LMFDB - Embedded newform 245.4.j.g.214.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(79,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("245.79");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.j (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:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			214.11
Character	$\chi$	$=$	245.214
Dual form			245.4.j.g.79.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.20246 - 2.42629i) q^{2} +(-0.991781 - 0.572605i) q^{3} +(7.77380 - 13.4646i) q^{4} +(6.75158 + 8.91157i) q^{5} -5.55723 q^{6} -36.6254i q^{8} +(-12.8442 - 22.2469i) q^{9} +O(q^{10})$	\(q+(4.20246 - 2.42629i) q^{2} +(-0.991781 - 0.572605i) q^{3} +(7.77380 - 13.4646i) q^{4} +(6.75158 + 8.91157i) q^{5} -5.55723 q^{6} -36.6254i q^{8} +(-12.8442 - 22.2469i) q^{9} +(49.9954 + 21.0693i) q^{10} +(19.8919 - 34.4537i) q^{11} +(-15.4198 + 8.90264i) q^{12} -61.1016i q^{13} +(-1.59328 - 12.7043i) q^{15} +(-26.6736 - 46.2001i) q^{16} +(68.4751 + 39.5341i) q^{17} +(-107.955 - 62.3278i) q^{18} +(-1.17292 - 2.03156i) q^{19} +(172.476 - 21.6307i) q^{20} -193.054i q^{22} +(161.523 - 93.2555i) q^{23} +(-20.9719 + 36.3244i) q^{24} +(-33.8323 + 120.334i) q^{25} +(-148.250 - 256.777i) q^{26} +60.3394i q^{27} -62.5696 q^{29} +(-37.5201 - 49.5237i) q^{30} +(-104.569 + 181.119i) q^{31} +(29.5585 + 17.0656i) q^{32} +(-39.4567 + 22.7804i) q^{33} +383.685 q^{34} -399.395 q^{36} +(-179.660 + 103.727i) q^{37} +(-9.85830 - 5.69169i) q^{38} +(-34.9871 + 60.5994i) q^{39} +(326.390 - 247.280i) q^{40} -346.718 q^{41} +271.573i q^{43} +(-309.271 - 535.673i) q^{44} +(111.536 - 264.664i) q^{45} +(452.531 - 783.806i) q^{46} +(-467.335 + 269.816i) q^{47} +61.0938i q^{48} +(149.788 + 587.788i) q^{50} +(-45.2749 - 78.4183i) q^{51} +(-822.710 - 474.992i) q^{52} +(514.798 + 297.219i) q^{53} +(146.401 + 253.574i) q^{54} +(441.338 - 55.3492i) q^{55} +2.68648i q^{57} +(-262.946 + 151.812i) q^{58} +(112.336 - 194.571i) q^{59} +(-183.445 - 77.3080i) q^{60} +(7.75441 + 13.4310i) q^{61} +1014.86i q^{62} +592.403 q^{64} +(544.511 - 412.532i) q^{65} +(-110.544 + 191.467i) q^{66} +(435.985 + 251.716i) q^{67} +(1064.62 - 614.661i) q^{68} -213.594 q^{69} -660.472 q^{71} +(-814.802 + 470.426i) q^{72} +(601.156 + 347.078i) q^{73} +(-503.344 + 871.817i) q^{74} +(102.458 - 99.9729i) q^{75} -36.4722 q^{76} +339.556i q^{78} +(84.6277 + 146.580i) q^{79} +(231.626 - 549.628i) q^{80} +(-312.244 + 540.822i) q^{81} +(-1457.07 + 841.239i) q^{82} -335.518i q^{83} +(110.004 + 877.138i) q^{85} +(658.917 + 1141.28i) q^{86} +(62.0553 + 35.8276i) q^{87} +(-1261.88 - 728.548i) q^{88} +(-136.809 - 236.961i) q^{89} +(-173.428 - 1382.86i) q^{90} -2899.80i q^{92} +(207.419 - 119.753i) q^{93} +(-1309.31 + 2267.79i) q^{94} +(10.1853 - 24.1688i) q^{95} +(-19.5437 - 33.8507i) q^{96} -251.125i q^{97} -1021.98 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 44 q^{4} - 140 q^{9}+O(q^{10}) $ 24 * q + 44 * q^4 - 140 * q^9	$ 24 q + 44 q^{4} - 140 q^{9} + 24 q^{11} - 272 q^{15} - 84 q^{16} - 584 q^{25} + 592 q^{29} + 632 q^{30} - 2200 q^{36} + 184 q^{39} - 2760 q^{44} + 2440 q^{46} + 1080 q^{50} + 1928 q^{51} + 1000 q^{60} + 4664 q^{64} + 588 q^{65} - 3680 q^{71} - 8656 q^{74} - 5032 q^{79} + 1284 q^{81} + 1032 q^{85} + 1680 q^{86} + 6416 q^{95} - 7008 q^{99}+O(q^{100}) $ 24 * q + 44 * q^4 - 140 * q^9 + 24 * q^11 - 272 * q^15 - 84 * q^16 - 584 * q^25 + 592 * q^29 + 632 * q^30 - 2200 * q^36 + 184 * q^39 - 2760 * q^44 + 2440 * q^46 + 1080 * q^50 + 1928 * q^51 + 1000 * q^60 + 4664 * q^64 + 588 * q^65 - 3680 * q^71 - 8656 * q^74 - 5032 * q^79 + 1284 * q^81 + 1032 * q^85 + 1680 * q^86 + 6416 * q^95 - 7008 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	4.20246	−	2.42629i	1.48580	−	0.857824i	0.485926	−	0.874000i	$-0.338482\pi$
$2$	4.20246	−	2.42629i	1.48580	−	0.857824i	0.999869	+	0.0161753i	$0.00514900\pi$
$3$	−0.991781	−	0.572605i	−0.190868	−	0.110198i	0.401521	−	0.915850i	$-0.368482\pi$
$3$	−0.991781	−	0.572605i	−0.190868	−	0.110198i	−0.592389	+	0.805652i	$0.701815\pi$
$4$	7.77380	−	13.4646i	0.971726	−	1.68308i
$5$	6.75158	+	8.91157i	0.603880	+	0.797075i
$5$	6.75158	+	8.91157i	0.603880	+	0.797075i
$6$	−5.55723			−0.378122
$7$		0			0
$7$		0			0
$8$		−	36.6254i		−	1.61863i
$9$	−12.8442	−	22.2469i	−0.475713	−	0.823959i
$10$	49.9954	+	21.0693i	1.58099	+	0.666268i
$11$	19.8919	−	34.4537i	0.545238	−	0.944380i	−0.453354	−	0.891331i	$-0.649773\pi$
$11$	19.8919	−	34.4537i	0.545238	−	0.944380i	0.998592	−	0.0530495i	$-0.0168941\pi$
$12$	−15.4198	+	8.90264i	−0.370943	+	0.214164i
$13$		−	61.1016i		−	1.30358i	−0.758400	−	0.651789i	$-0.774019\pi$
$13$		−	61.1016i		−	1.30358i	0.758400	−	0.651789i	$-0.225981\pi$
$14$		0			0
$15$	−1.59328	−	12.7043i	−0.0274255	−	0.218683i
$16$	−26.6736	−	46.2001i	−0.416775	−	0.721876i
$17$	68.4751	+	39.5341i	0.976920	+	0.564025i	0.901339	−	0.433115i	$-0.142585\pi$
$17$	68.4751	+	39.5341i	0.976920	+	0.564025i	0.0755812	+	0.997140i	$0.475919\pi$
$18$	−107.955	−	62.3278i	−1.41362	−	0.816156i
$19$	−1.17292	−	2.03156i	−0.0141624	−	0.0245300i	0.858857	−	0.512215i	$-0.171175\pi$
$19$	−1.17292	−	2.03156i	−0.0141624	−	0.0245300i	−0.873020	+	0.487685i	$0.837842\pi$
$20$	172.476	−	21.6307i	1.92835	−	0.241838i
$21$		0			0
$22$		−	193.054i		−	1.87087i
$23$	161.523	−	93.2555i	1.46434	−	0.845440i	0.465137	−	0.885239i	$-0.346005\pi$
$23$	161.523	−	93.2555i	1.46434	−	0.845440i	0.999208	+	0.0397987i	$0.0126717\pi$
$24$	−20.9719	+	36.3244i	−0.178370	+	0.308945i
$25$	−33.8323	+	120.334i	−0.270659	+	0.962675i
$26$	−148.250	−	256.777i	−1.11824	−	1.93685i
$27$			60.3394i			0.430086i
$28$		0			0
$29$	−62.5696			−0.400651			−0.200325	−	0.979729i	$-0.564200\pi$
$29$	−62.5696			−0.400651			−0.200325	+	0.979729i	$0.564200\pi$
$30$	−37.5201	−	49.5237i	−0.228340	−	0.301392i
$31$	−104.569	+	181.119i	−0.605843	+	1.04935i	0.386075	+	0.922468i	$0.373831\pi$
$31$	−104.569	+	181.119i	−0.605843	+	1.04935i	−0.991918	+	0.126883i	$0.959503\pi$
$32$	29.5585	+	17.0656i	0.163289	+	0.0942751i
$33$	−39.4567	+	22.7804i	−0.208137	+	0.120168i
$34$	383.685			1.93534
$35$		0			0
$36$	−399.395			−1.84905
$37$	−179.660	+	103.727i	−0.798270	+	0.460881i	−0.842866	−	0.538124i	$-0.819133\pi$
$37$	−179.660	+	103.727i	−0.798270	+	0.460881i	0.0445962	+	0.999005i	$0.485800\pi$
$38$	−9.85830	−	5.69169i	−0.0420849	−	0.0242977i
$39$	−34.9871	+	60.5994i	−0.143652	+	0.248812i
$40$	326.390	−	247.280i	1.29017	−	0.977458i
$41$	−346.718			−1.32069			−0.660344	−	0.750964i	$-0.729589\pi$
$41$	−346.718			−1.32069			−0.660344	+	0.750964i	$0.729589\pi$
$42$		0			0
$43$			271.573i			0.963129i	0.876411	+	0.481564i	$0.159931\pi$
$43$			271.573i			0.963129i	−0.876411	+	0.481564i	$0.840069\pi$
$44$	−309.271	−	535.673i	−1.05964	−	1.83536i
$45$	111.536	−	264.664i	0.369484	−	0.876751i
$46$	452.531	−	783.806i	1.45048	−	2.51230i
$47$	−467.335	+	269.816i	−1.45038	+	0.837377i	−0.998503	−	0.0547029i	$-0.982579\pi$
$47$	−467.335	+	269.816i	−1.45038	+	0.837377i	−0.451877	+	0.892080i	$0.649246\pi$
$48$			61.0938i			0.183711i
$49$		0			0
$50$	149.788	+	587.788i	0.423663	+	1.66252i
$51$	−45.2749	−	78.4183i	−0.124309	−	0.215309i
$52$	−822.710	−	474.992i	−2.19402	−	1.26672i
$53$	514.798	+	297.219i	1.33421	+	0.770305i	0.985941	−	0.167091i	$-0.0534375\pi$
$53$	514.798	+	297.219i	1.33421	+	0.770305i	0.348265	+	0.937396i	$0.386771\pi$
$54$	146.401	+	253.574i	0.368938	+	0.639020i
$55$	441.338	−	55.3492i	1.08200	−	0.135696i
$56$		0			0
$57$			2.68648i			0.00624268i
$58$	−262.946	+	151.812i	−0.595285	+	0.343688i
$59$	112.336	−	194.571i	0.247879	−	0.429339i	−0.715058	−	0.699065i	$-0.753600\pi$
$59$	112.336	−	194.571i	0.247879	−	0.429339i	0.962937	+	0.269726i	$0.0869330\pi$
$60$	−183.445	−	77.3080i	−0.394710	−	0.166340i
$61$	7.75441	+	13.4310i	0.0162762	+	0.0281913i	0.874049	−	0.485838i	$-0.161486\pi$
$61$	7.75441	+	13.4310i	0.0162762	+	0.0281913i	−0.857773	+	0.514029i	$0.828152\pi$
$62$			1014.86i			2.07883i
$63$		0			0
$64$	592.403			1.15704
$65$	544.511	−	412.532i	1.03905	−	0.787205i
$66$	−110.544	+	191.467i	−0.206166	+	0.357091i
$67$	435.985	+	251.716i	0.794986	+	0.458985i	0.841715	−	0.539922i	$-0.181546\pi$
$67$	435.985	+	251.716i	0.794986	+	0.458985i	−0.0467288	+	0.998908i	$0.514880\pi$
