.923639	−	0.383263i	$-0.874800\pi$
$331$	0.00873280	−	0.0210829i	0.000479998	−	0.00115882i	0.924119	+	0.382104i	$0.124800\pi$
$332$	6.49280	+	3.30825i	0.356339	+	0.181564i
$333$	2.70677	+	8.33057i	0.148330	+	0.456512i
$334$	−6.19094	−	1.48631i	−0.338753	−	0.0813274i
$335$	−16.6534	−	9.96665i	−0.909870	−	0.544536i
$336$	−9.75211	+	4.96895i	−0.532021	+	0.271078i
$337$		−	3.47987i		−	0.189561i	−0.995498	−	0.0947804i	$-0.969785\pi$
$337$		−	3.47987i		−	0.189561i	0.995498	−	0.0947804i	$-0.0302149\pi$
$338$	−4.49637	−	8.82462i	−0.244570	−	0.479996i
$339$	10.7185	+	9.15449i	0.582151	+	0.497204i
$340$	−16.3775	+	14.2872i	−0.888192	+	0.774832i
$341$	3.44547	−	2.11139i	0.186583	−	0.114338i
$342$	1.06877	−	2.58024i	0.0577926	−	0.139524i
$343$	17.1294	+	1.34811i	0.924900	+	0.0727912i
$344$	0.117900	+	0.162275i	0.00635672	+	0.00874928i
$345$	39.3383	−	3.51116i	2.11790	−	0.189035i
$346$	2.19481	+	1.59462i	0.117994	+	0.0857274i
$347$	−3.18322	−	13.2591i	−0.170884	−	0.711785i	−0.990342	−	0.138645i	$-0.955725\pi$
$347$	−3.18322	−	13.2591i	−0.170884	−	0.711785i	0.819458	−	0.573140i	$-0.194275\pi$
$348$	−8.67740	−	11.9434i	−0.465157	−	0.640234i
$349$	4.25524	−	26.8666i	0.227778	−	1.43813i	−0.563216	−	0.826310i	$-0.690436\pi$
$349$	4.25524	−	26.8666i	0.227778	−	1.43813i	0.790994	−	0.611824i	$-0.209564\pi$
$350$	7.40442	+	4.32664i	0.395783	+	0.231269i
$351$	−11.6345	+	16.0135i	−0.621005	+	0.854740i
$352$	11.6697	−	13.6634i	0.621994	−	0.728262i
$353$	−21.1278	−	3.34631i	−1.12452	−	0.178106i	−0.433646	−	0.901083i	$-0.642773\pi$
$353$	−21.1278	−	3.34631i	−1.12452	−	0.178106i	−0.690872	+	0.722977i	$0.742773\pi$
$354$	1.99039	+	2.33045i	0.105788	+	0.123862i
$355$	−12.7417	−	29.8718i	−0.676259	−	1.58543i
$356$	−2.05983	−	3.36133i	−0.109171	−	0.178150i
$357$	−22.3664	−	26.1877i	−1.18376	−	1.38600i
$358$	−2.38467	+	0.187678i	−0.126034	+	0.00991908i
$359$	0.490024	−	1.50814i	0.0258625	−	0.0795965i	−0.937292	−	0.348545i	$-0.886676\pi$
$359$	0.490024	−	1.50814i	0.0258625	−	0.0795965i	0.963155	+	0.268948i	$0.0866760\pi$
$360$	0.0631651	+	6.02704i	0.00332910	+	0.317653i
$361$	2.21593	+	4.34901i	0.116628	+	0.228895i
$362$	−2.37700	−	1.45663i	−0.124932	−	0.0765586i
$363$	−1.18560	+	0.726535i	−0.0622277	+	0.0381332i
$364$	11.2020	−	21.9852i	0.587147	−	1.15234i
$365$	−11.5781	+	23.3244i	−0.606025	+	1.22085i
$366$	1.71847	+	0.711815i	0.0898261	+	0.0372072i
$367$	13.4488	−	18.5106i	0.702020	−	0.966248i	−0.297912	−	0.954593i	$-0.596290\pi$
$367$	13.4488	−	18.5106i	0.702020	−	0.966248i	0.999932	−	0.0116542i	$-0.00370974\pi$
$368$	11.5505	+	11.5505i	0.602111	+	0.602111i
$369$	−7.26837	−	2.79817i	−0.378376	−	0.145667i
$370$	9.83924	−	0.103118i	0.511518	−	0.00536086i
$371$	3.88022	−	0.614566i	0.201451	−	0.0319067i
$372$	−3.88103	+	1.60758i	−0.201222	+	0.0833490i
$373$	−8.22883	+	16.1500i	−0.426073	+	0.836215i	0.573779	+	0.819010i	$0.305477\pi$
$373$	−8.22883	+	16.1500i	−0.426073	+	0.836215i	−0.999852	+	0.0172050i	$0.994523\pi$
$374$	10.4528	+	5.32596i	0.540501	+	0.275399i
$375$	−19.1877	+	12.6046i	−0.990847	+	0.650899i
$376$	2.11035	+	8.79025i	0.108833	+	0.453323i
$377$	22.7185	+	7.38168i	1.17006	+	0.380176i
$378$	6.28184			0.323103
$379$	−21.9249	−	7.12382i	−1.12620	−	0.365926i	−0.314072	−	0.949399i	$-0.601693\pi$
$379$	−21.9249	−	7.12382i	−1.12620	−	0.365926i	−0.812132	+	0.583473i	$0.801693\pi$
$380$	10.4848	+	8.76649i	0.537858	+	0.449711i
$381$	−0.259925	+	3.30266i	−0.0133164	+	0.169201i
$382$	1.97976	+	0.475299i	0.101294	+	0.0243184i
$383$	−29.0707	−	12.0415i	−1.48544	−	0.615291i	−0.515123	−	0.857116i	$-0.672254\pi$
$383$	−29.0707	−	12.0415i	−1.48544	−	0.615291i	−0.970320	+	0.241826i	$0.922254\pi$
$384$	−17.8277	+	15.2263i	−0.909766	+	0.777013i
$385$	−2.94564	+	19.9490i	−0.150124	+	1.01669i
$386$	12.4057	−	0.976349i	0.631433	−	0.0496949i
$387$	−0.0172224	−	0.108738i	−0.000875465	−	0.00552747i
$388$	−4.78110	+	1.14784i	−0.242724	+	0.0582728i
$389$	−17.8805	−	2.83199i	−0.906577	−	0.143588i	−0.314302	−	0.949323i	$-0.601770\pi$
$389$	−17.8805	−	2.83199i	−0.906577	−	0.143588i	−0.592276	+	0.805735i	$0.701770\pi$
$390$	−9.04078	−	12.1732i	−0.457797	−	0.616415i
$391$	−26.8556	+	43.8243i	−1.35815	+	2.21629i
$392$	−1.92270	+	0.304526i	−0.0971111	+	0.0153809i
$393$	−1.77643	−	1.51722i	−0.0896091	−	0.0765334i
$394$	−2.81448	+	2.04484i	−0.141791	+	0.103017i
$395$	−2.21640	+	1.93352i	−0.111519	+	0.0972861i
$396$	−5.87287	+	2.43262i	−0.295123	+	0.122244i
$397$	0.620276	−	2.58364i	0.0311308	−	0.129669i	−0.954641	−	0.297760i	$-0.903760\pi$
$397$	0.620276	−	2.58364i	0.0311308	−	0.129669i	0.985771	+	0.168091i	$0.0537604\pi$
$398$	−11.3624	+	9.70438i	−0.569544	+	0.486437i
$399$	−14.0648	+	16.4678i	−0.704121	+	0.824420i
$400$	−9.08990	−	2.74424i	−0.454495	−	0.137212i
$401$	13.4276	−	13.4276i	0.670541	−	0.670541i	−0.287300	−	0.957841i	$-0.592758\pi$
$401$	13.4276	−	13.4276i	0.670541	−	0.670541i	0.957841	+	0.287300i	$0.0927575\pi$
$402$	3.36537	−	10.3575i	0.167849	−	0.516587i
$403$	3.55156	−	5.79562i	0.176916	−	0.288700i
$404$	5.30630	−	22.1023i	0.263998	−	1.09963i
$405$	−11.1050	+	22.3712i	−0.551810	+	1.11164i
$406$	−2.34268	−	7.21002i	−0.116265	−	0.357827i
$407$	8.85425	+	21.3760i	0.438889	+	1.05957i
$408$	−21.9977	−	15.9823i	−1.08905	−	0.791240i
$409$	−20.8229			−1.02962			−0.514812	−	0.857303i	$-0.672138\pi$
$409$	−20.8229			−1.02962			−0.514812	+	0.857303i	$0.672138\pi$
$410$	−5.44111	+	6.85139i	−0.268717	+	0.338366i
$411$	14.3133			0.706022
$412$	−23.7908	−	17.2850i	−1.17209	−	0.851571i
$413$	−2.62360	−	6.33394i	−0.129099	−	0.311673i
$414$	1.97565	+	6.08044i	0.0970981	+	0.298837i
$415$	−9.49417	+	3.19523i	−0.466050	+	0.156847i
$416$	7.05586	−	29.3898i	0.345942	−	1.44095i
$417$	−4.84933	+	7.91339i	−0.237473	+	0.387520i
$418$	2.27967	−	7.01609i	0.111502	−	0.343168i
$419$	−11.9882	+	11.9882i	−0.585663	+	0.585663i	−0.936454	−	0.350791i	$-0.885913\pi$
$419$	−11.9882	+	11.9882i	−0.585663	+	0.585663i	0.350791	+	0.936454i	$0.385913\pi$
$420$	6.26863	−	20.0038i	0.305878	−	0.976084i
$421$	−10.9167	+	12.7818i	−0.532047	+	0.622947i	−0.959710	−	0.280991i	$-0.909337\pi$
