LMFDB - Embedded newform 600.2.w.k.293.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,2,Mod(293,600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("600.293"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [64,0,0,0,0,12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			293.3
Character	$\chi$	$=$	600.293
Dual form			600.2.w.k.557.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30189 - 0.552337i) q^{2} +(-1.65680 + 0.504984i) q^{3} +(1.38985 + 1.43817i) q^{4} +(2.43590 + 0.257678i) q^{6} +(-2.83719 + 2.83719i) q^{7} +(-1.01508 - 2.64000i) q^{8} +(2.48998 - 1.67332i) q^{9} -4.74897 q^{11} +(-3.02895 - 1.68091i) q^{12} +(0.867956 - 0.867956i) q^{13} +(5.26080 - 2.12663i) q^{14} +(-0.136650 + 3.99767i) q^{16} +(1.73117 + 1.73117i) q^{17} +(-4.16592 + 0.803169i) q^{18} -3.35370 q^{19} +(3.26792 - 6.13340i) q^{21} +(6.18265 + 2.62303i) q^{22} +(4.82662 - 4.82662i) q^{23} +(3.01494 + 3.86136i) q^{24} +(-1.60939 + 0.650581i) q^{26} +(-3.28041 + 4.02976i) q^{27} +(-8.02362 - 0.137093i) q^{28} -0.936190i q^{29} +5.49627 q^{31} +(2.38596 - 5.12905i) q^{32} +(7.86810 - 2.39815i) q^{33} +(-1.29761 - 3.20999i) q^{34} +(5.86720 + 1.25535i) q^{36} +(-0.749350 - 0.749350i) q^{37} +(4.36616 + 1.85238i) q^{38} +(-0.999726 + 1.87633i) q^{39} +2.24103i q^{41} +(-7.64219 + 6.18003i) q^{42} +(8.75448 - 8.75448i) q^{43} +(-6.60034 - 6.82981i) q^{44} +(-8.94967 + 3.61782i) q^{46} +(-6.71219 - 6.71219i) q^{47} +(-1.79236 - 6.69234i) q^{48} -9.09930i q^{49} +(-3.74242 - 1.99399i) q^{51} +(2.45459 + 0.0419396i) q^{52} +(-8.46720 - 8.46720i) q^{53} +(6.49652 - 3.43442i) q^{54} +(10.3702 + 4.61022i) q^{56} +(5.55642 - 1.69357i) q^{57} +(-0.517093 + 1.21882i) q^{58} -6.53585i q^{59} -5.10959i q^{61} +(-7.15555 - 3.03579i) q^{62} +(-2.31703 + 11.8121i) q^{63} +(-5.93923 + 5.35962i) q^{64} +(-11.5680 - 1.22370i) q^{66} +(4.85678 + 4.85678i) q^{67} +(-0.0836501 + 4.89577i) q^{68} +(-5.55939 + 10.4341i) q^{69} -8.34435i q^{71} +(-6.94509 - 4.87501i) q^{72} +(-1.57561 - 1.57561i) q^{73} +(0.561679 + 1.38947i) q^{74} +(-4.66114 - 4.82319i) q^{76} +(13.4737 - 13.4737i) q^{77} +(2.33791 - 1.89060i) q^{78} -7.75267i q^{79} +(3.40002 - 8.33306i) q^{81} +(1.23780 - 2.91758i) q^{82} +(9.15657 + 9.15657i) q^{83} +(13.3628 - 3.82466i) q^{84} +(-16.2328 + 6.56196i) q^{86} +(0.472761 + 1.55108i) q^{87} +(4.82057 + 12.5373i) q^{88} -4.97996 q^{89} +4.92511i q^{91} +(13.6498 + 0.233222i) q^{92} +(-9.10622 + 2.77553i) q^{93} +(5.03116 + 12.4459i) q^{94} +(-1.36297 + 9.70270i) q^{96} +(1.42918 - 1.42918i) q^{97} +(-5.02588 + 11.8463i) q^{98} +(-11.8248 + 7.94653i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 12 q^{6} - 40 q^{16} + 32 q^{31} - 84 q^{36} - 128 q^{46} - 180 q^{66} + 168 q^{76} + 48 q^{81} + 228 q^{96}+O(q^{100}) $ 64 * q + 12 * q^6 - 40 * q^16 + 32 * q^31 - 84 * q^36 - 128 * q^46 - 180 * q^66 + 168 * q^76 + 48 * q^81 + 228 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.30189	−	0.552337i	−0.920577	−	0.390561i
$2$	−1.30189	−	0.552337i	−0.920577	−	0.390561i
$3$	−1.65680	+	0.504984i	−0.956555	+	0.291553i
$3$	−1.65680	+	0.504984i	−0.956555	+	0.291553i
$4$	1.38985	+	1.43817i	0.694924	+	0.719084i
$5$		0			0
$5$		0			0
$6$	2.43590	+	0.257678i	0.994451	+	0.105197i
$7$	−2.83719	+	2.83719i	−1.07236	+	1.07236i	−0.0751879	+	0.997169i	$0.523956\pi$
$7$	−2.83719	+	2.83719i	−1.07236	+	1.07236i	−0.997169	+	0.0751879i	$0.976044\pi$
$8$	−1.01508	−	2.64000i	−0.358884	−	0.933382i
$9$	2.48998	−	1.67332i	0.829994	−	0.557772i
$10$		0			0
$11$	−4.74897			−1.43187			−0.715934	−	0.698168i	$-0.753999\pi$
$11$	−4.74897			−1.43187			−0.715934	+	0.698168i	$0.753999\pi$
$12$	−3.02895	−	1.68091i	−0.874383	−	0.485236i
$13$	0.867956	−	0.867956i	0.240728	−	0.240728i	−0.576424	−	0.817151i	$-0.695552\pi$
$13$	0.867956	−	0.867956i	0.240728	−	0.240728i	0.817151	+	0.576424i	$0.195552\pi$
$14$	5.26080	−	2.12663i	1.40601	−	0.568366i
$15$		0			0
$16$	−0.136650	+	3.99767i	−0.0341624	+	0.999416i
$17$	1.73117	+	1.73117i	0.419870	+	0.419870i	0.885159	−	0.465289i	$-0.154050\pi$
$17$	1.73117	+	1.73117i	0.419870	+	0.419870i	−0.465289	+	0.885159i	$0.654050\pi$
$18$	−4.16592	+	0.803169i	−0.981918	+	0.189309i
$19$	−3.35370			−0.769392			−0.384696	−	0.923043i	$-0.625694\pi$
$19$	−3.35370			−0.769392			−0.384696	+	0.923043i	$0.625694\pi$
$20$		0			0
$21$	3.26792	−	6.13340i	0.713120	−	1.33842i
$22$	6.18265	+	2.62303i	1.31814	+	0.559232i
$23$	4.82662	−	4.82662i	1.00642	−	1.00642i	0.00644154	−	0.999979i	$-0.497950\pi$
$23$	4.82662	−	4.82662i	1.00642	−	1.00642i	0.999979	−	0.00644154i	$-0.00205042\pi$
$24$	3.01494	+	3.86136i	0.615423	+	0.788197i
$25$		0			0
$26$	−1.60939	+	0.650581i	−0.315627	+	0.127589i
$27$	−3.28041	+	4.02976i	−0.631314	+	0.775527i
$28$	−8.02362	−	0.137093i	−1.51632	−	0.0259081i
$29$		−	0.936190i		−	0.173846i	−0.996215	−	0.0869231i	$-0.972297\pi$
$29$		−	0.936190i		−	0.173846i	0.996215	−	0.0869231i	$-0.0277034\pi$
$30$		0			0
$31$	5.49627			0.987159			0.493579	−	0.869701i	$-0.335688\pi$
$31$	5.49627			0.987159			0.493579	+	0.869701i	$0.335688\pi$
$32$	2.38596	−	5.12905i	0.421783	−	0.906697i
$33$	7.86810	−	2.39815i	1.36966	−	0.417465i
$34$	−1.29761	−	3.20999i	−0.222538	−	0.550508i
$35$		0			0
$36$	5.86720	+	1.25535i	0.977867	+	0.209226i
$37$	−0.749350	−	0.749350i	−0.123192	−	0.123192i	0.642823	−	0.766015i	$-0.277763\pi$
$37$	−0.749350	−	0.749350i	−0.123192	−	0.123192i	−0.766015	+	0.642823i	$0.777763\pi$
$38$	4.36616	+	1.85238i	0.708285	+	0.300495i
$39$	−0.999726	+	1.87633i	−0.160084	+	0.300454i
$40$		0			0
$41$			2.24103i			0.349990i	0.984569	+	0.174995i	$0.0559909\pi$
$41$			2.24103i			0.349990i	−0.984569	+	0.174995i	$0.944009\pi$
$42$	−7.64219	+	6.18003i	−1.17922	+	0.953599i
$43$	8.75448	−	8.75448i	1.33505	−	1.33505i	0.434256	−	0.900789i	$-0.357011\pi$
$43$	8.75448	−	8.75448i	1.33505	−	1.33505i	0.900789	−	0.434256i	$-0.142989\pi$
$44$	−6.60034	−	6.82981i	−0.995039	−	1.02963i
$45$		0			0
$46$	−8.94967	+	3.61782i	−1.31956	+	0.533419i
$47$	−6.71219	−	6.71219i	−0.979073	−	0.979073i	0.0207122	−	0.999785i	$-0.493407\pi$
$47$	−6.71219	−	6.71219i	−0.979073	−	0.979073i	−0.999785	+	0.0207122i	$0.993407\pi$
$48$	−1.79236	−	6.69234i	−0.258704	−	0.965957i
$49$		−	9.09930i		−	1.29990i
$50$		0			0
$51$	−3.74242	−	1.99399i	−0.524043	−	0.279214i
$52$	2.45459	+	0.0419396i	0.340391	+	0.00581598i
$53$	−8.46720	−	8.46720i	−1.16306	−	1.16306i	−0.983802	−	0.179258i	$-0.942630\pi$
$53$	−8.46720	−	8.46720i	−1.16306	−	1.16306i	−0.179258	−	0.983802i	$-0.557370\pi$
$54$	6.49652	−	3.43442i	0.884064	−	0.467365i
$55$		0			0
$56$	10.3702	+	4.61022i	1.38577	+	0.616067i
$57$	5.55642	−	1.69357i	0.735966	−	0.224319i
$58$	−0.517093	+	1.21882i	−0.0678976	+	0.160039i
$59$		−	6.53585i		−	0.850895i	−0.904983	−	0.425448i	$-0.860117\pi$
$59$		−	6.53585i		−	0.850895i	0.904983	−	0.425448i	$-0.139883\pi$
$60$		0			0
$61$		−	5.10959i		−	0.654216i	−0.944987	−	0.327108i	$-0.893926\pi$
$61$		−	5.10959i		−	0.654216i	0.944987	−	0.327108i	$-0.106074\pi$
$62$	−7.15555	−	3.03579i	−0.908756	−	0.385546i
$63$	−2.31703	+	11.8121i	−0.291919	+	1.48818i
$64$	−5.93923	+	5.35962i	−0.742404	+	0.669952i
$65$		0			0
$66$	−11.5680	−	1.22370i	−1.42392	−	0.150628i
$67$	4.85678	+	4.85678i	0.593350	+	0.593350i	0.938535	−	0.345185i	$-0.112184\pi$
$67$	4.85678	+	4.85678i	0.593350	+	0.593350i	−0.345185	+	0.938535i	$0.612184\pi$
$68$	−0.0836501	+	4.89577i	−0.0101441	+	0.593699i
$69$	−5.55939	+	10.4341i	−0.669272	+	1.25612i
$70$		0			0
$71$		−	8.34435i		−	0.990292i	−0.868810	−	0.495146i	$-0.835115\pi$
$71$		−	8.34435i		−	0.990292i	0.868810	−	0.495146i	$-0.164885\pi$
$72$	−6.94509	−	4.87501i	−0.818487	−	0.574526i
$73$	−1.57561	−	1.57561i	−0.184411	−	0.184411i	0.608864	−	0.793275i	$-0.291626\pi$
$73$	−1.57561	−	1.57561i	−0.184411	−	0.184411i	−0.793275	+	0.608864i	$0.791626\pi$
$74$	0.561679	+	1.38947i	0.0652939	+	0.161522i
$75$		0			0
$76$	−4.66114	−	4.82319i	−0.534669	−	0.553258i
$77$	13.4737	−	13.4737i	1.53547	−	1.53547i