$68$	1064.62	−	614.661i	1.89860	−	1.09616i
$69$	−213.594			−0.372663
$70$		0			0
$71$	−660.472			−1.10399			−0.551997	−	0.833846i	$-0.686134\pi$
$71$	−660.472			−1.10399			−0.551997	+	0.833846i	$0.686134\pi$
$72$	−814.802	+	470.426i	−1.33368	+	0.770003i
$73$	601.156	+	347.078i	0.963836	+	0.556471i	0.897351	−	0.441317i	$-0.145488\pi$
$73$	601.156	+	347.078i	0.963836	+	0.556471i	0.0664843	+	0.997787i	$0.478822\pi$
$74$	−503.344	+	871.817i	−0.790710	+	1.36955i
$75$	102.458	−	99.9729i	0.157745	−	0.153918i
$76$	−36.4722			−0.0550480
$77$		0			0
$78$			339.556i			0.492912i
$79$	84.6277	+	146.580i	0.120524	+	0.208753i	0.919974	−	0.391979i	$-0.128209\pi$
$79$	84.6277	+	146.580i	0.120524	+	0.208753i	−0.799451	+	0.600732i	$0.794876\pi$
$80$	231.626	−	549.628i	0.323708	−	0.768128i
$81$	−312.244	+	540.822i	−0.428318	+	0.741869i
$82$	−1457.07	+	841.239i	−1.96227	+	1.13292i
$83$		−	335.518i		−	0.443709i	−0.975080	−	0.221854i	$-0.928789\pi$
$83$		−	335.518i		−	0.443709i	0.975080	−	0.221854i	$-0.0712110\pi$
$84$		0			0
$85$	110.004	+	877.138i	0.140372	+	1.11928i
$86$	658.917	+	1141.28i	0.826196	+	1.43101i
$87$	62.0553	+	35.8276i	0.0764716	+	0.0441509i
$88$	−1261.88	−	728.548i	−1.52860	−	0.882539i
$89$	−136.809	−	236.961i	−0.162941	−	0.282222i	0.772981	−	0.634429i	$-0.218765\pi$
$89$	−136.809	−	236.961i	−0.162941	−	0.282222i	−0.935922	+	0.352207i	$0.885431\pi$
$90$	−173.428	−	1382.86i	−0.203121	−	1.61963i
$91$		0			0
$92$		−	2899.80i		−	3.28614i
$93$	207.419	−	119.753i	0.231273	−	0.133525i
$94$	−1309.31	+	2267.79i	−1.43665	+	2.48834i
$95$	10.1853	−	24.1688i	0.0109999	−	0.0261017i
$96$	−19.5437	−	33.8507i	−0.0207778	−	0.0359883i
$97$		−	251.125i		−	0.262865i	−0.991325	−	0.131433i	$-0.958042\pi$
$97$		−	251.125i		−	0.262865i	0.991325	−	0.131433i	$-0.0419577\pi$
$98$		0			0
$99$	−1021.98			−1.03751
$100$	1357.25	+	1391.00i	1.35725	+	1.39100i
$101$	701.493	−	1215.02i	0.691101	−	1.19702i	−0.280376	−	0.959890i	$-0.590459\pi$
$101$	701.493	−	1215.02i	0.691101	−	1.19702i	0.971477	−	0.237132i	$-0.0762074\pi$
$102$	−380.532	−	219.700i	−0.369395	−	0.213270i
$103$	−348.656	+	201.297i	−0.333535	+	0.192566i	−0.657409	−	0.753534i	$-0.728348\pi$
$103$	−348.656	+	201.297i	−0.333535	+	0.192566i	0.323875	+	0.946100i	$0.395014\pi$
$104$	−2237.87			−2.11001
$105$		0			0
$106$	2884.56			2.64314
$107$	391.024	−	225.758i	0.353287	−	0.203971i	−0.312845	−	0.949804i	$-0.601282\pi$
$107$	391.024	−	225.758i	0.353287	−	0.203971i	0.666132	+	0.745834i	$0.267949\pi$
$108$	812.447	+	469.067i	0.723868	+	0.417926i
$109$	187.530	−	324.812i	0.164790	−	0.285425i	−0.771790	−	0.635877i	$-0.780639\pi$
$109$	187.530	−	324.812i	0.164790	−	0.285425i	0.936581	+	0.350452i	$0.113972\pi$
$110$	1720.41	−	1303.42i	1.49123	−	1.12978i
$111$	237.578			0.203153
$112$		0			0
$113$		−	892.024i		−	0.742607i	−0.928512	−	0.371303i	$-0.878911\pi$
$113$		−	892.024i		−	0.742607i	0.928512	−	0.371303i	$-0.121089\pi$
$114$	6.51818	+	11.2898i	0.00535512	+	0.00927534i
$115$	1921.59	+	809.805i	1.55817	+	0.656649i
$116$	−486.403	+	842.475i	−0.389323	+	0.674327i
$117$	−1359.32	+	784.804i	−1.07410	+	0.620129i
$118$		−	1090.24i		−	0.850548i
$119$		0			0
$120$	−465.301	+	58.3545i	−0.353967	+	0.0443918i
$121$	−125.872	−	218.016i	−0.0945693	−	0.163799i
$122$	65.1752	+	37.6289i	0.0483663	+	0.0279243i
$123$	343.868	+	198.532i	0.252077	+	0.145537i
$124$	1625.80	+	2815.96i	1.17743	+	2.03936i
$125$	−1300.79	+	510.948i	−0.930770	+	0.365605i
$126$		0			0
$127$		−	1203.39i		−	0.840813i	−0.907336	−	0.420407i	$-0.861887\pi$
$127$		−	1203.39i		−	0.840813i	0.907336	−	0.420407i	$-0.138113\pi$
$128$	2253.08	−	1300.82i	1.55583	−	0.898259i
$129$	155.504	−	269.341i	0.106135	−	0.183831i
$130$	1287.36	−	3054.80i	0.868533	−	2.06095i
$131$	852.373	+	1476.35i	0.568490	+	0.984653i	0.996716	+	0.0809815i	$0.0258055\pi$
$131$	852.373	+	1476.35i	0.568490	+	0.984653i	−0.428226	+	0.903672i	$0.640861\pi$
$132$			708.360i			0.467082i
$133$		0			0
$134$	2442.95			1.57492
$135$	−537.719	+	407.386i	−0.342811	+	0.259720i
$136$	1447.95	−	2507.93i	0.912948	−	1.58127i
$137$	−465.784	−	268.921i	−0.290472	−	0.167704i	0.347683	−	0.937612i	$-0.386969\pi$
$137$	−465.784	−	268.921i	−0.290472	−	0.167704i	−0.638155	+	0.769908i	$0.720302\pi$
$138$	−897.623	+	518.243i	−0.553701	+	0.319679i
$139$	−1587.63			−0.968786			−0.484393	−	0.874851i	$-0.660959\pi$
$139$	−1587.63			−0.968786			−0.484393	+	0.874851i	$0.660959\pi$
$140$		0			0
$141$	617.992			0.369109
$142$	−2775.61	+	1602.50i	−1.64031	+	0.947034i
$143$	−2105.18	−	1215.42i	−1.23107	−	0.710761i
$144$	−685.205	+	1186.81i	−0.396531	+	0.686812i
$145$	−422.443	−	557.593i	−0.241945	−	0.319349i
$146$	3368.45			1.90942
$147$		0			0
$148$			3225.41i			1.79140i
$149$	−876.296	−	1517.79i	−0.481805	−	0.834511i	0.517977	−	0.855395i	$-0.326685\pi$
$149$	−876.296	−	1517.79i	−0.481805	−	0.834511i	−0.999782	+	0.0208837i	$0.993352\pi$
$150$	188.014	−	668.726i	0.102342	−	0.364009i
$151$	−1036.50	+	1795.26i	−0.558602	+	0.967526i	0.439012	+	0.898481i	$0.355329\pi$
$151$	−1036.50	+	1795.26i	−0.558602	+	0.967526i	−0.997614	+	0.0690451i	$0.978005\pi$
$152$	−74.4066	+	42.9587i	−0.0397051	+	0.0229237i
$153$		−	2031.14i		−	1.07326i
$154$		0			0
$155$	−2320.06	+	290.964i	−1.20227	+	0.150779i
$156$	543.965	+	942.175i	0.279180	+	0.483554i
$157$	−944.904	−	545.541i	−0.480328	−	0.277318i	0.240225	−	0.970717i	$-0.422779\pi$
$157$	−944.904	−	545.541i	−0.480328	−	0.277318i	−0.720553	+	0.693399i	$0.756112\pi$
$158$	711.290	+	410.663i	0.358147	+	0.206776i
$159$	−340.378	−	589.552i	−0.169772	−	0.294054i
$160$	47.4852	+	378.633i	0.0234627	+	0.187085i
$161$		0			0
$162$			3030.38i			1.46969i
$163$	−968.260	+	559.025i	−0.465276	+	0.268627i	−0.714260	−	0.699880i	$-0.753237\pi$
$163$	−968.260	+	559.025i	−0.465276	+	0.268627i	0.248984	+	0.968508i	$0.419903\pi$
$164$	−2695.31	+	4668.42i	−1.28335	+	2.22282i
$165$	−469.404	−	197.818i	−0.221473	−	0.0933341i
$166$	−814.064	−	1410.00i	−0.380624	−	0.659261i
$167$			3355.23i			1.55470i	0.629066	+	0.777352i	$0.283438\pi$
$167$			3355.23i			1.55470i	−0.629066	+	0.777352i	$0.716562\pi$
$168$		0			0
$169$	−1536.40			−0.699318
$170$	2590.48	+	3419.24i	1.16871	+	1.54261i
$171$	−30.1305	+	52.1876i	−0.0134745	+	0.0233385i
$172$	3656.63	+	2111.16i	1.62102	+	0.935897i
$173$	2831.07	−	1634.52i	1.24417	−	0.718323i	0.274232	−	0.961664i	$-0.411576\pi$
$173$	2831.07	−	1634.52i	1.24417	−	0.718323i	0.969941	+	0.243340i	$0.0782431\pi$
$174$	347.714			0.151495
$175$		0			0
$176$	−2122.35			−0.908967
$177$	−222.825	+	128.648i	−0.0946246	+	0.0546316i
$178$	−1149.87	−	663.879i	−0.484194	−	0.279550i
$179$	−1064.02	+	1842.93i	−0.444293	+	0.769539i	−0.998003	−	0.0631715i	$-0.979879\pi$
$179$	−1064.02	+	1842.93i	−0.444293	+	0.769539i	0.553709	+	0.832710i	$0.313212\pi$
$180$	−2696.55	−	3559.23i	−1.11660	−	1.47383i
$181$	922.343			0.378769			0.189385	−	0.981903i	$-0.439351\pi$
$181$	922.343			0.378769			0.189385	+	0.981903i	$0.439351\pi$
$182$		0			0
$183$		−	17.7609i		−	0.00717443i
$184$	−3415.52	−	5915.86i	−1.36845	−	2.37023i
$185$	−2137.36	−	900.736i	−0.849416	−	0.357964i
$186$	581.114	−	1006.52i	0.229082	−	0.396782i
$187$	2724.19	−	1572.81i	1.06531	−	0.615056i
$188$			8389.99i			3.25480i
$189$		0			0
$190$	−15.8372	−	126.281i	−0.00604710	−	0.0482178i
$191$	554.086	+	959.705i	0.209907	+	0.363570i	0.951685	−	0.307076i	$-0.0993505\pi$
$191$	554.086	+	959.705i	0.209907	+	0.363570i	−0.741778	+	0.670646i	$0.766017\pi$
$192$	−587.534	−	339.213i	−0.220842	−	0.127503i
$193$	241.661	+	139.523i	0.0901304	+	0.0520368i	0.544388	−	0.838834i	$-0.316762\pi$
$193$	241.661	+	139.523i	0.0901304	+	0.0520368i	−0.454257	+	0.890870i	$0.650095\pi$
$194$	−609.304	−	1055.35i	−0.225492	−	0.390564i
$195$	−776.254	+	97.3518i	−0.285070	+	0.0357513i
$196$		0			0
$197$			1232.54i			0.445759i	0.974846	+	0.222879i	$0.0715456\pi$
$197$			1232.54i			0.445759i	−0.974846	+	0.222879i	$0.928454\pi$
$198$	−4294.85	+	2479.63i	−1.54152	+	0.889999i
$199$	750.322	−	1299.60i	0.267281	−	0.462944i	−0.700878	−	0.713281i	$-0.747208\pi$
$199$	750.322	−	1299.60i	0.267281	−	0.462944i	0.968159	+	0.250337i	$0.0805415\pi$
$200$	4407.30	+	1239.12i	1.55822	+	0.438096i
