LMFDB - Embedded newform 197.3.c.a.14.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [197,3,Mod(14,197)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("197.14"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(197, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	197.c (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.36786120790$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			14.7
Character	$\chi$	$=$	197.14
Dual form			197.3.c.a.183.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.85403 + 1.85403i) q^{2} +(0.722049 - 0.722049i) q^{3} -2.87488i q^{4} +(-6.14279 + 6.14279i) q^{5} +2.67741i q^{6} -9.45582i q^{7} +(-2.08602 - 2.08602i) q^{8} +7.95729i q^{9} -22.7779i q^{10} +(3.71305 - 3.71305i) q^{11} +(-2.07580 - 2.07580i) q^{12} +(0.369578 - 0.369578i) q^{13} +(17.5314 + 17.5314i) q^{14} +8.87079i q^{15} +19.2346 q^{16} +(-15.3969 - 15.3969i) q^{17} +(-14.7531 - 14.7531i) q^{18} -17.7156i q^{19} +(17.6598 + 17.6598i) q^{20} +(-6.82756 - 6.82756i) q^{21} +13.7682i q^{22} -4.12352 q^{23} -3.01241 q^{24} -50.4678i q^{25} +1.37042i q^{26} +(12.2440 + 12.2440i) q^{27} -27.1843 q^{28} +10.3294 q^{29} +(-16.4467 - 16.4467i) q^{30} +(34.3182 - 34.3182i) q^{31} +(-27.3175 + 27.3175i) q^{32} -5.36201i q^{33} +57.0928 q^{34} +(58.0851 + 58.0851i) q^{35} +22.8762 q^{36} -53.7877 q^{37} +(32.8453 + 32.8453i) q^{38} -0.533706i q^{39} +25.6279 q^{40} +17.7713i q^{41} +25.3171 q^{42} -15.8937i q^{43} +(-10.6746 - 10.6746i) q^{44} +(-48.8800 - 48.8800i) q^{45} +(7.64514 - 7.64514i) q^{46} -59.0202i q^{47} +(13.8883 - 13.8883i) q^{48} -40.4125 q^{49} +(93.5689 + 93.5689i) q^{50} -22.2347 q^{51} +(-1.06249 - 1.06249i) q^{52} -65.5196 q^{53} -45.4015 q^{54} +45.6170i q^{55} +(-19.7250 + 19.7250i) q^{56} +(-12.7915 - 12.7915i) q^{57} +(-19.1510 + 19.1510i) q^{58} -1.87769 q^{59} +25.5024 q^{60} -67.6008 q^{61} +127.254i q^{62} +75.2427 q^{63} -24.3567i q^{64} +4.54048i q^{65} +(9.94135 + 9.94135i) q^{66} +(-73.0939 + 73.0939i) q^{67} +(-44.2642 + 44.2642i) q^{68} +(-2.97738 + 2.97738i) q^{69} -215.383 q^{70} +(-77.9060 - 77.9060i) q^{71} +(16.5990 - 16.5990i) q^{72} +(-37.2626 + 37.2626i) q^{73} +(99.7241 - 99.7241i) q^{74} +(-36.4402 - 36.4402i) q^{75} -50.9301 q^{76} +(-35.1099 - 35.1099i) q^{77} +(0.989509 + 0.989509i) q^{78} +(4.08633 + 4.08633i) q^{79} +(-118.154 + 118.154i) q^{80} -53.9341 q^{81} +(-32.9485 - 32.9485i) q^{82} +53.8331i q^{83} +(-19.6284 + 19.6284i) q^{84} +189.160 q^{85} +(29.4675 + 29.4675i) q^{86} +(7.45831 - 7.45831i) q^{87} -15.4910 q^{88} +(30.5612 + 30.5612i) q^{89} +181.250 q^{90} +(-3.49466 - 3.49466i) q^{91} +11.8546i q^{92} -49.5589i q^{93} +(109.425 + 109.425i) q^{94} +(108.823 + 108.823i) q^{95} +39.4492i q^{96} +8.46168i q^{97} +(74.9260 - 74.9260i) q^{98} +(29.5458 + 29.5458i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 2 q^{2} - 2 q^{3} - 10 q^{5} - 6 q^{8} + 10 q^{11} + 68 q^{12} + 2 q^{13} - 2 q^{14} - 280 q^{16} - 30 q^{17} - 68 q^{18} + 114 q^{20} - 20 q^{21} + 48 q^{23} + 60 q^{24} + 22 q^{27} + 392 q^{28}+ \cdots - 66 q^{99}+O(q^{100}) $ 64 * q - 2 * q^2 - 2 * q^3 - 10 * q^5 - 6 * q^8 + 10 * q^11 + 68 * q^12 + 2 * q^13 - 2 * q^14 - 280 * q^16 - 30 * q^17 - 68 * q^18 + 114 * q^20 - 20 * q^21 + 48 * q^23 + 60 * q^24 + 22 * q^27 + 392 * q^28 + 56 * q^29 - 70 * q^30 - 64 * q^31 - 156 * q^32 - 52 * q^34 - 92 * q^35 - 36 * q^36 - 160 * q^37 + 40 * q^38 + 52 * q^40 + 80 * q^42 + 140 * q^44 + 324 * q^45 + 214 * q^46 + 216 * q^48 - 836 * q^49 + 126 * q^50 + 124 * q^51 - 10 * q^52 - 16 * q^53 + 400 * q^54 - 40 * q^56 + 68 * q^57 - 266 * q^58 - 364 * q^59 - 68 * q^60 - 168 * q^61 - 12 * q^63 + 238 * q^66 - 112 * q^67 - 148 * q^68 - 48 * q^69 + 48 * q^70 + 150 * q^71 - 474 * q^72 + 18 * q^73 + 236 * q^74 + 64 * q^75 - 260 * q^76 - 388 * q^77 - 782 * q^78 + 202 * q^79 + 796 * q^80 - 516 * q^81 + 72 * q^82 - 294 * q^84 - 696 * q^85 + 618 * q^86 + 464 * q^87 - 244 * q^88 - 536 * q^89 + 1484 * q^90 + 212 * q^91 + 132 * q^94 + 370 * q^95 - 530 * q^98 - 66 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.85403	+	1.85403i	−0.927016	+	0.927016i	−0.997512	−	0.0704957i	$-0.977542\pi$
$2$	−1.85403	+	1.85403i	−0.927016	+	0.927016i	0.0704957	+	0.997512i	$0.477542\pi$
$3$	0.722049	−	0.722049i	0.240683	−	0.240683i	−0.576450	−	0.817133i	$-0.695562\pi$
$3$	0.722049	−	0.722049i	0.240683	−	0.240683i	0.817133	+	0.576450i	$0.195562\pi$
$4$		−	2.87488i		−	0.718719i
$5$	−6.14279	+	6.14279i	−1.22856	+	1.22856i	−0.264049	+	0.964509i	$0.585058\pi$
$5$	−6.14279	+	6.14279i	−1.22856	+	1.22856i	−0.964509	+	0.264049i	$0.914942\pi$
$6$			2.67741i			0.446234i
$7$		−	9.45582i		−	1.35083i	−0.737437	−	0.675415i	$-0.763964\pi$
$7$		−	9.45582i		−	1.35083i	0.737437	−	0.675415i	$-0.236036\pi$
$8$	−2.08602	−	2.08602i	−0.260752	−	0.260752i
$9$			7.95729i			0.884143i
$10$		−	22.7779i		−	2.27779i
$11$	3.71305	−	3.71305i	0.337550	−	0.337550i	−0.517894	−	0.855445i	$-0.673284\pi$
$11$	3.71305	−	3.71305i	0.337550	−	0.337550i	0.855445	+	0.517894i	$0.173284\pi$
$12$	−2.07580	−	2.07580i	−0.172983	−	0.172983i
$13$	0.369578	−	0.369578i	0.0284291	−	0.0284291i	−0.692749	−	0.721178i	$-0.743601\pi$
$13$	0.369578	−	0.369578i	0.0284291	−	0.0284291i	0.721178	+	0.692749i	$0.243601\pi$
$14$	17.5314	+	17.5314i	1.25224	+	1.25224i
$15$			8.87079i			0.591386i
$16$	19.2346			1.20216
$17$	−15.3969	−	15.3969i	−0.905701	−	0.905701i	0.0902205	−	0.995922i	$-0.471243\pi$
$17$	−15.3969	−	15.3969i	−0.905701	−	0.905701i	−0.995922	+	0.0902205i	$0.971243\pi$
$18$	−14.7531	−	14.7531i	−0.819615	−	0.819615i
$19$		−	17.7156i		−	0.932399i	−0.884680	−	0.466199i	$-0.845623\pi$
$19$		−	17.7156i		−	0.932399i	0.884680	−	0.466199i	$-0.154377\pi$
$20$	17.6598	+	17.6598i	0.882988	+	0.882988i
$21$	−6.82756	−	6.82756i	−0.325122	−	0.325122i
$22$			13.7682i			0.625829i
$23$	−4.12352			−0.179283			−0.0896417	−	0.995974i	$-0.528572\pi$
$23$	−4.12352			−0.179283			−0.0896417	+	0.995974i	$0.528572\pi$
$24$	−3.01241			−0.125517
$25$		−	50.4678i		−	2.01871i
$26$			1.37042i			0.0527084i
$27$	12.2440	+	12.2440i	0.453481	+	0.453481i
$28$	−27.1843			−0.970868
$29$	10.3294			0.356185			0.178093	−	0.984014i	$-0.443007\pi$
$29$	10.3294			0.356185			0.178093	+	0.984014i	$0.443007\pi$
$30$	−16.4467	−	16.4467i	−0.548225	−	0.548225i
$31$	34.3182	−	34.3182i	1.10704	−	1.10704i	0.113502	−	0.993538i	$-0.463793\pi$
$31$	34.3182	−	34.3182i	1.10704	−	1.10704i	0.993538	−	0.113502i	$-0.0362068\pi$
$32$	−27.3175	+	27.3175i	−0.853672	+	0.853672i
$33$		−	5.36201i		−	0.162485i
$34$	57.0928			1.67920
$35$	58.0851	+	58.0851i	1.65957	+	1.65957i
$36$	22.8762			0.635451
$37$	−53.7877			−1.45372			−0.726860	−	0.686785i	$-0.759021\pi$
$37$	−53.7877			−1.45372			−0.726860	+	0.686785i	$0.759021\pi$
$38$	32.8453	+	32.8453i	0.864349	+	0.864349i
$39$		−	0.533706i		−	0.0136848i
$40$	25.6279			0.640699
$41$			17.7713i			0.433446i	0.976233	+	0.216723i	$0.0695368\pi$
$41$			17.7713i			0.433446i	−0.976233	+	0.216723i	$0.930463\pi$
$42$	25.3171			0.602787
$43$		−	15.8937i		−	0.369621i	−0.982774	−	0.184811i	$-0.940833\pi$
$43$		−	15.8937i		−	0.369621i	0.982774	−	0.184811i	$-0.0591672\pi$
$44$	−10.6746	−	10.6746i	−0.242604	−	0.242604i
$45$	−48.8800	−	48.8800i	−1.08622	−	1.08622i
$46$	7.64514	−	7.64514i	0.166199	−	0.166199i
$47$		−	59.0202i		−	1.25575i	−0.778314	−	0.627875i	$-0.783925\pi$
$47$		−	59.0202i		−	1.25575i	0.778314	−	0.627875i	$-0.216075\pi$
$48$	13.8883	−	13.8883i	0.289340	−	0.289340i
$49$	−40.4125			−0.824744
$50$	93.5689	+	93.5689i	1.87138	+	1.87138i
$51$	−22.2347			−0.435974
$52$	−1.06249	−	1.06249i	−0.0204325	−	0.0204325i
$53$	−65.5196			−1.23622			−0.618109	−	0.786092i	$-0.712101\pi$
$53$	−65.5196			−1.23622			−0.618109	+	0.786092i	$0.712101\pi$
$54$	−45.4015			−0.840769
$55$			45.6170i			0.829400i
$56$	−19.7250	+	19.7250i	−0.352232	+	0.352232i
$57$	−12.7915	−	12.7915i	−0.224413	−	0.224413i
$58$	−19.1510	+	19.1510i	−0.330189	+	0.330189i
$59$	−1.87769			−0.0318253			−0.0159127	−	0.999873i	$-0.505065\pi$
$59$	−1.87769			−0.0318253			−0.0159127	+	0.999873i	$0.505065\pi$
$60$	25.5024			0.425040
