LMFDB - Embedded newform 600.2.w.k.293.19

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			293.19
Character	$\chi$	$=$	600.293
Dual form			600.2.w.k.557.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.552337 + 1.30189i) q^{2} +(-1.65680 + 0.504984i) q^{3} +(-1.38985 + 1.43817i) q^{4} +(-1.57255 - 1.87806i) q^{6} +(2.83719 - 2.83719i) q^{7} +(-2.64000 - 1.01508i) q^{8} +(2.48998 - 1.67332i) q^{9} +O(q^{10})$	\(q+(0.552337 + 1.30189i) q^{2} +(-1.65680 + 0.504984i) q^{3} +(-1.38985 + 1.43817i) q^{4} +(-1.57255 - 1.87806i) q^{6} +(2.83719 - 2.83719i) q^{7} +(-2.64000 - 1.01508i) q^{8} +(2.48998 - 1.67332i) q^{9} +4.74897 q^{11} +(1.57645 - 3.08461i) 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} +(3.55379 + 2.31745i) q^{18} +3.35370 q^{19} +(-3.26792 + 6.13340i) q^{21} +(2.62303 + 6.18265i) q^{22} +(-4.82662 + 4.82662i) q^{23} +(4.88656 + 0.348623i) q^{24} +(1.60939 + 0.650581i) q^{26} +(-3.28041 + 4.02976i) q^{27} +(0.137093 + 8.02362i) q^{28} +0.936190i q^{29} +5.49627 q^{31} +(5.12905 - 2.38596i) q^{32} +(-7.86810 + 2.39815i) q^{33} +(1.29761 - 3.20999i) q^{34} +(-1.05418 + 5.90667i) q^{36} +(-0.749350 - 0.749350i) q^{37} +(1.85238 + 4.36616i) q^{38} +(-0.999726 + 1.87633i) q^{39} +2.24103i q^{41} +(-9.79002 - 0.866782i) 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} +(2.24516 + 6.55433i) q^{48} -9.09930i q^{49} +(3.74242 + 1.99399i) q^{51} +(0.0419396 + 2.45459i) q^{52} +(-8.46720 - 8.46720i) q^{53} +(-7.05820 - 2.04495i) q^{54} +(-10.3702 + 4.61022i) q^{56} +(-5.55642 + 1.69357i) q^{57} +(-1.21882 + 0.517093i) q^{58} +6.53585i q^{59} +5.10959i q^{61} +(3.03579 + 7.15555i) q^{62} +(2.31703 - 11.8121i) q^{63} +(5.93923 + 5.35962i) q^{64} +(-7.46798 - 8.91883i) q^{66} +(4.85678 + 4.85678i) q^{67} +(4.89577 - 0.0836501i) q^{68} +(5.55939 - 10.4341i) q^{69} -8.34435i q^{71} +(-8.27211 + 1.89004i) q^{72} +(1.57561 + 1.57561i) q^{73} +(0.561679 - 1.38947i) q^{74} +(-4.66114 + 4.82319i) q^{76} +(13.4737 - 13.4737i) q^{77} +(-2.99497 - 0.265167i) q^{78} -7.75267i q^{79} +(3.40002 - 8.33306i) q^{81} +(-2.91758 + 1.23780i) q^{82} +(9.15657 + 9.15657i) q^{83} +(-4.27894 - 13.2243i) q^{84} +(16.2328 + 6.56196i) q^{86} +(-0.472761 - 1.55108i) q^{87} +(-12.5373 - 4.82057i) q^{88} -4.97996 q^{89} -4.92511i q^{91} +(-0.233222 - 13.6498i) q^{92} +(-9.10622 + 2.77553i) q^{93} +(-5.03116 + 12.4459i) q^{94} +(-7.29295 + 6.54316i) 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}+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 $

$2$	0.552337	+	1.30189i	0.390561	+	0.920577i
$2$	0.552337	+	1.30189i	0.390561	+	0.920577i
$3$	−1.65680	+	0.504984i	−0.956555	+	0.291553i
$3$	−1.65680	+	0.504984i	−0.956555	+	0.291553i
$4$	−1.38985	+	1.43817i	−0.694924	+	0.719084i
$5$		0			0
$5$		0			0
$6$	−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	$-0.0239557\pi$
$8$	−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	$-0.246001\pi$
$11$	4.74897			1.43187			0.715934	+	0.698168i	$0.246001\pi$
$12$	1.57645	−	3.08461i	0.455082	−	0.890450i
$13$	0.867956	−	0.867956i	0.240728	−	0.240728i	−0.576424	−	0.817151i	$-0.695552\pi$
$13$	0.867956	−	0.867956i	0.240728	−	0.240728i	0.817151	+	0.576424i	$0.195552\pi$
$14$	5.26080	+	2.12663i	1.40601	+	0.568366i
$15$		0			0
$16$	−0.136650	−	3.99767i	−0.0341624	−	0.999416i
$17$	−1.73117	−	1.73117i	−0.419870	−	0.419870i	0.465289	−	0.885159i	$-0.345950\pi$
$17$	−1.73117	−	1.73117i	−0.419870	−	0.419870i	−0.885159	+	0.465289i	$0.845950\pi$
$18$	3.55379	+	2.31745i	0.837636	+	0.546229i
$19$	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	$0.997950\pi$
$24$	4.88656	+	0.348623i	0.997465	+	0.0711623i
$25$		0			0
$26$	1.60939	+	0.650581i	0.315627	+	0.127589i
$27$	−3.28041	+	4.02976i	−0.631314	+	0.775527i
$28$	0.137093	+	8.02362i	0.0259081	+	1.51632i
$29$			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	$0.335688\pi$
$32$	5.12905	−	2.38596i	0.906697	−	0.421783i
$33$	−7.86810	+	2.39815i	−1.36966	+	0.417465i
$34$	1.29761	−	3.20999i	0.222538	−	0.550508i
$35$		0			0
$36$	−1.05418	+	5.90667i	−0.175697	+	0.984444i
$37$	−0.749350	−	0.749350i	−0.123192	−	0.123192i	0.642823	−	0.766015i	$-0.277763\pi$
$37$	−0.749350	−	0.749350i	−0.123192	−	0.123192i	−0.766015	+	0.642823i	$0.777763\pi$
$38$	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	$0.0559909\pi$
$41$			2.24103i			0.349990i	−0.984569	+	0.174995i	$0.944009\pi$
$42$	−9.79002	−	0.866782i	−1.51063	−	0.133747i
$43$	8.75448	−	8.75448i	1.33505	−	1.33505i	0.434256	−	0.900789i	$-0.357011\pi$
$43$	8.75448	−	8.75448i	1.33505	−	1.33505i	0.900789	−	0.434256i	$-0.142989\pi$
$44$	−6.60034	+	6.82981i	−0.995039	+	1.02963i
$45$		0			0
$46$	−8.94967	−	3.61782i	−1.31956	−	0.533419i
$47$	6.71219	+	6.71219i	0.979073	+	0.979073i	0.999785	−	0.0207122i	$-0.00659336\pi$
$47$	6.71219	+	6.71219i	0.979073	+	0.979073i	−0.0207122	+	0.999785i	$0.506593\pi$
