LMFDB - Embedded newform 525.2.q.g.299.18

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			299.18
Character	$\chi$	$=$	525.299
Dual form			525.2.q.g.374.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12521 - 1.94891i) q^{2} +(-1.42544 + 0.983931i) q^{3} +(-1.53217 - 2.65380i) q^{4} +(0.313682 + 3.88518i) q^{6} +(2.22667 + 1.42897i) q^{7} -2.39522 q^{8} +(1.06376 - 2.80507i) q^{9} +O(q^{10})$	\(q+(1.12521 - 1.94891i) q^{2} +(-1.42544 + 0.983931i) q^{3} +(-1.53217 - 2.65380i) q^{4} +(0.313682 + 3.88518i) q^{6} +(2.22667 + 1.42897i) q^{7} -2.39522 q^{8} +(1.06376 - 2.80507i) q^{9} +(1.64925 - 0.952197i) q^{11} +(4.79518 + 2.27529i) q^{12} +5.07948 q^{13} +(5.29039 - 2.73170i) q^{14} +(0.369233 - 0.639530i) q^{16} +(-3.85968 + 2.22839i) q^{17} +(-4.26988 - 5.22946i) q^{18} +(-3.85670 - 2.22667i) q^{19} +(-4.57999 + 0.153979i) q^{21} -4.28567i q^{22} +(1.42310 - 2.46489i) q^{23} +(3.41425 - 2.35673i) 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} +(-1.41402 + 2.98005i) q^{33} +10.0296i q^{34} +(-9.07397 + 1.47484i) q^{36} +(4.02342 + 2.32292i) q^{37} +(-8.67917 + 5.01092i) q^{38} +(-7.24050 + 4.99786i) q^{39} -0.250819 q^{41} +(-4.85334 + 9.09926i) 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} +(3.30916 - 6.97409i) q^{51} +(-7.78265 - 13.4799i) q^{52} +(-1.21077 - 2.09711i) q^{53} +(11.2319 + 3.25301i) 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} +(6.37700 - 4.72588i) q^{63} -13.0434 q^{64} +(4.21680 + 6.10897i) q^{66} +(-7.18573 + 4.14868i) q^{67} +(11.8274 + 6.82855i) q^{68} +(0.396729 + 4.91379i) q^{69} +9.68436i q^{71} +(-2.54794 + 6.71876i) 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} +(-6.73682 - 5.96785i) q^{81} +(-0.282223 + 0.488824i) q^{82} -8.98988i q^{83} +(7.42597 + 11.9185i) q^{84} +(18.0028 + 10.3939i) q^{86} +(8.68491 + 12.5820i) q^{87} +(-3.95033 + 2.28072i) q^{88} +(-5.43599 + 9.41541i) q^{89} +(11.3103 + 7.25841i) q^{91} -8.72178 q^{92} +(-4.12533 + 8.69416i) q^{93} +(5.99548 - 3.46149i) q^{94} +(10.0967 + 4.79084i) 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	$-0.540468\pi$
$2$	1.12521	−	1.94891i	0.795640	−	1.37809i	0.922432	−	0.386160i	$-0.126199\pi$
$3$	−1.42544	+	0.983931i	−0.822978	+	0.568073i
$3$	−1.42544	+	0.983931i	−0.822978	+	0.568073i
$4$	−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
$9$	1.06376	−	2.80507i	0.354587	−	0.935023i
$10$		0			0
$11$	1.64925	−	0.952197i	0.497269	−	0.287098i	−0.230316	−	0.973116i	$-0.573976\pi$
$11$	1.64925	−	0.952197i	0.497269	−	0.287098i	0.727585	+	0.686018i	$0.240643\pi$
$12$	4.79518	+	2.27529i	1.38425	+	0.656819i
$13$	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	−0.888739	−	0.458414i	$-0.848418\pi$
$17$	−3.85968	+	2.22839i	−0.936110	+	0.540463i	−0.0473710	+	0.998877i	$0.515084\pi$
$18$	−4.26988	−	5.22946i	−1.00642	−	1.23259i
$19$	−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
$21$	−4.57999	+	0.153979i	−0.999435	+	0.0336010i
$22$		−	4.28567i		−	0.913708i
$23$	1.42310	−	2.46489i	0.296738	−	0.513965i	−0.678650	−	0.734462i	$-0.737435\pi$
$23$	1.42310	−	2.46489i	0.296738	−	0.513965i	0.975388	+	0.220497i	$0.0707679\pi$
$24$	3.41425	−	2.35673i	0.696930	−	0.481066i
$25$		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	$-0.694227\pi$
$29$		−	8.82675i		−	1.63909i	0.573018	−	0.819543i	$-0.305773\pi$
$30$		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
$33$	−1.41402	+	2.98005i	−0.246149	+	0.518761i
$34$			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
$39$	−7.24050	+	4.99786i	−1.15941	+	0.800298i
$40$		0			0
$41$	−0.250819			−0.0391713			−0.0195857	−	0.999808i	$-0.506235\pi$
$41$	−0.250819			−0.0391713			−0.0195857	+	0.999808i	$0.506235\pi$
$42$	−4.85334	+	9.09926i	−0.748886	+	1.40405i
$43$			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	0.681557	−	0.731765i	$-0.261303\pi$
$47$	2.66417	+	1.53816i	0.388610	+	0.224364i	−0.292948	+	0.956128i	$0.594636\pi$
$48$	0.102934	+	1.27491i	0.0148572	+	0.184018i
$49$	2.91610	+	6.36367i	0.416586	+	0.909096i
$50$		0			0
$51$	3.30916	−	6.97409i	0.463376	−	0.976568i
$52$	−7.78265	−	13.4799i	−1.07926	−	1.86933i
$53$	−1.21077	−	2.09711i	−0.166312	−	0.288060i	0.770809	−	0.637067i	$-0.219852\pi$
$53$	−1.21077	−	2.09711i	−0.166312	−	0.288060i	−0.937120	+	0.349007i	$0.886519\pi$
$54$	11.2319	+	3.25301i	1.52847	+	0.442679i
$55$		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	$0.194283\pi$
$59$	6.95983	+	12.0548i	0.906093	+	1.56940i	0.0866494	+	0.996239i	$0.472384\pi$
$60$		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
$63$	6.37700	−	4.72588i	0.803426	−	0.595405i
$64$	−13.0434			−1.63042
