LMFDB - Embedded newform 976.2.bw.c.561.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [976,2,Mod(225,976)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(976, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 28]))

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

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

chi := DirichletCharacter("976.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 976 = 2^{4} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	976.bw (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.79339923728$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 61)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			561.1
Character	$\chi$	$=$	976.561
Dual form			976.2.bw.c.849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86941 + 1.35820i) q^{3} +(-1.20434 + 0.255990i) q^{5} +(-0.404506 + 3.84862i) q^{7} +(0.722916 - 2.22491i) q^{9} +O(q^{10})$	\(q+(-1.86941 + 1.35820i) q^{3} +(-1.20434 + 0.255990i) q^{5} +(-0.404506 + 3.84862i) q^{7} +(0.722916 - 2.22491i) q^{9} +1.98434 q^{11} +(2.72937 + 4.72741i) q^{13} +(1.90371 - 2.11428i) q^{15} +(3.60066 + 3.99894i) q^{17} +(-0.472909 - 4.49943i) q^{19} +(-4.47102 - 7.74404i) q^{21} +(-2.24547 + 6.91085i) q^{23} +(-3.18283 + 1.41709i) q^{25} +(-0.471699 - 1.45174i) q^{27} +(-0.207283 + 0.359024i) q^{29} +(2.26627 - 1.00901i) q^{31} +(-3.70954 + 2.69514i) q^{33} +(-0.498045 - 4.73858i) q^{35} +(-5.96555 - 4.33423i) q^{37} +(-11.5231 - 5.13041i) q^{39} +(-3.12409 - 2.26979i) q^{41} +(1.69649 - 1.88414i) q^{43} +(-0.301081 + 2.86459i) q^{45} +(-1.97577 + 3.42213i) q^{47} +(-7.80121 - 1.65820i) q^{49} +(-12.1625 - 2.58521i) q^{51} +(0.927961 + 2.85597i) q^{53} +(-2.38981 + 0.507970i) q^{55} +(6.99520 + 7.76896i) q^{57} +(1.34010 + 0.596653i) q^{59} +(1.71348 - 7.61997i) q^{61} +(8.27039 + 3.68221i) q^{63} +(-4.49725 - 4.99470i) q^{65} +(-5.93084 + 1.26064i) q^{67} +(-5.18865 - 15.9690i) q^{69} +(8.53723 + 1.81465i) q^{71} +(-6.01044 - 1.27756i) q^{73} +(4.02532 - 6.97205i) q^{75} +(-0.802678 + 7.63697i) q^{77} +(6.05353 - 6.72312i) q^{79} +(8.53141 + 6.19843i) q^{81} +(-4.66057 - 2.07502i) q^{83} +(-5.36009 - 3.89433i) q^{85} +(-0.100132 - 0.952694i) q^{87} +(-6.45373 + 4.68891i) q^{89} +(-19.2980 + 8.59204i) q^{91} +(-2.86615 + 4.96432i) q^{93} +(1.72135 + 5.29776i) q^{95} +(4.08831 - 1.82023i) q^{97} +(1.43451 - 4.41497i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} + 2 q^{5} - q^{7} - 2 q^{9}+O(q^{10}) $ 32 * q + 4 * q^3 + 2 * q^5 - q^7 - 2 * q^9	$ 32 q + 4 q^{3} + 2 q^{5} - q^{7} - 2 q^{9} + 18 q^{11} - 2 q^{15} - 24 q^{17} - 9 q^{19} - 3 q^{21} + 2 q^{23} + 28 q^{25} - 35 q^{27} - 4 q^{29} + 11 q^{31} - 35 q^{33} + 58 q^{35} - 14 q^{37} - 17 q^{39} + 11 q^{41} - 40 q^{43} + 12 q^{45} - 40 q^{47} + q^{49} + 9 q^{51} + 17 q^{53} + 60 q^{55} - 38 q^{57} + 11 q^{59} - 55 q^{61} + 58 q^{63} + 59 q^{65} + 13 q^{67} - 32 q^{69} - 63 q^{71} - 46 q^{73} - q^{75} - 31 q^{77} + 49 q^{79} + 48 q^{81} - 39 q^{83} + 21 q^{85} - 17 q^{87} + 32 q^{89} - 70 q^{91} + 67 q^{93} - 47 q^{95} + 37 q^{97} + 31 q^{99}+O(q^{100}) $ 32 * q + 4 * q^3 + 2 * q^5 - q^7 - 2 * q^9 + 18 * q^11 - 2 * q^15 - 24 * q^17 - 9 * q^19 - 3 * q^21 + 2 * q^23 + 28 * q^25 - 35 * q^27 - 4 * q^29 + 11 * q^31 - 35 * q^33 + 58 * q^35 - 14 * q^37 - 17 * q^39 + 11 * q^41 - 40 * q^43 + 12 * q^45 - 40 * q^47 + q^49 + 9 * q^51 + 17 * q^53 + 60 * q^55 - 38 * q^57 + 11 * q^59 - 55 * q^61 + 58 * q^63 + 59 * q^65 + 13 * q^67 - 32 * q^69 - 63 * q^71 - 46 * q^73 - q^75 - 31 * q^77 + 49 * q^79 + 48 * q^81 - 39 * q^83 + 21 * q^85 - 17 * q^87 + 32 * q^89 - 70 * q^91 + 67 * q^93 - 47 * q^95 + 37 * q^97 + 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/976\mathbb{Z}\right)^\times$.

$n$	$245$	$367$	$673$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{15}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.86941	+	1.35820i	−1.07930	+	0.784160i	−0.977561	−	0.210651i	$-0.932442\pi$
$3$	−1.86941	+	1.35820i	−1.07930	+	0.784160i	−0.101742	+	0.994811i	$0.532442\pi$
$4$		0			0
$5$	−1.20434	+	0.255990i	−0.538595	+	0.114482i	−0.469175	−	0.883105i	$-0.655448\pi$
$5$	−1.20434	+	0.255990i	−0.538595	+	0.114482i	−0.0694209	+	0.997587i	$0.522115\pi$
$6$		0			0
$7$	−0.404506	+	3.84862i	−0.152889	+	1.45464i	0.601846	+	0.798612i	$0.294432\pi$
$7$	−0.404506	+	3.84862i	−0.152889	+	1.45464i	−0.754735	+	0.656029i	$0.772235\pi$
$8$		0			0
$9$	0.722916	−	2.22491i	0.240972	−	0.741635i
$10$		0			0
$11$	1.98434			0.598301			0.299151	−	0.954206i	$-0.403297\pi$
$11$	1.98434			0.598301			0.299151	+	0.954206i	$0.403297\pi$
$12$		0			0
$13$	2.72937	+	4.72741i	0.756991	+	1.31115i	0.944378	+	0.328862i	$0.106665\pi$
$13$	2.72937	+	4.72741i	0.756991	+	1.31115i	−0.187387	+	0.982286i	$0.560002\pi$
$14$		0			0
$15$	1.90371	−	2.11428i	0.491536	−	0.545906i
$16$		0			0
$17$	3.60066	+	3.99894i	0.873288	+	0.969885i	0.999756	−	0.0220861i	$-0.00703079\pi$
$17$	3.60066	+	3.99894i	0.873288	+	0.969885i	−0.126468	+	0.991971i	$0.540364\pi$
$18$		0			0
$19$	−0.472909	−	4.49943i	−0.108493	−	1.03224i	−0.904361	−	0.426769i	$-0.859652\pi$
$19$	−0.472909	−	4.49943i	−0.108493	−	1.03224i	0.795868	−	0.605470i	$-0.207015\pi$
$20$		0			0
$21$	−4.47102	−	7.74404i	−0.975657	−	1.68989i
$22$		0			0
$23$	−2.24547	+	6.91085i	−0.468213	+	1.44101i	0.386683	+	0.922213i	$0.373621\pi$
$23$	−2.24547	+	6.91085i	−0.468213	+	1.44101i	−0.854896	+	0.518800i	$0.826379\pi$
$24$		0			0
$25$	−3.18283	+	1.41709i	−0.636567	+	0.283418i
$26$		0			0
$27$	−0.471699	−	1.45174i	−0.0907785	−	0.279387i
$28$		0			0
$29$	−0.207283	+	0.359024i	−0.0384914	+	0.0666691i	−0.884629	−	0.466295i	$-0.845589\pi$
$29$	−0.207283	+	0.359024i	−0.0384914	+	0.0666691i	0.846138	+	0.532964i	$0.178922\pi$
$30$		0			0
$31$	2.26627	−	1.00901i	0.407035	−	0.181224i	−0.192998	−	0.981199i	$-0.561821\pi$
$31$	2.26627	−	1.00901i	0.407035	−	0.181224i	0.600033	+	0.799976i	$0.295154\pi$
$32$		0			0
$33$	−3.70954	+	2.69514i	−0.645748	+	0.469164i
$34$		0			0
$35$	−0.498045	−	4.73858i	−0.0841849	−	0.800966i
$36$		0			0
$37$	−5.96555	−	4.33423i	−0.980730	−	0.712542i	−0.0228586	−	0.999739i	$-0.507277\pi$
$37$	−5.96555	−	4.33423i	−0.980730	−	0.712542i	−0.957872	+	0.287196i	$0.907277\pi$
$38$		0			0
$39$	−11.5231	−	5.13041i	−1.84517	−	0.821524i
$40$		0			0
$41$	−3.12409	−	2.26979i	−0.487902	−	0.354481i	0.316475	−	0.948601i	$-0.397501\pi$
$41$	−3.12409	−	2.26979i	−0.487902	−	0.354481i	−0.804377	+	0.594120i	$0.797501\pi$
$42$		0			0
$43$	1.69649	−	1.88414i	0.258712	−	0.287329i	−0.599770	−	0.800172i	$-0.704741\pi$
$43$	1.69649	−	1.88414i	0.258712	−	0.287329i	0.858482	+	0.512844i	$0.171408\pi$
$44$		0			0
$45$	−0.301081	+	2.86459i	−0.0448825	+	0.427028i
$46$		0			0
$47$	−1.97577	+	3.42213i	−0.288195	+	0.499169i	−0.973379	−	0.229201i	$-0.926389\pi$
$47$	−1.97577	+	3.42213i	−0.288195	+	0.499169i	0.685184	+	0.728370i	$0.259722\pi$
$48$		0			0
$49$	−7.80121	−	1.65820i	−1.11446	−	0.236885i
$50$		0			0
$51$	−12.1625	−	2.58521i	−1.70309	−	0.362002i
$52$		0			0
$53$	0.927961	+	2.85597i	0.127465	+	0.392298i	0.994342	−	0.106224i	$-0.0338762\pi$
$53$	0.927961	+	2.85597i	0.127465	+	0.392298i	−0.866877	+	0.498522i	$0.833876\pi$
