LMFDB - Embedded newform 936.2.j.a.755.33

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(755,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.755"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.j (of order $2$, degree $1$, 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:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			755.33
Character	$\chi$	$=$	936.755
Dual form			936.2.j.a.755.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.634171 - 1.26405i) q^{2} +(-1.19565 - 1.60325i) q^{4} -0.743520 q^{5} +1.72000i q^{7} +(-2.78484 + 0.494635i) q^{8} +(-0.471519 + 0.939848i) q^{10} +4.66933i q^{11} -1.00000i q^{13} +(2.17417 + 1.09077i) q^{14} +(-1.14082 + 3.83387i) q^{16} +6.58087i q^{17} -3.02593 q^{19} +(0.888993 + 1.19205i) q^{20} +(5.90228 + 2.96115i) q^{22} -7.02856 q^{23} -4.44718 q^{25} +(-1.26405 - 0.634171i) q^{26} +(2.75759 - 2.05653i) q^{28} +10.3540 q^{29} -0.619913i q^{31} +(4.12273 + 3.87338i) q^{32} +(8.31856 + 4.17339i) q^{34} -1.27886i q^{35} -0.689961i q^{37} +(-1.91896 + 3.82493i) q^{38} +(2.07059 - 0.367771i) q^{40} +5.53068i q^{41} +8.98383 q^{43} +(7.48610 - 5.58291i) q^{44} +(-4.45731 + 8.88447i) q^{46} +0.183800 q^{47} +4.04160 q^{49} +(-2.82027 + 5.62146i) q^{50} +(-1.60325 + 1.19565i) q^{52} -10.7059 q^{53} -3.47174i q^{55} +(-0.850773 - 4.78993i) q^{56} +(6.56622 - 13.0880i) q^{58} +13.2860i q^{59} -13.1575i q^{61} +(-0.783602 - 0.393131i) q^{62} +(7.51067 - 2.75496i) q^{64} +0.743520i q^{65} +0.268454 q^{67} +(10.5508 - 7.86844i) q^{68} +(-1.61654 - 0.811013i) q^{70} -10.4124 q^{71} +2.74597 q^{73} +(-0.872146 - 0.437553i) q^{74} +(3.61797 + 4.85132i) q^{76} -8.03125 q^{77} +11.0954i q^{79} +(0.848223 - 2.85056i) q^{80} +(6.99107 + 3.50740i) q^{82} +6.15784i q^{83} -4.89301i q^{85} +(5.69729 - 11.3560i) q^{86} +(-2.30961 - 13.0033i) q^{88} -13.1131i q^{89} +1.72000 q^{91} +(8.40373 + 11.2685i) q^{92} +(0.116561 - 0.232333i) q^{94} +2.24984 q^{95} -17.2096 q^{97} +(2.56306 - 5.10879i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{4} + 16 q^{10} + 8 q^{16} + 32 q^{19} + 48 q^{25} - 24 q^{28} + 32 q^{34} - 32 q^{40} - 32 q^{43} + 24 q^{46} - 48 q^{49} + 8 q^{52} - 40 q^{58} + 40 q^{64} + 32 q^{67} - 40 q^{70} + 40 q^{76}+ \cdots - 32 q^{97}+O(q^{100}) $ 48 * q - 8 * q^4 + 16 * q^10 + 8 * q^16 + 32 * q^19 + 48 * q^25 - 24 * q^28 + 32 * q^34 - 32 * q^40 - 32 * q^43 + 24 * q^46 - 48 * q^49 + 8 * q^52 - 40 * q^58 + 40 * q^64 + 32 * q^67 - 40 * q^70 + 40 * q^76 + 16 * q^82 + 48 * q^88 + 32 * q^94 - 32 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	0.634171	−	1.26405i	0.448427	−	0.893820i
$2$	0.634171	−	1.26405i	0.448427	−	0.893820i
$3$		0			0
$3$		0			0
$4$	−1.19565	−	1.60325i	−0.597827	−	0.801625i
$5$	−0.743520			−0.332512			−0.166256	−	0.986083i	$-0.553168\pi$
$5$	−0.743520			−0.332512			−0.166256	+	0.986083i	$0.553168\pi$
$6$		0			0
$7$			1.72000i			0.650099i	0.945697	+	0.325050i	$0.105381\pi$
$7$			1.72000i			0.650099i	−0.945697	+	0.325050i	$0.894619\pi$
$8$	−2.78484	+	0.494635i	−0.984590	+	0.174880i
$9$		0			0
$10$	−0.471519	+	0.939848i	−0.149107	+	0.297206i
$11$			4.66933i			1.40786i	0.710271	+	0.703928i	$0.248572\pi$
$11$			4.66933i			1.40786i	−0.710271	+	0.703928i	$0.751428\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	2.17417	+	1.09077i	0.581072	+	0.291522i
$15$		0			0
$16$	−1.14082	+	3.83387i	−0.285205	+	0.958467i
$17$			6.58087i			1.59609i	0.602595	+	0.798047i	$0.294134\pi$
$17$			6.58087i			1.59609i	−0.602595	+	0.798047i	$0.705866\pi$
$18$		0			0
$19$	−3.02593			−0.694196			−0.347098	−	0.937829i	$-0.612833\pi$
$19$	−3.02593			−0.694196			−0.347098	+	0.937829i	$0.612833\pi$
$20$	0.888993	+	1.19205i	0.198785	+	0.266550i
$21$		0			0
$22$	5.90228	+	2.96115i	1.25837	+	0.631320i
$23$	−7.02856			−1.46556			−0.732778	−	0.680468i	$-0.761777\pi$
$23$	−7.02856			−1.46556			−0.732778	+	0.680468i	$0.761777\pi$
$24$		0			0
$25$	−4.44718			−0.889436
$26$	−1.26405	−	0.634171i	−0.247901	−	0.124371i
$27$		0			0
$28$	2.75759	−	2.05653i	0.521136	−	0.388647i
$29$	10.3540			1.92269			0.961346	−	0.275342i	$-0.0887911\pi$
$29$	10.3540			1.92269			0.961346	+	0.275342i	$0.0887911\pi$
$30$		0			0
$31$		−	0.619913i		−	0.111340i	−0.998449	−	0.0556698i	$-0.982271\pi$
$31$		−	0.619913i		−	0.111340i	0.998449	−	0.0556698i	$-0.0177294\pi$
$32$	4.12273	+	3.87338i	0.728803	+	0.684724i
$33$		0			0
$34$	8.31856	+	4.17339i	1.42662	+	0.715731i
$35$		−	1.27886i		−	0.216166i
$36$		0			0
$37$		−	0.689961i		−	0.113429i	−0.998390	−	0.0567144i	$-0.981938\pi$
$37$		−	0.689961i		−	0.113429i	0.998390	−	0.0567144i	$-0.0180625\pi$
$38$	−1.91896	+	3.82493i	−0.311296	+	0.620486i
$39$		0			0
$40$	2.07059	−	0.367771i	0.327388	−	0.0581497i
$41$			5.53068i			0.863747i	0.901934	+	0.431874i	$0.142147\pi$
$41$			5.53068i			0.863747i	−0.901934	+	0.431874i	$0.857853\pi$
$42$		0			0
$43$	8.98383			1.37002			0.685011	−	0.728533i	$-0.259797\pi$
$43$	8.98383			1.37002			0.685011	+	0.728533i	$0.259797\pi$
$44$	7.48610	−	5.58291i	1.12857	−	0.841655i
$45$		0			0
$46$	−4.45731	+	8.88447i	−0.657194	+	1.30994i
$47$	0.183800			0.0268100			0.0134050	−	0.999910i	$-0.495733\pi$
$47$	0.183800			0.0268100			0.0134050	+	0.999910i	$0.495733\pi$
$48$		0			0
$49$	4.04160			0.577371
$50$	−2.82027	+	5.62146i	−0.398847	+	0.794995i
$51$		0			0
$52$	−1.60325	+	1.19565i	−0.222331	+	0.165807i
$53$	−10.7059			−1.47057			−0.735287	−	0.677755i	$-0.762953\pi$
$53$	−10.7059			−1.47057			−0.735287	+	0.677755i	$0.762953\pi$
$54$		0			0
$55$		−	3.47174i		−	0.468130i
$56$	−0.850773	−	4.78993i	−0.113689	−	0.640081i
$57$		0			0
$58$	6.56622	−	13.0880i	0.862186	−	1.71854i
$59$			13.2860i			1.72969i	0.502036	+	0.864847i	$0.332584\pi$
$59$			13.2860i			1.72969i	−0.502036	+	0.864847i	$0.667416\pi$
$60$		0			0
$61$		−	13.1575i		−	1.68465i	−0.538970	−	0.842325i	$-0.681186\pi$
$61$		−	13.1575i		−	1.68465i	0.538970	−	0.842325i	$-0.318814\pi$
$62$	−0.783602	−	0.393131i	−0.0995176	−	0.0499277i
$63$		0			0
$64$	7.51067	−	2.75496i	0.938834	−	0.344370i
$65$			0.743520i			0.0922223i
$66$		0			0
$67$	0.268454			0.0327969			0.0163984	−	0.999866i	$-0.494780\pi$
$67$	0.268454			0.0327969			0.0163984	+	0.999866i	$0.494780\pi$
$68$	10.5508	−	7.86844i	1.27947	−	0.954189i
$69$		0			0
$70$	−1.61654	−	0.811013i	−0.193213	−	0.0969346i
$71$	−10.4124			−1.23572			−0.617861	−	0.786287i	$-0.712001\pi$
$71$	−10.4124			−1.23572			−0.617861	+	0.786287i	$0.712001\pi$
$72$		0			0
$73$	2.74597			0.321391			0.160696	−	0.987004i	$-0.448626\pi$
$73$	2.74597			0.321391			0.160696	+	0.987004i	$0.448626\pi$
