LMFDB - Embedded newform 600.2.w.k.293.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(293,600)]

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

lf = mfeigenbasis(mf)

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")

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

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			293.29
Character	$\chi$	$=$	600.293
Dual form			600.2.w.k.557.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30189 + 0.552337i) q^{2} +(-0.504984 + 1.65680i) q^{3} +(1.38985 + 1.43817i) q^{4} +(-1.57255 + 1.87806i) q^{6} +(-2.83719 + 2.83719i) q^{7} +(1.01508 + 2.64000i) q^{8} +(-2.48998 - 1.67332i) q^{9} +O(q^{10})$	\(q+(1.30189 + 0.552337i) q^{2} +(-0.504984 + 1.65680i) q^{3} +(1.38985 + 1.43817i) q^{4} +(-1.57255 + 1.87806i) q^{6} +(-2.83719 + 2.83719i) q^{7} +(1.01508 + 2.64000i) q^{8} +(-2.48998 - 1.67332i) q^{9} +4.74897 q^{11} +(-3.08461 + 1.57645i) 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} +(-2.31745 - 3.55379i) q^{18} -3.35370 q^{19} +(-3.26792 - 6.13340i) q^{21} +(6.18265 + 2.62303i) q^{22} +(-4.82662 + 4.82662i) q^{23} +(-4.88656 + 0.348623i) q^{24} +(1.60939 - 0.650581i) q^{26} +(4.02976 - 3.28041i) q^{27} +(-8.02362 - 0.137093i) q^{28} +0.936190i q^{29} +5.49627 q^{31} +(-2.38596 + 5.12905i) q^{32} +(-2.39815 + 7.86810i) q^{33} +(-1.29761 - 3.20999i) q^{34} +(-1.05418 - 5.90667i) q^{36} +(-0.749350 - 0.749350i) q^{37} +(-4.36616 - 1.85238i) q^{38} +(0.999726 + 1.87633i) q^{39} -2.24103i q^{41} +(-0.866782 - 9.79002i) 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} +(-6.55433 - 2.24516i) q^{48} -9.09930i q^{49} +(3.74242 - 1.99399i) q^{51} +(2.45459 + 0.0419396i) q^{52} +(8.46720 + 8.46720i) q^{53} +(7.05820 - 2.04495i) q^{54} +(-10.3702 - 4.61022i) q^{56} +(1.69357 - 5.55642i) q^{57} +(-0.517093 + 1.21882i) q^{58} +6.53585i q^{59} -5.10959i q^{61} +(7.15555 + 3.03579i) q^{62} +(11.8121 - 2.31703i) q^{63} +(-5.93923 + 5.35962i) q^{64} +(-7.46798 + 8.91883i) q^{66} +(4.85678 + 4.85678i) q^{67} +(0.0836501 - 4.89577i) q^{68} +(-5.55939 - 10.4341i) q^{69} +8.34435i q^{71} +(1.89004 - 8.27211i) 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} +(0.265167 + 2.99497i) q^{78} -7.75267i q^{79} +(3.40002 + 8.33306i) q^{81} +(1.23780 - 2.91758i) q^{82} +(-9.15657 - 9.15657i) q^{83} +(4.27894 - 13.2243i) q^{84} +(16.2328 - 6.56196i) q^{86} +(-1.55108 - 0.472761i) q^{87} +(4.82057 + 12.5373i) q^{88} +4.97996 q^{89} +4.92511i q^{91} +(-13.6498 - 0.233222i) q^{92} +(-2.77553 + 9.10622i) q^{93} +(5.03116 + 12.4459i) q^{94} +(-7.29295 - 6.54316i) 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}+O(q^{10}) $ 64 * q + 12 * q^6	$ 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

Display 100 coefficients 10 coefficients

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
$3$	−0.504984	+	1.65680i	−0.291553	+	0.956555i
$3$	−0.504984	+	1.65680i	−0.291553	+	0.956555i
$4$	1.38985	+	1.43817i	0.694924	+	0.719084i
$5$		0			0
$5$		0			0
$6$	−1.57255	+	1.87806i	−0.641990	+	0.766713i
$7$	−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	$-0.246001\pi$
$11$	4.74897			1.43187			0.715934	+	0.698168i	$0.246001\pi$
$12$	−3.08461	+	1.57645i	−0.890450	+	0.455082i
$13$	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	0.465289	−	0.885159i	$-0.345950\pi$
$17$	−1.73117	−	1.73117i	−0.419870	−	0.419870i	−0.885159	+	0.465289i	$0.845950\pi$
$18$	−2.31745	−	3.55379i	−0.546229	−	0.837636i
$19$	−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	$0.502050\pi$
$23$	−4.82662	+	4.82662i	−1.00642	+	1.00642i	−0.999979	+	0.00644154i	$0.997950\pi$
$24$	−4.88656	+	0.348623i	−0.997465	+	0.0711623i
$25$		0			0
$26$	1.60939	−	0.650581i	0.315627	−	0.127589i
$27$	4.02976	−	3.28041i	0.775527	−	0.631314i
$28$	−8.02362	−	0.137093i	−1.51632	−	0.0259081i
$29$			0.936190i			0.173846i	0.996215	+	0.0869231i	$0.0277034\pi$
$29$			0.936190i			0.173846i	−0.996215	+	0.0869231i	$0.972297\pi$
$30$		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
$33$	−2.39815	+	7.86810i	−0.417465	+	1.36966i
$34$	−1.29761	−	3.20999i	−0.222538	−	0.550508i
$35$		0			0
$36$	−1.05418	−	5.90667i	−0.175697	−	0.984444i
$37$	−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	$-0.944009\pi$
$41$		−	2.24103i		−	0.349990i	0.984569	−	0.174995i	$-0.0559909\pi$
$42$	−0.866782	−	9.79002i	−0.133747	−	1.51063i
$43$	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	0.999785	−	0.0207122i	$-0.00659336\pi$
$47$	6.71219	+	6.71219i	0.979073	+	0.979073i	−0.0207122	+	0.999785i	$0.506593\pi$
$48$	−6.55433	−	2.24516i	−0.946036	−	0.324061i
$49$		−	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	$0.0573695\pi$
$53$	8.46720	+	8.46720i	1.16306	+	1.16306i	0.179258	+	0.983802i	$0.442630\pi$
$54$	7.05820	−	2.04495i	0.960499	−	0.278283i
$55$		0			0
$56$	−10.3702	−	4.61022i	−1.38577	−	0.616067i