$421$	−10.9167	+	12.7818i	−0.532047	+	0.622947i	0.427663	+	0.903938i	$0.359337\pi$
$422$	−0.537840	+	0.459358i	−0.0261816	+	0.0223612i
$423$	1.15831	−	4.82469i	0.0563188	−	0.234585i
$424$	2.86562	−	1.18698i	0.139167	−	0.0576448i
$425$	1.71936	−	29.8273i	0.0834010	−	1.44684i
$426$	14.7431	−	10.7115i	0.714304	−	0.518972i
$427$	−3.16400	−	2.70232i	−0.153117	−	0.130774i
$428$	−22.7785	+	3.60776i	−1.10104	+	0.174388i
$429$	18.6296	−	30.4007i	0.899443	−	1.46776i
$430$	−0.122348	−	0.0180657i	−0.00590013	−	0.000871207i
$431$	6.46396	+	1.02379i	0.311358	+	0.0493143i	0.310158	−	0.950685i	$-0.399618\pi$
$431$	6.46396	+	1.02379i	0.311358	+	0.0493143i	0.00120001	+	0.999999i	$0.499618\pi$
$432$	−6.76302	+	1.62366i	−0.325386	+	0.0781183i
$433$	0.621565	+	3.92441i	0.0298705	+	0.188595i	0.998112	−	0.0614224i	$-0.0195637\pi$
$433$	0.621565	+	3.92441i	0.0298705	+	0.188595i	−0.968241	+	0.250017i	$0.919564\pi$
$434$	−2.15055	+	0.169252i	−0.103230	+	0.00812437i
$435$	20.0767	+	2.96450i	0.962603	+	0.142137i
$436$	20.2676	−	17.3102i	0.970643	−	0.829008i
$437$	29.8609	+	12.3688i	1.42844	+	0.591679i
$438$	−14.2083	−	3.41111i	−0.678899	−	0.162989i
$439$	0.749755	−	9.52653i	0.0357838	−	0.454677i	−0.952758	−	0.303730i	$-0.901768\pi$
$439$	0.749755	−	9.52653i	0.0357838	−	0.454677i	0.988542	−	0.150947i	$-0.0482321\pi$
$440$	1.41542	+	15.8580i	0.0674773	+	0.756001i
$441$	1.01617	+	0.330174i	0.0483891	+	0.0157226i
$442$	19.7334			0.938623
$443$	19.7384	+	6.41340i	0.937800	+	0.304710i	0.737749	−	0.675076i	$-0.235889\pi$
$443$	19.7384	+	6.41340i	0.937800	+	0.304710i	0.200052	+	0.979785i	$0.435889\pi$
$444$	−5.61496	−	23.3880i	−0.266474	−	1.10994i
$445$	5.28262	+	1.20984i	0.250420	+	0.0573518i
$446$	−3.51628	−	1.79164i	−0.166501	−	0.0848364i
$447$	−6.22926	+	12.2256i	−0.294634	+	0.578251i
$448$	0.986955	−	0.408810i	0.0466293	−	0.0193145i
$449$	10.5604	−	1.67261i	0.498378	−	0.0789353i	0.0978152	−	0.995205i	$-0.468815\pi$
$449$	10.5604	−	1.67261i	0.498378	−	0.0789353i	0.400563	+	0.916269i	$0.368815\pi$
$450$	−2.68233	−	2.57218i	−0.126446	−	0.121254i
$451$	−19.7198	−	5.86212i	−0.928570	−	0.276037i
$452$	−7.89564	−	7.89564i	−0.371380	−	0.371380i
$453$	−11.6659	+	16.0568i	−0.548113	+	0.754413i
$454$	−6.66223	−	2.75959i	−0.312674	−	0.129514i
$455$	10.8193	+	32.1482i	0.507218	+	1.50713i
$456$	−7.76254	+	15.2348i	−0.363514	+	0.713437i
$457$	17.2549	−	10.5738i	0.807148	−	0.494621i	−0.0566892	−	0.998392i	$-0.518054\pi$
$457$	17.2549	−	10.5738i	0.807148	−	0.494621i	0.863837	+	0.503771i	$0.168054\pi$
$458$	12.6068	+	7.72547i	0.589078	+	0.360988i
$459$	−9.93552	−	19.4996i	−0.463750	−	0.910161i
$460$	−31.2843	+	0.327869i	−1.45864	+	0.0152870i
$461$	−0.757972	+	2.33280i	−0.0353023	+	0.108649i	−0.967155	−	0.254188i	$-0.918192\pi$
$461$	−0.757972	+	2.33280i	−0.0353023	+	0.108649i	0.931853	+	0.362837i	$0.118192\pi$
$462$	−11.2806	+	0.887806i	−0.524823	+	0.0413045i
$463$	−7.04751	−	8.25158i	−0.327526	−	0.383483i	0.572072	−	0.820204i	$-0.306140\pi$
$463$	−7.04751	−	8.25158i	−0.327526	−	0.383483i	−0.899597	+	0.436720i	$0.856140\pi$
$464$	4.38569	+	7.15679i	0.203600	+	0.332246i
$465$	2.15389	−	5.35808i	0.0998841	−	0.248475i
$466$	2.89999	+	3.39545i	0.134339	+	0.157291i
$467$	−10.3266	−	1.63557i	−0.477856	−	0.0756849i	−0.0871396	−	0.996196i	$-0.527773\pi$
$467$	−10.3266	−	1.63557i	−0.477856	−	0.0756849i	−0.390716	+	0.920511i	$0.627773\pi$
$468$	−6.94434	+	8.13077i	−0.321002	+	0.375845i
$469$	−14.3197	+	19.7093i	−0.661221	+	0.910092i
$470$	−4.78275	−	2.86236i	−0.220612	−	0.132031i
$471$	0.427009	−	2.69603i	0.0196755	−	0.124226i
$472$	−3.18160	−	4.37909i	−0.146445	−	0.201564i
$473$	−0.0678877	−	0.282772i	−0.00312148	−	0.0130019i
$474$	−1.33524	−	0.970111i	−0.0613297	−	0.0445587i
$475$	−18.6947	+	1.86628i	−0.857772	+	0.0856307i
$476$	16.0355	+	22.0710i	0.734987	+	1.01162i
$477$	−1.69719	−	0.133572i	−0.0777091	−	0.00611584i
$478$	−1.41785	+	3.42299i	−0.0648509	+	0.156564i
$479$	12.8460	−	7.87205i	0.586950	−	0.359683i	−0.197098	−	0.980384i	$-0.563152\pi$
$479$	12.8460	−	7.87205i	0.586950	−	0.359683i	0.784048	+	0.620701i	$0.213152\pi$
$480$	1.74632	−	25.6189i	0.0797081	−	1.16934i
$481$	29.5943	+	25.2759i	1.34939	+	1.15248i
$482$	−7.11205	−	13.9582i	−0.323945	−	0.635778i
$483$		−	49.5762i		−	2.25579i
$484$	0.981442	−	0.500070i	0.0446110	−	0.0227304i
$485$	3.47113	−	5.79993i	0.157616	−	0.263361i
$486$	−7.09910	−	1.70434i	−0.322021	−	0.0773105i
$487$	6.93677	+	21.3492i	0.314335	+	0.967424i	0.976027	+	0.217648i	$0.0698385\pi$
$487$	6.93677	+	21.3492i	0.314335	+	0.967424i	−0.661692	+	0.749775i	$0.730161\pi$
$488$	−2.92712	−	1.49144i	−0.132504	−	0.0675144i
$489$	9.71601	−	23.4565i	0.439373	−	1.06074i
$490$	0.695283	−	0.978375i	0.0314097	−	0.0441985i
$491$		−	35.0843i		−	1.58333i	−0.610954	−	0.791666i	$-0.709214\pi$
$491$		−	35.0843i		−	1.58333i	0.610954	−	0.791666i	$-0.290786\pi$
$492$	19.2942	+	9.22589i	0.869850	+	0.415935i
$493$	−18.6755	+	18.6755i	−0.841101	+	0.841101i
$494$	−1.94121	−	12.2563i	−0.0873391	−	0.551438i
$495$	3.25931	−	8.10798i	0.146495	−	0.364427i
$496$	2.27154	−	0.738067i	0.101995	−	0.0331402i
$497$	−38.7704	+	12.5973i	−1.73909	+	0.565065i
$498$	−2.93705	−	4.79283i	−0.131612	−	0.214772i
$499$	21.3380	−	5.12280i	0.955221	−	0.229328i	0.274266	−	0.961654i	$-0.411565\pi$
$499$	21.3380	−	5.12280i	0.955221	−	0.229328i	0.680955	+	0.732326i	$0.261565\pi$
$500$	15.9362	−	8.76152i	0.712690	−	0.391827i
$501$	−15.1283	−	15.1283i	−0.675882	−	0.675882i
$502$	−7.21707	+	3.67728i	−0.322114	+	0.164125i
$503$	−1.12882	−	14.3431i	−0.0503318	−	0.639526i	−0.969409	−	0.245449i	$-0.921064\pi$
$503$	−1.12882	−	14.3431i	−0.0503318	−	0.639526i	0.919078	−	0.394077i	$-0.128936\pi$
$504$	7.54261	+	0.593616i	0.335975	+	0.0264418i
$505$	16.6049	+	26.4701i	0.738909	+	1.17790i
$506$	6.46267	+	15.6023i	0.287301	+	0.693605i
$507$	2.61119	−	33.1783i	0.115967	−	1.47350i
$508$	0.410535	−	2.59202i	0.0182145	−	0.115002i
$509$	−1.30882	−	16.6301i	−0.0580124	−	0.737117i	−0.955294	−	0.295658i	$-0.904461\pi$
$509$	−1.30882	−	16.6301i	−0.0580124	−	0.737117i	0.897281	−	0.441459i	$-0.145539\pi$
$510$	16.5303	−	2.79602i	0.731972	−	0.123810i
$511$	27.8702	+	17.0789i	1.23291	+	0.755526i
