LMFDB - Embedded newform 525.2.q.g.299.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(299,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("525.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.q (of order $6$, degree $2$, not 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			299.4
Character	$\chi$	$=$	525.299
Dual form			525.2.q.g.374.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12521 + 1.94891i) q^{2} +(1.56483 - 0.742502i) q^{3} +(-1.53217 - 2.65380i) q^{4} +(-0.313682 + 3.88518i) q^{6} +(2.22667 + 1.42897i) q^{7} +2.39522 q^{8} +(1.89738 - 2.32378i) q^{9} +O(q^{10})$	\(q+(-1.12521 + 1.94891i) q^{2} +(1.56483 - 0.742502i) q^{3} +(-1.53217 - 2.65380i) q^{4} +(-0.313682 + 3.88518i) q^{6} +(2.22667 + 1.42897i) q^{7} +2.39522 q^{8} +(1.89738 - 2.32378i) q^{9} +(-1.64925 + 0.952197i) q^{11} +(-4.36805 - 3.01511i) q^{12} +5.07948 q^{13} +(-5.29039 + 2.73170i) q^{14} +(0.369233 - 0.639530i) q^{16} +(3.85968 - 2.22839i) q^{17} +(2.39390 + 6.31256i) q^{18} +(-3.85670 - 2.22667i) q^{19} +(4.54537 + 0.582783i) q^{21} -4.28567i q^{22} +(-1.42310 + 2.46489i) q^{23} +(3.74811 - 1.77846i) q^{24} +(-5.71546 + 9.89947i) q^{26} +(1.24366 - 5.04513i) q^{27} +(0.380555 - 8.09857i) q^{28} +8.82675i q^{29} +(4.81162 - 2.77799i) q^{31} +(3.22615 + 5.58785i) q^{32} +(-1.87379 + 2.71460i) q^{33} +10.0296i q^{34} +(-9.07397 - 1.47484i) q^{36} +(4.02342 + 2.32292i) q^{37} +(8.67917 - 5.01092i) q^{38} +(7.94852 - 3.77153i) q^{39} +0.250819 q^{41} +(-6.25027 + 8.20277i) q^{42} +9.23735i q^{43} +(5.05389 + 2.91786i) q^{44} +(-3.20257 - 5.54701i) q^{46} +(-2.66417 - 1.53816i) q^{47} +(0.102934 - 1.27491i) q^{48} +(2.91610 + 6.36367i) q^{49} +(4.38516 - 6.35287i) q^{51} +(-7.78265 - 13.4799i) q^{52} +(1.21077 + 2.09711i) q^{53} +(8.43313 + 8.10060i) q^{54} +(5.33336 + 3.42269i) q^{56} +(-7.68839 - 0.620744i) q^{57} +(-17.2026 - 9.93190i) q^{58} +(-6.95983 - 12.0548i) q^{59} +(-1.51554 - 0.874995i) q^{61} +12.5032i q^{62} +(7.54544 - 2.46299i) q^{63} -13.0434 q^{64} +(-3.18212 - 6.70634i) q^{66} +(-7.18573 + 4.14868i) q^{67} +(-11.8274 - 6.82855i) q^{68} +(-0.396729 + 4.91379i) q^{69} -9.68436i q^{71} +(4.54465 - 5.56596i) q^{72} +(-3.15855 - 5.47076i) q^{73} +(-9.05434 + 5.22752i) q^{74} +13.6466i q^{76} +(-5.03300 - 0.236503i) q^{77} +(-1.59334 + 19.7347i) q^{78} +(-1.59436 + 2.76150i) q^{79} +(-1.79990 - 8.81818i) q^{81} +(-0.282223 + 0.488824i) q^{82} +8.98988i q^{83} +(-5.41770 - 12.9554i) q^{84} +(-18.0028 - 10.3939i) q^{86} +(6.55388 + 13.8124i) q^{87} +(-3.95033 + 2.28072i) q^{88} +(5.43599 - 9.41541i) q^{89} +(11.3103 + 7.25841i) q^{91} +8.72178 q^{92} +(5.46670 - 7.91972i) q^{93} +(5.99548 - 3.46149i) q^{94} +(9.19736 + 6.34861i) q^{96} -8.94486 q^{97} +(-15.6835 - 1.47721i) q^{98} +(-0.916566 + 5.63918i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 28 q^{4} + 14 q^{9}+O(q^{10}) $ 40 * q - 28 * q^4 + 14 * q^9	$ 40 q - 28 q^{4} + 14 q^{9} - 36 q^{16} - 18 q^{21} - 36 q^{24} + 84 q^{31} - 72 q^{36} - 16 q^{46} + 8 q^{49} + 42 q^{51} + 150 q^{54} - 180 q^{61} + 240 q^{64} + 12 q^{66} - 92 q^{79} + 58 q^{81} - 150 q^{84} - 60 q^{91} - 12 q^{94} + 270 q^{96} - 188 q^{99}+O(q^{100}) $ 40 * q - 28 * q^4 + 14 * q^9 - 36 * q^16 - 18 * q^21 - 36 * q^24 + 84 * q^31 - 72 * q^36 - 16 * q^46 + 8 * q^49 + 42 * q^51 + 150 * q^54 - 180 * q^61 + 240 * q^64 + 12 * q^66 - 92 * q^79 + 58 * q^81 - 150 * q^84 - 60 * q^91 - 12 * q^94 + 270 * q^96 - 188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.12521	+	1.94891i	−0.795640	+	1.37809i	0.126791	+	0.991929i	$0.459532\pi$
$2$	−1.12521	+	1.94891i	−0.795640	+	1.37809i	−0.922432	+	0.386160i	$0.873801\pi$
$3$	1.56483	−	0.742502i	0.903455	−	0.428684i
$3$	1.56483	−	0.742502i	0.903455	−	0.428684i
$4$	−1.53217	−	2.65380i	−0.766087	−	1.32690i
$5$		0			0
$5$		0			0
$6$	−0.313682	+	3.88518i	−0.128060	+	1.58612i
$7$	2.22667	+	1.42897i	0.841602	+	0.540099i
$7$	2.22667	+	1.42897i	0.841602	+	0.540099i
$8$	2.39522			0.846839
$9$	1.89738	−	2.32378i	0.632460	−	0.774593i
$10$		0			0
$11$	−1.64925	+	0.952197i	−0.497269	+	0.287098i	−0.727585	−	0.686018i	$-0.759357\pi$
$11$	−1.64925	+	0.952197i	−0.497269	+	0.287098i	0.230316	+	0.973116i	$0.426024\pi$
$12$	−4.36805	−	3.01511i	−1.26095	−	0.870386i
$13$	5.07948			1.40879			0.704397	−	0.709806i	$-0.251217\pi$
$13$	5.07948			1.40879			0.704397	+	0.709806i	$0.251217\pi$
$14$	−5.29039	+	2.73170i	−1.41392	+	0.730078i
$15$		0			0
$16$	0.369233	−	0.639530i	0.0923082	−	0.159882i
$17$	3.85968	−	2.22839i	0.936110	−	0.540463i	0.0473710	−	0.998877i	$-0.484916\pi$
$17$	3.85968	−	2.22839i	0.936110	−	0.540463i	0.888739	+	0.458414i	$0.151582\pi$
$18$	2.39390	+	6.31256i	0.564248	+	1.48788i
$19$	−3.85670	−	2.22667i	−0.884788	−	0.510833i	−0.0125541	−	0.999921i	$-0.503996\pi$
$19$	−3.85670	−	2.22667i	−0.884788	−	0.510833i	−0.872234	+	0.489088i	$0.837330\pi$
$20$		0			0
$21$	4.54537	+	0.582783i	0.991880	+	0.127174i
$22$		−	4.28567i		−	0.913708i
$23$	−1.42310	+	2.46489i	−0.296738	+	0.513965i	−0.975388	−	0.220497i	$-0.929232\pi$
$23$	−1.42310	+	2.46489i	−0.296738	+	0.513965i	0.678650	+	0.734462i	$0.262565\pi$
$24$	3.74811	−	1.77846i	0.765080	−	0.363026i
$25$		0			0
$26$	−5.71546	+	9.89947i	−1.12089	+	1.94145i
$27$	1.24366	−	5.04513i	0.239343	−	0.970935i
$28$	0.380555	−	8.09857i	0.0719181	−	1.53049i
$29$			8.82675i			1.63909i	0.573018	+	0.819543i	$0.305773\pi$
$29$			8.82675i			1.63909i	−0.573018	+	0.819543i	$0.694227\pi$
$30$		0			0
$31$	4.81162	−	2.77799i	0.864193	−	0.498942i	−0.00122124	−	0.999999i	$-0.500389\pi$
$31$	4.81162	−	2.77799i	0.864193	−	0.498942i	0.865414	+	0.501057i	$0.167055\pi$
$32$	3.22615	+	5.58785i	0.570308	+	0.987802i
$33$	−1.87379	+	2.71460i	−0.326185	+	0.472551i
$34$			10.0296i			1.72006i
$35$		0			0
$36$	−9.07397	−	1.47484i	−1.51233	−	0.245807i
$37$	4.02342	+	2.32292i	0.661446	+	0.381886i	0.792828	−	0.609446i	$-0.208608\pi$
$37$	4.02342	+	2.32292i	0.661446	+	0.381886i	−0.131382	+	0.991332i	$0.541941\pi$
$38$	8.67917	−	5.01092i	1.40795	−	0.812878i
$39$	7.94852	−	3.77153i	1.27278	−	0.603928i
$40$		0			0
$41$	0.250819			0.0391713			0.0195857	−	0.999808i	$-0.493765\pi$
$41$	0.250819			0.0391713			0.0195857	+	0.999808i	$0.493765\pi$
$42$	−6.25027	+	8.20277i	−0.964437	+	1.26572i
$43$			9.23735i			1.40868i	0.709862	+	0.704341i	$0.248757\pi$
$43$			9.23735i			1.40868i	−0.709862	+	0.704341i	$0.751243\pi$
$44$	5.05389	+	2.91786i	0.761902	+	0.439885i
$45$		0			0
$46$	−3.20257	−	5.54701i	−0.472193	−	0.817863i
$47$	−2.66417	−	1.53816i	−0.388610	−	0.224364i	0.292948	−	0.956128i	$-0.405364\pi$
$47$	−2.66417	−	1.53816i	−0.388610	−	0.224364i	−0.681557	+	0.731765i	$0.738697\pi$
$48$	0.102934	−	1.27491i	0.0148572	−	0.184018i
$49$	2.91610	+	6.36367i	0.416586	+	0.909096i
$50$		0			0
$51$	4.38516	−	6.35287i	0.614045	−	0.889579i
$52$	−7.78265	−	13.4799i	−1.07926	−	1.86933i
$53$	1.21077	+	2.09711i	0.166312	+	0.288060i	0.937120	−	0.349007i	$-0.113481\pi$
$53$	1.21077	+	2.09711i	0.166312	+	0.288060i	−0.770809	+	0.637067i	$0.780148\pi$
$54$	8.43313	+	8.10060i	1.14760	+	1.10235i
$55$		0			0
$56$	5.33336	+	3.42269i	0.712701	+	0.457377i
$57$	−7.68839	−	0.620744i	−1.01835	−	0.0822196i
$58$	−17.2026	−	9.93190i	−2.25881	−	1.30412i
$59$	−6.95983	−	12.0548i	−0.906093	−	1.56940i	−0.819443	−	0.573160i	$-0.805717\pi$
$59$	−6.95983	−	12.0548i	−0.906093	−	1.56940i	−0.0866494	−	0.996239i	$-0.527616\pi$
$60$		0			0
$61$	−1.51554	−	0.874995i	−0.194044	−	0.112032i	0.399830	−	0.916589i	$-0.369069\pi$
$61$	−1.51554	−	0.874995i	−0.194044	−	0.112032i	−0.593875	+	0.804558i	$0.702402\pi$
$62$			12.5032i			1.58791i
$63$	7.54544	−	2.46299i	0.950636	−	0.310308i
$64$	−13.0434			−1.63042
$65$		0			0
$66$	−3.18212	−	6.70634i	−0.391692	−	0.825494i
$67$	−7.18573	+	4.14868i	−0.877876	+	0.506842i	−0.869958	−	0.493127i	$-0.835854\pi$
$67$	−7.18573	+	4.14868i	−0.877876	+	0.506842i	−0.00791862	+	0.999969i	$0.502521\pi$
$68$	−11.8274	−	6.82855i	−1.43428	−	0.828084i
$69$	−0.396729	+	4.91379i	−0.0477606	+	0.591551i
$70$		0			0
$71$		−	9.68436i		−	1.14932i	−0.818392	−	0.574661i	$-0.805134\pi$
