LMFDB - Embedded newform 603.2.v.a.8.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(8,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("603.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.v (of order $22$, degree $10$, 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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			8.2
Character	$\chi$	$=$	603.8
Dual form			603.2.v.a.377.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.382519 + 2.66048i) q^{2} +(-5.01283 - 1.47190i) q^{4} +(3.20794 + 2.06162i) q^{5} +(1.41064 + 0.202819i) q^{7} +(3.60033 - 7.88361i) q^{8} +O(q^{10})$	\(q+(-0.382519 + 2.66048i) q^{2} +(-5.01283 - 1.47190i) q^{4} +(3.20794 + 2.06162i) q^{5} +(1.41064 + 0.202819i) q^{7} +(3.60033 - 7.88361i) q^{8} +(-6.71198 + 7.74603i) q^{10} +(4.52660 + 2.90907i) q^{11} +(3.93742 - 1.79816i) q^{13} +(-1.07919 + 3.67539i) q^{14} +(10.8068 + 6.94510i) q^{16} +(-0.784978 - 2.67339i) q^{17} +(0.189848 + 1.32042i) q^{19} +(-13.0464 - 15.0563i) q^{20} +(-9.47101 + 10.9301i) q^{22} +(0.0169206 - 0.0146618i) q^{23} +(3.96352 + 8.67890i) q^{25} +(3.27782 + 11.1632i) q^{26} +(-6.77276 - 3.09301i) q^{28} -4.81170i q^{29} +(-1.32031 - 0.602967i) q^{31} +(-11.2600 + 12.9947i) q^{32} +(7.41276 - 1.06579i) q^{34} +(4.10710 + 3.55882i) q^{35} -10.9491 q^{37} -3.58557 q^{38} +(27.8026 - 17.8676i) q^{40} +(-7.78166 + 2.28490i) q^{41} +(-3.25126 - 11.0728i) q^{43} +(-18.4092 - 21.2454i) q^{44} +(0.0325350 + 0.0506254i) q^{46} +(3.91896 - 3.39580i) q^{47} +(-4.76769 - 1.39992i) q^{49} +(-24.6061 + 7.22502i) q^{50} +(-22.3843 + 3.21838i) q^{52} +(3.56245 + 1.04603i) q^{53} +(8.52366 + 18.6642i) q^{55} +(6.67770 - 10.3907i) q^{56} +(12.8014 + 1.84057i) q^{58} +(3.94598 + 1.80207i) q^{59} +(-5.44836 - 8.47781i) q^{61} +(2.10923 - 3.28202i) q^{62} +(-13.4402 - 15.5108i) q^{64} +(16.3381 + 2.34906i) q^{65} +(-3.77364 + 7.26358i) q^{67} +14.5567i q^{68} +(-11.0392 + 9.56553i) q^{70} +(0.866173 - 2.94991i) q^{71} +(-8.93614 + 5.74291i) q^{73} +(4.18825 - 29.1299i) q^{74} +(0.991852 - 6.89848i) q^{76} +(5.79537 + 5.02172i) q^{77} +(10.3746 - 4.73793i) q^{79} +(20.3494 + 44.5589i) q^{80} +(-3.10230 - 21.5770i) q^{82} +(-5.15163 + 8.01610i) q^{83} +(2.99334 - 10.1944i) q^{85} +(30.7025 - 4.41436i) q^{86} +(39.2312 - 25.2123i) q^{88} +(-3.53196 - 3.06046i) q^{89} +(5.91897 - 1.73797i) q^{91} +(-0.106401 + 0.0485917i) q^{92} +(7.53537 + 11.7253i) q^{94} +(-2.11318 + 4.62722i) q^{95} -0.0402137i q^{97} +(5.54819 - 12.1488i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 28 q^{4}+O(q^{10}) $ 240 * q - 28 * q^4	$ 240 q - 28 q^{4} - 28 q^{16} - 20 q^{19} + 12 q^{22} - 24 q^{25} + 44 q^{28} - 88 q^{31} + 24 q^{37} + 32 q^{40} + 44 q^{43} - 44 q^{46} + 8 q^{49} - 220 q^{52} + 52 q^{55} - 88 q^{58} - 88 q^{61} - 148 q^{64} + 8 q^{67} - 176 q^{70} - 120 q^{73} - 64 q^{76} - 264 q^{79} + 8 q^{82} + 256 q^{88} + 256 q^{91} - 88 q^{94}+O(q^{100}) $ 240 * q - 28 * q^4 - 28 * q^16 - 20 * q^19 + 12 * q^22 - 24 * q^25 + 44 * q^28 - 88 * q^31 + 24 * q^37 + 32 * q^40 + 44 * q^43 - 44 * q^46 + 8 * q^49 - 220 * q^52 + 52 * q^55 - 88 * q^58 - 88 * q^61 - 148 * q^64 + 8 * q^67 - 176 * q^70 - 120 * q^73 - 64 * q^76 - 264 * q^79 + 8 * q^82 + 256 * q^88 + 256 * q^91 - 88 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$-1$

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 $

$2$	−0.382519	+	2.66048i	−0.270482	+	1.88124i	0.172946	+	0.984931i	$0.444671\pi$
$2$	−0.382519	+	2.66048i	−0.270482	+	1.88124i	−0.443428	+	0.896310i	$0.646238\pi$
$3$		0			0
$3$		0			0
$4$	−5.01283	−	1.47190i	−2.50642	−	0.735950i
$5$	3.20794	+	2.06162i	1.43463	+	0.921983i	0.999769	+	0.0214862i	$0.00683979\pi$
$5$	3.20794	+	2.06162i	1.43463	+	0.921983i	0.434864	+	0.900496i	$0.356797\pi$
$6$		0			0
$7$	1.41064	+	0.202819i	0.533171	+	0.0766584i	0.403641	−	0.914917i	$-0.367744\pi$
$7$	1.41064	+	0.202819i	0.533171	+	0.0766584i	0.129529	+	0.991576i	$0.458653\pi$
$8$	3.60033	−	7.88361i	1.27291	−	2.78728i
$9$		0			0
$10$	−6.71198	+	7.74603i	−2.12251	+	2.44951i
$11$	4.52660	+	2.90907i	1.36482	+	0.877117i	0.998573	−	0.0534011i	$-0.0170062\pi$
$11$	4.52660	+	2.90907i	1.36482	+	0.877117i	0.366247	+	0.930518i	$0.380643\pi$
$12$		0			0
$13$	3.93742	−	1.79816i	1.09204	−	0.498719i	0.213773	−	0.976883i	$-0.431425\pi$
$13$	3.93742	−	1.79816i	1.09204	−	0.498719i	0.878271	+	0.478164i	$0.158698\pi$
$14$	−1.07919	+	3.67539i	−0.288426	+	0.982288i
$15$		0			0
$16$	10.8068	+	6.94510i	2.70170	+	1.73628i
$17$	−0.784978	−	2.67339i	−0.190385	−	0.648392i	−0.998256	−	0.0590328i	$-0.981198\pi$
$17$	−0.784978	−	2.67339i	−0.190385	−	0.648392i	0.807871	−	0.589360i	$-0.200620\pi$
$18$		0			0
$19$	0.189848	+	1.32042i	0.0435541	+	0.302925i	0.999941	+	0.0108237i	$0.00344537\pi$
$19$	0.189848	+	1.32042i	0.0435541	+	0.302925i	−0.956387	+	0.292101i	$0.905646\pi$
$20$	−13.0464	−	15.0563i	−2.91725	−	3.36669i
$21$		0			0
$22$	−9.47101	+	10.9301i	−2.01923	+	2.33031i
$23$	0.0169206	−	0.0146618i	0.00352820	−	0.00305720i	−0.653095	−	0.757276i	$-0.726530\pi$
$23$	0.0169206	−	0.0146618i	0.00352820	−	0.00305720i	0.656623	+	0.754219i	$0.271984\pi$
$24$		0			0
$25$	3.96352	+	8.67890i	0.792704	+	1.73578i
$26$	3.27782	+	11.1632i	0.642834	+	2.18929i
$27$		0			0
$28$	−6.77276	−	3.09301i	−1.27993	−	0.584525i
$29$		−	4.81170i		−	0.893510i	−0.894656	−	0.446755i	$-0.852580\pi$
$29$		−	4.81170i		−	0.893510i	0.894656	−	0.446755i	$-0.147420\pi$
$30$		0			0
$31$	−1.32031	−	0.602967i	−0.237135	−	0.108296i	0.293303	−	0.956019i	$-0.405245\pi$
$31$	−1.32031	−	0.602967i	−0.237135	−	0.108296i	−0.530439	+	0.847723i	$0.677973\pi$
$32$	−11.2600	+	12.9947i	−1.99050	+	2.29716i
$33$		0			0
$34$	7.41276	−	1.06579i	1.27128	−	0.182782i
$35$	4.10710	+	3.55882i	0.694226	+	0.601551i
$36$		0			0
$37$	−10.9491			−1.80003			−0.900013	−	0.435863i	$-0.856443\pi$
$37$	−10.9491			−1.80003			−0.900013	+	0.435863i	$0.856443\pi$
$38$	−3.58557			−0.581656
$39$		0			0
$40$	27.8026	−	17.8676i	4.39598	−	2.82512i
$41$	−7.78166	+	2.28490i	−1.21529	+	0.356842i	−0.825681	−	0.564138i	$-0.809209\pi$
$41$	−7.78166	+	2.28490i	−1.21529	+	0.356842i	−0.389611	+	0.920980i	$0.627390\pi$
$42$		0			0
$43$	−3.25126	−	11.0728i	−0.495812	−	1.68858i	−0.703757	−	0.710441i	$-0.748496\pi$
$43$	−3.25126	−	11.0728i	−0.495812	−	1.68858i	0.207944	−	0.978141i	$-0.433323\pi$
$44$	−18.4092	−	21.2454i	−2.77529	−	3.20286i
$45$		0			0
$46$	0.0325350	+	0.0506254i	0.00479702	+	0.00746431i
$47$	3.91896	−	3.39580i	0.571639	−	0.495328i	−0.320402	−	0.947282i	$-0.603818\pi$
$47$	3.91896	−	3.39580i	0.571639	−	0.495328i	0.892042	+	0.451953i	$0.149273\pi$
$48$		0			0
$49$	−4.76769	−	1.39992i	−0.681099	−	0.199989i
$50$	−24.6061	+	7.22502i	−3.47983	+	1.02177i
$51$		0			0
$52$	−22.3843	+	3.21838i	−3.10415	+	0.446309i
$53$	3.56245	+	1.04603i	0.489340	+	0.143683i	0.517089	−	0.855932i	$-0.327016\pi$
$53$	3.56245	+	1.04603i	0.489340	+	0.143683i	−0.0277487	+	0.999615i	$0.508834\pi$
$54$		0			0
$55$	8.52366	+	18.6642i	1.14933	+	2.51668i
$56$	6.67770	−	10.3907i	0.892345	−	1.38852i
$57$		0			0
$58$	12.8014	+	1.84057i	1.68091	+	0.241678i
$59$	3.94598	+	1.80207i	0.513722	+	0.234609i	0.655370	−	0.755308i	$-0.272513\pi$
$59$	3.94598	+	1.80207i	0.513722	+	0.234609i	−0.141648	+	0.989917i	$0.545240\pi$
$60$		0			0
$61$	−5.44836	−	8.47781i	−0.697591	−	1.08547i	−0.991559	−	0.129657i	$-0.958612\pi$
$61$	−5.44836	−	8.47781i	−0.697591	−	1.08547i	0.293968	−	0.955815i	$-0.405024\pi$
$62$	2.10923	−	3.28202i	0.267872	−	0.416817i
$63$		0			0
$64$	−13.4402	−	15.5108i	−1.68003	−	1.93885i
$65$	16.3381	+	2.34906i	2.02649	+	0.291365i
$66$		0			0
$67$	−3.77364	+	7.26358i	−0.461023	+	0.887388i
$67$	−3.77364	+	7.26358i	−0.461023	+	0.887388i
$68$			14.5567i			1.76526i
$69$		0			0
