LMFDB - Embedded newform 38.6.e.b.23.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,6,Mod(5,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, degree $6$, 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:	$6.09458515289$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			23.3
Character	$\chi$	$=$	38.23
Dual form			38.6.e.b.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.75877 - 1.36808i) q^{2} +(-0.196437 - 1.11405i) q^{3} +(12.2567 + 10.2846i) q^{4} +(8.74989 - 7.34203i) q^{5} +(-0.785748 + 4.45620i) q^{6} +(-7.74142 + 13.4085i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(227.143 - 82.6732i) q^{9} +(-42.9333 + 15.6265i) q^{10} +(-298.390 - 516.826i) q^{11} +(9.04988 - 15.6749i) q^{12} +(176.976 - 1003.68i) q^{13} +(47.4422 - 39.8087i) q^{14} +(-9.89819 - 8.30556i) q^{15} +(44.4539 + 252.111i) q^{16} +(-244.634 - 89.0396i) q^{17} -966.881 q^{18} +(1392.58 - 732.684i) q^{19} +182.755 q^{20} +(16.4585 + 5.99039i) q^{21} +(414.519 + 2350.85i) q^{22} +(144.742 + 121.453i) q^{23} +(-55.4609 + 46.5372i) q^{24} +(-519.995 + 2949.04i) q^{25} +(-2038.33 + 3530.49i) q^{26} +(-274.166 - 474.870i) q^{27} +(-232.786 + 84.7271i) q^{28} +(2818.93 - 1026.01i) q^{29} +(25.8423 + 44.7602i) q^{30} +(-2442.48 + 4230.50i) q^{31} +(177.816 - 1008.44i) q^{32} +(-517.155 + 433.944i) q^{33} +(797.711 + 669.359i) q^{34} +(30.7093 + 174.161i) q^{35} +(3634.28 + 1322.77i) q^{36} +3790.08 q^{37} +(-6236.75 + 848.834i) q^{38} -1152.91 q^{39} +(-686.933 - 250.023i) q^{40} +(-3040.19 - 17241.8i) q^{41} +(-53.6683 - 45.0330i) q^{42} +(2760.32 - 2316.18i) q^{43} +(1658.07 - 9403.41i) q^{44} +(1380.49 - 2391.07i) q^{45} +(-377.895 - 654.533i) q^{46} +(-11856.8 + 4315.52i) q^{47} +(272.131 - 99.0477i) q^{48} +(8283.64 + 14347.7i) q^{49} +(5989.07 - 10373.4i) q^{50} +(-51.1393 + 290.025i) q^{51} +(12491.6 - 10481.7i) q^{52} +(-4935.52 - 4141.40i) q^{53} +(380.868 + 2160.01i) q^{54} +(-6405.43 - 2331.39i) q^{55} +990.902 q^{56} +(-1089.80 - 1407.47i) q^{57} -11999.4 q^{58} +(1383.96 + 503.721i) q^{59} +(-35.8998 - 203.598i) q^{60} +(26681.7 + 22388.6i) q^{61} +(14968.4 - 12560.0i) q^{62} +(-649.881 + 3685.66i) q^{63} +(-2048.00 + 3547.24i) q^{64} +(-5820.53 - 10081.5i) q^{65} +(2537.54 - 923.588i) q^{66} +(-49505.7 + 18018.6i) q^{67} +(-2082.68 - 3607.30i) q^{68} +(106.872 - 185.108i) q^{69} +(122.837 - 696.644i) q^{70} +(-1981.49 + 1662.66i) q^{71} +(-11850.8 - 