LMFDB - Embedded newform 828.2.e.f.91.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [828,2,Mod(91,828)] 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("828.91"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(828, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 828 = 2^{2} \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	828.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,-4,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.61161328736$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 276)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.10
Character	$\chi$	$=$	828.91
Dual form			828.2.e.f.91.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.714279 - 1.22058i) q^{2} +(-0.979610 + 1.74366i) q^{4} +3.78153i q^{5} +1.02234 q^{7} +(2.82799 - 0.0497743i) q^{8} +(4.61564 - 2.70107i) q^{10} -4.16390 q^{11} +5.75925 q^{13} +(-0.730233 - 1.24784i) q^{14} +(-2.08073 - 3.41622i) q^{16} +2.80681i q^{17} -4.00376 q^{19} +(-6.59371 - 3.70442i) q^{20} +(2.97419 + 5.08236i) q^{22} +(4.42742 - 1.84336i) q^{23} -9.29995 q^{25} +(-4.11371 - 7.02960i) q^{26} +(-1.00149 + 1.78261i) q^{28} -0.341603 q^{29} +5.39782i q^{31} +(-2.68354 + 4.97982i) q^{32} +(3.42593 - 2.00485i) q^{34} +3.86599i q^{35} +10.6917i q^{37} +(2.85981 + 4.88690i) q^{38} +(0.188223 + 10.6941i) q^{40} -8.31977 q^{41} -8.92015 q^{43} +(4.07900 - 7.26045i) q^{44} +(-5.41237 - 4.08732i) q^{46} +2.69990i q^{47} -5.95483 q^{49} +(6.64276 + 11.3513i) q^{50} +(-5.64182 + 10.0422i) q^{52} +0.814576i q^{53} -15.7459i q^{55} +(2.89115 - 0.0508860i) q^{56} +(0.244000 + 0.416952i) q^{58} -2.67041i q^{59} +7.77081i q^{61} +(6.58844 - 3.85555i) q^{62} +(7.99505 - 0.281522i) q^{64} +21.7787i q^{65} +14.8080 q^{67} +(-4.89414 - 2.74958i) q^{68} +(4.71873 - 2.76140i) q^{70} -2.36679i q^{71} +5.19128 q^{73} +(13.0501 - 7.63689i) q^{74} +(3.92213 - 6.98122i) q^{76} -4.25691 q^{77} -6.91022 q^{79} +(12.9185 - 7.86833i) q^{80} +(5.94264 + 10.1549i) q^{82} +1.12198 q^{83} -10.6140 q^{85} +(6.37147 + 10.8877i) q^{86} +(-11.7755 + 0.207255i) q^{88} -9.76786i q^{89} +5.88788 q^{91} +(-1.12294 + 9.52570i) q^{92} +(3.29543 - 1.92848i) q^{94} -15.1403i q^{95} -10.8995i q^{97} +(4.25341 + 7.26832i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} - 4 q^{8} + 8 q^{16} - 24 q^{25} - 40 q^{26} + 32 q^{29} + 36 q^{32} - 16 q^{41} + 40 q^{49} + 12 q^{50} - 40 q^{52} + 24 q^{58} + 40 q^{62} + 48 q^{64} + 72 q^{70} - 16 q^{77} - 40 q^{82}+ \cdots + 52 q^{98}+O(q^{100}) $ 24 * q - 4 * q^2 - 4 * q^8 + 8 * q^16 - 24 * q^25 - 40 * q^26 + 32 * q^29 + 36 * q^32 - 16 * q^41 + 40 * q^49 + 12 * q^50 - 40 * q^52 + 24 * q^58 + 40 * q^62 + 48 * q^64 + 72 * q^70 - 16 * q^77 - 40 * q^82 - 64 * q^85 - 44 * q^92 + 72 * q^94 + 52 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/828\mathbb{Z}\right)^\times$.

$n$	$415$	$461$	$649$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−0.714279	−	1.22058i	−0.505072	−	0.863077i
$2$	−0.714279	−	1.22058i	−0.505072	−	0.863077i
$3$		0			0
$3$		0			0
$4$	−0.979610	+	1.74366i	−0.489805	+	0.871832i
$5$			3.78153i			1.69115i	0.533856	+	0.845575i	$0.320742\pi$
$5$			3.78153i			1.69115i	−0.533856	+	0.845575i	$0.679258\pi$
$6$		0			0
$7$	1.02234			0.386407			0.193203	−	0.981159i	$-0.438112\pi$
$7$	1.02234			0.386407			0.193203	+	0.981159i	$0.438112\pi$
$8$	2.82799	−	0.0497743i	0.999845	−	0.0175979i
$9$		0			0
$10$	4.61564	−	2.70107i	1.45959	−	0.854152i
$11$	−4.16390			−1.25546			−0.627732	−	0.778430i	$-0.716017\pi$
$11$	−4.16390			−1.25546			−0.627732	+	0.778430i	$0.716017\pi$
$12$		0			0
$13$	5.75925			1.59733			0.798664	−	0.601778i	$-0.205541\pi$
$13$	5.75925			1.59733			0.798664	+	0.601778i	$0.205541\pi$
$14$	−0.730233	−	1.24784i	−0.195163	−	0.333499i
$15$		0			0
$16$	−2.08073	−	3.41622i	−0.520182	−	0.854056i
$17$			2.80681i			0.680752i	0.940289	+	0.340376i	$0.110554\pi$
$17$			2.80681i			0.680752i	−0.940289	+	0.340376i	$0.889446\pi$
$18$		0			0
$19$	−4.00376			−0.918527			−0.459263	−	0.888300i	$-0.651887\pi$
$19$	−4.00376			−0.918527			−0.459263	+	0.888300i	$0.651887\pi$
$20$	−6.59371	−	3.70442i	−1.47440	−	0.828334i
$21$		0			0
$22$	2.97419	+	5.08236i	0.634099	+	1.08356i
$23$	4.42742	−	1.84336i	0.923180	−	0.384367i
$23$	4.42742	−	1.84336i	0.923180	−	0.384367i
$24$		0			0
$25$	−9.29995			−1.85999
$26$	−4.11371	−	7.02960i	−0.806765	−	1.37862i
$27$		0			0
$28$	−1.00149	+	1.78261i	−0.189264	+	0.336882i
$29$	−0.341603			−0.0634341			−0.0317170	−	0.999497i	$-0.510098\pi$
$29$	−0.341603			−0.0634341			−0.0317170	+	0.999497i	$0.510098\pi$
$30$		0			0
$31$			5.39782i			0.969477i	0.874659	+	0.484738i	$0.161085\pi$
$31$			5.39782i			0.969477i	−0.874659	+	0.484738i	$0.838915\pi$
$32$	−2.68354	+	4.97982i	−0.474387	+	0.880316i
$33$		0			0
$34$	3.42593	−	2.00485i	0.587542	−	0.343829i
$35$			3.86599i			0.653472i
$36$		0			0
$37$			10.6917i			1.75771i	0.477087	+	0.878856i	$0.341693\pi$
$37$			10.6917i			1.75771i	−0.477087	+	0.878856i	$0.658307\pi$
$38$	2.85981	+	4.88690i	0.463922	+	0.792759i
$39$		0			0
$40$	0.188223	+	10.6941i	0.0297606	+	1.69089i
$41$	−8.31977			−1.29933			−0.649665	−	0.760221i	$-0.725091\pi$
$41$	−8.31977			−1.29933			−0.649665	+	0.760221i	$0.725091\pi$
$42$		0			0
$43$	−8.92015			−1.36031			−0.680155	−	0.733069i	$-0.738087\pi$
$43$	−8.92015			−1.36031			−0.680155	+	0.733069i	$0.738087\pi$
$44$	4.07900	−	7.26045i	0.614933	−	1.09455i
$45$		0			0
$46$	−5.41237	−	4.08732i	−0.798011	−	0.602643i
$47$			2.69990i			0.393820i	0.980422	+	0.196910i	$0.0630907\pi$
$47$			2.69990i			0.393820i	−0.980422	+	0.196910i	$0.936909\pi$
$48$		0			0
$49$	−5.95483			−0.850690
$50$	6.64276	+	11.3513i	0.939428	+	1.60531i
$51$		0			0
$52$	−5.64182	+	10.0422i	−0.782379	+	1.39260i
$53$			0.814576i			0.111891i	0.998434	+	0.0559453i	$0.0178173\pi$
$53$			0.814576i			0.111891i	−0.998434	+	0.0559453i	$0.982183\pi$
$54$		0			0
$55$		−	15.7459i		−	2.12318i
$56$	2.89115	−	0.0508860i	0.386347	−	0.00679993i
$57$		0			0
$58$	0.244000	+	0.416952i	0.0320388	+	0.0547485i
$59$		−	2.67041i		−	0.347657i	−0.984776	−	0.173829i	$-0.944386\pi$
$59$		−	2.67041i		−	0.347657i	0.984776	−	0.173829i	$-0.0556139\pi$
$60$		0			0
$61$			7.77081i			0.994951i	0.867478	+	0.497475i	$0.165740\pi$
$61$			7.77081i			0.994951i	−0.867478	+	0.497475i	$0.834260\pi$
$62$	6.58844	−	3.85555i	0.836733	−	0.489655i
$63$		0			0
$64$	7.99505	−	0.281522i	0.999381	−	0.0351903i
$65$			21.7787i			2.70132i
$66$		0			0
$67$	14.8080			1.80909			0.904544	−	0.426380i	$-0.140211\pi$
$67$	14.8080			1.80909			0.904544	+	0.426380i	$0.140211\pi$
$68$	−4.89414	−	2.74958i	−0.593501	−	0.333436i
$69$		0			0