$78$	2.33791	−	1.89060i	0.264716	−	0.214068i
$79$		−	7.75267i		−	0.872243i	−0.899888	−	0.436122i	$-0.856352\pi$
$79$		−	7.75267i		−	0.872243i	0.899888	−	0.436122i	$-0.143648\pi$
$80$		0			0
$81$	3.40002	−	8.33306i	0.377780	−	0.925895i
$82$	1.23780	−	2.91758i	0.136693	−	0.322193i
$83$	9.15657	+	9.15657i	1.00506	+	1.00506i	0.999987	+	0.00507654i	$0.00161592\pi$
$83$	9.15657	+	9.15657i	1.00506	+	1.00506i	0.00507654	+	0.999987i	$0.498384\pi$
$84$	13.3628	−	3.82466i	1.45800	−	0.417305i
$85$		0			0
$86$	−16.2328	+	6.56196i	−1.75043	+	0.707595i
$87$	0.472761	+	1.55108i	0.0506853	+	0.166293i
$88$	4.82057	+	12.5373i	0.513875	+	1.33648i
$89$	−4.97996			−0.527875			−0.263938	−	0.964540i	$-0.585021\pi$
$89$	−4.97996			−0.527875			−0.263938	+	0.964540i	$0.585021\pi$
$90$		0			0
$91$			4.92511i			0.516292i
$92$	13.6498	+	0.233222i	1.42309	+	0.0243151i
$93$	−9.10622	+	2.77553i	−0.944272	+	0.287809i
$94$	5.03116	+	12.4459i	0.518924	+	1.28370i
$95$		0			0
$96$	−1.36297	+	9.70270i	−0.139108	+	0.990277i
$97$	1.42918	−	1.42918i	0.145112	−	0.145112i	−0.630819	−	0.775930i	$-0.717281\pi$
$97$	1.42918	−	1.42918i	0.145112	−	0.145112i	0.775930	+	0.630819i	$0.217281\pi$
$98$	−5.02588	+	11.8463i	−0.507691	+	1.19666i
$99$	−11.8248	+	7.94653i	−1.18844	+	0.798657i
$100$		0			0
$101$	4.79140			0.476762			0.238381	−	0.971172i	$-0.423383\pi$
$101$	4.79140			0.476762			0.238381	+	0.971172i	$0.423383\pi$
$102$	3.77087	+	4.66304i	0.373372	+	0.461709i
$103$	1.07832	+	1.07832i	0.106250	+	0.106250i	0.758233	−	0.651983i	$-0.226063\pi$
$103$	1.07832	+	1.07832i	0.106250	+	0.106250i	−0.651983	+	0.758233i	$0.726063\pi$
$104$	−3.17245	−	1.41036i	−0.311084	−	0.138297i
$105$		0			0
$106$	6.34663	+	15.7001i	0.616440	+	1.52493i
$107$	−6.51086	+	6.51086i	−0.629429	+	0.629429i	−0.947924	−	0.318496i	$-0.896822\pi$
$107$	−6.51086	+	6.51086i	−0.629429	+	0.629429i	0.318496	+	0.947924i	$0.396822\pi$
$108$	−10.3547	+	0.882973i	−0.996384	+	0.0849641i
$109$	8.99273			0.861347			0.430674	−	0.902508i	$-0.358276\pi$
$109$	8.99273			0.861347			0.430674	+	0.902508i	$0.358276\pi$
$110$		0			0
$111$	1.61993	+	0.863114i	0.153757	+	0.0819232i
$112$	−10.9544	−	11.7298i	−1.03510	−	1.10837i
$113$	−6.80391	+	6.80391i	−0.640058	+	0.640058i	−0.950570	−	0.310511i	$-0.899500\pi$
$113$	−6.80391	+	6.80391i	−0.640058	+	0.640058i	0.310511	+	0.950570i	$0.399500\pi$
$114$	−8.16928	−	0.864176i	−0.765123	−	0.0809375i
$115$		0			0
$116$	1.34640	−	1.30116i	0.125010	−	0.120810i
$117$	0.708829	−	3.61356i	0.0655312	−	0.334074i
$118$	−3.60999	+	8.50897i	−0.332327	+	0.783314i
$119$	−9.82331			−0.900502
$120$		0			0
$121$	11.5527			1.05025
$122$	−2.82222	+	6.65214i	−0.255512	+	0.602256i
$123$	−1.13168	−	3.71294i	−0.102041	−	0.334784i
$124$	7.63897	+	7.90455i	0.686000	+	0.709850i
$125$		0			0
$126$	9.54078	−	14.0983i	0.849960	−	1.25597i
$127$	0.0736760	−	0.0736760i	0.00653769	−	0.00653769i	−0.703830	−	0.710368i	$-0.748528\pi$
$127$	0.0736760	−	0.0736760i	0.00653769	−	0.00653769i	0.710368	+	0.703830i	$0.248528\pi$
$128$	10.6926	−	3.69719i	0.945098	−	0.326788i
$129$	−10.0836	+	18.9253i	−0.887808	+	1.66628i
$130$		0			0
$131$	−13.2979			−1.16184			−0.580922	−	0.813959i	$-0.697308\pi$
$131$	−13.2979			−1.16184			−0.580922	+	0.813959i	$0.697308\pi$
$132$	14.3844	+	7.98257i	1.25200	+	0.694794i
$133$	9.51510	−	9.51510i	0.825064	−	0.825064i
$134$	−3.64043	−	9.00559i	−0.314485	−	0.777964i
$135$		0			0
$136$	2.81302	−	6.32756i	0.241214	−	0.542584i
$137$	0.613004	+	0.613004i	0.0523724	+	0.0523724i	0.732808	−	0.680436i	$-0.238209\pi$
$137$	0.613004	+	0.613004i	0.0523724	+	0.0523724i	−0.680436	+	0.732808i	$0.738209\pi$
$138$	13.0009	−	10.5135i	1.10671	−	0.894965i
$139$	17.5621			1.48960			0.744798	−	0.667290i	$-0.232546\pi$
$139$	17.5621			1.48960			0.744798	+	0.667290i	$0.232546\pi$
$140$		0			0
$141$	14.5103	+	7.73121i	1.22199	+	0.651086i
$142$	−4.60890	+	10.8634i	−0.386770	+	0.911640i
$143$	−4.12189	+	4.12189i	−0.344690	+	0.344690i
$144$	6.34911	+	10.1828i	0.529092	+	0.848564i
$145$		0			0
$146$	1.18100	+	2.92154i	0.0977407	+	0.241788i
$147$	4.59501	+	15.0757i	0.378990	+	1.24343i
$148$	0.0362086	−	2.11917i	0.00297633	−	0.174195i
$149$			2.68064i			0.219607i	0.993953	+	0.109803i	$0.0350221\pi$
$149$			2.68064i			0.219607i	−0.993953	+	0.109803i	$0.964978\pi$
$150$		0			0
$151$	−15.6429			−1.27300			−0.636502	−	0.771275i	$-0.719619\pi$
$151$	−15.6429			−1.27300			−0.636502	+	0.771275i	$0.719619\pi$
$152$	3.40427	+	8.85379i	0.276123	+	0.718137i
$153$	7.20738	+	1.41378i	0.582682	+	0.114298i
$154$	−24.9834	+	10.0993i	−2.01322	+	0.813825i
$155$		0			0
$156$	−4.08795	+	1.17004i	−0.327298	+	0.0936785i
$157$	−14.1557	−	14.1557i	−1.12975	−	1.12975i	−0.990217	−	0.139534i	$-0.955440\pi$
$157$	−14.1557	−	14.1557i	−1.12975	−	1.12975i	−0.139534	−	0.990217i	$-0.544560\pi$
$158$	−4.28209	+	10.0931i	−0.340665	+	0.802967i
$159$	18.3043	+	9.75267i	1.45162	+	0.773437i
$160$		0			0
$161$			27.3881i			2.15849i
$162$	−9.02912	+	8.97079i	−0.709394	+	0.704812i
$163$	−5.09399	+	5.09399i	−0.398992	+	0.398992i	−0.877878	−	0.478885i	$-0.841041\pi$
$163$	−5.09399	+	5.09399i	−0.398992	+	0.398992i	0.478885	+	0.877878i	$0.341041\pi$
$164$	−3.22297	+	3.11469i	−0.251672	+	0.243216i
$165$		0			0
$166$	−6.86335	−	16.9784i	−0.532699	−	1.31778i
$167$	13.7751	+	13.7751i	1.06595	+	1.06595i	0.997666	+	0.0682869i	$0.0217533\pi$
$167$	13.7751	+	13.7751i	1.06595	+	1.06595i	0.0682869	+	0.997666i	$0.478247\pi$
$168$	−19.5094	−	2.40145i	−1.50518	−	0.185276i
$169$			11.4933i			0.884100i
$170$		0			0
$171$	−8.35066	+	5.61181i	−0.638591	+	0.429146i
$172$	24.7578	+	0.423016i	1.88776	+	0.0322547i
$173$	7.07803	+	7.07803i	0.538133	+	0.538133i	0.922980	−	0.384848i	$-0.125746\pi$
$173$	7.07803	+	7.07803i	0.538133	+	0.538133i	−0.384848	+	0.922980i	$0.625746\pi$
$174$	0.241236	−	2.28046i	0.0182880	−	0.172882i
$175$		0			0
$176$	0.648945	−	18.9848i	0.0489161	−	1.43103i
$177$	3.30050	+	10.8286i	0.248081	+	0.813928i
$178$	6.48338	+	2.75062i	0.485950	+	0.206168i
$179$		−	2.82136i		−	0.210879i	−0.994426	−	0.105439i	$-0.966375\pi$
$179$		−	2.82136i		−	0.210879i	0.994426	−	0.105439i	$-0.0336249\pi$
$180$		0			0
$181$		−	14.0239i		−	1.04239i	−0.853439	−	0.521194i	$-0.825487\pi$
$181$		−	14.0239i		−	1.04239i	0.853439	−	0.521194i	$-0.174513\pi$
$182$	2.72032	−	6.41197i	0.201644	−	0.475287i
$183$	2.58026	+	8.46558i	0.190739	+	0.625794i
$184$	−17.6417	−	7.84290i	−1.30056	−	0.578186i
$185$		0			0
$186$	13.3884	+	1.41627i	0.981682	+	0.103846i
$187$	−8.22127	−	8.22127i	−0.601199	−	0.601199i
$188$	0.324333	−	18.9822i	0.0236544	−	1.38442i
$189$	−2.12605	−	20.7403i	−0.154647	−	1.50864i
$190$		0			0
$191$		−	26.2648i		−	1.90045i	−0.311563	−	0.950225i	$-0.600853\pi$
$191$		−	26.2648i		−	1.90045i	0.311563	−	0.950225i	$-0.399147\pi$
$192$	7.13361	−	11.8790i	0.514824	−	0.857296i
$193$	−8.27030	−	8.27030i	−0.595309	−	0.595309i	0.343752	−	0.939061i	$-0.388302\pi$
$193$	−8.27030	−	8.27030i	−0.595309	−	0.595309i	−0.939061	+	0.343752i	$0.888302\pi$
$194$	−2.65003	+	1.07125i	−0.190261	+	0.0769114i
$195$		0			0
$196$	13.0863	−	12.6466i	0.934737	−	0.903332i
$197$	2.99822	−	2.99822i	0.213614	−	0.213614i	−0.592187	−	0.805801i	$-0.701735\pi$
$197$	2.99822	−	2.99822i	0.213614	−	0.213614i	0.805801	+	0.592187i	$0.201735\pi$
$198$	19.7838	−	3.81423i	1.40598	−	0.271065i
$199$		−	6.70234i		−	0.475116i	−0.971373	−	0.237558i	$-0.923653\pi$
$199$		−	6.70234i		−	0.475116i	0.971373	−	0.237558i	$-0.0763470\pi$
$200$		0			0
$201$	−10.4993	−	5.59412i	−0.740565	−	0.394579i
$202$	−6.23789	−	2.64647i	−0.438896	−	0.186205i
$203$	2.65615	+	2.65615i	0.186425	+	0.186425i
$204$	−2.33370	−	8.15356i	−0.163391	−	0.570864i
$205$		0			0
$206$	−0.808260	−	1.99945i	−0.0563142	−	0.139308i
$207$	3.94173	−	20.0947i	0.273969	−	1.39668i
$208$	3.35119	+	3.58840i	0.232363	+	0.248811i
$209$	15.9266			1.10167
$210$		0			0
$211$			9.44133i			0.649968i	0.945720	+	0.324984i	$0.105359\pi$
$211$			9.44133i			0.649968i	−0.945720	+	0.324984i	$0.894641\pi$
$212$	0.409135	−	23.9454i	0.0280995	−	1.64457i