$512$	15.4015	−	11.1898i	0.680656	−	0.494526i
$513$	−11.1337	+	8.08910i	−0.491564	+	0.357142i
$514$	−9.76897	−	5.98643i	−0.430891	−	0.264050i
$515$	39.8593	−	6.74202i	1.75641	−	0.297089i
$516$	0.0237191	+	0.301380i	0.00104417	+	0.0132675i
$517$	2.05028	−	12.9450i	0.0901714	−	0.569320i
$518$	0.969089	−	12.3134i	0.0425793	−	0.541022i
$519$	3.48866	+	8.42237i	0.153135	+	0.369701i
$520$	14.2314	+	22.6864i	0.624089	+	0.994866i
$521$	−23.7381	−	1.86823i	−1.03999	−	0.0818487i	−0.453053	−	0.891484i	$-0.649665\pi$
$521$	−23.7381	−	1.86823i	−1.03999	−	0.0818487i	−0.586934	+	0.809635i	$0.699665\pi$
$522$	0.257756	+	3.27510i	0.0112817	+	0.143347i
$523$	−22.2230	+	11.3232i	−0.971745	+	0.495129i	−0.866424	−	0.499309i	$-0.833587\pi$
$523$	−22.2230	+	11.3232i	−0.971745	+	0.495129i	−0.105321	+	0.994438i	$0.533587\pi$
$524$	1.30858	+	1.30858i	0.0571656	+	0.0571656i
$525$	13.6182	+	25.3968i	0.594346	+	1.10841i
$526$	12.1317	−	2.91257i	0.528969	−	0.126994i
$527$	3.92675	+	6.40787i	0.171052	+	0.279131i
$528$	11.9153	−	3.87150i	0.518545	−	0.168485i
$529$	−48.4940	+	15.7566i	−2.10843	+	0.685071i
$530$	−0.713305	+	1.77444i	−0.0309840	+	0.0770768i
$531$	0.464758	+	2.93437i	0.0201688	+	0.127341i
$532$	12.1307	−	12.1307i	0.525934	−	0.525934i
$533$	−34.0319	+	6.27324i	−1.47409	+	0.271724i
$534$			3.04103i			0.131598i
$535$	18.3652	−	25.8427i	0.793995	−	1.11728i
$536$	−7.36074	+	17.7704i	−0.317936	+	0.767564i
$537$	−7.16194	−	3.64919i	−0.309060	−	0.157474i
$538$	−2.96859	−	9.13638i	−0.127985	−	0.393897i
$539$	2.74432	+	0.658854i	0.118206	+	0.0283788i
$540$	6.84092	−	11.4306i	0.294386	−	0.491893i
$541$	−35.7702	+	18.2258i	−1.53788	+	0.783589i	−0.998297	−	0.0583427i	$-0.981418\pi$
$541$	−35.7702	+	18.2258i	−1.53788	+	0.783589i	−0.539584	+	0.841932i	$0.681418\pi$
$542$			6.69675i			0.287650i
$543$	−4.25295	−	8.34688i	−0.182512	−	0.358199i
$544$	25.4111	+	21.7032i	1.08949	+	0.930515i
$545$	−2.49183	+	36.5557i	−0.106738	+	1.56587i
$546$	−16.2290	+	9.94514i	−0.694537	+	0.425613i
$547$	0.533367	−	1.28766i	0.0228051	−	0.0550564i	−0.912067	−	0.410042i	$-0.865514\pi$
$547$	0.533367	−	1.28766i	0.0228051	−	0.0550564i	0.934872	+	0.354985i	$0.115514\pi$
$548$	−11.3034	−	0.889600i	−0.482859	−	0.0380018i
$549$	1.05985	+	1.45876i	0.0452335	+	0.0622586i
$550$	−7.59651	−	6.21747i	−0.323916	−	0.265114i
$551$	13.4364	+	9.76209i	0.572409	+	0.415879i
$552$	−9.13747	−	38.0603i	−0.388916	−	1.61995i
$553$	2.17013	+	2.98692i	0.0922832	+	0.127017i
$554$	−1.36248	+	8.60236i	−0.0578862	+	0.365479i
$555$	28.3719	+	16.9799i	1.20432	+	0.720757i
$556$	4.32143	−	5.94794i	0.183270	−	0.252249i
$557$	−21.8975	+	25.6387i	−0.927827	+	1.08635i	0.0682339	+	0.997669i	$0.478264\pi$
$557$	−21.8975	+	25.6387i	−0.927827	+	1.08635i	−0.996061	+	0.0886760i	$0.971736\pi$
$558$	0.923309	+	0.146238i	0.0390868	+	0.00619074i
$559$	−0.317688	−	0.371965i	−0.0134368	−	0.0157324i
$560$	−4.44550	+	11.0588i	−0.187857	+	0.467319i
$561$	20.5976	+	33.6122i	0.869631	+	1.41911i
$562$	3.72479	+	4.36117i	0.157121	+	0.183965i
$563$	18.9813	−	1.49386i	0.799966	−	0.0629587i	0.328116	−	0.944637i	$-0.393586\pi$
$563$	18.9813	−	1.49386i	0.799966	−	0.0629587i	0.471850	+	0.881679i	$0.343586\pi$
$564$	−4.21030	+	12.9580i	−0.177286	+	0.545629i
$565$	15.3491	−	0.160863i	0.645742	−	0.00676756i
$566$	5.68411	+	11.1557i	0.238921	+	0.468909i
$567$	26.7313	+	16.3810i	1.12261	+	0.687937i
$568$	−27.4428	+	16.8169i	−1.15147	+	0.705623i
$569$	17.6255	−	34.5919i	0.738898	−	1.45017i	−0.148378	−	0.988931i	$-0.547405\pi$
$569$	17.6255	−	34.5919i	0.738898	−	1.45017i	0.887276	−	0.461239i	$-0.152595\pi$
$570$	−3.36270	−	9.99180i	−0.140848	−	0.418510i
$571$	−21.9700	−	9.10027i	−0.919416	−	0.380835i	−0.127762	−	0.991805i	$-0.540780\pi$
$571$	−21.9700	−	9.10027i	−0.919416	−	0.380835i	−0.791654	+	0.610970i	$0.790780\pi$
$572$	−16.6015	+	22.8501i	−0.694146	+	0.955410i
$573$	4.83779	+	4.83779i	0.202102	+	0.202102i
$574$	7.95904	+	7.56756i	0.332204	+	0.315864i
$575$	29.7676	−	31.0424i	1.24140	−	1.29456i
$576$	−0.457233	+	0.0724187i	−0.0190514	+	0.00301744i
$577$	33.3056	−	13.7956i	1.38653	−	0.574320i	0.440311	−	0.897845i	$-0.354868\pi$
$577$	33.3056	−	13.7956i	1.38653	−	0.574320i	0.946219	+	0.323526i	$0.104868\pi$
$578$	−5.18909	+	10.1842i	−0.215838	+	0.423605i
$579$	37.2583	+	18.9840i	1.54840	+	0.788950i
$580$	−15.6706	−	3.58893i	−0.650688	−	0.149022i
$581$	2.93546	+	12.2271i	0.121783	+	0.507264i
$582$	3.60726	+	1.17207i	0.149526	+	0.0485839i
$583$	−4.49692			−0.186244
$584$	24.5442	+	7.97489i	1.01565	+	0.330003i
$585$	−1.30678	−	14.6409i	−0.0540288	−	0.605327i
$586$	−0.614902	+	7.81307i	−0.0254014	+	0.322755i
$587$	−1.68497	−	0.404526i	−0.0695462	−	0.0166966i	0.198523	−	0.980096i	$-0.436386\pi$
$587$	−1.68497	−	0.404526i	−0.0695462	−	0.0166966i	−0.268069	+	0.963400i	$0.586386\pi$
$588$	−2.71062	−	1.12277i	−0.111784	−	0.0463024i
$589$	3.59361	−	3.06923i	0.148072	−	0.126466i
$590$	3.30163	+	0.487515i	0.135926	+	0.0200707i
$591$	−11.6541	+	0.917198i	−0.479386	+	0.0377285i
$592$	2.13932	+	13.5071i	0.0879254	+	0.555139i
$593$	−24.9972	+	6.00129i	−1.02651	+	0.246444i	−0.711531	−	0.702655i	$-0.751998\pi$
$593$	−24.9972	+	6.00129i	−1.02651	+	0.246444i	−0.314980	+	0.949098i	$0.601998\pi$
$594$	−7.10209	−	1.12486i	−0.291402	−	0.0461536i
$595$	−37.1010	−	5.47829i	−1.52099	−	0.224588i
$596$	5.67920	−	9.26761i	0.232629	−	0.379616i
$597$	−49.5933	+	7.85481i	−2.02972	+	0.321476i
$598$	21.6008	+	18.4488i	0.883320	+	0.754427i
$599$	26.8751	−	19.5259i	1.09808	−	0.797805i	0.117339	−	0.993092i	$-0.462564\pi$
$599$	26.8751	−	19.5259i	1.09808	−	0.797805i	0.980746	+	0.195287i	$0.0625637\pi$
$600$	15.1358	+	16.9875i	0.617916	+	0.693512i
$601$	−16.4309	+	6.80589i	−0.670229	+	0.277618i	−0.691736	−	0.722151i	$-0.743154\pi$
$601$	−16.4309	+	6.80589i	−0.670229	+	0.277618i	0.0215066	+	0.999769i	$0.493154\pi$
$602$	−0.0362409	+	0.150954i	−0.00147707	+	0.00615244i
$603$	8.02778	−	6.85638i	0.326917	−	0.279213i
$604$	10.2108	−	11.9553i	0.415470	−	0.486452i
$605$	−0.452801	+	1.44493i	−0.0184090	+	0.0587448i
$606$	−12.3984	+	12.3984i	−0.503652	+	0.503652i