$57$	1.69357	−	5.55642i	0.224319	−	0.735966i
$58$	−0.517093	+	1.21882i	−0.0678976	+	0.160039i
$59$			6.53585i			0.850895i	0.904983	+	0.425448i	$0.139883\pi$
$59$			6.53585i			0.850895i	−0.904983	+	0.425448i	$0.860117\pi$
$60$		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
$63$	11.8121	−	2.31703i	1.48818	−	0.291919i
$64$	−5.93923	+	5.35962i	−0.742404	+	0.669952i
$65$		0			0
$66$	−7.46798	+	8.91883i	−0.919245	+	1.09783i
$67$	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	$0.164885\pi$
$71$			8.34435i			0.990292i	−0.868810	+	0.495146i	$0.835115\pi$
$72$	1.89004	−	8.27211i	0.222743	−	0.974877i
$73$	−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
$78$	0.265167	+	2.99497i	0.0300242	+	0.339114i
$79$		−	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	$-0.998384\pi$
$83$	−9.15657	−	9.15657i	−1.00506	−	1.00506i	−0.00507654	−	0.999987i	$-0.501616\pi$
$84$	4.27894	−	13.2243i	0.466870	−	1.44289i
$85$		0			0
$86$	16.2328	−	6.56196i	1.75043	−	0.707595i
$87$	−1.55108	−	0.472761i	−0.166293	−	0.0506853i
$88$	4.82057	+	12.5373i	0.513875	+	1.33648i
$89$	4.97996			0.527875			0.263938	−	0.964540i	$-0.414979\pi$
$89$	4.97996			0.527875			0.263938	+	0.964540i	$0.414979\pi$
$90$		0			0
$91$			4.92511i			0.516292i
$92$	−13.6498	−	0.233222i	−1.42309	−	0.0243151i
$93$	−2.77553	+	9.10622i	−0.287809	+	0.944272i
$94$	5.03116	+	12.4459i	0.518924	+	1.28370i
$95$		0			0
$96$	−7.29295	−	6.54316i	−0.744333	−	0.667808i
$97$	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	$-0.576617\pi$
$101$	−4.79140			−0.476762			−0.238381	+	0.971172i	$0.576617\pi$
$102$	5.97358	−	0.528885i	0.591472	−	0.0523674i
$103$	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	−0.318496	−	0.947924i	$-0.603178\pi$
$107$	6.51086	−	6.51086i	0.629429	−	0.629429i	0.947924	+	0.318496i	$0.103178\pi$
$108$	10.3185	+	1.23620i	0.992900	+	0.118953i
$109$	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	−0.310511	−	0.950570i	$-0.600500\pi$
$113$	6.80391	−	6.80391i	0.640058	−	0.640058i	0.950570	+	0.310511i	$0.100500\pi$
$114$	5.27386	−	6.29844i	0.493942	−	0.589903i
$115$		0			0
$116$	−1.34640	+	1.30116i	−0.125010	+	0.120810i
$117$	−3.61356	+	0.708829i	−0.334074	+	0.0655312i
$118$	−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
$123$	3.71294	+	1.13168i	0.334784	+	0.102041i
$124$	7.63897	+	7.90455i	0.686000	+	0.709850i
$125$		0			0
$126$	16.6578	+	3.50772i	1.48400	+	0.312493i
$127$	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	$-0.302692\pi$
$131$	13.2979			1.16184			0.580922	+	0.813959i	$0.302692\pi$
$132$	−14.6487	+	7.48651i	−1.27501	+	0.651617i
$133$	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	0.680436	−	0.732808i	$-0.261791\pi$
$137$	−0.613004	−	0.613004i	−0.0523724	−	0.0523724i	−0.732808	+	0.680436i	$0.761791\pi$
$138$	−1.47457	−	16.6548i	−0.125524	−	1.41775i
$139$	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
$144$	7.02962	−	9.72546i	0.585801	−	0.810455i
$145$		0			0
$146$	−1.18100	−	2.92154i	−0.0977407	−	0.241788i
$147$	15.0757	+	4.59501i	1.24343	+	0.378990i
$148$	0.0362086	−	2.11917i	0.00297633	−	0.174195i
$149$		−	2.68064i		−	0.219607i	−0.993953	−	0.109803i	$-0.964978\pi$
$149$		−	2.68064i		−	0.219607i	0.993953	−	0.109803i	$-0.0350221\pi$
$150$		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
$153$	1.41378	+	7.20738i	0.114298	+	0.582682i
$154$	−24.9834	+	10.0993i	−2.01322	+	0.813825i
$155$		0			0
$156$	−1.30902	+	4.04559i	−0.104805	+	0.323907i
$157$	−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
$162$	−0.176201	+	12.7267i	−0.0138437	+	0.999904i
$163$	−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	$-0.978247\pi$
$167$	−13.7751	−	13.7751i	−1.06595	−	1.06595i	−0.0682869	−	0.997666i	$-0.521753\pi$
$168$	12.8750	−	14.8532i	0.993327	−	1.14595i
$169$			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	0.384848	−	0.922980i	$-0.374254\pi$
$173$	−7.07803	−	7.07803i	−0.538133	−	0.538133i	−0.922980	+	0.384848i	$0.874254\pi$
$174$	−1.75822	−	1.47220i	−0.133290	−	0.111608i
$175$		0			0
$176$	−0.648945	+	18.9848i	−0.0489161	+	1.43103i
$177$	−10.8286	−	3.30050i	−0.813928	−	0.248081i
$178$	6.48338	+	2.75062i	0.485950	+	0.206168i
$179$			2.82136i			0.210879i	0.994426	+	0.105439i	$0.0336249\pi$
$179$			2.82136i			0.210879i	−0.994426	+	0.105439i	$0.966375\pi$
$180$		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
$183$	8.46558	+	2.58026i	0.625794	+	0.190739i
$184$	−17.6417	−	7.84290i	−1.30056	−	0.578186i
$185$		0			0
$186$	−8.64315	+	10.3223i	−0.633746	+	0.756867i
$187$	−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	$0.399147\pi$
$191$			26.2648i			1.90045i	−0.311563	+	0.950225i	$0.600853\pi$
$192$	−5.88060	−	12.5467i	−0.424396	−	0.905477i
$193$	−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	−0.805801	−	0.592187i	$-0.798265\pi$