$201$	−288.268	−	499.295i	−0.101158	−	0.175212i
$202$		−	6808.12i		−	2.37137i
$203$		0			0
$204$	−1407.83			−0.483176
$205$	−2340.89	−	3089.80i	−0.797536	−	1.05269i
$206$	−976.810	+	1691.88i	−0.330376	+	0.572229i
$207$	−4149.29	−	2395.59i	−1.39322	−	0.804373i
$208$	−2822.90	+	1629.80i	−0.941023	+	0.543300i
$209$	−93.3261			−0.0308876
$210$		0			0
$211$	−3971.90			−1.29591			−0.647955	−	0.761679i	$-0.724376\pi$
$211$	−3971.90			−1.29591			−0.647955	+	0.761679i	$0.724376\pi$
$212$	8003.88	−	4621.04i	2.59297	−	1.49705i
$213$	655.044	+	378.190i	0.210718	+	0.121658i
$214$	1095.51	−	1897.48i	0.349942	−	0.606117i
$215$	−2420.15	+	1833.55i	−0.767686	+	0.581614i
$216$	2209.96			0.696150
$217$		0			0
$218$		−	1820.01i		−	0.565445i
$219$	−397.477	−	688.450i	−0.122644	−	0.212425i
$220$	2685.62	−	6372.73i	0.823020	−	1.95295i
$221$	2415.60	−	4183.93i	0.735251	−	1.27349i
$222$	998.414	−	576.435i	0.301843	−	0.174269i
$223$		−	2861.98i		−	0.859429i	−0.902965	−	0.429715i	$-0.858614\pi$
$223$		−	2861.98i		−	0.859429i	0.902965	−	0.429715i	$-0.141386\pi$
$224$		0			0
$225$	3111.62	−	792.941i	0.921961	−	0.234946i
$226$	−2164.31	−	3748.70i	−0.637026	−	1.10336i
$227$	1793.50	+	1035.48i	0.524400	+	0.302763i	0.738733	−	0.673998i	$-0.235424\pi$
$227$	1793.50	+	1035.48i	0.524400	+	0.302763i	−0.214333	+	0.976761i	$0.568758\pi$
$228$	36.1724	+	20.8842i	0.0105069	+	0.00606617i
$229$	2879.11	+	4986.76i	0.830816	+	1.43902i	0.897392	+	0.441234i	$0.145459\pi$
$229$	2879.11	+	4986.76i	0.830816	+	1.43902i	−0.0665762	+	0.997781i	$0.521208\pi$
$230$	10040.2	−	1259.17i	2.87841	−	0.360988i
$231$		0			0
$232$			2291.64i			0.648506i
$233$	−1428.93	+	824.995i	−0.401771	+	0.231962i	−0.687248	−	0.726423i	$-0.741181\pi$
$233$	−1428.93	+	824.995i	−0.401771	+	0.231962i	0.285477	+	0.958386i	$0.407848\pi$
$234$	−3808.33	+	6596.22i	−1.06392	+	1.84277i
$235$	−5559.74	−	2343.01i	−1.54331	−	0.650387i
$236$	−1746.55	−	3025.12i	−0.481741	−	0.834400i
$237$		−	193.833i		−	0.0531258i
$238$		0			0
$239$	4008.31			1.08484			0.542419	−	0.840108i	$-0.317509\pi$
$239$	4008.31			1.08484			0.542419	+	0.840108i	$0.317509\pi$
$240$	−544.442	+	412.480i	−0.146432	+	0.110939i
$241$	1575.61	−	2729.03i	0.421136	−	0.729428i	−0.574915	−	0.818213i	$-0.694965\pi$
$241$	1575.61	−	2729.03i	0.421136	−	0.729428i	0.996051	+	0.0887847i	$0.0282983\pi$
$242$	−1057.94	−	610.804i	−0.281021	−	0.162248i
$243$	2030.25	−	1172.17i	0.535970	−	0.309443i
$244$	241.125			0.0632641
$245$		0			0
$246$	1926.79			0.499381
$247$	−124.131	+	71.6672i	−0.0319768	+	0.0184618i
$248$	6633.55	+	3829.88i	1.69851	+	0.980636i
$249$	−192.119	+	332.760i	−0.0488958	+	0.0846900i
$250$	−4226.82	+	5303.34i	−1.06931	+	1.34165i
$251$	−3531.54			−0.888084			−0.444042	−	0.896006i	$-0.646456\pi$
$251$	−3531.54			−0.888084			−0.444042	+	0.896006i	$0.646456\pi$
$252$		0			0
$253$		−	7420.10i		−	1.84386i
$254$	−2919.77	−	5057.19i	−0.721270	−	1.24928i
$255$	393.154	−	932.918i	0.0965501	−	0.229104i
$256$	3942.72	−	6829.00i	0.962579	−	1.66724i
$257$	4923.81	−	2842.76i	1.19509	−	0.689987i	0.235636	−	0.971841i	$-0.424283\pi$
$257$	4923.81	−	2842.76i	1.19509	−	0.689987i	0.959457	+	0.281854i	$0.0909495\pi$
$258$		−	1509.20i		−	0.364180i
$259$		0			0
$260$	−1321.67	−	10538.6i	−0.315255	−	2.51375i
$261$	803.659	+	1391.98i	0.190595	+	0.330120i
$262$	7164.13	+	4136.21i	1.68932	+	0.975329i
$263$	3846.85	+	2220.98i	0.901927	+	0.520728i	0.877825	−	0.478982i	$-0.158994\pi$
$263$	3846.85	+	2220.98i	0.901927	+	0.520728i	0.0241019	+	0.999710i	$0.492327\pi$
$264$	834.340	+	1445.12i	0.194508	+	0.336898i
$265$	827.013	+	6594.36i	0.191710	+	1.52863i
$266$		0			0
$267$			313.351i			0.0718230i
$268$	6778.53	−	3913.58i	1.54502	−	0.892016i
$269$	839.565	−	1454.17i	0.190294	−	0.329599i	−0.755053	−	0.655663i	$-0.772389\pi$
$269$	839.565	−	1454.17i	0.190294	−	0.329599i	0.945348	+	0.326064i	$0.105722\pi$
$270$	−1271.31	+	3016.69i	−0.286553	+	0.679963i
$271$	−570.883	−	988.799i	−0.127966	−	0.221643i	0.794923	−	0.606711i	$-0.207511\pi$
$271$	−570.883	−	988.799i	−0.127966	−	0.221643i	−0.922888	+	0.385068i	$0.874178\pi$
$272$		−	4218.07i		−	0.940287i
$273$		0			0
$274$	−2609.92			−0.575442
$275$	3472.98	+	3559.32i	0.761558	+	0.780492i
$276$	−1660.44	+	2875.97i	−0.362126	+	0.627221i
$277$	−2350.93	−	1357.31i	−0.509940	−	0.294414i	0.222869	−	0.974848i	$-0.428458\pi$
$277$	−2350.93	−	1357.31i	−0.509940	−	0.294414i	−0.732809	+	0.680434i	$0.761791\pi$
$278$	−6671.97	+	3852.06i	−1.43942	+	0.831048i
$279$	5372.44			1.15283
$280$		0			0
$281$	−5343.68			−1.13444			−0.567219	−	0.823567i	$-0.691981\pi$
$281$	−5343.68			−1.13444			−0.567219	+	0.823567i	$0.691981\pi$
$282$	2597.09	−	1499.43i	0.548420	−	0.316631i
$283$	−5887.65	−	3399.24i	−1.23669	−	0.714006i	−0.268277	−	0.963342i	$-0.586454\pi$
$283$	−5887.65	−	3399.24i	−1.23669	−	0.714006i	−0.968417	+	0.249336i	$0.919788\pi$
$284$	−5134.38	+	8893.01i	−1.07278	+	1.85811i
$285$	−23.9407	+	18.1380i	−0.00497589	+	0.00376983i
$286$	−11795.9			−2.43883
$287$		0			0
$288$		−	876.780i		−	0.179391i
$289$	669.389	+	1159.42i	0.136249	+	0.235990i
$290$	−3128.19	−	1318.29i	−0.633426	−	0.266941i
$291$	−143.796	+	249.061i	−0.0289672	+	0.0501726i
$292$	9346.54	−	5396.23i	1.87317	−	1.08147i
$293$		−	5119.59i		−	1.02078i	−0.859942	−	0.510392i	$-0.829500\pi$
$293$		−	5119.59i		−	1.02078i	0.859942	−	0.510392i	$-0.170500\pi$
$294$		0			0
$295$	2492.38	−	312.575i	0.491905	−	0.0616909i
$296$	3799.04	+	6580.14i	0.745996	+	1.29210i
$297$	2078.92	+	1200.26i	0.406165	+	0.234499i
$298$	−7365.21	−	4252.30i	−1.43173	−	0.826608i
$299$	−5698.06	−	9869.33i	−1.10210	−	1.90889i
$300$	−549.606	−	2156.73i	−0.105772	−	0.415063i
$301$		0			0
$302$			10059.4i			1.91673i
$303$	−1391.46	+	803.357i	−0.263819	+	0.152316i
$304$	−62.5720	+	108.378i	−0.0118051	+	0.0204470i
$305$	−67.3371	+	159.785i	−0.0126417	+	0.0299975i
$306$	−4928.15	−	8535.80i	−0.920665	−	1.59464i
$307$		−	4188.66i		−	0.778695i	−0.921091	−	0.389347i	$-0.872701\pi$
$307$		−	4188.66i		−	0.778695i	0.921091	−	0.389347i	$-0.127299\pi$
$308$		0			0
$309$	461.054			0.0848817
$310$	−9044.00	+	6851.91i	−1.65698	+	1.25536i
$311$	−4879.59	+	8451.70i	−0.889699	+	1.54100i	−0.0494671	+	0.998776i	$0.515752\pi$
$311$	−4879.59	+	8451.70i	−0.889699	+	1.54100i	−0.840232	+	0.542228i	$0.817581\pi$
$312$	2219.48	+	1281.42i	0.402735	+	0.232519i
$313$	−5162.12	+	2980.35i	−0.932205	+	0.538209i	−0.887508	−	0.460792i	$-0.847566\pi$
$313$	−5162.12	+	2980.35i	−0.932205	+	0.538209i	−0.0446970	+	0.999001i	$0.514232\pi$
$314$	−5294.57			−0.951560
$315$		0			0
$316$	2631.52			0.468463
$317$	−2357.62	+	1361.18i	−0.417720	+	0.241171i	−0.694102	−	0.719877i	$-0.744198\pi$
$317$	−2357.62	+	1361.18i	−0.417720	+	0.241171i	0.276381	+	0.961048i	$0.410865\pi$
$318$	−2860.85	−	1651.71i	−0.504493	−	0.291269i
$319$	−1244.62	+	2155.75i	−0.218450	+	0.378367i
$320$	3999.66	+	5279.24i	0.698711	+	0.922246i
$321$	−517.081			−0.0899085
$322$		0			0
$323$		−	185.481i		−	0.0319519i
$324$	4854.65	+	8408.50i	0.832416	+	1.44179i
$325$	7352.62	+	2067.21i	1.25492	+	0.352825i
$326$	−2712.72	+	4698.57i	−0.460870	+	0.798250i
$327$	−371.978	+	214.762i	−0.0629065	+	0.0363191i
$328$			12698.7i			2.13771i
$329$		0			0
$330$	−2452.62	+	307.588i	−0.409128	+	0.0513097i
$331$	−189.377	−	328.010i	−0.0314474	−	0.0544684i	0.849873	−	0.526987i	$-0.176678\pi$
$331$	−189.377	−	328.010i	−0.0314474	−	0.0544684i	−0.881321	+	0.472518i	$0.843345\pi$
$332$	−4517.62	−	2608.25i	−0.746797	−	0.431163i
$333$	4615.20	+	2664.59i	0.759494	+	0.438494i
$334$	8140.78	+	14100.2i	1.33366	+	2.30997i
$335$	700.402	+	5584.80i	0.114230	+	0.910836i
$336$		0			0
$337$			8031.54i			1.29824i	0.760687	+	0.649118i	$0.224862\pi$
$337$			8031.54i			1.29824i	−0.760687	+	0.649118i	$0.775138\pi$
$338$	−6456.67	+	3727.76i	−1.03904	+	0.599892i
$339$	−510.777	+	884.693i	−0.0818337	+	0.141740i
$340$	12665.5	+	5337.54i	2.02024	+	0.851379i
$341$	4160.14	+	7205.57i	0.660658	+	1.14429i
$342$			292.422i			0.0462350i
$343$		0			0
$344$	9946.49			1.55895
$345$	−1442.10	−	1903.46i	−0.225044	−	0.297040i
$346$	7931.63	−	13738.0i	1.23239	−	2.13456i
$347$	563.035	+	325.069i	0.0871047	+	0.0502899i	0.542920	−	0.839785i	$-0.317319\pi$