$607$	8.93104	−	27.4869i	0.362500	−	1.11566i	−0.589032	−	0.808110i	$-0.700491\pi$
$607$	8.93104	−	27.4869i	0.362500	−	1.11566i	0.951532	−	0.307550i	$-0.0995091\pi$
$608$	10.9800	−	17.9177i	0.445297	−	0.726658i
$609$	5.94696	−	24.7709i	0.240983	−	1.00377i
$610$	1.91975	−	0.646086i	0.0777286	−	0.0261593i
$611$	−6.81264	−	20.9671i	−0.275610	−	0.848240i
$612$	−4.52418	−	10.9223i	−0.182879	−	0.441509i
$613$	−28.7069	−	20.8568i	−1.15946	−	0.842398i	−0.169752	−	0.985487i	$-0.554297\pi$
$613$	−28.7069	−	20.8568i	−1.15946	−	0.842398i	−0.989710	+	0.143089i	$0.954297\pi$
$614$	−4.24159			−0.171177
$615$	−27.6189	+	10.0769i	−1.11370	+	0.406341i
$616$	19.9851			0.805222
$617$	−0.467203	−	0.339443i	−0.0188089	−	0.0136655i	0.578341	−	0.815795i	$-0.303700\pi$
$617$	−0.467203	−	0.339443i	−0.0188089	−	0.0136655i	−0.597150	+	0.802130i	$0.703700\pi$
$618$	8.68091	+	20.9576i	0.349198	+	0.843038i
$619$	−8.83304	−	27.1853i	−0.355030	−	1.09267i	−0.955992	−	0.293392i	$-0.905216\pi$
$619$	−8.83304	−	27.1853i	−0.355030	−	1.09267i	0.600962	−	0.799277i	$-0.294784\pi$
$620$	−2.03398	+	4.09750i	−0.0816865	+	0.164560i
$621$	7.35445	−	30.6335i	0.295124	−	1.22928i
$622$	4.35779	−	7.11127i	0.174732	−	0.285136i
$623$	2.10217	−	6.46981i	0.0842216	−	0.259207i
$624$	14.9016	−	14.9016i	0.596542	−	0.596542i
$625$	−6.72223	+	24.0793i	−0.268889	+	0.963171i
$626$	10.8693	−	12.7263i	0.434425	−	0.508647i
$627$	18.8501	−	16.0995i	0.752802	−	0.642954i
$628$	−0.504780	+	2.10256i	−0.0201429	+	0.0839013i
$629$	−39.7551	+	16.4671i	−1.58514	+	0.656586i
$630$	−3.51532	+	3.06666i	−0.140054	+	0.122179i
$631$	−31.0489	+	22.5584i	−1.23604	+	0.898034i	−0.997328	−	0.0730564i	$-0.976725\pi$
$631$	−31.0489	+	22.5584i	−1.23604	+	0.898034i	−0.238711	+	0.971091i	$0.576725\pi$
$632$	2.21656	+	1.89312i	0.0881701	+	0.0753044i
$633$	−2.34751	+	0.371809i	−0.0933051	+	0.0147781i
$634$	3.59369	−	5.86437i	0.142724	−	0.232904i
$635$	2.15098	+	2.89625i	0.0853591	+	0.114934i
$636$	4.61726	+	0.731303i	0.183086	+	0.0289980i
$637$	4.61622	−	1.10826i	0.182901	−	0.0439107i
$638$	1.35751	+	8.57096i	0.0537442	+	0.339327i
$639$	17.6112	−	1.38603i	0.696689	−	0.0548306i
$640$	−3.72944	+	25.2571i	−0.147419	+	0.998374i
$641$	17.2539	−	14.7362i	0.681488	−	0.582045i	−0.239849	−	0.970810i	$-0.577098\pi$
$641$	17.2539	−	14.7362i	0.681488	−	0.582045i	0.921337	+	0.388765i	$0.127098\pi$
$642$	16.4360	+	6.80802i	0.648677	+	0.268691i
$643$	−19.5001	−	4.68156i	−0.769008	−	0.184623i	−0.170085	−	0.985429i	$-0.554404\pi$
$643$	−19.5001	−	4.68156i	−0.769008	−	0.184623i	−0.598923	+	0.800807i	$0.704404\pi$
$644$	−3.08126	+	39.1512i	−0.121419	+	1.54277i
$645$	−0.318824	−	0.266574i	−0.0125537	−	0.0104963i
$646$	13.0485	+	4.23971i	0.513386	+	0.166809i
$647$	15.3422			0.603164			0.301582	−	0.953440i	$-0.402485\pi$
$647$	15.3422			0.603164			0.301582	+	0.953440i	$0.402485\pi$
$648$	23.5412	+	7.64900i	0.924786	+	0.300481i
$649$	1.83199	+	7.63079i	0.0719120	+	0.299535i
$650$	−16.1333	−	3.51737i	−0.632802	−	0.137963i
$651$	−6.45881	−	3.29093i	−0.253141	−	0.128982i
$652$	−9.13078	+	17.9202i	−0.357589	+	0.701808i
$653$	−2.26949	+	0.940054i	−0.0888120	+	0.0367871i	−0.426647	−	0.904418i	$-0.640305\pi$
$653$	−2.26949	+	0.940054i	−0.0888120	+	0.0367871i	0.337835	+	0.941205i	$0.390305\pi$
$654$	−20.3073	+	3.21636i	−0.794079	+	0.125770i
$655$	−2.54388	+	0.0266606i	−0.0993975	+	0.00104171i
$656$	−10.5247	−	6.09007i	−0.410919	−	0.237777i
$657$	−10.0160	−	10.0160i	−0.390763	−	0.390763i
$658$	−4.11253	+	5.66041i	−0.160323	+	0.220666i
$659$	23.3946	+	9.69036i	0.911324	+	0.377483i	0.788563	−	0.614954i	$-0.210825\pi$
$659$	23.3946	+	9.69036i	0.911324	+	0.377483i	0.122761	+	0.992436i	$0.460825\pi$
$660$	−10.6691	+	21.4933i	−0.415296	+	0.836625i
$661$	18.8943	−	37.0822i	0.734905	−	1.44233i	−0.155818	−	0.987786i	$-0.549801\pi$
$661$	18.8943	−	37.0822i	0.734905	−	1.44233i	0.890723	−	0.454546i	$-0.150199\pi$
$662$	0.0118896	−	0.00728596i	0.000462103	−	0.000283177i
$663$	56.5390	+	34.6471i	2.19579	+	1.34558i
$664$	4.50718	+	8.84584i	0.174913	+	0.343285i
$665$	0.247147	+	23.5821i	0.00958397	+	0.914475i
$666$	−1.65401	+	5.09052i	−0.0640916	+	0.197254i
$667$	−37.9024	+	2.98298i	−1.46759	+	0.115502i
$668$	11.0068	+	12.8873i	0.425867	+	0.498626i
$669$	−6.92896	−	11.3070i	−0.267889	−	0.437156i
$670$	−4.65302	−	10.9086i	−0.179762	−	0.421436i
$671$	3.09325	+	3.62173i	0.119414	+	0.139816i
$672$	−31.8362	−	5.04236i	−1.22811	−	0.194513i
$673$	−14.4330	+	16.8989i	−0.556352	+	0.651404i	−0.965297	−	0.261155i	$-0.915897\pi$
$673$	−14.4330	+	16.8989i	−0.556352	+	0.651404i	0.408945	+	0.912559i	$0.365897\pi$
$674$	1.24988	−	1.72032i	0.0481437	−	0.0662642i
$675$	4.64724	+	17.7131i	0.178872	+	0.681777i
$676$	−4.12420	+	26.0392i	−0.158623	+	1.00151i
$677$	−8.45403	−	11.6360i	−0.324915	−	0.447207i	0.615045	−	0.788492i	$-0.289138\pi$
$677$	−8.45403	−	11.6360i	−0.324915	−	0.447207i	−0.939960	+	0.341285i	$0.889138\pi$
$678$	2.01077	+	8.37547i	0.0772232	+	0.321658i
$679$	−6.86425	−	4.98717i	−0.263426	−	0.191390i
$680$	−29.4926	+	2.63238i	−1.13099	+	0.100947i
$681$	−14.2431	−	19.6039i	−0.545795	−	0.751223i
$682$	2.46167	+	0.193738i	0.0942622	+	0.00741860i
$683$	−0.704082	+	1.69980i	−0.0269409	+	0.0650412i	−0.936777	−	0.349926i	$-0.886207\pi$
$683$	−0.704082	+	1.69980i	−0.0269409	+	0.0650412i	0.909837	+	0.414967i	$0.136207\pi$
$684$	−6.33875	+	3.88439i	−0.242368	+	0.148523i
$685$	11.7455	−	10.2464i	0.448774	−	0.391497i
$686$	7.98392	+	6.81891i	0.304828	+	0.260347i
$687$	22.5562	+	44.2691i	0.860574	+	1.68897i
$688$		−	0.171884i		−	0.00655303i
$689$	−6.73981	+	3.43410i	−0.256766	+	0.130829i
$690$	20.7085	+	12.3935i	0.788358	+	0.471814i
$691$	41.4415	+	9.94922i	1.57651	+	0.378486i	0.924943	−	0.380106i	$-0.124112\pi$
$691$	41.4415	+	9.94922i	1.57651	+	0.378486i	0.651566	+	0.758592i	$0.274112\pi$
$692$	−2.23159	−	6.86812i	−0.0848322	−	0.261087i
$693$	−9.77362	−	4.97991i	−0.371269	−	0.189171i
$694$	3.18867	−	7.69813i	0.121040	−	0.292217i
$695$	1.68558	+	9.96525i	0.0639376	+	0.378004i
$696$		−	20.1130i		−	0.762383i
$697$	10.9023	−	36.6748i	0.412956	−	1.38916i
$698$	11.7534	−	11.7534i	0.444874	−	0.444874i
$699$	2.34728	+	14.8201i	0.0887822	+	0.560549i