$197$	−2.99822	+	2.99822i	−0.213614	+	0.213614i	0.592187	+	0.805801i	$0.298265\pi$
$198$	−11.0055	−	16.8768i	−0.782128	−	1.19938i
$199$		−	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
$204$	8.06908	+	2.61088i	0.564949	+	0.182798i
$205$		0			0
$206$	0.808260	+	1.99945i	0.0563142	+	0.139308i
$207$	20.0947	−	3.94173i	1.39668	−	0.273969i
$208$	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
$213$	−13.8249	−	4.21377i	−0.947269	−	0.288722i
$214$	12.0726	−	4.88025i	0.825268	−	0.333607i
$215$		0			0
$216$	12.7508	+	7.30870i	0.867582	+	0.497294i
$217$	−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
$222$	2.58571	−	0.228932i	0.173541	−	0.0153649i
$223$	−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	−0.436982	−	0.899470i	$-0.643953\pi$
$227$	6.96809	−	6.96809i	0.462489	−	0.462489i	0.899470	+	0.436982i	$0.143953\pi$
$228$	10.3449	−	5.28694i	0.685105	−	0.350136i
$229$	−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	−0.720520	−	0.693435i	$-0.756097\pi$
$233$	−0.413436	+	0.413436i	−0.0270851	+	0.0270851i	0.693435	+	0.720520i	$0.256097\pi$
$234$	−5.09598	−	1.07308i	−0.333134	−	0.0701498i
$235$		0			0
$236$	−9.39964	+	9.08383i	−0.611865	+	0.591307i
$237$	12.8446	+	3.91498i	0.834349	+	0.254305i
$238$	12.7889	+	5.42578i	0.828981	+	0.351701i
$239$	8.34435			0.539751			0.269876	−	0.962895i	$-0.413017\pi$
$239$	8.34435			0.539751			0.269876	+	0.962895i	$0.413017\pi$
$240$		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
$243$	−15.5232	+	1.42509i	−0.995812	+	0.0914196i
$244$	7.34845	−	7.10155i	0.470436	−	0.454630i
$245$		0			0
$246$	4.20878	+	3.52413i	0.268342	+	0.224690i
$247$	−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	$-0.713099\pi$
$251$	−19.6634			−1.24114			−0.620572	+	0.784150i	$0.713099\pi$
$252$	19.7493	+	13.7674i	1.24409	+	0.867266i
$253$	−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	0.985837	−	0.167709i	$-0.0536368\pi$
$257$	13.1156	+	13.1156i	0.818128	+	0.818128i	−0.167709	+	0.985837i	$0.553637\pi$
$258$	2.67456	+	30.2082i	0.166511	+	1.88068i
$259$	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	−0.929453	−	0.368940i	$-0.879721\pi$
$263$	−9.08999	+	9.08999i	−0.560513	+	0.560513i	0.368940	+	0.929453i	$0.379721\pi$
$264$	−23.2061	+	1.65560i	−1.42824	+	0.101895i
$265$		0			0
$266$	17.6432	−	7.13209i	1.08177	−	0.437297i
$267$	−2.51480	+	8.25081i	−0.153903	+	0.504941i
$268$	−0.234680	+	13.7350i	−0.0143353	+	0.839002i
$269$		−	11.3272i		−	0.690635i	−0.938486	−	0.345317i	$-0.887771\pi$
$269$		−	11.3272i		−	0.690635i	0.938486	−	0.345317i	$-0.112229\pi$
$270$		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
$273$	−8.15993	−	2.48710i	−0.493862	−	0.150526i
$274$	−0.459480	−	1.13665i	−0.0277582	−	0.0686675i
$275$		0			0
$276$	7.27932	−	22.4972i	0.438164	−	1.35417i
$277$	−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	$-0.873805\pi$
$281$		−	12.9461i		−	0.772301i	0.922436	−	0.386151i	$-0.126195\pi$
$282$	−23.1611	+	2.05062i	−1.37922	+	0.122113i
$283$	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
$288$	14.5235	−	8.77878i	0.855808	−	0.517294i
$289$		−	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	$0.00190327\pi$
$293$	17.2193	+	17.2193i	1.00596	+	1.00596i	0.00597927	+	0.999982i	$0.498097\pi$
$294$	17.0890	+	14.3091i	0.996650	+	0.834523i
$295$		0			0
$296$	1.21764	−	2.73893i	0.0707737	−	0.159197i
$297$	19.1372	−	15.5785i	1.11045	−	0.903959i
$298$	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
$303$	2.41958	−	7.93840i	0.139001	−	0.456049i
$304$	0.458282	−	13.4070i	0.0262843	−	0.768943i
$305$		0			0
$306$	−2.14031	+	10.1641i	−0.122353	+	0.581044i
$307$	−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	$-0.786538\pi$
$311$		−	21.9193i		−	1.24293i	0.783442	−	0.621465i	$-0.213462\pi$
$312$	−3.93873	+	4.54391i	−0.222987	+	0.257248i
$313$	−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	−0.0103899	−	0.999946i	$-0.503307\pi$
$317$	17.6185	−	17.6185i	0.989556	−	0.989556i	0.999946	+	0.0103899i	$0.00330728\pi$
$318$	−29.2170	+	2.58679i	−1.63841	+	0.145060i
$319$			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
$324$	−7.25883	+	16.4715i	−0.403268	+	0.915082i
$325$		0			0
$326$	−9.44543	+	3.81823i	−0.523134	+	0.211472i
$327$	−4.54119	+	14.8992i	−0.251128	+	0.823926i
$328$	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
$333$	0.611967	+	3.11977i	0.0335356	+	0.170962i
$334$	−10.3252	−	25.5423i	−0.564971	−	1.39761i
$335$		0			0
$336$	24.9658	−	12.2259i	1.36200	−	0.666980i
$337$	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
$342$	7.77205	+	11.9184i	0.420264	+	0.644471i
$343$	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	−0.747777	−	0.663950i	$-0.768879\pi$
$347$	−1.56152	+	1.56152i	−0.0838269	+	0.0838269i	0.663950	+	0.747777i	$0.268879\pi$
$348$	−1.47586	−	2.88778i	−0.0791142	−	0.154801i