$48$	2.24516	+	6.55433i	0.324061	+	0.946036i
$49$		−	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	$-0.557370\pi$
$54$	−7.05820	−	2.04495i	−0.960499	−	0.278283i
$55$		0			0
$56$	−10.3702	+	4.61022i	−1.38577	+	0.616067i
$57$	−5.55642	+	1.69357i	−0.735966	+	0.224319i
$58$	−1.21882	+	0.517093i	−0.160039	+	0.0678976i
$59$			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	$0.106074\pi$
$61$			5.10959i			0.654216i	−0.944987	+	0.327108i	$0.893926\pi$
$62$	3.03579	+	7.15555i	0.385546	+	0.908756i
$63$	2.31703	−	11.8121i	0.291919	−	1.48818i
$64$	5.93923	+	5.35962i	0.742404	+	0.669952i
$65$		0			0
$66$	−7.46798	−	8.91883i	−0.919245	−	1.09783i
$67$	4.85678	+	4.85678i	0.593350	+	0.593350i	0.938535	−	0.345185i	$-0.112184\pi$
$67$	4.85678	+	4.85678i	0.593350	+	0.593350i	−0.345185	+	0.938535i	$0.612184\pi$
$68$	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	$-0.835115\pi$
$71$		−	8.34435i		−	0.990292i	0.868810	−	0.495146i	$-0.164885\pi$
$72$	−8.27211	+	1.89004i	−0.974877	+	0.222743i
$73$	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
$78$	−2.99497	−	0.265167i	−0.339114	−	0.0300242i
$79$		−	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	$0.498384\pi$
$84$	−4.27894	−	13.2243i	−0.466870	−	1.44289i
$85$		0			0
$86$	16.2328	+	6.56196i	1.75043	+	0.707595i
$87$	−0.472761	−	1.55108i	−0.0506853	−	0.166293i
$88$	−12.5373	−	4.82057i	−1.33648	−	0.513875i
$89$	−4.97996			−0.527875			−0.263938	−	0.964540i	$-0.585021\pi$
$89$	−4.97996			−0.527875			−0.263938	+	0.964540i	$0.585021\pi$
$90$		0			0
$91$		−	4.92511i		−	0.516292i
$92$	−0.233222	−	13.6498i	−0.0243151	−	1.42309i
$93$	−9.10622	+	2.77553i	−0.944272	+	0.287809i
$94$	−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	$0.282719\pi$
$98$	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	$-0.576617\pi$
$101$	−4.79140			−0.476762			−0.238381	+	0.971172i	$0.576617\pi$
$102$	−0.528885	+	5.97358i	−0.0523674	+	0.591472i
$103$	−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	$0.396822\pi$
$108$	−1.23620	−	10.3185i	−0.118953	−	0.992900i
$109$	−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	$0.100500\pi$
$114$	−5.27386	−	6.29844i	−0.493942	−	0.589903i
$115$		0			0
$116$	−1.34640	−	1.30116i	−0.125010	−	0.120810i
$117$	0.708829	−	3.61356i	0.0655312	−	0.334074i
$118$	−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
$123$	−1.13168	−	3.71294i	−0.102041	−	0.334784i
$124$	−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	$0.251472\pi$
$128$	−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	$-0.302692\pi$
$131$	13.2979			1.16184			0.580922	+	0.813959i	$0.302692\pi$
$132$	7.48651	−	14.6487i	0.651617	−	1.27501i
$133$	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	$0.761791\pi$
$138$	16.6548	+	1.47457i	1.41775	+	0.125524i
$139$	−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
$144$	−7.02962	−	9.72546i	−0.585801	−	0.810455i
$145$		0			0
$146$	−1.18100	+	2.92154i	−0.0977407	+	0.241788i
$147$	4.59501	+	15.0757i	0.378990	+	1.24343i
$148$	2.11917	−	0.0362086i	0.174195	−	0.00297633i
$149$		−	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	$0.719619\pi$
$152$	−8.85379	−	3.40427i	−0.718137	−	0.276123i
$153$	−7.20738	−	1.41378i	−0.582682	−	0.114298i
$154$	24.9834	+	10.0993i	2.01322	+	0.813825i
$155$		0			0
$156$	−1.30902	−	4.04559i	−0.104805	−	0.323907i
$157$	−14.1557	−	14.1557i	−1.12975	−	1.12975i	−0.990217	−	0.139534i	$-0.955440\pi$
$157$	−14.1557	−	14.1557i	−1.12975	−	1.12975i	−0.139534	−	0.990217i	$-0.544560\pi$
$158$	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
$162$	12.7267	−	0.176201i	0.999904	−	0.0138437i
$163$	−5.09399	+	5.09399i	−0.398992	+	0.398992i	−0.877878	−	0.478885i	$-0.841041\pi$
$163$	−5.09399	+	5.09399i	−0.398992	+	0.398992i	0.478885	+	0.877878i	$0.341041\pi$
$164$	−3.22297	−	3.11469i	−0.251672	−	0.243216i
$165$		0			0
$166$	−6.86335	+	16.9784i	−0.532699	+	1.31778i
$167$	−13.7751	−	13.7751i	−1.06595	−	1.06595i	−0.997666	−	0.0682869i	$-0.978247\pi$
$167$	−13.7751	−	13.7751i	−1.06595	−	1.06595i	−0.0682869	−	0.997666i	$-0.521753\pi$
$168$	14.8532	−	12.8750i	1.14595	−	0.993327i
$169$			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	$0.625746\pi$
$174$	1.75822	−	1.47220i	0.133290	−	0.111608i
$175$		0			0
$176$	−0.648945	−	18.9848i	−0.0489161	−	1.43103i
$177$	−3.30050	−	10.8286i	−0.248081	−	0.813928i
$178$	−2.75062	−	6.48338i	−0.206168	−	0.485950i
$179$			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	$0.174513\pi$
$181$			14.0239i			1.04239i	−0.853439	+	0.521194i	$0.825487\pi$
$182$	6.41197	−	2.72032i	0.475287	−	0.201644i
$183$	−2.58026	−	8.46558i	−0.190739	−	0.625794i
$184$	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
$188$	−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	$-0.600853\pi$
$191$		−	26.2648i		−	1.90045i	0.311563	−	0.950225i	$-0.399147\pi$