$700$	−9.17604	−	20.9027i	−0.346822	−	0.790048i
$701$	−16.6496	+	5.40979i	−0.628848	+	0.204325i	−0.606065	−	0.795415i	$-0.707253\pi$
$701$	−16.6496	+	5.40979i	−0.628848	+	0.204325i	−0.0227833	+	0.999740i	$0.507253\pi$
$702$	−11.5033	+	3.73766i	−0.434166	+	0.141069i
$703$	14.1384	+	23.0717i	0.533239	+	0.870167i
$704$	−1.18903	+	0.285461i	−0.0448133	+	0.0107587i
$705$	−8.67762	−	16.5984i	−0.326818	−	0.625133i
$706$	−9.24286	−	9.24286i	−0.347860	−	0.347860i
$707$	34.9483	−	17.8071i	1.31437	−	0.669704i
$708$	−0.640075	−	8.13292i	−0.0240555	−	0.305654i
$709$	3.24595	+	0.255462i	0.121904	+	0.00959408i	0.139264	−	0.990255i	$-0.455526\pi$
$709$	3.24595	+	0.255462i	0.121904	+	0.00959408i	−0.0173601	+	0.999849i	$0.505526\pi$
$710$	4.43021	−	19.3440i	0.166263	−	0.725968i
$711$	−0.612269	−	1.47815i	−0.0229619	−	0.0554349i
$712$	0.421401	−	5.35441i	0.0157927	−	0.200665i
$713$	−1.69239	+	10.6854i	−0.0633807	+	0.400170i
$714$	−1.65114	−	20.9797i	−0.0617922	−	0.785145i
$715$	−6.47544	−	38.2833i	−0.242168	−	1.43171i
$716$	5.42910	+	3.32696i	0.202895	+	0.124334i
$717$	−10.0723	+	7.31794i	−0.376156	+	0.273293i
$718$	0.783936	−	0.569563i	0.0292562	−	0.0212559i
$719$	−38.3445	−	23.4976i	−1.43001	−	0.876311i	−0.430357	−	0.902659i	$-0.641612\pi$
$719$	−38.3445	−	23.4976i	−1.43001	−	0.876311i	−0.999653	+	0.0263480i	$0.991612\pi$
$720$	2.99196	−	4.21016i	0.111504	−	0.156903i
$721$	−3.98138	−	50.5882i	−0.148274	−	1.88400i
$722$	−0.466584	+	2.94590i	−0.0173645	+	0.109635i
$723$	4.13021	−	52.4792i	0.153604	−	1.95172i
$724$	2.83985	+	6.85601i	0.105542	+	0.254802i
$725$	18.5972	−	11.9396i	0.690683	−	0.443426i
$726$	−0.847068	−	0.0666657i	−0.0314376	−	0.00247420i
$727$	3.43898	+	43.6964i	0.127545	+	1.62061i	0.644505	+	0.764600i	$0.277063\pi$
$727$	3.43898	+	43.6964i	0.127545	+	1.62061i	−0.516960	+	0.856009i	$0.672937\pi$
$728$	29.9529	−	15.2617i	1.11013	−	0.565638i
$729$	6.34668	+	6.34668i	0.235062	+	0.235062i
$730$	−14.1013	+	7.37213i	−0.521913	+	0.272855i
$731$	0.525899	−	0.126257i	0.0194511	−	0.00466979i
$732$	−2.58705	−	4.22169i	−0.0956202	−	0.156038i
$733$	39.0512	−	12.6885i	1.44239	−	0.468660i	0.519746	−	0.854321i	$-0.326026\pi$
$733$	39.0512	−	12.6885i	1.44239	−	0.468660i	0.922641	+	0.385661i	$0.126026\pi$
$734$	13.2971	−	4.32050i	0.490806	−	0.159473i
$735$	3.70988	−	1.58243i	0.136841	−	0.0583689i
$736$	7.52544	+	47.5138i	0.277391	+	1.75138i
$737$	19.7187	−	19.7187i	0.726349	−	0.726349i
$738$	−2.58817	−	3.99393i	−0.0952720	−	0.147019i
$739$			14.0499i			0.516836i	0.966033	+	0.258418i	$0.0832011\pi$
$739$			14.0499i			0.516836i	−0.966033	+	0.258418i	$0.916799\pi$
$740$	−21.3504	−	15.1727i	−0.784857	−	0.557759i
$741$	15.9573	−	38.5244i	0.586206	−	1.41523i
$742$	2.13897	+	1.08986i	0.0785241	+	0.0400100i
$743$	12.3086	+	37.8820i	0.451559	+	1.38976i	0.875127	+	0.483893i	$0.160778\pi$
$743$	12.3086	+	37.8820i	0.451559	+	1.38976i	−0.423568	+	0.905864i	$0.639222\pi$
$744$	−5.56507	−	1.33605i	−0.204025	−	0.0489821i
$745$	3.64019	+	14.4917i	0.133366	+	0.530936i
$746$	−9.86871	+	5.02836i	−0.361319	+	0.184101i
$747$		−	5.44912i		−	0.199373i
$748$	−14.1772	−	27.8243i	−0.518370	−	1.01736i
$749$	−30.2615	−	25.8458i	−1.10573	−	0.944383i
$750$	−14.0129	−	0.660499i	−0.511680	−	0.0241180i
$751$	39.0253	−	23.9148i	1.42405	−	0.872662i	0.424590	−	0.905386i	$-0.360418\pi$
$751$	39.0253	−	23.9148i	1.42405	−	0.872662i	0.999464	+	0.0327239i	$0.0104182\pi$
$752$	2.96450	−	7.15695i	0.108104	−	0.260987i
$753$	−27.1343	−	2.13552i	−0.988830	−	0.0778226i
$754$	8.57984	+	11.8091i	0.312459	+	0.430063i
$755$	1.92146	+	21.5276i	0.0699289	+	0.783468i
$756$	−13.5281	−	9.82875i	−0.492013	−	0.357468i
$757$	6.32034	+	26.3261i	0.229717	+	0.956839i	0.961391	+	0.275185i	$0.0887391\pi$
$757$	6.32034	+	26.3261i	0.229717	+	0.956839i	−0.731674	+	0.681654i	$0.761261\pi$
$758$	−8.28012	−	11.3966i	−0.300748	−	0.413944i
$759$	−8.87738	+	56.0496i	−0.322228	+	2.03447i
$760$	4.53620	+	18.0588i	0.164545	+	0.655060i
$761$	−25.9915	+	35.7742i	−0.942190	+	1.29681i	0.0127211	+	0.999919i	$0.495951\pi$
$761$	−25.9915	+	35.7742i	−0.942190	+	1.29681i	−0.954911	+	0.296894i	$0.904049\pi$
$762$	−1.31473	+	1.53935i	−0.0476277	+	0.0557649i
$763$	45.4273	+	7.19497i	1.64458	+	0.260475i
$764$	−3.51981	−	4.12117i	−0.127342	−	0.149099i
$765$	15.0792	+	6.06165i	0.545189	+	0.219159i
$766$	−10.0465	−	16.3943i	−0.362993	−	0.592351i
$767$	8.57302	+	10.0377i	0.309554	+	0.362441i
$768$	−12.7241	+	1.00141i	−0.459140	+	0.0361351i
$769$	−4.57626	+	14.0843i	−0.165024	+	0.507892i	−0.999038	−	0.0438512i	$-0.986037\pi$
$769$	−4.57626	+	14.0843i	−0.165024	+	0.507892i	0.834014	+	0.551743i	$0.186037\pi$
$770$	−8.62139	+	8.80401i	−0.310693	+	0.317275i
$771$	−17.4787	−	34.3039i	−0.629481	−	1.23543i
$772$	−28.2436	−	17.3077i	−1.01651	−	0.622918i
$773$	−32.9023	+	20.1626i	−1.18341	+	0.725197i	−0.967908	−	0.251306i	$-0.919140\pi$
$773$	−32.9023	+	20.1626i	−1.18341	+	0.725197i	−0.215506	+	0.976502i	$0.569140\pi$
$774$	0.0305419	−	0.0599419i	0.00109781	−	0.00215457i
$775$	−2.06820	−	5.93877i	−0.0742921	−	0.213327i
$776$	−6.18897	−	2.56356i	−0.222171	−	0.0920263i
$777$	24.3960	−	33.5782i	0.875202	−	1.20461i
$778$	−7.82226	−	7.82226i	−0.280442	−	0.280442i
$779$	−23.8510	−	3.16362i	−0.854551	−	0.113349i
$780$	0.422993	+	40.3608i	0.0151456	+	1.44515i
$781$	46.0886	−	7.29972i	1.64918	−	0.261205i
$782$	−29.0170	+	12.0192i	−1.03765	+	0.429807i
$783$	7.34935	−	14.4239i	0.262644	−	0.515468i
$784$	1.48633	+	0.757323i	0.0530832	+	0.0270472i
$785$	−1.57960	−	2.51806i	−0.0563784	−	0.0898733i
$786$	−0.333254	−	1.38810i	−0.0118868	−	0.0495120i
$787$	−14.3491	−	4.66232i	−0.511491	−	0.166194i	0.0418890	−	0.999122i	$-0.486662\pi$
$787$	−14.3491	−	4.66232i	−0.511491	−	0.166194i	−0.553380	+	0.832929i	$0.686662\pi$
$788$	9.26046			0.329890
$789$	39.8729	+	12.9555i	1.41951	+	0.461228i
$790$	−1.79018	+	0.159784i	−0.0636917	+	0.00568485i
$791$	1.51177	−	19.2088i	0.0537523	−	0.682987i
$792$	−8.42119	−	2.02175i	−0.299234	−	0.0718398i
$793$	7.40180	+	3.06593i	0.262846	+	0.108874i
$794$	1.23462	−	1.05446i	0.0438150	−	0.0374216i
$795$	−5.15921	+	3.83163i	−0.182978	+	0.135894i