$74$	−0.872146	−	0.437553i	−0.101385	−	0.0508645i
$75$		0			0
$76$	3.61797	+	4.85132i	0.415009	+	0.556485i
$77$	−8.03125			−0.915246
$78$		0			0
$79$			11.0954i			1.24833i	0.781291	+	0.624167i	$0.214561\pi$
$79$			11.0954i			1.24833i	−0.781291	+	0.624167i	$0.785439\pi$
$80$	0.848223	−	2.85056i	0.0948342	−	0.318702i
$81$		0			0
$82$	6.99107	+	3.50740i	0.772034	+	0.387327i
$83$			6.15784i			0.675911i	0.941162	+	0.337955i	$0.109735\pi$
$83$			6.15784i			0.675911i	−0.941162	+	0.337955i	$0.890265\pi$
$84$		0			0
$85$		−	4.89301i		−	0.530721i
$86$	5.69729	−	11.3560i	0.614354	−	1.22455i
$87$		0			0
$88$	−2.30961	−	13.0033i	−0.246206	−	1.38616i
$89$		−	13.1131i		−	1.38998i	−0.719018	−	0.694991i	$-0.755408\pi$
$89$		−	13.1131i		−	1.38998i	0.719018	−	0.694991i	$-0.244592\pi$
$90$		0			0
$91$	1.72000			0.180305
$92$	8.40373	+	11.2685i	0.876149	+	1.17483i
$93$		0			0
$94$	0.116561	−	0.232333i	0.0120223	−	0.0239633i
$95$	2.24984			0.230829
$96$		0			0
$97$	−17.2096			−1.74737			−0.873685	−	0.486491i	$-0.838277\pi$
$97$	−17.2096			−1.74737			−0.873685	+	0.486491i	$0.838277\pi$
$98$	2.56306	−	5.10879i	0.258908	−	0.516066i
$99$		0			0
$100$	5.31729	+	7.12994i	0.531729	+	0.712994i
$101$	−0.508663			−0.0506139			−0.0253069	−	0.999680i	$-0.508056\pi$
$101$	−0.508663			−0.0506139			−0.0253069	+	0.999680i	$0.508056\pi$
$102$		0			0
$103$			13.6065i			1.34069i	0.742051	+	0.670344i	$0.233853\pi$
$103$			13.6065i			1.34069i	−0.742051	+	0.670344i	$0.766147\pi$
$104$	0.494635	+	2.78484i	0.0485030	+	0.273076i
$105$		0			0
$106$	−6.78940	+	13.5329i	−0.659445	+	1.31443i
$107$		−	9.51632i		−	0.919978i	−0.887925	−	0.459989i	$-0.847853\pi$
$107$		−	9.51632i		−	0.919978i	0.887925	−	0.459989i	$-0.152147\pi$
$108$		0			0
$109$		−	5.42029i		−	0.519169i	−0.965720	−	0.259585i	$-0.916414\pi$
$109$		−	5.42029i		−	0.519169i	0.965720	−	0.259585i	$-0.0835857\pi$
$110$	−4.38846	−	2.20168i	−0.418423	−	0.209922i
$111$		0			0
$112$	−6.59425	−	1.96221i	−0.623098	−	0.185412i
$113$			13.4980i			1.26979i	0.772599	+	0.634894i	$0.218956\pi$
$113$			13.4980i			1.26979i	−0.772599	+	0.634894i	$0.781044\pi$
$114$		0			0
$115$	5.22588			0.487316
$116$	−12.3798	−	16.6001i	−1.14944	−	1.54128i
$117$		0			0
$118$	16.7942	+	8.42561i	1.54603	+	0.775640i
$119$	−11.3191			−1.03762
$120$		0			0
$121$	−10.8026			−0.982059
$122$	−16.6318	−	8.34413i	−1.50577	−	0.755442i
$123$		0			0
$124$	−0.993876	+	0.741202i	−0.0892527	+	0.0665619i
$125$	7.02417			0.628261
$126$		0			0
$127$		−	9.79334i		−	0.869019i	−0.900667	−	0.434509i	$-0.856922\pi$
$127$		−	9.79334i		−	0.869019i	0.900667	−	0.434509i	$-0.143078\pi$
$128$	1.28064	−	11.2410i	0.113193	−	0.993573i
$129$		0			0
$130$	0.939848	+	0.471519i	0.0824301	+	0.0413549i
$131$			2.14770i			0.187645i	0.995589	+	0.0938225i	$0.0299086\pi$
$131$			2.14770i			0.187645i	−0.995589	+	0.0938225i	$0.970091\pi$
$132$		0			0
$133$		−	5.20460i		−	0.451296i
$134$	0.170246	−	0.339340i	0.0147070	−	0.0293145i
$135$		0			0
$136$	−3.25513	−	18.3267i	−0.279125	−	1.57150i
$137$		−	9.47000i		−	0.809077i	−0.914521	−	0.404538i	$-0.867432\pi$
$137$		−	9.47000i		−	0.809077i	0.914521	−	0.404538i	$-0.132568\pi$
$138$		0			0
$139$	2.93590			0.249020			0.124510	−	0.992218i	$-0.460264\pi$
$139$	2.93590			0.249020			0.124510	+	0.992218i	$0.460264\pi$
$140$	−2.05032	+	1.52907i	−0.173284	+	0.129230i
$141$		0			0
$142$	−6.60323	+	13.1618i	−0.554130	+	1.10451i
$143$	4.66933			0.390469
$144$		0			0
$145$	−7.69842			−0.639319
$146$	1.74141	−	3.47105i	0.144120	−	0.287266i
$147$		0			0
$148$	−1.10618	+	0.824955i	−0.0909274	+	0.0678109i
$149$	6.81718			0.558486			0.279243	−	0.960221i	$-0.409917\pi$
$149$	6.81718			0.558486			0.279243	+	0.960221i	$0.409917\pi$
$150$		0			0
$151$			18.6158i			1.51493i	0.652875	+	0.757466i	$0.273563\pi$
$151$			18.6158i			1.51493i	−0.652875	+	0.757466i	$0.726437\pi$
$152$	8.42673	−	1.49673i	0.683498	−	0.121401i
$153$		0			0
$154$	−5.09319	+	10.1519i	−0.410421	+	0.818065i
$155$			0.460918i			0.0370218i
$156$		0			0
$157$		−	9.01440i		−	0.719427i	−0.933063	−	0.359714i	$-0.882874\pi$
$157$		−	9.01440i		−	0.719427i	0.933063	−	0.359714i	$-0.117126\pi$
$158$	14.0252	+	7.03640i	1.11579	+	0.559786i
$159$		0			0
$160$	−3.06533	−	2.87994i	−0.242336	−	0.227679i
$161$		−	12.0891i		−	0.952757i
$162$		0			0
$163$	−8.20829			−0.642923			−0.321462	−	0.946923i	$-0.604174\pi$
$163$	−8.20829			−0.642923			−0.321462	+	0.946923i	$0.604174\pi$
$164$	8.86706	−	6.61278i	0.692401	−	0.516372i
$165$		0			0
$166$	7.78383	+	3.90512i	0.604143	+	0.303096i
$167$	−6.78711			−0.525202			−0.262601	−	0.964904i	$-0.584580\pi$
$167$	−6.78711			−0.525202			−0.262601	+	0.964904i	$0.584580\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	−6.18501	−	3.10300i	−0.474369	−	0.237989i
$171$		0			0
$172$	−10.7416	−	14.4033i	−0.819037	−	1.09824i
$173$	6.74312			0.512670			0.256335	−	0.966588i	$-0.417485\pi$
$173$	6.74312			0.512670			0.256335	+	0.966588i	$0.417485\pi$
$174$		0			0
$175$		−	7.64915i		−	0.578221i
$176$	−17.9016	−	5.32687i	−1.34938	−	0.401528i
$177$		0			0
$178$	−16.5756	−	8.31592i	−1.24239	−	0.623305i
$179$			7.33246i			0.548054i	0.961722	+	0.274027i	$0.0883558\pi$
$179$			7.33246i			0.548054i	−0.961722	+	0.274027i	$0.911644\pi$
$180$		0			0
$181$			1.57125i			0.116790i	0.998294	+	0.0583949i	$0.0185982\pi$
$181$			1.57125i			0.116790i	−0.998294	+	0.0583949i	$0.981402\pi$
$182$	1.09077	−	2.17417i	0.0808536	−	0.161160i
$183$		0			0
$184$	19.5734	−	3.47657i	1.44297	−	0.256296i
$185$			0.513000i			0.0377165i
$186$		0			0
$187$	−30.7282			−2.24707
$188$	−0.219761	−	0.294677i	−0.0160277	−	0.0214916i
$189$		0			0
$190$	1.42678	−	2.84391i	0.103510	−	0.206319i
$191$	−20.3374			−1.47156			−0.735781	−	0.677220i	$-0.763185\pi$
$191$	−20.3374			−1.47156			−0.735781	+	0.677220i	$0.763185\pi$
$192$		0			0
$193$	−2.56171			−0.184396			−0.0921980	−	0.995741i	$-0.529389\pi$
$193$	−2.56171			−0.184396			−0.0921980	+	0.995741i	$0.529389\pi$
$194$	−10.9138	+	21.7538i	−0.783568	+	1.56183i
$195$		0			0
$196$	−4.83235	−	6.47969i	−0.345168	−	0.462835i
$197$	21.0154			1.49728			0.748641	−	0.662975i	$-0.230707\pi$
$197$	21.0154			1.49728			0.748641	+	0.662975i	$0.230707\pi$
$198$		0			0
$199$		−	20.1058i		−	1.42527i	−0.701537	−	0.712633i	$-0.747503\pi$
$199$		−	20.1058i		−	1.42527i	0.701537	−	0.712633i	$-0.252497\pi$
$200$	12.3847	−	2.19973i	0.875729	−	0.155544i
$201$		0			0
$202$	−0.322579	+	0.642976i	−0.0226966	+	0.0452397i
$203$			17.8089i			1.24994i
$204$		0			0
$205$		−	4.11217i		−	0.287207i