$70$	4.71873	−	2.76140i	0.563997	−	0.330050i
$71$		−	2.36679i		−	0.280886i	−0.990089	−	0.140443i	$-0.955147\pi$
$71$		−	2.36679i		−	0.280886i	0.990089	−	0.140443i	$-0.0448527\pi$
$72$		0			0
$73$	5.19128			0.607594			0.303797	−	0.952737i	$-0.401746\pi$
$73$	5.19128			0.607594			0.303797	+	0.952737i	$0.401746\pi$
$74$	13.0501	−	7.63689i	1.51704	−	0.887771i
$75$		0			0
$76$	3.92213	−	6.98122i	0.449899	−	0.800801i
$77$	−4.25691			−0.485120
$78$		0			0
$79$	−6.91022			−0.777460			−0.388730	−	0.921352i	$-0.627086\pi$
$79$	−6.91022			−0.777460			−0.388730	+	0.921352i	$0.627086\pi$
$80$	12.9185	−	7.86833i	1.44434	−	0.879706i
$81$		0			0
$82$	5.94264	+	10.1549i	0.656255	+	1.12142i
$83$	1.12198			0.123153			0.0615766	−	0.998102i	$-0.480387\pi$
$83$	1.12198			0.123153			0.0615766	+	0.998102i	$0.480387\pi$
$84$		0			0
$85$	−10.6140			−1.15125
$86$	6.37147	+	10.8877i	0.687054	+	1.17405i
$87$		0			0
$88$	−11.7755	+	0.207255i	−1.25527	+	0.0220935i
$89$		−	9.76786i		−	1.03539i	−0.855565	−	0.517696i	$-0.826790\pi$
$89$		−	9.76786i		−	1.03539i	0.855565	−	0.517696i	$-0.173210\pi$
$90$		0			0
$91$	5.88788			0.617218
$92$	−1.12294	+	9.52570i	−0.117075	+	0.993123i
$93$		0			0
$94$	3.29543	−	1.92848i	0.339897	−	0.198907i
$95$		−	15.1403i		−	1.55337i
$96$		0			0
$97$		−	10.8995i		−	1.10668i	−0.832956	−	0.553339i	$-0.813354\pi$
$97$		−	10.8995i		−	1.10668i	0.832956	−	0.553339i	$-0.186646\pi$
$98$	4.25341	+	7.26832i	0.429659	+	0.734211i
$99$		0			0
$100$	9.11032	−	16.2160i	0.911032	−	1.62160i
$101$	7.92158			0.788226			0.394113	−	0.919062i	$-0.371052\pi$
$101$	7.92158			0.788226			0.394113	+	0.919062i	$0.371052\pi$
$102$		0			0
$103$	3.57377			0.352134			0.176067	−	0.984378i	$-0.443663\pi$
$103$	3.57377			0.352134			0.176067	+	0.984378i	$0.443663\pi$
$104$	16.2871	−	0.286662i	1.59708	−	0.0281095i
$105$		0			0
$106$	0.994252	−	0.581835i	0.0965703	−	0.0565128i
$107$	−3.49439			−0.337816			−0.168908	−	0.985632i	$-0.554024\pi$
$107$	−3.49439			−0.337816			−0.168908	+	0.985632i	$0.554024\pi$
$108$		0			0
$109$		−	2.15719i		−	0.206621i	−0.994649	−	0.103311i	$-0.967056\pi$
$109$		−	2.15719i		−	0.206621i	0.994649	−	0.103311i	$-0.0329436\pi$
$110$	−19.2191	+	11.2470i	−1.83247	+	1.07236i
$111$		0			0
$112$	−2.12720	−	3.49253i	−0.201002	−	0.330013i
$113$			0.687167i			0.0646433i	0.999478	+	0.0323216i	$0.0102901\pi$
$113$			0.687167i			0.0646433i	−0.999478	+	0.0323216i	$0.989710\pi$
$114$		0			0
$115$	6.97072	+	16.7424i	0.650023	+	1.56124i
$116$	0.334638	−	0.595641i	0.0310703	−	0.0553039i
$117$		0			0
$118$	−3.25943	+	1.90742i	−0.300055	+	0.175592i
$119$			2.86950i			0.263047i
$120$		0			0
$121$	6.33809			0.576190
$122$	9.48487	−	5.55053i	0.858719	−	0.502521i
$123$		0			0
$124$	−9.41198	−	5.28776i	−0.845221	−	0.474855i
$125$		−	16.2604i		−	1.45437i
$126$		0			0
$127$			4.32407i			0.383700i	0.981424	+	0.191850i	$0.0614486\pi$
$127$			4.32407i			0.383700i	−0.981424	+	0.191850i	$0.938551\pi$
$128$	−6.05431	−	9.55747i	−0.535131	−	0.844769i
$129$		0			0
$130$	26.5826	−	15.5561i	2.33145	−	1.36436i
$131$			10.2833i			0.898452i	0.893418	+	0.449226i	$0.148300\pi$
$131$			10.2833i			0.898452i	−0.893418	+	0.449226i	$0.851700\pi$
$132$		0			0
$133$	−4.09319			−0.354925
$134$	−10.5771	−	18.0743i	−0.913719	−	1.56138i
$135$		0			0
$136$	0.139707	+	7.93763i	0.0119798	+	0.680646i
$137$			7.32794i			0.626068i	0.949742	+	0.313034i	$0.101345\pi$
$137$			7.32794i			0.626068i	−0.949742	+	0.313034i	$0.898655\pi$
$138$		0			0
$139$			0.706954i			0.0599631i	0.999550	+	0.0299815i	$0.00954485\pi$
$139$			0.706954i			0.0599631i	−0.999550	+	0.0299815i	$0.990455\pi$
$140$	−6.74099	−	3.78716i	−0.569717	−	0.320074i
$141$		0			0
$142$	−2.88885	+	1.69055i	−0.242427	+	0.141868i
$143$	−23.9809			−2.00539
$144$		0			0
$145$		−	1.29178i		−	0.107277i
$146$	−3.70802	−	6.33635i	−0.306878	−	0.524400i
$147$		0			0
$148$	−18.6428	−	10.4737i	−1.53243	−	0.860937i
$149$			0.382789i			0.0313593i	0.999877	+	0.0156797i	$0.00499120\pi$
$149$			0.382789i			0.0313593i	−0.999877	+	0.0156797i	$0.995009\pi$
$150$		0			0
$151$		−	6.34904i		−	0.516678i	−0.966054	−	0.258339i	$-0.916825\pi$
$151$		−	6.34904i		−	0.516678i	0.966054	−	0.258339i	$-0.0831751\pi$
$152$	−11.3226	+	0.199284i	−0.918384	+	0.0161641i
$153$		0			0
$154$	3.04062	+	5.19588i	0.245020	+	0.418696i
$155$	−20.4120			−1.63953
$156$		0			0
$157$			14.4032i			1.14950i	0.818329	+	0.574749i	$0.194901\pi$
$157$			14.4032i			1.14950i	−0.818329	+	0.574749i	$0.805099\pi$
$158$	4.93583	+	8.43445i	0.392673	+	0.671009i
$159$		0			0
$160$	−18.8313	−	10.1479i	−1.48875	−	0.802260i
$161$	4.52631	−	1.88453i	0.356723	−	0.148522i
$162$		0			0
$163$			13.7153i			1.07426i	0.843499	+	0.537131i	$0.180492\pi$
$163$			13.7153i			1.07426i	−0.843499	+	0.537131i	$0.819508\pi$
$164$	8.15013	−	14.5069i	0.636419	−	1.13280i
$165$		0			0
$166$	−0.801407	−	1.36946i	−0.0622012	−	0.106291i
$167$		−	13.6811i		−	1.05867i	−0.848412	−	0.529337i	$-0.822441\pi$
$167$		−	13.6811i		−	1.05867i	0.848412	−	0.529337i	$-0.177559\pi$
$168$		0			0
$169$	20.1689			1.55145
$170$	7.58138	+	12.9552i	0.581466	+	0.993621i
$171$		0			0
$172$	8.73827	−	15.5537i	0.666287	−	1.18596i
$173$	3.49528			0.265741			0.132871	−	0.991133i	$-0.457581\pi$
$173$	3.49528			0.265741			0.132871	+	0.991133i	$0.457581\pi$
$174$		0			0
$175$	−9.50767			−0.718712
$176$	8.66395	+	14.2248i	0.653070	+	1.07224i
$177$		0			0
$178$	−11.9224	+	6.97698i	−0.893623	+	0.522947i
$179$			26.0258i			1.94526i	0.232363	+	0.972629i	$0.425354\pi$
$179$			26.0258i			1.94526i	−0.232363	+	0.972629i	$0.574646\pi$
$180$		0			0
$181$			6.69764i			0.497832i	0.968525	+	0.248916i	$0.0800743\pi$
$181$			6.69764i			0.497832i	−0.968525	+	0.248916i	$0.919926\pi$
$182$	−4.20559	−	7.18661i	−0.311739	−	0.532707i
$183$		0			0
$184$	12.4289	−	5.43337i	0.916273	−	0.400554i
$185$	−40.4311			−2.97256
$186$		0			0
$187$		−	11.6873i		−	0.854659i
$188$	−4.70771	−	2.64485i	−0.343345	−	0.192895i
$189$		0			0
$190$	−18.4799	+	10.8144i	−1.34068	+	0.784561i
$191$	17.1708			1.24243			0.621217	−	0.783639i	$-0.286639\pi$
$191$	17.1708			1.24243			0.621217	+	0.783639i	$0.286639\pi$
$192$		0			0
$193$	8.99448			0.647437			0.323718	−	0.946153i	$-0.395067\pi$
$193$	8.99448			0.647437			0.323718	+	0.946153i	$0.395067\pi$
$194$	−13.3037	+	7.78529i	−0.955148	+	0.558951i
$195$		0			0
$196$	5.83341	−	10.3832i	0.416672	−	0.741659i
$197$	15.7039			1.11886			0.559429	−	0.828878i	$-0.311020\pi$
$197$	15.7039			1.11886			0.559429	+	0.828878i	$0.311020\pi$
$198$		0			0
$199$	−17.4402			−1.23630			−0.618152	−	0.786058i	$-0.712119\pi$
$199$	−17.4402			−1.23630			−0.618152	+	0.786058i	$0.712119\pi$