$796$	39.6529	−	3.12075i	1.40546	−	0.110612i
$797$	−0.459226	−	2.89944i	−0.0162666	−	0.102703i	0.978219	−	0.207575i	$-0.0665570\pi$
$797$	−0.459226	−	2.89944i	−0.0162666	−	0.102703i	−0.994486	+	0.104871i	$0.966557\pi$
$798$	−12.8679	+	3.08932i	−0.455520	+	0.109361i
$799$	24.0750	+	3.81311i	0.851713	+	0.134898i
$800$	−16.9068	−	22.2731i	−0.597745	−	0.787474i
$801$	−1.54030	+	2.51355i	−0.0544239	+	0.0888118i
$802$	11.4609	−	1.81524i	0.404700	−	0.0640982i
$803$	−28.4511	−	24.2996i	−1.00402	−	0.857513i
$804$	−23.4531	+	17.0397i	−0.827128	+	0.600943i
$805$	−35.4901	−	40.6824i	−1.25086	−	1.43387i
$806$	3.83740	−	1.58950i	0.135167	−	0.0559879i
$807$	7.53587	−	31.3891i	0.265275	−	1.10495i
$808$	23.5483	−	20.1121i	0.828425	−	0.707542i
$809$	−30.9841	+	36.2777i	−1.08934	+	1.27546i	−0.130523	+	0.991445i	$0.541665\pi$
$809$	−30.9841	+	36.2777i	−1.08934	+	1.27546i	−0.958821	+	0.284012i	$0.908335\pi$
$810$	−13.5251	+	7.07088i	−0.475223	+	0.248445i
$811$	−17.9514	+	17.9514i	−0.630360	+	0.630360i	−0.948158	−	0.317799i	$-0.897056\pi$
$811$	−17.9514	+	17.9514i	−0.630360	+	0.630360i	0.317799	+	0.948158i	$0.397056\pi$
$812$	−6.23598	+	19.1924i	−0.218840	+	0.673521i
$813$	−11.7579	+	19.1871i	−0.412367	+	0.672922i
$814$	−3.30054	+	13.7477i	−0.115684	+	0.481858i
$815$	−8.81883	−	26.2039i	−0.308910	−	0.917884i
$816$	7.20020	+	22.1599i	0.252057	+	0.775753i
$817$	−0.130151	−	0.314213i	−0.00455341	−	0.0109929i
$818$	−10.2940	−	7.47906i	−0.359923	−	0.261499i
$819$	−18.4512			−0.644739
$820$	22.4375	−	6.24135i	0.783550	−	0.217957i
$821$	−8.93610			−0.311872			−0.155936	−	0.987767i	$-0.549839\pi$
$821$	−8.93610			−0.311872			−0.155936	+	0.987767i	$0.549839\pi$
$822$	7.07594	+	5.14097i	0.246802	+	0.179312i
$823$	17.2013	+	41.5275i	0.599599	+	1.44756i	0.873991	+	0.485941i	$0.161523\pi$
$823$	17.2013	+	41.5275i	0.599599	+	1.44756i	−0.274393	+	0.961618i	$0.588477\pi$
$824$	−12.3805	−	38.1034i	−0.431297	−	1.32739i
$825$	−10.8487	−	31.1516i	−0.377702	−	1.08456i
$826$	0.977984	−	4.07360i	0.0340284	−	0.141739i
$827$	−4.07155	+	6.64417i	−0.141582	+	0.231041i	−0.915569	−	0.402161i	$-0.868259\pi$
$827$	−4.07155	+	6.64417i	−0.141582	+	0.231041i	0.773987	+	0.633201i	$0.218259\pi$
$828$	5.25901	−	16.1856i	0.182763	−	0.562487i
$829$	27.0396	−	27.0396i	0.939125	−	0.939125i	−0.0591253	−	0.998251i	$-0.518831\pi$
$829$	27.0396	−	27.0396i	0.939125	−	0.939125i	0.998251	+	0.0591253i	$0.0188312\pi$
$830$	−5.84121	−	1.83047i	−0.202751	−	0.0635366i
$831$	−19.0074	+	22.2548i	−0.659358	+	0.772009i
$832$	−1.56408	+	1.33585i	−0.0542246	+	0.0463122i
$833$	−1.22533	+	5.10388i	−0.0424553	+	0.176839i
$834$	−5.23962	+	2.17032i	−0.181433	+	0.0751521i
$835$	−23.2442	−	1.58445i	−0.804400	−	0.0548321i
$836$	−15.8869	+	11.5425i	−0.549460	+	0.399206i
$837$	−3.50275	−	2.99163i	−0.121073	−	0.103406i
$838$	−10.2324	+	1.62065i	−0.353473	+	0.0559845i
$839$	12.9785	−	21.1790i	0.448067	−	0.731179i	−0.546252	−	0.837621i	$-0.683946\pi$
$839$	12.9785	−	21.1790i	0.448067	−	0.731179i	0.994319	+	0.106442i	$0.0339457\pi$
$840$	22.9284	−	17.0284i	0.791106	−	0.587537i
$841$	9.34707	+	1.48043i	0.322313	+	0.0510493i
$842$	−9.98772	+	2.39784i	−0.344199	+	0.0826350i
$843$	3.01488	+	19.0352i	0.103838	+	0.655607i
$844$	1.87698	−	0.147721i	0.0646082	−	0.00508478i
$845$	−21.6086	−	29.0955i	−0.743359	−	1.00092i
$846$	2.30553	−	1.96911i	0.0792659	−	0.0676995i
$847$	1.75606	+	0.727382i	0.0603388	+	0.0249931i
$848$	−2.58451	−	0.620485i	−0.0887524	−	0.0213076i
$849$	−3.30095	+	41.9425i	−0.113288	+	1.43946i
$850$	11.5632	−	14.1279i	0.396615	−	0.484584i
$851$	−58.9121	−	19.1417i	−2.01948	−	0.656169i
$852$	−48.5091			−1.66189
$853$	−13.6494	−	4.43495i	−0.467345	−	0.151850i	0.0658718	−	0.997828i	$-0.479017\pi$
$853$	−13.6494	−	4.43495i	−0.467345	−	0.151850i	−0.533217	+	0.845978i	$0.679017\pi$
$854$	−0.593560	−	2.47236i	−0.0203112	−	0.0846023i
$855$	2.28149	−	9.96188i	0.0780254	−	0.340689i
$856$	−27.9958	−	14.2646i	−0.956878	−	0.487554i
$857$	16.9771	−	33.3194i	0.579926	−	1.13817i	−0.395629	−	0.918411i	$-0.629473\pi$
$857$	16.9771	−	33.3194i	0.579926	−	1.13817i	0.975554	−	0.219758i	$-0.0705267\pi$
$858$	20.1289	−	8.33767i	0.687190	−	0.284643i
$859$	−11.0497	+	1.75010i	−0.377010	+	0.0597125i	−0.342064	−	0.939677i	$-0.611126\pi$
$859$	−11.0497	+	1.75010i	−0.377010	+	0.0597125i	−0.0349460	+	0.999389i	$0.511126\pi$
$860$	0.235213	+	0.230334i	0.00802069	+	0.00785431i
$861$	9.51695	+	35.6563i	0.324337	+	1.21516i
$862$	2.82782	+	2.82782i	0.0963159	+	0.0963159i
$863$	−26.4196	+	36.3634i	−0.899333	+	1.23783i	0.0713475	+	0.997452i	$0.477270\pi$
$863$	−26.4196	+	36.3634i	−0.899333	+	1.23783i	−0.970680	+	0.240374i	$0.922730\pi$
$864$	−18.9238	−	7.83851i	−0.643802	−	0.266671i
$865$	8.89213	+	4.41401i	0.302342	+	0.150081i
$866$	−1.10227	+	2.16333i	−0.0374567	+	0.0735129i
$867$	−32.7484	+	20.0683i	−1.11219	+	0.681554i
$868$	4.89609	+	3.00033i	0.166184	+	0.101838i
$869$	−1.91864	−	3.76554i	−0.0650853	−	0.127737i
$870$	8.86038	+	8.67658i	0.300395	+	0.294164i
$871$	14.4953	−	44.6119i	0.491155	−	1.51162i
$872$	36.2012	−	2.84910i	1.22593	−	0.0964827i
$873$	2.38790	+	2.79587i	0.0808181	+	0.0946259i
$874$	10.3195	+	16.8399i	0.349063	+	0.569620i
$875$	29.3560	+	11.0919i	0.992413	+	0.374975i
$876$	25.2608	+	29.5766i	0.853485	+	0.999302i
$877$	30.8068	+	4.87932i	1.04027	+	0.164763i	0.653121	−	0.757253i	$-0.273459\pi$
$877$	30.8068	+	4.87932i	1.04027	+	0.164763i	0.387151	+	0.922016i	$0.373459\pi$
$878$	3.79235	−	4.44027i	0.127986	−	0.149852i
$879$	−15.4797	+	21.3059i	−0.522116	+	0.718631i
$880$	7.00622	−	11.7067i	0.236180	−	0.394634i
$881$	−6.99211	+	44.1464i	−0.235570	+	1.48733i	0.532207	+	0.846614i	$0.321363\pi$
$881$	−6.99211	+	44.1464i	−0.235570	+	1.48733i	−0.767777	+	0.640717i	$0.778637\pi$
$882$	0.383766	+	0.528209i	0.0129221	+	0.0177857i
$883$	−2.98446	−	12.4312i	−0.100435	−	0.418342i	0.899388	−	0.437151i	$-0.144013\pi$
$883$	−2.98446	−	12.4312i	−0.100435	−	0.418342i	−0.999823	+	0.0188089i	$0.994013\pi$
$884$	−42.4964	−	30.8755i	−1.42931	−	1.03845i
$885$	8.60367	+	7.19367i	0.289209	+	0.241812i
$886$	7.45439	+	10.2601i	0.250435	+	0.344695i
