LMFDB - Embedded newform 348.3.v.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [348,3,Mod(11,348)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(348, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([14, 14, 25]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("348.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 348 = 2^{2} \cdot 3 \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	348.v (of order $28$, degree $12$, 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:	$9.48231319974$
Analytic rank:	$0$
Dimension:	$1392$
Relative dimension:	$116$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	348.11
Dual form			348.3.v.a.95.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.96981 + 0.346217i) q^{2} +(-2.38019 - 1.82612i) q^{3} +(3.76027 - 1.36396i) q^{4} +(0.175987 + 0.0847507i) q^{5} +(5.32074 + 2.77304i) q^{6} +(-0.380227 - 0.303221i) q^{7} +(-6.93477 + 3.98860i) q^{8} +(2.33057 + 8.69301i) q^{9} +O(q^{10})$	\(q+(-1.96981 + 0.346217i) q^{2} +(-2.38019 - 1.82612i) q^{3} +(3.76027 - 1.36396i) q^{4} +(0.175987 + 0.0847507i) q^{5} +(5.32074 + 2.77304i) q^{6} +(-0.380227 - 0.303221i) q^{7} +(-6.93477 + 3.98860i) q^{8} +(2.33057 + 8.69301i) q^{9} +(-0.376002 - 0.106013i) q^{10} +(-9.36512 - 14.9045i) q^{11} +(-11.4409 - 3.62022i) q^{12} +(10.4717 + 2.39009i) q^{13} +(0.853953 + 0.465645i) q^{14} +(-0.264116 - 0.523095i) q^{15} +(12.2792 - 10.2577i) q^{16} +(-11.7944 - 11.7944i) q^{17} +(-7.60044 - 16.3167i) q^{18} +(-1.53113 + 13.5892i) q^{19} +(0.777353 + 0.0786466i) q^{20} +(0.351293 + 1.41606i) q^{21} +(23.6077 + 26.1166i) q^{22} +(-6.10902 + 2.94195i) q^{23} +(23.7897 + 3.17010i) q^{24} +(-15.5635 - 19.5160i) q^{25} +(-21.4546 - 1.08254i) q^{26} +(10.3273 - 24.9469i) q^{27} +(-1.84334 - 0.621577i) q^{28} +(28.5264 - 5.21975i) q^{29} +(0.701362 + 0.938954i) q^{30} +(12.9580 + 37.0318i) q^{31} +(-20.6363 + 24.4570i) q^{32} +(-4.92668 + 52.5773i) q^{33} +(27.3161 + 19.1492i) q^{34} +(-0.0412167 - 0.0855873i) q^{35} +(20.6205 + 29.5092i) q^{36} +(-31.9660 + 50.8735i) q^{37} +(-1.68877 - 27.2981i) q^{38} +(-20.5599 - 24.8114i) q^{39} +(-1.55846 + 0.114214i) q^{40} +(-57.0285 + 57.0285i) q^{41} +(-1.18224 - 2.66774i) q^{42} +(-22.0161 - 7.70376i) q^{43} +(-55.5445 - 43.2713i) q^{44} +(-0.326589 + 1.72737i) q^{45} +(11.0150 - 7.91012i) q^{46} +(-39.0281 + 24.5230i) q^{47} +(-47.9587 + 1.99192i) q^{48} +(-10.8509 - 47.5409i) q^{49} +(37.4137 + 33.0543i) q^{50} +(6.53488 + 49.6108i) q^{51} +(42.6363 - 5.29556i) q^{52} +(-40.4877 + 84.0735i) q^{53} +(-11.7057 + 52.7160i) q^{54} +(-0.384969 - 3.41669i) q^{55} +(3.84621 + 0.586192i) q^{56} +(28.4598 - 29.5487i) q^{57} +(-54.3843 + 20.1582i) q^{58} +2.58781 q^{59} +(-1.70663 - 1.60673i) q^{60} +(1.66431 + 14.7712i) q^{61} +(-38.3458 - 68.4592i) q^{62} +(1.74975 - 4.01199i) q^{63} +(32.1821 - 55.3201i) q^{64} +(1.64031 + 1.30810i) q^{65} +(-8.49857 - 105.273i) q^{66} +(8.15653 + 35.7361i) q^{67} +(-60.4371 - 28.2630i) q^{68} +(19.9130 + 4.15342i) q^{69} +(0.110821 + 0.154320i) q^{70} +(78.7376 + 17.9713i) q^{71} +(-50.8350 - 50.9883i) q^{72} +(-80.6798 - 28.2311i) q^{73} +(45.3534 - 111.278i) q^{74} +(1.40545 + 74.8723i) q^{75} +(12.7776 + 53.1873i) q^{76} +(-0.958485 + 8.50679i) q^{77} +(49.0892 + 41.7554i) q^{78} +(6.96752 - 11.0887i) q^{79} +(3.03033 - 0.764547i) q^{80} +(-70.1369 + 40.5194i) q^{81} +(92.5909 - 132.079i) q^{82} +(59.9157 + 75.1319i) q^{83} +(3.25241 + 4.84562i) q^{84} +(-1.07607 - 3.07524i) q^{85} +(46.0346 + 7.55257i) q^{86} +(-77.4300 - 39.6686i) q^{87} +(124.393 + 66.0056i) q^{88} +(22.2656 + 63.6315i) q^{89} +(0.0452713 - 3.51566i) q^{90} +(-3.25688 - 4.08400i) q^{91} +(-18.9589 + 19.3950i) q^{92} +(36.7821 - 111.805i) q^{93} +(68.3875 - 61.8177i) q^{94} +(-1.42115 + 2.26175i) q^{95} +(93.7796 - 20.5278i) q^{96} +(6.23212 - 55.3116i) q^{97} +(37.8336 + 89.8895i) q^{98} +(107.739 - 116.147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1392 q - 28 q^{4} - 14 q^{6} - 28 q^{9}+O(q^{10}) $ 1392 * q - 28 * q^4 - 14 * q^6 - 28 * q^9	$ 1392 q - 28 q^{4} - 14 q^{6} - 28 q^{9} - 8 q^{10} + 36 q^{12} - 56 q^{13} - 52 q^{16} - 32 q^{18} - 76 q^{21} - 28 q^{22} - 10 q^{24} - 1040 q^{25} + 272 q^{30} - 28 q^{33} - 28 q^{34} + 58 q^{36} - 80 q^{37} - 36 q^{40} - 14 q^{42} + 180 q^{45} + 1032 q^{46} - 216 q^{48} + 1088 q^{49} + 120 q^{52} - 10 q^{54} - 308 q^{58} + 240 q^{60} + 112 q^{61} - 1792 q^{64} + 92 q^{66} + 124 q^{69} - 1096 q^{70} + 148 q^{72} - 160 q^{73} + 68 q^{76} - 154 q^{78} - 180 q^{81} - 20 q^{82} + 72 q^{84} - 72 q^{85} + 760 q^{88} + 256 q^{90} - 28 q^{93} - 632 q^{94} - 812 q^{96} + 32 q^{97}+O(q^{100}) $ 1392 * q - 28 * q^4 - 14 * q^6 - 28 * q^9 - 8 * q^10 + 36 * q^12 - 56 * q^13 - 52 * q^16 - 32 * q^18 - 76 * q^21 - 28 * q^22 - 10 * q^24 - 1040 * q^25 + 272 * q^30 - 28 * q^33 - 28 * q^34 + 58 * q^36 - 80 * q^37 - 36 * q^40 - 14 * q^42 + 180 * q^45 + 1032 * q^46 - 216 * q^48 + 1088 * q^49 + 120 * q^52 - 10 * q^54 - 308 * q^58 + 240 * q^60 + 112 * q^61 - 1792 * q^64 + 92 * q^66 + 124 * q^69 - 1096 * q^70 + 148 * q^72 - 160 * q^73 + 68 * q^76 - 154 * q^78 - 180 * q^81 - 20 * q^82 + 72 * q^84 - 72 * q^85 + 760 * q^88 + 256 * q^90 - 28 * q^93 - 632 * q^94 - 812 * q^96 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/348\mathbb{Z}\right)^\times$.

$n$	$175$	$205$	$233$
$\chi(n)$	$-1$	$e\left(\frac{25}{28}\right)$	$-1$

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 $

$2$	−1.96981	+	0.346217i	−0.984903	+	0.173108i
$2$	−1.96981	+	0.346217i	−0.984903	+	0.173108i
$3$	−2.38019	−	1.82612i	−0.793395	−	0.608707i
$3$	−2.38019	−	1.82612i	−0.793395	−	0.608707i
$4$	3.76027	−	1.36396i	0.940067	−	0.340990i
$5$	0.175987	+	0.0847507i	0.0351973	+	0.0169501i	0.451400	−	0.892322i	$-0.350925\pi$
$5$	0.175987	+	0.0847507i	0.0351973	+	0.0169501i	−0.416202	+	0.909272i	$0.636639\pi$
$6$	5.32074	+	2.77304i	0.886790	+	0.462173i
$7$	−0.380227	−	0.303221i	−0.0543181	−	0.0433172i	0.595954	−	0.803018i	$-0.296774\pi$
$7$	−0.380227	−	0.303221i	−0.0543181	−	0.0433172i	−0.650273	+	0.759701i	$0.725345\pi$
$8$	−6.93477	+	3.98860i	−0.866846	+	0.498576i
$9$	2.33057	+	8.69301i	0.258953	+	0.965890i
$10$	−0.376002	−	0.106013i	−0.0376002	−	0.0106013i
$11$	−9.36512	−	14.9045i	−0.851375	−	1.35496i	−0.933591	−	0.358341i	$-0.883343\pi$
$11$	−9.36512	−	14.9045i	−0.851375	−	1.35496i	0.0822159	−	0.996615i	$-0.473800\pi$
$12$	−11.4409	−	3.62022i	−0.953408	−	0.301685i
$13$	10.4717	+	2.39009i	0.805513	+	0.183853i	0.605402	−	0.795920i	$-0.293012\pi$
$13$	10.4717	+	2.39009i	0.805513	+	0.183853i	0.200111	+	0.979773i	$0.435870\pi$
$14$	0.853953	+	0.465645i	0.0609966	+	0.0332604i
$15$	−0.264116	−	0.523095i	−0.0176077	−	0.0348730i
$16$	12.2792	−	10.2577i	0.767452	−	0.641107i
$17$	−11.7944	−	11.7944i	−0.693787	−	0.693787i	0.269276	−	0.963063i	$-0.413216\pi$
$17$	−11.7944	−	11.7944i	−0.693787	−	0.693787i	−0.963063	+	0.269276i	$0.913216\pi$
$18$	−7.60044	−	16.3167i	−0.422247	−	0.906481i
$19$	−1.53113	+	13.5892i	−0.0805859	+	0.715220i	0.886842	+	0.462073i	$0.152894\pi$
$19$	−1.53113	+	13.5892i	−0.0805859	+	0.715220i	−0.967428	+	0.253147i	$0.918534\pi$
$20$	0.777353	+	0.0786466i	0.0388677	+	0.00393233i
$21$	0.351293	+	1.41606i	0.0167282	+	0.0674315i
$22$	23.6077	+	26.1166i	1.07308	+	1.18712i
$23$	−6.10902	+	2.94195i	−0.265610	+	0.127911i	−0.561949	−	0.827172i	$-0.689948\pi$
$23$	−6.10902	+	2.94195i	−0.265610	+	0.127911i	0.296339	+	0.955083i	$0.404234\pi$
$24$	23.7897	+	3.17010i	0.991238	+	0.132087i
$25$	−15.5635	−	19.5160i	−0.622538	−	0.780638i
$26$	−21.4546	−	1.08254i	−0.825178	−	0.0416363i
$27$	10.3273	−	24.9469i	0.382492	−	0.923959i
$28$	−1.84334	−	0.621577i	−0.0658334	−	0.0221992i
$29$	28.5264	−	5.21975i	0.983668	−	0.179991i
$29$	28.5264	−	5.21975i	0.983668	−	0.179991i
$30$	0.701362	+	0.938954i	0.0233787	+	0.0312985i
$31$	12.9580	+	37.0318i	0.418000	+	1.19457i	0.939865	+	0.341547i	$0.110951\pi$
$31$	12.9580	+	37.0318i	0.418000	+	1.19457i	−0.521865	+	0.853028i	$0.674763\pi$
$32$	−20.6363	+	24.4570i	−0.644884	+	0.764280i
$33$	−4.92668	+	52.5773i	−0.149293	+	1.59325i
$34$	27.3161	+	19.1492i	0.803414	+	0.563213i
$35$	−0.0412167	−	0.0855873i	−0.00117762	−	0.00244535i
$36$	20.6205	+	29.5092i	0.572792	+	0.819701i
$37$	−31.9660	+	50.8735i	−0.863945	+	1.37496i	0.0623081	+	0.998057i	$0.480154\pi$
$37$	−31.9660	+	50.8735i	−0.863945	+	1.37496i	−0.926253	+	0.376903i	$0.876989\pi$
$38$	−1.68877	−	27.2981i	−0.0444413	−	0.718372i
$39$	−20.5599	−	24.8114i	−0.527178	−	0.636189i
$40$	−1.55846	+	0.114214i	−0.0389616	+	0.00285536i
$41$	−57.0285	+	57.0285i	−1.39094	+	1.39094i	−0.567714	+	0.823226i	$0.692172\pi$
$41$	−57.0285	+	57.0285i	−1.39094	+	1.39094i	−0.823226	+	0.567714i	$0.807828\pi$
$42$	−1.18224	−	2.66774i	−0.0281487	−	0.0635177i
$43$	−22.0161	−	7.70376i	−0.512002	−	0.179157i	0.0618982	−	0.998082i	$-0.480285\pi$
$43$	−22.0161	−	7.70376i	−0.512002	−	0.179157i	−0.573900	+	0.818925i	$0.694570\pi$
$44$	−55.5445	−	43.2713i	−1.26238	−	0.983438i
$45$	−0.326589	+	1.72737i	−0.00725753	+	0.0383860i
$46$	11.0150	−	7.91012i	0.239457	−	0.171959i
$47$	−39.0281	+	24.5230i	−0.830385	+	0.521766i	−0.878872	−	0.477058i	$-0.841703\pi$
$47$	−39.0281	+	24.5230i	−0.830385	+	0.521766i	0.0484865	+	0.998824i	$0.484560\pi$
$48$	−47.9587	+	1.99192i	−0.999139	+	0.0414984i
$49$	−10.8509	−	47.5409i	−0.221447	−	0.970222i
$50$	37.4137	+	33.0543i	0.748275	+	0.661086i
$51$	6.53488	+	49.6108i	0.128135	+	0.972761i
$52$	42.6363	−	5.29556i	0.819928	−	0.101838i
$53$	−40.4877	+	84.0735i	−0.763918	+	1.58629i	0.0454327	+	0.998967i	$0.485533\pi$
$53$	−40.4877	+	84.0735i	−0.763918	+	1.58629i	−0.809351	+	0.587325i	$0.800181\pi$
$54$	−11.7057	+	52.7160i	−0.216772	+	0.976222i
$55$	−0.384969	−	3.41669i	−0.00699944	−	0.0621217i
$56$	3.84621	+	0.586192i	0.0686824	+	0.0104677i
$57$	28.4598	−	29.5487i	0.499295	−	0.518399i
