LMFDB - Embedded newform 512.2.k.a.497.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [512,2,Mod(17,512)] 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("512.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(512, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.k (of order $32$, degree $16$, not 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	no (minimal twist has level 128)
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			497.5
Character	$\chi$	$=$	512.497
Dual form			512.2.k.a.273.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.731810 + 0.391160i) q^{3} +(-0.0771150 - 0.0939649i) q^{5} +(3.30773 - 2.21015i) q^{7} +(-1.28417 + 1.92190i) q^{9} +(-0.0222437 + 0.00674755i) q^{11} +(0.466044 + 0.382472i) q^{13} +(0.0931888 + 0.0386001i) q^{15} +(4.59132 - 1.90179i) q^{17} +(-0.166080 - 1.68624i) q^{19} +(-1.55610 + 2.91126i) q^{21} +(3.40974 - 0.678239i) q^{23} +(0.972569 - 4.88943i) q^{25} +(0.432000 - 4.38616i) q^{27} +(-1.44800 + 4.77342i) q^{29} +(6.39673 + 6.39673i) q^{31} +(0.0136388 - 0.0136388i) q^{33} +(-0.462752 - 0.140374i) q^{35} +(8.75672 + 0.862462i) q^{37} +(-0.490664 - 0.0975990i) q^{39} +(0.0606195 + 0.304755i) q^{41} +(4.91504 + 2.62714i) q^{43} +(0.279620 - 0.0275402i) q^{45} +(-0.167395 - 0.404127i) q^{47} +(3.37751 - 8.15402i) q^{49} +(-2.61607 + 3.18769i) q^{51} +(1.85360 + 6.11049i) q^{53} +(0.00234935 + 0.00156979i) q^{55} +(0.781127 + 1.16904i) q^{57} +(-7.95889 + 6.53169i) q^{59} +(-6.59803 - 12.3440i) q^{61} +9.19534i q^{63} -0.0732861i q^{65} +(-5.13746 - 9.61151i) q^{67} +(-2.22998 + 1.83010i) q^{69} +(-3.99036 - 5.97200i) q^{71} +(-8.64165 - 5.77416i) q^{73} +(1.20082 + 3.95857i) q^{75} +(-0.0586630 + 0.0714811i) q^{77} +(0.504221 - 1.21730i) q^{79} +(-1.25411 - 3.02768i) q^{81} +(-16.2560 + 1.60107i) q^{83} +(-0.532760 - 0.284766i) q^{85} +(-0.807512 - 4.05964i) q^{87} +(2.00759 + 0.399335i) q^{89} +(2.38687 + 0.235086i) q^{91} +(-7.18334 - 2.17904i) q^{93} +(-0.145640 + 0.145640i) q^{95} +(5.29993 + 5.29993i) q^{97} +(0.0155966 - 0.0514152i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{9}{32}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.731810	+	0.391160i	−0.422510	+	0.225837i	−0.668928	−	0.743327i	$-0.733247\pi$
$3$	−0.731810	+	0.391160i	−0.422510	+	0.225837i	0.246418	+	0.969164i	$0.420747\pi$
$4$		0			0
$5$	−0.0771150	−	0.0939649i	−0.0344869	−	0.0420224i	0.755481	−	0.655170i	$-0.227403\pi$
$5$	−0.0771150	−	0.0939649i	−0.0344869	−	0.0420224i	−0.789968	+	0.613148i	$0.789903\pi$
$6$		0			0
$7$	3.30773	−	2.21015i	1.25020	−	0.835360i	0.258766	−	0.965940i	$-0.416684\pi$
$7$	3.30773	−	2.21015i	1.25020	−	0.835360i	0.991438	+	0.130580i	$0.0416840\pi$
$8$		0			0
$9$	−1.28417	+	1.92190i	−0.428057	+	0.640633i
$10$		0			0
$11$	−0.0222437	+	0.00674755i	−0.00670673	+	0.00203446i	−0.293636	−	0.955917i	$-0.594865\pi$
$11$	−0.0222437	+	0.00674755i	−0.00670673	+	0.00203446i	0.286930	+	0.957952i	$0.407365\pi$
$12$		0			0
$13$	0.466044	+	0.382472i	0.129257	+	0.106079i	0.696801	−	0.717265i	$-0.254606\pi$
$13$	0.466044	+	0.382472i	0.129257	+	0.106079i	−0.567544	+	0.823343i	$0.692106\pi$
$14$		0			0
$15$	0.0931888	+	0.0386001i	0.0240612	+	0.00996650i
$16$		0			0
$17$	4.59132	−	1.90179i	1.11356	−	0.461251i	0.251396	−	0.967884i	$-0.419110\pi$
$17$	4.59132	−	1.90179i	1.11356	−	0.461251i	0.862162	+	0.506633i	$0.169110\pi$
$18$		0			0
$19$	−0.166080	−	1.68624i	−0.0381013	−	0.386849i	−0.995257	−	0.0972765i	$-0.968987\pi$
$19$	−0.166080	−	1.68624i	−0.0381013	−	0.386849i	0.957156	−	0.289572i	$-0.0935131\pi$
$20$		0			0
$21$	−1.55610	+	2.91126i	−0.339570	+	0.635290i
$22$		0			0
$23$	3.40974	−	0.678239i	0.710979	−	0.141423i	0.173665	−	0.984805i	$-0.444439\pi$
$23$	3.40974	−	0.678239i	0.710979	−	0.141423i	0.537314	+	0.843382i	$0.319439\pi$
$24$		0			0
$25$	0.972569	−	4.88943i	0.194514	−	0.977887i
$26$		0			0
$27$	0.432000	−	4.38616i	0.0831383	−	0.844118i
$28$		0			0
$29$	−1.44800	+	4.77342i	−0.268887	+	0.886403i	0.713676	+	0.700476i	$0.247029\pi$
$29$	−1.44800	+	4.77342i	−0.268887	+	0.886403i	−0.982564	+	0.185927i	$0.940471\pi$
$30$		0			0
$31$	6.39673	+	6.39673i	1.14889	+	1.14889i	0.986772	+	0.162115i	$0.0518316\pi$
$31$	6.39673	+	6.39673i	1.14889	+	1.14889i	0.162115	+	0.986772i	$0.448168\pi$
$32$		0			0
$33$	0.0136388	−	0.0136388i	0.00237421	−	0.00237421i
$34$		0			0
$35$	−0.462752	−	0.140374i	−0.0782194	−	0.0237276i
$36$		0			0
$37$	8.75672	+	0.862462i	1.43960	+	0.141788i	0.787484	−	0.616335i	$-0.211383\pi$
$37$	8.75672	+	0.862462i	1.43960	+	0.141788i	0.652112	+	0.758123i	$0.273883\pi$
$38$		0			0
$39$	−0.490664	−	0.0975990i	−0.0785690	−	0.0156284i
$40$		0			0
$41$	0.0606195	+	0.304755i	0.00946718	+	0.0475947i	0.985230	−	0.171236i	$-0.0547759\pi$
$41$	0.0606195	+	0.304755i	0.00946718	+	0.0475947i	−0.975763	+	0.218830i	$0.929776\pi$
$42$		0			0
$43$	4.91504	+	2.62714i	0.749536	+	0.400635i	0.801485	−	0.598014i	$-0.204043\pi$
$43$	4.91504	+	2.62714i	0.749536	+	0.400635i	−0.0519494	+	0.998650i	$0.516543\pi$
$44$		0			0
$45$	0.279620	−	0.0275402i	0.0416833	−	0.00410544i
$46$		0			0
$47$	−0.167395	−	0.404127i	−0.0244171	−	0.0589480i	0.911201	−	0.411963i	$-0.135157\pi$
$47$	−0.167395	−	0.404127i	−0.0244171	−	0.0589480i	−0.935618	+	0.353015i	$0.885157\pi$
$48$		0			0
$49$	3.37751	−	8.15402i	0.482501	−	1.16486i
$50$		0			0
$51$	−2.61607	+	3.18769i	−0.366323	+	0.446365i
$52$		0			0
$53$	1.85360	+	6.11049i	0.254611	+	0.839341i	0.987312	+	0.158790i	$0.0507594\pi$
$53$	1.85360	+	6.11049i	0.254611	+	0.839341i	−0.732701	+	0.680551i	$0.761741\pi$
$54$		0			0
$55$	0.00234935	+	0.00156979i	0.000316787	+	0.000211670i
$56$		0			0
$57$	0.781127	+	1.16904i	0.103463	+	0.154843i
$58$		0			0
$59$	−7.95889	+	6.53169i	−1.03616	+	0.850354i	−0.988908	−	0.148529i	$-0.952546\pi$
$59$	−7.95889	+	6.53169i	−1.03616	+	0.850354i	−0.0472513	+	0.998883i	$0.515046\pi$
$60$		0			0
$61$	−6.59803	−	12.3440i	−0.844791	−	1.58049i	−0.813925	−	0.580969i	$-0.802674\pi$
$61$	−6.59803	−	12.3440i	−0.844791	−	1.58049i	−0.0308657	−	0.999524i	$-0.509826\pi$
$62$		0			0
$63$			9.19534i			1.15850i
$64$		0			0
$65$		−	0.0732861i		−	0.00909002i
$66$		0			0
$67$	−5.13746	−	9.61151i	−0.627641	−	1.17423i	−0.971908	−	0.235361i	$-0.924373\pi$
$67$	−5.13746	−	9.61151i	−0.627641	−	1.17423i	0.344267	−	0.938872i	$-0.388127\pi$
$68$		0			0
$69$	−2.22998	+	1.83010i	−0.268458	+	0.220318i
$70$		0			0
$71$	−3.99036	−	5.97200i	−0.473569	−	0.708746i	0.515387	−	0.856958i	$-0.327648\pi$
$71$	−3.99036	−	5.97200i	−0.473569	−	0.708746i	−0.988956	+	0.148212i	$0.952648\pi$
$72$		0			0
$73$	−8.64165	−	5.77416i	−1.01143	−	0.675815i	−0.0647187	−	0.997904i	$-0.520615\pi$
$73$	−8.64165	−	5.77416i	−1.01143	−	0.675815i	−0.946709	+	0.322089i	$0.895615\pi$
$74$		0			0
$75$	1.20082	+	3.95857i	0.138658	+	0.457096i
$76$		0			0
$77$	−0.0586630	+	0.0714811i	−0.00668527	+	0.00814602i