$213$	4.21377	+	13.8249i	0.288722	+	0.947269i
$214$	12.0726	−	4.88025i	0.825268	−	0.333607i
$215$		0			0
$216$	13.9684	+	4.56977i	0.950432	+	0.310933i
$217$	−15.5940	+	15.5940i	−1.05859	+	1.05859i
$218$	−11.7076	−	4.96702i	−0.792936	−	0.336409i
$219$	3.40613	+	1.81481i	0.230165	+	0.122634i
$220$		0			0
$221$	3.00516			0.202149
$222$	−1.63225	−	2.01843i	−0.109549	−	0.135468i
$223$	−17.3049	−	17.3049i	−1.15882	−	1.15882i	−0.984729	−	0.174091i	$-0.944301\pi$
$223$	−17.3049	−	17.3049i	−1.15882	−	1.15882i	−0.174091	−	0.984729i	$-0.555699\pi$
$224$	7.78267	+	21.3215i	0.520002	+	1.42460i
$225$		0			0
$226$	12.6160	−	5.09991i	0.839205	−	0.339241i
$227$	−6.96809	+	6.96809i	−0.462489	+	0.462489i	−0.899470	−	0.436982i	$-0.856047\pi$
$227$	−6.96809	+	6.96809i	−0.462489	+	0.462489i	0.436982	+	0.899470i	$0.356047\pi$
$228$	10.1582	+	5.63726i	0.672744	+	0.373337i
$229$	−2.90511			−0.191975			−0.0959874	−	0.995383i	$-0.530601\pi$
$229$	−2.90511			−0.191975			−0.0959874	+	0.995383i	$0.530601\pi$
$230$		0			0
$231$	−15.5193	+	29.1273i	−1.02109	+	1.91644i
$232$	−2.47155	+	0.950306i	−0.162265	+	0.0623907i
$233$	0.413436	−	0.413436i	0.0270851	−	0.0270851i	−0.693435	−	0.720520i	$-0.743903\pi$
$233$	0.413436	−	0.413436i	0.0270851	−	0.0270851i	0.720520	+	0.693435i	$0.243903\pi$
$234$	−2.91872	+	4.31295i	−0.190803	+	0.281947i
$235$		0			0
$236$	9.39964	−	9.08383i	0.611865	−	0.591307i
$237$	3.91498	+	12.8446i	0.254305	+	0.834349i
$238$	12.7889	+	5.42578i	0.828981	+	0.351701i
$239$	−8.34435			−0.539751			−0.269876	−	0.962895i	$-0.586983\pi$
$239$	−8.34435			−0.539751			−0.269876	+	0.962895i	$0.586983\pi$
$240$		0			0
$241$	−15.4459			−0.994960			−0.497480	−	0.867475i	$-0.665741\pi$
$241$	−15.4459			−0.994960			−0.497480	+	0.867475i	$0.665741\pi$
$242$	−15.0404	−	6.38099i	−0.966832	−	0.410186i
$243$	−1.42509	+	15.5232i	−0.0914196	+	0.995812i
$244$	7.34845	−	7.10155i	0.470436	−	0.454630i
$245$		0			0
$246$	−0.577464	+	5.45892i	−0.0368177	+	0.348048i
$247$	−2.91087	+	2.91087i	−0.185214	+	0.185214i
$248$	−5.57914	−	14.5102i	−0.354276	−	0.921396i
$249$	−19.7945	−	10.5467i	−1.25443	−	0.668369i
$250$		0			0
$251$	19.6634			1.24114			0.620572	−	0.784150i	$-0.286901\pi$
$251$	19.6634			1.24114			0.620572	+	0.784150i	$0.286901\pi$
$252$	−20.2081	+	13.0847i	−1.27299	+	0.824258i
$253$	−22.9215	+	22.9215i	−1.44106	+	1.44106i
$254$	−0.136612	+	0.0552242i	−0.00857181	+	0.00346508i
$255$		0			0
$256$	−15.9627	−	1.09256i	−0.997666	−	0.0682849i
$257$	−13.1156	−	13.1156i	−0.818128	−	0.818128i	0.167709	−	0.985837i	$-0.446363\pi$
$257$	−13.1156	−	13.1156i	−0.818128	−	0.818128i	−0.985837	+	0.167709i	$0.946363\pi$
$258$	23.5809	−	19.0692i	1.46808	−	1.18720i
$259$	4.25210			0.264212
$260$		0			0
$261$	−1.56654	−	2.33110i	−0.0969666	−	0.144291i
$262$	17.3125	+	7.34494i	1.06957	+	0.453772i
$263$	9.08999	−	9.08999i	0.560513	−	0.560513i	−0.368940	−	0.929453i	$-0.620279\pi$
$263$	9.08999	−	9.08999i	0.560513	−	0.560513i	0.929453	+	0.368940i	$0.120279\pi$
$264$	−14.3179	−	18.3375i	−0.881204	−	1.12859i
$265$		0			0
$266$	−17.6432	+	7.13209i	−1.08177	+	0.437297i
$267$	8.25081	−	2.51480i	0.504941	−	0.153903i
$268$	−0.234680	+	13.7350i	−0.0143353	+	0.839002i
$269$			11.3272i			0.690635i	0.938486	+	0.345317i	$0.112229\pi$
$269$			11.3272i			0.690635i	−0.938486	+	0.345317i	$0.887771\pi$
$270$		0			0
$271$	2.39400			0.145425			0.0727126	−	0.997353i	$-0.476834\pi$
$271$	2.39400			0.145425			0.0727126	+	0.997353i	$0.476834\pi$
$272$	−7.15720	+	6.68407i	−0.433969	+	0.405281i
$273$	−2.48710	−	8.15993i	−0.150526	−	0.493862i
$274$	−0.459480	−	1.13665i	−0.0277582	−	0.0686675i
$275$		0			0
$276$	−22.7327	+	6.50651i	−1.36835	+	0.391646i
$277$	−2.60387	−	2.60387i	−0.156451	−	0.156451i	0.624541	−	0.780992i	$-0.285286\pi$
$277$	−2.60387	−	2.60387i	−0.156451	−	0.156451i	−0.780992	+	0.624541i	$0.785286\pi$
$278$	−22.8639	−	9.70018i	−1.37129	−	0.581778i
$279$	13.6856	−	9.19700i	0.819336	−	0.550610i
$280$		0			0
$281$			12.9461i			0.772301i	0.922436	+	0.386151i	$0.126195\pi$
$281$			12.9461i			0.772301i	−0.922436	+	0.386151i	$0.873805\pi$
$282$	−14.6206	−	18.0798i	−0.870646	−	1.07664i
$283$	1.95205	−	1.95205i	0.116037	−	0.116037i	−0.646704	−	0.762741i	$-0.723853\pi$
$283$	1.95205	−	1.95205i	0.116037	−	0.116037i	0.762741	+	0.646704i	$0.223853\pi$
$284$	12.0006	−	11.5974i	0.712103	−	0.688177i
$285$		0			0
$286$	7.64294	−	3.08959i	0.451936	−	0.182691i
$287$	−6.35823	−	6.35823i	−0.375314	−	0.375314i
$288$	−2.64153	−	16.7637i	−0.155654	−	0.987812i
$289$		−	11.0061i		−	0.647418i
$290$		0			0
$291$	−1.64616	+	3.08959i	−0.0964995	+	0.181115i
$292$	0.0761334	−	4.45584i	0.00445537	−	0.260758i
$293$	−17.2193	−	17.2193i	−1.00596	−	1.00596i	−0.999982	−	0.00597927i	$-0.998097\pi$
$293$	−17.2193	−	17.2193i	−1.00596	−	1.00596i	−0.00597927	−	0.999982i	$-0.501903\pi$
$294$	2.34469	−	22.1650i	0.136745	−	1.29269i
$295$		0			0
$296$	−1.21764	+	2.73893i	−0.0707737	+	0.159197i
$297$	15.5785	−	19.1372i	0.903959	−	1.11045i
$298$	1.48062	−	3.48991i	0.0857699	−	0.202165i
$299$		−	8.37859i		−	0.484547i
$300$		0			0
$301$			49.6763i			2.86329i
$302$	20.3654	+	8.64018i	1.17190	+	0.497186i
$303$	−7.93840	+	2.41958i	−0.456049	+	0.139001i
$304$	0.458282	−	13.4070i	0.0262843	−	0.768943i
$305$		0			0
$306$	−8.60234	−	5.82150i	−0.491763	−	0.332793i
$307$	−7.34204	−	7.34204i	−0.419033	−	0.419033i	0.465838	−	0.884870i	$-0.345753\pi$
$307$	−7.34204	−	7.34204i	−0.419033	−	0.419033i	−0.884870	+	0.465838i	$0.845753\pi$
$308$	38.1039	+	0.651051i	2.17117	+	0.0370970i
$309$	−2.33110	−	1.24203i	−0.132611	−	0.0706565i
$310$		0			0
$311$			21.9193i			1.24293i	0.783442	+	0.621465i	$0.213462\pi$
$311$			21.9193i			1.24293i	−0.783442	+	0.621465i	$0.786538\pi$
$312$	5.96833	+	0.734655i	0.337890	+	0.0415916i
$313$	−14.8922	−	14.8922i	−0.841759	−	0.841759i	0.147329	−	0.989088i	$-0.452933\pi$
$313$	−14.8922	−	14.8922i	−0.841759	−	0.841759i	−0.989088	+	0.147329i	$0.952933\pi$
$314$	10.6105	+	26.2480i	0.598786	+	1.48126i
$315$		0			0
$316$	11.1496	−	10.7750i	0.627216	−	0.606142i
$317$	−17.6185	+	17.6185i	−0.989556	+	0.989556i	−0.999946	−	0.0103899i	$-0.996693\pi$
$317$	−17.6185	+	17.6185i	−0.989556	+	0.989556i	0.0103899	+	0.999946i	$0.496693\pi$
$318$	−18.4434	−	22.8071i	−1.03426	−	1.27896i
$319$			4.44594i			0.248925i
$320$		0			0
$321$	7.49932	−	14.0751i	0.418571	−	0.785595i
$322$	15.1275	−	35.6564i	0.843021	−	1.98705i
$323$	−5.80583	−	5.80583i	−0.323045	−	0.323045i
$324$	16.7098	−	6.69188i	0.928324	−	0.371771i
$325$		0			0
$326$	9.44543	−	3.81823i	0.523134	−	0.211472i
$327$	−14.8992	+	4.54119i	−0.823926	+	0.251128i
$328$	5.91632	−	2.27482i	0.326674	−	0.125606i
$329$	38.0875			2.09983
$330$		0			0
$331$		−	7.13080i		−	0.391944i	−0.980609	−	0.195972i	$-0.937214\pi$
$331$		−	7.13080i		−	0.391944i	0.980609	−	0.195972i	$-0.0627862\pi$
$332$	−0.442445	+	25.8949i	−0.0242823	+	1.42117i
$333$	−3.11977	−	0.611967i	−0.170962	−	0.0335356i
$334$	−10.3252	−	25.5423i	−0.564971	−	1.39761i
$335$		0			0
$336$	24.0727	+	13.9022i	1.31327	+	0.758427i
$337$	18.6144	−	18.6144i	1.01399	−	1.01399i	0.0140911	−	0.999901i	$-0.495515\pi$
$337$	18.6144	−	18.6144i	1.01399	−	1.01399i	0.999901	−	0.0140911i	$-0.00448549\pi$
$338$	6.34818	−	14.9630i	0.345295	−	0.813882i
$339$	7.83687	−	14.7086i	0.425640	−	0.798862i
$340$		0			0
$341$	−26.1016			−1.41348
$342$	13.9713	−	2.69359i	0.755480	−	0.145653i
$343$	5.95612	+	5.95612i	0.321600	+	0.321600i
$344$	−31.9983	−	14.2254i	−1.72523	−	0.766981i
$345$		0			0
$346$	−5.30537	−	13.1243i	−0.285219	−	0.705566i
$347$	1.56152	−	1.56152i	0.0838269	−	0.0838269i	−0.663950	−	0.747777i	$-0.731121\pi$
$347$	1.56152	−	1.56152i	0.0838269	−	0.0838269i	0.747777	+	0.663950i	$0.231121\pi$
$348$	−1.57365	+	2.83568i	−0.0843564	+	0.152008i
$349$	26.5812			1.42286			0.711430	−	0.702757i	$-0.248048\pi$
$349$	26.5812			1.42286			0.711430	+	0.702757i	$0.248048\pi$
$350$		0			0
$351$	0.650403	+	6.34490i	0.0347159	+	0.338666i
$352$	−11.3309	+	24.3577i	−0.603937	+	1.29827i
