LMFDB - Embedded newform 600.2.w.k.293.20

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)

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);

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")

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			293.20
Character	$\chi$	$=$	600.293
Dual form			600.2.w.k.557.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

$2$	0.552337	+	1.30189i	0.390561	+	0.920577i
$2$	0.552337	+	1.30189i	0.390561	+	0.920577i
$3$	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
$6$	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	$0.976044\pi$
$8$	−2.64000	−	1.01508i	−0.933382	−	0.358884i
$9$	−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	$0.753999\pi$
$12$	1.68091	+	3.02895i	0.485236	+	0.874383i
$13$	−0.867956	+	0.867956i	−0.240728	+	0.240728i	−0.817151	−	0.576424i	$-0.804448\pi$
$13$	−0.867956	+	0.867956i	−0.240728	+	0.240728i	0.576424	+	0.817151i	$0.304448\pi$
$14$	−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	$0.845950\pi$
$18$	0.803169	−	4.16592i	0.189309	−	0.981918i
$19$	3.35370			0.769392			0.384696	−	0.923043i	$-0.374306\pi$
$19$	3.35370			0.769392			0.384696	+	0.923043i	$0.374306\pi$
$20$		0			0
$21$	3.26792	+	6.13340i	0.713120	+	1.33842i
$22$	−2.62303	−	6.18265i	−0.559232	−	1.31814i
$23$	−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	$0.997950\pi$
$24$	−3.01494	+	3.86136i	−0.615423	+	0.788197i
$25$		0			0
$26$	−1.60939	−	0.650581i	−0.315627	−	0.127589i
$27$	−4.02976	+	3.28041i	−0.775527	+	0.631314i
$28$	−0.137093	−	8.02362i	−0.0259081	−	1.51632i
$29$		−	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	$0.335688\pi$
$32$	5.12905	−	2.38596i	0.906697	−	0.421783i
$33$	−2.39815	+	7.86810i	−0.417465	+	1.36966i
$34$	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	0.766015	−	0.642823i	$-0.222237\pi$
$37$	0.749350	+	0.749350i	0.123192	+	0.123192i	−0.642823	+	0.766015i	$0.722237\pi$
$38$	1.85238	+	4.36616i	0.300495	+	0.708285i
$39$	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	$-0.0559909\pi$
$42$	−6.18003	+	7.64219i	−0.953599	+	1.17922i
$43$	−8.75448	+	8.75448i	−1.33505	+	1.33505i	−0.434256	+	0.900789i	$0.642989\pi$
$43$	−8.75448	+	8.75448i	−1.33505	+	1.33505i	−0.900789	+	0.434256i	$0.857011\pi$
$44$	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	$0.506593\pi$
$48$	−6.69234	−	1.79236i	−0.965957	−	0.258704i
$49$		−	9.09930i		−	1.29990i
$50$		0			0
$51$	−3.74242	+	1.99399i	−0.524043	+	0.279214i
$52$	−0.0419396	−	2.45459i	−0.00581598	−	0.340391i
$53$	−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
$57$	1.69357	−	5.55642i	0.224319	−	0.735966i
$58$	1.21882	−	0.517093i	0.160039	−	0.0678976i
$59$		−	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	$0.106074\pi$
$61$			5.10959i			0.654216i	−0.944987	+	0.327108i	$0.893926\pi$
$62$	3.03579	+	7.15555i	0.385546	+	0.908756i
$63$	11.8121	−	2.31703i	1.48818	−	0.291919i
$64$	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	0.345185	−	0.938535i	$-0.387816\pi$
$67$	−4.85678	−	4.85678i	−0.593350	−	0.593350i	−0.938535	+	0.345185i	$0.887816\pi$
$68$	4.89577	−	0.0836501i	0.593699	−	0.0101441i
$69$	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	$0.835115\pi$
$72$	4.87501	+	6.94509i	0.574526	+	0.818487i
$73$	−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
$78$	−1.89060	+	2.33791i	−0.214068	+	0.264716i
$79$		−	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
$82$	2.91758	−	1.23780i	0.322193	−	0.136693i
$83$	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
$87$	−1.55108	−	0.472761i	−0.166293	−	0.0506853i
$88$	12.5373	+	4.82057i	1.33648	+	0.513875i
$89$	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
$92$	−0.233222	−	13.6498i	−0.0243151	−	1.42309i
$93$	2.77553	−	9.10622i	0.287809	−	0.944272i
$94$	−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	$0.217281\pi$
$98$	11.8463	−	5.02588i	1.19666	−	0.507691i
$99$	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	$0.423383\pi$
$102$	−4.66304	−	3.77087i	−0.461709	−	0.373372i
$103$	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	$0.396822\pi$
$108$	0.882973	−	10.3547i	0.0849641	−	0.996384i
$109$	−8.99273			−0.861347			−0.430674	−	0.902508i	$-0.641724\pi$
$109$	−8.99273			−0.861347			−0.430674	+	0.902508i	$0.641724\pi$
$110$		0			0
$111$	1.61993	−	0.863114i	0.153757	−	0.0819232i
$112$	11.7298	+	10.9544i	1.10837	+	1.03510i
$113$	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	$0.100500\pi$
$114$	8.16928	−	0.864176i	0.765123	−	0.0809375i
$115$		0			0
$116$	1.34640	+	1.30116i	0.125010	+	0.120810i
$117$	3.61356	−	0.708829i	0.334074	−	0.0655312i
$118$	8.50897	−	3.60999i	0.783314	−	0.332327i
$119$	9.82331			0.900502
$120$		0			0
$121$	11.5527			1.05025