$61$	−67.6008			−1.10821			−0.554105	−	0.832447i	$-0.686939\pi$
$61$	−67.6008			−1.10821			−0.554105	+	0.832447i	$0.686939\pi$
$62$			127.254i			2.05249i
$63$	75.2427			1.19433
$64$		−	24.3567i		−	0.380573i
$65$			4.54048i			0.0698535i
$66$	9.94135	+	9.94135i	0.150626	+	0.150626i
$67$	−73.0939	+	73.0939i	−1.09095	+	1.09095i	−0.0955263	+	0.995427i	$0.530453\pi$
$67$	−73.0939	+	73.0939i	−1.09095	+	1.09095i	−0.995427	+	0.0955263i	$0.969547\pi$
$68$	−44.2642	+	44.2642i	−0.650945	+	0.650945i
$69$	−2.97738	+	2.97738i	−0.0431505	+	0.0431505i
$70$	−215.383			−3.07691
$71$	−77.9060	−	77.9060i	−1.09727	−	1.09727i	−0.994729	−	0.102539i	$-0.967303\pi$
$71$	−77.9060	−	77.9060i	−1.09727	−	1.09727i	−0.102539	−	0.994729i	$-0.532697\pi$
$72$	16.5990	−	16.5990i	0.230542	−	0.230542i
$73$	−37.2626	+	37.2626i	−0.510446	+	0.510446i	−0.914663	−	0.404217i	$-0.867544\pi$
$73$	−37.2626	+	37.2626i	−0.510446	+	0.510446i	0.404217	+	0.914663i	$0.367544\pi$
$74$	99.7241	−	99.7241i	1.34762	−	1.34762i
$75$	−36.4402	−	36.4402i	−0.485869	−	0.485869i
$76$	−50.9301			−0.670133
$77$	−35.1099	−	35.1099i	−0.455973	−	0.455973i
$78$	0.989509	+	0.989509i	0.0126860	+	0.0126860i
$79$	4.08633	+	4.08633i	0.0517257	+	0.0517257i	0.732497	−	0.680771i	$-0.238355\pi$
$79$	4.08633	+	4.08633i	0.0517257	+	0.0517257i	−0.680771	+	0.732497i	$0.738355\pi$
$80$	−118.154	+	118.154i	−1.47693	+	1.47693i
$81$	−53.9341			−0.665853
$82$	−32.9485	−	32.9485i	−0.401811	−	0.401811i
$83$			53.8331i			0.648592i	0.945956	+	0.324296i	$0.105127\pi$
$83$			53.8331i			0.648592i	−0.945956	+	0.324296i	$0.894873\pi$
$84$	−19.6284	+	19.6284i	−0.233671	+	0.233671i
$85$	189.160			2.22541
$86$	29.4675	+	29.4675i	0.342645	+	0.342645i
$87$	7.45831	−	7.45831i	0.0857277	−	0.0857277i
$88$	−15.4910			−0.176034
$89$	30.5612	+	30.5612i	0.343385	+	0.343385i	0.857638	−	0.514254i	$-0.171931\pi$
$89$	30.5612	+	30.5612i	0.343385	+	0.343385i	−0.514254	+	0.857638i	$0.671931\pi$
$90$	181.250			2.01389
$91$	−3.49466	−	3.49466i	−0.0384028	−	0.0384028i
$92$			11.8546i			0.128854i
$93$		−	49.5589i		−	0.532891i
$94$	109.425	+	109.425i	1.16410	+	1.16410i
$95$	108.823	+	108.823i	1.14551	+	1.14551i
$96$			39.4492i			0.410929i
$97$			8.46168i			0.0872338i	0.999048	+	0.0436169i	$0.0138881\pi$
$97$			8.46168i			0.0872338i	−0.999048	+	0.0436169i	$0.986112\pi$
$98$	74.9260	−	74.9260i	0.764551	−	0.764551i
$99$	29.5458	+	29.5458i	0.298443	+	0.298443i
$100$	−145.089			−1.45089
$101$	95.6836			0.947362			0.473681	−	0.880696i	$-0.342925\pi$
$101$	95.6836			0.947362			0.473681	+	0.880696i	$0.342925\pi$
$102$	41.2238	−	41.2238i	0.404155	−	0.404155i
$103$	29.6005	−	29.6005i	0.287384	−	0.287384i	−0.548661	−	0.836045i	$-0.684862\pi$
$103$	29.6005	−	29.6005i	0.287384	−	0.287384i	0.836045	+	0.548661i	$0.184862\pi$
$104$	−1.54189			−0.0148259
$105$	83.8806			0.798863
$106$	121.475	−	121.475i	1.14599	−	1.14599i
$107$		−	191.609i		−	1.79074i	−0.445323	−	0.895370i	$-0.646911\pi$
$107$		−	191.609i		−	1.79074i	0.445323	−	0.895370i	$-0.353089\pi$
$108$	35.2000	−	35.2000i	0.325926	−	0.325926i
$109$		−	65.0326i		−	0.596629i	−0.954468	−	0.298315i	$-0.903576\pi$
$109$		−	65.0326i		−	0.596629i	0.954468	−	0.298315i	$-0.0964245\pi$
$110$	−84.5754	−	84.5754i	−0.768867	−	0.768867i
$111$	−38.8373	+	38.8373i	−0.349886	+	0.349886i
$112$		−	181.879i		−	1.62392i
$113$	57.6292	+	57.6292i	0.509993	+	0.509993i	0.914524	−	0.404531i	$-0.132565\pi$
$113$	57.6292	+	57.6292i	0.509993	+	0.509993i	−0.404531	+	0.914524i	$0.632565\pi$
$114$	47.4318			0.416068
$115$	25.3299	−	25.3299i	0.220260	−	0.220260i
$116$		−	29.6956i		−	0.255997i
$117$	2.94084	+	2.94084i	0.0251354	+	0.0251354i
$118$	3.48131	−	3.48131i	0.0295026	−	0.0295026i
$119$	−145.590	+	145.590i	−1.22345	+	1.22345i
$120$	18.5046	−	18.5046i	0.154205	−	0.154205i
$121$			93.4265i			0.772120i
$122$	125.334	−	125.334i	1.02733	−	1.02733i
$123$	12.8317	+	12.8317i	0.104323	+	0.104323i
$124$	−98.6606	−	98.6606i	−0.795650	−	0.795650i
$125$	156.443	+	156.443i	1.25155	+	1.25155i
$126$	−139.502	+	139.502i	−1.10716	+	1.10716i
$127$		−	136.940i		−	1.07826i	−0.842221	−	0.539132i	$-0.818752\pi$
$127$		−	136.940i		−	1.07826i	0.842221	−	0.539132i	$-0.181248\pi$
$128$	−64.1119	−	64.1119i	−0.500874	−	0.500874i
$129$	−11.4760	−	11.4760i	−0.0889616	−	0.0889616i
$130$	−8.41819	−	8.41819i	−0.0647553	−	0.0647553i
$131$	−126.763	+	126.763i	−0.967653	+	0.967653i	−0.999493	−	0.0318401i	$-0.989863\pi$
$131$	−126.763	+	126.763i	−0.967653	+	0.967653i	0.0318401	+	0.999493i	$0.489863\pi$
$132$	−15.4151			−0.116781
$133$	−167.515			−1.25951
$134$		−	271.037i		−	2.02266i
$135$	−150.425			−1.11426
$136$			64.2365i			0.472327i
$137$		−	247.589i		−	1.80722i	−0.428359	−	0.903609i	$-0.640908\pi$
$137$		−	247.589i		−	1.80722i	0.428359	−	0.903609i	$-0.359092\pi$
$138$		−	11.0403i		−	0.0800024i
$139$	79.3138	+	79.3138i	0.570603	+	0.570603i	0.932297	−	0.361694i	$-0.117801\pi$
$139$	79.3138	+	79.3138i	0.570603	+	0.570603i	−0.361694	+	0.932297i	$0.617801\pi$
$140$	166.987	−	166.987i	1.19277	−	1.19277i
$141$	−42.6155	−	42.6155i	−0.302238	−	0.302238i
$142$	288.881			2.03437
$143$		−	2.74452i		−	0.0191925i
$144$			153.055i			1.06288i
$145$	−63.4511	+	63.4511i	−0.437594	+	0.437594i
$146$		−	138.172i		−	0.946384i
$147$	−29.1798	+	29.1798i	−0.198502	+	0.198502i
$148$			154.633i			1.04482i
$149$	91.5706	+	91.5706i	0.614568	+	0.614568i	0.944133	−	0.329565i	$-0.106902\pi$
$149$	91.5706	+	91.5706i	0.614568	+	0.614568i	−0.329565	+	0.944133i	$0.606902\pi$
$150$	135.123			0.900818
$151$	−63.1800	−	63.1800i	−0.418410	−	0.418410i	0.466245	−	0.884656i	$-0.345606\pi$
$151$	−63.1800	−	63.1800i	−0.418410	−	0.418410i	−0.884656	+	0.466245i	$0.845606\pi$
$152$	−36.9550	+	36.9550i	−0.243125	+	0.243125i
$153$	122.518	−	122.518i	0.800770	−	0.800770i
$154$	130.190			0.845389
$155$			421.619i			2.72012i
$156$	−1.53434			−0.00983551
$157$			51.2253i			0.326276i	0.986603	+	0.163138i	$0.0521615\pi$
$157$			51.2253i			0.326276i	−0.986603	+	0.163138i	$0.947838\pi$
$158$	−15.1524			−0.0959012
$159$	−47.3084	+	47.3084i	−0.297537	+	0.297537i
$160$		−	335.611i		−	2.09757i
$161$			38.9912i			0.242182i
$162$	99.9955	−	99.9955i	0.617256	−	0.617256i
$163$		−	163.659i		−	1.00405i	−0.864854	−	0.502023i	$-0.832589\pi$
$163$		−	163.659i		−	1.00405i	0.864854	−	0.502023i	$-0.167411\pi$
$164$	51.0902			0.311526
$165$	32.9377	+	32.9377i	0.199623	+	0.199623i
$166$	−99.8084	−	99.8084i	−0.601255	−	0.601255i
$167$	193.902	−	193.902i	1.16109	−	1.16109i	0.176855	−	0.984237i	$-0.443408\pi$
$167$	193.902	−	193.902i	1.16109	−	1.16109i	0.984237	−	0.176855i	$-0.0565924\pi$
$168$			28.4848i			0.169553i
$169$			168.727i			0.998384i
$170$	−350.709	+	350.709i	−2.06299	+	2.06299i
$171$	140.968			0.824374
$172$	−45.6925			−0.265654
$173$			330.377i			1.90969i	0.297099	+	0.954847i	$0.403981\pi$
$173$			330.377i			1.90969i	−0.297099	+	0.954847i	$0.596019\pi$
$174$			27.6559i			0.158942i
$175$	−477.214			−2.72694
$176$	71.4190	−	71.4190i	0.405790	−	0.405790i
$177$	−1.35579	+	1.35579i	−0.00765982	+	0.00765982i
$178$	−113.323			−0.636646
$179$	167.632	−	167.632i	0.936490	−	0.936490i	−0.0616104	−	0.998100i	$-0.519624\pi$
$179$	167.632	−	167.632i	0.936490	−	0.936490i	0.998100	+	0.0616104i	$0.0196236\pi$
$180$	−140.524	+	140.524i	−0.780688	+	0.780688i
$181$		−	250.908i		−	1.38623i	−0.720827	−	0.693115i	$-0.756238\pi$
$181$		−	250.908i		−	1.38623i	0.720827	−	0.693115i	$-0.243762\pi$
$182$	12.9584			0.0712001
$183$	−48.8111	+	48.8111i	−0.266727	+	0.266727i
$184$	8.60173	+	8.60173i	0.0467486	+	0.0467486i
$185$	330.406	−	330.406i	1.78598	−	1.78598i
$186$	91.8838	+	91.8838i	0.493999	+	0.493999i
$187$	−114.339			−0.611439
$188$	−169.676			−0.902531
$189$	115.777	−	115.777i	0.612577	−	0.612577i
$190$	−403.523			−2.12381
$191$	−317.466			−1.66212			−0.831062	−	0.556179i	$-0.812267\pi$
$191$	−317.466			−1.66212			−0.831062	+	0.556179i	$0.812267\pi$
$192$	−17.5867	−	17.5867i	−0.0915976	−	0.0915976i
$193$	179.490			0.930002			0.465001	−	0.885310i	$-0.346054\pi$
$193$	179.490			0.930002			0.465001	+	0.885310i	$0.346054\pi$
$194$	−15.6882	−	15.6882i	−0.0808672	−	0.0808672i