9943.99i) q^{72} +(3929.94 + 22287.8i) q^{73} +(-14246.0 - 5185.14i) q^{74} +3387.52 q^{75} +(24603.8 + 5341.81i) q^{76} +9239.84 q^{77} +(4333.54 + 1577.28i) q^{78} +(6692.16 + 37953.1i) q^{79} +(2239.97 + 1879.56i) q^{80} +(44520.8 - 37357.4i) q^{81} +(-12160.8 + 68967.1i) q^{82} +(-45084.8 + 78089.2i) q^{83} +(140.118 + 242.691i) q^{84} +(-2794.26 + 1017.03i) q^{85} +(-13544.1 + 4929.66i) q^{86} +(-1696.76 - 2938.88i) q^{87} +(-19096.9 + 33076.9i) q^{88} +(15545.0 - 88159.9i) q^{89} +(-8460.11 + 7098.87i) q^{90} +(12087.8 + 10142.9i) q^{91} +(524.966 + 2977.23i) q^{92} +(5192.77 + 1890.02i) q^{93} +50471.0 q^{94} +(6805.51 - 16635.3i) q^{95} -1158.38 q^{96} +(126019. + 45867.1i) q^{97} +(-11507.5 - 65262.3i) q^{98} +(-110505. - 92724.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9} - 126 q^{11} - 2610 q^{13} - 864 q^{14} - 5160 q^{15} + 1902 q^{17} + 17016 q^{18} - 2400 q^{19} + 3456 q^{20} - 6426 q^{21} + 216 q^{22} - 3306 q^{23}+ \cdots - 1068531 q^{99}+O(q^{100}) $ 30 * q + 15 * q^3 + 60 * q^6 - 84 * q^7 - 960 * q^8 - 345 * q^9 - 126 * q^11 - 2610 * q^13 - 864 * q^14 - 5160 * q^15 + 1902 * q^17 + 17016 * q^18 - 2400 * q^19 + 3456 * q^20 - 6426 * q^21 + 216 * q^22 - 3306 * q^23 + 960 * q^24 - 18060 * q^25 + 456 * q^26 + 13017 * q^27 + 6048 * q^28 + 5988 * q^29 - 6840 * q^31 + 51867 * q^33 - 10752 * q^34 + 24408 * q^35 - 5520 * q^36 - 8556 * q^37 + 2772 * q^38 + 9912 * q^39 - 40527 * q^41 + 27432 * q^42 + 3678 * q^43 + 864 * q^44 - 31770 * q^45 - 15744 * q^46 - 133740 * q^47 - 7680 * q^48 - 63777 * q^49 - 107580 * q^50 + 45657 * q^51 + 5760 * q^52 - 64626 * q^53 + 1476 * q^54 + 142056 * q^55 + 10752 * q^56 + 232824 * q^57 + 117264 * q^58 + 169041 * q^59 - 56640 * q^60 + 61698 * q^61 - 101616 * q^62 - 188064 * q^63 - 61440 * q^64 - 80646 * q^65 - 173772 * q^66 - 72129 * q^67 - 65904 * q^68 - 124224 * q^69 + 97632 * q^70 + 417828 * q^71 + 44160 * q^72 + 239082 * q^73 - 116112 * q^74 - 174960 * q^75 + 6912 * q^76 + 242436 * q^77 + 336624 * q^78 - 145740 * q^79 + 14781 * q^81 - 162108 * q^82 - 201630 * q^83 - 54528 * q^84 - 46512 * q^85 - 75720 * q^86 - 376512 * q^87 - 8064 * q^88 + 416928 * q^89 + 560640 * q^90 - 380316 * q^91 + 269376 * q^92 - 205146 * q^93 + 5616 * q^94 + 708168 * q^95 + 858363 * q^97 + 308328 * q^98 - 1068531 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$	−3.75877	−	1.36808i	−0.664463	−	0.241845i
$2$	−3.75877	−	1.36808i	−0.664463	−	0.241845i