$347$	563.035	+	325.069i	0.0871047	+	0.0502899i	−0.455815	+	0.890075i	$0.650652\pi$
$348$	964.812	−	557.034i	0.148619	−	0.0858051i
$349$	−1240.68			−0.190292			−0.0951462	−	0.995463i	$-0.530332\pi$
$349$	−1240.68			−0.190292			−0.0951462	+	0.995463i	$0.530332\pi$
$350$		0			0
$351$	3686.83			0.560651
$352$	1175.95	−	678.933i	0.178063	−	0.102805i
$353$	−6818.95	−	3936.92i	−1.02815	−	0.593601i	−0.111694	−	0.993743i	$-0.535628\pi$
$353$	−6818.95	−	3936.92i	−1.02815	−	0.593601i	−0.916453	+	0.400141i	$0.868961\pi$
$354$	−624.276	+	1081.28i	−0.0937286	+	0.162343i
$355$	−4459.23	−	5885.85i	−0.666680	−	0.879967i
$356$	−4254.11			−0.633336
$357$		0			0
$358$			10326.5i			1.52450i
$359$	−203.360	−	352.231i	−0.0298968	−	0.0517828i	0.850690	−	0.525668i	$-0.176185\pi$
$359$	−203.360	−	352.231i	−0.0298968	−	0.0517828i	−0.880587	+	0.473885i	$0.842851\pi$
$360$	−9693.44	−	4085.05i	−1.41914	−	0.598058i
$361$	3426.75	−	5935.30i	0.499599	−	0.865331i
$362$	3876.11	−	2237.88i	0.562774	−	0.324917i
$363$			288.299i			0.0416854i
$364$		0			0
$365$	965.746	+	7700.57i	0.138492	+	1.10429i
$366$	−43.0930	−	74.6393i	−0.00615440	−	0.0106597i
$367$	566.619	+	327.138i	0.0805920	+	0.0465298i	0.539754	−	0.841822i	$-0.318517\pi$
$367$	566.619	+	327.138i	0.0805920	+	0.0465298i	−0.459162	+	0.888352i	$0.651850\pi$
$368$	−8616.82	−	4974.93i	−1.22061	−	0.704717i
$369$	4453.33	+	7713.39i	0.628268	+	1.08819i
$370$	−11167.6	+	1400.56i	−1.56913	+	0.196788i
$371$		0			0
$372$		−	3723.76i		−	0.519000i
$373$	4763.50	−	2750.21i	0.661245	−	0.381770i	−0.131506	−	0.991315i	$-0.541981\pi$
$373$	4763.50	−	2750.21i	0.661245	−	0.381770i	0.792751	+	0.609545i	$0.208648\pi$
$374$	7632.21	−	13219.4i	1.05522	−	1.82769i
$375$	1582.67	+	238.090i	0.217943	+	0.0327865i
$376$	9882.13	+	17116.4i	1.35540	+	2.34763i
$377$			3823.10i			0.522280i
$378$		0			0
$379$	1771.48			0.240091			0.120046	−	0.992768i	$-0.461696\pi$
$379$	1771.48			0.240091			0.120046	+	0.992768i	$0.461696\pi$
$380$	−246.245	−	325.024i	−0.0332423	−	0.0438774i
$381$	−689.065	+	1193.50i	−0.0926559	+	0.160485i
$382$	4657.05	+	2688.75i	0.623758	+	0.360127i
$383$	7712.17	−	4452.62i	1.02891	−	0.594043i	0.112240	−	0.993681i	$-0.464198\pi$
$383$	7712.17	−	4452.62i	1.02891	−	0.594043i	0.916673	+	0.399638i	$0.130864\pi$
$384$	−2979.42			−0.395945
$385$		0			0
$386$	1354.10			0.178554
$387$	6041.66	−	3488.15i	0.793579	−	0.458173i
$388$	−3381.31	−	1952.20i	−0.442422	−	0.255433i
$389$	4686.74	−	8117.67i	0.610866	−	1.05805i	−0.380228	−	0.924893i	$-0.624155\pi$
$389$	4686.74	−	8117.67i	0.610866	−	1.05805i	0.991095	−	0.133159i	$-0.0425121\pi$
$390$	−3025.98	+	2292.54i	−0.392888	+	0.297659i
$391$	14747.1			1.90740
$392$		0			0
$393$		−	1952.29i		−	0.250586i
$394$	2990.49	+	5179.68i	0.382383	+	0.662306i
$395$	−734.883	+	1743.81i	−0.0936101	+	0.222128i
$396$	−7944.70	+	13760.6i	−1.00817	+	1.74621i
$397$	−9092.24	+	5249.41i	−1.14944	+	0.663628i	−0.948750	−	0.316027i	$-0.897651\pi$
$397$	−9092.24	+	5249.41i	−1.14944	+	0.663628i	−0.200687	+	0.979655i	$0.564317\pi$
$398$		−	7282.01i		−	0.917121i
$399$		0			0
$400$	6461.89	−	1646.70i	0.807736	−	0.205837i
$401$	1399.27	+	2423.60i	0.174255	+	0.301818i	0.939903	−	0.341441i	$-0.110915\pi$
$401$	1399.27	+	2423.60i	0.174255	+	0.301818i	−0.765648	+	0.643259i	$0.777582\pi$
$402$	−2422.87	−	1398.85i	−0.300602	−	0.173552i
$403$	11066.6	+	6389.33i	1.36791	+	0.789764i
$404$	−10906.5	−	18890.7i	−1.34312	−	2.32635i
$405$	−6927.72	+	868.821i	−0.849978	+	0.106598i
$406$		0			0
$407$			8253.28i			1.00516i
$408$	−2872.11	+	1658.21i	−0.348506	+	0.201210i
$409$	−3795.09	+	6573.29i	−0.458815	+	0.794690i	−0.998899	−	0.0469208i	$-0.985059\pi$
$409$	−3795.09	+	6573.29i	−0.458815	+	0.794690i	0.540084	+	0.841611i	$0.318392\pi$
$410$	−17334.3	−	7305.08i	−2.08800	−	0.879932i
$411$	307.971	+	533.421i	0.0369612	+	0.0640187i
$412$			6259.36i			0.748487i
$413$		0			0
$414$	−23249.7			−2.76004
$415$	2989.99	−	2265.27i	0.353669	−	0.267947i
$416$	1042.74	−	1806.07i	0.122895	−	0.212860i
$417$	1574.58	+	909.086i	0.184911	+	0.106758i
$418$	−392.200	+	226.437i	−0.0458926	+	0.0264961i
$419$	−11070.5			−1.29076			−0.645382	−	0.763860i	$-0.723302\pi$
$419$	−11070.5			−1.29076			−0.645382	+	0.763860i	$0.723302\pi$
$420$		0			0
$421$	8891.82			1.02936			0.514680	−	0.857382i	$-0.327911\pi$
$421$	8891.82			1.02936			0.514680	+	0.857382i	$0.327911\pi$
$422$	−16691.8	+	9637.00i	−1.92546	+	1.11166i
$423$	12005.1	+	6931.17i	1.37993	+	0.796702i
$424$	10885.8	−	18854.7i	1.24684	−	2.15959i
$425$	−7073.98	+	6902.38i	−0.807385	+	0.787799i
$426$	3670.40			0.417444
$427$		0			0
$428$		−	7019.99i		−	0.792814i
$429$	1391.92	+	2410.87i	0.156649	+	0.271324i
$430$	−5721.85	+	13577.4i	−0.641702	+	1.52270i
$431$	−7619.87	+	13198.0i	−0.851592	+	1.47500i	0.0281792	+	0.999603i	$0.491029\pi$
$431$	−7619.87	+	13198.0i	−0.851592	+	1.47500i	−0.879771	+	0.475398i	$0.842304\pi$
$432$	2787.68	−	1609.47i	0.310469	−	0.179249i
$433$		−	15959.0i		−	1.77123i	−0.464421	−	0.885615i	$-0.653737\pi$
$433$		−	15959.0i		−	1.77123i	0.464421	−	0.885615i	$-0.346263\pi$
$434$		0			0
$435$	99.6907	+	794.904i	0.0109880	+	0.0876154i
$436$	−2915.65	−	5050.05i	−0.320262	−	0.554710i
$437$	−378.907	−	218.762i	−0.0414774	−	0.0239470i
$438$	−3340.77	−	1928.79i	−0.364447	−	0.210414i
$439$	−5417.23	−	9382.92i	−0.588953	−	1.02010i	−0.994370	−	0.105964i	$-0.966207\pi$
$439$	−5417.23	−	9382.92i	−0.588953	−	1.02010i	0.405417	−	0.914132i	$-0.367126\pi$
$440$	−2027.19	−	16164.2i	−0.219642	−	1.75136i
$441$		0			0
$442$		−	23443.8i		−	2.52287i
$443$	−7147.51	+	4126.62i	−0.766565	+	0.442577i	−0.831648	−	0.555303i	$-0.812602\pi$
$443$	−7147.51	+	4126.62i	−0.766565	+	0.442577i	0.0650828	+	0.997880i	$0.479269\pi$
$444$	1846.89	−	3198.90i	0.197409	−	0.341922i
$445$	1188.01	−	2819.04i	0.126556	−	0.300304i
$446$	−6944.02	−	12027.4i	−0.737239	−	1.27694i
$447$			2007.09i			0.212376i
$448$		0			0
$449$	11022.5			1.15853			0.579267	−	0.815138i	$-0.303339\pi$
$449$	11022.5			1.15853			0.579267	+	0.815138i	$0.303339\pi$
$450$	11152.6	−	10882.0i	1.16830	−	1.13996i
$451$	−6896.85	+	11945.7i	−0.720089	+	1.24723i
$452$	−12010.8	−	6934.42i	−1.24986	−	0.721610i
$453$	2055.95	−	1187.01i	0.213239	−	0.123113i
$454$	10049.5			1.03887
$455$		0			0
$456$	98.3934			0.0101046
$457$	8078.79	−	4664.29i	0.826936	−	0.477432i	−0.0258662	−	0.999665i	$-0.508234\pi$
$457$	8078.79	−	4664.29i	0.826936	−	0.477432i	0.852803	+	0.522234i	$0.174901\pi$
$458$	24198.7	+	13971.1i	2.46885	+	1.42539i
$459$	−2385.46	+	4131.74i	−0.242579	+	0.420160i
$460$	25841.8	−	19578.2i	2.61930	−	1.98443i
$461$	16806.4			1.69794			0.848972	−	0.528438i	$-0.177222\pi$
$461$	16806.4			1.69794			0.848972	+	0.528438i	$0.177222\pi$
$462$		0			0
$463$		−	8238.55i		−	0.826950i	−0.910515	−	0.413475i	$-0.864315\pi$
$463$		−	8238.55i		−	0.826950i	0.910515	−	0.413475i	$-0.135685\pi$
$464$	1668.96	+	2890.72i	0.166981	+	0.289220i
$465$	2467.60	+	1039.90i	0.246091	+	0.103708i
$466$	−4003.36	+	6934.03i	−0.397966	+	0.689297i
$467$	−16943.0	+	9782.06i	−1.67886	+	0.969293i	−0.716478	+	0.697610i	$0.754247\pi$
$467$	−16943.0	+	9782.06i	−1.67886	+	0.969293i	−0.962387	+	0.271683i	$0.912420\pi$
$468$			24403.6i			2.41038i
$469$		0			0
$470$	−29049.4	+	3643.15i	−2.85096	+	0.357545i
$471$	624.759	+	1082.11i	0.0611197	+	0.105862i
$472$	−7126.26	−	4114.35i	−0.694942	−	0.401225i
$473$	9356.71	+	5402.10i	0.909560	+	0.525135i
$474$	−470.296	−	814.577i	−0.0455726	−	0.0789341i
$475$	284.149	−	72.4103i	0.0274476	−	0.00699455i
$476$		0			0
$477$		−	15270.2i		−	1.46578i
$478$	16844.8	−	9725.35i	1.61185	−	0.930601i
$479$	−626.668	+	1085.42i	−0.0597770	+	0.103537i	−0.894365	−	0.447337i	$-0.852372\pi$
$479$	−626.668	+	1085.42i	−0.0597770	+	0.103537i	0.834588	+	0.550874i	$0.185706\pi$
$480$	169.712	−	402.711i	0.0161380	−	0.0382941i
$481$	6337.88	+	10977.5i	0.600795	+	1.04061i
$482$		−	15291.5i		−	1.44504i
$483$		0			0
$484$	−3914.01			−0.367582
$485$	2237.92	−	1695.49i	0.209523	−	0.158739i
$486$	5688.04	−	9851.98i	0.530895	−	0.919537i
$487$	−3085.94	−	1781.67i	−0.287141	−	0.165781i	0.349511	−	0.936932i	$-0.386348\pi$
$487$	−3085.94	−	1781.67i	−0.287141	−	0.165781i	−0.636652	+	0.771152i	$0.719681\pi$
$488$	491.917	−	284.008i	0.0456312	−	0.0263452i