$65$		0			0
$66$	4.21680	+	6.10897i	0.519052	+	0.751962i
$67$	−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	$0.194866\pi$
$71$			9.68436i			1.14932i	−0.818392	+	0.574661i	$0.805134\pi$
$72$	−2.54794	+	6.71876i	−0.300278	+	0.791814i
$73$	−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
$81$	−6.73682	−	5.96785i	−0.748536	−	0.663094i
$82$	−0.282223	+	0.488824i	−0.0311663	+	0.0539816i
$83$		−	8.98988i		−	0.986768i	−0.869812	−	0.493384i	$-0.835760\pi$
$83$		−	8.98988i		−	0.986768i	0.869812	−	0.493384i	$-0.164240\pi$
$84$	7.42597	+	11.9185i	0.810240	+	1.30041i
$85$		0			0
$86$	18.0028	+	10.3939i	1.94129	+	1.12080i
$87$	8.68491	+	12.5820i	0.931120	+	1.34893i
$88$	−3.95033	+	2.28072i	−0.421106	+	0.243126i
$89$	−5.43599	+	9.41541i	−0.576213	+	0.998031i	0.419695	+	0.907665i	$0.362137\pi$
$89$	−5.43599	+	9.41541i	−0.576213	+	0.998031i	−0.995909	+	0.0903658i	$0.971196\pi$
$90$		0			0
$91$	11.3103	+	7.25841i	1.18564	+	0.760889i
$92$	−8.72178			−0.909308
$93$	−4.12533	+	8.69416i	−0.427777	+	0.901543i
$94$	5.99548	−	3.46149i	0.618387	−	0.357026i
$95$		0			0
$96$	10.0967	+	4.79084i	1.03049	+	0.488963i
$97$	−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	0.530365	−	0.847769i	$-0.322055\pi$
$101$	−4.71346	−	8.16395i	−0.469007	−	0.812344i	−0.999372	+	0.0354254i	$0.988721\pi$
$102$	−9.86840	−	14.2966i	−0.977117	−	1.41557i
$103$	−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	$0.463279\pi$
$107$	−8.30336	+	14.3818i	−0.802716	+	1.39034i	−0.917822	+	0.396991i	$0.870054\pi$
$108$	11.4833	−	11.0305i	1.10498	−	1.06141i
$109$	−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	$-0.433999\pi$
$113$	4.37678			0.411733			0.205866	+	0.978580i	$0.433999\pi$
$114$	7.44124	−	15.6825i	0.696936	−	1.46880i
$115$		0			0
$116$	−23.4245	+	13.5241i	−2.17491	+	1.25568i
$117$	5.40336	−	14.2483i	0.499540	−	1.31726i
$118$	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
$123$	0.357528	−	0.246788i	0.0322372	−	0.0222522i
$124$	−14.7445	−	8.51273i	−1.32409	−	0.764466i
$125$		0			0
$126$	−2.03489	−	17.7458i	−0.181283	−	1.58092i
$127$		−	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
$129$	−9.08891	−	13.1673i	−0.800234	−	1.15932i
$130$		0			0
$131$	−2.59617	+	4.49669i	−0.226828	+	0.392878i	−0.956866	−	0.290528i	$-0.906169\pi$
$131$	−2.59617	+	4.49669i	−0.226828	+	0.392878i	0.730038	+	0.683406i	$0.239502\pi$
$132$	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	$0.0287135\pi$
$137$	6.74170	+	11.6770i	0.575982	+	0.997630i	−0.419952	+	0.907546i	$0.637953\pi$
$138$	10.0229	+	4.75583i	0.853210	+	0.404843i
$139$			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
$144$	−1.40115	−	1.71603i	−0.116762	−	0.143003i
$145$		0			0
$146$	−14.2161			−1.17653
$147$	−10.4181	−	6.20179i	−0.859274	−	0.511515i
$148$		−	14.2365i		−	1.17023i
$149$	−1.11049	−	0.641143i	−0.0909750	−	0.0525244i	0.453822	−	0.891092i	$-0.350060\pi$
$149$	−1.11049	−	0.641143i	−0.0909750	−	0.0525244i	−0.544797	+	0.838568i	$0.683393\pi$
$150$		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
$156$	24.3570	+	11.5573i	1.95012	+	0.925323i
$157$	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
$159$	3.78928	+	1.79799i	0.300510	+	0.142590i
$160$		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	$0.0407348\pi$
$167$			3.29851i			0.255246i	−0.991823	+	0.127623i	$0.959265\pi$
$168$	10.9701	−	0.368814i	0.846360	−	0.0284546i
$169$	12.8011			0.984703
$170$		0			0
$171$	−10.3486	+	8.44967i	−0.791375	+	0.646163i
$172$	24.5141	−	14.1532i	1.86918	−	1.07917i
$173$	−15.1038	−	8.72018i	−1.14832	−	0.662983i	−0.199843	−	0.979828i	$-0.564043\pi$
$173$	−15.1038	−	8.72018i	−1.14832	−	0.662983i	−0.948477	+	0.316845i	$0.897376\pi$
$174$	34.2935	−	2.76879i	2.59979	−	0.209901i
$175$		0			0
$176$		−	1.40633i		−	0.106006i
$177$	−21.7819	−	10.3354i	−1.63723	−	0.776855i
$178$	12.2332	+	21.1885i	0.916917	+	1.58815i
$179$	19.5347	−	11.2784i	1.46009	−	0.842985i	0.461077	−	0.887360i	$-0.347463\pi$
$179$	19.5347	−	11.2784i	1.46009	−	0.842985i	0.999015	+	0.0443755i	$0.0141298\pi$
$180$		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
$186$	12.3023	+	17.8226i	0.902050	+	1.30682i
$187$	−4.24373	+	7.35035i	−0.310332	+	0.537511i
$188$		−	9.42692i		−	0.687529i
$189$	−4.44009	+	13.0110i	−0.322969	+	0.946409i
$190$		0			0
$191$	8.27801	+	4.77931i	0.598976	+	0.345819i	0.768638	−	0.639683i	$-0.220935\pi$
$191$	8.27801	+	4.77931i	0.598976	+	0.345819i	−0.169663	+	0.985502i	$0.554268\pi$
$192$	18.5926	−	12.8338i	1.34180	−	0.926198i
$193$	−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	$-0.450532\pi$
$197$	4.34500			0.309568			0.154784	+	0.987948i	$0.450532\pi$