$3$	−0.196437	−	1.11405i	−0.0126014	−	0.0714663i	0.977859	−	0.209267i	$-0.0671078\pi$
$3$	−0.196437	−	1.11405i	−0.0126014	−	0.0714663i	−0.990460	+	0.137801i	$0.955997\pi$
$4$	12.2567	+	10.2846i	0.383022	+	0.321394i
$5$	8.74989	−	7.34203i	0.156523	−	0.131338i	−0.561163	−	0.827705i	$-0.689646\pi$
$5$	8.74989	−	7.34203i	0.156523	−	0.131338i	0.717686	+	0.696367i	$0.245201\pi$
$6$	−0.785748	+	4.45620i	−0.00891056	+	0.0505343i
$7$	−7.74142	+	13.4085i	−0.0597139	+	0.103428i	−0.894337	−	0.447394i	$-0.852352\pi$
$7$	−7.74142	+	13.4085i	−0.0597139	+	0.103428i	0.834623	+	0.550822i	$0.185686\pi$
$8$	−32.0000	−	55.4256i	−0.176777	−	0.306186i
$9$	227.143	−	82.6732i	0.934744	−	0.340219i
$10$	−42.9333	+	15.6265i	−0.135767	+	0.0494152i
$11$	−298.390	−	516.826i	−0.743536	−	1.28784i	−0.950876	−	0.309573i	$-0.899814\pi$
$11$	−298.390	−	516.826i	−0.743536	−	1.28784i	0.207340	−	0.978269i	$-0.433519\pi$
$12$	9.04988	−	15.6749i	0.0181422	−	0.0314232i
$13$	176.976	−	1003.68i	0.290439	−	1.64716i	−0.394742	−	0.918792i	$-0.629166\pi$
$13$	176.976	−	1003.68i	0.290439	−	1.64716i	0.685182	−	0.728372i	$-0.259723\pi$
$14$	47.4422	−	39.8087i	0.0646911	−	0.0542823i
$15$	−9.89819	−	8.30556i	−0.0113587	−	0.00953106i
$16$	44.4539	+	252.111i	0.0434120	+	0.246202i
$17$	−244.634	−	89.0396i	−0.205303	−	0.0747241i	0.237322	−	0.971431i	$-0.423730\pi$
$17$	−244.634	−	89.0396i	−0.205303	−	0.0747241i	−0.442625	+	0.896707i	$0.645953\pi$
$18$	−966.881			−0.703383
$19$	1392.58	−	732.684i	0.884984	−	0.465621i
$19$	1392.58	−	732.684i	0.884984	−	0.465621i
$20$	182.755			0.102163
$21$	16.4585	+	5.99039i	0.00814406	+	0.00296420i
$22$	414.519	+	2350.85i	0.182594	+	1.03554i
$23$	144.742	+	121.453i	0.0570526	+	0.0478728i	0.670868	−	0.741577i	$-0.265922\pi$
$23$	144.742	+	121.453i	0.0570526	+	0.0478728i	−0.613815	+	0.789450i	$0.710366\pi$
$24$	−55.4609	+	46.5372i	−0.0196544	+	0.0164920i
$25$	−519.995	+	2949.04i	−0.166399	+	0.943693i
$26$	−2038.33	+	3530.49i	−0.591344	+	1.02424i
$27$	−274.166	−	474.870i	−0.0723777	−	0.125362i
$28$	−232.786	+	84.7271i	−0.0561127	+	0.0204234i
$29$	2818.93	−	1026.01i	0.622428	−	0.226545i	−0.0115043	−	0.999934i	$-0.503662\pi$
$29$	2818.93	−	1026.01i	0.622428	−	0.226545i	0.633932	+	0.773389i	$0.281440\pi$
$30$	25.8423	+	44.7602i	0.00524238	+	0.00908007i
$31$	−2442.48	+	4230.50i	−0.456485	+	0.790655i	−0.998772	−	0.0495380i	$-0.984225\pi$
$31$	−2442.48	+	4230.50i	−0.456485	+	0.790655i	0.542287	+	0.840193i	$0.317558\pi$