$200$	−26.3001	+	0.462898i	−1.85970	+	0.0327318i
$201$		0			0
$202$	−5.65822	−	9.66889i	−0.398111	−	0.680300i
$203$	−0.349233			−0.0245113
$204$		0			0
$205$		−	31.4614i		−	2.19736i
$206$	−2.55267	−	4.36205i	−0.177853	−	0.303919i
$207$		0			0
$208$	−11.9834	−	19.6749i	−0.830901	−	1.36421i
$209$	16.6713			1.15318
$210$		0			0
$211$		−	2.65058i		−	0.182474i	−0.995829	−	0.0912368i	$-0.970918\pi$
$211$		−	2.65058i		−	0.182474i	0.995829	−	0.0912368i	$-0.0290820\pi$
$212$	−1.42035	−	0.797967i	−0.0975498	−	0.0548046i
$213$		0			0
$214$	2.49597	+	4.26517i	0.170621	+	0.291561i
$215$		−	33.7318i		−	2.30049i
$216$		0			0
$217$			5.51838i			0.374612i
$218$	−2.63301	+	1.54084i	−0.178330	+	0.104359i
$219$		0			0
$220$	27.4556	+	15.4249i	1.85105	+	1.03994i
$221$			16.1651i			1.08738i
$222$		0			0
$223$		−	24.2438i		−	1.62349i	−0.584014	−	0.811743i	$-0.698519\pi$
$223$		−	24.2438i		−	1.62349i	0.584014	−	0.811743i	$-0.301481\pi$
$224$	−2.74348	+	5.09105i	−0.183306	+	0.340160i
$225$		0			0
$226$	0.838740	−	0.490829i	0.0557921	−	0.0326495i
$227$	−6.20857			−0.412078			−0.206039	−	0.978544i	$-0.566057\pi$
$227$	−6.20857			−0.412078			−0.206039	+	0.978544i	$0.566057\pi$
$228$		0			0
$229$		−	11.1620i		−	0.737604i	−0.929508	−	0.368802i	$-0.879768\pi$
$229$		−	11.1620i		−	0.737604i	0.929508	−	0.368802i	$-0.120232\pi$
$230$	15.4563	−	20.4670i	1.01916	−	1.34956i
$231$		0			0
$232$	−0.966049	+	0.0170030i	−0.0634243	+	0.00111630i
$233$	23.6813			1.55141			0.775707	−	0.631094i	$-0.217394\pi$
$233$	23.6813			1.55141			0.775707	+	0.631094i	$0.217394\pi$
$234$		0			0
$235$	−10.2097			−0.666009
$236$	4.65629	+	2.61596i	0.303099	+	0.170284i
$237$		0			0
$238$	3.50245	−	2.04963i	0.227030	−	0.132858i
$239$			5.75021i			0.371950i	0.982554	+	0.185975i	$0.0595444\pi$
$239$			5.75021i			0.371950i	−0.982554	+	0.185975i	$0.940456\pi$
$240$		0			0
$241$		−	12.3285i		−	0.794151i	−0.917786	−	0.397076i	$-0.870025\pi$
$241$		−	12.3285i		−	0.794151i	0.917786	−	0.397076i	$-0.129975\pi$
$242$	−4.52717	−	7.73612i	−0.291017	−	0.497296i
$243$		0			0
$244$	−13.5497	−	7.61237i	−0.867430	−	0.487332i
$245$		−	22.5183i		−	1.43864i
$246$		0			0
$247$	−23.0587			−1.46719
$248$	0.268672	+	15.2650i	0.0170607	+	0.969326i
$249$		0			0
$250$	−19.8470	+	11.6144i	−1.25523	+	0.734562i
$251$	21.0263			1.32717			0.663583	−	0.748103i	$-0.269035\pi$
$251$	21.0263			1.32717			0.663583	+	0.748103i	$0.269035\pi$
$252$		0			0
$253$	−18.4353	+	7.67557i	−1.15902	+	0.482559i
$254$	5.27786	−	3.08860i	0.331162	−	0.193796i
$255$		0			0
$256$	−7.34115	+	14.2165i	−0.458822	+	0.888528i
$257$	19.1154			1.19239			0.596193	−	0.802841i	$-0.296679\pi$
$257$	19.1154			1.19239			0.596193	+	0.802841i	$0.296679\pi$
$258$		0			0
$259$			10.9306i			0.679192i
$260$	−37.9748	−	21.3347i	−2.35510	−	1.32312i
$261$		0			0
$262$	12.5515	−	7.34512i	0.775434	−	0.453783i
$263$	−4.96561			−0.306192			−0.153096	−	0.988211i	$-0.548924\pi$
$263$	−4.96561			−0.306192			−0.153096	+	0.988211i	$0.548924\pi$
$264$		0			0
$265$	−3.08034			−0.189224
$266$	2.92368	+	4.99605i	0.179262	+	0.306328i
$267$		0			0
$268$	−14.5061	+	25.8202i	−0.886101	+	1.57722i
$269$	−9.04263			−0.551339			−0.275669	−	0.961252i	$-0.588900\pi$
$269$	−9.04263			−0.551339			−0.275669	+	0.961252i	$0.588900\pi$
$270$		0			0
$271$			6.06709i			0.368550i	0.982875	+	0.184275i	$0.0589936\pi$
$271$			6.06709i			0.368550i	−0.982875	+	0.184275i	$0.941006\pi$
$272$	9.58869	−	5.84021i	0.581400	−	0.354115i
$273$		0			0
$274$	8.94431	−	5.23420i	0.540345	−	0.316209i
$275$	38.7241			2.33515
$276$		0			0
$277$	31.4785			1.89136			0.945681	−	0.325097i	$-0.105397\pi$
$277$	31.4785			1.89136			0.945681	+	0.325097i	$0.105397\pi$
$278$	0.862891	−	0.504963i	0.0517528	−	0.0302856i
$279$		0			0
$280$	0.192427	+	10.9330i	0.0114997	+	0.653371i
$281$		−	3.23860i		−	0.193199i	−0.995323	−	0.0965993i	$-0.969203\pi$
$281$		−	3.23860i		−	0.193199i	0.995323	−	0.0965993i	$-0.0307965\pi$
$282$		0			0
$283$	23.0191			1.36834			0.684172	−	0.729321i	$-0.260164\pi$
$283$	23.0191			1.36834			0.684172	+	0.729321i	$0.260164\pi$
$284$	4.12688	+	2.31853i	0.244886	+	0.137580i
$285$		0			0
$286$	17.1291	+	29.2706i	1.01286	+	1.73080i
$287$	−8.50560			−0.502070
$288$		0			0
$289$	9.12181			0.536577
$290$	−1.57672	+	0.922692i	−0.0925880	+	0.0541824i
$291$		0			0
$292$	−5.08543	+	9.05185i	−0.297602	+	0.529719i
$293$		−	30.4767i		−	1.78047i	−0.455506	−	0.890233i	$-0.650542\pi$
$293$		−	30.4767i		−	1.78047i	0.455506	−	0.890233i	$-0.349458\pi$
$294$		0			0
$295$	10.0982			0.587941
$296$	0.532174	+	30.2361i	0.0309320	+	1.75744i
$297$		0			0
$298$	0.467224	−	0.273419i	0.0270655	−	0.0158387i
$299$	25.4986	−	10.6164i	1.47462	−	0.613960i
$300$		0			0
$301$	−9.11938			−0.525633
$302$	−7.74949	+	4.53499i	−0.445933	+	0.260959i
$303$		0			0
$304$	8.33074	+	13.6777i	0.477801	+	0.784473i
$305$	−29.3855			−1.68261
$306$		0			0
$307$		−	28.6158i		−	1.63319i	−0.577211	−	0.816595i	$-0.695859\pi$
$307$		−	28.6158i		−	1.63319i	0.577211	−	0.816595i	$-0.304141\pi$
$308$	4.17011	−	7.42262i	0.237614	−	0.422943i
$309$		0			0
$310$	14.5799	+	24.9144i	0.828080	+	1.41504i
$311$			27.4154i			1.55458i	0.629141	+	0.777291i	$0.283407\pi$
$311$			27.4154i			1.55458i	−0.629141	+	0.777291i	$0.716593\pi$
$312$		0			0
$313$		−	9.19221i		−	0.519574i	−0.965666	−	0.259787i	$-0.916348\pi$
$313$		−	9.19221i		−	0.519574i	0.965666	−	0.259787i	$-0.0836524\pi$
$314$	17.5802	−	10.2879i	0.992107	−	0.580579i
$315$		0			0
$316$	6.76932	−	12.0491i	0.380804	−	0.677815i
$317$	−4.89112			−0.274713			−0.137356	−	0.990522i	$-0.543861\pi$
$317$	−4.89112			−0.274713			−0.137356	+	0.990522i	$0.543861\pi$
$318$		0			0
$319$	1.42240			0.0796392
$320$	1.06458	+	30.2335i	0.0595120	+	1.69010i
$321$		0			0
$322$	−5.53326	−	4.17862i	−0.308357	−	0.232865i
$323$		−	11.2378i		−	0.625289i
$324$		0			0
$325$	−53.5607			−2.97101
$326$	16.7405	−	9.79653i	0.927171	−	0.542579i
$327$		0			0
$328$	−23.5282	+	0.414111i	−1.29913	+	0.0228654i
$329$			2.76020i			0.152175i
$330$		0			0
$331$			9.27238i			0.509656i	0.966986	+	0.254828i	$0.0820189\pi$
$331$			9.27238i			0.509656i	−0.966986	+	0.254828i	$0.917981\pi$
$332$	−1.09910	+	1.95636i	−0.0603211	+	0.107369i
$333$		0			0
$334$	−16.6988	+	9.77211i	−0.913717	+	0.534706i
$335$			55.9970i			3.05944i
$336$		0			0
$337$		−	31.9595i		−	1.74095i	−0.492216	−	0.870473i	$-0.663813\pi$
$337$		−	31.9595i		−	1.74095i	0.492216	−	0.870473i	$-0.336187\pi$
$338$	−14.4062	−	24.6177i	−0.783596	−	1.33903i
$339$		0			0
$340$	10.3976	−	18.5073i	0.563890	−	1.00370i
$341$		−	22.4760i		−	1.21714i
$342$		0			0
$343$	−13.2442			−0.715119
$344$	−25.2261	+	0.443994i	−1.36010	+	0.0239385i
$345$		0			0