$122$	−6.65214	+	2.82222i	−0.602256	+	0.255512i
$123$	−3.71294	−	1.13168i	−0.334784	−	0.102041i
$124$	−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	$0.248528\pi$
$128$	−3.69719	+	10.6926i	−0.326788	+	0.945098i
$129$	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	$0.697308\pi$
$132$	−7.98257	−	14.3844i	−0.694794	−	1.25200i
$133$	−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	$0.761791\pi$
$138$	−10.5135	+	13.0009i	−0.894965	+	1.10671i
$139$	−17.5621			−1.48960			−0.744798	−	0.667290i	$-0.767454\pi$
$139$	−17.5621			−1.48960			−0.744798	+	0.667290i	$0.767454\pi$
$140$		0			0
$141$	14.5103	−	7.73121i	1.22199	−	0.651086i
$142$	−10.8634	+	4.60890i	−0.911640	+	0.386770i
$143$	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
$147$	−15.0757	−	4.59501i	−1.24343	−	0.378990i
$148$	−2.11917	+	0.0362086i	−0.174195	+	0.00297633i
$149$			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	$0.719619\pi$
$152$	−8.85379	−	3.40427i	−0.718137	−	0.276123i
$153$	1.41378	+	7.20738i	0.114298	+	0.582682i
$154$	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	$0.0445604\pi$
$157$	14.1557	+	14.1557i	1.12975	+	1.12975i	0.139534	+	0.990217i	$0.455440\pi$
$158$	10.0931	−	4.28209i	0.802967	−	0.340665i
$159$	−18.3043	+	9.75267i	−1.45162	+	0.773437i
$160$		0			0
$161$		−	27.3881i		−	2.15849i
$162$	−8.97079	+	9.02912i	−0.704812	+	0.709394i
$163$	5.09399	−	5.09399i	0.398992	−	0.398992i	−0.478885	−	0.877878i	$-0.658959\pi$
$163$	5.09399	−	5.09399i	0.398992	−	0.398992i	0.877878	+	0.478885i	$0.158959\pi$
$164$	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	$-0.521753\pi$
$168$	−2.40145	−	19.5094i	−0.185276	−	1.50518i
$169$			11.4933i			0.884100i
$170$		0			0
$171$	−8.35066	−	5.61181i	−0.638591	−	0.429146i
$172$	−0.423016	−	24.7578i	−0.0322547	−	1.88776i
$173$	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
$177$	−10.8286	−	3.30050i	−0.813928	−	0.248081i
$178$	2.75062	+	6.48338i	0.206168	+	0.485950i
$179$		−	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	$0.174513\pi$
$181$			14.0239i			1.04239i	−0.853439	+	0.521194i	$0.825487\pi$
$182$	6.41197	−	2.72032i	0.475287	−	0.201644i
$183$	8.46558	+	2.58026i	0.625794	+	0.190739i
$184$	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
$188$	−18.9822	+	0.324333i	−1.38442	+	0.0236544i
$189$	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	$0.600853\pi$
$192$	11.8790	−	7.13361i	0.857296	−	0.514824i
$193$	−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	$0.201735\pi$
$198$	−3.81423	+	19.7838i	−0.271065	+	1.40598i
$199$		−	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
$202$	2.64647	+	6.23789i	0.186205	+	0.438896i
$203$	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
$207$	20.0947	−	3.94173i	1.39668	−	0.273969i
$208$	3.58840	+	3.35119i	0.248811	+	0.232363i
$209$	−15.9266			−1.10167
$210$		0			0
$211$		−	9.44133i		−	0.649968i	−0.945720	−	0.324984i	$-0.894641\pi$
$211$		−	9.44133i		−	0.649968i	0.945720	−	0.324984i	$-0.105359\pi$
$212$	23.9454	−	0.409135i	1.64457	−	0.0280995i
$213$	13.8249	+	4.21377i	0.947269	+	0.288722i
$214$	−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
$218$	−4.96702	−	11.7076i	−0.336409	−	0.792936i
$219$	−3.40613	+	1.81481i	−0.230165	+	0.122634i
$220$		0			0
$221$	3.00516			0.202149
$222$	2.01843	+	1.63225i	0.135468	+	0.109549i
$223$	−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	$0.356047\pi$
$228$	5.63726	+	10.1582i	0.373337	+	0.672744i
$229$	2.90511			0.191975			0.0959874	−	0.995383i	$-0.469399\pi$
$229$	2.90511			0.191975			0.0959874	+	0.995383i	$0.469399\pi$
$230$		0			0
$231$	−15.5193	−	29.1273i	−1.02109	−	1.91644i
$232$	−0.950306	+	2.47155i	−0.0623907	+	0.162265i
$233$	−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	$0.256097\pi$
$234$	2.91872	+	4.31295i	0.190803	+	0.281947i
$235$		0			0
$236$	9.39964	+	9.08383i	0.611865	+	0.591307i
$237$	−12.8446	−	3.91498i	−0.834349	−	0.254305i
$238$	5.42578	+	12.7889i	0.351701	+	0.828981i
$239$	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	$0.665741\pi$
$242$	6.38099	+	15.0404i	0.410186	+	0.966832i
$243$	15.5232	−	1.42509i	0.995812	−	0.0914196i
$244$	−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
$248$	−14.5102	−	5.57914i	−0.921396	−	0.354276i
$249$	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	$0.286901\pi$
$252$	−13.0847	+	20.2081i	−0.824258	+	1.27299i
$253$	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	$0.553637\pi$
$258$	−19.0692	+	23.5809i	−1.18720	+	1.46808i
$259$	−4.25210			−0.264212
$260$		0			0
$261$	−1.56654	+	2.33110i	−0.0969666	+	0.144291i
$262$	−7.34494	−	17.3125i	−0.453772	−	1.06957i
$263$	−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	$0.379721\pi$
$264$	14.3179	−	18.3375i	0.881204	−	1.12859i