$54$		0			0
$55$	−2.38981	+	0.507970i	−0.322242	+	0.0684947i
$56$		0			0
$57$	6.99520	+	7.76896i	0.926537	+	1.02902i
$58$		0			0
$59$	1.34010	+	0.596653i	0.174467	+	0.0776776i	0.492111	−	0.870532i	$-0.336225\pi$
$59$	1.34010	+	0.596653i	0.174467	+	0.0776776i	−0.317645	+	0.948210i	$0.602892\pi$
$60$		0			0
$61$	1.71348	−	7.61997i	0.219389	−	0.975637i
$61$	1.71348	−	7.61997i	0.219389	−	0.975637i
$62$		0			0
$63$	8.27039	+	3.68221i	1.04197	+	0.463915i
$64$		0			0
$65$	−4.49725	−	4.99470i	−0.557815	−	0.619516i
$66$		0			0
$67$	−5.93084	+	1.26064i	−0.724568	+	0.154012i	−0.555409	−	0.831577i	$-0.687438\pi$
$67$	−5.93084	+	1.26064i	−0.724568	+	0.154012i	−0.169159	+	0.985589i	$0.554105\pi$
$68$		0			0
$69$	−5.18865	−	15.9690i	−0.624640	−	1.92244i
$70$		0			0
$71$	8.53723	+	1.81465i	1.01318	+	0.215359i	0.684447	−	0.729063i	$-0.260044\pi$
$71$	8.53723	+	1.81465i	1.01318	+	0.215359i	0.328737	+	0.944422i	$0.393377\pi$
$72$		0			0
$73$	−6.01044	−	1.27756i	−0.703469	−	0.149527i	−0.157730	−	0.987482i	$-0.550418\pi$
$73$	−6.01044	−	1.27756i	−0.703469	−	0.149527i	−0.545739	+	0.837955i	$0.683751\pi$
$74$		0			0
$75$	4.02532	−	6.97205i	0.464804	−	0.805063i
$76$		0			0
$77$	−0.802678	+	7.63697i	−0.0914736	+	0.870314i
$78$		0			0
$79$	6.05353	−	6.72312i	0.681075	−	0.756411i	−0.299169	−	0.954200i	$-0.596710\pi$
$79$	6.05353	−	6.72312i	0.681075	−	0.756411i	0.980245	+	0.197789i	$0.0633762\pi$
$80$		0			0
$81$	8.53141	+	6.19843i	0.947934	+	0.688715i
$82$		0			0
$83$	−4.66057	−	2.07502i	−0.511565	−	0.227763i	0.134686	−	0.990888i	$-0.456997\pi$
$83$	−4.66057	−	2.07502i	−0.511565	−	0.227763i	−0.646251	+	0.763125i	$0.723664\pi$
$84$		0			0
$85$	−5.36009	−	3.89433i	−0.581383	−	0.422400i
$86$		0			0
$87$	−0.100132	−	0.952694i	−0.0107353	−	0.102140i
$88$		0			0
$89$	−6.45373	+	4.68891i	−0.684093	+	0.497023i	−0.874713	−	0.484641i	$-0.838950\pi$
$89$	−6.45373	+	4.68891i	−0.684093	+	0.497023i	0.190620	+	0.981664i	$0.438950\pi$
$90$		0			0
$91$	−19.2980	+	8.59204i	−2.02299	+	0.900691i
$92$		0			0
$93$	−2.86615	+	4.96432i	−0.297206	+	0.514776i
$94$		0			0
$95$	1.72135	+	5.29776i	0.176607	+	0.543539i
$96$		0			0
$97$	4.08831	−	1.82023i	0.415105	−	0.184817i	−0.188548	−	0.982064i	$-0.560378\pi$
$97$	4.08831	−	1.82023i	0.415105	−	0.184817i	0.603653	+	0.797247i	$0.293711\pi$
$98$		0			0
$99$	1.43451	−	4.41497i	0.144174	−	0.443721i
$100$		0			0
$101$	−2.32112	−	4.02029i	−0.230960	−	0.400034i	0.727131	−	0.686499i	$-0.240853\pi$
$101$	−2.32112	−	4.02029i	−0.230960	−	0.400034i	−0.958091	+	0.286465i	$0.907520\pi$
$102$		0			0
$103$	−0.0983275	−	0.935524i	−0.00968850	−	0.0921799i	0.988609	−	0.150506i	$-0.0480903\pi$
$103$	−0.0983275	−	0.935524i	−0.00968850	−	0.0921799i	−0.998298	+	0.0583262i	$0.981424\pi$
$104$		0			0
$105$	7.36701	+	8.18189i	0.718946	+	0.798471i
$106$		0			0
$107$	−9.70753	+	10.7813i	−0.938462	+	1.04227i	0.0605646	+	0.998164i	$0.480710\pi$
$107$	−9.70753	+	10.7813i	−0.938462	+	1.04227i	−0.999027	+	0.0441038i	$0.985957\pi$
$108$		0			0
$109$	−0.198787	−	0.344309i	−0.0190404	−	0.0329789i	0.856348	−	0.516399i	$-0.172728\pi$
$109$	−0.198787	−	0.344309i	−0.0190404	−	0.0329789i	−0.875389	+	0.483420i	$0.839394\pi$
$110$		0			0
$111$	17.0388			1.61725
$112$		0			0
$113$	−1.84819	+	5.68814i	−0.173863	+	0.535095i	−0.999580	−	0.0289897i	$-0.990771\pi$
$113$	−1.84819	+	5.68814i	−0.173863	+	0.535095i	0.825717	+	0.564085i	$0.190771\pi$
$114$		0			0
$115$	0.935197	−	8.89781i	0.0872076	−	0.829725i
$116$		0			0
$117$	12.4911	−	2.65508i	1.15481	−	0.245462i
$118$		0			0
$119$	−16.8469	+	12.2400i	−1.54435	+	1.12204i
$120$		0			0
$121$	−7.06239			−0.642036
$122$		0			0
$123$	8.92304			0.804563
$124$		0			0
$125$	8.45092	−	6.13995i	0.755873	−	0.549174i
$126$		0			0
$127$	2.51029	−	0.533579i	0.222752	−	0.0473475i	−0.0951833	−	0.995460i	$-0.530344\pi$
$127$	2.51029	−	0.533579i	0.222752	−	0.0473475i	0.317936	+	0.948112i	$0.397010\pi$
$128$		0			0
$129$	−0.612380	+	5.82641i	−0.0539171	+	0.512987i
$130$		0			0
$131$	4.15159	−	12.7773i	0.362726	−	1.11636i	−0.588667	−	0.808376i	$-0.700347\pi$
$131$	4.15159	−	12.7773i	0.362726	−	1.11636i	0.951393	−	0.307980i	$-0.0996531\pi$
$132$		0			0
$133$	17.5079			1.51813
$134$		0			0
$135$	0.939714	+	1.62763i	0.0808777	+	0.140084i
$136$		0			0
$137$	9.39015	−	10.4288i	0.802255	−	0.890994i	−0.193681	−	0.981065i	$-0.562043\pi$
$137$	9.39015	−	10.4288i	0.802255	−	0.890994i	0.995935	+	0.0900705i	$0.0287092\pi$
$138$		0			0
$139$	−3.86611	−	4.29375i	−0.327919	−	0.364191i	0.556530	−	0.830827i	$-0.312132\pi$
$139$	−3.86611	−	4.29375i	−0.327919	−	0.364191i	−0.884449	+	0.466637i	$0.845466\pi$
$140$		0			0
$141$	−0.954436	−	9.08085i	−0.0803780	−	0.764746i
$142$		0			0
$143$	5.41600	+	9.38079i	0.452909	+	0.784461i
$144$		0			0
$145$	0.157731	−	0.485447i	0.0130989	−	0.0403142i
$146$		0			0
$147$	16.8358	−	7.49578i	1.38859	−	0.618242i
$148$		0			0
$149$	7.04785	+	21.6911i	0.577383	+	1.77700i	0.627919	+	0.778279i	$0.283907\pi$
$149$	7.04785	+	21.6911i	0.577383	+	1.77700i	−0.0505360	+	0.998722i	$0.516093\pi$
$150$		0			0
$151$	5.55147	−	9.61543i	0.451772	−	0.782492i	−0.546724	−	0.837313i	$-0.684125\pi$
$151$	5.55147	−	9.61543i	0.451772	−	0.782492i	0.998496	+	0.0548206i	$0.0174587\pi$
$152$		0			0
$153$	11.5002	−	5.12023i	0.929738	−	0.413946i
$154$		0			0
$155$	−2.47106	+	1.79533i	−0.198480	+	0.144204i
$156$		0			0
$157$	−0.905118	−	8.61162i	−0.0722363	−	0.687282i	−0.969384	−	0.245551i	$-0.921031\pi$
$157$	−0.905118	−	8.61162i	−0.0722363	−	0.687282i	0.897147	−	0.441731i	$-0.145636\pi$
$158$		0			0
$159$	−5.61373	−	4.07861i	−0.445198	−	0.323455i
$160$		0			0
$161$	−25.6889	−	11.4374i	−2.02457	−	0.901397i
$162$		0			0
$163$	16.0936	+	11.6927i	1.26055	+	0.915842i	0.998785	−	0.0492895i	$-0.0156957\pi$
$163$	16.0936	+	11.6927i	1.26055	+	0.915842i	0.261764	+	0.965132i	$0.415696\pi$
$164$		0			0
$165$	3.77761	−	4.19546i	0.294086	−	0.326616i
$166$		0			0
$167$	−1.18071	+	11.2337i	−0.0913660	+	0.869290i	0.848832	+	0.528662i	$0.177306\pi$
$167$	−1.18071	+	11.2337i	−0.0913660	+	0.869290i	−0.940198	+	0.340628i	$0.889360\pi$
$168$		0			0
$169$	−8.39894	+	14.5474i	−0.646072	+	1.11903i
$170$		0			0
$171$	−10.3527	−	2.20053i	−0.791689	−	0.168279i
$172$		0			0
$173$	−9.25127	−	1.96642i	−0.703361	−	0.149504i	−0.157672	−	0.987492i	$-0.550399\pi$
$173$	−9.25127	−	1.96642i	−0.703361	−	0.149504i	−0.545689	+	0.837988i	$0.683732\pi$
$174$		0			0
$175$	−4.16636	−	12.8227i	−0.314947	−	0.969307i
$176$		0			0
$177$	−3.31558	+	0.704748i	−0.249214	+	0.0529721i
$178$		0			0
$179$	−1.16770	−	1.29686i	−0.0872777	−	0.0969317i	0.697924	−	0.716172i	$-0.254107\pi$
$179$	−1.16770	−	1.29686i	−0.0872777	−	0.0969317i	−0.785202	+	0.619240i	$0.787441\pi$
$180$		0			0
$181$	20.1978	+	8.99263i	1.50129	+	0.668417i	0.982462	−	0.186462i	$-0.0597023\pi$
$181$	20.1978	+	8.99263i	1.50129	+	0.668417i	0.518827	+	0.854879i	$0.326369\pi$
$182$		0			0
$183$	7.14628	+	16.5721i	0.528268	+	1.22504i
$184$		0			0
$185$	8.29404	+	3.69275i	0.609790	+	0.271496i
$186$		0			0
$187$	7.14493	+	7.93525i	0.522489	+	0.580283i
$188$		0			0
$189$	5.77800	−	1.22815i	0.420287	−	0.0893348i
$190$		0			0