$346$	−2.49661	−	4.26625i	−0.134218	−	0.229355i
$347$			17.4157i			0.934922i	0.884014	+	0.467461i	$0.154831\pi$
$347$			17.4157i			0.934922i	−0.884014	+	0.467461i	$0.845169\pi$
$348$		0			0
$349$	14.0294			0.750976			0.375488	−	0.926827i	$-0.377475\pi$
$349$	14.0294			0.750976			0.375488	+	0.926827i	$0.377475\pi$
$350$	6.79113	+	11.6048i	0.363001	+	0.620304i
$351$		0			0
$352$	11.1740	−	20.7355i	0.595576	−	1.10521i
$353$	−10.5138			−0.559594			−0.279797	−	0.960059i	$-0.590267\pi$
$353$	−10.5138			−0.559594			−0.279797	+	0.960059i	$0.590267\pi$
$354$		0			0
$355$	8.95008			0.475021
$356$	17.0319	+	9.56870i	0.902687	+	0.507140i
$357$		0			0
$358$	31.7664	−	18.5897i	1.67891	−	0.982495i
$359$	26.7026			1.40931			0.704654	−	0.709551i	$-0.251102\pi$
$359$	26.7026			1.40931			0.704654	+	0.709551i	$0.251102\pi$
$360$		0			0
$361$	−2.96987			−0.156309
$362$	8.17498	−	4.78399i	0.429668	−	0.251441i
$363$		0			0
$364$	−5.76783	+	10.2665i	−0.302317	+	0.538110i
$365$			19.6310i			1.02753i
$366$		0			0
$367$	22.7892			1.18959			0.594794	−	0.803878i	$-0.297234\pi$
$367$	22.7892			1.18959			0.594794	+	0.803878i	$0.297234\pi$
$368$	−15.5096	−	11.2895i	−0.808492	−	0.588507i
$369$		0			0
$370$	28.8791	+	49.3493i	1.50135	+	2.56555i
$371$			0.832771i			0.0432353i
$372$		0			0
$373$			29.4873i			1.52679i	0.645930	+	0.763397i	$0.276470\pi$
$373$			29.4873i			1.52679i	−0.645930	+	0.763397i	$0.723530\pi$
$374$	−14.2652	+	8.34799i	−0.737637	+	0.431664i
$375$		0			0
$376$	0.134385	+	7.63527i	0.00693039	+	0.393759i
$377$	−1.96738			−0.101325
$378$		0			0
$379$	−2.86951			−0.147397			−0.0736984	−	0.997281i	$-0.523480\pi$
$379$	−2.86951			−0.147397			−0.0736984	+	0.997281i	$0.523480\pi$
$380$	26.3997	+	14.8316i	1.35427	+	0.760847i
$381$		0			0
$382$	−12.2647	−	20.9582i	−0.627518	−	1.07232i
$383$	−27.8917			−1.42520			−0.712599	−	0.701572i	$-0.752482\pi$
$383$	−27.8917			−1.42520			−0.712599	+	0.701572i	$0.752482\pi$
$384$		0			0
$385$		−	16.0976i		−	0.820410i
$386$	−6.42457	−	10.9784i	−0.327002	−	0.558788i
$387$		0			0
$388$	19.0051	+	10.6773i	0.964837	+	0.542056i
$389$		−	2.26388i		−	0.114783i	−0.998352	−	0.0573917i	$-0.981722\pi$
$389$		−	2.26388i		−	0.114783i	0.998352	−	0.0573917i	$-0.0182784\pi$
$390$		0			0
$391$	5.17396	+	12.4269i	0.261659	+	0.628457i
$392$	−16.8402	+	0.296397i	−0.850558	+	0.0149703i
$393$		0			0
$394$	−11.2170	−	19.1678i	−0.565104	−	0.965662i
$395$		−	26.1312i		−	1.31480i
$396$		0			0
$397$	14.1054			0.707930			0.353965	−	0.935259i	$-0.384833\pi$
$397$	14.1054			0.707930			0.353965	+	0.935259i	$0.384833\pi$
$398$	12.4572	+	21.2871i	0.624423	+	1.06703i
$399$		0			0
$400$	19.3507	+	31.7707i	0.967533	+	1.58853i
$401$			27.7645i			1.38649i	0.720701	+	0.693246i	$0.243820\pi$
$401$			27.7645i			1.38649i	−0.720701	+	0.693246i	$0.756180\pi$
$402$		0			0
$403$			31.0874i			1.54857i
$404$	−7.76006	+	13.8126i	−0.386077	+	0.687201i
$405$		0			0
$406$	0.249450	+	0.426265i	0.0123800	+	0.0211552i
$407$		−	44.5194i		−	2.20674i
$408$		0			0
$409$	−30.1790			−1.49225			−0.746127	−	0.665804i	$-0.768089\pi$
$409$	−30.1790			−1.49225			−0.746127	+	0.665804i	$0.768089\pi$
$410$	−38.4011	+	22.4723i	−1.89649	+	1.10983i
$411$		0			0
$412$	−3.50090	+	6.23145i	−0.172477	+	0.307001i
$413$		−	2.73005i		−	0.134337i
$414$		0			0
$415$			4.24280i			0.208271i
$416$	−15.4552	+	28.6800i	−0.757751	+	1.40615i
$417$		0			0
$418$	−11.9080	−	20.3486i	−0.582437	−	0.995281i
$419$	24.3639			1.19026			0.595128	−	0.803631i	$-0.297101\pi$
$419$	24.3639			1.19026			0.595128	+	0.803631i	$0.297101\pi$
$420$		0			0
$421$			20.0093i			0.975196i	0.873068	+	0.487598i	$0.162127\pi$
$421$			20.0093i			0.975196i	−0.873068	+	0.487598i	$0.837873\pi$
$422$	−3.23524	+	1.89326i	−0.157489	+	0.0921622i
$423$		0			0
$424$	0.0405449	+	2.30361i	0.00196904	+	0.111873i
$425$		−	26.1032i		−	1.26619i
$426$		0			0
$427$			7.94438i			0.384456i
$428$	3.42314	−	6.09305i	0.165464	−	0.294518i
$429$		0			0
$430$	−41.1722	+	24.0939i	−1.98550	+	1.16191i
$431$	−11.9663			−0.576394			−0.288197	−	0.957571i	$-0.593056\pi$
$431$	−11.9663			−0.576394			−0.288197	+	0.957571i	$0.593056\pi$
$432$		0			0
$433$			8.07822i			0.388215i	0.980980	+	0.194107i	$0.0621810\pi$
$433$			8.07822i			0.388215i	−0.980980	+	0.194107i	$0.937819\pi$
$434$	6.73560	−	3.94167i	0.323319	−	0.189206i
$435$		0			0
$436$	3.76141	+	2.11321i	0.180139	+	0.101204i
$437$	−17.7263	+	7.38038i	−0.847966	+	0.353051i
$438$		0			0
$439$		−	21.9504i		−	1.04764i	−0.851830	−	0.523818i	$-0.824507\pi$
$439$		−	21.9504i		−	1.04764i	0.851830	−	0.523818i	$-0.175493\pi$
$440$	−0.783741	−	44.5293i	−0.0373634	−	2.12285i
$441$		0			0
$442$	19.7308	−	11.5464i	0.938496	−	0.549207i
$443$			2.92531i			0.138986i	0.997582	+	0.0694928i	$0.0221381\pi$
$443$			2.92531i			0.138986i	−0.997582	+	0.0694928i	$0.977862\pi$
$444$		0			0
$445$	36.9374			1.75100
$446$	−29.5914	+	17.3169i	−1.40119	+	0.819977i
$447$		0			0
$448$	8.17362	−	0.287810i	0.386167	−	0.0135978i
$449$	31.0423			1.46498			0.732489	−	0.680779i	$-0.238359\pi$
$449$	31.0423			1.46498			0.732489	+	0.680779i	$0.238359\pi$
$450$		0			0
$451$	34.6427			1.63126
$452$	−1.19819	−	0.673156i	−0.0563581	−	0.0316626i
$453$		0			0
$454$	4.43466	+	7.57804i	0.208129	+	0.355655i
$455$			22.2652i			1.04381i
$456$		0			0
$457$		−	7.04266i		−	0.329442i	−0.986340	−	0.164721i	$-0.947328\pi$
$457$		−	7.04266i		−	0.329442i	0.986340	−	0.164721i	$-0.0526723\pi$
$458$	−13.6240	+	7.97276i	−0.636609	+	0.372543i
$459$		0			0
$460$	−36.0217	−	4.24644i	−1.67952	−	0.197991i
$461$	4.88736			0.227627			0.113813	−	0.993502i	$-0.463693\pi$
$461$	4.88736			0.227627			0.113813	+	0.993502i	$0.463693\pi$
$462$		0			0
$463$			17.4728i			0.812032i	0.913866	+	0.406016i	$0.133082\pi$
$463$			17.4728i			0.812032i	−0.913866	+	0.406016i	$0.866918\pi$
$464$	0.710783	+	1.16699i	0.0329973	+	0.0541762i
$465$		0			0
$466$	−16.9151	−	28.9048i	−0.783575	−	1.33899i
$467$	−21.6721			−1.00286			−0.501432	−	0.865197i	$-0.667193\pi$
$467$	−21.6721			−1.00286			−0.501432	+	0.865197i	$0.667193\pi$
$468$		0			0
$469$	15.1388			0.699044
$470$	7.29260	+	12.4617i	0.336382	+	0.574817i
$471$		0			0
$472$	−0.132918	−	7.55188i	−0.00611803	−	0.347604i
$473$	37.1426			1.70782
$474$		0			0
$475$	37.2348			1.70845
$476$	−5.00345	−	2.81100i	−0.229333	−	0.128842i
$477$		0			0
$478$	7.01857	−	4.10726i	0.321022	−	0.187862i
$479$	38.7920			1.77245			0.886226	−	0.463254i	$-0.153318\pi$
$479$	38.7920			1.77245			0.886226	+	0.463254i	$0.153318\pi$
$480$		0			0
$481$			61.5764i			2.80764i
$482$	−15.0479	+	8.80602i	−0.685414	+	0.401103i
$483$		0			0
$484$	−6.20886	+	11.0515i	−0.282221	+	0.502341i