$195$	3.27845	+	3.27845i	0.0168126	+	0.0168126i
$196$			116.181i			0.592759i
$197$	40.5037	−	192.791i	0.205603	−	0.978636i
$197$	40.5037	−	192.791i	0.205603	−	0.978636i
$198$	−109.558			−0.553323
$199$	−42.9467	+	42.9467i	−0.215812	+	0.215812i	−0.806731	−	0.590919i	$-0.798765\pi$
$199$	−42.9467	+	42.9467i	−0.215812	+	0.215812i	0.590919	+	0.806731i	$0.298765\pi$
$200$	−105.277	+	105.277i	−0.526383	+	0.526383i
$201$			105.555i			0.525148i
$202$	−177.400	+	177.400i	−0.878220	+	0.878220i
$203$		−	97.6726i		−	0.481146i
$204$			63.9219i			0.313343i
$205$	−109.165	−	109.165i	−0.532513	−	0.532513i
$206$			109.761i			0.532819i
$207$		−	32.8120i		−	0.158512i
$208$	7.10868	−	7.10868i	0.0341763	−	0.0341763i
$209$	−65.7789	−	65.7789i	−0.314731	−	0.314731i
$210$	−155.517	+	155.517i	−0.740559	+	0.740559i
$211$	177.017	+	177.017i	0.838944	+	0.838944i	0.988720	−	0.149776i	$-0.0478552\pi$
$211$	177.017	+	177.017i	0.838944	+	0.838944i	−0.149776	+	0.988720i	$0.547855\pi$
$212$			188.361i			0.888494i
$213$	−112.504			−0.528188
$214$	355.250	+	355.250i	1.66005	+	1.66005i
$215$	97.6318	+	97.6318i	0.454101	+	0.454101i
$216$		−	51.0824i		−	0.236493i
$217$	−324.507	−	324.507i	−1.49542	−	1.49542i
$218$	120.573	+	120.573i	0.553085	+	0.553085i
$219$			53.8108i			0.245712i
$220$	131.143			0.596105
$221$	−11.3807			−0.0514965
$222$		−	144.011i		−	0.648700i
$223$			104.788i			0.469904i	0.972007	+	0.234952i	$0.0754932\pi$
$223$			104.788i			0.469904i	−0.972007	+	0.234952i	$0.924507\pi$
$224$	258.309	+	258.309i	1.15317	+	1.15317i
$225$	401.587			1.78483
$226$	−213.693			−0.945544
$227$	−48.7907	−	48.7907i	−0.214937	−	0.214937i	0.591424	−	0.806361i	$-0.298566\pi$
$227$	−48.7907	−	48.7907i	−0.214937	−	0.214937i	−0.806361	+	0.591424i	$0.798566\pi$
$228$	−36.7740	+	36.7740i	−0.161290	+	0.161290i
$229$	133.506	−	133.506i	0.582996	−	0.582996i	−0.352730	−	0.935725i	$-0.614746\pi$
$229$	133.506	−	133.506i	0.582996	−	0.582996i	0.935725	+	0.352730i	$0.114746\pi$
$230$			93.9250i			0.408370i
$231$	−50.7022			−0.219490
$232$	−21.5472	−	21.5472i	−0.0928760	−	0.0928760i
$233$	349.226			1.49882			0.749411	−	0.662105i	$-0.230337\pi$
$233$	349.226			1.49882			0.749411	+	0.662105i	$0.230337\pi$
$234$	−10.9048			−0.0466018
$235$	362.549	+	362.549i	1.54276	+	1.54276i
$236$			5.39814i			0.0228735i
$237$	5.90107			0.0248990
$238$		−	539.859i		−	2.26832i
$239$	−404.019			−1.69046			−0.845229	−	0.534405i	$-0.820536\pi$
$239$	−404.019			−1.69046			−0.845229	+	0.534405i	$0.820536\pi$
$240$			170.626i			0.710942i
$241$	−56.3505	−	56.3505i	−0.233819	−	0.233819i	0.580465	−	0.814285i	$-0.302871\pi$
$241$	−56.3505	−	56.3505i	−0.233819	−	0.233819i	−0.814285	+	0.580465i	$0.802871\pi$
$242$	−173.216	−	173.216i	−0.715768	−	0.715768i
$243$	−149.139	+	149.139i	−0.613741	+	0.613741i
$244$			194.344i			0.796492i
$245$	248.245	−	248.245i	1.01325	−	1.01325i
$246$	−47.5809			−0.193418
$247$	−6.54728	−	6.54728i	−0.0265072	−	0.0265072i
$248$	−143.177			−0.577326
$249$	38.8702	+	38.8702i	0.156105	+	0.156105i
$250$	−580.101			−2.32041
$251$	30.6780			0.122223			0.0611116	−	0.998131i	$-0.480535\pi$
$251$	30.6780			0.122223			0.0611116	+	0.998131i	$0.480535\pi$
$252$		−	216.313i		−	0.858386i
$253$	−15.3108	+	15.3108i	−0.0605172	+	0.0605172i
$254$	253.890	+	253.890i	0.999569	+	0.999569i
$255$	136.583	−	136.583i	0.535619	−	0.535619i
$256$	335.158			1.30921
$257$	−329.837			−1.28341			−0.641706	−	0.766950i	$-0.721773\pi$
$257$	−329.837			−1.28341			−0.641706	+	0.766950i	$0.721773\pi$
$258$	42.5539			0.164938
$259$			508.606i			1.96373i
$260$	13.0533			0.0502050
$261$			82.1938i			0.314919i
$262$		−	470.044i		−	1.79406i
$263$	63.3241	+	63.3241i	0.240776	+	0.240776i	0.817171	−	0.576395i	$-0.195541\pi$
$263$	63.3241	+	63.3241i	0.240776	+	0.240776i	−0.576395	+	0.817171i	$0.695541\pi$
$264$	−11.1853	+	11.1853i	−0.0423684	+	0.0423684i
$265$	402.473	−	402.473i	1.51877	−	1.51877i
$266$	310.579	−	310.579i	1.16759	−	1.16759i
$267$	44.1334			0.165294
$268$	210.136	+	210.136i	0.784089	+	0.784089i
$269$	−346.391	+	346.391i	−1.28770	+	1.28770i	−0.351517	+	0.936181i	$0.614334\pi$
$269$	−346.391	+	346.391i	−1.28770	+	1.28770i	−0.936181	+	0.351517i	$0.885666\pi$
$270$	278.892	−	278.892i	1.03293	−	1.03293i
$271$	27.6402	−	27.6402i	0.101993	−	0.101993i	−0.654269	−	0.756262i	$-0.727023\pi$
$271$	27.6402	−	27.6402i	0.101993	−	0.101993i	0.756262	+	0.654269i	$0.227023\pi$
$272$	−296.154	−	296.154i	−1.08880	−	1.08880i
$273$	−5.04663			−0.0184858
$274$	459.038	+	459.038i	1.67532	+	1.67532i
$275$	−187.389	−	187.389i	−0.681416	−	0.681416i
$276$	8.55961	+	8.55961i	0.0310131	+	0.0310131i
$277$	−316.919	+	316.919i	−1.14411	+	1.14411i	−0.156422	+	0.987690i	$0.549996\pi$
$277$	−316.919	+	316.919i	−1.14411	+	1.14411i	−0.987690	+	0.156422i	$0.950004\pi$
$278$	−294.101			−1.05792
$279$	273.080	+	273.080i	0.978782	+	0.978782i
$280$		−	242.333i		−	0.865475i
$281$	214.995	−	214.995i	0.765105	−	0.765105i	−0.212135	−	0.977240i	$-0.568042\pi$
$281$	214.995	−	214.995i	0.765105	−	0.765105i	0.977240	+	0.212135i	$0.0680417\pi$
$282$	158.021			0.560358
$283$	19.6373	+	19.6373i	0.0693897	+	0.0693897i	0.740950	−	0.671560i	$-0.234376\pi$
$283$	19.6373	+	19.6373i	0.0693897	+	0.0693897i	−0.671560	+	0.740950i	$0.734376\pi$
$284$	−223.970	+	223.970i	−0.788627	+	0.788627i
$285$	157.151			0.551408
$286$	5.08843	+	5.08843i	0.0177917	+	0.0177917i
$287$	168.042			0.585512
$288$	−217.373	−	217.373i	−0.754768	−	0.754768i
$289$			185.130i			0.640590i
$290$		−	235.281i		−	0.811314i
$291$	6.10975	+	6.10975i	0.0209957	+	0.0209957i
$292$	107.125	+	107.125i	0.366867	+	0.366867i
$293$			504.154i			1.72066i	0.509736	+	0.860331i	$0.329743\pi$
$293$			504.154i			1.72066i	−0.509736	+	0.860331i	$0.670257\pi$
$294$		−	108.201i		−	0.368029i
$295$	11.5343	−	11.5343i	0.0390993	−	0.0390993i
$296$	112.202	+	112.202i	0.379061	+	0.379061i
$297$	90.9252			0.306145
$298$	−339.550			−1.13943
$299$	−1.52396	+	1.52396i	−0.00509686	+	0.00509686i
$300$	−104.761	+	104.761i	−0.349204	+	0.349204i
$301$	−150.288			−0.499296
$302$	234.275			0.775746
$303$	69.0882	−	69.0882i	0.228014	−	0.228014i
$304$		−	340.752i		−	1.12089i
$305$	415.258	−	415.258i	1.36150	−	1.36150i
$306$			454.304i			1.48465i
$307$	391.840	+	391.840i	1.27635	+	1.27635i	0.942695	+	0.333656i	$0.108282\pi$
$307$	391.840	+	391.840i	1.27635	+	1.27635i	0.333656	+	0.942695i	$0.391718\pi$
$308$	−100.937	+	100.937i	−0.327717	+	0.327717i
$309$		−	42.7461i		−	0.138337i
$310$	−781.696	−	781.696i	−2.52160	−	2.52160i
$311$	−302.162			−0.971582			−0.485791	−	0.874075i	$-0.661468\pi$
$311$	−302.162			−0.971582			−0.485791	+	0.874075i	$0.661468\pi$
$312$	−1.11332	+	1.11332i	−0.00356834	+	0.00356834i
$313$		−	76.7248i		−	0.245127i	−0.992461	−	0.122564i	$-0.960888\pi$
$313$		−	76.7248i		−	0.245127i	0.992461	−	0.122564i	$-0.0391115\pi$
$314$	−94.9733	−	94.9733i	−0.302463	−	0.302463i
$315$	−462.200	+	462.200i	−1.46730	+	1.46730i
$316$	11.7477	−	11.7477i	0.0371763	−	0.0371763i
$317$	−218.686	+	218.686i	−0.689861	+	0.689861i	−0.962201	−	0.272340i	$-0.912203\pi$
$317$	−218.686	+	218.686i	−0.689861	+	0.689861i	0.272340	+	0.962201i	$0.412203\pi$
$318$		−	175.423i		−	0.551643i
$319$	38.3535	−	38.3535i	0.120230	−	0.120230i
$320$	149.618	+	149.618i	0.467557	+	0.467557i
$321$	−138.351	−	138.351i	−0.431001	−	0.431001i
$322$	−72.2910	−	72.2910i	−0.224506	−	0.224506i
$323$	−272.765	+	272.765i	−0.844475	+	0.844475i
$324$			155.054i			0.478561i
$325$	−18.6518	−	18.6518i	−0.0573900	−	0.0573900i
$326$	303.430	+	303.430i	0.930767	+	0.930767i
$327$	−46.9567	−	46.9567i	−0.143599	−	0.143599i
$328$	37.0712	−	37.0712i	0.113022	−	0.113022i
$329$	−558.084			−1.69630
$330$	−122.135			−0.370107
$331$		−	285.481i		−	0.862479i	−0.902237	−	0.431240i	$-0.858076\pi$
$331$		−	285.481i		−	0.862479i	0.902237	−	0.431240i	$-0.141924\pi$
$332$	154.764			0.466155
$333$		−	428.004i		−	1.28530i
$334$			719.003i			2.15270i
$335$		−	898.001i		−	2.68060i
$336$	−131.325	−	131.325i	−0.390849	−	0.390849i
$337$	−267.588	+	267.588i	−0.794029	+	0.794029i	−0.982146	−	0.188118i	$-0.939761\pi$