$887$	−11.2750	−	0.887362i	−0.378577	−	0.0297947i	−0.112257	−	0.993679i	$-0.535808\pi$
$887$	−11.2750	−	0.887362i	−0.378577	−	0.0297947i	−0.266321	+	0.963885i	$0.585808\pi$
$888$	12.5403	−	30.2749i	0.420825	−	1.01596i
$889$	3.86120	−	2.36615i	0.129501	−	0.0793581i
$890$	2.17699	+	2.49548i	0.0729727	+	0.0836488i
$891$	−27.2885	−	23.3066i	−0.914200	−	0.780800i
$892$	4.76917	+	9.36002i	0.159684	+	0.313397i
$893$		−	15.3280i		−	0.512931i
$894$	−7.47065	+	3.80648i	−0.249856	+	0.127308i
$895$	−8.48947	+	2.13248i	−0.283772	+	0.0712809i
$896$	31.1625	+	7.48146i	1.04107	+	0.249938i
$897$	29.4975	+	90.7841i	0.984894	+	3.03119i
$898$	5.82145	+	2.96618i	0.194264	+	0.0989825i
$899$	−2.12738	+	5.13596i	−0.0709522	+	0.171294i
$900$	1.75197	+	9.73613i	0.0583988	+	0.324538i
$901$		−	8.36336i		−	0.278624i
$902$	−7.64321	−	9.98089i	−0.254491	−	0.332327i
$903$	−0.368875	+	0.368875i	−0.0122754	+	0.0122754i
$904$	−2.37981	−	15.0255i	−0.0791512	−	0.499741i
$905$	−9.46528	−	3.80493i	−0.314636	−	0.126480i
$906$	−11.5344	+	3.74775i	−0.383205	+	0.124511i
$907$	0.210492	−	0.0683930i	0.00698928	−	0.00227095i	−0.305520	−	0.952186i	$-0.598830\pi$
$907$	0.210492	−	0.0683930i	0.00698928	−	0.00227095i	0.312510	+	0.949915i	$0.398830\pi$
$908$	10.0296	+	16.3668i	0.332843	+	0.543150i
$909$	−16.5277	+	3.96796i	−0.548190	+	0.131609i
$910$	−6.19815	+	19.7789i	−0.205467	+	0.655663i
$911$	−15.9502	−	15.9502i	−0.528454	−	0.528454i	0.391657	−	0.920111i	$-0.371902\pi$
$911$	−15.9502	−	15.9502i	−0.528454	−	0.528454i	−0.920111	+	0.391657i	$0.871902\pi$
$912$	13.0551	−	6.65191i	0.432298	−	0.220267i
$913$	−1.12931	−	14.3493i	−0.0373747	−	0.474891i
$914$	12.3280	+	0.970234i	0.407774	+	0.0320925i
$915$	6.63474	+	1.51950i	0.219338	+	0.0502332i
$916$	−15.0616	−	36.3620i	−0.497650	−	1.20143i
$917$	−0.250552	+	3.18356i	−0.00827396	+	0.105131i
$918$	2.09201	−	13.2084i	0.0690467	−	0.435943i
$919$	−0.0119698	−	0.152091i	−0.000394848	−	0.00501702i	0.996717	−	0.0809674i	$-0.0258010\pi$
$919$	−0.0119698	−	0.152091i	−0.000394848	−	0.00501702i	−0.997112	+	0.0759503i	$0.975801\pi$
$920$	−34.7445	−	24.6912i	−1.14549	−	0.814045i
$921$	−12.1527	−	7.44721i	−0.400447	−	0.245394i
$922$	−1.21260	+	0.881003i	−0.0399347	+	0.0290143i
$923$	63.5013	−	46.1364i	2.09017	−	1.51860i
$924$	25.6822	+	15.7381i	0.844884	+	0.517746i
$925$	35.4375	−	6.37679i	1.16518	−	0.209668i
$926$	−0.520262	−	6.61056i	−0.0170969	−	0.217237i
$927$	−3.44000	+	21.7193i	−0.112984	+	0.713355i
$928$	−1.93946	+	24.6431i	−0.0636658	+	0.808950i
$929$	−3.23947	−	7.82077i	−0.106284	−	0.256591i	0.861786	−	0.507271i	$-0.169346\pi$
$929$	−3.23947	−	7.82077i	−0.106284	−	0.256591i	−0.968070	+	0.250680i	$0.919346\pi$
$930$	2.98929	−	1.87521i	0.0980227	−	0.0614906i
$931$	3.29053	+	0.258970i	0.107843	+	0.00848740i
$932$	−0.932584	−	11.8496i	−0.0305478	−	0.388147i
$933$	24.9714	−	12.7236i	0.817526	−	0.416550i
$934$	−4.51760	−	4.51760i	−0.147821	−	0.147821i
$935$	40.9645	+	12.8371i	1.33968	+	0.419819i
$936$	−14.1653	+	3.40078i	−0.463006	+	0.111158i
$937$	−21.3589	−	34.8546i	−0.697765	−	1.13865i	−0.983599	−	0.180370i	$-0.942271\pi$
$937$	−21.3589	−	34.8546i	−0.697765	−	1.13865i	0.285834	−	0.958279i	$-0.407729\pi$
$938$	−14.1582	+	4.60028i	−0.462282	+	0.150205i
$939$	53.4865	−	17.3788i	1.74547	−	0.567136i
$940$	5.82124	+	13.6474i	0.189868	+	0.445129i
$941$	3.32767	+	21.0101i	0.108479	+	0.684910i	0.980659	+	0.195724i	$0.0627058\pi$
$941$	3.32767	+	21.0101i	0.108479	+	0.684910i	−0.872180	+	0.489185i	$0.837294\pi$
$942$	1.17944	−	1.17944i	0.0384284	−	0.0384284i
$943$	46.2213	−	29.9527i	1.50517	−	0.975393i
$944$			4.63841i			0.150967i
$945$	22.6652	−	3.83371i	0.737298	−	0.124711i
$946$	0.0680038	−	0.164176i	0.00221099	−	0.00533781i
$947$	9.02929	+	4.60065i	0.293413	+	0.149501i	0.594501	−	0.804095i	$-0.297350\pi$
$947$	9.02929	+	4.60065i	0.293413	+	0.149501i	−0.301088	+	0.953596i	$0.597350\pi$
$948$	1.35762	+	4.17832i	0.0440934	+	0.135706i
$949$	−61.1980	−	14.6923i	−1.98657	−	0.476933i
$950$	−9.91228	−	5.79206i	−0.321597	−	0.187919i
$951$	20.5928	−	10.4926i	0.667769	−	0.340245i
$952$			37.1682i			1.20463i
$953$	3.70439	+	7.27028i	0.119997	+	0.235508i	0.943190	−	0.332255i	$-0.107809\pi$
$953$	3.70439	+	7.27028i	0.119997	+	0.235508i	−0.823193	+	0.567762i	$0.807809\pi$
$954$	−0.791052	−	0.675623i	−0.0256113	−	0.0218741i
$955$	7.43315	+	0.506682i	0.240531	+	0.0163958i
$956$	8.40908	−	5.15309i	0.271969	−	0.166663i
$957$	−11.1591	+	26.9405i	−0.360722	+	0.870861i
$958$	9.17804	+	0.722327i	0.296529	+	0.0233373i
$959$	−11.5003	−	15.8288i	−0.371364	−	0.511139i
$960$	−1.12092	+	1.34062i	−0.0361775	+	0.0432685i
$961$	−23.7998	−	17.2915i	−0.767735	−	0.557792i
$962$	5.55183	+	23.1250i	0.178998	+	0.745581i
$963$	10.1368	+	13.9521i	0.326653	+	0.449599i
$964$	−6.52339	+	41.1871i	−0.210104	+	1.32655i
$965$	44.1644	−	11.0937i	1.42170	−	0.357119i
$966$	17.8065	−	24.5086i	0.572916	−	0.788551i
$967$	−26.1569	+	30.6258i	−0.841149	+	0.984859i	−0.999997	−	0.00244426i	$-0.999222\pi$
$967$	−26.1569	+	30.6258i	−0.841149	+	0.984859i	0.158848	+	0.987303i	$0.449222\pi$
$968$	1.48221	+	0.234759i	0.0476401	+	0.00754546i
$969$	29.9418	+	35.0574i	0.961870	+	1.12621i
$970$	3.79919	−	1.62053i	0.121985	−	0.0520320i
$971$	20.0377	+	32.6986i	0.643041	+	1.04935i	0.993616	+	0.112813i	$0.0359860\pi$
$971$	20.0377	+	32.6986i	0.643041	+	1.04935i	−0.350575	+	0.936534i	$0.614014\pi$
$972$	12.6214	+	14.7778i	0.404833	+	0.473998i
$973$	12.6476	−	0.995386i	0.405463	−	0.0319106i
$974$	−4.23882	+	13.0457i	−0.135821	+	0.418013i
$975$	−40.0486	−	38.4040i	−1.28258	−	1.22991i
$976$	1.27805	+	2.50832i	0.0409095	+	0.0802893i
$977$	−23.6121	−	14.4695i	−0.755419	−	0.462922i	0.0907245	−	0.995876i	$-0.471082\pi$
$977$	−23.6121	−	14.4695i	−0.755419	−	0.462922i	−0.846144	+	0.532954i	$0.821082\pi$
$978$	13.2282	−	8.10628i	0.422992	−	0.259210i
$979$	−3.53518	+	6.93818i	−0.112985	+	0.221745i
$980$	−3.02811	+	1.01910i	−0.0967293	+	0.0325539i
$981$	−18.4140	−	7.62732i	−0.587913	−	0.243522i
$982$	12.6014	−	17.3444i	0.402127	−	0.553480i
$983$	14.6233	+	14.6233i	0.466410	+	0.466410i	0.900749	−	0.434339i	$-0.143018\pi$