$70$	−11.0392	+	9.56553i	−1.31944	+	1.14330i
$71$	0.866173	−	2.94991i	0.102796	−	0.350090i	−0.891993	−	0.452050i	$-0.850693\pi$
$71$	0.866173	−	2.94991i	0.102796	−	0.350090i	0.994789	+	0.101959i	$0.0325112\pi$
$72$		0			0
$73$	−8.93614	+	5.74291i	−1.04590	+	0.672156i	−0.946438	−	0.322885i	$-0.895347\pi$
$73$	−8.93614	+	5.74291i	−1.04590	+	0.672156i	−0.0994576	+	0.995042i	$0.531711\pi$
$74$	4.18825	−	29.1299i	0.486874	−	3.38628i
$75$		0			0
$76$	0.991852	−	6.89848i	0.113773	−	0.791310i
$77$	5.79537	+	5.02172i	0.660444	+	0.572278i
$78$		0			0
$79$	10.3746	−	4.73793i	1.16724	−	0.533059i	0.264978	−	0.964254i	$-0.414635\pi$
$79$	10.3746	−	4.73793i	1.16724	−	0.533059i	0.902259	+	0.431195i	$0.141908\pi$
$80$	20.3494	+	44.5589i	2.27513	+	4.98184i
$81$		0			0
$82$	−3.10230	−	21.5770i	−0.342591	−	2.38278i
$83$	−5.15163	+	8.01610i	−0.565465	+	0.879881i	−0.999782	−	0.0208790i	$-0.993354\pi$
$83$	−5.15163	+	8.01610i	−0.565465	+	0.879881i	0.434317	+	0.900760i	$0.356990\pi$
$84$		0			0
$85$	2.99334	−	10.1944i	0.324674	−	1.10574i
$86$	30.7025	−	4.41436i	3.31074	−	0.476012i
$87$		0			0
$88$	39.2312	−	25.2123i	4.18206	−	2.68765i
$89$	−3.53196	−	3.06046i	−0.374388	−	0.324409i	0.447261	−	0.894404i	$-0.352400\pi$
$89$	−3.53196	−	3.06046i	−0.374388	−	0.324409i	−0.821648	+	0.569995i	$0.806945\pi$
$90$		0			0
$91$	5.91897	−	1.73797i	0.620476	−	0.182188i
$92$	−0.106401	+	0.0485917i	−0.0110931	+	0.00506604i
$93$		0			0
$94$	7.53537	+	11.7253i	0.777214	+	1.20937i
$95$	−2.11318	+	4.62722i	−0.216808	+	0.474742i
$96$		0			0
$97$		−	0.0402137i		−	0.00408308i	−0.999998	−	0.00204154i	$-0.999350\pi$
$97$		−	0.0402137i		−	0.00408308i	0.999998	−	0.00204154i	$-0.000649843\pi$
$98$	5.54819	−	12.1488i	0.560452	−	1.22722i
$99$		0			0
$100$	−7.09399	−	49.3398i	−0.709399	−	4.93398i
$101$	1.06228	+	7.38835i	0.105701	+	0.735168i	0.971887	+	0.235447i	$0.0756553\pi$
$101$	1.06228	+	7.38835i	0.105701	+	0.735168i	−0.866186	+	0.499722i	$0.833436\pi$
$102$		0			0
$103$	−0.548545	+	1.20115i	−0.0540498	+	0.118353i	−0.934730	−	0.355359i	$-0.884359\pi$
$103$	−0.548545	+	1.20115i	−0.0540498	+	0.118353i	0.880680	+	0.473711i	$0.157086\pi$
$104$		−	37.5150i		−	3.67865i
$105$		0			0
$106$	−4.14564	+	9.07769i	−0.402660	+	0.881703i
$107$	−2.79790	−	4.35362i	−0.270483	−	0.420880i	0.679266	−	0.733892i	$-0.262298\pi$
$107$	−2.79790	−	4.35362i	−0.270483	−	0.420880i	−0.949749	+	0.313012i	$0.898662\pi$
$108$		0			0
$109$	−15.7832	+	7.20796i	−1.51176	+	0.690397i	−0.986980	−	0.160841i	$-0.948579\pi$
$109$	−15.7832	+	7.20796i	−1.51176	+	0.690397i	−0.524779	+	0.851238i	$0.675852\pi$
$110$	−52.9161	+	15.5376i	−5.04536	+	1.48145i
$111$		0			0
$112$	13.8359	+	11.9888i	1.30737	+	1.13284i
$113$	−1.45660	+	0.936100i	−0.137025	+	0.0880609i	−0.607358	−	0.794429i	$-0.707770\pi$
$113$	−1.45660	+	0.936100i	−0.137025	+	0.0880609i	0.470332	+	0.882489i	$0.344134\pi$
$114$		0			0
$115$	0.0845074	−	0.0121503i	0.00788035	−	0.00113302i
$116$	−7.08234	+	24.1202i	−0.657579	+	2.23951i
$117$		0			0
$118$	−6.30377	+	9.80886i	−0.580309	+	0.902979i
$119$	−0.565105	−	3.93039i	−0.0518031	−	0.360298i
$120$		0			0
$121$	7.45784	+	16.3304i	0.677985	+	1.48458i
$122$	24.6391	−	11.2523i	2.23072	−	1.01874i
$123$		0			0
$124$	5.73101	+	4.96595i	0.514660	+	0.445955i
$125$	−2.46440	+	17.1403i	−0.220423	+	1.53307i
$126$		0			0
$127$	2.62576	−	18.2626i	0.232998	−	1.62054i	−0.452016	−	0.892010i	$-0.649295\pi$
$127$	2.62576	−	18.2626i	0.232998	−	1.62054i	0.685014	−	0.728530i	$-0.259796\pi$
$128$	17.4775	−	11.2321i	1.54481	−	0.992789i
$129$		0			0
$130$	−12.4993	+	42.5686i	−1.09626	+	3.73351i
$131$	4.21763	−	3.65459i	0.368496	−	0.319303i	−0.450854	−	0.892598i	$-0.648880\pi$
$131$	4.21763	−	3.65459i	0.368496	−	0.319303i	0.819349	+	0.573295i	$0.194335\pi$
$132$		0			0
$133$			1.90114i			0.164850i
$134$	−17.8811	−	12.8181i	−1.54469	−	1.10732i
$135$		0			0
$136$	−23.9022	−	3.43661i	−2.04959	−	0.294687i
$137$	10.4163	+	12.0210i	0.889921	+	1.02702i	0.999454	+	0.0330400i	$0.0105189\pi$
$137$	10.4163	+	12.0210i	0.889921	+	1.02702i	−0.109533	+	0.993983i	$0.534936\pi$
$138$		0			0
$139$	−1.53139	+	2.38289i	−0.129891	+	0.202114i	−0.900107	−	0.435669i	$-0.856512\pi$
$139$	−1.53139	+	2.38289i	−0.129891	+	0.202114i	0.770216	+	0.637783i	$0.220148\pi$
$140$	−15.3500	−	23.8850i	−1.29731	−	2.01865i
$141$		0			0
$142$	7.51685	+	3.43283i	0.630800	+	0.288077i
$143$	23.0541	+	3.31467i	1.92788	+	0.277187i
$144$		0			0
$145$	9.91987	−	15.4356i	0.823801	−	1.28186i
$146$	−11.8606	−	25.9712i	−0.981593	−	2.14939i
$147$		0			0
$148$	54.8862	+	16.1160i	4.51162	+	1.32473i
$149$	−14.7257	+	2.11723i	−1.20638	+	0.173451i	−0.716025	−	0.698075i	$-0.754040\pi$
$149$	−14.7257	+	2.11723i	−1.20638	+	0.173451i	−0.490350	+	0.871525i	$0.663131\pi$
$150$		0			0
$151$	−2.78406	+	0.817473i	−0.226563	+	0.0665250i	−0.393044	−	0.919520i	$-0.628578\pi$
$151$	−2.78406	+	0.817473i	−0.226563	+	0.0665250i	0.166480	+	0.986045i	$0.446760\pi$
$152$	11.0932	+	3.25726i	0.899777	+	0.264198i
$153$		0			0
$154$	−15.5770	+	13.4975i	−1.25523	+	1.08766i
$155$	−2.99240	−	4.65626i	−0.240355	−	0.374000i
$156$		0			0
$157$	1.36965	+	1.58066i	0.109310	+	0.126150i	0.807768	−	0.589501i	$-0.200676\pi$
$157$	1.36965	+	1.58066i	0.109310	+	0.126150i	−0.698458	+	0.715651i	$0.746130\pi$
$158$	8.63667	+	29.4138i	0.687097	+	2.34004i
$159$		0			0
$160$	−62.9114	+	18.4724i	−4.97358	+	1.46038i
$161$	0.0268426	−	0.0172507i	0.00211549	−	0.00135954i
$162$		0			0
$163$	11.4935			0.900243			0.450122	−	0.892967i	$-0.351381\pi$
$163$	11.4935			0.900243			0.450122	+	0.892967i	$0.351381\pi$
$164$	42.3713			3.30864
$165$		0			0
$166$	−19.3561	−	16.7721i	−1.50232	−	1.30177i
$167$	19.7362	−	2.83764i	1.52724	−	0.219583i	0.673068	−	0.739581i	$-0.264976\pi$
$167$	19.7362	−	2.83764i	1.52724	−	0.219583i	0.854168	+	0.519998i	$0.174067\pi$
$168$		0			0
$169$	3.75669	−	4.33546i	0.288976	−	0.333497i
$170$	25.9769	+	11.8633i	1.99234	+	0.909871i
$171$		0			0
$172$			60.2915i			4.59718i
$173$	−7.70879	−	3.52049i	−0.586089	−	0.267658i	0.100223	−	0.994965i	$-0.468044\pi$
$173$	−7.70879	−	3.52049i	−0.586089	−	0.267658i	−0.686312	+	0.727307i	$0.740772\pi$
$174$		0			0
$175$	3.83084	+	13.0467i	0.289585	+	0.986235i
$176$	28.7142	+	62.8754i	2.16442	+	4.73941i
$177$		0			0
$178$	9.49334	−	8.22603i	0.711556	−	0.616567i
$179$	−13.8656	+	16.0017i	−1.03636	+	1.19603i	−0.0560798	+	0.998426i	$0.517860\pi$
$179$	−13.8656	+	16.0017i	−1.03636	+	1.19603i	−0.980283	+	0.197600i	$0.936685\pi$
$180$		0			0
$181$	1.74403	+	2.01272i	0.129633	+	0.149604i	0.816855	−	0.576843i	$-0.195716\pi$
$181$	1.74403	+	2.01272i	0.129633	+	0.149604i	−0.687222	+	0.726447i	$0.741170\pi$
$182$	2.35970	+	16.4121i	0.174913	+	1.21654i
$183$		0			0
$184$	−0.0546683	−	0.186183i	−0.00403020	−	0.0137256i
$185$	−35.1241	−	22.5729i	−2.58238	−	1.65959i
$186$		0			0
$187$	4.22379	−	14.3849i	0.308874	−	1.05193i
$188$	−24.6434	+	11.2543i	−1.79730	+	0.820801i
$189$		0			0
$190$	−11.5023	−	7.39206i	−0.834462	−	0.536276i
$191$	−7.82801	+	9.03401i	−0.566415	+	0.653678i	−0.964628	−	0.263615i	$-0.915085\pi$
$191$	−7.82801	+	9.03401i	−0.566415	+	0.653678i	0.398213	+	0.917293i	$0.369631\pi$
$192$		0			0
$193$	0.485983	−	1.06415i	0.0349818	−	0.0765995i	−0.891334	−	0.453346i	$-0.850230\pi$
$193$	0.485983	−	1.06415i	0.0349818	−	0.0765995i	0.926316	+	0.376747i	$0.122957\pi$
$194$	0.106988	+	0.0153825i	0.00768126	+	0.00110440i
$195$		0			0
$196$	21.8391	+	14.0351i	1.55993	+	1.00251i
$197$	11.4019	+	3.34791i	0.812355	+	0.238529i	0.661421	−	0.750015i	$-0.269954\pi$
$197$	11.4019	+	3.34791i	0.812355	+	0.238529i	0.150934	+	0.988544i	$0.451772\pi$
$198$		0			0
$199$	1.69544	−	11.7920i	0.120187	−	0.835916i	−0.837157	−	0.546963i	$-0.815784\pi$