$485$	41.2168			1.87156
$486$		0			0
$487$			29.5419i			1.33867i	0.742960	+	0.669336i	$0.233421\pi$
$487$			29.5419i			1.33867i	−0.742960	+	0.669336i	$0.766579\pi$
$488$	0.386787	+	21.9758i	0.0175090	+	0.994797i
$489$		0			0
$490$	−27.4853	+	16.0844i	−1.24166	+	0.726619i
$491$		−	15.6437i		−	0.705991i	−0.935625	−	0.352996i	$-0.885163\pi$
$491$		−	15.6437i		−	0.705991i	0.935625	−	0.352996i	$-0.114837\pi$
$492$		0			0
$493$		−	0.958815i		−	0.0431829i
$494$	16.4703	+	28.1448i	0.741035	+	1.26630i
$495$		0			0
$496$	18.4401	−	11.2314i	0.827987	−	0.504304i
$497$		−	2.41965i		−	0.108536i
$498$		0			0
$499$		−	35.1984i		−	1.57570i	−0.615868	−	0.787849i	$-0.711195\pi$
$499$		−	35.1984i		−	1.57570i	0.615868	−	0.787849i	$-0.288805\pi$
$500$	28.3526	+	15.9288i	1.26797	+	0.712358i
$501$		0			0
$502$	−15.0186	−	25.6642i	−0.670314	−	1.14545i
$503$	−26.6899			−1.19004			−0.595022	−	0.803709i	$-0.702857\pi$
$503$	−26.6899			−1.19004			−0.595022	+	0.803709i	$0.702857\pi$
$504$		0			0
$505$			29.9557i			1.33301i
$506$	22.5366	+	17.0192i	1.00187	+	0.756597i
$507$		0			0
$508$	−7.53973	−	4.23591i	−0.334521	−	0.187938i
$509$	4.70015			0.208330			0.104165	−	0.994560i	$-0.466783\pi$
$509$	4.70015			0.208330			0.104165	+	0.994560i	$0.466783\pi$
$510$		0			0
$511$	5.30723			0.234778
$512$	22.5959	−	1.19409i	0.998607	−	0.0527718i
$513$		0			0
$514$	−13.6537	−	23.3318i	−0.602241	−	1.02912i
$515$			13.5143i			0.595511i
$516$		0			0
$517$		−	11.2421i		−	0.494427i
$518$	13.3416	−	7.80747i	0.586195	−	0.343041i
$519$		0			0
$520$	1.08402	+	61.5901i	0.0475375	+	2.70090i
$521$		−	1.58918i		−	0.0696231i	−0.999394	−	0.0348116i	$-0.988917\pi$
$521$		−	1.58918i		−	0.0696231i	0.999394	−	0.0348116i	$-0.0110831\pi$
$522$		0			0
$523$	2.47426			0.108192			0.0540959	−	0.998536i	$-0.482772\pi$
$523$	2.47426			0.108192			0.0540959	+	0.998536i	$0.482772\pi$
$524$	−17.9305	−	10.0736i	−0.783299	−	0.440067i
$525$		0			0
$526$	3.54683	+	6.06090i	0.154649	+	0.264268i
$527$	−15.1507			−0.659973
$528$		0			0
$529$	16.2040	−	16.3226i	0.704524	−	0.709680i
$530$	2.20022	+	3.75979i	0.0955716	+	0.163315i
$531$		0			0
$532$	4.00973	−	7.13715i	0.173844	−	0.309435i
$533$	−47.9156			−2.07546
$534$		0			0
$535$		−	13.2141i		−	0.571297i
$536$	41.8769	−	0.737059i	1.80881	−	0.0318361i
$537$		0			0
$538$	6.45896	+	11.0372i	0.278466	+	0.475848i
$539$	24.7953			1.06801
$540$		0			0
$541$	9.66457			0.415512			0.207756	−	0.978181i	$-0.433384\pi$
$541$	9.66457			0.415512			0.207756	+	0.978181i	$0.433384\pi$
$542$	7.40535	−	4.33360i	0.318087	−	0.186144i
$543$		0			0
$544$	−13.9774	−	7.53219i	−0.599277	−	0.322940i
$545$	8.15747			0.349428
$546$		0			0
$547$			10.7576i			0.459962i	0.973195	+	0.229981i	$0.0738664\pi$
$547$			10.7576i			0.459962i	−0.973195	+	0.229981i	$0.926134\pi$
$548$	−12.7775	−	7.17853i	−0.545826	−	0.306652i
$549$		0			0
$550$	−27.6598	−	47.2657i	−1.17942	−	2.01541i
$551$	1.36770			0.0582659
$552$		0			0
$553$	−7.06457			−0.300416
$554$	−22.4845	−	38.4219i	−0.955273	−	1.63239i
$555$		0			0
$556$	−1.23269	−	0.692539i	−0.0522777	−	0.0293702i
$557$		−	19.7483i		−	0.836762i	−0.908272	−	0.418381i	$-0.862598\pi$
$557$		−	19.7483i		−	0.836762i	0.908272	−	0.418381i	$-0.137402\pi$
$558$		0			0
$559$	−51.3733			−2.17286
$560$	13.2071	−	8.04407i	0.558101	−	0.339924i
$561$		0			0
$562$	−3.95296	+	2.31326i	−0.166745	+	0.0975791i
$563$	−13.5629			−0.571606			−0.285803	−	0.958288i	$-0.592260\pi$
$563$	−13.5629			−0.571606			−0.285803	+	0.958288i	$0.592260\pi$
$564$		0			0
$565$	−2.59854			−0.109321
$566$	−16.4421	−	28.0966i	−0.691112	−	1.18099i
$567$		0			0
$568$	−0.117805	−	6.69325i	−0.00494300	−	0.280843i
$569$		−	22.1659i		−	0.929243i	−0.885509	−	0.464621i	$-0.846190\pi$
$569$		−	22.1659i		−	0.929243i	0.885509	−	0.464621i	$-0.153810\pi$
$570$		0			0
$571$	−0.830063			−0.0347370			−0.0173685	−	0.999849i	$-0.505529\pi$
$571$	−0.830063			−0.0347370			−0.0173685	+	0.999849i	$0.505529\pi$
$572$	23.4920	−	41.8147i	0.982249	−	1.74836i
$573$		0			0
$574$	6.07537	+	10.3817i	0.253581	+	0.433325i
$575$	−41.1747	+	17.1431i	−1.71711	+	0.714919i
$576$		0			0
$577$	−3.58731			−0.149342			−0.0746708	−	0.997208i	$-0.523791\pi$
$577$	−3.58731			−0.149342			−0.0746708	+	0.997208i	$0.523791\pi$
$578$	−6.51552	−	11.1339i	−0.271010	−	0.463107i
$579$		0			0
$580$	2.25243	+	1.26544i	0.0935271	+	0.0525446i
$581$	1.14704			0.0475872
$582$		0			0
$583$		−	3.39182i		−	0.140475i
$584$	14.6809	−	0.258392i	0.607499	−	0.0106923i
$585$		0			0
$586$	−37.1991	+	21.7688i	−1.53668	+	0.899262i
$587$		−	27.3709i		−	1.12972i	−0.825187	−	0.564860i	$-0.808930\pi$
$587$		−	27.3709i		−	1.12972i	0.825187	−	0.564860i	$-0.191070\pi$
$588$		0			0
$589$		−	21.6116i		−	0.890490i
$590$	−7.21295	−	12.3256i	−0.296952	−	0.507439i
$591$		0			0
$592$	36.5254	−	22.2466i	1.50118	−	0.914330i
$593$	−29.7156			−1.22027			−0.610137	−	0.792296i	$-0.708886\pi$
$593$	−29.7156			−1.22027			−0.610137	+	0.792296i	$0.708886\pi$
$594$		0			0
$595$	−10.8511			−0.444852
$596$	−0.667456	−	0.374984i	−0.0273401	−	0.0153600i
$597$		0			0
$598$	−31.1712	−	23.5399i	−1.27468	−	0.962618i
$599$		−	2.73087i		−	0.111580i	−0.998443	−	0.0557902i	$-0.982232\pi$
$599$		−	2.73087i		−	0.111580i	0.998443	−	0.0557902i	$-0.0177678\pi$
$600$		0			0
$601$	−33.8681			−1.38151			−0.690753	−	0.723090i	$-0.742721\pi$
$601$	−33.8681			−1.38151			−0.690753	+	0.723090i	$0.742721\pi$
$602$	6.51379	+	11.1309i	0.265482	+	0.453662i
$603$		0			0
$604$	11.0706	+	6.21959i	0.450456	+	0.253071i
$605$			23.9677i			0.974424i
$606$		0			0
$607$			28.8726i			1.17190i	0.810346	+	0.585952i	$0.199279\pi$
$607$			28.8726i			1.17190i	−0.810346	+	0.585952i	$0.800721\pi$
$608$	10.7443	−	19.9380i	0.435737	−	0.808594i
$609$		0			0
$610$	20.9895	+	35.8673i	0.849839	+	1.45222i
$611$			15.5494i			0.629060i
$612$		0			0
$613$		−	1.07656i		−	0.0434818i	−0.999764	−	0.0217409i	$-0.993079\pi$
$613$		−	1.07656i		−	0.0434818i	0.999764	−	0.0217409i	$-0.00692088\pi$
$614$	−34.9277	+	20.4397i	−1.40957	+	0.824878i
$615$		0			0
$616$	−12.0385	+	0.211884i	−0.485045	+	0.00853707i
$617$			8.83195i			0.355561i	0.984070	+	0.177781i	$0.0568917\pi$
$617$			8.83195i			0.355561i	−0.984070	+	0.177781i	$0.943108\pi$
$618$		0			0
$619$	20.3851			0.819347			0.409674	−	0.912232i	$-0.365643\pi$
$619$	20.3851			0.819347			0.409674	+	0.912232i	$0.365643\pi$
$620$	19.9958	−	35.5916i	0.803051	−	1.42940i
$621$		0			0
$622$	33.4625	−	19.5822i	1.34172	−	0.785175i
$623$		−	9.98604i		−	0.400082i
$624$		0			0
$625$	14.9893			0.599571
$626$	−11.2198	+	6.56580i	−0.448433	+	0.262422i
$627$		0			0
$628$	−25.1143	−	14.1095i	−1.00217	−	0.563031i
$629$	−30.0097			−1.19657