$191$	1.26390	+	3.88989i	0.0914528	+	0.281463i	0.986313	−	0.164884i	$-0.0527249\pi$
$191$	1.26390	+	3.88989i	0.0914528	+	0.281463i	−0.894860	+	0.446347i	$0.852725\pi$
$192$		0			0
$193$	20.8189	+	4.42519i	1.49858	+	0.318532i	0.882935	−	0.469494i	$-0.155564\pi$
$193$	20.8189	+	4.42519i	1.49858	+	0.318532i	0.615641	+	0.788027i	$0.288897\pi$
$194$		0			0
$195$	15.1910	+	3.22895i	1.08785	+	0.231230i
$196$		0			0
$197$	0.463455	−	0.802727i	0.0330198	−	0.0571919i	−0.849043	−	0.528323i	$-0.822821\pi$
$197$	0.463455	−	0.802727i	0.0330198	−	0.0571919i	0.882063	+	0.471131i	$0.156154\pi$
$198$		0			0
$199$	−2.90050	+	27.5964i	−0.205611	+	1.95626i	0.0770244	+	0.997029i	$0.475458\pi$
$199$	−2.90050	+	27.5964i	−0.205611	+	1.95626i	−0.282635	+	0.959227i	$0.591209\pi$
$200$		0			0
$201$	9.37496	−	10.4119i	0.661258	−	0.734402i
$202$		0			0
$203$	−1.29790	−	0.942979i	−0.0910946	−	0.0661841i
$204$		0			0
$205$	4.34350	+	1.93385i	0.303363	+	0.135066i
$206$		0			0
$207$	13.7527	+	9.99193i	0.955879	+	0.694487i
$208$		0			0
$209$	−0.938413	−	8.92840i	−0.0649114	−	0.617590i
$210$		0			0
$211$	−1.39195	+	1.01131i	−0.0958255	+	0.0696213i	−0.634666	−	0.772786i	$-0.718862\pi$
$211$	−1.39195	+	1.01131i	−0.0958255	+	0.0696213i	0.538841	+	0.842408i	$0.318862\pi$
$212$		0			0
$213$	−18.4242	+	8.20300i	−1.26241	+	0.562060i
$214$		0			0
$215$	−1.56082	+	2.70342i	−0.106447	+	0.184372i
$216$		0			0
$217$	2.96657	+	9.13018i	0.201384	+	0.619797i
$218$		0			0
$219$	12.9712	−	5.77513i	0.876510	−	0.390247i
$220$		0			0
$221$	−9.07708	+	27.9364i	−0.610590	+	1.87920i
$222$		0			0
$223$	−7.37302	−	12.7704i	−0.493734	−	0.855172i	0.506240	−	0.862393i	$-0.331035\pi$
$223$	−7.37302	−	12.7704i	−0.493734	−	0.855172i	−0.999974	+	0.00722039i	$0.997702\pi$
$224$		0			0
$225$	0.851968	+	8.10594i	0.0567979	+	0.540396i
$226$		0			0
$227$	4.20101	+	4.66570i	0.278831	+	0.309673i	0.866251	−	0.499609i	$-0.166523\pi$
$227$	4.20101	+	4.66570i	0.278831	+	0.309673i	−0.587420	+	0.809282i	$0.699856\pi$
$228$		0			0
$229$	−1.22133	+	1.35642i	−0.0807077	+	0.0896350i	−0.782146	−	0.623095i	$-0.785875\pi$
$229$	−1.22133	+	1.35642i	−0.0807077	+	0.0896350i	0.701438	+	0.712730i	$0.252542\pi$
$230$		0			0
$231$	−8.87203	−	15.3668i	−0.583737	−	1.01106i
$232$		0			0
$233$	−11.4021			−0.746974			−0.373487	−	0.927635i	$-0.621838\pi$
$233$	−11.4021			−0.746974			−0.373487	+	0.927635i	$0.621838\pi$
$234$		0			0
$235$	1.50346	−	4.62717i	0.0980748	−	0.301843i
$236$		0			0
$237$	−2.18514	+	20.7902i	−0.141940	+	1.35047i
$238$		0			0
$239$	−5.69764	+	1.21107i	−0.368549	+	0.0783376i	−0.388464	−	0.921464i	$-0.626994\pi$
$239$	−5.69764	+	1.21107i	−0.368549	+	0.0783376i	0.0199141	+	0.999802i	$0.493661\pi$
$240$		0			0
$241$	14.0356	−	10.1975i	0.904113	−	0.656876i	−0.0354063	−	0.999373i	$-0.511273\pi$
$241$	14.0356	−	10.1975i	0.904113	−	0.656876i	0.939519	+	0.342497i	$0.111273\pi$
$242$		0			0
$243$	−19.7881			−1.26941
$244$		0			0
$245$	9.81975			0.627361
$246$		0			0
$247$	19.9799	−	14.5162i	1.27129	−	0.923647i
$248$		0			0
$249$	11.5308	−	2.45095i	0.730736	−	0.155323i
$250$		0			0
$251$	0.530194	−	5.04446i	0.0334656	−	0.318403i	−0.964964	−	0.262382i	$-0.915492\pi$
$251$	0.530194	−	5.04446i	0.0334656	−	0.318403i	0.998430	−	0.0560213i	$-0.0178415\pi$
$252$		0			0
$253$	−4.45578	+	13.7135i	−0.280133	+	0.862160i
$254$		0			0
$255$	15.3095			0.958717
$256$		0			0
$257$	−10.8484	−	18.7901i	−0.676707	−	1.17209i	−0.975967	−	0.217920i	$-0.930073\pi$
$257$	−10.8484	−	18.7901i	−0.676707	−	1.17209i	0.299259	−	0.954172i	$-0.403260\pi$
$258$		0			0
$259$	19.0939	−	21.2059i	1.18644	−	1.31767i
$260$		0			0
$261$	0.648946	+	0.720728i	0.0401688	+	0.0446119i
$262$		0			0
$263$	−0.0382994	−	0.364395i	−0.00236164	−	0.0224695i	0.993278	−	0.115757i	$-0.0369292\pi$
$263$	−0.0382994	−	0.364395i	−0.00236164	−	0.0224695i	−0.995639	+	0.0932870i	$0.970263\pi$
$264$		0			0
$265$	−1.84868	−	3.20200i	−0.113563	−	0.196697i
$266$		0			0
$267$	5.69615	−	17.5310i	0.348599	−	1.07288i
$268$		0			0
$269$	−18.8038	+	8.37201i	−1.14649	+	0.510450i	−0.889939	−	0.456080i	$-0.849253\pi$
$269$	−18.8038	+	8.37201i	−1.14649	+	0.510450i	−0.256551	+	0.966531i	$0.582586\pi$
$270$		0			0
$271$	10.0125	+	30.8152i	0.608215	+	1.87189i	0.472967	+	0.881080i	$0.343183\pi$
$271$	10.0125	+	30.8152i	0.608215	+	1.87189i	0.135248	+	0.990812i	$0.456817\pi$
$272$		0			0
$273$	24.4062	−	42.2727i	1.47713	−	2.55846i
$274$		0			0
$275$	−6.31583	+	2.81199i	−0.380859	+	0.169569i
$276$		0			0
$277$	−3.40946	+	2.47712i	−0.204855	+	0.148836i	−0.685483	−	0.728089i	$-0.740409\pi$
$277$	−3.40946	+	2.47712i	−0.204855	+	0.148836i	0.480628	+	0.876925i	$0.340409\pi$
$278$		0			0
$279$	−0.606628	−	5.77168i	−0.0363178	−	0.345541i
$280$		0			0
$281$	−2.97726	−	2.16310i	−0.177608	−	0.129040i	0.495429	−	0.868648i	$-0.335011\pi$
$281$	−2.97726	−	2.16310i	−0.177608	−	0.129040i	−0.673037	+	0.739608i	$0.735011\pi$
$282$		0			0
$283$	−18.0382	−	8.03111i	−1.07226	−	0.477400i	−0.206801	−	0.978383i	$-0.566305\pi$
$283$	−18.0382	−	8.03111i	−1.07226	−	0.477400i	−0.865457	+	0.500983i	$0.832972\pi$
$284$		0			0
$285$	−10.4133	−	7.56574i	−0.616833	−	0.448156i
$286$		0			0
$287$	9.99926	−	11.1053i	0.590238	−	0.655525i
$288$		0			0
$289$	−1.24977	+	11.8907i	−0.0735157	+	0.699455i
$290$		0			0
$291$	−5.17047	+	8.95552i	−0.303098	+	0.524982i
$292$		0			0
$293$	−1.67272	−	0.355547i	−0.0977212	−	0.0207713i	0.158792	−	0.987312i	$-0.449240\pi$
$293$	−1.67272	−	0.355547i	−0.0977212	−	0.0207713i	−0.256513	+	0.966541i	$0.582574\pi$
$294$		0			0
$295$	−1.76667	−	0.375518i	−0.102860	−	0.0218635i
$296$		0			0
$297$	−0.936011	−	2.88075i	−0.0543129	−	0.167158i
$298$		0			0
$299$	−38.7992	+	8.24702i	−2.24381	+	0.476937i
$300$		0			0
$301$	6.56510	+	7.29128i	0.378406	+	0.420263i
$302$		0			0
$303$	9.79949	+	4.36301i	0.562966	+	0.250649i
$304$		0			0
$305$	−0.112976	+	9.61564i	−0.00646901	+	0.550590i
$306$		0			0
$307$	−15.9872	−	7.11797i	−0.912439	−	0.406244i	−0.103833	−	0.994595i	$-0.533111\pi$
$307$	−15.9872	−	7.11797i	−0.912439	−	0.406244i	−0.808606	+	0.588351i	$0.799778\pi$
$308$		0			0
$309$	1.45445	+	1.61533i	0.0827406	+	0.0918927i
$310$		0			0
$311$	14.4204	−	3.06514i	0.817704	−	0.173808i	0.219974	−	0.975506i	$-0.429403\pi$
$311$	14.4204	−	3.06514i	0.817704	−	0.173808i	0.597730	+	0.801697i	$0.296069\pi$
$312$		0			0
$313$	−3.98839	−	12.2750i	−0.225437	−	0.693825i	−0.998247	−	0.0591867i	$-0.981149\pi$
$313$	−3.98839	−	12.2750i	−0.225437	−	0.693825i	0.772810	−	0.634638i	$-0.218851\pi$
$314$		0			0
$315$	−10.9029	−	2.31749i	−0.614311	−	0.130576i
$316$		0			0
$317$	14.3518	+	3.05057i	0.806078	+	0.171337i	0.592481	−	0.805584i	$-0.298149\pi$
$317$	14.3518	+	3.05057i	0.806078	+	0.171337i	0.213598	+	0.976922i	$0.431482\pi$
$318$		0			0
$319$	−0.411319	+	0.712426i	−0.0230295	+	0.0398882i
$320$		0			0
$321$	3.50412	−	33.3395i	0.195581	−	1.86083i
$322$		0			0
$323$	16.2901	−	18.0920i	0.906408	−	1.00667i
$324$		0			0
$325$	−15.3863	−	11.1788i	−0.853478	−	0.620088i
$326$		0			0
$327$	0.839257	+	0.373661i	0.0464110	+	0.0206635i
$328$		0			0
$329$	−12.3713	−	8.98825i	−0.682050	−	0.495538i
$330$		0			0
$331$	0.117148	+	1.11458i	0.00643901	+	0.0612631i	0.997270	−	0.0738473i	$-0.0235277\pi$