$58$	−54.3843	+	20.1582i	−0.937660	+	0.347555i
$59$	2.58781			0.0438613			0.0219306	−	0.999759i	$-0.493019\pi$
$59$	2.58781			0.0438613			0.0219306	+	0.999759i	$0.493019\pi$
$60$	−1.70663	−	1.60673i	−0.0284438	−	0.0267789i
$61$	1.66431	+	14.7712i	0.0272838	+	0.242151i	0.999951	+	0.00994500i	$0.00316564\pi$
$61$	1.66431	+	14.7712i	0.0272838	+	0.242151i	−0.972667	+	0.232206i	$0.925406\pi$
$62$	−38.3458	−	68.4592i	−0.618480	−	1.10418i
$63$	1.74975	−	4.01199i	0.0277739	−	0.0636824i
$64$	32.1821	−	55.3201i	0.502845	−	0.864377i
$65$	1.64031	+	1.30810i	0.0252356	+	0.0201247i
$66$	−8.49857	−	105.273i	−0.128766	−	1.59504i
$67$	8.15653	+	35.7361i	0.121739	+	0.533375i	0.998613	+	0.0526537i	$0.0167679\pi$
$67$	8.15653	+	35.7361i	0.121739	+	0.533375i	−0.876874	+	0.480721i	$0.840375\pi$
$68$	−60.4371	−	28.2630i	−0.888781	−	0.415632i
$69$	19.9130	+	4.15342i	0.288594	+	0.0601944i
$70$	0.110821	+	0.154320i	0.00158315	+	0.00220458i
$71$	78.7376	+	17.9713i	1.10898	+	0.253118i	0.737516	−	0.675330i	$-0.235999\pi$
$71$	78.7376	+	17.9713i	1.10898	+	0.253118i	0.371464	+	0.928447i	$0.378856\pi$
$72$	−50.8350	−	50.9883i	−0.706041	−	0.708171i
$73$	−80.6798	−	28.2311i	−1.10520	−	0.386727i	−0.284843	−	0.958574i	$-0.591941\pi$
$73$	−80.6798	−	28.2311i	−1.10520	−	0.386727i	−0.820360	+	0.571847i	$0.806227\pi$
$74$	45.3534	−	111.278i	0.612884	−	1.50376i
$75$	1.40545	+	74.8723i	0.0187394	+	0.998298i
$76$	12.7776	+	53.1873i	0.168127	+	0.699833i
$77$	−0.958485	+	8.50679i	−0.0124479	+	0.110478i
$78$	49.0892	+	41.7554i	0.629349	+	0.535326i
$79$	6.96752	−	11.0887i	0.0881964	−	0.140364i	−0.799712	−	0.600383i	$-0.795015\pi$
$79$	6.96752	−	11.0887i	0.0881964	−	0.140364i	0.887909	+	0.460019i	$0.152158\pi$
$80$	3.03033	−	0.764547i	0.0378791	−	0.00955683i
$81$	−70.1369	+	40.5194i	−0.865887	+	0.500240i
$82$	92.5909	−	132.079i	1.12916	−	1.61072i
$83$	59.9157	+	75.1319i	0.721876	+	0.905203i	0.998442	−	0.0557913i	$-0.0177681\pi$
$83$	59.9157	+	75.1319i	0.721876	+	0.905203i	−0.276567	+	0.960995i	$0.589197\pi$
$84$	3.25241	+	4.84562i	0.0387191	+	0.0576859i
$85$	−1.07607	−	3.07524i	−0.0126597	−	0.0361792i
$86$	46.0346	+	7.55257i	0.535286	+	0.0878206i
$87$	−77.4300	−	39.6686i	−0.890000	−	0.455961i
$88$	124.393	+	66.0056i	1.41356	+	0.750063i
$89$	22.2656	+	63.6315i	0.250175	+	0.714960i	0.998657	+	0.0518051i	$0.0164974\pi$
$89$	22.2656	+	63.6315i	0.250175	+	0.714960i	−0.748482	+	0.663155i	$0.769217\pi$
$90$	0.0452713	−	3.51566i	0.000503014	−	0.0390628i
$91$	−3.25688	−	4.08400i	−0.0357899	−	0.0448792i
$92$	−18.9589	+	19.3950i	−0.206075	+	0.210815i
$93$	36.7821	−	111.805i	0.395506	−	1.20221i
$94$	68.3875	−	61.8177i	0.727527	−	0.657635i
$95$	−1.42115	+	2.26175i	−0.0149595	+	0.0238079i
$96$	93.7796	−	20.5278i	0.976871	−	0.213831i
$97$	6.23212	−	55.3116i	0.0642487	−	0.570223i	−0.919808	−	0.392369i	$-0.871656\pi$
$97$	6.23212	−	55.3116i	0.0642487	−	0.570223i	0.984057	−	0.177854i	$-0.0569156\pi$
$98$	37.8336	+	89.8895i	0.386057	+	0.917240i
$99$	107.739	−	116.147i	1.08827	−	1.17320i
$100$	−85.1417	−	52.1573i	−0.851417	−	0.521573i
$101$	−10.6382	−	3.72246i	−0.105329	−	0.0368561i	0.277100	−	0.960841i	$-0.410627\pi$
$101$	−10.6382	−	3.72246i	−0.105329	−	0.0368561i	−0.382429	+	0.923985i	$0.624912\pi$
$102$	−30.0485	−	95.4611i	−0.294593	−	0.935893i
$103$	−152.556	−	34.8200i	−1.48113	−	0.338058i	−0.595842	−	0.803102i	$-0.703182\pi$
$103$	−152.556	−	34.8200i	−1.48113	−	0.338058i	−0.885288	+	0.465044i	$0.846039\pi$
$104$	−82.1517	+	25.1926i	−0.789921	+	0.242237i
$105$	−0.0581893	+	0.278980i	−0.000554183	+	0.00265695i
$106$	50.6452	−	179.626i	0.477785	−	1.69458i
$107$	−2.13603	−	9.35857i	−0.0199629	−	0.0874633i	0.963965	−	0.266029i	$-0.0857116\pi$
$107$	−2.13603	−	9.35857i	−0.0199629	−	0.0874633i	−0.983928	+	0.178565i	$0.942854\pi$
$108$	4.80677	−	107.893i	0.0445071	−	0.999009i
$109$	62.7797	+	50.0652i	0.575961	+	0.459313i	0.867633	−	0.497205i	$-0.165640\pi$
$109$	62.7797	+	50.0652i	0.575961	+	0.459313i	−0.291672	+	0.956518i	$0.594212\pi$
$110$	1.94123	+	6.59694i	0.0176476	+	0.0599722i
$111$	168.986	−	62.7148i	1.52240	−	0.564998i
$112$	−7.77924	+	0.176939i	−0.0694575	+	0.00157982i
$113$	−22.4427	−	199.184i	−0.198608	−	1.76269i	−0.558316	−	0.829628i	$-0.688552\pi$
$113$	−22.4427	−	199.184i	−0.198608	−	1.76269i	0.359709	−	0.933065i	$-0.382876\pi$
$114$	−45.8301	+	68.0585i	−0.402018	+	0.597005i
$115$	−1.32444			−0.0115169
$116$	100.147	−	58.5365i	0.863339	−	0.504625i
$117$	3.62792	+	96.6006i	0.0310079	+	0.825646i
$118$	−5.09749	+	0.895945i	−0.0431991	+	0.00759275i
$119$	0.908239	+	8.06084i	0.00763226	+	0.0677382i
$120$	3.91800	+	2.57409i	0.0326500	+	0.0214507i
$121$	−81.9389	+	170.148i	−0.677181	+	1.40618i
$122$	−8.39241	−	28.5201i	−0.0687902	−	0.233772i
$123$	239.879	−	31.5976i	1.95024	−	0.256891i
$124$	99.2355	+	121.575i	0.800286	+	0.980447i
$125$	−2.17160	−	9.51439i	−0.0173728	−	0.0761151i
$126$	−2.05766	+	8.50864i	−0.0163306	+	0.0675289i
$127$	−86.1040	+	54.1028i	−0.677985	+	0.426006i	−0.826525	−	0.562900i	$-0.809685\pi$
$127$	−86.1040	+	54.1028i	−0.677985	+	0.426006i	0.148540	+	0.988906i	$0.452543\pi$
$128$	−44.2397	+	120.112i	−0.345622	+	0.938374i
$129$	38.3344	+	58.5404i	0.297166	+	0.453802i
$130$	−3.68398	−	2.00881i	−0.0283383	−	0.0154524i
$131$	34.8054	+	12.1789i	0.265690	+	0.0929689i	0.459836	−	0.888004i	$-0.347908\pi$
$131$	34.8054	+	12.1789i	0.265690	+	0.0929689i	−0.194147	+	0.980973i	$0.562194\pi$
$132$	53.1878	+	204.425i	0.402938	+	1.54867i
$133$	4.70270	−	4.70270i	0.0353586	−	0.0353586i
$134$	−28.4392	−	67.5693i	−0.212233	−	0.504248i
$135$	3.93173	−	3.51507i	0.0291239	−	0.0260376i
$136$	128.834	+	34.7482i	0.947312	+	0.255502i
$137$	13.9608	−	22.2186i	0.101904	−	0.162179i	−0.791880	−	0.610676i	$-0.790898\pi$
$137$	13.9608	−	22.2186i	0.101904	−	0.162179i	0.893784	+	0.448497i	$0.148041\pi$
$138$	−40.6626	−	1.28722i	−0.294657	−	0.00932767i
$139$	−66.5720	−	138.238i	−0.478935	−	0.994519i	−0.990785	−	0.135444i	$-0.956754\pi$
$139$	−66.5720	−	138.238i	−0.478935	−	0.994519i	0.511850	−	0.859075i	$-0.328960\pi$
$140$	−0.271723	−	0.265613i	−0.00194088	−	0.00189724i
$141$	137.676	+	12.9007i	0.976426	+	0.0914945i
$142$	−161.320	−	8.13976i	−1.13605	−	0.0573223i
$143$	−62.4454	−	178.459i	−0.436681	−	1.24796i
$144$	117.788	+	82.8371i	0.817972	+	0.575258i
$145$	5.46264	+	1.49902i	0.0376734	+	0.0103381i
$146$	168.698	+	27.6770i	1.15546	+	0.189569i
$147$	−60.9882	+	132.971i	−0.414886	+	0.904566i
$148$	−50.8111	+	234.898i	−0.343318	+	1.58715i
$149$	−59.8521	−	75.0522i	−0.401692	−	0.503706i	0.539310	−	0.842107i	$-0.318685\pi$
$149$	−59.8521	−	75.0522i	−0.401692	−	0.503706i	−0.941002	+	0.338402i	$0.890114\pi$
$150$	−28.6905	−	146.997i	−0.191270	−	0.979982i
$151$	63.3011	−	30.4842i	0.419213	−	0.201882i	−0.212372	−	0.977189i	$-0.568119\pi$
$151$	63.3011	−	30.4842i	0.419213	−	0.201882i	0.631585	+	0.775307i	$0.282405\pi$
$152$	−43.5838	−	100.345i	−0.286735	−	0.660164i
$153$	75.0410	−	130.016i	0.490464	−	0.849780i
$154$	−1.05717	−	17.0886i	−0.00686471	−	0.110965i
$155$	−0.858039	+	7.61530i	−0.00553573	+	0.0491310i
$156$	−111.153	−	65.2545i	−0.712517	−	0.418298i
$157$	90.5310	+	90.5310i	0.576631	+	0.576631i	0.933973	−	0.357343i	$-0.116317\pi$
$157$	90.5310	+	90.5310i	0.576631	+	0.576631i	−0.357343	+	0.933973i	$0.616317\pi$
$158$	−9.88554	+	24.2549i	−0.0625667	+	0.153512i
$159$	249.896	−	126.175i	1.57168	−	0.793555i
$160$	−5.70446	+	2.55516i	−0.0356529	+	0.0159697i
$161$	3.21487	+	0.733774i	0.0199682	+	0.00455760i
$162$	124.127	−	104.098i	0.766219	−	0.642580i
$163$	−113.832	−	181.162i	−0.698353	−	1.11142i	−0.988025	−	0.154297i	$-0.950689\pi$
$163$	−113.832	−	181.162i	−0.698353	−	1.11142i	0.289671	−	0.957126i	$-0.406454\pi$
$164$	−136.658	+	292.227i	−0.833280	+	1.78187i
$165$	−5.32300	+	8.83537i	−0.0322606	+	0.0535477i
$166$	−144.034	−	127.251i	−0.867676	−	0.766575i
$167$	−31.8390	−	25.3908i	−0.190653	−	0.152041i	0.523512	−	0.852019i	$-0.324622\pi$
$167$	−31.8390	−	25.3908i	−0.190653	−	0.152041i	−0.714164	+	0.699978i	$0.753193\pi$
$168$	−8.08425	−	8.41889i	−0.0481205	−	0.0501124i
$169$	−48.3204	−	23.2699i	−0.285920	−	0.137692i
$170$	3.18435	+	5.68506i	0.0187315	+	0.0334415i
$171$	−121.699	+	18.3604i	−0.711691	+	0.107371i
$172$	−93.2940	+	1.06085i	−0.542407	+	0.00616775i
$173$	−201.537			−1.16495			−0.582476	−	0.812848i	$-0.697916\pi$
$173$	−201.537			−1.16495			−0.582476	+	0.812848i	$0.697916\pi$
$174$	166.256	+	51.3319i	0.955494	+	0.295011i
$175$			12.1397i			0.0693694i
$176$	−267.883	−	86.9511i	−1.52206	−	0.494041i
$177$	−6.15948	−	4.72566i	−0.0347993	−	0.0266986i
$178$	−65.8892	−	117.633i	−0.370164	−	0.660859i
$179$	−123.921	+	257.324i	−0.692296	+	1.43757i	0.197079	+	0.980388i	$0.436854\pi$
$179$	−123.921	+	257.324i	−0.692296	+	1.43757i	−0.889375	+	0.457179i	$0.848860\pi$
$180$	1.12800	+	6.94083i	0.00626669	+	0.0385602i
$181$	108.636	−	136.225i	0.600199	−	0.752625i	−0.385210	−	0.922829i	$-0.625871\pi$
$181$	108.636	−	136.225i	0.600199	−	0.752625i	0.985409	+	0.170203i	$0.0544425\pi$
$182$	7.82938	+	6.91710i	0.0430186	+	0.0380061i
$183$	23.0126	−	38.1974i	0.125752	−	0.208729i
$184$	30.6304	−	44.7682i	0.166470	−	0.243306i
$185$	−9.93714	+	6.24392i	−0.0537143	+	0.0337509i
$186$	−33.7446	+	232.970i	−0.181423	+	1.25253i
$187$	−65.3336	+	286.245i	−0.349378	+	1.53072i
$188$	−113.308	+	145.446i	−0.602701	+	0.773648i
$189$	−11.4911	+	6.35403i	−0.0607996	+	0.0336192i
$190$	2.01633	−	4.94723i	0.0106123	−	0.0260381i
$191$	178.644	−	178.644i	0.935310	−	0.935310i	−0.0627213	−	0.998031i	$-0.519978\pi$
$191$	178.644	−	178.644i	0.935310	−	0.935310i	0.998031	+	0.0627213i	$0.0199779\pi$
$192$	−177.620	+	72.9038i	−0.925107	+	0.379707i
$193$	−49.3272	−	5.55784i	−0.255581	−	0.0287971i	−0.0167558	−	0.999860i	$-0.505334\pi$
$193$	−49.3272	−	5.55784i	−0.255581	−	0.0287971i	−0.238825	+	0.971063i	$0.576762\pi$