$489$	1280.40			0.118409
$490$		0			0
$491$	−10148.4			−0.932774			−0.466387	−	0.884581i	$-0.654445\pi$
$491$	−10148.4			−0.932774			−0.466387	+	0.884581i	$0.654445\pi$
$492$	5346.32	−	3086.70i	0.489900	−	0.282844i
$493$	−4284.45	−	2473.63i	−0.391404	−	0.225977i
$494$	−347.771	+	602.358i	−0.0316740	+	0.0548610i
$495$	−6900.00	−	9107.48i	−0.626530	−	0.826972i
$496$	11156.9			1.01000
$497$		0			0
$498$			1864.55i			0.167776i
$499$	4105.28	+	7110.55i	0.368292	+	0.637900i	0.989299	−	0.145905i	$-0.0466095\pi$
$499$	4105.28	+	7110.55i	0.368292	+	0.637900i	−0.621007	+	0.783805i	$0.713276\pi$
$500$	−3232.36	+	21486.7i	−0.289112	+	1.92183i
$501$	1921.22	−	3327.66i	0.171325	−	0.296744i
$502$	−14841.2	+	8568.56i	−1.31951	+	0.761820i
$503$		−	8479.88i		−	0.751688i	−0.926683	−	0.375844i	$-0.877353\pi$
$503$		−	8479.88i		−	0.751688i	0.926683	−	0.375844i	$-0.122647\pi$
$504$		0			0
$505$	15564.0	−	1951.91i	1.37146	−	0.171998i
$506$	−18003.3	−	31182.7i	−1.58171	−	2.73961i
$507$	1523.77	+	879.751i	0.133478	+	0.0770634i
$508$	−16203.1	−	9354.89i	−1.41515	−	0.817040i
$509$	−3511.50	−	6082.10i	−0.305785	−	0.529636i	0.671651	−	0.740868i	$-0.265586\pi$
$509$	−3511.50	−	6082.10i	−0.305785	−	0.529636i	−0.977436	+	0.211232i	$0.932252\pi$
$510$	−611.317	−	4874.46i	−0.0530776	−	0.423225i
$511$		0			0
$512$		−	17451.7i		−	1.50638i
$513$	122.583	−	70.7732i	0.0105500	−	0.00609106i
$514$	13794.8	−	23893.2i	1.18378	−	2.05036i
$515$	−4147.85	−	1748.00i	−0.354905	−	0.149565i
$516$	−2417.72	−	4187.61i	−0.206268	−	0.357266i
$517$			21468.6i			1.82628i
$518$		0			0
$519$	−3743.73			−0.316631
$520$	−15109.2	−	19943.0i	−1.27419	−	1.68184i
$521$	3279.25	−	5679.82i	0.275751	−	0.477615i	−0.694573	−	0.719422i	$-0.744407\pi$
$521$	3279.25	−	5679.82i	0.275751	−	0.477615i	0.970324	+	0.241807i	$0.0777400\pi$
$522$	6754.69	+	3899.82i	0.566370	+	0.326994i
$523$	−91.9094	+	53.0639i	−0.00768435	+	0.00443656i	−0.503837	−	0.863799i	$-0.668079\pi$
$523$	−91.9094	+	53.0639i	−0.00768435	+	0.00443656i	0.496153	+	0.868235i	$0.334746\pi$
$524$	26504.7			2.20966
$525$		0			0
$526$	21555.0			1.78677
$527$	−14320.7	+	8268.08i	−1.18372	+	0.683421i
$528$	2104.91	+	1215.27i	0.173493	+	0.100166i
$529$	11309.7	−	19588.9i	0.929537	−	1.61001i
$530$	19475.3	+	25706.0i	1.59614	+	2.10679i
$531$	−5771.48			−0.471677
$532$		0			0
$533$			21185.0i			1.72162i
$534$	760.281	+	1316.84i	0.0616115	+	0.106714i
$535$	4651.89	+	1960.42i	0.375923	+	0.158423i
$536$	9219.21	−	15968.1i	0.742928	−	1.28679i
$537$	2110.55	−	1218.53i	0.169603	−	0.0979204i
$538$		−	8148.12i		−	0.652956i
$539$		0			0
$540$	1305.18	+	10407.1i	0.104011	+	0.829354i
$541$	685.454	+	1187.24i	0.0544732	+	0.0943503i	0.891976	−	0.452082i	$-0.149319\pi$
$541$	685.454	+	1187.24i	0.0544732	+	0.0943503i	−0.837503	+	0.546433i	$0.815985\pi$
$542$	−4798.23	−	2770.26i	−0.380262	−	0.219544i
$543$	−914.763	−	528.138i	−0.0722951	−	0.0417396i
$544$	1349.35	+	2337.14i	0.106347	+	0.184198i
$545$	4160.71	−	521.804i	0.327019	−	0.0410122i
$546$		0			0
$547$		−	5324.93i		−	0.416229i	−0.978104	−	0.208115i	$-0.933267\pi$
$547$		−	5324.93i		−	0.416229i	0.978104	−	0.208115i	$-0.0667327\pi$
$548$	−7241.83	+	4181.07i	−0.564517	+	0.325924i
$549$	199.199	−	345.023i	0.0154856	−	0.0268219i
$550$	23231.0	+	6531.46i	1.80104	+	0.506368i
$551$	73.3890	+	127.114i	0.00567419	+	0.00982798i
$552$			7822.98i			0.603203i
$553$		0			0
$554$	−13172.9			−1.01022
$555$	1604.03	+	2117.20i	0.122680	+	0.161928i
$556$	−12341.9	+	21376.9i	−0.941394	+	1.63054i
$557$	13757.7	+	7942.99i	1.04655	+	0.604229i	0.921683	−	0.387944i	$-0.126815\pi$
$557$	13757.7	+	7942.99i	1.04655	+	0.604229i	0.124872	+	0.992173i	$0.460148\pi$
$558$	22577.5	−	13035.1i	1.71287	−	0.988925i
$559$	16593.6			1.25551
$560$		0			0
$561$	−3602.40			−0.271112
$562$	−22456.6	+	12965.3i	−1.68554	+	0.973148i
$563$	−15538.1	−	8970.95i	−1.16315	−	0.671546i	−0.211095	−	0.977466i	$-0.567703\pi$
$563$	−15538.1	−	8970.95i	−1.16315	−	0.671546i	−0.952057	+	0.305919i	$0.901036\pi$
$564$	4804.15	−	8321.04i	0.358673	−	0.621239i
$565$	7949.34	−	6022.57i	0.591914	−	0.448445i
$566$	−32990.2			−2.44997
$567$		0			0
$568$			24190.1i			1.78696i
$569$	−9403.52	−	16287.4i	−0.692823	−	1.20000i	−0.970909	−	0.239448i	$-0.923033\pi$
$569$	−9403.52	−	16287.4i	−0.692823	−	1.20000i	0.278086	−	0.960556i	$-0.410300\pi$
$570$	−56.6021	+	134.311i	−0.00415930	+	0.00986963i
$571$	2965.75	−	5136.83i	0.217360	−	0.376479i	−0.736640	−	0.676285i	$-0.763589\pi$
$571$	2965.75	−	5136.83i	0.217360	−	0.376479i	0.954000	+	0.299806i	$0.0969220\pi$
$572$	−32730.4	+	18896.9i	−2.39253	+	1.38133i
$573$		−	1269.09i		−	0.0925253i
$574$		0			0
$575$	5757.14	+	22591.9i	0.417547	+	1.63851i
$576$	−7608.97	−	13179.1i	−0.550417	−	0.953351i
$577$	9949.81	+	5744.53i	0.717879	+	0.414467i	0.813971	−	0.580905i	$-0.197301\pi$
$577$	9949.81	+	5744.53i	0.717879	+	0.414467i	−0.0960927	+	0.995372i	$0.530635\pi$
$578$	5626.17	+	3248.27i	0.404875	+	0.233755i
$579$	−159.784	−	276.753i	−0.0114687	−	0.0198644i
$580$	−10791.8	+	1353.42i	−0.772593	+	0.0968926i
$581$		0			0
$582$			1395.56i			0.0993950i
$583$	20480.6	−	11824.5i	1.45492	−	0.839999i
$584$	12711.9	−	22017.6i	0.900721	−	1.56009i
$585$	−16171.4	−	6815.01i	−1.14291	−	0.481652i
$586$	−12421.6	−	21514.9i	−0.875653	−	1.51668i
$587$			4853.49i			0.341269i	0.985334	+	0.170634i	$0.0545817\pi$
$587$			4853.49i			0.341269i	−0.985334	+	0.170634i	$0.945418\pi$
$588$		0			0
$589$	490.604			0.0343208
$590$	9715.74	−	7360.84i	0.677951	−	0.513628i
$591$	705.756	−	1222.41i	0.0491217	−	0.0850813i
$592$	9584.38	+	5533.55i	0.665398	+	0.384168i
$593$	2327.99	−	1344.07i	0.161213	−	0.0930762i	−0.417223	−	0.908804i	$-0.636997\pi$
$593$	2327.99	−	1344.07i	0.161213	−	0.0930762i	0.578436	+	0.815728i	$0.303663\pi$
$594$	11648.8			0.804637
$595$		0			0
$596$	−27248.6			−1.87273
$597$	−1488.31	+	859.277i	−0.102031	+	0.0589076i
$598$	−47891.8	−	27650.3i	−3.27498	−	1.89081i
$599$	−11479.1	+	19882.3i	−0.783008	+	1.35621i	0.147174	+	0.989111i	$0.452982\pi$
$599$	−11479.1	+	19882.3i	−0.783008	+	1.35621i	−0.930182	+	0.367099i	$0.880351\pi$
$600$	−3661.55	−	3752.58i	−0.249137	−	0.255331i
$601$	−7566.12			−0.513525			−0.256762	−	0.966475i	$-0.582656\pi$
$601$	−7566.12			−0.513525			−0.256762	+	0.966475i	$0.582656\pi$
$602$		0			0
$603$		−	12932.4i		−	0.873381i
$604$	16115.0	+	27912.1i	1.08561	+	1.88034i
$605$	1093.04	−	2593.67i	0.0734516	−	0.174294i
$606$	−3898.36	+	6752.16i	−0.261320	+	0.452620i
$607$	20087.6	−	11597.6i	1.34321	−	0.775505i	0.355937	−	0.934510i	$-0.384162\pi$
$607$	20087.6	−	11597.6i	1.34321	−	0.775505i	0.987278	+	0.159004i	$0.0508284\pi$
$608$		−	80.0663i		−	0.00534065i
$609$		0			0
$610$	104.703	+	834.869i	0.00694966	+	0.0554145i
$611$	16486.2	+	28554.9i	1.09159	+	1.89068i
$612$	−27348.6	−	15789.7i	−1.80637	−	1.04291i
$613$	−8163.80	−	4713.37i	−0.537900	−	0.310557i	0.206328	−	0.978483i	$-0.433849\pi$
$613$	−8163.80	−	4713.37i	−0.537900	−	0.310557i	−0.744227	+	0.667926i	$0.767182\pi$
$614$	−10162.9	−	17602.7i	−0.667983	−	1.15698i
$615$	552.417	+	4404.81i	0.0362205	+	0.288812i
$616$		0			0
$617$			811.353i			0.0529398i	0.999650	+	0.0264699i	$0.00842662\pi$
$617$			811.353i			0.0529398i	−0.999650	+	0.0264699i	$0.991573\pi$
$618$	1937.56	−	1118.65i	0.126117	−	0.0728136i
$619$	−4641.44	+	8039.20i	−0.301381	+	0.522008i	−0.976449	−	0.215748i	$-0.930781\pi$
$619$	−4641.44	+	8039.20i	−0.301381	+	0.522008i	0.675068	+	0.737756i	$0.264114\pi$
$620$	−14118.0	+	33500.6i	−0.914502	+	2.17003i
$621$	5626.98	+	9746.22i	0.363612	+	0.629794i
$622$			47357.3i			3.05282i
$623$		0			0
$624$	3732.93			0.239482
$625$	−13335.7	−	8142.38i	−0.853488	−	0.521113i
$626$	−14462.4	+	25049.6i	−0.923378	+	1.59934i
$627$	92.5591	+	53.4390i	0.00589546	+	0.00340375i
$628$	−14691.0	+	8481.85i	−0.933495	+	0.538954i
$629$	−16403.0			−1.03979
$630$		0			0
$631$	−26078.4			−1.64527			−0.822634	−	0.568572i	$-0.807496\pi$
$631$	−26078.4			−1.64527			−0.822634	+	0.568572i	$0.807496\pi$
$632$	5368.54	−	3099.53i	0.337894	−	0.195083i
$633$	3939.26	+	2274.33i	0.247348	+	0.142807i
$634$	−6605.22	+	11440.6i	−0.413765	+	0.716662i
$635$	10724.1	−	8124.76i	0.670192	−	0.507750i
$636$	−10584.1			−0.659887
$637$		0			0