$71$		−	9.68436i		−	1.14932i	0.818392	−	0.574661i	$-0.194866\pi$
$72$	4.54465	−	5.56596i	0.535592	−	0.655955i
$73$	−3.15855	−	5.47076i	−0.369680	−	0.640304i	0.619835	−	0.784732i	$-0.287199\pi$
$73$	−3.15855	−	5.47076i	−0.369680	−	0.640304i	−0.989515	+	0.144427i	$0.953866\pi$
$74$	−9.05434	+	5.22752i	−1.05255	+	0.607687i
$75$		0			0
$76$			13.6466i			1.56537i
$77$	−5.03300	−	0.236503i	−0.573564	−	0.0269520i
$78$	−1.59334	+	19.7347i	−0.180410	+	2.23452i
$79$	−1.59436	+	2.76150i	−0.179379	+	0.310694i	−0.941668	−	0.336543i	$-0.890742\pi$
$79$	−1.59436	+	2.76150i	−0.179379	+	0.310694i	0.762289	+	0.647237i	$0.224076\pi$
$80$		0			0
$81$	−1.79990	−	8.81818i	−0.199988	−	0.979798i
$82$	−0.282223	+	0.488824i	−0.0311663	+	0.0539816i
$83$			8.98988i			0.986768i	0.869812	+	0.493384i	$0.164240\pi$
$83$			8.98988i			0.986768i	−0.869812	+	0.493384i	$0.835760\pi$
$84$	−5.41770	−	12.9554i	−0.591120	−	1.41355i
$85$		0			0
$86$	−18.0028	−	10.3939i	−1.94129	−	1.12080i
$87$	6.55388	+	13.8124i	0.702650	+	1.48084i
$88$	−3.95033	+	2.28072i	−0.421106	+	0.243126i
$89$	5.43599	−	9.41541i	0.576213	−	0.998031i	−0.419695	−	0.907665i	$-0.637863\pi$
$89$	5.43599	−	9.41541i	0.576213	−	0.998031i	0.995909	−	0.0903658i	$-0.0288036\pi$
$90$		0			0
$91$	11.3103	+	7.25841i	1.18564	+	0.760889i
$92$	8.72178			0.909308
$93$	5.46670	−	7.91972i	0.566871	−	0.821237i
$94$	5.99548	−	3.46149i	0.618387	−	0.357026i
$95$		0			0
$96$	9.19736	+	6.34861i	0.938702	+	0.647952i
$97$	−8.94486			−0.908213			−0.454107	−	0.890947i	$-0.650041\pi$
$97$	−8.94486			−0.908213			−0.454107	+	0.890947i	$0.650041\pi$
$98$	−15.6835	−	1.47721i	−1.58427	−	0.149220i
$99$	−0.916566	+	5.63918i	−0.0921184	+	0.566759i
$100$		0			0
$101$	4.71346	+	8.16395i	0.469007	+	0.812344i	0.999372	−	0.0354254i	$-0.0112786\pi$
$101$	4.71346	+	8.16395i	0.469007	+	0.812344i	−0.530365	+	0.847769i	$0.677945\pi$
$102$	7.44698	+	15.6946i	0.737361	+	1.55399i
$103$	−3.15056	+	5.45692i	−0.310433	+	0.537686i	−0.978456	−	0.206454i	$-0.933808\pi$
$103$	−3.15056	+	5.45692i	−0.310433	+	0.537686i	0.668023	+	0.744141i	$0.267141\pi$
$104$	12.1665			1.19302
$105$		0			0
$106$	−5.44944			−0.529297
$107$	8.30336	−	14.3818i	0.802716	−	1.39034i	−0.115107	−	0.993353i	$-0.536721\pi$
$107$	8.30336	−	14.3818i	0.802716	−	1.39034i	0.917822	−	0.396991i	$-0.129946\pi$
$108$	−15.2943	+	4.42957i	−1.47169	+	0.426236i
$109$	−9.20177	−	15.9379i	−0.881370	−	1.52658i	−0.849818	−	0.527076i	$-0.823288\pi$
$109$	−9.20177	−	15.9379i	−0.881370	−	1.52658i	−0.0315518	−	0.999502i	$-0.510045\pi$
$110$		0			0
$111$	8.02073	+	0.647577i	0.761294	+	0.0614653i
$112$	1.73603	−	0.896399i	0.164039	−	0.0847018i
$113$	−4.37678			−0.411733			−0.205866	−	0.978580i	$-0.566001\pi$
$113$	−4.37678			−0.411733			−0.205866	+	0.978580i	$0.566001\pi$
$114$	9.86079	−	14.2855i	0.923548	−	1.33796i
$115$		0			0
$116$	23.4245	−	13.5241i	2.17491	−	1.25568i
$117$	9.63771	−	11.8036i	0.891007	−	1.09124i
$118$	31.3250			2.88370
$119$	11.7785	+	0.553477i	1.07973	+	0.0507372i
$120$		0			0
$121$	−3.68664	+	6.38545i	−0.335149	+	0.580495i
$122$	3.41058	−	1.96910i	0.308779	−	0.178274i
$123$	0.392489	−	0.186234i	0.0353895	−	0.0167921i
$124$	−14.7445	−	8.51273i	−1.32409	−	0.764466i
$125$		0			0
$126$	−3.69002	+	17.4768i	−0.328733	+	1.55696i
$127$		−	12.7846i		−	1.13445i	−0.823564	−	0.567223i	$-0.808018\pi$
$127$		−	12.7846i		−	1.13445i	0.823564	−	0.567223i	$-0.191982\pi$
$128$	8.22419	−	14.2447i	0.726922	−	1.25907i
$129$	6.85875	+	14.4549i	0.603880	+	1.27268i
$130$		0			0
$131$	2.59617	−	4.49669i	0.226828	−	0.392878i	−0.730038	−	0.683406i	$-0.760498\pi$
$131$	2.59617	−	4.49669i	0.226828	−	0.392878i	0.956866	+	0.290528i	$0.0938311\pi$
$132$	10.0750	+	0.813434i	0.876916	+	0.0708003i
$133$	−5.40576	−	10.4692i	−0.468739	−	0.907791i
$134$		−	18.6725i		−	1.61306i
$135$		0			0
$136$	9.24478	−	5.33748i	0.792734	−	0.457685i
$137$	−6.74170	−	11.6770i	−0.575982	−	0.997630i	−0.995934	−	0.0900838i	$-0.971287\pi$
$137$	−6.74170	−	11.6770i	−0.575982	−	0.997630i	0.419952	−	0.907546i	$-0.362047\pi$
$138$	−9.13015	−	6.30221i	−0.777210	−	0.536480i
$139$			2.02188i			0.171493i	0.996317	+	0.0857466i	$0.0273276\pi$
$139$			2.02188i			0.171493i	−0.996317	+	0.0857466i	$0.972672\pi$
$140$		0			0
$141$	−5.31106	−	0.428804i	−0.447272	−	0.0361118i
$142$	18.8740	+	10.8969i	1.58387	+	0.914447i
$143$	−8.37736	+	4.83667i	−0.700550	+	0.404463i
$144$	−0.785551	−	2.07145i	−0.0654626	−	0.172621i
$145$		0			0
$146$	14.2161			1.17653
$147$	9.28825	+	7.79285i	0.766082	+	0.642743i
$148$		−	14.2365i		−	1.17023i
$149$	1.11049	+	0.641143i	0.0909750	+	0.0525244i	0.544797	−	0.838568i	$-0.316607\pi$
$149$	1.11049	+	0.641143i	0.0909750	+	0.0525244i	−0.453822	+	0.891092i	$0.649940\pi$
$150$		0			0
$151$	−3.50501	−	6.07085i	−0.285233	−	0.494039i	0.687432	−	0.726248i	$-0.258738\pi$
$151$	−3.50501	−	6.07085i	−0.285233	−	0.494039i	−0.972666	+	0.232210i	$0.925404\pi$
$152$	−9.23766	−	5.33336i	−0.749273	−	0.432593i
$153$	2.14500	−	13.1971i	0.173413	−	1.06693i
$154$	6.12408	−	9.54277i	0.493493	−	0.768978i
$155$		0			0
$156$	−22.1874	−	15.3152i	−1.77641	−	1.22620i
$157$	1.25671	+	2.17668i	0.100296	+	0.173718i	0.911807	−	0.410620i	$-0.134688\pi$
$157$	1.25671	+	2.17668i	0.100296	+	0.173718i	−0.811511	+	0.584338i	$0.801354\pi$
$158$	−3.58795	−	6.21452i	−0.285442	−	0.494401i
$159$	3.45175	+	2.38262i	0.273742	+	0.188954i
$160$		0			0
$161$	−6.69103	+	3.45492i	−0.527327	+	0.272286i
$162$	19.2111	+	6.41443i	1.50937	+	0.503965i
$163$	3.00033	+	1.73224i	0.235004	+	0.135680i	0.612879	−	0.790177i	$-0.290011\pi$
$163$	3.00033	+	1.73224i	0.235004	+	0.135680i	−0.377874	+	0.925857i	$0.623345\pi$
$164$	−0.384298	−	0.665624i	−0.0300087	−	0.0519765i
$165$		0			0
$166$	−17.5205	−	10.1155i	−1.35985	−	0.785112i
$167$		−	3.29851i		−	0.255246i	−0.991823	−	0.127623i	$-0.959265\pi$
$167$		−	3.29851i		−	0.255246i	0.991823	−	0.127623i	$-0.0407348\pi$
$168$	10.8872	+	1.39589i	0.839963	+	0.107696i
$169$	12.8011			0.984703
$170$		0			0
$171$	−12.4919	+	4.73729i	−0.955281	+	0.362269i
$172$	24.5141	−	14.1532i	1.86918	−	1.07917i
$173$	15.1038	+	8.72018i	1.14832	+	0.662983i	0.948477	−	0.316845i	$-0.102624\pi$
$173$	15.1038	+	8.72018i	1.14832	+	0.662983i	0.199843	+	0.979828i	$0.435957\pi$
$174$	−34.2935	−	2.76879i	−2.59979	−	0.209901i
$175$		0			0
$176$			1.40633i			0.106006i
$177$	−19.8417	−	13.6960i	−1.49139	−	1.02945i
$178$	12.2332	+	21.1885i	0.916917	+	1.58815i
$179$	−19.5347	+	11.2784i	−1.46009	+	0.842985i	−0.999015	−	0.0443755i	$-0.985870\pi$
$179$	−19.5347	+	11.2784i	−1.46009	+	0.842985i	−0.461077	+	0.887360i	$0.652537\pi$
$180$		0			0
$181$			3.48204i			0.258818i	0.991591	+	0.129409i	$0.0413080\pi$
$181$			3.48204i			0.258818i	−0.991591	+	0.129409i	$0.958692\pi$
$182$	−26.8725	+	13.8756i	−1.99192	+	1.02853i
$183$	−3.02124	−	0.243929i	−0.223336	−	0.0180317i
$184$	−3.40865	+	5.90396i	−0.251289	+	0.435245i
$185$		0			0
$186$	9.28369	+	19.5654i	0.680713	+	1.43461i
$187$	−4.24373	+	7.35035i	−0.310332	+	0.537511i
$188$			9.42692i			0.687529i
$189$	9.97855	−	9.45667i	0.725833	−	0.687871i
$190$		0			0
$191$	−8.27801	−	4.77931i	−0.598976	−	0.345819i	0.169663	−	0.985502i	$-0.445732\pi$
$191$	−8.27801	−	4.77931i	−0.598976	−	0.345819i	−0.768638	+	0.639683i	$0.779065\pi$
$192$	−20.4107	+	9.68474i	−1.47301	+	0.698936i
$193$	−4.99714	+	2.88510i	−0.359702	+	0.207674i	−0.668950	−	0.743307i	$-0.733256\pi$
$193$	−4.99714	+	2.88510i	−0.359702	+	0.207674i	0.309248	+	0.950981i	$0.399923\pi$
$194$	10.0648	−	17.4328i	0.722611	−	1.25160i
$195$		0			0
$196$	12.4200	−	17.4890i	0.887140	−	1.24922i
$197$	−4.34500			−0.309568			−0.154784	−	0.987948i	$-0.549468\pi$
$197$	−4.34500			−0.309568			−0.154784	+	0.987948i	$0.549468\pi$
$198$	−9.95895	−	8.13155i	−0.707752	−	0.577884i
$199$	−7.53338	+	4.34940i	−0.534027	+	0.308321i	−0.742655	−	0.669674i	$-0.766434\pi$
$199$	−7.53338	+	4.34940i	−0.534027	+	0.308321i	0.208628	+	0.977995i	$0.433100\pi$
$200$		0			0
$201$	−8.16403	+	11.8274i	−0.575846	+	0.834240i
$202$	−21.2144			−1.49264
$203$	−12.6131	+	19.6542i	−0.885269	+	1.37946i
$204$	−23.5781	−	1.90364i	−1.65080	−	0.133282i
$205$		0			0