$32$	177.816	−	1008.44i	0.0306970	−	0.174091i
$33$	−517.155	+	433.944i	−0.0826677	+	0.0693664i
$34$	797.711	+	669.359i	0.118345	+	0.0993029i
$35$	30.7093	+	174.161i	0.00423740	+	0.0240315i
$36$	3634.28	+	1322.77i	0.467372	+	0.170109i
$37$	3790.08			0.455139			0.227570	−	0.973762i	$-0.426922\pi$
$37$	3790.08			0.455139			0.227570	+	0.973762i	$0.426922\pi$
$38$	−6236.75	+	848.834i	−0.700647	+	0.0953594i
$39$	−1152.91			−0.121377
$40$	−686.933	−	250.023i	−0.0678835	−	0.0247076i
$41$	−3040.19	−	17241.8i	−0.282450	−	1.60185i	−0.714255	−	0.699886i	$-0.753234\pi$
$41$	−3040.19	−	17241.8i	−0.282450	−	1.60185i	0.431805	−	0.901967i	$-0.357877\pi$
$42$	−53.6683	−	45.0330i	−0.00469455	−	0.00393920i
$43$	2760.32	−	2316.18i	0.227661	−	0.191030i	−0.521821	−	0.853055i	$-0.674747\pi$
$43$	2760.32	−	2316.18i	0.227661	−	0.191030i	0.749482	+	0.662025i	$0.230303\pi$
$44$	1658.07	−	9403.41i	0.129114	−	0.732240i
$45$	1380.49	−	2391.07i	0.101625	−	0.176020i
$46$	−377.895	−	654.533i	−0.0263315	−	0.0456076i
$47$	−11856.8	+	4315.52i	−0.782930	+	0.284963i	−0.702394	−	0.711789i	$-0.747885\pi$
$47$	−11856.8	+	4315.52i	−0.782930	+	0.284963i	−0.0805360	+	0.996752i	$0.525663\pi$
$48$	272.131	−	99.0477i	0.0170481	−	0.00620500i
$49$	8283.64	+	14347.7i	0.492868	+	0.853673i
$50$	5989.07	−	10373.4i	0.338793	−	0.586806i
$51$	−51.1393	+	290.025i	−0.00275315	+	0.0156139i
$52$	12491.6	−	10481.7i	0.640633	−	0.537555i
$53$	−4935.52	−	4141.40i	−0.241348	−	0.202515i	0.514088	−	0.857737i	$-0.328130\pi$
$53$	−4935.52	−	4141.40i	−0.241348	−	0.202515i	−0.755436	+	0.655222i	$0.772575\pi$
$54$	380.868	+	2160.01i	0.0177742	+	0.100802i
$55$	−6405.43	−	2331.39i	−0.285523	−	0.103922i
$56$	990.902			0.0422241
$57$	−1089.80	−	1407.47i	−0.0444283	−	0.0573790i
$58$	−11999.4			−0.468369
$59$	1383.96	+	503.721i	0.0517600	+	0.0188391i	0.367770	−	0.929917i	$-0.380121\pi$
$59$	1383.96	+	503.721i	0.0517600	+	0.0188391i	−0.316010	+	0.948756i	$0.602343\pi$
$60$	−35.8998	−	203.598i	−0.00128740	−	0.00730121i
$61$	26681.7	+	22388.6i	0.918097	+	0.770375i	0.973642	−	0.228081i	$-0.0732452\pi$
$61$	26681.7	+	22388.6i	0.918097	+	0.770375i	−0.0555449	+	0.998456i	$0.517690\pi$
$62$	14968.4	−	12560.0i	0.494533	−	0.414963i
$63$	−649.881	+	3685.66i	−0.0206292	+	0.116994i
$64$	−2048.00	+	3547.24i	−0.0625000	+	0.108253i
$65$	−5820.53	−	10081.5i	−0.170875	−	0.295965i
$66$	2537.54	−	923.588i	0.0717055	−	0.0260987i