$198$	−12.0216	−	4.55893i	−0.854338	−	0.323989i
$199$	−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
$201$	6.16081	−	12.9840i	0.434550	−	0.915817i
$202$	−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
$207$	−5.40034	−	6.61396i	−0.375350	−	0.459702i
$208$	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
$213$	−9.52873	−	13.8045i	−0.652898	−	0.945867i
$214$	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
$219$	9.88517	+	4.69046i	0.667978	+	0.316952i
$220$		0			0
$221$	−19.6052	+	11.3190i	−1.31879	+	0.761402i
$222$	−7.76290	+	16.3604i	−0.521012	+	1.09804i
$223$	−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	−0.568249	−	0.822857i	$-0.692379\pi$
$227$	−2.10568	+	1.21572i	−0.139759	+	0.0806899i	0.428490	+	0.903546i	$0.359046\pi$
$228$	−13.4273	−	19.4524i	−0.889244	−	1.28827i
$229$	−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
$231$	−7.40695	+	4.61500i	−0.487341	+	0.303645i
$232$			21.1420i			1.38804i
$233$	−5.54068	+	9.59675i	−0.362982	+	0.628704i	−0.988450	−	0.151546i	$-0.951575\pi$
$233$	−5.54068	+	9.59675i	−0.362982	+	0.628704i	0.625468	+	0.780250i	$0.284908\pi$
$234$	−21.6888	−	26.5629i	−1.41784	−	1.73647i
$235$		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	$0.101316\pi$
$239$			9.67610i			0.625895i	−0.949770	+	0.312948i	$0.898684\pi$
$240$		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
$243$	15.4749	+	1.87825i	0.992715	+	0.120490i
$244$			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
$249$	8.84542	+	12.8145i	0.560556	+	0.812089i
$250$		0			0
$251$	14.3809			0.907716			0.453858	−	0.891074i	$-0.350047\pi$
$251$	14.3809			0.907716			0.453858	+	0.891074i	$0.350047\pi$
$252$	−22.3122	−	9.68243i	−1.40554	−	0.609936i
$253$		−	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	0.365898	−	0.930655i	$-0.380762\pi$
$257$	−4.12202	−	2.37985i	−0.257125	−	0.148451i	−0.623022	+	0.782204i	$0.714095\pi$
$258$	−35.8888	+	2.89759i	−2.23434	+	0.180396i
$259$	5.63944	+	10.9217i	0.350417	+	0.678642i
$260$		0			0
$261$	−24.7596	−	9.38955i	−1.53258	−	0.581199i
$262$	5.84244	+	10.1194i	0.360947	+	0.625179i
$263$	2.82469	+	4.89251i	0.174178	+	0.301685i	0.939877	−	0.341514i	$-0.110940\pi$
$263$	2.82469	+	4.89251i	0.174178	+	0.301685i	−0.765698	+	0.643200i	$0.777607\pi$
$264$	3.38689	−	7.13788i	0.208448	−	0.439306i
$265$		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	0.854967	−	0.518682i	$-0.173577\pi$
$269$	−0.356044	−	0.616686i	−0.0217084	−	0.0376000i	−0.876676	+	0.481082i	$0.840244\pi$
$270$		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
$273$	−23.2640	+	0.782133i	−1.40800	+	0.0473369i
$274$	30.3432			1.83310
$275$		0			0
$276$	12.4324	−	8.58162i	0.748341	−	0.516553i
$277$	−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	$-0.883135\pi$
$281$		−	12.0342i		−	0.717900i	0.933357	−	0.358950i	$-0.116865\pi$
$282$	−5.14034	+	10.8333i	−0.306102	+	0.645113i
$283$	−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
$291$	12.7504	−	8.80112i	0.747440	−	0.515931i
$292$	−9.67889	+	16.7643i	−0.566414	+	0.981058i
$293$		−	8.87318i		−	0.518377i	−0.965827	−	0.259188i	$-0.916545\pi$
$293$		−	8.87318i		−	0.518377i	0.965827	−	0.259188i	$-0.0834550\pi$
$294$	−23.8093	+	13.3258i	−1.38859	+	0.777174i
$295$		0			0
$296$	−9.63697	−	5.56391i	−0.560138	−	0.323396i
$297$	6.85507	+	7.13648i	0.397772	+	0.414101i
$298$	−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
$303$	14.7515	+	6.99951i	0.847453	+	0.402111i
$304$	−2.84804	+	1.64432i	−0.163346	+	0.0943081i
$305$		0			0
$306$	28.1336	+	10.6691i	1.60829	+	0.609910i
$307$	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	0.944262	−	0.329194i	$-0.106777\pi$
$311$	3.29851	+	5.71318i	0.187041	+	0.323965i	−0.757221	+	0.653159i	$0.773444\pi$
$312$	17.3426	−	11.9710i	0.981831	−	0.677723i
$313$	−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	$-0.652217\pi$
$317$	9.59278	−	16.6152i	0.538784	−	0.933202i	0.998970	−	0.0453790i	$-0.0144496\pi$
$318$	7.76786	−	5.36187i	0.435600	−	0.300679i
$319$	−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
$324$	−5.51551	+	27.0220i	−0.306417	+	1.50122i
$325$		0			0
$326$	6.75198	−	3.89826i	0.373958	−	0.215905i
$327$	28.7984	+	13.6647i	1.59256	+	0.755659i
$328$	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
$333$	10.7959	−	8.81493i	0.591612	−	0.483055i
$334$	6.42851	+	3.71150i	0.351752	+	0.203084i
$335$		0			0
$336$	−1.59261	+	2.98589i	−0.0868839	+	0.162894i
$337$			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
$339$	−6.23884	+	4.30644i	−0.338847	+	0.233894i