$194$	6.87375	+	111.111i	0.0354317	+	0.572736i
$195$	−1.51549	−	6.10894i	−0.00777175	−	0.0313279i
$196$	−105.646	−	163.966i	−0.539011	−	0.836563i
$197$	6.20947	+	12.8941i	0.0315202	+	0.0654523i	0.916134	−	0.400871i	$-0.131293\pi$
$197$	6.20947	+	12.8941i	0.0315202	+	0.0654523i	−0.884614	+	0.466324i	$0.845578\pi$
$198$	−172.013	+	266.088i	−0.868751	+	1.34388i
$199$	−147.870	+	117.923i	−0.743066	+	0.592575i	−0.920125	−	0.391625i	$-0.871913\pi$
$199$	−147.870	+	117.923i	−0.743066	+	0.592575i	0.177059	+	0.984200i	$0.443342\pi$
$200$	185.770	+	73.2622i	0.928852	+	0.366311i
$201$	45.8443	−	99.9534i	0.228081	−	0.497281i
$202$	22.2439	+	3.64941i	0.110119	+	0.0180664i
$203$	−12.4292	−	6.66510i	−0.0612277	−	0.0328330i
$204$	92.2400	+	177.637i	0.452157	+	0.870767i
$205$	−14.8695	+	5.20305i	−0.0725340	+	0.0253807i
$206$	312.562	+	15.7710i	1.51729	+	0.0765584i
$207$	−39.8119	−	46.2494i	−0.192328	−	0.223427i
$208$	153.101	−	78.0669i	0.736062	−	0.375322i
$209$	216.879	−	104.444i	1.03770	−	0.499730i
$210$	0.0180339	−	0.569683i	8.58757e−5	−	0.00271278i
$211$	−163.605	−	102.800i	−0.775377	−	0.487202i	0.0852984	−	0.996355i	$-0.472816\pi$
$211$	−163.605	−	102.800i	−0.775377	−	0.487202i	−0.860676	+	0.509154i	$0.829959\pi$
$212$	−37.5716	+	371.362i	−0.177224	+	1.75171i
$213$	−154.592	−	186.559i	−0.725786	−	0.875866i
$214$	7.44767	+	17.6950i	0.0348022	+	0.0826871i
$215$	−3.22164	−	3.22164i	−0.0149844	−	0.0149844i
$216$	27.8860	+	214.192i	0.129102	+	0.991631i
$217$	6.30184	−	18.0096i	0.0290407	−	0.0829937i
$218$	−140.997	−	76.8832i	−0.646776	−	0.352675i
$219$	140.480	+	214.526i	0.641460	+	0.979572i
$220$	−6.10782	−	12.3226i	−0.0277628	−	0.0560118i
$221$	−95.3173	−	151.697i	−0.431300	−	0.686410i
$222$	−311.157	+	182.042i	−1.40161	+	0.820008i
$223$	−159.188	+	36.3337i	−0.713848	+	0.162931i	−0.563996	−	0.825777i	$-0.690737\pi$
$223$	−159.188	+	36.3337i	−0.713848	+	0.162931i	−0.149852	+	0.988708i	$0.547880\pi$
$224$	15.2623	−	3.04184i	0.0681354	−	0.0135796i
$225$	133.381	−	180.777i	0.592803	−	0.803452i
$226$	113.169	+	384.584i	0.500746	+	1.70170i
$227$	−254.604	−	122.611i	−1.12161	−	0.540137i	−0.221217	−	0.975225i	$-0.571003\pi$
$227$	−254.604	−	122.611i	−1.12161	−	0.540137i	−0.900388	+	0.435088i	$0.856717\pi$
$228$	66.7133	−	149.929i	0.292602	−	0.657584i
$229$	271.844	−	30.6294i	1.18709	−	0.133753i	0.503748	−	0.863851i	$-0.331954\pi$
$229$	271.844	−	30.6294i	1.18709	−	0.133753i	0.683343	+	0.730098i	$0.260525\pi$
$230$	2.60889	−	0.458543i	0.0113430	−	0.00199366i
$231$	17.8158	−	18.4974i	0.0771247	−	0.0800755i
$232$	−177.004	+	149.978i	−0.762950	+	0.646458i
$233$			127.974i			0.549244i	0.961552	+	0.274622i	$0.0885527\pi$
$233$			127.974i			0.549244i	−0.961552	+	0.274622i	$0.911447\pi$
$234$	−40.5911	−	189.028i	−0.173466	−	0.807813i
$235$	−8.94676	+	1.00806i	−0.0380713	+	0.00428961i
$236$	9.73087	−	3.52967i	0.0412325	−	0.0149562i
$237$	−36.8333	+	13.6697i	−0.155415	+	0.0576782i
$238$	−4.57985	−	15.5638i	−0.0192431	−	0.0653943i
$239$	−39.2793	+	49.2547i	−0.164349	+	0.206087i	−0.857186	−	0.515008i	$-0.827789\pi$
$239$	−39.2793	+	49.2547i	−0.164349	+	0.206087i	0.692837	+	0.721094i	$0.256361\pi$
$240$	−8.60890	−	3.71398i	−0.0358704	−	0.0154749i
$241$	289.412	−	66.0563i	1.20088	−	0.274093i	0.425128	−	0.905133i	$-0.360229\pi$
$241$	289.412	−	66.0563i	1.20088	−	0.274093i	0.775750	+	0.631041i	$0.217372\pi$
$242$	102.496	−	363.527i	0.423536	−	1.50218i
$243$	240.932	+	31.6345i	0.991490	+	0.130183i
$244$	26.4056	+	53.2736i	0.108220	+	0.218334i
$245$	2.11951	−	9.28618i	0.00865106	−	0.0379028i
$246$	−461.576	+	145.291i	−1.87633	+	0.590616i
$247$	−48.5129	+	138.642i	−0.196408	+	0.561303i
$248$	−237.566	−	205.123i	−0.957927	−	0.827108i
$249$	−5.41067	−	288.241i	−0.0217296	−	1.15759i
$250$	7.57166	+	17.9896i	0.0302867	+	0.0719586i
$251$	−10.3498	−	1.16615i	−0.0412344	−	0.00464600i	0.0913232	−	0.995821i	$-0.470890\pi$
$251$	−10.3498	−	1.16615i	−0.0412344	−	0.00464600i	−0.132558	+	0.991175i	$0.542319\pi$
$252$	1.10735	−	17.4728i	0.00439423	−	0.0693364i
$253$	101.060	+	63.5003i	0.399447	+	0.250989i
$254$	150.877	−	136.383i	0.594004	−	0.536939i
$255$	−3.05450	+	9.28467i	−0.0119784	+	0.0364105i
$256$	45.5588	−	251.913i	0.177964	−	0.984037i
$257$	−85.7169	+	68.3569i	−0.333529	+	0.265980i	−0.775906	−	0.630849i	$-0.782707\pi$
$257$	−85.7169	+	68.3569i	−0.333529	+	0.265980i	0.442377	+	0.896829i	$0.354135\pi$
$258$	−95.7790	−	102.041i	−0.371236	−	0.395508i
$259$	27.5802	−	9.65073i	0.106487	−	0.0372615i
$260$	7.95221	+	2.68151i	0.0305854	+	0.0103135i
$261$	111.858	+	235.815i	0.428575	+	0.903506i
$262$	−72.7763	−	11.9399i	−0.277772	−	0.0455721i
$263$	85.6272	−	29.9623i	0.325579	−	0.113925i	−0.162541	−	0.986702i	$-0.551969\pi$
$263$	85.6272	−	29.9623i	0.325579	−	0.113925i	0.488119	+	0.872777i	$0.337683\pi$
$264$	−175.545	−	384.262i	−0.664943	−	1.45554i
$265$	−14.2506	+	11.3645i	−0.0537758	+	0.0428847i
$266$	−7.63524	+	10.8915i	−0.0287039	+	0.0409457i
$267$	63.2024	−	192.114i	0.236713	−	0.719530i
$268$	79.4134	+	123.252i	0.296319	+	0.459896i
$269$	139.308	+	87.5329i	0.517873	+	0.325401i	0.765480	−	0.643459i	$-0.222501\pi$
$269$	139.308	+	87.5329i	0.517873	+	0.325401i	−0.247608	+	0.968860i	$0.579644\pi$
$270$	−6.52776	+	8.28524i	−0.0241769	+	0.0306861i
$271$	28.6376	+	3.22668i	0.105674	+	0.0119066i	0.164643	−	0.986353i	$-0.447353\pi$
$271$	28.6376	+	3.22668i	0.105674	+	0.0119066i	−0.0589693	+	0.998260i	$0.518781\pi$
$272$	−265.809	−	23.8426i	−0.977240	−	0.0876565i
$273$	0.294112	+	15.6681i	0.00107733	+	0.0573925i
$274$	−19.8077	+	48.5997i	−0.0722909	+	0.177371i
$275$	−145.122	+	414.735i	−0.527717	+	1.50813i
$276$	80.5432	−	11.5425i	0.291823	−	0.0418208i
$277$	−77.2445	+	338.430i	−0.278861	+	1.22177i	0.620375	+	0.784306i	$0.286981\pi$
$277$	−77.2445	+	338.430i	−0.278861	+	1.22177i	−0.899236	+	0.437464i	$0.855877\pi$
$278$	178.994	+	249.254i	0.643864	+	0.896596i
$279$	−291.718	+	198.949i	−1.04559	+	0.713080i
$280$	0.627202	+	0.429131i	0.00224001	+	0.00153261i
$281$	−112.531	+	25.6844i	−0.400465	+	0.0914034i	−0.418010	−	0.908443i	$-0.637272\pi$
$281$	−112.531	+	25.6844i	−0.400465	+	0.0914034i	0.0175449	+	0.999846i	$0.494415\pi$
$282$	−275.662	+	22.2539i	−0.977523	+	0.0789144i
$283$	−168.302	+	211.044i	−0.594705	+	0.745737i	−0.984542	−	0.175147i	$-0.943960\pi$
$283$	−168.302	+	211.044i	−0.594705	+	0.745737i	0.389837	+	0.920884i	$0.372531\pi$
$284$	320.587	−	39.8179i	1.12883	−	0.140204i
$285$	7.51283	−	2.78819i	0.0263608	−	0.00978313i
$286$	184.791	+	329.909i	0.646121	+	1.15353i
$287$	38.9760	−	4.39154i	0.135805	−	0.0153015i
$288$	−260.699	−	122.393i	−0.905205	−	0.424975i
$289$		−	10.7849i		−	0.0373181i
$290$	−11.2793	−	1.06153i	−0.0388942	−	0.00366045i
$291$	−115.839	+	120.271i	−0.398073	+	0.413304i
$292$	−341.884	+	3.88758i	−1.17083	+	0.0133136i
$293$	363.562	−	40.9636i	1.24083	−	0.139808i	0.532952	−	0.846146i	$-0.321083\pi$
$293$	363.562	−	40.9636i	1.24083	−	0.139808i	0.707874	+	0.706338i	$0.249654\pi$
$294$	74.0980	−	283.043i	0.252034	−	0.962730i
$295$	0.455421	+	0.219319i	0.00154380	+	0.000743454i
$296$	18.7622	−	480.296i	0.0633858	−	1.62262i
$297$	−468.537	+	79.7077i	−1.57757	+	0.268376i
$298$	143.881	+	127.116i	0.482823	+	0.426565i
$299$	−71.0032	+	16.2060i	−0.237469	+	0.0542007i
$300$	107.408	+	279.623i	0.358026	+	0.932077i
$301$	6.03517	+	9.60491i	0.0200504	+	0.0319100i
$302$	−114.137	+	81.9639i	−0.377936	+	0.271404i
$303$	18.5232	+	28.2868i	0.0611327	+	0.0933556i
$304$	120.593	+	182.570i	0.396686	+	0.600561i
$305$	−0.958971	+	2.74058i	−0.00314417	+	0.00898552i
$306$	−102.802	+	282.088i	−0.335955	+	0.921855i
$307$	352.346	+	352.346i	1.14771	+	1.14771i	0.987003	+	0.160703i	$0.0513760\pi$
$307$	352.346	+	352.346i	1.14771	+	1.14771i	0.160703	+	0.987003i	$0.448624\pi$
$308$	7.99876	+	33.2952i	0.0259700	+	0.108101i
$309$	299.527	+	361.464i	0.969343	+	1.16979i
$310$	−0.946378	−	15.2977i	−0.00305283	−	0.0493475i
$311$	−42.6027	−	26.7691i	−0.136986	−	0.0860742i	0.461795	−	0.886986i	$-0.347205\pi$
$311$	−42.6027	−	26.7691i	−0.136986	−	0.0860742i	−0.598782	+	0.800912i	$0.704348\pi$
$312$	241.541	+	90.0558i	0.774170	+	0.288640i
$313$	314.311	−	151.364i	1.00419	−	0.483591i	0.141830	−	0.989891i	$-0.454701\pi$
$313$	314.311	−	151.364i	1.00419	−	0.483591i	0.862358	+	0.506300i	$0.168987\pi$
$314$	−209.672	−	146.985i	−0.667745	−	0.468105i
$315$	0.647952	−	0.557764i	0.00205699	−	0.00177068i
$316$	11.0751	−	51.2000i	0.0350479	−	0.162025i
$317$	435.555	−	152.407i	1.37399	−	0.480780i	0.460507	−	0.887656i	$-0.347668\pi$
$317$	435.555	−	152.407i	1.37399	−	0.480780i	0.913483	+	0.406876i	$0.133382\pi$
$318$	−448.563	+	335.059i	−1.41058	+	1.05365i
$319$	−344.951	−	376.288i	−1.08135	−	1.17959i
$320$	10.3520	−	7.00814i	0.0323501	−	0.0219005i
$321$	−12.0057	+	26.1758i	−0.0374010	+	0.0815445i
$322$	−6.58672	−	0.332348i	−0.0204557	−	0.00103214i
$323$	178.335	−	142.217i	0.552120	−	0.440301i
$324$	−208.466	+	248.028i	−0.643415	+	0.765517i
$325$	−116.330	−	241.563i	−0.357940	−	0.743270i
$326$	286.947	+	317.443i	0.880207	+	0.973753i
$327$	−58.0025	−	233.808i	−0.177378	−	0.715008i
$328$	168.016	−	622.944i	0.512243	−	1.89922i
$329$	22.2754	+	2.50984i	0.0677064	+	0.00762868i
$330$	7.42631	−	19.2469i	0.0225040	−	0.0583238i
$331$	344.425	−	344.425i	1.04056	−	1.04056i	0.0414177	−	0.999142i	$-0.486813\pi$
$331$	344.425	−	344.425i	1.04056	−	1.04056i	0.999142	−	0.0414177i	$-0.0131874\pi$
$332$	327.776	+	200.793i	0.987277	+	0.604799i
$333$	−516.743	−	159.316i	−1.55178	−	0.478426i
$334$	71.5074	+	38.9917i	0.214094	+	0.116742i
$335$	−1.59322	+	6.98035i	−0.00475588	+	0.0208369i
$336$	18.8392	+	13.7847i	0.0560689	+	0.0410258i
$337$	−445.178	+	279.724i	−1.32100	+	0.830040i	−0.993392	−	0.114773i	$-0.963386\pi$
$337$	−445.178	+	279.724i	−1.32100	+	0.830040i	−0.327610	+	0.944813i	$0.606243\pi$
$338$	103.238	+	29.1078i	0.305439	+	0.0861178i