$337$	−267.588	+	267.588i	−0.794029	+	0.794029i	0.188118	+	0.982146i	$0.439761\pi$
$338$	−312.825	−	312.825i	−0.925518	−	0.925518i
$339$	83.2223			0.245494
$340$		−	543.812i		−	1.59945i
$341$		−	254.851i		−	0.747363i
$342$	−261.359	+	261.359i	−0.764209	+	0.764209i
$343$		−	81.2023i		−	0.236741i
$344$	−33.1546	+	33.1546i	−0.0963796	+	0.0963796i
$345$		−	36.5789i		−	0.106026i
$346$	−612.530	−	612.530i	−1.77032	−	1.77032i
$347$	−182.404			−0.525660			−0.262830	−	0.964842i	$-0.584656\pi$
$347$	−182.404			−0.525660			−0.262830	+	0.964842i	$0.584656\pi$
$348$	−21.4417	−	21.4417i	−0.0616141	−	0.0616141i
$349$	130.381	−	130.381i	0.373584	−	0.373584i	−0.495197	−	0.868781i	$-0.664904\pi$
$349$	130.381	−	130.381i	0.373584	−	0.373584i	0.868781	+	0.495197i	$0.164904\pi$
$350$	884.770	−	884.770i	2.52791	−	2.52791i
$351$	9.05022			0.0257841
$352$			202.863i			0.576314i
$353$	−51.1331			−0.144853			−0.0724264	−	0.997374i	$-0.523074\pi$
$353$	−51.1331			−0.144853			−0.0724264	+	0.997374i	$0.523074\pi$
$354$		−	5.02735i		−	0.0142016i
$355$	957.121			2.69612
$356$	87.8597	−	87.8597i	0.246797	−	0.246797i
$357$			210.247i			0.588927i
$358$			621.589i			1.73628i
$359$	228.229	−	228.229i	0.635735	−	0.635735i	−0.313766	−	0.949500i	$-0.601591\pi$
$359$	228.229	−	228.229i	0.635735	−	0.635735i	0.949500	+	0.313766i	$0.101591\pi$
$360$			203.929i			0.566469i
$361$	47.1582			0.130632
$362$	465.191	+	465.191i	1.28506	+	1.28506i
$363$	67.4585	+	67.4585i	0.185836	+	0.185836i
$364$	−10.0467	+	10.0467i	−0.0276008	+	0.0276008i
$365$		−	457.792i		−	1.25423i
$366$		−	180.995i		−	0.494521i
$367$	−72.8879	+	72.8879i	−0.198605	+	0.198605i	−0.799402	−	0.600797i	$-0.794850\pi$
$367$	−72.8879	+	72.8879i	−0.198605	+	0.198605i	0.600797	+	0.799402i	$0.294850\pi$
$368$	−79.3142			−0.215528
$369$	−141.411			−0.383228
$370$			1225.17i			3.31127i
$371$			619.541i			1.66992i
$372$	−142.476			−0.382999
$373$	499.449	−	499.449i	1.33900	−	1.33900i	0.441979	−	0.897025i	$-0.354277\pi$
$373$	499.449	−	499.449i	1.33900	−	1.33900i	0.897025	−	0.441979i	$-0.145723\pi$
$374$	211.989	−	211.989i	0.566814	−	0.566814i
$375$	225.919			0.602451
$376$	−123.117	+	123.117i	−0.327439	+	0.327439i
$377$	3.81750	−	3.81750i	0.0101260	−	0.0101260i
$378$			429.309i			1.13574i
$379$	−421.103			−1.11109			−0.555545	−	0.831486i	$-0.687490\pi$
$379$	−421.103			−1.11109			−0.555545	+	0.831486i	$0.687490\pi$
$380$	312.853	−	312.853i	0.823297	−	0.823297i
$381$	−98.8771	−	98.8771i	−0.259520	−	0.259520i
$382$	588.592	−	588.592i	1.54082	−	1.54082i
$383$	−404.963	−	404.963i	−1.05735	−	1.05735i	−0.998253	−	0.0590925i	$-0.981179\pi$
$383$	−404.963	−	404.963i	−1.05735	−	1.05735i	−0.0590925	−	0.998253i	$-0.518821\pi$
$384$	−92.5838			−0.241104
$385$	431.346			1.12038
$386$	−332.781	+	332.781i	−0.862127	+	0.862127i
$387$	126.471			0.326798
$388$	24.3263			0.0626966
$389$	80.5272	+	80.5272i	0.207011	+	0.207011i	0.802996	−	0.595985i	$-0.203238\pi$
$389$	80.5272	+	80.5272i	0.207011	+	0.207011i	−0.595985	+	0.802996i	$0.703238\pi$
$390$	−12.1567			−0.0311710
$391$	63.4895	+	63.4895i	0.162377	+	0.162377i
$392$	84.3011	+	84.3011i	0.215054	+	0.215054i
$393$			183.058i			0.465795i
$394$	282.346	+	432.536i	0.716614	+	1.09781i
$395$	−50.2030			−0.127096
$396$	84.9406	−	84.9406i	0.214496	−	0.214496i
$397$	436.406	−	436.406i	1.09926	−	1.09926i	0.104761	−	0.994497i	$-0.466592\pi$
$397$	436.406	−	436.406i	1.09926	−	1.09926i	0.994497	−	0.104761i	$-0.0334077\pi$
$398$		−	159.249i		−	0.400123i
$399$	−120.954	+	120.954i	−0.303143	+	0.303143i
$400$		−	970.727i		−	2.42682i
$401$		−	275.830i		−	0.687855i	−0.938996	−	0.343927i	$-0.888243\pi$
$401$		−	275.830i		−	0.687855i	0.938996	−	0.343927i	$-0.111757\pi$
$402$	−195.702	−	195.702i	−0.486821	−	0.486821i
$403$		−	25.3665i		−	0.0629442i
$404$		−	275.078i		−	0.680887i
$405$	331.306	−	331.306i	0.818039	−	0.818039i
$406$	181.088	+	181.088i	0.446030	+	0.446030i
$407$	−199.716	+	199.716i	−0.490704	+	0.490704i
$408$	46.3819	+	46.3819i	0.113681	+	0.113681i
$409$			392.872i			0.960567i	0.877113	+	0.480284i	$0.159466\pi$
$409$			392.872i			0.960567i	−0.877113	+	0.480284i	$0.840534\pi$
$410$	404.792			0.987297
$411$	−178.771	−	178.771i	−0.434967	−	0.434967i
$412$	−85.0979	−	85.0979i	−0.206548	−	0.206548i
$413$			17.7551i			0.0429906i
$414$	60.8346	+	60.8346i	0.146943	+	0.146943i
$415$	−330.686	−	330.686i	−0.796833	−	0.796833i
$416$			20.1919i			0.0485382i
$417$	114.537			0.274669
$418$	243.912			0.583522
$419$		−	330.235i		−	0.788149i	−0.919078	−	0.394075i	$-0.871065\pi$
$419$		−	330.235i		−	0.788149i	0.919078	−	0.394075i	$-0.128935\pi$
$420$		−	241.146i		−	0.574158i
$421$	312.913	+	312.913i	0.743260	+	0.743260i	0.973204	−	0.229944i	$-0.0738542\pi$
$421$	312.913	+	312.913i	0.743260	+	0.743260i	−0.229944	+	0.973204i	$0.573854\pi$
$422$	−656.391			−1.55543
$423$	469.641			1.11026
$424$	136.675	+	136.675i	0.322347	+	0.322347i
$425$	−777.048	+	777.048i	−1.82835	+	1.82835i
$426$	208.586	−	208.586i	0.489639	−	0.489639i
$427$			639.221i			1.49700i
$428$	−550.852			−1.28704
$429$	−1.98168	−	1.98168i	−0.00461930	−	0.00461930i
$430$	−362.025			−0.841919
$431$	25.5939			0.0593827			0.0296913	−	0.999559i	$-0.490548\pi$
$431$	25.5939			0.0593827			0.0296913	+	0.999559i	$0.490548\pi$
$432$	235.508	+	235.508i	0.545158	+	0.545158i
$433$			679.762i			1.56989i	0.619566	+	0.784944i	$0.287308\pi$
$433$			679.762i			1.56989i	−0.619566	+	0.784944i	$0.712692\pi$
$434$	1203.29			2.77256
$435$			91.6297i			0.210643i
$436$	−186.961			−0.428809
$437$			73.0505i			0.167164i
$438$	−99.7670	−	99.7670i	−0.227779	−	0.227779i
$439$	−63.7721	−	63.7721i	−0.145267	−	0.145267i	0.630733	−	0.776000i	$-0.282754\pi$
$439$	−63.7721	−	63.7721i	−0.145267	−	0.145267i	−0.776000	+	0.630733i	$0.782754\pi$
$440$	95.1579	−	95.1579i	0.216268	−	0.216268i
$441$		−	321.574i		−	0.729192i
$442$	21.1002	−	21.1002i	0.0477381	−	0.0477381i
$443$	109.670			0.247563			0.123781	−	0.992310i	$-0.460498\pi$
$443$	109.670			0.247563			0.123781	+	0.992310i	$0.460498\pi$
$444$	111.653	+	111.653i	0.251470	+	0.251470i
$445$	−375.463			−0.843736
$446$	−194.281	−	194.281i	−0.435608	−	0.435608i
$447$	132.237			0.295832
$448$	−230.312			−0.514090
$449$		−	441.656i		−	0.983643i	−0.870696	−	0.491822i	$-0.836331\pi$
$449$		−	441.656i		−	0.983643i	0.870696	−	0.491822i	$-0.163669\pi$
$450$	−744.555	+	744.555i	−1.65457	+	1.65457i
$451$	65.9857	+	65.9857i	0.146310	+	0.146310i
$452$	165.677	−	165.677i	0.366542	−	0.366542i
$453$	−91.2381			−0.201409
$454$	180.919			0.398500
$455$	42.9339			0.0943602
$456$			53.3667i			0.117032i
$457$	−147.026			−0.321719			−0.160860	−	0.986977i	$-0.551427\pi$
$457$	−147.026			−0.321719			−0.160860	+	0.986977i	$0.551427\pi$
$458$			495.049i			1.08089i
$459$		−	377.040i		−	0.821437i
$460$	−72.8204	−	72.8204i	−0.158305	−	0.158305i
$461$	51.9508	−	51.9508i	0.112692	−	0.112692i	−0.648512	−	0.761204i	$-0.724609\pi$
$461$	51.9508	−	51.9508i	0.112692	−	0.112692i	0.761204	+	0.648512i	$0.224609\pi$
$462$	94.0035	−	94.0035i	0.203471	−	0.203471i
$463$	−186.723	+	186.723i	−0.403290	+	0.403290i	−0.879391	−	0.476101i	$-0.842050\pi$
$463$	−186.723	+	186.723i	−0.403290	+	0.403290i	0.476101	+	0.879391i	$0.342050\pi$
$464$	198.681			0.428192
$465$	304.430	+	304.430i	0.654688	+	0.654688i
$466$	−647.476	+	647.476i	−1.38943	+	1.38943i
$467$	−120.368	+	120.368i	−0.257748	+	0.257748i	−0.824137	−	0.566390i	$-0.808340\pi$
$467$	−120.368	+	120.368i	−0.257748	+	0.257748i	0.566390	+	0.824137i	$0.308340\pi$
$468$	8.45454	−	8.45454i	0.0180653	−	0.0180653i
$469$	691.162	+	691.162i	1.47369	+	1.47369i
$470$	−1344.35			−2.86033
$471$	36.9872	+	36.9872i	0.0785290	+	0.0785290i
$472$	3.91690	+	3.91690i	0.00829853	+	0.00829853i
$473$	−59.0142	−	59.0142i	−0.124766	−	0.124766i
$474$	−10.9408	+	10.9408i	−0.0230818	+	0.0230818i
$475$	−894.066			−1.88224
$476$	418.554	+	418.554i	0.879316	+	0.879316i
$477$		−	521.358i		−	1.09299i
$478$	749.065	−	749.065i	1.56708	−	1.56708i
$479$	−303.233			−0.633054			−0.316527	−	0.948584i	$-0.602517\pi$
$479$	−303.233			−0.633054			−0.316527	+	0.948584i	$0.602517\pi$