$78$		0			0
$79$	0.504221	−	1.21730i	0.0567293	−	0.136957i	−0.892974	−	0.450109i	$-0.851385\pi$
$79$	0.504221	−	1.21730i	0.0567293	−	0.136957i	0.949703	+	0.313153i	$0.101385\pi$
$80$		0			0
$81$	−1.25411	−	3.02768i	−0.139345	−	0.336409i
$82$		0			0
$83$	−16.2560	+	1.60107i	−1.78433	+	0.175741i	−0.935593	−	0.353081i	$-0.885134\pi$
$83$	−16.2560	+	1.60107i	−1.78433	+	0.175741i	−0.848733	+	0.528822i	$0.822634\pi$
$84$		0			0
$85$	−0.532760	−	0.284766i	−0.0577860	−	0.0308872i
$86$		0			0
$87$	−0.807512	−	4.05964i	−0.0865744	−	0.435239i
$88$		0			0
$89$	2.00759	+	0.399335i	0.212805	+	0.0423294i	0.300341	−	0.953832i	$-0.402899\pi$
$89$	2.00759	+	0.399335i	0.212805	+	0.0423294i	−0.0875366	+	0.996161i	$0.527899\pi$
$90$		0			0
$91$	2.38687	+	0.235086i	0.250212	+	0.0246437i
$92$		0			0
$93$	−7.18334	−	2.17904i	−0.744878	−	0.225956i
$94$		0			0
$95$	−0.145640	+	0.145640i	−0.0149423	+	0.0149423i
$96$		0			0
$97$	5.29993	+	5.29993i	0.538126	+	0.538126i	0.922978	−	0.384852i	$-0.125748\pi$
$97$	5.29993	+	5.29993i	0.538126	+	0.538126i	−0.384852	+	0.922978i	$0.625748\pi$
$98$		0			0
$99$	0.0155966	−	0.0514152i	0.00156752	−	0.00516742i
$100$		0			0
$101$	−1.09246	+	11.0919i	−0.108703	+	1.10369i	0.773816	+	0.633410i	$0.218345\pi$
$101$	−1.09246	+	11.0919i	−0.108703	+	1.10369i	−0.882520	+	0.470275i	$0.844155\pi$
$102$		0			0
$103$	−2.45829	+	12.3587i	−0.242223	+	1.21774i	0.647797	+	0.761813i	$0.275691\pi$
$103$	−2.45829	+	12.3587i	−0.242223	+	1.21774i	−0.890019	+	0.455923i	$0.849309\pi$
$104$		0			0
$105$	0.393555	−	0.0782830i	0.0384071	−	0.00763964i
$106$		0			0
$107$	5.68486	−	10.6356i	0.549577	−	1.02819i	−0.441796	−	0.897115i	$-0.645659\pi$
$107$	5.68486	−	10.6356i	0.549577	−	1.02819i	0.991373	−	0.131070i	$-0.0418413\pi$
$108$		0			0
$109$	0.501099	+	5.08775i	0.0479966	+	0.487318i	0.988894	+	0.148625i	$0.0474847\pi$
$109$	0.501099	+	5.08775i	0.0479966	+	0.487318i	−0.940897	+	0.338693i	$0.890015\pi$
$110$		0			0
$111$	−6.74561	+	2.79412i	−0.640265	+	0.265207i
$112$		0			0
$113$	−5.35557	−	2.21835i	−0.503810	−	0.208685i	0.116279	−	0.993217i	$-0.462903\pi$
$113$	−5.35557	−	2.21835i	−0.503810	−	0.208685i	−0.620089	+	0.784532i	$0.712903\pi$
$114$		0			0
$115$	−0.326672	−	0.268093i	−0.0304624	−	0.0249998i
$116$		0			0
$117$	−1.33355	+	0.404529i	−0.123287	+	0.0373987i
$118$		0			0
$119$	10.9836	−	16.4381i	1.00686	−	1.50688i
$120$		0			0
$121$	−9.14572	+	6.11097i	−0.831429	+	0.555543i
$122$		0			0
$123$	−0.163570	−	0.199311i	−0.0147486	−	0.0179712i
$124$		0			0
$125$	−1.07045	+	0.572169i	−0.0957443	+	0.0511764i
$126$		0			0
$127$	−8.77440			−0.778602			−0.389301	−	0.921111i	$-0.627283\pi$
$127$	−8.77440			−0.778602			−0.389301	+	0.921111i	$0.627283\pi$
$128$		0			0
$129$	−4.62450			−0.407165
$130$		0			0
$131$	9.40916	−	5.02930i	0.822082	−	0.439412i	−0.00602507	−	0.999982i	$-0.501918\pi$
$131$	9.40916	−	5.02930i	0.822082	−	0.439412i	0.828107	+	0.560570i	$0.189418\pi$
$132$		0			0
$133$	−4.27619	−	5.21055i	−0.370792	−	0.451812i
$134$		0			0
$135$	−0.445459	+	0.297646i	−0.0383390	+	0.0256173i
$136$		0			0
$137$	−12.1619	+	18.2015i	−1.03906	+	1.55506i	−0.224929	+	0.974375i	$0.572215\pi$
$137$	−12.1619	+	18.2015i	−1.03906	+	1.55506i	−0.814129	+	0.580684i	$0.802785\pi$
$138$		0			0
$139$	10.1020	−	3.06440i	0.856839	−	0.259919i	0.168851	−	0.985642i	$-0.445994\pi$
$139$	10.1020	−	3.06440i	0.856839	−	0.259919i	0.687988	+	0.725722i	$0.258494\pi$
$140$		0			0
$141$	0.280580	+	0.230266i	0.0236291	+	0.0193919i
$142$		0			0
$143$	−0.0129473	−	0.00536294i	−0.00108271	−	0.000448472i
$144$		0			0
$145$	0.560197	−	0.232041i	0.0465218	−	0.0192700i
$146$		0			0
$147$	0.717839	+	7.28834i	0.0592063	+	0.601132i
$148$		0			0
$149$	−5.30179	+	9.91895i	−0.434339	+	0.812592i	−0.999927	−	0.0120964i	$-0.996150\pi$
$149$	−5.30179	+	9.91895i	−0.434339	+	0.812592i	0.565587	+	0.824688i	$0.308650\pi$
$150$		0			0
$151$	−0.817708	+	0.162652i	−0.0665441	+	0.0132364i	−0.228250	−	0.973603i	$-0.573300\pi$
$151$	−0.817708	+	0.162652i	−0.0665441	+	0.0132364i	0.161706	+	0.986839i	$0.448300\pi$
$152$		0			0
$153$	−2.24100	+	11.2663i	−0.181174	+	0.910824i
$154$		0			0
$155$	0.107784	−	1.09435i	0.00865744	−	0.0879005i
$156$		0			0
$157$	2.36481	−	7.79574i	0.188732	−	0.622167i	−0.810599	−	0.585602i	$-0.800858\pi$
$157$	2.36481	−	7.79574i	0.188732	−	0.622167i	0.999331	−	0.0365656i	$-0.0116418\pi$
$158$		0			0
$159$	−3.74666	−	3.74666i	−0.297130	−	0.297130i
$160$		0			0
$161$	9.77947	−	9.77947i	0.770730	−	0.770730i
$162$		0			0
$163$	−7.21798	−	2.18955i	−0.565356	−	0.171499i	−0.00534748	−	0.999986i	$-0.501702\pi$
$163$	−7.21798	−	2.18955i	−0.565356	−	0.171499i	−0.560009	+	0.828487i	$0.689202\pi$
$164$		0			0
$165$	−0.00233332		0.000229812i	−0.000181649		1.78908e-5i
$166$		0			0
$167$	−12.6226	−	2.51078i	−0.976763	−	0.194290i	−0.319198	−	0.947688i	$-0.603413\pi$
$167$	−12.6226	−	2.51078i	−0.976763	−	0.194290i	−0.657565	+	0.753398i	$0.728413\pi$
$168$		0			0
$169$	−2.46526	−	12.3937i	−0.189636	−	0.953362i
$170$		0			0
$171$	3.45405	+	1.84623i	0.264138	+	0.141185i
$172$		0			0
$173$	14.9849	−	1.47588i	1.13928	−	0.112209i	0.489268	−	0.872134i	$-0.337264\pi$
$173$	14.9849	−	1.47588i	1.13928	−	0.112209i	0.650012	+	0.759924i	$0.274764\pi$
$174$		0			0
$175$	−7.58941	−	18.3225i	−0.573705	−	1.38505i
$176$		0			0
$177$	3.26945	−	7.89316i	0.245747	−	0.593286i
$178$		0			0
$179$	−7.82617	+	9.53622i	−0.584956	+	0.712771i	−0.978433	−	0.206564i	$-0.933772\pi$
$179$	−7.82617	+	9.53622i	−0.584956	+	0.712771i	0.393477	+	0.919334i	$0.371272\pi$
$180$		0			0
$181$	−2.60365	−	8.58308i	−0.193528	−	0.637976i	−0.998973	−	0.0453056i	$-0.985574\pi$
$181$	−2.60365	−	8.58308i	−0.193528	−	0.637976i	0.805445	−	0.592670i	$-0.201926\pi$
$182$		0			0
$183$	9.65700	+	6.45260i	0.713866	+	0.476990i
$184$		0			0
$185$	−0.594233	−	0.889333i	−0.0436889	−	0.0653850i
$186$		0			0
$187$	−0.0892955	+	0.0732829i	−0.00652993	+	0.00535898i
$188$		0			0
$189$	−8.26516	−	15.4630i	−0.601202	−	1.12477i
$190$		0			0
$191$			20.3929i			1.47558i	0.675032	+	0.737789i	$0.264130\pi$
$191$			20.3929i			1.47558i	−0.675032	+	0.737789i	$0.735870\pi$
$192$		0			0
$193$			26.1565i			1.88279i	0.337311	+	0.941393i	$0.390482\pi$
$193$			26.1565i			1.88279i	−0.337311	+	0.941393i	$0.609518\pi$
$194$		0			0
$195$	0.0286666	+	0.0536315i	0.00205286	+	0.00384063i
$196$		0			0
$197$	16.7316	−	13.7313i	1.19208	−	0.978313i	0.192082	−	0.981379i	$-0.438476\pi$
$197$	16.7316	−	13.7313i	1.19208	−	0.978313i	0.999995	+	0.00306612i	$0.000975976\pi$
$198$		0			0
$199$	−3.48100	−	5.20969i	−0.246762	−	0.369305i	0.687326	−	0.726349i	$-0.258785\pi$
$199$	−3.48100	−	5.20969i	−0.246762	−	0.369305i	−0.934087	+	0.357044i	$0.883785\pi$
$200$		0			0
$201$	7.51929	+	5.02423i	0.530370	+	0.354382i
$202$		0			0
$203$	5.76040	+	18.9895i	0.404301	+	1.33280i
$204$		0			0
$205$	0.0239616	−	0.0291973i	0.00167355	−	0.00203923i