$349$	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	−0.512268	−	0.858826i	$-0.671194\pi$
$353$	6.51124	−	6.51124i	0.346558	−	0.346558i	0.858826	+	0.512268i	$0.171194\pi$
$354$	−12.2747	−	10.2779i	−0.652392	−	0.546266i
$355$		0			0
$356$	6.92139	+	7.16202i	0.366833	+	0.379586i
$357$	−4.96062	+	16.2753i	−0.262544	+	0.861379i
$358$	−1.55834	+	3.67311i	−0.0823611	+	0.194130i
$359$	−9.82331			−0.518455			−0.259227	−	0.965816i	$-0.583468\pi$
$359$	−9.82331			−0.518455			−0.259227	+	0.965816i	$0.583468\pi$
$360$		0			0
$361$	−7.75267			−0.408035
$362$	7.74591	−	18.2576i	0.407116	−	0.959597i
$363$	−5.83393	+	19.1405i	−0.306202	+	1.00462i
$364$	−7.08313	+	6.84515i	−0.371257	+	0.358784i
$365$		0			0
$366$	9.59610	+	8.03508i	0.501596	+	0.420000i
$367$	−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
$372$	−16.9538	+	8.66459i	−0.879015	+	0.449238i
$373$	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
$378$	−14.2235	+	25.8274i	−0.731580	+	1.32842i
$379$	−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	−0.977901	−	0.209070i	$-0.932957\pi$
$383$	−15.0463	+	15.0463i	−0.768831	+	0.768831i	0.209070	+	0.977901i	$0.432957\pi$
$384$	−0.725930	−	19.5825i	−0.0370450	−	0.999314i
$385$		0			0
$386$	−6.19904	−	15.3350i	−0.315523	−	0.780532i
$387$	−36.4475	+	7.14947i	−1.85273	+	0.363428i
$388$	4.04175	+	0.0690581i	0.205189	+	0.00350589i
$389$			3.98314i			0.201953i	0.994889	+	0.100977i	$0.0321967\pi$
$389$			3.98314i			0.201953i	−0.994889	+	0.100977i	$0.967803\pi$
$390$		0			0
$391$	16.7114			0.845132
$392$	24.0222	−	9.23650i	1.21330	−	0.466514i
$393$	−6.71524	+	22.0320i	−0.338739	+	1.11137i
$394$	−5.55939	+	2.24733i	−0.280078	+	0.113219i
$395$		0			0
$396$	−5.00629	−	28.0506i	−0.251575	−	1.40959i
$397$	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	$0.191636\pi$
$401$			22.6814i			1.13265i	−0.824181	+	0.566327i	$0.808364\pi$
$402$	−16.7588	+	1.48378i	−0.835854	+	0.0740043i
$403$	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
$408$	9.06299	+	7.85594i	0.448685	+	0.388927i
$409$			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
$414$	28.3383	+	5.96733i	1.39275	+	0.293278i
$415$		0			0
$416$	2.38088	+	6.52270i	0.116732	+	0.319802i
$417$	−8.86857	+	29.0969i	−0.434296	+	1.42488i
$418$	−20.7348	−	8.79687i	−1.01417	−	0.430269i
$419$		−	11.4558i		−	0.559653i	−0.960051	−	0.279827i	$-0.909723\pi$
$419$		−	11.4558i		−	0.559653i	0.960051	−	0.279827i	$-0.0902770\pi$
$420$		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
$423$	−5.48161	−	27.9448i	−0.266525	−	1.35873i
$424$	−13.7586	+	30.9483i	−0.668175	+	1.50298i
$425$		0			0
$426$	−15.6712	−	13.1219i	−0.759270	−	0.635758i
$427$	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	$0.298409\pi$
$431$			33.4688i			1.61214i	−0.591822	+	0.806069i	$0.701591\pi$
$432$	12.5633	+	16.5579i	0.604452	+	0.796641i
$433$	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
$438$	5.43680	−	0.481359i	0.259780	−	0.0230002i
$439$			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	0.582880	−	0.812558i	$-0.301926\pi$
$443$	−4.83418	−	4.83418i	−0.229679	−	0.229679i	−0.812558	+	0.582880i	$0.801926\pi$
$444$	3.49276	+	1.13014i	0.165759	+	0.0536340i
$445$		0			0
$446$	−12.9710	−	32.0872i	−0.614193	−	1.51937i
$447$	4.44129	+	1.35368i	0.210066	+	0.0640269i
$448$	1.64448	−	32.0570i	0.0776942	−	1.51455i
$449$	8.70564			0.410845			0.205422	−	0.978673i	$-0.434143\pi$
$449$	8.70564			0.410845			0.205422	+	0.978673i	$0.434143\pi$
$450$		0			0
$451$		−	10.6426i		−	0.501139i
$452$	19.2416	+	0.328765i	0.905047	+	0.0154638i
$453$	7.89944	−	25.9172i	0.371148	−	1.21770i
$454$	12.9204	−	5.22297i	0.606386	−	0.245126i
$455$		0			0
$456$	16.3881	−	1.16918i	0.767442	−	0.0547517i
$457$	−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	$-0.659514\pi$
$461$	−20.6299			−0.960829			−0.480415	+	0.877042i	$0.659514\pi$
$462$	−4.11632	−	46.4925i	−0.191509	−	2.16303i
$463$	−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	−0.987322	−	0.158729i	$-0.949260\pi$
$467$	−17.9061	+	17.9061i	−0.828593	+	0.828593i	0.158729	+	0.987322i	$0.449260\pi$
$468$	−6.04171	−	4.21174i	−0.279278	−	0.194688i
$469$	−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
$474$	14.5599	+	12.1914i	0.668760	+	0.559972i
$475$		0			0
$476$	13.6529	+	14.1276i	0.625780	+	0.647536i
$477$	−6.91486	−	35.2515i	−0.316610	−	1.61406i
$478$	10.8634	+	4.60890i	0.496882	+	0.210806i
$479$	18.1677			0.830102			0.415051	−	0.909798i	$-0.363764\pi$
$479$	18.1677			0.830102			0.415051	+	0.909798i	$0.363764\pi$
$480$		0			0
$481$	−1.30081			−0.0593116
$482$	−20.1089	−	8.53137i	−0.915937	−	0.388593i
$483$	45.3767	+	13.8306i	2.06471	+	0.629312i
$484$	16.0565	+	16.6147i	0.729841	+	0.755215i
$485$		0			0
$486$	−20.9966	−	6.71872i	−0.952427	−	0.304767i