$340$		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	0.780866	−	0.624699i	$-0.214778\pi$
$347$	−2.80486	−	4.85815i	−0.150573	−	0.260799i	−0.931438	+	0.363900i	$0.881445\pi$
$348$	20.0834	−	42.3259i	1.07658	−	2.26890i
$349$		−	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	$0.766086\pi$
$353$	−31.8188	+	18.3706i	−1.69354	+	0.977767i	−0.951619	+	0.307281i	$0.900581\pi$
$354$	−44.6519	+	30.8216i	−2.37322	+	1.63815i
$355$		0			0
$356$	33.3155			1.76572
$357$	17.3342	−	10.8003i	0.917421	−	0.571612i
$358$		−	50.7619i		−	2.68285i
$359$	21.1388	+	12.2045i	1.11566	+	0.644127i	0.940290	−	0.340375i	$-0.110554\pi$
$359$	21.1388	+	12.2045i	1.11566	+	0.644127i	0.175371	+	0.984502i	$0.443887\pi$
$360$		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
$366$	2.92412	−	6.16260i	0.152846	−	0.322124i
$367$	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
$369$	−0.266812	+	0.703565i	−0.0138897	+	0.0366261i
$370$		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
$378$	20.3612	+	23.2934i	1.04727	+	1.19808i
$379$	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
$381$	12.5791	+	18.2236i	0.644447	+	0.933624i
$382$	18.6289	−	10.7554i	0.953138	−	0.550295i
$383$	5.48580	+	3.16723i	0.280311	+	0.161838i	0.633564	−	0.773690i	$-0.281591\pi$
$383$	5.48580	+	3.16723i	0.280311	+	0.161838i	−0.353253	+	0.935528i	$0.614924\pi$
$384$	−2.29272	−	28.3970i	−0.117000	−	1.44913i
$385$		0			0
$386$			12.9853i			0.660936i
$387$	25.9114	+	9.82633i	1.31715	+	0.499501i
$388$	13.7051	+	23.7379i	0.695770	+	1.20511i
$389$	10.7869	−	6.22784i	0.546919	−	0.315764i	−0.200959	−	0.979600i	$-0.564406\pi$
$389$	10.7869	−	6.22784i	0.546919	−	0.315764i	0.747879	+	0.663836i	$0.231073\pi$
$390$		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
$396$	−13.5609	+	11.0726i	−0.681463	+	0.556419i
$397$	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
$399$	18.0065	+	9.60426i	0.901453	+	0.480815i
$400$		0			0
$401$	12.7515	+	7.36207i	0.636779	+	0.367644i	0.783373	−	0.621552i	$-0.213498\pi$
$401$	12.7515	+	7.36207i	0.636779	+	0.367644i	−0.146594	+	0.989197i	$0.546831\pi$
$402$	−18.3724	−	26.6165i	−0.916333	−	1.32751i
$403$	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
$408$	−7.92618	+	16.7045i	−0.392404	+	0.826995i
$409$	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
$411$	−21.0992	−	10.0115i	−1.04075	−	0.493828i
$412$	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
$417$	−1.98939	−	2.88206i	−0.0974206	−	0.141135i
$418$	−9.54277	+	16.5286i	−0.466752	+	0.808438i
$419$	−30.1515			−1.47299			−0.736497	−	0.676440i	$-0.763522\pi$
$419$	−30.1515			−1.47299			−0.736497	+	0.676440i	$0.763522\pi$
$420$		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
$423$	7.14869	−	5.83695i	0.347581	−	0.283802i
$424$	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
$429$	−7.18248	+	15.1371i	−0.346773	+	0.730827i
$430$		0			0
$431$	11.9349	−	6.89063i	0.574885	−	0.331910i	−0.184213	−	0.982886i	$-0.558974\pi$
$431$	11.9349	−	6.89063i	0.574885	−	0.331910i	0.759098	+	0.650976i	$0.225640\pi$
$432$	3.68571	+	1.06747i	0.177329	+	0.0513584i
$433$	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
$438$	20.2641	−	13.9876i	0.968258	−	0.668354i
$439$	−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
$441$	20.9526	−	1.41044i	0.997742	−	0.0671640i
$442$			50.9450i			2.42321i
$443$	−8.25313	+	14.2948i	−0.392118	+	0.679169i	−0.992729	−	0.120373i	$-0.961591\pi$
$443$	−8.25313	+	14.2948i	−0.392118	+	0.679169i	0.600611	+	0.799542i	$0.294924\pi$
$444$	14.0077	+	20.2932i	0.664776	+	0.963075i
$445$		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	$-0.789925\pi$
$449$		−	25.9824i		−	1.22618i	0.790012	−	0.613092i	$-0.210075\pi$
$450$		0			0
$451$	−0.413664	+	0.238829i	−0.0194787	+	0.0112460i
$452$	−6.70598	−	11.6151i	−0.315423	−	0.546329i
$453$	10.9695	+	5.20495i	0.515391	+	0.244550i
$454$			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
$459$	−16.0426	−	16.7012i	−0.748806	−	0.779545i
$460$		0			0
$461$	1.40468			0.0654225			0.0327113	−	0.999465i	$-0.489586\pi$
$461$	1.40468			0.0654225			0.0327113	+	0.999465i	$0.489586\pi$
$462$	0.659903	+	19.6283i	0.0307015	+	0.913192i
$463$		−	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	$-0.980889\pi$
$467$	−33.4798	−	19.3296i	−1.54926	−	0.894467i	−0.551064	−	0.834463i	$-0.685778\pi$
$468$	−46.0911	+	7.49143i	−2.13056	+	0.346291i
$469$	−21.9286	−	1.03043i	−1.01257	−	0.0475809i
$470$		0			0
$471$	−3.93306	−	1.86621i	−0.181226	−	0.0859906i
$472$	−16.6703	−	28.8739i	−0.767314	−	1.32903i
$473$	8.79578	+	15.2347i	0.404430	+	0.700494i
$474$	−11.2291	−	5.32813i	−0.515768	−	0.244729i