$206$	−7.09004	−	12.2803i	−0.493987	−	0.855610i
$207$	3.02769	+	7.98381i	0.210439	+	0.554913i
$208$	1.87551	−	3.24848i	0.130043	−	0.225242i
$209$	8.48091			0.586637
$210$		0			0
$211$	10.6975			0.736446			0.368223	−	0.929737i	$-0.379966\pi$
$211$	10.6975			0.736446			0.368223	+	0.929737i	$0.379966\pi$
$212$	3.71021	−	6.42627i	0.254818	−	0.441358i
$213$	−7.19066	−	15.1544i	−0.492696	−	1.03836i
$214$	18.6860	+	32.3650i	1.27735	+	2.21243i
$215$		0			0
$216$	2.97885	−	12.0842i	0.202685	−	0.822225i
$217$	14.6835	+	0.689986i	0.996784	+	0.0468393i
$218$	41.4155			2.80501
$219$	−9.00464	−	6.21558i	−0.608477	−	0.420010i
$220$		0			0
$221$	19.6052	−	11.3190i	1.31879	−	0.761402i
$222$	−10.2870	+	14.9031i	−0.690421	+	1.00023i
$223$	−16.9483			−1.13494			−0.567471	−	0.823394i	$-0.692078\pi$
$223$	−16.9483			−1.13494			−0.567471	+	0.823394i	$0.692078\pi$
$224$	−0.801297	+	17.0523i	−0.0535389	+	1.13936i
$225$		0			0
$226$	4.92477	−	8.52996i	0.327591	−	0.567404i
$227$	2.10568	−	1.21572i	0.139759	−	0.0806899i	−0.428490	−	0.903546i	$-0.640954\pi$
$227$	2.10568	−	1.21572i	0.139759	−	0.0806899i	0.568249	+	0.822857i	$0.307621\pi$
$228$	10.1326	+	21.3546i	0.671049	+	1.41424i
$229$	−0.204081	−	0.117826i	−0.0134861	−	0.00778618i	0.493242	−	0.869892i	$-0.335812\pi$
$229$	−0.204081	−	0.117826i	−0.0134861	−	0.00778618i	−0.506728	+	0.862106i	$0.669145\pi$
$230$		0			0
$231$	−8.05139	+	3.36693i	−0.529743	+	0.221528i
$232$			21.1420i			1.38804i
$233$	5.54068	−	9.59675i	0.362982	−	0.628704i	−0.625468	−	0.780250i	$-0.715092\pi$
$233$	5.54068	−	9.59675i	0.362982	−	0.628704i	0.988450	+	0.151546i	$0.0484252\pi$
$234$	12.1598	+	32.0645i	0.794909	+	2.09612i
$235$		0			0
$236$	−21.3273	+	36.9401i	−1.38829	+	2.40459i
$237$	−0.444470	+	5.50510i	−0.0288714	+	0.357594i
$238$	−14.3319	+	22.3325i	−0.929001	+	1.44760i
$239$		−	9.67610i		−	0.625895i	−0.949770	−	0.312948i	$-0.898684\pi$
$239$		−	9.67610i		−	0.625895i	0.949770	−	0.312948i	$-0.101316\pi$
$240$		0			0
$241$	−13.9240	+	8.03902i	−0.896923	+	0.517839i	−0.876201	−	0.481947i	$-0.839930\pi$
$241$	−13.9240	+	8.03902i	−0.896923	+	0.517839i	−0.0207223	+	0.999785i	$0.506597\pi$
$242$	−8.29646	−	14.3699i	−0.533316	−	0.923731i
$243$	−9.36405	−	12.4625i	−0.600704	−	0.799471i
$244$			5.36258i			0.343304i
$245$		0			0
$246$	−0.0786773	+	0.974478i	−0.00501628	+	0.0621304i
$247$	−19.5901	−	11.3103i	−1.24649	−	0.719659i
$248$	11.5249	−	6.65390i	0.731832	−	0.422523i
$249$	6.67501	+	14.0676i	0.423012	+	0.891500i
$250$		0			0
$251$	−14.3809			−0.907716			−0.453858	−	0.891074i	$-0.649953\pi$
$251$	−14.3809			−0.907716			−0.453858	+	0.891074i	$0.649953\pi$
$252$	−18.0972	−	16.2504i	−1.14002	−	1.02368i
$253$		−	5.42031i		−	0.340772i
$254$	24.9160	+	14.3852i	1.56337	+	0.902611i
$255$		0			0
$256$	5.46442	+	9.46465i	0.341526	+	0.591541i
$257$	4.12202	+	2.37985i	0.257125	+	0.148451i	0.623022	−	0.782204i	$-0.285905\pi$
$257$	4.12202	+	2.37985i	0.257125	+	0.148451i	−0.365898	+	0.930655i	$0.619238\pi$
$258$	−35.8888	−	2.89759i	−2.23434	−	0.180396i
$259$	5.63944	+	10.9217i	0.350417	+	0.678642i
$260$		0			0
$261$	20.5114	+	16.7477i	1.26962	+	1.03666i
$262$	5.84244	+	10.1194i	0.360947	+	0.625179i
$263$	−2.82469	−	4.89251i	−0.174178	−	0.301685i	0.765698	−	0.643200i	$-0.222393\pi$
$263$	−2.82469	−	4.89251i	−0.174178	−	0.301685i	−0.939877	+	0.341514i	$0.889060\pi$
$264$	−4.48815	+	6.50207i	−0.276226	+	0.400175i
$265$		0			0
$266$	26.4861	+	1.24459i	1.62396	+	0.0763108i
$267$	1.51543	−	18.7697i	0.0927427	−	1.14869i
$268$	22.0196	+	12.7130i	1.34506	+	0.776570i
$269$	0.356044	+	0.616686i	0.0217084	+	0.0376000i	0.876676	−	0.481082i	$-0.159756\pi$
$269$	0.356044	+	0.616686i	0.0217084	+	0.0376000i	−0.854967	+	0.518682i	$0.826423\pi$
$270$		0			0
$271$	2.80074	+	1.61701i	0.170133	+	0.0982264i	0.582649	−	0.812724i	$-0.302016\pi$
$271$	2.80074	+	1.61701i	0.170133	+	0.0982264i	−0.412516	+	0.910951i	$0.635350\pi$
$272$		−	3.29117i		−	0.199557i
$273$	23.0881	+	2.96024i	1.39736	+	0.179162i
$274$	30.3432			1.83310
$275$		0			0
$276$	13.6481	−	6.47594i	0.821518	−	0.389806i
$277$	−19.8435	+	11.4567i	−1.19228	+	0.688364i	−0.958824	−	0.284002i	$-0.908338\pi$
$277$	−19.8435	+	11.4567i	−1.19228	+	0.688364i	−0.233459	+	0.972367i	$0.575004\pi$
$278$	−3.94046	−	2.27503i	−0.236333	−	0.136447i
$279$	2.67404	−	16.4521i	0.160091	−	0.984959i
$280$		0			0
$281$			12.0342i			0.717900i	0.933357	+	0.358950i	$0.116865\pi$
$281$			12.0342i			0.717900i	−0.933357	+	0.358950i	$0.883135\pi$
$282$	6.81174	−	9.86831i	0.405633	−	0.587649i
$283$	−8.95065	−	15.5030i	−0.532061	−	0.921556i	−0.999299	−	0.0374249i	$-0.988084\pi$
$283$	−8.95065	−	15.5030i	−0.532061	−	0.921556i	0.467239	−	0.884131i	$-0.345249\pi$
$284$	−25.7004	+	14.8381i	−1.52504	+	0.880481i
$285$		0			0
$286$		−	21.7690i		−	1.28723i
$287$	0.558491	+	0.358412i	0.0329667	+	0.0211564i
$288$	19.1062	+	3.10542i	1.12584	+	0.182989i
$289$	1.43141	−	2.47928i	0.0842008	−	0.145840i
$290$		0			0
$291$	−13.9972	+	6.64158i	−0.820529	+	0.389336i
$292$	−9.67889	+	16.7643i	−0.566414	+	0.981058i
$293$			8.87318i			0.518377i	0.965827	+	0.259188i	$0.0834550\pi$
$293$			8.87318i			0.518377i	−0.965827	+	0.259188i	$0.916545\pi$
$294$	−25.6388	+	9.33343i	−1.49528	+	0.544337i
$295$		0			0
$296$	9.63697	+	5.56391i	0.560138	+	0.323396i
$297$	2.75284	+	9.50491i	0.159736	+	0.551531i
$298$	−2.49906	+	1.44283i	−0.144767	+	0.0835811i
$299$	−7.22863	+	12.5204i	−0.418043	+	0.724071i
$300$		0			0
$301$	−13.1999	+	20.5685i	−0.760828	+	1.18555i
$302$	15.7754			0.907773
$303$	13.4375	+	9.27544i	0.771965	+	0.532860i
$304$	−2.84804	+	1.64432i	−0.163346	+	0.0943081i
$305$		0			0
$306$	23.3065	+	19.0299i	1.33234	+	1.08787i
$307$	8.99889			0.513594			0.256797	−	0.966465i	$-0.417333\pi$
$307$	8.99889			0.513594			0.256797	+	0.966465i	$0.417333\pi$
$308$	7.08380	+	13.7190i	0.403637	+	0.781710i
$309$	−0.878303	+	10.8784i	−0.0499649	+	0.618853i
$310$		0			0
$311$	−3.29851	−	5.71318i	−0.187041	−	0.323965i	0.757221	−	0.653159i	$-0.226556\pi$
$311$	−3.29851	−	5.71318i	−0.187041	−	0.323965i	−0.944262	+	0.329194i	$0.893223\pi$
$312$	19.0385	−	9.03364i	1.07784	−	0.511429i
$313$	−9.64215	+	16.7007i	−0.545007	+	0.943979i	0.453600	+	0.891205i	$0.350139\pi$
$313$	−9.64215	+	16.7007i	−0.545007	+	0.943979i	−0.998607	+	0.0527736i	$0.983194\pi$
$314$	−5.65621			−0.319198
$315$		0			0
$316$	9.77132			0.549680
$317$	−9.59278	+	16.6152i	−0.538784	+	0.933202i	0.460186	+	0.887823i	$0.347783\pi$
$317$	−9.59278	+	16.6152i	−0.538784	+	0.933202i	−0.998970	+	0.0453790i	$0.985550\pi$
$318$	−8.52745	+	4.04622i	−0.478195	+	0.226901i
$319$	−8.40481	−	14.5576i	−0.470579	−	0.815066i
$320$		0			0
$321$	2.31479	−	28.6704i	0.129199	−	1.60022i
$322$	0.795441	−	16.9277i	0.0443282	−	0.943345i
$323$	−19.8475			−1.10435
$324$	−20.6440	+	18.2876i	−1.14689	+	1.01598i
$325$		0			0
$326$	−6.75198	+	3.89826i	−0.373958	+	0.215905i
$327$	−26.2332	−	18.1078i	−1.45070	−	1.00136i
$328$	0.600767			0.0331718
$329$	−3.73425	−	7.23199i	−0.205876	−	0.398713i
$330$		0			0
$331$	−5.98753	+	10.3707i	−0.329104	+	0.570026i	−0.982334	−	0.187134i	$-0.940080\pi$
$331$	−5.98753	+	10.3707i	−0.329104	+	0.570026i	0.653230	+	0.757160i	$0.273413\pi$
$332$	23.8574	−	13.7741i	1.30934	−	0.755950i
$333$	13.0319	−	4.94207i	0.714144	−	0.270824i
$334$	6.42851	+	3.71150i	0.351752	+	0.203084i
$335$		0			0
$336$	2.05101	−	2.69172i	0.111892	−	0.146845i
$337$			12.6992i			0.691769i	0.938277	+	0.345885i	$0.112421\pi$
$337$			12.6992i			0.691769i	−0.938277	+	0.345885i	$0.887579\pi$
$338$	−14.4039	+	24.9483i	−0.783469	+	1.35701i
$339$	−6.84891	+	3.24977i	−0.371982	+	0.176503i
$340$		0			0
$341$	−5.29039	+	9.16323i	−0.286491	+	0.496217i
$342$	4.82341	−	29.6761i	0.260820	−	1.60470i
$343$	−2.60028	+	18.3368i	−0.140402	+	0.990095i
$344$			22.1255i			1.19293i
$345$		0			0
$346$	−33.9897	+	19.6240i	−1.82730	+	1.05499i
$347$	2.80486	+	4.85815i	0.150573	+	0.260799i	0.931438	−	0.363900i	$-0.118555\pi$
$347$	2.80486	+	4.85815i	0.150573	+	0.260799i	−0.780866	+	0.624699i	$0.785222\pi$
$348$	26.6136	−	38.5556i	1.42664	−	2.06680i
$349$		−	33.8725i		−	1.81315i	−0.422041	−	0.906577i	$-0.638686\pi$