$353$	−6.51124	+	6.51124i	−0.346558	+	0.346558i	−0.858826	−	0.512268i	$-0.828806\pi$
$353$	−6.51124	+	6.51124i	−0.346558	+	0.346558i	0.512268	+	0.858826i	$0.328806\pi$
$354$	1.68414	−	15.9207i	0.0895113	−	0.846174i
$355$		0			0
$356$	−6.92139	−	7.16202i	−0.366833	−	0.379586i
$357$	16.2753	−	4.96062i	0.861379	−	0.262544i
$358$	−1.55834	+	3.67311i	−0.0823611	+	0.194130i
$359$	9.82331			0.518455			0.259227	−	0.965816i	$-0.416532\pi$
$359$	9.82331			0.518455			0.259227	+	0.965816i	$0.416532\pi$
$360$		0			0
$361$	−7.75267			−0.408035
$362$	−7.74591	+	18.2576i	−0.407116	+	0.959597i
$363$	−19.1405	+	5.83393i	−1.00462	+	0.306202i
$364$	−7.08313	+	6.84515i	−0.371257	+	0.358784i
$365$		0			0
$366$	1.31663	−	12.4465i	0.0688213	−	0.650586i
$367$	−0.983469	+	0.983469i	−0.0513367	+	0.0513367i	−0.732309	−	0.680972i	$-0.761557\pi$
$367$	−0.983469	+	0.983469i	−0.0513367	+	0.0513367i	0.680972	+	0.732309i	$0.261557\pi$
$368$	18.6357	+	19.9548i	0.971452	+	1.04022i
$369$	3.74995	+	5.58012i	0.195215	+	0.290489i
$370$		0			0
$371$	48.0461			2.49443
$372$	−16.6479	−	9.23871i	−0.863155	−	0.479005i
$373$	18.9116	−	18.9116i	0.979205	−	0.979205i	−0.0205831	−	0.999788i	$-0.506552\pi$
$373$	18.9116	−	18.9116i	0.979205	−	0.979205i	0.999788	+	0.0205831i	$0.00655226\pi$
$374$	6.16229	+	15.2441i	0.318645	+	0.788255i
$375$		0			0
$376$	−10.9068	+	24.5336i	−0.562475	+	1.26522i
$377$	−0.812572	−	0.812572i	−0.0418496	−	0.0418496i
$378$	−8.68777	+	28.1760i	−0.446851	+	1.44922i
$379$	−24.3755			−1.25209			−0.626043	−	0.779788i	$-0.715327\pi$
$379$	−24.3755			−1.25209			−0.626043	+	0.779788i	$0.715327\pi$
$380$		0			0
$381$	−0.0848613	+	0.159272i	−0.00434758	+	0.00815974i
$382$	−14.5070	+	34.1939i	−0.742243	+	1.74951i
$383$	15.0463	−	15.0463i	0.768831	−	0.768831i	−0.209070	−	0.977901i	$-0.567043\pi$
$383$	15.0463	−	15.0463i	0.768831	−	0.768831i	0.977901	+	0.209070i	$0.0670435\pi$
$384$	−15.8484	+	11.5251i	−0.808762	+	0.588137i
$385$		0			0
$386$	6.19904	+	15.3350i	0.315523	+	0.780532i
$387$	7.14947	−	36.4475i	0.363428	−	1.85273i
$388$	4.04175	+	0.0690581i	0.205189	+	0.00350589i
$389$		−	3.98314i		−	0.201953i	−0.994889	−	0.100977i	$-0.967803\pi$
$389$		−	3.98314i		−	0.201953i	0.994889	−	0.100977i	$-0.0321967\pi$
$390$		0			0
$391$	16.7114			0.845132
$392$	−24.0222	+	9.23650i	−1.21330	+	0.466514i
$393$	22.0320	−	6.71524i	1.11137	−	0.338739i
$394$	−5.55939	+	2.24733i	−0.280078	+	0.113219i
$395$		0			0
$396$	−27.8632	−	5.96164i	−1.40018	−	0.299584i
$397$	18.0470	+	18.0470i	0.905755	+	0.905755i	0.995926	−	0.0901716i	$-0.0287416\pi$
$397$	18.0470	+	18.0470i	0.905755	+	0.905755i	−0.0901716	+	0.995926i	$0.528742\pi$
$398$	−3.70195	+	8.72572i	−0.185562	+	0.437381i
$399$	−10.9597	+	20.5696i	−0.548669	+	1.02977i
$400$		0			0
$401$		−	22.6814i		−	1.13265i	−0.824181	−	0.566327i	$-0.808364\pi$
$401$		−	22.6814i		−	1.13265i	0.824181	−	0.566327i	$-0.191636\pi$
$402$	10.5791	+	13.0821i	0.527640	+	0.652477i
$403$	4.77052	−	4.77052i	0.237636	−	0.237636i
$404$	6.65931	+	6.89083i	0.331313	+	0.342832i
$405$		0			0
$406$	−1.99093	−	4.92511i	−0.0988082	−	0.244429i
$407$	3.55864	+	3.55864i	0.176395	+	0.176395i
$408$	−1.46530	+	11.9040i	−0.0725429	+	0.589338i
$409$			1.51280i			0.0748032i	0.999300	+	0.0374016i	$0.0119081\pi$
$409$			1.51280i			0.0748032i	−0.999300	+	0.0374016i	$0.988092\pi$
$410$		0			0
$411$	−1.32518	−	0.706068i	−0.0653664	−	0.0348278i
$412$	−0.0521044	+	3.04950i	−0.00256700	+	0.150238i
$413$	18.5435	+	18.5435i	0.912464	+	0.912464i
$414$	−16.2308	+	23.9839i	−0.797698	+	1.17875i
$415$		0			0
$416$	−2.38088	−	6.52270i	−0.116732	−	0.319802i
$417$	−29.0969	+	8.86857i	−1.42488	+	0.434296i
$418$	−20.7348	−	8.79687i	−1.01417	−	0.430269i
$419$			11.4558i			0.559653i	0.960051	+	0.279827i	$0.0902770\pi$
$419$			11.4558i			0.559653i	−0.960051	+	0.279827i	$0.909723\pi$
$420$		0			0
$421$		−	18.1975i		−	0.886894i	−0.896301	−	0.443447i	$-0.853755\pi$
$421$		−	18.1975i		−	0.886894i	0.896301	−	0.443447i	$-0.146245\pi$
$422$	5.21480	−	12.2916i	0.253852	−	0.598345i
$423$	−27.9448	−	5.48161i	−1.35873	−	0.266525i
$424$	−13.7586	+	30.9483i	−0.668175	+	1.50298i
$425$		0			0
$426$	2.15015	−	20.3260i	0.104175	−	0.984797i
$427$	14.4969	+	14.4969i	0.701554	+	0.701554i
$428$	−18.4128	−	0.314605i	−0.890017	−	0.0152070i
$429$	4.74767	−	8.91065i	0.229220	−	0.430210i
$430$		0			0
$431$		−	33.4688i		−	1.61214i	−0.591822	−	0.806069i	$-0.701591\pi$
$431$		−	33.4688i		−	1.61214i	0.591822	−	0.806069i	$-0.298409\pi$
$432$	−15.6613	−	13.6646i	−0.753507	−	0.657440i
$433$	16.3942	+	16.3942i	0.787853	+	0.787853i	0.981142	−	0.193289i	$-0.0619153\pi$
$433$	16.3942	+	16.3942i	0.787853	+	0.787853i	−0.193289	+	0.981142i	$0.561915\pi$
$434$	28.9148	−	11.6885i	1.38795	−	0.561068i
$435$		0			0
$436$	12.4985	+	12.9330i	0.598570	+	0.619381i
$437$	−16.1871	+	16.1871i	−0.774333	+	0.774333i
$438$	−3.43202	−	4.24402i	−0.163988	−	0.202787i
$439$			24.1557i			1.15289i	0.817136	+	0.576445i	$0.195561\pi$
$439$			24.1557i			1.15289i	−0.817136	+	0.576445i	$0.804439\pi$
$440$		0			0
$441$	−15.2260	−	22.6571i	−0.725049	−	1.07891i
$442$	−3.91239	−	1.65986i	−0.186093	−	0.0789515i
$443$	4.83418	+	4.83418i	0.229679	+	0.229679i	0.812558	−	0.582880i	$-0.198074\pi$
$443$	4.83418	+	4.83418i	0.229679	+	0.229679i	−0.582880	+	0.812558i	$0.698074\pi$
$444$	1.01016	+	3.52933i	0.0479400	+	0.167495i
$445$		0			0
$446$	12.9710	+	32.0872i	0.614193	+	1.51937i
$447$	−1.35368	−	4.44129i	−0.0640269	−	0.210066i
$448$	1.64448	−	32.0570i	0.0776942	−	1.51455i
$449$	−8.70564			−0.410845			−0.205422	−	0.978673i	$-0.565857\pi$
$449$	−8.70564			−0.410845			−0.205422	+	0.978673i	$0.565857\pi$
$450$		0			0
$451$		−	10.6426i		−	0.501139i
$452$	−19.2416	−	0.328765i	−0.905047	−	0.0154638i
$453$	25.9172	−	7.89944i	1.21770	−	0.371148i
$454$	12.9204	−	5.22297i	0.606386	−	0.245126i
$455$		0			0
$456$	−10.1112	−	12.9499i	−0.473502	−	0.606433i
$457$	−5.80514	+	5.80514i	−0.271553	+	0.271553i	−0.829725	−	0.558172i	$-0.811503\pi$
$457$	−5.80514	+	5.80514i	−0.271553	+	0.271553i	0.558172	+	0.829725i	$0.311503\pi$
$458$	3.78214	+	1.60460i	0.176728	+	0.0749780i
$459$	−12.6551	+	1.29725i	−0.590691	+	0.0605505i
$460$		0			0
$461$	20.6299			0.960829			0.480415	−	0.877042i	$-0.340486\pi$
$461$	20.6299			0.960829			0.480415	+	0.877042i	$0.340486\pi$
$462$	36.2925	−	29.3488i	1.68848	−	1.36543i
$463$	−9.79796	−	9.79796i	−0.455350	−	0.455350i	0.441776	−	0.897126i	$-0.354349\pi$
$463$	−9.79796	−	9.79796i	−0.455350	−	0.455350i	−0.897126	+	0.441776i	$0.854349\pi$
$464$	3.74257	+	0.127930i	0.173745	+	0.00593900i
$465$		0			0
$466$	−0.766605	+	0.309893i	−0.0355123	+	0.0143555i
$467$	17.9061	−	17.9061i	0.828593	−	0.828593i	−0.158729	−	0.987322i	$-0.550740\pi$
$467$	17.9061	−	17.9061i	0.828593	−	0.828593i	0.987322	+	0.158729i	$0.0507395\pi$
$468$	6.18207	−	4.00288i	0.285766	−	0.185033i
$469$	−27.5592			−1.27257
$470$		0			0
$471$	30.6017	+	16.3048i	1.41005	+	0.751287i
$472$	−17.2547	+	6.63440i	−0.794210	+	0.305373i
$473$	−41.5747	+	41.5747i	−1.91161	+	1.91161i
$474$	1.99769	−	18.8847i	0.0917570	−	0.867404i
$475$		0			0
$476$	−13.6529	−	14.1276i	−0.625780	−	0.647536i
$477$	−35.2515	−	6.91486i	−1.61406	−	0.316610i
$478$	10.8634	+	4.60890i	0.496882	+	0.210806i
$479$	−18.1677			−0.830102			−0.415051	−	0.909798i	$-0.636236\pi$
$479$	−18.1677			−0.830102			−0.415051	+	0.909798i	$0.636236\pi$
$480$		0			0
$481$	−1.30081			−0.0593116
$482$	20.1089	+	8.53137i	0.915937	+	0.388593i
$483$	−13.8306	−	45.3767i	−0.629312	−	2.06471i
$484$	16.0565	+	16.6147i	0.729841	+	0.755215i
$485$		0			0
$486$	10.4293	−	19.4224i	0.473085	−	0.881017i
$487$	−2.60795	+	2.60795i	−0.118177	+	0.118177i	−0.763722	−	0.645545i	$-0.776630\pi$
$487$	−2.60795	+	2.60795i	−0.118177	+	0.118177i	0.645545	+	0.763722i	$0.276630\pi$
$488$	−13.4893	+	5.18664i	−0.610634	+	0.234788i
$489$	5.86735	−	11.0121i	0.265331	−	0.497985i
$490$		0			0
$491$	−10.4772			−0.472829			−0.236415	−	0.971652i	$-0.575972\pi$