$192$	−12.5467	−	5.88060i	−0.905477	−	0.424396i
$193$	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	$0.201735\pi$
$198$	16.8768	+	11.0055i	1.19938	+	0.782128i
$199$		−	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
$204$	−8.06908	+	2.61088i	−0.564949	+	0.182798i
$205$		0			0
$206$	0.808260	−	1.99945i	0.0563142	−	0.139308i
$207$	−3.94173	+	20.0947i	−0.273969	+	1.39668i
$208$	−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
$213$	4.21377	+	13.8249i	0.288722	+	0.947269i
$214$	−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
$218$	−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
$222$	−0.228932	+	2.58571i	−0.0153649	+	0.173541i
$223$	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	$0.356047\pi$
$228$	5.28694	−	10.3449i	0.350136	−	0.685105i
$229$	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	$0.256097\pi$
$234$	5.09598	−	1.07308i	0.333134	−	0.0701498i
$235$		0			0
$236$	−9.39964	−	9.08383i	−0.611865	−	0.591307i
$237$	3.91498	+	12.8446i	0.254305	+	0.834349i
$238$	−5.42578	−	12.7889i	−0.351701	−	0.828981i
$239$	−8.34435			−0.539751			−0.269876	−	0.962895i	$-0.586983\pi$
$239$	−8.34435			−0.539751			−0.269876	+	0.962895i	$0.586983\pi$
$240$		0			0
$241$	−15.4459			−0.994960			−0.497480	−	0.867475i	$-0.665741\pi$
$241$	−15.4459			−0.994960			−0.497480	+	0.867475i	$0.665741\pi$
$242$	6.38099	+	15.0404i	0.410186	+	0.966832i
$243$	−1.42509	+	15.5232i	−0.0914196	+	0.995812i
$244$	−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
$248$	−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	$-0.713099\pi$
$251$	−19.6634			−1.24114			−0.620572	+	0.784150i	$0.713099\pi$
$252$	13.7674	+	19.7493i	0.867266	+	1.24409i
$253$	−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	$0.553637\pi$
$258$	−30.2082	−	2.67456i	−1.88068	−	0.166511i
$259$	−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	$0.379721\pi$
$264$	23.2061	+	1.65560i	1.42824	+	0.101895i
$265$		0			0
$266$	17.6432	+	7.13209i	1.08177	+	0.437297i
$267$	8.25081	−	2.51480i	0.504941	−	0.153903i
$268$	−13.7350	+	0.234680i	−0.839002	+	0.0143353i
$269$		−	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	$0.476834\pi$
$272$	−6.68407	+	7.15720i	−0.405281	+	0.433969i
$273$	2.48710	+	8.15993i	0.150526	+	0.493862i
$274$	0.459480	−	1.13665i	0.0277582	−	0.0686675i
$275$		0			0
$276$	7.27932	+	22.4972i	0.438164	+	1.35417i
$277$	−2.60387	−	2.60387i	−0.156451	−	0.156451i	0.624541	−	0.780992i	$-0.285286\pi$
$277$	−2.60387	−	2.60387i	−0.156451	−	0.156451i	−0.780992	+	0.624541i	$0.785286\pi$
$278$	−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	$0.126195\pi$
$281$			12.9461i			0.772301i	−0.922436	+	0.386151i	$0.873805\pi$
$282$	2.05062	−	23.1611i	0.122113	−	1.37922i
$283$	1.95205	−	1.95205i	0.116037	−	0.116037i	−0.646704	−	0.762741i	$-0.723853\pi$
$283$	1.95205	−	1.95205i	0.116037	−	0.116037i	0.762741	+	0.646704i	$0.223853\pi$
$284$	12.0006	+	11.5974i	0.712103	+	0.688177i
$285$		0			0
$286$	7.64294	+	3.08959i	0.451936	+	0.182691i
$287$	6.35823	+	6.35823i	0.375314	+	0.375314i
$288$	8.77878	−	14.5235i	0.517294	−	0.855808i
$289$		−	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	$-0.501903\pi$
$294$	−17.0890	+	14.3091i	−0.996650	+	0.834523i
$295$		0			0
$296$	1.21764	+	2.73893i	0.0707737	+	0.159197i
$297$	−15.5785	+	19.1372i	−0.903959	+	1.11045i
$298$	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
$303$	7.93840	−	2.41958i	0.456049	−	0.139001i
$304$	−0.458282	−	13.4070i	−0.0262843	−	0.768943i
$305$		0			0
$306$	−2.14031	−	10.1641i	−0.122353	−	0.581044i
$307$	−7.34204	−	7.34204i	−0.419033	−	0.419033i	0.465838	−	0.884870i	$-0.345753\pi$
$307$	−7.34204	−	7.34204i	−0.419033	−	0.419033i	−0.884870	+	0.465838i	$0.845753\pi$
$308$	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	$0.213462\pi$
$311$			21.9193i			1.24293i	−0.783442	+	0.621465i	$0.786538\pi$
$312$	4.54391	−	3.93873i	0.257248	−	0.222987i
$313$	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	$0.496693\pi$
$318$	−2.58679	+	29.2170i	−0.145060	+	1.63841i
$319$			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
$324$	7.25883	+	16.4715i	0.403268	+	0.915082i
$325$		0			0
$326$	−9.44543	−	3.81823i	−0.523134	−	0.211472i
$327$	14.8992	−	4.54119i	0.823926	−	0.251128i
$328$	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
$333$	−3.11977	−	0.611967i	−0.170962	−	0.0335356i
$334$	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	$0.995515\pi$
$338$	−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
$342$	11.9184	+	7.77205i	0.644471	+	0.420264i
$343$	−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	$0.231121\pi$
$348$	2.88778	+	1.47586i	0.154801	+	0.0791142i
$349$	−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	$0.171194\pi$
$354$	12.2747	−	10.2779i	0.652392	−	0.546266i
$355$		0			0
