LMFDB - Embedded newform 76.6.f.a.31.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(27,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("76.27");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.f (of order $6$, degree $2$, 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:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.10
Character	$\chi$	$=$	76.31
Dual form			76.6.f.a.27.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.70334 - 3.14303i) q^{2} +(7.75035 + 13.4240i) q^{3} +(12.2427 + 29.5654i) q^{4} +(-8.78700 - 15.2195i) q^{5} +(5.73951 - 87.4972i) q^{6} -77.0445i q^{7} +(35.3433 - 177.535i) q^{8} +(1.36406 - 2.36263i) q^{9} +O(q^{10})$	\(q+(-4.70334 - 3.14303i) q^{2} +(7.75035 + 13.4240i) q^{3} +(12.2427 + 29.5654i) q^{4} +(-8.78700 - 15.2195i) q^{5} +(5.73951 - 87.4972i) q^{6} -77.0445i q^{7} +(35.3433 - 177.535i) q^{8} +(1.36406 - 2.36263i) q^{9} +(-6.50720 + 99.2004i) q^{10} -67.5657i q^{11} +(-302.001 + 393.489i) q^{12} +(538.434 + 310.865i) q^{13} +(-242.153 + 362.366i) q^{14} +(136.205 - 235.914i) q^{15} +(-724.230 + 723.924i) q^{16} +(1125.58 + 1949.56i) q^{17} +(-13.8415 + 6.82494i) q^{18} +(-344.019 - 1535.50i) q^{19} +(342.395 - 446.121i) q^{20} +(1034.25 - 597.122i) q^{21} +(-212.361 + 317.784i) q^{22} +(1743.96 + 1006.88i) q^{23} +(2657.16 - 901.514i) q^{24} +(1408.08 - 2438.86i) q^{25} +(-1555.38 - 3154.42i) q^{26} +3808.96 q^{27} +(2277.85 - 943.236i) q^{28} +(4570.26 + 2638.64i) q^{29} +(-1382.10 + 681.485i) q^{30} -1021.36 q^{31} +(5681.61 - 1128.58i) q^{32} +(907.002 - 523.658i) q^{33} +(833.546 - 12707.2i) q^{34} +(-1172.58 + 676.990i) q^{35} +(86.5520 + 11.4041i) q^{36} +4516.66i q^{37} +(-3208.07 + 8303.22i) q^{38} +9637.26i q^{39} +(-3012.57 + 1022.10i) q^{40} +(5424.50 - 3131.83i) q^{41} +(-6741.17 - 442.198i) q^{42} +(-7439.38 + 4295.13i) q^{43} +(1997.61 - 827.189i) q^{44} -47.9441 q^{45} +(-5037.79 - 10217.0i) q^{46} +(-7786.40 - 4495.48i) q^{47} +(-15331.0 - 4111.40i) q^{48} +10871.2 q^{49} +(-14288.1 + 7045.16i) q^{50} +(-17447.3 + 30219.6i) q^{51} +(-2598.95 + 19724.9i) q^{52} +(1949.39 + 1125.48i) q^{53} +(-17914.8 - 11971.7i) q^{54} +(-1028.32 + 593.700i) q^{55} +(-13678.1 - 2723.00i) q^{56} +(17946.2 - 16518.8i) q^{57} +(-13202.2 - 26774.9i) q^{58} +(5922.01 + 10257.2i) q^{59} +(8642.41 + 1138.72i) q^{60} +(-3585.06 + 6209.50i) q^{61} +(4803.82 + 3210.18i) q^{62} +(-182.027 - 105.094i) q^{63} +(-30269.7 - 12549.4i) q^{64} -10926.3i q^{65} +(-5911.81 - 387.794i) q^{66} +(26378.3 - 45688.6i) q^{67} +(-43859.4 + 57146.2i) q^{68} +31214.6i q^{69} +(7642.84 + 501.344i) q^{70} +(23847.8 + 41305.6i) q^{71} +(-371.240 - 325.673i) q^{72} +(-18567.2 - 32159.3i) q^{73} +(14196.0 - 21243.3i) q^{74} +43652.4 q^{75} +(41185.9 - 28969.8i) q^{76} -5205.56 q^{77} +(30290.2 - 45327.3i) q^{78} +(-47435.6 - 82160.8i) q^{79} +(17381.6 + 4661.33i) q^{80} +(29189.3 + 50557.4i) q^{81} +(-35356.7 - 2319.28i) q^{82} -33741.0i q^{83} +(30316.2 + 23267.5i) q^{84} +(19780.9 - 34261.6i) q^{85} +(48489.6 + 3180.75i) q^{86} +81801.7i q^{87} +(-11995.3 - 2387.99i) q^{88} +(-16595.2 - 9581.25i) q^{89} +(225.497 + 150.690i) q^{90} +(23950.4 - 41483.4i) q^{91} +(-8417.87 + 63887.9i) q^{92} +(-7915.94 - 13710.8i) q^{93} +(22492.6 + 45616.6i) q^{94} +(-20346.6 + 18728.2i) q^{95} +(59184.6 + 67523.1i) q^{96} +(-9978.63 + 5761.16i) q^{97} +(-51130.7 - 34168.3i) q^{98} +(-159.633 - 92.1639i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 3 q^{2} - 11 q^{4} - 2 q^{5} - 27 q^{6} - 3588 q^{9}+O(q^{10}) $ 96 * q - 3 * q^2 - 11 * q^4 - 2 * q^5 - 27 * q^6 - 3588 * q^9	$ 96 q - 3 q^{2} - 11 q^{4} - 2 q^{5} - 27 q^{6} - 3588 q^{9} + 648 q^{10} - 354 q^{13} + 2154 q^{14} - 611 q^{16} - 1006 q^{17} + 10524 q^{20} + 7824 q^{21} + 93 q^{22} - 5311 q^{24} - 25002 q^{25} - 13428 q^{26} + 1556 q^{28} - 6 q^{29} - 12656 q^{30} - 30453 q^{32} + 8586 q^{33} + 30102 q^{34} - 2306 q^{36} + 29846 q^{38} - 1392 q^{40} + 29064 q^{41} + 18616 q^{42} + 9155 q^{44} + 13464 q^{45} + 38217 q^{48} - 116224 q^{49} + 36858 q^{52} + 26262 q^{53} - 26355 q^{54} + 53974 q^{57} - 112740 q^{58} - 108810 q^{60} - 77370 q^{61} - 106848 q^{62} + 337966 q^{64} + 166855 q^{66} + 175796 q^{68} + 148122 q^{70} - 259842 q^{72} - 52040 q^{73} + 103690 q^{74} - 194709 q^{76} + 197584 q^{77} + 253206 q^{78} - 171934 q^{80} - 313100 q^{81} + 63919 q^{82} - 161762 q^{85} - 38442 q^{86} + 10482 q^{89} - 372450 q^{90} + 64544 q^{92} + 94012 q^{93} + 537614 q^{96} + 177180 q^{97} - 509397 q^{98}+O(q^{100}) $ 96 * q - 3 * q^2 - 11 * q^4 - 2 * q^5 - 27 * q^6 - 3588 * q^9 + 648 * q^10 - 354 * q^13 + 2154 * q^14 - 611 * q^16 - 1006 * q^17 + 10524 * q^20 + 7824 * q^21 + 93 * q^22 - 5311 * q^24 - 25002 * q^25 - 13428 * q^26 + 1556 * q^28 - 6 * q^29 - 12656 * q^30 - 30453 * q^32 + 8586 * q^33 + 30102 * q^34 - 2306 * q^36 + 29846 * q^38 - 1392 * q^40 + 29064 * q^41 + 18616 * q^42 + 9155 * q^44 + 13464 * q^45 + 38217 * q^48 - 116224 * q^49 + 36858 * q^52 + 26262 * q^53 - 26355 * q^54 + 53974 * q^57 - 112740 * q^58 - 108810 * q^60 - 77370 * q^61 - 106848 * q^62 + 337966 * q^64 + 166855 * q^66 + 175796 * q^68 + 148122 * q^70 - 259842 * q^72 - 52040 * q^73 + 103690 * q^74 - 194709 * q^76 + 197584 * q^77 + 253206 * q^78 - 171934 * q^80 - 313100 * q^81 + 63919 * q^82 - 161762 * q^85 - 38442 * q^86 + 10482 * q^89 - 372450 * q^90 + 64544 * q^92 + 94012 * q^93 + 537614 * q^96 + 177180 * q^97 - 509397 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−4.70334	−	3.14303i	−0.831440	−	0.555614i
$2$	−4.70334	−	3.14303i	−0.831440	−	0.555614i
$3$	7.75035	+	13.4240i	0.497185	+	0.861150i	0.999995	−	0.00324702i	$-0.00103356\pi$
$3$	7.75035	+	13.4240i	0.497185	+	0.861150i	−0.502809	+	0.864397i	$0.667700\pi$
$4$	12.2427	+	29.5654i	0.382586	+	0.923920i
$5$	−8.78700	−	15.2195i	−0.157187	−	0.272255i	0.776666	−	0.629912i	$-0.216909\pi$
$5$	−8.78700	−	15.2195i	−0.157187	−	0.272255i	−0.933853	+	0.357657i	$0.883576\pi$
$6$	5.73951	−	87.4972i	0.0650874	−	0.992238i
$7$		−	77.0445i		−	0.594287i	−0.954833	−	0.297144i	$-0.903966\pi$
$7$		−	77.0445i		−	0.594287i	0.954833	−	0.297144i	$-0.0960340\pi$
$8$	35.3433	−	177.535i	0.195246	−	0.980754i
$9$	1.36406	−	2.36263i	0.00561343	−	0.00972275i
$10$	−6.50720	+	99.2004i	−0.0205776	+	0.313699i
$11$		−	67.5657i		−	0.168362i	−0.996450	−	0.0841811i	$-0.973173\pi$
$11$		−	67.5657i		−	0.168362i	0.996450	−	0.0841811i	$-0.0268274\pi$
$12$	−302.001	+	393.489i	−0.605418	+	0.788823i
$13$	538.434	+	310.865i	0.883638	+	0.510168i	0.871856	−	0.489762i	$-0.162916\pi$
$13$	538.434	+	310.865i	0.883638	+	0.510168i	0.0117816	+	0.999931i	$0.496250\pi$
$14$	−242.153	+	362.366i	−0.330194	+	0.494114i
$15$	136.205	−	235.914i	0.156302	−	0.270723i
$16$	−724.230	+	723.924i	−0.707256	+	0.706957i
$17$	1125.58	+	1949.56i	0.944612	+	1.63612i	0.756526	+	0.653964i	$0.226895\pi$
$17$	1125.58	+	1949.56i	0.944612	+	1.63612i	0.188087	+	0.982152i	$0.439771\pi$
$18$	−13.8415	+	6.82494i	−0.0100693	+	0.00496498i
$19$	−344.019	−	1535.50i	−0.218624	−	0.975809i
$19$	−344.019	−	1535.50i	−0.218624	−	0.975809i
$20$	342.395	−	446.121i	0.191405	−	0.249389i
$21$	1034.25	−	597.122i	0.511771	−	0.295471i
$22$	−212.361	+	317.784i	−0.0935444	+	0.139983i
$23$	1743.96	+	1006.88i	0.687412	+	0.396877i	0.802642	−	0.596461i	$-0.203427\pi$
$23$	1743.96	+	1006.88i	0.687412	+	0.396877i	−0.115230	+	0.993339i	$0.536760\pi$
$24$	2657.16	−	901.514i	0.941650	−	0.319481i
$25$	1408.08	−	2438.86i	0.450585	−	0.780436i
$26$	−1555.38	−	3154.42i	−0.451235	−	0.915136i
$27$	3808.96			1.00553
$28$	2277.85	−	943.236i	0.549074	−	0.227366i
$29$	4570.26	+	2638.64i	1.00913	+	0.582620i	0.910936	−	0.412547i	$-0.135361\pi$
$29$	4570.26	+	2638.64i	1.00913	+	0.582620i	0.0981919	+	0.995167i	$0.468694\pi$
$30$	−1382.10	+	681.485i	−0.280373	+	0.138246i
$31$	−1021.36			−0.190887			−0.0954435	−	0.995435i	$-0.530427\pi$
$31$	−1021.36			−0.190887			−0.0954435	+	0.995435i	$0.530427\pi$
$32$	5681.61	−	1128.58i	0.980837	−	0.194831i
$33$	907.002	−	523.658i	0.144985	−	0.0837072i
$34$	833.546	−	12707.2i	0.123661	−	1.88517i
$35$	−1172.58	+	676.990i	−0.161798	+	0.0934140i
$36$	86.5520	+	11.4041i	0.0111307	+	0.00146658i
$37$			4516.66i			0.542391i	0.962524	+	0.271196i	$0.0874190\pi$
$37$			4516.66i			0.542391i	−0.962524	+	0.271196i	$0.912581\pi$
$38$	−3208.07	+	8303.22i	−0.360400	+	0.932798i
$39$			9637.26i			1.01459i
$40$	−3012.57	+	1022.10i	−0.297706	+	0.101005i
$41$	5424.50	−	3131.83i	0.503964	−	0.290964i	−0.226385	−	0.974038i	$-0.572691\pi$
$41$	5424.50	−	3131.83i	0.503964	−	0.290964i	0.730349	+	0.683074i	$0.239357\pi$
$42$	−6741.17	−	442.198i	−0.589674	−	0.0386806i
$43$	−7439.38	+	4295.13i	−0.613572	+	0.354246i	−0.774362	−	0.632743i	$-0.781929\pi$
$43$	−7439.38	+	4295.13i	−0.613572	+	0.354246i	0.160790	+	0.986989i	$0.448596\pi$
$44$	1997.61	−	827.189i	0.155553	−	0.0644130i
$45$	−47.9441			−0.00352943
$46$	−5037.79	−	10217.0i	−0.351031	−	0.711916i
$47$	−7786.40	−	4495.48i	−0.514152	−	0.296846i	0.220386	−	0.975413i	$-0.429268\pi$
$47$	−7786.40	−	4495.48i	−0.514152	−	0.296846i	−0.734539	+	0.678567i	$0.762601\pi$
$48$	−15331.0	−	4111.40i	−0.960434	−	0.257565i
$49$	10871.2			0.646823
$50$	−14288.1	+	7045.16i	−0.808255	+	0.398534i
$51$	−17447.3	+	30219.6i	−0.939295	+	1.62691i
$52$	−2598.95	+	19724.9i	−0.133288	+	1.01159i
$53$	1949.39	+	1125.48i	0.0953257	+	0.0550363i	0.546905	−	0.837195i	$-0.315806\pi$
$53$	1949.39	+	1125.48i	0.0953257	+	0.0550363i	−0.451579	+	0.892231i	$0.649139\pi$
$54$	−17914.8	−	11971.7i	−0.836042	−	0.558689i
$55$	−1028.32	+	593.700i	−0.0458375	+	0.0264643i
$56$	−13678.1	−	2723.00i	−0.582850	−	0.116032i
$57$	17946.2	−	16518.8i	0.731621	−	0.673426i