$339$	−310.317	+	515.079i	−0.915388	+	1.51941i
$340$	−8.24082	−	10.0960i	−0.0242377	−	0.0296941i
$341$	430.588	−	539.940i	1.26272	−	1.58340i
$342$	233.367	−	78.3008i	0.682360	−	0.228950i
$343$	−20.6291	+	42.8367i	−0.0601430	+	0.124888i
$344$	183.404	−	34.3896i	0.533151	−	0.0999699i
$345$	3.15241	+	2.41858i	0.00913742	+	0.00701039i
$346$	396.988	−	69.7754i	1.14736	−	0.201663i
$347$		−	306.357i		−	0.882873i	−0.897293	−	0.441436i	$-0.854469\pi$
$347$		−	306.357i		−	0.882873i	0.897293	−	0.441436i	$-0.145531\pi$
$348$	−345.264	−	43.5532i	−0.992137	−	0.125153i
$349$	6.60967			0.0189389			0.00946944	−	0.999955i	$-0.496986\pi$
$349$	6.60967			0.0189389			0.00946944	+	0.999955i	$0.496986\pi$
$350$	−4.20295	−	23.9128i	−0.0120084	−	0.0683221i
$351$	167.769	−	236.552i	0.477975	−	0.673939i
$352$	557.781	+	78.5313i	1.58460	+	0.223100i
$353$	−137.189	−	66.0669i	−0.388638	−	0.187158i	0.229353	−	0.973343i	$-0.426339\pi$
$353$	−137.189	−	66.0669i	−0.388638	−	0.187158i	−0.617991	+	0.786185i	$0.712053\pi$
$354$	13.7691	+	7.17611i	0.0388957	+	0.0202715i
$355$	12.3337	+	9.83578i	0.0347428	+	0.0277064i
$356$	170.515	+	208.902i	0.478976	+	0.586803i
$357$	12.5583	−	20.8449i	0.0351773	−	0.0583890i
$358$	155.010	−	549.783i	0.432989	−	1.53571i
$359$	−102.672	−	163.401i	−0.285993	−	0.455156i	0.672571	−	0.740033i	$-0.265190\pi$
$359$	−102.672	−	163.401i	−0.285993	−	0.455156i	−0.958564	+	0.284877i	$0.908047\pi$
$360$	−4.62498	−	13.2816i	−0.0128472	−	0.0368932i
$361$	169.628	+	38.7164i	0.469883	+	0.107248i
$362$	−166.828	+	305.949i	−0.460852	+	0.845162i
$363$	505.740	−	255.353i	1.39322	−	0.703453i
$364$	−17.8172	−	10.9147i	−0.0489483	−	0.0299854i
$365$	−11.8060	−	11.8060i	−0.0323451	−	0.0323451i
$366$	−32.1057	+	83.2088i	−0.0877205	+	0.227346i
$367$	55.1954	−	489.872i	0.150396	−	1.33480i	−0.661036	−	0.750355i	$-0.729883\pi$
$367$	55.1954	−	489.872i	0.150396	−	1.33480i	0.811432	−	0.584447i	$-0.198689\pi$
$368$	−44.8364	+	98.7894i	−0.121838	+	0.268450i
$369$	−628.659	−	362.840i	−1.70368	−	0.983307i
$370$	17.4125	−	15.7397i	0.0470608	−	0.0425398i
$371$	40.8873	−	19.6903i	0.110208	−	0.0530736i
$372$	−14.1877	−	470.588i	−0.0381389	−	1.26502i
$373$	−65.8676	−	82.5953i	−0.176589	−	0.221435i	0.685658	−	0.727924i	$-0.259515\pi$
$373$	−65.8676	−	82.5953i	−0.176589	−	0.221435i	−0.862247	+	0.506489i	$0.830943\pi$
$374$	29.5916	−	586.467i	0.0791219	−	1.56809i
$375$	−12.2056	+	26.6116i	−0.0325483	+	0.0709643i
$376$	172.838	−	325.729i	0.459677	−	0.866300i
$377$	311.194	+	13.5212i	0.825449	+	0.0358652i
$378$	20.4354	−	16.4946i	0.0540619	−	0.0436366i
$379$	36.9643	+	105.638i	0.0975312	+	0.278728i	0.982304	−	0.187295i	$-0.0599720\pi$
$379$	36.9643	+	105.638i	0.0975312	+	0.278728i	−0.884772	+	0.466023i	$0.845686\pi$
$380$	−2.25897	+	10.4432i	−0.00594466	+	0.0274820i
$381$	303.742	+	28.4616i	0.797222	+	0.0747025i
$382$	−290.045	+	413.744i	−0.759279	+	1.08310i
$383$	−105.197	−	218.443i	−0.274665	−	0.570347i	0.717314	−	0.696750i	$-0.245371\pi$
$383$	−105.197	−	218.443i	−0.274665	−	0.570347i	−0.991979	+	0.126403i	$0.959657\pi$
$384$	324.637	−	205.102i	0.845409	−	0.534119i
$385$	−0.889637	+	1.41585i	−0.00231075	+	0.00367753i
$386$	99.0892	−	6.13004i	0.256708	−	0.0158809i
$387$	15.6588	−	209.340i	0.0404619	−	0.540931i
$388$	−52.0084	−	216.487i	−0.134042	−	0.557956i
$389$	−274.880	+	274.880i	−0.706632	+	0.706632i	−0.965825	−	0.259193i	$-0.916543\pi$
$389$	−274.880	+	274.880i	−0.706632	+	0.706632i	0.259193	+	0.965825i	$0.416543\pi$
$390$	5.10024	+	11.5087i	0.0130775	+	0.0295096i
$391$	106.751	+	37.3537i	0.273020	+	0.0955337i
$392$	264.870	+	286.405i	0.675689	+	0.730625i
$393$	−60.6031	−	92.5468i	−0.154206	−	0.235488i
$394$	−16.6956	−	23.2491i	−0.0423746	−	0.0590077i
$395$	2.16597	−	1.36097i	0.00548346	−	0.00344549i
$396$	246.707	−	583.696i	0.622998	−	1.47398i
$397$	30.9755	+	135.712i	0.0780239	+	0.341845i	0.998840	−	0.0481520i	$-0.0153332\pi$
$397$	30.9755	+	135.712i	0.0780239	+	0.341845i	−0.920816	+	0.389997i	$0.872476\pi$
$398$	250.449	−	283.480i	0.629268	−	0.712260i
$399$	−19.7810	+	2.60561i	−0.0495764	+	0.00653034i
$400$	−391.296	−	79.9955i	−0.978241	−	0.199989i
$401$	−259.617	+	539.100i	−0.647424	+	1.34439i	0.276204	+	0.961099i	$0.410923\pi$
$401$	−259.617	+	539.100i	−0.647424	+	1.34439i	−0.923628	+	0.383290i	$0.874791\pi$
$402$	−55.6989	+	212.761i	−0.138554	+	0.529256i
$403$	47.1824	+	418.756i	0.117078	+	1.03910i
$404$	−45.0797	+	0.512605i	−0.111583	+	0.00126882i
$405$	−15.7772	+	1.18673i	−0.0389560	+	0.00293019i
$406$	26.7907	+	8.82575i	0.0659870	+	0.0217383i
$407$	1057.61			2.59855
$408$	−243.196	−	317.974i	−0.596068	−	0.779349i
$409$	−65.5619	−	581.878i	−0.160298	−	1.42268i	−0.774020	−	0.633161i	$-0.781757\pi$
$409$	−65.5619	−	581.878i	−0.160298	−	1.42268i	0.613722	−	0.789522i	$-0.289672\pi$
$410$	27.4886	−	15.3971i	0.0670453	−	0.0375538i
$411$	−73.8031	+	27.3901i	−0.179570	+	0.0666426i
$412$	−621.146	+	77.1483i	−1.50764	+	0.187253i
$413$	−0.983956	−	0.784679i	−0.00238246	−	0.00189995i
$414$	94.4341	+	77.3187i	0.228102	+	0.186760i
$415$	4.17688	+	18.3001i	0.0100648	+	0.0440966i
$416$	−274.551	+	206.783i	−0.659978	+	0.497074i
$417$	−93.9856	+	450.601i	−0.225385	+	1.08058i
$418$	−391.050	+	280.821i	−0.935526	+	0.671820i
$419$	176.705	+	40.3318i	0.421731	+	0.0962573i	0.428119	−	0.903722i	$-0.359176\pi$
$419$	176.705	+	40.3318i	0.421731	+	0.0962573i	−0.00638848	+	0.999980i	$0.502034\pi$
$420$	0.161711	+	1.12841i	0.000385025	+	0.00268669i
$421$	−686.286	−	240.142i	−1.63013	−	0.570408i	−0.648505	−	0.761211i	$-0.724605\pi$
$421$	−686.286	−	240.142i	−1.63013	−	0.570408i	−0.981628	+	0.190802i	$0.938891\pi$
$422$	357.860	+	145.853i	0.848010	+	0.345622i
$423$	−304.136	−	282.119i	−0.718999	−	0.666948i
$424$	−54.5633	−	744.520i	−0.128687	−	1.75594i
$425$	−46.6173	+	413.740i	−0.109688	+	0.973506i
$426$	369.107	+	313.963i	0.866448	+	0.737003i
$427$	3.84611	−	6.12105i	0.00900729	−	0.0143350i
$428$	−20.7968	−	32.2773i	−0.0485906	−	0.0754142i
$429$	−177.255	+	538.797i	−0.413182	+	1.25594i
$430$	7.46138	+	5.23061i	0.0173521	+	0.0121642i
$431$	206.771	+	259.283i	0.479748	+	0.601584i	0.961528	−	0.274708i	$-0.0885811\pi$
$431$	206.771	+	259.283i	0.479748	+	0.601584i	−0.481780	+	0.876292i	$0.660010\pi$
$432$	−129.087	−	412.263i	−0.298812	−	0.954312i
$433$	−27.3903	−	78.2768i	−0.0632569	−	0.180778i	0.907917	−	0.419150i	$-0.137672\pi$
$433$	−27.3903	−	78.2768i	−0.0632569	−	0.180778i	−0.971174	+	0.238372i	$0.923386\pi$
$434$	−6.17816	+	37.6573i	−0.0142354	+	0.0867679i
$435$	−10.2647	−	13.5434i	−0.0235970	−	0.0311342i
$436$	304.355	+	102.629i	0.698063	+	0.235389i
$437$	−30.6249	−	87.5211i	−0.0700800	−	0.200277i
$438$	−350.990	−	373.939i	−0.801347	−	0.853741i
$439$	6.79845	+	8.52498i	0.0154862	+	0.0194191i	0.789514	−	0.613732i	$-0.210333\pi$
$439$	6.79845	+	8.52498i	0.0154862	+	0.0194191i	−0.774028	+	0.633151i	$0.781761\pi$
$440$	16.2975	+	22.1585i	0.0370398	+	0.0503602i
$441$	387.985	−	205.124i	0.879784	−	0.465135i
$442$	240.276	+	265.812i	0.543612	+	0.601385i
$443$	−152.626	+	242.903i	−0.344529	+	0.548314i	−0.973376	−	0.229215i	$-0.926384\pi$
$443$	−152.626	+	242.903i	−0.344529	+	0.548314i	0.628847	+	0.777529i	$0.283527\pi$
$444$	549.892	−	466.315i	1.23850	−	1.05026i
$445$	−1.47436	+	13.0853i	−0.00331317	+	0.0294052i
$446$	300.990	−	126.684i	0.674866	−	0.284045i
$447$	5.40493	+	287.935i	0.0120916	+	0.644150i
$448$	−29.0107	+	11.2759i	−0.0647560	+	0.0251694i
$449$	−129.952	−	45.4722i	−0.289426	−	0.101274i	0.181661	−	0.983361i	$-0.441853\pi$
$449$	−129.952	−	45.4722i	−0.289426	−	0.101274i	−0.471087	+	0.882087i	$0.656138\pi$
$450$	−200.146	+	402.274i	−0.444769	+	0.893941i
$451$	1384.06	+	315.903i	3.06887	+	0.700450i
$452$	−356.070	−	718.375i	−0.787765	−	1.58933i
$453$	−206.336	−	43.0373i	−0.455489	−	0.0950051i
$454$	543.971	+	153.371i	1.19817	+	0.337823i
$455$	−0.227046	−	0.994753i	−0.000499002	−	0.00218627i
$456$	−79.5042	+	318.429i	−0.174351	+	0.698309i
$457$	48.1151	+	38.3705i	0.105285	+	0.0839618i	0.674717	−	0.738076i	$-0.264266\pi$
$457$	48.1151	+	38.3705i	0.105285	+	0.0839618i	−0.569433	+	0.822038i	$0.692837\pi$
$458$	−524.875	+	154.451i	−1.14602	+	0.337229i
$459$	−416.037	+	172.429i	−0.906399	+	0.375663i
$460$	−4.98024	+	1.80648i	−0.0108266	+	0.00392713i
$461$	46.0488	+	408.694i	0.0998889	+	0.886538i	0.939313	+	0.343061i	$0.111464\pi$
$461$	46.0488	+	408.694i	0.0998889	+	0.886538i	−0.839424	+	0.543477i	$0.817108\pi$
$462$	−28.6895	+	42.6045i	−0.0620985	+	0.0922175i
$463$	−822.067			−1.77552			−0.887761	−	0.460304i	$-0.847740\pi$
$463$	−822.067			−1.77552			−0.887761	+	0.460304i	$0.847740\pi$
$464$	296.739	−	356.710i	0.639524	−	0.768771i
$465$	15.9487	−	16.5590i	0.0342984	−	0.0356107i
$466$	−44.3067	−	252.083i	−0.0950787	−	0.540952i
$467$	−45.3894	−	402.842i	−0.0971936	−	0.862617i	−0.943827	−	0.330440i	$-0.892803\pi$
$467$	−45.3894	−	402.842i	−0.0971936	−	0.862617i	0.846633	−	0.532177i	$-0.178626\pi$
$468$	145.401	+	358.296i	0.310687	+	0.765589i
$469$	7.73460	−	16.0611i	0.0164917	−	0.0342453i
$470$	17.2744	−	5.08320i	0.0367540	−	0.0108153i
$471$	−50.1602	−	380.801i	−0.106497	−	0.808495i
$472$	−17.9459	+	10.3218i	−0.0380210	+	0.0218681i
$473$	91.3626	+	400.286i	0.193156	+	0.846270i
$474$	67.8218	−	39.6791i	0.143084	−	0.0837111i
$475$	289.035	−	181.613i	0.608496	−	0.382343i
$476$	14.4099	+	29.0721i	0.0302729	+	0.0610759i
$477$	−825.211	−	156.020i	−1.73000	−	0.327086i
$478$	60.3198	−	110.621i	0.126192	−	0.231425i
$479$	−814.948	−	285.163i	−1.70135	−	0.595329i	−0.707568	−	0.706645i	$-0.750208\pi$
$479$	−814.948	−	285.163i	−1.70135	−	0.595329i	−0.993785	+	0.111316i	$0.964493\pi$
$480$	18.2437	+	4.33527i	0.0380077	+	0.00903181i
$481$	−456.329	+	456.329i	−0.948709	+	0.948709i
$482$	−547.215	+	230.317i	−1.13530	+	0.477837i
$483$	−6.31204	−	7.61726i	−0.0130684	−	0.0157707i
$484$	−76.0373	+	751.563i	−0.157102	+	1.55282i