$67$	−49505.7	+	18018.6i	−1.34731	+	0.490382i	−0.912108	−	0.409950i	$-0.865546\pi$
$67$	−49505.7	+	18018.6i	−1.34731	+	0.490382i	−0.435205	+	0.900332i	$0.643324\pi$
$68$	−2082.68	−	3607.30i	−0.0546197	−	0.0946041i
$69$	106.872	−	185.108i	0.00270235	−	0.00468060i
$70$	122.837	−	696.644i	0.00299629	−	0.0169928i
$71$	−1981.49	+	1662.66i	−0.0466493	+	0.0391434i	−0.665814	−	0.746118i	$-0.731916\pi$
$71$	−1981.49	+	1662.66i	−0.0466493	+	0.0391434i	0.619165	+	0.785261i	$0.287471\pi$
$72$	−11850.8	−	9943.99i	−0.269411	−	0.226063i
$73$	3929.94	+	22287.8i	0.0863136	+	0.489509i	0.997065	+	0.0765545i	$0.0243919\pi$
$73$	3929.94	+	22287.8i	0.0863136	+	0.489509i	−0.910752	+	0.412954i	$0.864497\pi$
$74$	−14246.0	−	5185.14i	−0.302423	−	0.110073i
$75$	3387.52			0.0695391
$76$	24603.8	+	5341.81i	0.488616	+	0.106085i
$77$	9239.84			0.177598
$78$	4333.54	+	1577.28i	0.0806503	+	0.0293543i
$79$	6692.16	+	37953.1i	0.120642	+	0.684195i	0.983801	+	0.179263i	$0.0573713\pi$
$79$	6692.16	+	37953.1i	0.120642	+	0.684195i	−0.863159	+	0.504932i	$0.831518\pi$
$80$	2239.97	+	1879.56i	0.0391307	+	0.0328346i
$81$	44520.8	−	37357.4i	0.753963	−	0.632650i
$82$	−12160.8	+	68967.1i	−0.199722	+	1.13268i
$83$	−45084.8	+	78089.2i	−0.718348	+	1.24422i	0.243305	+	0.969950i	$0.421768\pi$
$83$	−45084.8	+	78089.2i	−0.718348	+	1.24422i	−0.961654	+	0.274266i	$0.911565\pi$
$84$	140.118	+	242.691i	0.00216668	+	0.00375280i
$85$	−2794.26	+	1017.03i	−0.0419487	+	0.0152681i
$86$	−13544.1	+	4929.66i	−0.197472	+	0.0718739i
$87$	−1696.76	−	2938.88i	−0.0240338	−	0.0416278i
$88$	−19096.9	+	33076.9i	−0.262880	+	0.455321i
$89$	15545.0	−	88159.9i	0.208025	−	1.17977i	−0.684584	−	0.728934i	$-0.740016\pi$
$89$	15545.0	−	88159.9i	0.208025	−	1.17977i	0.892609	−	0.450832i	$-0.148873\pi$
$90$	−8460.11	+	7098.87i	−0.110095	+	0.0923811i
$91$	12087.8	+	10142.9i	0.153019	+	0.128398i
$92$	524.966	+	2977.23i	0.00646639	+	0.0366727i
$93$	5192.77	+	1890.02i	0.0622576	+	0.0226599i
$94$	50471.0			0.589145
$95$	6805.51	−	16635.3i	0.0773663	−	0.189113i
$96$	−1158.38			−0.0128285
$97$	126019.	+	45867.1i	1.35990	+	0.494962i	0.916023	−	0.401127i	$-0.131381\pi$
$97$	126019.	+	45867.1i	1.35990	+	0.494962i	0.443875	+	0.896089i	$0.353604\pi$
$98$	−11507.5	−	65262.3i	−0.121036	−	0.686432i
$99$	−110505.	−	92724.5i	−1.13316	−	0.950838i
$100$	−36703.1	+	30797.6i	−0.367031	+	0.307976i
$101$	7053.13	−	40000.3i	0.0687985	−	0.390175i	−0.930892	−	0.365295i	$-0.880968\pi$