$265$		0			0
$266$	−17.6432	−	7.13209i	−1.08177	−	0.437297i
$267$	2.51480	−	8.25081i	0.153903	−	0.504941i
$268$	13.7350	−	0.234680i	0.839002	−	0.0143353i
$269$			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	$0.476834\pi$
$272$	−6.68407	+	7.15720i	−0.405281	+	0.433969i
$273$	−8.15993	−	2.48710i	−0.493862	−	0.150526i
$274$	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	0.780992	−	0.624541i	$-0.214714\pi$
$277$	2.60387	+	2.60387i	0.156451	+	0.156451i	−0.624541	+	0.780992i	$0.714714\pi$
$278$	−9.70018	−	22.8639i	−0.581778	−	1.37129i
$279$	−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	$-0.126195\pi$
$282$	18.0798	+	14.6206i	1.07664	+	0.870646i
$283$	−1.95205	+	1.95205i	−0.116037	+	0.116037i	−0.762741	−	0.646704i	$-0.776147\pi$
$283$	−1.95205	+	1.95205i	−0.116037	+	0.116037i	0.646704	+	0.762741i	$0.276147\pi$
$284$	−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
$288$	−16.7637	−	2.64153i	−0.987812	−	0.155654i
$289$		−	11.0061i		−	0.647418i
$290$		0			0
$291$	−1.64616	−	3.08959i	−0.0964995	−	0.181115i
$292$	4.45584	−	0.0761334i	0.260758	−	0.00445537i
$293$	−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
$297$	19.1372	−	15.5785i	1.11045	−	0.903959i
$298$	−3.48991	+	1.48062i	−0.202165	+	0.0857699i
$299$		−	8.37859i		−	0.484547i
$300$		0			0
$301$		−	49.6763i		−	2.86329i
$302$	−8.64018	−	20.3654i	−0.497186	−	1.17190i
$303$	2.41958	−	7.93840i	0.139001	−	0.456049i
$304$	−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	0.884870	−	0.465838i	$-0.154247\pi$
$307$	7.34204	+	7.34204i	0.419033	+	0.419033i	−0.465838	+	0.884870i	$0.654247\pi$
$308$	0.651051	+	38.1039i	0.0370970	+	2.17117i
$309$	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	$-0.213462\pi$
$312$	−0.734655	−	5.96833i	−0.0415916	−	0.337890i
$313$	−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	$0.496693\pi$
$318$	−22.8071	−	18.4434i	−1.27896	−	1.03426i
$319$			4.44594i			0.248925i
$320$		0			0
$321$	7.49932	+	14.0751i	0.418571	+	0.785595i
$322$	35.6564	−	15.1275i	1.98705	−	0.843021i
$323$	−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
$327$	−4.54119	+	14.8992i	−0.251128	+	0.823926i
$328$	−2.27482	+	5.91632i	−0.125606	+	0.326674i
$329$	−38.0875			−2.09983
$330$		0			0
$331$			7.13080i			0.391944i	0.980609	+	0.195972i	$0.0627862\pi$
$331$			7.13080i			0.391944i	−0.980609	+	0.195972i	$0.937214\pi$
$332$	−25.8949	+	0.442445i	−1.42117	+	0.0242823i
$333$	−0.611967	−	3.11977i	−0.0335356	−	0.170962i
$334$	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	$-0.00448549\pi$
$338$	−14.9630	+	6.34818i	−0.813882	+	0.345295i
$339$	−7.83687	−	14.7086i	−0.425640	−	0.798862i
$340$		0			0
$341$	−26.1016			−1.41348
$342$	2.69359	−	13.9713i	0.145653	−	0.755480i
$343$	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	$0.231121\pi$
$348$	2.83568	−	1.57365i	0.152008	−	0.0843564i
$349$	−26.5812			−1.42286			−0.711430	−	0.702757i	$-0.751952\pi$
$349$	−26.5812			−1.42286			−0.711430	+	0.702757i	$0.751952\pi$
$350$		0			0
$351$	0.650403	−	6.34490i	0.0347159	−	0.338666i
$352$	−24.3577	+	11.3309i	−1.29827	+	0.603937i
$353$	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	$0.171194\pi$
$354$	−1.68414	−	15.9207i	−0.0895113	−	0.846174i
$355$		0			0
$356$	−6.92139	+	7.16202i	−0.366833	+	0.379586i
$357$	4.96062	−	16.2753i	0.262544	−	0.861379i
$358$	3.67311	−	1.55834i	0.194130	−	0.0823611i
$359$	−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
$362$	−18.2576	+	7.74591i	−0.959597	+	0.407116i
$363$	5.83393	−	19.1405i	0.306202	−	1.00462i
$364$	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	$0.261557\pi$
$368$	19.9548	+	18.6357i	1.04022	+	0.971452i
$369$	−3.74995	+	5.58012i	−0.195215	+	0.290489i
$370$		0			0
$371$	48.0461			2.49443
$372$	9.23871	+	16.6479i	0.479005	+	0.863155i
$373$	−18.9116	+	18.9116i	−0.979205	+	0.979205i	−0.999788	−	0.0205831i	$-0.993448\pi$
$373$	−18.9116	+	18.9116i	−0.979205	+	0.979205i	0.0205831	+	0.999788i	$0.493448\pi$
$374$	−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
$378$	28.1760	−	8.68777i	1.44922	−	0.446851i
$379$	24.3755			1.25209			0.626043	−	0.779788i	$-0.284673\pi$
$379$	24.3755			1.25209			0.626043	+	0.779788i	$0.284673\pi$
$380$		0			0
$381$	−0.0848613	−	0.159272i	−0.00434758	−	0.00815974i
$382$	−34.1939	+	14.5070i	−1.74951	+	0.742243i
$383$	−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	$0.432957\pi$
$384$	15.8484	+	11.5251i	0.808762	+	0.588137i
$385$		0			0
$386$	6.19904	−	15.3350i	0.315523	−	0.780532i
$387$	36.4475	−	7.14947i	1.85273	−	0.363428i
$388$	0.0690581	+	4.04175i	0.00350589	+	0.205189i
$389$		−	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
$392$	−9.23650	+	24.0222i	−0.466514	+	1.21330i
$393$	−6.71524	+	22.0320i	−0.338739	+	1.11137i