$485$	5.78447	−	9.20593i	0.0119267	−	0.0189813i
$486$	−485.542	+	21.1008i	−0.999057	+	0.0434174i
$487$	−376.366	−	781.531i	−0.772825	−	1.60479i	−0.796180	−	0.605060i	$-0.793149\pi$
$487$	−376.366	−	781.531i	−0.772825	−	1.60479i	0.0233549	−	0.999727i	$-0.492565\pi$
$488$	−70.4580	−	95.7965i	−0.144381	−	0.196304i
$489$	−59.8830	+	639.069i	−0.122460	+	1.30689i
$490$	−0.959990	+	19.0258i	−0.00195916	+	0.0388281i
$491$	214.641	+	613.409i	0.437151	+	1.24931i	0.926195	+	0.377046i	$0.123060\pi$
$491$	214.641	+	613.409i	0.437151	+	1.24931i	−0.489044	+	0.872259i	$0.662654\pi$
$492$	858.913	−	446.001i	1.74576	−	0.906507i
$493$	−398.015	−	274.887i	−0.807332	−	0.557581i
$494$	47.5608	−	289.893i	0.0962769	−	0.586829i
$495$	28.8042	−	11.3094i	0.0581902	−	0.0228473i
$496$	538.976	+	321.803i	1.08664	+	0.648796i
$497$	−24.4889	−	30.7081i	−0.0492734	−	0.0617868i
$498$	110.452	+	565.906i	0.221791	+	1.13636i
$499$	−96.4005	+	46.4241i	−0.193187	+	0.0930342i	−0.527977	−	0.849259i	$-0.677049\pi$
$499$	−96.4005	+	46.4241i	−0.193187	+	0.0930342i	0.334789	+	0.942293i	$0.391335\pi$
$500$	−21.1430	−	32.8147i	−0.0422861	−	0.0656293i
$501$	29.4162	+	118.577i	0.0587150	+	0.236680i
$502$	20.7909	−	1.28621i	0.0414161	−	0.00256216i
$503$	59.8701	−	531.362i	0.119026	−	1.05639i	−0.782197	−	0.623031i	$-0.785901\pi$
$503$	59.8701	−	531.362i	0.119026	−	1.05639i	0.901223	−	0.433355i	$-0.142670\pi$
$504$	3.86811	+	34.8013i	0.00767482	+	0.0690503i
$505$	−1.55670	−	1.55670i	−0.00308257	−	0.00308257i
$506$	−221.054	−	90.0944i	−0.436865	−	0.178052i
$507$	72.5180	+	143.626i	0.143034	+	0.283285i
$508$	−249.980	+	320.883i	−0.492087	+	0.631660i
$509$	−495.064	−	112.995i	−0.972620	−	0.221994i	−0.293449	−	0.955975i	$-0.594803\pi$
$509$	−495.064	−	112.995i	−0.972620	−	0.221994i	−0.679171	+	0.733980i	$0.737660\pi$
$510$	2.80226	−	19.3465i	0.00549462	−	0.0379343i
$511$	22.1164	+	35.1980i	0.0432806	+	0.0688806i
$512$	−2.52531	+	511.994i	−0.00493224	+	0.999988i
$513$	323.195	+	178.536i	0.630010	+	0.348024i
$514$	145.179	−	164.326i	0.282450	−	0.319701i
$515$	−23.8969	−	19.0571i	−0.0464017	−	0.0370041i
$516$	223.994	+	167.841i	0.434098	+	0.325273i
$517$	731.006	+	352.034i	1.41394	+	0.680917i
$518$	−50.9864	+	28.5588i	−0.0984294	+	0.0551328i
$519$	479.695	+	368.030i	0.924267	+	0.709114i
$520$	−16.5927	−	2.52885i	−0.0319090	−	0.00486318i
$521$	628.257			1.20587			0.602934	−	0.797791i	$-0.293998\pi$
$521$	628.257			1.20587			0.602934	+	0.797791i	$0.293998\pi$
$522$	−301.982	−	425.783i	−0.578509	−	0.815676i
$523$			579.514i			1.10806i	0.832498	+	0.554029i	$0.186910\pi$
$523$			579.514i			1.10806i	−0.832498	+	0.554029i	$0.813090\pi$
$524$	147.489	−	1.67711i	0.281468	−	0.00320059i
$525$	22.1685	−	28.8946i	0.0422256	−	0.0550374i
$526$	−158.295	+	88.6654i	−0.300942	+	0.168565i
$527$	283.936	−	589.599i	0.538778	−	1.11878i
$528$	478.827	+	696.146i	0.906870	+	1.31846i
$529$	−301.161	+	377.644i	−0.569303	+	0.713883i
$530$	24.1363	−	27.3196i	0.0455402	−	0.0515463i
$531$	6.03109	+	22.4959i	0.0113580	+	0.0423651i
$532$	11.2691	−	24.0977i	0.0211825	−	0.0452964i
$533$	−733.487	+	460.881i	−1.37615	+	0.864692i
$534$	−57.9831	+	400.310i	−0.108583	+	0.749644i
$535$	0.417232	−	1.82801i	0.000779873	−	0.00341685i
$536$	−199.101	−	215.289i	−0.371457	−	0.401658i
$537$	764.860	−	386.186i	1.42432	−	0.719154i
$538$	−304.715	−	124.192i	−0.566384	−	0.230840i
$539$	−606.954	+	606.954i	−1.12607	+	1.12607i
$540$	9.98993	−	18.5803i	0.0184999	−	0.0344080i
$541$	−994.127	−	112.011i	−1.83757	−	0.207045i	−0.876135	−	0.482065i	$-0.839887\pi$
$541$	−994.127	−	112.011i	−1.83757	−	0.207045i	−0.961438	+	0.275020i	$0.911315\pi$
$542$	−57.5276	+	3.55888i	−0.106139	+	0.00656620i
$543$	−507.337	+	125.859i	−0.934323	+	0.231785i
$544$	531.847	−	45.0625i	0.977661	−	0.0828354i
$545$	6.80534	+	14.1314i	0.0124869	+	0.0259292i
$546$	−6.00392	−	30.7614i	−0.0109962	−	0.0563395i
$547$	430.108	−	343.000i	0.786304	−	0.627056i	−0.145773	−	0.989318i	$-0.546567\pi$
$547$	430.108	−	343.000i	0.786304	−	0.627056i	0.932076	+	0.362262i	$0.117995\pi$
$548$	22.1913	−	102.590i	0.0404951	−	0.187208i
$549$	−124.527	+	48.8932i	−0.226826	+	0.0890587i
$550$	142.274	−	867.191i	0.258680	−	1.57671i
$551$	27.2544	+	395.642i	0.0494635	+	0.718044i
$552$	−154.658	+	50.6219i	−0.280178	+	0.0917064i
$553$	−6.01157	+	2.10354i	−0.0108708	+	0.00380387i
$554$	34.9864	−	693.385i	0.0631523	−	1.25160i
$555$	35.0544	+	3.28472i	0.0631611	+	0.00591841i
$556$	−438.880	−	429.011i	−0.789352	−	0.771602i
$557$	519.871	−	250.357i	0.933341	−	0.449473i	0.0955255	−	0.995427i	$-0.469547\pi$
$557$	519.871	−	250.357i	0.933341	−	0.449473i	0.837815	+	0.545954i	$0.183833\pi$
$558$	505.749	−	492.889i	0.906360	−	0.883314i
$559$	−212.133	−	133.292i	−0.379486	−	0.238447i
$560$	−1.38404	−	0.628157i	−0.00247150	−	0.00112171i
$561$	678.225	−	562.010i	1.20896	−	1.00180i
$562$	212.771	−	89.5532i	0.378596	−	0.159347i
$563$	700.605	+	700.605i	1.24441	+	1.24441i	0.958151	+	0.286262i	$0.0924127\pi$
$563$	700.605	+	700.605i	1.24441	+	1.24441i	0.286262	+	0.958151i	$0.407587\pi$
$564$	535.295	−	139.274i	0.949105	−	0.246941i
$565$	12.9314	−	36.9558i	0.0228874	−	0.0654085i
$566$	258.455	−	473.984i	0.456633	−	0.837427i
$567$	38.9542	+	5.86038i	0.0687023	+	0.0103358i
$568$	−617.708	+	189.426i	−1.08751	+	0.333496i
$569$	−234.467	−	373.152i	−0.412069	−	0.655804i	0.574621	−	0.818420i	$-0.305150\pi$
$569$	−234.467	−	373.152i	−0.412069	−	0.655804i	−0.986689	+	0.162616i	$0.948007\pi$
$570$	−13.8335	+	8.09326i	−0.0242693	+	0.0141987i
$571$	−888.539	+	202.803i	−1.55611	+	0.355172i	−0.912140	−	0.409879i	$-0.865571\pi$
$571$	−888.539	+	202.803i	−1.55611	+	0.355172i	−0.643970	+	0.765051i	$0.722714\pi$
$572$	−478.222	−	585.879i	−0.836052	−	1.02426i
$573$	−751.432	+	98.9808i	−1.31140	+	0.172741i
$574$	−75.2547	+	22.1446i	−0.131106	+	0.0385795i
$575$	152.492	+	73.4365i	0.265204	+	0.127716i
$576$	555.901	+	150.832i	0.965106	+	0.261860i
$577$	353.343	−	39.8122i	0.612379	−	0.0689985i	0.199673	−	0.979863i	$-0.436012\pi$
$577$	353.343	−	39.8122i	0.612379	−	0.0689985i	0.412706	+	0.910864i	$0.364584\pi$
$578$	3.73393	+	21.2442i	0.00646008	+	0.0367547i
$579$	107.259	+	103.306i	0.185248	+	0.178421i
$580$	22.5856	−	1.81408i	0.0389407	−	0.00312773i
$581$		−	46.7348i		−	0.0804386i
$582$	186.541	−	277.017i	0.320517	−	0.475974i
$583$	1632.25	−	183.910i	2.79974	−	0.315455i
$584$	672.099	−	126.024i	1.15085	−	0.215794i
$585$	−7.54850	+	17.3079i	−0.0129034	+	0.0295861i
$586$	−701.964	+	206.562i	−1.19789	+	0.352494i
$587$	−275.675	+	345.686i	−0.469635	+	0.588903i	−0.959082	−	0.283130i	$-0.908627\pi$
$587$	−275.675	+	345.686i	−0.469635	+	0.588903i	0.489447	+	0.872033i	$0.337199\pi$
$588$	−47.9645	+	583.193i	−0.0815723	+	0.991824i
$589$	−523.072	+	119.388i	−0.888068	+	0.202696i
$590$	−0.973022	−	0.274341i	−0.00164919	−	0.000464986i
$591$	8.76647	−	42.0296i	0.0148333	−	0.0711161i
$592$	129.329	+	952.585i	0.218460	+	1.60910i
$593$	−4.96401	+	21.7488i	−0.00837101	+	0.0366758i	−0.978941	−	0.204144i	$-0.934559\pi$
$593$	−4.96401	+	21.7488i	−0.00837101	+	0.0366758i	0.970570	+	0.240819i	$0.0774162\pi$
$594$	895.331	−	319.224i	1.50729	−	0.537415i
$595$	−0.523324	+	1.49557i	−0.000879536	+	0.00251357i
$596$	−327.428	−	200.580i	−0.549376	−	0.336544i
$597$	567.299	−	10.6490i	0.950250	−	0.0178374i
$598$	134.252	−	56.5052i	0.224501	−	0.0944903i
$599$	−782.106	−	88.1222i	−1.30569	−	0.147116i	−0.568432	−	0.822730i	$-0.692450\pi$
$599$	−782.106	−	88.1222i	−1.30569	−	0.147116i	−0.737255	+	0.675615i	$0.763878\pi$
$600$	−308.383	−	513.617i	−0.513971	−	0.856028i
$601$	815.060	+	512.136i	1.35617	+	0.852140i	0.996712	−	0.0810209i	$-0.0258181\pi$
$601$	815.060	+	512.136i	1.35617	+	0.852140i	0.359460	+	0.933161i	$0.382961\pi$
$602$	−15.2135	−	16.8303i	−0.0252716	−	0.0279574i
$603$	−291.645	+	154.190i	−0.483657	+	0.255706i
$604$	196.450	−	200.969i	0.325248	−	0.332730i
$605$	−28.8403	+	22.9994i	−0.0476699	+	0.0380155i
$606$	−46.2805	−	49.3064i	−0.0763704	−	0.0813636i
$607$	−1016.13	+	355.560i	−1.67402	+	0.585766i	−0.989667	−	0.143382i	$-0.954202\pi$
$607$	−1016.13	+	355.560i	−1.67402	+	0.585766i	−0.684356	+	0.729148i	$0.739917\pi$
$608$	−300.753	−	317.877i	−0.494660	−	0.522824i
$609$	17.4126	+	38.5614i	0.0285921	+	0.0633193i
$610$	0.940151	−	5.73043i	0.00154123	−	0.00939414i
$611$	−467.302	+	163.516i	−0.764814	+	0.267620i
$612$	104.837	−	591.249i	0.171303	−	0.966094i
$613$	622.789	−	496.657i	1.01597	−	0.810208i	0.0340323	−	0.999421i	$-0.489165\pi$
$613$	622.789	−	496.657i	1.01597	−	0.810208i	0.981936	+	0.189213i	$0.0605937\pi$
$614$	−816.040	−	572.064i	−1.32906	−	0.931701i
$615$	44.8935	+	14.7692i	0.0729975	+	0.0240149i
$616$	−27.2834	−	62.8157i	−0.0442912	−	0.101973i
$617$	299.533	+	188.209i	0.485467	+	0.305039i	0.752435	−	0.658666i	$-0.228879\pi$
$617$	299.533	+	188.209i	0.485467	+	0.305039i	−0.266968	+	0.963705i	$0.586022\pi$
$618$	−715.155	−	608.313i	−1.15721	−	0.984325i
$619$	224.796	+	25.3284i	0.363159	+	0.0409182i	0.291659	−	0.956522i	$-0.405793\pi$
$619$	224.796	+	25.3284i	0.363159	+	0.0409182i	0.0715003	+	0.997441i	$0.477221\pi$
$620$	7.16051	+	29.8059i	0.0115492	+	0.0480741i
$621$	10.3029	+	182.783i	0.0165909	+	0.294337i
$622$	93.1870	+	37.9801i	0.149818	+	0.0610612i
$623$	10.8284	−	30.9458i	0.0173811	−	0.0496722i
$624$	−506.968	−	93.7668i	−0.812449	−	0.150267i
$625$	−138.439	+	606.542i	−0.221503	+	0.970466i
$626$	−566.726	+	406.977i	−0.905313	+	0.650124i
$627$	−706.939	−	147.452i	−1.12749	−	0.235171i
$628$	463.901	+	216.940i	0.738697	+	0.345446i
$629$	977.041	−	223.003i	1.55332	−	0.354536i
$630$	−1.08323	+	1.32302i	−0.00171942	+	0.00210003i
$631$	77.7965	−	97.5537i	0.123291	−	0.154602i	−0.716355	−	0.697736i	$-0.754191\pi$
$631$	77.7965	−	97.5537i	0.123291	−	0.154602i	0.839646	+	0.543134i	$0.182762\pi$
$632$	−4.08954	+	104.689i	−0.00647079	+	0.165646i