$491$	−10.4772			−0.472829			−0.236415	+	0.971652i	$0.575972\pi$
$492$	3.76696	−	6.78797i	0.169828	−	0.306025i
$493$	1.62070	−	1.62070i	0.0729928	−	0.0729928i
$494$	5.39742	−	2.18186i	0.242841	−	0.0981663i
$495$		0			0
$496$	−0.751063	+	21.9722i	−0.0337237	+	0.986583i
$497$	23.6745	+	23.6745i	1.06195	+	1.06195i
$498$	19.9450	+	24.6639i	0.893758	+	1.10522i
$499$	16.6637			0.745969			0.372984	−	0.927838i	$-0.378335\pi$
$499$	16.6637			0.745969			0.372984	+	0.927838i	$0.378335\pi$
$500$		0			0
$501$	−29.7789	−	15.8664i	−1.33042	−	0.708861i
$502$	−25.5996	−	10.8608i	−1.14257	−	0.484743i
$503$	11.7513	−	11.7513i	0.523965	−	0.523965i	−0.394802	−	0.918766i	$-0.629187\pi$
$503$	11.7513	−	11.7513i	0.523965	−	0.523965i	0.918766	+	0.394802i	$0.129187\pi$
$504$	33.5359	−	5.87320i	1.49381	−	0.261613i
$505$		0			0
$506$	42.5017	−	17.1809i	1.88943	−	0.763785i
$507$	−5.80394	−	19.0421i	−0.257762	−	0.845690i
$508$	0.208357	+	0.00356002i	0.00924434	+	0.000157951i
$509$			16.9269i			0.750272i	0.926970	+	0.375136i	$0.122404\pi$
$509$			16.9269i			0.750272i	−0.926970	+	0.375136i	$0.877596\pi$
$510$		0			0
$511$	8.94060			0.395509
$512$	20.1782	+	10.2392i	0.891759	+	0.452511i
$513$	11.0015	−	13.5146i	0.485729	−	0.596685i
$514$	9.83086	+	24.3193i	0.433620	+	1.07268i
$515$		0			0
$516$	−41.2324	+	11.8014i	−1.81515	+	0.519530i
$517$	31.8760	+	31.8760i	1.40190	+	1.40190i
$518$	−5.53577	−	2.34859i	−0.243228	−	0.103191i
$519$	−15.3012	−	8.15260i	−0.671647	−	0.357859i
$520$		0			0
$521$			17.4056i			0.762553i	0.924461	+	0.381277i	$0.124515\pi$
$521$			17.4056i			0.762553i	−0.924461	+	0.381277i	$0.875485\pi$
$522$	0.751919	+	3.90010i	0.0329106	+	0.170703i
$523$	−22.7980	+	22.7980i	−0.996888	+	0.996888i	−0.999995	−	0.00310741i	$-0.999011\pi$
$523$	−22.7980	+	22.7980i	−0.996888	+	0.996888i	0.00310741	+	0.999995i	$0.499011\pi$
$524$	−18.4821	−	19.1246i	−0.807393	−	0.835464i
$525$		0			0
$526$	−16.8549	+	6.81345i	−0.734910	+	0.297081i
$527$	9.51497	+	9.51497i	0.414479	+	0.414479i
$528$	8.51185	+	31.7817i	0.370431	+	1.38312i
$529$		−	23.5926i		−	1.02577i
$530$		0			0
$531$	−10.9366	−	16.2741i	−0.474606	−	0.706238i
$532$	26.9088	+	0.459769i	1.16665	+	0.0199335i
$533$	1.94511	+	1.94511i	0.0842522	+	0.0842522i
$534$	−12.1307	−	1.28323i	−0.524946	−	0.0555306i
$535$		0			0
$536$	7.89191	−	17.7519i	0.340878	−	0.766767i
$537$	1.42474	+	4.67444i	0.0614823	+	0.201717i
$538$	6.25646	−	14.7469i	0.269735	−	0.635782i
$539$			43.2123i			1.86129i
$540$		0			0
$541$			2.53614i			0.109037i	0.998513	+	0.0545187i	$0.0173624\pi$
$541$			2.53614i			0.109037i	−0.998513	+	0.0545187i	$0.982638\pi$
$542$	−3.11673	−	1.32230i	−0.133875	−	0.0567975i
$543$	7.08184	+	23.2348i	0.303911	+	0.997100i
$544$	13.0098	−	4.74875i	0.557789	−	0.203601i
$545$		0			0
$546$	−1.26909	+	11.9971i	−0.0543122	+	0.513427i
$547$	−14.4630	−	14.4630i	−0.618394	−	0.618394i	0.326726	−	0.945119i	$-0.394055\pi$
$547$	−14.4630	−	14.4630i	−0.618394	−	0.618394i	−0.945119	+	0.326726i	$0.894055\pi$
$548$	−0.0296203	+	1.73358i	−0.00126532	+	0.0740550i
$549$	−8.54997	−	12.7228i	−0.364904	−	0.542996i
$550$		0			0
$551$			3.13970i			0.133756i
$552$	33.1893	+	4.08535i	1.41263	+	0.173884i
$553$	21.9958	+	21.9958i	0.935357	+	0.935357i
$554$	1.95174	+	4.82817i	0.0829216	+	0.205129i
$555$		0			0
$556$	24.4086	+	25.2572i	1.03515	+	1.07114i
$557$	−17.5535	+	17.5535i	−0.743767	+	0.743767i	−0.973301	−	0.229533i	$-0.926280\pi$
$557$	−17.5535	+	17.5535i	−0.743767	+	0.743767i	0.229533	+	0.973301i	$0.426280\pi$
$558$	−22.8970	+	4.41443i	−0.969309	+	0.186878i
$559$		−	15.1970i		−	0.642765i
$560$		0			0
$561$	17.7726	+	9.46940i	0.750361	+	0.399798i
$562$	7.15063	−	16.8545i	0.301631	−	0.710963i
$563$	−14.6880	−	14.6880i	−0.619024	−	0.619024i	0.326257	−	0.945281i	$-0.394212\pi$
$563$	−14.6880	−	14.6880i	−0.619024	−	0.619024i	−0.945281	+	0.326257i	$0.894212\pi$
$564$	9.04834	+	31.6135i	0.381004	+	1.33117i
$565$		0			0
$566$	−3.61955	+	1.46317i	−0.152141	+	0.0615016i
$567$	13.9960	+	33.2890i	0.587776	+	1.39801i
$568$	−22.0291	+	8.47017i	−0.924321	+	0.355400i
$569$	−27.6388			−1.15868			−0.579338	−	0.815087i	$-0.696689\pi$
$569$	−27.6388			−1.15868			−0.579338	+	0.815087i	$0.696689\pi$
$570$		0			0
$571$		−	2.71823i		−	0.113754i	−0.998381	−	0.0568772i	$-0.981886\pi$
$571$		−	2.71823i		−	0.113754i	0.998381	−	0.0568772i	$-0.0181143\pi$
$572$	−11.6568	−	0.199170i	−0.487394	−	0.00832771i
$573$	13.2633	+	43.5155i	0.554082	+	1.81789i
$574$	4.76584	+	11.7896i	0.198922	+	0.492089i
$575$		0			0
$576$	−5.82024	+	23.2836i	−0.242510	+	0.970149i
$577$	6.19740	−	6.19740i	0.258001	−	0.258001i	−0.566240	−	0.824241i	$-0.691602\pi$
$577$	6.19740	−	6.19740i	0.258001	−	0.258001i	0.824241	+	0.566240i	$0.191602\pi$
$578$	−6.07908	+	14.3288i	−0.252856	+	0.595998i
$579$	17.8786	+	9.52587i	0.743010	+	0.395882i
$580$		0			0
$581$	−51.9578			−2.15557
$582$	3.84961	−	3.11308i	0.159572	−	0.129041i
$583$	40.2105	+	40.2105i	1.66535	+	1.66535i
$584$	−2.56024	+	5.75897i	−0.105944	+	0.238308i
$585$		0			0
$586$	12.9068	+	31.9285i	0.533175	+	1.31895i
$587$	23.7301	−	23.7301i	0.979448	−	0.979448i	−0.0203450	−	0.999793i	$-0.506476\pi$
$587$	23.7301	−	23.7301i	0.979448	−	0.979448i	0.999793	+	0.0203450i	$0.00647647\pi$
$588$	−15.2951	+	27.5614i	−0.630758	+	1.13661i
$589$	−18.4329			−0.759513
$590$		0			0
$591$	−3.45340	+	6.48151i	−0.142054	+	0.266614i
$592$	3.09805	−	2.89325i	0.127329	−	0.118912i
$593$	−1.82747	+	1.82747i	−0.0750452	+	0.0750452i	−0.743633	−	0.668588i	$-0.766899\pi$
$593$	−1.82747	+	1.82747i	−0.0750452	+	0.0750452i	0.668588	+	0.743633i	$0.266899\pi$
$594$	−30.8518	+	16.3099i	−1.26586	+	0.669205i
$595$		0			0
$596$	−3.85521	+	3.72568i	−0.157916	+	0.152610i
$597$	3.38458	+	11.1044i	0.138521	+	0.454475i
$598$	−4.62781	+	10.9080i	−0.189245	+	0.446062i
$599$	−20.1671			−0.824006			−0.412003	−	0.911182i	$-0.635171\pi$
$599$	−20.1671			−0.824006			−0.412003	+	0.911182i	$0.635171\pi$
$600$		0			0
$601$	17.2324			0.702924			0.351462	−	0.936202i	$-0.385685\pi$
$601$	17.2324			0.702924			0.351462	+	0.936202i	$0.385685\pi$
$602$	27.4380	−	64.6731i	1.11829	−	2.63588i
$603$	20.2202	+	3.96636i	0.823432	+	0.161523i
$604$	−21.7413	−	22.4972i	−0.884641	−	0.915397i
$605$		0			0
$606$	11.6714	+	1.23464i	0.474117	+	0.0501537i
$607$	20.5409	−	20.5409i	0.833729	−	0.833729i	−0.154296	−	0.988025i	$-0.549311\pi$
$607$	20.5409	−	20.5409i	0.833729	−	0.833729i	0.988025	+	0.154296i	$0.0493109\pi$
$608$	−8.00181	+	17.2013i	−0.324516	+	0.697606i
$609$	−5.74203	−	3.05940i	−0.232679	−	0.123973i
$610$		0			0
$611$	−11.6518			−0.471380
$612$	7.98389	+	12.3304i	0.322730	+	0.498425i
$613$	17.7138	−	17.7138i	0.715452	−	0.715452i	−0.252218	−	0.967670i	$-0.581160\pi$
$613$	17.7138	−	17.7138i	0.715452	−	0.715452i	0.967670	+	0.252218i	$0.0811602\pi$
$614$	5.50327	+	13.6138i	0.222094	+	0.549410i
$615$		0			0
$616$	−49.2476	−	21.8938i	−1.98424	−	0.882126i
$617$	−13.8378	−	13.8378i	−0.557089	−	0.557089i	0.371388	−	0.928478i	$-0.378882\pi$
$617$	−13.8378	−	13.8378i	−0.557089	−	0.557089i	−0.928478	+	0.371388i	$0.878882\pi$
$618$	2.34882	+	2.90454i	0.0944833	+	0.116838i
$619$	−4.67429			−0.187876			−0.0939378	−	0.995578i	$-0.529945\pi$
$619$	−4.67429			−0.187876			−0.0939378	+	0.995578i	$0.529945\pi$
$620$		0			0
$621$	3.61683	+	35.2834i	0.145138	+	1.41587i
$622$	12.1068	−	28.5366i	0.485440	−	1.14421i
$623$	14.1291	−	14.1291i	0.566071	−	0.566071i
$624$	−7.36434	−	4.25297i	−0.294810	−	0.170255i
$625$		0			0
$626$	11.1626	+	27.6136i	0.446145	+	1.10366i
$627$	−26.3873	+	8.04270i	−1.05381	+	0.321195i
$628$	0.684005	−	40.0326i	0.0272948	−	1.59748i
$629$		−	2.59450i		−	0.103450i
$630$		0			0
$631$	−26.9009			−1.07091			−0.535455	−	0.844564i	$-0.679860\pi$
$631$	−26.9009			−1.07091			−0.535455	+	0.844564i	$0.679860\pi$
$632$	−20.4671	+	7.86956i	−0.814136	+	0.313034i
$633$	−4.76772	−	15.6424i	−0.189500	−	0.621730i
$634$	32.6688	−	13.2061i	1.29744	−	0.524480i
$635$		0			0
$636$	11.4142	+	39.8793i	0.452602	+	1.58132i
$637$	−7.89779	−	7.89779i	−0.312922	−	0.312922i