$331$	0.117148	+	1.11458i	0.00643901	+	0.0612631i	−0.990831	+	0.135110i	$0.956861\pi$
$332$		0			0
$333$	−13.9558	+	10.1395i	−0.764775	+	0.555641i
$334$		0			0
$335$	6.82002	−	3.03647i	0.372617	−	0.165900i
$336$		0			0
$337$	9.71207	−	16.8218i	0.529050	−	0.916342i	−0.470376	−	0.882466i	$-0.655882\pi$
$337$	9.71207	−	16.8218i	0.529050	−	0.916342i	0.999426	−	0.0338755i	$-0.0107850\pi$
$338$		0			0
$339$	−4.27064	−	13.1437i	−0.231949	−	0.713866i
$340$		0			0
$341$	4.49706	−	2.00222i	0.243530	−	0.108426i
$342$		0			0
$343$	1.16653	−	3.59021i	0.0629867	−	0.193853i
$344$		0			0
$345$	10.3368	+	17.9038i	0.556513	+	0.963909i
$346$		0			0
$347$	2.93642	+	27.9382i	0.157635	+	1.49980i	0.732059	+	0.681242i	$0.238560\pi$
$347$	2.93642	+	27.9382i	0.157635	+	1.49980i	−0.574423	+	0.818559i	$0.694774\pi$
$348$		0			0
$349$	−7.40721	−	8.22654i	−0.396499	−	0.440356i	0.511529	−	0.859266i	$-0.329079\pi$
$349$	−7.40721	−	8.22654i	−0.396499	−	0.440356i	−0.908028	+	0.418909i	$0.862412\pi$
$350$		0			0
$351$	5.57553	−	6.19225i	0.297600	−	0.330518i
$352$		0			0
$353$	5.25836	+	9.10774i	0.279874	+	0.484756i	0.971353	−	0.237640i	$-0.0763739\pi$
$353$	5.25836	+	9.10774i	0.279874	+	0.484756i	−0.691479	+	0.722397i	$0.743041\pi$
$354$		0			0
$355$	−10.7462			−0.570351
$356$		0			0
$357$	14.8693	−	45.7630i	0.786966	−	2.42203i
$358$		0			0
$359$	−1.23915	+	11.7897i	−0.0653997	+	0.622236i	0.911906	+	0.410400i	$0.134611\pi$
$359$	−1.23915	+	11.7897i	−0.0653997	+	0.622236i	−0.977305	+	0.211836i	$0.932056\pi$
$360$		0			0
$361$	−1.43641	+	0.305319i	−0.0756007	+	0.0160694i
$362$		0			0
$363$	13.2025	−	9.59217i	0.692951	−	0.503458i
$364$		0			0
$365$	7.56564			0.396004
$366$		0			0
$367$	8.31934			0.434266			0.217133	−	0.976142i	$-0.430329\pi$
$367$	8.31934			0.434266			0.217133	+	0.976142i	$0.430329\pi$
$368$		0			0
$369$	−7.30852	+	5.30995i	−0.380466	+	0.276425i
$370$		0			0
$371$	−11.3669	+	2.41611i	−0.590140	+	0.125438i
$372$		0			0
$373$	0.790781	−	7.52378i	0.0409451	−	0.389567i	−0.954788	−	0.297287i	$-0.903918\pi$
$373$	0.790781	−	7.52378i	0.0409451	−	0.389567i	0.995733	−	0.0922793i	$-0.0294153\pi$
$374$		0			0
$375$	−7.45890	+	22.9561i	−0.385176	+	1.18545i
$376$		0			0
$377$	−2.26300			−0.116551
$378$		0			0
$379$	−10.9280	−	18.9278i	−0.561333	−	0.972257i	−0.997381	−	0.0723332i	$-0.976955\pi$
$379$	−10.9280	−	18.9278i	−0.561333	−	0.972257i	0.436048	−	0.899923i	$-0.356378\pi$
$380$		0			0
$381$	−3.96805	+	4.40697i	−0.203289	+	0.225776i
$382$		0			0
$383$	−20.8527	−	23.1592i	−1.06552	−	1.18338i	−0.982390	−	0.186842i	$-0.940175\pi$
$383$	−20.8527	−	23.1592i	−1.06552	−	1.18338i	−0.0831307	−	0.996539i	$-0.526492\pi$
$384$		0			0
$385$	−0.988290	−	9.40296i	−0.0503679	−	0.479219i
$386$		0			0
$387$	−2.96562	−	5.13660i	−0.150751	−	0.261108i
$388$		0			0
$389$	−7.42504	+	22.8519i	−0.376465	+	1.15864i	0.566021	+	0.824391i	$0.308482\pi$
$389$	−7.42504	+	22.8519i	−0.376465	+	1.15864i	−0.942485	+	0.334248i	$0.891518\pi$
$390$		0			0
$391$	−35.7212	+	15.9041i	−1.80650	+	0.804306i
$392$		0			0
$393$	9.59314	+	29.5247i	0.483910	+	1.48932i
$394$		0			0
$395$	−5.56943	+	9.64654i	−0.280229	+	0.485370i
$396$		0			0
$397$	−1.19276	+	0.531050i	−0.0598628	+	0.0266526i	−0.436450	−	0.899729i	$-0.643764\pi$
$397$	−1.19276	+	0.531050i	−0.0598628	+	0.0266526i	0.376587	+	0.926381i	$0.377098\pi$
$398$		0			0
$399$	−32.7294	+	23.7793i	−1.63852	+	1.19045i
$400$		0			0
$401$	2.08242	+	19.8129i	0.103991	+	0.989410i	0.914747	+	0.404026i	$0.132390\pi$
$401$	2.08242	+	19.8129i	0.103991	+	0.989410i	−0.810756	+	0.585384i	$0.800944\pi$
$402$		0			0
$403$	10.9555	+	7.95965i	0.545733	+	0.396498i
$404$		0			0
$405$	−11.8614	−	5.28104i	−0.589398	−	0.262417i
$406$		0			0
$407$	−11.8377	−	8.60058i	−0.586772	−	0.426315i
$408$		0			0
$409$	−7.27309	+	8.07759i	−0.359631	+	0.399411i	−0.895624	−	0.444811i	$-0.853271\pi$
$409$	−7.27309	+	8.07759i	−0.359631	+	0.399411i	0.535993	+	0.844222i	$0.319937\pi$
$410$		0			0
$411$	−3.38955	+	32.2495i	−0.167194	+	1.59075i
$412$		0			0
$413$	−2.83837	+	4.91620i	−0.139667	+	0.241910i
$414$		0			0
$415$	6.14408	+	1.30596i	0.301601	+	0.0641073i
$416$		0			0
$417$	13.0591	+	2.77580i	0.639508	+	0.135932i
$418$		0			0
$419$	11.5266	+	35.4752i	0.563111	+	1.73308i	0.673499	+	0.739188i	$0.264791\pi$
$419$	11.5266	+	35.4752i	0.563111	+	1.73308i	−0.110388	+	0.993889i	$0.535209\pi$
$420$		0			0
$421$	10.1823	−	2.16431i	0.496254	−	0.105482i	0.0470162	−	0.998894i	$-0.485029\pi$
$421$	10.1823	−	2.16431i	0.496254	−	0.105482i	0.449238	+	0.893412i	$0.351695\pi$
$422$		0			0
$423$	6.18560	+	6.86981i	0.300754	+	0.334022i
$424$		0			0
$425$	−17.1271	−	7.62549i	−0.830788	−	0.369891i
$426$		0			0
$427$	28.6333	+	9.67687i	1.38566	+	0.468296i
$428$		0			0
$429$	−22.8658	−	10.1805i	−1.10397	−	0.491519i
$430$		0			0
$431$	12.8860	+	14.3113i	0.620695	+	0.689352i	0.968726	−	0.248131i	$-0.0798164\pi$
$431$	12.8860	+	14.3113i	0.620695	+	0.689352i	−0.348031	+	0.937483i	$0.613150\pi$
$432$		0			0
$433$	−15.3817	+	3.26947i	−0.739195	+	0.157121i	−0.562096	−	0.827072i	$-0.690005\pi$
$433$	−15.3817	+	3.26947i	−0.739195	+	0.157121i	−0.177100	+	0.984193i	$0.556671\pi$
$434$		0			0
$435$	0.364472	+	1.12173i	0.0174751	+	0.0537829i
$436$		0			0
$437$	32.1568	+	6.83514i	1.53827	+	0.326969i
$438$		0			0
$439$	−22.8168	−	4.84986i	−1.08899	−	0.231471i	−0.371772	−	0.928324i	$-0.621250\pi$
$439$	−22.8168	−	4.84986i	−1.08899	−	0.231471i	−0.717214	+	0.696853i	$0.754583\pi$
$440$		0			0
$441$	−9.32895	+	16.1582i	−0.444236	+	0.769439i
$442$		0			0
$443$	1.49567	−	14.2304i	0.0710616	−	0.676106i	−0.899773	−	0.436357i	$-0.856268\pi$
$443$	1.49567	−	14.2304i	0.0710616	−	0.676106i	0.970835	−	0.239749i	$-0.0770650\pi$
$444$		0			0
$445$	6.57214	−	7.29910i	0.311549	−	0.346011i
$446$		0			0
$447$	−42.6362	−	30.9770i	−2.01662	−	1.46516i
$448$		0			0
$449$	7.26491	+	3.23455i	0.342852	+	0.152648i	0.570938	−	0.820994i	$-0.306580\pi$
$449$	7.26491	+	3.23455i	0.342852	+	0.152648i	−0.228085	+	0.973641i	$0.573247\pi$
$450$		0			0
$451$	−6.19927	−	4.50403i	−0.291912	−	0.212087i
$452$		0			0
$453$	2.68175	+	25.5152i	0.126000	+	1.19881i
$454$		0			0
$455$	21.0419	−	15.2878i	0.986458	−	0.716703i
$456$		0			0
$457$	−29.4136	+	13.0958i	−1.37591	+	0.612595i	−0.955568	−	0.294770i	$-0.904757\pi$
$457$	−29.4136	+	13.0958i	−1.37591	+	0.612595i	−0.420343	+	0.907365i	$0.638090\pi$
$458$		0			0
$459$	4.10699	−	7.11351i	0.191698	−	0.332030i
$460$		0			0
$461$	9.73046	+	29.9473i	0.453193	+	1.39478i	0.873244	+	0.487283i	$0.162012\pi$
$461$	9.73046	+	29.9473i	0.453193	+	1.39478i	−0.420052	+	0.907500i	$0.637988\pi$
$462$		0			0
$463$	−14.0725	+	6.26547i	−0.654004	+	0.291181i	−0.706789	−	0.707425i	$-0.749857\pi$
$463$	−14.0725	+	6.26547i	−0.654004	+	0.291181i	0.0527851	+	0.998606i	$0.483190\pi$
$464$		0			0
$465$	2.18099	−	6.71241i	0.101141	−	0.311280i
$466$		0			0
$467$	−12.3112	−	21.3237i	−0.569696	−	0.986743i	−0.996596	−	0.0824437i	$-0.973728\pi$
$467$	−12.3112	−	21.3237i	−0.569696	−	0.986743i	0.426900	−	0.904299i	$-0.359606\pi$
$468$		0			0
$469$	−2.45266	−	23.3355i	−0.113253	−	1.07753i
$470$		0			0
$471$	13.3884	+	14.8693i	0.616904	+	0.685141i