$199$	1.69544	−	11.7920i	0.120187	−	0.835916i	0.957343	−	0.288953i	$-0.0933072\pi$
$200$	82.6911			5.84714
$201$		0			0
$202$	−20.0629			−1.41162
$203$	0.975904	−	6.78756i	0.0684950	−	0.476393i
$204$		0			0
$205$	−29.6737	−	8.71297i	−2.07250	−	0.608541i
$206$	−2.98579	−	1.91885i	−0.208030	−	0.133693i
$207$		0			0
$208$	55.0393	+	7.91345i	3.81629	+	0.548699i
$209$	−2.98183	+	6.52929i	−0.206257	+	0.451640i
$210$		0			0
$211$	−0.877292	+	1.01245i	−0.0603952	+	0.0696998i	−0.785143	−	0.619314i	$-0.787411\pi$
$211$	−0.877292	+	1.01245i	−0.0603952	+	0.0696998i	0.724748	+	0.689014i	$0.241956\pi$
$212$	−16.3183	−	10.4871i	−1.12075	−	0.720260i
$213$		0			0
$214$	12.6529	−	5.77841i	0.864938	−	0.395004i
$215$	12.3980	−	42.2236i	0.845534	−	2.87962i
$216$		0			0
$217$	−1.74019	−	1.11835i	−0.118132	−	0.0759187i
$218$	−13.1392	−	44.7481i	−0.889901	−	3.03072i
$219$		0			0
$220$	−15.2558	−	106.106i	−1.02855	−	7.15370i
$221$	−7.89797	−	9.11474i	−0.531275	−	0.613124i
$222$		0			0
$223$	11.2719	−	13.0084i	0.754821	−	0.871109i	−0.240206	−	0.970722i	$-0.577215\pi$
$223$	11.2719	−	13.0084i	0.754821	−	0.871109i	0.995026	+	0.0996126i	$0.0317604\pi$
$224$	−18.5193	+	16.0471i	−1.23737	+	1.07219i
$225$		0			0
$226$	−1.93330	−	4.23333i	−0.128601	−	0.281597i
$227$	0.0362425	+	0.123431i	0.00240550	+	0.00819239i	0.960687	−	0.277634i	$-0.0895502\pi$
$227$	0.0362425	+	0.123431i	0.00240550	+	0.00819239i	−0.958281	+	0.285826i	$0.907732\pi$
$228$		0			0
$229$	−21.3438	−	9.74738i	−1.41044	−	0.644125i	−0.442834	−	0.896603i	$-0.646027\pi$
$229$	−21.3438	−	9.74738i	−1.41044	−	0.644125i	−0.967602	+	0.252479i	$0.918754\pi$
$230$			0.229478i			0.0151313i
$231$		0			0
$232$	−37.9336	−	17.3237i	−2.49046	−	1.13736i
$233$	13.4520	−	15.5244i	0.881270	−	1.01704i	−0.118440	−	0.992961i	$-0.537789\pi$
$233$	13.4520	−	15.5244i	0.881270	−	1.01704i	0.999710	−	0.0240789i	$-0.00766529\pi$
$234$		0			0
$235$	19.5726	−	2.81412i	1.27678	−	0.183573i
$236$	−17.1281	−	14.8415i	−1.11494	−	0.966102i
$237$		0			0
$238$	10.6729			0.691820
$239$	2.42194			0.156662			0.0783311	−	0.996927i	$-0.475041\pi$
$239$	2.42194			0.156662			0.0783311	+	0.996927i	$0.475041\pi$
$240$		0			0
$241$	7.95544	−	5.11265i	0.512455	−	0.329335i	−0.258726	−	0.965951i	$-0.583303\pi$
$241$	7.95544	−	5.11265i	0.512455	−	0.329335i	0.771181	+	0.636616i	$0.219666\pi$
$242$	−46.2994	+	13.5947i	−2.97624	+	0.873902i
$243$		0			0
$244$	14.8332	+	50.5173i	0.949599	+	3.23404i
$245$	−12.4083	−	14.3200i	−0.792740	−	0.914871i
$246$		0			0
$247$	3.12183	+	4.85767i	0.198638	+	0.309086i
$248$	−9.50712	+	8.23797i	−0.603703	+	0.523112i
$249$		0			0
$250$	−44.6587	−	13.1130i	−2.82446	−	0.829337i
$251$	21.5489	−	6.32734i	1.36016	−	0.399378i	0.481339	−	0.876535i	$-0.340151\pi$
$251$	21.5489	−	6.32734i	1.36016	−	0.399378i	0.878818	+	0.477156i	$0.158332\pi$
$252$		0			0
$253$	0.119245	−	0.0171449i	0.00749688	−	0.00107789i
$254$	47.5827	+	13.9715i	2.98560	+	0.876652i
$255$		0			0
$256$	6.14557	+	13.4569i	0.384098	+	0.841058i
$257$	0.00808248	−	0.0125766i	0.000504171	−	0.000784506i	−0.841001	−	0.541033i	$-0.818033\pi$
$257$	0.00808248	−	0.0125766i	0.000504171	−	0.000784506i	0.841506	+	0.540249i	$0.181670\pi$
$258$		0			0
$259$	−15.4453	−	2.22069i	−0.959721	−	0.137987i
$260$	−78.4425	−	35.8235i	−4.86480	−	2.22168i
$261$		0			0
$262$	8.10964	+	12.6188i	0.501015	+	0.779595i
$263$	−8.86628	+	13.7962i	−0.546718	+	0.850710i	−0.999156	−	0.0410862i	$-0.986918\pi$
$263$	−8.86628	+	13.7962i	−0.546718	+	0.850710i	0.452438	+	0.891796i	$0.350555\pi$
$264$		0			0
$265$	9.27160	+	10.7000i	0.569550	+	0.657296i
$266$	−5.05793	−	0.727221i	−0.310122	−	0.0445888i
$267$		0			0
$268$	29.6079	−	30.8567i	1.80859	−	1.88487i
$269$		−	10.3278i		−	0.629696i	−0.949142	−	0.314848i	$-0.898046\pi$
$269$		−	10.3278i		−	0.629696i	0.949142	−	0.314848i	$-0.101954\pi$
$270$		0			0
$271$	0.117703	−	0.101990i	0.00714997	−	0.00619548i	−0.651278	−	0.758839i	$-0.725767\pi$
$271$	0.117703	−	0.101990i	0.00714997	−	0.00619548i	0.658428	+	0.752643i	$0.271222\pi$
$272$	10.0839	−	34.3425i	0.611425	−	2.08232i
$273$		0			0
$274$	−35.9660	+	23.1139i	−2.17279	+	1.39636i
$275$	−7.30624	+	50.8160i	−0.440583	+	3.06432i
$276$		0			0
$277$	−0.554520	+	3.85677i	−0.0333179	+	0.231731i	−0.999676	−	0.0254709i	$-0.991891\pi$
$277$	−0.554520	+	3.85677i	−0.0333179	+	0.231731i	0.966358	+	0.257202i	$0.0828006\pi$
$278$	−5.75385	−	4.98574i	−0.345093	−	0.299025i
$279$		0			0
$280$	42.8433	−	19.5659i	2.56038	−	1.16928i
$281$	0.196180	+	0.429575i	0.0117031	+	0.0256263i	0.915393	−	0.402561i	$-0.131880\pi$
$281$	0.196180	+	0.429575i	0.0117031	+	0.0256263i	−0.903690	+	0.428187i	$0.859152\pi$
$282$		0			0
$283$	−0.770382	−	5.35813i	−0.0457945	−	0.318508i	−0.999823	−	0.0187930i	$-0.994018\pi$
$283$	−0.770382	−	5.35813i	−0.0457945	−	0.318508i	0.954029	−	0.299715i	$-0.0968915\pi$
$284$	−8.68396	+	13.5125i	−0.515298	+	0.801819i
$285$		0			0
$286$	−17.6372	+	60.0669i	−1.04291	+	3.55183i
$287$	−11.4405	+	1.64490i	−0.675313	+	0.0970953i
$288$		0			0
$289$	7.77049	−	4.99379i	0.457087	−	0.293752i
$290$	37.2716	+	32.2960i	2.18866	+	1.89649i
$291$		0			0
$292$	53.2483	−	15.6351i	3.11612	−	0.914976i
$293$	−7.17803	+	3.27809i	−0.419345	+	0.191508i	−0.613901	−	0.789383i	$-0.710401\pi$
$293$	−7.17803	+	3.27809i	−0.419345	+	0.191508i	0.194556	+	0.980891i	$0.437673\pi$
$294$		0			0
$295$	8.94327	+	13.9160i	0.520698	+	0.810221i
$296$	−39.4204	+	86.3187i	−2.29127	+	5.01717i
$297$		0			0
$298$		−	39.9872i		−	2.31640i
$299$	0.0402594	−	0.0881557i	0.00232826	−	0.00509818i
$300$		0			0
$301$	−2.34058	−	16.2791i	−0.134909	−	0.938310i
$302$	−1.10991	−	7.71962i	−0.0638684	−	0.444214i
$303$		0			0
$304$	−7.11881	+	15.5880i	−0.408292	+	0.894034i
$305$		−	38.4287i		−	2.20042i
$306$		0			0
$307$	10.9475	−	23.9717i	0.624808	−	1.36814i	−0.287162	−	0.957882i	$-0.592712\pi$
$307$	10.9475	−	23.9717i	0.624808	−	1.36814i	0.911970	−	0.410256i	$-0.134561\pi$
$308$	−21.6597	−	33.7032i	−1.23418	−	1.92042i
$309$		0			0
$310$	13.5325	−	6.18010i	0.768596	−	0.351006i
$311$	−2.29480	+	0.673813i	−0.130126	+	0.0382084i	−0.346147	−	0.938180i	$-0.612510\pi$
$311$	−2.29480	+	0.673813i	−0.130126	+	0.0382084i	0.216021	+	0.976389i	$0.430692\pi$
$312$		0			0
$313$	6.10519	+	5.29018i	0.345086	+	0.299018i	0.810108	−	0.586280i	$-0.199408\pi$
$313$	6.10519	+	5.29018i	0.345086	+	0.299018i	−0.465022	+	0.885299i	$0.653954\pi$
$314$	−4.72921	+	3.03928i	−0.266885	+	0.171517i
$315$		0			0
$316$	−58.9800	+	8.48005i	−3.31789	+	0.477040i
$317$	0.176217	−	0.600140i	0.00989734	−	0.0337072i	−0.954396	−	0.298543i	$-0.903499\pi$
$317$	0.176217	−	0.600140i	0.00989734	−	0.0337072i	0.964294	+	0.264835i	$0.0853176\pi$
$318$		0			0
$319$	13.9976	−	21.7806i	0.783712	−	1.21948i
$320$	−11.1380	−	77.4663i	−0.622631	−	4.33050i
$321$		0			0
$322$	0.0356272	+	0.0780128i	0.00198543	+	0.00434748i
$323$	3.38097	−	1.54404i	0.188122	−	0.0859126i
$324$		0			0
$325$	31.2121	+	27.0454i	1.73133	+	1.50021i
$326$	−4.39649	+	30.5783i	−0.243499	+	1.69357i
$327$		0			0
$328$	−10.0032	+	69.5740i	−0.552336	+	3.84158i
$329$	6.21696	−	3.99540i	0.342752	−	0.220274i
$330$		0			0
$331$	1.62863	−	5.54661i	0.0895176	−	0.304869i	−0.902548	−	0.430589i	$-0.858306\pi$
$331$	1.62863	−	5.54661i	0.0895176	−	0.304869i	0.992066	+	0.125720i	$0.0401241\pi$
$332$	37.6232	−	32.6007i	2.06484	−	1.78919i
$333$		0			0
$334$			53.5932i			2.93249i
$335$	−27.0803	+	15.5213i	−1.47956	+	0.848020i
$336$		0			0
$337$	18.5681	+	2.66969i	1.01147	+	0.145427i	0.628072	−	0.778155i	$-0.283844\pi$
$337$	18.5681	+	2.66969i	1.01147	+	0.145427i	0.383399	+	0.923583i	$0.374754\pi$
$338$	10.0974	+	11.6530i	0.549225	+	0.633839i
$339$		0			0
$340$	−30.0102	+	46.6969i	−1.62753	+	2.53249i