$480$	−242.328	−	242.328i	−0.504850	−	0.504850i
$481$	−19.8787	+	19.8787i	−0.0413279	+	0.0413279i
$482$	208.951			0.433509
$483$	28.1536	+	28.1536i	0.0582890	+	0.0582890i
$484$	268.590			0.554937
$485$	−51.9783	−	51.9783i	−0.107172	−	0.107172i
$486$		−	553.017i		−	1.13790i
$487$			105.371i			0.216367i	0.994131	+	0.108184i	$0.0345034\pi$
$487$			105.371i			0.216367i	−0.994131	+	0.108184i	$0.965497\pi$
$488$	141.017	+	141.017i	0.288968	+	0.288968i
$489$	−118.170	−	118.170i	−0.241657	−	0.241657i
$490$			920.510i			1.87859i
$491$		−	115.702i		−	0.235646i	−0.993035	−	0.117823i	$-0.962408\pi$
$491$		−	115.702i		−	0.235646i	0.993035	−	0.117823i	$-0.0375916\pi$
$492$	36.8896	−	36.8896i	0.0749789	−	0.0749789i
$493$	−159.040	−	159.040i	−0.322597	−	0.322597i
$494$	24.2778			0.0491453
$495$	−362.988			−0.733308
$496$	660.097	−	660.097i	1.33084	−	1.33084i
$497$	−736.665	+	736.665i	−1.48222	+	1.48222i
$498$	−144.133			−0.289424
$499$	498.032			0.998060			0.499030	−	0.866585i	$-0.333690\pi$
$499$	498.032			0.998060			0.499030	+	0.866585i	$0.333690\pi$
$500$	449.755	−	449.755i	0.899509	−	0.899509i
$501$		−	280.014i		−	0.558910i
$502$	−56.8781	+	56.8781i	−0.113303	+	0.113303i
$503$		−	889.271i		−	1.76793i	−0.467550	−	0.883967i	$-0.654863\pi$
$503$		−	889.271i		−	1.76793i	0.467550	−	0.883967i	$-0.345137\pi$
$504$	−156.958	−	156.958i	−0.311424	−	0.311424i
$505$	−587.764	+	587.764i	−1.16389	+	1.16389i
$506$		−	56.7736i		−	0.112201i
$507$	121.829	+	121.829i	0.240294	+	0.240294i
$508$	−393.684			−0.774969
$509$	121.369	−	121.369i	0.238446	−	0.238446i	−0.577760	−	0.816206i	$-0.696073\pi$
$509$	121.369	−	121.369i	0.238446	−	0.238446i	0.816206	+	0.577760i	$0.196073\pi$
$510$			506.458i			0.993056i
$511$	352.348	+	352.348i	0.689527	+	0.689527i
$512$	−364.946	+	364.946i	−0.712785	+	0.712785i
$513$	216.910	−	216.910i	0.422826	−	0.422826i
$514$	611.529	−	611.529i	1.18974	−	1.18974i
$515$			363.660i			0.706136i
$516$	−32.9922	+	32.9922i	−0.0639384	+	0.0639384i
$517$	−219.145	−	219.145i	−0.423878	−	0.423878i
$518$	−942.973	−	942.973i	−1.82041	−	1.82041i
$519$	238.548	+	238.548i	0.459631	+	0.459631i
$520$	9.47151	−	9.47151i	0.0182145	−	0.0182145i
$521$			460.242i			0.883382i	0.897167	+	0.441691i	$0.145621\pi$
$521$			460.242i			0.883382i	−0.897167	+	0.441691i	$0.854379\pi$
$522$	−152.390	−	152.390i	−0.291935	−	0.291935i
$523$	189.728	+	189.728i	0.362768	+	0.362768i	0.864831	−	0.502063i	$-0.167425\pi$
$523$	189.728	+	189.728i	0.362768	+	0.362768i	−0.502063	+	0.864831i	$0.667425\pi$
$524$	364.426	+	364.426i	0.695470	+	0.695470i
$525$	−344.572	+	344.572i	−0.656327	+	0.656327i
$526$	−234.810			−0.446406
$527$	−1056.79			−2.00529
$528$		−	103.136i		−	0.195334i
$529$	−511.997			−0.967857
$530$			1492.40i			2.81584i
$531$		−	14.9414i		−	0.0281382i
$532$			481.586i			0.905236i
$533$	6.56787	+	6.56787i	0.0123224	+	0.0123224i
$534$	−81.8248	+	81.8248i	−0.153230	+	0.153230i
$535$	1177.02	+	1177.02i	2.20003	+	2.20003i
$536$	304.950			0.568937
$537$		−	242.077i		−	0.450794i
$538$		−	1284.44i		−	2.38744i
$539$	−150.054	+	150.054i	−0.278392	+	0.278392i
$540$			432.452i			0.800837i
$541$	−368.331	+	368.331i	−0.680833	+	0.680833i	−0.960188	−	0.279355i	$-0.909879\pi$
$541$	−368.331	+	368.331i	−0.680833	+	0.680833i	0.279355	+	0.960188i	$0.409879\pi$
$542$			102.492i			0.189099i
$543$	−181.168	−	181.168i	−0.333642	−	0.333642i
$544$	841.211			1.54634
$545$	399.482	+	399.482i	0.732994	+	0.732994i
$546$	9.35662	−	9.35662i	0.0171367	−	0.0171367i
$547$	363.420	−	363.420i	0.664388	−	0.664388i	−0.292023	−	0.956411i	$-0.594328\pi$
$547$	363.420	−	363.420i	0.664388	−	0.664388i	0.956411	+	0.292023i	$0.0943284\pi$
$548$	−711.787			−1.29888
$549$		−	537.919i		−	0.979817i
$550$	694.852			1.26337
$551$		−	182.991i		−	0.332107i
$552$	12.4217			0.0225032
$553$	38.6396	−	38.6396i	0.0698727	−	0.0698727i
$554$		−	1175.16i		−	2.12122i
$555$		−	477.139i		−	0.859711i
$556$	228.017	−	228.017i	0.410103	−	0.410103i
$557$		−	112.919i		−	0.202728i	−0.994849	−	0.101364i	$-0.967679\pi$
$557$		−	112.919i		−	0.202728i	0.994849	−	0.101364i	$-0.0323206\pi$
$558$	−1012.60			−1.81469
$559$	−5.87396	−	5.87396i	−0.0105080	−	0.0105080i
$560$	1117.24	+	1117.24i	1.99508	+	1.99508i
$561$	−82.5585	+	82.5585i	−0.147163	+	0.147163i
$562$			797.214i			1.41853i
$563$			539.374i			0.958035i	0.877805	+	0.479018i	$0.159007\pi$
$563$			539.374i			0.958035i	−0.877805	+	0.479018i	$0.840993\pi$
$564$	−122.514	+	122.514i	−0.217224	+	0.217224i
$565$	−708.009			−1.25311
$566$	−72.8163			−0.128651
$567$			509.991i			0.899454i
$568$			325.027i			0.572230i
$569$	618.784			1.08749			0.543747	−	0.839249i	$-0.317005\pi$
$569$	618.784			1.08749			0.543747	+	0.839249i	$0.317005\pi$
$570$	−291.364	+	291.364i	−0.511164	+	0.511164i
$571$	−222.155	+	222.155i	−0.389063	+	0.389063i	−0.874353	−	0.485290i	$-0.838714\pi$
$571$	−222.155	+	222.155i	−0.389063	+	0.389063i	0.485290	+	0.874353i	$0.338714\pi$
$572$	−7.89016			−0.0137940
$573$	−229.226	+	229.226i	−0.400045	+	0.400045i
$574$	−311.555	+	311.555i	−0.542779	+	0.542779i
$575$			208.105i			0.361921i
$576$	193.813			0.336481
$577$	360.038	−	360.038i	0.623982	−	0.623982i	−0.322565	−	0.946547i	$-0.604545\pi$
$577$	360.038	−	360.038i	0.623982	−	0.623982i	0.946547	+	0.322565i	$0.104545\pi$
$578$	−343.238	−	343.238i	−0.593837	−	0.593837i
$579$	129.601	−	129.601i	0.223836	−	0.223836i
$580$	182.414	+	182.414i	0.314507	+	0.314507i
$581$	509.036			0.876138
$582$	−22.6554			−0.0389267
$583$	−243.278	+	243.278i	−0.417286	+	0.417286i
$584$	155.461			0.266200
$585$	−36.1299			−0.0617605
$586$	−934.718	−	934.718i	−1.59508	−	1.59508i
$587$	850.848			1.44949			0.724743	−	0.689020i	$-0.241959\pi$
$587$	850.848			1.44949			0.724743	+	0.689020i	$0.241959\pi$
$588$	83.8882	+	83.8882i	0.142667	+	0.142667i
$589$	−607.967	−	607.967i	−1.03220	−	1.03220i
$590$			42.7699i			0.0724913i
$591$	−109.959	−	168.450i	−0.186056	−	0.285026i
$592$	−1034.58			−1.74761
$593$	−457.521	+	457.521i	−0.771536	+	0.771536i	−0.978375	−	0.206839i	$-0.933682\pi$
$593$	−457.521	+	457.521i	−0.771536	+	0.771536i	0.206839	+	0.978375i	$0.433682\pi$
$594$	−168.578	+	168.578i	−0.283802	+	0.283802i
$595$		−	1788.66i		−	3.00616i
$596$	263.254	−	263.254i	0.441701	−	0.441701i
$597$			62.0192i			0.103885i
$598$		−	5.65095i		−	0.00944974i
$599$	−188.629	−	188.629i	−0.314906	−	0.314906i	0.531901	−	0.846807i	$-0.321478\pi$
$599$	−188.629	−	188.629i	−0.314906	−	0.314906i	−0.846807	+	0.531901i	$0.821478\pi$
$600$			152.030i			0.253383i
$601$		−	739.711i		−	1.23080i	−0.788215	−	0.615400i	$-0.788994\pi$
$601$		−	739.711i		−	1.23080i	0.788215	−	0.615400i	$-0.211006\pi$
$602$	278.639	−	278.639i	0.462855	−	0.462855i
$603$	−581.629	−	581.629i	−0.964559	−	0.964559i
$604$	−181.635	+	181.635i	−0.300719	+	0.300719i
$605$	−573.899	−	573.899i	−0.948594	−	0.948594i
$606$			256.184i			0.422745i
$607$	−235.745			−0.388378			−0.194189	−	0.980964i	$-0.562207\pi$
$607$	−235.745			−0.388378			−0.194189	+	0.980964i	$0.562207\pi$
$608$	483.945	+	483.945i	0.795963	+	0.795963i
$609$	−70.5244	−	70.5244i	−0.115804	−	0.115804i
$610$			1539.80i			2.52427i
$611$	−21.8126	−	21.8126i	−0.0356998	−	0.0356998i
$612$	−352.223	−	352.223i	−0.575528	−	0.575528i
$613$		−	986.467i		−	1.60924i	−0.593787	−	0.804622i	$-0.702368\pi$
$613$		−	986.467i		−	1.60924i	0.593787	−	0.804622i	$-0.297632\pi$
$614$	−1452.97			−2.36640
$615$	−157.645			−0.256334
$616$			146.480i			0.237792i
$617$			887.836i			1.43896i	0.694515	+	0.719478i	$0.255619\pi$
$617$			887.836i			1.43896i	−0.694515	+	0.719478i	$0.744381\pi$
$618$	79.2527	+	79.2527i	0.128241	+	0.128241i
$619$	336.542			0.543686			0.271843	−	0.962342i	$-0.412367\pi$
$619$	336.542			0.543686			0.271843	+	0.962342i	$0.412367\pi$
$620$	1212.10			1.95501
$621$	−50.4884	−	50.4884i	−0.0813017	−	0.0813017i
$622$	560.219	−	560.219i	0.900673	−	0.900673i
$623$	288.981	−	288.981i	0.463855	−	0.463855i
$624$		−	10.2656i		−	0.0164513i
$625$	−660.301			−1.05648
$626$	142.250	+	142.250i	0.227237	+	0.227237i
$627$	−94.9911			−0.151501
$628$	147.266			0.234500