$58$	−13202.2	−	26774.9i	−0.515318	−	1.04510i
$59$	5922.01	+	10257.2i	0.221482	+	0.383619i	0.955258	−	0.295773i	$-0.0955772\pi$
$59$	5922.01	+	10257.2i	0.221482	+	0.383619i	−0.733776	+	0.679391i	$0.762244\pi$
$60$	8642.41	+	1138.72i	0.309925	+	0.0408357i
$61$	−3585.06	+	6209.50i	−0.123359	+	0.213664i	−0.921090	−	0.389349i	$-0.872700\pi$
$61$	−3585.06	+	6209.50i	−0.123359	+	0.213664i	0.797731	+	0.603013i	$0.206033\pi$
$62$	4803.82	+	3210.18i	0.158711	+	0.106060i
$63$	−182.027	−	105.094i	−0.00577810	−	0.00333599i
$64$	−30269.7	−	12549.4i	−0.923758	−	0.382976i
$65$		−	10926.3i		−	0.320767i
$66$	−5911.81	−	387.794i	−0.167055	−	0.0109583i
$67$	26378.3	−	45688.6i	0.717893	−	1.24343i	−0.243939	−	0.969790i	$-0.578440\pi$
$67$	26378.3	−	45688.6i	0.717893	−	1.24343i	0.961833	−	0.273637i	$-0.0882268\pi$
$68$	−43859.4	+	57146.2i	−1.15025	+	1.49870i
$69$			31214.6i			0.789287i
$70$	7642.84	+	501.344i	0.186427	+	0.0122290i
$71$	23847.8	+	41305.6i	0.561439	+	0.972440i	0.997371	+	0.0724610i	$0.0230853\pi$
$71$	23847.8	+	41305.6i	0.561439	+	0.972440i	−0.435933	+	0.899979i	$0.643581\pi$
$72$	−371.240	−	325.673i	−0.00843963	−	0.00740372i
$73$	−18567.2	−	32159.3i	−0.407793	−	0.706318i	0.586849	−	0.809696i	$-0.300368\pi$
$73$	−18567.2	−	32159.3i	−0.407793	−	0.706318i	−0.994642	+	0.103378i	$0.967035\pi$
$74$	14196.0	−	21243.3i	0.301360	−	0.450966i
$75$	43652.4			0.896096
$76$	41185.9	−	28969.8i	0.817927	−	0.575322i
$77$	−5205.56			−0.100055
$78$	30290.2	−	45327.3i	0.563722	−	0.843574i
$79$	−47435.6	−	82160.8i	−0.855138	−	1.48114i	−0.876517	−	0.481371i	$-0.840139\pi$
$79$	−47435.6	−	82160.8i	−0.855138	−	1.48114i	0.0213786	−	0.999771i	$-0.493194\pi$
$80$	17381.6	+	4661.33i	0.303644	+	0.0814300i
$81$	29189.3	+	50557.4i	0.494324	+	0.856193i
$82$	−35356.7	−	2319.28i	−0.580680	−	0.0380906i
$83$		−	33741.0i		−	0.537604i	−0.963196	−	0.268802i	$-0.913372\pi$
$83$		−	33741.0i		−	0.537604i	0.963196	−	0.268802i	$-0.0866277\pi$
$84$	30316.2	+	23267.5i	0.468788	+	0.359792i
$85$	19780.9	−	34261.6i	0.296961	−	0.514352i
$86$	48489.6	+	3180.75i	0.706973	+	0.0463750i
$87$			81801.7i			1.15868i
$88$	−11995.3	−	2387.99i	−0.165122	−	0.0328720i
$89$	−16595.2	−	9581.25i	−0.222079	−	0.128218i	0.384833	−	0.922986i	$-0.374259\pi$
$89$	−16595.2	−	9581.25i	−0.222079	−	0.128218i	−0.606913	+	0.794769i	$0.707592\pi$
$90$	225.497	+	150.690i	0.00293451	+	0.00196100i
$91$	23950.4	−	41483.4i	0.303187	−	0.525134i
$92$	−8417.87	+	63887.9i	−0.103689	+	0.786953i
$93$	−7915.94	−	13710.8i	−0.0949063	−	0.164382i
$94$	22492.6	+	45616.6i	0.262555	+	0.532480i
$95$	−20346.6	+	18728.2i	−0.231304	+	0.212906i
$96$	59184.6	+	67523.1i	0.655437	+	0.747781i
$97$	−9978.63	+	5761.16i	−0.107682	+	0.0621700i	−0.552874	−	0.833265i	$-0.686469\pi$
$97$	−9978.63	+	5761.16i	−0.107682	+	0.0621700i	0.445192	+	0.895435i	$0.353135\pi$
$98$	−51130.7	−	34168.3i	−0.537795	−	0.359384i
$99$	−159.633	−	92.1639i	−0.00163694	−	0.000945089i
$100$	89344.7	+	11772.1i	0.893447	+	0.117721i
$101$	−69628.8	+	120601.i	−0.679181	+	1.17638i	0.296047	+	0.955174i	$0.404332\pi$
$101$	−69628.8	+	120601.i	−0.679181	+	1.17638i	−0.975228	+	0.221203i	$0.929002\pi$
$102$	177041.	−	87295.5i	1.68490	−	0.830790i
$103$	−65055.7			−0.604216			−0.302108	−	0.953274i	$-0.597690\pi$
$103$	−65055.7			−0.604216			−0.302108	+	0.953274i	$0.597690\pi$
$104$	74219.6	−	84604.2i	0.672876	−	0.767023i
$105$	−18175.8	−	10493.8i	−0.160887	−	0.0928882i
$106$	−5631.23	−	11420.5i	−0.0486786	−	0.0987237i
$107$	−76328.6			−0.644507			−0.322254	−	0.946653i	$-0.604440\pi$
$107$	−76328.6			−0.644507			−0.322254	+	0.946653i	$0.604440\pi$
$108$	46632.1	+	112614.i	0.384703	+	0.929033i
$109$	−131111.	+	75697.2i	−1.05700	+	0.610258i	−0.924601	−	0.380938i	$-0.875601\pi$
$109$	−131111.	+	75697.2i	−1.05700	+	0.610258i	−0.132398	+	0.991197i	$0.542268\pi$
$110$	6702.54	+	439.664i	0.0528151	+	0.00346449i
$111$	−60631.6	+	35005.7i	−0.467080	+	0.269669i
$112$	55774.4	+	55797.9i	0.420136	+	0.420313i
$113$		−	189550.i		−	1.39646i	−0.715874	−	0.698229i	$-0.753972\pi$
$113$		−	189550.i		−	1.39646i	0.715874	−	0.698229i	$-0.246028\pi$
$114$	−136326.	+	21287.7i	−0.982465	+	0.153415i
$115$		−	35389.7i		−	0.249535i
$116$	−22060.1	+	167426.i	−0.152217	+	1.15526i
$117$	1468.92	−	848.080i	0.00992048	−	0.00572759i
$118$	4385.53	−	66856.2i	0.0289946	−	0.442015i
$119$	150203.	−	86719.6i	0.972323	−	0.561371i
$120$	−37069.1	−	32519.1i	−0.234995	−	0.206151i
$121$	156486.			0.971654
$122$	36378.4	−	17937.4i	0.221281	−	0.109109i
$123$	84083.5	+	48545.6i	0.501127	+	0.289326i
$124$	−12504.3	−	30197.1i	−0.0730307	−	0.176364i
$125$	−104410.			−0.597677
$126$	525.824	+	1066.41i	0.00295063	+	0.00598407i
$127$	151316.	−	262088.i	0.832485	−	1.44191i	−0.0635762	−	0.997977i	$-0.520251\pi$
$127$	151316.	−	262088.i	0.832485	−	1.44191i	0.896062	−	0.443930i	$-0.146416\pi$
$128$	102926.	+	154162.i	0.555263	+	0.831675i
$129$	−115316.	−	66577.5i	−0.610118	−	0.352252i
$130$	−34341.6	+	51390.0i	−0.178223	+	0.266698i
$131$	−5181.34	+	2991.45i	−0.0263793	+	0.0152301i	−0.513132	−	0.858310i	$-0.671515\pi$
$131$	−5181.34	+	2991.45i	−0.0263793	+	0.0152301i	0.486752	+	0.873540i	$0.338181\pi$
$132$	26586.4	+	20404.9i	0.132808	+	0.101929i
$133$	−118302.	+	26504.8i	−0.579911	+	0.129926i
$134$	−267667.	+	131981.i	−1.28775	+	0.634964i
$135$	−33469.3	−	57970.6i	−0.158057	−	0.273762i
$136$	385898.	−	130926.i	1.78906	−	0.606988i
$137$	−110125.	+	190743.i	−0.501286	+	0.868253i	0.498713	+	0.866767i	$0.333806\pi$
$137$	−110125.	+	190743.i	−0.501286	+	0.868253i	−0.999999	+	0.00148602i	$0.999527\pi$
$138$	98108.3	−	146813.i	0.438539	−	0.656245i
$139$	−46053.6	−	26589.1i	−0.202175	−	0.116726i	0.395495	−	0.918468i	$-0.370573\pi$
$139$	−46053.6	−	26589.1i	−0.202175	−	0.116726i	−0.597669	+	0.801743i	$0.703906\pi$
$140$	−34371.1	−	26379.7i	−0.148209	−	0.113749i
$141$		−	139366.i		−	0.590350i
$142$	17660.5	−	269228.i	0.0734989	−	1.12047i
$143$	21003.8	−	36379.7i	0.0858931	−	0.148771i
$144$	722.467	+	2698.57i	0.00290343	+	0.0108449i
$145$		−	92743.1i		−	0.366321i
$146$	−13749.9	+	209614.i	−0.0533849	+	0.813836i
$147$	84255.3	+	145934.i	0.321591	+	0.557012i
$148$	−133537.	+	55296.3i	−0.501126	+	0.207511i
$149$	−131395.	−	227583.i	−0.484857	−	0.839797i	0.514991	−	0.857195i	$-0.327795\pi$
$149$	−131395.	−	227583.i	−0.484857	−	0.839797i	−0.999849	+	0.0173980i	$0.994462\pi$
$150$	−205312.	−	137201.i	−0.745051	−	0.497884i
$151$	−148656.			−0.530566			−0.265283	−	0.964171i	$-0.585465\pi$
$151$	−148656.			−0.530566			−0.265283	+	0.964171i	$0.585465\pi$
$152$	−284764.	+	6806.15i	−0.999714	+	0.0238942i
$153$	6141.45			0.0212101
$154$	24483.5	+	16361.2i	0.0831901	+	0.0555922i
$155$	8974.73	+	15544.7i	0.0300049	+	0.0519700i
$156$	−284930.	+	117986.i	−0.937403	+	0.388169i
$157$	219910.	+	380894.i	0.712024	+	1.23326i	0.964096	+	0.265554i	$0.0855548\pi$
$157$	219910.	+	380894.i	0.712024	+	1.23326i	−0.252072	+	0.967709i	$0.581112\pi$
$158$	−35128.3	+	535521.i	−0.111948	+	1.70661i
$159$			34891.6i			0.109453i
$160$	−67100.9	−	76554.7i	−0.207218	−	0.236413i
$161$	77574.2	−	134363.i	0.235859	−	0.408520i
$162$	21616.1	−	329531.i	0.0647128	−	0.986527i
$163$			185957.i			0.548206i	0.961700	+	0.274103i	$0.0883809\pi$
$163$			185957.i			0.548206i	−0.961700	+	0.274103i	$0.911619\pi$
$164$	159005.	+	122035.i	0.461637	+	0.354304i
$165$	−15939.7	−	9202.77i	−0.0455795	−	0.0263153i
$166$	−106049.	+	158695.i	−0.298700	+	0.446985i
$167$	−210812.	+	365136.i	−0.584929	+	1.01313i	0.409955	+	0.912106i	$0.365544\pi$
$167$	−210812.	+	365136.i	−0.584929	+	1.01313i	−0.994884	+	0.101022i	$0.967789\pi$
$168$	−69456.7	−	204719.i	−0.189863	−	0.559611i
$169$	7627.72	+	13211.6i	0.0205437	+	0.0355827i
$170$	−200721.	+	98971.7i	−0.532686	+	0.262657i
$171$	−4097.07	−	1281.73i	−0.0107148	−	0.00335201i
$172$	−218066.	−	167364.i	−0.562039	−	0.431362i
$173$	−21745.6	+	12554.8i	−0.0552402	+	0.0318929i	−0.527366	−	0.849638i	$-0.676820\pi$
$173$	−21745.6	+	12554.8i	−0.0552402	+	0.0318929i	0.472126	+	0.881531i	$0.343487\pi$
$174$	257105.	−	384741.i	0.643780	−	0.963374i
$175$	−187901.	−	108485.i	−0.463803	−	0.267777i
$176$	48912.4	+	48933.1i	0.119025	+	0.119075i
$177$	−91795.3	+	158994.i	−0.220235	+	0.381459i
$178$	47938.7	+	97223.1i	0.113406	+	0.229996i
$179$	−17513.1			−0.0408535			−0.0204268	−	0.999791i	$-0.506502\pi$
$179$	−17513.1			−0.0408535			−0.0204268	+	0.999791i	$0.506502\pi$
$180$	−586.968	−	1417.49i	−0.00135031	−	0.00326091i
$181$	72289.0	+	41736.1i	0.164012	+	0.0946924i	0.579759	−	0.814788i	$-0.303147\pi$
$181$	72289.0	+	41736.1i	0.164012	+	0.0946924i	−0.415747	+	0.909480i	$0.636480\pi$
$182$	−243030.	+	119833.i	−0.543854	+	0.268163i
$183$	−111142.			−0.245330
$184$	240394.	−	274029.i	0.523454	−	0.596694i
$185$	68741.4	−	39687.9i	0.147669	−	0.0852567i
$186$	−5862.14	+	89366.5i	−0.0124243	+	0.189405i
$187$	131723.	−	76050.5i	0.275460	−	0.159037i
$188$	37583.9	−	285245.i	0.0775546	−	0.588605i
$189$		−	293459.i		−	0.597576i
$190$	154560.	−	24135.1i	0.310609	−	0.0485025i
$191$			941340.i			1.86708i	0.358472	+	0.933540i	$0.383298\pi$
$191$			941340.i			1.86708i	−0.358472	+	0.933540i	$0.616702\pi$
$192$	−66138.1	−	503603.i	−0.129479	−	0.985905i
$193$	554750.	−	320285.i	1.07202	−	0.618933i	0.143290	−	0.989681i	$-0.454232\pi$
$193$	554750.	−	320285.i	1.07202	−	0.618933i	0.928734	+	0.370748i	$0.120899\pi$
$194$	65040.3	+	4266.42i	0.124073	+	0.00813878i
$195$	146675.	−	84682.6i	0.276228	−	0.159481i
$196$	133093.	+	321410.i	0.247465	+	0.597613i
$197$	720073.			1.32194			0.660968	−	0.750414i	$-0.270146\pi$
$197$	720073.			1.32194			0.660968	+	0.750414i	$0.270146\pi$
$198$	461.132	+	935.208i	0.000835915	+	0.00169529i