$630$		0			0
$631$	6.21298			0.247335			0.123667	−	0.992324i	$-0.460534\pi$
$631$	6.21298			0.247335			0.123667	+	0.992324i	$0.460534\pi$
$632$	−19.5420	+	0.343951i	−0.777340	+	0.0136816i
$633$		0			0
$634$	3.49363	+	5.96999i	0.138750	+	0.237098i
$635$	−16.3516			−0.648894
$636$		0			0
$637$	−34.2953			−1.35883
$638$	−1.01599	−	1.73615i	−0.0402235	−	0.0687348i
$639$		0			0
$640$	36.1418	−	22.8946i	1.42863	−	0.904987i
$641$		−	16.1002i		−	0.635921i	−0.948104	−	0.317960i	$-0.897002\pi$
$641$		−	16.1002i		−	0.635921i	0.948104	−	0.317960i	$-0.102998\pi$
$642$		0			0
$643$	−8.14353			−0.321150			−0.160575	−	0.987024i	$-0.551335\pi$
$643$	−8.14353			−0.321150			−0.160575	+	0.987024i	$0.551335\pi$
$644$	−1.14803	+	9.73847i	−0.0452386	+	0.383749i
$645$		0			0
$646$	−13.7166	+	8.02694i	−0.539673	+	0.315816i
$647$			25.7912i			1.01396i	0.861959	+	0.506978i	$0.169238\pi$
$647$			25.7912i			1.01396i	−0.861959	+	0.506978i	$0.830762\pi$
$648$		0			0
$649$			11.1193i			0.436471i
$650$	38.2573	+	65.3749i	1.50057	+	2.56421i
$651$		0			0
$652$	−23.9148	−	13.4356i	−0.936576	−	0.526179i
$653$	36.8619			1.44252			0.721260	−	0.692665i	$-0.243563\pi$
$653$	36.8619			1.44252			0.721260	+	0.692665i	$0.243563\pi$
$654$		0			0
$655$	−38.8864			−1.51942
$656$	17.3112	+	28.4222i	0.675888	+	1.10970i
$657$		0			0
$658$	3.36903	−	1.97155i	0.131339	−	0.0768592i
$659$	−23.0516			−0.897963			−0.448982	−	0.893541i	$-0.648213\pi$
$659$	−23.0516			−0.897963			−0.448982	+	0.893541i	$0.648213\pi$
$660$		0			0
$661$			15.4291i			0.600123i	0.953920	+	0.300061i	$0.0970072\pi$
$661$			15.4291i			0.600123i	−0.953920	+	0.300061i	$0.902993\pi$
$662$	11.3176	−	6.62307i	0.439873	−	0.257413i
$663$		0			0
$664$	3.17295	−	0.0558457i	0.123134	−	0.00216723i
$665$		−	15.4785i		−	0.600231i
$666$		0			0
$667$	−1.51242	+	0.629697i	−0.0585611	+	0.0243820i
$668$	23.8552	+	13.4021i	0.922985	+	0.518544i
$669$		0			0
$670$	68.3485	−	39.9975i	2.64053	−	1.54524i
$671$		−	32.3569i		−	1.24912i
$672$		0			0
$673$	11.2843			0.434978			0.217489	−	0.976063i	$-0.430213\pi$
$673$	11.2843			0.434978			0.217489	+	0.976063i	$0.430213\pi$
$674$	−39.0090	+	22.8280i	−1.50257	+	0.879302i
$675$		0			0
$676$	−19.7577	+	35.1678i	−0.759911	+	1.35261i
$677$			28.5070i			1.09561i	0.836606	+	0.547806i	$0.184537\pi$
$677$			28.5070i			1.09561i	−0.836606	+	0.547806i	$0.815463\pi$
$678$		0			0
$679$		−	11.1430i		−	0.427627i
$680$	−30.0164	+	0.528306i	−1.15108	+	0.0202596i
$681$		0			0
$682$	−27.4336	+	16.0541i	−1.05049	+	0.614744i
$683$		−	26.1642i		−	1.00115i	−0.865694	−	0.500573i	$-0.833123\pi$
$683$		−	26.1642i		−	1.00115i	0.865694	−	0.500573i	$-0.166877\pi$
$684$		0			0
$685$	−27.7108			−1.05878
$686$	9.46005	+	16.1655i	0.361186	+	0.617203i
$687$		0			0
$688$	18.5604	+	30.4732i	0.707608	+	1.16178i
$689$			4.69134i			0.178726i
$690$		0			0
$691$			42.6495i			1.62246i	0.584725	+	0.811232i	$0.301203\pi$
$691$			42.6495i			1.62246i	−0.584725	+	0.811232i	$0.698797\pi$
$692$	−3.42401	+	6.09459i	−0.130161	+	0.231682i
$693$		0			0
$694$	21.2571	−	12.4397i	0.806910	−	0.472203i
$695$	−2.67337			−0.101407
$696$		0			0
$697$		−	23.3520i		−	0.884521i
$698$	−10.0209	−	17.1239i	−0.379296	−	0.648150i
$699$		0			0
$700$	9.31381	−	16.5782i	0.352029	−	0.626596i
$701$		−	8.56934i		−	0.323659i	−0.986819	−	0.161830i	$-0.948260\pi$
$701$		−	8.56934i		−	0.323659i	0.986819	−	0.161830i	$-0.0517395\pi$
$702$		0			0
$703$		−	42.8072i		−	1.61451i
$704$	−33.2906	+	1.17223i	−1.25469	+	0.0441801i
$705$		0			0
$706$	7.50980	+	12.8329i	0.282635	+	0.482973i
$707$	8.09851			0.304576
$708$		0			0
$709$		−	50.0440i		−	1.87944i	−0.341943	−	0.939721i	$-0.611085\pi$
$709$		−	50.0440i		−	1.87944i	0.341943	−	0.939721i	$-0.388915\pi$
$710$	−6.39285	−	10.9242i	−0.239920	−	0.409980i
$711$		0			0
$712$	−0.486188	−	27.6234i	−0.0182207	−	1.03523i
$713$	9.95012	+	23.8984i	0.372635	+	0.895002i
$714$		0			0
$715$		−	90.6846i		−	3.39141i
$716$	−45.3802	−	25.4951i	−1.69594	−	0.952798i
$717$		0			0
$718$	−19.0731	−	32.5925i	−0.711802	−	1.21634i
$719$			32.9114i			1.22739i	0.789543	+	0.613695i	$0.210317\pi$
$719$			32.9114i			1.22739i	−0.789543	+	0.613695i	$0.789683\pi$
$720$		0			0
$721$	3.65359			0.136067
$722$	2.12132	+	3.62495i	0.0789473	+	0.134907i
$723$		0			0
$724$	−11.6784	−	6.56108i	−0.434026	−	0.243841i
$725$	3.17689			0.117987
$726$		0			0
$727$	−0.793020			−0.0294115			−0.0147057	−	0.999892i	$-0.504681\pi$
$727$	−0.793020			−0.0294115			−0.0147057	+	0.999892i	$0.504681\pi$
$728$	16.6509	−	0.293065i	0.617122	−	0.0108617i
$729$		0			0
$730$	23.9611	−	14.0220i	0.886840	−	0.518977i
$731$		−	25.0372i		−	0.926033i
$732$		0			0
$733$		−	28.1816i		−	1.04091i	−0.853889	−	0.520456i	$-0.825762\pi$
$733$		−	28.1816i		−	1.04091i	0.853889	−	0.520456i	$-0.174238\pi$
$734$	−16.2779	−	27.8160i	−0.600827	−	1.02671i
$735$		0			0
$736$	−2.70154	+	26.9945i	−0.0995800	+	0.995030i
$737$	−61.6592			−2.27125
$738$		0			0
$739$			28.9097i			1.06346i	0.846914	+	0.531730i	$0.178458\pi$
$739$			28.9097i			1.06346i	−0.846914	+	0.531730i	$0.821542\pi$
$740$	39.6068	−	70.4983i	1.45597	−	2.59157i
$741$		0			0
$742$	1.01646	−	0.594831i	0.0373154	−	0.0218369i
$743$	34.6908			1.27268			0.636341	−	0.771408i	$-0.280447\pi$
$743$	34.6908			1.27268			0.636341	+	0.771408i	$0.280447\pi$
$744$		0			0
$745$	−1.44753			−0.0530333
$746$	35.9915	−	21.0621i	1.31774	−	0.771140i
$747$		0			0
$748$	20.3787	+	11.4490i	0.745119	+	0.418617i
$749$	−3.57244			−0.130534
$750$		0			0
$751$	−41.9033			−1.52907			−0.764536	−	0.644581i	$-0.777032\pi$
$751$	−41.9033			−1.52907			−0.764536	+	0.644581i	$0.777032\pi$
$752$	9.22344	−	5.61775i	0.336344	−	0.204858i
$753$		0			0
$754$	1.40526	+	2.40133i	0.0511764	+	0.0874513i
$755$	24.0091			0.873780
$756$		0			0
$757$			5.44668i			0.197963i	0.995089	+	0.0989815i	$0.0315585\pi$
$757$			5.44668i			0.197963i	−0.995089	+	0.0989815i	$0.968442\pi$
$758$	2.04963	+	3.50245i	0.0744460	+	0.127215i
$759$		0			0
$760$	−0.753600	−	42.8167i	−0.0273359	−	1.55313i
$761$	2.39310			0.0867498			0.0433749	−	0.999059i	$-0.486189\pi$
$761$	2.39310			0.0867498			0.0433749	+	0.999059i	$0.486189\pi$
$762$		0			0
$763$		−	2.20537i		−	0.0798398i
$764$	−16.8207	+	29.9401i	−0.608551	+	1.08319i
$765$		0			0
$766$	19.9224	+	34.0439i	0.719827	+	1.23006i
$767$		−	15.3795i		−	0.555323i
$768$		0			0
$769$		−	40.1929i		−	1.44939i	−0.689068	−	0.724697i	$-0.741980\pi$
$769$		−	40.1929i		−	1.44939i	0.689068	−	0.724697i	$-0.258020\pi$
$770$	−19.6484	+	11.4982i	−0.708078	+	0.414366i
$771$		0			0
$772$	−8.81109	+	15.6834i	−0.317118	+	0.564456i
$773$		−	1.02655i		−	0.0369225i	−0.999830	−	0.0184612i	$-0.994123\pi$