$638$			12079.3i			0.749567i
$639$	8483.27	+	14693.4i	0.525184	+	0.909646i
$640$	26804.2	+	11295.9i	1.65551	+	0.697674i
$641$	15485.7	−	26822.0i	0.954210	−	1.65274i	0.218046	−	0.975939i	$-0.430032\pi$
$641$	15485.7	−	26822.0i	0.954210	−	1.65274i	0.736165	−	0.676802i	$-0.236635\pi$
$642$	−2173.01	+	1254.59i	−0.133586	+	0.0771257i
$643$		−	7482.92i		−	0.458939i	−0.973316	−	0.229469i	$-0.926301\pi$
$643$		−	7482.92i		−	0.458939i	0.973316	−	0.229469i	$-0.0736990\pi$
$644$		0			0
$645$	3450.15	−	432.692i	0.210620	−	0.0264143i
$646$	−450.032	−	779.478i	−0.0274091	−	0.0474739i
$647$	−23400.2	−	13510.1i	−1.42188	−	0.820925i	−0.425423	−	0.904995i	$-0.639875\pi$
$647$	−23400.2	−	13510.1i	−1.42188	−	0.820925i	−0.996460	+	0.0840701i	$0.973208\pi$
$648$	19807.9	+	11436.1i	1.20081	+	0.693289i
$649$	−4469.14	−	7740.77i	−0.270306	−	0.468185i
$650$	35914.8	−	9152.26i	2.16722	−	0.552279i
$651$		0			0
$652$			17383.0i			1.04413i
$653$	−27125.2	+	15660.7i	−1.62556	+	0.938518i	−0.640165	+	0.768237i	$0.721134\pi$
$653$	−27125.2	+	15660.7i	−1.62556	+	0.938518i	−0.985396	+	0.170280i	$0.945533\pi$
$654$	−1042.15	+	1805.06i	−0.0623108	+	0.107926i
$655$	−7401.77	+	17563.7i	−0.441543	+	1.04774i
$656$	9248.21	+	16018.4i	0.550430	+	0.953373i
$657$		−	17831.8i		−	1.05888i
$658$		0			0
$659$	14051.9			0.830627			0.415314	−	0.909678i	$-0.363672\pi$
$659$	14051.9			0.830627			0.415314	+	0.909678i	$0.363672\pi$
$660$	−6312.60	+	4782.55i	−0.372300	+	0.282061i
$661$	−598.051	+	1035.86i	−0.0351914	+	0.0609533i	−0.883085	−	0.469214i	$-0.844537\pi$
$661$	−598.051	+	1035.86i	−0.0351914	+	0.0609533i	0.847893	+	0.530167i	$0.177871\pi$
$662$	−1591.70	−	918.966i	−0.0934487	−	0.0539526i
$663$	−4791.48	+	2766.36i	−0.280672	+	0.162046i
$664$	−12288.5			−0.718201
$665$		0			0
$666$	25860.3			1.50460
$667$	−10106.4	+	5834.96i	−0.586691	+	0.338726i
$668$	45176.9	+	26082.9i	2.61669	+	1.51075i
$669$	−1638.79	+	2838.46i	−0.0947073	+	0.164038i
$670$	16493.8	+	21770.5i	0.951060	+	1.25533i
$671$	616.998			0.0354977
$672$		0			0
$673$		−	4801.54i		−	0.275016i	−0.990501	−	0.137508i	$-0.956091\pi$
$673$		−	4801.54i		−	0.275016i	0.990501	−	0.137508i	$-0.0439093\pi$
$674$	19486.9	+	33752.3i	1.11366	+	1.92891i
$675$	−7260.91	−	2041.42i	−0.414033	−	0.116406i
$676$	−11943.7	+	20687.1i	−0.679545	+	1.17701i
$677$	1252.62	−	723.199i	0.0711108	−	0.0410558i	−0.464023	−	0.885823i	$-0.653595\pi$
$677$	1252.62	−	723.199i	0.0711108	−	0.0410558i	0.535134	+	0.844767i	$0.320261\pi$
$678$			4957.18i			0.280796i
$679$		0			0
$680$	32125.6	−	4028.94i	1.81170	−	0.227210i
$681$	−1185.84	−	2053.94i	−0.0667276	−	0.115576i
$682$	34965.7	+	20187.4i	1.96320	+	1.13346i
$683$	−11612.3	−	6704.37i	−0.650560	−	0.375601i	0.138111	−	0.990417i	$-0.455897\pi$
$683$	−11612.3	−	6704.37i	−0.650560	−	0.375601i	−0.788671	+	0.614816i	$0.789230\pi$
$684$	468.458	+	811.392i	0.0261870	+	0.0453573i
$685$	−748.273	−	5966.51i	−0.0417373	−	0.332801i
$686$		0			0
$687$		−	6594.37i		−	0.366217i
$688$	12546.7	−	7243.85i	0.695260	−	0.401408i
$689$	18160.5	−	31455.0i	1.00415	−	1.73924i
$690$	−10678.7	−	4500.27i	−0.589177	−	0.248293i
$691$	−1306.74	−	2263.34i	−0.0719403	−	0.124604i	0.827811	−	0.561007i	$-0.189586\pi$
$691$	−1306.74	−	2263.34i	−0.0719403	−	0.124604i	−0.899752	+	0.436402i	$0.856252\pi$
$692$		−	50825.6i		−	2.79205i
$693$		0			0
$694$	3154.85			0.172560
$695$	−10719.0	−	14148.3i	−0.585030	−	0.772195i
$696$	1312.20	−	2272.80i	0.0714640	−	0.123779i
$697$	−23741.5	−	13707.2i	−1.29021	−	0.744901i
$698$	−5213.91	+	3010.25i	−0.282736	+	0.163237i
$699$	1889.59			0.102247
$700$		0			0
$701$	−4957.94			−0.267131			−0.133566	−	0.991040i	$-0.542643\pi$
$701$	−4957.94			−0.267131			−0.133566	+	0.991040i	$0.542643\pi$
$702$	15493.8	−	8945.34i	0.833013	−	0.480940i
$703$	421.454	+	243.327i	0.0226109	+	0.0130544i
$704$	11784.0	−	20410.5i	0.630861	−	1.09268i
$705$	4172.43	+	5507.29i	0.222897	+	0.294208i
$706$	−38208.5			−2.03682
$707$		0			0
$708$			4000.34i			0.212347i
$709$	−15870.8	−	27489.0i	−0.840676	−	1.45609i	−0.889324	−	0.457277i	$-0.848825\pi$
$709$	−15870.8	−	27489.0i	−0.840676	−	1.45609i	0.0486488	−	0.998816i	$-0.484508\pi$
$710$	−33020.6	−	13915.7i	−1.74541	−	0.735557i
$711$	2173.96	−	3765.41i	0.114669	−	0.198613i
$712$	−8678.78	+	5010.70i	−0.456813	+	0.263741i
$713$			39006.5i			2.04882i
$714$		0			0
$715$	−3381.92	−	26966.5i	−0.176891	−	1.41047i
$716$	16542.9	+	28653.2i	0.863462	+	1.49556i
$717$	−3975.37	−	2295.18i	−0.207061	−	0.119547i
$718$	−1709.23	−	986.824i	−0.0888411	−	0.0512924i
$719$	12439.5	+	21545.9i	0.645224	+	1.11756i	0.984250	+	0.176784i	$0.0565693\pi$
$719$	12439.5	+	21545.9i	0.645224	+	1.11756i	−0.339026	+	0.940777i	$0.610097\pi$
$720$	−15202.6	+	1906.59i	−0.786898	+	0.0986866i
$721$		0			0
$722$		−	33257.2i		−	1.71427i
$723$	−3125.31	+	1804.40i	−0.160763	+	0.0928165i
$724$	7170.11	−	12419.0i	0.368060	−	0.637498i
$725$	2116.87	−	7529.27i	0.108440	−	0.385697i
$726$	699.499	+	1211.57i	0.0357587	+	0.0619359i
$727$		−	5429.27i		−	0.276974i	−0.990364	−	0.138487i	$-0.955776\pi$
$727$		−	5429.27i		−	0.276974i	0.990364	−	0.138487i	$-0.0442240\pi$
$728$		0			0
$729$	14176.4			0.720237
$730$	22742.4	+	30018.2i	1.15306	+	1.52195i
$731$	−10736.4	+	18596.0i	−0.543229	+	0.940900i
$732$	−239.143	−	138.069i	−0.0120751	−	0.00697157i
$733$	10730.6	−	6195.34i	0.540716	−	0.312183i	−0.204653	−	0.978835i	$-0.565607\pi$
$733$	10730.6	−	6195.34i	0.540716	−	0.312183i	0.745369	+	0.666652i	$0.232273\pi$
$734$	3174.93			0.159658
$735$		0			0
$736$	6365.85			0.318816
$737$	17345.1	−	10014.2i	0.866914	−	0.500513i
$738$	37429.9	+	21610.2i	1.86696	+	1.07789i
$739$	−4087.22	+	7079.27i	−0.203452	+	0.352389i	−0.949638	−	0.313348i	$-0.898549\pi$
$739$	−4087.22	+	7079.27i	−0.203452	+	0.352389i	0.746187	+	0.665737i	$0.231883\pi$
$740$	−28743.5	+	21776.6i	−1.42788	+	1.08179i
$741$	164.148			0.00813782
$742$		0			0
$743$		−	17213.0i		−	0.849911i	−0.905214	−	0.424956i	$-0.860290\pi$
$743$		−	17213.0i		−	0.849911i	0.905214	−	0.424956i	$-0.139710\pi$
$744$	−4386.02	−	7596.81i	−0.216128	−	0.374345i
$745$	7609.51	−	18056.7i	0.374216	−	0.887979i
$746$	13345.6	−	23115.3i	0.654983	−	1.13446i
$747$	−7464.22	+	4309.47i	−0.365598	+	0.211078i
$748$		−	48907.0i		−	2.39066i
$749$		0			0
$750$	7228.80	−	2839.46i	0.351945	−	0.138243i
$751$	−1487.50	−	2576.42i	−0.0722763	−	0.125186i	0.827622	−	0.561285i	$-0.189693\pi$
$751$	−1487.50	−	2576.42i	−0.0722763	−	0.125186i	−0.899899	+	0.436099i	$0.856360\pi$
$752$	24931.1	+	14394.0i	1.20897	+	0.697996i
$753$	3502.52	+	2022.18i	0.169507	+	0.0978650i
$754$	9275.96	+	16066.4i	0.448025	+	0.776001i
$755$	−22996.6	+	2884.06i	−1.10852	+	0.139022i
$756$		0			0
$757$			1108.45i			0.0532198i	0.999646	+	0.0266099i	$0.00847120\pi$
$757$			1108.45i			0.0532198i	−0.999646	+	0.0266099i	$0.991529\pi$
$758$	7444.56	−	4298.12i	0.356726	−	0.205956i
$759$	−4248.79	+	7359.12i	−0.203190	+	0.351935i
$760$	−885.191	−	373.041i	−0.0422490	−	0.0178048i
$761$	13462.1	+	23317.1i	0.641264	+	1.11070i	0.985151	+	0.171691i	$0.0549231\pi$
$761$	13462.1	+	23317.1i	0.641264	+	1.11070i	−0.343886	+	0.939011i	$0.611744\pi$
$762$			6687.50i			0.317930i
$763$		0			0
$764$	17229.4			0.815888
$765$	18100.7	−	13713.4i	0.855466	−	0.648118i
$766$	21606.7	−	37424.0i	1.01917	−	1.76525i
$767$	−11888.6	−	6863.89i	−0.559678	−	0.323130i
$768$	−7820.64	+	4515.25i	−0.367452	+	0.212148i
$769$	−15160.3			−0.710914			−0.355457	−	0.934693i	$-0.615675\pi$
$769$	−15160.3			−0.710914			−0.355457	+	0.934693i	$0.615675\pi$
$770$		0			0
$771$	−6511.12			−0.304141
$772$	3757.26	−	2169.25i	0.175164	−	0.101131i
$773$	8006.82	+	4622.74i	0.372556	+	0.215095i	0.674574	−	0.738207i	$-0.264327\pi$
$773$	8006.82	+	4622.74i	0.372556	+	0.215095i	−0.302019	+	0.953302i	$0.597661\pi$
$774$	16926.6	−	29317.7i	0.786064	−	1.36150i
$775$	−18257.0	−	18710.9i	−0.846208	−	0.867246i
$776$	−9197.57			−0.425481
$777$		0			0
$778$		−	45485.6i		−	2.09606i
$779$	406.672	+	704.376i	0.0187041	+	0.0323965i
$780$	−4723.64	+	11208.8i	−0.216838	+	0.514536i
$781$	−13138.0	+	22755.7i	−0.601940	+	1.04259i
$782$	61974.1	−	35780.8i	2.83400	−	1.63621i
$783$		−	3775.41i		−	0.172314i
$784$		0			0
$785$	−1517.97	−	12103.8i	−0.0690174	−	0.550325i