$206$	17.1993	+	8.62884i	1.19833	+	0.601200i
$207$		0			0
$208$	3.83387	+	1.14082i	0.265831	+	0.0791017i
$209$		−	14.1291i		−	0.977328i
$210$		0			0
$211$	14.5749			1.00337			0.501687	−	0.865049i	$-0.332713\pi$
$211$	14.5749			1.00337			0.501687	+	0.865049i	$0.332713\pi$
$212$	12.8006	+	17.1643i	0.879150	+	1.17885i
$213$		0			0
$214$	−12.0291	−	6.03498i	−0.822294	−	0.412542i
$215$	−6.67966			−0.455549
$216$		0			0
$217$	1.06625			0.0723818
$218$	−6.85152	−	3.43739i	−0.464044	−	0.232809i
$219$		0			0
$220$	−5.56607	+	4.15100i	−0.375264	+	0.279861i
$221$	6.58087			0.442677
$222$		0			0
$223$			14.0882i			0.943418i	0.881754	+	0.471709i	$0.156363\pi$
$223$			14.0882i			0.943418i	−0.881754	+	0.471709i	$0.843637\pi$
$224$	−6.66222	+	7.09110i	−0.445138	+	0.473794i
$225$		0			0
$226$	17.0622	+	8.56006i	1.13496	+	0.569407i
$227$			10.0126i			0.664558i	0.943181	+	0.332279i	$0.107818\pi$
$227$			10.0126i			0.664558i	−0.943181	+	0.332279i	$0.892182\pi$
$228$		0			0
$229$			11.3711i			0.751426i	0.926736	+	0.375713i	$0.122602\pi$
$229$			11.3711i			0.751426i	−0.926736	+	0.375713i	$0.877398\pi$
$230$	3.31410	−	6.60578i	0.218525	−	0.435572i
$231$		0			0
$232$	−28.8343	+	5.12146i	−1.89306	+	0.336240i
$233$			5.49317i			0.359869i	0.983679	+	0.179935i	$0.0575887\pi$
$233$			5.49317i			0.359869i	−0.983679	+	0.179935i	$0.942411\pi$
$234$		0			0
$235$	−0.136659			−0.00891465
$236$	21.3008	−	15.8855i	1.38657	−	1.03406i
$237$		0			0
$238$	−7.17824	+	14.3079i	−0.465296	+	0.927445i
$239$	18.0075			1.16481			0.582404	−	0.812899i	$-0.302112\pi$
$239$	18.0075			1.16481			0.582404	+	0.812899i	$0.302112\pi$
$240$		0			0
$241$	7.74211			0.498713			0.249357	−	0.968412i	$-0.419781\pi$
$241$	7.74211			0.498713			0.249357	+	0.968412i	$0.419781\pi$
$242$	−6.85073	+	13.6551i	−0.440381	+	0.877784i
$243$		0			0
$244$	−21.0948	+	15.7319i	−1.35046	+	1.00713i
$245$	−3.00501			−0.191983
$246$		0			0
$247$			3.02593i			0.192535i
$248$	0.306631	+	1.72636i	0.0194711	+	0.109624i
$249$		0			0
$250$	4.45452	−	8.87891i	0.281729	−	0.561552i
$251$		−	19.3627i		−	1.22216i	−0.791567	−	0.611082i	$-0.790734\pi$
$251$		−	19.3627i		−	1.22216i	0.791567	−	0.611082i	$-0.209266\pi$
$252$		0			0
$253$		−	32.8187i		−	2.06329i
$254$	−12.3793	−	6.21065i	−0.776746	−	0.389691i
$255$		0			0
$256$	−13.3971	−	8.74750i	−0.837316	−	0.546719i
$257$		−	4.17899i		−	0.260678i	−0.991469	−	0.130339i	$-0.958393\pi$
$257$		−	4.17899i		−	0.260678i	0.991469	−	0.130339i	$-0.0416066\pi$
$258$		0			0
$259$	1.18673			0.0737400
$260$	1.19205	−	0.888993i	0.0739277	−	0.0551330i
$261$		0			0
$262$	2.71480	+	1.36201i	0.167721	+	0.0841450i
$263$	24.6071			1.51734			0.758670	−	0.651475i	$-0.225850\pi$
$263$	24.6071			1.51734			0.758670	+	0.651475i	$0.225850\pi$
$264$		0			0
$265$	7.96009			0.488984
$266$	−6.57889	−	3.30061i	−0.403377	−	0.202373i
$267$		0			0
$268$	−0.320978	−	0.430399i	−0.0196069	−	0.0262908i
$269$	8.95889			0.546233			0.273116	−	0.961981i	$-0.411946\pi$
$269$	8.95889			0.546233			0.273116	+	0.961981i	$0.411946\pi$
$270$		0			0
$271$			21.8098i			1.32485i	0.749128	+	0.662426i	$0.230473\pi$
$271$			21.8098i			1.32485i	−0.749128	+	0.662426i	$0.769527\pi$
$272$	−25.2302	−	7.50759i	−1.52980	−	0.455214i
$273$		0			0
$274$	−11.9706	−	6.00560i	−0.723169	−	0.362811i
$275$		−	20.7653i		−	1.25220i
$276$		0			0
$277$		−	7.26899i		−	0.436751i	−0.975865	−	0.218376i	$-0.929924\pi$
$277$		−	7.26899i		−	0.436751i	0.975865	−	0.218376i	$-0.0700758\pi$
$278$	1.86186	−	3.71113i	0.111667	−	0.222579i
$279$		0			0
$280$	0.632567	+	3.56141i	0.0378031	+	0.212835i
$281$		−	0.361353i		−	0.0215565i	−0.999942	−	0.0107783i	$-0.996569\pi$
$281$		−	0.361353i		−	0.0215565i	0.999942	−	0.0107783i	$-0.00343089\pi$
$282$		0			0
$283$	11.2756			0.670262			0.335131	−	0.942172i	$-0.391219\pi$
$283$	11.2756			0.670262			0.335131	+	0.942172i	$0.391219\pi$
$284$	12.4496	+	16.6936i	0.738748	+	0.990585i
$285$		0			0
$286$	2.96115	−	5.90228i	0.175097	−	0.349009i
$287$	−9.51278			−0.561521
$288$		0			0
$289$	−26.3078			−1.54752
$290$	−4.88211	+	9.73120i	−0.286688	+	0.571436i
$291$		0			0
$292$	−3.28323	−	4.40247i	−0.192137	−	0.257635i
$293$	−19.6966			−1.15069			−0.575343	−	0.817913i	$-0.695131\pi$
$293$	−19.6966			−1.15069			−0.575343	+	0.817913i	$0.695131\pi$
$294$		0			0
$295$		−	9.87843i		−	0.575144i
$296$	0.341279	+	1.92143i	0.0198364	+	0.111681i
$297$		0			0
$298$	4.32326	−	8.61728i	0.250440	−	0.499185i
$299$			7.02856i			0.406472i
$300$		0			0
$301$			15.4522i			0.890650i
$302$	23.5313	+	11.8056i	1.35408	+	0.679336i
$303$		0			0
$304$	3.45204	−	11.6010i	0.197988	−	0.665363i
$305$			9.78290i			0.560167i
$306$		0			0
$307$	−7.93961			−0.453138			−0.226569	−	0.973995i	$-0.572751\pi$
$307$	−7.93961			−0.453138			−0.226569	+	0.973995i	$0.572751\pi$
$308$	9.60260	+	12.8761i	0.547159	+	0.733684i
$309$		0			0
$310$	0.582624	+	0.292301i	0.0330908	+	0.0166016i
$311$	−23.4955			−1.33231			−0.666153	−	0.745815i	$-0.732060\pi$
$311$	−23.4955			−1.33231			−0.666153	+	0.745815i	$0.732060\pi$
$312$		0			0
$313$	8.59126			0.485607			0.242803	−	0.970076i	$-0.421933\pi$
$313$	8.59126			0.485607			0.242803	+	0.970076i	$0.421933\pi$
$314$	−11.3947	−	5.71667i	−0.643038	−	0.322610i
$315$		0			0
$316$	17.7888	−	13.2663i	1.00070	−	0.746288i
$317$	3.57136			0.200588			0.100294	−	0.994958i	$-0.468022\pi$
$317$	3.57136			0.200588			0.100294	+	0.994958i	$0.468022\pi$
$318$		0			0
$319$			48.3463i			2.70687i
$320$	−5.58434	+	2.04837i	−0.312174	+	0.114507i
$321$		0			0
$322$	−15.2813	−	7.66657i	−0.851593	−	0.427242i
$323$		−	19.9132i		−	1.10800i
$324$		0			0
$325$			4.44718i			0.246685i
$326$	−5.20546	+	10.3757i	−0.288304	+	0.574657i
$327$		0			0
$328$	−2.73567	−	15.4021i	−0.151052	−	0.850437i
$329$			0.316136i			0.0174292i
$330$		0			0
$331$	22.6506			1.24499			0.622494	−	0.782625i	$-0.286120\pi$
$331$	22.6506			1.24499			0.622494	+	0.782625i	$0.286120\pi$
$332$	9.87256	−	7.36265i	0.541827	−	0.404078i
$333$		0			0
$334$	−4.30419	+	8.57926i	−0.235515	+	0.469436i
$335$	−0.199601			−0.0109054
$336$		0			0
$337$	−13.1565			−0.716679			−0.358340	−	0.933591i	$-0.616657\pi$
$337$	−13.1565			−0.716679			−0.358340	+	0.933591i	$0.616657\pi$
$338$	−0.634171	+	1.26405i	−0.0344943	+	0.0687554i
$339$		0			0
$340$	−7.84471	+	5.85035i	−0.425439	+	0.317280i
$341$	2.89458			0.156750
$342$		0			0
$343$			18.9916i			1.02545i
$344$	−25.0185	+	4.44372i	−1.34891	+	0.239589i
$345$		0			0
$346$	4.27629	−	8.52366i	0.229895	−	0.458235i
$347$		−	7.91878i		−	0.425102i	−0.977150	−	0.212551i	$-0.931823\pi$