$983$	14.6233	+	14.6233i	0.466410	+	0.466410i	−0.434339	+	0.900749i	$0.643018\pi$
$984$	13.8782	+	25.6197i	0.442420	+	0.816727i
$985$	−8.90682	+	9.09549i	−0.283795	+	0.289806i
$986$	−15.9402	+	2.52468i	−0.507640	+	0.0804023i
$987$	−21.7213	+	8.99725i	−0.691396	+	0.286386i
$988$	−14.9961	+	29.4316i	−0.477091	+	0.936343i
$989$	0.693701	+	0.353458i	0.0220584	+	0.0112393i
$990$	4.52347	−	2.83762i	0.143765	−	0.0901853i
$991$	−5.11121	−	21.2897i	−0.162363	−	0.676290i	−0.992862	−	0.119270i	$-0.961945\pi$
$991$	−5.11121	−	21.2897i	−0.162363	−	0.676290i	0.830499	−	0.557020i	$-0.188055\pi$
$992$	6.68966	+	2.17360i	0.212397	+	0.0690120i
$993$	0.0468578			0.00148699
$994$	−23.6913	−	7.69776i	−0.751441	−	0.244158i
$995$	−35.0735	+	41.9481i	−1.11190	+	1.32984i
$996$	−1.17399	+	14.9169i	−0.0371991	+	0.472660i
$997$	37.9131	+	9.10213i	1.20072	+	0.288267i	0.783996	−	0.620766i	$-0.213178\pi$
$997$	37.9131	+	9.10213i	1.20072	+	0.288267i	0.416724	+	0.909033i	$0.363178\pi$
$998$	12.3887	+	5.13157i	0.392157	+	0.162437i
$999$	20.0557	−	17.1292i	0.634534	−	0.541943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	205.2.y.a.112.13	yes	304
5.3	odd	4		205.2.bb.a.153.13	yes	304
41.26	odd	40		205.2.bb.a.67.13	yes	304
205.108	even	40	inner	205.2.y.a.108.13	✓	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
205.2.y.a.108.13	✓	304	205.108	even	40	inner
205.2.y.a.112.13	yes	304	1.1	even	1	trivial
205.2.bb.a.67.13	yes	304	41.26	odd	40
205.2.bb.a.153.13	yes	304	5.3	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 205 = 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	205.y (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.494362 + 0.359175i) q^{2} +(0.785792 + 1.89707i) q^{3} +(-0.502647 - 1.54699i) q^{4} +(2.00288 + 0.994219i) q^{5} +(-0.292915 + 1.22008i) q^{6} +(1.46658 - 2.39324i) q^{7} +(0.684809 - 2.10763i) q^{8} +(-0.860084 + 0.860084i) q^{9} +(0.633050 + 1.21089i) q^{10} +(-2.08662 + 2.44312i) q^{11} +(2.53977 - 2.16917i) q^{12} +(-1.26164 + 5.25511i) q^{13} +(1.58461 - 0.656368i) q^{14} +(-0.312255 + 4.58085i) q^{15} +(-1.53634 + 1.11622i) q^{16} +(-4.54370 - 3.88069i) q^{17} +(-0.734114 + 0.116272i) q^{18} +(-1.96330 + 3.20382i) q^{19} +(0.531303 - 3.59817i) q^{20} +(5.69256 + 0.901613i) q^{21} +(-1.90906 + 0.458324i) q^{22} +(-1.34561 - 8.49582i) q^{23} +(4.53643 - 0.357025i) q^{24} +(3.02306 + 3.98260i) q^{25} +(-2.51121 + 2.14478i) q^{26} +(3.38372 + 1.40158i) q^{27} +(-4.43948 - 1.06582i) q^{28} +(0.346789 - 4.40638i) q^{29} +(-1.79970 + 2.15245i) q^{30} +(-1.19616 - 0.388657i) q^{31} -5.59261 q^{32} +(-6.27442 - 2.03868i) q^{33} +(-0.852388 - 3.55045i) q^{34} +(5.31678 - 3.33527i) q^{35} +(1.76286 + 0.898220i) q^{36} +(3.26934 - 6.41643i) q^{37} +(-2.12131 + 0.878677i) q^{38} +(-10.9607 + 1.73600i) q^{39} +(3.46703 - 3.54047i) q^{40} +(2.59870 + 5.85207i) q^{41} +(2.49035 + 2.49035i) q^{42} +(-0.0532016 + 0.0732258i) q^{43} +(4.82831 + 1.99995i) q^{44} +(-2.57776 + 0.867533i) q^{45} +(2.38627 - 4.68332i) q^{46} +(-3.47815 + 2.13141i) q^{47} +(-3.32479 - 2.03743i) q^{48} +(-0.398796 - 0.782682i) q^{49} +(0.0640344 + 3.05466i) q^{50} +(3.79153 - 11.6691i) q^{51} +(8.76375 - 0.689722i) q^{52} +(0.908993 + 1.06429i) q^{53} +(1.16937 + 1.90824i) q^{54} +(-6.60825 + 2.81872i) q^{55} +(-4.03972 - 4.72991i) q^{56} +(-7.62061 - 1.20699i) q^{57} +(1.75410 - 2.05379i) q^{58} +(1.43568 - 1.97604i) q^{59} +(7.24347 - 1.81950i) q^{60} +(0.231902 - 1.46417i) q^{61} +(-0.451742 - 0.621769i) q^{62} +(0.797004 + 3.31976i) q^{63} +(0.307907 + 0.223708i) q^{64} +(-7.75164 + 9.27101i) q^{65} +(-2.36959 - 3.26146i) q^{66} +(-8.65274 - 0.680986i) q^{67} +(-3.71950 + 8.97966i) q^{68} +(15.0598 - 9.22865i) q^{69} +(3.82636 + 0.260825i) q^{70} +(-11.0438 - 9.43233i) q^{71} +(1.22374 + 2.40173i) q^{72} +11.6454i q^{73} +(3.92086 - 1.99778i) q^{74} +(-5.17978 + 8.86445i) q^{75} +(5.94311 + 1.42681i) q^{76} +(2.78677 + 8.57680i) q^{77} +(-6.04209 - 3.07860i) q^{78} +(-0.503369 + 1.21524i) q^{79} +(-4.18687 + 0.708190i) q^{80} +11.1695i q^{81} +(-0.817220 + 3.82643i) q^{82} +(-3.16779 + 3.16779i) q^{83} +(-1.46656 - 9.25951i) q^{84} +(-5.24224 - 12.2900i) q^{85} +(-0.0526018 + 0.0170914i) q^{86} +(8.63171 - 2.80461i) q^{87} +(3.72025 + 6.07089i) q^{88} +(2.35666 - 0.565784i) q^{89} +(-1.58594 - 0.496990i) q^{90} +(10.7264 + 10.7264i) q^{91} +(-12.4666 + 6.35203i) q^{92} +(-0.202626 - 2.57461i) q^{93} +(-2.48502 - 0.195575i) q^{94} +(-7.11755 + 4.46491i) q^{95} +(-4.39462 - 10.6096i) q^{96} +(0.237170 - 3.01353i) q^{97} +(0.0839701 - 0.530166i) q^{98} +(-0.306618 - 3.89596i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q - 16 q^{2} - 16 q^{3} - 68 q^{4} - 16 q^{5} - 32 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{9} - 12 q^{10} - 32 q^{11} + 20 q^{12} - 4 q^{13} - 16 q^{14} + 16 q^{15} - 76 q^{16} - 16 q^{17} + 28 q^{18} - 40 q^{20}+ \cdots - 72 q^{99}+O(q^{100}) \) 304 * q - 16 * q^2 - 16 * q^3 - 68 * q^4 - 16 * q^5 - 32 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^9 - 12 * q^10 - 32 * q^11 + 20 * q^12 - 4 * q^13 - 16 * q^14 + 16 * q^15 - 76 * q^16 - 16 * q^17 + 28 * q^18 - 40 * q^20 - 40 * q^21 - 40 * q^22 - 20 * q^23 + 40 * q^24 - 20 * q^25 - 24 * q^26 - 76 * q^27 - 4 * q^28 + 76 * q^29 - 8 * q^30 - 40 * q^31 + 48 * q^32 - 120 * q^33 + 16 * q^34 - 80 * q^35 - 24 * q^36 + 24 * q^37 - 20 * q^38 - 16 * q^39 + 56 * q^40 - 32 * q^41 + 176 * q^42 + 20 * q^43 + 16 * q^44 - 32 * q^46 + 40 * q^47 + 76 * q^48 - 8 * q^49 - 8 * q^50 - 24 * q^51 - 80 * q^52 - 16 * q^53 + 40 * q^54 + 48 * q^55 + 24 * q^56 + 12 * q^57 + 20 * q^58 - 40 * q^59 + 120 * q^60 + 4 * q^61 - 20 * q^62 + 108 * q^63 - 68 * q^64 - 92 * q^65 - 40 * q^66 + 8 * q^67 + 76 * q^68 + 32 * q^69 + 48 * q^70 - 40 * q^71 - 220 * q^72 + 144 * q^74 + 44 * q^75 - 48 * q^76 + 72 * q^77 - 212 * q^78 + 232 * q^80 - 72 * q^82 - 112 * q^83 - 256 * q^84 + 116 * q^85 - 40 * q^86 - 20 * q^87 + 92 * q^88 - 80 * q^89 + 212 * q^90 - 72 * q^91 + 20 * q^92 + 96 * q^93 - 40 * q^94 - 36 * q^95 - 8 * q^96 - 136 * q^97 - 12 * q^98 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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