$349$		−	33.8725i		−	1.81315i	0.422041	−	0.906577i	$-0.361314\pi$
$350$		0			0
$351$	6.31717	−	25.6266i	0.337186	−	1.36785i
$352$	−10.6415	−	6.14386i	−0.567192	−	0.327469i
$353$	31.8188	−	18.3706i	1.69354	−	0.977767i	0.741923	−	0.670485i	$-0.233914\pi$
$353$	31.8188	−	18.3706i	1.69354	−	0.977767i	0.951619	−	0.307281i	$-0.0994192\pi$
$354$	49.0182	−	23.2589i	2.60529	−	1.23619i
$355$		0			0
$356$	−33.3155			−1.76572
$357$	18.8423	−	7.87948i	0.997242	−	0.417026i
$358$		−	50.7619i		−	2.68285i
$359$	−21.1388	−	12.2045i	−1.11566	−	0.644127i	−0.175371	−	0.984502i	$-0.556113\pi$
$359$	−21.1388	−	12.2045i	−1.11566	−	0.644127i	−0.940290	+	0.340375i	$0.889446\pi$
$360$		0			0
$361$	0.416104	+	0.720714i	0.0219002	+	0.0379323i
$362$	−6.78619	−	3.91801i	−0.356674	−	0.205926i
$363$	−1.02775	+	12.7295i	−0.0539429	+	0.668124i
$364$	1.93302	−	41.1365i	0.101318	−	2.15614i
$365$		0			0
$366$	3.87491	−	5.61366i	0.202545	−	0.293431i
$367$	10.3327	+	17.8968i	0.539362	+	0.934203i	0.998938	+	0.0460646i	$0.0146680\pi$
$367$	10.3327	+	17.8968i	0.539362	+	0.934203i	−0.459576	+	0.888138i	$0.651999\pi$
$368$	1.05091	+	1.82024i	0.0547827	+	0.0948864i
$369$	0.475899	−	0.582848i	0.0247743	−	0.0303418i
$370$		0			0
$371$	−0.300725	+	6.39971i	−0.0156129	+	0.332256i
$372$	−29.3933	−	2.37316i	−1.52397	−	0.123042i
$373$	18.0759	+	10.4361i	0.935936	+	0.540363i	0.888684	−	0.458520i	$-0.151620\pi$
$373$	18.0759	+	10.4361i	0.935936	+	0.540363i	0.0472520	+	0.998883i	$0.484954\pi$
$374$	−9.55013	−	16.5413i	−0.493825	−	0.855331i
$375$		0			0
$376$	−6.38128	−	3.68424i	−0.329090	−	0.190000i
$377$			44.8353i			2.30914i
$378$	7.20230	+	30.0880i	0.370446	+	1.54756i
$379$	27.0384			1.38887			0.694435	−	0.719556i	$-0.255655\pi$
$379$	27.0384			1.38887			0.694435	+	0.719556i	$0.255655\pi$
$380$		0			0
$381$	−9.49256	−	20.0056i	−0.486319	−	1.02492i
$382$	18.6289	−	10.7554i	0.953138	−	0.550295i
$383$	−5.48580	−	3.16723i	−0.280311	−	0.161838i	0.353253	−	0.935528i	$-0.385076\pi$
$383$	−5.48580	−	3.16723i	−0.280311	−	0.161838i	−0.633564	+	0.773690i	$0.718409\pi$
$384$	2.29272	−	28.3970i	0.117000	−	1.44913i
$385$		0			0
$386$		−	12.9853i		−	0.660936i
$387$	21.4656	+	17.5268i	1.09116	+	0.890935i
$388$	13.7051	+	23.7379i	0.695770	+	1.20511i
$389$	−10.7869	+	6.22784i	−0.546919	+	0.315764i	−0.747879	−	0.663836i	$-0.768927\pi$
$389$	−10.7869	+	6.22784i	−0.546919	+	0.315764i	0.200959	+	0.979600i	$0.435594\pi$
$390$		0			0
$391$			12.6849i			0.641503i
$392$	6.98471	+	15.2424i	0.352781	+	0.769858i
$393$	0.723752	−	8.96422i	0.0365085	−	0.452185i
$394$	4.88902	−	8.46803i	0.246305	−	0.426613i
$395$		0			0
$396$	16.3696	−	6.20782i	0.822604	−	0.311955i
$397$	14.2381	−	24.6611i	0.714591	−	1.23771i	−0.248527	−	0.968625i	$-0.579946\pi$
$397$	14.2381	−	24.6611i	0.714591	−	1.23771i	0.963117	−	0.269082i	$-0.0867203\pi$
$398$		−	19.5759i		−	0.981250i
$399$	−16.2325	−	12.3686i	−0.812640	−	0.619207i
$400$		0			0
$401$	−12.7515	−	7.36207i	−0.636779	−	0.367644i	0.146594	−	0.989197i	$-0.453169\pi$
$401$	−12.7515	−	7.36207i	−0.636779	−	0.367644i	−0.783373	+	0.621552i	$0.786502\pi$
$402$	−13.8644	−	29.2192i	−0.691491	−	1.45732i
$403$	24.4405	−	14.1108i	1.21747	−	0.702907i
$404$	14.4437	−	25.0172i	0.718600	−	1.24465i
$405$		0			0
$406$	−24.1120	−	46.6970i	−1.19666	−	2.31753i
$407$	−8.84751			−0.438555
$408$	10.5034	−	15.2165i	0.519997	−	0.753330i
$409$	0.810609	−	0.468005i	0.0400820	−	0.0231414i	−0.479825	−	0.877364i	$-0.659300\pi$
$409$	0.810609	−	0.468005i	0.0400820	−	0.0231414i	0.519907	+	0.854223i	$0.325967\pi$
$410$		0			0
$411$	−19.2198	−	13.2667i	−0.948041	−	0.654399i
$412$	19.3088			0.951276
$413$	1.72865	−	36.7874i	0.0850615	−	1.81019i
$414$	−18.9665	−	3.08273i	−0.932154	−	0.151508i
$415$		0			0
$416$	16.3872	+	28.3834i	0.803446	+	1.39161i
$417$	1.50125	+	3.16389i	0.0735164	+	0.154936i
$418$	−9.54277	+	16.5286i	−0.466752	+	0.808438i
$419$	30.1515			1.47299			0.736497	−	0.676440i	$-0.236478\pi$
$419$	30.1515			1.47299			0.736497	+	0.676440i	$0.236478\pi$
$420$		0			0
$421$	36.3685			1.77249			0.886245	−	0.463217i	$-0.153305\pi$
$421$	36.3685			1.77249			0.886245	+	0.463217i	$0.153305\pi$
$422$	−12.0369	+	20.8485i	−0.585946	+	1.01489i
$423$	−8.62929	+	3.27247i	−0.419571	+	0.159113i
$424$	2.90005	+	5.02304i	0.140839	+	0.243940i
$425$		0			0
$426$	37.6255	+	3.03780i	1.82296	+	0.147182i
$427$	−2.12426	−	4.11397i	−0.102800	−	0.199089i
$428$	−50.8887			−2.45980
$429$	−9.51789	+	13.7888i	−0.459528	+	0.665728i
$430$		0			0
$431$	−11.9349	+	6.89063i	−0.574885	+	0.331910i	−0.759098	−	0.650976i	$-0.774360\pi$
$431$	−11.9349	+	6.89063i	−0.574885	+	0.331910i	0.184213	+	0.982886i	$0.441026\pi$
$432$	−2.76731	−	2.65819i	−0.133142	−	0.127892i
$433$	1.16840			0.0561499			0.0280750	−	0.999606i	$-0.491062\pi$
$433$	1.16840			0.0561499			0.0280750	+	0.999606i	$0.491062\pi$
$434$	−17.8667	+	27.8406i	−0.857630	+	1.33639i
$435$		0			0
$436$	−28.1974	+	48.8394i	−1.35041	+	2.33898i
$437$	10.9770	−	6.33756i	0.525100	−	0.303167i
$438$	22.2457	−	10.5555i	1.06294	−	0.504359i
$439$	−2.50353	−	1.44541i	−0.119487	−	0.0689858i	0.439065	−	0.898455i	$-0.355310\pi$
$439$	−2.50353	−	1.44541i	−0.119487	−	0.0689858i	−0.558552	+	0.829469i	$0.688643\pi$
$440$		0			0
$441$	20.3207	+	5.29793i	0.967654	+	0.252282i
$442$			50.9450i			2.42321i
$443$	8.25313	−	14.2948i	0.392118	−	0.679169i	−0.600611	−	0.799542i	$-0.705076\pi$
$443$	8.25313	−	14.2948i	0.392118	−	0.679169i	0.992729	+	0.120373i	$0.0384091\pi$
$444$	−10.5706	−	22.2776i	−0.501659	−	1.05725i
$445$		0			0
$446$	19.0703	−	33.0307i	0.903005	−	1.56405i
$447$	2.21378	+	0.178736i	0.104708	+	0.00845392i
$448$	−29.0433	−	18.6386i	−1.37217	−	0.880589i
$449$			25.9824i			1.22618i	0.790012	+	0.613092i	$0.210075\pi$
$449$			25.9824i			1.22618i	−0.790012	+	0.613092i	$0.789925\pi$
$450$		0			0
$451$	−0.413664	+	0.238829i	−0.0194787	+	0.0112460i
$452$	6.70598	+	11.6151i	0.315423	+	0.546329i
$453$	−9.99236	−	6.89737i	−0.469482	−	0.324067i
$454$			5.47172i			0.256801i
$455$		0			0
$456$	−18.4154	−	1.48682i	−0.862380	−	0.0696267i
$457$	1.30069	+	0.750953i	0.0608436	+	0.0351281i	0.530113	−	0.847927i	$-0.322149\pi$
$457$	1.30069	+	0.750953i	0.0608436	+	0.0351281i	−0.469270	+	0.883055i	$0.655483\pi$
$458$	0.459266	−	0.265158i	0.0214601	−	0.0123900i
$459$	−6.44235	−	22.2439i	−0.300703	−	1.03826i
$460$		0			0
$461$	−1.40468			−0.0654225			−0.0327113	−	0.999465i	$-0.510414\pi$
$461$	−1.40468			−0.0654225			−0.0327113	+	0.999465i	$0.510414\pi$
$462$	2.49762	−	19.4799i	0.116200	−	0.906289i
$463$		−	20.2056i		−	0.939033i	−0.882924	−	0.469516i	$-0.844428\pi$
$463$		−	20.2056i		−	0.939033i	0.882924	−	0.469516i	$-0.155572\pi$
$464$	5.64497	+	3.25912i	0.262061	+	0.151301i
$465$		0			0
$466$	12.4688	+	21.5966i	0.577607	+	1.00044i
$467$	33.4798	+	19.3296i	1.54926	+	0.894467i	0.998198	+	0.0600041i	$0.0191114\pi$
$467$	33.4798	+	19.3296i	1.54926	+	0.894467i	0.551064	+	0.834463i	$0.314222\pi$
$468$	−46.0911	−	7.49143i	−2.13056	−	0.346291i
$469$	−21.9286	−	1.03043i	−1.01257	−	0.0475809i
$470$		0			0
$471$	3.58272	+	2.47302i	0.165083	+	0.113951i
$472$	−16.6703	−	28.8739i	−0.767314	−	1.32903i
$473$	−8.79578	−	15.2347i	−0.404430	−	0.700494i
$474$	−10.2288	−	7.06060i	−0.469826	−	0.324304i
$475$		0			0
$476$	−16.5779	−	32.1059i	−0.759848	−	1.47157i
$477$	7.17050	+	1.16546i	0.328315	+	0.0533627i
$478$	18.8579	+	10.8876i	0.862539	+	0.497987i
$479$	−15.3467	−	26.5813i	−0.701210	−	1.21453i	−0.968042	−	0.250788i	$-0.919310\pi$
$479$	−15.3467	−	26.5813i	−0.701210	−	1.21453i	0.266832	−	0.963743i	$-0.414023\pi$
$480$		0			0
$481$	20.4369	+	11.7992i	0.931841	+	0.537999i
$482$		−	36.1822i		−	1.64805i
$483$	−7.90503	+	10.3745i	−0.359691	+	0.472055i
$484$	22.5943			1.02701
$485$		0			0
$486$	34.8249	−	4.22682i	1.57969	−	0.191733i
$487$	−25.7209	+	14.8500i	−1.16552	+	0.672915i	−0.952622	−	0.304158i	$-0.901625\pi$
$487$	−25.7209	+	14.8500i	−1.16552	+	0.672915i	−0.212902	+	0.977074i	$0.568292\pi$
$488$	−3.63004	−	2.09581i	−0.164324	−	0.0948727i
$489$	5.98120	+	0.482910i	0.270479	+	0.0218379i
$490$		0			0