$629$	828.165	+	828.165i	1.31664	+	1.31664i
$630$		−	1713.87i		−	2.72043i
$631$	−1073.26			−1.70089			−0.850447	−	0.526060i	$-0.823669\pi$
$631$	−1073.26			−1.70089			−0.850447	+	0.526060i	$0.823669\pi$
$632$		−	17.0483i		−	0.0269752i
$633$	255.630			0.403839
$634$		−	810.902i		−	1.27903i
$635$	841.191	+	841.191i	1.32471	+	1.32471i
$636$	136.006	+	136.006i	0.213845	+	0.213845i
$637$	−14.9355	+	14.9355i	−0.0234467	+	0.0234467i
$638$			142.217i			0.222911i
$639$	619.921	−	619.921i	0.970142	−	0.970142i
$640$	787.652			1.23071
$641$	19.5087	+	19.5087i	0.0304347	+	0.0304347i	0.722160	−	0.691726i	$-0.243149\pi$
$641$	19.5087	+	19.5087i	0.0304347	+	0.0304347i	−0.691726	+	0.722160i	$0.743149\pi$
$642$	513.015			0.799090
$643$	362.004	+	362.004i	0.562992	+	0.562992i	0.930156	−	0.367164i	$-0.119671\pi$
$643$	362.004	+	362.004i	0.562992	+	0.562992i	−0.367164	+	0.930156i	$0.619671\pi$
$644$	112.095			0.174060
$645$	140.990			0.218589
$646$		−	1011.43i		−	1.56568i
$647$	−387.472	+	387.472i	−0.598875	+	0.598875i	−0.940013	−	0.341138i	$-0.889188\pi$
$647$	−387.472	+	387.472i	−0.598875	+	0.598875i	0.341138	+	0.940013i	$0.389188\pi$
$648$	112.507	+	112.507i	0.173623	+	0.173623i
$649$	−6.97198	+	6.97198i	−0.0107426	+	0.0107426i
$650$	69.1619			0.106403
$651$	−468.620			−0.719846
$652$	−470.500			−0.721626
$653$		−	819.997i		−	1.25574i	−0.778319	−	0.627869i	$-0.783927\pi$
$653$		−	819.997i		−	1.25574i	0.778319	−	0.627869i	$-0.216073\pi$
$654$	174.119			0.266236
$655$		−	1557.35i		−	2.37764i
$656$			341.823i			0.521072i
$657$	−296.509	−	296.509i	−0.451308	−	0.451308i
$658$	1034.71	−	1034.71i	1.57250	−	1.57250i
$659$	−614.405	+	614.405i	−0.932330	+	0.932330i	−0.997851	−	0.0655216i	$-0.979129\pi$
$659$	−614.405	+	614.405i	−0.932330	+	0.932330i	0.0655216	+	0.997851i	$0.479129\pi$
$660$	94.6918	−	94.6918i	0.143472	−	0.143472i
$661$	353.118			0.534218			0.267109	−	0.963666i	$-0.413932\pi$
$661$	353.118			0.534218			0.267109	+	0.963666i	$0.413932\pi$
$662$	529.291	+	529.291i	0.799533	+	0.799533i
$663$	−8.21744	+	8.21744i	−0.0123943	+	0.0123943i
$664$	112.297	−	112.297i	0.169122	−	0.169122i
$665$	1029.01	−	1029.01i	1.54739	−	1.54739i
$666$	793.534	+	793.534i	1.19149	+	1.19149i
$667$	−42.5933			−0.0638581
$668$	−557.445	−	557.445i	−0.834499	−	0.834499i
$669$	75.6624	+	75.6624i	0.113098	+	0.113098i
$670$	1664.92	+	1664.92i	2.48496	+	2.48496i
$671$	−251.005	+	251.005i	−0.374077	+	0.374077i
$672$	373.024			0.555095
$673$	202.588	+	202.588i	0.301022	+	0.301022i	0.841414	−	0.540391i	$-0.181724\pi$
$673$	202.588	+	202.588i	0.301022	+	0.301022i	−0.540391	+	0.841414i	$0.681724\pi$
$674$		−	992.232i		−	1.47216i
$675$	617.927	−	617.927i	0.915448	−	0.915448i
$676$	485.069			0.717557
$677$	578.791	+	578.791i	0.854935	+	0.854935i	0.990736	−	0.135801i	$-0.0433608\pi$
$677$	578.791	+	578.791i	0.854935	+	0.854935i	−0.135801	+	0.990736i	$0.543361\pi$
$678$	−154.297	+	154.297i	−0.227577	+	0.227577i
$679$	80.0121			0.117838
$680$	−394.591	−	394.591i	−0.580281	−	0.580281i
$681$	−70.4585			−0.103463
$682$	472.502	+	472.502i	0.692818	+	0.692818i
$683$		−	750.269i		−	1.09849i	−0.835661	−	0.549245i	$-0.814915\pi$
$683$		−	750.269i		−	1.09849i	0.835661	−	0.549245i	$-0.185085\pi$
$684$		−	405.265i		−	0.592493i
$685$	1520.89	+	1520.89i	2.22027	+	2.22027i
$686$	150.552	+	150.552i	0.219463	+	0.219463i
$687$		−	192.796i		−	0.280634i
$688$		−	305.709i		−	0.444345i
$689$	−24.2146	+	24.2146i	−0.0351445	+	0.0351445i
$690$	67.8185	+	67.8185i	0.0982876	+	0.0982876i
$691$	−308.137			−0.445929			−0.222965	−	0.974827i	$-0.571573\pi$
$691$	−308.137			−0.445929			−0.222965	+	0.974827i	$0.571573\pi$
$692$	949.793			1.37253
$693$	279.380	−	279.380i	0.403146	−	0.403146i
$694$	338.183	−	338.183i	0.487296	−	0.487296i
$695$	−974.417			−1.40204
$696$	−31.1163			−0.0447074
$697$	273.623	−	273.623i	0.392572	−	0.392572i
$698$			483.460i			0.692636i
$699$	252.158	−	252.158i	0.360741	−	0.360741i
$700$			1371.93i			1.95990i
$701$	−503.113	−	503.113i	−0.717708	−	0.717708i	0.250428	−	0.968135i	$-0.419429\pi$
$701$	−503.113	−	503.113i	−0.717708	−	0.717708i	−0.968135	+	0.250428i	$0.919429\pi$
$702$	−16.7794	+	16.7794i	−0.0239023	+	0.0239023i
$703$			952.880i			1.35545i
$704$	−90.4377	−	90.4377i	−0.128463	−	0.128463i
$705$	523.556			0.742633
$706$	94.8024	−	94.8024i	0.134281	−	0.134281i
$707$		−	904.766i		−	1.27973i
$708$	3.89772	+	3.89772i	0.00550526	+	0.00550526i
$709$	707.551	−	707.551i	0.997957	−	0.997957i	−0.00204137	−	0.999998i	$-0.500650\pi$
$709$	707.551	−	707.551i	0.997957	−	0.997957i	0.999998	+	0.00204137i	$0.000649790\pi$
$710$	−1774.53	+	1774.53i	−2.49934	+	2.49934i
$711$	−32.5161	+	32.5161i	−0.0457330	+	0.0457330i
$712$		−	127.503i		−	0.179077i
$713$	−141.512	+	141.512i	−0.198474	+	0.198474i
$714$	−389.805	−	389.805i	−0.545945	−	0.545945i
$715$	16.8590	+	16.8590i	0.0235791	+	0.0235791i
$716$	−481.920	−	481.920i	−0.673073	−	0.673073i
$717$	−291.722	+	291.722i	−0.406864	+	0.406864i
$718$			846.287i			1.17867i
$719$	222.026	+	222.026i	0.308798	+	0.308798i	0.844443	−	0.535645i	$-0.179932\pi$
$719$	222.026	+	222.026i	0.308798	+	0.308798i	−0.535645	+	0.844443i	$0.679932\pi$
$720$	−940.186	−	940.186i	−1.30581	−	1.30581i
$721$	−279.897	−	279.897i	−0.388207	−	0.388207i
$722$	−87.4329	+	87.4329i	−0.121098	+	0.121098i
$723$	−81.3756			−0.112553
$724$	−721.329			−0.996310
$725$		−	521.300i		−	0.719034i
$726$	−250.141			−0.344546
$727$		−	328.362i		−	0.451667i	−0.974166	−	0.225834i	$-0.927489\pi$
$727$		−	328.362i		−	0.451667i	0.974166	−	0.225834i	$-0.0725106\pi$
$728$			14.5798i			0.0200272i
$729$		−	270.035i		−	0.370419i
$730$	848.762	+	848.762i	1.16269	+	1.16269i
$731$	−244.714	+	244.714i	−0.334766	+	0.334766i
$732$	140.326	+	140.326i	0.191702	+	0.191702i
$733$	−67.1611			−0.0916250			−0.0458125	−	0.998950i	$-0.514588\pi$
$733$	−67.1611			−0.0916250			−0.0458125	+	0.998950i	$0.514588\pi$
$734$		−	270.273i		−	0.368220i
$735$		−	358.491i		−	0.487742i
$736$	112.644	−	112.644i	0.153049	−	0.153049i
$737$			542.803i			0.736503i
$738$	262.181	−	262.181i	0.355259	−	0.355259i
$739$		−	735.935i		−	0.995852i	−0.867220	−	0.497926i	$-0.834095\pi$
$739$		−	735.935i		−	0.995852i	0.867220	−	0.497926i	$-0.165905\pi$
$740$	−949.877	−	949.877i	−1.28362	−	1.28362i
$741$	−9.45492			−0.0127597
$742$	−1148.65	−	1148.65i	−1.54805	−	1.54805i
$743$	720.697	−	720.697i	0.969983	−	0.969983i	−0.0295796	−	0.999562i	$-0.509417\pi$
$743$	720.697	−	720.697i	0.969983	−	0.969983i	0.999562	+	0.0295796i	$0.00941684\pi$
$744$	−103.381	+	103.381i	−0.138953	+	0.138953i
$745$	−1125.00			−1.51006
$746$			1851.99i			2.48256i
$747$	−428.366			−0.573448
$748$			328.711i			0.439453i
$749$	−1811.82			−2.41899
$750$	−418.862	+	418.862i	−0.558482	+	0.558482i
$751$			677.410i			0.902011i	0.892521	+	0.451005i	$0.148934\pi$
$751$			677.410i			0.902011i	−0.892521	+	0.451005i	$0.851066\pi$
$752$		−	1135.23i		−	1.50961i
$753$	22.1510	−	22.1510i	0.0294171	−	0.0294171i
$754$			14.1556i			0.0187739i
$755$	776.203			1.02808
$756$	−332.844	−	332.844i	−0.440270	−	0.440270i
$757$	459.992	+	459.992i	0.607651	+	0.607651i	0.942332	−	0.334680i	$-0.108628\pi$
$757$	459.992	+	459.992i	0.607651	+	0.607651i	−0.334680	+	0.942332i	$0.608628\pi$
$758$	780.739	−	780.739i	1.03000	−	1.03000i
$759$			22.1104i			0.0291309i
$760$		−	454.014i		−	0.597387i
$761$	225.532	−	225.532i	0.296362	−	0.296362i	−0.543225	−	0.839587i	$-0.682797\pi$
$761$	225.532	−	225.532i	0.296362	−	0.296362i	0.839587	+	0.543225i	$0.182797\pi$
$762$	366.643			0.481158
$763$	−614.936			−0.805945
$764$			912.675i			1.19460i
$765$			1505.20i			1.96758i
$766$	1501.63			1.96035
$767$	−0.693954	+	0.693954i	−0.000904764	+	0.000904764i
$768$	242.000	−	242.000i	0.315105	−	0.315105i
$769$	274.038			0.356357			0.178178	−	0.983998i	$-0.442980\pi$
$769$	274.038			0.356357			0.178178	+	0.983998i	$0.442980\pi$
$770$	−799.730	+	799.730i	−1.03861	+	1.03861i
$771$	−238.159	+	238.159i	−0.308896	+	0.308896i
$772$		−	516.012i		−	0.668410i
$773$	−205.270			−0.265550			−0.132775	−	0.991146i	$-0.542389\pi$
$773$	−205.270			−0.265550			−0.132775	+	0.991146i	$0.542389\pi$