$475$		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	$0.0806898\pi$
$479$	15.3467	+	26.5813i	0.701210	+	1.21453i	−0.266832	+	0.963743i	$0.585977\pi$
$480$		0			0
$481$	20.4369	+	11.7992i	0.931841	+	0.537999i
$482$			36.1822i			1.64805i
$483$	−6.13826	+	11.5083i	−0.279301	+	0.523645i
$484$	22.5943			1.02701
$485$		0			0
$486$	21.0730	−	28.0458i	0.955889	−	1.27218i
$487$	−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	$-0.948516\pi$
$491$		−	7.13665i		−	0.322073i	0.986948	−	0.161036i	$-0.0514836\pi$
$492$	−1.20272	−	0.570685i	−0.0542229	−	0.0257285i
$493$	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
$501$	−3.24550	−	4.70183i	−0.144998	−	0.210062i
$502$	16.1815	−	28.0272i	0.722216	−	1.25091i
$503$		−	30.4353i		−	1.35704i	−0.734580	−	0.678522i	$-0.762621\pi$
$503$		−	30.4353i		−	1.35704i	0.734580	−	0.678522i	$-0.237379\pi$
$504$	−15.2743	+	11.3195i	−0.680372	+	0.504212i
$505$		0			0
$506$	−10.5637	−	6.09896i	−0.469614	−	0.271132i
$507$	−18.2473	+	12.5954i	−0.810389	+	0.559383i
$508$	−33.9277	+	19.5882i	−1.50530	+	0.869084i
$509$	16.4870	−	28.5563i	0.730774	−	1.26574i	−0.225779	−	0.974179i	$-0.572493\pi$
$509$	16.4870	−	28.5563i	0.730774	−	1.26574i	0.956553	−	0.291559i	$-0.0941740\pi$
$510$		0			0
$511$	0.784506	−	16.6950i	0.0347045	−	0.738545i
$512$	−8.30237			−0.366916
$513$	6.43738	−	22.2268i	0.284217	−	0.981336i
$514$	−9.27624	+	5.35564i	−0.409157	+	0.236227i
$515$		0			0
$516$	−21.0176	+	44.2948i	−0.925249	+	1.94997i
$517$	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	$-0.978423\pi$
$521$	−12.7254	−	22.0411i	−0.557511	−	0.965638i	0.440192	−	0.897904i	$-0.354910\pi$
$522$	−46.1591	+	37.6892i	−2.02033	+	1.64961i
$523$	−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
$528$	1.38373	+	2.00464i	0.0602192	+	0.0872407i
$529$	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
$534$	−38.2857	−	18.1664i	−1.65679	−	0.786136i
$535$		0			0
$536$	17.2114	−	9.93701i	0.743419	−	0.429213i
$537$	−16.7484	+	35.2974i	−0.722748	+	1.52320i
$538$	−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
$543$	−3.42609	−	4.96344i	−0.147027	−	0.213002i
$544$	24.9038	+	14.3782i	1.06774	+	0.616460i
$545$		0			0
$546$	−24.6524	+	46.2195i	−1.05503	+	1.97801i
$547$		−	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
$549$	−4.06659	+	3.32040i	−0.173558	+	0.141711i
$550$		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	$-0.934760\pi$
$557$	−15.7133	−	27.2162i	−0.665792	−	1.15319i	0.313278	−	0.949661i	$-0.398573\pi$
$558$	−35.0725	−	13.3005i	−1.48474	−	0.563054i
$559$			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	0.216615	−	0.976257i	$-0.430498\pi$
$563$	27.7705	−	16.0333i	1.17039	−	0.675723i	0.953771	+	0.300535i	$0.0971651\pi$
$564$	9.27544	+	13.4375i	0.390566	+	0.565822i
$565$		0			0
$566$	−40.2853			−1.69332
$567$	−6.47281	−	22.9151i	−0.271833	−	0.962345i
$568$		−	23.1962i		−	0.973290i
$569$	−17.1344	−	9.89257i	−0.718313	−	0.414718i	0.0958187	−	0.995399i	$-0.469453\pi$
$569$	−17.1344	−	9.89257i	−0.718313	−	0.414718i	−0.814131	+	0.580681i	$0.802786\pi$
$570$		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
$576$	−13.8750	+	36.5876i	−0.578127	+	1.52448i
$577$	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
$579$	4.28439	−	9.02938i	0.178053	−	0.375248i
$580$		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	$-0.731499\pi$
$587$		−	36.1962i		−	1.49398i	0.664837	−	0.746988i	$-0.268501\pi$
$588$	−0.495928	+	37.1499i	−0.0204517	+	1.53204i
$589$	−24.7427			−1.01950
$590$		0			0
$591$	−6.19354	+	4.27518i	−0.254768	+	0.175857i
$592$	2.97115	−	1.71540i	0.122114	−	0.0705024i
$593$	12.9981	+	7.50446i	0.533768	+	0.308171i	0.742550	−	0.669791i	$-0.233616\pi$
$593$	12.9981	+	7.50446i	0.533768	+	0.308171i	−0.208781	+	0.977962i	$0.566950\pi$
$594$	21.6217	−	5.32994i	0.887151	−	0.218690i
$595$		0			0
$596$			3.92937i			0.160953i
$597$	6.45888	−	13.6121i	0.264344	−	0.557108i
$598$	−16.2674	−	28.1760i	−0.665223	−	1.15220i
$599$	−11.3793	+	6.56986i	−0.464947	+	0.268437i	−0.714122	−	0.700021i	$-0.753174\pi$
$599$	−11.3793	+	6.56986i	−0.464947	+	0.268437i	0.249175	+	0.968458i	$0.419841\pi$
$600$		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
$606$	30.2399	−	20.8735i	1.22841	−	0.847930i
$607$	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
$609$	1.35913	+	40.4264i	0.0550749	+	1.63816i
$610$		0			0
$611$	13.5326	+	7.81306i	0.547471	+	0.316083i
$612$	31.7361	−	25.9127i	1.28286	−	1.04746i
$613$	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	$-0.171241\pi$
$617$	42.6618			1.71750			0.858751	+	0.512394i	$0.171241\pi$
$618$	−22.1894	−	10.5287i	−0.892589	−	0.423528i