$341$	−4.22246	−	6.57027i	−0.228659	−	0.355800i
$342$		0			0
$343$	−15.5160	−	7.08594i	−0.837787	−	0.382605i
$344$	−98.9990	−	14.2339i	−5.33767	−	0.767441i
$345$		0			0
$346$	12.3149	−	19.1624i	0.662055	−	1.03018i
$347$	−3.73510	−	8.17872i	−0.200511	−	0.439057i	0.782489	−	0.622664i	$-0.213950\pi$
$347$	−3.73510	−	8.17872i	−0.200511	−	0.439057i	−0.983000	+	0.183607i	$0.941222\pi$
$348$		0			0
$349$	−13.2604	−	3.89360i	−0.709813	−	0.208420i	−0.0931554	−	0.995652i	$-0.529695\pi$
$349$	−13.2604	−	3.89360i	−0.709813	−	0.208420i	−0.616657	+	0.787232i	$0.711514\pi$
$350$	−36.1757	+	5.20128i	−1.93367	+	0.278020i
$351$		0			0
$352$	−88.7718	+	26.0658i	−4.73156	+	1.38931i
$353$	2.36431	+	0.694223i	0.125839	+	0.0369498i	0.344046	−	0.938953i	$-0.388202\pi$
$353$	2.36431	+	0.694223i	0.125839	+	0.0369498i	−0.218206	+	0.975903i	$0.570021\pi$
$354$		0			0
$355$	8.86021	−	7.67742i	0.470251	−	0.407475i
$356$	13.2004	+	20.5403i	0.699622	+	1.08863i
$357$		0			0
$358$	−37.2684	−	43.0100i	−1.96970	−	2.27315i
$359$	3.62226	+	12.3363i	0.191176	+	0.651085i	0.998167	+	0.0605211i	$0.0192762\pi$
$359$	3.62226	+	12.3363i	0.191176	+	0.651085i	−0.806991	+	0.590563i	$0.798906\pi$
$360$		0			0
$361$	16.5229	−	4.85156i	0.869626	−	0.255345i
$362$	−6.02191	+	3.87005i	−0.316504	+	0.203405i
$363$		0			0
$364$	−32.2289			−1.68925
$365$	−40.5062			−2.12019
$366$		0			0
$367$	−10.6804	−	9.25461i	−0.557512	−	0.483087i	0.329931	−	0.944005i	$-0.392975\pi$
$367$	−10.6804	−	9.25461i	−0.557512	−	0.483087i	−0.887443	+	0.460918i	$0.847520\pi$
$368$	0.284686	−	0.0409316i	0.0148403	−	0.00213371i
$369$		0			0
$370$	73.4903	−	84.8124i	3.82058	−	4.40918i
$371$	4.81317	+	2.19810i	0.249887	+	0.114120i
$372$		0			0
$373$			4.94211i			0.255893i	0.991781	+	0.127946i	$0.0408385\pi$
$373$			4.94211i			0.255893i	−0.991781	+	0.127946i	$0.959161\pi$
$374$	36.6550	+	16.7398i	1.89539	+	0.865594i
$375$		0			0
$376$	−12.6616	−	43.1216i	−0.652974	−	2.22383i
$377$	−8.65220	−	18.9457i	−0.445611	−	0.975751i
$378$		0			0
$379$	−7.25235	+	6.28420i	−0.372528	+	0.322798i	−0.820924	−	0.571038i	$-0.806541\pi$
$379$	−7.25235	+	6.28420i	−0.372528	+	0.322798i	0.448396	+	0.893835i	$0.351996\pi$
$380$	17.4038	−	20.0851i	0.892797	−	1.03034i
$381$		0			0
$382$	−21.0404	−	24.2819i	−1.07652	−	1.24237i
$383$	4.63381	+	32.2288i	0.236777	+	1.64682i	0.667701	+	0.744429i	$0.267278\pi$
$383$	4.63381	+	32.2288i	0.236777	+	1.64682i	−0.430925	+	0.902388i	$0.641813\pi$
$384$		0			0
$385$	8.23833	+	28.0572i	0.419864	+	1.42993i
$386$	2.64526	+	1.70001i	0.134640	+	0.0865280i
$387$		0			0
$388$	−0.0591905	+	0.201584i	−0.00300494	+	0.0102339i
$389$	−6.69367	+	3.05690i	−0.339383	+	0.154991i	−0.577814	−	0.816169i	$-0.696094\pi$
$389$	−6.69367	+	3.05690i	−0.339383	+	0.154991i	0.238431	+	0.971159i	$0.423367\pi$
$390$		0			0
$391$	−0.0524791	−	0.0337263i	−0.00265398	−	0.00170561i
$392$	−28.2017	+	32.5465i	−1.42440	+	1.64384i
$393$		0			0
$394$	−13.2685	+	29.0540i	−0.668457	+	1.46372i
$395$	43.0489	+	6.18950i	2.16603	+	0.311428i
$396$		0			0
$397$	27.2526	+	17.5142i	1.36777	+	0.879011i	0.998729	−	0.0504037i	$-0.0160508\pi$
$397$	27.2526	+	17.5142i	1.36777	+	0.879011i	0.369038	+	0.929414i	$0.379687\pi$
$398$	30.7239	+	9.02136i	1.54005	+	0.452200i
$399$		0			0
$400$	−17.4429	+	121.318i	−0.872146	+	6.06591i
$401$	−18.8681			−0.942227			−0.471113	−	0.882073i	$-0.656148\pi$
$401$	−18.8681			−0.942227			−0.471113	+	0.882073i	$0.656148\pi$
$402$		0			0
$403$	−6.28286			−0.312971
$404$	5.54986	−	38.6001i	0.276116	−	1.92043i
$405$		0			0
$406$	17.6848	+	5.19274i	0.877684	+	0.257711i
$407$	−49.5623	−	31.8518i	−2.45671	−	1.57883i
$408$		0			0
$409$	−35.0943	−	5.04580i	−1.73530	−	0.249499i	−0.799160	−	0.601119i	$-0.794722\pi$
$409$	−35.0943	−	5.04580i	−1.73530	−	0.249499i	−0.936143	+	0.351620i	$0.885631\pi$
$410$	34.5314	−	75.6132i	1.70538	−	3.73427i
$411$		0			0
$412$	4.51773	−	5.21374i	0.222573	−	0.256863i
$413$	5.20085	+	3.34238i	0.255917	+	0.164468i
$414$		0			0
$415$	−33.0522	+	15.0944i	−1.62247	+	0.740957i
$416$	−20.9687	+	71.4128i	−1.02807	+	3.50130i
$417$		0			0
$418$	−16.2304	−	10.4307i	−0.793856	−	0.510180i
$419$	10.4959	+	35.7458i	0.512759	+	1.74630i	0.654173	+	0.756345i	$0.273017\pi$
$419$	10.4959	+	35.7458i	0.512759	+	1.74630i	−0.141414	+	0.989951i	$0.545165\pi$
$420$		0			0
$421$	0.334227	+	2.32460i	0.0162892	+	0.113294i	0.996344	−	0.0854345i	$-0.0272278\pi$
$421$	0.334227	+	2.32460i	0.0162892	+	0.113294i	−0.980055	+	0.198729i	$0.936319\pi$
$422$	−2.35802	−	2.72130i	−0.114786	−	0.132471i
$423$		0			0
$424$	21.0725	−	24.3189i	1.02337	−	1.18103i
$425$	20.0908	−	17.4088i	0.974548	−	0.844450i
$426$		0			0
$427$	−5.96619	−	13.0641i	−0.288724	−	0.632218i
$428$	7.61731	+	25.9422i	0.368197	+	1.25396i
$429$		0			0
$430$	107.592	+	49.1358i	5.18857	+	2.36954i
$431$			13.2460i			0.638039i	0.947748	+	0.319019i	$0.103353\pi$
$431$			13.2460i			0.638039i	−0.947748	+	0.319019i	$0.896647\pi$
$432$		0			0
$433$	−27.8929	−	12.7382i	−1.34045	−	0.612161i	−0.389359	−	0.921086i	$-0.627303\pi$
$433$	−27.8929	−	12.7382i	−1.34045	−	0.612161i	−0.951086	+	0.308925i	$0.900031\pi$
$434$	3.64101	−	4.20195i	0.174774	−	0.201700i
$435$		0			0
$436$	89.7281	−	12.9010i	4.29720	−	0.617844i
$437$	0.0225721	+	0.0195588i	0.00107977	+	0.000935626i
$438$		0			0
$439$	−15.3015			−0.730299			−0.365150	−	0.930949i	$-0.618982\pi$
$439$	−15.3015			−0.730299			−0.365150	+	0.930949i	$0.618982\pi$
$440$	177.829			8.47768
$441$		0			0
$442$	27.2707	−	17.5258i	1.29713	−	0.833617i
$443$	−2.24117	+	0.658068i	−0.106481	+	0.0312657i	−0.334539	−	0.942382i	$-0.608581\pi$
$443$	−2.24117	+	0.658068i	−0.106481	+	0.0312657i	0.228058	+	0.973648i	$0.426762\pi$
$444$		0			0
$445$	−5.02082	−	17.0993i	−0.238010	−	0.810586i
$446$	30.2969	+	34.9645i	1.43460	+	1.65562i
$447$		0			0
$448$	−15.8134	−	24.6061i	−0.747111	−	1.16253i
$449$	8.73540	−	7.56927i	0.412249	−	0.357216i	−0.423909	−	0.905705i	$-0.639342\pi$
$449$	8.73540	−	7.56927i	0.412249	−	0.357216i	0.836158	+	0.548489i	$0.184797\pi$
$450$		0			0
$451$	−41.8714	−	12.2945i	−1.97165	−	0.578927i
$452$	8.67954	−	2.54854i	0.408251	−	0.119873i
$453$		0			0
$454$	−0.342248	+	0.0492079i	−0.0160625	+	0.00230944i
$455$	22.5707	+	6.62735i	1.05813	+	0.310695i
$456$		0			0
$457$	6.36889	+	13.9459i	0.297924	+	0.652363i	0.998100	−	0.0616070i	$-0.0196225\pi$
$457$	6.36889	+	13.9459i	0.297924	+	0.652363i	−0.700176	+	0.713970i	$0.746895\pi$
$458$	34.0971	−	53.0561i	1.59325	−	2.47915i
$459$		0			0
$460$	−0.441505	−	0.0634789i	−0.0205853	−	0.00295972i
$461$	29.8019	+	13.6101i	1.38801	+	0.633884i	0.962553	−	0.271093i	$-0.0873853\pi$
$461$	29.8019	+	13.6101i	1.38801	+	0.633884i	0.425459	+	0.904978i	$0.360113\pi$
$462$		0			0
$463$	20.4096	+	31.7580i	0.948515	+	1.47592i	0.878143	+	0.478398i	$0.158782\pi$
$463$	20.4096	+	31.7580i	0.948515	+	1.47592i	0.0703721	+	0.997521i	$0.477581\pi$
$464$	33.4177	−	51.9990i	1.55138	−	2.41399i
$465$		0			0
$466$	36.1568	+	41.7272i	1.67493	+	1.93297i
$467$	−21.5470	−	3.09800i	−0.997078	−	0.143358i	−0.375594	−	0.926784i	$-0.622561\pi$
$467$	−21.5470	−	3.09800i	−0.997078	−	0.143358i	−0.621485	+	0.783426i	$0.713470\pi$
$468$		0			0
$469$	−6.79643	+	9.48091i	−0.313830	+	0.437788i
$470$			53.1489i			2.45158i
$471$		0			0
$472$	28.4136	−	24.6205i	1.30784	−	1.13325i
$473$	17.4943	−	59.5801i	0.804388	−	2.73950i
$474$		0			0
$475$	−10.7073	+	6.88118i	−0.491286	+	0.315730i
$476$	−2.95237	+	20.5342i	−0.135322	+	0.941182i
$477$		0			0
$478$	−0.926437	+	6.44351i	−0.0423742	+	0.294719i
$479$	20.3112	+	17.5997i	0.928042	+	0.804153i	0.980913	−	0.194448i	$-0.0622917\pi$
$479$	20.3112	+	17.5997i	0.928042	+	0.804153i	−0.0528707	+	0.998601i	$0.516837\pi$
$480$		0			0
$481$	−43.1113	+	19.6883i	−1.96571	+	0.897708i