$347$		−	7.91878i		−	0.425102i	0.977150	−	0.212551i	$-0.0681772\pi$
$348$		0			0
$349$			7.78876i			0.416923i	0.978031	+	0.208461i	$0.0668456\pi$
$349$			7.78876i			0.416923i	−0.978031	+	0.208461i	$0.933154\pi$
$350$	−9.66892	−	4.85087i	−0.516826	−	0.259290i
$351$		0			0
$352$	−18.0861	+	19.2504i	−0.963993	+	1.02605i
$353$			9.64415i			0.513306i	0.966504	+	0.256653i	$0.0826198\pi$
$353$			9.64415i			0.513306i	−0.966504	+	0.256653i	$0.917380\pi$
$354$		0			0
$355$	7.74181			0.410893
$356$	−21.0235	+	15.6787i	−1.11424	+	0.830969i
$357$		0			0
$358$	9.26861	+	4.65003i	0.489861	+	0.245762i
$359$	13.0246			0.687410			0.343705	−	0.939078i	$-0.388318\pi$
$359$	13.0246			0.687410			0.343705	+	0.939078i	$0.388318\pi$
$360$		0			0
$361$	−9.84375			−0.518092
$362$	1.98614	+	0.996438i	0.104389	+	0.0523716i
$363$		0			0
$364$	−2.05653	−	2.75759i	−0.107791	−	0.144537i
$365$	−2.04168			−0.106867
$366$		0			0
$367$			9.32427i			0.486723i	0.969936	+	0.243362i	$0.0782502\pi$
$367$			9.32427i			0.486723i	−0.969936	+	0.243362i	$0.921750\pi$
$368$	8.01832	−	26.9466i	0.417984	−	1.40469i
$369$		0			0
$370$	0.648458	+	0.325329i	0.0337117	+	0.0169131i
$371$		−	18.4142i		−	0.956020i
$372$		0			0
$373$		−	33.2225i		−	1.72020i	−0.510129	−	0.860098i	$-0.670402\pi$
$373$		−	33.2225i		−	1.72020i	0.510129	−	0.860098i	$-0.329598\pi$
$374$	−19.4870	+	38.8421i	−1.00765	+	2.00848i
$375$		0			0
$376$	−0.511854	+	0.0909139i	−0.0263968	+	0.00468853i
$377$		−	10.3540i		−	0.533259i
$378$		0			0
$379$	4.21971			0.216752			0.108376	−	0.994110i	$-0.465435\pi$
$379$	4.21971			0.216752			0.108376	+	0.994110i	$0.465435\pi$
$380$	−2.69003	−	3.60706i	−0.137996	−	0.185038i
$381$		0			0
$382$	−12.8974	+	25.7075i	−0.659887	+	1.31531i
$383$	31.8136			1.62560			0.812800	−	0.582542i	$-0.197942\pi$
$383$	31.8136			1.62560			0.812800	+	0.582542i	$0.197942\pi$
$384$		0			0
$385$	5.97140			0.304331
$386$	−1.62456	+	3.23814i	−0.0826881	+	0.164817i
$387$		0			0
$388$	20.5767	+	27.5913i	1.04463	+	1.40074i
$389$	18.6833			0.947282			0.473641	−	0.880718i	$-0.342939\pi$
$389$	18.6833			0.947282			0.473641	+	0.880718i	$0.342939\pi$
$390$		0			0
$391$		−	46.2540i		−	2.33917i
$392$	−11.2552	+	1.99912i	−0.568474	+	0.100971i
$393$		0			0
$394$	13.3273	−	26.5645i	0.671421	−	1.33830i
$395$		−	8.24968i		−	0.415086i
$396$		0			0
$397$			11.2388i			0.564059i	0.959406	+	0.282029i	$0.0910076\pi$
$397$			11.2388i			0.564059i	−0.959406	+	0.282029i	$0.908992\pi$
$398$	−25.4148	−	12.7505i	−1.27393	−	0.639127i
$399$		0			0
$400$	5.07343	−	17.0499i	0.253672	−	0.852494i
$401$		−	29.1439i		−	1.45537i	−0.685909	−	0.727687i	$-0.740595\pi$
$401$		−	29.1439i		−	1.45537i	0.685909	−	0.727687i	$-0.259405\pi$
$402$		0			0
$403$	−0.619913			−0.0308801
$404$	0.608185	+	0.815514i	0.0302583	+	0.0405733i
$405$		0			0
$406$	22.5114	+	11.2939i	1.11722	+	0.560507i
$407$	3.22165			0.159691
$408$		0			0
$409$	32.8717			1.62540			0.812700	−	0.582682i	$-0.197997\pi$
$409$	32.8717			1.62540			0.812700	+	0.582682i	$0.197997\pi$
$410$	−5.19800	−	2.60782i	−0.256711	−	0.128791i
$411$		0			0
$412$	21.8146	−	16.2687i	1.07473	−	0.801500i
$413$	−22.8520			−1.12447
$414$		0			0
$415$		−	4.57848i		−	0.224749i
$416$	3.87338	−	4.12273i	0.189908	−	0.202134i
$417$		0			0
$418$	−17.8599	−	8.96024i	−0.873555	−	0.438260i
$419$			9.13194i			0.446125i	0.974804	+	0.223062i	$0.0716053\pi$
$419$			9.13194i			0.446125i	−0.974804	+	0.223062i	$0.928395\pi$
$420$		0			0
$421$			31.0989i			1.51567i	0.652449	+	0.757833i	$0.273742\pi$
$421$			31.0989i			1.51567i	−0.652449	+	0.757833i	$0.726258\pi$
$422$	9.24295	−	18.4234i	0.449940	−	0.896836i
$423$		0			0
$424$	29.8143	−	5.29554i	1.44791	−	0.257174i
$425$		−	29.2663i		−	1.41962i
$426$		0			0
$427$	22.6310			1.09519
$428$	−15.2570	+	11.3782i	−0.737477	+	0.549988i
$429$		0			0
$430$	−4.23605	+	8.44344i	−0.204280	+	0.407179i
$431$	19.3891			0.933941			0.466970	−	0.884273i	$-0.345345\pi$
$431$	19.3891			0.933941			0.466970	+	0.884273i	$0.345345\pi$
$432$		0			0
$433$	34.0276			1.63526			0.817632	−	0.575742i	$-0.195287\pi$
$433$	34.0276			1.63526			0.817632	+	0.575742i	$0.195287\pi$
$434$	0.676185	−	1.34780i	0.0324579	−	0.0646963i
$435$		0			0
$436$	−8.69008	+	6.48079i	−0.416179	+	0.310374i
$437$	21.2679			1.01738
$438$		0			0
$439$		−	16.8226i		−	0.802899i	−0.915881	−	0.401449i	$-0.868507\pi$
$439$		−	16.8226i		−	0.802899i	0.915881	−	0.401449i	$-0.131493\pi$
$440$	1.71725	+	9.66825i	0.0818664	+	0.460916i
$441$		0			0
$442$	4.17339	−	8.31856i	0.198508	−	0.395673i
$443$		−	8.46566i		−	0.402216i	−0.979569	−	0.201108i	$-0.935546\pi$
$443$		−	8.46566i		−	0.402216i	0.979569	−	0.201108i	$-0.0644542\pi$
$444$		0			0
$445$			9.74983i			0.462186i
$446$	17.8083	+	8.93435i	0.843245	+	0.423054i
$447$		0			0
$448$	4.73853	+	12.9184i	0.223875	+	0.610335i
$449$			11.6157i			0.548177i	0.961705	+	0.274088i	$0.0883761\pi$
$449$			11.6157i			0.548177i	−0.961705	+	0.274088i	$0.911624\pi$
$450$		0			0
$451$	−25.8246			−1.21603
$452$	21.6407	−	16.1390i	1.01789	−	0.759114i
$453$		0			0
$454$	12.6564	+	6.34969i	0.593995	+	0.298006i
$455$	−1.27886			−0.0599537
$456$		0			0
$457$	25.4077			1.18852			0.594262	−	0.804272i	$-0.297444\pi$
$457$	25.4077			1.18852			0.594262	+	0.804272i	$0.297444\pi$
$458$	14.3737	+	7.21124i	0.671639	+	0.336959i
$459$		0			0
$460$	−6.24834	−	8.37839i	−0.291331	−	0.390644i
$461$	10.4445			0.486449			0.243224	−	0.969970i	$-0.421795\pi$
$461$	10.4445			0.486449			0.243224	+	0.969970i	$0.421795\pi$
$462$		0			0
$463$		−	4.65934i		−	0.216538i	−0.994122	−	0.108269i	$-0.965469\pi$
$463$		−	4.65934i		−	0.216538i	0.994122	−	0.108269i	$-0.0345308\pi$
$464$	−11.8121	+	39.6959i	−0.548362	+	1.84284i
$465$		0			0
$466$	6.94365	+	3.48361i	0.321658	+	0.161375i
$467$			23.2887i			1.07767i	0.842410	+	0.538837i	$0.181136\pi$
$467$			23.2887i			1.07767i	−0.842410	+	0.538837i	$0.818864\pi$
$468$		0			0
$469$			0.461741i			0.0213212i
$470$	−0.0866652	+	0.172744i	−0.00399757	+	0.00796809i
$471$		0			0
$472$	−6.57173	−	36.9995i	−0.302489	−	1.70304i
$473$			41.9485i			1.92879i
$474$		0			0
$475$	13.4568			0.617442
$476$	13.5337	+	18.1473i	0.620317	+	0.831782i
$477$		0			0
$478$	11.4198	−	22.7624i	0.522331	−	1.04113i
$479$	−35.1469			−1.60590			−0.802952	−	0.596044i	$-0.796738\pi$
$479$	−35.1469			−1.60590			−0.802952	+	0.596044i	$0.796738\pi$
$480$		0			0
$481$	−0.689961			−0.0314595
$482$	4.90982	−	9.78643i	0.223636	−	0.445760i
$483$		0			0
$484$	12.9162	+	17.3193i	0.587102	+	0.787243i
$485$	12.7957			0.581022
$486$		0			0