$394$	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	0.0901716	−	0.995926i	$-0.471258\pi$
$397$	−18.0470	−	18.0470i	−0.905755	−	0.905755i	−0.995926	+	0.0901716i	$0.971258\pi$
$398$	8.72572	−	3.70195i	0.437381	−	0.185562i
$399$	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	$0.808364\pi$
$402$	−13.0821	−	10.5791i	−0.652477	−	0.527640i
$403$	−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
$408$	11.9040	−	1.46530i	0.589338	−	0.0725429i
$409$			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
$412$	−3.04950	+	0.0521044i	−0.150238	+	0.00256700i
$413$	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
$417$	−8.86857	+	29.0969i	−0.434296	+	1.42488i
$418$	−8.79687	−	20.7348i	−0.430269	−	1.01417i
$419$			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	$0.146245\pi$
$421$			18.1975i			0.886894i	−0.896301	+	0.443447i	$0.853755\pi$
$422$	12.2916	−	5.21480i	0.598345	−	0.253852i
$423$	−5.48161	−	27.9448i	−0.266525	−	1.35873i
$424$	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
$428$	−0.314605	−	18.4128i	−0.0152070	−	0.890017i
$429$	−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	$0.701591\pi$
$432$	13.6646	+	15.6613i	0.657440	+	0.753507i
$433$	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
$438$	−4.24402	−	3.43202i	−0.202787	−	0.163988i
$439$			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
$442$	1.65986	+	3.91239i	0.0789515	+	0.186093i
$443$	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
$447$	4.44129	+	1.35368i	0.210066	+	0.0640269i
$448$	−32.0570	+	1.64448i	−1.51455	+	0.0776942i
$449$	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
$452$	0.328765	+	19.2416i	0.0154638	+	0.905047i
$453$	−7.89944	+	25.9172i	−0.371148	+	1.21770i
$454$	−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	$0.311503\pi$
$458$	1.60460	+	3.78214i	0.0749780	+	0.176728i
$459$	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	$0.340486\pi$
$462$	29.3488	−	36.2925i	1.36543	−	1.68848i
$463$	−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	$0.0507395\pi$
$468$	−4.00288	+	6.18207i	−0.185033	+	0.285766i
$469$	27.5592			1.27257
$470$		0			0
$471$	30.6017	−	16.3048i	1.41005	−	0.751287i
$472$	−6.63440	+	17.2547i	−0.305373	+	0.794210i
$473$	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
$477$	6.91486	+	35.2515i	0.316610	+	1.61406i
$478$	4.60890	+	10.8634i	0.210806	+	0.496882i
$479$	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
$482$	−8.53137	−	20.1089i	−0.388593	−	0.915937i
$483$	−45.3767	−	13.8306i	−2.06471	−	0.629312i
$484$	−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	$0.276630\pi$
$488$	5.18664	−	13.4893i	0.234788	−	0.610634i
$489$	−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	$0.575972\pi$
$492$	6.78797	−	3.76696i	0.306025	−	0.169828i
$493$	−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
$498$	24.6639	+	19.9450i	1.10522	+	0.893758i
$499$	−16.6637			−0.745969			−0.372984	−	0.927838i	$-0.621665\pi$
$499$	−16.6637			−0.745969			−0.372984	+	0.927838i	$0.621665\pi$
$500$		0			0
$501$	−29.7789	+	15.8664i	−1.33042	+	0.708861i
$502$	10.8608	+	25.5996i	0.484743	+	1.14257i
$503$	−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	$0.370813\pi$
$504$	−33.5359	−	5.87320i	−1.49381	−	0.261613i
$505$		0			0
$506$	42.5017	+	17.1809i	1.88943	+	0.763785i
$507$	19.0421	+	5.80394i	0.845690	+	0.257762i
$508$	0.00356002	+	0.208357i	0.000157951	+	0.00924434i
$509$			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
$512$	−10.2392	−	20.1782i	−0.452511	−	0.891759i
$513$	−13.5146	+	11.0015i	−0.596685	+	0.485729i
$514$	−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
$518$	−2.34859	−	5.53577i	−0.103191	−	0.243228i
$519$	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	$-0.124515\pi$
$522$	−3.90010	−	0.751919i	−0.170703	−	0.0329106i
$523$	22.7980	−	22.7980i	0.996888	−	0.996888i	−0.00310741	−	0.999995i	$-0.500989\pi$
$523$	22.7980	−	22.7980i	0.996888	−	0.996888i	0.999995	+	0.00310741i	$0.000989121\pi$
$524$	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
$528$	31.7817	+	8.51185i	1.38312	+	0.370431i
$529$		−	23.5926i		−	1.02577i
$530$		0			0
$531$	−10.9366	+	16.2741i	−0.474606	+	0.706238i
$532$	−0.459769	−	26.9088i	−0.0199335	−	1.16665i
$533$	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
$537$	−4.67444	−	1.42474i	−0.201717	−	0.0614823i
$538$	−14.7469	+	6.25646i	−0.635782	+	0.269735i
$539$			43.2123i			1.86129i
$540$		0			0
$541$		−	2.53614i		−	0.109037i	−0.998513	−	0.0545187i	$-0.982638\pi$
$541$		−	2.53614i		−	0.109037i	0.998513	−	0.0545187i	$-0.0173624\pi$
$542$	1.32230	+	3.11673i	0.0567975	+	0.133875i
$543$	23.2348	+	7.08184i	0.997100	+	0.303911i
$544$	−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	0.945119	−	0.326726i	$-0.105945\pi$