$199$	−603659.	−	348522.i	−1.08058	−	0.623876i	−0.149530	−	0.988757i	$-0.547776\pi$
$199$	−603659.	−	348522.i	−1.08058	−	0.623876i	−0.931054	+	0.364881i	$0.881110\pi$
$200$	−383218.	−	336181.i	−0.677441	−	0.594290i
$201$	817765.			1.42770
$202$	706539.	−	348380.i	1.21831	−	0.600724i
$203$	203293.	−	352114.i	0.346244	−	0.599712i
$204$	−1.10706e6	−	145866.i	−1.86249	−	0.245402i
$205$	−95330.1	−	55038.9i	−0.158433	−	0.0914713i
$206$	305979.	+	204472.i	0.502369	+	0.335711i
$207$	4757.75	−	2746.89i	0.00771748	−	0.00445569i
$208$	−614993.	+	164648.i	−0.985626	+	0.263874i
$209$	−103747.	+	23243.9i	−0.164289	+	0.0368081i
$210$	52504.7	+	106483.i	0.0821580	+	0.166622i
$211$	552464.	+	956896.i	0.854275	+	1.47965i	0.877316	+	0.479914i	$0.159332\pi$
$211$	552464.	+	956896.i	0.854275	+	1.47965i	−0.0230403	+	0.999735i	$0.507335\pi$
$212$	−9409.47	+	71413.7i	−0.0143789	+	0.109129i
$213$	−369658.	+	640266.i	−0.558278	+	0.966966i
$214$	358999.	+	239903.i	0.535869	+	0.358097i
$215$	130740.	+	75482.6i	0.192891	+	0.111366i
$216$	134621.	−	676225.i	0.196326	−	0.986182i
$217$			78690.5i			0.113442i
$218$	854580.	+	56057.5i	1.21790	+	0.0798900i
$219$	287805.	−	498493.i	0.405497	−	0.702342i
$220$	−30142.4	−	23134.2i	−0.0419877	−	0.0322253i
$221$			1.39961e6i			1.92765i
$222$	395195.	+	25923.4i	0.538181	+	0.0353028i
$223$	−363165.	−	629020.i	−0.489037	−	0.847037i	0.510883	−	0.859650i	$-0.329318\pi$
$223$	−363165.	−	629020.i	−0.489037	−	0.847037i	−0.999920	+	0.0126128i	$0.995985\pi$
$224$	−86951.0	−	437737.i	−0.115786	−	0.582899i
$225$	−3841.41	−	6653.53i	−0.00505865	−	0.00876184i
$226$	−595762.	+	891518.i	−0.775892	+	1.16107i
$227$	345997.			0.445665			0.222832	−	0.974857i	$-0.428470\pi$
$227$	345997.			0.445665			0.222832	+	0.974857i	$0.428470\pi$
$228$	708096.	+	328354.i	0.902100	+	0.418316i
$229$	627836.			0.791148			0.395574	−	0.918434i	$-0.370546\pi$
$229$	627836.			0.791148			0.395574	+	0.918434i	$0.370546\pi$
$230$	−111231.	+	166450.i	−0.138645	+	0.207474i
$231$	−40344.9	−	69879.5i	−0.0497461	−	0.0861628i
$232$	629981.	−	718126.i	0.768436	−	0.875953i
$233$	656862.	+	1.13772e6i	0.792655	+	1.37292i	0.924318	+	0.381624i	$0.124635\pi$
$233$	656862.	+	1.13772e6i	0.792655	+	1.37292i	−0.131663	+	0.991295i	$0.542032\pi$
$234$	−9574.35	−	628.044i	−0.0114306	−	0.000749809i
$235$			158007.i			0.186641i
$236$	−230758.	+	300663.i	−0.269697	+	0.351399i
$237$	735285.	−	1.27355e6i	0.850324	−	1.47280i
$238$	−979016.	−	64220.1i	−1.12033	−	0.0734900i
$239$		−	362958.i		−	0.411019i	−0.978655	−	0.205510i	$-0.934115\pi$
$239$		−	362958.i		−	0.411019i	0.978655	−	0.205510i	$-0.0658852\pi$
$240$	72139.9	+	269458.i	0.0808440	+	0.301969i
$241$	−897929.	−	518420.i	−0.995863	−	0.574962i	−0.0888413	−	0.996046i	$-0.528316\pi$
$241$	−897929.	−	518420.i	−0.995863	−	0.574962i	−0.907022	+	0.421084i	$0.861650\pi$
$242$	−736006.	−	491840.i	−0.807872	−	0.539865i
$243$	10333.6	−	17898.4i	0.0112263	−	0.0194446i
$244$	−227478.	−	29972.5i	−0.244604	−	0.0322291i
$245$	−95524.9	−	165454.i	−0.101672	−	0.176101i
$246$	−242893.	−	492603.i	−0.255904	−	0.518991i
$247$	292101.	−	933707.i	0.304642	−	0.973797i
$248$	−36098.4	+	181328.i	−0.0372699	+	0.187213i
$249$	452939.	−	261504.i	0.462957	−	0.267289i
$250$	491075.	+	328163.i	0.496933	+	0.332078i
$251$	470315.	+	271536.i	0.471199	+	0.272047i	0.716741	−	0.697339i	$-0.245633\pi$
$251$	470315.	+	271536.i	0.471199	+	0.272047i	−0.245543	+	0.969386i	$0.578966\pi$
$252$	878.623	−	6668.35i	0.000871568	−	0.00661481i
$253$	68030.3	−	117832.i	0.0668191	−	0.115734i
$254$	−1.53544e6	+	757095.i	−1.49331	+	0.736319i
$255$	613237.			0.590579
$256$	443.402	−	1.04858e6i	0.000422861	−	1.00000i
$257$	−1.63112e6	−	941728.i	−1.54047	−	0.889391i	−0.998809	−	0.0487946i	$-0.984462\pi$
$257$	−1.63112e6	−	941728.i	−1.54047	−	0.889391i	−0.541662	−	0.840597i	$-0.682205\pi$
$258$	333113.	+	675577.i	0.311561	+	0.631867i
$259$	347983.			0.322336
$260$	323041.	−	133768.i	0.296363	−	0.122721i
$261$	12468.3	−	7198.56i	0.0113293	−	0.00654100i
$262$	33771.8	+	2215.31i	0.0303949	+	0.00199380i
$263$	−282697.	+	163215.i	−0.252018	+	0.145503i	−0.620688	−	0.784058i	$-0.713147\pi$
$263$	−282697.	+	163215.i	−0.252018	+	0.145503i	0.368670	+	0.929560i	$0.379813\pi$
$264$	−60911.4	−	179533.i	−0.0537885	−	0.158538i
$265$		−	39558.5i		−	0.0346039i
$266$	639717.	+	247164.i	0.554350	+	0.214181i
$267$		−	297032.i		−	0.254991i
$268$	1.67375e6	+	220533.i	1.42348	+	0.187558i
$269$	−259798.	+	149994.i	−0.218904	+	0.126385i	−0.605443	−	0.795889i	$-0.707004\pi$
$269$	−259798.	+	149994.i	−0.218904	+	0.126385i	0.386538	+	0.922273i	$0.373671\pi$
$270$	−24785.7	+	377850.i	−0.0206915	+	0.315435i
$271$	−1.64828e6	+	951638.i	−1.36336	+	0.787133i	−0.990069	−	0.140583i	$-0.955102\pi$
$271$	−1.64828e6	+	951638.i	−1.36336	+	0.787133i	−0.373286	+	0.927716i	$0.621769\pi$
$272$	−2.22651e6	−	597097.i	−1.82475	−	0.489353i
$273$	742497.			0.602960
$274$	1.11747e6	−	551000.i	0.899204	−	0.443379i
$275$	−164783.	−	95137.7i	−0.131396	−	0.0758614i
$276$	−922873.	+	382152.i	−0.729238	+	0.301970i
$277$	−1.31044e6			−1.02617			−0.513083	−	0.858339i	$-0.671497\pi$
$277$	−1.31044e6			−1.02617			−0.513083	+	0.858339i	$0.671497\pi$
$278$	133035.	+	269805.i	0.103242	+	0.209381i
$279$	−1393.21	+	2413.10i	−0.00107153	+	0.00185595i
$280$	78746.9	+	232102.i	0.0600259	+	0.176923i
$281$	−1.60615e6	−	927312.i	−1.21345	−	0.700584i	−0.249939	−	0.968262i	$-0.580410\pi$
$281$	−1.60615e6	−	927312.i	−1.21345	−	0.700584i	−0.963509	+	0.267678i	$0.913744\pi$
$282$	−438032.	+	655486.i	−0.328007	+	0.490841i
$283$	−1.47700e6	+	852748.i	−1.09626	+	0.632929i	−0.935237	−	0.354021i	$-0.884814\pi$
$283$	−1.47700e6	+	852748.i	−1.09626	+	0.632929i	−0.161027	+	0.986950i	$0.551481\pi$
$284$	−929256.	+	1.21076e6i	−0.683659	+	0.890766i
$285$	−409102.	−	127983.i	−0.298345	−	0.0933342i
$286$	−213130.	+	105090.i	−0.154074	+	0.0759709i
$287$	−241290.	−	417927.i	−0.172916	−	0.299499i
$288$	5083.66	−	14963.0i	0.00361157	−	0.0106301i
$289$	−1.82393e6	+	3.15913e6i	−1.28458	+	2.22497i
$290$	−291494.	+	436202.i	−0.203533	+	0.304574i
$291$	−154676.	−	89302.1i	−0.107075	−	0.0618200i
$292$	723492.	−	942666.i	0.496565	−	0.646995i
$293$		−	2.70650e6i		−	1.84178i	−0.389819	−	0.920892i	$-0.627462\pi$
$293$		−	2.70650e6i		−	1.84178i	0.389819	−	0.920892i	$-0.372538\pi$
$294$	62395.1	−	951195.i	0.0421000	−	0.641802i
$295$	104073.	−	180260.i	0.0696281	−	0.120599i
$296$	801867.	+	159633.i	0.531953	+	0.105900i
$297$		−	257355.i		−	0.169294i
$298$	−97304.6	+	1.48338e6i	−0.0634735	+	0.967635i
$299$	626005.	+	1.08427e6i	0.404949	+	0.701392i
$300$	534425.	+	1.29060e6i	0.342834	+	0.827921i
$301$	330916.	+	573163.i	0.210524	+	0.364638i
$302$	699178.	+	467229.i	0.441134	+	0.294790i
$303$	−2.15859e6			−1.35072
$304$	1.36073e6	+	863009.i	0.844479	+	0.535589i
$305$	126008.			0.0775617
$306$	−28885.3	−	19302.7i	−0.0176349	−	0.0117846i
$307$	540.216	+	935.682i	0.000327131	+	0.000566607i	0.866189	−	0.499717i	$-0.166563\pi$
$307$	540.216	+	935.682i	0.000327131	+	0.000566607i	−0.865862	+	0.500283i	$0.833229\pi$
$308$	−63730.4	−	153905.i	−0.0382798	−	0.0924432i
$309$	−504204.	−	873308.i	−0.300407	−	0.520321i
$310$	6646.23	−	101320.i	0.00392800	−	0.0598811i
$311$			1.87564e6i			1.09963i	0.835286	+	0.549816i	$0.185302\pi$
$311$			1.87564e6i			1.09963i	−0.835286	+	0.549816i	$0.814698\pi$
$312$	1.71096e6	+	340612.i	0.995067	+	0.198095i
$313$	−1.48391e6	+	2.57021e6i	−0.856144	+	1.48288i	0.0194360	+	0.999811i	$0.493813\pi$
$313$	−1.48391e6	+	2.57021e6i	−0.856144	+	1.48288i	−0.875580	+	0.483074i	$0.839520\pi$
$314$	162854.	−	2.48266e6i	0.0932124	−	1.42099i
$315$			3693.83i			0.00209749i
$316$	1.84838e6	−	2.40833e6i	1.04129	−	1.35674i
$317$	−1.98485e6	−	1.14595e6i	−1.10938	−	0.640498i	−0.170708	−	0.985322i	$-0.554606\pi$
$317$	−1.98485e6	−	1.14595e6i	−1.10938	−	0.640498i	−0.938668	+	0.344823i	$0.887939\pi$
$318$	109665.	−	164107.i	0.0608136	−	0.0910036i
$319$	178282.	−	308793.i	0.0980912	−	0.169899i
$320$	74984.4	+	570962.i	0.0409351	+	0.311697i
$321$	−591574.	−	1.02464e6i	−0.320440	−	0.555018i
$322$	−787163.	+	388134.i	−0.423082	+	0.208613i
$323$	2.60632e6	−	2.39901e6i	1.39002	−	1.27946i
$324$	−1.13739e6	+	1.48196e6i	−0.601933	+	0.784283i
$325$	1.51631e6	−	875444.i	0.796307	−	0.459748i
$326$	584468.	−	874618.i	0.304591	−	0.455800i
$327$	−2.03232e6	−	1.17336e6i	−1.05105	−	0.606823i
$328$	−364292.	−	1.07373e6i	−0.186967	−	0.551075i
$329$	−346352.	+	599899.i	−0.176412	+	0.305554i
$330$	46045.0	+	93382.5i	0.0232754	+	0.0472042i
$331$	2.08577e6			1.04639			0.523197	−	0.852212i	$-0.324739\pi$
$331$	2.08577e6			1.04639			0.523197	+	0.852212i	$0.324739\pi$
$332$	997566.	−	413082.i	0.496703	−	0.205679i
$333$	10671.2	+	6161.01i	0.00527353	+	0.00304468i
$334$	2.13915e6	−	1.05477e6i	1.04924	−	0.517360i
$335$	−927145.			−0.451373
$336$	−316761.	+	1.18117e6i	−0.153068	+	0.570773i
$337$	1.33681e6	−	771807.i	0.641202	−	0.370198i	−0.143876	−	0.989596i	$-0.545957\pi$
$337$	1.33681e6	−	771807.i	0.641202	−	0.370198i	0.785077	+	0.619398i	$0.212623\pi$
$338$	5648.70	−	86112.7i	0.00268941	−	0.0409992i
$339$	2.54452e6	−	1.46908e6i	1.20256	−	0.694299i
$340$	1.25513e6	+	165376.i	0.588833	+	0.0775846i
$341$			69009.2i			0.0321382i
$342$	15241.4	+	18905.6i	0.00704628	+	0.00874028i
$343$		−	2.13245e6i		−	0.978686i
$344$	499606.	+	1.47256e6i	0.227631	+	0.670929i
$345$	475071.	−	274283.i	0.214888	−	0.124065i
$346$	141737.	+	9297.44i	0.0636491	+	0.00417516i
$347$	3.09129e6	−	1.78476e6i	1.37821	−	0.795711i	0.386267	−	0.922387i	$-0.373764\pi$
$347$	3.09129e6	−	1.78476e6i	1.37821	−	0.795711i	0.991944	+	0.126676i	$0.0404309\pi$