$774$	−234.481	+	234.481i	−0.302947	+	0.302947i
$775$	−1731.96	−	1731.96i	−2.23479	−	2.23479i
$776$	17.6512	−	17.6512i	0.0227464	−	0.0227464i
$777$	367.239	+	367.239i	0.472637	+	0.472637i
$778$	−298.600			−0.383805
$779$	314.828			0.404144
$780$	9.42513	−	9.42513i	0.0120835	−	0.0120835i
$781$	−578.538			−0.740766
$782$	−235.423			−0.301053
$783$	126.473	+	126.473i	0.161523	+	0.161523i
$784$	−777.317			−0.991476
$785$	−314.666	−	314.666i	−0.400849	−	0.400849i
$786$	−339.395	−	339.395i	−0.431800	−	0.431800i
$787$			572.372i			0.727283i	0.931539	+	0.363641i	$0.118467\pi$
$787$			572.372i			0.727283i	−0.931539	+	0.363641i	$0.881533\pi$
$788$	−554.251	−	116.443i	−0.703364	−	0.147771i
$789$	91.4462			0.115901
$790$	93.0780	−	93.0780i	0.117820	−	0.117820i
$791$	544.932	−	544.932i	0.688915	−	0.688915i
$792$		−	123.266i		−	0.155639i
$793$	−24.9838	+	24.9838i	−0.0315054	+	0.0315054i
$794$			1618.22i			2.03806i
$795$		−	581.211i		−	0.731083i
$796$	123.466	+	123.466i	0.155108	+	0.155108i
$797$		−	71.8433i		−	0.0901421i	−0.998984	−	0.0450711i	$-0.985649\pi$
$797$		−	71.8433i		−	0.0901421i	0.998984	−	0.0450711i	$-0.0143514\pi$
$798$		−	448.506i		−	0.562038i
$799$	−908.730	+	908.730i	−1.13733	+	1.13733i
$800$	1378.65	+	1378.65i	1.72332	+	1.72332i
$801$	−243.185	+	243.185i	−0.303601	+	0.303601i
$802$	511.397	+	511.397i	0.637653	+	0.637653i
$803$			276.716i			0.344602i
$804$	303.457			0.377434
$805$	−239.515	−	239.515i	−0.297534	−	0.297534i
$806$	47.0303	+	47.0303i	0.0583503	+	0.0583503i
$807$			500.223i			0.619855i
$808$	−199.598	−	199.598i	−0.247027	−	0.247027i
$809$	839.505	+	839.505i	1.03771	+	1.03771i	0.999261	+	0.0384469i	$0.0122410\pi$
$809$	839.505	+	839.505i	1.03771	+	1.03771i	0.0384469	+	0.999261i	$0.487759\pi$
$810$			1228.50i			1.51667i
$811$	231.621			0.285599			0.142800	−	0.989752i	$-0.454390\pi$
$811$	231.621			0.285599			0.142800	+	0.989752i	$0.454390\pi$
$812$	−280.797			−0.345809
$813$		−	39.9152i		−	0.0490961i
$814$		−	740.562i		−	0.909781i
$815$	1005.33	+	1005.33i	1.23353	+	1.23353i
$816$	−427.675			−0.524111
$817$	−281.566			−0.344634
$818$	−728.398	−	728.398i	−0.890462	−	0.890462i
$819$	27.8080	−	27.8080i	0.0339536	−	0.0339536i
$820$	−313.836	+	313.836i	−0.382727	+	0.382727i
$821$		−	550.744i		−	0.670821i	−0.942072	−	0.335410i	$-0.891125\pi$
$821$		−	550.744i		−	0.670821i	0.942072	−	0.335410i	$-0.108875\pi$
$822$	662.896			0.806442
$823$	848.633	+	848.633i	1.03115	+	1.03115i	0.999499	+	0.0316463i	$0.0100750\pi$
$823$	848.633	+	848.633i	1.03115	+	1.03115i	0.0316463	+	0.999499i	$0.489925\pi$
$824$	−123.495			−0.149872
$825$	−270.609			−0.328011
$826$	−32.9186	−	32.9186i	−0.0398530	−	0.0398530i
$827$		−	744.994i		−	0.900839i	−0.892817	−	0.450420i	$-0.851274\pi$
$827$		−	744.994i		−	0.900839i	0.892817	−	0.450420i	$-0.148726\pi$
$828$	−94.3305			−0.113926
$829$			651.677i			0.786101i	0.919517	+	0.393050i	$0.128580\pi$
$829$			651.677i			0.786101i	−0.919517	+	0.393050i	$0.871420\pi$
$830$	1226.20			1.47735
$831$			457.662i			0.550737i
$832$	−9.00169	−	9.00169i	−0.0108193	−	0.0108193i
$833$	622.227	+	622.227i	0.746972	+	0.746972i
$834$	−212.355	+	212.355i	−0.254623	+	0.254623i
$835$			2382.20i			2.85294i
$836$	−189.106	+	189.106i	−0.226203	+	0.226203i
$837$	840.385			1.00404
$838$	612.266	+	612.266i	0.730627	+	0.730627i
$839$	413.702			0.493089			0.246545	−	0.969131i	$-0.420705\pi$
$839$	413.702			0.493089			0.246545	+	0.969131i	$0.420705\pi$
$840$	−174.976	−	174.976i	−0.208305	−	0.208305i
$841$	−734.304			−0.873132
$842$	−1160.30			−1.37803
$843$		−	310.473i		−	0.368296i
$844$	508.902	−	508.902i	0.602965	−	0.602965i
$845$	−1036.45	−	1036.45i	−1.22657	−	1.22657i
$846$	−870.730	+	870.730i	−1.02923	+	1.02923i
$847$	883.424			1.04300
$848$	−1260.24			−1.48614
$849$	28.3582			0.0334018
$850$		−	2881.35i		−	3.38982i
$851$	221.795			0.260628
$852$			323.435i			0.379618i
$853$		−	1132.63i		−	1.32782i	−0.747813	−	0.663910i	$-0.768896\pi$
$853$		−	1132.63i		−	1.32782i	0.747813	−	0.663910i	$-0.231104\pi$
$854$	−1185.14	−	1185.14i	−1.38775	−	1.38775i
$855$	−865.937	+	865.937i	−1.01279	+	1.01279i
$856$	−399.700	+	399.700i	−0.466939	+	0.466939i
$857$	815.254	−	815.254i	0.951289	−	0.951289i	−0.0475787	−	0.998867i	$-0.515150\pi$
$857$	815.254	−	815.254i	0.951289	−	0.951289i	0.998867	+	0.0475787i	$0.0151505\pi$
$858$	7.34820			0.00856433
$859$	386.924	+	386.924i	0.450436	+	0.450436i	0.895499	−	0.445063i	$-0.146819\pi$
$859$	386.924	+	386.924i	0.450436	+	0.450436i	−0.445063	+	0.895499i	$0.646819\pi$
$860$	280.679	−	280.679i	0.326371	−	0.326371i
$861$	121.334	−	121.334i	0.140923	−	0.140923i
$862$	−47.4520	+	47.4520i	−0.0550487	+	0.0550487i
$863$	78.1715	+	78.1715i	0.0905811	+	0.0905811i	0.750945	−	0.660364i	$-0.229598\pi$
$863$	78.1715	+	78.1715i	0.0905811	+	0.0905811i	−0.660364	+	0.750945i	$0.729598\pi$
$864$	−668.951			−0.774248
$865$	−2029.44	−	2029.44i	−2.34617	−	2.34617i
$866$	−1260.30	−	1260.30i	−1.45531	−	1.45531i
$867$	133.673	+	133.673i	0.154179	+	0.154179i
$868$	−932.917	+	932.917i	−1.07479	+	1.07479i
$869$	30.3455			0.0349201
$870$	−169.884	−	169.884i	−0.195269	−	0.195269i
$871$			54.0277i			0.0620295i
$872$	−135.659	+	135.659i	−0.155572	+	0.155572i
$873$	−67.3320			−0.0771272
$874$	−135.438	−	135.438i	−0.154963	−	0.154963i
$875$	1479.30	−	1479.30i	1.69063	−	1.69063i
$876$	154.699			0.176598
$877$	−409.252	−	409.252i	−0.466650	−	0.466650i	0.434178	−	0.900827i	$-0.357039\pi$
$877$	−409.252	−	409.252i	−0.466650	−	0.466650i	−0.900827	+	0.434178i	$0.857039\pi$
$878$	236.471			0.269329
$879$	364.024	+	364.024i	0.414134	+	0.414134i
$880$			877.424i			0.997073i
$881$			611.913i			0.694566i	0.937760	+	0.347283i	$0.112896\pi$
$881$			611.913i			0.694566i	−0.937760	+	0.347283i	$0.887104\pi$
$882$	596.208	+	596.208i	0.675973	+	0.675973i
$883$	−9.00464	−	9.00464i	−0.0101978	−	0.0101978i	0.701990	−	0.712187i	$-0.252295\pi$
$883$	−9.00464	−	9.00464i	−0.0101978	−	0.0101978i	−0.712187	+	0.701990i	$0.752295\pi$
$884$			32.7181i			0.0370115i
$885$		−	16.6566i		−	0.0188211i
$886$	−203.332	+	203.332i	−0.229495	+	0.229495i
$887$	−319.405	−	319.405i	−0.360096	−	0.360096i	0.503752	−	0.863848i	$-0.331952\pi$
$887$	−319.405	−	319.405i	−0.360096	−	0.360096i	−0.863848	+	0.503752i	$0.831952\pi$
$888$	162.031			0.182467
$889$	−1294.88			−1.45655
$890$	696.120	−	696.120i	0.782157	−	0.782157i
$891$	−200.260	+	200.260i	−0.224759	+	0.224759i
$892$	301.254			0.337729
$893$	−1045.58			−1.17086
$894$	−245.172	+	245.172i	−0.274241	+	0.274241i
$895$			2059.45i			2.30106i
$896$	−606.230	+	606.230i	−0.676596	+	0.676596i
$897$			2.20075i			0.00245345i
$898$	818.844	+	818.844i	0.911853	+	0.911853i
$899$	354.486	−	354.486i	0.394311	−	0.394311i
$900$		−	1154.51i		−	1.28279i
$901$	1008.80	+	1008.80i	1.11964	+	1.11964i
$902$	−244.679			−0.271263
$903$	−108.515	+	108.515i	−0.120172	+	0.120172i
$904$		−	240.431i		−	0.265964i
$905$	1541.27	+	1541.27i	1.70307	+	1.70307i
$906$	169.158	−	169.158i	0.186709	−	0.186709i
$907$	−903.099	+	903.099i	−0.995699	+	0.995699i	−0.999991	−	0.00429189i	$-0.998634\pi$
$907$	−903.099	+	903.099i	−0.995699	+	0.995699i	0.00429189	+	0.999991i	$0.498634\pi$
$908$	−140.267	+	140.267i	−0.154479	+	0.154479i
$909$			761.382i			0.837604i
$910$	−79.6009	+	79.6009i	−0.0874735	+	0.0874735i
$911$	−438.747	−	438.747i	−0.481610	−	0.481610i	0.424035	−	0.905646i	$-0.360613\pi$
$911$	−438.747	−	438.747i	−0.481610	−	0.481610i	−0.905646	+	0.424035i	$0.860613\pi$
$912$	−246.040	−	246.040i	−0.269780	−	0.269780i
$913$	199.885	+	199.885i	0.218932	+	0.218932i
$914$	272.590	−	272.590i	0.298239	−	0.298239i
$915$		−	599.673i		−	0.655380i
$916$	−383.813	−	383.813i	−0.419010	−	0.419010i
$917$	1198.64	+	1198.64i	1.30714	+	1.30714i
$918$	699.044	+	699.044i	0.761486	+	0.761486i
$919$	869.501	−	869.501i	0.946138	−	0.946138i	−0.0524835	−	0.998622i	$-0.516714\pi$
$919$	869.501	−	869.501i	0.946138	−	0.946138i	0.998622	+	0.0524835i	$0.0167137\pi$
$920$	−105.677			−0.114867
$921$	565.855			0.614392
$922$			192.637i			0.208934i
$923$	−57.5847			−0.0623886
$924$			145.763i			0.157752i