$472$		0			0
$473$	3.36641	−	3.73878i	0.154788	−	0.171909i
$474$		0			0
$475$	7.88128	+	13.6508i	0.361618	+	0.626341i
$476$		0			0
$477$	7.02510			0.321657
$478$		0			0
$479$	2.73131	−	8.40611i	0.124797	−	0.384085i	−0.869067	−	0.494694i	$-0.835280\pi$
$479$	2.73131	−	8.40611i	0.124797	−	0.384085i	0.993864	+	0.110609i	$0.0352802\pi$
$480$		0			0
$481$	4.20746	−	40.0313i	0.191844	−	1.82527i
$482$		0			0
$483$	63.5575	−	13.5096i	2.89197	−	0.614706i
$484$		0			0
$485$	−4.45774	+	3.23874i	−0.202416	+	0.147064i
$486$		0			0
$487$	14.6614			0.664373			0.332187	−	0.943214i	$-0.392214\pi$
$487$	14.6614			0.664373			0.332187	+	0.943214i	$0.392214\pi$
$488$		0			0
$489$	−45.9666			−2.07868
$490$		0			0
$491$	−21.4615	+	15.5927i	−0.968545	+	0.703689i	−0.955120	−	0.296220i	$-0.904274\pi$
$491$	−21.4615	+	15.5927i	−0.968545	+	0.703689i	−0.0134259	+	0.999910i	$0.504274\pi$
$492$		0			0
$493$	−2.18207	+	0.463813i	−0.0982754	+	0.0208891i
$494$		0			0
$495$	−0.597447	+	5.68433i	−0.0268532	+	0.255492i
$496$		0			0
$497$	−10.4372	+	32.1225i	−0.468174	+	1.44089i
$498$		0			0
$499$	−15.8024			−0.707412			−0.353706	−	0.935357i	$-0.615079\pi$
$499$	−15.8024			−0.707412			−0.353706	+	0.935357i	$0.615079\pi$
$500$		0			0
$501$	−13.0504	−	22.6040i	−0.583050	−	1.00987i
$502$		0			0
$503$	23.2485	−	25.8201i	1.03660	−	1.15126i	0.0482846	−	0.998834i	$-0.484625\pi$
$503$	23.2485	−	25.8201i	1.03660	−	1.15126i	0.988315	−	0.152427i	$-0.0487088\pi$
$504$		0			0
$505$	3.82456	+	4.24760i	0.170190	+	0.189016i
$506$		0			0
$507$	−4.05728	−	38.6025i	−0.180190	−	1.71440i
$508$		0			0
$509$	−13.6496	−	23.6418i	−0.605009	−	1.04791i	−0.992050	−	0.125843i	$-0.959836\pi$
$509$	−13.6496	−	23.6418i	−0.605009	−	1.04791i	0.387042	−	0.922062i	$-0.373497\pi$
$510$		0			0
$511$	7.34810	−	22.6151i	0.325061	−	1.00043i
$512$		0			0
$513$	−6.30893	+	2.80892i	−0.278546	+	0.124017i
$514$		0			0
$515$	0.357904	+	1.10151i	0.0157711	+	0.0485385i
$516$		0			0
$517$	−3.92060	+	6.79067i	−0.172428	+	0.298653i
$518$		0			0
$519$	19.9652	−	8.88908i	0.876375	−	0.390187i
$520$		0			0
$521$	11.2871	−	8.20059i	0.494499	−	0.359274i	−0.312413	−	0.949946i	$-0.601137\pi$
$521$	11.2871	−	8.20059i	0.494499	−	0.359274i	0.806912	+	0.590672i	$0.201137\pi$
$522$		0			0
$523$	−1.81900	−	17.3067i	−0.0795395	−	0.756768i	−0.959498	−	0.281717i	$-0.909096\pi$
$523$	−1.81900	−	17.3067i	−0.0795395	−	0.756768i	0.879958	−	0.475051i	$-0.157570\pi$
$524$		0			0
$525$	25.2045	+	18.3121i	1.10001	+	0.799208i
$526$		0			0
$527$	12.1951	+	5.42959i	0.531225	+	0.236516i
$528$		0			0
$529$	−24.1104	−	17.5172i	−1.04828	−	0.761617i
$530$		0			0
$531$	2.29628	−	2.55027i	0.0996500	−	0.110672i
$532$		0			0
$533$	2.20340	−	20.9640i	0.0954399	−	0.908050i
$534$		0			0
$535$	8.93123	−	15.4693i	0.386131	−	0.668798i
$536$		0			0
$537$	3.94430	+	0.838387i	0.170209	+	0.0361791i
$538$		0			0
$539$	−15.4803	−	3.29043i	−0.666782	−	0.141729i
$540$		0			0
$541$	10.2665	+	31.5970i	0.441391	+	1.35846i	0.886394	+	0.462932i	$0.153202\pi$
$541$	10.2665	+	31.5970i	0.441391	+	1.35846i	−0.445003	+	0.895529i	$0.646798\pi$
$542$		0			0
$543$	−49.9717	+	10.6218i	−2.14449	+	0.455826i
$544$		0			0
$545$	0.327546	+	0.363777i	0.0140305	+	0.0155825i
$546$		0			0
$547$	40.2659	+	17.9275i	1.72165	+	0.766527i	0.997000	+	0.0774068i	$0.0246640\pi$
$547$	40.2659	+	17.9275i	1.72165	+	0.766527i	0.724647	+	0.689120i	$0.242003\pi$
$548$		0			0
$549$	−15.7150	−	9.32093i	−0.670700	−	0.397808i
$550$		0			0
$551$	1.71343	+	0.762867i	0.0729945	+	0.0324992i
$552$		0			0
$553$	23.4261	+	26.0173i	0.996177	+	1.10637i
$554$		0			0
$555$	−20.5204	+	4.36176i	−0.871045	+	0.185146i
$556$		0			0
$557$	12.3150	+	37.9017i	0.521803	+	1.60594i	0.770552	+	0.637377i	$0.219981\pi$
$557$	12.3150	+	37.9017i	0.521803	+	1.60594i	−0.248749	+	0.968568i	$0.580019\pi$
$558$		0			0
$559$	13.5375	+	2.87748i	0.572573	+	0.121704i
$560$		0			0
$561$	−24.1345	−	5.12994i	−1.01896	−	0.216586i
$562$		0			0
$563$	−12.7079	+	22.0107i	−0.535573	+	0.927639i	0.463563	+	0.886064i	$0.346571\pi$
$563$	−12.7079	+	22.0107i	−0.535573	+	0.927639i	−0.999135	+	0.0415751i	$0.986762\pi$
$564$		0			0
$565$	0.769736	−	7.32355i	0.0323830	−	0.308104i
$566$		0			0
$567$	−27.3064	+	30.3268i	−1.14676	+	1.27361i
$568$		0			0
$569$	11.2939	+	8.20552i	0.473466	+	0.343993i	0.798791	−	0.601609i	$-0.205473\pi$
$569$	11.2939	+	8.20552i	0.473466	+	0.343993i	−0.325324	+	0.945602i	$0.605473\pi$
$570$		0			0
$571$	20.0858	+	8.94279i	0.840566	+	0.374244i	0.781420	−	0.624005i	$-0.214496\pi$
$571$	20.0858	+	8.94279i	0.840566	+	0.374244i	0.0591457	+	0.998249i	$0.481162\pi$
$572$		0			0
$573$	−7.64602	−	5.55516i	−0.319417	−	0.232070i
$574$		0			0
$575$	−2.64633	−	25.1781i	−0.110359	−	1.05000i
$576$		0			0
$577$	26.6247	−	19.3440i	1.10840	−	0.805301i	0.125990	−	0.992032i	$-0.459789\pi$
$577$	26.6247	−	19.3440i	1.10840	−	0.805301i	0.982411	+	0.186731i	$0.0597893\pi$
$578$		0			0
$579$	−44.9293	+	20.0038i	−1.86720	+	0.831330i
$580$		0			0
$581$	9.87120	−	17.0974i	0.409526	−	0.709320i
$582$		0			0
$583$	1.84139	+	5.66722i	0.0762626	+	0.234712i
$584$		0			0
$585$	−14.3639	+	6.39520i	−0.593873	+	0.264409i
$586$		0			0
$587$	−7.85604	+	24.1784i	−0.324253	+	0.997949i	0.647523	+	0.762046i	$0.275805\pi$
$587$	−7.85604	+	24.1784i	−0.324253	+	0.997949i	−0.971777	+	0.235903i	$0.924195\pi$
$588$		0			0
$589$	−5.61171	−	9.71977i	−0.231227	−	0.400496i
$590$		0			0
$591$	0.223882	+	2.13009i	0.00920926	+	0.0876202i
$592$		0			0
$593$	13.7052	+	15.2211i	0.562804	+	0.625057i	0.955635	−	0.294553i	$-0.0951709\pi$
$593$	13.7052	+	15.2211i	0.562804	+	0.625057i	−0.392831	+	0.919611i	$0.628504\pi$
$594$		0			0
$595$	17.1560	−	19.0537i	0.703327	−	0.781124i
$596$		0			0
$597$	−32.0593	−	55.5284i	−1.31210	−	2.27263i
$598$		0			0
$599$	−24.3177			−0.993593			−0.496797	−	0.867867i	$-0.665490\pi$
$599$	−24.3177			−0.993593			−0.496797	+	0.867867i	$0.665490\pi$
$600$		0			0
$601$	−6.20409	+	19.0942i	−0.253070	+	0.778870i	0.741133	+	0.671358i	$0.234289\pi$
$601$	−6.20409	+	19.0942i	−0.253070	+	0.778870i	−0.994204	+	0.107513i	$0.965711\pi$
$602$		0			0
$603$	−1.48269	+	14.1069i	−0.0603800	+	0.574477i
$604$		0			0
$605$	8.50549	−	1.80790i	0.345797	−	0.0735015i
$606$		0			0
$607$	0.0186590	−	0.0135565i	0.000757344	−	0.000550243i	−0.587407	−	0.809292i	$-0.699851\pi$
$607$	0.0186590	−	0.0135565i	0.000757344	−	0.000550243i	0.588164	+	0.808742i	$0.299851\pi$
$608$		0			0
$609$	3.70706			0.150218
$610$		0			0
$611$	−21.5704			−0.872646
$612$		0			0
$613$	−33.7387	+	24.5126i	−1.36269	+	0.990056i	−0.364427	+	0.931232i	$0.618735\pi$
$613$	−33.7387	+	24.5126i	−1.36269	+	0.990056i	−0.998268	+	0.0588237i	$0.981265\pi$
$614$		0			0
$615$	−10.7463	+	2.28420i	−0.433334	+	0.0921080i
$616$		0			0
$617$	−4.43511	+	42.1972i	−0.178551	+	1.69880i	0.428021	+	0.903769i	$0.359211\pi$
$617$	−4.43511	+	42.1972i	−0.178551	+	1.69880i	−0.606572	+	0.795028i	$0.707456\pi$
$618$		0			0
$619$	−0.767447	+	2.36196i	−0.0308463	+	0.0949351i	−0.965294	−	0.261164i	$-0.915894\pi$
$619$	−0.767447	+	2.36196i	−0.0308463	+	0.0949351i	0.934448	+	0.356099i	$0.115894\pi$
$620$		0			0
$621$	11.0919			0.445104
$622$		0			0