$633$	201.685	+	543.444i	0.318618	+	0.858521i
$634$	−805.193	+	451.009i	−1.27002	+	0.711371i
$635$	−19.7384	+	2.22398i	−0.0310841	+	0.00350234i
$636$	767.580	−	815.302i	1.20689	−	1.28192i
$637$		−	523.767i		−	0.822240i
$638$	809.763	+	621.787i	1.26922	+	0.974587i
$639$	27.2787	+	726.350i	0.0426897	+	1.13670i
$640$	−17.9651	+	17.3887i	−0.0280705	+	0.0271699i
$641$	−575.306	+	64.8214i	−0.897513	+	0.101125i	−0.548654	−	0.836050i	$-0.684859\pi$
$641$	−575.306	+	64.8214i	−0.897513	+	0.101125i	−0.348859	+	0.937175i	$0.613431\pi$
$642$	14.5864	−	55.7178i	0.0227203	−	0.0867879i
$643$	827.863	+	398.678i	1.28750	+	0.620027i	0.947307	−	0.320328i	$-0.103793\pi$
$643$	827.863	+	398.678i	1.28750	+	0.620027i	0.340194	+	0.940355i	$0.389507\pi$
$644$	13.0896	−	1.62577i	0.0203255	−	0.00252449i
$645$	1.78500	+	13.5512i	0.00276744	+	0.0210096i
$646$	−302.047	+	341.883i	−0.467565	+	0.529230i
$647$	−210.561	+	48.0591i	−0.325441	+	0.0742799i	−0.382120	−	0.924113i	$-0.624806\pi$
$647$	−210.561	+	48.0591i	−0.325441	+	0.0742799i	0.0566789	+	0.998392i	$0.481949\pi$
$648$	324.767	−	560.741i	0.501184	−	0.865341i
$649$	−24.2352	−	38.5701i	−0.0373424	−	0.0594300i
$650$	312.781	+	435.556i	0.481202	+	0.670086i
$651$	−47.8873	+	31.3583i	−0.0735596	+	0.0481695i
$652$	−675.135	−	525.956i	−1.03548	−	0.806680i
$653$	90.3107	−	258.093i	0.138301	−	0.395242i	−0.853813	−	0.520580i	$-0.825716\pi$
$653$	90.3107	−	258.093i	0.138301	−	0.395242i	0.992114	+	0.125338i	$0.0400015\pi$
$654$	195.202	+	440.474i	0.298474	+	0.673508i
$655$	5.09310	+	5.09310i	0.00777573	+	0.00777573i
$656$	−115.284	+	1285.25i	−0.175738	+	1.95922i
$657$	57.3829	−	767.145i	0.0873407	−	1.16765i
$658$	−44.7472	+	2.76823i	−0.0680048	+	0.00420704i
$659$	−406.762	−	255.586i	−0.617241	−	0.387838i	0.186812	−	0.982396i	$-0.440184\pi$
$659$	−406.762	−	255.586i	−0.617241	−	0.387838i	−0.804053	+	0.594557i	$0.797327\pi$
$660$	−7.96480	+	40.4837i	−0.0120679	+	0.0613389i
$661$	356.398	−	171.632i	0.539181	−	0.259656i	−0.144414	−	0.989517i	$-0.546130\pi$
$661$	356.398	−	171.632i	0.539181	−	0.259656i	0.683595	+	0.729862i	$0.260415\pi$
$662$	−559.205	+	797.697i	−0.844720	+	1.20498i
$663$	−50.1432	+	535.127i	−0.0756308	+	0.807129i
$664$	−715.173	−	282.042i	−1.07707	−	0.424763i
$665$	1.22617	−	0.429055i	0.00184386	−	0.000645195i
$666$	1073.04	+	134.916i	1.61117	+	0.202577i
$667$	−158.912	+	115.811i	−0.238249	+	0.173629i
$668$	−154.355	−	52.0490i	−0.231071	−	0.0779176i
$669$	445.247	+	204.216i	0.665541	+	0.305255i
$670$	0.721617	−	14.3015i	0.00107704	−	0.0213456i
$671$	204.571	−	163.140i	0.304874	−	0.243129i
$672$	−41.8820	−	20.6307i	−0.0623243	−	0.0307004i
$673$	−345.470	−	717.376i	−0.513329	−	1.06594i	−0.983086	−	0.183143i	$-0.941373\pi$
$673$	−345.470	−	717.376i	−0.513329	−	1.06594i	0.469758	−	0.882795i	$-0.344341\pi$
$674$	780.068	−	705.129i	1.15737	−	1.04619i
$675$	−647.591	+	186.713i	−0.959393	+	0.276612i
$676$	−213.437	−	21.5939i	−0.315735	−	0.0319436i
$677$	−458.579	−	51.6695i	−0.677370	−	0.0763213i	−0.233424	−	0.972375i	$-0.574993\pi$
$677$	−458.579	−	51.6695i	−0.677370	−	0.0763213i	−0.443946	+	0.896054i	$0.646422\pi$
$678$	432.934	−	1122.04i	0.638546	−	1.65493i
$679$	−19.1413	+	19.1413i	−0.0281904	+	0.0281904i
$680$	19.7282	+	17.0340i	0.0290121	+	0.0250500i
$681$	382.103	+	756.775i	0.561092	+	1.11127i
$682$	−661.238	+	1212.65i	−0.969557	+	1.77809i
$683$	189.523	−	830.355i	0.277486	−	1.21575i	−0.623474	−	0.781844i	$-0.714279\pi$
$683$	189.523	−	830.355i	0.277486	−	1.21575i	0.900960	−	0.433902i	$-0.142864\pi$
$684$	−432.579	+	235.033i	−0.632425	+	0.343615i
$685$	4.33996	−	2.72698i	0.00633571	−	0.00398099i
$686$	25.8045	−	91.5221i	0.0376158	−	0.133414i
$687$	−702.972	−	423.516i	−1.02325	−	0.616471i
$688$	−349.363	+	131.238i	−0.507796	+	0.190753i
$689$	−624.917	+	783.621i	−0.906991	+	1.13733i
$690$	−7.04699	−	3.67272i	−0.0102130	−	0.00532278i
$691$	387.549	−	804.755i	0.560853	−	1.16462i	−0.407075	−	0.913395i	$-0.633451\pi$
$691$	387.549	−	804.755i	0.560853	−	1.16462i	0.967928	−	0.251229i	$-0.0808346\pi$
$692$	−757.832	+	274.888i	−1.09513	+	0.397237i
$693$	−76.1835	+	11.4936i	−0.109933	+	0.0165853i
$694$	106.066	+	603.463i	0.152833	+	0.869544i
$695$		−	29.9701i		−	0.0431224i
$696$	695.181	−	33.7448i	0.998824	−	0.0484839i
$697$	1345.23			1.93003
$698$	−13.0198	+	2.28838i	−0.0186530	+	0.00327848i
$699$	233.695	−	304.601i	0.334328	−	0.435767i
$700$	16.5580	+	45.6483i	0.0236543	+	0.0652119i
$701$	−741.936	−	357.297i	−1.05840	−	0.509697i	−0.178047	−	0.984022i	$-0.556978\pi$
$701$	−741.936	−	357.297i	−1.05840	−	0.509697i	−0.880350	+	0.474325i	$0.842692\pi$
$702$	−248.574	+	524.047i	−0.354094	+	0.746505i
$703$	−642.385	−	512.285i	−0.913777	−	0.728713i
$704$	−1125.91	+	38.4216i	−1.59930	+	0.0545761i
$705$	23.1358	+	13.9385i	0.0328167	+	0.0197709i
$706$	293.110	+	82.6416i	0.415169	+	0.117056i
$707$	2.91620	+	4.64110i	0.00412475	+	0.00656450i
$708$	−29.6069	−	9.36846i	−0.0418177	−	0.0132323i
$709$	−54.8349	−	12.5157i	−0.0773412	−	0.0176526i	0.183675	−	0.982987i	$-0.441201\pi$
$709$	−54.8349	−	12.5157i	−0.0773412	−	0.0176526i	−0.261016	+	0.965334i	$0.584058\pi$
$710$	−27.7003	−	15.1044i	−0.0390145	−	0.0212739i
$711$	112.633	+	34.7256i	0.158415	+	0.0488405i
$712$	−408.208	−	352.461i	−0.573325	−	0.495029i
$713$	−188.106	−	188.106i	−0.263824	−	0.263824i
$714$	−17.5205	+	45.4082i	−0.0245386	+	0.0635969i
$715$	4.13494	−	36.6986i	0.00578313	−	0.0513267i
$716$	−114.996	+	1136.63i	−0.160608	+	1.58747i
$717$	183.437	−	45.5066i	0.255840	−	0.0634681i
$718$	258.815	+	286.322i	0.360467	+	0.398777i
$719$	1029.22	−	495.648i	1.43147	−	0.689358i	0.452196	−	0.891918i	$-0.350641\pi$
$719$	1029.22	−	495.648i	1.43147	−	0.689358i	0.979270	+	0.202561i	$0.0649263\pi$
$720$	13.7086	+	24.5608i	0.0190397	+	0.0341123i
$721$	47.4479	+	59.4977i	0.0658084	+	0.0825211i
$722$	−347.538	−	17.5358i	−0.481354	−	0.0242879i
$723$	−809.480	−	371.274i	−1.11961	−	0.513519i
$724$	222.695	−	660.418i	0.307589	−	0.912180i
$725$	−545.837	−	475.482i	−0.752879	−	0.655838i
$726$	−907.802	+	678.093i	−1.25042	+	0.934012i
$727$	251.412	+	718.494i	0.345821	+	0.988300i	0.977107	+	0.212750i	$0.0682419\pi$
$727$	251.412	+	718.494i	0.345821	+	0.988300i	−0.631286	+	0.775550i	$0.717472\pi$
$728$	38.8752	+	15.3312i	0.0534000	+	0.0210593i
$729$	−515.695	−	515.267i	−0.707400	−	0.706813i
$730$	27.3429	+	19.1680i	0.0374560	+	0.0262576i
$731$	168.805	+	350.527i	0.230924	+	0.479518i
$732$	34.4337	−	175.021i	0.0470406	−	0.239099i
$733$	−561.849	+	894.178i	−0.766507	+	1.21989i	0.204037	+	0.978963i	$0.434594\pi$
$733$	−561.849	+	894.178i	−0.766507	+	1.21989i	−0.970544	+	0.240925i	$0.922549\pi$
$734$	60.8780	+	984.063i	0.0829400	+	1.34068i
$735$	−22.0025	+	18.2324i	−0.0299354	+	0.0248059i
$736$	54.1164	−	210.119i	0.0735277	−	0.285488i
$737$	456.242	−	456.242i	0.619053	−	0.619053i
$738$	1363.96	+	497.073i	1.84818	+	0.673540i
$739$	−97.7821	−	34.2154i	−0.132317	−	0.0462997i	0.263308	−	0.964712i	$-0.415186\pi$
$739$	−97.7821	−	34.2154i	−0.132317	−	0.0462997i	−0.395625	+	0.918412i	$0.629472\pi$
$740$	−28.8499	+	37.0327i	−0.0389863	+	0.0500442i
$741$	368.646	−	241.403i	0.497498	−	0.325780i
$742$	−73.7230	+	52.9419i	−0.0993571	+	0.0713503i
$743$	−171.229	+	107.590i	−0.230456	+	0.144805i	−0.642311	−	0.766444i	$-0.722024\pi$
$743$	−171.229	+	107.590i	−0.230456	+	0.144805i	0.411854	+	0.911250i	$0.364881\pi$
$744$	190.872	+	922.055i	0.256549	+	1.23932i
$745$	−4.17245	−	18.2807i	−0.00560060	−	0.0245378i
$746$	158.342	+	139.892i	0.212255	+	0.187523i
$747$	−513.484	+	695.948i	−0.687395	+	0.931657i
$748$	144.755	+	1165.47i	0.193523	+	1.55812i
$749$	−2.02554	+	4.20607i	−0.00270432	+	0.00561558i
$750$	14.8293	−	56.6455i	0.0197724	−	0.0755273i
$751$	61.9534	+	549.852i	0.0824945	+	0.732159i	0.965071	+	0.261990i	$0.0843787\pi$
$751$	61.9534	+	549.852i	0.0824945	+	0.732159i	−0.882576	+	0.470170i	$0.844193\pi$
$752$	−227.685	+	701.462i	−0.302773	+	0.932796i
$753$	22.5050	+	21.6757i	0.0298871	+	0.0287858i
$754$	−617.674	+	81.1067i	−0.819196	+	0.107569i
$755$	13.7237			0.0181771
$756$	−34.5430	+	39.5663i	−0.0456919	+	0.0523364i
$757$	19.5437	+	173.455i	0.0258173	+	0.229135i	0.999994	+	0.00334977i	$0.00106627\pi$
$757$	19.5437	+	173.455i	0.0258173	+	0.229135i	−0.974177	+	0.225785i	$0.927505\pi$
$758$	−109.386	−	195.289i	−0.144309	−	0.257637i
$759$	−124.583	−	335.690i	−0.164141	−	0.442280i
$760$	0.834135	−	21.3531i	0.00109755	−	0.0280962i
$761$	−700.430	−	558.574i	−0.920407	−	0.734000i	0.0438308	−	0.999039i	$-0.486044\pi$
$761$	−700.430	−	558.574i	−0.920407	−	0.734000i	−0.964238	+	0.265039i	$0.914615\pi$
$762$	−608.166	+	49.0966i	−0.798118	+	0.0644313i
$763$	−8.68974	−	38.0722i	−0.0113889	−	0.0498981i
$764$	428.086	−	915.413i	0.560323	−	1.19819i
$765$	24.2252	−	16.5214i	0.0316669	−	0.0215966i
$766$	282.845	+	393.869i	0.369250	+	0.514190i
$767$	27.0987	+	6.18511i	0.0353308	+	0.00806403i
$768$	−568.463	+	516.405i	−0.740186	+	0.672403i
$769$	−251.639	−	88.0522i	−0.327229	−	0.114502i	0.161665	−	0.986846i	$-0.448314\pi$
$769$	−251.639	−	88.0522i	−0.327229	−	0.114502i	−0.488894	+	0.872343i	$0.662599\pi$
$770$	1.26222	−	3.09696i	0.00163925	−	0.00402202i
$771$	328.850	−	6.17295i	0.426524	−	0.00800642i
$772$	−193.064	+	46.3813i	−0.250083	+	0.0600795i
$773$	75.2767	−	668.099i	0.0973825	−	0.864294i	−0.846134	−	0.532970i	$-0.821076\pi$
$773$	75.2767	−	668.099i	0.0973825	−	0.864294i	0.943517	−	0.331324i	$-0.107495\pi$
$774$	41.6324	+	417.781i	0.0537887	+	0.539769i
$775$	521.040	−	829.231i	0.672310	−	1.06998i
$776$	177.398	+	408.431i	0.228605	+	0.526329i
$777$	−83.2694	−	27.3942i	−0.107168	−	0.0352564i
$778$	446.292	−	636.628i	0.573640	−	0.818288i
$779$	−687.652	−	862.289i	−0.882737	−	1.10692i
$780$	−14.0310	−	20.9042i	−0.0179885	−	0.0268002i
$781$	−469.533	−	1341.85i	−0.601195	−	1.71812i