$101$	7053.13	−	40000.3i	0.0687985	−	0.390175i	0.999690	−	0.0248808i	$-0.00792064\pi$
$102$	588.999	−	1020.18i	0.00560550	−	0.00970900i
$103$	−67023.8	−	116089.i	−0.622495	−	1.07819i	−0.989020	−	0.147784i	$-0.952786\pi$
$103$	−67023.8	−	116089.i	−0.622495	−	1.07819i	0.366525	−	0.930408i	$-0.380547\pi$
$104$	−61292.8	+	22308.8i	−0.555682	+	0.202252i
$105$	187.991	−	68.4233i	0.00166404	−	0.000605663i
$106$	12885.7	+	22318.8i	0.111390	+	0.192932i
$107$	35751.7	−	61923.7i	0.301882	−	0.522874i	−0.674681	−	0.738110i	$-0.735719\pi$
$107$	35751.7	−	61923.7i	0.301882	−	0.522874i	0.976562	+	0.215236i	$0.0690519\pi$
$108$	1523.47	−	8640.04i	0.0125683	−	0.0712781i
$109$	124463.	−	104437.i	1.00340	−	0.841953i	0.0159489	−	0.999873i	$-0.494923\pi$
$109$	124463.	−	104437.i	1.00340	−	0.841953i	0.987452	+	0.157920i	$0.0504787\pi$
$110$	20887.0	+	17526.3i	0.164587	+	0.138105i
$111$	−744.512	−	4222.34i	−0.00573541	−	0.0325271i
$112$	−3724.57	−	1355.63i	−0.0280564	−	0.0102117i
$113$	6880.02			0.0506866			0.0253433	−	0.999679i	$-0.491932\pi$
$113$	6880.02			0.0506866			0.0253433	+	0.999679i	$0.491932\pi$
$114$	2170.77	+	6781.31i	0.0156441	+	0.0488710i
$115$	2158.19			0.0152176
$116$	45102.9	+	16416.1i	0.311214	+	0.113273i
$117$	−42778.7	−	242610.i	−0.288910	−	1.63849i
$118$	−4512.86	−	3786.74i	−0.0298365	−	0.0250358i
$119$	3087.71	−	2590.89i	0.0199880	−	0.0167719i
$120$	−143.599	+	814.391i	−0.000910330	+	0.00516274i
$121$	−97547.2	+	168957.i	−0.605692	+	1.04909i
$122$	−69660.9	−	120656.i	−0.423730	−	0.733923i
$123$	−18611.0	+	6773.85i	−0.110919	+	0.0403713i
$124$	−73445.7	+	26732.1i	−0.428956	+	0.156127i
$125$	34949.2	+	60533.8i	0.200061	+	0.346515i
$126$	7485.03	−	12964.5i	0.0420018	−	0.0727492i
$127$	−41924.1	+	237763.i	−0.230650	+	1.30808i	0.620933	+	0.783864i	$0.286754\pi$
$127$	−41924.1	+	237763.i	−0.230650	+	1.30808i	−0.851583	+	0.524220i	$0.824357\pi$
$128$	12550.9	−	10531.4i	0.0677094	−	0.0568149i
$129$	−3122.57	−	2620.15i	−0.0165211	−	0.0138628i
$130$	8085.79	+	45856.8i	0.0419628	+	0.237983i
$131$	195107.	+	71013.2i	0.993333	+	0.361544i	0.787010	−	0.616940i	$-0.211628\pi$
$131$	195107.	+	71013.2i	0.993333	+	0.361544i	0.206323	+	0.978484i	$0.433850\pi$
$132$	−10801.6			−0.0539575
$133$	−956.307	+	24344.4i	−0.00468779	+	0.119336i
$134$	210732.			1.01384
$135$	−5885.44	−	2142.12i	−0.0277936	−	0.0101160i
$136$	2893.22	+	16408.3i	0.0134133	+	0.0760704i