$623$	−15.4352	−	26.7346i	−0.618400	−	1.07110i
$624$		0			0
$625$	3.05042	−	3.38784i	0.122017	−	0.135514i
$626$		0			0
$627$	13.8809	+	15.4163i	0.554348	+	0.615666i
$628$		0			0
$629$	−4.14762	−	39.4619i	−0.165376	−	1.57345i
$630$		0			0
$631$	8.73991	+	15.1380i	0.347930	+	0.602633i	0.985882	−	0.167444i	$-0.0535512\pi$
$631$	8.73991	+	15.1380i	0.347930	+	0.602633i	−0.637951	+	0.770077i	$0.720218\pi$
$632$		0			0
$633$	1.22855	−	3.78109i	0.0488305	−	0.150285i
$634$		0			0
$635$	−2.88664	+	1.28522i	−0.114553	+	0.0510023i
$636$		0			0
$637$	−13.4534	−	41.4053i	−0.533044	−	1.64054i
$638$		0			0
$639$	10.2091	−	17.6827i	0.403866	−	0.699517i
$640$		0			0
$641$	35.5364	−	15.8218i	1.40360	−	0.624925i	0.441415	−	0.897303i	$-0.354477\pi$
$641$	35.5364	−	15.8218i	1.40360	−	0.624925i	0.962190	+	0.272378i	$0.0878101\pi$
$642$		0			0
$643$	7.93799	−	5.76729i	0.313044	−	0.227440i	−0.420158	−	0.907451i	$-0.638025\pi$
$643$	7.93799	−	5.76729i	0.313044	−	0.227440i	0.733201	+	0.680012i	$0.238025\pi$
$644$		0			0
$645$	−0.753988	−	7.17371i	−0.0296882	−	0.282465i
$646$		0			0
$647$	29.8155	+	21.6622i	1.17217	+	0.851629i	0.991267	−	0.131873i	$-0.0420990\pi$
$647$	29.8155	+	21.6622i	1.17217	+	0.851629i	0.180900	+	0.983502i	$0.442099\pi$
$648$		0			0
$649$	2.65922	+	1.18396i	0.104384	+	0.0464746i
$650$		0			0
$651$	−17.9464	−	13.0388i	−0.703374	−	0.511031i
$652$		0			0
$653$	14.6834	−	16.3076i	0.574607	−	0.638166i	−0.383852	−	0.923395i	$-0.625403\pi$
$653$	14.6834	−	16.3076i	0.574607	−	0.638166i	0.958460	+	0.285228i	$0.0920694\pi$
$654$		0			0
$655$	−1.72906	+	16.4509i	−0.0675599	+	0.642790i
$656$		0			0
$657$	−7.18749	+	12.4491i	−0.280411	+	0.485686i
$658$		0			0
$659$	−1.97929	−	0.420712i	−0.0771023	−	0.0163886i	0.169199	−	0.985582i	$-0.445882\pi$
$659$	−1.97929	−	0.420712i	−0.0771023	−	0.0163886i	−0.246301	+	0.969193i	$0.579215\pi$
$660$		0			0
$661$	38.0775	+	8.09362i	1.48104	+	0.314805i	0.876358	−	0.481660i	$-0.159966\pi$
$661$	38.0775	+	8.09362i	1.48104	+	0.314805i	0.604685	+	0.796465i	$0.293299\pi$
$662$		0			0
$663$	−20.9745	−	64.5530i	−0.814584	−	2.50703i
$664$		0			0
$665$	−21.0854	+	4.48183i	−0.817656	+	0.173798i
$666$		0			0
$667$	−2.01571	−	2.23868i	−0.0780488	−	0.0866819i
$668$		0			0
$669$	31.1281	+	13.8591i	1.20348	+	0.535824i
$670$		0			0
$671$	3.40013	−	15.1206i	0.131261	−	0.583725i
$672$		0			0
$673$	−30.4872	−	13.5738i	−1.17519	−	0.523230i	−0.276161	−	0.961111i	$-0.589062\pi$
$673$	−30.4872	−	13.5738i	−1.17519	−	0.523230i	−0.899033	+	0.437881i	$0.855729\pi$
$674$		0			0
$675$	3.55858	+	3.95220i	0.136970	+	0.152120i
$676$		0			0
$677$	−23.8568	+	5.07092i	−0.916892	+	0.194891i	−0.642108	−	0.766615i	$-0.721940\pi$
$677$	−23.8568	+	5.07092i	−0.916892	+	0.194891i	−0.274784	+	0.961506i	$0.588606\pi$
$678$		0			0
$679$	5.35164	+	16.4706i	0.205377	+	0.632085i
$680$		0			0
$681$	−14.1904	−	3.01626i	−0.543777	−	0.115583i
$682$		0			0
$683$	12.9711	+	2.75710i	0.496326	+	0.105497i	0.449272	−	0.893395i	$-0.351683\pi$
$683$	12.9711	+	2.75710i	0.496326	+	0.105497i	0.0470542	+	0.998892i	$0.485017\pi$
$684$		0			0
$685$	−8.63923	+	14.9636i	−0.330088	+	0.571729i
$686$		0			0
$687$	0.440862	−	4.19452i	0.0168199	−	0.160031i
$688$		0			0
$689$	−10.9686	+	12.1819i	−0.417870	+	0.464092i
$690$		0			0
$691$	−6.43016	−	4.67178i	−0.244615	−	0.177723i	0.458722	−	0.888580i	$-0.348307\pi$
$691$	−6.43016	−	4.67178i	−0.244615	−	0.177723i	−0.703337	+	0.710857i	$0.748307\pi$
$692$		0			0
$693$	16.4113	+	7.30677i	0.623413	+	0.277561i
$694$		0			0
$695$	5.75524	+	4.18143i	0.218309	+	0.158611i
$696$		0			0
$697$	−2.17206	−	20.6658i	−0.0822727	−	0.782772i
$698$		0			0
$699$	21.3151	−	15.4863i	0.806211	−	0.585747i
$700$		0			0
$701$	−20.9030	+	9.30662i	−0.789495	+	0.351506i	−0.761552	−	0.648103i	$-0.775562\pi$
$701$	−20.9030	+	9.30662i	−0.789495	+	0.351506i	−0.0279432	+	0.999610i	$0.508896\pi$
$702$		0			0
$703$	−16.6804	+	28.8913i	−0.629112	+	1.08965i
$704$		0			0
$705$	3.47407	+	10.6921i	0.130841	+	0.402687i
$706$		0			0
$707$	16.4115	−	7.30686i	0.617217	−	0.274803i
$708$		0			0
$709$	12.4938	−	38.4519i	0.469214	−	1.44409i	−0.384390	−	0.923171i	$-0.625588\pi$
$709$	12.4938	−	38.4519i	0.469214	−	1.44409i	0.853604	−	0.520922i	$-0.174412\pi$
$710$		0			0
$711$	−10.5821	−	18.3288i	−0.396861	−	0.687383i
$712$		0			0
$713$	1.88427	+	17.9276i	0.0705663	+	0.671394i
$714$		0			0
$715$	−8.92407	−	9.91119i	−0.333741	−	0.370657i
$716$		0			0
$717$	9.00632	−	10.0025i	0.336347	−	0.373552i
$718$		0			0
$719$	−5.40177	−	9.35614i	−0.201452	−	0.348925i	0.747544	−	0.664212i	$-0.231233\pi$
$719$	−5.40177	−	9.35614i	−0.201452	−	0.348925i	−0.948996	+	0.315287i	$0.897899\pi$
$720$		0			0
$721$	3.64025			0.135570
$722$		0			0
$723$	−12.3880	+	38.1264i	−0.460716	+	1.41794i
$724$		0			0
$725$	0.150977	−	1.43645i	0.00560715	−	0.0533484i
$726$		0			0
$727$	−36.8424	+	7.83110i	−1.36641	+	0.290440i	−0.831995	−	0.554782i	$-0.812801\pi$
$727$	−36.8424	+	7.83110i	−1.36641	+	0.290440i	−0.534415	+	0.845222i	$0.679468\pi$
$728$		0			0
$729$	11.3977	−	8.28095i	0.422139	−	0.306702i
$730$		0			0
$731$	13.6430			0.504606
$732$		0			0
$733$	2.42808			0.0896831			0.0448416	−	0.998994i	$-0.485722\pi$
$733$	2.42808			0.0896831			0.0448416	+	0.998994i	$0.485722\pi$
$734$		0			0
$735$	−18.3571	+	13.3372i	−0.677113	+	0.491951i
$736$		0			0
$737$	−11.7688	+	2.50154i	−0.433510	+	0.0921453i
$738$		0			0
$739$	0.144334	−	1.37325i	0.00530942	−	0.0505158i	−0.991546	−	0.129753i	$-0.958582\pi$
$739$	0.144334	−	1.37325i	0.00530942	−	0.0505158i	0.996856	+	0.0792369i	$0.0252483\pi$
$740$		0			0
$741$	−17.6346	+	54.2736i	−0.647822	+	1.99379i
$742$		0			0
$743$	33.5407			1.23049			0.615245	−	0.788336i	$-0.289057\pi$
$743$	33.5407			1.23049			0.615245	+	0.788336i	$0.289057\pi$
$744$		0			0
$745$	−14.0407	−	24.3192i	−0.514410	−	0.890985i
$746$		0			0
$747$	−7.98593	+	8.86927i	−0.292190	+	0.324510i
$748$		0			0
$749$	−37.5664	−	41.7217i	−1.37265	−	1.52448i
$750$		0			0
$751$	−2.83605	−	26.9833i	−0.103489	−	0.984633i	−0.915862	−	0.401494i	$-0.868491\pi$
$751$	−2.83605	−	26.9833i	−0.103489	−	0.984633i	0.812373	−	0.583139i	$-0.198176\pi$
$752$		0			0
$753$	5.86026	+	10.1503i	0.213560	+	0.369896i
$754$		0			0
$755$	−4.22439	+	13.0013i	−0.153741	+	0.473167i
$756$		0			0
$757$	3.14580	−	1.40060i	0.114336	−	0.0509057i	−0.348771	−	0.937208i	$-0.613401\pi$
$757$	3.14580	−	1.40060i	0.114336	−	0.0509057i	0.463107	+	0.886302i	$0.346734\pi$
$758$		0			0
$759$	−10.2960	−	31.6880i	−0.373723	−	1.15020i
$760$		0			0
$761$	13.2840	−	23.0085i	0.481543	−	0.834057i	−0.518233	−	0.855240i	$-0.673410\pi$
$761$	13.2840	−	23.0085i	0.481543	−	0.834057i	0.999776	+	0.0211827i	$0.00674317\pi$
$762$		0			0
$763$	1.40553	−	0.625781i	0.0508835	−	0.0226548i
$764$		0			0
$765$	−12.5394	+	9.11042i	−0.453363	+	0.329388i
$766$		0			0
$767$	0.837019	+	7.96371i	0.0302230	+	0.287553i
$768$		0			0
$769$	11.1719	+	8.11685i	0.402869	+	0.292701i	0.770708	−	0.637188i	$-0.219903\pi$
$769$	11.1719	+	8.11685i	0.402869	+	0.292701i	−0.367840	+	0.929889i	$0.619903\pi$
$770$		0			0
$771$	45.8009	+	20.3919i	1.64948	+	0.734395i
$772$		0			0
$773$	10.7009	+	7.77468i	0.384885	+	0.279636i	0.763356	−	0.645978i	$-0.223550\pi$