$487$	−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	$-0.424028\pi$
$491$	10.4772			0.472829			0.236415	+	0.971652i	$0.424028\pi$
$492$	3.53287	+	6.91270i	0.159274	+	0.311648i
$493$	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
$498$	31.5957	−	2.79740i	1.41584	−	0.125354i
$499$	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	−0.918766	−	0.394802i	$-0.870813\pi$
$503$	−11.7513	+	11.7513i	−0.523965	+	0.523965i	0.394802	+	0.918766i	$0.370813\pi$
$504$	18.1072	+	28.8319i	0.806557	+	1.28428i
$505$		0			0
$506$	−42.5017	+	17.1809i	−1.88943	+	0.763785i
$507$	−19.0421	−	5.80394i	−0.845690	−	0.257762i
$508$	0.208357	+	0.00356002i	0.00924434	+	0.000157951i
$509$		−	16.9269i		−	0.750272i	−0.926970	−	0.375136i	$-0.877596\pi$
$509$		−	16.9269i		−	0.750272i	0.926970	−	0.375136i	$-0.122404\pi$
$510$		0			0
$511$	8.94060			0.395509
$512$	−20.1782	−	10.2392i	−0.891759	−	0.452511i
$513$	−13.5146	+	11.0015i	−0.596685	+	0.485729i
$514$	9.83086	+	24.3193i	0.433620	+	1.07268i
$515$		0			0
$516$	−13.2032	+	40.8051i	−0.581236	+	1.79635i
$517$	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	$-0.875485\pi$
$521$		−	17.4056i		−	0.762553i	0.924461	−	0.381277i	$-0.124515\pi$
$522$	3.32702	−	2.16958i	0.145620	−	0.0949598i
$523$	−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
$528$	−31.1263	−	10.6622i	−1.35460	−	0.464012i
$529$		−	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
$534$	−7.83123	+	9.35265i	−0.338891	+	0.404729i
$535$		0			0
$536$	−7.89191	+	17.7519i	−0.340878	+	0.766767i
$537$	−4.67444	−	1.42474i	−0.201717	−	0.0614823i
$538$	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
$543$	23.2348	+	7.08184i	0.997100	+	0.303911i
$544$	13.0098	−	4.74875i	0.557789	−	0.203601i
$545$		0			0
$546$	−9.24963	−	7.74498i	−0.395848	−	0.331454i
$547$	−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
$552$	21.9029	−	25.2683i	0.932250	−	1.07549i
$553$	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	−0.229533	−	0.973301i	$-0.573720\pi$
$557$	17.5535	−	17.5535i	0.743767	−	0.743767i	0.973301	+	0.229533i	$0.0737200\pi$
$558$	−12.7373	−	19.5326i	−0.539215	−	0.826880i
$559$		−	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	0.945281	−	0.326257i	$-0.105788\pi$
$563$	14.6880	+	14.6880i	0.619024	+	0.619024i	−0.326257	+	0.945281i	$0.605788\pi$
$564$	−31.2859	−	10.1231i	−1.31737	−	0.426257i
$565$		0			0
$566$	3.61955	−	1.46317i	0.152141	−	0.0615016i
$567$	−33.2890	−	13.9960i	−1.39801	−	0.587776i
$568$	−22.0291	+	8.47017i	−0.924321	+	0.355400i
$569$	27.6388			1.15868			0.579338	−	0.815087i	$-0.303311\pi$
$569$	27.6388			1.15868			0.579338	+	0.815087i	$0.303311\pi$
$570$		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
$573$	−43.5155	−	13.2633i	−1.81789	−	0.554082i
$574$	4.76584	+	11.7896i	0.198922	+	0.492089i
$575$		0			0
$576$	23.7569	−	3.40713i	0.989872	−	0.141964i
$577$	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
$582$	0.436626	+	4.93154i	0.0180987	+	0.204419i
$583$	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	−0.999793	−	0.0203450i	$-0.993524\pi$
$587$	−23.7301	+	23.7301i	−0.979448	+	0.979448i	0.0203450	+	0.999793i	$0.493524\pi$
$588$	14.3446	+	28.0678i	0.591561	+	1.15750i
$589$	−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	−0.668588	−	0.743633i	$-0.733101\pi$
$593$	1.82747	−	1.82747i	0.0750452	−	0.0750452i	0.743633	+	0.668588i	$0.233101\pi$
$594$	33.5192	−	9.71141i	1.37531	−	0.398464i
$595$		0			0
$596$	3.85521	−	3.72568i	0.157916	−	0.152610i
$597$	11.1044	+	3.38458i	0.454475	+	0.138521i
$598$	−4.62781	+	10.9080i	−0.189245	+	0.446062i
$599$	20.1671			0.824006			0.412003	−	0.911182i	$-0.364829\pi$
$599$	20.1671			0.824006			0.412003	+	0.911182i	$0.364829\pi$
$600$		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
$603$	−3.96636	−	20.2202i	−0.161523	−	0.823432i
$604$	−21.7413	−	22.4972i	−0.884641	−	0.915397i
$605$		0			0
$606$	7.53471	−	8.99851i	0.306077	−	0.365540i
$607$	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
$612$	−8.40047	+	12.0504i	−0.339569	+	0.487109i
$613$	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	0.928478	−	0.371388i	$-0.121118\pi$
$617$	13.8378	+	13.8378i	0.557089	+	0.557089i	−0.371388	+	0.928478i	$0.621118\pi$
$618$	−3.72085	+	0.329434i	−0.149675	+	0.0132518i
$619$	−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
$624$	−7.63757	+	3.74017i	−0.305747	+	0.149727i
$625$		0			0
$626$	−11.1626	−	27.6136i	−0.446145	−	1.10366i
$627$	8.04270	−	26.3873i	0.321195	−	1.05381i
$628$	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
$633$	−15.6424	−	4.76772i	−0.621730	−	0.189500i
$634$	32.6688	−	13.2061i	1.29744	−	0.524480i
$635$		0			0
$636$	−39.4661	−	12.7699i	−1.56493	−	0.506359i
$637$	−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	$0.126833\pi$
$641$			19.6466i			0.775995i	−0.921660	+	0.387998i	$0.873167\pi$