$782$	−223.211	−	36.6206i	−0.285435	−	0.0468294i
$783$	164.383	−	765.550i	0.209940	−	0.977714i
$784$	−620.901	−	472.460i	−0.791966	−	0.602627i
$785$	8.25968	+	23.6048i	0.0105219	+	0.0300698i
$786$	151.418	+	161.317i	0.192643	+	0.205239i
$787$	145.381	+	182.302i	0.184728	+	0.231641i	0.865569	−	0.500790i	$-0.166957\pi$
$787$	145.381	+	182.302i	0.184728	+	0.231641i	−0.680841	+	0.732431i	$0.738386\pi$
$788$	40.9363	+	40.0158i	0.0519496	+	0.0507815i
$789$	−258.523	−	85.0498i	−0.327659	−	0.107794i
$790$	−3.79534	+	3.43074i	−0.00480423	+	0.00434270i
$791$	−51.8635	+	82.5403i	−0.0655670	+	0.104349i
$792$	−283.880	+	1235.18i	−0.358434	+	1.55957i
$793$	−17.8763	+	158.657i	−0.0225427	+	0.200072i
$794$	−108.002	−	256.603i	−0.136022	−	0.323178i
$795$	54.6719	−	1.02626i	0.0687697	−	0.00129090i
$796$	−395.190	+	645.109i	−0.496470	+	0.810439i
$797$	951.263	+	332.861i	1.19355	+	0.417643i	0.852664	−	0.522460i	$-0.174986\pi$
$797$	951.263	+	332.861i	1.19355	+	0.417643i	0.340891	+	0.940103i	$0.389271\pi$
$798$	38.0626	−	11.9810i	0.0476975	−	0.0150138i
$799$	749.546	+	171.079i	0.938105	+	0.214116i
$800$	798.473	+	22.1021i	0.998092	+	0.0276277i
$801$	−501.257	+	341.853i	−0.625790	+	0.426783i
$802$	324.749	−	1151.81i	0.404924	−	1.43617i
$803$	334.806	+	1466.88i	0.416944	+	1.82675i
$804$	36.0546	−	438.381i	0.0448440	−	0.545251i
$805$	0.503587	+	0.401597i	0.000625574	+	0.000498878i
$806$	−237.921	−	808.532i	−0.295187	−	1.00314i
$807$	−171.733	−	462.737i	−0.212804	−	0.573404i
$808$	88.6208	−	16.6171i	0.109679	−	0.0205657i
$809$	100.008	+	887.593i	0.123619	+	1.09715i	0.890381	+	0.455217i	$0.150438\pi$
$809$	100.008	+	887.593i	0.123619	+	1.09715i	−0.766762	+	0.641932i	$0.778133\pi$
$810$	30.6671	−	7.79995i	0.0378607	−	0.00962957i
$811$	1023.32			1.26180			0.630899	−	0.775865i	$-0.282686\pi$
$811$	1023.32			1.26180			0.630899	+	0.775865i	$0.282686\pi$
$812$	−55.8282	−	8.10960i	−0.0687539	−	0.00998719i
$813$	−62.2704	−	59.9757i	−0.0765934	−	0.0737709i
$814$	−2083.29	+	366.162i	−2.55932	+	0.449831i
$815$	−4.67924	−	41.5294i	−0.00574139	−	0.0509563i
$816$	589.136	+	542.149i	0.721981	+	0.664399i
$817$	138.397	−	287.385i	0.169397	−	0.351756i
$818$	330.600	+	1123.49i	0.404157	+	1.37346i
$819$	27.9119	−	37.8302i	0.0340804	−	0.0461907i
$820$	−48.8164	+	39.8462i	−0.0595322	+	0.0485930i
$821$	−113.596	−	497.696i	−0.138363	−	0.606207i	−0.995795	−	0.0916101i	$-0.970799\pi$
$821$	−113.596	−	497.696i	−0.138363	−	0.606207i	0.857432	−	0.514597i	$-0.172058\pi$
$822$	135.895	−	79.5051i	0.165322	−	0.0967216i
$823$	1176.17	−	739.038i	1.42913	−	0.897980i	0.429141	−	0.903238i	$-0.358816\pi$
$823$	1176.17	−	739.038i	1.42913	−	0.897980i	0.999986	+	0.00525757i	$0.00167355\pi$
$824$	1196.83	−	367.018i	1.45246	−	0.445410i
$825$	1102.77	−	722.136i	1.33669	−	0.875317i
$826$	2.20987	+	1.20500i	0.00267539	+	0.00145884i
$827$	−81.1102	−	28.3817i	−0.0980776	−	0.0343188i	0.280794	−	0.959768i	$-0.409402\pi$
$827$	−81.1102	−	28.3817i	−0.0980776	−	0.0343188i	−0.378872	+	0.925449i	$0.623688\pi$
$828$	−212.786	−	119.608i	−0.256988	−	0.144454i
$829$	−473.091	+	473.091i	−0.570677	+	0.570677i	−0.932318	−	0.361640i	$-0.882217\pi$
$829$	−473.091	+	473.091i	−0.570677	+	0.570677i	0.361640	+	0.932318i	$0.382217\pi$
$830$	−14.5634	−	34.6015i	−0.0175463	−	0.0416886i
$831$	801.870	−	664.469i	0.964946	−	0.799602i
$832$	469.220	−	502.376i	0.563966	−	0.603817i
$833$	−432.736	+	688.695i	−0.519491	+	0.826765i
$834$	29.1278	−	920.135i	0.0349254	−	1.10328i
$835$	−3.45136	−	7.16681i	−0.00413336	−	0.00858301i
$836$	673.067	−	688.550i	0.805104	−	0.823625i
$837$	1057.65	+	59.1762i	1.26362	+	0.0707003i
$838$	−362.038	−	18.2675i	−0.432027	−	0.0217989i
$839$	193.119	+	551.901i	0.230177	+	0.657808i	0.999813	+	0.0193255i	$0.00615190\pi$
$839$	193.119	+	551.901i	0.230177	+	0.657808i	−0.769636	+	0.638483i	$0.779562\pi$
$840$	−0.709212	−	2.16676i	−0.000844300	−	0.00257947i
$841$	786.509	−	297.801i	0.935206	−	0.354103i
$842$	1434.99	+	235.429i	1.70427	+	0.279607i
$843$	314.746	+	144.361i	0.373365	+	0.171246i
$844$	−755.412	−	163.404i	−0.895037	−	0.193606i
$845$	−6.53161	−	8.19038i	−0.00772971	−	0.00969275i
$846$	696.764	+	450.423i	0.823598	+	0.532414i
$847$	82.7477	−	39.8492i	0.0976951	−	0.0470475i
$848$	365.244	+	1447.67i	0.430713	+	1.70716i
$849$	785.980	−	194.984i	0.925771	−	0.229663i
$850$	−51.4168	−	831.127i	−0.0604903	−	0.977797i
$851$	45.6134	−	404.830i	0.0535997	−	0.475711i
$852$	−835.768	−	490.656i	−0.980949	−	0.575887i
$853$	902.043	+	902.043i	1.05749	+	1.05749i	0.998243	+	0.0592519i	$0.0188715\pi$
$853$	902.043	+	902.043i	1.05749	+	1.05749i	0.0592519	+	0.998243i	$0.481128\pi$
$854$	−5.45688	+	13.3889i	−0.00638979	+	0.0156778i
$855$	−22.9735	−	7.08290i	−0.0268696	−	0.00828410i
$856$	52.1405	+	56.3798i	0.0609118	+	0.0658642i
$857$	−1436.35	−	327.837i	−1.67602	−	0.382540i	−0.724293	−	0.689492i	$-0.757834\pi$
$857$	−1436.35	−	327.837i	−1.67602	−	0.382540i	−0.951725	+	0.306952i	$0.900691\pi$
$858$	162.617	−	1122.69i	0.189531	−	1.30850i
$859$	−676.694	−	1076.95i	−0.787770	−	1.25373i	−0.963080	−	0.269215i	$-0.913236\pi$
$859$	−676.694	−	1076.95i	−0.787770	−	1.25373i	0.175310	−	0.984513i	$-0.443907\pi$
$860$	−16.5084	−	7.72004i	−0.0191958	−	0.00897679i
$861$	−100.790	−	60.7222i	−0.117061	−	0.0705252i
$862$	−497.067	−	439.149i	−0.576644	−	0.509454i
$863$	−657.719	−	524.513i	−0.762130	−	0.607779i	0.163353	−	0.986568i	$-0.447769\pi$
$863$	−657.719	−	524.513i	−0.762130	−	0.607779i	−0.925483	+	0.378789i	$0.876341\pi$
$864$	397.009	+	767.385i	0.459501	+	0.888177i
$865$	−35.4677	−	17.0804i	−0.0410032	−	0.0197461i
$866$	81.0542	+	144.707i	0.0935961	+	0.167098i
$867$	−19.6946	+	25.6701i	−0.0227158	+	0.0296080i
$868$	−0.867800	−	76.3165i	−0.000999769	−	0.0879222i
$869$	−230.524			−0.265275
$870$	24.9084	+	23.1240i	0.0286304	+	0.0265793i
$871$			393.712i			0.452022i
$872$	−635.053	−	96.7869i	−0.728272	−	0.110994i
$873$	495.349	−	74.7319i	0.567410	−	0.0856036i
$874$	90.6265	+	161.797i	0.103692	+	0.185122i
$875$	−2.05926	+	4.27610i	−0.00235344	+	0.00488697i
$876$	820.846	+	615.068i	0.937039	+	0.702132i
$877$	−284.142	+	356.303i	−0.323993	+	0.406275i	−0.916977	−	0.398940i	$-0.869378\pi$
$877$	−284.142	+	356.303i	−0.323993	+	0.406275i	0.592984	+	0.805214i	$0.297950\pi$
$878$	−16.3431	−	14.4388i	−0.0186140	−	0.0164451i
$879$	−940.150	−	566.407i	−1.06957	−	0.644376i
$880$	−39.7746	−	38.0055i	−0.0451984	−	0.0431880i
$881$	439.466	−	276.135i	0.498827	−	0.313434i	−0.259014	−	0.965874i	$-0.583397\pi$
$881$	439.466	−	276.135i	0.498827	−	0.313434i	0.757840	+	0.652440i	$0.226255\pi$
$882$	−693.237	+	538.382i	−0.785982	+	0.610411i
$883$	−146.447	+	641.625i	−0.165851	+	0.726642i	0.821775	+	0.569813i	$0.192984\pi$
$883$	−146.447	+	641.625i	−0.165851	+	0.726642i	−0.987626	+	0.156829i	$0.949873\pi$
$884$	−565.326	−	440.411i	−0.639510	−	0.498202i
$885$	−0.683483	−	1.35367i	−0.000772297	−	0.00152957i
$886$	216.547	−	531.314i	0.244409	−	0.599677i
$887$	291.549	−	291.549i	0.328692	−	0.328692i	−0.523397	−	0.852089i	$-0.675336\pi$
$887$	291.549	−	291.549i	0.328692	−	0.328692i	0.852089	+	0.523397i	$0.175336\pi$
$888$	−921.735	+	1108.93i	−1.03799	+	1.24880i
$889$	49.1441	+	5.53721i	0.0552802	+	0.00622859i
$890$	−1.62615	−	26.2860i	−0.00182714	−	0.0295348i
$891$	1260.76	+	665.886i	1.41500	+	0.747347i
$892$	−549.032	+	353.750i	−0.615507	+	0.396581i
$893$	−273.490	−	567.908i	−0.306260	−	0.635955i
$894$	−110.335	−	565.305i	−0.123417	−	0.632332i
$895$	−43.6168	+	34.7833i	−0.0487339	+	0.0388640i
$896$	53.2415	−	32.2553i	0.0594213	−	0.0359993i
$897$	198.595	+	91.0870i	0.221399	+	0.101546i
$898$	271.724	+	44.5798i	0.302588	+	0.0496435i
$899$	562.941	+	988.746i	0.626186	+	1.09983i
$900$	254.975	−	861.694i	0.283305	−	0.957438i
$901$	1469.12	−	514.068i	1.63055	−	0.570553i
$902$	−2835.70	−	143.082i	−3.14380	−	0.158628i
$903$	3.17490	−	33.8824i	0.00351594	−	0.0375220i
$904$	950.102	+	1291.78i	1.05100	+	1.42896i
$905$	30.6637	−	14.7668i	0.0338825	−	0.0163169i
$906$	421.343	+	13.3380i	0.465058	+	0.0147219i
$907$	−830.784	−	522.016i	−0.915969	−	0.575542i	−0.0104959	−	0.999945i	$-0.503341\pi$
$907$	−830.784	−	522.016i	−0.915969	−	0.575542i	−0.905473	+	0.424403i	$0.860484\pi$
$908$	−1124.62	−	113.780i	−1.23856	−	0.125308i
$909$	7.56632	−	101.153i	0.00832379	−	0.111280i
$910$	0.791636	+	1.88086i	0.000869930	+	0.00206688i
$911$	673.989	+	673.989i	0.739834	+	0.739834i	0.972546	−	0.232711i	$-0.0747598\pi$
$911$	673.989	+	673.989i	0.739834	+	0.739834i	−0.232711	+	0.972546i	$0.574760\pi$
$912$	46.3625	−	654.768i	0.0508360	−	0.717948i
$913$	558.686	−	1596.63i	0.611923	−	1.74878i
$914$	−108.062	−	58.9242i	−0.118230	−	0.0644685i
$915$	7.28716	−	4.77190i	0.00796411	−	0.00521519i
$916$	980.428	−	485.959i	1.07034	−	0.530523i
$917$	−9.54103	−	15.1845i	−0.0104046	−	0.0165588i
$918$	759.814	−	483.691i	0.827684	−	0.526897i
$919$	−1240.61	+	283.160i	−1.34995	+	0.308118i	−0.835542	−	0.549426i	$-0.814846\pi$
$919$	−1240.61	+	283.160i	−1.34995	+	0.308118i	−0.514411	+	0.857544i	$0.671989\pi$
$920$	9.18468	−	5.28266i	0.00998334	−	0.00574202i
$921$	−195.223	−	1482.07i	−0.211968	−	1.60920i
$922$	−232.204	−	789.105i	−0.251848	−	0.855862i
$923$	781.561	+	376.380i	0.846762	+	0.407779i
$924$	41.7624	−	93.8554i	0.0451974	−	0.101575i
$925$	1490.35	−	167.922i	1.61119	−	0.181537i
$926$	1619.31	−	284.614i	1.74872	−	0.307358i
$927$	−52.8533	−	1407.32i	−0.0570154	−	1.51815i
$928$	−461.020	+	805.385i	−0.496788	+	0.867872i
$929$		−	918.514i		−	0.988713i	−0.869259	−	0.494356i	$-0.835404\pi$
$929$		−	918.514i		−	0.988713i	0.869259	−	0.494356i	$-0.164596\pi$
$930$	−25.6829	+	38.1397i	−0.0276161	+	0.0410104i
$931$	662.655	−	74.6633i	0.711767	−	0.0801969i
$932$	174.551	+	481.216i	0.187287	+	0.516326i
$933$	52.5189	+	141.513i	0.0562904	+	0.151675i
$934$	228.879	+	777.806i	0.245053	+	0.832769i
$935$	−35.7573	+	44.8383i	−0.0382431	+	0.0479554i