$487$		−	3.43122i		−	0.155483i	−0.996974	−	0.0777417i	$-0.975229\pi$
$487$		−	3.43122i		−	0.155483i	0.996974	−	0.0777417i	$-0.0247710\pi$
$488$	6.50818	+	36.6417i	0.294612	+	1.65869i
$489$		0			0
$490$	−1.90569	+	3.79849i	−0.0860903	+	0.171598i
$491$		−	6.49646i		−	0.293181i	−0.989197	−	0.146591i	$-0.953170\pi$
$491$		−	6.49646i		−	0.293181i	0.989197	−	0.146591i	$-0.0468300\pi$
$492$		0			0
$493$			68.1384i			3.06880i
$494$	3.82493	+	1.91896i	0.172092	+	0.0863379i
$495$		0			0
$496$	2.37666	+	0.707209i	0.106715	+	0.0317546i
$497$		−	17.9093i		−	0.803342i
$498$		0			0
$499$	22.7906			1.02025			0.510123	−	0.860101i	$-0.329600\pi$
$499$	22.7906			1.02025			0.510123	+	0.860101i	$0.329600\pi$
$500$	−8.39848	−	11.2615i	−0.375591	−	0.503629i
$501$		0			0
$502$	−24.4755	−	12.2793i	−1.09239	−	0.548051i
$503$	−6.22278			−0.277460			−0.138730	−	0.990330i	$-0.544302\pi$
$503$	−6.22278			−0.277460			−0.138730	+	0.990330i	$0.544302\pi$
$504$		0			0
$505$	0.378201			0.0168297
$506$	−41.4845	−	20.8126i	−1.84421	−	0.925235i
$507$		0			0
$508$	−15.7012	+	11.7095i	−0.696627	+	0.519523i
$509$	−0.0362228			−0.00160555			−0.000802774	−	1.00000i	$-0.500256\pi$
$509$	−0.0362228			−0.00160555			−0.000802774		1.00000i	$0.500256\pi$
$510$		0			0
$511$			4.72307i			0.208936i
$512$	−19.5533	+	11.3872i	−0.864143	+	0.503246i
$513$		0			0
$514$	−5.28246	−	2.65019i	−0.232999	−	0.116895i
$515$		−	10.1167i		−	0.445795i
$516$		0			0
$517$			0.858223i			0.0377446i
$518$	0.752592	−	1.50009i	0.0330670	−	0.0659103i
$519$		0			0
$520$	−0.367771	−	2.07059i	−0.0161278	−	0.0908012i
$521$		−	18.2499i		−	0.799542i	−0.916615	−	0.399771i	$-0.869090\pi$
$521$		−	18.2499i		−	0.799542i	0.916615	−	0.399771i	$-0.130910\pi$
$522$		0			0
$523$	19.9310			0.871521			0.435761	−	0.900063i	$-0.356479\pi$
$523$	19.9310			0.871521			0.435761	+	0.900063i	$0.356479\pi$
$524$	3.44329	−	2.56790i	0.150421	−	0.112179i
$525$		0			0
$526$	15.6051	−	31.1047i	0.680415	−	1.35623i
$527$	4.07957			0.177709
$528$		0			0
$529$	26.4007			1.14786
$530$	5.04806	−	10.0620i	0.219274	−	0.437064i
$531$		0			0
$532$	−8.34428	+	6.22291i	−0.361770	+	0.269797i
$533$	5.53068			0.239560
$534$		0			0
$535$			7.07558i			0.305904i
$536$	−0.747602	+	0.132787i	−0.0322915	+	0.00573552i
$537$		0			0
$538$	5.68146	−	11.3245i	0.244945	−	0.488234i
$539$			18.8716i			0.812855i
$540$		0			0
$541$		−	7.30595i		−	0.314107i	−0.987590	−	0.157054i	$-0.949800\pi$
$541$		−	7.30595i		−	0.314107i	0.987590	−	0.157054i	$-0.0501995\pi$
$542$	27.5687	+	13.8311i	1.18418	+	0.594098i
$543$		0			0
$544$	−25.4902	+	27.1311i	−1.09288	+	1.16324i
$545$			4.03009i			0.172630i
$546$		0			0
$547$	21.5397			0.920970			0.460485	−	0.887667i	$-0.347676\pi$
$547$	21.5397			0.920970			0.460485	+	0.887667i	$0.347676\pi$
$548$	−15.1828	+	11.3228i	−0.648576	+	0.483688i
$549$		0			0
$550$	−26.2485	−	13.1688i	−1.11924	−	0.561519i
$551$	−31.3305			−1.33473
$552$		0			0
$553$	−19.0842			−0.811541
$554$	−9.18838	−	4.60978i	−0.390377	−	0.195851i
$555$		0			0
$556$	−3.51032	−	4.70698i	−0.148871	−	0.199620i
$557$	−31.4672			−1.33331			−0.666653	−	0.745368i	$-0.732274\pi$
$557$	−31.4672			−1.33331			−0.666653	+	0.745368i	$0.732274\pi$
$558$		0			0
$559$		−	8.98383i		−	0.379976i
$560$	4.90296	+	1.45894i	0.207188	+	0.0616516i
$561$		0			0
$562$	−0.456769	−	0.229160i	−0.0192676	−	0.00966652i
$563$			23.3682i			0.984853i	0.870354	+	0.492427i	$0.163890\pi$
$563$			23.3682i			0.984853i	−0.870354	+	0.492427i	$0.836110\pi$
$564$		0			0
$565$		−	10.0361i		−	0.422220i
$566$	7.15063	−	14.2529i	0.300563	−	0.599093i
$567$		0			0
$568$	28.9968	−	5.15033i	1.21668	−	0.216103i
$569$		−	9.05265i		−	0.379507i	−0.981832	−	0.189753i	$-0.939231\pi$
$569$		−	9.05265i		−	0.379507i	0.981832	−	0.189753i	$-0.0607688\pi$
$570$		0			0
$571$	11.1599			0.467025			0.233513	−	0.972354i	$-0.424978\pi$
$571$	11.1599			0.467025			0.233513	+	0.972354i	$0.424978\pi$
$572$	−5.58291	−	7.48610i	−0.233433	−	0.313010i
$573$		0			0
$574$	−6.03273	+	12.0246i	−0.251801	+	0.501899i
$575$	31.2573			1.30352
$576$		0			0
$577$	16.9468			0.705506			0.352753	−	0.935716i	$-0.385246\pi$
$577$	16.9468			0.705506			0.352753	+	0.935716i	$0.385246\pi$
$578$	−16.6836	+	33.2544i	−0.693948	+	1.38320i
$579$		0			0
$580$	9.20465	+	12.3425i	0.382202	+	0.512494i
$581$	−10.5915			−0.439409
$582$		0			0
$583$		−	49.9896i		−	2.07036i
$584$	−7.64709	+	1.35825i	−0.316439	+	0.0562049i
$585$		0			0
$586$	−12.4910	+	24.8975i	−0.515998	+	1.02851i
$587$			1.11604i			0.0460640i	0.999735	+	0.0230320i	$0.00733196\pi$
$587$			1.11604i			0.0460640i	−0.999735	+	0.0230320i	$0.992668\pi$
$588$		0			0
$589$			1.87581i			0.0772915i
$590$	−12.4868	−	6.26461i	−0.514075	−	0.257910i
$591$		0			0
$592$	2.64522	+	0.787121i	0.108718	+	0.0323505i
$593$			26.3257i			1.08107i	0.841323	+	0.540533i	$0.181777\pi$
$593$			26.3257i			1.08107i	−0.841323	+	0.540533i	$0.818223\pi$
$594$		0			0
$595$	8.41598			0.345021
$596$	−8.15100	−	10.9297i	−0.333878	−	0.447696i
$597$		0			0
$598$	8.88447	+	4.45731i	0.363313	+	0.182273i
$599$	6.69893			0.273711			0.136855	−	0.990591i	$-0.456300\pi$
$599$	6.69893			0.273711			0.136855	+	0.990591i	$0.456300\pi$
$600$		0			0
$601$	24.9360			1.01716			0.508580	−	0.861015i	$-0.330170\pi$
$601$	24.9360			1.01716			0.508580	+	0.861015i	$0.330170\pi$
$602$	19.5324	+	9.79934i	0.796081	+	0.399391i
$603$		0			0
$604$	29.8458	−	22.2581i	1.21441	−	0.905668i
$605$	8.03199			0.326547
$606$		0			0
$607$			12.1079i			0.491443i	0.969341	+	0.245721i	$0.0790248\pi$
$607$			12.1079i			0.491443i	−0.969341	+	0.245721i	$0.920975\pi$
$608$	−12.4751	−	11.7206i	−0.505932	−	0.475332i
$609$		0			0
$610$	12.3661	+	6.20403i	0.500688	+	0.251194i
$611$		−	0.183800i		−	0.00743575i
$612$		0			0
$613$		−	35.3445i		−	1.42755i	−0.700375	−	0.713775i	$-0.746984\pi$
$613$		−	35.3445i		−	1.42755i	0.700375	−	0.713775i	$-0.253016\pi$
$614$	−5.03507	+	10.0361i	−0.203199	+	0.405023i
$615$		0			0
$616$	22.3658	−	3.97254i	0.901142	−	0.160058i
$617$			4.27008i			0.171907i	0.996299	+	0.0859534i	$0.0273936\pi$
$617$			4.27008i			0.171907i	−0.996299	+	0.0859534i	$0.972606\pi$
$618$		0			0
$619$	0.994984			0.0399918			0.0199959	−	0.999800i	$-0.493635\pi$
$619$	0.994984			0.0399918			0.0199959	+	0.999800i	$0.493635\pi$
$620$	0.738967	−	0.551099i	0.0296776	−	0.0221327i
$621$		0			0
$622$	−14.9001	+	29.6995i	−0.597441	+	1.19084i
$623$	22.5545			0.903626
$624$		0			0
$625$	17.0133			0.680531
$626$	5.44833	−	10.8598i	0.217759	−	0.434045i
$627$		0			0
$628$	−14.4523	+	10.7781i	−0.576711	+	0.430093i
$629$	4.54054			0.181043