$642$	1.98911	+	22.4664i	0.0785041	+	0.886678i
$643$	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	0.352597	−	0.935775i	$-0.385299\pi$
$647$	−14.8338	−	14.8338i	−0.583178	−	0.583178i	−0.935775	+	0.352597i	$0.885299\pi$
$648$	−18.5480	+	17.4348i	−0.728635	+	0.684902i
$649$			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	0.871352	−	0.490659i	$-0.163244\pi$
$653$	9.72818	+	9.72818i	0.380693	+	0.380693i	−0.490659	+	0.871352i	$0.663244\pi$
$654$	−14.1415	+	16.8888i	−0.552976	+	0.660406i
$655$		0			0
$656$	8.95888	+	0.306236i	0.349786	+	0.0119565i
$657$	1.28674	+	6.55973i	0.0502006	+	0.255919i
$658$	−49.5858	−	21.0372i	−1.93306	−	0.820114i
$659$			28.9095i			1.12616i	0.826404	+	0.563078i	$0.190383\pi$
$659$			28.9095i			1.12616i	−0.826404	+	0.563078i	$0.809617\pi$
$660$		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
$663$	1.51756	−	4.97895i	0.0589370	−	0.193366i
$664$	14.8787	−	33.4680i	0.577407	−	1.29881i
$665$		0			0
$666$	−0.926448	+	4.39961i	−0.0358991	+	0.170482i
$667$	−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
$672$	39.2557	−	2.12730i	1.51432	−	0.0820624i
$673$	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	−0.804348	−	0.594158i	$-0.797485\pi$
$677$	−5.46898	+	5.46898i	−0.210190	+	0.210190i	0.594158	+	0.804348i	$0.297485\pi$
$678$	2.07864	+	23.4776i	0.0798299	+	0.901652i
$679$			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	0.804040	−	0.594575i	$-0.202680\pi$
$683$	5.47421	+	5.47421i	0.209465	+	0.209465i	−0.594575	+	0.804040i	$0.702680\pi$
$684$	3.53542	+	19.8092i	0.135180	+	0.757424i
$685$		0			0
$686$	4.46444	+	11.0440i	0.170453	+	0.421663i
$687$	1.46703	−	4.81318i	0.0559708	−	0.183634i
$688$	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
$693$	56.0952	−	11.0035i	2.13088	−	0.417989i
$694$	−2.89542	+	1.17045i	−0.109909	+	0.0444296i
$695$		0			0
$696$	−0.326377	−	4.57475i	−0.0123713	−	0.173405i
$697$	−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	$-0.286466\pi$
$701$	32.9176			1.24328			0.621641	+	0.783302i	$0.286466\pi$
$702$	4.35128	−	7.90113i	0.164228	−	0.298209i
$703$	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
$708$	−10.3034	−	20.1605i	−0.387227	−	0.757679i
$709$	−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
$714$	−15.4476	+	18.4487i	−0.578113	+	0.690426i
$715$		0			0
$716$	−4.05759	+	3.92127i	−0.151639	+	0.146545i
$717$	−4.21377	+	13.8249i	−0.157366	+	0.516302i
$718$	−12.7889	−	5.42578i	−0.477277	−	0.202488i
$719$	−44.9529			−1.67646			−0.838230	−	0.545317i	$-0.816409\pi$
$719$	−44.9529			−1.67646			−0.838230	+	0.545317i	$0.816409\pi$
$720$		0			0
$721$	−6.11880			−0.227876
$722$	−10.0931	−	4.28209i	−0.375628	−	0.159363i
$723$	7.79996	−	25.5909i	0.290083	−	0.951734i
$724$	20.1687	−	19.4911i	0.749563	−	0.724379i
$725$		0			0
$726$	−18.1672	+	21.6966i	−0.674248	+	0.805237i
$727$	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
$732$	8.05501	+	15.7611i	0.297722	+	0.582547i
$733$	−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
$738$	−7.96414	+	5.19348i	−0.293164	+	0.191175i
$739$	−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	−0.762583	−	0.646890i	$-0.776069\pi$
$743$	−3.15355	+	3.15355i	−0.115692	+	0.115692i	0.646890	+	0.762583i	$0.276069\pi$
$744$	−26.8578	+	1.91612i	−0.984656	+	0.0702485i
$745$		0			0
$746$	35.0664	−	14.1753i	1.28387	−	0.518994i
$747$	7.47784	+	38.1215i	0.273600	+	1.39479i
$748$	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
$753$	9.92971	−	32.5784i	0.361859	−	1.18722i
$754$	0.609067	+	1.50669i	0.0221809	+	0.0548706i
$755$		0			0
$756$	−32.7829	+	25.7683i	−1.19230	+	0.937183i
$757$	−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	$0.0621558\pi$
$761$			10.7051i			0.388059i	−0.980996	+	0.194030i	$0.937844\pi$
$762$	0.0225085	+	0.254227i	0.000815399	+	0.00920966i
$763$	−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
$768$	9.87104	−	25.8952i	0.356191	−	0.934413i
$769$			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	0.868447	−	0.495783i	$-0.165119\pi$
$773$	10.3611	+	10.3611i	0.372664	+	0.372664i	−0.495783	+	0.868447i	$0.665119\pi$
$774$	−51.3997	−	10.8235i	−1.84752	−	0.389042i
$775$		0			0
$776$	5.22378	+	2.32232i	0.187523	+	0.0833663i
$777$	−2.14724	+	7.04488i	−0.0770319	+	0.252734i
$778$	−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
$783$	3.07108	+	3.77262i	0.109752	+	0.134822i
$784$	36.3760	+	1.24342i	1.29914	+	0.0444077i
$785$		0			0
$786$	−20.9116	+	24.9742i	−0.745893	+	0.890801i
$787$	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
$792$	8.97573	−	39.2840i	0.318939	−	1.39590i
$793$	−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	−0.833603	−	0.552363i	$-0.813726\pi$
$797$	−7.93974	+	7.93974i	−0.281240	+	0.281240i	0.552363	+	0.833603i	$0.313726\pi$
$798$	2.90693	+	32.8328i	0.102904	+	1.16227i