$925$			2714.54i			2.93464i
$926$		−	692.382i		−	0.747712i
$927$	235.540	+	235.540i	0.254089	+	0.254089i
$928$	−282.172	+	282.172i	−0.304065	+	0.304065i
$929$	869.767	+	869.767i	0.936240	+	0.936240i	0.998086	−	0.0618461i	$-0.0196988\pi$
$929$	869.767	+	869.767i	0.936240	+	0.936240i	−0.0618461	+	0.998086i	$0.519699\pi$
$930$	−1128.85			−1.21381
$931$			715.930i			0.768990i
$932$		−	1003.98i		−	1.07723i
$933$	−218.176	+	218.176i	−0.233843	+	0.233843i
$934$		−	446.333i		−	0.477872i
$935$	702.361	−	702.361i	0.751189	−	0.751189i
$936$		−	12.2693i		−	0.0131082i
$937$	495.066	+	495.066i	0.528353	+	0.528353i	0.920081	−	0.391728i	$-0.128123\pi$
$937$	495.066	+	495.066i	0.528353	+	0.528353i	−0.391728	+	0.920081i	$0.628123\pi$
$938$	−2562.87			−2.73228
$939$	−55.3991	−	55.3991i	−0.0589979	−	0.0589979i
$940$	1042.28	−	1042.28i	1.10881	−	1.10881i
$941$	243.881	−	243.881i	0.259172	−	0.259172i	−0.565545	−	0.824717i	$-0.691334\pi$
$941$	243.881	−	243.881i	0.259172	−	0.259172i	0.824717	+	0.565545i	$0.191334\pi$
$942$	−137.151			−0.145595
$943$		−	73.2802i		−	0.0777096i
$944$	−36.1167			−0.0382592
$945$			1422.39i			1.50517i
$946$	218.828			0.231320
$947$	1158.75	−	1158.75i	1.22360	−	1.22360i	0.257262	−	0.966342i	$-0.417180\pi$
$947$	1158.75	−	1158.75i	1.22360	−	1.22360i	0.966342	−	0.257262i	$-0.0828205\pi$
$948$		−	16.9648i		−	0.0178954i
$949$			27.5428i			0.0290230i
$950$	1657.63	−	1657.63i	1.74487	−	1.74487i
$951$			315.804i			0.332076i
$952$	607.409			0.638034
$953$	−1078.74	−	1078.74i	−1.13194	−	1.13194i	−0.989854	−	0.142091i	$-0.954617\pi$
$953$	−1078.74	−	1078.74i	−1.13194	−	1.13194i	−0.142091	−	0.989854i	$-0.545383\pi$
$954$	966.615	+	966.615i	1.01322	+	1.01322i
$955$	1950.13	−	1950.13i	2.04202	−	2.04202i
$956$			1161.51i			1.21496i
$957$		−	55.3862i		−	0.0578748i
$958$	562.204	−	562.204i	0.586851	−	0.586851i
$959$	−2341.15			−2.44124
$960$	216.063			0.225066
$961$		−	1394.48i		−	1.45107i
$962$		−	73.7116i		−	0.0766233i
$963$	1524.69			1.58327
$964$	−162.001	+	162.001i	−0.168050	+	0.168050i
$965$	−1102.57	+	1102.57i	−1.14256	+	1.14256i
$966$	−104.395			−0.108070
$967$	102.834	−	102.834i	0.106343	−	0.106343i	−0.651933	−	0.758276i	$-0.726042\pi$
$967$	102.834	−	102.834i	0.106343	−	0.106343i	0.758276	+	0.651933i	$0.226042\pi$
$968$	194.889	−	194.889i	0.201332	−	0.201332i
$969$			393.900i			0.406502i
$970$	192.739			0.198700
$971$	719.327	−	719.327i	0.740810	−	0.740810i	−0.231924	−	0.972734i	$-0.574502\pi$
$971$	719.327	−	719.327i	0.740810	−	0.740810i	0.972734	+	0.231924i	$0.0745019\pi$
$972$	428.756	+	428.756i	0.441107	+	0.441107i
$973$	749.977	−	749.977i	0.770788	−	0.770788i
$974$	−195.361	−	195.361i	−0.200576	−	0.200576i
$975$	−26.9350			−0.0276256
$976$	−1300.27			−1.33225
$977$	−105.553	+	105.553i	−0.108038	+	0.108038i	−0.759059	−	0.651021i	$-0.774341\pi$
$977$	−105.553	+	105.553i	−0.108038	+	0.108038i	0.651021	+	0.759059i	$0.274341\pi$
$978$	438.183			0.448039
$979$	226.951			0.231819
$980$	−713.674	−	713.674i	−0.728239	−	0.728239i
$981$	517.483			0.527506
$982$	214.516	+	214.516i	0.218448	+	0.218448i
$983$	45.1105	+	45.1105i	0.0458907	+	0.0458907i	0.729680	−	0.683789i	$-0.239669\pi$
$983$	45.1105	+	45.1105i	0.0458907	+	0.0458907i	−0.683789	+	0.729680i	$0.739669\pi$
$984$		−	53.5344i		−	0.0544049i
$985$	935.470	+	1433.08i	0.949716	+	1.45491i
$986$	589.732			0.598106
$987$	−402.964	+	402.964i	−0.408272	+	0.408272i
$988$	−18.8226	+	18.8226i	−0.0190512	+	0.0190512i
$989$			65.5380i			0.0662670i
$990$	672.991	−	672.991i	0.679789	−	0.679789i
$991$		−	1821.25i		−	1.83779i	−0.394500	−	0.918896i	$-0.629082\pi$
$991$		−	1821.25i		−	1.83779i	0.394500	−	0.918896i	$-0.370918\pi$
$992$			1874.98i			1.89010i
$993$	−206.131	−	206.131i	−0.207584	−	0.207584i
$994$		−	2731.60i		−	2.74809i
$995$		−	527.625i		−	0.530276i
$996$	111.747	−	111.747i	0.112196	−	0.112196i
$997$	−132.251	−	132.251i	−0.132649	−	0.132649i	0.637665	−	0.770314i	$-0.279900\pi$
$997$	−132.251	−	132.251i	−0.132649	−	0.132649i	−0.770314	+	0.637665i	$0.779900\pi$
$998$	−923.368	+	923.368i	−0.925218	+	0.925218i
$999$	−658.576	−	658.576i	−0.659235	−	0.659235i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.3.c.a.14.7	✓	64
197.183	odd	4	inner	197.3.c.a.183.7	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.3.c.a.14.7	✓	64	1.1	even	1	trivial
197.3.c.a.183.7	yes	64	197.183	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	197.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.85403 + 1.85403i) q^{2} +(0.722049 - 0.722049i) q^{3} -2.87488i q^{4} +(-6.14279 + 6.14279i) q^{5} +2.67741i q^{6} -9.45582i q^{7} +(-2.08602 - 2.08602i) q^{8} +7.95729i q^{9} -22.7779i q^{10} +(3.71305 - 3.71305i) q^{11} +(-2.07580 - 2.07580i) q^{12} +(0.369578 - 0.369578i) q^{13} +(17.5314 + 17.5314i) q^{14} +8.87079i q^{15} +19.2346 q^{16} +(-15.3969 - 15.3969i) q^{17} +(-14.7531 - 14.7531i) q^{18} -17.7156i q^{19} +(17.6598 + 17.6598i) q^{20} +(-6.82756 - 6.82756i) q^{21} +13.7682i q^{22} -4.12352 q^{23} -3.01241 q^{24} -50.4678i q^{25} +1.37042i q^{26} +(12.2440 + 12.2440i) q^{27} -27.1843 q^{28} +10.3294 q^{29} +(-16.4467 - 16.4467i) q^{30} +(34.3182 - 34.3182i) q^{31} +(-27.3175 + 27.3175i) q^{32} -5.36201i q^{33} +57.0928 q^{34} +(58.0851 + 58.0851i) q^{35} +22.8762 q^{36} -53.7877 q^{37} +(32.8453 + 32.8453i) q^{38} -0.533706i q^{39} +25.6279 q^{40} +17.7713i q^{41} +25.3171 q^{42} -15.8937i q^{43} +(-10.6746 - 10.6746i) q^{44} +(-48.8800 - 48.8800i) q^{45} +(7.64514 - 7.64514i) q^{46} -59.0202i q^{47} +(13.8883 - 13.8883i) q^{48} -40.4125 q^{49} +(93.5689 + 93.5689i) q^{50} -22.2347 q^{51} +(-1.06249 - 1.06249i) q^{52} -65.5196 q^{53} -45.4015 q^{54} +45.6170i q^{55} +(-19.7250 + 19.7250i) q^{56} +(-12.7915 - 12.7915i) q^{57} +(-19.1510 + 19.1510i) q^{58} -1.87769 q^{59} +25.5024 q^{60} -67.6008 q^{61} +127.254i q^{62} +75.2427 q^{63} -24.3567i q^{64} +4.54048i q^{65} +(9.94135 + 9.94135i) q^{66} +(-73.0939 + 73.0939i) q^{67} +(-44.2642 + 44.2642i) q^{68} +(-2.97738 + 2.97738i) q^{69} -215.383 q^{70} +(-77.9060 - 77.9060i) q^{71} +(16.5990 - 16.5990i) q^{72} +(-37.2626 + 37.2626i) q^{73} +(99.7241 - 99.7241i) q^{74} +(-36.4402 - 36.4402i) q^{75} -50.9301 q^{76} +(-35.1099 - 35.1099i) q^{77} +(0.989509 + 0.989509i) q^{78} +(4.08633 + 4.08633i) q^{79} +(-118.154 + 118.154i) q^{80} -53.9341 q^{81} +(-32.9485 - 32.9485i) q^{82} +53.8331i q^{83} +(-19.6284 + 19.6284i) q^{84} +189.160 q^{85} +(29.4675 + 29.4675i) q^{86} +(7.45831 - 7.45831i) q^{87} -15.4910 q^{88} +(30.5612 + 30.5612i) q^{89} +181.250 q^{90} +(-3.49466 - 3.49466i) q^{91} +11.8546i q^{92} -49.5589i q^{93} +(109.425 + 109.425i) q^{94} +(108.823 + 108.823i) q^{95} +39.4492i q^{96} +8.46168i q^{97} +(74.9260 - 74.9260i) q^{98} +(29.5458 + 29.5458i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 2 q^{2} - 2 q^{3} - 10 q^{5} - 6 q^{8} + 10 q^{11} + 68 q^{12} + 2 q^{13} - 2 q^{14} - 280 q^{16} - 30 q^{17} - 68 q^{18} + 114 q^{20} - 20 q^{21} + 48 q^{23} + 60 q^{24} + 22 q^{27} + 392 q^{28}+ \cdots - 66 q^{99}+O(q^{100}) \) 64 * q - 2 * q^2 - 2 * q^3 - 10 * q^5 - 6 * q^8 + 10 * q^11 + 68 * q^12 + 2 * q^13 - 2 * q^14 - 280 * q^16 - 30 * q^17 - 68 * q^18 + 114 * q^20 - 20 * q^21 + 48 * q^23 + 60 * q^24 + 22 * q^27 + 392 * q^28 + 56 * q^29 - 70 * q^30 - 64 * q^31 - 156 * q^32 - 52 * q^34 - 92 * q^35 - 36 * q^36 - 160 * q^37 + 40 * q^38 + 52 * q^40 + 80 * q^42 + 140 * q^44 + 324 * q^45 + 214 * q^46 + 216 * q^48 - 836 * q^49 + 126 * q^50 + 124 * q^51 - 10 * q^52 - 16 * q^53 + 400 * q^54 - 40 * q^56 + 68 * q^57 - 266 * q^58 - 364 * q^59 - 68 * q^60 - 168 * q^61 - 12 * q^63 + 238 * q^66 - 112 * q^67 - 148 * q^68 - 48 * q^69 + 48 * q^70 + 150 * q^71 - 474 * q^72 + 18 * q^73 + 236 * q^74 + 64 * q^75 - 260 * q^76 - 388 * q^77 - 782 * q^78 + 202 * q^79 + 796 * q^80 - 516 * q^81 + 72 * q^82 - 294 * q^84 - 696 * q^85 + 618 * q^86 + 464 * q^87 - 244 * q^88 - 536 * q^89 + 1484 * q^90 + 212 * q^91 + 132 * q^94 + 370 * q^95 - 530 * q^98 - 66 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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