$356$	6.92139	−	7.16202i	0.366833	−	0.379586i
$357$	16.2753	−	4.96062i	0.861379	−	0.262544i
$358$	−3.67311	+	1.55834i	−0.194130	+	0.0823611i
$359$	9.82331			0.518455			0.259227	−	0.965816i	$-0.416532\pi$
$359$	9.82331			0.518455			0.259227	+	0.965816i	$0.416532\pi$
$360$		0			0
$361$	−7.75267			−0.408035
$362$	−18.2576	+	7.74591i	−0.959597	+	0.407116i
$363$	−19.1405	+	5.83393i	−1.00462	+	0.306202i
$364$	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	$0.238443\pi$
$368$	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
$372$	8.66459	−	16.9538i	0.449238	−	0.879015i
$373$	18.9116	−	18.9116i	0.979205	−	0.979205i	−0.0205831	−	0.999788i	$-0.506552\pi$
$373$	18.9116	−	18.9116i	0.979205	−	0.979205i	0.999788	+	0.0205831i	$0.00655226\pi$
$374$	6.16229	−	15.2441i	0.318645	−	0.788255i
$375$		0			0
$376$	−10.9068	−	24.5336i	−0.562475	−	1.26522i
$377$	0.812572	+	0.812572i	0.0418496	+	0.0418496i
$378$	−25.8274	+	14.2235i	−1.32842	+	0.731580i
$379$	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	$0.432957\pi$
$384$	0.725930	−	19.5825i	0.0370450	−	0.999314i
$385$		0			0
$386$	−6.19904	+	15.3350i	−0.315523	+	0.780532i
$387$	7.14947	−	36.4475i	0.363428	−	1.85273i
$388$	−0.0690581	−	4.04175i	−0.00350589	−	0.205189i
$389$			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
$392$	−9.23650	+	24.0222i	−0.466514	+	1.21330i
$393$	−22.0320	+	6.71524i	−1.11137	+	0.338739i
$394$	5.55939	+	2.24733i	0.280078	+	0.113219i
$395$		0			0
$396$	−5.00629	+	28.0506i	−0.251575	+	1.40959i
$397$	18.0470	+	18.0470i	0.905755	+	0.905755i	0.995926	−	0.0901716i	$-0.0287416\pi$
$397$	18.0470	+	18.0470i	0.905755	+	0.905755i	−0.0901716	+	0.995926i	$0.528742\pi$
$398$	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	$-0.808364\pi$
$401$		−	22.6814i		−	1.13265i	0.824181	−	0.566327i	$-0.191636\pi$
$402$	1.48378	−	16.7588i	0.0740043	−	0.835854i
$403$	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
$408$	−7.85594	−	9.06299i	−0.388927	−	0.448685i
$409$			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
$414$	−28.3383	+	5.96733i	−1.39275	+	0.293278i
$415$		0			0
$416$	2.38088	−	6.52270i	0.116732	−	0.319802i
$417$	29.0969	−	8.86857i	1.42488	−	0.434296i
$418$	8.79687	+	20.7348i	0.430269	+	1.01417i
$419$		−	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	$0.146245\pi$
$421$			18.1975i			0.886894i	−0.896301	+	0.443447i	$0.853755\pi$
$422$	12.2916	−	5.21480i	0.598345	−	0.253852i
$423$	27.9448	+	5.48161i	1.35873	+	0.266525i
$424$	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
$428$	−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	$-0.701591\pi$
$431$		−	33.4688i		−	1.61214i	0.591822	−	0.806069i	$-0.298409\pi$
$432$	16.5579	+	12.5633i	0.796641	+	0.604452i
$433$	−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
$438$	0.481359	−	5.43680i	0.0230002	−	0.259780i
$439$			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	$0.698074\pi$
$444$	−3.49276	+	1.13014i	−0.165759	+	0.0536340i
$445$		0			0
$446$	−12.9710	+	32.0872i	−0.614193	+	1.51937i
$447$	1.35368	+	4.44129i	0.0640269	+	0.210066i
$448$	32.0570	−	1.64448i	1.51455	−	0.0776942i
$449$	−8.70564			−0.410845			−0.205422	−	0.978673i	$-0.565857\pi$
$449$	−8.70564			−0.410845			−0.205422	+	0.978673i	$0.565857\pi$
$450$		0			0
$451$			10.6426i			0.501139i
$452$	0.328765	+	19.2416i	0.0154638	+	0.905047i
$453$	25.9172	−	7.89944i	1.21770	−	0.371148i
$454$	−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	$0.188497\pi$
$458$	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	$-0.659514\pi$
$461$	−20.6299			−0.960829			−0.480415	+	0.877042i	$0.659514\pi$
$462$	−46.4925	−	4.11632i	−2.16303	−	0.191509i
$463$	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	$0.0507395\pi$
$468$	4.21174	+	6.04171i	0.194688	+	0.279278i
$469$	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
$474$	−14.5599	+	12.1914i	−0.668760	+	0.559972i
$475$		0			0
$476$	13.6529	−	14.1276i	0.625780	−	0.647536i
$477$	−35.2515	−	6.91486i	−1.61406	−	0.316610i
$478$	−4.60890	−	10.8634i	−0.210806	−	0.496882i
$479$	−18.1677			−0.830102			−0.415051	−	0.909798i	$-0.636236\pi$
$479$	−18.1677			−0.830102			−0.415051	+	0.909798i	$0.636236\pi$
$480$		0			0
$481$	−1.30081			−0.0593116
$482$	−8.53137	−	20.1089i	−0.388593	−	0.915937i
$483$	−13.8306	−	45.3767i	−0.629312	−	2.06471i
$484$	−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	$0.223370\pi$
$488$	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	$-0.424028\pi$
$491$	10.4772			0.472829			0.236415	+	0.971652i	$0.424028\pi$
$492$	6.91270	+	3.53287i	0.311648	+	0.159274i
$493$	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
$498$	2.79740	−	31.5957i	0.125354	−	1.41584i
$499$	−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	$0.370813\pi$
$504$	−18.1072	+	28.8319i	−0.806557	+	1.28428i
$505$		0			0
$506$	−42.5017	−	17.1809i	−1.88943	−	0.763785i