$638$	2.45566	−	5.78813i	0.0972204	−	0.229154i
$639$	−13.9627	−	20.7773i	−0.552358	−	0.821936i
$640$		0			0
$641$		−	19.6466i		−	0.775995i	−0.921660	−	0.387998i	$-0.873167\pi$
$641$		−	19.6466i		−	0.775995i	0.921660	−	0.387998i	$-0.126833\pi$
$642$	−17.5375	+	14.1821i	−0.692150	+	0.559723i
$643$	18.4955	−	18.4955i	0.729392	−	0.729392i	−0.241107	−	0.970499i	$-0.577510\pi$
$643$	18.4955	−	18.4955i	0.729392	−	0.729392i	0.970499	+	0.241107i	$0.0775103\pi$
$644$	−39.3887	+	38.0653i	−1.55213	+	1.49998i
$645$		0			0
$646$	4.35179	+	10.7653i	0.171219	+	0.423557i
$647$	14.8338	+	14.8338i	0.583178	+	0.583178i	0.935775	−	0.352597i	$-0.114701\pi$
$647$	14.8338	+	14.8338i	0.583178	+	0.583178i	−0.352597	+	0.935775i	$0.614701\pi$
$648$	−25.4506	−	0.517352i	−0.999793	−	0.0203235i
$649$			31.0385i			1.21837i
$650$		0			0
$651$	17.9614	−	33.7108i	0.703962	−	1.32123i
$652$	−14.4059	−	0.246142i	−0.564178	−	0.00963965i
$653$	−9.72818	−	9.72818i	−0.380693	−	0.380693i	0.490659	−	0.871352i	$-0.336756\pi$
$653$	−9.72818	−	9.72818i	−0.380693	−	0.380693i	−0.871352	+	0.490659i	$0.836756\pi$
$654$	21.9054	+	2.31723i	0.856568	+	0.0906108i
$655$		0			0
$656$	−8.95888	−	0.306236i	−0.349786	−	0.0119565i
$657$	−6.55973	−	1.28674i	−0.255919	−	0.0502006i
$658$	−49.5858	−	21.0372i	−1.93306	−	0.820114i
$659$		−	28.9095i		−	1.12616i	−0.826404	−	0.563078i	$-0.809617\pi$
$659$		−	28.9095i		−	1.12616i	0.826404	−	0.563078i	$-0.190383\pi$
$660$		0			0
$661$		−	39.6271i		−	1.54131i	−0.637250	−	0.770657i	$-0.719928\pi$
$661$		−	39.6271i		−	1.54131i	0.637250	−	0.770657i	$-0.280072\pi$
$662$	−3.93860	+	9.28353i	−0.153078	+	0.360815i
$663$	−4.97895	+	1.51756i	−0.193366	+	0.0589370i
$664$	14.8787	−	33.4680i	0.577407	−	1.29881i
$665$		0			0
$666$	3.72359	+	2.51988i	0.144286	+	0.0976434i
$667$	−4.51864	−	4.51864i	−0.174962	−	0.174962i
$668$	−0.665615	+	38.9563i	−0.0257534	+	1.50726i
$669$	37.4095	+	19.9321i	1.44633	+	0.770618i
$670$		0			0
$671$			24.2653i			0.936751i
$672$	−23.6614	−	31.3954i	−0.912758	−	1.21110i
$673$	25.5135	+	25.5135i	0.983475	+	0.983475i	0.999866	−	0.0163909i	$-0.00521761\pi$
$673$	25.5135	+	25.5135i	0.983475	+	0.983475i	−0.0163909	+	0.999866i	$0.505218\pi$
$674$	−34.5154	+	13.9525i	−1.32948	+	0.537431i
$675$		0			0
$676$	−16.5293	+	15.9739i	−0.635742	+	0.614382i
$677$	5.46898	−	5.46898i	0.210190	−	0.210190i	−0.594158	−	0.804348i	$-0.702515\pi$
$677$	5.46898	−	5.46898i	0.210190	−	0.210190i	0.804348	+	0.594158i	$0.202515\pi$
$678$	−18.3269	+	14.8204i	−0.703839	+	0.569175i
$679$			8.10973i			0.311223i
$680$		0			0
$681$	8.02597	−	15.0635i	0.307556	−	0.577235i
$682$	33.9815	+	14.4169i	1.30122	+	0.552051i
$683$	−5.47421	−	5.47421i	−0.209465	−	0.209465i	0.594575	−	0.804040i	$-0.297320\pi$
$683$	−5.47421	−	5.47421i	−0.209465	−	0.209465i	−0.804040	+	0.594575i	$0.797320\pi$
$684$	−19.6769	−	4.21009i	−0.752364	−	0.160977i
$685$		0			0
$686$	−4.46444	−	11.0440i	−0.170453	−	0.421663i
$687$	4.81318	−	1.46703i	0.183634	−	0.0559708i
$688$	33.8012	+	36.1938i	1.28866	+	1.37987i
$689$	−14.6983			−0.559961
$690$		0			0
$691$		−	20.5069i		−	0.780118i	−0.920790	−	0.390059i	$-0.872455\pi$
$691$		−	20.5069i		−	0.780118i	0.920790	−	0.390059i	$-0.127545\pi$
$692$	−0.342010	+	20.0168i	−0.0130013	+	0.760923i
$693$	11.0035	−	56.0952i	0.417989	−	2.13088i
$694$	−2.89542	+	1.17045i	−0.109909	+	0.0444296i
$695$		0			0
$696$	3.61497	−	2.82256i	0.137025	−	0.106989i
$697$	−3.87960	+	3.87960i	−0.146950	+	0.146950i
$698$	−34.6059	−	14.6818i	−1.30985	−	0.555714i
$699$	−0.476202	+	0.893760i	−0.0180116	+	0.0338051i
$700$		0			0
$701$	−32.9176			−1.24328			−0.621641	−	0.783302i	$-0.713534\pi$
$701$	−32.9176			−1.24328			−0.621641	+	0.783302i	$0.713534\pi$
$702$	2.65777	−	8.61961i	0.100311	−	0.325326i
$703$	2.51310	+	2.51310i	0.0947833	+	0.0947833i
$704$	28.2052	−	25.4527i	1.06302	−	0.959283i
$705$		0			0
$706$	12.0733	−	4.88053i	0.454386	−	0.183681i
$707$	−13.5941	+	13.5941i	−0.511259	+	0.511259i
$708$	−10.9862	+	19.7968i	−0.412885	+	0.744009i
$709$	−31.3218			−1.17632			−0.588158	−	0.808746i	$-0.700147\pi$
$709$	−31.3218			−1.17632			−0.588158	+	0.808746i	$0.700147\pi$
$710$		0			0
$711$	−12.9727	−	19.3040i	−0.486513	−	0.723957i
$712$	5.05505	+	13.1471i	0.189446	+	0.492709i
$713$	26.5284	−	26.5284i	0.993497	−	0.993497i
$714$	−23.9286	−	2.53125i	−0.895505	−	0.0947297i
$715$		0			0
$716$	4.05759	−	3.92127i	0.151639	−	0.146545i
$717$	13.8249	−	4.21377i	0.516302	−	0.157366i
$718$	−12.7889	−	5.42578i	−0.477277	−	0.202488i
$719$	44.9529			1.67646			0.838230	−	0.545317i	$-0.183591\pi$
$719$	44.9529			1.67646			0.838230	+	0.545317i	$0.183591\pi$
$720$		0			0
$721$	−6.11880			−0.227876
$722$	10.0931	+	4.28209i	0.375628	+	0.159363i
$723$	25.5909	−	7.79996i	0.951734	−	0.290083i
$724$	20.1687	−	19.4911i	0.749563	−	0.724379i
$725$		0			0
$726$	28.1412	+	2.97688i	1.04442	+	0.110482i
$727$	19.0849	−	19.0849i	0.707821	−	0.707821i	−0.258256	−	0.966077i	$-0.583148\pi$
$727$	19.0849	−	19.0849i	0.707821	−	0.707821i	0.966077	+	0.258256i	$0.0831477\pi$
$728$	13.0023	−	4.99937i	0.481898	−	0.185289i
$729$	−5.47787	−	26.4385i	−0.202884	−	0.979203i
$730$		0			0
$731$	30.3110			1.12109
$732$	−8.58875	+	15.4767i	−0.317449	+	0.572036i
$733$	−10.9177	+	10.9177i	−0.403256	+	0.403256i	−0.879379	−	0.476123i	$-0.842042\pi$
$733$	−10.9177	+	10.9177i	−0.403256	+	0.403256i	0.476123	+	0.879379i	$0.342042\pi$
$734$	1.82358	−	0.737164i	0.0673095	−	0.0272092i
$735$		0			0
$736$	−13.2399	−	36.2722i	−0.488028	−	1.33701i
$737$	−23.0647	−	23.0647i	−0.849599	−	0.849599i
$738$	−1.79993	−	9.33595i	−0.0662562	−	0.343661i
$739$	−13.6946			−0.503765			−0.251882	−	0.967758i	$-0.581050\pi$
$739$	−13.6946			−0.503765			−0.251882	+	0.967758i	$0.581050\pi$
$740$		0			0
$741$	3.35279	−	6.29267i	0.123168	−	0.231167i
$742$	−62.5509	−	26.5377i	−2.29632	−	0.974229i
$743$	3.15355	−	3.15355i	0.115692	−	0.115692i	−0.646890	−	0.762583i	$-0.723931\pi$
$743$	3.15355	−	3.15355i	0.115692	−	0.115692i	0.762583	+	0.646890i	$0.223931\pi$
$744$	16.5709	+	21.2231i	0.607520	+	0.778076i
$745$		0			0
$746$	−35.0664	+	14.1753i	−1.28387	+	0.518994i
$747$	38.1215	+	7.47784i	1.39479	+	0.273600i
$748$	0.397252	−	23.2499i	0.0145250	−	0.850099i
$749$		−	36.9451i		−	1.34995i
$750$		0			0
$751$	32.4641			1.18463			0.592315	−	0.805706i	$-0.298214\pi$
$751$	32.4641			1.18463			0.592315	+	0.805706i	$0.298214\pi$
$752$	27.7503	−	25.9159i	1.01195	−	0.945054i
$753$	−32.5784	+	9.92971i	−1.18722	+	0.361859i
$754$	0.609067	+	1.50669i	0.0221809	+	0.0548706i
$755$		0			0
$756$	26.8732	−	31.8835i	0.977368	−	1.15959i
$757$	−23.2548	−	23.2548i	−0.845209	−	0.845209i	0.144322	−	0.989531i	$-0.453900\pi$
$757$	−23.2548	−	23.2548i	−0.845209	−	0.845209i	−0.989531	+	0.144322i	$0.953900\pi$
$758$	31.7343	+	13.4635i	1.15264	+	0.489017i
$759$	26.4014	−	49.5513i	0.958309	−	1.79860i
$760$		0			0
$761$		−	10.7051i		−	0.388059i	−0.980996	−	0.194030i	$-0.937844\pi$
$761$		−	10.7051i		−	0.388059i	0.980996	−	0.194030i	$-0.0621558\pi$
$762$	0.198452	−	0.160483i	0.00718916	−	0.00581367i
$763$	−25.5141	+	25.5141i	−0.923672	+	0.923672i
$764$	37.7731	−	36.5040i	1.36658	−	1.32067i
$765$		0			0
$766$	−27.8993	+	11.2780i	−1.00804	+	0.407492i
$767$	−5.67283	−	5.67283i	−0.204834	−	0.204834i
$768$	26.9987	−	6.25074i	0.974231	−	0.225554i
$769$			38.8506i			1.40099i	0.713658	+	0.700495i	$0.247037\pi$
$769$			38.8506i			1.40099i	−0.713658	+	0.700495i	$0.752963\pi$
$770$		0			0
$771$	28.3531	+	15.1068i	1.02111	+	0.544057i
$772$	0.399621	−	23.3885i	0.0143827	−	0.841771i
$773$	−10.3611	−	10.3611i	−0.372664	−	0.372664i	0.495783	−	0.868447i	$-0.334881\pi$
$773$	−10.3611	−	10.3611i	−0.372664	−	0.372664i	−0.868447	+	0.495783i	$0.834881\pi$
$774$	−29.4392	+	43.5018i	−1.05817	+	1.56364i
$775$		0			0
$776$	−5.22378	−	2.32232i	−0.187523	−	0.0833663i
$777$	−7.04488	+	2.14724i	−0.252734	+	0.0770319i
$778$	−2.20004	+	5.18562i	−0.0788751	+	0.185913i
$779$		−	7.51575i		−	0.269280i
$780$		0			0
$781$			39.6271i			1.41797i