$482$	10.5590	+	23.1210i	0.480949	+	1.05313i
$483$		0			0
$484$	−13.3482	−	92.8387i	−0.606736	−	4.21994i
$485$	0.0829052	−	0.129003i	0.00376453	−	0.00585772i
$486$		0			0
$487$	−5.05660	+	17.2212i	−0.229136	+	0.780367i	0.762007	+	0.647569i	$0.224214\pi$
$487$	−5.05660	+	17.2212i	−0.229136	+	0.780367i	−0.991143	+	0.132798i	$0.957604\pi$
$488$	−86.4517	+	12.4299i	−3.91348	+	0.562674i
$489$		0			0
$490$	42.8445	−	27.5345i	1.93552	−	1.24388i
$491$	14.9927	+	12.9912i	0.676609	+	0.586285i	0.923890	−	0.382659i	$-0.124992\pi$
$491$	14.9927	+	12.9912i	0.676609	+	0.586285i	−0.247281	+	0.968944i	$0.579537\pi$
$492$		0			0
$493$	−12.8635	+	3.77708i	−0.579345	+	0.170111i
$494$	−14.1179	+	6.44742i	−0.635193	+	0.290083i
$495$		0			0
$496$	−10.0807	−	15.6859i	−0.452636	−	0.704316i
$497$	1.82015	−	3.98558i	0.0816450	−	0.178778i
$498$		0			0
$499$			9.67393i			0.433065i	0.976275	+	0.216532i	$0.0694747\pi$
$499$			9.67393i			0.433065i	−0.976275	+	0.216532i	$0.930525\pi$
$500$	37.5824	−	82.2940i	1.68074	−	3.68030i
$501$		0			0
$502$	8.59087	+	59.7508i	0.383429	+	2.66681i
$503$	3.62252	+	25.1952i	0.161520	+	1.12340i	0.895770	+	0.444519i	$0.146625\pi$
$503$	3.62252	+	25.1952i	0.161520	+	1.12340i	−0.734249	+	0.678880i	$0.762466\pi$
$504$		0			0
$505$	−11.8242	+	25.8914i	−0.526170	+	1.15215i
$506$			0.323807i			0.0143950i
$507$		0			0
$508$	−40.0431	+	87.6823i	−1.77663	+	3.89027i
$509$	−1.39399	−	2.16910i	−0.0617877	−	0.0961435i	0.808985	−	0.587829i	$-0.200017\pi$
$509$	−1.39399	−	2.16910i	−0.0617877	−	0.0961435i	−0.870773	+	0.491686i	$0.836381\pi$
$510$		0			0
$511$	−13.7704	+	6.28874i	−0.609167	+	0.278197i
$512$	1.71540	−	0.503688i	0.0758109	−	0.0222601i
$513$		0			0
$514$	0.0303680	+	0.0263140i	0.00133948	+	0.00116066i
$515$	−4.23600	+	2.72231i	−0.186661	+	0.119959i
$516$		0			0
$517$	27.6182	−	3.97089i	1.21465	−	0.174640i
$518$	11.8162	−	40.2423i	0.519174	−	1.76814i
$519$		0			0
$520$	77.3416	−	120.346i	3.39165	−	5.27751i
$521$	−5.14342	−	35.7733i	−0.225337	−	1.56725i	−0.717379	−	0.696683i	$-0.754658\pi$
$521$	−5.14342	−	35.7733i	−0.225337	−	1.56725i	0.492042	−	0.870572i	$-0.336251\pi$
$522$		0			0
$523$	16.0576	+	35.1613i	0.702152	+	1.53750i	0.837343	+	0.546678i	$0.184108\pi$
$523$	16.0576	+	35.1613i	0.702152	+	1.53750i	−0.135191	+	0.990820i	$0.543165\pi$
$524$	−26.5214	+	12.1119i	−1.15859	+	0.529113i
$525$		0			0
$526$	−33.3129	−	28.8658i	−1.45251	−	1.25861i
$527$	−0.575549	+	4.00303i	−0.0250713	+	0.174375i
$528$		0			0
$529$	−3.27317	+	22.7654i	−0.142312	+	0.989800i
$530$	−32.0137	+	20.5739i	−1.39058	+	0.893675i
$531$		0			0
$532$	2.79829	−	9.53008i	0.121321	−	0.413182i
$533$	−26.5310	+	22.9893i	−1.14919	+	0.995776i
$534$		0			0
$535$		−	19.7343i		−	0.853189i
$536$	43.6770	+	55.9012i	1.88656	+	2.41456i
$537$		0			0
$538$	27.4768	+	3.95057i	1.18461	+	0.170321i
$539$	−17.5089	−	20.2064i	−0.754164	−	0.870351i
$540$		0			0
$541$	19.0858	−	29.6981i	0.820563	−	1.27682i	−0.137569	−	0.990492i	$-0.543929\pi$
$541$	19.0858	−	29.6981i	0.820563	−	1.27682i	0.958132	−	0.286328i	$-0.0924347\pi$
$542$	0.226320	+	0.352160i	0.00972126	+	0.0151266i
$543$		0			0
$544$	43.5788	+	19.9018i	1.86842	+	0.853281i
$545$	−65.4917	−	9.41628i	−2.80535	−	0.403349i
$546$		0			0
$547$	8.25572	−	12.8461i	0.352989	−	0.549261i	−0.618669	−	0.785651i	$-0.712328\pi$
$547$	8.25572	−	12.8461i	0.352989	−	0.549261i	0.971658	+	0.236390i	$0.0759643\pi$
$548$	−34.5212	−	75.5909i	−1.47467	−	3.22908i
$549$		0			0
$550$	−132.400	−	38.8762i	−5.64556	−	1.65769i
$551$	6.35346	−	0.913490i	0.270667	−	0.0389160i
$552$		0			0
$553$	15.5958	−	4.57933i	0.663200	−	0.194733i
$554$	−10.0487	−	2.95058i	−0.426930	−	0.125358i
$555$		0			0
$556$	11.1840	−	9.69099i	0.474307	−	0.410990i
$557$	−7.21007	−	11.2191i	−0.305501	−	0.475368i	0.654228	−	0.756297i	$-0.272994\pi$
$557$	−7.21007	−	11.2191i	−0.305501	−	0.475368i	−0.959728	+	0.280929i	$0.909357\pi$
$558$		0			0
$559$	−32.7122	−	37.7518i	−1.38358	−	1.59673i
$560$	19.6682	+	66.9837i	0.831132	+	2.83058i
$561$		0			0
$562$	−1.21792	+	0.357613i	−0.0513748	+	0.0150850i
$563$	−10.0156	+	6.43665i	−0.422108	+	0.271272i	−0.734404	−	0.678713i	$-0.762538\pi$
$563$	−10.0156	+	6.43665i	−0.422108	+	0.271272i	0.312296	+	0.949985i	$0.398902\pi$
$564$		0			0
$565$	−6.60256			−0.277772
$566$	14.5499			0.611576
$567$		0			0
$568$	−20.1375	−	17.4492i	−0.844950	−	0.732153i
$569$	17.1212	−	2.46166i	0.717759	−	0.103198i	0.226248	−	0.974070i	$-0.427354\pi$
$569$	17.1212	−	2.46166i	0.717759	−	0.103198i	0.491511	+	0.870872i	$0.336445\pi$
$570$		0			0
$571$	−13.5337	+	15.6187i	−0.566366	+	0.653621i	−0.964617	−	0.263655i	$-0.915072\pi$
$571$	−13.5337	+	15.6187i	−0.566366	+	0.653621i	0.398251	+	0.917277i	$0.369617\pi$
$572$	−110.687	−	50.5492i	−4.62807	−	2.11357i
$573$		0			0
$574$		−	31.0664i		−	1.29669i
$575$	0.194314	+	0.0887402i	0.00810345	+	0.00370072i
$576$		0			0
$577$	11.4528	+	39.0047i	0.476787	+	1.62379i	0.749722	+	0.661753i	$0.230187\pi$
$577$	11.4528	+	39.0047i	0.476787	+	1.62379i	−0.272935	+	0.962032i	$0.587994\pi$
$578$	10.3135	+	22.5834i	0.428985	+	0.939346i
$579$		0			0
$580$	−72.4464	+	62.7751i	−3.00817	+	2.60660i
$581$	−8.89290	+	10.2630i	−0.368940	+	0.425779i
$582$		0			0
$583$	13.0828	+	15.0984i	0.541834	+	0.625310i
$584$	13.1019	+	91.1254i	0.542159	+	3.77080i
$585$		0			0
$586$	−5.97556	−	20.3509i	−0.246848	−	0.840688i
$587$	6.77026	+	4.35098i	0.279439	+	0.179584i	0.672851	−	0.739778i	$-0.265069\pi$
$587$	6.77026	+	4.35098i	0.279439	+	0.179584i	−0.393413	+	0.919362i	$0.628706\pi$
$588$		0			0
$589$	0.545511	−	1.85784i	0.0224774	−	0.0765510i
$590$	−40.4442	+	18.4702i	−1.66506	+	0.760408i
$591$		0			0
$592$	−118.325	−	76.0429i	−4.86313	−	3.12534i
$593$	19.5766	−	22.5926i	0.803914	−	0.927766i	−0.194675	−	0.980868i	$-0.562365\pi$
$593$	19.5766	−	22.5926i	0.803914	−	0.927766i	0.998589	+	0.0531017i	$0.0169107\pi$
$594$		0			0
$595$	6.29013	−	13.7735i	0.257870	−	0.564657i
$596$	76.9338	+	11.0614i	3.15133	+	0.453093i
$597$		0			0
$598$	0.219136	+	0.140830i	0.00896115	+	0.00575898i
$599$	−22.2407	−	6.53045i	−0.908730	−	0.266827i	−0.206224	−	0.978505i	$-0.566117\pi$
$599$	−22.2407	−	6.53045i	−0.908730	−	0.266827i	−0.702506	+	0.711678i	$0.747936\pi$
$600$		0			0
$601$	−3.43406	+	23.8844i	−0.140078	+	0.974266i	0.791615	+	0.611020i	$0.209241\pi$
$601$	−3.43406	+	23.8844i	−0.140078	+	0.974266i	−0.931693	+	0.363246i	$0.881668\pi$
$602$	44.2054			1.80168
$603$		0			0
$604$	15.1593			0.616821
$605$	−9.74271	+	67.7620i	−0.396098	+	2.75492i
$606$		0			0
$607$	12.2124	+	3.58588i	0.495686	+	0.145547i	0.520014	−	0.854158i	$-0.325927\pi$
$607$	12.2124	+	3.58588i	0.495686	+	0.145547i	−0.0243285	+	0.999704i	$0.507745\pi$
$608$	−19.2961	−	12.4009i	−0.782562	−	0.502922i
$609$		0			0
$610$	102.239	+	14.6997i	4.13952	+	0.595174i
$611$	9.32440	−	20.4176i	0.377225	−	0.826007i
$612$		0			0
$613$	3.73915	−	4.31521i	0.151023	−	0.174290i	−0.675197	−	0.737637i	$-0.735941\pi$
$613$	3.73915	−	4.31521i	0.151023	−	0.174290i	0.826220	+	0.563348i	$0.190487\pi$
$614$	59.5886	+	38.2953i	2.40480	+	1.54547i
$615$		0			0
$616$	60.4545	−	27.6086i	2.43578	−	1.11238i
$617$	0.490874	−	1.67176i	0.0197619	−	0.0673027i	−0.949022	−	0.315211i	$-0.897925\pi$
$617$	0.490874	−	1.67176i	0.0197619	−	0.0673027i	0.968784	+	0.247908i	$0.0797430\pi$
$618$		0			0
$619$	−2.81846	−	1.81132i	−0.113284	−	0.0728029i	0.482772	−	0.875746i	$-0.339630\pi$
$619$	−2.81846	−	1.81132i	−0.113284	−	0.0728029i	−0.596056	+	0.802943i	$0.703266\pi$
$620$	8.14683	+	27.7456i	0.327185	+	1.11429i
$621$		0			0
$622$	−0.914861	−	6.36300i	−0.0366826	−	0.255133i
$623$	−4.36160	−	5.03355i	−0.174744	−	0.201665i
$624$		0			0
$625$	−12.0018	+	13.8508i	−0.480073	+	0.554034i