$507$	−5.80394	−	19.0421i	−0.257762	−	0.845690i
$508$	−0.00356002	−	0.208357i	−0.000157951	−	0.00924434i
$509$		−	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
$512$	−10.2392	−	20.1782i	−0.452511	−	0.891759i
$513$	−11.0015	+	13.5146i	−0.485729	+	0.596685i
$514$	−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
$518$	−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	$0.124515\pi$
$521$			17.4056i			0.762553i	−0.924461	+	0.381277i	$0.875485\pi$
$522$	−2.16958	+	3.32702i	−0.0949598	+	0.145620i
$523$	−22.7980	+	22.7980i	−0.996888	+	0.996888i	−0.999995	−	0.00310741i	$-0.999011\pi$
$523$	−22.7980	+	22.7980i	−0.996888	+	0.996888i	0.00310741	+	0.999995i	$0.499011\pi$
$524$	−18.4821	+	19.1246i	−0.807393	+	0.835464i
$525$		0			0
$526$	−16.8549	−	6.81345i	−0.734910	−	0.297081i
$527$	−9.51497	−	9.51497i	−0.414479	−	0.414479i
$528$	10.6622	+	31.1263i	0.464012	+	1.35460i
$529$		−	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
$534$	7.83123	+	9.35265i	0.338891	+	0.404729i
$535$		0			0
$536$	−7.89191	−	17.7519i	−0.340878	−	0.766767i
$537$	−1.42474	−	4.67444i	−0.0614823	−	0.201717i
$538$	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
$543$	−7.08184	−	23.2348i	−0.303911	−	0.997100i
$544$	−13.0098	−	4.74875i	−0.557789	−	0.203601i
$545$		0			0
$546$	−9.24963	+	7.74498i	−0.395848	+	0.331454i
$547$	−14.4630	−	14.4630i	−0.618394	−	0.618394i	0.326726	−	0.945119i	$-0.394055\pi$
$547$	−14.4630	−	14.4630i	−0.618394	−	0.618394i	−0.945119	+	0.326726i	$0.894055\pi$
$548$	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
$552$	−25.2683	+	21.9029i	−1.07549	+	0.932250i
$553$	−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	$0.426280\pi$
$558$	19.5326	+	12.7373i	0.826880	+	0.539215i
$559$		−	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	$0.894212\pi$
$564$	31.2859	−	10.1231i	1.31737	−	0.426257i
$565$		0			0
$566$	3.61955	+	1.46317i	0.152141	+	0.0615016i
$567$	−13.9960	−	33.2890i	−0.587776	−	1.39801i
$568$	−8.47017	+	22.0291i	−0.355400	+	0.924321i
$569$	−27.6388			−1.15868			−0.579338	−	0.815087i	$-0.696689\pi$
$569$	−27.6388			−1.15868			−0.579338	+	0.815087i	$0.696689\pi$
$570$		0			0
$571$			2.71823i			0.113754i	0.998381	+	0.0568772i	$0.0181143\pi$
$571$			2.71823i			0.113754i	−0.998381	+	0.0568772i	$0.981886\pi$
$572$	0.199170	+	11.6568i	0.00832771	+	0.487394i
$573$	13.2633	+	43.5155i	0.554082	+	1.81789i
$574$	−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	$0.308398\pi$
$578$	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
$582$	4.93154	+	0.436626i	0.204419	+	0.0180987i
$583$	−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	$0.00647647\pi$
$588$	−28.0678	−	14.3446i	−1.15750	−	0.591561i
$589$	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	$0.233101\pi$
$594$	−33.5192	−	9.71141i	−1.37531	−	0.398464i
$595$		0			0
$596$	3.85521	+	3.72568i	0.157916	+	0.152610i
$597$	3.38458	+	11.1044i	0.138521	+	0.454475i
$598$	−10.9080	+	4.62781i	−0.446062	+	0.189245i
$599$	−20.1671			−0.824006			−0.412003	−	0.911182i	$-0.635171\pi$
$599$	−20.1671			−0.824006			−0.412003	+	0.911182i	$0.635171\pi$
$600$		0			0
$601$	17.2324			0.702924			0.351462	−	0.936202i	$-0.385685\pi$
$601$	17.2324			0.702924			0.351462	+	0.936202i	$0.385685\pi$
$602$	64.6731	−	27.4380i	2.63588	−	1.11829i
$603$	20.2202	+	3.96636i	0.823432	+	0.161523i
$604$	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	$0.450689\pi$
$608$	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
$612$	12.0504	−	8.40047i	0.487109	−	0.339569i
$613$	17.7138	−	17.7138i	0.715452	−	0.715452i	−0.252218	−	0.967670i	$-0.581160\pi$
$613$	17.7138	−	17.7138i	0.715452	−	0.715452i	0.967670	+	0.252218i	$0.0811602\pi$
$614$	5.50327	−	13.6138i	0.222094	−	0.549410i
$615$		0			0
$616$	−49.2476	+	21.8938i	−1.98424	+	0.882126i
$617$	13.8378	+	13.8378i	0.557089	+	0.557089i	0.928478	−	0.371388i	$-0.121118\pi$
$617$	13.8378	+	13.8378i	0.557089	+	0.557089i	−0.371388	+	0.928478i	$0.621118\pi$
$618$	−0.329434	+	3.72085i	−0.0132518	+	0.149675i
$619$	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
$624$	7.63757	+	3.74017i	0.305747	+	0.149727i
$625$		0			0
$626$	−11.1626	+	27.6136i	−0.446145	+	1.10366i
$627$	−26.3873	+	8.04270i	−1.05381	+	0.321195i
$628$	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
$633$	4.76772	+	15.6424i	0.189500	+	0.621730i
$634$	−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
$638$	−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	$-0.873167\pi$
$641$		−	19.6466i		−	0.775995i	0.921660	−	0.387998i	$-0.126833\pi$
$642$	22.4664	+	1.98911i	0.886678	+	0.0785041i
$643$	18.4955	−	18.4955i	0.729392	−	0.729392i	−0.241107	−	0.970499i	$-0.577510\pi$
$643$	18.4955	−	18.4955i	0.729392	−	0.729392i	0.970499	+	0.241107i	$0.0775103\pi$
$644$	−39.3887	−	38.0653i	−1.55213	−	1.49998i
$645$		0			0
$646$	4.35179	−	10.7653i	0.171219	−	0.423557i