$630$		0			0
$631$			7.71126i			0.306981i	0.988150	+	0.153490i	$0.0490514\pi$
$631$			7.71126i			0.306981i	−0.988150	+	0.153490i	$0.950949\pi$
$632$	−5.48819	−	30.8990i	−0.218308	−	1.22910i
$633$		0			0
$634$	2.26485	−	4.51439i	0.0899489	−	0.179289i
$635$			7.28155i			0.288959i
$636$		0			0
$637$		−	4.04160i		−	0.160134i
$638$	61.1123	+	30.6598i	2.41946	+	1.21383i
$639$		0			0
$640$	−0.952180	+	8.35791i	−0.0376382	+	0.330375i
$641$		−	1.31766i		−	0.0520443i	−0.999661	−	0.0260221i	$-0.991716\pi$
$641$		−	1.31766i		−	0.0520443i	0.999661	−	0.0260221i	$-0.00828404\pi$
$642$		0			0
$643$	−46.5222			−1.83466			−0.917328	−	0.398133i	$-0.869658\pi$
$643$	−46.5222			−1.83466			−0.917328	+	0.398133i	$0.869658\pi$
$644$	−19.3819	+	14.4544i	−0.763754	+	0.569584i
$645$		0			0
$646$	−25.1714	−	12.6284i	−0.990354	−	0.496858i
$647$	−9.96272			−0.391675			−0.195837	−	0.980636i	$-0.562743\pi$
$647$	−9.96272			−0.391675			−0.195837	+	0.980636i	$0.562743\pi$
$648$		0			0
$649$	−62.0368			−2.43516
$650$	5.62146	+	2.82027i	0.220492	+	0.110620i
$651$		0			0
$652$	9.81428	+	13.1599i	0.384357	+	0.515383i
$653$	−28.7123			−1.12360			−0.561800	−	0.827273i	$-0.689891\pi$
$653$	−28.7123			−1.12360			−0.561800	+	0.827273i	$0.689891\pi$
$654$		0			0
$655$		−	1.59685i		−	0.0623943i
$656$	−21.2039	−	6.30951i	−0.827873	−	0.246345i
$657$		0			0
$658$	0.399613	+	0.200484i	0.0155785	+	0.00781569i
$659$		−	40.3362i		−	1.57128i	−0.618686	−	0.785638i	$-0.712335\pi$
$659$		−	40.3362i		−	1.57128i	0.618686	−	0.785638i	$-0.287665\pi$
$660$		0			0
$661$			14.9302i			0.580717i	0.956918	+	0.290358i	$0.0937745\pi$
$661$			14.9302i			0.580717i	−0.956918	+	0.290358i	$0.906225\pi$
$662$	14.3643	−	28.6315i	0.558285	−	1.11279i
$663$		0			0
$664$	−3.04588	−	17.1486i	−0.118203	−	0.665495i
$665$			3.86973i			0.150062i
$666$		0			0
$667$	−72.7738			−2.81781
$668$	8.11504	+	10.8814i	0.313980	+	0.421015i
$669$		0			0
$670$	−0.126581	+	0.252306i	−0.00489026	+	0.00974744i
$671$	61.4369			2.37175
$672$		0			0
$673$	−1.18247			−0.0455809			−0.0227905	−	0.999740i	$-0.507255\pi$
$673$	−1.18247			−0.0455809			−0.0227905	+	0.999740i	$0.507255\pi$
$674$	−8.34346	+	16.6305i	−0.321378	+	0.640582i
$675$		0			0
$676$	1.19565	+	1.60325i	0.0459867	+	0.0616635i
$677$	−14.2359			−0.547129			−0.273564	−	0.961854i	$-0.588203\pi$
$677$	−14.2359			−0.547129			−0.273564	+	0.961854i	$0.588203\pi$
$678$		0			0
$679$		−	29.6005i		−	1.13596i
$680$	2.42025	+	13.6262i	0.0928125	+	0.522543i
$681$		0			0
$682$	1.83566	−	3.65890i	0.0702910	−	0.140106i
$683$		−	45.4893i		−	1.74060i	−0.492521	−	0.870300i	$-0.663925\pi$
$683$		−	45.4893i		−	1.74060i	0.492521	−	0.870300i	$-0.336075\pi$
$684$		0			0
$685$			7.04114i			0.269028i
$686$	24.0063	+	12.0439i	0.916565	+	0.459838i
$687$		0			0
$688$	−10.2489	+	34.4428i	−0.390737	+	1.31312i
$689$			10.7059i			0.407864i
$690$		0			0
$691$	−30.8877			−1.17502			−0.587511	−	0.809216i	$-0.699892\pi$
$691$	−30.8877			−1.17502			−0.587511	+	0.809216i	$0.699892\pi$
$692$	−8.06245	−	10.8109i	−0.306488	−	0.410969i
$693$		0			0
$694$	−10.0097	−	5.02186i	−0.379965	−	0.190627i
$695$	−2.18290			−0.0828022
$696$		0			0
$697$	−36.3967			−1.37862
$698$	9.84540	+	4.93941i	0.372654	+	0.186959i
$699$		0			0
$700$	−12.2635	+	9.14574i	−0.463517	+	0.345677i
$701$	−24.6794			−0.932128			−0.466064	−	0.884751i	$-0.654328\pi$
$701$	−24.6794			−0.932128			−0.466064	+	0.884751i	$0.654328\pi$
$702$		0			0
$703$			2.08777i			0.0787418i
$704$	12.8638	+	35.0698i	0.484823	+	1.32174i
$705$		0			0
$706$	12.1907	+	6.11604i	0.458803	+	0.230180i
$707$		−	0.874901i		−	0.0329040i
$708$		0			0
$709$			41.0911i			1.54321i	0.636103	+	0.771605i	$0.280546\pi$
$709$			41.0911i			1.54321i	−0.636103	+	0.771605i	$0.719454\pi$
$710$	4.90963	−	9.78605i	0.184255	−	0.367264i
$711$		0			0
$712$	6.48618	+	36.5178i	0.243080	+	1.36856i
$713$			4.35710i			0.163175i
$714$		0			0
$715$	−3.47174			−0.129836
$716$	11.7558	−	8.76709i	0.439334	−	0.327642i
$717$		0			0
$718$	8.25980	−	16.4637i	0.308253	−	0.614421i
$719$	48.3260			1.80225			0.901127	−	0.433554i	$-0.142741\pi$
$719$	48.3260			1.80225			0.901127	+	0.433554i	$0.142741\pi$
$720$		0			0
$721$	−23.4032			−0.871580
$722$	−6.24262	+	12.4430i	−0.232326	+	0.463081i
$723$		0			0
$724$	2.51910	−	1.87867i	0.0936216	−	0.0698201i
$725$	−46.0462			−1.71011
$726$		0			0
$727$			26.1871i			0.971225i	0.874174	+	0.485612i	$0.161403\pi$
$727$			26.1871i			0.971225i	−0.874174	+	0.485612i	$0.838597\pi$
$728$	−4.78993	+	0.850773i	−0.177527	+	0.0315317i
$729$		0			0
$730$	−1.29478	+	2.58079i	−0.0479218	+	0.0955195i
$731$			59.1214i			2.18668i
$732$		0			0
$733$			25.1869i			0.930300i	0.885232	+	0.465150i	$0.154000\pi$
$733$			25.1869i			0.930300i	−0.885232	+	0.465150i	$0.846000\pi$
$734$	11.7864	+	5.91318i	0.435043	+	0.218260i
$735$		0			0
$736$	−28.9769	−	27.2243i	−1.06810	−	1.00350i
$737$			1.25350i			0.0461733i
$738$		0			0
$739$	21.7993			0.801900			0.400950	−	0.916100i	$-0.368680\pi$
$739$	21.7993			0.801900			0.400950	+	0.916100i	$0.368680\pi$
$740$	0.822467	−	0.613370i	0.0302345	−	0.0225479i
$741$		0			0
$742$	−23.2766	−	11.6778i	−0.854509	−	0.428705i
$743$	−12.0393			−0.441680			−0.220840	−	0.975310i	$-0.570880\pi$
$743$	−12.0393			−0.441680			−0.220840	+	0.975310i	$0.570880\pi$
$744$		0			0
$745$	−5.06871			−0.185703
$746$	−41.9950	−	21.0687i	−1.53755	−	0.771382i
$747$		0			0
$748$	36.7404	+	49.2650i	1.34336	+	1.80131i
$749$	16.3681			0.598077
$750$		0			0
$751$		−	7.16475i		−	0.261446i	−0.991419	−	0.130723i	$-0.958270\pi$
$751$		−	7.16475i		−	0.261446i	0.991419	−	0.130723i	$-0.0417298\pi$
$752$	−0.209683	+	0.704665i	−0.00764634	+	0.0256965i
$753$		0			0
$754$	−13.0880	−	6.56622i	−0.476637	−	0.239127i
$755$		−	13.8412i		−	0.503734i
$756$		0			0
$757$			2.57105i			0.0934464i	0.998908	+	0.0467232i	$0.0148779\pi$
$757$			2.57105i			0.0934464i	−0.998908	+	0.0467232i	$0.985122\pi$
$758$	2.67602	−	5.33393i	0.0971973	−	0.193737i
$759$		0			0
$760$	−6.26544	+	1.11285i	−0.227272	+	0.0403673i
$761$			47.1405i			1.70884i	0.519581	+	0.854421i	$0.326088\pi$
$761$			47.1405i			1.70884i	−0.519581	+	0.854421i	$0.673912\pi$
$762$		0			0
$763$	9.32290			0.337512
$764$	24.3165	+	32.6059i	0.879740	+	1.17964i
$765$		0			0
$766$	20.1753	−	40.2141i	0.728963	−	1.45299i
$767$	13.2860			0.479731
$768$		0			0
$769$	54.3586			1.96022			0.980110	−	0.198456i	$-0.0635927\pi$
$769$	54.3586			1.96022			0.980110	+	0.198456i	$0.0635927\pi$
$770$	3.78689	−	7.54816i	0.136470	−	0.272017i
$771$		0			0
$772$	3.06292	+	4.10706i	0.110237	+	0.147816i