$547$	14.4630	+	14.4630i	0.618394	+	0.618394i	−0.326726	+	0.945119i	$0.605945\pi$
$548$	1.73358	−	0.0296203i	0.0740550	−	0.00126532i
$549$	8.54997	−	12.7228i	0.364904	−	0.542996i
$550$		0			0
$551$		−	3.13970i		−	0.133756i
$552$	−4.08535	−	33.1893i	−0.173884	−	1.41263i
$553$	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	$0.426280\pi$
$558$	4.41443	−	22.8970i	0.186878	−	0.969309i
$559$		−	15.1970i		−	0.642765i
$560$		0			0
$561$	17.7726	−	9.46940i	0.750361	−	0.399798i
$562$	16.8545	−	7.15063i	0.710963	−	0.301631i
$563$	−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
$567$	−33.2890	−	13.9960i	−1.39801	−	0.587776i
$568$	8.47017	−	22.0291i	0.355400	−	0.924321i
$569$	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	$0.0181143\pi$
$571$			2.71823i			0.113754i	−0.998381	+	0.0568772i	$0.981886\pi$
$572$	0.199170	+	11.6568i	0.00832771	+	0.487394i
$573$	43.5155	+	13.2633i	1.81789	+	0.554082i
$574$	−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	$0.191602\pi$
$578$	14.3288	−	6.07908i	0.595998	−	0.252856i
$579$	−17.8786	+	9.52587i	−0.743010	+	0.395882i
$580$		0			0
$581$	−51.9578			−2.15557
$582$	3.11308	−	3.84961i	0.129041	−	0.159572i
$583$	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	$0.00647647\pi$
$588$	27.5614	−	15.2951i	1.13661	−	0.630758i
$589$	18.4329			0.759513
$590$		0			0
$591$	−3.45340	−	6.48151i	−0.142054	−	0.266614i
$592$	2.89325	−	3.09805i	0.118912	−	0.127329i
$593$	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	$0.233101\pi$
$594$	30.8518	+	16.3099i	1.26586	+	0.669205i
$595$		0			0
$596$	−3.85521	−	3.72568i	−0.157916	−	0.152610i
$597$	−11.1044	−	3.38458i	−0.454475	−	0.138521i
$598$	10.9080	−	4.62781i	0.446062	−	0.189245i
$599$	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	$0.385685\pi$
$602$	64.6731	−	27.4380i	2.63588	−	1.11829i
$603$	3.96636	+	20.2202i	0.161523	+	0.823432i
$604$	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	$0.0493109\pi$
$608$	17.2013	−	8.00181i	0.697606	−	0.324516i
$609$	5.74203	−	3.05940i	0.232679	−	0.123973i
$610$		0			0
$611$	−11.6518			−0.471380
$612$	−12.3304	−	7.98389i	−0.498425	−	0.322730i
$613$	−17.7138	+	17.7138i	−0.715452	+	0.715452i	−0.967670	−	0.252218i	$-0.918840\pi$
$613$	−17.7138	+	17.7138i	−0.715452	+	0.715452i	0.252218	+	0.967670i	$0.418840\pi$
$614$	−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	$0.621118\pi$
$618$	2.90454	+	2.34882i	0.116838	+	0.0944833i
$619$	4.67429			0.187876			0.0939378	−	0.995578i	$-0.470055\pi$
$619$	4.67429			0.187876			0.0939378	+	0.995578i	$0.470055\pi$
$620$		0			0
$621$	3.61683	−	35.2834i	0.145138	−	1.41587i
$622$	28.5366	−	12.1068i	1.14421	−	0.485440i
$623$	−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
$627$	−8.04270	+	26.3873i	−0.321195	+	1.05381i
$628$	−40.0326	+	0.684005i	−1.59748	+	0.0272948i
$629$		−	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	$0.679860\pi$
$632$	−7.86956	+	20.4671i	−0.313034	+	0.814136i
$633$	−15.6424	−	4.76772i	−0.621730	−	0.189500i
$634$	−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
$638$	−5.78813	+	2.45566i	−0.229154	+	0.0972204i
$639$	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	$0.873167\pi$
$642$	−14.1821	+	17.5375i	−0.559723	+	0.692150i
$643$	−18.4955	+	18.4955i	−0.729392	+	0.729392i	−0.970499	−	0.241107i	$-0.922490\pi$
$643$	−18.4955	+	18.4955i	−0.729392	+	0.729392i	0.241107	+	0.970499i	$0.422490\pi$
$644$	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	$0.885299\pi$
$648$	−0.517352	−	25.4506i	−0.0203235	−	0.999793i
$649$			31.0385i			1.21837i
$650$		0			0
$651$	17.9614	+	33.7108i	0.703962	+	1.32123i
$652$	0.246142	+	14.4059i	0.00963965	+	0.564178i
$653$	−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
$657$	1.28674	+	6.55973i	0.0502006	+	0.255919i
$658$	−21.0372	−	49.5858i	−0.820114	−	1.93306i
$659$		−	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	$0.280072\pi$
$661$			39.6271i			1.54131i	−0.637250	+	0.770657i	$0.719928\pi$
$662$	−9.28353	+	3.93860i	−0.360815	+	0.153078i
$663$	1.51756	−	4.97895i	0.0589370	−	0.193366i
$664$	−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
$668$	38.9563	−	0.665615i	1.50726	−	0.0257534i
$669$	−37.4095	+	19.9321i	−1.44633	+	0.770618i
$670$		0			0
$671$		−	24.2653i		−	0.936751i
$672$	31.3954	+	23.6614i	1.21110	+	0.912758i
$673$	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	$0.202515\pi$
$678$	14.8204	−	18.3269i	0.569175	−	0.703839i
$679$			8.10973i			0.311223i
$680$		0			0
$681$	8.02597	+	15.0635i	0.307556	+	0.577235i
$682$	−14.4169	−	33.9815i	−0.552051	−	1.30122i
$683$	−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
$687$	1.46703	−	4.81318i	0.0559708	−	0.183634i