$619$	−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
$621$	14.2055	+	4.11425i	0.570049	+	0.165099i
$622$	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
$627$	12.0890	−	8.34463i	0.482790	−	0.333252i
$628$	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
$633$	−15.2487	+	10.5256i	−0.606079	+	0.418355i
$634$	−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
$639$	27.1653	+	10.3018i	1.07464	+	0.407535i
$640$		0			0
$641$	−11.0323	+	6.36950i	−0.435750	+	0.251580i	−0.701793	−	0.712381i	$-0.747617\pi$
$641$	−11.0323	+	6.36950i	−0.435750	+	0.251580i	0.266043	+	0.963961i	$0.414284\pi$
$642$	−58.4807	−	27.7487i	−2.30805	−	1.09516i
$643$	−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	0.384230	−	0.923238i	$-0.374467\pi$
$647$	34.9974	−	20.2058i	1.37589	−	0.794371i	0.991662	+	0.128866i	$0.0411338\pi$
$648$	16.1362	+	14.2943i	0.633889	+	0.561534i
$649$	22.9571	+	13.2543i	0.901143	+	0.520275i
$650$		0			0
$651$	−21.6094	+	13.4641i	−0.846940	+	0.527698i
$652$		−	10.6164i		−	0.415770i
$653$	−21.3460	+	36.9723i	−0.835332	+	1.44684i	0.0584277	+	0.998292i	$0.481391\pi$
$653$	−21.3460	+	36.9723i	−0.835332	+	1.44684i	−0.893760	+	0.448546i	$0.851942\pi$
$654$	59.0354	−	40.7500i	2.30847	−	1.59345i
$655$		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	$-0.987054\pi$
$659$		−	2.08754i		−	0.0813192i	0.999173	−	0.0406596i	$-0.0129459\pi$
$660$		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
$663$	16.8088	−	35.4248i	0.652801	−	1.37578i
$664$			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
$669$	24.1588	−	16.6759i	0.934032	−	0.644729i
$670$		0			0
$671$	−3.33267			−0.128656
$672$	15.6361	+	25.0955i	0.603177	+	0.968081i
$673$			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	0.945462	−	0.325734i	$-0.105611\pi$
$677$	29.5604	+	17.0667i	1.13610	+	0.655927i	0.190637	+	0.981661i	$0.438945\pi$
$678$	1.37291	+	17.0046i	0.0527265	+	0.653057i
$679$	−19.9172	−	12.7819i	−0.764354	−	0.490525i
$680$		0			0
$681$	1.80534	−	3.80478i	0.0691809	−	0.145799i
$682$	−11.9056	−	20.6210i	−0.455887	−	0.789620i
$683$	9.83481	+	17.0344i	0.376319	+	0.651803i	0.990523	−	0.137344i	$-0.0438565\pi$
$683$	9.83481	+	17.0344i	0.376319	+	0.651803i	−0.614205	+	0.789147i	$0.710523\pi$
$684$	38.2796	+	14.5167i	1.46366	+	0.555060i
$685$		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
$693$	6.01732	−	13.8663i	0.228579	−	0.526738i
$694$	−12.6242			−0.479206
$695$		0			0
$696$	−20.8023	−	30.1367i	−0.788508	−	1.14233i
$697$	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	$0.00124119\pi$
$701$			0.206478i			0.00779858i	−0.999992	+	0.00389929i	$0.998759\pi$
$702$	57.0522	+	16.5236i	2.15330	+	0.623643i
$703$	−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
$711$	6.05020	+	7.40986i	0.226900	+	0.277891i
$712$	13.0204	−	22.5520i	0.487960	−	0.845171i
$713$		−	15.8135i		−	0.592220i
$714$	−1.54434	−	45.9353i	−0.0577956	−	1.71909i
$715$		0			0
$716$	−59.8611	−	34.5608i	−2.23712	−	1.29160i
$717$	−9.52061	−	13.7927i	−0.355554	−	0.515098i
$718$	47.5709	−	27.4651i	1.77533	−	1.02499i
$719$	−4.36496	+	7.56034i	−0.162786	+	0.281953i	−0.935867	−	0.352354i	$-0.885381\pi$
$719$	−4.36496	+	7.56034i	−0.162786	+	0.281953i	0.773081	+	0.634307i	$0.218715\pi$
$720$		0			0
$721$	−14.8130	+	7.64871i	−0.551665	+	0.284853i
$722$	1.87281			0.0696988
$723$	11.9380	−	25.1594i	0.443978	−	0.935687i
$724$	9.24065	−	5.33509i	0.343426	−	0.198277i
$725$		0			0
$726$	−25.9651	−	12.3203i	−0.963654	−	0.457248i
$727$	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
$732$	−5.27640	−	7.64404i	−0.195022	−	0.282532i
$733$	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
$738$	1.07097	+	1.31165i	0.0394229	+	0.0482824i
$739$	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	$-0.625526\pi$
$743$	−20.9456			−0.768419			−0.384209	+	0.923246i	$0.625526\pi$
$744$	9.88108	−	20.8244i	0.362258	−	0.763461i
$745$		0			0
$746$	40.6783	−	23.4856i	1.48934	−	0.859869i
$747$	−25.2172	−	9.56309i	−0.922651	−	0.349895i
$748$	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
$753$	−20.4992	+	14.1498i	−0.747031	+	0.515649i
$754$	−87.3801	−	50.4489i	−3.18220	−	1.83724i
$755$		0			0
$756$	41.3316	−	8.15195i	1.50321	−	0.296484i
$757$		−	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
$759$	5.33320	+	7.72632i	0.193583	+	0.280448i
$760$		0			0
$761$	−21.1371	+	36.6105i	−0.766219	+	1.32713i	0.173381	+	0.984855i	$0.444531\pi$
$761$	−21.1371	+	36.6105i	−0.766219	+	1.32713i	−0.939600	+	0.342275i	$0.888803\pi$
$762$	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
$768$	−17.1018	−	8.11469i	−0.617107	−	0.292814i