$647$	−14.8338	−	14.8338i	−0.583178	−	0.583178i	0.352597	−	0.935775i	$-0.385299\pi$
$647$	−14.8338	−	14.8338i	−0.583178	−	0.583178i	−0.935775	+	0.352597i	$0.885299\pi$
$648$	−17.4348	+	18.5480i	−0.684902	+	0.728635i
$649$			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	$0.836756\pi$
$654$	14.1415	+	16.8888i	0.552976	+	0.660406i
$655$		0			0
$656$	8.95888	−	0.306236i	0.349786	−	0.0119565i
$657$	6.55973	+	1.28674i	0.255919	+	0.0502006i
$658$	21.0372	+	49.5858i	0.820114	+	1.93306i
$659$			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	$0.280072\pi$
$661$			39.6271i			1.54131i	−0.637250	+	0.770657i	$0.719928\pi$
$662$	−9.28353	+	3.93860i	−0.360815	+	0.153078i
$663$	4.97895	−	1.51756i	0.193366	−	0.0589370i
$664$	−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
$668$	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
$672$	−2.12730	+	39.2557i	−0.0820624	+	1.51432i
$673$	−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	$0.202515\pi$
$678$	−23.4776	−	2.07864i	−0.901652	−	0.0798299i
$679$			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	$0.797320\pi$
$684$	−3.53542	+	19.8092i	−0.135180	+	0.757424i
$685$		0			0
$686$	4.46444	−	11.0440i	0.170453	−	0.421663i
$687$	−4.81318	+	1.46703i	−0.183634	+	0.0559708i
$688$	−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
$693$	11.0035	−	56.0952i	0.417989	−	2.13088i
$694$	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
$698$	−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	$-0.286466\pi$
$701$	32.9176			1.24328			0.621641	+	0.783302i	$0.286466\pi$
$702$	−7.90113	+	4.35128i	−0.298209	+	0.164228i
$703$	−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
$708$	20.1605	+	10.3034i	0.757679	+	0.387227i
$709$	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
$714$	15.4476	+	18.4487i	0.578113	+	0.690426i
$715$		0			0
$716$	−4.05759	−	3.92127i	−0.151639	−	0.146545i
$717$	13.8249	−	4.21377i	0.516302	−	0.157366i
$718$	5.42578	+	12.7889i	0.202488	+	0.477277i
$719$	44.9529			1.67646			0.838230	−	0.545317i	$-0.183591\pi$
$719$	44.9529			1.67646			0.838230	+	0.545317i	$0.183591\pi$
$720$		0			0
$721$	−6.11880			−0.227876
$722$	−4.28209	−	10.0931i	−0.159363	−	0.375628i
$723$	25.5909	−	7.79996i	0.951734	−	0.290083i
$724$	−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	$0.416852\pi$
$728$	−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
$732$	15.7611	+	8.05501i	0.582547	+	0.297722i
$733$	−10.9177	+	10.9177i	−0.403256	+	0.403256i	−0.879379	−	0.476123i	$-0.842042\pi$
$733$	−10.9177	+	10.9177i	−0.403256	+	0.403256i	0.476123	+	0.879379i	$0.342042\pi$
$734$	1.82358	+	0.737164i	0.0673095	+	0.0272092i
$735$		0			0
$736$	−13.2399	+	36.2722i	−0.488028	+	1.33701i
$737$	23.0647	+	23.0647i	0.849599	+	0.849599i
$738$	−5.19348	+	7.96414i	−0.191175	+	0.293164i
$739$	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	$0.276069\pi$
$744$	26.8578	+	1.91612i	0.984656	+	0.0702485i
$745$		0			0
$746$	35.0664	+	14.1753i	1.28387	+	0.518994i
$747$	38.1215	+	7.47784i	1.39479	+	0.273600i
$748$	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
$753$	32.5784	−	9.92971i	1.18722	−	0.361859i
$754$	−0.609067	+	1.50669i	−0.0221809	+	0.0548706i
$755$		0			0
$756$	−32.7829	−	25.7683i	−1.19230	−	0.937183i
$757$	−23.2548	−	23.2548i	−0.845209	−	0.845209i	0.144322	−	0.989531i	$-0.453900\pi$
$757$	−23.2548	−	23.2548i	−0.845209	−	0.845209i	−0.989531	+	0.144322i	$0.953900\pi$
$758$	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	$-0.937844\pi$
$761$		−	10.7051i		−	0.388059i	0.980996	−	0.194030i	$-0.0621558\pi$
$762$	0.254227	+	0.0225085i	0.00920966	+	0.000815399i
$763$	−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
$768$	25.8952	−	9.87104i	0.934413	−	0.356191i
$769$			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	$0.834881\pi$
$774$	51.3997	−	10.8235i	1.84752	−	0.389042i
$775$		0			0
$776$	5.22378	−	2.32232i	0.187523	−	0.0833663i
$777$	7.04488	−	2.14724i	0.252734	−	0.0770319i
$778$	−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
$783$	−3.77262	−	3.07108i	−0.134822	−	0.109752i
$784$	−36.3760	+	1.24342i	−1.29914	+	0.0444077i
$785$		0			0
$786$	−20.9116	−	24.9742i	−0.745893	−	0.890801i
$787$	15.0090	+	15.0090i	0.535014	+	0.535014i	0.922060	−	0.387046i	$-0.126505\pi$
$787$	15.0090	+	15.0090i	0.535014	+	0.535014i	−0.387046	+	0.922060i	$0.626505\pi$
$788$	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
$792$	−39.2840	+	8.97573i	−1.39590	+	0.318939i
$793$	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	$0.186274\pi$
$798$	−32.8328	−	2.90693i	−1.16227	−	0.102904i
$799$		−	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
$804$	22.6377	−	7.32480i	0.798371	−	0.258326i
$805$		0			0
$806$	8.84563	+	3.57577i	0.311574	+	0.125951i
$807$	5.72008	+	18.7670i	0.201356	+	0.660630i