$206$		0			0
$207$	−3.07518	+	7.42414i	−0.213740	+	0.516014i
$208$		0			0
$209$	0.0150722	+	0.0363875i	0.00104256	+	0.00251697i
$210$		0			0
$211$	8.19563	−	0.807199i	0.564210	−	0.0555698i	0.188108	−	0.982148i	$-0.439764\pi$
$211$	8.19563	−	0.807199i	0.564210	−	0.0555698i	0.376102	+	0.926578i	$0.377264\pi$
$212$		0			0
$213$	5.25620	+	2.80950i	0.360149	+	0.192503i
$214$		0			0
$215$	−0.132164	−	0.664433i	−0.00901350	−	0.0453139i
$216$		0			0
$217$	35.2964	+	7.02089i	2.39608	+	0.476609i
$218$		0			0
$219$	8.58266	+	0.845319i	0.579963	+	0.0571213i
$220$		0			0
$221$	2.86714	+	0.869736i	0.192864	+	0.0585048i
$222$		0			0
$223$	11.6133	−	11.6133i	0.777684	−	0.777684i	−0.201753	−	0.979436i	$-0.564664\pi$
$223$	11.6133	−	11.6133i	0.777684	−	0.777684i	0.979436	+	0.201753i	$0.0646638\pi$
$224$		0			0
$225$	8.14805	+	8.14805i	0.543204	+	0.543204i
$226$		0			0
$227$	−3.16640	+	10.4382i	−0.210161	+	0.692809i	0.786961	+	0.617003i	$0.211653\pi$
$227$	−3.16640	+	10.4382i	−0.210161	+	0.692809i	−0.997123	+	0.0758068i	$0.975847\pi$
$228$		0			0
$229$	2.11359	−	21.4596i	0.139670	−	1.41809i	−0.628481	−	0.777825i	$-0.716323\pi$
$229$	2.11359	−	21.4596i	0.139670	−	1.41809i	0.768151	−	0.640269i	$-0.221177\pi$
$230$		0			0
$231$	0.0149696	−	0.0752572i	0.000984926	−	0.00495156i
$232$		0			0
$233$	−16.2550	+	3.23332i	−1.06490	+	0.211822i	−0.696288	−	0.717762i	$-0.745167\pi$
$233$	−16.2550	+	3.23332i	−1.06490	+	0.211822i	−0.368611	+	0.929584i	$0.620167\pi$
$234$		0			0
$235$	−0.0250651	+	0.0468935i	−0.00163507	+	0.00305900i
$236$		0			0
$237$	0.107165	+	1.08806i	0.00696109	+	0.0706771i
$238$		0			0
$239$	11.1084	−	4.60123i	0.718540	−	0.297629i	0.00670690	−	0.999978i	$-0.497865\pi$
$239$	11.1084	−	4.60123i	0.718540	−	0.297629i	0.711833	+	0.702348i	$0.247865\pi$
$240$		0			0
$241$	−5.46474	−	2.26357i	−0.352015	−	0.145809i	0.199667	−	0.979864i	$-0.436014\pi$
$241$	−5.46474	−	2.26357i	−0.352015	−	0.145809i	−0.551682	+	0.834054i	$0.686014\pi$
$242$		0			0
$243$	12.3229	+	10.1132i	0.790517	+	0.648761i
$244$		0			0
$245$	−1.02665	+	0.311430i	−0.0655901	+	0.0198966i
$246$		0			0
$247$	0.567538	−	0.849381i	0.0361116	−	0.0540448i
$248$		0			0
$249$	11.2700	−	7.53038i	0.714207	−	0.477218i
$250$		0			0
$251$	−10.6829	−	13.0172i	−0.674301	−	0.821638i	0.317657	−	0.948206i	$-0.397104\pi$
$251$	−10.6829	−	13.0172i	−0.674301	−	0.821638i	−0.991958	+	0.126568i	$0.959604\pi$
$252$		0			0
$253$	−0.0712687	+	0.0380939i	−0.00448062	+	0.00239494i
$254$		0			0
$255$	0.501268			0.0313906
$256$		0			0
$257$	−23.9405			−1.49337			−0.746684	−	0.665178i	$-0.768355\pi$
$257$	−23.9405			−1.49337			−0.746684	+	0.665178i	$0.768355\pi$
$258$		0			0
$259$	30.8710	−	16.5009i	1.91823	−	1.02532i
$260$		0			0
$261$	−7.31455	−	8.91281i	−0.452760	−	0.551689i
$262$		0			0
$263$	−10.9676	+	7.32835i	−0.676294	+	0.451885i	−0.845698	−	0.533661i	$-0.820816\pi$
$263$	−10.9676	+	7.32835i	−0.676294	+	0.451885i	0.169404	+	0.985547i	$0.445816\pi$
$264$		0			0
$265$	0.431232	−	0.645384i	0.0264904	−	0.0396456i
$266$		0			0
$267$	−1.62538	+	0.493054i	−0.0994717	+	0.0301744i
$268$		0			0
$269$	−8.79097	−	7.21456i	−0.535995	−	0.439880i	0.327050	−	0.945007i	$-0.393946\pi$
$269$	−8.79097	−	7.21456i	−0.535995	−	0.439880i	−0.863045	+	0.505127i	$0.831446\pi$
$270$		0			0
$271$	−1.68682	−	0.698705i	−0.102467	−	0.0424433i	0.330861	−	0.943680i	$-0.392661\pi$
$271$	−1.68682	−	0.698705i	−0.102467	−	0.0424433i	−0.433328	+	0.901236i	$0.642661\pi$
$272$		0			0
$273$	−1.83869	+	0.761611i	−0.111283	+	0.0460948i
$274$		0			0
$275$	0.0113582	+	0.115322i	0.000684924	+	0.00695415i
$276$		0			0
$277$	−10.7417	+	20.0963i	−0.645405	+	1.20747i	0.320174	+	0.947359i	$0.396259\pi$
$277$	−10.7417	+	20.0963i	−0.645405	+	1.20747i	−0.965579	+	0.260109i	$0.916241\pi$
$278$		0			0
$279$	−20.5084	+	4.07937i	−1.22780	+	0.244226i
$280$		0			0
$281$	1.26582	−	6.36368i	0.0755122	−	0.379626i	−0.924487	−	0.381215i	$-0.875506\pi$
$281$	1.26582	−	6.36368i	0.0755122	−	0.379626i	0.999999	+	0.00158916i	$0.000505845\pi$
$282$		0			0
$283$	−0.0748010	+	0.759467i	−0.00444646	+	0.0451456i	−0.997152	−	0.0754191i	$-0.975971\pi$
$283$	−0.0748010	+	0.759467i	−0.00444646	+	0.0451456i	0.992705	+	0.120565i	$0.0384705\pi$
$284$		0			0
$285$	0.0496120	−	0.163549i	0.00293876	−	0.00968781i
$286$		0			0
$287$	0.874068	+	0.874068i	0.0515946	+	0.0515946i
$288$		0			0
$289$	5.44259	−	5.44259i	0.320152	−	0.320152i
$290$		0			0
$291$	−5.95166	−	1.80542i	−0.348892	−	0.105835i
$292$		0			0
$293$	31.9981	+	3.15153i	1.86935	+	0.184115i	0.968331	−	0.249671i	$-0.0803225\pi$
$293$	31.9981	+	3.15153i	1.86935	+	0.184115i	0.901016	+	0.433786i	$0.142823\pi$
$294$		0			0
$295$	1.22750	+	0.244165i	0.0714678	+	0.0142158i
$296$		0			0
$297$	0.0199866	+	0.100479i	0.00115974	+	0.00583041i
$298$		0			0
$299$	1.84849	+	0.988041i	0.106901	+	0.0571399i
$300$		0			0
$301$	22.0640	−	2.17311i	1.27175	−	0.125256i
$302$		0			0
$303$	−3.53924	−	8.54448i	−0.203324	−	0.490868i
$304$		0			0
$305$	−0.651100	+	1.57189i	−0.0372819	+	0.0900064i
$306$		0			0
$307$	15.6652	−	19.0882i	0.894062	−	1.08942i	−0.101455	−	0.994840i	$-0.532350\pi$
$307$	15.6652	−	19.0882i	0.894062	−	1.08942i	0.995517	−	0.0945782i	$-0.0301502\pi$
$308$		0			0
$309$	−3.03522	−	10.0058i	−0.172668	−	0.569209i
$310$		0			0
$311$	15.6555	+	10.4607i	0.887745	+	0.593172i	0.913654	−	0.406492i	$-0.133248\pi$
$311$	15.6555	+	10.4607i	0.887745	+	0.593172i	−0.0259096	+	0.999664i	$0.508248\pi$
$312$		0			0
$313$	−12.9159	−	19.3301i	−0.730052	−	1.09260i	−0.991842	−	0.127475i	$-0.959313\pi$
$313$	−12.9159	−	19.3301i	−0.730052	−	1.09260i	0.261790	−	0.965125i	$-0.415687\pi$
$314$		0			0
$315$	0.864039	−	0.709098i	0.0486831	−	0.0399532i
$316$		0			0
$317$	4.77352	+	8.93063i	0.268108	+	0.501594i	0.979563	−	0.201137i	$-0.0644636\pi$
$317$	4.77352	+	8.93063i	0.268108	+	0.501594i	−0.711455	+	0.702731i	$0.751964\pi$
$318$		0			0
$319$		−	0.115949i		−	0.00649190i
$320$		0			0
$321$			10.0070i			0.558534i
$322$		0			0
$323$	−3.96938	−	7.42619i	−0.220862	−	0.413204i
$324$		0			0
$325$	2.32333	−	1.90671i	0.128875	−	0.105765i
$326$		0			0
$327$	−2.35683	−	3.52725i	−0.130333	−	0.195057i
$328$		0			0
$329$	−1.44688	−	0.966775i	−0.0797691	−	0.0533000i
$330$		0			0
$331$	7.57606	+	24.9749i	0.416418	+	1.37275i	0.875012	+	0.484101i	$0.160853\pi$
$331$	7.57606	+	24.9749i	0.416418	+	1.37275i	−0.458594	+	0.888646i	$0.651647\pi$
$332$		0			0
$333$	−12.9027	+	15.7220i	−0.707063	+	0.861559i
$334$		0			0
$335$	−0.506969	+	1.22393i	−0.0276987	+	0.0668706i
$336$		0			0
$337$	8.11390	+	19.5887i	0.441992	+	1.06706i	0.975249	+	0.221110i	$0.0709681\pi$
$337$	8.11390	+	19.5887i	0.441992	+	1.06706i	−0.533256	+	0.845954i	$0.679032\pi$
$338$		0			0
$339$	4.78699	−	0.471477i	0.259994	−	0.0256071i
$340$		0			0
$341$	−0.185449	−	0.0991247i	−0.0100426	−	0.00536790i
$342$		0			0