$491$			7.13665i			0.322073i	0.986948	+	0.161036i	$0.0514836\pi$
$491$			7.13665i			0.322073i	−0.986948	+	0.161036i	$0.948516\pi$
$492$	−1.09559	−	0.756246i	−0.0493930	−	0.0340942i
$493$	19.6694	+	34.0684i	0.885866	+	1.53436i
$494$	44.0857	−	25.4529i	1.98351	−	1.14518i
$495$		0			0
$496$		−	4.10290i		−	0.184226i
$497$	13.8386	−	21.5639i	0.620747	−	0.967271i
$498$	−34.9273	−	2.81996i	−1.56513	−	0.126365i
$499$	−6.67079	+	11.5541i	−0.298626	+	0.517235i	−0.975822	−	0.218568i	$-0.929861\pi$
$499$	−6.67079	+	11.5541i	−0.298626	+	0.517235i	0.677196	+	0.735802i	$0.263195\pi$
$500$		0			0
$501$	−2.44915	−	5.16160i	−0.109420	−	0.230603i
$502$	16.1815	−	28.0272i	0.722216	−	1.25091i
$503$			30.4353i			1.35704i	0.734580	+	0.678522i	$0.237379\pi$
$503$			30.4353i			1.35704i	−0.734580	+	0.678522i	$0.762621\pi$
$504$	18.0730	−	5.89941i	0.805035	−	0.262780i
$505$		0			0
$506$	10.5637	+	6.09896i	0.469614	+	0.271132i
$507$	20.0316	−	9.50488i	0.889634	−	0.422126i
$508$	−33.9277	+	19.5882i	−1.50530	+	0.869084i
$509$	−16.4870	+	28.5563i	−0.730774	+	1.26574i	0.225779	+	0.974179i	$0.427507\pi$
$509$	−16.4870	+	28.5563i	−0.730774	+	1.26574i	−0.956553	+	0.291559i	$0.905826\pi$
$510$		0			0
$511$	0.784506	−	16.6950i	0.0347045	−	0.738545i
$512$	8.30237			0.366916
$513$	−16.0303	+	16.6883i	−0.707754	+	0.736808i
$514$	−9.27624	+	5.35564i	−0.409157	+	0.236227i
$515$		0			0
$516$	27.8516	−	40.3492i	1.22610	−	1.77627i
$517$	5.85853			0.257658
$518$	−27.6310	−	1.29839i	−1.21404	−	0.0570480i
$519$	30.1096	+	2.43099i	1.32167	+	0.106708i
$520$		0			0
$521$	12.7254	+	22.0411i	0.557511	+	0.965638i	0.997703	+	0.0677342i	$0.0215770\pi$
$521$	12.7254	+	22.0411i	0.557511	+	0.965638i	−0.440192	+	0.897904i	$0.645090\pi$
$522$	−55.7194	+	21.1304i	−2.43877	+	0.924850i
$523$	−12.0969	+	20.9524i	−0.528959	+	0.916184i	0.470470	+	0.882416i	$0.344084\pi$
$523$	−12.0969	+	20.9524i	−0.528959	+	0.916184i	−0.999430	+	0.0337685i	$0.989249\pi$
$524$	−15.9111			−0.695081
$525$		0			0
$526$	12.7134			0.554332
$527$	12.3809	−	21.4443i	0.539320	−	0.934129i
$528$	1.04420	+	2.20067i	0.0454431	+	0.0957717i
$529$	7.44955	+	12.9030i	0.323893	+	0.561000i
$530$		0			0
$531$	−41.2181	−	6.69940i	−1.78871	−	0.290729i
$532$	−19.5005	+	30.3864i	−0.845454	+	1.31742i
$533$	1.27403			0.0551844
$534$	34.8754	+	24.0732i	1.50921	+	1.04175i
$535$		0			0
$536$	−17.2114	+	9.93701i	−0.743419	+	0.429213i
$537$	−22.1943	+	32.1533i	−0.957753	+	1.38752i
$538$	−1.60249			−0.0690882
$539$	−10.8689	−	7.71861i	−0.468155	−	0.332464i
$540$		0			0
$541$	17.8529	−	30.9222i	0.767557	−	1.32945i	−0.171328	−	0.985214i	$-0.554806\pi$
$541$	17.8529	−	30.9222i	0.767557	−	1.32945i	0.938884	−	0.344233i	$-0.111861\pi$
$542$	−6.30282	+	3.63894i	−0.270729	+	0.156306i
$543$	2.58542	+	5.44880i	0.110951	+	0.233830i
$544$	24.9038	+	14.3782i	1.06774	+	0.616460i
$545$		0			0
$546$	−31.7481	+	41.6658i	−1.35869	+	1.78313i
$547$		−	14.1119i		−	0.603380i	−0.953406	−	0.301690i	$-0.902449\pi$
$547$		−	14.1119i		−	0.603380i	0.953406	−	0.301690i	$-0.0975507\pi$
$548$	−20.6589	+	35.7823i	−0.882505	+	1.52854i
$549$	−4.90884	+	1.86157i	−0.209504	+	0.0794499i
$550$		0			0
$551$	19.6542	−	34.0421i	0.837299	−	1.45024i
$552$	−0.950254	+	11.7696i	−0.0404455	+	0.500948i
$553$	−7.49620	+	3.87067i	−0.318771	+	0.164598i
$554$		−	51.5644i		−	2.19076i
$555$		0			0
$556$	5.36566	−	3.09787i	0.227555	−	0.131379i
$557$	15.7133	+	27.2162i	0.665792	+	1.15319i	0.979070	+	0.203524i	$0.0652395\pi$
$557$	15.7133	+	27.2162i	0.665792	+	1.15319i	−0.313278	+	0.949661i	$0.601427\pi$
$558$	29.0548	+	23.7234i	1.22999	+	1.00429i
$559$			46.9209i			1.98454i
$560$		0			0
$561$	−1.18305	+	14.6530i	−0.0499486	+	0.618651i
$562$	−23.4536	−	13.5409i	−0.989330	−	0.571190i
$563$	−27.7705	+	16.0333i	−1.17039	+	0.675723i	−0.953771	−	0.300535i	$-0.902835\pi$
$563$	−27.7705	+	16.0333i	−1.17039	+	0.675723i	−0.216615	+	0.976257i	$0.569502\pi$
$564$	6.99951	+	14.7515i	0.294733	+	0.621151i
$565$		0			0
$566$	40.2853			1.69332
$567$	8.59313	−	22.2072i	0.360877	−	0.932613i
$568$		−	23.1962i		−	0.973290i
$569$	17.1344	+	9.89257i	0.718313	+	0.414718i	0.814131	−	0.580681i	$-0.197214\pi$
$569$	17.1344	+	9.89257i	0.718313	+	0.414718i	−0.0958187	+	0.995399i	$0.530547\pi$
$570$		0			0
$571$	−12.9459	−	22.4229i	−0.541768	−	0.938370i	−0.998803	−	0.0489208i	$-0.984422\pi$
$571$	−12.9459	−	22.4229i	−0.541768	−	0.938370i	0.457035	−	0.889449i	$-0.348912\pi$
$572$	25.6711	+	14.8212i	1.07336	+	0.619707i
$573$	−16.5023	−	1.33236i	−0.689394	−	0.0556602i
$574$	−1.32693	+	0.685162i	−0.0553850	+	0.0285981i
$575$		0			0
$576$	−24.7482	+	30.3099i	−1.03118	+	1.26291i
$577$	11.7388	+	20.3323i	0.488694	+	0.846443i	0.999915	−	0.0130060i	$-0.00414005\pi$
$577$	11.7388	+	20.3323i	0.488694	+	0.846443i	−0.511221	+	0.859449i	$0.670807\pi$
$578$	3.22127	+	5.57940i	0.133987	+	0.232073i
$579$	−5.67748	+	8.22508i	−0.235948	+	0.341823i
$580$		0			0
$581$	−12.8463	+	20.0175i	−0.532952	+	0.830465i
$582$	2.80584	−	34.7524i	0.116306	−	1.44053i
$583$	−3.99372	−	2.30578i	−0.165403	−	0.0954955i
$584$	−7.56542	−	13.1037i	−0.313059	−	0.542234i
$585$		0			0
$586$	−17.2930	−	9.98415i	−0.714369	−	0.412441i
$587$			36.1962i			1.49398i	0.664837	+	0.746988i	$0.268501\pi$
$587$			36.1962i			1.49398i	−0.664837	+	0.746988i	$0.731499\pi$
$588$	6.44947	−	36.5892i	0.265972	−	1.50891i
$589$	−24.7427			−1.01950
$590$		0			0
$591$	−6.79918	+	3.22617i	−0.279681	+	0.132707i
$592$	2.97115	−	1.71540i	0.122114	−	0.0705024i
$593$	−12.9981	−	7.50446i	−0.533768	−	0.308171i	0.208781	−	0.977962i	$-0.433050\pi$
$593$	−12.9981	−	7.50446i	−0.533768	−	0.308171i	−0.742550	+	0.669791i	$0.766384\pi$
$594$	−21.6217	−	5.32994i	−0.887151	−	0.218690i
$595$		0			0
$596$		−	3.92937i		−	0.160953i
$597$	−8.55901	+	12.3996i	−0.350297	+	0.507483i
$598$	−16.2674	−	28.1760i	−0.665223	−	1.15220i
$599$	11.3793	−	6.56986i	0.464947	−	0.268437i	−0.249175	−	0.968458i	$-0.580159\pi$
$599$	11.3793	−	6.56986i	0.464947	−	0.268437i	0.714122	+	0.700021i	$0.246826\pi$
$600$		0			0
$601$		−	17.2898i		−	0.705267i	−0.935762	−	0.352633i	$-0.885286\pi$
$601$		−	17.2898i		−	0.705267i	0.935762	−	0.352633i	$-0.114714\pi$
$602$	−25.2337	−	48.8692i	−1.02845	−	1.99176i
$603$	−3.99344	+	24.5697i	−0.162625	+	1.00055i
$604$	−10.7406	+	18.6032i	−0.437027	+	0.756954i
$605$		0			0
$606$	−33.1970	+	15.7518i	−1.34854	+	0.639872i
$607$	0.225991	−	0.391428i	0.00917270	−	0.0158876i	−0.861403	−	0.507923i	$-0.830414\pi$
$607$	0.225991	−	0.391428i	0.00917270	−	0.0158876i	0.870575	+	0.492035i	$0.163747\pi$
$608$		−	28.7342i		−	1.16533i
$609$	−5.14408	+	40.1208i	−0.208449	+	1.62578i
$610$		0			0
$611$	−13.5326	−	7.81306i	−0.547471	−	0.316083i
$612$	−38.3091	+	14.5279i	−1.54855	+	0.587256i
$613$	1.34205	−	0.774834i	0.0542050	−	0.0312953i	−0.472653	−	0.881249i	$-0.656703\pi$
$613$	1.34205	−	0.774834i	0.0542050	−	0.0312953i	0.526858	+	0.849954i	$0.323370\pi$
$614$	−10.1256	+	17.5380i	−0.408636	+	0.707778i
$615$		0			0
$616$	−12.0552	−	0.566476i	−0.485716	−	0.0228240i
$617$	−42.6618			−1.71750			−0.858751	−	0.512394i	$-0.828759\pi$
$617$	−42.6618			−1.71750			−0.858751	+	0.512394i	$0.828759\pi$
$618$	−20.2129	−	13.9522i	−0.813081	−	0.561241i
$619$	−21.8956	+	12.6414i	−0.880058	+	0.508102i	−0.870677	−	0.491854i	$-0.836319\pi$
$619$	−21.8956	+	12.6414i	−0.880058	+	0.508102i	−0.00938032	+	0.999956i	$0.502986\pi$
$620$		0			0
$621$	10.6658	+	10.2452i	0.428004	+	0.411127i
$622$	14.8460			0.595270
$623$	25.5584	−	13.1971i	1.02398	−	0.528732i
$624$	0.522850	−	6.47589i	0.0209307	−	0.259243i
$625$		0			0
$626$	−21.6988	−	37.5834i	−0.867258	−	1.50214i
$627$	13.2712	−	6.29710i	0.530000	−	0.251482i
$628$	3.85098	−	6.67010i	0.153671	−	0.266166i
$629$	20.7055			0.825581
$630$		0			0
$631$	4.91791			0.195779			0.0978895	−	0.995197i	$-0.468791\pi$
$631$	4.91791			0.195779			0.0978895	+	0.995197i	$0.468791\pi$
$632$	−3.81883	+	6.61441i	−0.151905	+	0.263107i
$633$	16.7398	−	7.94292i	0.665346	−	0.315703i
$634$	−21.5877	−	37.3910i	−0.857357	−	1.48499i
$635$		0			0
$636$	1.03432	−	12.8109i	0.0410135	−	0.507983i
$637$	14.8123	+	32.3242i	0.586885	+	1.28073i
$638$	37.8285			1.49765