$808$	12.6493	+	4.86364i	0.445001	+	0.171102i
$809$	−1.99039			−0.0699782			−0.0349891	−	0.999388i	$-0.511140\pi$
$809$	−1.99039			−0.0699782			−0.0349891	+	0.999388i	$0.511140\pi$
$810$		0			0
$811$			39.1133i			1.37345i	0.726915	+	0.686727i	$0.240953\pi$
$811$			39.1133i			1.37345i	−0.726915	+	0.686727i	$0.759047\pi$
$812$	−7.51163	+	0.128345i	−0.263607	+	0.00450403i
$813$	−3.96639	+	1.20893i	−0.139107	+	0.0423991i
$814$	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
$818$	−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	$-0.509923\pi$
$821$	−1.78624			−0.0623403			−0.0311702	+	0.999514i	$0.509923\pi$
$822$	−0.187277	+	2.11523i	−0.00653204	+	0.0737772i
$823$	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	$0.266404\pi$
$828$	−23.4211	−	33.5974i	−0.813940	−	1.16759i
$829$	−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
$834$	27.6172	+	32.9825i	0.956305	+	1.14209i
$835$		0			0
$836$	−22.1356	+	22.9052i	−0.765575	+	0.792192i
$837$	−18.0300	+	22.1486i	−0.623208	+	0.765568i
$838$	14.9142	−	6.32747i	0.515204	−	0.218579i
$839$	−20.7869			−0.717643			−0.358821	−	0.933406i	$-0.616821\pi$
$839$	−20.7869			−0.717643			−0.358821	+	0.933406i	$0.616821\pi$
$840$		0			0
$841$	28.1235			0.969778
$842$	−23.6912	+	10.0512i	−0.816454	+	0.346387i
$843$	−6.53759	−	21.4492i	−0.225167	−	0.738748i
$844$	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
$848$	−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
$852$	−25.7391	−	13.1544i	−0.881805	−	0.450664i
$853$	−12.6345	+	12.6345i	−0.432597	+	0.432597i	−0.889511	−	0.456914i	$-0.848955\pi$
$853$	−12.6345	+	12.6345i	−0.432597	+	0.432597i	0.456914	+	0.889511i	$0.348955\pi$
$854$	−10.8662	+	26.8806i	−0.371834	+	0.919834i
$855$		0			0
$856$	23.7977	−	10.5797i	0.813390	−	0.361605i
$857$	−4.87637	−	4.87637i	−0.166574	−	0.166574i	0.618898	−	0.785472i	$-0.287579\pi$
$857$	−4.87637	−	4.87637i	−0.166574	−	0.166574i	−0.785472	+	0.618898i	$0.787579\pi$
$858$	−14.2230	−	1.25927i	−0.485566	−	0.0429907i
$859$	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	$-0.0253904\pi$
$864$	−7.21053	+	28.4958i	−0.245307	+	0.969445i
$865$		0			0
$866$	12.2883	−	30.3985i	0.417575	−	1.03298i
$867$	5.55791	+	18.2349i	0.188757	+	0.619291i
$868$	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
$873$	−1.16716	+	5.95012i	−0.0395025	+	0.201381i
$874$	−30.0145	−	12.1331i	−1.01526	−	0.410408i
$875$		0			0
$876$	7.34400	−	2.37627i	0.248131	−	0.0802867i
$877$	13.4991	+	13.4991i	0.455831	+	0.455831i	0.897284	−	0.441453i	$-0.145537\pi$
$877$	13.4991	+	13.4991i	0.455831	+	0.455831i	−0.441453	+	0.897284i	$0.645537\pi$
$878$	−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	$0.221729\pi$
$881$			38.0875i			1.28320i	−0.767039	+	0.641601i	$0.778271\pi$
$882$	21.0872	−	32.3370i	0.710043	−	1.08884i
$883$	−8.86328	+	8.86328i	−0.298273	+	0.298273i	−0.840337	−	0.542064i	$-0.817643\pi$
$883$	−8.86328	+	8.86328i	−0.298273	+	0.298273i	0.542064	+	0.840337i	$0.317643\pi$
$884$	4.17671	−	4.32192i	0.140478	−	0.145362i
$885$		0			0
$886$	−3.62348	+	8.96368i	−0.121733	+	0.301141i
$887$	27.3410	+	27.3410i	0.918021	+	0.918021i	0.996885	−	0.0788646i	$-0.0251295\pi$
$887$	27.3410	+	27.3410i	0.918021	+	0.918021i	−0.0788646	+	0.996885i	$0.525129\pi$
$888$	−3.40050	−	3.92298i	−0.114113	−	0.131647i
$889$			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
$894$	−5.03439	+	4.21544i	−0.168375	+	0.140985i
$895$		0			0
$896$	19.8472	+	40.8265i	0.663049	+	1.36392i
$897$	−4.23106	−	13.8817i	−0.141271	−	0.463495i
$898$	−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
$903$	25.0857	+	82.3037i	0.834801	+	2.73890i
$904$	−24.8689	+	11.0559i	−0.827126	+	0.367712i
$905$		0			0
$906$	24.5993	+	29.3783i	0.817256	+	0.976029i
$907$	11.1000	+	11.1000i	0.368569	+	0.368569i	0.866955	−	0.498386i	$-0.166074\pi$
$907$	11.1000	+	11.1000i	0.368569	+	0.368569i	−0.498386	+	0.866955i	$0.666074\pi$
$908$	−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	$0.158611\pi$
$911$			28.8502i			0.955849i	−0.878401	+	0.477925i	$0.841389\pi$
$912$	7.52960	+	21.9813i	0.249330	+	0.727873i
$913$	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
$918$	8.67878	+	15.7591i	0.286442	+	0.520128i
$919$			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
$924$	−20.3205	−	62.8018i	−0.668496	−	2.06603i
$925$		0			0
$926$	−7.34411	+	18.1677i	−0.241342	+	0.597027i
$927$	−4.48937	−	0.880625i	−0.147450	−	0.0289235i
$928$	2.23371	+	4.80177i	0.0733253	+	0.157626i
$929$	55.0325			1.80556			0.902780	−	0.430103i	$-0.141523\pi$
$929$	55.0325			1.80556			0.902780	+	0.430103i	$0.141523\pi$
$930$		0			0
$931$		−	30.5164i		−	1.00013i
$932$	−0.0199772	−	1.16920i	−0.000654375	−	0.0382985i
$933$	−11.0689	−	36.3159i	−0.362380	−	1.18893i
$934$	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	$0.358727\pi$
$938$	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	$-0.860546\pi$