$343$	−1.41705	−	7.12399i	−0.0765134	−	0.384659i
$344$		0			0
$345$	0.343929	+	0.0684118i	0.0185165	+	0.00368317i
$346$		0			0
$347$	−5.66595	−	0.558048i	−0.304164	−	0.0299576i	−0.0552163	−	0.998474i	$-0.517585\pi$
$347$	−5.66595	−	0.558048i	−0.304164	−	0.0299576i	−0.248948	+	0.968517i	$0.580085\pi$
$348$		0			0
$349$	20.0761	+	6.09002i	1.07465	+	0.325991i	0.777528	−	0.628848i	$-0.216473\pi$
$349$	20.0761	+	6.09002i	1.07465	+	0.325991i	0.297122	+	0.954840i	$0.403973\pi$
$350$		0			0
$351$	1.87892	−	1.87892i	0.100289	−	0.100289i
$352$		0			0
$353$	−4.75045	−	4.75045i	−0.252841	−	0.252841i	0.569293	−	0.822134i	$-0.307217\pi$
$353$	−4.75045	−	4.75045i	−0.252841	−	0.252841i	−0.822134	+	0.569293i	$0.807217\pi$
$354$		0			0
$355$	−0.253442	+	0.835485i	−0.0134513	+	0.0443429i
$356$		0			0
$357$	−1.60796	+	16.3259i	−0.0851024	+	0.864059i
$358$		0			0
$359$	−2.60517	+	13.0971i	−0.137495	+	0.691237i	0.849124	+	0.528194i	$0.177131\pi$
$359$	−2.60517	+	13.0971i	−0.137495	+	0.691237i	−0.986619	+	0.163042i	$0.947869\pi$
$360$		0			0
$361$	15.8191	−	3.14662i	0.832585	−	0.165611i
$362$		0			0
$363$	4.30255	−	8.04951i	0.225825	−	0.422490i
$364$		0			0
$365$	0.123832	+	1.25729i	0.00648165	+	0.0658093i
$366$		0			0
$367$	−11.3928	+	4.71905i	−0.594700	+	0.246333i	−0.659671	−	0.751555i	$-0.729304\pi$
$367$	−11.3928	+	4.71905i	−0.594700	+	0.246333i	0.0649715	+	0.997887i	$0.479304\pi$
$368$		0			0
$369$	−0.663554	−	0.274853i	−0.0345433	−	0.0143083i
$370$		0			0
$371$	19.6363	+	16.1151i	1.01947	+	0.836656i
$372$		0			0
$373$	8.71947	−	2.64502i	0.451477	−	0.136954i	−0.0563537	−	0.998411i	$-0.517947\pi$
$373$	8.71947	−	2.64502i	0.451477	−	0.136954i	0.507831	+	0.861457i	$0.330447\pi$
$374$		0			0
$375$	0.559558	−	0.837438i	0.0288955	−	0.0432451i
$376$		0			0
$377$	−2.50054	+	1.67080i	−0.128784	+	0.0860508i
$378$		0			0
$379$	−11.4836	−	13.9928i	−0.589871	−	0.718760i	0.389455	−	0.921045i	$-0.372663\pi$
$379$	−11.4836	−	13.9928i	−0.589871	−	0.718760i	−0.979327	+	0.202285i	$0.935163\pi$
$380$		0			0
$381$	6.42119	−	3.43220i	0.328967	−	0.175837i
$382$		0			0
$383$	9.09522			0.464744			0.232372	−	0.972627i	$-0.425351\pi$
$383$	9.09522			0.464744			0.232372	+	0.972627i	$0.425351\pi$
$384$		0			0
$385$	0.0112405			0.000572869
$386$		0			0
$387$	−11.3609	+	6.07250i	−0.577505	+	0.308683i
$388$		0			0
$389$	−15.2648	−	18.6002i	−0.773954	−	0.943066i	0.225560	−	0.974229i	$-0.427579\pi$
$389$	−15.2648	−	18.6002i	−0.773954	−	0.943066i	−0.999514	+	0.0311635i	$0.990079\pi$
$390$		0			0
$391$	14.3653	−	9.59860i	0.726485	−	0.485422i
$392$		0			0
$393$	−4.91845	+	7.36098i	−0.248103	+	0.371312i
$394$		0			0
$395$	−0.153266	+	0.0464928i	−0.00771165	+	0.00233930i
$396$		0			0
$397$	−4.06935	−	3.33963i	−0.204235	−	0.167611i	0.526716	−	0.850041i	$-0.323423\pi$
$397$	−4.06935	−	3.33963i	−0.204235	−	0.167611i	−0.730951	+	0.682430i	$0.760923\pi$
$398$		0			0
$399$	5.16751	+	2.14045i	0.258699	+	0.107157i
$400$		0			0
$401$	−5.81542	+	2.40882i	−0.290408	+	0.120291i	−0.523131	−	0.852252i	$-0.675236\pi$
$401$	−5.81542	+	2.40882i	−0.290408	+	0.120291i	0.232723	+	0.972543i	$0.425236\pi$
$402$		0			0
$403$	0.534585	+	5.42773i	0.0266296	+	0.270375i
$404$		0			0
$405$	−0.187785	+	0.351321i	−0.00933112	+	0.0174573i
$406$		0			0
$407$	−0.200601	+	0.0399021i	−0.00994344	+	0.00197787i
$408$		0			0
$409$	−0.477282	+	2.39946i	−0.0236001	+	0.118646i	−0.990790	−	0.135410i	$-0.956765\pi$
$409$	−0.477282	+	2.39946i	−0.0236001	+	0.118646i	0.967190	+	0.254056i	$0.0817647\pi$
$410$		0			0
$411$	1.78046	−	18.0773i	0.0878234	−	0.891686i
$412$		0			0
$413$	−11.8898	+	39.1954i	−0.585059	+	1.92868i
$414$		0			0
$415$	1.40402	+	1.40402i	0.0689208	+	0.0689208i
$416$		0			0
$417$	−6.19405	+	6.19405i	−0.303324	+	0.303324i
$418$		0			0
$419$	8.91320	+	2.70379i	0.435438	+	0.132089i	0.500391	−	0.865800i	$-0.333190\pi$
$419$	8.91320	+	2.70379i	0.435438	+	0.132089i	−0.0649526	+	0.997888i	$0.520690\pi$
$420$		0			0
$421$	−39.1667	−	3.85758i	−1.90887	−	0.188007i	−0.926673	−	0.375869i	$-0.877344\pi$
$421$	−39.1667	−	3.85758i	−1.90887	−	0.188007i	−0.982196	+	0.187862i	$0.939844\pi$
$422$		0			0
$423$	0.991656	+	0.197253i	0.0482160	+	0.00959075i
$424$		0			0
$425$	−4.83328	−	24.2986i	−0.234449	−	1.17865i
$426$		0			0
$427$	−49.1067	−	26.2481i	−2.37644	−	1.27023i
$428$		0			0
$429$	0.0115727	−	0.00113981i	0.000558736	−	5.50307e-5i
$430$		0			0
$431$	−8.66423	−	20.9173i	−0.417341	−	1.00755i	−0.983115	−	0.182990i	$-0.941422\pi$
$431$	−8.66423	−	20.9173i	−0.417341	−	1.00755i	0.565773	−	0.824561i	$-0.308578\pi$
$432$		0			0
$433$	3.05834	−	7.38350i	0.146975	−	0.354828i	−0.833198	−	0.552975i	$-0.813492\pi$
$433$	3.05834	−	7.38350i	0.146975	−	0.354828i	0.980172	+	0.198147i	$0.0634924\pi$
$434$		0			0
$435$	−0.319192	+	0.388937i	−0.0153041	+	0.0186481i
$436$		0			0
$437$	−1.70996	−	5.63698i	−0.0817984	−	0.269653i
$438$		0			0
$439$	14.1963	+	9.48567i	0.677553	+	0.452726i	0.846140	−	0.532960i	$-0.178921\pi$
$439$	14.1963	+	9.48567i	0.677553	+	0.452726i	−0.168587	+	0.985687i	$0.553921\pi$
$440$		0			0
$441$	11.3339	+	16.9624i	0.539710	+	0.807733i
$442$		0			0
$443$	−27.7871	+	22.8043i	−1.32021	+	1.08346i	−0.329980	+	0.943988i	$0.607042\pi$
$443$	−27.7871	+	22.8043i	−1.32021	+	1.08346i	−0.990225	+	0.139476i	$0.955458\pi$
$444$		0			0
$445$	−0.117292	−	0.219438i	−0.00556018	−	0.0104024i
$446$		0			0
$447$		−	9.33263i		−	0.441418i
$448$		0			0
$449$		−	17.0810i		−	0.806100i	−0.915178	−	0.403050i	$-0.867950\pi$
$449$		−	17.0810i		−	0.806100i	0.915178	−	0.403050i	$-0.132050\pi$
$450$		0			0
$451$	−0.00340475	−	0.00636984i	−0.000160324	−	0.000299944i
$452$		0			0
$453$	0.534783	−	0.438885i	0.0251263	−	0.0206206i
$454$		0			0
$455$	−0.161974	−	0.242411i	−0.00759344	−	0.0113644i
$456$		0			0
$457$	3.38358	+	2.26083i	0.158277	+	0.105757i	0.632187	−	0.774816i	$-0.282158\pi$
$457$	3.38358	+	2.26083i	0.158277	+	0.105757i	−0.473910	+	0.880574i	$0.657158\pi$
$458$		0			0
$459$	−6.35810	−	20.9598i	−0.296771	−	0.978322i
$460$		0			0
$461$	−14.1236	+	17.2096i	−0.657800	+	0.801532i	−0.989908	−	0.141710i	$-0.954740\pi$
$461$	−14.1236	+	17.2096i	−0.657800	+	0.801532i	0.332108	+	0.943241i	$0.392240\pi$
$462$		0			0
$463$	4.50354	−	10.8725i	0.209297	−	0.505288i	−0.784016	−	0.620741i	$-0.786832\pi$
$463$	4.50354	−	10.8725i	0.209297	−	0.505288i	0.993313	+	0.115453i	$0.0368319\pi$
$464$		0			0
$465$	0.349190	+	0.843018i	0.0161933	+	0.0390940i
$466$		0			0
$467$	−37.3627	+	3.67991i	−1.72894	+	0.170286i	−0.913030	−	0.407893i	$-0.866264\pi$
$467$	−37.3627	+	3.67991i	−1.72894	+	0.170286i	−0.815910	+	0.578179i	$0.803764\pi$
$468$		0			0
$469$	−38.2362	−	20.4377i	−1.76559	−	0.943725i
$470$		0			0
$471$	1.31879	+	6.63001i	0.0607667	+	0.305495i
$472$		0			0
$473$	−0.127055	−	0.0252729i	−0.00584201	−	0.00116205i
$474$		0			0
$475$	−8.40626	−	0.827944i	−0.385706	−	0.0379887i
$476$		0			0