$786$	−4736.83	−	8204.44i	−0.214958	−	0.372319i
$787$	26128.4	+	15085.2i	1.18345	+	0.683266i	0.956811	−	0.290712i	$-0.0938921\pi$
$787$	26128.4	+	15085.2i	1.18345	+	0.683266i	0.226641	+	0.973978i	$0.427225\pi$
$788$	16595.6	+	9581.49i	0.750247	+	0.433155i
$789$	−2543.49	−	4405.45i	−0.114766	−	0.198781i
$790$	1142.67	+	9111.34i	0.0514614	+	0.410338i
$791$		0			0
$792$			37430.6i			1.67934i
$793$	820.657	−	473.806i	0.0367495	−	0.0212174i
$794$	−25473.2	+	44120.9i	−1.13855	+	1.97203i
$795$	2955.75	−	7013.71i	0.131861	−	0.312894i
$796$	−11665.7	−	20205.6i	−0.519448	−	0.899710i
$797$		−	14025.3i		−	0.623340i	−0.950190	−	0.311670i	$-0.899112\pi$
$797$		−	14025.3i		−	0.623340i	0.950190	−	0.311670i	$-0.100888\pi$
$798$		0			0
$799$	−42667.8			−1.88921
$800$	−3053.61	+	2979.54i	−0.134952	+	0.131678i
$801$	−3514.42	+	6087.16i	−0.155026	+	0.268513i
$802$	11760.8	+	6790.07i	0.517814	+	0.298960i
$803$	23916.2	−	13808.0i	1.05104	−	0.606818i
$804$	−8963.75			−0.393193
$805$		0			0
$806$	62009.5			2.70992
$807$	−1665.33	+	961.478i	−0.0726423	+	0.0419401i
$808$	−44500.7	−	25692.5i	−1.93754	−	1.11864i
$809$	−4213.27	+	7297.60i	−0.183104	+	0.317145i	−0.942936	−	0.332974i	$-0.891948\pi$
$809$	−4213.27	+	7297.60i	−0.183104	+	0.317145i	0.759832	+	0.650119i	$0.225281\pi$
$810$	−27005.5	+	20459.9i	−1.17145	+	0.887514i
$811$	16791.3			0.727031			0.363515	−	0.931588i	$-0.381576\pi$
$811$	16791.3			0.727031			0.363515	+	0.931588i	$0.381576\pi$
$812$		0			0
$813$			1307.56i			0.0564062i
$814$	20024.9	+	34684.1i	0.862251	+	1.49346i
$815$	−11519.1	−	4854.42i	−0.495087	−	0.208642i
$816$	−2415.29	+	4183.40i	−0.103618	+	0.179471i
$817$	551.716	−	318.534i	0.0236256	−	0.0136402i
$818$			36832.0i			1.57433i
$819$		0			0
$820$	−59800.6	+	7499.73i	−2.54674	+	0.319393i
$821$	−5254.05	−	9100.29i	−0.223347	−	0.386848i	0.732475	−	0.680794i	$-0.238365\pi$
$821$	−5254.05	−	9100.29i	−0.223347	−	0.386848i	−0.955822	+	0.293946i	$0.905032\pi$
$822$	2588.47	+	1494.45i	0.109834	+	0.0634125i
$823$	−29431.5	−	16992.3i	−1.24656	−	0.719701i	−0.276137	−	0.961118i	$-0.589054\pi$
$823$	−29431.5	−	16992.3i	−1.24656	−	0.719701i	−0.970421	+	0.241418i	$0.922388\pi$
$824$	7372.58	+	12769.7i	0.311694	+	0.539870i
$825$	−1406.35	−	5518.72i	−0.0593488	−	0.232893i
$826$		0			0
$827$			31679.9i			1.33207i	0.745922	+	0.666033i	$0.232009\pi$
$827$			31679.9i			1.33207i	−0.745922	+	0.666033i	$0.767991\pi$
$828$	−64511.5	+	37245.8i	−2.70765	+	1.56326i
$829$	6342.91	−	10986.2i	0.265740	−	0.460275i	−0.702017	−	0.712160i	$-0.747717\pi$
$829$	6342.91	−	10986.2i	0.265740	−	0.460275i	0.967757	+	0.251885i	$0.0810504\pi$
$830$	7069.11	−	16774.3i	0.295629	−	0.701501i
$831$	1554.40	+	2692.30i	0.0648876	+	0.112389i
$832$		−	36196.7i		−	1.50829i
$833$		0			0
$834$	8822.84			0.366319
$835$	−29900.4	+	22653.1i	−1.23922	+	0.938854i
$836$	−725.499	+	1256.60i	−0.0300142	+	0.0519862i
$837$	−10928.6	−	6309.63i	−0.451311	−	0.260565i
$838$	−46523.4	+	26860.3i	−1.91781	+	1.10725i
$839$	31557.8			1.29857			0.649283	−	0.760547i	$-0.275069\pi$
$839$	31557.8			1.29857			0.649283	+	0.760547i	$0.275069\pi$
$840$		0			0
$841$	−20474.1			−0.839479
$842$	37367.5	−	21574.2i	1.52942	−	0.883010i
$843$	5299.76	+	3059.82i	0.216528	+	0.125013i
$844$	−30876.8	+	53480.2i	−1.25927	+	2.18112i
$845$	−10373.1	−	13691.8i	−0.422304	−	0.557409i
$846$	67268.2			2.73372
$847$		0			0
$848$		−	31711.6i		−	1.28418i
$849$	3892.84	+	6742.60i	0.157364	+	0.272562i
$850$	−12981.0	+	46170.6i	−0.523816	+	1.86310i
$851$	−19346.2	+	33508.6i	−0.779295	+	1.34978i
$852$	10184.4	−	5879.95i	0.409519	−	0.236436i
$853$		−	5455.96i		−	0.219002i	−0.993987	−	0.109501i	$-0.965075\pi$
$853$		−	5455.96i		−	0.219002i	0.993987	−	0.109501i	$-0.0349252\pi$
$854$		0			0
$855$	−668.502	+	83.8384i	−0.0267395	+	0.00335346i
$856$	−8268.48	−	14321.4i	−0.330153	−	0.571842i
$857$	−22801.2	−	13164.3i	−0.908836	−	0.524717i	−0.0287796	−	0.999586i	$-0.509162\pi$
$857$	−22801.2	−	13164.3i	−0.908836	−	0.524717i	−0.880056	+	0.474869i	$0.842495\pi$
$858$	11699.0	+	6754.39i	0.465496	+	0.268754i
$859$	−13244.5	−	22940.1i	−0.526072	−	0.911183i	−0.999539	−	0.0303717i	$-0.990331\pi$
$859$	−13244.5	−	22940.1i	−0.526072	−	0.911183i	0.473467	−	0.880812i	$-0.343002\pi$
$860$	5874.31	+	46840.0i	0.232921	+	1.85725i
$861$		0			0
$862$			73952.2i			2.92207i
$863$	7073.39	−	4083.83i	0.279005	−	0.161083i	−0.353968	−	0.935258i	$-0.615168\pi$
$863$	7073.39	−	4083.83i	0.279005	−	0.161083i	0.632973	+	0.774174i	$0.281835\pi$
$864$	−1029.73	+	1783.54i	−0.0405464	+	0.0702284i
$865$	33680.3	+	14193.7i	1.32389	+	0.557919i
$866$	−38721.3	−	67067.3i	−1.51940	−	2.63168i
$867$		−	1533.18i		−	0.0600573i
$868$		0			0
$869$	6733.61			0.262856
$870$	2347.62	+	3098.68i	0.0914847	+	0.120753i
$871$	15380.3	−	26639.4i	0.598324	−	1.03633i
$872$	−11896.4	−	6868.38i	−0.461998	−	0.266735i
$873$	−5586.76	+	3225.52i	−0.216590	+	0.125048i
$874$	−2123.13			−0.0821691
$875$		0			0
$876$	−12359.6			−0.476705
$877$	−4480.15	+	2586.62i	−0.172502	+	0.0995939i	−0.583765	−	0.811923i	$-0.698421\pi$
$877$	−4480.15	+	2586.62i	−0.172502	+	0.0995939i	0.411263	+	0.911517i	$0.365088\pi$
$878$	−45531.4	−	26287.6i	−1.75013	−	1.01044i
$879$	−2931.50	+	5077.51i	−0.112488	+	0.194835i
$880$	−14329.2	−	18913.5i	−0.548907	−	0.724516i
$881$	−8713.88			−0.333233			−0.166616	−	0.986022i	$-0.553284\pi$
$881$	−8713.88			−0.333233			−0.166616	+	0.986022i	$0.553284\pi$
$882$		0			0
$883$			32124.1i			1.22431i	0.790740	+	0.612153i	$0.209696\pi$
$883$			32124.1i			1.22431i	−0.790740	+	0.612153i	$0.790304\pi$
$884$	−37556.7	−	65050.2i	−1.42892	−	2.47497i
$885$	−2650.88	−	1117.14i	−0.100687	−	0.0424321i
$886$	−20024.8	+	34683.9i	−0.759306	+	1.31516i
$887$	13441.5	−	7760.43i	0.508816	−	0.293765i	−0.223531	−	0.974697i	$-0.571758\pi$
$887$	13441.5	−	7760.43i	0.508816	−	0.293765i	0.732347	+	0.680932i	$0.238425\pi$
$888$		−	8701.41i		−	0.328829i
$889$		0			0
$890$	−1847.25	−	14729.4i	−0.0695729	−	0.554753i
$891$	12422.2	+	21515.9i	0.467071	+	0.808991i
$892$	−38535.5	−	22248.5i	−1.44649	−	0.835129i
$893$	1096.29	+	632.945i	0.0410818	+	0.0237186i
$894$	4869.78	+	8434.71i	0.182181	+	0.315547i
$895$	−23607.3	+	2960.64i	−0.881680	+	0.110573i
$896$		0			0
$897$			13050.9i			0.485795i
$898$	46321.5	−	26743.7i	1.72134	−	0.993819i
$899$	6542.83	−	11332.5i	0.242732	−	0.420423i
$900$	13512.4	−	48060.9i	0.500461	−	1.78003i
$901$	23500.6	+	40704.2i	0.868942	+	1.50505i
$902$			66935.2i			2.47084i
$903$		0			0
$904$	−32670.8			−1.20201
$905$	6227.27	+	8219.53i	0.228731	+	0.301908i
$906$	5760.05	−	9976.70i	0.211219	−	0.365843i
$907$	45614.0	+	26335.2i	1.66989	+	0.964109i	0.967696	+	0.252120i	$0.0811277\pi$
$907$	45614.0	+	26335.2i	1.66989	+	0.964109i	0.702190	+	0.711989i	$0.252206\pi$
$908$	27884.6	−	16099.2i	1.01915	−	0.588404i
$909$	−36040.6			−1.31506
$910$		0			0
$911$	−19502.8			−0.709283			−0.354641	−	0.935002i	$-0.615397\pi$
$911$	−19502.8			−0.709283			−0.354641	+	0.935002i	$0.615397\pi$
$912$	124.115	−	71.6581i	0.00450644	−	0.00260179i
$913$	−11559.8	−	6674.07i	−0.419030	−	0.241927i
$914$	22633.9	−	39203.0i	0.819106	−	1.41873i
$915$	158.277	−	119.914i	0.00571856	−	0.00433249i
$916$	89526.5			3.22930
$917$		0			0
$918$			23151.3i			0.832362i
$919$	−22640.2	−	39214.0i	−0.812656	−	1.40756i	−0.910999	−	0.412410i	$-0.864687\pi$
$919$	−22640.2	−	39214.0i	−0.812656	−	1.40756i	0.0983421	−	0.995153i	$-0.468646\pi$
$920$	29659.4	−	70379.1i	1.06287	−	2.52210i
$921$	−2398.45	+	4154.23i	−0.0858105	+	0.148628i
$922$	70628.3	−	40777.3i	2.52280	−	1.45654i
$923$			40355.9i			1.43914i
$924$		0			0
$925$	−6403.60	−	25128.6i	−0.227620	−	0.893216i
$926$	−19989.1	−	34622.2i	−0.709378	−	1.22868i
$927$	8956.45	+	5171.01i	0.317334	+	0.183213i
$928$	−1849.46	−	1067.79i	−0.0654220	−	0.0377714i
$929$	1600.78	+	2772.63i	0.0565337	+	0.0979192i	0.892907	−	0.450241i	$-0.148662\pi$
$929$	1600.78	+	2772.63i	0.0565337	+	0.0979192i	−0.836374	+	0.548160i	$0.815328\pi$
$930$	12893.1	−	1616.95i	0.454604	−	0.0570129i
$931$		0			0
$932$			25653.4i			0.901615i
$933$	9678.98	−	5588.16i	0.339631	−	0.196086i
$934$	−47468.3	+	82217.5i	−1.66297	+	2.88034i
$935$	32408.8	+	13657.9i	1.13356	+	0.477711i
$936$	28743.8	+	49785.7i	1.00376	+	1.73856i