$936$	−410.460	−	655.433i	−0.438526	−	0.700249i
$937$	−619.219	+	141.333i	−0.660853	+	0.150835i	−0.539777	−	0.841808i	$-0.681492\pi$
$937$	−619.219	+	141.333i	−0.660853	+	0.150835i	−0.121076	+	0.992643i	$0.538634\pi$
$938$	−9.67504	+	34.3150i	−0.0103145	+	0.0365832i
$939$	−1024.53	−	213.694i	−1.09108	−	0.227576i
$940$	−32.2673	+	15.9936i	−0.0343269	+	0.0170145i
$941$	352.159	−	1542.91i	0.374239	−	1.63965i	−0.340490	−	0.940248i	$-0.610593\pi$
$941$	352.159	−	1542.91i	0.374239	−	1.63965i	0.714729	−	0.699402i	$-0.246550\pi$
$942$	230.646	+	732.738i	0.244847	+	0.777853i
$943$	180.613	−	516.164i	0.191531	−	0.547363i
$944$	31.7764	−	26.5450i	0.0336614	−	0.0281197i
$945$	−2.56079	+	0.144344i	−0.00270983	+	0.000152745i
$946$	−318.552	−	756.854i	−0.336736	−	0.800057i
$947$	−1148.53	−	129.409i	−1.21281	−	0.136651i	−0.517707	−	0.855558i	$-0.673214\pi$
$947$	−1148.53	−	129.409i	−1.21281	−	0.136651i	−0.695106	+	0.718907i	$0.744643\pi$
$948$	−119.858	+	101.641i	−0.126433	+	0.107216i
$949$	−777.377	−	488.459i	−0.819154	−	0.514709i
$950$	−506.466	+	457.811i	−0.533122	+	0.481907i
$951$	−1315.02	−	432.618i	−1.38277	−	0.454908i
$952$	−38.4499	−	52.2775i	−0.0403886	−	0.0549133i
$953$	−220.559	+	175.890i	−0.231436	+	0.184564i	−0.732341	−	0.680938i	$-0.761572\pi$
$953$	−220.559	+	175.890i	−0.231436	+	0.184564i	0.500904	+	0.865503i	$0.333001\pi$
$954$	1679.52	+	21.6273i	1.76051	+	0.0226701i
$955$	46.5792	−	16.2988i	0.0487740	−	0.0170668i
$956$	−80.5193	+	238.786i	−0.0842252	+	0.249776i
$957$	133.900	+	1525.56i	0.139917	+	1.59410i
$958$	1704.02	+	279.566i	1.77872	+	0.291823i
$959$	−12.0454	+	4.21487i	−0.0125604	+	0.00439507i
$960$	−37.4375	−	2.22336i	−0.0389974	−	0.00231600i
$961$	−452.106	+	360.543i	−0.470454	+	0.375175i
$962$	740.891	−	1056.87i	0.770157	−	1.09862i
$963$	76.3760	−	40.3794i	0.0793105	−	0.0419308i
$964$	998.167	−	643.135i	1.03544	−	0.667153i
$965$	−8.20989	−	5.15862i	−0.00850766	−	0.00534572i
$966$	15.0707	+	12.8192i	0.0156012	+	0.0132704i
$967$	542.550	+	61.1307i	0.561065	+	0.0632169i	0.387943	−	0.921683i	$-0.373186\pi$
$967$	542.550	+	61.1307i	0.561065	+	0.0632169i	0.173123	+	0.984900i	$0.444614\pi$
$968$	−110.425	−	1506.76i	−0.114076	−	1.55657i
$969$	−684.175	+	12.8429i	−0.706063	+	0.0132537i
$970$	−8.20703	+	20.1366i	−0.00846086	+	0.0207594i
$971$	443.978	−	1268.82i	0.457238	−	1.30671i	−0.452587	−	0.891720i	$-0.649499\pi$
$971$	443.978	−	1268.82i	0.457238	−	1.30671i	0.909825	−	0.414992i	$-0.136215\pi$
$972$	949.117	−	209.667i	0.976458	−	0.215707i
$973$	−16.6042	+	72.7478i	−0.0170650	+	0.0747665i
$974$	1011.95	+	1409.16i	1.03896	+	1.44678i
$975$	−164.234	+	787.398i	−0.168445	+	0.807587i
$976$	171.955	+	164.307i	0.176183	+	0.168347i
$977$	55.5452	−	12.6778i	0.0568528	−	0.0129763i	−0.194000	−	0.981002i	$-0.562146\pi$
$977$	55.5452	−	12.6778i	0.0568528	−	0.0129763i	0.250853	+	0.968025i	$0.419289\pi$
$978$	−103.299	−	1279.57i	−0.105622	−	1.30836i
$979$	739.876	−	927.775i	0.755746	−	0.947676i
$980$	−4.69605	−	37.8094i	−0.00479189	−	0.0385811i
$981$	−288.904	+	662.425i	−0.294500	+	0.675255i
$982$	−635.174	−	1133.98i	−0.646816	−	1.15477i
$983$	360.350	−	40.6017i	0.366582	−	0.0413038i	0.0732474	−	0.997314i	$-0.476664\pi$
$983$	360.350	−	40.6017i	0.366582	−	0.0413038i	0.293334	+	0.956010i	$0.405235\pi$
$984$	−1537.48	+	1175.91i	−1.56248	+	1.19503i
$985$			2.79545i			0.00283802i
$986$	879.182	+	403.675i	0.891666	+	0.409407i
$987$	−48.4364	−	46.6514i	−0.0490743	−	0.0472659i
$988$	6.68050	+	587.500i	0.00676164	+	0.594635i
$989$	157.161	−	17.7078i	0.158909	−	0.0179047i
$990$	−52.8231	+	32.2498i	−0.0533567	+	0.0325756i
$991$	−386.517	−	186.137i	−0.390027	−	0.187827i	0.228585	−	0.973524i	$-0.426590\pi$
$991$	−386.517	−	186.137i	−0.390027	−	0.187827i	−0.618612	+	0.785697i	$0.712305\pi$
$992$	−1173.09	−	447.286i	−1.18255	−	0.450894i
$993$	−1448.76	+	190.835i	−1.45897	+	0.192180i
$994$	58.8699	+	52.0104i	0.0592253	+	0.0523244i
$995$	−36.0172	+	8.22069i	−0.0361982	+	0.00826200i
$996$	−413.495	−	1076.48i	−0.415155	−	1.08081i
$997$	580.771	+	924.292i	0.582519	+	0.927074i	0.999832	+	0.0183109i	$0.00582888\pi$
$997$	580.771	+	924.292i	0.582519	+	0.927074i	−0.417313	+	0.908763i	$0.637028\pi$
$998$	173.818	−	124.822i	0.174166	−	0.125072i
$999$	939.015	+	1322.84i	0.939955	+	1.32416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	348.3.v.a.11.6	✓	1392
3.2	odd	2	inner	348.3.v.a.11.111	yes	1392
4.3	odd	2	inner	348.3.v.a.11.99	yes	1392
12.11	even	2	inner	348.3.v.a.11.18	yes	1392
29.8	odd	28	inner	348.3.v.a.95.18	yes	1392
87.8	even	28	inner	348.3.v.a.95.99	yes	1392
116.95	even	28	inner	348.3.v.a.95.111	yes	1392
348.95	odd	28	inner	348.3.v.a.95.6	yes	1392

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
348.3.v.a.11.6	✓	1392	1.1	even	1	trivial
348.3.v.a.11.18	yes	1392	12.11	even	2	inner
348.3.v.a.11.99	yes	1392	4.3	odd	2	inner
348.3.v.a.11.111	yes	1392	3.2	odd	2	inner
348.3.v.a.95.6	yes	1392	348.95	odd	28	inner
348.3.v.a.95.18	yes	1392	29.8	odd	28	inner
348.3.v.a.95.99	yes	1392	87.8	even	28	inner
348.3.v.a.95.111	yes	1392	116.95	even	28	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	348.v (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.96981 + 0.346217i) q^{2} +(-2.38019 - 1.82612i) q^{3} +(3.76027 - 1.36396i) q^{4} +(0.175987 + 0.0847507i) q^{5} +(5.32074 + 2.77304i) q^{6} +(-0.380227 - 0.303221i) q^{7} +(-6.93477 + 3.98860i) q^{8} +(2.33057 + 8.69301i) q^{9} +O(q^{10})\)	\(q+(-1.96981 + 0.346217i) q^{2} +(-2.38019 - 1.82612i) q^{3} +(3.76027 - 1.36396i) q^{4} +(0.175987 + 0.0847507i) q^{5} +(5.32074 + 2.77304i) q^{6} +(-0.380227 - 0.303221i) q^{7} +(-6.93477 + 3.98860i) q^{8} +(2.33057 + 8.69301i) q^{9} +(-0.376002 - 0.106013i) q^{10} +(-9.36512 - 14.9045i) q^{11} +(-11.4409 - 3.62022i) q^{12} +(10.4717 + 2.39009i) q^{13} +(0.853953 + 0.465645i) q^{14} +(-0.264116 - 0.523095i) q^{15} +(12.2792 - 10.2577i) q^{16} +(-11.7944 - 11.7944i) q^{17} +(-7.60044 - 16.3167i) q^{18} +(-1.53113 + 13.5892i) q^{19} +(0.777353 + 0.0786466i) q^{20} +(0.351293 + 1.41606i) q^{21} +(23.6077 + 26.1166i) q^{22} +(-6.10902 + 2.94195i) q^{23} +(23.7897 + 3.17010i) q^{24} +(-15.5635 - 19.5160i) q^{25} +(-21.4546 - 1.08254i) q^{26} +(10.3273 - 24.9469i) q^{27} +(-1.84334 - 0.621577i) q^{28} +(28.5264 - 5.21975i) q^{29} +(0.701362 + 0.938954i) q^{30} +(12.9580 + 37.0318i) q^{31} +(-20.6363 + 24.4570i) q^{32} +(-4.92668 + 52.5773i) q^{33} +(27.3161 + 19.1492i) q^{34} +(-0.0412167 - 0.0855873i) q^{35} +(20.6205 + 29.5092i) q^{36} +(-31.9660 + 50.8735i) q^{37} +(-1.68877 - 27.2981i) q^{38} +(-20.5599 - 24.8114i) q^{39} +(-1.55846 + 0.114214i) q^{40} +(-57.0285 + 57.0285i) q^{41} +(-1.18224 - 2.66774i) q^{42} +(-22.0161 - 7.70376i) q^{43} +(-55.5445 - 43.2713i) q^{44} +(-0.326589 + 1.72737i) q^{45} +(11.0150 - 7.91012i) q^{46} +(-39.0281 + 24.5230i) q^{47} +(-47.9587 + 1.99192i) q^{48} +(-10.8509 - 47.5409i) q^{49} +(37.4137 + 33.0543i) q^{50} +(6.53488 + 49.6108i) q^{51} +(42.6363 - 5.29556i) q^{52} +(-40.4877 + 84.0735i) q^{53} +(-11.7057 + 52.7160i) q^{54} +(-0.384969 - 3.41669i) q^{55} +(3.84621 + 0.586192i) q^{56} +(28.4598 - 29.5487i) q^{57} +(-54.3843 + 20.1582i) q^{58} +2.58781 q^{59} +(-1.70663 - 1.60673i) q^{60} +(1.66431 + 14.7712i) q^{61} +(-38.3458 - 68.4592i) q^{62} +(1.74975 - 4.01199i) q^{63} +(32.1821 - 55.3201i) q^{64} +(1.64031 + 1.30810i) q^{65} +(-8.49857 - 105.273i) q^{66} +(8.15653 + 35.7361i) q^{67} +(-60.4371 - 28.2630i) q^{68} +(19.9130 + 4.15342i) q^{69} +(0.110821 + 0.154320i) q^{70} +(78.7376 + 17.9713i) q^{71} +(-50.8350 - 50.9883i) q^{72} +(-80.6798 - 28.2311i) q^{73} +(45.3534 - 111.278i) q^{74} +(1.40545 + 74.8723i) q^{75} +(12.7776 + 53.1873i) q^{76} +(-0.958485 + 8.50679i) q^{77} +(49.0892 + 41.7554i) q^{78} +(6.96752 - 11.0887i) q^{79} +(3.03033 - 0.764547i) q^{80} +(-70.1369 + 40.5194i) q^{81} +(92.5909 - 132.079i) q^{82} +(59.9157 + 75.1319i) q^{83} +(3.25241 + 4.84562i) q^{84} +(-1.07607 - 3.07524i) q^{85} +(46.0346 + 7.55257i) q^{86} +(-77.4300 - 39.6686i) q^{87} +(124.393 + 66.0056i) q^{88} +(22.2656 + 63.6315i) q^{89} +(0.0452713 - 3.51566i) q^{90} +(-3.25688 - 4.08400i) q^{91} +(-18.9589 + 19.3950i) q^{92} +(36.7821 - 111.805i) q^{93} +(68.3875 - 61.8177i) q^{94} +(-1.42115 + 2.26175i) q^{95} +(93.7796 - 20.5278i) q^{96} +(6.23212 - 55.3116i) q^{97} +(37.8336 + 89.8895i) q^{98} +(107.739 - 116.147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1392 q - 28 q^{4} - 14 q^{6} - 28 q^{9}+O(q^{10}) \) 1392 * q - 28 * q^4 - 14 * q^6 - 28 * q^9	\( 1392 q - 28 q^{4} - 14 q^{6} - 28 q^{9} - 8 q^{10} + 36 q^{12} - 56 q^{13} - 52 q^{16} - 32 q^{18} - 76 q^{21} - 28 q^{22} - 10 q^{24} - 1040 q^{25} + 272 q^{30} - 28 q^{33} - 28 q^{34} + 58 q^{36} - 80 q^{37} - 36 q^{40} - 14 q^{42} + 180 q^{45} + 1032 q^{46} - 216 q^{48} + 1088 q^{49} + 120 q^{52} - 10 q^{54} - 308 q^{58} + 240 q^{60} + 112 q^{61} - 1792 q^{64} + 92 q^{66} + 124 q^{69} - 1096 q^{70} + 148 q^{72} - 160 q^{73} + 68 q^{76} - 154 q^{78} - 180 q^{81} - 20 q^{82} + 72 q^{84} - 72 q^{85} + 760 q^{88} + 256 q^{90} - 28 q^{93} - 632 q^{94} - 812 q^{96} + 32 q^{97}+O(q^{100}) \) 1392 * q - 28 * q^4 - 14 * q^6 - 28 * q^9 - 8 * q^10 + 36 * q^12 - 56 * q^13 - 52 * q^16 - 32 * q^18 - 76 * q^21 - 28 * q^22 - 10 * q^24 - 1040 * q^25 + 272 * q^30 - 28 * q^33 - 28 * q^34 + 58 * q^36 - 80 * q^37 - 36 * q^40 - 14 * q^42 + 180 * q^45 + 1032 * q^46 - 216 * q^48 + 1088 * q^49 + 120 * q^52 - 10 * q^54 - 308 * q^58 + 240 * q^60 + 112 * q^61 - 1792 * q^64 + 92 * q^66 + 124 * q^69 - 1096 * q^70 + 148 * q^72 - 160 * q^73 + 68 * q^76 - 154 * q^78 - 180 * q^81 - 20 * q^82 + 72 * q^84 - 72 * q^85 + 760 * q^88 + 256 * q^90 - 28 * q^93 - 632 * q^94 - 812 * q^96 + 32 * q^97

Introduction

L-functions

Modular forms

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