$773$	10.7009	+	7.77468i	0.384885	+	0.279636i	−0.378471	+	0.925613i	$0.623550\pi$
$774$		0			0
$775$	−5.78332	+	6.42302i	−0.207743	+	0.230722i
$776$		0			0
$777$	−6.89230	+	65.5759i	−0.247260	+	2.35252i
$778$		0			0
$779$	−8.73533	+	15.1300i	−0.312976	+	0.542090i
$780$		0			0
$781$	16.9408	+	3.60087i	0.606189	+	0.128849i
$782$		0			0
$783$	0.618984	+	0.131569i	0.0221207	+	0.00470190i
$784$		0			0
$785$	3.29455	+	10.1396i	0.117588	+	0.361897i
$786$		0			0
$787$	−13.7088	+	2.91390i	−0.488666	+	0.103869i	−0.445654	−	0.895205i	$-0.647029\pi$
$787$	−13.7088	+	2.91390i	−0.488666	+	0.103869i	−0.0430124	+	0.999075i	$0.513695\pi$
$788$		0			0
$789$	0.566520	+	0.629184i	0.0201686	+	0.0223995i
$790$		0			0
$791$	−21.1439	−	9.41386i	−0.751790	−	0.334718i
$792$		0			0
$793$	40.6995	−	12.6974i	1.44528	−	0.450898i
$794$		0			0
$795$	7.80490	+	3.47496i	0.276811	+	0.123244i
$796$		0			0
$797$	−6.51823	−	7.23922i	−0.230887	−	0.256426i	0.616557	−	0.787310i	$-0.288527\pi$
$797$	−6.51823	−	7.23922i	−0.230887	−	0.256426i	−0.847445	+	0.530884i	$0.821860\pi$
$798$		0			0
$799$	−20.7989	+	4.42095i	−0.735814	+	0.156402i
$800$		0			0
$801$	5.76687	+	17.7486i	0.203762	+	0.627116i
$802$		0			0
$803$	−11.9268	−	2.53511i	−0.420887	−	0.0894622i
$804$		0			0
$805$	33.8660	+	7.19843i	1.19362	+	0.253711i
$806$		0			0
$807$	23.7811	−	41.1901i	0.837136	−	1.44996i
$808$		0			0
$809$	−3.66154	+	34.8372i	−0.128733	+	1.22481i	0.719237	+	0.694765i	$0.244492\pi$
$809$	−3.66154	+	34.8372i	−0.128733	+	1.22481i	−0.847969	+	0.530045i	$0.822175\pi$
$810$		0			0
$811$	11.7247	−	13.0216i	0.411711	−	0.457251i	−0.501247	−	0.865304i	$-0.667125\pi$
$811$	11.7247	−	13.0216i	0.411711	−	0.457251i	0.912958	+	0.408053i	$0.133792\pi$
$812$		0			0
$813$	−60.5708	−	44.0072i	−2.12431	−	1.54340i
$814$		0			0
$815$	−22.3753	−	9.96213i	−0.783773	−	0.348958i
$816$		0			0
$817$	−9.27985	−	6.74220i	−0.324661	−	0.235880i
$818$		0			0
$819$	5.16563	+	49.1477i	0.180502	+	1.71736i
$820$		0			0
$821$	10.2058	−	7.41496i	0.356185	−	0.258784i	−0.395274	−	0.918563i	$-0.629350\pi$
$821$	10.2058	−	7.41496i	0.356185	−	0.258784i	0.751459	+	0.659780i	$0.229350\pi$
$822$		0			0
$823$	37.3573	−	16.6325i	1.30219	−	0.579774i	0.365790	−	0.930698i	$-0.380799\pi$
$823$	37.3573	−	16.6325i	1.30219	−	0.579774i	0.936404	+	0.350924i	$0.114132\pi$
$824$		0			0
$825$	7.98760	−	13.8349i	0.278093	−	0.481670i
$826$		0			0
$827$	3.64368	+	11.2141i	0.126703	+	0.389952i	0.994208	−	0.107477i	$-0.0342773\pi$
$827$	3.64368	+	11.2141i	0.126703	+	0.389952i	−0.867504	+	0.497429i	$0.834277\pi$
$828$		0			0
$829$	12.6123	−	5.61538i	0.438045	−	0.195030i	−0.175852	−	0.984417i	$-0.556268\pi$
$829$	12.6123	−	5.61538i	0.438045	−	0.195030i	0.613896	+	0.789387i	$0.289601\pi$
$830$		0			0
$831$	3.00924	−	9.26150i	0.104389	−	0.321278i
$832$		0			0
$833$	−21.4585	−	37.1671i	−0.743491	−	1.28776i
$834$		0			0
$835$	−1.45374	−	13.8314i	−0.0503087	−	0.478655i
$836$		0			0
$837$	−2.53382	−	2.81409i	−0.0875816	−	0.0972692i
$838$		0			0
$839$	−7.79560	+	8.65789i	−0.269134	+	0.298903i	−0.862529	−	0.506008i	$-0.831121\pi$
$839$	−7.79560	+	8.65789i	−0.269134	+	0.298903i	0.593395	+	0.804912i	$0.297787\pi$
$840$		0			0
$841$	14.4141	+	24.9659i	0.497037	+	0.860893i
$842$		0			0
$843$	8.50364			0.292881
$844$		0			0
$845$	6.39117	−	19.6700i	0.219863	−	0.676668i
$846$		0			0
$847$	2.85678	−	27.1805i	0.0981601	−	0.933931i
$848$		0			0
$849$	44.6286	−	9.48610i	1.53165	−	0.325562i
$850$		0			0
$851$	43.3487	−	31.4947i	1.48597	−	1.07962i
$852$		0			0
$853$	−18.2376			−0.624444			−0.312222	−	0.950009i	$-0.601073\pi$
$853$	−18.2376			−0.624444			−0.312222	+	0.950009i	$0.601073\pi$
$854$		0			0
$855$	13.0314			0.445665
$856$		0			0
$857$	40.7310	−	29.5928i	1.39134	−	1.01087i	0.395629	−	0.918411i	$-0.370527\pi$
$857$	40.7310	−	29.5928i	1.39134	−	1.01087i	0.995716	−	0.0924606i	$-0.0294732\pi$
$858$		0			0
$859$	49.8985	−	10.6063i	1.70252	−	0.361881i	0.748848	−	0.662741i	$-0.230607\pi$
$859$	49.8985	−	10.6063i	1.70252	−	0.361881i	0.953668	+	0.300860i	$0.0972738\pi$
$860$		0			0
$861$	−3.60942	+	34.3414i	−0.123009	+	1.17035i
$862$		0			0
$863$	−9.13512	+	28.1150i	−0.310963	+	0.957046i	0.666421	+	0.745575i	$0.267825\pi$
$863$	−9.13512	+	28.1150i	−0.310963	+	0.957046i	−0.977384	+	0.211470i	$0.932175\pi$
$864$		0			0
$865$	11.6450			0.395943
$866$		0			0
$867$	−13.8137	−	23.9261i	−0.469139	−	0.812572i
$868$		0			0
$869$	12.0123	−	13.3410i	0.407488	−	0.452561i
$870$		0			0
$871$	−22.1470	−	24.5968i	−0.750424	−	0.833430i
$872$		0			0
$873$	−1.09434	−	10.4120i	−0.0370379	−	0.352392i
$874$		0			0
$875$	20.2119	+	35.0080i	0.683286	+	1.18349i
$876$		0			0
$877$	−1.77511	+	5.46322i	−0.0599411	+	0.184480i	−0.976543	−	0.215320i	$-0.930920\pi$
$877$	−1.77511	+	5.46322i	−0.0599411	+	0.184480i	0.916602	+	0.399800i	$0.130920\pi$
$878$		0			0
$879$	3.60990	−	1.60723i	0.121759	−	0.0542105i
$880$		0			0
$881$	−10.8991	−	33.5439i	−0.367199	−	1.13012i	−0.948593	−	0.316500i	$-0.897492\pi$
$881$	−10.8991	−	33.5439i	−0.367199	−	1.13012i	0.581393	−	0.813623i	$-0.302508\pi$
$882$		0			0
$883$	−20.2089	+	35.0028i	−0.680083	+	1.17794i	0.294872	+	0.955537i	$0.404723\pi$
$883$	−20.2089	+	35.0028i	−0.680083	+	1.17794i	−0.974955	+	0.222401i	$0.928610\pi$
$884$		0			0
$885$	3.81266	−	1.69751i	0.128161	−	0.0570610i
$886$		0			0
$887$	18.8828	−	13.7192i	0.634023	−	0.460644i	−0.223769	−	0.974642i	$-0.571836\pi$
$887$	18.8828	−	13.7192i	0.634023	−	0.460644i	0.857792	+	0.513998i	$0.171836\pi$
$888$		0			0
$889$	1.03811	+	9.87699i	0.0348172	+	0.331264i
$890$		0			0
$891$	16.9292	+	12.2998i	0.567150	+	0.412059i
$892$		0			0
$893$	16.3320	+	7.27147i	0.546529	+	0.243330i
$894$		0			0
$895$	1.73828	+	1.26293i	0.0581043	+	0.0422153i
$896$		0			0
$897$	61.3303	−	68.1142i	2.04776	−	2.27427i
$898$		0			0
$899$	−0.107500	+	1.02280i	−0.00358533	+	0.0341122i
$900$		0			0
$901$	−8.07957	+	13.9942i	−0.269170	+	0.466216i
$902$		0			0
$903$	−22.1759	−	4.71363i	−0.737968	−	0.156860i
$904$		0			0
$905$	−26.6269	−	5.65973i	−0.885109	−	0.188136i
$906$		0			0
$907$	−0.499891	−	1.53850i	−0.0165986	−	0.0510852i	0.942414	−	0.334448i	$-0.108550\pi$
$907$	−0.499891	−	1.53850i	−0.0165986	−	0.0510852i	−0.959013	+	0.283363i	$0.908550\pi$
$908$		0			0
$909$	−10.6227	+	2.25793i	−0.352334	+	0.0748909i
$910$		0			0
$911$	24.3368	+	27.0288i	0.806314	+	0.895503i	0.996270	−	0.0862900i	$-0.0275012\pi$
$911$	24.3368	+	27.0288i	0.806314	+	0.895503i	−0.189956	+	0.981793i	$0.560834\pi$
$912$		0			0
$913$	−9.24817	−	4.11755i	−0.306070	−	0.136271i
$914$		0			0
$915$	−12.8488	−	18.1290i	−0.424768	−	0.599326i
$916$		0			0
$917$	47.4955	+	21.1464i	1.56844	+	0.698315i
$918$		0			0
$919$	−11.4978	−	12.7696i	−0.379277	−	0.421230i	0.523037	−	0.852310i	$-0.324799\pi$
$919$	−11.4978	−	12.7696i	−0.379277	−	0.421230i	−0.902313	+	0.431081i	$0.858132\pi$
$920$		0			0
$921$	39.5543	−	8.40753i	1.30336	−	0.277037i
$922$		0			0
$923$	14.7227	+	45.3119i	0.484604	+	1.49146i
$924$		0			0
$925$	25.1293	+	5.34140i	0.826247	+	0.175624i
$926$		0			0
$927$	−2.15253	−	0.457535i	−0.0706985	−	0.0150274i
$928$		0			0
$929$	−11.5819	+	20.0604i	−0.379990	+	0.658162i	−0.991060	−	0.133415i	$-0.957406\pi$