$348$	−2.41850e6	+	1.00148e6i	−1.07053	+	0.443295i
$349$	−611182.			−0.268601			−0.134300	−	0.990941i	$-0.542879\pi$
$349$	−611182.			−0.268601			−0.134300	+	0.990941i	$0.542879\pi$
$350$	542790.	+	1.10082e6i	0.236844	+	0.480336i
$351$	2.05087e6	+	1.18407e6i	0.888528	+	0.512992i
$352$	−76253.4	−	383882.i	−0.0328022	−	0.165136i
$353$	2.42704e6			1.03667			0.518335	−	0.855178i	$-0.326552\pi$
$353$	2.42704e6			1.03667			0.518335	+	0.855178i	$0.326552\pi$
$354$	931467.	−	459288.i	0.395057	−	0.194794i
$355$	419101.	−	725905.i	0.176501	−	0.305709i
$356$	80103.0	−	607946.i	0.0334984	−	0.254238i
$357$	2.32825e6	+	1.34422e6i	0.966849	+	0.558211i
$358$	82369.8	+	55044.1i	0.0339673	+	0.0226988i
$359$	−2.52906e6	+	1.46016e6i	−1.03567	+	0.597947i	−0.918605	−	0.395176i	$-0.870683\pi$
$359$	−2.52906e6	+	1.46016e6i	−1.03567	+	0.597947i	−0.117070	+	0.993124i	$0.537350\pi$
$360$	−1694.50	+	8511.79i	−0.000689106	+	0.00346150i
$361$	−2.23940e6	+	1.05648e6i	−0.904407	+	0.426671i
$362$	−208822.	−	423505.i	−0.0837538	−	0.169859i
$363$	1.21282e6	+	2.10067e6i	0.483092	+	0.836740i
$364$	1.51969e6	+	200235.i	0.601177	+	0.0792111i
$365$	−326300.	+	565169.i	−0.128199	+	0.222048i
$366$	522737.	+	349322.i	0.203977	+	0.136309i
$367$	−3.54145e6	−	2.04466e6i	−1.37251	−	0.792420i	−0.381268	−	0.924464i	$-0.624513\pi$
$367$	−3.54145e6	−	2.04466e6i	−1.37251	−	0.792420i	−0.991244	+	0.132044i	$0.957846\pi$
$368$	−1.99193e6	+	533285.i	−0.766752	+	0.205277i
$369$		−	17088.1i		−	0.00653322i
$370$	−448054.	−	29390.8i	−0.170148	−	0.0111611i
$371$	86712.2	−	150190.i	0.0327074	−	0.0566508i
$372$	308453.	−	401896.i	0.115566	−	0.150576i
$373$			540870.i			0.201290i	0.994922	+	0.100645i	$0.0320906\pi$
$373$			540870.i			0.201290i	−0.994922	+	0.100645i	$0.967909\pi$
$374$	−858568.	−	56319.1i	−0.317392	−	0.0208198i
$375$	−809214.	−	1.40160e6i	−0.297156	−	0.514690i
$376$	−1.07330e6	+	1.22348e6i	−0.391519	+	0.446299i
$377$	1.64052e6	+	2.84147e6i	0.594469	+	1.02965i
$378$	−922351.	+	1.38024e6i	−0.332022	+	0.496849i
$379$	1.40440e6			0.502220			0.251110	−	0.967959i	$-0.419204\pi$
$379$	1.40440e6			0.502220			0.251110	+	0.967959i	$0.419204\pi$
$380$	−802807.	−	372273.i	−0.285202	−	0.132252i
$381$	4.69102e6			1.65560
$382$	2.95866e6	−	4.42744e6i	1.03738	−	1.55237i
$383$	−177690.	−	307769.i	−0.0618966	−	0.107208i	0.833417	−	0.552645i	$-0.186382\pi$
$383$	−177690.	−	307769.i	−0.0618966	−	0.107208i	−0.895313	+	0.445437i	$0.853048\pi$
$384$	−1.27177e6	+	2.57649e6i	−0.440129	+	0.891661i
$385$	45741.3	+	79226.2i	0.0157274	+	0.0272406i
$386$	−3.61584e6	−	237187.i	−1.23521	−	0.0810256i
$387$			23435.3i			0.00795415i
$388$	−292497.	−	224490.i	−0.0986375	−	0.0757038i
$389$	929284.	−	1.60957e6i	0.311368	−	0.539306i	−0.667291	−	0.744798i	$-0.732546\pi$
$389$	929284.	−	1.60957e6i	0.311368	−	0.539306i	0.978659	+	0.205492i	$0.0658794\pi$
$390$	−956020.	−	62711.6i	−0.318277	−	0.0208779i
$391$			4.53327e6i			1.49958i
$392$	384222.	−	1.93002e6i	0.126289	−	0.634374i
$393$	−80314.4	−	46369.6i	−0.0262308	−	0.0151444i
$394$	−3.38674e6	−	2.26321e6i	−1.09911	−	0.734487i
$395$	−833633.	+	1.44389e6i	−0.268833	+	0.465632i
$396$	770.526	−	5847.95i	0.000246916	−	0.00187398i
$397$	1.80443e6	+	3.12536e6i	0.574597	+	0.995232i	0.996085	+	0.0883977i	$0.0281746\pi$
$397$	1.80443e6	+	3.12536e6i	0.574597	+	0.995232i	−0.421488	+	0.906834i	$0.638492\pi$
$398$	1.74379e6	+	3.53653e6i	0.551807	+	1.11910i
$399$	−1.27268e6	−	1.38266e6i	−0.400209	−	0.434793i
$400$	745778.	+	2.78564e6i	0.233056	+	0.870512i
$401$	1.00781e6	−	581861.i	0.312981	−	0.180700i	−0.335278	−	0.942119i	$-0.608830\pi$
$401$	1.00781e6	−	581861.i	0.312981	−	0.180700i	0.648260	+	0.761419i	$0.275497\pi$
$402$	−3.84622e6	−	2.57026e6i	−1.18705	−	0.793253i
$403$	−549938.	−	317507.i	−0.168675	−	0.0973846i
$404$	−4.41806e6	−	582124.i	−1.34672	−	0.177444i
$405$	512973.	−	888496.i	0.155402	−	0.269164i
$406$	−2.06286e6	+	1.01715e6i	−0.621089	+	0.306247i
$407$	305171.			0.0913181
$408$	4.74840e6	+	4.16557e6i	1.41220	+	1.23886i
$409$	−1.85106e6	−	1.06871e6i	−0.547156	−	0.315901i	0.200818	−	0.979629i	$-0.435640\pi$
$409$	−1.85106e6	−	1.06871e6i	−0.547156	−	0.315901i	−0.747974	+	0.663728i	$0.768973\pi$
$410$	275381.	+	558492.i	0.0809048	+	0.164081i
$411$	−3.41404e6			−0.996929
$412$	−796460.	−	1.92340e6i	−0.231164	−	0.558247i
$413$	790262.	−	456258.i	0.227980	−	0.131624i
$414$	−31010.8	−	2034.20i	−0.00889227	−	0.000583302i
$415$	−513522.	+	296482.i	−0.146365	+	0.0845041i
$416$	3.41001e6	+	1.15855e6i	0.966101	+	0.328232i
$417$		−	824299.i		−	0.232137i
$418$	561013.	+	216756.i	0.157048	+	0.0606777i
$419$			7.03090e6i			1.95648i	0.207469	+	0.978242i	$0.433477\pi$
$419$			7.03090e6i			1.95648i	−0.207469	+	0.978242i	$0.566523\pi$
$420$	87732.4	−	665850.i	0.0242682	−	0.184184i
$421$	−5.81387e6	+	3.35664e6i	−1.59867	+	0.922995i	−0.606931	+	0.794755i	$0.707600\pi$
$421$	−5.81387e6	+	3.35664e6i	−1.59867	+	0.922995i	−0.991743	+	0.128240i	$0.959067\pi$
$422$	409127.	−	6.23701e6i	0.111835	−	1.70489i
$423$	−21242.3	+	12264.2i	−0.00577232	+	0.00333265i
$424$	268711.	−	306308.i	0.0725890	−	0.0827454i
$425$	6.33961e6			1.70251
$426$	3.75100e6	−	1.84954e6i	1.00144	−	0.493787i
$427$	478408.	+	276209.i	0.126978	+	0.0733108i
$428$	−934472.	−	2.25669e6i	−0.246579	−	0.595473i
$429$	651148.			0.170819
$430$	−377669.	−	765939.i	−0.0985009	−	0.199767i
$431$	206908.	−	358375.i	0.0536518	−	0.0929277i	−0.837952	−	0.545744i	$-0.816247\pi$
$431$	206908.	−	358375.i	0.0536518	−	0.0929277i	0.891604	+	0.452816i	$0.149581\pi$
$432$	−2.75856e6	+	2.75740e6i	−0.711171	+	0.710870i
$433$	−3.36244e6	−	1.94131e6i	−0.861857	−	0.497593i	0.00277682	−	0.999996i	$-0.499116\pi$
$433$	−3.36244e6	−	1.94131e6i	−0.861857	−	0.497593i	−0.864634	+	0.502403i	$0.832449\pi$
$434$	247326.	−	370108.i	0.0630298	−	0.0943200i
$435$	1.24498e6	−	718792.i	0.315457	−	0.182129i
$436$	−3.84319e6	−	2.94963e6i	−0.968223	−	0.743106i
$437$	946099.	−	3.02423e6i	0.236992	−	0.757550i
$438$	−2.92042e6	+	1.44000e6i	−0.727378	+	0.358655i
$439$	1.71768e6	+	2.97510e6i	0.425383	+	0.736785i	0.996456	−	0.0841143i	$-0.0268061\pi$
$439$	1.71768e6	+	2.97510e6i	0.425383	+	0.736785i	−0.571073	+	0.820899i	$0.693473\pi$
$440$	69058.7	+	203546.i	0.0170054	+	0.0501224i
$441$	14828.9	−	25684.5i	0.00363090	−	0.00628890i
$442$	4.39902e6	−	6.58285e6i	1.07103	−	1.60272i
$443$	−2.23712e6	−	1.29160e6i	−0.541603	−	0.312694i	0.204126	−	0.978945i	$-0.434565\pi$
$443$	−2.23712e6	−	1.29160e6i	−0.541603	−	0.312694i	−0.745728	+	0.666250i	$0.767898\pi$
$444$	−1.77726e6	−	1.36403e6i	−0.427851	−	0.328373i
$445$			336762.i			0.0806164i
$446$	−268941.	+	4.09993e6i	−0.0640207	+	0.975977i
$447$	2.03672e6	−	3.52770e6i	0.482128	−	0.835070i
$448$	−966860.	+	2.33211e6i	−0.227598	+	0.548978i
$449$		−	4.76530e6i		−	1.11551i	−0.830005	−	0.557756i	$-0.811663\pi$
$449$		−	4.76530e6i		−	1.11551i	0.830005	−	0.557756i	$-0.188337\pi$
$450$	−2844.75	+	43367.4i	−0.000662237	+	0.0100956i
$451$	−211604.	−	366510.i	−0.0489873	−	0.0848485i
$452$	5.60413e6	−	2.32061e6i	1.29022	−	0.534265i
$453$	−1.15213e6	−	1.99556e6i	−0.263790	−	0.456897i
$454$	−1.62734e6	−	1.08748e6i	−0.370543	−	0.247618i
$455$	−841810.			−0.190628
$456$	−2.29839e6	−	3.76992e6i	−0.517620	−	0.849025i
$457$	4.88977e6			1.09521			0.547606	−	0.836736i	$-0.315539\pi$
$457$	4.88977e6			1.09521			0.547606	+	0.836736i	$0.315539\pi$
$458$	−2.95292e6	−	1.97331e6i	−0.657792	−	0.439573i
$459$	4.28728e6	+	7.42579e6i	0.949840	+	1.64517i
$460$	1.04631e6	−	433267.i	0.230551	−	0.0954687i
$461$	−589922.	−	1.02178e6i	−0.129283	−	0.223925i	0.794116	−	0.607767i	$-0.207934\pi$
$461$	−589922.	−	1.02178e6i	−0.129283	−	0.223925i	−0.923399	+	0.383841i	$0.874601\pi$
$462$	−29877.4	+	455472.i	−0.00651235	+	0.0992788i
$463$		−	4.05981e6i		−	0.880142i	−0.897963	−	0.440071i	$-0.854953\pi$
$463$		−	4.05981e6i		−	0.880142i	0.897963	−	0.440071i	$-0.145047\pi$
$464$	−5.22010e6	+	1.39754e6i	−1.12560	+	0.301349i
$465$	−139115.	+	240954.i	−0.0298360	+	0.0516775i
$466$	486438.	−	7.41560e6i	0.103768	−	1.58191i
$467$			3.32385e6i			0.705260i	0.935763	+	0.352630i	$0.114713\pi$
$467$			3.32385e6i			0.705260i	−0.935763	+	0.352630i	$0.885287\pi$
$468$	43057.4	+	33046.4i	0.00908727	+	0.00697443i
$469$	−3.52005e6	−	2.03230e6i	−0.738953	−	0.426635i
$470$	496621.	−	743161.i	0.103700	−	0.155181i
$471$	−3.40875e6	+	5.90413e6i	−0.708016	+	1.22632i
$472$	2.03032e6	−	688843.i	0.419479	−	0.142320i
$473$	290203.	+	502647.i	0.0596416	+	0.103302i
$474$	−7.46110e6	+	3.67891e6i	−1.52531	+	0.752097i
$475$	−4.22927e6	−	1.32308e6i	−0.860065	−	0.269062i
$476$	4.40280e6	+	3.37912e6i	0.890659	+	0.683576i
$477$	5318.19	−	3070.46i	0.00107021	−	0.000617885i
$478$	−1.14079e6	+	1.70712e6i	−0.228368	+	0.341738i
$479$	335084.	+	193461.i	0.0667291	+	0.0385261i	0.532993	−	0.846119i	$-0.321067\pi$
$479$	335084.	+	193461.i	0.0667291	+	0.0385261i	−0.466264	+	0.884645i	$0.654400\pi$
$480$	507615.	−	1.49409e6i	0.100561	−	0.295987i
$481$	−1.40407e6	+	2.43192e6i	−0.276711	+	0.479277i
$482$	2.59386e6	+	5.26052e6i	0.508544	+	1.03136i
$483$	2.40491e6			0.469063
$484$	1.91582e6	+	4.62657e6i	0.371741	+	0.897731i
$485$	175364.	+	101247.i	0.0338522	+	0.0195446i
$486$	−104858.	+	51703.2i	−0.0201377	+	0.00992949i
$487$	−4.62343e6			−0.883369			−0.441684	−	0.897171i	$-0.645619\pi$
$487$	−4.62343e6			−0.883369			−0.441684	+	0.897171i	$0.645619\pi$
$488$	975699.	+	855939.i	0.185467	+	0.162702i
$489$	−2.49629e6	+	1.44123e6i	−0.472088	+	0.272560i
$490$	−70740.8	+	1.07842e6i	−0.0133101	+	0.202908i
$491$	7.26837e6	−	4.19640e6i	1.36061	−	0.785548i	0.370904	−	0.928671i	$-0.379048\pi$
$491$	7.26837e6	−	4.19640e6i	1.36061	−	0.785548i	0.989705	+	0.143123i	$0.0457145\pi$