$626$	−16.4097	+	14.2191i	−0.655865	+	0.568311i
$627$		0			0
$628$	−4.53924	−	9.93955i	−0.181135	−	0.396631i
$629$	8.59483	+	29.2713i	0.342698	+	1.16712i
$630$		0			0
$631$	−4.36904	−	1.99527i	−0.173929	−	0.0794306i	0.326548	−	0.945181i	$-0.394115\pi$
$631$	−4.36904	−	1.99527i	−0.173929	−	0.0794306i	−0.500477	+	0.865750i	$0.666842\pi$
$632$		−	98.8476i		−	3.93195i
$633$		0			0
$634$	1.52925	+	0.698387i	0.0607344	+	0.0277365i
$635$	46.0736	−	53.1718i	1.82838	−	2.11006i
$636$		0			0
$637$	−21.2897	+	3.06099i	−0.843527	+	0.121281i
$638$	52.5925	+	45.5717i	2.08216	+	1.80420i
$639$		0			0
$640$	79.2231			3.13157
$641$	−15.6535			−0.618277			−0.309138	−	0.951017i	$-0.600041\pi$
$641$	−15.6535			−0.618277			−0.309138	+	0.951017i	$0.600041\pi$
$642$		0			0
$643$	17.1049	−	10.9927i	0.674553	−	0.433509i	−0.158012	−	0.987437i	$-0.550508\pi$
$643$	17.1049	−	10.9927i	0.674553	−	0.433509i	0.832564	+	0.553929i	$0.186872\pi$
$644$	−0.159949	+	0.0469651i	−0.00630286	+	0.00185069i
$645$		0			0
$646$	2.81459	+	9.58562i	0.110739	+	0.377141i
$647$	22.3737	+	25.8206i	0.879601	+	1.01511i	0.999750	+	0.0223579i	$0.00711733\pi$
$647$	22.3737	+	25.8206i	0.879601	+	1.01511i	−0.120149	+	0.992756i	$0.538337\pi$
$648$		0			0
$649$	12.6195	+	19.6363i	0.495359	+	0.770794i
$650$	−83.8929	+	72.6937i	−3.29055	+	2.85128i
$651$		0			0
$652$	−57.6152	−	16.9173i	−2.25638	−	0.662534i
$653$	−8.16737	+	2.39816i	−0.319614	+	0.0938471i	−0.437604	−	0.899168i	$-0.644173\pi$
$653$	−8.16737	+	2.39816i	−0.319614	+	0.0938471i	0.117990	+	0.993015i	$0.462355\pi$
$654$		0			0
$655$	21.0642	−	3.02858i	0.823048	−	0.118336i
$656$	−99.9637	−	29.3520i	−3.90293	−	1.14600i
$657$		0			0
$658$	8.25157	+	18.0684i	0.321680	+	0.704380i
$659$	−1.38423	+	2.15391i	−0.0539220	+	0.0839043i	−0.867168	−	0.498016i	$-0.834062\pi$
$659$	−1.38423	+	2.15391i	−0.0539220	+	0.0839043i	0.813246	+	0.581920i	$0.197698\pi$
$660$		0			0
$661$	−3.39015	−	0.487430i	−0.131862	−	0.0189588i	0.0760680	−	0.997103i	$-0.475763\pi$
$661$	−3.39015	−	0.487430i	−0.131862	−	0.0189588i	−0.207930	+	0.978144i	$0.566672\pi$
$662$	14.1336	+	6.45462i	0.549319	+	0.250866i
$663$		0			0
$664$	44.6483	+	69.4741i	1.73269	+	2.69612i
$665$	−3.91941	+	6.09873i	−0.151988	+	0.236499i
$666$		0			0
$667$	−0.0705483	−	0.0814170i	−0.00273164	−	0.00315248i
$668$	−103.111	−	14.8251i	−3.98949	−	0.573602i
$669$		0			0
$670$	−30.9354	−	77.9837i	−1.19514	−	3.01278i
$671$		−	54.2253i		−	2.09334i
$672$		0			0
$673$	−0.500705	+	0.433863i	−0.0193007	+	0.0167242i	−0.664458	−	0.747326i	$-0.731337\pi$
$673$	−0.500705	+	0.433863i	−0.0193007	+	0.0167242i	0.645157	+	0.764050i	$0.276792\pi$
$674$	−14.2053	+	48.3789i	−0.547168	+	1.86348i
$675$		0			0
$676$	−25.2130	+	16.2034i	−0.969732	+	0.623209i
$677$	6.72761	−	46.7915i	0.258563	−	1.79834i	−0.284525	−	0.958669i	$-0.591836\pi$
$677$	6.72761	−	46.7915i	0.258563	−	1.79834i	0.543088	−	0.839676i	$-0.317255\pi$
$678$		0			0
$679$	0.00815610	−	0.0567269i	0.000313002	−	0.00217698i
$680$	−69.5916	−	60.3015i	−2.66872	−	2.31246i
$681$		0			0
$682$	19.0952	−	8.72050i	0.731194	−	0.333925i
$683$	−8.79151	−	19.2507i	−0.336398	−	0.736609i	0.663535	−	0.748145i	$-0.269055\pi$
$683$	−8.79151	−	19.2507i	−0.336398	−	0.736609i	−0.999933	+	0.0115360i	$0.996328\pi$
$684$		0			0
$685$	8.63200	+	60.0369i	0.329812	+	2.29389i
$686$	24.7872	−	38.5696i	0.946378	−	1.47259i
$687$		0			0
$688$	41.7659	−	142.241i	1.59231	−	5.42291i
$689$	15.9078	−	2.28719i	0.606038	−	0.0871351i
$690$		0			0
$691$	−29.7177	+	19.0984i	−1.13051	+	0.726537i	−0.965667	−	0.259782i	$-0.916349\pi$
$691$	−29.7177	+	19.0984i	−1.13051	+	0.726537i	−0.164846	+	0.986319i	$0.552713\pi$
$692$	33.4611	+	28.9942i	1.27200	+	1.10219i
$693$		0			0
$694$	23.1881	−	6.80863i	0.880206	−	0.258452i
$695$	−9.82522	+	4.48703i	−0.372692	+	0.170203i
$696$		0			0
$697$	12.2169	+	19.0098i	0.462747	+	0.720048i
$698$	15.4312	−	33.7896i	0.584079	−	1.27896i
$699$		0			0
$700$		−	71.0393i		−	2.68503i
$701$	−10.1500	+	22.2254i	−0.383360	+	0.839441i	0.615330	+	0.788270i	$0.289023\pi$
$701$	−10.1500	+	22.2254i	−0.383360	+	0.839441i	−0.998690	+	0.0511714i	$0.983705\pi$
$702$		0			0
$703$	−2.07867	−	14.4575i	−0.0783984	−	0.545273i
$704$	−15.7164	−	109.310i	−0.592333	−	4.11976i
$705$		0			0
$706$	−2.75136	+	6.02463i	−0.103549	+	0.226740i
$707$			10.6377i			0.400073i
$708$		0			0
$709$	4.66817	−	10.2219i	0.175317	−	0.383890i	−0.801491	−	0.598006i	$-0.795960\pi$
$709$	4.66817	−	10.2219i	0.175317	−	0.383890i	0.976808	+	0.214116i	$0.0686870\pi$
$710$	17.0364	+	26.5092i	0.639365	+	0.994871i
$711$		0			0
$712$	−36.8437	+	16.8260i	−1.38078	+	0.630580i
$713$	−0.0311812	+	0.00915561i	−0.00116774	+	0.000342880i
$714$		0			0
$715$	67.1224	+	58.1619i	2.51023	+	2.17513i
$716$	93.0588	−	59.8053i	3.47777	−	2.23503i
$717$		0			0
$718$	−34.2060	+	4.91808i	−1.27656	+	0.183541i
$719$	4.92496	−	16.7729i	0.183670	−	0.625522i	−0.815252	−	0.579106i	$-0.803402\pi$
$719$	4.92496	−	16.7729i	0.183670	−	0.625522i	0.998922	−	0.0464163i	$-0.0147801\pi$
$720$		0			0
$721$	−1.01741	+	1.58313i	−0.0378905	+	0.0589587i
$722$	6.58715	+	45.8146i	0.245148	+	1.70504i
$723$		0			0
$724$	−5.78000	−	12.6564i	−0.214812	−	0.470373i
$725$	41.7603	−	19.0713i	1.55094	−	0.708289i
$726$		0			0
$727$	−8.52431	−	7.38636i	−0.316149	−	0.273945i	0.482301	−	0.876005i	$-0.339801\pi$
$727$	−8.52431	−	7.38636i	−0.316149	−	0.273945i	−0.798450	+	0.602061i	$0.794347\pi$
$728$	7.60876	−	52.9201i	0.281999	−	1.96135i
$729$		0			0
$730$	15.4944	−	107.766i	0.573473	−	3.98859i
$731$	−27.0497	+	17.3838i	−1.00047	+	0.642962i
$732$		0			0
$733$	12.5526	−	42.7502i	0.463641	−	1.57902i	−0.313436	−	0.949609i	$-0.601480\pi$
$733$	12.5526	−	42.7502i	0.463641	−	1.57902i	0.777077	−	0.629406i	$-0.216702\pi$
$734$	28.7071	−	24.8749i	1.05960	−	0.918148i
$735$		0			0
$736$			0.384971i			0.0141902i
$737$	−38.2120	+	21.9015i	−1.40756	+	0.806754i
$738$		0			0
$739$	−6.24593	−	0.898029i	−0.229760	−	0.0330345i	0.0264729	−	0.999650i	$-0.491572\pi$
$739$	−6.24593	−	0.898029i	−0.229760	−	0.0330345i	−0.256233	+	0.966615i	$0.582482\pi$
$740$	142.846	+	164.853i	5.25113	+	6.06013i
$741$		0			0
$742$	−7.68912	+	11.9645i	−0.282277	+	0.439231i
$743$	18.4308	+	28.6789i	0.676161	+	1.05213i	0.994559	+	0.104171i	$0.0332188\pi$
$743$	18.4308	+	28.6789i	0.676161	+	1.05213i	−0.318398	+	0.947957i	$0.603145\pi$
$744$		0			0
$745$	−51.6040	−	23.5668i	−1.89062	−	0.863419i
$746$	−13.1484	−	1.89045i	−0.481396	−	0.0692143i
$747$		0			0
$748$	−42.3463	+	65.8921i	−1.54833	+	2.40926i
$749$	−3.06382	−	6.70884i	−0.111950	−	0.245136i
$750$		0			0
$751$	13.9944	+	4.10912i	0.510662	+	0.149944i	0.526905	−	0.849924i	$-0.323352\pi$
$751$	13.9944	+	4.10912i	0.510662	+	0.149944i	−0.0162431	+	0.999868i	$0.505171\pi$
$752$	65.9356	−	9.48011i	2.40442	−	0.345704i
$753$		0			0
$754$	53.7141	−	15.7719i	1.95615	−	0.574379i
$755$	−10.6164	−	3.11725i	−0.386370	−	0.113449i
$756$		0			0
$757$	23.3409	−	20.2250i	0.848338	−	0.735089i	−0.117821	−	0.993035i	$-0.537591\pi$
$757$	23.3409	−	20.2250i	0.848338	−	0.735089i	0.966159	+	0.257946i	$0.0830455\pi$
$758$	−13.9448	−	21.6985i	−0.506498	−	0.788127i
$759$		0			0
$760$	28.8711	+	33.3190i	1.04726	+	1.20861i
$761$	8.31213	+	28.3085i	0.301315	+	1.02618i	0.961437	+	0.275025i	$0.0886861\pi$
$761$	8.31213	+	28.3085i	0.301315	+	1.02618i	−0.660123	+	0.751158i	$0.729496\pi$
$762$		0			0
$763$	−23.7263	+	6.96668i	−0.858951	+	0.252211i
$764$	52.5377	−	33.7639i	1.90075	−	1.22154i
$765$		0			0
$766$	−87.5166			−3.16210
$767$	18.7774			0.678011
$768$		0			0
$769$	−32.9680	−	28.5670i	−1.18886	−	1.03015i	−0.998829	−	0.0483725i	$-0.984597\pi$
$769$	−32.9680	−	28.5670i	−1.18886	−	1.03015i	−0.190028	−	0.981779i	$-0.560858\pi$
$770$	−77.7968	+	11.1855i	−2.80360	+	0.403097i