$688$	36.1938	+	33.8012i	1.37987	+	1.28866i
$689$	14.6983			0.559961
$690$		0			0
$691$			20.5069i			0.780118i	0.920790	+	0.390059i	$0.127545\pi$
$691$			20.5069i			0.780118i	−0.920790	+	0.390059i	$0.872455\pi$
$692$	−20.0168	+	0.342010i	−0.760923	+	0.0130013i
$693$	−56.0952	+	11.0035i	−2.13088	+	0.417989i
$694$	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
$698$	−14.6818	−	34.6059i	−0.555714	−	1.30985i
$699$	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	$0.713534\pi$
$702$	8.61961	−	2.65777i	0.325326	−	0.100311i
$703$	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
$708$	19.7968	−	10.9862i	0.744009	−	0.412885i
$709$	31.3218			1.17632			0.588158	−	0.808746i	$-0.299853\pi$
$709$	31.3218			1.17632			0.588158	+	0.808746i	$0.299853\pi$
$710$		0			0
$711$	−12.9727	+	19.3040i	−0.486513	+	0.723957i
$712$	−13.1471	−	5.05505i	−0.492709	−	0.189446i
$713$	−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
$717$	4.21377	−	13.8249i	0.157366	−	0.516302i
$718$	−5.42578	−	12.7889i	−0.202488	−	0.477277i
$719$	−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
$722$	−4.28209	−	10.0931i	−0.159363	−	0.375628i
$723$	−7.79996	+	25.5909i	−0.290083	+	0.951734i
$724$	−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	$0.0831477\pi$
$728$	−4.99937	+	13.0023i	−0.185289	+	0.481898i
$729$	5.47787	−	26.4385i	0.202884	−	0.979203i
$730$		0			0
$731$	30.3110			1.12109
$732$	−15.4767	+	8.58875i	−0.572036	+	0.317449i
$733$	10.9177	−	10.9177i	0.403256	−	0.403256i	−0.476123	−	0.879379i	$-0.657958\pi$
$733$	10.9177	−	10.9177i	0.403256	−	0.403256i	0.879379	+	0.476123i	$0.157958\pi$
$734$	−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
$738$	−9.33595	−	1.79993i	−0.343661	−	0.0662562i
$739$	13.6946			0.503765			0.251882	−	0.967758i	$-0.418950\pi$
$739$	13.6946			0.503765			0.251882	+	0.967758i	$0.418950\pi$
$740$		0			0
$741$	3.35279	+	6.29267i	0.123168	+	0.231167i
$742$	26.5377	+	62.5509i	0.974229	+	2.29632i
$743$	−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	$0.276069\pi$
$744$	−16.5709	+	21.2231i	−0.607520	+	0.778076i
$745$		0			0
$746$	−35.0664	−	14.1753i	−1.28387	−	0.518994i
$747$	−7.47784	−	38.1215i	−0.273600	−	1.39479i
$748$	−23.2499	+	0.397252i	−0.850099	+	0.0145250i
$749$		−	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	$0.298214\pi$
$752$	25.9159	−	27.7503i	0.945054	−	1.01195i
$753$	9.92971	−	32.5784i	0.361859	−	1.18722i
$754$	−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	0.989531	−	0.144322i	$-0.0461001\pi$
$757$	23.2548	+	23.2548i	0.845209	+	0.845209i	−0.144322	+	0.989531i	$0.546100\pi$
$758$	13.4635	+	31.7343i	0.489017	+	1.15264i
$759$	−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	$0.937844\pi$
$762$	0.160483	−	0.198452i	0.00581367	−	0.00718916i
$763$	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
$768$	−6.25074	+	26.9987i	−0.225554	+	0.974231i
$769$			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
$772$	23.3885	−	0.399621i	0.841771	−	0.0143827i
$773$	−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
$777$	−2.14724	+	7.04488i	−0.0770319	+	0.252734i
$778$	5.18562	−	2.20004i	0.185913	−	0.0788751i
$779$		−	7.51575i		−	0.269280i
$780$		0			0
$781$		−	39.6271i		−	1.41797i
$782$	9.23033	+	21.7565i	0.330076	+	0.778009i
$783$	3.07108	+	3.77262i	0.109752	+	0.134822i
$784$	−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	0.387046	−	0.922060i	$-0.373495\pi$
$787$	−15.0090	−	15.0090i	−0.535014	−	0.535014i	−0.922060	+	0.387046i	$0.873495\pi$
$788$	0.144874	+	8.47901i	0.00516092	+	0.302052i
$789$	10.4700	+	19.6506i	0.372742	+	0.699581i
$790$		0			0
$791$			38.6080i			1.37274i
$792$	−23.1513	−	32.9820i	−0.822645	−	1.17196i
$793$	−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	$0.186274\pi$
$798$	−20.7260	+	25.6296i	−0.733692	+	0.907280i
$799$		−	23.2399i		−	0.822167i
$800$		0			0
$801$	−12.4000	−	8.33306i	−0.438133	−	0.294434i
$802$	−29.5287	+	12.5278i	−1.04269	+	0.442371i
$803$	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
$807$	18.7670	+	5.72008i	0.660630	+	0.201356i
$808$	−12.6493	−	4.86364i	−0.445001	−	0.171102i
$809$	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	$0.240953\pi$
$811$			39.1133i			1.37345i	−0.726915	+	0.686727i	$0.759047\pi$
$812$	−7.51163	+	0.128345i	−0.263607	+	0.00450403i
$813$	1.20893	−	3.96639i	0.0423991	−	0.139107i
$814$	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
$818$	−1.96950	+	0.835576i	−0.0688621	+	0.0292152i
$819$	−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	$0.490077\pi$
$822$	−1.65117	−	1.33526i	−0.0575913	−	0.0465725i
$823$	−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	$0.266404\pi$
$828$	−22.2597	+	34.3779i	−0.773577	+	1.19472i
$829$	−2.73512			−0.0949945			−0.0474973	−	0.998871i	$-0.515125\pi$