$782$	−21.7565	−	9.23033i	−0.778009	−	0.330076i
$783$	3.77262	+	3.07108i	0.134822	+	0.109752i
$784$	36.3760	+	1.24342i	1.29914	+	0.0444077i
$785$		0			0
$786$	−32.3924	−	3.42658i	−1.15540	−	0.122222i
$787$	15.0090	+	15.0090i	0.535014	+	0.535014i	0.922060	−	0.387046i	$-0.126505\pi$
$787$	15.0090	+	15.0090i	0.535014	+	0.535014i	−0.387046	+	0.922060i	$0.626505\pi$
$788$	8.47901	+	0.144874i	0.302052	+	0.00516092i
$789$	−10.4700	+	19.6506i	−0.372742	+	0.699581i
$790$		0			0
$791$		−	38.6080i		−	1.37274i
$792$	32.9820	+	23.1513i	1.17196	+	0.822645i
$793$	−4.43490	−	4.43490i	−0.157488	−	0.157488i
$794$	−13.5272	−	33.4633i	−0.480064	−	1.18757i
$795$		0			0
$796$	9.63908	−	9.31523i	0.341648	−	0.330169i
$797$	7.93974	−	7.93974i	0.281240	−	0.281240i	−0.552363	−	0.833603i	$-0.686274\pi$
$797$	7.93974	−	7.93974i	0.281240	−	0.281240i	0.833603	+	0.552363i	$0.186274\pi$
$798$	25.6296	−	20.7260i	0.907280	−	0.733692i
$799$		−	23.2399i		−	0.822167i
$800$		0			0
$801$	−12.4000	+	8.33306i	−0.438133	+	0.294434i
$802$	−12.5278	+	29.5287i	−0.442371	+	1.04269i
$803$	7.48251	+	7.48251i	0.264052	+	0.264052i
$804$	−6.54717	−	22.8748i	−0.230901	−	0.806730i
$805$		0			0
$806$	−8.84563	+	3.57577i	−0.311574	+	0.125951i
$807$	−5.72008	−	18.7670i	−0.201356	−	0.660630i
$808$	−4.86364	−	12.6493i	−0.171102	−	0.445001i
$809$	−1.99039			−0.0699782			−0.0349891	−	0.999388i	$-0.511140\pi$
$809$	−1.99039			−0.0699782			−0.0349891	+	0.999388i	$0.511140\pi$
$810$		0			0
$811$		−	39.1133i		−	1.37345i	−0.726915	−	0.686727i	$-0.759047\pi$
$811$		−	39.1133i		−	1.37345i	0.726915	−	0.686727i	$-0.240953\pi$
$812$	−0.128345	+	7.51163i	−0.00450403	+	0.263607i
$813$	−3.96639	+	1.20893i	−0.139107	+	0.0423991i
$814$	−2.66740	−	6.59853i	−0.0934922	−	0.231279i
$815$		0			0
$816$	8.48271	−	14.6885i	0.296954	−	0.514199i
$817$	−29.3599	+	29.3599i	−1.02717	+	1.02717i
$818$	0.835576	−	1.96950i	0.0292152	−	0.0688621i
$819$	8.24128	+	12.2634i	0.287973	+	0.428519i
$820$		0			0
$821$	1.78624			0.0623403			0.0311702	−	0.999514i	$-0.490077\pi$
$821$	1.78624			0.0623403			0.0311702	+	0.999514i	$0.490077\pi$
$822$	1.33526	+	1.65117i	0.0465725	+	0.0575913i
$823$	−14.7321	−	14.7321i	−0.513529	−	0.513529i	0.402077	−	0.915606i	$-0.368288\pi$
$823$	−14.7321	−	14.7321i	−0.513529	−	0.513529i	−0.915606	+	0.402077i	$0.868288\pi$
$824$	1.75219	−	3.94135i	0.0610404	−	0.137303i
$825$		0			0
$826$	−13.8993	−	34.3838i	−0.483620	−	1.19637i
$827$	−2.09499	+	2.09499i	−0.0728498	+	0.0728498i	−0.742593	−	0.669743i	$-0.766404\pi$
$827$	−2.09499	+	2.09499i	−0.0728498	+	0.0728498i	0.669743	+	0.742593i	$0.266404\pi$
$828$	34.3779	−	22.2597i	1.19472	−	0.773577i
$829$	2.73512			0.0949945			0.0474973	−	0.998871i	$-0.484875\pi$
$829$	2.73512			0.0949945			0.0474973	+	0.998871i	$0.484875\pi$
$830$		0			0
$831$	5.62900	+	2.99918i	0.195268	+	0.104040i
$832$	−0.503080	+	9.80690i	−0.0174411	+	0.339993i
$833$	15.7524	−	15.7524i	0.545789	−	0.545789i
$834$	42.7794	+	4.52536i	1.48133	+	0.156700i
$835$		0			0
$836$	22.1356	+	22.9052i	0.765575	+	0.792192i
$837$	−18.0300	+	22.1486i	−0.623208	+	0.765568i
$838$	6.32747	−	14.9142i	0.218579	−	0.515204i
$839$	−20.7869			−0.717643			−0.358821	−	0.933406i	$-0.616821\pi$
$839$	−20.7869			−0.717643			−0.358821	+	0.933406i	$0.616821\pi$
$840$		0			0
$841$	28.1235			0.969778
$842$	−10.0512	+	23.6912i	−0.346387	+	0.816454i
$843$	−6.53759	−	21.4492i	−0.225167	−	0.738748i
$844$	−13.5782	+	13.1220i	−0.467381	+	0.451678i
$845$		0			0
$846$	33.3535	+	22.5714i	1.14672	+	0.776022i
$847$	−32.7772	+	32.7772i	−1.12624	+	1.12624i
$848$	35.0061	−	32.6920i	1.20211	−	1.12265i
$849$	−2.24841	+	4.21992i	−0.0771651	+	0.144827i
$850$		0			0
$851$	−7.23366			−0.247967
$852$	−14.0261	+	25.2746i	−0.480525	+	0.865895i
$853$	−12.6345	+	12.6345i	−0.432597	+	0.432597i	−0.889511	−	0.456914i	$-0.848955\pi$
$853$	−12.6345	+	12.6345i	−0.432597	+	0.432597i	0.456914	+	0.889511i	$0.348955\pi$
$854$	−10.8662	−	26.8806i	−0.371834	−	0.919834i
$855$		0			0
$856$	23.7977	+	10.5797i	0.813390	+	0.361605i
$857$	4.87637	+	4.87637i	0.166574	+	0.166574i	0.785472	−	0.618898i	$-0.212421\pi$
$857$	4.87637	+	4.87637i	0.166574	+	0.166574i	−0.618898	+	0.785472i	$0.712421\pi$
$858$	−11.1026	+	8.97840i	−0.379038	+	0.306517i
$859$	−55.4601			−1.89227			−0.946136	−	0.323768i	$-0.895050\pi$
$859$	−55.4601			−1.89227			−0.946136	+	0.323768i	$0.895050\pi$
$860$		0			0
$861$	13.7451	+	7.32351i	0.468432	+	0.249585i
$862$	−18.4861	+	43.5728i	−0.629639	+	1.48410i
$863$	−31.6243	+	31.6243i	−1.07650	+	1.07650i	−0.0796816	+	0.996820i	$0.525390\pi$
$863$	−31.6243	+	31.6243i	−1.07650	+	1.07650i	−0.996820	+	0.0796816i	$0.974610\pi$
$864$	12.8419	+	26.4402i	0.436891	+	0.899515i
$865$		0			0
$866$	−12.2883	−	30.3985i	−0.417575	−	1.03298i
$867$	5.55791	+	18.2349i	0.188757	+	0.619291i
$868$	−44.0999	−	0.753500i	−1.49685	−	0.0255755i
$869$			36.8172i			1.24894i
$870$		0			0
$871$	8.43094			0.285672
$872$	−9.12832	−	23.7408i	−0.309124	−	0.803966i
$873$	1.16716	−	5.95012i	0.0395025	−	0.201381i
$874$	30.0145	−	12.1331i	1.01526	−	0.410408i
$875$		0			0
$876$	2.12399	+	7.42089i	0.0717630	+	0.250729i
$877$	13.4991	+	13.4991i	0.455831	+	0.455831i	0.897284	−	0.441453i	$-0.145537\pi$
$877$	13.4991	+	13.4991i	0.455831	+	0.455831i	−0.441453	+	0.897284i	$0.645537\pi$
$878$	13.3421	−	31.4482i	0.450275	−	1.06132i
$879$	37.2244	+	19.8335i	1.25555	+	0.668966i
$880$		0			0
$881$			38.0875i			1.28320i	0.767039	+	0.641601i	$0.221729\pi$
$881$			38.0875i			1.28320i	−0.767039	+	0.641601i	$0.778271\pi$
$882$	7.30828	+	37.9070i	0.246083	+	1.27640i
$883$	−8.86328	+	8.86328i	−0.298273	+	0.298273i	−0.840337	−	0.542064i	$-0.817643\pi$
$883$	−8.86328	+	8.86328i	−0.298273	+	0.298273i	0.542064	+	0.840337i	$0.317643\pi$
$884$	4.17671	+	4.32192i	0.140478	+	0.145362i
$885$		0			0
$886$	−3.62348	−	8.96368i	−0.121733	−	0.301141i
$887$	−27.3410	−	27.3410i	−0.918021	−	0.918021i	0.0788646	−	0.996885i	$-0.474871\pi$
$887$	−27.3410	−	27.3410i	−0.918021	−	0.918021i	−0.996885	+	0.0788646i	$0.974871\pi$
$888$	0.634264	−	5.15276i	0.0212845	−	0.172915i
$889$			0.418066i			0.0140215i
$890$		0			0
$891$	−16.1466	+	39.5734i	−0.540931	+	1.32576i
$892$	0.836172	−	48.9385i	0.0279971	−	1.63858i
$893$	22.5107	+	22.5107i	0.753292	+	0.753292i
$894$	−0.690742	+	6.52977i	−0.0231019	+	0.218388i
$895$		0			0
$896$	−19.8472	+	40.8265i	−0.663049	+	1.36392i
$897$	4.23106	+	13.8817i	0.141271	+	0.463495i
$898$	11.3338	+	4.80845i	0.378214	+	0.160460i
$899$		−	5.14555i		−	0.171614i
$900$		0			0
$901$		−	29.3163i		−	0.976668i
$902$	−5.87829	+	13.8555i	−0.195726	+	0.461337i
$903$	−25.0857	−	82.3037i	−0.834801	−	2.73890i
$904$	24.8689	+	11.0559i	0.827126	+	0.367712i
$905$		0			0
$906$	−38.1046	−	4.03084i	−1.26594	−	0.133916i
$907$	11.1000	+	11.1000i	0.368569	+	0.368569i	0.866955	−	0.498386i	$-0.166074\pi$
$907$	11.1000	+	11.1000i	0.368569	+	0.368569i	−0.498386	+	0.866955i	$0.666074\pi$
$908$	−19.7059	−	0.336698i	−0.653962	−	0.0111737i
$909$	11.9305	−	8.01753i	0.395710	−	0.265925i
$910$		0			0
$911$			28.8502i			0.955849i	0.878401	+	0.477925i	$0.158611\pi$
$911$			28.8502i			0.955849i	−0.878401	+	0.477925i	$0.841389\pi$
$912$	6.01103	+	22.4441i	0.199045	+	0.743200i
$913$	−43.4842	−	43.4842i	−1.43912	−	1.43912i
$914$	10.7641	−	4.35127i	0.356044	−	0.143927i
$915$		0			0
$916$	−4.03765	−	4.17803i	−0.133408	−	0.138046i
$917$	37.7287	−	37.7287i	1.24591	−	1.24591i
$918$	17.1921	+	5.30102i	0.567425	+	0.174960i
$919$			45.6949i			1.50733i	0.657256	+	0.753667i	$0.271717\pi$
$919$			45.6949i			1.50733i	−0.657256	+	0.753667i	$0.728283\pi$
$920$		0			0
$921$	15.8719	+	8.45669i	0.522998	+	0.278657i
$922$	−26.8579	−	11.3946i	−0.884517	−	0.375263i
$923$	−7.24253	−	7.24253i	−0.238391	−	0.238391i
$924$	−63.4594	+	18.1632i	−2.08766	+	0.597526i
$925$		0			0
$926$	7.34411	+	18.1677i	0.241342	+	0.597027i
$927$	4.48937	+	0.880625i	0.147450	+	0.0289235i
$928$	−4.80177	−	2.23371i	−0.157626	−	0.0733253i
$929$	55.0325			1.80556			0.902780	−	0.430103i	$-0.141523\pi$