$771$		0			0
$772$	−4.00248	+	4.61911i	−0.144052	+	0.166245i
$773$	36.9628	+	16.8803i	1.32946	+	0.607144i	0.948303	−	0.317366i	$-0.102799\pi$
$773$	36.9628	+	16.8803i	1.32946	+	0.607144i	0.381157	+	0.924510i	$0.375526\pi$
$774$		0			0
$775$		−	13.8488i		−	0.497462i
$776$	−0.317029	−	0.144782i	−0.0113807	−	0.00519739i
$777$		0			0
$778$	−5.57235	−	18.9777i	−0.199778	−	0.680383i
$779$	−4.49436	−	9.84128i	−0.161027	−	0.352600i
$780$		0			0
$781$	12.5023	−	10.8333i	0.447368	−	0.387646i
$782$	0.109802	−	0.126719i	0.00392652	−	0.00453144i
$783$		0			0
$784$	−41.8009	−	48.2408i	−1.49289	−	1.72288i
$785$	1.13503	+	7.89433i	0.0405111	+	0.281761i
$786$		0			0
$787$	−1.46134	−	4.97687i	−0.0520911	−	0.177406i	0.929338	−	0.369229i	$-0.120378\pi$
$787$	−1.46134	−	4.97687i	−0.0520911	−	0.177406i	−0.981430	+	0.191823i	$0.938560\pi$
$788$	−52.2282	−	33.5650i	−1.86055	−	1.19571i
$789$		0			0
$790$	−32.9341	+	112.163i	−1.17174	+	3.99058i
$791$	−2.24459	+	1.02507i	−0.0798085	+	0.0364473i
$792$		0			0
$793$	−36.6969	−	23.5837i	−1.30315	−	0.837481i
$794$	−57.0206	+	65.8053i	−2.02359	+	2.33534i
$795$		0			0
$796$	−25.8557	+	56.6160i	−0.916430	+	2.00670i
$797$	19.1369	+	2.75147i	0.677864	+	0.0974622i	0.472644	−	0.881254i	$-0.343300\pi$
$797$	19.1369	+	2.75147i	0.677864	+	0.0974622i	0.205220	+	0.978716i	$0.434209\pi$
$798$		0			0
$799$	−12.1546	−	7.81129i	−0.429999	−	0.276343i
$800$	−157.409	−	46.2194i	−5.56525	−	1.63410i
$801$		0			0
$802$	7.21740	−	50.1981i	0.254855	−	1.77256i
$803$	−57.1568			−2.01702
$804$		0			0
$805$	0.121674			0.00428843
$806$	2.40331	−	16.7154i	0.0846531	−	0.588775i
$807$		0			0
$808$	62.0715	+	18.2258i	2.18367	+	0.641182i
$809$	−23.3618	−	15.0137i	−0.821356	−	0.527853i	0.0611643	−	0.998128i	$-0.480519\pi$
$809$	−23.3618	−	15.0137i	−0.821356	−	0.527853i	−0.882520	+	0.470274i	$0.844155\pi$
$810$		0			0
$811$	55.2002	+	7.93659i	1.93834	+	0.278691i	0.998089	−	0.0617890i	$-0.0196806\pi$
$811$	55.2002	+	7.93659i	1.93834	+	0.278691i	0.940252	+	0.340480i	$0.110590\pi$
$812$	−14.8827	+	32.5885i	−0.522279	+	1.14363i
$813$		0			0
$814$	103.699	−	119.675i	3.63466	−	4.19462i
$815$	36.8705	+	23.6952i	1.29152	+	0.830008i
$816$		0			0
$817$	14.0035	−	6.39517i	0.489919	−	0.223739i
$818$	26.8485	−	91.4375i	0.938735	−	3.19704i
$819$		0			0
$820$	135.924	+	87.3534i	4.74669	+	3.05051i
$821$	8.89412	+	30.2906i	0.310407	+	1.05715i	0.955975	+	0.293447i	$0.0948023\pi$
$821$	8.89412	+	30.2906i	0.310407	+	1.05715i	−0.645569	+	0.763702i	$0.723380\pi$
$822$		0			0
$823$	−4.62915	−	32.1965i	−0.161362	−	1.12230i	−0.896069	−	0.443914i	$-0.853590\pi$
$823$	−4.62915	−	32.1965i	−0.161362	−	1.12230i	0.734707	−	0.678384i	$-0.237320\pi$
$824$	7.49444	+	8.64904i	0.261081	+	0.301304i
$825$		0			0
$826$	−10.8818	+	12.5582i	−0.378625	+	0.436956i
$827$	18.2836	−	15.8429i	0.635784	−	0.550910i	−0.276218	−	0.961095i	$-0.589081\pi$
$827$	18.2836	−	15.8429i	0.635784	−	0.550910i	0.912002	+	0.410185i	$0.134536\pi$
$828$		0			0
$829$	10.3885	+	22.7477i	0.360809	+	0.790061i	0.999783	+	0.0208327i	$0.00663174\pi$
$829$	10.3885	+	22.7477i	0.360809	+	0.790061i	−0.638974	+	0.769228i	$0.720641\pi$
$830$	−27.5153	−	93.7086i	−0.955071	−	3.25267i
$831$		0			0
$832$	−80.8106	−	36.9050i	−2.80160	−	1.27945i
$833$			13.8448i			0.479694i
$834$		0			0
$835$	69.1627	+	31.5855i	2.39347	+	1.09306i
$836$	24.5579	−	28.3413i	0.849351	−	0.980203i
$837$		0			0
$838$	−99.1157	+	14.2507i	−3.42390	+	0.492282i
$839$	0.134645	+	0.116671i	0.00464846	+	0.00402791i	0.657182	−	0.753732i	$-0.271748\pi$
$839$	0.134645	+	0.116671i	0.00464846	+	0.00402791i	−0.652533	+	0.757760i	$0.726294\pi$
$840$		0			0
$841$	5.84756			0.201640
$842$	−6.31240			−0.217540
$843$		0			0
$844$	5.88794	−	3.78395i	0.202671	−	0.130249i
$845$	20.9893	−	6.16301i	0.722053	−	0.212014i
$846$		0			0
$847$	7.20819	+	24.5488i	0.247676	+	0.843508i
$848$	31.2339	+	36.0458i	1.07258	+	1.23782i
$849$		0			0
$850$	38.6306	+	60.1103i	1.32502	+	2.06177i
$851$	−0.185266	+	0.160534i	−0.00635085	+	0.00550304i
$852$		0			0
$853$	33.1455	+	9.73239i	1.13488	+	0.333231i	0.794624	−	0.607102i	$-0.207668\pi$
$853$	33.1455	+	9.73239i	1.13488	+	0.333231i	0.340256	+	0.940333i	$0.389486\pi$
$854$	37.0390	−	10.8756i	1.26745	−	0.372157i
$855$		0			0
$856$	−44.3956	+	6.38312i	−1.51741	+	0.218171i
$857$	−18.3643	−	5.39224i	−0.627312	−	0.184195i	−0.0474019	−	0.998876i	$-0.515094\pi$
$857$	−18.3643	−	5.39224i	−0.627312	−	0.184195i	−0.579910	+	0.814680i	$0.696912\pi$
$858$		0			0
$859$	18.2195	+	39.8950i	0.621640	+	1.36120i	0.914321	+	0.404991i	$0.132725\pi$
$859$	18.2195	+	39.8950i	0.621640	+	1.36120i	−0.292681	+	0.956210i	$0.594547\pi$
$860$	−124.298	+	193.411i	−4.23852	+	6.59527i
$861$		0			0
$862$	−35.2407	−	5.06685i	−1.20030	−	0.172578i
$863$	−36.3784	−	16.6135i	−1.23834	−	0.565529i	−0.314843	−	0.949144i	$-0.601952\pi$
$863$	−36.3784	−	16.6135i	−1.23834	−	0.565529i	−0.923493	+	0.383615i	$0.874679\pi$
$864$		0			0
$865$	−17.4714	−	27.1861i	−0.594046	−	0.924354i
$866$	44.5593	−	69.3357i	1.51419	−	2.35612i
$867$		0			0
$868$	7.07718	+	8.16750i	0.240215	+	0.277223i
$869$	60.7447	+	8.73377i	2.06062	+	0.296273i
$870$		0			0
$871$	−1.79732	+	35.3854i	−0.0608998	+	1.19899i
$872$			150.380i			5.09251i
$873$		0			0
$874$	−0.0606701	+	0.0525709i	−0.00205220	+	0.00177824i
$875$	−6.95275	+	23.6789i	−0.235046	+	0.800493i
$876$		0			0
$877$	−25.0611	+	16.1058i	−0.846252	+	0.543853i	−0.890404	−	0.455172i	$-0.849578\pi$
$877$	−25.0611	+	16.1058i	−0.846252	+	0.543853i	0.0441518	+	0.999025i	$0.485941\pi$
$878$	5.85310	−	40.7092i	0.197533	−	1.37387i
$879$		0			0
$880$	−37.5114	+	260.898i	−1.26451	+	8.79486i
$881$	−29.4371	−	25.5074i	−0.991761	−	0.859365i	−0.00169886	−	0.999999i	$-0.500541\pi$
$881$	−29.4371	−	25.5074i	−0.991761	−	0.859365i	−0.990062	+	0.140633i	$0.955086\pi$
$882$		0			0
$883$	−27.3075	+	12.4709i	−0.918971	+	0.419680i	−0.818006	−	0.575210i	$-0.804920\pi$
$883$	−27.3075	+	12.4709i	−0.918971	+	0.419680i	−0.100965	+	0.994890i	$0.532193\pi$
$884$	26.1752	+	57.3157i	0.880367	+	1.92773i
$885$		0			0
$886$	−0.893483	−	6.21431i	−0.0300172	−	0.208774i
$887$	−12.4964	+	19.4448i	−0.419589	+	0.652894i	−0.985127	−	0.171829i	$-0.945032\pi$
$887$	−12.4964	+	19.4448i	−0.419589	+	0.652894i	0.565538	+	0.824723i	$0.308669\pi$
$888$		0			0
$889$	7.40798	−	25.2293i	0.248456	−	0.846163i
$890$	47.4129	−	6.81695i	1.58929	−	0.228505i
$891$		0			0
$892$	−75.6511	+	48.6180i	−2.53299	+	1.62785i
$893$	5.22789	+	4.52999i	0.174945	+	0.151590i
$894$		0			0
$895$	−77.4694	+	22.7471i	−2.58951	+	0.760350i
$896$	26.9325	−	12.2997i	0.899753	−	0.410903i
$897$		0			0
$898$	16.7964	+	26.1357i	0.560503	+	0.872160i
$899$	−2.90130	+	6.35295i	−0.0967637	+	0.211883i
$900$		0			0
$901$		−	10.3449i		−	0.344640i
$902$	48.7259	−	106.695i	1.62240	−	3.55255i
$903$		0			0
$904$	2.13562	+	14.8535i	0.0710296	+	0.494022i
$905$	1.44529	+	10.0522i	0.0480429	+	0.334146i
$906$		0			0
$907$	3.83546	−	8.39850i	0.127355	−	0.278868i	−0.835205	−	0.549939i	$-0.814651\pi$
$907$	3.83546	−	8.39850i	0.127355	−	0.278868i	0.962559	+	0.271072i	$0.0873781\pi$
$908$		−	0.672083i		−	0.0223039i
$909$		0			0
$910$	−26.2656	+	57.5137i	−0.870697	+	1.90656i
$911$	−23.8929	−	37.1780i	−0.791606	−	1.23176i	−0.968863	−	0.247598i	$-0.920359\pi$
$911$	−23.8929	−	37.1780i	−0.791606	−	1.23176i	0.177257	−	0.984165i	$-0.443278\pi$
$912$		0			0
$913$	−46.6387	+	21.2992i	−1.54352	+	0.704900i
$914$	−39.5391	+	11.6097i	−1.30784	+	0.384015i
$915$		0			0
$916$	92.6456	+	80.2779i	3.06110	+	2.65246i
$917$	6.69076	−	4.29989i	0.220948	−	0.141995i
$918$		0			0
$919$	51.8341	−	7.45262i	1.70985	−	0.245839i	0.783201	−	0.621768i	$-0.213585\pi$
$919$	51.8341	−	7.45262i	1.70985	−	0.245839i	0.926648	+	0.375929i	$0.122676\pi$