$829$	−2.73512			−0.0949945			−0.0474973	+	0.998871i	$0.515125\pi$
$830$		0			0
$831$	5.62900	−	2.99918i	0.195268	−	0.104040i
$832$	−9.80690	+	0.503080i	−0.339993	+	0.0174411i
$833$	−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
$837$	−22.1486	+	18.0300i	−0.765568	+	0.623208i
$838$	−14.9142	+	6.32747i	−0.515204	+	0.218579i
$839$	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
$842$	−23.6912	+	10.0512i	−0.816454	+	0.346387i
$843$	−21.4492	−	6.53759i	−0.738748	−	0.225167i
$844$	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
$848$	−32.6920	+	35.0061i	−1.12265	+	1.20211i
$849$	2.24841	+	4.21992i	0.0771651	+	0.144827i
$850$		0			0
$851$	−7.23366			−0.247967
$852$	−25.2746	+	14.0261i	−0.865895	+	0.480525i
$853$	12.6345	−	12.6345i	0.432597	−	0.432597i	−0.456914	−	0.889511i	$-0.651045\pi$
$853$	12.6345	−	12.6345i	0.432597	−	0.432597i	0.889511	+	0.456914i	$0.151045\pi$
$854$	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	$0.787579\pi$
$858$	8.97840	−	11.1026i	0.306517	−	0.379038i
$859$	55.4601			1.89227			0.946136	−	0.323768i	$-0.104950\pi$
$859$	55.4601			1.89227			0.946136	+	0.323768i	$0.104950\pi$
$860$		0			0
$861$	13.7451	−	7.32351i	0.468432	−	0.249585i
$862$	−43.5728	+	18.4861i	−1.48410	+	0.629639i
$863$	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	$-0.0253904\pi$
$864$	−12.8419	+	26.4402i	−0.436891	+	0.899515i
$865$		0			0
$866$	−12.2883	+	30.3985i	−0.417575	+	1.03298i
$867$	−18.2349	−	5.55791i	−0.619291	−	0.188757i
$868$	−0.753500	−	44.0999i	−0.0255755	−	1.49685i
$869$			36.8172i			1.24894i
$870$		0			0
$871$	8.43094			0.285672
$872$	23.7408	+	9.12832i	0.803966	+	0.309124i
$873$	−5.95012	+	1.16716i	−0.201381	+	0.0395025i
$874$	−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	0.441453	−	0.897284i	$-0.354463\pi$
$877$	−13.4991	−	13.4991i	−0.455831	−	0.455831i	−0.897284	+	0.441453i	$0.854463\pi$
$878$	−31.4482	+	13.3421i	−1.06132	+	0.450275i
$879$	−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	$-0.221729\pi$
$882$	−37.9070	−	7.30828i	−1.27640	−	0.246083i
$883$	8.86328	−	8.86328i	0.298273	−	0.298273i	−0.542064	−	0.840337i	$-0.682357\pi$
$883$	8.86328	−	8.86328i	0.298273	−	0.298273i	0.840337	+	0.542064i	$0.182357\pi$
$884$	−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	$0.525129\pi$
$888$	−5.15276	+	0.634264i	−0.172915	+	0.0212845i
$889$			0.418066i			0.0140215i
$890$		0			0
$891$	−16.1466	−	39.5734i	−0.540931	−	1.32576i
$892$	48.9385	−	0.836172i	1.63858	−	0.0279971i
$893$	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
$897$	−13.8817	−	4.23106i	−0.463495	−	0.141271i
$898$	4.80845	+	11.3338i	0.160460	+	0.378214i
$899$		−	5.14555i		−	0.171614i
$900$		0			0
$901$			29.3163i			0.976668i
$902$	−13.8555	+	5.87829i	−0.461337	+	0.195726i
$903$	−82.3037	−	25.0857i	−2.73890	−	0.834801i
$904$	−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	0.498386	−	0.866955i	$-0.333926\pi$
$907$	−11.1000	−	11.1000i	−0.368569	−	0.368569i	−0.866955	+	0.498386i	$0.833926\pi$
$908$	−0.336698	−	19.7059i	−0.0111737	−	0.653962i
$909$	−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	$-0.158611\pi$
$912$	−22.4441	−	6.01103i	−0.743200	−	0.199045i
$913$	−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
$918$	5.30102	+	17.1921i	0.174960	+	0.567425i
$919$			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
$922$	11.3946	+	26.8579i	0.375263	+	0.884517i
$923$	−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
$927$	−0.880625	−	4.48937i	−0.0289235	−	0.147450i
$928$	−2.23371	−	4.80177i	−0.0733253	−	0.157626i
$929$	−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
$932$	−0.0199772	−	1.16920i	−0.000654375	−	0.0382985i
$933$	−36.3159	−	11.0689i	−1.18893	−	0.362380i
$934$	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	$0.141273\pi$
$938$	15.2220	+	35.8792i	0.497016	+	1.17150i
$939$	−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	$0.139454\pi$
$942$	38.1296	+	30.8343i	1.24233	+	1.00464i
$943$	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	$0.158943\pi$
$948$	23.4825	−	13.0315i	0.762675	−	0.423244i
$949$	2.73512			0.0887856
$950$		0			0
$951$	20.2933	+	38.0875i	0.658057	+	1.23507i
$952$	−25.9336	−	9.97143i	−0.840512	−	0.323176i
$953$	−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	$0.328557\pi$
$954$	−42.0743	+	28.4731i	−1.36221	+	0.921851i
$955$		0			0
$956$	−11.5974	+	12.0006i	−0.375086	+	0.388126i
$957$	7.36604	+	2.24513i	0.238110	+	0.0725747i
$958$	10.0347	+	23.6523i	0.324206	+	0.764173i
$959$	3.47842			0.112324
$960$		0			0
$961$	−0.791035			−0.0255173
$962$	−0.718483	−	1.69351i	−0.0231648	−	0.0546009i
$963$	27.1067	−	5.31719i	0.873500	−	0.171344i
$964$	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	$-0.0839436\pi$