$773$	22.6180			0.813512			0.406756	−	0.913537i	$-0.366660\pi$
$773$	22.6180			0.813512			0.406756	+	0.913537i	$0.366660\pi$
$774$		0			0
$775$			2.75686i			0.0990295i
$776$	47.9260	−	8.51248i	1.72044	−	0.305580i
$777$		0			0
$778$	11.8484	−	23.6167i	0.424786	−	0.846699i
$779$		−	16.7355i		−	0.599610i
$780$		0			0
$781$		−	48.6188i		−	1.73972i
$782$	−58.4675	−	29.3330i	−2.09079	−	1.04894i
$783$		0			0
$784$	−4.61074	+	15.4949i	−0.164669	+	0.553391i
$785$			6.70238i			0.239218i
$786$		0			0
$787$	−38.6165			−1.37653			−0.688264	−	0.725460i	$-0.741627\pi$
$787$	−38.6165			−1.37653			−0.688264	+	0.725460i	$0.741627\pi$
$788$	−25.1271	−	33.6929i	−0.895116	−	1.20026i
$789$		0			0
$790$	−10.4280	−	5.23171i	−0.371012	−	0.186136i
$791$	−23.2166			−0.825488
$792$		0			0
$793$	−13.1575			−0.467238
$794$	14.2064	+	7.12731i	0.504167	+	0.252939i
$795$		0			0
$796$	−32.2347	+	24.0397i	−1.14253	+	0.852063i
$797$	−32.2392			−1.14197			−0.570986	−	0.820960i	$-0.693439\pi$
$797$	−32.2392			−1.14197			−0.570986	+	0.820960i	$0.693439\pi$
$798$		0			0
$799$			1.20956i			0.0427913i
$800$	−18.3345	−	17.2256i	−0.648223	−	0.609018i
$801$		0			0
$802$	−36.8393	−	18.4822i	−1.30084	−	0.652629i
$803$			12.8218i			0.452473i
$804$		0			0
$805$			8.98851i			0.316803i
$806$	−0.393131	+	0.783602i	−0.0138474	+	0.0276012i
$807$		0			0
$808$	1.41655	−	0.251603i	0.0498339	−	0.00885135i
$809$			8.34642i			0.293445i	0.989178	+	0.146722i	$0.0468724\pi$
$809$			8.34642i			0.293445i	−0.989178	+	0.146722i	$0.953128\pi$
$810$		0			0
$811$	−53.8372			−1.89048			−0.945241	−	0.326374i	$-0.894173\pi$
$811$	−53.8372			−1.89048			−0.945241	+	0.326374i	$0.894173\pi$
$812$	28.5521	−	21.2933i	1.00198	−	0.747249i
$813$		0			0
$814$	2.04308	−	4.07234i	0.0716099	−	0.142735i
$815$	6.10303			0.213780
$816$		0			0
$817$	−27.1845			−0.951064
$818$	20.8463	−	41.5515i	0.728873	−	1.45282i
$819$		0			0
$820$	−6.59284	+	4.91674i	−0.230232	+	0.171700i
$821$	14.3765			0.501742			0.250871	−	0.968021i	$-0.419283\pi$
$821$	14.3765			0.501742			0.250871	+	0.968021i	$0.419283\pi$
$822$		0			0
$823$		−	36.1630i		−	1.26056i	−0.776366	−	0.630282i	$-0.782939\pi$
$823$		−	36.1630i		−	1.26056i	0.776366	−	0.630282i	$-0.217061\pi$
$824$	−6.73025	−	37.8919i	−0.234459	−	1.32003i
$825$		0			0
$826$	−14.4921	+	28.8861i	−0.504243	+	1.00508i
$827$			6.07633i			0.211295i	0.994404	+	0.105647i	$0.0336915\pi$
$827$			6.07633i			0.211295i	−0.994404	+	0.105647i	$0.966309\pi$
$828$		0			0
$829$			21.2242i			0.737146i	0.929599	+	0.368573i	$0.120154\pi$
$829$			21.2242i			0.737146i	−0.929599	+	0.368573i	$0.879846\pi$
$830$	−5.78744	−	2.90354i	−0.200885	−	0.100783i
$831$		0			0
$832$	−2.75496	−	7.51067i	−0.0955110	−	0.260386i
$833$			26.5972i			0.921539i
$834$		0			0
$835$	5.04635			0.174636
$836$	−22.6524	+	16.8935i	−0.783450	+	0.584273i
$837$		0			0
$838$	11.5433	+	5.79121i	0.398755	+	0.200054i
$839$	−34.8560			−1.20336			−0.601681	−	0.798736i	$-0.705502\pi$
$839$	−34.8560			−1.20336			−0.601681	+	0.798736i	$0.705502\pi$
$840$		0			0
$841$	78.2057			2.69675
$842$	39.3106	+	19.7220i	1.35473	+	0.679665i
$843$		0			0
$844$	−17.4265	−	23.3671i	−0.599845	−	0.804330i
$845$	0.743520			0.0255779
$846$		0			0
$847$		−	18.5806i		−	0.638436i
$848$	12.2136	−	41.0452i	0.419415	−	1.40950i
$849$		0			0
$850$	−36.9941	−	18.5598i	−1.26889	−	0.636597i
$851$			4.84943i			0.166236i
$852$		0			0
$853$			29.9766i			1.02638i	0.858275	+	0.513190i	$0.171536\pi$
$853$			29.9766i			1.02638i	−0.858275	+	0.513190i	$0.828464\pi$
$854$	14.3519	−	28.6067i	0.491112	−	0.978902i
$855$		0			0
$856$	4.70711	+	26.5014i	0.160886	+	0.905801i
$857$		−	1.09615i		−	0.0374439i	−0.999825	−	0.0187220i	$-0.994040\pi$
$857$		−	1.09615i		−	0.0374439i	0.999825	−	0.0187220i	$-0.00595974\pi$
$858$		0			0
$859$	−1.19251			−0.0406879			−0.0203440	−	0.999793i	$-0.506476\pi$
$859$	−1.19251			−0.0406879			−0.0203440	+	0.999793i	$0.506476\pi$
$860$	7.98657	+	10.7092i	0.272340	+	0.365180i
$861$		0			0
$862$	12.2960	−	24.5088i	0.418804	−	0.834775i
$863$	8.53819			0.290643			0.145322	−	0.989384i	$-0.453578\pi$
$863$	8.53819			0.290643			0.145322	+	0.989384i	$0.453578\pi$
$864$		0			0
$865$	−5.01365			−0.170469
$866$	21.5793	−	43.0127i	0.733295	−	1.46163i
$867$		0			0
$868$	−1.27487	−	1.70947i	−0.0432718	−	0.0580231i
$869$	−51.8082			−1.75747
$870$		0			0
$871$		−	0.268454i		−	0.00909622i
$872$	2.68106	+	15.0946i	0.0907923	+	0.511169i
$873$		0			0
$874$	13.4875	−	26.8838i	0.456222	−	0.909357i
$875$			12.0816i			0.408432i
$876$		0			0
$877$			54.5232i			1.84112i	0.390606	+	0.920558i	$0.372266\pi$
$877$			54.5232i			1.84112i	−0.390606	+	0.920558i	$0.627734\pi$
$878$	−21.2646	−	10.6684i	−0.717647	−	0.360041i
$879$		0			0
$880$	13.3102	+	3.96063i	0.448686	+	0.133513i
$881$		−	24.2338i		−	0.816458i	−0.912879	−	0.408229i	$-0.866146\pi$
$881$		−	24.2338i		−	0.816458i	0.912879	−	0.408229i	$-0.133854\pi$
$882$		0			0
$883$	−27.7907			−0.935232			−0.467616	−	0.883932i	$-0.654887\pi$
$883$	−27.7907			−0.935232			−0.467616	+	0.883932i	$0.654887\pi$
$884$	−7.86844	−	10.5508i	−0.264644	−	0.354861i
$885$		0			0
$886$	−10.7010	−	5.36868i	−0.359508	−	0.180364i
$887$	−37.5606			−1.26116			−0.630581	−	0.776123i	$-0.717183\pi$
$887$	−37.5606			−1.26116			−0.630581	+	0.776123i	$0.717183\pi$
$888$		0			0
$889$	16.8446			0.564948
$890$	12.3243	+	6.18306i	0.413111	+	0.207257i
$891$		0			0
$892$	22.5870	−	16.8447i	0.756267	−	0.564001i
$893$	−0.556166			−0.0186114
$894$		0			0
$895$		−	5.45183i		−	0.182235i
$896$	19.3345	+	2.20270i	0.645921	+	0.0735870i
$897$		0			0
$898$	14.6828	+	7.36631i	0.489971	+	0.245817i
$899$		−	6.41859i		−	0.214072i
$900$		0			0
$901$		−	70.4544i		−	2.34718i
$902$	−16.3772	+	32.6436i	−0.545301	+	1.08691i
$903$		0			0
$904$	−6.67660	−	37.5899i	−0.222060	−	1.25022i
$905$		−	1.16825i		−	0.0388340i
$906$		0			0
$907$	−26.8748			−0.892362			−0.446181	−	0.894943i	$-0.647216\pi$
$907$	−26.8748			−0.892362			−0.446181	+	0.894943i	$0.647216\pi$
$908$	16.0527	−	11.9716i	0.532727	−	0.397291i
$909$		0			0
$910$	−0.811013	+	1.61654i	−0.0268848	+	0.0535878i
$911$	−22.3775			−0.741400			−0.370700	−	0.928753i	$-0.620882\pi$
$911$	−22.3775			−0.741400			−0.370700	+	0.928753i	$0.620882\pi$
$912$		0			0
$913$	−28.7530			−0.951585
$914$	16.1128	−	32.1167i	0.532965	−	1.06233i
$915$		0			0
$916$	18.2308	−	13.5960i	0.602362	−	0.449223i
$917$	−3.69404			−0.121988
$918$		0			0
$919$		−	38.2831i		−	1.26284i	−0.775439	−	0.631422i	$-0.782472\pi$
$919$		−	38.2831i		−	1.26284i	0.775439	−	0.631422i	$-0.217528\pi$
