LMFDB - Embedded newform 600.2.w.k.293.4

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			293.4
Character	$\chi$	$=$	600.293
Dual form			600.2.w.k.557.4

$q$-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	$-0.476044\pi$
$7$	2.83719	−	2.83719i	1.07236	−	1.07236i	0.997169	−	0.0751879i	$-0.0239557\pi$
$8$	−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	−0.817151	−	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	0.885159	−	0.465289i	$-0.154050\pi$
$17$	1.73117	+	1.73117i	0.419870	+	0.419870i	−0.465289	+	0.885159i	$0.654050\pi$
$18$	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	$-0.497950\pi$
$23$	4.82662	−	4.82662i	1.00642	−	1.00642i	0.999979	−	0.00644154i	$-0.00205042\pi$
$24$	−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	0.766015	−	0.642823i	$-0.222237\pi$
$37$	0.749350	+	0.749350i	0.123192	+	0.123192i	−0.642823	+	0.766015i	$0.722237\pi$
$38$	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	$0.642989\pi$
$43$	−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	0.0207122	−	0.999785i	$-0.493407\pi$
$47$	−6.71219	−	6.71219i	−0.979073	−	0.979073i	−0.999785	+	0.0207122i	$0.993407\pi$
$48$	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	$-0.942630\pi$
$53$	−8.46720	−	8.46720i	−1.16306	−	1.16306i	−0.179258	−	0.983802i	$-0.557370\pi$
$54$	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	0.345185	−	0.938535i	$-0.387816\pi$
$67$	−4.85678	−	4.85678i	−0.593350	−	0.593350i	−0.938535	+	0.345185i	$0.887816\pi$
$68$	−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	0.793275	−	0.608864i	$-0.208374\pi$
$73$	1.57561	+	1.57561i	0.184411	+	0.184411i	−0.608864	+	0.793275i	$0.708374\pi$
$74$	−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	$0.00161592\pi$
$83$	9.15657	+	9.15657i	1.00506	+	1.00506i	0.00507654	+	0.999987i	$0.498384\pi$
$84$	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	−0.775930	−	0.630819i	$-0.782719\pi$
$97$	−1.42918	+	1.42918i	−0.145112	+	0.145112i	0.630819	+	0.775930i	$0.282719\pi$
$98$	−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	0.651983	−	0.758233i	$-0.273937\pi$
$103$	−1.07832	−	1.07832i	−0.106250	−	0.106250i	−0.758233	+	0.651983i	$0.773937\pi$
$104$	3.17245	+	1.41036i	0.311084	+	0.138297i
$105$		0			0
$106$	6.34663	+	15.7001i	0.616440	+	1.52493i
$107$	−6.51086	+	6.51086i	−0.629429	+	0.629429i	−0.947924	−	0.318496i	$-0.896822\pi$
$107$	−6.51086	+	6.51086i	−0.629429	+	0.629429i	0.318496	+	0.947924i	$0.396822\pi$
$108$	−10.3185	−	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	−0.950570	−	0.310511i	$-0.899500\pi$
$113$	−6.80391	+	6.80391i	−0.640058	+	0.640058i	0.310511	+	0.950570i	$0.399500\pi$
$114$	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	−0.710368	−	0.703830i	$-0.751472\pi$
$127$	−0.0736760	+	0.0736760i	−0.00653769	+	0.00653769i	0.703830	+	0.710368i	$0.251472\pi$
$128$	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	0.732808	−	0.680436i	$-0.238209\pi$
$137$	0.613004	+	0.613004i	0.0523724	+	0.0523724i	−0.680436	+	0.732808i	$0.738209\pi$
$138$	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	$0.0445604\pi$
$157$	14.1557	+	14.1557i	1.12975	+	1.12975i	0.139534	+	0.990217i	$0.455440\pi$
$158$	−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	−0.478885	−	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	$0.0217533\pi$
$167$	13.7751	+	13.7751i	1.06595	+	1.06595i	0.0682869	+	0.997666i	$0.478247\pi$
$168$	−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	0.922980	−	0.384848i	$-0.125746\pi$
$173$	7.07803	+	7.07803i	0.538133	+	0.538133i	−0.384848	+	0.922980i	$0.625746\pi$
$174$	−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	0.939061	−	0.343752i	$-0.111698\pi$
$193$	8.27030	+	8.27030i	0.595309	+	0.595309i	−0.343752	+	0.939061i	$0.611698\pi$
$194$	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	$0.201735\pi$