$968$	−30.4992	−	11.7269i	−0.980281	−	0.376917i
$969$	−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	$0.661177\pi$
$972$	−19.5253	+	24.3056i	−0.626275	+	0.779602i
$973$	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	$0.669472\pi$
$978$	11.0958	−	13.7211i	0.354806	−	0.438751i
$979$	−23.6497			−0.755847
$980$		0			0
$981$	22.3917	+	15.0477i	0.714913	+	0.480436i
$982$	−5.78695	−	13.6402i	−0.184669	−	0.435276i
$983$	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	$0.182197\pi$
$984$	8.65342	+	6.75657i	0.275861	+	0.215392i
$985$		0			0
$986$	−3.00516	−	1.21481i	−0.0957037	−	0.0386873i
$987$	−19.2336	+	63.1035i	−0.612212	+	2.00861i
$988$	−0.140653	−	8.23197i	−0.00447477	−	0.261894i
$989$		−	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	$0.804391\pi$
$992$	28.1907	−	13.1139i	0.895054	−	0.416366i
$993$	11.8143	+	3.60094i	0.374916	+	0.114272i
$994$	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	0.726800	−	0.686849i	$-0.241007\pi$
$997$	1.26149	+	1.26149i	0.0399517	+	0.0399517i	−0.686849	+	0.726800i	$0.741007\pi$
$998$	−9.20397	−	21.6943i	−0.291347	−	0.686721i
$999$	−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.293.20	yes	64
3.2	odd	2	inner	600.2.w.k.293.14	yes	64
5.2	odd	4	inner	600.2.w.k.557.3	yes	64
5.3	odd	4	inner	600.2.w.k.557.30	yes	64
5.4	even	2	inner	600.2.w.k.293.13	yes	64
8.5	even	2	inner	600.2.w.k.293.29	yes	64
15.2	even	4	inner	600.2.w.k.557.29	yes	64
15.8	even	4	inner	600.2.w.k.557.4	yes	64
15.14	odd	2	inner	600.2.w.k.293.19	yes	64
24.5	odd	2	inner	600.2.w.k.293.3	✓	64
40.13	odd	4	inner	600.2.w.k.557.19	yes	64
40.29	even	2	inner	600.2.w.k.293.4	yes	64
40.37	odd	4	inner	600.2.w.k.557.14	yes	64
120.29	odd	2	inner	600.2.w.k.293.30	yes	64
120.53	even	4	inner	600.2.w.k.557.13	yes	64
120.77	even	4	inner	600.2.w.k.557.20	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.w.k.293.3	✓	64	24.5	odd	2	inner
600.2.w.k.293.4	yes	64	40.29	even	2	inner
600.2.w.k.293.13	yes	64	5.4	even	2	inner
600.2.w.k.293.14	yes	64	3.2	odd	2	inner
600.2.w.k.293.19	yes	64	15.14	odd	2	inner
600.2.w.k.293.20	yes	64	1.1	even	1	trivial
600.2.w.k.293.29	yes	64	8.5	even	2	inner
600.2.w.k.293.30	yes	64	120.29	odd	2	inner
600.2.w.k.557.3	yes	64	5.2	odd	4	inner
600.2.w.k.557.4	yes	64	15.8	even	4	inner
600.2.w.k.557.13	yes	64	120.53	even	4	inner
600.2.w.k.557.14	yes	64	40.37	odd	4	inner
600.2.w.k.557.19	yes	64	40.13	odd	4	inner
600.2.w.k.557.20	yes	64	120.77	even	4	inner
600.2.w.k.557.29	yes	64	15.2	even	4	inner
600.2.w.k.557.30	yes	64	5.3	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 $\F_{q}$
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+(0.552337 + 1.30189i) q^{2} +(0.504984 - 1.65680i) q^{3} +(-1.38985 + 1.43817i) q^{4} +(2.43590 - 0.257678i) q^{6} +(-2.83719 + 2.83719i) q^{7} +(-2.64000 - 1.01508i) q^{8} +(-2.48998 - 1.67332i) q^{9} -4.74897 q^{11} +(1.68091 + 3.02895i) 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} +(0.803169 - 4.16592i) q^{18} +3.35370 q^{19} +(3.26792 + 6.13340i) q^{21} +(-2.62303 - 6.18265i) q^{22} +(-4.82662 + 4.82662i) q^{23} +(-3.01494 + 3.86136i) q^{24} +(-1.60939 - 0.650581i) q^{26} +(-4.02976 + 3.28041i) q^{27} +(-0.137093 - 8.02362i) q^{28} -0.936190i q^{29} +5.49627 q^{31} +(5.12905 - 2.38596i) q^{32} +(-2.39815 + 7.86810i) q^{33} +(1.29761 - 3.20999i) q^{34} +(5.86720 - 1.25535i) q^{36} +(0.749350 + 0.749350i) q^{37} +(1.85238 + 4.36616i) q^{38} +(0.999726 + 1.87633i) q^{39} -2.24103i q^{41} +(-6.18003 + 7.64219i) 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} +(-6.69234 - 1.79236i) q^{48} -9.09930i q^{49} +(-3.74242 + 1.99399i) q^{51} +(-0.0419396 - 2.45459i) q^{52} +(-8.46720 - 8.46720i) q^{53} +(-6.49652 - 3.43442i) q^{54} +(10.3702 - 4.61022i) q^{56} +(1.69357 - 5.55642i) q^{57} +(1.21882 - 0.517093i) q^{58} -6.53585i q^{59} +5.10959i q^{61} +(3.03579 + 7.15555i) q^{62} +(11.8121 - 2.31703i) q^{63} +(5.93923 + 5.35962i) q^{64} +(-11.5680 + 1.22370i) q^{66} +(-4.85678 - 4.85678i) q^{67} +(4.89577 - 0.0836501i) q^{68} +(5.55939 + 10.4341i) q^{69} +8.34435i q^{71} +(4.87501 + 6.94509i) 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} +(-1.89060 + 2.33791i) q^{78} -7.75267i q^{79} +(3.40002 + 8.33306i) q^{81} +(2.91758 - 1.23780i) q^{82} +(9.15657 + 9.15657i) q^{83} +(-13.3628 - 3.82466i) q^{84} +(-16.2328 - 6.56196i) q^{86} +(-1.55108 - 0.472761i) q^{87} +(12.5373 + 4.82057i) q^{88} +4.97996 q^{89} -4.92511i q^{91} +(-0.233222 - 13.6498i) q^{92} +(2.77553 - 9.10622i) q^{93} +(-5.03116 + 12.4459i) q^{94} +(-1.36297 - 9.70270i) q^{96} +(1.42918 - 1.42918i) q^{97} +(11.8463 - 5.02588i) 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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