$477$	−14.1241	−	4.28450i	−0.646698	−	0.196174i
$478$		0			0
$479$	16.9780	−	16.9780i	0.775746	−	0.775746i	−0.203358	−	0.979104i	$-0.565186\pi$
$479$	16.9780	−	16.9780i	0.775746	−	0.775746i	0.979104	+	0.203358i	$0.0651856\pi$
$480$		0			0
$481$	3.75115	+	3.75115i	0.171038	+	0.171038i
$482$		0			0
$483$	−3.33137	+	10.9821i	−0.151583	+	0.499701i
$484$		0			0
$485$	0.0893032	−	0.906710i	0.00405505	−	0.0411716i
$486$		0			0
$487$	−7.02462	+	35.3151i	−0.318316	+	1.60028i	0.408041	+	0.912964i	$0.366212\pi$
$487$	−7.02462	+	35.3151i	−0.318316	+	1.60028i	−0.726357	+	0.687318i	$0.758788\pi$
$488$		0			0
$489$	6.13865	−	1.22105i	0.277600	−	0.0552180i
$490$		0			0
$491$	−5.35809	+	10.0243i	−0.241807	+	0.452389i	−0.973324	−	0.229434i	$-0.926313\pi$
$491$	−5.35809	+	10.0243i	−0.241807	+	0.452389i	0.731517	+	0.681823i	$0.238813\pi$
$492$		0			0
$493$	2.42979	+	24.6701i	0.109432	+	1.11109i
$494$		0			0
$495$	−0.00603395	+	0.00249934i	−0.000271206	+	0.000112337i
$496$		0			0
$497$	−26.3981	−	10.9344i	−1.18412	−	0.490477i
$498$		0			0
$499$	3.89647	+	3.19775i	0.174430	+	0.143151i	0.717558	−	0.696499i	$-0.245260\pi$
$499$	3.89647	+	3.19775i	0.174430	+	0.143151i	−0.543128	+	0.839650i	$0.682760\pi$
$500$		0			0
$501$	10.2194	−	3.10003i	0.456570	−	0.138499i
$502$		0			0
$503$	0.917582	−	1.37326i	0.0409130	−	0.0612306i	−0.810449	−	0.585809i	$-0.800777\pi$
$503$	0.917582	−	1.37326i	0.0409130	−	0.0612306i	0.851362	+	0.524578i	$0.175777\pi$
$504$		0			0
$505$	1.12649	−	0.752699i	0.0501283	−	0.0334947i
$506$		0			0
$507$	6.65203	+	8.10552i	0.295427	+	0.359979i
$508$		0			0
$509$	9.24185	−	4.93987i	0.409638	−	0.218956i	−0.253689	−	0.967286i	$-0.581644\pi$
$509$	9.24185	−	4.93987i	0.409638	−	0.218956i	0.663327	+	0.748330i	$0.269144\pi$
$510$		0			0
$511$	−41.3460			−1.82904
$512$		0			0
$513$	−7.46785			−0.329714
$514$		0			0
$515$	1.35085	−	0.722045i	0.0595257	−	0.0318171i
$516$		0			0
$517$	0.00645035	+	0.00785978i	0.000283686	+	0.000345673i
$518$		0			0
$519$	−10.3888	+	6.94156i	−0.456017	+	0.304701i
$520$		0			0
$521$	11.7661	−	17.6092i	0.515482	−	0.771473i	−0.478839	−	0.877903i	$-0.658942\pi$
$521$	11.7661	−	17.6092i	0.515482	−	0.771473i	0.994320	+	0.106430i	$0.0339421\pi$
$522$		0			0
$523$	−4.31365	+	1.30853i	−0.188623	+	0.0572181i	−0.383183	−	0.923673i	$-0.625172\pi$
$523$	−4.31365	+	1.30853i	−0.188623	+	0.0572181i	0.194560	+	0.980891i	$0.437672\pi$
$524$		0			0
$525$	12.7210	+	10.4399i	0.555191	+	0.455633i
$526$		0			0
$527$	41.5346	+	17.2042i	1.80928	+	0.749427i
$528$		0			0
$529$	−10.0829	+	4.17649i	−0.438389	+	0.181586i
$530$		0			0
$531$	−2.33267	−	23.6840i	−0.101229	−	1.02780i
$532$		0			0
$533$	−0.0883090	+	0.165215i	−0.00382509	+	0.00715624i
$534$		0			0
$535$	−1.43776	+	0.285989i	−0.0621600	+	0.0123644i
$536$		0			0
$537$	1.99708	−	10.0400i	0.0861803	−	0.433257i
$538$		0			0
$539$	−0.0201085	+	0.204166i	−0.000866137	+	0.00879403i
$540$		0			0
$541$	−1.60334	+	5.28551i	−0.0689330	+	0.227242i	−0.984638	−	0.174610i	$-0.944133\pi$
$541$	−1.60334	+	5.28551i	−0.0689330	+	0.227242i	0.915705	+	0.401852i	$0.131633\pi$
$542$		0			0
$543$	5.26274	+	5.26274i	0.225846	+	0.225846i
$544$		0			0
$545$	0.439427	−	0.439427i	0.0188230	−	0.0188230i
$546$		0			0
$547$	30.7204	+	9.31895i	1.31351	+	0.398449i	0.867883	−	0.496769i	$-0.165480\pi$
$547$	30.7204	+	9.31895i	1.31351	+	0.398449i	0.445628	+	0.895218i	$0.352980\pi$
$548$		0			0
$549$	32.1970	+	3.17113i	1.37413	+	0.135340i
$550$		0			0
$551$	8.28960	+	1.64890i	0.353149	+	0.0702457i
$552$		0			0
$553$	−1.02259	−	5.14089i	−0.0434848	−	0.218613i
$554$		0			0
$555$	0.782737	+	0.418382i	0.0332253	+	0.0177593i
$556$		0			0
$557$	1.22883	−	0.121029i	0.0520672	−	0.00512817i	−0.0719500	−	0.997408i	$-0.522922\pi$
$557$	1.22883	−	0.121029i	0.0520672	−	0.00512817i	0.124017	+	0.992280i	$0.460422\pi$
$558$		0			0
$559$	1.28581	+	3.10423i	0.0543841	+	0.131295i
$560$		0			0
$561$	0.0366819	−	0.0885580i	0.00154871	−	0.00373892i
$562$		0			0
$563$	−19.6923	+	23.9952i	−0.829933	+	1.01128i	0.169735	+	0.985490i	$0.445709\pi$
$563$	−19.6923	+	23.9952i	−0.829933	+	1.01128i	−0.999667	+	0.0257864i	$0.991791\pi$
$564$		0			0
$565$	0.204548	+	0.674304i	0.00860539	+	0.0283682i
$566$		0			0
$567$	−10.8399	−	7.24298i	−0.455232	−	0.304177i
$568$		0			0
$569$	−16.8146	−	25.1648i	−0.704905	−	1.05496i	−0.995184	−	0.0980224i	$-0.968748\pi$
$569$	−16.8146	−	25.1648i	−0.704905	−	1.05496i	0.290280	−	0.956942i	$-0.406252\pi$
$570$		0			0
$571$	−15.3113	+	12.5656i	−0.640756	+	0.525855i	−0.897720	−	0.440566i	$-0.854778\pi$
$571$	−15.3113	+	12.5656i	−0.640756	+	0.525855i	0.256964	+	0.966421i	$0.417278\pi$
$572$		0			0
$573$	−7.97689	−	14.9237i	−0.333239	−	0.623447i
$574$		0			0
$575$		−	17.3313i		−	0.722766i
$576$		0			0
$577$		−	8.22211i		−	0.342291i	−0.985246	−	0.171146i	$-0.945253\pi$
$577$		−	8.22211i		−	0.342291i	0.985246	−	0.171146i	$-0.0547468\pi$
$578$		0			0
$579$	−10.2314	−	19.1416i	−0.425202	−	0.795497i
$580$		0			0
$581$	−50.2318	+	41.2241i	−2.08396	+	1.71027i
$582$		0			0
$583$	−0.0824618	−	0.123413i	−0.00341522	−	0.00511123i
$584$		0			0
$585$	0.140849	+	0.0941120i	0.00582337	+	0.00389105i
$586$		0			0
$587$	−3.60109	−	11.8712i	−0.148633	−	0.489978i	0.850732	−	0.525599i	$-0.176159\pi$
$587$	−3.60109	−	11.8712i	−0.148633	−	0.489978i	−0.999365	+	0.0356217i	$0.988659\pi$
$588$		0			0
$589$	9.72403	−	11.8488i	0.400672	−	0.488220i
$590$		0			0
$591$	−6.87322	+	16.5934i	−0.282726	+	0.682562i
$592$		0			0
$593$	2.11689	+	5.11064i	0.0869304	+	0.209869i	0.961366	−	0.275273i	$-0.0887681\pi$
$593$	2.11689	+	5.11064i	0.0869304	+	0.209869i	−0.874436	+	0.485141i	$0.838768\pi$
$594$		0			0
$595$	−2.39160	+	0.235552i	−0.0980462	+	0.00965671i
$596$		0			0
$597$	4.58526	+	2.45087i	0.187662	+	0.100307i
$598$		0			0
$599$	−0.665937	−	3.34789i	−0.0272094	−	0.136791i	0.964793	−	0.263011i	$-0.0847155\pi$
$599$	−0.665937	−	3.34789i	−0.0272094	−	0.136791i	−0.992002	+	0.126220i	$0.959716\pi$
$600$		0			0
$601$	7.99415	+	1.59013i	0.326088	+	0.0648629i	0.355420	−	0.934707i	$-0.384338\pi$
$601$	7.99415	+	1.59013i	0.326088	+	0.0648629i	−0.0293318	+	0.999570i	$0.509338\pi$
$602$		0			0
$603$	25.0697	+	2.46915i	1.02092	+	0.100552i
$604$		0			0
$605$	1.27949	+	0.388129i	0.0520186	+	0.0157797i
$606$		0			0
$607$	−2.14223	+	2.14223i	−0.0869506	+	0.0869506i	−0.749244	−	0.662294i	$-0.769583\pi$
$607$	−2.14223	+	2.14223i	−0.0869506	+	0.0869506i	0.662294	+	0.749244i	$0.269583\pi$
$608$		0			0
$609$	−11.6435	−	11.6435i	−0.471817	−	0.471817i
$610$		0			0
$611$	0.0765541	−	0.252365i	0.00309705	−	0.0102096i
$612$		0			0
$613$	−0.970077	+	9.84936i	−0.0391810	+	0.397812i	0.955514	+	0.294945i	$0.0953014\pi$
$613$	−0.970077	+	9.84936i	−0.0391810	+	0.397812i	−0.994695	+	0.102866i	$0.967199\pi$
$614$		0			0
$615$	−0.00611450	+	0.0307397i	−0.000246560	+	0.00123954i
$616$		0			0