$492$	−405860.	+	3.08030e6i	−0.0755899	+	0.573693i
$493$			1.18800e7i			2.20140i
$494$	−4.30852e6	+	3.47346e6i	−0.794347	+	0.640390i
$495$			3239.38i			0.000594222i
$496$	739703.	−	739391.i	0.135006	−	0.134949i
$497$	3.18237e6	−	1.83734e6i	0.577909	−	0.333656i
$498$	−2.95224e6	−	193657.i	−0.533431	−	0.0349912i
$499$	1.57567e6	−	909712.i	0.283278	−	0.163551i	−0.351628	−	0.936140i	$-0.614372\pi$
$499$	1.57567e6	−	909712.i	0.283278	−	0.163551i	0.634907	+	0.772589i	$0.281039\pi$
$500$	−1.27826e6	−	3.08692e6i	−0.228663	−	0.552206i
$501$	−6.53546e6			−1.16327
$502$	−1.35860e6	−	2.75534e6i	−0.240621	−	0.487995i
$503$	−6.31427e6	−	3.64555e6i	−1.11276	−	0.642455i	−0.173220	−	0.984883i	$-0.555417\pi$
$503$	−6.31427e6	−	3.64555e6i	−1.11276	−	0.642455i	−0.939544	+	0.342428i	$0.888751\pi$
$504$	−25091.3	+	28602.0i	−0.00439994	+	0.00501556i
$505$	2.44732e6			0.427033
$506$	−690318.	+	340382.i	−0.119860	+	0.0591004i
$507$	−118235.	+	204789.i	−0.0204280	+	0.0353824i
$508$	9.60126e6	+	1.26506e6i	1.65070	+	0.217497i
$509$	6.32806e6	+	3.65351e6i	1.08262	+	0.625051i	0.931602	−	0.363480i	$-0.118411\pi$
$509$	6.32806e6	+	3.65351e6i	1.08262	+	0.625051i	0.151018	+	0.988531i	$0.451745\pi$
$510$	−2.88426e6	−	1.92742e6i	−0.491031	−	0.328134i
$511$	−2.47770e6	+	1.43050e6i	−0.419756	+	0.242346i
$512$	−3.29779e6	+	4.93041e6i	−0.555966	+	0.831205i
$513$	−1.31036e6	−	5.84864e6i	−0.219834	−	0.981210i
$514$	4.71183e6	+	9.55592e6i	0.786651	+	1.59538i
$515$	571645.	+	990117.i	0.0949747	+	0.164501i
$516$	556614.	−	4.22445e6i	0.0920301	−	0.698467i
$517$	−303740.	+	526093.i	−0.0499776	+	0.0865638i
$518$	−1.63668e6	−	1.09372e6i	−0.268003	−	0.179095i
$519$	−337071.	−	194608.i	−0.0549292	−	0.0317134i
$520$	−1.93980e6	−	386171.i	−0.314593	−	0.0626284i
$521$		−	3.02807e6i		−	0.488734i	−0.969683	−	0.244367i	$-0.921420\pi$
$521$		−	3.02807e6i		−	0.488734i	0.969683	−	0.244367i	$-0.0785801\pi$
$522$	−81267.7	−	5330.88i	−0.0130539	−	0.000856294i
$523$	6.00291e6	−	1.03973e7i	0.959638	−	1.66214i	0.236260	−	0.971690i	$-0.424078\pi$
$523$	6.00291e6	−	1.03973e7i	0.959638	−	1.66214i	0.723378	−	0.690452i	$-0.242588\pi$
$524$	−151877.	−	116565.i	−0.0241638	−	0.0185456i
$525$		−	3.36317e6i		−	0.532539i
$526$	1.84261e6	+	120869.i	0.290381	+	0.0190480i
$527$	−1.14963e6	−	1.99121e6i	−0.180314	−	0.312314i
$528$	−277790.	+	1.03585e6i	−0.0433642	+	0.161701i
$529$	−1.19057e6	−	2.06213e6i	−0.184977	−	0.320389i
$530$	−124333.	+	186057.i	−0.0192264	+	0.0287711i
$531$	32312.0			0.00497310
$532$	−2.23196e6	−	3.17314e6i	−0.341907	−	0.486083i
$533$	3.89431e6			0.593762
$534$	−933581.	+	1.39704e6i	−0.141677	+	0.212010i
$535$	670700.	+	1.16169e6i	0.101308	+	0.175471i
$536$	−7.17905e6	−	6.29787e6i	−1.07933	−	0.946851i
$537$	−135732.	−	235095.i	−0.0203118	−	0.0351810i
$538$	1.69335e6	+	111078.i	0.252227	+	0.0165452i
$539$		−	734517.i		−	0.108900i
$540$	1.30417e6	−	1.69926e6i	0.192464	−	0.250769i
$541$	−2.01566e6	+	3.49123e6i	−0.296091	+	0.512845i	−0.975238	−	0.221158i	$-0.929016\pi$
$541$	−2.01566e6	+	3.49123e6i	−0.296091	+	0.512845i	0.679147	+	0.734002i	$0.262350\pi$
$542$	1.07435e7	+	704734.i	1.57089	+	0.103045i
$543$			1.29388e6i			0.188319i
$544$	8.59534e6	+	9.80634e6i	1.24528	+	1.42072i
$545$	2.30415e6	+	1.33030e6i	0.332292	+	0.191849i
$546$	−3.49221e6	−	2.33369e6i	−0.501325	−	0.335013i
$547$	1.95436e6	−	3.38506e6i	0.279278	−	0.483724i	−0.691927	−	0.721967i	$-0.743238\pi$
$547$	1.95436e6	−	3.38506e6i	0.279278	−	0.483724i	0.971206	+	0.238243i	$0.0765715\pi$
$548$	−6.98763e6	−	920690.i	−0.993982	−	0.130967i
$549$	9780.50	+	16940.3i	0.00138494	+	0.00239878i
$550$	476011.	+	965383.i	0.0670981	+	0.136080i
$551$	2.47937e6	−	7.92537e6i	0.347906	−	1.11209i
$552$	5.54170e6	+	1.10323e6i	0.774096	+	0.154105i
$553$	−6.33003e6	+	3.65465e6i	−0.880224	+	0.508198i
$554$	6.16343e6	+	4.11875e6i	0.853195	+	0.570152i
$555$	1.06554e6	+	615190.i	0.146838	+	0.0847768i
$556$	222295.	−	1.68712e6i	0.0304960	−	0.231451i
$557$	−572838.	+	992185.i	−0.0782337	+	0.135505i	−0.902488	−	0.430715i	$-0.858261\pi$
$557$	−572838.	+	992185.i	−0.0782337	+	0.135505i	0.824254	+	0.566220i	$0.191595\pi$
$558$	14137.2	−	6970.75i	0.00192211	−	0.000947751i
$559$	−5.34082e6			−0.722901
$560$	359129.	−	1.33916e6i	0.0483928	−	0.180452i
$561$	2.04180e6	+	1.17884e6i	0.273909	+	0.158142i
$562$	4.63970e6	+	9.40964e6i	0.619654	+	1.25670i
$563$	1.51588e6			0.201555			0.100777	−	0.994909i	$-0.467867\pi$
$563$	1.51588e6			0.201555			0.100777	+	0.994909i	$0.467867\pi$
$564$	4.12042e6	−	1.70622e6i	0.545436	−	0.225860i
$565$	−2.88487e6	+	1.66558e6i	−0.380193	+	0.219505i
$566$	9.62706e6	+	631502.i	1.26314	+	0.0828578i
$567$	3.89517e6	−	2.24887e6i	0.508825	−	0.293770i
$568$	8.17607e6	−	2.77396e6i	1.06334	−	0.360769i
$569$			2.49528e6i			0.323101i	0.986864	+	0.161551i	$0.0516495\pi$
$569$			2.49528e6i			0.323101i	−0.986864	+	0.161551i	$0.948350\pi$
$570$	1.52189e6	+	1.88777e6i	0.196198	+	0.243367i
$571$		−	9.84454e6i		−	1.26359i	−0.775137	−	0.631793i	$-0.782319\pi$
$571$		−	9.84454e6i		−	1.26359i	0.775137	−	0.631793i	$-0.217681\pi$
$572$	1.33273e6	+	175600.i	0.170314	+	0.0224406i
$573$	−1.26366e7	+	7.29572e6i	−1.60784	+	0.928285i
$574$	−178687.	+	2.72404e6i	−0.0226367	+	0.345091i
$575$	4.91126e6	−	2.83552e6i	0.619475	−	0.357654i
$576$	−70939.3	+	54397.9i	−0.00890904	+	0.00683166i
$577$	−6.44138e6			−0.805452			−0.402726	−	0.915321i	$-0.631937\pi$
$577$	−6.44138e6			−0.805452			−0.402726	+	0.915321i	$0.631937\pi$
$578$	1.85078e7	−	9.12582e6i	2.30428	−	1.13619i
$579$	8.59902e6	+	4.96465e6i	1.06599	+	0.615449i
$580$	2.74199e6	−	1.13543e6i	0.338451	−	0.140149i
$581$	−2.59955e6			−0.319491
$582$	446813.	+	906168.i	0.0546787	+	0.110892i
$583$	76044.0	−	131712.i	0.00926603	−	0.0160492i
$584$	−6.36565e6	+	2.15972e6i	−0.772344	+	0.262039i
$585$	−25814.8	−	14904.2i	−0.00311874	−	0.00180060i
$586$	−8.50660e6	+	1.27296e7i	−1.02332	+	1.53133i
$587$	−1.01036e7	+	5.83331e6i	−1.21026	+	0.698746i	−0.962817	−	0.270155i	$-0.912925\pi$
$587$	−1.01036e7	+	5.83331e6i	−1.21026	+	0.698746i	−0.247447	+	0.968901i	$0.579592\pi$
$588$	−3.28310e6	+	4.27768e6i	−0.391598	+	0.510229i
$589$	351369.	+	1.56830e6i	0.0417326	+	0.186269i
$590$	−1.05606e6	+	520720.i	−0.124898	+	0.0615849i
$591$	5.58082e6	+	9.66626e6i	0.657248	+	1.13839i
$592$	−3.26972e6	−	3.27110e6i	−0.383447	−	0.383610i
$593$	3.02925e6	−	5.24682e6i	0.353752	−	0.612717i	−0.633151	−	0.774028i	$-0.718239\pi$
$593$	3.02925e6	−	5.24682e6i	0.353752	−	0.612717i	0.986904	+	0.161311i	$0.0515723\pi$
$594$	−808874.	+	1.21043e6i	−0.0940621	+	0.140758i
$595$	−2.63966e6	−	1.52401e6i	−0.305672	−	0.176480i
$596$	5.11996e6	−	6.67100e6i	0.590406	−	0.769264i
$597$		−	1.08047e7i		−	1.24073i
$598$	463587.	−	7.06725e6i	0.0530125	−	0.808161i
$599$	216618.	−	375193.i	0.0246676	−	0.0427256i	−0.853428	−	0.521211i	$-0.825481\pi$
$599$	216618.	−	375193.i	0.0246676	−	0.0427256i	0.878096	+	0.478485i	$0.158814\pi$
$600$	1.54282e6	−	7.74985e6i	0.174959	−	0.878850i
$601$		−	6.99772e6i		−	0.790261i	−0.918625	−	0.395130i	$-0.870699\pi$
$601$		−	6.99772e6i		−	0.790261i	0.918625	−	0.395130i	$-0.129301\pi$
$602$	245059.	−	3.73586e6i	0.0275601	−	0.420145i
$603$	−71963.4	−	124644.i	−0.00805969	−	0.0139598i
$604$	−1.81995e6	−	4.39507e6i	−0.202987	−	0.490201i
$605$	−1.37504e6	−	2.38164e6i	−0.152731	−	0.264538i
$606$	1.01526e7	+	6.78452e6i	1.12304	+	0.750477i
$607$	−3.77598e6			−0.415966			−0.207983	−	0.978132i	$-0.566690\pi$
$607$	−3.77598e6			−0.415966			−0.207983	+	0.978132i	$0.566690\pi$
$608$	−3.68752e6	−	8.33584e6i	−0.404553	−	0.914515i
$609$	6.30237e6			0.688589
$610$	−592656.	−	396046.i	−0.0644879	−	0.0430944i
$611$	−2.79497e6	−	4.84104e6i	−0.302883	−	0.524609i
$612$	75188.2	+	181575.i	0.00811467	+	0.0195964i
$613$	−5.94393e6	−	1.02952e7i	−0.638885	−	1.10658i	−0.985678	−	0.168639i	$-0.946063\pi$
$613$	−5.94393e6	−	1.02952e7i	−0.638885	−	1.10658i	0.346793	−	0.937942i	$-0.387271\pi$
$614$	400.056	−	6098.74i	4.28253e−5	−	0.000652859i
$615$		−	1.70628e6i		−	0.181913i
$616$	−183982.	+	924172.i	−0.0195354	+	0.0981298i
$617$	5.27200e6	−	9.13138e6i	0.557523	−	0.965658i	−0.440180	−	0.897910i	$-0.645085\pi$
$617$	5.27200e6	−	9.13138e6i	0.557523	−	0.965658i	0.997702	−	0.0677481i	$-0.0215814\pi$
$618$	−373388.	+	5.69219e6i	−0.0393268	+	0.599526i
$619$			1.46850e7i			1.54044i	0.637776	+	0.770222i	$0.279855\pi$
$619$			1.46850e7i			1.54044i	−0.637776	+	0.770222i	$0.720145\pi$
$620$	−349710.	+	455652.i	−0.0365367	+	0.0476051i
$621$	6.64268e6	+	3.83515e6i	0.691216	+	0.399074i
$622$	5.89518e6	−	8.82175e6i	0.610972	−	0.914279i
$623$	−738183.	+	1.27857e6i	−0.0761980	+	0.131979i
$624$	−6.97664e6	−	6.97959e6i	−0.717274	−	0.717577i
$625$	−3.48279e6	−	6.03237e6i	−0.356638	−	0.617715i
$626$	1.50576e7	−	7.42458e6i	1.53574	−	0.757244i
$627$	−1.11610e6	−	1.21255e6i	−0.113380	−	0.123177i
$628$	−8.56902e6	+	1.11649e7i	−0.867025	+	1.12968i
$629$	−8.80549e6	+	5.08385e6i	−0.887415	+	0.512349i
$630$	11609.8	−	17373.3i	0.00116540	−	0.00174394i
$631$	6.06636e6	+	3.50242e6i	0.606534	+	0.350183i	0.771608	−	0.636099i	$-0.219453\pi$
$631$	6.06636e6	+	3.50242e6i	0.606534	+	0.350183i	−0.165074	+	0.986281i	$0.552786\pi$
$632$	−1.62630e7	+	5.51766e6i	−1.61960	+	0.549493i
$633$	−8.56358e6	+	1.48326e7i	−0.849466	+	1.47132i
$634$	5.73364e6	+	1.16282e7i	0.566510	+	1.14892i
$635$	−5.31847e6			−0.523423
$636$	−1.03158e6	+	427168.i	−0.101126	+	0.0418751i
$637$	5.85340e6	+	3.37946e6i	0.571557	+	0.329989i
$638$	−1.80906e6	+	892013.i	−0.175955	+	0.0867600i
$639$	130120.			0.0126064
$640$	1.44187e6	−	2.92111e6i	0.139148	−	0.281901i
$641$	−7.59725e6	+	4.38627e6i	−0.730317	+	0.421648i	−0.818538	−	0.574452i	$-0.805215\pi$