$773$		−	1.02655i		−	0.0369225i	0.999830	−	0.0184612i	$-0.00587673\pi$
$774$		0			0
$775$		−	50.1994i		−	1.80322i
$776$	−0.542515	−	30.8237i	−0.0194752	−	1.10651i
$777$		0			0
$778$	−2.76324	+	1.61705i	−0.0990670	+	0.0579739i
$779$	33.3104			1.19347
$780$		0			0
$781$			9.85508i			0.352642i
$782$	11.4724	−	15.1915i	0.410250	−	0.543247i
$783$		0			0
$784$	12.3904	+	20.3430i	0.442513	+	0.726536i
$785$	−54.4660			−1.94398
$786$		0			0
$787$	−29.7905			−1.06192			−0.530958	−	0.847398i	$-0.678168\pi$
$787$	−29.7905			−1.06192			−0.530958	+	0.847398i	$0.678168\pi$
$788$	−15.3837	+	27.3824i	−0.548023	+	0.975457i
$789$		0			0
$790$	−31.8951	+	18.6650i	−1.13478	+	0.664070i
$791$			0.702516i			0.0249786i
$792$		0			0
$793$			44.7540i			1.58926i
$794$	−10.0752	−	17.2167i	−0.357555	−	0.610998i
$795$		0			0
$796$	17.0846	−	30.4099i	0.605548	−	1.07785i
$797$			42.4174i			1.50250i	0.660017	+	0.751251i	$0.270549\pi$
$797$			42.4174i			1.50250i	−0.660017	+	0.751251i	$0.729451\pi$
$798$		0			0
$799$	−7.57810			−0.268094
$800$	24.9568	−	46.3121i	0.882355	−	1.63738i
$801$		0			0
$802$	33.8887	−	19.8316i	1.19665	−	0.700278i
$803$	−21.6160			−0.762812
$804$		0			0
$805$	7.12641	+	17.1164i	0.251173	+	0.603272i
$806$	37.9445	−	22.2051i	1.33654	−	0.782140i
$807$		0			0
$808$	22.4021	−	0.394291i	0.788104	−	0.0138711i
$809$	29.6442			1.04224			0.521118	−	0.853485i	$-0.325515\pi$
$809$	29.6442			1.04224			0.521118	+	0.853485i	$0.325515\pi$
$810$		0			0
$811$		−	2.07439i		−	0.0728418i	−0.999337	−	0.0364209i	$-0.988404\pi$
$811$		−	2.07439i		−	0.0728418i	0.999337	−	0.0364209i	$-0.0115957\pi$
$812$	0.342112	−	0.608945i	0.0120058	−	0.0213698i
$813$		0			0
$814$	−54.3393	+	31.7993i	−1.90459	+	1.11456i
$815$	−51.8646			−1.81674
$816$		0			0
$817$	35.7142			1.24948
$818$	21.5562	+	36.8357i	0.753695	+	1.28793i
$819$		0			0
$820$	54.8582	+	30.8200i	1.91573	+	1.07628i
$821$	14.6390			0.510904			0.255452	−	0.966822i	$-0.417776\pi$
$821$	14.6390			0.510904			0.255452	+	0.966822i	$0.417776\pi$
$822$		0			0
$823$			36.8036i			1.28289i	0.767168	+	0.641446i	$0.221665\pi$
$823$			36.8036i			1.28289i	−0.767168	+	0.641446i	$0.778335\pi$
$824$	10.1066	−	0.177882i	0.352079	−	0.00619680i
$825$		0			0
$826$	−3.33224	+	1.95002i	−0.115943	+	0.0678499i
$827$	−20.8771			−0.725970			−0.362985	−	0.931795i	$-0.618242\pi$
$827$	−20.8771			−0.725970			−0.362985	+	0.931795i	$0.618242\pi$
$828$		0			0
$829$	17.8407			0.619632			0.309816	−	0.950797i	$-0.399733\pi$
$829$	17.8407			0.619632			0.309816	+	0.950797i	$0.399733\pi$
$830$	5.17865	−	3.03054i	0.179754	−	0.105192i
$831$		0			0
$832$	46.0454	−	1.62136i	1.59634	−	0.0562104i
$833$		−	16.7141i		−	0.579109i
$834$		0			0
$835$	51.7353			1.79038
$836$	−16.3314	+	29.0691i	−0.564832	+	1.00538i
$837$		0			0
$838$	−17.4026	−	29.7380i	−0.601164	−	1.02728i
$839$	−30.5659			−1.05525			−0.527625	−	0.849477i	$-0.676917\pi$
$839$	−30.5659			−1.05525			−0.527625	+	0.849477i	$0.676917\pi$
$840$		0			0
$841$	−28.8833			−0.995976
$842$	24.4229	−	14.2923i	0.841669	−	0.492544i
$843$		0			0
$844$	4.62172	+	2.59654i	0.159086	+	0.0893765i
$845$			76.2693i			2.62374i
$846$		0			0
$847$	6.47966			0.222644
$848$	2.78277	−	1.69491i	0.0955608	−	0.0582035i
$849$		0			0
$850$	−31.8609	+	18.6450i	−1.09282	+	0.639517i
$851$	19.7087	+	47.3368i	0.675607	+	1.62269i
$852$		0			0
$853$	24.6193			0.842948			0.421474	−	0.906840i	$-0.361513\pi$
$853$	24.6193			0.842948			0.421474	+	0.906840i	$0.361513\pi$
$854$	9.69672	−	5.67451i	0.331815	−	0.194178i
$855$		0			0
$856$	−9.88210	+	0.173931i	−0.337763	+	0.00594483i
$857$	29.1797			0.996760			0.498380	−	0.866959i	$-0.333928\pi$
$857$	29.1797			0.996760			0.498380	+	0.866959i	$0.333928\pi$
$858$		0			0
$859$			4.44412i			0.151631i	0.997122	+	0.0758157i	$0.0241561\pi$
$859$			4.44412i			0.151631i	−0.997122	+	0.0758157i	$0.975844\pi$
$860$	58.8169	+	33.0440i	2.00564	+	1.12679i
$861$		0			0
$862$	8.54724	+	14.6057i	0.291120	+	0.497473i
$863$		−	11.8945i		−	0.404895i	−0.979293	−	0.202447i	$-0.935111\pi$
$863$		−	11.8945i		−	0.404895i	0.979293	−	0.202447i	$-0.0648895\pi$
$864$		0			0
$865$			13.2175i			0.449408i
$866$	9.86008	−	5.77011i	0.335059	−	0.196076i
$867$		0			0
$868$	−9.62220	−	5.40586i	−0.326599	−	0.183487i
$869$	28.7735			0.976074
$870$		0			0
$871$	85.2831			2.88971
$872$	−0.107373	−	6.10051i	−0.00363609	−	0.206589i
$873$		0			0
$874$	21.6699	+	16.3647i	0.732994	+	0.553544i
$875$		−	16.6236i		−	0.561979i
$876$		0			0
$877$	−18.3997			−0.621314			−0.310657	−	0.950522i	$-0.600549\pi$
$877$	−18.3997			−0.621314			−0.310657	+	0.950522i	$0.600549\pi$
$878$	−26.7921	+	15.6787i	−0.904190	+	0.529131i
$879$		0			0
$880$	−53.7915	+	32.7629i	−1.81331	+	1.10444i
$881$			2.28963i			0.0771395i	0.999256	+	0.0385697i	$0.0122802\pi$
$881$			2.28963i			0.0771395i	−0.999256	+	0.0385697i	$0.987720\pi$
$882$		0			0
$883$		−	33.2434i		−	1.11873i	−0.828921	−	0.559366i	$-0.811045\pi$
$883$		−	33.2434i		−	1.11873i	0.828921	−	0.559366i	$-0.188955\pi$
$884$	−28.1865	−	15.8355i	−0.948016	−	0.532606i
$885$		0			0
$886$	3.57056	−	2.08949i	0.119955	−	0.0701977i
$887$			7.21083i			0.242116i	0.992645	+	0.121058i	$0.0386287\pi$
$887$			7.21083i			0.242116i	−0.992645	+	0.121058i	$0.961371\pi$
$888$		0			0
$889$			4.42066i			0.148264i
$890$	−26.3836	−	45.0849i	−0.884382	−	1.51125i
$891$		0			0
$892$	42.2731	+	23.7495i	1.41541	+	0.795192i
$893$		−	10.8097i		−	0.361734i
$894$		0			0
$895$	−98.4172			−3.28972
$896$	−6.18954	−	9.77095i	−0.206778	−	0.326424i
$897$		0			0
$898$	−22.1729	−	37.8895i	−0.739919	−	1.26439i
$899$		−	1.84391i		−	0.0614979i
$900$		0			0
$901$	−2.28636			−0.0761698
$902$	−24.7446	−	42.2841i	−0.823904	−	1.40791i
$903$		0			0
$904$	0.0342033	+	1.94330i	0.00113758	+	0.0646333i
$905$	−25.3273			−0.841909
$906$		0			0
$907$	−19.2080			−0.637792			−0.318896	−	0.947790i	$-0.603312\pi$
$907$	−19.2080			−0.637792			−0.318896	+	0.947790i	$0.603312\pi$
$908$	6.08198	−	10.8257i	0.201838	−	0.359262i
$909$		0			0
$910$	27.1764	−	15.9036i	0.900887	−	0.527198i
$911$	24.6794			0.817665			0.408833	−	0.912609i	$-0.365936\pi$
$911$	24.6794			0.817665			0.408833	+	0.912609i	$0.365936\pi$
$912$		0			0
$913$	−4.67181			−0.154614
$914$	−8.59610	+	5.03043i	−0.284334	+	0.166392i
$915$		0			0
$916$	19.4627	+	10.9344i	0.643066	+	0.361282i
$917$			10.5129i			0.347168i
$918$		0			0
$919$	−36.1695			−1.19312			−0.596560	−	0.802568i	$-0.703466\pi$
$919$	−36.1695			−1.19312			−0.596560	+	0.802568i	$0.703466\pi$
$920$	20.5464	+	47.0004i	0.677396	+	1.54956i
$921$		0			0
$922$	−3.49094	−	5.96539i	−0.114968	−	0.196460i
$923$		−	13.6309i		−	0.448667i
$924$		0			0