$617$	38.5540	−	7.66886i	1.55212	−	0.308737i	0.656770	−	0.754091i	$-0.271922\pi$
$617$	38.5540	−	7.66886i	1.55212	−	0.308737i	0.895355	+	0.445354i	$0.146922\pi$
$618$		0			0
$619$	−0.0636802	+	0.119137i	−0.00255952	+	0.00478853i	−0.883198	−	0.469001i	$-0.844614\pi$
$619$	−0.0636802	+	0.119137i	−0.00255952	+	0.00478853i	0.880638	+	0.473789i	$0.157114\pi$
$620$		0			0
$621$	−1.50186	−	15.2487i	−0.0602677	−	0.611908i
$622$		0			0
$623$	7.52317	−	3.11620i	0.301409	−	0.124848i
$624$		0			0
$625$	−22.8924	−	9.48235i	−0.915697	−	0.379294i
$626$		0			0
$627$	−0.0252633	−	0.0207331i	−0.00100892	−	0.000827999i
$628$		0			0
$629$	41.8451	−	12.6936i	1.66847	−	0.506126i
$630$		0			0
$631$	−22.5931	+	33.8130i	−0.899419	+	1.34608i	0.0385138	+	0.999258i	$0.487738\pi$
$631$	−22.5931	+	33.8130i	−0.899419	+	1.34608i	−0.937933	+	0.346817i	$0.887262\pi$
$632$		0			0
$633$	−5.68189	+	3.79652i	−0.225835	+	0.150898i
$634$		0			0
$635$	0.676637	+	0.824485i	0.0268515	+	0.0327187i
$636$		0			0
$637$	4.69276	−	2.50833i	0.185934	−	0.0993837i
$638$		0			0
$639$	16.6019			0.656761
$640$		0			0
$641$	23.1593			0.914737			0.457369	−	0.889277i	$-0.348792\pi$
$641$	23.1593			0.914737			0.457369	+	0.889277i	$0.348792\pi$
$642$		0			0
$643$	−19.7142	+	10.5374i	−0.777451	+	0.415556i	−0.811860	−	0.583852i	$-0.801545\pi$
$643$	−19.7142	+	10.5374i	−0.777451	+	0.415556i	0.0344096	+	0.999408i	$0.489045\pi$
$644$		0			0
$645$	0.356619	+	0.434541i	0.0140418	+	0.0171100i
$646$		0			0
$647$	16.9366	−	11.3167i	0.665848	−	0.444906i	−0.176166	−	0.984360i	$-0.556370\pi$
$647$	16.9366	−	11.3167i	0.665848	−	0.444906i	0.842015	+	0.539455i	$0.181370\pi$
$648$		0			0
$649$	0.132962	−	0.198992i	0.00521922	−	0.00781112i
$650$		0			0
$651$	−28.5766	+	8.66860i	−1.12000	+	0.339749i
$652$		0			0
$653$	−4.07582	−	3.34494i	−0.159499	−	0.130898i	0.551259	−	0.834334i	$-0.314148\pi$
$653$	−4.07582	−	3.34494i	−0.159499	−	0.130898i	−0.710758	+	0.703437i	$0.751648\pi$
$654$		0			0
$655$	−1.19816	−	0.496296i	−0.0468162	−	0.0193919i
$656$		0			0
$657$	22.1947	−	9.19335i	0.865898	−	0.358667i
$658$		0			0
$659$	−4.24986	−	43.1495i	−0.165551	−	1.68087i	−0.615753	−	0.787939i	$-0.711148\pi$
$659$	−4.24986	−	43.1495i	−0.165551	−	1.68087i	0.450202	−	0.892927i	$-0.351352\pi$
$660$		0			0
$661$	−0.696171	+	1.30244i	−0.0270779	+	0.0506592i	−0.895096	−	0.445873i	$-0.852893\pi$
$661$	−0.696171	+	1.30244i	−0.0270779	+	0.0506592i	0.868018	+	0.496532i	$0.165393\pi$
$662$		0			0
$663$	−2.43840	+	0.485029i	−0.0946998	+	0.0188370i
$664$		0			0
$665$	−0.159850	+	0.803623i	−0.00619874	+	0.0311631i
$666$		0			0
$667$	−1.69979	+	17.2582i	−0.0658159	+	0.668240i
$668$		0			0
$669$	−3.95606	+	13.0414i	−0.152950	+	0.504209i
$670$		0			0
$671$	0.230057	+	0.230057i	0.00888124	+	0.00888124i
$672$		0			0
$673$	−1.82208	+	1.82208i	−0.0702360	+	0.0702360i	−0.741352	−	0.671116i	$-0.765815\pi$
$673$	−1.82208	+	1.82208i	−0.0702360	+	0.0702360i	0.671116	+	0.741352i	$0.265815\pi$
$674$		0			0
$675$	−21.0257	−	6.37808i	−0.809280	−	0.245492i
$676$		0			0
$677$	−0.419455	−	0.0413127i	−0.0161210	−	0.00158778i	0.0899534	−	0.995946i	$-0.471328\pi$
$677$	−0.419455	−	0.0413127i	−0.0161210	−	0.00158778i	−0.106074	+	0.994358i	$0.533828\pi$
$678$		0			0
$679$	29.2444	+	5.81707i	1.12230	+	0.223239i
$680$		0			0
$681$	−1.76582	−	8.87737i	−0.0676663	−	0.340181i
$682$		0			0
$683$	17.5556	+	9.38369i	0.671748	+	0.359057i	0.771746	−	0.635931i	$-0.219384\pi$
$683$	17.5556	+	9.38369i	0.671748	+	0.359057i	−0.0999979	+	0.994988i	$0.531884\pi$
$684$		0			0
$685$	2.64816	−	0.260821i	0.101181	−	0.00996547i
$686$		0			0
$687$	6.84742	+	16.5311i	0.261245	+	0.630702i
$688$		0			0
$689$	−1.47324	+	3.55671i	−0.0561259	+	0.135500i
$690$		0			0
$691$	29.5091	−	35.9570i	1.12258	−	1.36787i	0.201040	−	0.979583i	$-0.435568\pi$
$691$	29.5091	−	35.9570i	1.12258	−	1.36787i	0.921540	−	0.388284i	$-0.126932\pi$
$692$		0			0
$693$	−0.0620460	−	0.204538i	−0.00235693	−	0.00776977i
$694$		0			0
$695$	−1.06696	−	0.712920i	−0.0404721	−	0.0270426i
$696$		0			0
$697$	0.857902	+	1.28394i	0.0324954	+	0.0486327i
$698$		0			0
$699$	10.6308	−	8.72448i	0.402094	−	0.329990i
$700$		0			0
$701$	4.39214	+	8.21711i	0.165889	+	0.310356i	0.951106	−	0.308864i	$-0.0999488\pi$
$701$	4.39214	+	8.21711i	0.165889	+	0.310356i	−0.785217	+	0.619220i	$0.787449\pi$
$702$		0			0
$703$		−	14.9091i		−	0.562308i
$704$		0			0
$705$		−	0.0441216i		−	0.00166172i
$706$		0			0
$707$	20.9012	+	39.1035i	0.786072	+	1.47064i
$708$		0			0
$709$	−9.64803	+	7.91793i	−0.362339	+	0.297364i	−0.797894	−	0.602798i	$-0.794052\pi$
$709$	−9.64803	+	7.91793i	−0.362339	+	0.297364i	0.435554	+	0.900162i	$0.356552\pi$
$710$		0			0
$711$	1.69202	+	2.53228i	0.0634555	+	0.0949679i
$712$		0			0
$713$	26.1497	+	17.4727i	0.979313	+	0.654356i
$714$		0			0
$715$	0.000494502		0.00163015i	1.84933e−5		6.09643e-5i
$716$		0			0
$717$	−6.32939	+	7.71238i	−0.236375	+	0.288024i
$718$		0			0
$719$	12.7225	−	30.7147i	0.474468	−	1.14547i	−0.487701	−	0.873011i	$-0.662164\pi$
$719$	12.7225	−	30.7147i	0.474468	−	1.14547i	0.962168	−	0.272456i	$-0.0878358\pi$
$720$		0			0
$721$	19.1832	+	46.3123i	0.714420	+	1.72476i
$722$		0			0
$723$	4.88457	−	0.481088i	0.181659	−	0.0178919i
$724$		0			0
$725$	21.9311	+	11.7224i	0.814499	+	0.435359i
$726$		0			0
$727$	1.56729	+	7.87929i	0.0581275	+	0.292227i	0.998904	−	0.0468000i	$-0.0149023\pi$
$727$	1.56729	+	7.87929i	0.0581275	+	0.292227i	−0.940777	+	0.339027i	$0.889902\pi$
$728$		0			0
$729$	−3.33142	−	0.662661i	−0.123386	−	0.0245430i
$730$		0			0
$731$	27.5628	+	2.71469i	1.01945	+	0.100407i
$732$		0			0
$733$	21.0691	+	6.39125i	0.778206	+	0.236066i	0.654308	−	0.756229i	$-0.272960\pi$
$733$	21.0691	+	6.39125i	0.778206	+	0.236066i	0.123899	+	0.992295i	$0.460460\pi$
$734$		0			0
$735$	0.629492	−	0.629492i	0.0232192	−	0.0232192i
$736$		0			0
$737$	0.179130	+	0.179130i	0.00659835	+	0.00659835i
$738$		0			0
$739$	−3.47126	+	11.4432i	−0.127692	+	0.420946i	−0.997354	−	0.0727036i	$-0.976837\pi$
$739$	−3.47126	+	11.4432i	−0.127692	+	0.420946i	0.869661	+	0.493649i	$0.164337\pi$
$740$		0			0
$741$	−0.0830857	+	0.843583i	−0.00305223	+	0.0309898i
$742$		0			0
$743$	5.67291	−	28.5196i	0.208119	−	1.04628i	−0.725556	−	0.688163i	$-0.758418\pi$
$743$	5.67291	−	28.5196i	0.208119	−	1.04628i	0.933675	−	0.358121i	$-0.116582\pi$
$744$		0			0
$745$	1.34088	−	0.266718i	0.0491260	−	0.00977178i
$746$		0			0
$747$	17.7984	−	33.2984i	0.651208	−	1.21832i
$748$		0			0
$749$	−4.70240	−	47.7442i	−0.171822	−	1.74454i
$750$		0			0
$751$	−11.2356	+	4.65395i	−0.409994	+	0.169825i	−0.578141	−	0.815937i	$-0.696222\pi$
$751$	−11.2356	+	4.65395i	−0.409994	+	0.169825i	0.168147	+	0.985762i	$0.446222\pi$
$752$		0			0
$753$	12.9097	+	5.34737i	0.470455	+	0.194869i
$754$		0			0
$755$	0.0783411	+	0.0642929i	0.00285112	+	0.00233986i
$756$		0			0
$757$	−22.4907	+	6.82249i	−0.817440	+	0.247968i	−0.671195	−	0.741281i	$-0.734219\pi$