$769$		−	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	−0.466612	−	0.884462i	$-0.654526\pi$
$773$	1.83633	−	1.06021i	0.0660483	−	0.0381330i	0.532661	+	0.846329i	$0.321192\pi$
$774$	48.3063	−	39.4424i	1.73633	−	1.41773i
$775$		0			0
$776$	21.4249			0.769110
$777$	−18.7849	−	10.0194i	−0.673904	−	0.359445i
$778$		−	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
$786$	−18.2849	−	8.67606i	−0.652199	−	0.309465i
$787$	−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
$789$	−8.84032	−	4.19468i	−0.314724	−	0.149335i
$790$		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	$0.122935\pi$
$797$			21.2684i			0.753365i	−0.926342	+	0.376682i	$0.877065\pi$
$798$	38.9789	−	24.2864i	1.37984	−	0.859728i
$799$	−13.7105			−0.485042
$800$		0			0
$801$	20.6283	+	25.2641i	0.728864	+	0.892662i
$802$	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
$807$	1.11429	+	0.528726i	0.0392250	+	0.0186121i
$808$	11.2898	+	19.5545i	0.397173	+	0.687924i
$809$	19.3311	−	11.1608i	0.679646	−	0.392394i	−0.120075	−	0.992765i	$-0.538314\pi$
$809$	19.3311	−	11.1608i	0.679646	−	0.392394i	0.799722	+	0.600371i	$0.204980\pi$
$810$		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
$816$	−3.23829	−	4.69137i	−0.113363	−	0.164231i
$817$	20.5685	−	35.6257i	0.719601	−	1.24639i
$818$		−	2.10641i		−	0.0736488i
$819$	32.3918	−	24.0050i	1.13186	−	0.838803i
$820$		0			0
$821$	−34.1580	−	19.7211i	−1.19212	−	0.688272i	−0.233335	−	0.972397i	$-0.574964\pi$
$821$	−34.1580	−	19.7211i	−1.19212	−	0.688272i	−0.958787	+	0.284125i	$0.908297\pi$
$822$	−43.2524	+	29.8556i	−1.50860	+	1.04133i
$823$	−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	$-0.750527\pi$
$827$	−40.7367			−1.41655			−0.708277	+	0.705935i	$0.750527\pi$
$828$	−9.27789	+	24.4652i	−0.322429	+	0.850224i
$829$	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
$831$	17.0132	−	35.8555i	0.590182	−	1.24381i
$832$	−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
$837$	19.9994	+	20.8204i	0.691279	+	0.719657i
$838$	−33.9266	+	58.7626i	−1.17197	+	2.02992i
$839$	−9.40638			−0.324744			−0.162372	−	0.986730i	$-0.551915\pi$
$839$	−9.40638			−0.324744			−0.162372	+	0.986730i	$0.551915\pi$
$840$		0			0
$841$	−48.9115			−1.68660
$842$	40.9220	−	70.8790i	1.41026	−	2.44265i
$843$	11.8408	+	17.1540i	0.407819	+	0.590816i
$844$	−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
$849$	28.0125	+	13.2918i	0.961385	+	0.456172i
$850$		0			0
$851$	11.4515	−	6.61152i	0.392552	−	0.226640i
$852$	−22.0347	+	46.4382i	−0.754896	+	1.59095i
$853$	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	−0.231226	−	0.972900i	$-0.574274\pi$
$857$	14.5119	−	8.37845i	0.495717	−	0.286202i	0.726943	+	0.686698i	$0.240940\pi$
$858$	21.4192	+	31.0304i	0.731238	+	1.05936i
$859$	−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
$861$	1.14875	−	0.0386209i	0.0391492	−	0.00131620i
$862$		−	31.0135i		−	1.05632i
$863$	−11.0039	+	19.0593i	−0.374576	+	0.648785i	−0.990263	−	0.139206i	$-0.955545\pi$
$863$	−11.0039	+	19.0593i	−0.374576	+	0.648785i	0.615687	+	0.787990i	$0.288878\pi$
$864$	24.1792	−	23.2257i	0.822592	−	0.790155i
$865$		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
$873$	−9.51520	+	25.0910i	−0.322041	+	0.849200i
$874$			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
$879$	8.73059	+	12.6482i	0.294475	+	0.426613i
$880$		0			0
$881$	−44.3021			−1.49258			−0.746288	−	0.665623i	$-0.768166\pi$
$881$	−44.3021			−1.49258			−0.746288	+	0.665623i	$0.768166\pi$
$882$	20.8271	−	42.4218i	0.701286	−	1.42842i
$883$		−	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	0.608401	−	0.793630i	$-0.291811\pi$
$887$	6.70992	+	3.87397i	0.225297	+	0.130075i	−0.383104	+	0.923705i	$0.625145\pi$
$888$	19.2114	−	1.55109i	0.644693	−	0.0520512i
$889$	18.2687	−	28.4670i	0.612713	−	0.954751i
$890$		0			0
$891$	−16.7933	−	3.42771i	−0.562597	−	0.114833i
$892$	25.9677	+	44.9774i	0.869464	+	1.50596i
$893$	−6.84995	−	11.8645i	−0.229225	−	0.397029i
$894$	2.14262	−	4.51558i	0.0716598	−	0.151024i
$895$		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
$903$	−1.42236	−	42.3069i	−0.0473331	−	1.40789i
$904$	−10.4833			−0.348671
$905$		0			0
$906$	22.4869	−	15.5219i	0.747078	−	0.515681i
$907$	−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	$0.259060\pi$
$911$			43.8824i			1.45389i	−0.686697	+	0.726944i	$0.740940\pi$
$912$	2.44182	−	5.14615i	0.0808567	−	0.170406i
$913$	−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
$921$	−12.8274	+	8.85428i	−0.422676	+	0.291758i
$922$	1.58056	−	2.73760i	0.0520528	−	0.0901581i
$923$			49.1915i			1.61916i
$924$	23.5960	+	12.5856i	0.776253	+	0.414036i