$929$	55.0325			1.80556			0.902780	+	0.430103i	$0.141523\pi$
$930$		0			0
$931$			30.5164i			1.00013i
$932$	1.16920	+	0.0199772i	0.0382985	+	0.000654375i
$933$	−11.0689	−	36.3159i	−0.362380	−	1.18893i
$934$	−33.2019	+	13.4216i	−1.08640	+	0.439167i
$935$		0			0
$936$	−10.2593	+	1.79674i	−0.335337	+	0.0587281i
$937$	14.5009	−	14.5009i	0.473724	−	0.473724i	−0.429394	−	0.903117i	$-0.641273\pi$
$937$	14.5009	−	14.5009i	0.473724	−	0.473724i	0.903117	+	0.429394i	$0.141273\pi$
$938$	35.8792	+	15.2220i	1.17150	+	0.497016i
$939$	32.1938	+	17.1531i	1.05061	+	0.559771i
$940$		0			0
$941$	55.5572			1.81111			0.905556	−	0.424226i	$-0.139454\pi$
$941$	55.5572			1.81111			0.905556	+	0.424226i	$0.139454\pi$
$942$	−30.8343	−	38.1296i	−1.00464	−	1.24233i
$943$	10.8166	+	10.8166i	0.352237	+	0.352237i
$944$	26.1281	+	0.893121i	0.850398	+	0.0290686i
$945$		0			0
$946$	77.0891	−	31.1626i	2.50638	−	1.01318i
$947$	12.2804	−	12.2804i	0.399059	−	0.399059i	−0.478842	−	0.877901i	$-0.658943\pi$
$947$	12.2804	−	12.2804i	0.399059	−	0.399059i	0.877901	+	0.478842i	$0.158943\pi$
$948$	−13.0315	+	23.4825i	−0.423244	+	0.762675i
$949$	−2.73512			−0.0887856
$950$		0			0
$951$	20.2933	−	38.0875i	0.658057	−	1.23507i
$952$	9.97143	+	25.9336i	0.323176	+	0.840512i
$953$	10.6654	−	10.6654i	0.345486	−	0.345486i	−0.512939	−	0.858425i	$-0.671443\pi$
$953$	10.6654	−	10.6654i	0.345486	−	0.345486i	0.858425	+	0.512939i	$0.171443\pi$
$954$	42.0743	+	28.4731i	1.36221	+	0.921851i
$955$		0			0
$956$	−11.5974	−	12.0006i	−0.375086	−	0.388126i
$957$	−2.24513	−	7.36604i	−0.0725747	−	0.238110i
$958$	23.6523	+	10.0347i	0.764173	+	0.324206i
$959$	−3.47842			−0.112324
$960$		0			0
$961$	−0.791035			−0.0255173
$962$	1.69351	+	0.718483i	0.0546009	+	0.0231648i
$963$	−5.31719	+	27.1067i	−0.171344	+	0.873500i
$964$	−21.4675	−	22.2138i	−0.691421	−	0.715460i
$965$		0			0
$966$	−7.05731	+	66.7147i	−0.227065	+	2.14651i
$967$	38.1275	−	38.1275i	1.22610	−	1.22610i	0.260670	−	0.965428i	$-0.416056\pi$
$967$	38.1275	−	38.1275i	1.22610	−	1.22610i	0.965428	−	0.260670i	$-0.0839436\pi$
$968$	−11.7269	−	30.4992i	−0.376917	−	0.980281i
$969$	12.5510	+	6.68725i	0.403195	+	0.214826i
$970$		0			0
$971$	−30.2255			−0.969981			−0.484991	−	0.874519i	$-0.661177\pi$
$971$	−30.2255			−0.969981			−0.484991	+	0.874519i	$0.661177\pi$
$972$	−24.3056	+	19.5253i	−0.779602	+	0.626275i
$973$	−49.8269	+	49.8269i	−1.59738	+	1.59738i
$974$	4.83574	−	1.95480i	0.154947	−	0.0626359i
$975$		0			0
$976$	20.4264	+	0.698224i	0.653835	+	0.0223496i
$977$	−11.0641	−	11.0641i	−0.353972	−	0.353972i	0.507613	−	0.861585i	$-0.330528\pi$
$977$	−11.0641	−	11.0641i	−0.353972	−	0.353972i	−0.861585	+	0.507613i	$0.830528\pi$
$978$	−13.7211	+	11.0958i	−0.438751	+	0.354806i
$979$	23.6497			0.755847
$980$		0			0
$981$	22.3917	−	15.0477i	0.714913	−	0.480436i
$982$	13.6402	+	5.78695i	0.435276	+	0.184669i
$983$	−9.37350	+	9.37350i	−0.298968	+	0.298968i	−0.840610	−	0.541641i	$-0.817803\pi$
$983$	−9.37350	+	9.37350i	−0.298968	+	0.298968i	0.541641	+	0.840610i	$0.317803\pi$
$984$	−8.65342	+	6.75657i	−0.275861	+	0.215392i
$985$		0			0
$986$	−3.00516	+	1.21481i	−0.0957037	+	0.0386873i
$987$	−63.1035	+	19.2336i	−2.00861	+	0.612212i
$988$	−8.23197	−	0.140653i	−0.261894	−	0.00447477i
$989$		−	84.5092i		−	2.68724i
$990$		0			0
$991$	−51.4416			−1.63410			−0.817048	−	0.576569i	$-0.804391\pi$
$991$	−51.4416			−1.63410			−0.817048	+	0.576569i	$0.804391\pi$
$992$	13.1139	−	28.1907i	0.416366	−	0.895054i
$993$	3.60094	+	11.8143i	0.114272	+	0.374916i
$994$	−17.7454	−	43.8980i	−0.562848	−	1.39236i
$995$		0			0
$996$	−12.3435	−	43.1261i	−0.391118	−	1.36650i
$997$	−1.26149	−	1.26149i	−0.0399517	−	0.0399517i	0.686849	−	0.726800i	$-0.258993\pi$
$997$	−1.26149	−	1.26149i	−0.0399517	−	0.0399517i	−0.726800	+	0.686849i	$0.758993\pi$
$998$	−21.6943	−	9.20397i	−0.686721	−	0.291347i
$999$	5.47787	−	0.561525i	0.173312	−	0.0177659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.w.k.293.3	✓	64
3.2	odd	2	inner	600.2.w.k.293.29	yes	64
5.2	odd	4	inner	600.2.w.k.557.20	yes	64
5.3	odd	4	inner	600.2.w.k.557.13	yes	64
5.4	even	2	inner	600.2.w.k.293.30	yes	64
8.5	even	2	inner	600.2.w.k.293.14	yes	64
15.2	even	4	inner	600.2.w.k.557.14	yes	64
15.8	even	4	inner	600.2.w.k.557.19	yes	64
15.14	odd	2	inner	600.2.w.k.293.4	yes	64
24.5	odd	2	inner	600.2.w.k.293.20	yes	64
40.13	odd	4	inner	600.2.w.k.557.4	yes	64
40.29	even	2	inner	600.2.w.k.293.19	yes	64
40.37	odd	4	inner	600.2.w.k.557.29	yes	64
120.29	odd	2	inner	600.2.w.k.293.13	yes	64
120.53	even	4	inner	600.2.w.k.557.30	yes	64
120.77	even	4	inner	600.2.w.k.557.3	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.w.k.293.3	✓	64	1.1	even	1	trivial
600.2.w.k.293.4	yes	64	15.14	odd	2	inner
600.2.w.k.293.13	yes	64	120.29	odd	2	inner
600.2.w.k.293.14	yes	64	8.5	even	2	inner
600.2.w.k.293.19	yes	64	40.29	even	2	inner
600.2.w.k.293.20	yes	64	24.5	odd	2	inner
600.2.w.k.293.29	yes	64	3.2	odd	2	inner
600.2.w.k.293.30	yes	64	5.4	even	2	inner
600.2.w.k.557.3	yes	64	120.77	even	4	inner
600.2.w.k.557.4	yes	64	40.13	odd	4	inner
600.2.w.k.557.13	yes	64	5.3	odd	4	inner
600.2.w.k.557.14	yes	64	15.2	even	4	inner
600.2.w.k.557.19	yes	64	15.8	even	4	inner
600.2.w.k.557.20	yes	64	5.2	odd	4	inner
600.2.w.k.557.29	yes	64	40.37	odd	4	inner
600.2.w.k.557.30	yes	64	120.53	even	4	inner

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30189 - 0.552337i) q^{2} +(-1.65680 + 0.504984i) q^{3} +(1.38985 + 1.43817i) q^{4} +(2.43590 + 0.257678i) q^{6} +(-2.83719 + 2.83719i) q^{7} +(-1.01508 - 2.64000i) q^{8} +(2.48998 - 1.67332i) q^{9} -4.74897 q^{11} +(-3.02895 - 1.68091i) q^{12} +(0.867956 - 0.867956i) q^{13} +(5.26080 - 2.12663i) q^{14} +(-0.136650 + 3.99767i) q^{16} +(1.73117 + 1.73117i) q^{17} +(-4.16592 + 0.803169i) q^{18} -3.35370 q^{19} +(3.26792 - 6.13340i) q^{21} +(6.18265 + 2.62303i) q^{22} +(4.82662 - 4.82662i) q^{23} +(3.01494 + 3.86136i) q^{24} +(-1.60939 + 0.650581i) q^{26} +(-3.28041 + 4.02976i) q^{27} +(-8.02362 - 0.137093i) q^{28} -0.936190i q^{29} +5.49627 q^{31} +(2.38596 - 5.12905i) q^{32} +(7.86810 - 2.39815i) q^{33} +(-1.29761 - 3.20999i) q^{34} +(5.86720 + 1.25535i) q^{36} +(-0.749350 - 0.749350i) q^{37} +(4.36616 + 1.85238i) q^{38} +(-0.999726 + 1.87633i) q^{39} +2.24103i q^{41} +(-7.64219 + 6.18003i) q^{42} +(8.75448 - 8.75448i) q^{43} +(-6.60034 - 6.82981i) q^{44} +(-8.94967 + 3.61782i) q^{46} +(-6.71219 - 6.71219i) q^{47} +(-1.79236 - 6.69234i) q^{48} -9.09930i q^{49} +(-3.74242 - 1.99399i) q^{51} +(2.45459 + 0.0419396i) q^{52} +(-8.46720 - 8.46720i) q^{53} +(6.49652 - 3.43442i) q^{54} +(10.3702 + 4.61022i) q^{56} +(5.55642 - 1.69357i) q^{57} +(-0.517093 + 1.21882i) q^{58} -6.53585i q^{59} -5.10959i q^{61} +(-7.15555 - 3.03579i) q^{62} +(-2.31703 + 11.8121i) q^{63} +(-5.93923 + 5.35962i) q^{64} +(-11.5680 - 1.22370i) q^{66} +(4.85678 + 4.85678i) q^{67} +(-0.0836501 + 4.89577i) q^{68} +(-5.55939 + 10.4341i) q^{69} -8.34435i q^{71} +(-6.94509 - 4.87501i) q^{72} +(-1.57561 - 1.57561i) q^{73} +(0.561679 + 1.38947i) q^{74} +(-4.66114 - 4.82319i) q^{76} +(13.4737 - 13.4737i) q^{77} +(2.33791 - 1.89060i) q^{78} -7.75267i q^{79} +(3.40002 - 8.33306i) q^{81} +(1.23780 - 2.91758i) q^{82} +(9.15657 + 9.15657i) q^{83} +(13.3628 - 3.82466i) q^{84} +(-16.2328 + 6.56196i) q^{86} +(0.472761 + 1.55108i) q^{87} +(4.82057 + 12.5373i) q^{88} -4.97996 q^{89} +4.92511i q^{91} +(13.6498 + 0.233222i) q^{92} +(-9.10622 + 2.77553i) q^{93} +(5.03116 + 12.4459i) q^{94} +(-1.36297 + 9.70270i) q^{96} +(1.42918 - 1.42918i) q^{97} +(-5.02588 + 11.8463i) q^{98} +(-11.8248 + 7.94653i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 12 q^{6} - 40 q^{16} + 32 q^{31} - 84 q^{36} - 128 q^{46} - 180 q^{66} + 168 q^{76} + 48 q^{81} + 228 q^{96}+O(q^{100}) \) 64 * q + 12 * q^6 - 40 * q^16 + 32 * q^31 - 84 * q^36 - 128 * q^46 - 180 * q^66 + 168 * q^76 + 48 * q^81 + 228 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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