$641$	−7.59725e6	+	4.38627e6i	−0.730317	+	0.421648i	0.0882214	+	0.996101i	$0.471882\pi$
$642$	−438089.	+	6.67854e6i	−0.0419493	+	0.639505i
$643$	−1.26575e7	+	7.30783e6i	−1.20732	+	0.697045i	−0.962172	−	0.272441i	$-0.912169\pi$
$643$	−1.26575e7	+	7.30783e6i	−1.20732	+	0.697045i	−0.245145	+	0.969486i	$0.578836\pi$
$644$	4.92221e6	+	648550.i	0.467676	+	0.0616210i
$645$			2.34007e6i			0.221477i
$646$	−1.97986e7	+	3.09160e6i	−1.86660	+	0.291476i
$647$		−	1.55671e7i		−	1.46200i	−0.682378	−	0.730999i	$-0.739054\pi$
$647$		−	1.55671e7i		−	1.46200i	0.682378	−	0.730999i	$-0.260946\pi$
$648$	1.00074e7	−	3.39528e6i	0.936230	−	0.317642i
$649$	693036.	−	400124.i	0.0645868	−	0.0372892i
$650$	−9.88328e6	−	648309.i	−0.917524	−	0.0601864i
$651$	−1.05634e6	+	609879.i	−0.0976904	+	0.0564016i
$652$	−5.49790e6	+	2.27662e6i	−0.506498	+	0.209736i
$653$	−3.21129e6			−0.294711			−0.147356	−	0.989084i	$-0.547076\pi$
$653$	−3.21129e6			−0.294711			−0.147356	+	0.989084i	$0.547076\pi$
$654$	5.87078e6	+	1.19064e7i	0.536725	+	1.08851i
$655$	91056.9	+	52571.7i	0.00829296	+	0.00478795i
$656$	−1.66137e6	+	6.19509e6i	−0.150733	+	0.562067i
$657$	−101307.			−0.00915647
$658$	3.51451e6	−	1.73293e6i	0.316446	−	0.156033i
$659$	3.71539e6	−	6.43525e6i	0.333266	−	0.577234i	−0.649884	−	0.760033i	$-0.725183\pi$
$659$	3.71539e6	−	6.43525e6i	0.333266	−	0.577234i	0.983150	+	0.182800i	$0.0585160\pi$
$660$	76938.7	−	583930.i	0.00687519	−	0.0521796i
$661$	7.18895e6	+	4.15054e6i	0.639974	+	0.369489i	0.784604	−	0.619997i	$-0.212866\pi$
$661$	7.18895e6	+	4.15054e6i	0.639974	+	0.369489i	−0.144631	+	0.989486i	$0.546199\pi$
$662$	−9.81006e6	−	6.55562e6i	−0.870015	−	0.581392i
$663$	−1.87884e7	+	1.08475e7i	−1.65999	+	0.958397i
$664$	−5.99022e6	−	1.19252e6i	−0.527257	−	0.104965i
$665$	1.44291e6	+	1.56760e6i	0.126527	+	0.137461i
$666$	−30825.9	−	62517.1i	−0.00269296	−	0.00546152i
$667$	5.31357e6	+	9.20338e6i	0.462458	+	0.801001i
$668$	−1.33763e7	−	1.76247e6i	−1.15983	−	0.152820i
$669$	5.62931e6	−	9.75026e6i	0.486284	−	0.842269i
$670$	4.36068e6	+	2.91404e6i	0.375290	+	0.250789i
$671$	419549.	+	242227.i	0.0359730	+	0.0207690i
$672$	5.20228e6	−	4.55985e6i	0.444396	−	0.389517i
$673$			2.52088e6i			0.214543i	0.994230	+	0.107272i	$0.0342114\pi$
$673$			2.52088e6i			0.214543i	−0.994230	+	0.107272i	$0.965789\pi$
$674$	−8.71327e6	−	571561.i	−0.738808	−	0.0484632i
$675$	5.36331e6	−	9.28952e6i	0.453078	−	0.784755i
$676$	−297222.	+	387263.i	−0.0250158	+	0.0325941i
$677$		−	1.25333e7i		−	1.05098i	−0.850801	−	0.525488i	$-0.823883\pi$
$677$		−	1.25333e7i		−	1.05098i	0.850801	−	0.525488i	$-0.176117\pi$
$678$	−1.65851e7	−	1.08793e6i	−1.38562	−	0.0908919i
$679$	443866.	+	768798.i	0.0369468	+	0.0639938i
$680$	−5.38352e6	−	4.72273e6i	−0.446472	−	0.391671i
$681$	2.68160e6	+	4.64467e6i	0.221578	+	0.383784i
$682$	216898.	−	324573.i	0.0178564	−	0.0267210i
$683$	908242.			0.0744989			0.0372494	−	0.999306i	$-0.488140\pi$
$683$	908242.			0.0744989			0.0372494	+	0.999306i	$0.488140\pi$
$684$	−12264.6	−	136824.i	−0.00100234	−	0.0111820i
$685$	3.87069e6			0.315182
$686$	−6.70235e6	+	1.00296e7i	−0.543772	+	0.813719i
$687$	4.86595e6	+	8.42807e6i	0.393347	+	0.681297i
$688$	2.27848e6	−	8.49621e6i	0.183516	−	0.684312i
$689$	699747.	+	1.21200e6i	0.0561556	+	0.0972643i
$690$	−3.09650e6	−	203120.i	−0.247599	−	0.0162416i
$691$		−	6.35971e6i		−	0.506690i	−0.967376	−	0.253345i	$-0.918469\pi$
$691$		−	6.35971e6i		−	0.506690i	0.967376	−	0.253345i	$-0.0815308\pi$
$692$	−637413.	−	489212.i	−0.0506006	−	0.0388357i
$693$	−7100.72	+	12298.8i	−0.000561654	+	0.000972814i
$694$	−2.01489e7	−	1.32170e6i	−1.58801	−	0.104168i
$695$			934553.i			0.0733908i
$696$	1.45227e7	+	2.89114e6i	1.13638	+	0.226228i
$697$	1.22114e7	+	7.05025e6i	0.952102	+	0.549696i
$698$	2.87460e6	+	1.92096e6i	0.223325	+	0.149238i
$699$	−1.01818e7	+	1.76354e7i	−0.788193	+	1.36519i
$700$	906972.	−	6.88352e6i	0.0699599	−	0.530964i
$701$	−2.08770e6	−	3.61600e6i	−0.160462	−	0.277928i	0.774572	−	0.632485i	$-0.217965\pi$
$701$	−2.08770e6	−	3.61600e6i	−0.160462	−	0.277928i	−0.935034	+	0.354557i	$0.884632\pi$
$702$	−5.92438e6	−	1.20150e7i	−0.453732	−	0.920201i
$703$	6.93531e6	−	1.55382e6i	0.529270	−	0.118580i
$704$	−847907.	+	2.04519e6i	−0.0644787	+	0.155526i
$705$	−2.12109e6	+	1.22461e6i	−0.160726	+	0.0927952i
$706$	−1.14152e7	−	7.62826e6i	−0.861929	−	0.575989i
$707$	9.29161e6	+	5.36452e6i	0.699105	+	0.403629i
$708$	−5.82456e6	−	767444.i	−0.436697	−	0.0575392i
$709$	−927540.	+	1.60655e6i	−0.0692974	+	0.120027i	−0.898592	−	0.438785i	$-0.855409\pi$
$709$	−927540.	+	1.60655e6i	−0.0692974	+	0.120027i	0.829295	+	0.558811i	$0.188742\pi$
$710$	−4.25271e6	+	2.09693e6i	−0.316607	+	0.156112i
$711$	−258821.			−0.0192010
$712$	−2.28754e6	+	2.60761e6i	−0.169110	+	0.192771i
$713$	−1.78122e6	−	1.02839e6i	−0.131218	−	0.0757588i
$714$	−6.72563e6	−	1.36400e7i	−0.493728	−	1.00131i
$715$	−738242.			−0.0540050
$716$	−214408.	−	517781.i	−0.0156300	−	0.0377454i
$717$	4.87236e6	−	2.81306e6i	0.353949	−	0.204353i
$718$	1.64843e7	+	1.08132e6i	1.19333	+	0.0782783i
$719$	1.21955e7	−	7.04107e6i	0.879786	−	0.507944i	0.00919783	−	0.999958i	$-0.497072\pi$
$719$	1.21955e7	−	7.04107e6i	0.879786	−	0.507944i	0.870588	+	0.492013i	$0.163739\pi$
$720$	34722.6	−	34707.9i	0.00249621	−	0.00249515i
$721$			5.01218e6i			0.359078i
$722$	1.38532e7	+	2.06952e6i	0.989025	+	0.147749i
$723$		−	1.60717e7i		−	1.14345i
$724$	−348930.	+	2.64822e6i	−0.0247395	+	0.187762i
$725$	1.28706e7	−	7.43083e6i	0.909395	−	0.525040i
$726$	898153.	−	1.36921e7i	0.0632424	−	0.964112i
$727$	−91194.3	+	52651.0i	−0.00639929	+	0.00369463i	−0.503196	−	0.864172i	$-0.667843\pi$
$727$	−91194.3	+	52651.0i	−0.00639929	+	0.00369463i	0.496797	+	0.867867i	$0.334509\pi$
$728$	−6.51828e6	−	5.71821e6i	−0.455832	−	0.399882i
$729$	1.45064e7			1.01097
$730$	3.31104e6	−	1.63261e6i	0.229963	−	0.113390i
$731$	−1.67472e7	−	9.66901e6i	−1.15918	−	0.669251i
$732$	−1.36068e6	−	3.28596e6i	−0.0938596	−	0.226665i
$733$	3.05573e6			0.210066			0.105033	−	0.994469i	$-0.466505\pi$
$733$	3.05573e6			0.210066			0.105033	+	0.994469i	$0.466505\pi$
$734$	1.02302e7	+	2.07476e7i	0.700882	+	1.42144i
$735$	1.48070e6	−	2.56465e6i	0.101100	−	0.175110i
$736$	1.10449e7	+	3.75248e6i	0.751563	+	0.255343i
$737$	−3.08698e6	−	1.78227e6i	−0.209346	−	0.120866i
$738$	−53708.3	+	80371.0i	−0.00362995	+	0.00543199i
$739$	−3.36720e6	+	1.94405e6i	−0.226808	+	0.130948i	−0.609099	−	0.793095i	$-0.708469\pi$
$739$	−3.36720e6	+	1.94405e6i	−0.226808	+	0.130948i	0.382291	+	0.924042i	$0.375135\pi$
$740$	2.01497e6	+	1.54648e6i	0.135266	+	0.103816i
$741$	1.47980e7	−	3.31540e6i	0.990049	−	0.221815i
$742$	−879888.	+	433855.i	−0.0586702	+	0.0289291i
$743$	1.49115e7	+	2.58275e7i	0.990944	+	1.71637i	0.611759	+	0.791044i	$0.290462\pi$
$743$	1.49115e7	+	2.58275e7i	0.990944	+	1.71637i	0.379185	+	0.925321i	$0.376204\pi$
$744$	−2.71393e6	+	920775.i	−0.179749	+	0.0609847i
$745$	−2.30914e6	+	3.99955e6i	−0.152426	+	0.264010i
$746$	1.69997e6	−	2.54390e6i	0.111839	−	0.167360i
$747$	−79717.3	−	46024.8i	−0.00522699	−	0.00301780i
$748$	3.86112e6	+	2.96339e6i	0.252325	+	0.193658i
$749$			5.88070e6i			0.383022i
$750$	−599262.	+	9.13557e6i	−0.0389013	+	0.593038i
$751$	296978.	−	514381.i	0.0192143	−	0.0332801i	−0.856258	−	0.516548i	$-0.827217\pi$
$751$	296978.	−	514381.i	0.0192143	−	0.0332801i	0.875473	+	0.483268i	$0.160550\pi$
$752$	8.89353e6	−	2.38100e6i	0.573495	−	0.153538i
$753$			8.41801e6i			0.541031i
$754$	1.21489e6	−	1.85206e7i	0.0778230	−	1.18639i
$755$	1.30624e6	+	2.26247e6i	0.0833979	+	0.144449i
$756$	8.67625e6	−	3.59275e6i	0.552113	−	0.228624i
$757$	7.12232e6	+	1.23362e7i	0.451733	+	0.782424i	0.998494	−	0.0548644i	$-0.0174726\pi$
$757$	7.12232e6	+	1.23362e7i	0.451733	+	0.782424i	−0.546761	+	0.837289i	$0.684139\pi$
$758$	−6.60539e6	−	4.41408e6i	−0.417566	−	0.279041i
$759$	2.10903e6			0.132886
$760$	2.60581e6	+	4.27417e6i	0.163647	+	0.268422i
$761$	−9.17339e6			−0.574206			−0.287103	−	0.957900i	$-0.592692\pi$
$761$	−9.17339e6			−0.574206			−0.287103	+	0.957900i	$0.592692\pi$
$762$	−2.20634e7	−	1.47440e7i	−1.37653	−	0.919874i
$763$	5.83205e6	+	1.01014e7i	0.362669	+	0.628161i
$764$	−2.78311e7	+	1.15246e7i	−1.72503	+	0.714318i
$765$	−53964.9	−	93470.0i	−0.00333394	−	0.00577456i
$766$	−131588.	+	2.00603e6i	−0.00810300	+	0.123528i
$767$			7.36378e6i			0.451973i
$768$	1.40795e7	−	8.12088e6i	0.861360	−	0.496821i
$769$	1.11806e7	−	1.93654e7i	0.681790	−	1.18089i	−0.292644	−	0.956221i	$-0.594535\pi$
$769$	1.11806e7	−	1.93654e7i	0.681790	−	1.18089i	0.974434	−	0.224673i	$-0.0721314\pi$
$770$	33873.7	−	516394.i	0.00205890	−	0.0313873i
$771$		−	2.91949e7i		−	1.76877i
$772$	1.62610e7	+	1.24803e7i	0.981985	+	0.753669i
$773$	2.02174e7	+	1.16725e7i	1.21696	+	0.702612i	0.964267	−	0.264934i	$-0.0853502\pi$
$773$	2.02174e7	+	1.16725e7i	1.21696	+	0.702612i	0.252694	+	0.967546i	$0.418684\pi$
$774$	73657.9	−	110224.i	0.00441944	−	0.00661340i
$775$	−1.43816e6	+	2.49097e6i	−0.0860108	+	0.148975i
$776$	670134.	+	1.97518e6i	0.0399491	+	0.117748i
$777$	2.69699e6	+	4.67133e6i	0.160261	+	0.277580i
$778$	−9.42965e6	+	4.64957e6i	−0.558530	+	0.275400i
$779$	−6.67505e6	−	7.25188e6i	−0.394104	−	0.428161i
$780$	4.29938e6	+	3.29975e6i	0.253028	+	0.194198i
$781$	2.79084e6	−	1.61129e6i	0.163722	−	0.0945250i
$782$	1.42482e7	−	2.13215e7i	0.833189	−	1.24681i
$783$	1.74080e7	+	1.00505e7i	1.01471	+	0.585845i
$784$	−7.87322e6	+	7.86989e6i	−0.457470	+	0.457276i
$785$	3.86469e6	−	6.69384e6i	0.223842	−	0.387705i
$786$	232005.	+	470522.i	0.0133949	+	0.0271659i
$787$	927008.			0.0533515			0.0266757	−	0.999644i	$-0.491508\pi$
$787$	927008.			0.0533515			0.0266757	+	0.999644i	$0.491508\pi$