$937$		−	23678.3i		−	0.825546i	−0.910834	−	0.412773i	$-0.864560\pi$
$937$		−	23678.3i		−	0.825546i	0.910834	−	0.412773i	$-0.135440\pi$
$938$		0			0
$939$	6826.26			0.237238
$940$	−74768.0	+	56645.7i	−2.59432	+	1.96551i
$941$	17363.3	−	30074.2i	0.601518	−	1.04186i	−0.391073	−	0.920360i	$-0.627896\pi$
$941$	17363.3	−	30074.2i	0.601518	−	1.04186i	0.992591	−	0.121501i	$-0.0387707\pi$
$942$	5251.05	+	3031.70i	0.181623	+	0.104860i
$943$	−56003.0	+	32333.3i	−1.93394	+	1.11656i
$944$	−11985.6			−0.413240
$945$		0			0
$946$	52428.3			1.80189
$947$	25366.7	−	14645.5i	0.870440	−	0.502549i	0.00294538	−	0.999996i	$-0.499062\pi$
$947$	25366.7	−	14645.5i	0.870440	−	0.502549i	0.867494	+	0.497447i	$0.165729\pi$
$948$	−2609.89	−	1506.82i	−0.0894148	−	0.0516237i
$949$	21207.0	−	36731.6i	0.725404	−	1.25644i
$950$	1018.44	−	993.730i	0.0347815	−	0.0339377i
$951$	3117.66			0.106306
$952$		0			0
$953$			23209.3i			0.788900i	0.918917	+	0.394450i	$0.129065\pi$
$953$			23209.3i			0.788900i	−0.918917	+	0.394450i	$0.870935\pi$
$954$	−37050.0	−	64172.5i	−1.25738	−	2.17784i
$955$	−4811.53	+	11417.3i	−0.163034	+	0.386864i
$956$	31159.9	−	53970.4i	1.05416	−	1.82587i
$957$	2468.79	−	1425.36i	0.0833904	−	0.0481455i
$958$			6081.93i			0.205113i
$959$		0			0
$960$	−943.862	−	7526.08i	−0.0317323	−	0.253024i
$961$	−6973.82	−	12079.0i	−0.234092	−	0.405459i
$962$	53269.4	+	30755.1i	1.78532	+	1.03075i
$963$	−10044.8	−	5799.38i	−0.336127	−	0.194063i
$964$	−24496.9	−	42429.9i	−0.818457	−	1.41761i
$965$	388.224	+	3095.59i	0.0129507	+	0.103265i
$966$		0			0
$967$		−	25503.9i		−	0.848140i	−0.905629	−	0.424070i	$-0.860601\pi$
$967$		−	25503.9i		−	0.848140i	0.905629	−	0.424070i	$-0.139399\pi$
$968$	−7984.94	+	4610.11i	−0.265130	+	0.153073i
$969$	−106.207	+	183.957i	−0.00352103	+	0.00609860i
$970$	5291.02	−	12555.1i	0.175139	−	0.415588i
$971$	6915.82	+	11978.6i	0.228568	+	0.395891i	0.957384	−	0.288819i	$-0.0932625\pi$
$971$	6915.82	+	11978.6i	0.228568	+	0.395891i	−0.728816	+	0.684709i	$0.759929\pi$
$972$		−	36448.8i		−	1.20277i
$973$		0			0
$974$	−17291.4			−0.568843
$975$	−6108.50	−	6260.37i	−0.200645	−	0.205633i
$976$	413.676	−	716.508i	0.0135671	−	0.0234988i
$977$	33487.9	+	19334.3i	1.09659	+	0.633119i	0.935324	−	0.353791i	$-0.115108\pi$
$977$	33487.9	+	19334.3i	1.09659	+	0.633119i	0.161270	+	0.986910i	$0.448441\pi$
$978$	5380.85	−	3106.63i	0.175931	−	0.101574i
$979$	−10885.6			−0.355367
$980$		0			0
$981$	−9634.74			−0.313572
$982$	−42648.4	+	24623.1i	−1.38591	+	0.800157i
$983$	24374.2	+	14072.4i	0.790860	+	0.456603i	0.840265	−	0.542175i	$-0.182399\pi$
$983$	24374.2	+	14072.4i	0.790860	+	0.456603i	−0.0494050	+	0.998779i	$0.515732\pi$
$984$	7271.33	−	12594.3i	0.235571	−	0.408020i
$985$	−10983.8	+	8321.56i	−0.355303	+	0.269185i
$986$	−24007.0			−0.775395
$987$		0			0
$988$			2228.51i			0.0717594i
$989$	25325.7	+	43865.4i	0.814268	+	1.41035i
$990$	−51094.5	−	21532.4i	−1.64029	−	0.691258i
$991$	15598.9	−	27018.2i	0.500017	−	0.866055i	−0.499983	−	0.866035i	$-0.666660\pi$
$991$	15598.9	−	27018.2i	0.500017	−	0.866055i	1.00000		1.95269e-5i	$-6.21562e-6\pi$
$992$	−6181.80	+	3569.07i	−0.197855	+	0.114232i
$993$			433.752i			0.0138617i
$994$		0			0
$995$	16647.3	−	2087.78i	0.530407	−	0.0665195i
$996$	2986.99	+	5173.62i	0.0950266	+	0.164591i
$997$	35534.4	+	20515.8i	1.12877	+	0.651696i	0.943626	−	0.331015i	$-0.107391\pi$
$997$	35534.4	+	20515.8i	1.12877	+	0.651696i	0.185146	+	0.982711i	$0.440724\pi$
$998$	34504.6	+	19921.2i	1.09441	+	0.631859i
$999$	−6258.82	−	10840.6i	−0.198219	−	0.343325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.j.g.214.11		24
5.4	even	2	inner	245.4.j.g.214.2		24
7.2	even	3	inner	245.4.j.g.79.2		24
7.3	odd	6		245.4.b.g.99.11	yes	12
7.4	even	3		245.4.b.g.99.12	yes	12
7.5	odd	6	inner	245.4.j.g.79.1		24
7.6	odd	2	inner	245.4.j.g.214.12		24
35.3	even	12		1225.4.a.bs.1.12		12
35.4	even	6		245.4.b.g.99.1	✓	12
35.9	even	6	inner	245.4.j.g.79.11		24
35.17	even	12		1225.4.a.bs.1.1		12
35.18	odd	12		1225.4.a.bs.1.11		12
35.19	odd	6	inner	245.4.j.g.79.12		24
35.24	odd	6		245.4.b.g.99.2	yes	12
35.32	odd	12		1225.4.a.bs.1.2		12
35.34	odd	2	inner	245.4.j.g.214.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.4.b.g.99.1	✓	12	35.4	even	6
245.4.b.g.99.2	yes	12	35.24	odd	6
245.4.b.g.99.11	yes	12	7.3	odd	6
245.4.b.g.99.12	yes	12	7.4	even	3
245.4.j.g.79.1		24	7.5	odd	6	inner
245.4.j.g.79.2		24	7.2	even	3	inner
245.4.j.g.79.11		24	35.9	even	6	inner
245.4.j.g.79.12		24	35.19	odd	6	inner
245.4.j.g.214.1		24	35.34	odd	2	inner
245.4.j.g.214.2		24	5.4	even	2	inner
245.4.j.g.214.11		24	1.1	even	1	trivial
245.4.j.g.214.12		24	7.6	odd	2	inner
1225.4.a.bs.1.1		12	35.17	even	12
1225.4.a.bs.1.2		12	35.32	odd	12
1225.4.a.bs.1.11		12	35.18	odd	12
1225.4.a.bs.1.12		12	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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.20246 - 2.42629i) q^{2} +(-0.991781 - 0.572605i) q^{3} +(7.77380 - 13.4646i) q^{4} +(6.75158 + 8.91157i) q^{5} -5.55723 q^{6} -36.6254i q^{8} +(-12.8442 - 22.2469i) q^{9} +O(q^{10})\)	\(q+(4.20246 - 2.42629i) q^{2} +(-0.991781 - 0.572605i) q^{3} +(7.77380 - 13.4646i) q^{4} +(6.75158 + 8.91157i) q^{5} -5.55723 q^{6} -36.6254i q^{8} +(-12.8442 - 22.2469i) q^{9} +(49.9954 + 21.0693i) q^{10} +(19.8919 - 34.4537i) q^{11} +(-15.4198 + 8.90264i) q^{12} -61.1016i q^{13} +(-1.59328 - 12.7043i) q^{15} +(-26.6736 - 46.2001i) q^{16} +(68.4751 + 39.5341i) q^{17} +(-107.955 - 62.3278i) q^{18} +(-1.17292 - 2.03156i) q^{19} +(172.476 - 21.6307i) q^{20} -193.054i q^{22} +(161.523 - 93.2555i) q^{23} +(-20.9719 + 36.3244i) q^{24} +(-33.8323 + 120.334i) q^{25} +(-148.250 - 256.777i) q^{26} +60.3394i q^{27} -62.5696 q^{29} +(-37.5201 - 49.5237i) q^{30} +(-104.569 + 181.119i) q^{31} +(29.5585 + 17.0656i) q^{32} +(-39.4567 + 22.7804i) q^{33} +383.685 q^{34} -399.395 q^{36} +(-179.660 + 103.727i) q^{37} +(-9.85830 - 5.69169i) q^{38} +(-34.9871 + 60.5994i) q^{39} +(326.390 - 247.280i) q^{40} -346.718 q^{41} +271.573i q^{43} +(-309.271 - 535.673i) q^{44} +(111.536 - 264.664i) q^{45} +(452.531 - 783.806i) q^{46} +(-467.335 + 269.816i) q^{47} +61.0938i q^{48} +(149.788 + 587.788i) q^{50} +(-45.2749 - 78.4183i) q^{51} +(-822.710 - 474.992i) q^{52} +(514.798 + 297.219i) q^{53} +(146.401 + 253.574i) q^{54} +(441.338 - 55.3492i) q^{55} +2.68648i q^{57} +(-262.946 + 151.812i) q^{58} +(112.336 - 194.571i) q^{59} +(-183.445 - 77.3080i) q^{60} +(7.75441 + 13.4310i) q^{61} +1014.86i q^{62} +592.403 q^{64} +(544.511 - 412.532i) q^{65} +(-110.544 + 191.467i) q^{66} +(435.985 + 251.716i) q^{67} +(1064.62 - 614.661i) q^{68} -213.594 q^{69} -660.472 q^{71} +(-814.802 + 470.426i) q^{72} +(601.156 + 347.078i) q^{73} +(-503.344 + 871.817i) q^{74} +(102.458 - 99.9729i) q^{75} -36.4722 q^{76} +339.556i q^{78} +(84.6277 + 146.580i) q^{79} +(231.626 - 549.628i) q^{80} +(-312.244 + 540.822i) q^{81} +(-1457.07 + 841.239i) q^{82} -335.518i q^{83} +(110.004 + 877.138i) q^{85} +(658.917 + 1141.28i) q^{86} +(62.0553 + 35.8276i) q^{87} +(-1261.88 - 728.548i) q^{88} +(-136.809 - 236.961i) q^{89} +(-173.428 - 1382.86i) q^{90} -2899.80i q^{92} +(207.419 - 119.753i) q^{93} +(-1309.31 + 2267.79i) q^{94} +(10.1853 - 24.1688i) q^{95} +(-19.5437 - 33.8507i) q^{96} -251.125i q^{97} -1021.98 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 44 q^{4} - 140 q^{9}+O(q^{10}) \) 24 * q + 44 * q^4 - 140 * q^9	\( 24 q + 44 q^{4} - 140 q^{9} + 24 q^{11} - 272 q^{15} - 84 q^{16} - 584 q^{25} + 592 q^{29} + 632 q^{30} - 2200 q^{36} + 184 q^{39} - 2760 q^{44} + 2440 q^{46} + 1080 q^{50} + 1928 q^{51} + 1000 q^{60} + 4664 q^{64} + 588 q^{65} - 3680 q^{71} - 8656 q^{74} - 5032 q^{79} + 1284 q^{81} + 1032 q^{85} + 1680 q^{86} + 6416 q^{95} - 7008 q^{99}+O(q^{100}) \) 24 * q + 44 * q^4 - 140 * q^9 + 24 * q^11 - 272 * q^15 - 84 * q^16 - 584 * q^25 + 592 * q^29 + 632 * q^30 - 2200 * q^36 + 184 * q^39 - 2760 * q^44 + 2440 * q^46 + 1080 * q^50 + 1928 * q^51 + 1000 * q^60 + 4664 * q^64 + 588 * q^65 - 3680 * q^71 - 8656 * q^74 - 5032 * q^79 + 1284 * q^81 + 1032 * q^85 + 1680 * q^86 + 6416 * q^95 - 7008 * q^99

Introduction

L-functions

Modular forms

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