$639$	−22.5043	−	18.3749i	−0.890256	−	0.726900i
$640$		0			0
$641$	11.0323	−	6.36950i	0.435750	−	0.251580i	−0.266043	−	0.963961i	$-0.585716\pi$
$641$	11.0323	−	6.36950i	0.435750	−	0.251580i	0.701793	+	0.712381i	$0.252383\pi$
$642$	53.2714	+	36.7714i	2.10246	+	1.45125i
$643$	−2.51652			−0.0992419			−0.0496210	−	0.998768i	$-0.515801\pi$
$643$	−2.51652			−0.0992419			−0.0496210	+	0.998768i	$0.515801\pi$
$644$	19.4205	+	12.4631i	0.765275	+	0.491116i
$645$		0			0
$646$	22.3325	−	38.6811i	0.878662	−	1.52189i
$647$	−34.9974	+	20.2058i	−1.37589	+	0.794371i	−0.991662	−	0.128866i	$-0.958866\pi$
$647$	−34.9974	+	20.2058i	−1.37589	+	0.794371i	−0.384230	+	0.923238i	$0.625533\pi$
$648$	−4.31115	−	21.1215i	−0.169358	−	0.829731i
$649$	22.9571	+	13.2543i	0.901143	+	0.520275i
$650$		0			0
$651$	23.4896	−	9.82286i	0.920628	−	0.384988i
$652$		−	10.6164i		−	0.415770i
$653$	21.3460	−	36.9723i	0.835332	−	1.44684i	−0.0584277	−	0.998292i	$-0.518609\pi$
$653$	21.3460	−	36.9723i	0.835332	−	1.44684i	0.893760	−	0.448546i	$-0.148058\pi$
$654$	64.8082	−	30.7511i	2.53420	−	1.20246i
$655$		0			0
$656$	0.0926106	−	0.160406i	0.00361584	−	0.00626281i
$657$	−18.7058	−	3.04035i	−0.729783	−	0.118616i
$658$	18.2963	+	0.859751i	0.713265	+	0.0335166i
$659$			2.08754i			0.0813192i	0.999173	+	0.0406596i	$0.0129459\pi$
$659$			2.08754i			0.0813192i	−0.999173	+	0.0406596i	$0.987054\pi$
$660$		0			0
$661$	20.5058	−	11.8391i	0.797585	−	0.460486i	−0.0450412	−	0.998985i	$-0.514342\pi$
$661$	20.5058	−	11.8391i	0.797585	−	0.460486i	0.842626	+	0.538499i	$0.181009\pi$
$662$	−13.4744	−	23.3384i	−0.523698	−	0.907071i
$663$	22.2743	−	32.2693i	0.865063	−	1.25323i
$664$			21.5328i			0.835633i
$665$		0			0
$666$	−5.03191	+	30.9589i	−0.194983	+	1.19963i
$667$	−21.7570	−	12.5614i	−0.842433	−	0.486379i
$668$	−8.75359	+	5.05389i	−0.338687	+	0.195541i
$669$	−26.5212	+	12.5841i	−1.02537	+	0.486531i
$670$		0			0
$671$	3.33267			0.128656
$672$	11.4075	+	27.2790i	0.440054	+	1.05231i
$673$			29.6317i			1.14222i	0.820875	+	0.571108i	$0.193486\pi$
$673$			29.6317i			1.14222i	−0.820875	+	0.571108i	$0.806514\pi$
$674$	−24.7496	−	14.2892i	−0.953320	−	0.550400i
$675$		0			0
$676$	−19.6136	−	33.9717i	−0.754368	−	1.30660i
$677$	−29.5604	−	17.0667i	−1.13610	−	0.655927i	−0.190637	−	0.981661i	$-0.561055\pi$
$677$	−29.5604	−	17.0667i	−1.13610	−	0.655927i	−0.945462	+	0.325734i	$0.894389\pi$
$678$	1.37291	−	17.0046i	0.0527265	−	0.653057i
$679$	−19.9172	−	12.7819i	−0.764354	−	0.490525i
$680$		0			0
$681$	2.39236	−	3.46586i	0.0916755	−	0.132812i
$682$	−11.9056	−	20.6210i	−0.455887	−	0.789620i
$683$	−9.83481	−	17.0344i	−0.376319	−	0.651803i	0.614205	−	0.789147i	$-0.289477\pi$
$683$	−9.83481	−	17.0344i	−0.376319	−	0.651803i	−0.990523	+	0.137344i	$0.956143\pi$
$684$	31.7116	+	25.8927i	1.21252	+	0.990034i
$685$		0			0
$686$	−32.8110	−	25.7004i	−1.25273	−	0.981246i
$687$	−0.406838	−	0.0328473i	−0.0155219	−	0.00125320i
$688$	5.90756	+	3.41073i	0.225224	+	0.130033i
$689$	6.15006	+	10.6522i	0.234299	+	0.405817i
$690$		0			0
$691$	−0.800772	−	0.462326i	−0.0304628	−	0.0175877i	0.484691	−	0.874685i	$-0.338932\pi$
$691$	−0.800772	−	0.462326i	−0.0304628	−	0.0175877i	−0.515154	+	0.857098i	$0.672265\pi$
$692$		−	53.4433i		−	2.03161i
$693$	−10.0991	+	11.2468i	−0.383633	+	0.427232i
$694$	−12.6242			−0.479206
$695$		0			0
$696$	15.6980	+	33.0836i	0.595031	+	1.25403i
$697$	0.968081	−	0.558922i	0.0366687	−	0.0211707i
$698$	66.0145	+	38.1135i	2.49869	+	1.44262i
$699$	1.54462	−	19.1312i	0.0584228	−	0.723610i
$700$		0			0
$701$		−	0.206478i		−	0.00779858i	−0.999992	−	0.00389929i	$-0.998759\pi$
$701$		−	0.206478i		−	0.00779858i	0.999992	−	0.00389929i	$-0.00124119\pi$
$702$	42.8359	+	41.1468i	1.61674	+	1.55299i
$703$	−10.3447	−	17.9176i	−0.390160	−	0.675776i
$704$	21.5118	−	12.4199i	0.810758	−	0.468091i
$705$		0			0
$706$			82.6826i			3.11180i
$707$	−1.17071	+	24.9138i	−0.0440291	+	0.936980i
$708$	−5.94558	+	73.6405i	−0.223449	+	2.76758i
$709$	20.5452	−	35.5852i	0.771589	−	1.33643i	−0.165102	−	0.986276i	$-0.552795\pi$
$709$	20.5452	−	35.5852i	0.771589	−	1.33643i	0.936692	−	0.350156i	$-0.113871\pi$
$710$		0			0
$711$	3.39203	+	8.94455i	0.127211	+	0.335447i
$712$	13.0204	−	22.5520i	0.487960	−	0.845171i
$713$			15.8135i			0.592220i
$714$	−5.84506	+	45.5881i	−0.218746	+	1.70609i
$715$		0			0
$716$	59.8611	+	34.5608i	2.23712	+	1.29160i
$717$	−7.18453	−	15.1414i	−0.268311	−	0.565468i
$718$	47.5709	−	27.4651i	1.77533	−	1.02499i
$719$	4.36496	−	7.56034i	0.162786	−	0.281953i	−0.773081	−	0.634307i	$-0.781285\pi$
$719$	4.36496	−	7.56034i	0.162786	−	0.281953i	0.935867	+	0.352354i	$0.114619\pi$
$720$		0			0
$721$	−14.8130	+	7.64871i	−0.551665	+	0.284853i
$722$	−1.87281			−0.0696988
$723$	−15.8197	+	22.9183i	−0.588340	+	0.852340i
$724$	9.24065	−	5.33509i	0.343426	−	0.198277i
$725$		0			0
$726$	−23.6522	−	16.3263i	−0.877816	−	0.605925i
$727$	26.6400			0.988024			0.494012	−	0.869455i	$-0.335530\pi$
$727$	26.6400			0.988024			0.494012	+	0.869455i	$0.335530\pi$
$728$	27.0907	+	17.3855i	1.00405	+	0.644350i
$729$	−23.9066	−	12.5489i	−0.885430	−	0.464774i
$730$		0			0
$731$	20.5844	+	35.6532i	0.761341	+	1.31868i
$732$	3.98173	+	8.39152i	0.147169	+	0.310159i
$733$	15.6975	−	27.1888i	0.579800	−	1.00424i	−0.415702	−	0.909501i	$-0.636464\pi$
$733$	15.6975	−	27.1888i	0.579800	−	1.00424i	0.995502	−	0.0947418i	$-0.0302025\pi$
$734$	−46.5056			−1.71655
$735$		0			0
$736$	−18.3646			−0.676927
$737$	7.90073	−	13.6845i	0.291027	−	0.504074i
$738$	0.600436	+	1.58331i	0.0221023	+	0.0582824i
$739$	6.49377	+	11.2475i	0.238877	+	0.413747i	0.960392	−	0.278651i	$-0.0898873\pi$
$739$	6.49377	+	11.2475i	0.238877	+	0.413747i	−0.721515	+	0.692399i	$0.756554\pi$
$740$		0			0
$741$	−39.0530	−	3.15306i	−1.43465	−	0.115831i
$742$	−12.1341	−	7.78708i	−0.445457	−	0.285873i
$743$	20.9456			0.768419			0.384209	−	0.923246i	$-0.374474\pi$
$743$	20.9456			0.768419			0.384209	+	0.923246i	$0.374474\pi$
$744$	13.0940	−	18.9695i	0.480048	−	0.695455i
$745$		0			0
$746$	−40.6783	+	23.4856i	−1.48934	+	0.859869i
$747$	20.8905	+	17.0572i	0.764343	+	0.624091i
$748$	26.0085			0.950966
$749$	39.0400	−	20.1583i	1.42649	−	0.736570i
$750$		0			0
$751$	−2.17046	+	3.75935i	−0.0792014	+	0.137181i	−0.902906	−	0.429839i	$-0.858570\pi$
$751$	−2.17046	+	3.75935i	−0.0792014	+	0.137181i	0.823704	+	0.567020i	$0.191904\pi$
$752$	−1.96740	+	1.13588i	−0.0717437	+	0.0414212i
$753$	−22.5037	+	10.6779i	−0.820080	+	0.389123i
$754$	−87.3801	−	50.4489i	−3.18220	−	1.83724i
$755$		0			0
$756$	−40.3850	−	11.9918i	−1.46879	−	0.436139i
$757$		−	0.401257i		−	0.0145839i	−0.999973	−	0.00729196i	$-0.997679\pi$
$757$		−	0.401257i		−	0.0145839i	0.999973	−	0.00729196i	$-0.00232112\pi$
$758$	−30.4238	+	52.6955i	−1.10504	+	1.91399i
$759$	−4.02459	−	8.48185i	−0.146083	−	0.307872i
$760$		0			0
$761$	21.1371	−	36.6105i	0.766219	−	1.32713i	−0.173381	−	0.984855i	$-0.555469\pi$
$761$	21.1371	−	36.6105i	0.766219	−	1.32713i	0.939600	−	0.342275i	$-0.111197\pi$
$762$	49.6703	+	4.01028i	1.79937	+	0.145277i
$763$	2.28550	−	48.6375i	0.0827406	−	1.76080i
$764$			29.2909i			1.05971i
$765$		0			0
$766$	12.3453	−	7.12757i	0.446054	−	0.257530i
$767$	−35.3523	−	61.2320i	−1.27650	−	2.21096i
$768$	15.5784	+	10.7532i	0.562137	+	0.388023i
$769$		−	0.306962i		−	0.0110693i	−0.999985	−	0.00553466i	$-0.998238\pi$
$769$		−	0.306962i		−	0.0110693i	0.999985	−	0.00553466i	$-0.00176175\pi$
$770$		0			0
$771$	8.21730	+	0.663448i	0.295939	+	0.0238935i
$772$	15.3130	+	8.84096i	0.551126	+	0.318193i
$773$	−1.83633	+	1.06021i	−0.0660483	+	0.0381330i	−0.532661	−	0.846329i	$-0.678808\pi$
$773$	−1.83633	+	1.06021i	−0.0660483	+	0.0381330i	0.466612	+	0.884462i	$0.345474\pi$
$774$	−58.3113	+	22.1133i	−2.09596	+	0.794846i
$775$		0			0
$776$	−21.4249			−0.769110
$777$	16.9341	+	12.9033i	0.607509	+	0.462903i
$778$		−	28.0304i		−	1.00494i
$779$	−0.967334	−	0.558491i	−0.0346583	−	0.0200100i
$780$		0			0
$781$	9.22142	+	15.9720i	0.329968	+	0.571522i
$782$	−24.7218	−	14.2731i	−0.884049	−	0.510406i
$783$	44.5321	+	10.9775i	1.59145	+	0.392304i
$784$	5.14648	+	0.484741i	0.183803	+	0.0173122i