$788$	8.81566e6	+	2.12893e7i	0.505754	+	1.22136i
$789$	−4.38200e6	−	2.52995e6i	−0.250599	−	0.144683i
$790$	8.45906e6	−	4.17099e6i	0.482230	−	0.237778i
$791$	−1.46038e7			−0.829897
$792$	−22004.3	+	25083.1i	−0.00124651	+	0.00142091i
$793$	−3.86063e6	+	2.22894e6i	−0.218010	+	0.125868i
$794$	1.33627e6	−	2.03710e7i	0.0752215	−	1.14673i
$795$	531033.	−	306592.i	0.0297992	−	0.0172045i
$796$	2.91378e6	−	2.21143e7i	0.162995	−	1.23706i
$797$			2.00518e7i			1.11817i	0.829111	+	0.559085i	$0.188847\pi$
$797$			2.00518e7i			1.11817i	−0.829111	+	0.559085i	$0.811153\pi$
$798$	1.64010e6	+	1.05032e7i	0.0911724	+	0.583866i
$799$		−	2.02401e7i		−	1.12162i
$800$	5.24769e6	−	1.54458e7i	0.289897	−	0.853268i
$801$	−45273.9	+	26138.9i	−0.00249325	+	0.00143948i
$802$	−6.56888e6	−	430896.i	−0.360625	−	0.0236557i
$803$	−2.17287e6	+	1.25451e6i	−0.118917	+	0.0686569i
$804$	1.00117e7	+	2.41776e7i	0.546219	+	1.31908i
$805$	−2.72658e6			−0.148296
$806$	1.58861e6	+	3.22181e6i	0.0861350	+	0.174688i
$807$	−4.02705e6	−	2.32502e6i	−0.217672	−	0.125673i
$808$	1.89500e7	+	1.66240e7i	1.02113	+	0.895793i
$809$	−1.57681e7			−0.847049			−0.423524	−	0.905885i	$-0.639207\pi$
$809$	−1.57681e7			−0.847049			−0.423524	+	0.905885i	$0.639207\pi$
$810$	−5.20525e6	+	2.56660e6i	−0.278759	+	0.137451i
$811$	−1.81116e7	+	3.13702e7i	−0.966951	+	1.67481i	−0.262673	+	0.964885i	$0.584604\pi$
$811$	−1.81116e7	+	3.13702e7i	−0.966951	+	1.67481i	−0.704278	+	0.709924i	$0.748729\pi$
$812$	1.28993e7	+	1.69961e6i	0.686554	+	0.0904604i
$813$	−2.55496e7	−	1.47511e7i	−1.35568	−	0.782702i
$814$	−1.43532e6	−	959161.i	−0.0759256	−	0.0507377i
$815$	2.83018e6	−	1.63401e6i	0.149252	−	0.0861707i
$816$	−9.24082e6	−	3.45164e7i	−0.485831	−	1.81468i
$817$	9.15445e6	+	9.94554e6i	0.479819	+	0.521283i
$818$	5.34716e6	+	1.08444e7i	0.279409	+	0.566661i
$819$	−65339.8	−	113172.i	−0.00340383	−	0.00589561i
$820$	460146.	−	3.49230e6i	0.0238980	−	0.181375i
$821$	−6.33482e6	+	1.09722e7i	−0.328002	+	0.568116i	−0.982115	−	0.188280i	$-0.939709\pi$
$821$	−6.33482e6	+	1.09722e7i	−0.328002	+	0.568116i	0.654113	+	0.756397i	$0.273042\pi$
$822$	1.60574e7	+	1.07304e7i	0.828887	+	0.553908i
$823$	7.12457e6	+	4.11337e6i	0.366656	+	0.211689i	0.671997	−	0.740554i	$-0.265437\pi$
$823$	7.12457e6	+	4.11337e6i	0.366656	+	0.211689i	−0.305341	+	0.952243i	$0.598770\pi$
$824$	−2.29928e6	+	1.15497e7i	−0.117971	+	0.592587i
$825$		−	2.94940e6i		−	0.150869i
$826$	−5.15090e6	−	337881.i	−0.262684	−	0.0172311i
$827$	−5.59763e6	+	9.69538e6i	−0.284604	+	0.492948i	−0.972513	−	0.232849i	$-0.925195\pi$
$827$	−5.59763e6	+	9.69538e6i	−0.284604	+	0.492948i	0.687909	+	0.725797i	$0.258529\pi$
$828$	139461.	+	107035.i	0.00706930	+	0.00542565i
$829$		−	3.51211e7i		−	1.77493i	−0.460872	−	0.887467i	$-0.652463\pi$
$829$		−	3.51211e7i		−	1.77493i	0.460872	−	0.887467i	$-0.347537\pi$
$830$	3.34712e6	+	219559.i	0.168646	+	0.0110626i
$831$	−1.01564e7	−	1.75913e7i	−0.510194	−	0.883683i
$832$	−1.23971e7	−	1.61668e7i	−0.620885	−	0.809685i
$833$	1.22363e7	+	2.11940e7i	0.610997	+	1.05828i
$834$	−2.59079e6	+	3.87695e6i	−0.128979	+	0.193008i
$835$	7.40961e6			0.367772
$836$	−1.95736e6	−	2.78275e6i	−0.0968625	−	0.137708i
$837$	−3.89034e6			−0.191944
$838$	2.20983e7	−	3.30687e7i	1.08705	−	1.62670i
$839$	1.71253e7	+	2.96619e7i	0.839910	+	1.45477i	0.889969	+	0.456021i	$0.150726\pi$
$839$	1.71253e7	+	2.96619e7i	0.839910	+	1.45477i	−0.0500591	+	0.998746i	$0.515941\pi$
$840$	−2.50542e6	+	2.85597e6i	−0.122513	+	0.139655i
$841$	3.66931e6	+	6.35542e6i	0.178893	+	0.309852i
$842$	3.78946e7	+	2.48575e6i	1.84203	+	0.120831i
$843$		−	2.87480e7i		−	1.39328i
$844$	−2.15274e7	+	2.80489e7i	−1.04024	+	1.35537i
$845$	134050.	−	232181.i	0.00645838	−	0.0111862i
$846$	138456.	+	9082.27i	0.00665101	+	0.000436283i
$847$		−	1.20564e7i		−	0.577442i
$848$	−2.22657e6	+	596104.i	−0.106328	+	0.0284664i
$849$	−2.28946e7	−	1.32182e7i	−1.09009	−	0.629366i
$850$	−2.98173e7	−	1.99256e7i	−1.41554	−	0.945939i
$851$	−4.54771e6	+	7.87687e6i	−0.215263	+	0.372846i
$852$	−2.34554e7	−	3.09048e6i	−1.10699	−	0.145857i
$853$	−1.01635e7	−	1.76037e7i	−0.478269	−	0.828385i	0.521421	−	0.853300i	$-0.325402\pi$
$853$	−1.01635e7	−	1.76037e7i	−0.478269	−	0.828385i	−0.999690	+	0.0249141i	$0.992069\pi$
$854$	−1.38198e6	−	2.80275e6i	−0.0648421	−	0.131504i
$855$	16493.7	+	73618.1i	0.000771619	+	0.00344405i
$856$	−2.69770e6	+	1.35510e7i	−0.125837	+	0.632103i
$857$	−7.71153e6	+	4.45226e6i	−0.358665	+	0.207075i	−0.668495	−	0.743717i	$-0.733061\pi$
$857$	−7.71153e6	+	4.45226e6i	−0.358665	+	0.207075i	0.309830	+	0.950792i	$0.399728\pi$
$858$	−3.06257e6	−	2.04658e6i	−0.142026	−	0.0949095i
$859$	2.04703e7	+	1.18185e7i	0.946545	+	0.546488i	0.892006	−	0.452024i	$-0.149298\pi$
$859$	2.04703e7	+	1.18185e7i	0.946545	+	0.546488i	0.0545389	+	0.998512i	$0.482631\pi$
$860$	−631064.	+	4.78949e6i	−0.0290956	+	0.220823i
$861$	3.74017e6	−	6.47817e6i	0.171943	−	0.297813i
$862$	−2.09954e6	+	1.03524e6i	−0.0962402	+	0.0474541i
$863$	−2.61235e7			−1.19400			−0.597001	−	0.802240i	$-0.703641\pi$
$863$	−2.61235e7			−1.19400			−0.597001	+	0.802240i	$0.703641\pi$
$864$	2.16410e7	−	4.29872e6i	0.986265	−	0.195909i
$865$	382156.	+	220638.i	0.0173660	+	0.0100263i
$866$	9.71311e6	+	1.96989e7i	0.440113	+	0.892579i
$867$	−5.65443e7			−2.55471
$868$	−2.32652e6	+	963387.i	−0.104811	+	0.0434012i
$869$	−5.55125e6	+	3.20502e6i	−0.249368	+	0.143973i
$870$	−8.11476e6	−	532300.i	−0.363477	−	0.0238429i
$871$	2.84060e7	−	1.64002e7i	1.26872	−	0.732493i
$872$	8.80504e6	+	2.59523e7i	0.392139	+	1.15581i
$873$			31434.4i			0.00139595i
$874$	−1.39551e7	+	1.12504e7i	−0.617950	+	0.498182i
$875$			8.04420e6i			0.355192i
$876$	1.82617e7	+	2.40616e6i	0.804045	+	0.105941i
$877$	1.53016e7	−	8.83439e6i	0.671797	−	0.387862i	−0.124960	−	0.992162i	$-0.539880\pi$
$877$	1.53016e7	−	8.83439e6i	0.671797	−	0.387862i	0.796757	+	0.604300i	$0.206547\pi$
$878$	1.27202e6	−	1.93916e7i	0.0556876	−	0.848941i
$879$	3.63320e7	−	2.09763e7i	1.58605	−	0.915708i
$880$	314946.	−	1.17440e6i	0.0137097	−	0.0511222i
$881$	−3.15544e7			−1.36968			−0.684842	−	0.728692i	$-0.740129\pi$
$881$	−3.15544e7			−1.36968			−0.684842	+	0.728692i	$0.740129\pi$
$882$	−150473.	+	74195.0i	−0.00651307	+	0.00321146i
$883$	−2.18189e7	−	1.25971e7i	−0.941739	−	0.543713i	−0.0512338	−	0.998687i	$-0.516315\pi$
$883$	−2.18189e7	−	1.25971e7i	−0.941739	−	0.543713i	−0.890505	+	0.454974i	$0.849649\pi$
$884$	−4.13802e7	+	1.71351e7i	−1.78099	+	0.737490i
$885$	3.22642e6			0.138472
$886$	6.46240e6	+	1.31062e7i	0.276573	+	0.560909i
$887$	7.35622e6	−	1.27413e7i	0.313939	−	0.543759i	−0.665272	−	0.746601i	$-0.731684\pi$
$887$	7.35622e6	−	1.27413e7i	0.313939	−	0.543759i	0.979211	+	0.202842i	$0.0650178\pi$
$888$	4.07183e6	+	1.20015e7i	0.173284	+	0.510743i
$889$	−2.01924e7	−	1.16581e7i	−0.856907	−	0.494735i
$890$	1.05845e6	−	1.58391e6i	0.0447916	−	0.0670277i
$891$	3.41594e6	−	1.97220e6i	0.144151	−	0.0832254i
$892$	1.41511e7	−	1.84381e7i	0.595496	−	0.775896i
$893$	−4.22412e6	+	1.35025e7i	−0.177259	+	0.566612i
$894$	−2.06670e7	+	1.01905e7i	−0.864837	+	0.426434i
$895$	153887.	+	266541.i	0.00642163	+	0.0111226i
$896$	1.18774e7	−	7.92985e6i	0.494254	−	0.329985i
$897$	−9.70352e6	+	1.68070e7i	−0.402669	+	0.697443i
$898$	−1.49775e7	+	2.24128e7i	−0.619794	+	0.927481i
$899$	−4.66791e6	−	2.69502e6i	−0.192630	−	0.111215i
$900$	149685.	−	195031.i	0.00615987	−	0.00802595i
$901$			5.06728e6i			0.207952i
$902$	−156703.	+	2.38890e6i	−0.00641301	+	0.0977645i
$903$	−5.12943e6	+	8.88443e6i	−0.209339	+	0.362585i
$904$	−3.36519e7	−	6.69932e6i	−1.36958	−	0.272653i
$905$		−	1.46694e6i		−	0.0595376i
$906$	−853212.	+	1.30070e7i	−0.0345332	+	0.526448i
$907$	−2.73353e6	−	4.73461e6i	−0.110333	−	0.191103i	0.805571	−	0.592499i	$-0.201858\pi$
$907$	−2.73353e6	−	4.73461e6i	−0.110333	−	0.191103i	−0.915905	+	0.401396i	$0.868525\pi$
$908$	4.23596e6	+	1.02296e7i	0.170505	+	0.411758i
$909$	189956.	+	329014.i	0.00762508	+	0.0132070i
$910$	3.95932e6	+	2.64583e6i	0.158495	+	0.105915i
$911$	3.39884e7			1.35686			0.678430	−	0.734665i	$-0.262661\pi$
$911$	3.39884e7			1.35686			0.678430	+	0.734665i	$0.262661\pi$
$912$	−1.03889e6	+	2.49551e7i	−0.0413601	+	0.993510i
$913$	−2.27973e6			−0.0905121
$914$	−2.29982e7	−	1.53687e7i	−0.910603	−	0.608515i
$915$	976604.	+	1.69153e6i	0.0385625	+	0.0667923i
$916$	7.68644e6	+	1.85622e7i	0.302682	+	0.730957i
$917$	230475.	+	399194.i	0.00905106	+	0.0156769i
$918$	3.17494e6	−	4.84011e7i	0.124345	−	1.89561i
$919$			2.21124e6i			0.0863668i	0.999067	+	0.0431834i	$0.0137500\pi$
$919$			2.21124e6i			0.0863668i	−0.999067	+	0.0431834i	$0.986250\pi$
$920$	−6.28293e6	−	1.25079e6i	−0.244733	−	0.0487208i
$921$	−8373.73	+	14503.7i	−0.000325289	+	0.000563418i
$922$	−436866.	+	6.65990e6i	−0.0169247	+	0.258012i
$923$			2.96538e7i			1.14571i
$924$	1.57208e6	−	2.04833e6i	0.0605754	−	0.0789261i
$925$	1.10155e7	+	6.35980e6i	0.423301	+	0.244393i
$926$	−1.27601e7	+	1.90946e7i	−0.489019	+	0.731785i
$927$	−88740.1	+	153702.i	−0.00339172	+	0.00587464i
$928$	2.89444e7	+	9.83383e6i	1.10330	+	0.374846i
$929$	−1.16563e7	−	2.01893e7i	−0.443119	−	0.767505i	0.554800	−	0.831984i	$-0.312795\pi$
$929$	−1.16563e7	−	2.01893e7i	−0.443119	−	0.767505i	−0.997919	+	0.0644790i	$0.979461\pi$
$930$	1.41163e6	−	696045.i	0.0535196	−	0.0263894i
$931$	−3.73989e6	−	1.66926e7i	−0.141411	−	0.631176i
$932$	−2.55953e7	+	3.33492e7i	−0.965208	+	1.25761i
$933$	−2.51786e7	+	1.45368e7i	−0.946949	+	0.546721i
$934$	1.04470e7	−	1.56332e7i	0.391853	−	0.586382i
$935$	−2.31491e6	−	1.33651e6i	−0.0865973	−	0.0499970i
$936$	−98647.9	−	290759.i	−0.00368043	−	0.0108478i
$937$	2.00554e7	−	3.47370e7i	0.746248	−	1.29254i	−0.203361	−	0.979104i	$-0.565187\pi$