$799$		−	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
$804$	−22.6377	−	7.32480i	−0.798371	−	0.258326i
$805$		0			0
$806$	8.84563	−	3.57577i	0.311574	−	0.125951i
$807$	18.7670	+	5.72008i	0.660630	+	0.201356i
$808$	−4.86364	−	12.6493i	−0.171102	−	0.445001i
$809$	1.99039			0.0699782			0.0349891	−	0.999388i	$-0.488860\pi$
$809$	1.99039			0.0699782			0.0349891	+	0.999388i	$0.488860\pi$
$810$		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
$813$	−1.20893	+	3.96639i	−0.0423991	+	0.139107i
$814$	−2.66740	−	6.59853i	−0.0934922	−	0.231279i
$815$		0			0
$816$	7.45991	+	15.2334i	0.261149	+	0.533276i
$817$	−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	$-0.509923\pi$
$821$	−1.78624			−0.0623403			−0.0311702	+	0.999514i	$0.509923\pi$
$822$	2.11523	−	0.187277i	0.0737772	−	0.00653204i
$823$	−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	−0.669743	−	0.742593i	$-0.733596\pi$
$827$	2.09499	−	2.09499i	0.0728498	−	0.0728498i	0.742593	+	0.669743i	$0.233596\pi$
$828$	33.5974	+	23.4211i	1.16759	+	0.813940i
$829$	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
$834$	−27.6172	+	32.9825i	−0.956305	+	1.14209i
$835$		0			0
$836$	−22.1356	−	22.9052i	−0.765575	−	0.792192i
$837$	22.1486	−	18.0300i	0.765568	−	0.623208i
$838$	6.32747	−	14.9142i	0.218579	−	0.515204i
$839$	20.7869			0.717643			0.358821	−	0.933406i	$-0.383179\pi$
$839$	20.7869			0.717643			0.358821	+	0.933406i	$0.383179\pi$
$840$		0			0
$841$	28.1235			0.969778
$842$	10.0512	−	23.6912i	0.346387	−	0.816454i
$843$	21.4492	+	6.53759i	0.738748	+	0.225167i
$844$	−13.5782	+	13.1220i	−0.467381	+	0.451678i
$845$		0			0
$846$	8.29852	−	39.4089i	0.285309	−	1.35491i
$847$	−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
$852$	−13.1544	−	25.7391i	−0.450664	−	0.881805i
$853$	−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	0.618898	−	0.785472i	$-0.287579\pi$
$857$	−4.87637	−	4.87637i	−0.166574	−	0.166574i	−0.785472	+	0.618898i	$0.787579\pi$
$858$	1.25927	+	14.2230i	0.0429907	+	0.485566i
$859$	−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	$-0.474610\pi$
$863$	31.6243	−	31.6243i	1.07650	−	1.07650i	0.996820	−	0.0796816i	$-0.0253904\pi$
$864$	7.21053	+	28.4958i	0.245307	+	0.969445i
$865$		0			0
$866$	12.2883	+	30.3985i	0.417575	+	1.03298i
$867$	18.2349	+	5.55791i	0.619291	+	0.188757i
$868$	−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
$873$	−5.95012	+	1.16716i	−0.201381	+	0.0395025i
$874$	30.0145	−	12.1331i	1.01526	−	0.410408i
$875$		0			0
$876$	7.34400	+	2.37627i	0.248131	+	0.0802867i
$877$	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	$-0.778271\pi$
$881$		−	38.0875i		−	1.28320i	0.767039	−	0.641601i	$-0.221729\pi$
$882$	−32.3370	+	21.0872i	−1.08884	+	0.710043i
$883$	−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	0.996885	−	0.0788646i	$-0.0251295\pi$
$887$	27.3410	+	27.3410i	0.918021	+	0.918021i	−0.0788646	+	0.996885i	$0.525129\pi$
$888$	3.92298	+	3.40050i	0.131647	+	0.114113i
$889$			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
$894$	5.03439	+	4.21544i	0.168375	+	0.140985i
$895$		0			0
$896$	19.8472	−	40.8265i	0.663049	−	1.36392i
$897$	−13.8817	−	4.23106i	−0.463495	−	0.141271i
$898$	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
$903$	−82.3037	−	25.0857i	−2.73890	−	0.834801i
$904$	24.8689	+	11.0559i	0.827126	+	0.367712i
$905$		0			0
$906$	24.5993	−	29.3783i	0.817256	−	0.976029i
$907$	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	$-0.841389\pi$
$911$		−	28.8502i		−	0.955849i	0.878401	−	0.477925i	$-0.158611\pi$
$912$	21.9813	+	7.52960i	0.727873	+	0.249330i
$913$	−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
$918$	−15.7591	−	8.67878i	−0.520128	−	0.286442i
$919$			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
$924$	20.3205	−	62.8018i	0.668496	−	2.06603i
$925$		0			0
$926$	−7.34411	−	18.1677i	−0.241342	−	0.597027i
$927$	−0.880625	−	4.48937i	−0.0289235	−	0.147450i
$928$	−4.80177	−	2.23371i	−0.157626	−	0.0733253i
$929$	−55.0325			−1.80556			−0.902780	−	0.430103i	$-0.858477\pi$
$929$	−55.0325			−1.80556			−0.902780	+	0.430103i	$0.858477\pi$
$930$		0			0
$931$			30.5164i			1.00013i
$932$	−1.16920	−	0.0199772i	−0.0382985	−	0.000654375i
$933$	36.3159	+	11.0689i	1.18893	+	0.362380i
$934$	−33.2019	+	13.4216i	−1.08640	+	0.439167i
$935$		0			0
$936$	−5.53935	−	8.82029i	−0.181059	−	0.288300i
$937$	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	$-0.860546\pi$
$941$	−55.5572			−1.81111			−0.905556	+	0.424226i	$0.860546\pi$
$942$	48.8459	−	4.32468i	1.59148	−	0.140906i
$943$	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	−0.877901	−	0.478842i	$-0.841057\pi$
$947$	−12.2804	+	12.2804i	−0.399059	+	0.399059i	0.478842	+	0.877901i	$0.341057\pi$
$948$	12.2217	+	23.9139i	0.396942	+	0.776689i
$949$	−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	−0.858425	−	0.512939i	$-0.828557\pi$