$920$	−14.5532	+	2.58490i	−0.479806	+	0.0852217i
$921$		0			0
$922$	6.62359	−	13.2024i	0.218136	−	0.434797i
$923$			10.4124i			0.342728i
$924$		0			0
$925$			3.06838i			0.100888i
$926$	−5.88965	−	2.95482i	−0.193546	−	0.0971013i
$927$		0			0
$928$	42.6868	+	40.1051i	1.40126	+	1.31651i
$929$		−	0.192447i		−	0.00631398i	−0.999995	−	0.00315699i	$-0.998995\pi$
$929$		−	0.192447i		−	0.00631398i	0.999995	−	0.00315699i	$-0.00100490\pi$
$930$		0			0
$931$	−12.2296			−0.400809
$932$	8.80692	−	6.56793i	0.288480	−	0.215140i
$933$		0			0
$934$	29.4382	+	14.7690i	0.963246	+	0.483258i
$935$	22.8471			0.747179
$936$		0			0
$937$	−54.7439			−1.78841			−0.894203	−	0.447662i	$-0.852257\pi$
$937$	−54.7439			−1.78841			−0.894203	+	0.447662i	$0.852257\pi$
$938$	0.583665	+	0.292823i	0.0190573	+	0.00956101i
$939$		0			0
$940$	0.163397	+	0.219099i	0.00532942	+	0.00714621i
$941$	54.6373			1.78113			0.890563	−	0.454859i	$-0.150310\pi$
$941$	54.6373			1.78113			0.890563	+	0.454859i	$0.150310\pi$
$942$		0			0
$943$		−	38.8727i		−	1.26587i
$944$	−50.9368	−	15.1570i	−1.65785	−	0.493317i
$945$		0			0
$946$	53.0251	+	26.6025i	1.72399	+	0.864922i
$947$		−	6.29630i		−	0.204602i	−0.994753	−	0.102301i	$-0.967379\pi$
$947$		−	6.29630i		−	0.204602i	0.994753	−	0.102301i	$-0.0326205\pi$
$948$		0			0
$949$		−	2.74597i		−	0.0891379i
$950$	8.53394	−	17.0102i	0.276878	−	0.551882i
$951$		0			0
$952$	31.5219	−	5.59882i	1.02163	−	0.181459i
$953$		−	37.1157i		−	1.20229i	−0.799138	−	0.601147i	$-0.794710\pi$
$953$		−	37.1157i		−	1.20229i	0.799138	−	0.601147i	$-0.205290\pi$
$954$		0			0
$955$	15.1213			0.489312
$956$	−21.5308	−	28.8705i	−0.696355	−	0.933740i
$957$		0			0
$958$	−22.2891	+	44.4275i	−0.720130	+	1.43539i
$959$	16.2884			0.525980
$960$		0			0
$961$	30.6157			0.987603
$962$	−0.437553	+	0.872146i	−0.0141073	+	0.0281191i
$963$		0			0
$964$	−9.25689	−	12.4125i	−0.298144	−	0.399781i
$965$	1.90468			0.0613139
$966$		0			0
$967$			10.8250i			0.348109i	0.984736	+	0.174054i	$0.0556869\pi$
$967$			10.8250i			0.348109i	−0.984736	+	0.174054i	$0.944313\pi$
$968$	30.0837	−	5.34337i	0.966925	−	0.171742i
$969$		0			0
$970$	8.11465	−	16.1744i	0.260546	−	0.519329i
$971$		−	16.8746i		−	0.541531i	−0.962645	−	0.270765i	$-0.912723\pi$
$971$		−	16.8746i		−	0.541531i	0.962645	−	0.270765i	$-0.0872768\pi$
$972$		0			0
$973$			5.04975i			0.161888i
$974$	−4.33724	−	2.17598i	−0.138974	−	0.0697229i
$975$		0			0
$976$	50.4442	+	15.0104i	1.61468	+	0.480471i
$977$		−	4.05555i		−	0.129749i	−0.997893	−	0.0648743i	$-0.979335\pi$
$977$		−	4.05555i		−	0.129749i	0.997893	−	0.0648743i	$-0.0206646\pi$
$978$		0			0
$979$	61.2292			1.95689
$980$	3.59295	+	4.81778i	0.114773	+	0.153898i
$981$		0			0
$982$	−8.21186	−	4.11986i	−0.262051	−	0.131470i
$983$	−39.7911			−1.26914			−0.634569	−	0.772866i	$-0.718822\pi$
$983$	−39.7911			−1.26914			−0.634569	+	0.772866i	$0.718822\pi$
$984$		0			0
$985$	−15.6253			−0.497865
$986$	86.1305	+	43.2114i	2.74295	+	1.37613i
$987$		0			0
$988$	4.85132	−	3.61797i	0.154341	−	0.115103i
$989$	−63.1434			−2.00784
$990$		0			0
$991$		−	48.1323i		−	1.52897i	−0.644640	−	0.764486i	$-0.722993\pi$
$991$		−	48.1323i		−	1.52897i	0.644640	−	0.764486i	$-0.277007\pi$
$992$	2.40116	−	2.55573i	0.0762369	−	0.0811447i
$993$		0			0
$994$	−22.6383	−	11.3576i	−0.718043	−	0.360240i
$995$			14.9491i			0.473918i
$996$		0			0
$997$		−	30.0514i		−	0.951738i	−0.879516	−	0.475869i	$-0.842134\pi$
$997$		−	30.0514i		−	0.951738i	0.879516	−	0.475869i	$-0.157866\pi$
$998$	14.4531	−	28.8085i	0.457505	−	0.911916i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.j.a.755.33	yes	48
3.2	odd	2	inner	936.2.j.a.755.16	yes	48
4.3	odd	2		3744.2.j.a.2159.18		48
8.3	odd	2	inner	936.2.j.a.755.15	✓	48
8.5	even	2		3744.2.j.a.2159.31		48
12.11	even	2		3744.2.j.a.2159.32		48
24.5	odd	2		3744.2.j.a.2159.17		48
24.11	even	2	inner	936.2.j.a.755.34	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.j.a.755.15	✓	48	8.3	odd	2	inner
936.2.j.a.755.16	yes	48	3.2	odd	2	inner
936.2.j.a.755.33	yes	48	1.1	even	1	trivial
936.2.j.a.755.34	yes	48	24.11	even	2	inner
3744.2.j.a.2159.17		48	24.5	odd	2
3744.2.j.a.2159.18		48	4.3	odd	2
3744.2.j.a.2159.31		48	8.5	even	2
3744.2.j.a.2159.32		48	12.11	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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.634171 - 1.26405i) q^{2} +(-1.19565 - 1.60325i) q^{4} -0.743520 q^{5} +1.72000i q^{7} +(-2.78484 + 0.494635i) q^{8} +(-0.471519 + 0.939848i) q^{10} +4.66933i q^{11} -1.00000i q^{13} +(2.17417 + 1.09077i) q^{14} +(-1.14082 + 3.83387i) q^{16} +6.58087i q^{17} -3.02593 q^{19} +(0.888993 + 1.19205i) q^{20} +(5.90228 + 2.96115i) q^{22} -7.02856 q^{23} -4.44718 q^{25} +(-1.26405 - 0.634171i) q^{26} +(2.75759 - 2.05653i) q^{28} +10.3540 q^{29} -0.619913i q^{31} +(4.12273 + 3.87338i) q^{32} +(8.31856 + 4.17339i) q^{34} -1.27886i q^{35} -0.689961i q^{37} +(-1.91896 + 3.82493i) q^{38} +(2.07059 - 0.367771i) q^{40} +5.53068i q^{41} +8.98383 q^{43} +(7.48610 - 5.58291i) q^{44} +(-4.45731 + 8.88447i) q^{46} +0.183800 q^{47} +4.04160 q^{49} +(-2.82027 + 5.62146i) q^{50} +(-1.60325 + 1.19565i) q^{52} -10.7059 q^{53} -3.47174i q^{55} +(-0.850773 - 4.78993i) q^{56} +(6.56622 - 13.0880i) q^{58} +13.2860i q^{59} -13.1575i q^{61} +(-0.783602 - 0.393131i) q^{62} +(7.51067 - 2.75496i) q^{64} +0.743520i q^{65} +0.268454 q^{67} +(10.5508 - 7.86844i) q^{68} +(-1.61654 - 0.811013i) q^{70} -10.4124 q^{71} +2.74597 q^{73} +(-0.872146 - 0.437553i) q^{74} +(3.61797 + 4.85132i) q^{76} -8.03125 q^{77} +11.0954i q^{79} +(0.848223 - 2.85056i) q^{80} +(6.99107 + 3.50740i) q^{82} +6.15784i q^{83} -4.89301i q^{85} +(5.69729 - 11.3560i) q^{86} +(-2.30961 - 13.0033i) q^{88} -13.1131i q^{89} +1.72000 q^{91} +(8.40373 + 11.2685i) q^{92} +(0.116561 - 0.232333i) q^{94} +2.24984 q^{95} -17.2096 q^{97} +(2.56306 - 5.10879i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{4} + 16 q^{10} + 8 q^{16} + 32 q^{19} + 48 q^{25} - 24 q^{28} + 32 q^{34} - 32 q^{40} - 32 q^{43} + 24 q^{46} - 48 q^{49} + 8 q^{52} - 40 q^{58} + 40 q^{64} + 32 q^{67} - 40 q^{70} + 40 q^{76}+ \cdots - 32 q^{97}+O(q^{100}) \) 48 * q - 8 * q^4 + 16 * q^10 + 8 * q^16 + 32 * q^19 + 48 * q^25 - 24 * q^28 + 32 * q^34 - 32 * q^40 - 32 * q^43 + 24 * q^46 - 48 * q^49 + 8 * q^52 - 40 * q^58 + 40 * q^64 + 32 * q^67 - 40 * q^70 + 40 * q^76 + 16 * q^82 + 48 * q^88 + 32 * q^94 - 32 * q^97

Introduction

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Database

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