$198$	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	$0.0556989\pi$
$223$	17.3049	+	17.3049i	1.15882	+	1.15882i	0.174091	+	0.984729i	$0.444301\pi$
$224$	−7.78267	−	21.3215i	−0.520002	−	1.42460i
$225$		0			0
$226$	12.6160	−	5.09991i	0.839205	−	0.339241i
$227$	−6.96809	+	6.96809i	−0.462489	+	0.462489i	−0.899470	−	0.436982i	$-0.856047\pi$
$227$	−6.96809	+	6.96809i	−0.462489	+	0.462489i	0.436982	+	0.899470i	$0.356047\pi$
$228$	−10.3449	+	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	−0.693435	−	0.720520i	$-0.743903\pi$
$233$	0.413436	−	0.413436i	0.0270851	−	0.0270851i	0.720520	+	0.693435i	$0.243903\pi$
$234$	−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	0.167709	−	0.985837i	$-0.446363\pi$
$257$	−13.1156	−	13.1156i	−0.818128	−	0.818128i	−0.985837	+	0.167709i	$0.946363\pi$
$258$	−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	−0.368940	−	0.929453i	$-0.620279\pi$
$263$	9.08999	−	9.08999i	0.560513	−	0.560513i	0.929453	+	0.368940i	$0.120279\pi$
$264$	−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	0.780992	−	0.624541i	$-0.214714\pi$
$277$	2.60387	+	2.60387i	0.156451	+	0.156451i	−0.624541	+	0.780992i	$0.714714\pi$
$278$	−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	−0.762741	−	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
$288$	−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	$-0.998097\pi$
$293$	−17.2193	−	17.2193i	−1.00596	−	1.00596i	−0.00597927	−	0.999982i	$-0.501903\pi$
$294$	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	0.884870	−	0.465838i	$-0.154247\pi$
$307$	7.34204	+	7.34204i	0.419033	+	0.419033i	−0.465838	+	0.884870i	$0.654247\pi$
$308$	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	0.989088	−	0.147329i	$-0.0470675\pi$
$313$	14.8922	+	14.8922i	0.841759	+	0.841759i	−0.147329	+	0.989088i	$0.547067\pi$
$314$	−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	$0.496693\pi$
$318$	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	$0.504485\pi$
$337$	−18.6144	+	18.6144i	−1.01399	+	1.01399i	−0.999901	+	0.0140911i	$0.995515\pi$
$338$	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	−0.663950	−	0.747777i	$-0.731121\pi$
$347$	1.56152	−	1.56152i	0.0838269	−	0.0838269i	0.747777	+	0.663950i	$0.231121\pi$
$348$	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	−0.858826	−	0.512268i	$-0.828806\pi$
$353$	−6.51124	+	6.51124i	−0.346558	+	0.346558i	0.512268	+	0.858826i	$0.328806\pi$
$354$	−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	−0.680972	−	0.732309i	$-0.738443\pi$
$367$	0.983469	−	0.983469i	0.0513367	−	0.0513367i	0.732309	+	0.680972i	$0.238443\pi$
$368$	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	−0.999788	−	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
$378$	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	−0.209070	−	0.977901i	$-0.567043\pi$
$383$	15.0463	−	15.0463i	0.768831	−	0.768831i	0.977901	+	0.209070i	$0.0670435\pi$
$384$	−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	0.0901716	−	0.995926i	$-0.471258\pi$
$397$	−18.0470	−	18.0470i	−0.905755	−	0.905755i	−0.995926	+	0.0901716i	$0.971258\pi$
$398$	−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	0.193289	−	0.981142i	$-0.438085\pi$
$433$	−16.3942	−	16.3942i	−0.787853	−	0.787853i	−0.981142	+	0.193289i	$0.938085\pi$
$434$	−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	0.812558	−	0.582880i	$-0.198074\pi$
$443$	4.83418	+	4.83418i	0.229679	+	0.229679i	−0.582880	+	0.812558i	$0.698074\pi$
$444$	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	−0.558172	−	0.829725i	$-0.688497\pi$
$457$	5.80514	−	5.80514i	0.271553	−	0.271553i	0.829725	+	0.558172i	$0.188497\pi$
$458$	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	0.897126	−	0.441776i	$-0.145651\pi$
$463$	9.79796	+	9.79796i	0.455350	+	0.455350i	−0.441776	+	0.897126i	$0.645651\pi$