$785$		0			0
$786$	16.6561	+	11.4971i	0.594104	+	0.410089i
$787$	−10.2260	−	17.7119i	−0.364516	−	0.631360i	0.624183	−	0.781279i	$-0.285432\pi$
$787$	−10.2260	−	17.7119i	−0.364516	−	0.631360i	−0.988698	+	0.149919i	$0.952099\pi$
$788$	6.65730	+	11.5308i	0.237156	+	0.410767i
$789$	−8.05286	−	5.55860i	−0.286690	−	0.197892i
$790$		0			0
$791$	−9.74563	−	6.25427i	−0.346515	−	0.222376i
$792$	−2.19538	+	13.5071i	−0.0780094	+	0.479954i
$793$	−7.69814	−	4.44452i	−0.273369	−	0.157830i
$794$	32.0416	+	55.4977i	1.13711	+	1.96954i
$795$		0			0
$796$	23.0849	+	13.3281i	0.818223	+	0.472401i
$797$		−	21.2684i		−	0.753365i	−0.926342	−	0.376682i	$-0.877065\pi$
$797$		−	21.2684i		−	0.753365i	0.926342	−	0.376682i	$-0.122935\pi$
$798$	42.3703	−	17.7184i	1.49989	−	0.627224i
$799$	−13.7105			−0.485042
$800$		0			0
$801$	−11.5652	−	30.4966i	−0.408636	−	1.07755i
$802$	28.6961	−	16.5677i	1.01329	−	0.585025i
$803$	10.4185	+	6.01512i	0.367661	+	0.212269i
$804$	43.8963	+	3.54410i	1.54810	+	0.124991i
$805$		0			0
$806$			63.5100i			2.23704i
$807$	1.01504	+	0.700644i	0.0357310	+	0.0246638i
$808$	11.2898	+	19.5545i	0.397173	+	0.687924i
$809$	−19.3311	+	11.1608i	−0.679646	+	0.392394i	−0.799722	−	0.600371i	$-0.795020\pi$
$809$	−19.3311	+	11.1608i	−0.679646	+	0.392394i	0.120075	+	0.992765i	$0.461686\pi$
$810$		0			0
$811$			39.7633i			1.39628i	0.715962	+	0.698139i	$0.245988\pi$
$811$			39.7633i			1.39628i	−0.715962	+	0.698139i	$0.754012\pi$
$812$	71.4840	+	3.35906i	2.50860	+	0.117880i
$813$	5.58332	+	0.450786i	0.195816	+	0.0158097i
$814$	9.95527	−	17.2430i	0.348932	−	0.604368i
$815$		0			0
$816$	−2.44370	−	5.15012i	−0.0855468	−	0.180290i
$817$	20.5685	−	35.6257i	0.719601	−	1.24639i
$818$			2.10641i			0.0736488i
$819$	38.3269	−	12.5107i	1.33925	−	0.437160i
$820$		0			0
$821$	34.1580	+	19.7211i	1.19212	+	0.688272i	0.958787	−	0.284125i	$-0.0917030\pi$
$821$	34.1580	+	19.7211i	1.19212	+	0.688272i	0.233335	+	0.972397i	$0.425036\pi$
$822$	47.4819	−	22.5299i	1.65612	−	0.785820i
$823$	−41.3948	+	23.8993i	−1.44293	+	0.833077i	−0.998044	−	0.0625104i	$-0.980089\pi$
$823$	−41.3948	+	23.8993i	−1.44293	+	0.833077i	−0.444887	+	0.895587i	$0.646756\pi$
$824$	−7.54628	+	13.0705i	−0.262887	+	0.455334i
$825$		0			0
$826$	69.7503	+	44.7623i	2.42692	+	1.55748i
$827$	40.7367			1.41655			0.708277	−	0.705935i	$-0.249473\pi$
$827$	40.7367			1.41655			0.708277	+	0.705935i	$0.249473\pi$
$828$	16.5485	−	20.2675i	0.575101	−	0.704344i
$829$	18.8083	−	10.8590i	0.653238	−	0.377147i	−0.136458	−	0.990646i	$-0.543572\pi$
$829$	18.8083	−	10.8590i	0.653238	−	0.377147i	0.789696	+	0.613499i	$0.210238\pi$
$830$		0			0
$831$	−22.5451	+	32.6616i	−0.782082	+	1.13302i
$832$	−66.2536			−2.29693
$833$	25.4360	+	18.0635i	0.881303	+	0.625864i
$834$	−7.85536	−	0.634225i	−0.272009	−	0.0219614i
$835$		0			0
$836$	−12.9942	−	22.5067i	−0.449415	−	0.778410i
$837$	−8.03127	−	27.7301i	−0.277601	−	0.958494i
$838$	−33.9266	+	58.7626i	−1.17197	+	2.02992i
$839$	9.40638			0.324744			0.162372	−	0.986730i	$-0.448085\pi$
$839$	9.40638			0.324744			0.162372	+	0.986730i	$0.448085\pi$
$840$		0			0
$841$	−48.9115			−1.68660
$842$	−40.9220	+	70.8790i	−1.41026	+	2.44265i
$843$	8.93542	+	18.8315i	0.307752	+	0.648590i
$844$	−16.3904	−	28.3891i	−0.564182	−	0.977192i
$845$		0			0
$846$	3.33197	−	20.4999i	0.114555	−	0.704803i
$847$	−17.3335	+	8.95019i	−0.595587	+	0.307532i
$848$	1.78822			0.0614077
$849$	−25.5172	−	17.6136i	−0.875749	−	0.604498i
$850$		0			0
$851$	−11.4515	+	6.61152i	−0.392552	+	0.226640i
$852$	−29.1994	+	42.3017i	−1.00035	+	1.44923i
$853$	28.2296			0.966562			0.483281	−	0.875465i	$-0.339445\pi$
$853$	28.2296			0.966562			0.483281	+	0.875465i	$0.339445\pi$
$854$	10.4080	+	0.489076i	0.356154	+	0.0167358i
$855$		0			0
$856$	19.8884	−	34.4477i	0.679771	−	1.17740i
$857$	−14.5119	+	8.37845i	−0.495717	+	0.286202i	−0.726943	−	0.686698i	$-0.759060\pi$
$857$	−14.5119	+	8.37845i	−0.495717	+	0.286202i	0.231226	+	0.972900i	$0.425726\pi$
$858$	−16.1635	−	34.0647i	−0.551814	−	1.16295i
$859$	−8.38608	−	4.84171i	−0.286129	−	0.165197i	0.350066	−	0.936725i	$-0.386159\pi$
$859$	−8.38608	−	4.84171i	−0.286129	−	0.165197i	−0.636195	+	0.771528i	$0.719493\pi$
$860$		0			0
$861$	1.14006	+	0.146173i	0.0388533	+	0.00498157i
$862$		−	31.0135i		−	1.05632i
$863$	11.0039	−	19.0593i	0.374576	−	0.648785i	−0.615687	−	0.787990i	$-0.711122\pi$
$863$	11.0039	−	19.0593i	0.374576	−	0.648785i	0.990263	+	0.139206i	$0.0444549\pi$
$864$	32.2037	−	9.32691i	1.09559	−	0.317308i
$865$		0			0
$866$	−1.31469	+	2.27712i	−0.0446751	+	0.0773796i
$867$	0.399046	−	4.94248i	0.0135523	−	0.167855i
$868$	−20.6667	−	40.0244i	−0.701472	−	1.35852i
$869$		−	6.07256i		−	0.205998i
$870$		0			0
$871$	−36.4998	+	21.0732i	−1.23675	+	0.714036i
$872$	−22.0403	−	38.1749i	−0.746378	−	1.29276i
$873$	−16.9718	+	20.7859i	−0.574409	+	0.703496i
$874$			28.5242i			0.964847i
$875$		0			0
$876$	−2.69825	+	33.4199i	−0.0911655	+	1.12915i
$877$	18.2921	+	10.5609i	0.617679	+	0.356617i	0.775965	−	0.630776i	$-0.217263\pi$
$877$	18.2921	+	10.5609i	0.617679	+	0.356617i	−0.158286	+	0.987393i	$0.550597\pi$
$878$	5.63397	−	3.25277i	0.190137	−	0.109776i
$879$	6.58836	+	13.8850i	0.222220	+	0.468330i
$880$		0			0
$881$	44.3021			1.49258			0.746288	−	0.665623i	$-0.231834\pi$
$881$	44.3021			1.49258			0.746288	+	0.665623i	$0.231834\pi$
$882$	−33.1902	+	33.6421i	−1.11757	+	1.13279i
$883$		−	5.12282i		−	0.172397i	−0.996278	−	0.0861984i	$-0.972528\pi$
$883$		−	5.12282i		−	0.172397i	0.996278	−	0.0861984i	$-0.0274719\pi$
$884$	−60.0771	−	34.6855i	−2.02061	−	1.16660i
$885$		0			0
$886$	18.5729	+	32.1693i	0.623970	+	1.08075i
$887$	−6.70992	−	3.87397i	−0.225297	−	0.130075i	0.383104	−	0.923705i	$-0.374855\pi$
$887$	−6.70992	−	3.87397i	−0.225297	−	0.130075i	−0.608401	+	0.793630i	$0.708189\pi$
$888$	19.2114	+	1.55109i	0.644693	+	0.0520512i
$889$	18.2687	−	28.4670i	0.612713	−	0.954751i
$890$		0			0
$891$	11.3651	+	12.8296i	0.380746	+	0.429807i
$892$	25.9677	+	44.9774i	0.869464	+	1.50596i
$893$	6.84995	+	11.8645i	0.229225	+	0.397029i
$894$	−2.83930	+	4.11335i	−0.0949603	+	0.137571i
$895$		0			0
$896$	38.6678	−	19.9661i	1.29180	−	0.667022i
$897$	−2.01518	+	24.9595i	−0.0672848	+	0.833374i
$898$	−50.6374	−	29.2355i	−1.68979	−	0.975601i
$899$	24.5206	+	42.4710i	0.817809	+	1.41649i
$900$		0			0
$901$	9.34634	+	5.39611i	0.311372	+	0.179770i
$902$		−	1.07493i		−	0.0357912i
$903$	−5.38337	+	41.9871i	−0.179147	+	1.39724i
$904$	−10.4833			−0.348671
$905$		0			0
$906$	24.6858	−	11.7133i	0.820132	−	0.389148i
$907$	−21.2416	+	12.2639i	−0.705316	+	0.407215i	−0.809324	−	0.587362i	$-0.800167\pi$
$907$	−21.2416	+	12.2639i	−0.705316	+	0.407215i	0.104008	+	0.994576i	$0.466833\pi$
$908$	−6.45254	−	3.72538i	−0.214135	−	0.123631i
$909$	27.9145	+	4.53708i	0.925864	+	0.150486i
$910$		0			0
$911$		−	43.8824i		−	1.45389i	−0.686697	−	0.726944i	$-0.740940\pi$
$911$		−	43.8824i		−	1.45389i	0.686697	−	0.726944i	$-0.259060\pi$
$912$	−3.23579	+	4.68775i	−0.107148	+	0.155227i
$913$	−8.56014	−	14.8266i	−0.283299	−	0.490689i
$914$	−2.92708	+	1.68995i	−0.0968193	+	0.0558986i
$915$		0			0
$916$			0.722122i			0.0238596i
$917$	12.2064	−	6.30281i	0.403092	−	0.208137i
$918$	50.6004	+	12.4734i	1.67006	+	0.411684i
$919$	−7.85902	+	13.6122i	−0.259245	+	0.449026i	−0.966040	−	0.258393i	$-0.916807\pi$
$919$	−7.85902	+	13.6122i	−0.259245	+	0.449026i	0.706795	+	0.707419i	$0.250140\pi$
$920$		0			0
$921$	14.0817	−	6.68169i	0.464008	−	0.220169i
$922$	1.58056	−	2.73760i	0.0520528	−	0.0901581i
$923$		−	49.1915i		−	1.61916i
$924$	21.2713	+	16.2081i	0.699774	+	0.533207i
$925$		0			0
$926$	39.3789	+	22.7354i	1.29407	+	0.747132i
$927$	6.70288	+	17.6750i	0.220151	+	0.580525i
$928$	−49.3225	+	28.4764i	−1.61909	+	0.934783i
$929$	9.87128	−	17.0976i	0.323866	−	0.560952i	−0.657416	−	0.753528i	$-0.728351\pi$
$929$	9.87128	−	17.0976i	0.323866	−	0.560952i	0.981282	+	0.192575i	$0.0616839\pi$
$930$		0			0
$931$	2.92324	−	31.0360i	0.0958054	−	1.01716i
$932$	−33.9572			−1.11230
$933$	−9.40365	−	6.49101i	−0.307862	−	0.212506i
$934$	−75.3434	+	43.4995i	−2.46531	+	1.42335i
$935$		0			0