$953$	−10.6654	+	10.6654i	−0.345486	+	0.345486i	0.512939	+	0.858425i	$0.328557\pi$
$954$	10.4683	−	49.7130i	0.338924	−	1.60952i
$955$		0			0
$956$	11.5974	+	12.0006i	0.375086	+	0.388126i
$957$	−7.36604	−	2.24513i	−0.238110	−	0.0725747i
$958$	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
$963$	−27.1067	+	5.31719i	−0.873500	+	0.171344i
$964$	−21.4675	−	22.2138i	−0.691421	−	0.715460i
$965$		0			0
$966$	51.4364	+	43.0691i	1.65494	+	1.38573i
$967$	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	$-0.338823\pi$
$971$	30.2255			0.969981			0.484991	+	0.874519i	$0.338823\pi$
$972$	−23.6244	−	20.3443i	−0.757752	−	0.652543i
$973$	−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	0.861585	−	0.507613i	$-0.169472\pi$
$977$	11.0641	+	11.0641i	0.353972	+	0.353972i	−0.507613	+	0.861585i	$0.669472\pi$
$978$	−1.55625	−	17.5774i	−0.0497634	−	0.562062i
$979$	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	−0.541641	−	0.840610i	$-0.682197\pi$
$983$	9.37350	−	9.37350i	0.298968	−	0.298968i	0.840610	+	0.541641i	$0.182197\pi$
$984$	0.781273	+	10.9509i	0.0249061	+	0.349103i
$985$		0			0
$986$	3.00516	−	1.21481i	0.0957037	−	0.0386873i
$987$	19.2336	−	63.1035i	0.612212	−	2.00861i
$988$	−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
$993$	11.8143	+	3.60094i	0.374916	+	0.114272i
$994$	−17.7454	−	43.8980i	−0.562848	−	1.39236i
$995$		0			0
$996$	42.6793	+	13.8096i	1.35234	+	0.437573i
$997$	−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.293.29	yes	64
3.2	odd	2	inner	600.2.w.k.293.3	✓	64
5.2	odd	4	inner	600.2.w.k.557.14	yes	64
5.3	odd	4	inner	600.2.w.k.557.19	yes	64
5.4	even	2	inner	600.2.w.k.293.4	yes	64
8.5	even	2	inner	600.2.w.k.293.20	yes	64
15.2	even	4	inner	600.2.w.k.557.20	yes	64
15.8	even	4	inner	600.2.w.k.557.13	yes	64
15.14	odd	2	inner	600.2.w.k.293.30	yes	64
24.5	odd	2	inner	600.2.w.k.293.14	yes	64
40.13	odd	4	inner	600.2.w.k.557.30	yes	64
40.29	even	2	inner	600.2.w.k.293.13	yes	64
40.37	odd	4	inner	600.2.w.k.557.3	yes	64
120.29	odd	2	inner	600.2.w.k.293.19	yes	64
120.53	even	4	inner	600.2.w.k.557.4	yes	64
120.77	even	4	inner	600.2.w.k.557.29	yes	64

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

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

\(f(q)\)	\(=\)	\(q+(1.30189 + 0.552337i) q^{2} +(-0.504984 + 1.65680i) q^{3} +(1.38985 + 1.43817i) q^{4} +(-1.57255 + 1.87806i) q^{6} +(-2.83719 + 2.83719i) q^{7} +(1.01508 + 2.64000i) q^{8} +(-2.48998 - 1.67332i) q^{9} +O(q^{10})\)	\(q+(1.30189 + 0.552337i) q^{2} +(-0.504984 + 1.65680i) q^{3} +(1.38985 + 1.43817i) q^{4} +(-1.57255 + 1.87806i) q^{6} +(-2.83719 + 2.83719i) q^{7} +(1.01508 + 2.64000i) q^{8} +(-2.48998 - 1.67332i) q^{9} +4.74897 q^{11} +(-3.08461 + 1.57645i) 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} +(-2.31745 - 3.55379i) q^{18} -3.35370 q^{19} +(-3.26792 - 6.13340i) q^{21} +(6.18265 + 2.62303i) q^{22} +(-4.82662 + 4.82662i) q^{23} +(-4.88656 + 0.348623i) q^{24} +(1.60939 - 0.650581i) q^{26} +(4.02976 - 3.28041i) q^{27} +(-8.02362 - 0.137093i) q^{28} +0.936190i q^{29} +5.49627 q^{31} +(-2.38596 + 5.12905i) q^{32} +(-2.39815 + 7.86810i) q^{33} +(-1.29761 - 3.20999i) q^{34} +(-1.05418 - 5.90667i) q^{36} +(-0.749350 - 0.749350i) q^{37} +(-4.36616 - 1.85238i) q^{38} +(0.999726 + 1.87633i) q^{39} -2.24103i q^{41} +(-0.866782 - 9.79002i) 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} +(-6.55433 - 2.24516i) q^{48} -9.09930i q^{49} +(3.74242 - 1.99399i) q^{51} +(2.45459 + 0.0419396i) q^{52} +(8.46720 + 8.46720i) q^{53} +(7.05820 - 2.04495i) q^{54} +(-10.3702 - 4.61022i) q^{56} +(1.69357 - 5.55642i) q^{57} +(-0.517093 + 1.21882i) q^{58} +6.53585i q^{59} -5.10959i q^{61} +(7.15555 + 3.03579i) q^{62} +(11.8121 - 2.31703i) q^{63} +(-5.93923 + 5.35962i) q^{64} +(-7.46798 + 8.91883i) q^{66} +(4.85678 + 4.85678i) q^{67} +(0.0836501 - 4.89577i) q^{68} +(-5.55939 - 10.4341i) q^{69} +8.34435i q^{71} +(1.89004 - 8.27211i) 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} +(0.265167 + 2.99497i) q^{78} -7.75267i q^{79} +(3.40002 + 8.33306i) q^{81} +(1.23780 - 2.91758i) q^{82} +(-9.15657 - 9.15657i) q^{83} +(4.27894 - 13.2243i) q^{84} +(16.2328 - 6.56196i) q^{86} +(-1.55108 - 0.472761i) q^{87} +(4.82057 + 12.5373i) q^{88} +4.97996 q^{89} +4.92511i q^{91} +(-13.6498 - 0.233222i) q^{92} +(-2.77553 + 9.10622i) q^{93} +(5.03116 + 12.4459i) q^{94} +(-7.29295 - 6.54316i) q^{96} +(1.42918 - 1.42918i) q^{97} +(5.02588 - 11.8463i) q^{98} +(-11.8248 - 7.94653i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 12 q^{6}+O(q^{10}) \) 64 * q + 12 * q^6	\( 64 q + 12 q^{6} - 40 q^{16} + 32 q^{31} - 84 q^{36} - 128 q^{46} - 180 q^{66} + 168 q^{76} + 48 q^{81} + 228 q^{96}+O(q^{100}) \) 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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