$464$	−3.74257	−	0.127930i	−0.173745	−	0.00593900i
$465$		0			0
$466$	−0.766605	+	0.309893i	−0.0355123	+	0.0143555i
$467$	17.9061	−	17.9061i	0.828593	−	0.828593i	−0.158729	−	0.987322i	$-0.550740\pi$
$467$	17.9061	−	17.9061i	0.828593	−	0.828593i	0.987322	+	0.158729i	$0.0507395\pi$
$468$	6.04171	+	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	−0.645545	−	0.763722i	$-0.723370\pi$
$487$	2.60795	−	2.60795i	0.118177	−	0.118177i	0.763722	+	0.645545i	$0.223370\pi$
$488$	−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	−0.394802	−	0.918766i	$-0.629187\pi$
$503$	11.7513	−	11.7513i	0.523965	−	0.523965i	0.918766	+	0.394802i	$0.129187\pi$
$504$	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	−0.00310741	−	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
$528$	31.1263	+	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	0.945119	−	0.326726i	$-0.105945\pi$
$547$	14.4630	+	14.4630i	0.618394	+	0.618394i	−0.326726	+	0.945119i	$0.605945\pi$
$548$	−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	−0.973301	−	0.229533i	$-0.926280\pi$
$557$	−17.5535	+	17.5535i	−0.743767	+	0.743767i	0.229533	+	0.973301i	$0.426280\pi$
$558$	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	0.326257	−	0.945281i	$-0.394212\pi$
$563$	−14.6880	−	14.6880i	−0.619024	−	0.619024i	−0.945281	+	0.326257i	$0.894212\pi$
$564$	−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	−0.824241	−	0.566240i	$-0.808398\pi$
$577$	−6.19740	+	6.19740i	−0.258001	+	0.258001i	0.566240	+	0.824241i	$0.308398\pi$
$578$	−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	−0.0203450	−	0.999793i	$-0.506476\pi$
$587$	23.7301	−	23.7301i	0.979448	−	0.979448i	0.999793	+	0.0203450i	$0.00647647\pi$
$588$	−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	−0.743633	−	0.668588i	$-0.766899\pi$
$593$	−1.82747	+	1.82747i	−0.0750452	+	0.0750452i	0.668588	+	0.743633i	$0.266899\pi$
$594$	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	−0.988025	−	0.154296i	$-0.950689\pi$
$607$	−20.5409	+	20.5409i	−0.833729	+	0.833729i	0.154296	+	0.988025i	$0.450689\pi$
$608$	−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	−0.967670	−	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	0.371388	−	0.928478i	$-0.378882\pi$
$617$	−13.8378	−	13.8378i	−0.557089	−	0.557089i	−0.928478	+	0.371388i	$0.878882\pi$
$618$	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	−0.970499	−	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	0.935775	−	0.352597i	$-0.114701\pi$
$647$	14.8338	+	14.8338i	0.583178	+	0.583178i	−0.352597	+	0.935775i	$0.614701\pi$
$648$	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	0.490659	−	0.871352i	$-0.336756\pi$
$653$	−9.72818	−	9.72818i	−0.380693	−	0.380693i	−0.871352	+	0.490659i	$0.836756\pi$
$654$	−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	0.0163909	−	0.999866i	$-0.494782\pi$
$673$	−25.5135	−	25.5135i	−0.983475	−	0.983475i	−0.999866	+	0.0163909i	$0.994782\pi$
$674$	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	$0.202515\pi$
$678$	−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	0.594575	−	0.804040i	$-0.297320\pi$
$683$	−5.47421	−	5.47421i	−0.209465	−	0.209465i	−0.804040	+	0.594575i	$0.797320\pi$
$684$	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	−0.966077	−	0.258256i	$-0.916852\pi$
$727$	−19.0849	+	19.0849i	−0.707821	+	0.707821i	0.258256	+	0.966077i	$0.416852\pi$
$728$	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	−0.476123	−	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
$738$	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	−0.646890	−	0.762583i	$-0.723931\pi$
$743$	3.15355	−	3.15355i	0.115692	−	0.115692i	0.762583	+	0.646890i	$0.223931\pi$
$744$	−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	0.989531	−	0.144322i	$-0.0461001\pi$
$757$	23.2548	+	23.2548i	0.845209	+	0.845209i	−0.144322	+	0.989531i	$0.546100\pi$