$941$	−55.5572			−1.81111			−0.905556	+	0.424226i	$0.860546\pi$
$942$	−4.32468	+	48.8459i	−0.140906	+	1.59148i
$943$	−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	$0.158943\pi$
$948$	−23.9139	−	12.2217i	−0.776689	−	0.396942i
$949$	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	$0.328557\pi$
$954$	−10.4683	−	49.7130i	−0.338924	−	1.60952i
$955$		0			0
$956$	11.5974	−	12.0006i	0.375086	−	0.388126i
$957$	−2.24513	−	7.36604i	−0.0725747	−	0.238110i
$958$	−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
$963$	−5.31719	+	27.1067i	−0.171344	+	0.873500i
$964$	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	$0.916056\pi$
$968$	−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	$-0.338823\pi$
$971$	30.2255			0.969981			0.484991	+	0.874519i	$0.338823\pi$
$972$	−20.3443	−	23.6244i	−0.652543	−	0.757752i
$973$	−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	$0.669472\pi$
$978$	17.5774	+	1.55625i	0.562062	+	0.0497634i
$979$	−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	$0.182197\pi$
$984$	−0.781273	+	10.9509i	−0.0249061	+	0.349103i
$985$		0			0
$986$	3.00516	+	1.21481i	0.0957037	+	0.0386873i
$987$	−63.1035	+	19.2336i	−2.00861	+	0.612212i
$988$	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
$993$	−3.60094	−	11.8143i	−0.114272	−	0.374916i
$994$	17.7454	−	43.8980i	0.562848	−	1.39236i
$995$		0			0
$996$	42.6793	−	13.8096i	1.35234	−	0.437573i
$997$	−1.26149	−	1.26149i	−0.0399517	−	0.0399517i	0.686849	−	0.726800i	$-0.258993\pi$
$997$	−1.26149	−	1.26149i	−0.0399517	−	0.0399517i	−0.726800	+	0.686849i	$0.758993\pi$
$998$	−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.293.19	yes	64
3.2	odd	2	inner	600.2.w.k.293.13	yes	64
5.2	odd	4	inner	600.2.w.k.557.4	yes	64
5.3	odd	4	inner	600.2.w.k.557.29	yes	64
5.4	even	2	inner	600.2.w.k.293.14	yes	64
8.5	even	2	inner	600.2.w.k.293.30	yes	64
15.2	even	4	inner	600.2.w.k.557.30	yes	64
15.8	even	4	inner	600.2.w.k.557.3	yes	64
15.14	odd	2	inner	600.2.w.k.293.20	yes	64
24.5	odd	2	inner	600.2.w.k.293.4	yes	64
40.13	odd	4	inner	600.2.w.k.557.20	yes	64
40.29	even	2	inner	600.2.w.k.293.3	✓	64
40.37	odd	4	inner	600.2.w.k.557.13	yes	64
120.29	odd	2	inner	600.2.w.k.293.29	yes	64
120.53	even	4	inner	600.2.w.k.557.14	yes	64
120.77	even	4	inner	600.2.w.k.557.19	yes	64

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.552337 + 1.30189i) q^{2} +(-1.65680 + 0.504984i) q^{3} +(-1.38985 + 1.43817i) q^{4} +(-1.57255 - 1.87806i) q^{6} +(2.83719 - 2.83719i) q^{7} +(-2.64000 - 1.01508i) q^{8} +(2.48998 - 1.67332i) q^{9} +O(q^{10})\)	\(q+(0.552337 + 1.30189i) q^{2} +(-1.65680 + 0.504984i) q^{3} +(-1.38985 + 1.43817i) q^{4} +(-1.57255 - 1.87806i) q^{6} +(2.83719 - 2.83719i) q^{7} +(-2.64000 - 1.01508i) q^{8} +(2.48998 - 1.67332i) q^{9} +4.74897 q^{11} +(1.57645 - 3.08461i) 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} +(3.55379 + 2.31745i) q^{18} +3.35370 q^{19} +(-3.26792 + 6.13340i) q^{21} +(2.62303 + 6.18265i) q^{22} +(-4.82662 + 4.82662i) q^{23} +(4.88656 + 0.348623i) q^{24} +(1.60939 + 0.650581i) q^{26} +(-3.28041 + 4.02976i) q^{27} +(0.137093 + 8.02362i) q^{28} +0.936190i q^{29} +5.49627 q^{31} +(5.12905 - 2.38596i) q^{32} +(-7.86810 + 2.39815i) q^{33} +(1.29761 - 3.20999i) q^{34} +(-1.05418 + 5.90667i) q^{36} +(-0.749350 - 0.749350i) q^{37} +(1.85238 + 4.36616i) q^{38} +(-0.999726 + 1.87633i) q^{39} +2.24103i q^{41} +(-9.79002 - 0.866782i) 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} +(2.24516 + 6.55433i) q^{48} -9.09930i q^{49} +(3.74242 + 1.99399i) q^{51} +(0.0419396 + 2.45459i) q^{52} +(-8.46720 - 8.46720i) q^{53} +(-7.05820 - 2.04495i) q^{54} +(-10.3702 + 4.61022i) q^{56} +(-5.55642 + 1.69357i) q^{57} +(-1.21882 + 0.517093i) q^{58} +6.53585i q^{59} +5.10959i q^{61} +(3.03579 + 7.15555i) q^{62} +(2.31703 - 11.8121i) q^{63} +(5.93923 + 5.35962i) q^{64} +(-7.46798 - 8.91883i) q^{66} +(4.85678 + 4.85678i) q^{67} +(4.89577 - 0.0836501i) q^{68} +(5.55939 - 10.4341i) q^{69} -8.34435i q^{71} +(-8.27211 + 1.89004i) q^{72} +(1.57561 + 1.57561i) q^{73} +(0.561679 - 1.38947i) q^{74} +(-4.66114 + 4.82319i) q^{76} +(13.4737 - 13.4737i) q^{77} +(-2.99497 - 0.265167i) q^{78} -7.75267i q^{79} +(3.40002 - 8.33306i) q^{81} +(-2.91758 + 1.23780i) q^{82} +(9.15657 + 9.15657i) q^{83} +(-4.27894 - 13.2243i) q^{84} +(16.2328 + 6.56196i) q^{86} +(-0.472761 - 1.55108i) q^{87} +(-12.5373 - 4.82057i) q^{88} -4.97996 q^{89} -4.92511i q^{91} +(-0.233222 - 13.6498i) q^{92} +(-9.10622 + 2.77553i) q^{93} +(-5.03116 + 12.4459i) q^{94} +(-7.29295 + 6.54316i) q^{96} +(-1.42918 + 1.42918i) q^{97} +(11.8463 - 5.02588i) q^{98} +(11.8248 - 7.94653i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 12 q^{6}+O(q^{10}) \) 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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