$936$	23.0844	−	28.2722i	0.754539	−	0.924106i
$937$	−37.1538			−1.21376			−0.606881	−	0.794793i	$-0.707580\pi$
$937$	−37.1538			−1.21376			−0.606881	+	0.794793i	$0.707580\pi$
$938$	26.6824	−	41.5774i	0.871210	−	1.35755i
$939$	−2.68801	+	33.2930i	−0.0877199	+	1.08648i
$940$		0			0
$941$	−16.1049	−	27.8945i	−0.525005	−	0.909336i	−0.999576	−	0.0291183i	$-0.990730\pi$
$941$	−16.1049	−	27.8945i	−0.525005	−	0.909336i	0.474571	−	0.880217i	$-0.342603\pi$
$942$	−8.85100	+	4.19975i	−0.288381	+	0.136835i
$943$	−0.356942	+	0.618241i	−0.0116236	+	0.0201327i
$944$	−10.2792			−0.334559
$945$		0			0
$946$	39.5882			1.28712
$947$	14.1852	−	24.5694i	0.460956	−	0.798400i	−0.538053	−	0.842911i	$-0.680840\pi$
$947$	14.1852	−	24.5694i	0.460956	−	0.798400i	0.999009	+	0.0445115i	$0.0141731\pi$
$948$	15.2904	−	7.25523i	0.496611	−	0.235639i
$949$	−16.0438	−	27.7886i	−0.520803	−	0.902057i
$950$		0			0
$951$	−2.67425	+	33.1226i	−0.0867185	+	1.07407i
$952$	28.2122	+	1.32570i	0.914361	+	0.0429662i
$953$	−28.4105			−0.920305			−0.460153	−	0.887840i	$-0.652205\pi$
$953$	−28.4105			−0.920305			−0.460153	+	0.887840i	$0.652205\pi$
$954$	−10.3397	+	12.6633i	−0.334759	+	0.409989i
$955$		0			0
$956$	−25.6785	+	14.8255i	−0.830501	+	0.479490i
$957$	−23.9611	−	16.5395i	−0.774552	−	0.534646i
$958$	69.0729			2.23164
$959$	1.67447	−	35.6344i	0.0540716	−	1.15069i
$960$		0			0
$961$	−0.0655266	+	0.113495i	−0.00211376	+	0.00366114i
$962$	−45.9913	+	26.5531i	−1.48282	+	0.856107i
$963$	−17.6656	−	46.5830i	−0.569265	−	1.50112i
$964$	42.6680	+	24.6344i	1.37424	+	0.793419i
$965$		0			0
$966$	−11.3241	−	27.0796i	−0.364349	−	0.871272i
$967$		−	42.3117i		−	1.36065i	−0.732909	−	0.680326i	$-0.761838\pi$
$967$		−	42.3117i		−	1.36065i	0.732909	−	0.680326i	$-0.238162\pi$
$968$	−8.83032	+	15.2946i	−0.283817	+	0.491586i
$969$	−31.0580	+	14.7368i	−0.997726	+	0.473415i
$970$		0			0
$971$	−11.7297	+	20.3164i	−0.376424	+	0.651985i	−0.990539	−	0.137231i	$-0.956180\pi$
$971$	−11.7297	+	20.3164i	−0.376424	+	0.651985i	0.614115	+	0.789216i	$0.289513\pi$
$972$	−18.7257	+	43.9451i	−0.600628	+	1.40954i
$973$	−2.88919	+	4.50205i	−0.0926233	+	0.144329i
$974$		−	66.8370i		−	2.14159i
$975$		0			0
$976$	−1.11917	+	0.646154i	−0.0358238	+	0.0206829i
$977$	17.5848	+	30.4577i	0.562587	+	0.974429i	0.997270	+	0.0738456i	$0.0235272\pi$
$977$	17.5848	+	30.4577i	0.562587	+	0.974429i	−0.434683	+	0.900584i	$0.643139\pi$
$978$	−7.67123	+	11.1135i	−0.245299	+	0.355370i
$979$			20.7045i			0.661720i
$980$		0			0
$981$	−54.4955	−	8.85745i	−1.73991	−	0.282796i
$982$	−13.9087	−	8.03020i	−0.443845	−	0.256254i
$983$	−36.0944	+	20.8391i	−1.15123	+	0.664665i	−0.949187	−	0.314711i	$-0.898092\pi$
$983$	−36.0944	+	20.8391i	−1.15123	+	0.664665i	−0.202046	+	0.979376i	$0.564759\pi$
$984$	0.940098	−	0.446071i	0.0299692	−	0.0142202i
$985$		0			0
$986$	−88.5285			−2.81932
$987$	−11.2132	−	8.54414i	−0.356921	−	0.271963i
$988$			69.3175i			2.20528i
$989$	−22.7690	−	13.1457i	−0.724013	−	0.418009i
$990$		0			0
$991$	−22.1571	−	38.3773i	−0.703844	−	1.21909i	−0.967107	−	0.254370i	$-0.918132\pi$
$991$	−22.1571	−	38.3773i	−0.703844	−	1.21909i	0.263262	−	0.964724i	$-0.415201\pi$
$992$	31.0460	+	17.9244i	0.985711	+	0.569101i
$993$	−1.66919	+	20.6741i	−0.0529700	+	0.656074i
$994$	26.4548	+	51.2340i	0.839094	+	1.62505i
$995$		0			0
$996$	27.1055	−	39.2682i	0.858869	−	1.24426i
$997$	−22.3412	−	38.6961i	−0.707552	−	1.22552i	−0.965763	−	0.259428i	$-0.916466\pi$
$997$	−22.3412	−	38.6961i	−0.707552	−	1.22552i	0.258210	−	0.966089i	$-0.416867\pi$
$998$	−15.0120	−	26.0016i	−0.475197	−	0.823065i
$999$	16.7232	−	17.4097i	0.529099	−	0.550819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.q.g.299.4		40
3.2	odd	2	inner	525.2.q.g.299.18		40
5.2	odd	4		525.2.t.h.26.2	✓	20
5.3	odd	4		525.2.t.i.26.9	yes	20
5.4	even	2	inner	525.2.q.g.299.17		40
7.3	odd	6	inner	525.2.q.g.374.3		40
15.2	even	4		525.2.t.h.26.9	yes	20
15.8	even	4		525.2.t.i.26.2	yes	20
15.14	odd	2	inner	525.2.q.g.299.3		40
21.17	even	6	inner	525.2.q.g.374.17		40
35.3	even	12		525.2.t.i.101.2	yes	20
35.17	even	12		525.2.t.h.101.9	yes	20
35.24	odd	6	inner	525.2.q.g.374.18		40
105.17	odd	12		525.2.t.h.101.2	yes	20
105.38	odd	12		525.2.t.i.101.9	yes	20
105.59	even	6	inner	525.2.q.g.374.4		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.q.g.299.3		40	15.14	odd	2	inner
525.2.q.g.299.4		40	1.1	even	1	trivial
525.2.q.g.299.17		40	5.4	even	2	inner
525.2.q.g.299.18		40	3.2	odd	2	inner
525.2.q.g.374.3		40	7.3	odd	6	inner
525.2.q.g.374.4		40	105.59	even	6	inner
525.2.q.g.374.17		40	21.17	even	6	inner
525.2.q.g.374.18		40	35.24	odd	6	inner
525.2.t.h.26.2	✓	20	5.2	odd	4
525.2.t.h.26.9	yes	20	15.2	even	4
525.2.t.h.101.2	yes	20	105.17	odd	12
525.2.t.h.101.9	yes	20	35.17	even	12
525.2.t.i.26.2	yes	20	15.8	even	4
525.2.t.i.26.9	yes	20	5.3	odd	4
525.2.t.i.101.2	yes	20	35.3	even	12
525.2.t.i.101.9	yes	20	105.38	odd	12

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.12521 + 1.94891i) q^{2} +(1.56483 - 0.742502i) q^{3} +(-1.53217 - 2.65380i) q^{4} +(-0.313682 + 3.88518i) q^{6} +(2.22667 + 1.42897i) q^{7} +2.39522 q^{8} +(1.89738 - 2.32378i) q^{9} +O(q^{10})\)	\(q+(-1.12521 + 1.94891i) q^{2} +(1.56483 - 0.742502i) q^{3} +(-1.53217 - 2.65380i) q^{4} +(-0.313682 + 3.88518i) q^{6} +(2.22667 + 1.42897i) q^{7} +2.39522 q^{8} +(1.89738 - 2.32378i) q^{9} +(-1.64925 + 0.952197i) q^{11} +(-4.36805 - 3.01511i) q^{12} +5.07948 q^{13} +(-5.29039 + 2.73170i) q^{14} +(0.369233 - 0.639530i) q^{16} +(3.85968 - 2.22839i) q^{17} +(2.39390 + 6.31256i) q^{18} +(-3.85670 - 2.22667i) q^{19} +(4.54537 + 0.582783i) q^{21} -4.28567i q^{22} +(-1.42310 + 2.46489i) q^{23} +(3.74811 - 1.77846i) q^{24} +(-5.71546 + 9.89947i) q^{26} +(1.24366 - 5.04513i) q^{27} +(0.380555 - 8.09857i) q^{28} +8.82675i q^{29} +(4.81162 - 2.77799i) q^{31} +(3.22615 + 5.58785i) q^{32} +(-1.87379 + 2.71460i) q^{33} +10.0296i q^{34} +(-9.07397 - 1.47484i) q^{36} +(4.02342 + 2.32292i) q^{37} +(8.67917 - 5.01092i) q^{38} +(7.94852 - 3.77153i) q^{39} +0.250819 q^{41} +(-6.25027 + 8.20277i) q^{42} +9.23735i q^{43} +(5.05389 + 2.91786i) q^{44} +(-3.20257 - 5.54701i) q^{46} +(-2.66417 - 1.53816i) q^{47} +(0.102934 - 1.27491i) q^{48} +(2.91610 + 6.36367i) q^{49} +(4.38516 - 6.35287i) q^{51} +(-7.78265 - 13.4799i) q^{52} +(1.21077 + 2.09711i) q^{53} +(8.43313 + 8.10060i) q^{54} +(5.33336 + 3.42269i) q^{56} +(-7.68839 - 0.620744i) q^{57} +(-17.2026 - 9.93190i) q^{58} +(-6.95983 - 12.0548i) q^{59} +(-1.51554 - 0.874995i) q^{61} +12.5032i q^{62} +(7.54544 - 2.46299i) q^{63} -13.0434 q^{64} +(-3.18212 - 6.70634i) q^{66} +(-7.18573 + 4.14868i) q^{67} +(-11.8274 - 6.82855i) q^{68} +(-0.396729 + 4.91379i) q^{69} -9.68436i q^{71} +(4.54465 - 5.56596i) q^{72} +(-3.15855 - 5.47076i) q^{73} +(-9.05434 + 5.22752i) q^{74} +13.6466i q^{76} +(-5.03300 - 0.236503i) q^{77} +(-1.59334 + 19.7347i) q^{78} +(-1.59436 + 2.76150i) q^{79} +(-1.79990 - 8.81818i) q^{81} +(-0.282223 + 0.488824i) q^{82} +8.98988i q^{83} +(-5.41770 - 12.9554i) q^{84} +(-18.0028 - 10.3939i) q^{86} +(6.55388 + 13.8124i) q^{87} +(-3.95033 + 2.28072i) q^{88} +(5.43599 - 9.41541i) q^{89} +(11.3103 + 7.25841i) q^{91} +8.72178 q^{92} +(5.46670 - 7.91972i) q^{93} +(5.99548 - 3.46149i) q^{94} +(9.19736 + 6.34861i) q^{96} -8.94486 q^{97} +(-15.6835 - 1.47721i) q^{98} +(-0.916566 + 5.63918i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 28 q^{4} + 14 q^{9}+O(q^{10}) \) 40 * q - 28 * q^4 + 14 * q^9	\( 40 q - 28 q^{4} + 14 q^{9} - 36 q^{16} - 18 q^{21} - 36 q^{24} + 84 q^{31} - 72 q^{36} - 16 q^{46} + 8 q^{49} + 42 q^{51} + 150 q^{54} - 180 q^{61} + 240 q^{64} + 12 q^{66} - 92 q^{79} + 58 q^{81} - 150 q^{84} - 60 q^{91} - 12 q^{94} + 270 q^{96} - 188 q^{99}+O(q^{100}) \) 40 * q - 28 * q^4 + 14 * q^9 - 36 * q^16 - 18 * q^21 - 36 * q^24 + 84 * q^31 - 72 * q^36 - 16 * q^46 + 8 * q^49 + 42 * q^51 + 150 * q^54 - 180 * q^61 + 240 * q^64 + 12 * q^66 - 92 * q^79 + 58 * q^81 - 150 * q^84 - 60 * q^91 - 12 * q^94 + 270 * q^96 - 188 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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