$925$		−	99.4327i		−	3.26933i
$926$	21.3269	−	12.4805i	0.700846	−	0.410134i
$927$		0			0
$928$	0.916704	−	1.70112i	0.0300923	−	0.0558421i
$929$	−19.8450			−0.651095			−0.325547	−	0.945526i	$-0.605549\pi$
$929$	−19.8450			−0.651095			−0.325547	+	0.945526i	$0.605549\pi$
$930$		0			0
$931$	23.8417			0.781381
$932$	−23.1984	+	41.2922i	−0.759890	+	1.35257i
$933$		0			0
$934$	15.4799	+	26.4524i	0.506518	+	0.865548i
$935$	44.1958			1.44536
$936$		0			0
$937$			33.2780i			1.08715i	0.839362	+	0.543573i	$0.182929\pi$
$937$			33.2780i			1.08715i	−0.839362	+	0.543573i	$0.817071\pi$
$938$	−10.8133	−	18.4780i	−0.353067	−	0.603329i
$939$		0			0
$940$	10.0016	−	17.8023i	0.326215	−	0.580648i
$941$			17.6138i			0.574194i	0.957901	+	0.287097i	$0.0926903\pi$
$941$			17.6138i			0.574194i	−0.957901	+	0.287097i	$0.907310\pi$
$942$		0			0
$943$	−36.8351	+	15.3363i	−1.19952	+	0.499420i
$944$	−9.12271	+	5.55639i	−0.296919	+	0.180845i
$945$		0			0
$946$	−26.5302	−	45.3354i	−0.862571	−	1.47398i
$947$			45.0168i			1.46285i	0.681921	+	0.731425i	$0.261145\pi$
$947$			45.0168i			1.46285i	−0.681921	+	0.731425i	$0.738855\pi$
$948$		0			0
$949$	29.8979			0.970526
$950$	−26.5960	−	45.4479i	−0.862889	−	1.47452i
$951$		0			0
$952$	0.142827	+	8.11493i	0.00462907	+	0.263006i
$953$		−	39.4151i		−	1.27678i	−0.769713	−	0.638390i	$-0.779601\pi$
$953$		−	39.4151i		−	1.27678i	0.769713	−	0.638390i	$-0.220399\pi$
$954$		0			0
$955$			64.9318i			2.10114i
$956$	−10.0264	−	5.63297i	−0.324278	−	0.182183i
$957$		0			0
$958$	−27.7083	−	47.3486i	−0.895215	−	1.52976i
$959$			7.49162i			0.241917i
$960$		0			0
$961$	1.86357			0.0601152
$962$	75.1587	−	43.9827i	2.42321	−	1.41806i
$963$		0			0
$964$	21.4968	+	12.0772i	0.692367	+	0.388979i
$965$			34.0129i			1.09491i
$966$		0			0
$967$			24.3005i			0.781450i	0.920507	+	0.390725i	$0.127776\pi$
$967$			24.3005i			0.781450i	−0.920507	+	0.390725i	$0.872224\pi$
$968$	17.9240	−	0.315474i	0.576101	−	0.0101397i
$969$		0			0
$970$	−29.4403	−	50.3082i	−0.945271	−	1.61530i
$971$	−15.5499			−0.499020			−0.249510	−	0.968372i	$-0.580270\pi$
$971$	−15.5499			−0.499020			−0.249510	+	0.968372i	$0.580270\pi$
$972$		0			0
$973$			0.722745i			0.0231701i
$974$	36.0582	−	21.1012i	1.15538	−	0.676125i
$975$		0			0
$976$	26.5468	−	16.1689i	0.849743	−	0.517555i
$977$			37.7336i			1.20720i	0.797286	+	0.603602i	$0.206268\pi$
$977$			37.7336i			1.20720i	−0.797286	+	0.603602i	$0.793732\pi$
$978$		0			0
$979$			40.6724i			1.29990i
$980$	39.2644	+	22.0592i	1.25426	+	0.704655i
$981$		0			0
$982$	−19.0943	+	11.1740i	−0.609325	+	0.356576i
$983$	19.1931			0.612166			0.306083	−	0.952005i	$-0.400982\pi$
$983$	19.1931			0.612166			0.306083	+	0.952005i	$0.400982\pi$
$984$		0			0
$985$			59.3848i			1.89216i
$986$	−1.17031	+	0.684862i	−0.0372702	+	0.0218104i
$987$		0			0
$988$	22.5885	−	40.2066i	0.718636	−	1.27914i
$989$	−39.4932	+	16.4430i	−1.25581	+	0.522858i
$990$		0			0
$991$		−	24.2887i		−	0.771555i	−0.922592	−	0.385778i	$-0.873933\pi$
$991$		−	24.2887i		−	0.771555i	0.922592	−	0.385778i	$-0.126067\pi$
$992$	−26.8802	−	14.4852i	−0.853446	−	0.459907i
$993$		0			0
$994$	−2.95337	+	1.72831i	−0.0936752	+	0.0548186i
$995$		−	65.9507i		−	2.09078i
$996$		0			0
$997$	4.39684			0.139249			0.0696247	−	0.997573i	$-0.477820\pi$
$997$	4.39684			0.139249			0.0696247	+	0.997573i	$0.477820\pi$
$998$	−42.9624	+	25.1415i	−1.35995	+	0.795841i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	828.2.e.f.91.10		24
3.2	odd	2		276.2.e.a.91.15	yes	24
4.3	odd	2	inner	828.2.e.f.91.12		24
12.11	even	2		276.2.e.a.91.13	✓	24
23.22	odd	2	inner	828.2.e.f.91.9		24
24.5	odd	2		4416.2.i.d.1471.23		24
24.11	even	2		4416.2.i.d.1471.22		24
69.68	even	2		276.2.e.a.91.16	yes	24
92.91	even	2	inner	828.2.e.f.91.11		24
276.275	odd	2		276.2.e.a.91.14	yes	24
552.275	odd	2		4416.2.i.d.1471.21		24
552.413	even	2		4416.2.i.d.1471.24		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.e.a.91.13	✓	24	12.11	even	2
276.2.e.a.91.14	yes	24	276.275	odd	2
276.2.e.a.91.15	yes	24	3.2	odd	2
276.2.e.a.91.16	yes	24	69.68	even	2
828.2.e.f.91.9		24	23.22	odd	2	inner
828.2.e.f.91.10		24	1.1	even	1	trivial
828.2.e.f.91.11		24	92.91	even	2	inner
828.2.e.f.91.12		24	4.3	odd	2	inner
4416.2.i.d.1471.21		24	552.275	odd	2
4416.2.i.d.1471.22		24	24.11	even	2
4416.2.i.d.1471.23		24	24.5	odd	2
4416.2.i.d.1471.24		24	552.413	even	2

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:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.714279 - 1.22058i) q^{2} +(-0.979610 + 1.74366i) q^{4} +3.78153i q^{5} +1.02234 q^{7} +(2.82799 - 0.0497743i) q^{8} +(4.61564 - 2.70107i) q^{10} -4.16390 q^{11} +5.75925 q^{13} +(-0.730233 - 1.24784i) q^{14} +(-2.08073 - 3.41622i) q^{16} +2.80681i q^{17} -4.00376 q^{19} +(-6.59371 - 3.70442i) q^{20} +(2.97419 + 5.08236i) q^{22} +(4.42742 - 1.84336i) q^{23} -9.29995 q^{25} +(-4.11371 - 7.02960i) q^{26} +(-1.00149 + 1.78261i) q^{28} -0.341603 q^{29} +5.39782i q^{31} +(-2.68354 + 4.97982i) q^{32} +(3.42593 - 2.00485i) q^{34} +3.86599i q^{35} +10.6917i q^{37} +(2.85981 + 4.88690i) q^{38} +(0.188223 + 10.6941i) q^{40} -8.31977 q^{41} -8.92015 q^{43} +(4.07900 - 7.26045i) q^{44} +(-5.41237 - 4.08732i) q^{46} +2.69990i q^{47} -5.95483 q^{49} +(6.64276 + 11.3513i) q^{50} +(-5.64182 + 10.0422i) q^{52} +0.814576i q^{53} -15.7459i q^{55} +(2.89115 - 0.0508860i) q^{56} +(0.244000 + 0.416952i) q^{58} -2.67041i q^{59} +7.77081i q^{61} +(6.58844 - 3.85555i) q^{62} +(7.99505 - 0.281522i) q^{64} +21.7787i q^{65} +14.8080 q^{67} +(-4.89414 - 2.74958i) q^{68} +(4.71873 - 2.76140i) q^{70} -2.36679i q^{71} +5.19128 q^{73} +(13.0501 - 7.63689i) q^{74} +(3.92213 - 6.98122i) q^{76} -4.25691 q^{77} -6.91022 q^{79} +(12.9185 - 7.86833i) q^{80} +(5.94264 + 10.1549i) q^{82} +1.12198 q^{83} -10.6140 q^{85} +(6.37147 + 10.8877i) q^{86} +(-11.7755 + 0.207255i) q^{88} -9.76786i q^{89} +5.88788 q^{91} +(-1.12294 + 9.52570i) q^{92} +(3.29543 - 1.92848i) q^{94} -15.1403i q^{95} -10.8995i q^{97} +(4.25341 + 7.26832i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} - 4 q^{8} + 8 q^{16} - 24 q^{25} - 40 q^{26} + 32 q^{29} + 36 q^{32} - 16 q^{41} + 40 q^{49} + 12 q^{50} - 40 q^{52} + 24 q^{58} + 40 q^{62} + 48 q^{64} + 72 q^{70} - 16 q^{77} - 40 q^{82}+ \cdots + 52 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 - 4 * q^8 + 8 * q^16 - 24 * q^25 - 40 * q^26 + 32 * q^29 + 36 * q^32 - 16 * q^41 + 40 * q^49 + 12 * q^50 - 40 * q^52 + 24 * q^58 + 40 * q^62 + 48 * q^64 + 72 * q^70 - 16 * q^77 - 40 * q^82 - 64 * q^85 - 44 * q^92 + 72 * q^94 + 52 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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