$758$	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	0.495783	−	0.868447i	$-0.334881\pi$
$773$	−10.3611	−	10.3611i	−0.372664	−	0.372664i	−0.868447	+	0.495783i	$0.834881\pi$
$774$	−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	0.387046	−	0.922060i	$-0.373495\pi$
$787$	−15.0090	−	15.0090i	−0.535014	−	0.535014i	−0.922060	+	0.387046i	$0.873495\pi$
$788$	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	−0.552363	−	0.833603i	$-0.686274\pi$
$797$	7.93974	−	7.93974i	0.281240	−	0.281240i	0.833603	+	0.552363i	$0.186274\pi$
$798$	−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	0.915606	−	0.402077i	$-0.131712\pi$
$823$	14.7321	+	14.7321i	0.513529	+	0.513529i	−0.402077	+	0.915606i	$0.631712\pi$
$824$	−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	$0.266404\pi$
$828$	−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	−0.456914	−	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	0.785472	−	0.618898i	$-0.212421\pi$
$857$	4.87637	+	4.87637i	0.166574	+	0.166574i	−0.618898	+	0.785472i	$0.712421\pi$
$858$	−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	$0.525390\pi$
$863$	−31.6243	+	31.6243i	−1.07650	+	1.07650i	−0.996820	+	0.0796816i	$0.974610\pi$
$864$	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	0.441453	−	0.897284i	$-0.354463\pi$
$877$	−13.4991	−	13.4991i	−0.455831	−	0.455831i	−0.897284	+	0.441453i	$0.854463\pi$
$878$	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	−0.542064	−	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	0.0788646	−	0.996885i	$-0.474871\pi$
$887$	−27.3410	−	27.3410i	−0.918021	−	0.918021i	−0.996885	+	0.0788646i	$0.974871\pi$
$888$	−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	0.498386	−	0.866955i	$-0.333926\pi$
$907$	−11.1000	−	11.1000i	−0.368569	−	0.368569i	−0.866955	+	0.498386i	$0.833926\pi$
$908$	−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	−0.903117	−	0.429394i	$-0.858727\pi$
$937$	−14.5009	+	14.5009i	−0.473724	+	0.473724i	0.429394	+	0.903117i	$0.358727\pi$
$938$	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	−0.478842	−	0.877901i	$-0.658943\pi$
$947$	12.2804	−	12.2804i	0.399059	−	0.399059i	0.877901	+	0.478842i	$0.158943\pi$
$948$	−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	−0.512939	−	0.858425i	$-0.671443\pi$
$953$	10.6654	−	10.6654i	0.345486	−	0.345486i	0.858425	+	0.512939i	$0.171443\pi$
$954$	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	$0.583944\pi$
$967$	−38.1275	+	38.1275i	−1.22610	+	1.22610i	−0.965428	+	0.260670i	$0.916056\pi$
$968$	−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	0.507613	−	0.861585i	$-0.330528\pi$
$977$	−11.0641	−	11.0641i	−0.353972	−	0.353972i	−0.861585	+	0.507613i	$0.830528\pi$
$978$	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	−0.840610	−	0.541641i	$-0.817803\pi$
$983$	−9.37350	+	9.37350i	−0.298968	+	0.298968i	0.541641	+	0.840610i	$0.317803\pi$
$984$	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	0.726800	−	0.686849i	$-0.241007\pi$
$997$	1.26149	+	1.26149i	0.0399517	+	0.0399517i	−0.686849	+	0.726800i	$0.741007\pi$
$998$	−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.293.4	yes	64
3.2	odd	2	inner	600.2.w.k.293.30	yes	64
5.2	odd	4	inner	600.2.w.k.557.19	yes	64
5.3	odd	4	inner	600.2.w.k.557.14	yes	64
5.4	even	2	inner	600.2.w.k.293.29	yes	64
8.5	even	2	inner	600.2.w.k.293.13	yes	64
15.2	even	4	inner	600.2.w.k.557.13	yes	64
15.8	even	4	inner	600.2.w.k.557.20	yes	64
15.14	odd	2	inner	600.2.w.k.293.3	✓	64
24.5	odd	2	inner	600.2.w.k.293.19	yes	64
40.13	odd	4	inner	600.2.w.k.557.3	yes	64
40.29	even	2	inner	600.2.w.k.293.20	yes	64
40.37	odd	4	inner	600.2.w.k.557.30	yes	64
120.29	odd	2	inner	600.2.w.k.293.14	yes	64
120.53	even	4	inner	600.2.w.k.557.29	yes	64
120.77	even	4	inner	600.2.w.k.557.4	yes	64

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