$757$	−22.4907	+	6.82249i	−0.817440	+	0.247968i	−0.146245	+	0.989248i	$0.546719\pi$
$758$		0			0
$759$	0.0372543	−	0.0557550i	0.00135224	−	0.00202378i
$760$		0			0
$761$	−13.4730	+	9.00236i	−0.488395	+	0.326335i	−0.775267	−	0.631634i	$-0.782385\pi$
$761$	−13.4730	+	9.00236i	−0.488395	+	0.326335i	0.286872	+	0.957969i	$0.407385\pi$
$762$		0			0
$763$	12.9022	+	15.7214i	0.467091	+	0.569152i
$764$		0			0
$765$	1.23145	−	0.658223i	0.0445231	−	0.0237981i
$766$		0			0
$767$	−6.20739			−0.224136
$768$		0			0
$769$	−18.8181			−0.678600			−0.339300	−	0.940678i	$-0.610190\pi$
$769$	−18.8181			−0.678600			−0.339300	+	0.940678i	$0.610190\pi$
$770$		0			0
$771$	17.5199	−	9.36458i	0.630964	−	0.337257i
$772$		0			0
$773$	4.01518	+	4.89251i	0.144416	+	0.175971i	0.840195	−	0.542285i	$-0.182441\pi$
$773$	4.01518	+	4.89251i	0.144416	+	0.175971i	−0.695779	+	0.718256i	$0.744941\pi$
$774$		0			0
$775$	37.4977	−	25.0551i	1.34696	−	0.900007i
$776$		0			0
$777$	−16.1372	+	24.1510i	−0.578919	+	0.866414i
$778$		0			0
$779$	0.503821	−	0.152832i	0.0180513	−	0.00547579i
$780$		0			0
$781$	0.129057	+	0.105914i	0.00461802	+	0.00378991i
$782$		0			0
$783$	20.3115	+	8.41329i	0.725873	+	0.300667i
$784$		0			0
$785$	−0.914888	+	0.378959i	−0.0326537	+	0.0135256i
$786$		0			0
$787$	0.0914796	+	0.928808i	0.00326090	+	0.0331084i	0.996677	−	0.0814494i	$-0.0259549\pi$
$787$	0.0914796	+	0.928808i	0.00326090	+	0.0331084i	−0.993417	+	0.114558i	$0.963455\pi$
$788$		0			0
$789$	5.15967	−	9.65307i	0.183689	−	0.343658i
$790$		0			0
$791$	−22.6177	+	4.49893i	−0.804192	+	0.159964i
$792$		0			0
$793$	1.64628	−	8.27643i	0.0584613	−	0.293905i
$794$		0			0
$795$	−0.0631309	+	0.640979i	−0.00223902	+	0.0227332i
$796$		0			0
$797$	−1.61413	+	5.32107i	−0.0571754	+	0.188482i	−0.980876	−	0.194633i	$-0.937649\pi$
$797$	−1.61413	+	5.32107i	−0.0571754	+	0.188482i	0.923701	+	0.383115i	$0.125149\pi$
$798$		0			0
$799$	−1.53713	−	1.53713i	−0.0543797	−	0.0543797i
$800$		0			0
$801$	−3.34558	+	3.34558i	−0.118210	+	0.118210i
$802$		0			0
$803$	0.231184	+	0.0701288i	0.00815829	+	0.00247479i
$804$		0			0
$805$	−1.67307	−	0.164783i	−0.0589680	−	0.00580784i
$806$		0			0
$807$	9.25537	+	1.84101i	0.325804	+	0.0648065i
$808$		0			0
$809$	7.22202	+	36.3076i	0.253913	+	1.27651i	0.871653	+	0.490124i	$0.163048\pi$
$809$	7.22202	+	36.3076i	0.253913	+	1.27651i	−0.617740	+	0.786382i	$0.711952\pi$
$810$		0			0
$811$	−21.4330	−	11.4562i	−0.752615	−	0.402281i	0.0500228	−	0.998748i	$-0.484071\pi$
$811$	−21.4330	−	11.4562i	−0.752615	−	0.402281i	−0.802637	+	0.596467i	$0.796571\pi$
$812$		0			0
$813$	1.50774	−	0.148499i	0.0528787	−	0.00520810i
$814$		0			0
$815$	0.350874	+	0.847084i	0.0122906	+	0.0296721i
$816$		0			0
$817$	3.61369	−	8.72422i	0.126427	−	0.305222i
$818$		0			0
$819$	−3.51696	+	4.28543i	−0.122893	+	0.149745i
$820$		0			0
$821$	−0.847368	−	2.79340i	−0.0295734	−	0.0974903i	0.940911	−	0.338653i	$-0.109971\pi$
$821$	−0.847368	−	2.79340i	−0.0295734	−	0.0974903i	−0.970485	+	0.241163i	$0.922471\pi$
$822$		0			0
$823$	−7.77987	−	5.19834i	−0.271189	−	0.181203i	0.412538	−	0.910940i	$-0.364642\pi$
$823$	−7.77987	−	5.19834i	−0.271189	−	0.181203i	−0.683727	+	0.729737i	$0.739642\pi$
$824$		0			0
$825$	−0.0534212	−	0.0799505i	−0.00185989	−	0.00278352i
$826$		0			0
$827$	38.7516	−	31.8026i	1.34752	−	1.10588i	0.362781	−	0.931875i	$-0.381827\pi$
$827$	38.7516	−	31.8026i	1.34752	−	1.10588i	0.984744	−	0.174010i	$-0.0556726\pi$
$828$		0			0
$829$	14.2850	+	26.7253i	0.496138	+	0.928208i	0.997997	+	0.0632592i	$0.0201495\pi$
$829$	14.2850	+	26.7253i	0.496138	+	0.928208i	−0.501859	+	0.864949i	$0.667351\pi$
$830$		0			0
$831$		−	18.9084i		−	0.655924i
$832$		0			0
$833$		−	43.8610i		−	1.51969i
$834$		0			0
$835$	0.737463	+	1.37970i	0.0255209	+	0.0477463i
$836$		0			0
$837$	30.8205	−	25.2937i	1.06531	−	0.874279i
$838$		0			0
$839$	−17.3312	−	25.9380i	−0.598340	−	0.895479i	0.401452	−	0.915880i	$-0.368506\pi$
$839$	−17.3312	−	25.9380i	−0.598340	−	0.895479i	−0.999792	+	0.0204013i	$0.993506\pi$
$840$		0			0
$841$	3.42375	+	2.28768i	0.118060	+	0.0788855i
$842$		0			0
$843$	1.56289	+	5.15214i	0.0538286	+	0.177449i
$844$		0			0
$845$	−0.974465	+	1.18739i	−0.0335226	+	0.0408474i
$846$		0			0
$847$	−16.7454	+	40.4269i	−0.575377	+	1.38908i
$848$		0			0
$849$	−0.242333	−	0.585044i	−0.00831686	−	0.0200787i
$850$		0			0
$851$	30.4431	−	2.99838i	1.04357	−	0.102783i
$852$		0			0
$853$	−4.67174	−	2.49710i	−0.159957	−	0.0854989i	0.389476	−	0.921037i	$-0.372656\pi$
$853$	−4.67174	−	2.49710i	−0.159957	−	0.0854989i	−0.549433	+	0.835538i	$0.685156\pi$
$854$		0			0
$855$	−0.0928784	−	0.466931i	−0.00317637	−	0.0159687i
$856$		0			0
$857$	−36.9016	−	7.34018i	−1.26053	−	0.250736i	−0.480791	−	0.876835i	$-0.659650\pi$
$857$	−36.9016	−	7.34018i	−1.26053	−	0.250736i	−0.779743	+	0.626099i	$0.784650\pi$
$858$		0			0
$859$	9.02225	+	0.888615i	0.307835	+	0.0303191i	0.250755	−	0.968050i	$-0.419321\pi$
$859$	9.02225	+	0.888615i	0.307835	+	0.0303191i	0.0570799	+	0.998370i	$0.481821\pi$
$860$		0			0
$861$	−0.981553	−	0.297751i	−0.0334512	−	0.0101473i
$862$		0			0
$863$	−10.3112	+	10.3112i	−0.350998	+	0.350998i	−0.860481	−	0.509483i	$-0.829837\pi$
$863$	−10.3112	+	10.3112i	−0.350998	+	0.350998i	0.509483	+	0.860481i	$0.329837\pi$
$864$		0			0
$865$	−1.29424	−	1.29424i	−0.0440055	−	0.0440055i
$866$		0			0
$867$	−1.85401	+	6.11186i	−0.0629656	+	0.207570i
$868$		0			0
$869$	−0.00300196	+	0.0304794i	−0.000101835	+	0.00103394i
$870$		0			0
$871$	1.28186	−	6.44432i	0.0434340	−	0.218358i
$872$		0			0
$873$	−16.9919	+	3.37991i	−0.575090	+	0.114393i
$874$		0			0
$875$	−2.27619	+	4.25845i	−0.0769492	+	0.143962i
$876$		0			0
$877$	−0.273707	−	2.77900i	−0.00924244	−	0.0938401i	0.989457	−	0.144828i	$-0.0462629\pi$
$877$	−0.273707	−	2.77900i	−0.00924244	−	0.0938401i	−0.998699	+	0.0509881i	$0.983763\pi$
$878$		0			0
$879$	−24.6492	+	10.2101i	−0.831398	+	0.344376i
$880$		0			0
$881$	27.6632	+	11.4585i	0.931997	+	0.386046i	0.796436	−	0.604723i	$-0.206716\pi$
$881$	27.6632	+	11.4585i	0.931997	+	0.386046i	0.135561	+	0.990769i	$0.456716\pi$
$882$		0			0
$883$	2.57191	+	2.11071i	0.0865518	+	0.0710312i	0.676674	−	0.736283i	$-0.263421\pi$
$883$	2.57191	+	2.11071i	0.0865518	+	0.0710312i	−0.590122	+	0.807314i	$0.700921\pi$
$884$		0			0
$885$	−0.993803	+	0.301467i	−0.0334063	+	0.0101337i
$886$		0			0
$887$	6.53796	−	9.78474i	0.219523	−	0.328540i	−0.705320	−	0.708890i	$-0.749196\pi$
$887$	6.53796	−	9.78474i	0.219523	−	0.328540i	0.924843	+	0.380350i	$0.124196\pi$
$888$		0			0
$889$	−29.0233	+	19.3928i	−0.973411	+	0.650413i
$890$		0			0
$891$	0.0483254	+	0.0588847i	0.00161896	+	0.00197271i
$892$		0			0
$893$	−0.653653	+	0.349385i	−0.0218737	+	0.0116917i
$894$		0			0
$895$	1.49958			0.0501256
$896$		0			0
$897$	−1.73923			−0.0580712
$898$		0			0
$899$	−39.7968	+	21.2718i	−1.32730	+	0.709455i