$920$	0.208466	−	0.709969i	0.00687291	−	0.0234070i
$921$		0			0
$922$	−47.6091	+	74.0811i	−1.56792	+	2.43973i
$923$	−1.89393	−	13.1726i	−0.0623394	−	0.433580i
$924$		0			0
$925$	−43.3971	−	95.0265i	−1.42689	−	3.12445i
$926$	−92.2985	+	42.1513i	−3.03312	+	1.38518i
$927$		0			0
$928$	62.5266	+	54.1796i	2.05254	+	1.77853i
$929$	0.934828	−	6.50187i	0.0306707	−	0.213319i	−0.968723	−	0.248146i	$-0.920179\pi$
$929$	0.934828	−	6.50187i	0.0306707	−	0.213319i	0.999393	+	0.0348264i	$0.0110878\pi$
$930$		0			0
$931$	0.943347	−	6.56112i	0.0309170	−	0.215032i
$932$	−90.2831	+	58.0214i	−2.95732	+	1.90055i
$933$		0			0
$934$	16.4843	−	56.1404i	0.539383	−	1.83697i
$935$	43.2058	−	37.4380i	1.41298	−	1.22436i
$936$		0			0
$937$			6.65411i			0.217380i	0.994076	+	0.108690i	$0.0346656\pi$
$937$			6.65411i			0.217380i	−0.994076	+	0.108690i	$0.965334\pi$
$938$	−22.6240	−	21.7084i	−0.738700	−	0.708803i
$939$		0			0
$940$	−102.256	−	14.7022i	−3.33523	−	0.479534i
$941$	−18.2207	−	21.0278i	−0.593979	−	0.685488i	0.376571	−	0.926388i	$-0.377103\pi$
$941$	−18.2207	−	21.0278i	−0.593979	−	0.685488i	−0.970550	+	0.240900i	$0.922558\pi$
$942$		0			0
$943$	−0.0981699	+	0.152755i	−0.00319685	+	0.00497440i
$944$	30.1278	+	46.8798i	0.980577	+	1.52581i
$945$		0			0
$946$	151.820	+	69.3337i	4.93608	+	2.25423i
$947$	44.7789	+	6.43824i	1.45512	+	0.209215i	0.824052	−	0.566514i	$-0.191708\pi$
$947$	44.7789	+	6.43824i	1.45512	+	0.209215i	0.631067	+	0.775728i	$0.282617\pi$
$948$		0			0
$949$	−24.8586	+	38.6808i	−0.806946	+	1.25563i
$950$	−14.2115	−	31.1188i	−0.461081	−	1.00963i
$951$		0			0
$952$	−33.0203	−	9.69562i	−1.07019	−	0.314237i
$953$	−8.91821	+	1.28224i	−0.288889	+	0.0415360i	−0.285236	−	0.958457i	$-0.592072\pi$
$953$	−8.91821	+	1.28224i	−0.288889	+	0.0415360i	−0.00365316	+	0.999993i	$0.501163\pi$
$954$		0			0
$955$	−43.7364	+	12.8422i	−1.41528	+	0.415563i
$956$	−12.1408	−	3.56485i	−0.392660	−	0.115296i
$957$		0			0
$958$	−54.5931	+	47.3052i	−1.76382	+	1.52836i
$959$	12.2555	+	19.0699i	0.395750	+	0.615798i
$960$		0			0
$961$	−18.9210	−	21.8360i	−0.610356	−	0.704388i
$962$	−35.8893	−	122.228i	−1.15712	−	3.94078i
$963$		0			0
$964$	−47.4046	+	13.9193i	−1.52680	+	0.448309i
$965$	3.75288	−	2.41183i	0.120809	−	0.0776395i
$966$		0			0
$967$	35.8520			1.15292			0.576461	−	0.817125i	$-0.304433\pi$
$967$	35.8520			1.15292			0.576461	+	0.817125i	$0.304433\pi$
$968$	155.593			5.00095
$969$		0			0
$970$	0.311497	+	0.269913i	0.0100016	+	0.00866640i
$971$	−25.2247	+	3.62677i	−0.809500	+	0.116389i	−0.534623	−	0.845091i	$-0.679546\pi$
$971$	−25.2247	+	3.62677i	−0.809500	+	0.116389i	−0.274877	+	0.961479i	$0.588637\pi$
$972$		0			0
$973$	−2.64354	+	3.05080i	−0.0847479	+	0.0978043i
$974$	−43.8823	−	20.0404i	−1.40608	−	0.642136i
$975$		0			0
$976$		−	129.457i		−	4.14383i
$977$	−26.6248	−	12.1591i	−0.851802	−	0.389005i	−0.0588339	−	0.998268i	$-0.518738\pi$
$977$	−26.6248	−	12.1591i	−0.851802	−	0.389005i	−0.792968	+	0.609263i	$0.791466\pi$
$978$		0			0
$979$	−7.08468	−	24.1282i	−0.226427	−	0.771141i
$980$	41.1234	+	90.0476i	1.31364	+	2.87647i
$981$		0			0
$982$	−40.2978	+	34.9182i	−1.28595	+	1.11429i
$983$	19.1713	−	22.1248i	0.611469	−	0.705673i	−0.362594	−	0.931947i	$-0.618109\pi$
$983$	19.1713	−	22.1248i	0.611469	−	0.705673i	0.974064	+	0.226274i	$0.0726544\pi$
$984$		0			0
$985$	29.6746	+	34.2463i	0.945511	+	1.09118i
$986$	−5.12828	−	35.6680i	−0.163318	−	1.13590i
$987$		0			0
$988$	−8.49923	−	28.9457i	−0.270396	−	0.920885i
$989$	−0.217360	−	0.139689i	−0.00691166	−	0.00444185i
$990$		0			0
$991$	12.9099	−	43.9672i	0.410097	−	1.39666i	−0.452948	−	0.891537i	$-0.649628\pi$
$991$	12.9099	−	43.9672i	0.410097	−	1.39666i	0.863046	−	0.505126i	$-0.168554\pi$
$992$	22.7021	−	10.3677i	0.720792	−	0.329175i
$993$		0			0
$994$	9.90730	+	6.36704i	0.314241	+	0.201950i
$995$	29.7495	−	34.3328i	0.943124	−	1.08842i
$996$		0			0
$997$	7.63520	−	16.7188i	0.241809	−	0.529488i	−0.749349	−	0.662175i	$-0.769633\pi$
$997$	7.63520	−	16.7188i	0.241809	−	0.529488i	0.991158	+	0.132687i	$0.0423606\pi$
$998$	−25.7373	−	3.70046i	−0.814699	−	0.117136i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.v.a.8.2	✓	240
3.2	odd	2	inner	603.2.v.a.8.23	yes	240
67.42	odd	22	inner	603.2.v.a.377.23	yes	240
201.176	even	22	inner	603.2.v.a.377.2	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.v.a.8.2	✓	240	1.1	even	1	trivial
603.2.v.a.8.23	yes	240	3.2	odd	2	inner
603.2.v.a.377.2	yes	240	201.176	even	22	inner
603.2.v.a.377.23	yes	240	67.42	odd	22	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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.v (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.382519 + 2.66048i) q^{2} +(-5.01283 - 1.47190i) q^{4} +(3.20794 + 2.06162i) q^{5} +(1.41064 + 0.202819i) q^{7} +(3.60033 - 7.88361i) q^{8} +O(q^{10})\)	\(q+(-0.382519 + 2.66048i) q^{2} +(-5.01283 - 1.47190i) q^{4} +(3.20794 + 2.06162i) q^{5} +(1.41064 + 0.202819i) q^{7} +(3.60033 - 7.88361i) q^{8} +(-6.71198 + 7.74603i) q^{10} +(4.52660 + 2.90907i) q^{11} +(3.93742 - 1.79816i) q^{13} +(-1.07919 + 3.67539i) q^{14} +(10.8068 + 6.94510i) q^{16} +(-0.784978 - 2.67339i) q^{17} +(0.189848 + 1.32042i) q^{19} +(-13.0464 - 15.0563i) q^{20} +(-9.47101 + 10.9301i) q^{22} +(0.0169206 - 0.0146618i) q^{23} +(3.96352 + 8.67890i) q^{25} +(3.27782 + 11.1632i) q^{26} +(-6.77276 - 3.09301i) q^{28} -4.81170i q^{29} +(-1.32031 - 0.602967i) q^{31} +(-11.2600 + 12.9947i) q^{32} +(7.41276 - 1.06579i) q^{34} +(4.10710 + 3.55882i) q^{35} -10.9491 q^{37} -3.58557 q^{38} +(27.8026 - 17.8676i) q^{40} +(-7.78166 + 2.28490i) q^{41} +(-3.25126 - 11.0728i) q^{43} +(-18.4092 - 21.2454i) q^{44} +(0.0325350 + 0.0506254i) q^{46} +(3.91896 - 3.39580i) q^{47} +(-4.76769 - 1.39992i) q^{49} +(-24.6061 + 7.22502i) q^{50} +(-22.3843 + 3.21838i) q^{52} +(3.56245 + 1.04603i) q^{53} +(8.52366 + 18.6642i) q^{55} +(6.67770 - 10.3907i) q^{56} +(12.8014 + 1.84057i) q^{58} +(3.94598 + 1.80207i) q^{59} +(-5.44836 - 8.47781i) q^{61} +(2.10923 - 3.28202i) q^{62} +(-13.4402 - 15.5108i) q^{64} +(16.3381 + 2.34906i) q^{65} +(-3.77364 + 7.26358i) q^{67} +14.5567i q^{68} +(-11.0392 + 9.56553i) q^{70} +(0.866173 - 2.94991i) q^{71} +(-8.93614 + 5.74291i) q^{73} +(4.18825 - 29.1299i) q^{74} +(0.991852 - 6.89848i) q^{76} +(5.79537 + 5.02172i) q^{77} +(10.3746 - 4.73793i) q^{79} +(20.3494 + 44.5589i) q^{80} +(-3.10230 - 21.5770i) q^{82} +(-5.15163 + 8.01610i) q^{83} +(2.99334 - 10.1944i) q^{85} +(30.7025 - 4.41436i) q^{86} +(39.2312 - 25.2123i) q^{88} +(-3.53196 - 3.06046i) q^{89} +(5.91897 - 1.73797i) q^{91} +(-0.106401 + 0.0485917i) q^{92} +(7.53537 + 11.7253i) q^{94} +(-2.11318 + 4.62722i) q^{95} -0.0402137i q^{97} +(5.54819 - 12.1488i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 28 q^{4}+O(q^{10}) \) 240 * q - 28 * q^4	\( 240 q - 28 q^{4} - 28 q^{16} - 20 q^{19} + 12 q^{22} - 24 q^{25} + 44 q^{28} - 88 q^{31} + 24 q^{37} + 32 q^{40} + 44 q^{43} - 44 q^{46} + 8 q^{49} - 220 q^{52} + 52 q^{55} - 88 q^{58} - 88 q^{61} - 148 q^{64} + 8 q^{67} - 176 q^{70} - 120 q^{73} - 64 q^{76} - 264 q^{79} + 8 q^{82} + 256 q^{88} + 256 q^{91} - 88 q^{94}+O(q^{100}) \) 240 * q - 28 * q^4 - 28 * q^16 - 20 * q^19 + 12 * q^22 - 24 * q^25 + 44 * q^28 - 88 * q^31 + 24 * q^37 + 32 * q^40 + 44 * q^43 - 44 * q^46 + 8 * q^49 - 220 * q^52 + 52 * q^55 - 88 * q^58 - 88 * q^61 - 148 * q^64 + 8 * q^67 - 176 * q^70 - 120 * q^73 - 64 * q^76 - 264 * q^79 + 8 * q^82 + 256 * q^88 + 256 * q^91 - 88 * q^94

Introduction

L-functions

Modular forms

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Representations

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Database

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