$925$		0			0
$926$	−39.3789	−	22.7354i	−1.29407	−	0.747132i
$927$	11.9556	+	14.6424i	0.392674	+	0.480919i
$928$	−49.3225	+	28.4764i	−1.61909	+	0.934783i
$929$	−9.87128	+	17.0976i	−0.323866	+	0.560952i	−0.981282	−	0.192575i	$-0.938316\pi$
$929$	−9.87128	+	17.0976i	−0.323866	+	0.560952i	0.657416	+	0.753528i	$0.271649\pi$
$930$		0			0
$931$	2.92324	−	31.0360i	0.0958054	−	1.01716i
$932$	33.9572			1.11230
$933$	−10.3232	−	4.89830i	−0.337967	−	0.160363i
$934$	−75.3434	+	43.4995i	−2.46531	+	1.42335i
$935$		0			0
$936$	−12.9422	+	34.1278i	−0.423030	+	1.11550i
$937$	−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	$0.00926996\pi$
$941$	16.1049	+	27.8945i	0.525005	+	0.909336i	−0.474571	+	0.880217i	$0.657397\pi$
$942$	−8.06259	+	5.56532i	−0.262693	+	0.181328i
$943$	−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	−0.999009	−	0.0445115i	$-0.985827\pi$
$947$	−14.1852	+	24.5694i	−0.460956	+	0.798400i	0.538053	+	0.842911i	$0.319160\pi$
$948$	−13.9284	+	9.61430i	−0.452375	+	0.312258i
$949$	−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	$-0.347795\pi$
$953$	28.4105			0.920305			0.460153	+	0.887840i	$0.347795\pi$
$954$	−5.79691	+	15.2861i	−0.187682	+	0.494904i
$955$		0			0
$956$	25.6785	−	14.8255i	0.830501	−	0.479490i
$957$	26.3042	+	12.4812i	0.850293	+	0.403459i
$958$	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
$963$	31.5092	+	38.5903i	1.01537	+	1.24356i
$964$	42.6680	+	24.6344i	1.37424	+	0.793419i
$965$		0			0
$966$	15.5219	+	24.9121i	0.499407	+	0.801535i
$967$		−	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
$969$	−28.2914	+	19.5286i	−0.908852	+	0.627348i
$970$		0			0
$971$	11.7297	−	20.3164i	0.376424	−	0.651985i	−0.614115	−	0.789216i	$-0.710487\pi$
$971$	11.7297	−	20.3164i	0.376424	−	0.651985i	0.990539	+	0.137231i	$0.0438203\pi$
$972$	−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	$-0.976473\pi$
$977$	−17.5848	−	30.4577i	−0.562587	−	0.974429i	0.434683	−	0.900584i	$-0.356861\pi$
$978$	−5.78893	+	12.2002i	−0.185110	+	0.390120i
$979$			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	0.202046	−	0.979376i	$-0.435241\pi$
$983$	36.0944	−	20.8391i	1.15123	−	0.664665i	0.949187	+	0.314711i	$0.101908\pi$
$984$	−0.856358	+	0.591113i	−0.0272997	+	0.0188440i
$985$		0			0
$986$	88.5285			2.81932
$987$	−12.4387	−	6.63453i	−0.395929	−	0.211179i
$988$			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
$996$	20.4546	−	43.1081i	0.648127	−	1.36593i
$997$	−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
$999$	−6.71565	+	23.1876i	−0.212474	+	0.733622i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.12521 - 1.94891i) q^{2} +(-1.42544 + 0.983931i) q^{3} +(-1.53217 - 2.65380i) q^{4} +(0.313682 + 3.88518i) q^{6} +(2.22667 + 1.42897i) q^{7} -2.39522 q^{8} +(1.06376 - 2.80507i) q^{9} +O(q^{10})\)	\(q+(1.12521 - 1.94891i) q^{2} +(-1.42544 + 0.983931i) q^{3} +(-1.53217 - 2.65380i) q^{4} +(0.313682 + 3.88518i) q^{6} +(2.22667 + 1.42897i) q^{7} -2.39522 q^{8} +(1.06376 - 2.80507i) q^{9} +(1.64925 - 0.952197i) q^{11} +(4.79518 + 2.27529i) q^{12} +5.07948 q^{13} +(5.29039 - 2.73170i) q^{14} +(0.369233 - 0.639530i) q^{16} +(-3.85968 + 2.22839i) q^{17} +(-4.26988 - 5.22946i) q^{18} +(-3.85670 - 2.22667i) q^{19} +(-4.57999 + 0.153979i) q^{21} -4.28567i q^{22} +(1.42310 - 2.46489i) q^{23} +(3.41425 - 2.35673i) 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} +(-1.41402 + 2.98005i) q^{33} +10.0296i q^{34} +(-9.07397 + 1.47484i) q^{36} +(4.02342 + 2.32292i) q^{37} +(-8.67917 + 5.01092i) q^{38} +(-7.24050 + 4.99786i) q^{39} -0.250819 q^{41} +(-4.85334 + 9.09926i) 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} +(3.30916 - 6.97409i) q^{51} +(-7.78265 - 13.4799i) q^{52} +(-1.21077 - 2.09711i) q^{53} +(11.2319 + 3.25301i) 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} +(6.37700 - 4.72588i) q^{63} -13.0434 q^{64} +(4.21680 + 6.10897i) q^{66} +(-7.18573 + 4.14868i) q^{67} +(11.8274 + 6.82855i) q^{68} +(0.396729 + 4.91379i) q^{69} +9.68436i q^{71} +(-2.54794 + 6.71876i) 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} +(-6.73682 - 5.96785i) q^{81} +(-0.282223 + 0.488824i) q^{82} -8.98988i q^{83} +(7.42597 + 11.9185i) q^{84} +(18.0028 + 10.3939i) q^{86} +(8.68491 + 12.5820i) q^{87} +(-3.95033 + 2.28072i) q^{88} +(-5.43599 + 9.41541i) q^{89} +(11.3103 + 7.25841i) q^{91} -8.72178 q^{92} +(-4.12533 + 8.69416i) q^{93} +(5.99548 - 3.46149i) q^{94} +(10.0967 + 4.79084i) 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

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Database

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