$900$		0			0
$901$	20.1313	+	24.5301i	0.670671	+	0.817215i
$902$		0			0
$903$	−15.2966	+	10.2209i	−0.509039	+	0.340129i
$904$		0			0
$905$	−0.605728	+	0.906536i	−0.0201351	+	0.0301343i
$906$		0			0
$907$	32.6753	−	9.91195i	1.08497	−	0.329121i	0.303349	−	0.952879i	$-0.401895\pi$
$907$	32.6753	−	9.91195i	1.08497	−	0.329121i	0.781617	+	0.623758i	$0.214395\pi$
$908$		0			0
$909$	−19.9146	−	16.3435i	−0.660526	−	0.542079i
$910$		0			0
$911$	−40.8439	−	16.9181i	−1.35322	−	0.560522i	−0.416032	−	0.909350i	$-0.636580\pi$
$911$	−40.8439	−	16.9181i	−1.35322	−	0.560522i	−0.937187	+	0.348828i	$0.886580\pi$
$912$		0			0
$913$	0.350790	−	0.145302i	0.0116094	−	0.00480879i
$914$		0			0
$915$	−0.138382	−	1.40501i	−0.00457475	−	0.0464482i
$916$		0			0
$917$	20.0074	−	37.4313i	0.660703	−	1.23609i
$918$		0			0
$919$	−19.7682	+	3.93214i	−0.652093	+	0.129709i	−0.510041	−	0.860150i	$-0.670370\pi$
$919$	−19.7682	+	3.93214i	−0.652093	+	0.129709i	−0.142052	+	0.989859i	$0.545370\pi$
$920$		0			0
$921$	−3.99744	+	20.0965i	−0.131720	+	0.662203i
$922$		0			0
$923$	0.424441	−	4.30942i	0.0139706	−	0.141846i
$924$		0			0
$925$	12.7335	−	41.9766i	0.418674	−	1.38018i
$926$		0			0
$927$	−20.5952	−	20.5952i	−0.676437	−	0.676437i
$928$		0			0
$929$	38.1736	−	38.1736i	1.25244	−	1.25244i	0.297811	−	0.954625i	$-0.403743\pi$
$929$	38.1736	−	38.1736i	1.25244	−	1.25244i	0.954625	−	0.297811i	$-0.0962567\pi$
$930$		0			0
$931$	−14.3105	−	4.34105i	−0.469009	−	0.142272i
$932$		0			0
$933$	−15.5487	−	1.53141i	−0.509041	−	0.0501362i
$934$		0			0
$935$	0.0137720	+	0.00273943i	0.000450394	+	8.95889e-5i
$936$		0			0
$937$	−0.605903	−	3.04608i	−0.0197940	−	0.0995111i	0.969625	−	0.244595i	$-0.0786549\pi$
$937$	−0.605903	−	3.04608i	−0.0197940	−	0.0995111i	−0.989419	+	0.145084i	$0.953655\pi$
$938$		0			0
$939$	17.0132	+	9.09373i	0.555204	+	0.296763i
$940$		0			0
$941$	−20.0122	+	1.97103i	−0.652380	+	0.0642539i	−0.418793	−	0.908082i	$-0.637547\pi$
$941$	−20.0122	+	1.97103i	−0.652380	+	0.0642539i	−0.233588	+	0.972336i	$0.575047\pi$
$942$		0			0
$943$	0.413393	+	0.998020i	0.0134619	+	0.0325000i
$944$		0			0
$945$	−0.815614	+	1.96907i	−0.0265319	+	0.0640537i
$946$		0			0
$947$	−2.67002	+	3.25343i	−0.0867641	+	0.105722i	−0.814583	−	0.580047i	$-0.803034\pi$
$947$	−2.67002	+	3.25343i	−0.0867641	+	0.105722i	0.727819	+	0.685769i	$0.240534\pi$
$948$		0			0
$949$	−1.81893	−	5.99621i	−0.0590449	−	0.194645i
$950$		0			0
$951$	−6.98662	−	4.66831i	−0.226557	−	0.151380i
$952$		0			0
$953$	−13.5272	−	20.2448i	−0.438188	−	0.655795i	0.544990	−	0.838442i	$-0.316533\pi$
$953$	−13.5272	−	20.2448i	−0.438188	−	0.655795i	−0.983178	+	0.182648i	$0.941533\pi$
$954$		0			0
$955$	1.91621	−	1.57260i	0.0620072	−	0.0508880i
$956$		0			0
$957$	0.0453547	+	0.0848526i	0.00146611	+	0.00274290i
$958$		0			0
$959$			87.0852i			2.81213i
$960$		0			0
$961$			50.8364i			1.63988i
$962$		0			0
$963$	13.1403	+	24.5837i	0.423439	+	0.792199i
$964$		0			0
$965$	2.45779	−	2.01706i	0.0791191	−	0.0649314i
$966$		0			0
$967$	8.71721	+	13.0462i	0.280327	+	0.419538i	0.944737	−	0.327830i	$-0.106317\pi$
$967$	8.71721	+	13.0462i	0.280327	+	0.419538i	−0.664410	+	0.747368i	$0.731317\pi$
$968$		0			0
$969$	5.80967	+	3.88189i	0.186633	+	0.124704i
$970$		0			0
$971$	6.60194	+	21.7637i	0.211866	+	0.698430i	0.996879	+	0.0789496i	$0.0251566\pi$
$971$	6.60194	+	21.7637i	0.211866	+	0.698430i	−0.785012	+	0.619480i	$0.787343\pi$
$972$		0			0
$973$	26.6418	−	32.4631i	0.854097	−	1.04072i
$974$		0			0
$975$	−0.954408	+	2.30415i	−0.0305655	+	0.0737917i
$976$		0			0
$977$	−2.46663	−	5.95497i	−0.0789145	−	0.190516i	0.879498	−	0.475902i	$-0.157878\pi$
$977$	−2.46663	−	5.95497i	−0.0789145	−	0.190516i	−0.958413	+	0.285386i	$0.907878\pi$
$978$		0			0
$979$	−0.0473508	+	0.00466365i	−0.00151334	+	0.000149051i
$980$		0			0
$981$	−10.4216	−	5.57048i	−0.332737	−	0.177852i
$982$		0			0
$983$	−2.93264	−	14.7434i	−0.0935366	−	0.470240i	−0.998954	−	0.0457186i	$-0.985442\pi$
$983$	−2.93264	−	14.7434i	−0.0935366	−	0.470240i	0.905418	−	0.424522i	$-0.139558\pi$
$984$		0			0
$985$	−2.58051	−	0.513296i	−0.0822220	−	0.0163550i
$986$		0			0
$987$	1.43701	+	0.141533i	0.0457404	+	0.00450503i
$988$		0			0
$989$	18.5408	+	5.62429i	0.589563	+	0.178842i
$990$		0			0
$991$	−1.22693	+	1.22693i	−0.0389747	+	0.0389747i	−0.726326	−	0.687351i	$-0.758773\pi$
$991$	−1.22693	+	1.22693i	−0.0389747	+	0.0389747i	0.687351	+	0.726326i	$0.258773\pi$
$992$		0			0
$993$	−15.3134	−	15.3134i	−0.485957	−	0.485957i
$994$		0			0
$995$	−0.221090	+	0.728837i	−0.00700903	+	0.0231057i
$996$		0			0
$997$	−1.48445	+	15.0719i	−0.0470130	+	0.477331i	0.942636	+	0.333822i	$0.108339\pi$
$997$	−1.48445	+	15.0719i	−0.0470130	+	0.477331i	−0.989649	+	0.143509i	$0.954161\pi$
$998$		0			0
$999$	7.56580	−	38.0358i	0.239371	−	1.20340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.497.5		240
4.3	odd	2		128.2.k.a.101.14	✓	240
128.19	odd	32		128.2.k.a.109.14	yes	240
128.109	even	32	inner	512.2.k.a.273.5		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.101.14	✓	240	4.3	odd	2
128.2.k.a.109.14	yes	240	128.19	odd	32
512.2.k.a.273.5		240	128.109	even	32	inner
512.2.k.a.497.5		240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.k (of order \(32\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.731810 + 0.391160i) q^{3} +(-0.0771150 - 0.0939649i) q^{5} +(3.30773 - 2.21015i) q^{7} +(-1.28417 + 1.92190i) q^{9} +(-0.0222437 + 0.00674755i) q^{11} +(0.466044 + 0.382472i) q^{13} +(0.0931888 + 0.0386001i) q^{15} +(4.59132 - 1.90179i) q^{17} +(-0.166080 - 1.68624i) q^{19} +(-1.55610 + 2.91126i) q^{21} +(3.40974 - 0.678239i) q^{23} +(0.972569 - 4.88943i) q^{25} +(0.432000 - 4.38616i) q^{27} +(-1.44800 + 4.77342i) q^{29} +(6.39673 + 6.39673i) q^{31} +(0.0136388 - 0.0136388i) q^{33} +(-0.462752 - 0.140374i) q^{35} +(8.75672 + 0.862462i) q^{37} +(-0.490664 - 0.0975990i) q^{39} +(0.0606195 + 0.304755i) q^{41} +(4.91504 + 2.62714i) q^{43} +(0.279620 - 0.0275402i) q^{45} +(-0.167395 - 0.404127i) q^{47} +(3.37751 - 8.15402i) q^{49} +(-2.61607 + 3.18769i) q^{51} +(1.85360 + 6.11049i) q^{53} +(0.00234935 + 0.00156979i) q^{55} +(0.781127 + 1.16904i) q^{57} +(-7.95889 + 6.53169i) q^{59} +(-6.59803 - 12.3440i) q^{61} +9.19534i q^{63} -0.0732861i q^{65} +(-5.13746 - 9.61151i) q^{67} +(-2.22998 + 1.83010i) q^{69} +(-3.99036 - 5.97200i) q^{71} +(-8.64165 - 5.77416i) q^{73} +(1.20082 + 3.95857i) q^{75} +(-0.0586630 + 0.0714811i) q^{77} +(0.504221 - 1.21730i) q^{79} +(-1.25411 - 3.02768i) q^{81} +(-16.2560 + 1.60107i) q^{83} +(-0.532760 - 0.284766i) q^{85} +(-0.807512 - 4.05964i) q^{87} +(2.00759 + 0.399335i) q^{89} +(2.38687 + 0.235086i) q^{91} +(-7.18334 - 2.17904i) q^{93} +(-0.145640 + 0.145640i) q^{95} +(5.29993 + 5.29993i) q^{97} +(0.0155966 - 0.0514152i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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