$937$	2.00554e7	−	3.47370e7i	0.746248	−	1.29254i	0.949609	−	0.313436i	$-0.101480\pi$
$938$	1.01684e7	+	2.06222e7i	0.377351	+	0.765294i
$939$	−4.60033e7			−1.70265
$940$	−4.67155e6	+	1.93444e6i	−0.172441	+	0.0714062i
$941$	−1.81803e7	−	1.04964e7i	−0.669308	−	0.386425i	0.126506	−	0.991966i	$-0.459624\pi$
$941$	−1.81803e7	−	1.04964e7i	−0.669308	−	0.386425i	−0.795815	+	0.605540i	$0.792957\pi$
$942$	3.45894e7	−	1.70553e7i	1.27003	−	0.626228i
$943$	1.26135e7			0.461908
$944$	−1.17143e7	−	3.14150e6i	−0.427847	−	0.114738i
$945$	−4.46631e6	+	2.57863e6i	−0.162693	+	0.0939310i
$946$	214910.	−	3.27623e6i	0.00780779	−	0.119027i
$947$	3.31834e7	−	1.91584e7i	1.20239	−	0.694200i	0.241304	−	0.970450i	$-0.422425\pi$
$947$	3.31834e7	−	1.91584e7i	1.20239	−	0.694200i	0.961086	+	0.276249i	$0.0890915\pi$
$948$	4.66550e7	+	6.14726e6i	1.68608	+	0.222157i
$949$		−	2.30876e7i		−	0.832172i
$950$	1.57332e7	+	1.95156e7i	0.565598	+	0.701574i
$951$		−	3.55261e7i		−	1.27379i
$952$	−1.00872e7	−	2.97313e7i	−0.360725	−	1.06322i
$953$	−4.13111e7	+	2.38509e7i	−1.47345	+	0.850694i	−0.999553	−	0.0298890i	$-0.990485\pi$
$953$	−4.13111e7	+	2.38509e7i	−1.47345	+	0.850694i	−0.473892	+	0.880583i	$0.657151\pi$
$954$	−34663.8	−	2273.83i	−0.00123312	−	8.08884e-5i
$955$	1.43268e7	−	8.27156e6i	0.508323	−	0.293480i
$956$	1.07310e7	−	4.44361e6i	0.379749	−	0.157250i
$957$	5.52699e6			0.195078
$958$	−967961.	−	1.96309e6i	−0.0340756	−	0.0691078i
$959$	1.46957e7	+	8.48455e6i	0.515992	+	0.297908i
$960$	−7.08345e6	+	5.43175e6i	−0.248066	+	0.190222i
$961$	−2.75860e7			−0.963562
$962$	1.42474e7	−	7.02511e6i	0.496362	−	0.244746i
$963$	−104117.	+	180336.i	−0.00361790	+	0.00626638i
$964$	4.33419e6	−	3.28946e7i	0.150216	−	1.14007i
$965$	−9.74918e6	−	5.62869e6i	−0.337016	−	0.194576i
$966$	−1.13111e7	−	7.55870e6i	−0.389998	−	0.260618i
$967$	−1.99195e7	+	1.15005e7i	−0.685035	+	0.395505i	−0.801749	−	0.597661i	$-0.796097\pi$
$967$	−1.99195e7	+	1.15005e7i	−0.685035	+	0.395505i	0.116715	+	0.993165i	$0.462764\pi$
$968$	5.53072e6	−	2.77818e7i	0.189711	−	0.952954i
$969$	5.24042e7	+	1.63941e7i	1.79290	+	0.560891i
$970$	−506577.	−	1.02737e6i	−0.0172869	−	0.0350589i
$971$	−1.73122e7	−	2.99857e7i	−0.589257	−	1.02062i	−0.994330	−	0.106339i	$-0.966087\pi$
$971$	−1.73122e7	−	2.99857e7i	−0.589257	−	1.02062i	0.405072	−	0.914285i	$-0.367246\pi$
$972$	655686.	+	86393.2i	0.0222603	+	0.00293301i
$973$	−2.04854e6	+	3.54818e6i	−0.0693685	+	0.120150i
$974$	2.17456e7	+	1.45316e7i	0.734468	+	0.490812i
$975$	2.35039e7	+	1.35700e7i	0.791825	+	0.457160i
$976$	−1.89880e6	−	7.09242e6i	−0.0638050	−	0.238325i
$977$		−	4.33567e6i		−	0.145318i	−0.997357	−	0.0726591i	$-0.976851\pi$
$977$		−	4.33567e6i		−	0.145318i	0.997357	−	0.0726591i	$-0.0231485\pi$
$978$	1.62707e7	+	1.06730e6i	0.543951	+	0.0356813i
$979$	−647364.	+	1.12127e6i	−0.0215870	+	0.0373897i
$980$	3.72223e6	−	4.84984e6i	0.123805	−	0.161310i
$981$			413024.i			0.0137026i
$982$	−4.73750e7	−	3.10764e6i	−1.56773	−	0.102837i
$983$	2.53456e7	+	4.38999e7i	0.836602	+	1.44904i	0.892719	+	0.450614i	$0.148795\pi$
$983$	2.53456e7	+	4.38999e7i	0.836602	+	1.44904i	−0.0561167	+	0.998424i	$0.517872\pi$
$984$	1.15904e7	−	1.32120e7i	0.381601	−	0.434993i
$985$	−6.32728e6	−	1.09592e7i	−0.207791	−	0.359904i
$986$	3.73392e7	−	5.58757e7i	1.22313	−	1.83033i
$987$	−1.07374e7			−0.350837
$988$	3.11816e7	−	2.79506e6i	1.01626	−	0.0910958i
$989$	−1.72987e7			−0.562369
$990$	10181.5	−	15235.9i	0.000330158	−	0.000494060i
$991$	−943540.	−	1.63426e6i	−0.0305194	−	0.0528612i	0.850362	−	0.526198i	$-0.176383\pi$
$991$	−943540.	−	1.63426e6i	−0.0305194	−	0.0528612i	−0.880882	+	0.473336i	$0.843049\pi$
$992$	−5.80300e6	+	1.15269e6i	−0.187229	+	0.0371907i
$993$	1.61654e7	+	2.79993e7i	0.520252	+	0.901103i
$994$	−2.07426e7	−	1.36064e6i	−0.665881	−	0.0436795i
$995$			1.22499e7i			0.392260i
$996$	1.32767e7	+	1.01898e7i	0.424074	+	0.325475i
$997$	2.60186e6	−	4.50655e6i	0.0828983	−	0.143584i	−0.821595	−	0.570071i	$-0.806916\pi$
$997$	2.60186e6	−	4.50655e6i	0.0828983	−	0.143584i	0.904494	+	0.426487i	$0.140249\pi$
$998$	−1.02701e7	−	673686.i	−0.326400	−	0.0214107i
$999$			1.72038e7i			0.545393i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.f.a.31.10	yes	96
4.3	odd	2	inner	76.6.f.a.31.26	yes	96
19.8	odd	6	inner	76.6.f.a.27.26	yes	96
76.27	even	6	inner	76.6.f.a.27.10	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.f.a.27.10	✓	96	76.27	even	6	inner
76.6.f.a.27.26	yes	96	19.8	odd	6	inner
76.6.f.a.31.10	yes	96	1.1	even	1	trivial
76.6.f.a.31.26	yes	96	4.3	odd	2	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.70334 - 3.14303i) q^{2} +(7.75035 + 13.4240i) q^{3} +(12.2427 + 29.5654i) q^{4} +(-8.78700 - 15.2195i) q^{5} +(5.73951 - 87.4972i) q^{6} -77.0445i q^{7} +(35.3433 - 177.535i) q^{8} +(1.36406 - 2.36263i) q^{9} +O(q^{10})\)	\(q+(-4.70334 - 3.14303i) q^{2} +(7.75035 + 13.4240i) q^{3} +(12.2427 + 29.5654i) q^{4} +(-8.78700 - 15.2195i) q^{5} +(5.73951 - 87.4972i) q^{6} -77.0445i q^{7} +(35.3433 - 177.535i) q^{8} +(1.36406 - 2.36263i) q^{9} +(-6.50720 + 99.2004i) q^{10} -67.5657i q^{11} +(-302.001 + 393.489i) q^{12} +(538.434 + 310.865i) q^{13} +(-242.153 + 362.366i) q^{14} +(136.205 - 235.914i) q^{15} +(-724.230 + 723.924i) q^{16} +(1125.58 + 1949.56i) q^{17} +(-13.8415 + 6.82494i) q^{18} +(-344.019 - 1535.50i) q^{19} +(342.395 - 446.121i) q^{20} +(1034.25 - 597.122i) q^{21} +(-212.361 + 317.784i) q^{22} +(1743.96 + 1006.88i) q^{23} +(2657.16 - 901.514i) q^{24} +(1408.08 - 2438.86i) q^{25} +(-1555.38 - 3154.42i) q^{26} +3808.96 q^{27} +(2277.85 - 943.236i) q^{28} +(4570.26 + 2638.64i) q^{29} +(-1382.10 + 681.485i) q^{30} -1021.36 q^{31} +(5681.61 - 1128.58i) q^{32} +(907.002 - 523.658i) q^{33} +(833.546 - 12707.2i) q^{34} +(-1172.58 + 676.990i) q^{35} +(86.5520 + 11.4041i) q^{36} +4516.66i q^{37} +(-3208.07 + 8303.22i) q^{38} +9637.26i q^{39} +(-3012.57 + 1022.10i) q^{40} +(5424.50 - 3131.83i) q^{41} +(-6741.17 - 442.198i) q^{42} +(-7439.38 + 4295.13i) q^{43} +(1997.61 - 827.189i) q^{44} -47.9441 q^{45} +(-5037.79 - 10217.0i) q^{46} +(-7786.40 - 4495.48i) q^{47} +(-15331.0 - 4111.40i) q^{48} +10871.2 q^{49} +(-14288.1 + 7045.16i) q^{50} +(-17447.3 + 30219.6i) q^{51} +(-2598.95 + 19724.9i) q^{52} +(1949.39 + 1125.48i) q^{53} +(-17914.8 - 11971.7i) q^{54} +(-1028.32 + 593.700i) q^{55} +(-13678.1 - 2723.00i) q^{56} +(17946.2 - 16518.8i) q^{57} +(-13202.2 - 26774.9i) q^{58} +(5922.01 + 10257.2i) q^{59} +(8642.41 + 1138.72i) q^{60} +(-3585.06 + 6209.50i) q^{61} +(4803.82 + 3210.18i) q^{62} +(-182.027 - 105.094i) q^{63} +(-30269.7 - 12549.4i) q^{64} -10926.3i q^{65} +(-5911.81 - 387.794i) q^{66} +(26378.3 - 45688.6i) q^{67} +(-43859.4 + 57146.2i) q^{68} +31214.6i q^{69} +(7642.84 + 501.344i) q^{70} +(23847.8 + 41305.6i) q^{71} +(-371.240 - 325.673i) q^{72} +(-18567.2 - 32159.3i) q^{73} +(14196.0 - 21243.3i) q^{74} +43652.4 q^{75} +(41185.9 - 28969.8i) q^{76} -5205.56 q^{77} +(30290.2 - 45327.3i) q^{78} +(-47435.6 - 82160.8i) q^{79} +(17381.6 + 4661.33i) q^{80} +(29189.3 + 50557.4i) q^{81} +(-35356.7 - 2319.28i) q^{82} -33741.0i q^{83} +(30316.2 + 23267.5i) q^{84} +(19780.9 - 34261.6i) q^{85} +(48489.6 + 3180.75i) q^{86} +81801.7i q^{87} +(-11995.3 - 2387.99i) q^{88} +(-16595.2 - 9581.25i) q^{89} +(225.497 + 150.690i) q^{90} +(23950.4 - 41483.4i) q^{91} +(-8417.87 + 63887.9i) q^{92} +(-7915.94 - 13710.8i) q^{93} +(22492.6 + 45616.6i) q^{94} +(-20346.6 + 18728.2i) q^{95} +(59184.6 + 67523.1i) q^{96} +(-9978.63 + 5761.16i) q^{97} +(-51130.7 - 34168.3i) q^{98} +(-159.633 - 92.1639i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 3 q^{2} - 11 q^{4} - 2 q^{5} - 27 q^{6} - 3588 q^{9}+O(q^{10}) \) 96 * q - 3 * q^2 - 11 * q^4 - 2 * q^5 - 27 * q^6 - 3588 * q^9	\( 96 q - 3 q^{2} - 11 q^{4} - 2 q^{5} - 27 q^{6} - 3588 q^{9} + 648 q^{10} - 354 q^{13} + 2154 q^{14} - 611 q^{16} - 1006 q^{17} + 10524 q^{20} + 7824 q^{21} + 93 q^{22} - 5311 q^{24} - 25002 q^{25} - 13428 q^{26} + 1556 q^{28} - 6 q^{29} - 12656 q^{30} - 30453 q^{32} + 8586 q^{33} + 30102 q^{34} - 2306 q^{36} + 29846 q^{38} - 1392 q^{40} + 29064 q^{41} + 18616 q^{42} + 9155 q^{44} + 13464 q^{45} + 38217 q^{48} - 116224 q^{49} + 36858 q^{52} + 26262 q^{53} - 26355 q^{54} + 53974 q^{57} - 112740 q^{58} - 108810 q^{60} - 77370 q^{61} - 106848 q^{62} + 337966 q^{64} + 166855 q^{66} + 175796 q^{68} + 148122 q^{70} - 259842 q^{72} - 52040 q^{73} + 103690 q^{74} - 194709 q^{76} + 197584 q^{77} + 253206 q^{78} - 171934 q^{80} - 313100 q^{81} + 63919 q^{82} - 161762 q^{85} - 38442 q^{86} + 10482 q^{89} - 372450 q^{90} + 64544 q^{92} + 94012 q^{93} + 537614 q^{96} + 177180 q^{97} - 509397 q^{98}+O(q^{100}) \) 96 * q - 3 * q^2 - 11 * q^4 - 2 * q^5 - 27 * q^6 - 3588 * q^9 + 648 * q^10 - 354 * q^13 + 2154 * q^14 - 611 * q^16 - 1006 * q^17 + 10524 * q^20 + 7824 * q^21 + 93 * q^22 - 5311 * q^24 - 25002 * q^25 - 13428 * q^26 + 1556 * q^28 - 6 * q^29 - 12656 * q^30 - 30453 * q^32 + 8586 * q^33 + 30102 * q^34 - 2306 * q^36 + 29846 * q^38 - 1392 * q^40 + 29064 * q^41 + 18616 * q^42 + 9155 * q^44 + 13464 * q^45 + 38217 * q^48 - 116224 * q^49 + 36858 * q^52 + 26262 * q^53 - 26355 * q^54 + 53974 * q^57 - 112740 * q^58 - 108810 * q^60 - 77370 * q^61 - 106848 * q^62 + 337966 * q^64 + 166855 * q^66 + 175796 * q^68 + 148122 * q^70 - 259842 * q^72 - 52040 * q^73 + 103690 * q^74 - 194709 * q^76 + 197584 * q^77 + 253206 * q^78 - 171934 * q^80 - 313100 * q^81 + 63919 * q^82 - 161762 * q^85 - 38442 * q^86 + 10482 * q^89 - 372450 * q^90 + 64544 * q^92 + 94012 * q^93 + 537614 * q^96 + 177180 * q^97 - 509397 * q^98

Introduction

L-functions

Modular forms

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