$929$	−11.5819	+	20.0604i	−0.379990	+	0.658162i	0.611071	+	0.791576i	$0.290739\pi$
$930$		0			0
$931$	−3.77168	+	35.8852i	−0.123612	+	1.17609i
$932$		0			0
$933$	−22.7945	+	25.3158i	−0.746257	+	0.828802i
$934$		0			0
$935$	−10.6362	−	7.72768i	−0.347842	−	0.252722i
$936$		0			0
$937$	2.44613	+	1.08909i	0.0799116	+	0.0355789i	0.446303	−	0.894882i	$-0.352740\pi$
$937$	2.44613	+	1.08909i	0.0799116	+	0.0355789i	−0.366392	+	0.930461i	$0.619407\pi$
$938$		0			0
$939$	24.1279	+	17.5299i	0.787384	+	0.572068i
$940$		0			0
$941$	5.08037	+	48.3365i	0.165615	+	1.57572i	0.689723	+	0.724073i	$0.257732\pi$
$941$	5.08037	+	48.3365i	0.165615	+	1.57572i	−0.524108	+	0.851652i	$0.675601\pi$
$942$		0			0
$943$	22.7012	−	16.4934i	0.739254	−	0.537099i
$944$		0			0
$945$	−6.64425	+	2.95821i	−0.216138	+	0.0962307i
$946$		0			0
$947$	27.8693	−	48.2710i	0.905630	−	1.56860i	0.0855598	−	0.996333i	$-0.472732\pi$
$947$	27.8693	−	48.2710i	0.905630	−	1.56860i	0.820070	−	0.572263i	$-0.193935\pi$
$948$		0			0
$949$	−10.3652	−	31.9008i	−0.336468	−	1.03554i
$950$		0			0
$951$	−30.9727	+	13.7899i	−1.00436	+	0.447169i
$952$		0			0
$953$	−8.35678	+	25.7195i	−0.270703	+	0.833137i	0.719622	+	0.694366i	$0.244315\pi$
$953$	−8.35678	+	25.7195i	−0.270703	+	0.833137i	−0.990325	+	0.138771i	$0.955685\pi$
$954$		0			0
$955$	−2.51794	−	4.36119i	−0.0814785	−	0.141125i
$956$		0			0
$957$	−0.198696	−	1.89047i	−0.00642294	−	0.0611102i
$958$		0			0
$959$	36.3382	+	40.3576i	1.17342	+	1.30322i
$960$		0			0
$961$	−16.6252	+	18.4641i	−0.536295	+	0.595616i
$962$		0			0
$963$	16.9697	+	29.3923i	0.546840	+	0.947154i
$964$		0			0
$965$	−26.2057			−0.843593
$966$		0			0
$967$	6.20814	−	19.1067i	0.199640	−	0.614430i	−0.800251	−	0.599666i	$-0.795300\pi$
$967$	6.20814	−	19.1067i	0.199640	−	0.614430i	0.999891	−	0.0147641i	$-0.00469974\pi$
$968$		0			0
$969$	−5.88024	+	55.9467i	−0.188901	+	1.79727i
$970$		0			0
$971$	20.4636	−	4.34968i	0.656710	−	0.139588i	0.132508	−	0.991182i	$-0.457697\pi$
$971$	20.4636	−	4.34968i	0.656710	−	0.139588i	0.524202	+	0.851594i	$0.324364\pi$
$972$		0			0
$973$	18.0889	−	13.1423i	0.579902	−	0.421323i
$974$		0			0
$975$	43.9463			1.40741
$976$		0			0
$977$	60.1275			1.92365			0.961824	−	0.273669i	$-0.0882372\pi$
$977$	60.1275			1.92365			0.961824	+	0.273669i	$0.0882372\pi$
$978$		0			0
$979$	−12.8064	+	9.30439i	−0.409294	+	0.297369i
$980$		0			0
$981$	−0.909762	+	0.193376i	−0.0290465	+	0.00617402i
$982$		0			0
$983$	−3.48984	+	33.2036i	−0.111309	+	1.05903i	0.786182	+	0.617996i	$0.212055\pi$
$983$	−3.48984	+	33.2036i	−0.111309	+	1.05903i	−0.897490	+	0.441035i	$0.854612\pi$
$984$		0			0
$985$	−0.352665	+	1.08539i	−0.0112369	+	0.0345835i
$986$		0			0
$987$	35.3348			1.12472
$988$		0			0
$989$	9.21161	+	15.9550i	0.292912	+	0.507339i
$990$		0			0
$991$	20.1793	−	22.4114i	0.641018	−	0.711922i	−0.331838	−	0.943337i	$-0.607669\pi$
$991$	20.1793	−	22.4114i	0.641018	−	0.711922i	0.972855	+	0.231414i	$0.0743353\pi$
$992$		0			0
$993$	−1.73283	−	1.92450i	−0.0549897	−	0.0610723i
$994$		0			0
$995$	−3.57121	−	33.9778i	−0.113215	−	1.07717i
$996$		0			0
$997$	18.2499	+	31.6097i	0.577979	+	1.00109i	0.995711	+	0.0925188i	$0.0294918\pi$
$997$	18.2499	+	31.6097i	0.577979	+	1.00109i	−0.417732	+	0.908570i	$0.637175\pi$
$998$		0			0
$999$	−3.47822	+	10.7049i	−0.110046	+	0.338687i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	976.2.bw.c.561.1		32
4.3	odd	2		61.2.i.a.12.2	✓	32
12.11	even	2		549.2.bl.b.73.3		32
61.56	even	15	inner	976.2.bw.c.849.1		32
244.19	odd	30		3721.2.a.l.1.13		16
244.103	odd	30		3721.2.a.j.1.4		16
244.239	odd	30		61.2.i.a.56.2	yes	32
732.239	even	30		549.2.bl.b.361.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.i.a.12.2	✓	32	4.3	odd	2
61.2.i.a.56.2	yes	32	244.239	odd	30
549.2.bl.b.73.3		32	12.11	even	2
549.2.bl.b.361.3		32	732.239	even	30
976.2.bw.c.561.1		32	1.1	even	1	trivial
976.2.bw.c.849.1		32	61.56	even	15	inner
3721.2.a.j.1.4		16	244.103	odd	30
3721.2.a.l.1.13		16	244.19	odd	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 976 = 2^{4} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	976.bw (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.86941 + 1.35820i) q^{3} +(-1.20434 + 0.255990i) q^{5} +(-0.404506 + 3.84862i) q^{7} +(0.722916 - 2.22491i) q^{9} +O(q^{10})\)	\(q+(-1.86941 + 1.35820i) q^{3} +(-1.20434 + 0.255990i) q^{5} +(-0.404506 + 3.84862i) q^{7} +(0.722916 - 2.22491i) q^{9} +1.98434 q^{11} +(2.72937 + 4.72741i) q^{13} +(1.90371 - 2.11428i) q^{15} +(3.60066 + 3.99894i) q^{17} +(-0.472909 - 4.49943i) q^{19} +(-4.47102 - 7.74404i) q^{21} +(-2.24547 + 6.91085i) q^{23} +(-3.18283 + 1.41709i) q^{25} +(-0.471699 - 1.45174i) q^{27} +(-0.207283 + 0.359024i) q^{29} +(2.26627 - 1.00901i) q^{31} +(-3.70954 + 2.69514i) q^{33} +(-0.498045 - 4.73858i) q^{35} +(-5.96555 - 4.33423i) q^{37} +(-11.5231 - 5.13041i) q^{39} +(-3.12409 - 2.26979i) q^{41} +(1.69649 - 1.88414i) q^{43} +(-0.301081 + 2.86459i) q^{45} +(-1.97577 + 3.42213i) q^{47} +(-7.80121 - 1.65820i) q^{49} +(-12.1625 - 2.58521i) q^{51} +(0.927961 + 2.85597i) q^{53} +(-2.38981 + 0.507970i) q^{55} +(6.99520 + 7.76896i) q^{57} +(1.34010 + 0.596653i) q^{59} +(1.71348 - 7.61997i) q^{61} +(8.27039 + 3.68221i) q^{63} +(-4.49725 - 4.99470i) q^{65} +(-5.93084 + 1.26064i) q^{67} +(-5.18865 - 15.9690i) q^{69} +(8.53723 + 1.81465i) q^{71} +(-6.01044 - 1.27756i) q^{73} +(4.02532 - 6.97205i) q^{75} +(-0.802678 + 7.63697i) q^{77} +(6.05353 - 6.72312i) q^{79} +(8.53141 + 6.19843i) q^{81} +(-4.66057 - 2.07502i) q^{83} +(-5.36009 - 3.89433i) q^{85} +(-0.100132 - 0.952694i) q^{87} +(-6.45373 + 4.68891i) q^{89} +(-19.2980 + 8.59204i) q^{91} +(-2.86615 + 4.96432i) q^{93} +(1.72135 + 5.29776i) q^{95} +(4.08831 - 1.82023i) q^{97} +(1.43451 - 4.41497i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} + 2 q^{5} - q^{7} - 2 q^{9}+O(q^{10}) \) 32 * q + 4 * q^3 + 2 * q^5 - q^7 - 2 * q^9	\( 32 q + 4 q^{3} + 2 q^{5} - q^{7} - 2 q^{9} + 18 q^{11} - 2 q^{15} - 24 q^{17} - 9 q^{19} - 3 q^{21} + 2 q^{23} + 28 q^{25} - 35 q^{27} - 4 q^{29} + 11 q^{31} - 35 q^{33} + 58 q^{35} - 14 q^{37} - 17 q^{39} + 11 q^{41} - 40 q^{43} + 12 q^{45} - 40 q^{47} + q^{49} + 9 q^{51} + 17 q^{53} + 60 q^{55} - 38 q^{57} + 11 q^{59} - 55 q^{61} + 58 q^{63} + 59 q^{65} + 13 q^{67} - 32 q^{69} - 63 q^{71} - 46 q^{73} - q^{75} - 31 q^{77} + 49 q^{79} + 48 q^{81} - 39 q^{83} + 21 q^{85} - 17 q^{87} + 32 q^{89} - 70 q^{91} + 67 q^{93} - 47 q^{95} + 37 q^{97} + 31 q^{99}+O(q^{100}) \) 32 * q + 4 * q^3 + 2 * q^5 - q^7 - 2 * q^9 + 18 * q^11 - 2 * q^15 - 24 * q^17 - 9 * q^19 - 3 * q^21 + 2 * q^23 + 28 * q^25 - 35 * q^27 - 4 * q^29 + 11 * q^31 - 35 * q^33 + 58 * q^35 - 14 * q^37 - 17 * q^39 + 11 * q^41 - 40 * q^43 + 12 * q^45 - 40 * q^47 + q^49 + 9 * q^51 + 17 * q^53 + 60 * q^55 - 38 * q^57 + 11 * q^59 - 55 * q^61 + 58 * q^63 + 59 * q^65 + 13 * q^67 - 32 * q^69 - 63 * q^71 - 46 * q^73 - q^75 - 31 * q^77 + 49 * q^79 + 48 * q^81 - 39 * q^83 + 21 * q^85 - 17 * q^87 + 32 * q^89 - 70 * q^91 + 67 * q^93 - 47 * q^95 + 37 * q^97 + 31 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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