$137$	−5020.60	−	4212.78i	−0.0228536	−	0.0191764i	0.631289	−	0.775547i	$-0.282526\pi$
$137$	−5020.60	−	4212.78i	−0.0228536	−	0.0191764i	−0.654143	+	0.756371i	$0.726971\pi$
$138$	−654.950	+	549.568i	−0.00292759	+	0.00245654i
$139$	−51049.7	+	289517.i	−0.224107	+	1.27098i	0.640277	+	0.768144i	$0.278819\pi$
$139$	−51049.7	+	289517.i	−0.224107	+	1.27098i	−0.864385	+	0.502831i	$0.832292\pi$
$140$	−1414.78	+	2450.47i	−0.00610055	+	0.0105665i
$141$	7136.82	+	12361.3i	0.0302313	+	0.0523621i
$142$	9722.61	−	3538.74i	0.0404634	−	0.0147275i
$143$	−571536.	+	208022.i	−2.33724	+	0.850686i
$144$	30940.2	+	53590.0i	0.124342	+	0.215366i
$145$	17132.3	−	29674.1i	0.0676701	−	0.117208i
$146$	15719.8	−	89151.3i	0.0610329	−	0.346135i
$147$	14356.8	−	12046.8i	0.0547980	−	0.0459810i
$148$	46453.9	+	38979.5i	0.174328	+	0.146279i
$149$	74430.8	+	422118.i	0.274655	+	1.55764i	0.740057	+	0.672545i	$0.234799\pi$
$149$	74430.8	+	422118.i	0.274655	+	1.55764i	−0.465402	+	0.885099i	$0.654090\pi$
$150$	−12732.9	−	4634.40i	−0.0462062	−	0.0168177i
$151$	486171.			1.73519			0.867595	−	0.497271i	$-0.165665\pi$
$151$	486171.			1.73519			0.867595	+	0.497271i	$0.165665\pi$
$152$	−85172.0	−	53738.6i	−0.299011	−	0.188659i
$153$	−62928.1			−0.217328
$154$	−34730.4	−	12640.8i	−0.118007	−	0.0429511i
$155$	9689.02	+	54949.1i	0.0323929	+	0.183710i
$156$	−14130.9	−	11857.3i	−0.0464900	−	0.0390097i
$157$	31919.5	−	26783.6i	0.103349	−	0.0867202i	−0.589649	−	0.807660i	$-0.700734\pi$
$157$	31919.5	−	26783.6i	0.103349	−	0.0867202i	0.692998	+	0.720939i	$0.256289\pi$
$158$	26768.6	−	151812.i	0.0853068	−	0.483799i
$159$	−3644.20	+	6311.94i	−0.0114317	+	0.0198002i
$160$	−5848.15	−	10129.3i	−0.0180600	−	0.0312809i
$161$	−2749.02	+	1000.56i	−0.00835820	+	0.00304214i
$162$	−218451.	+	79509.8i	−0.653984	+	0.238031i
$163$	−223334.	−	386825.i	−0.658393	−	1.14037i	−0.981032	−	0.193848i	$-0.937903\pi$
$163$	−223334.	−	386825.i	−0.658393	−	1.14037i	0.322639	−	0.946522i	$-0.395430\pi$
$164$	140062.	−	242595.i	0.406641	−	0.704323i
$165$	−1339.02	+	7593.93i	−0.00382891	+	0.0217149i
$166$	276296.	−	231840.i	0.778223	−	0.653007i
$167$	−266600.	−	223704.i	−0.739723	−	0.620701i	0.193040	−	0.981191i	$-0.438165\pi$
$167$	−266600.	−	223704.i	−0.739723	−	0.620701i	−0.932763	+	0.360489i	$0.882610\pi$
$168$	−194.650	−	1103.91i	−0.000532084	−	0.00301760i
$169$	−627152.	−	228265.i	−1.68910	−	0.614783i
$170$	11894.3			0.0315659
$171$	255741.	−	281553.i	0.668820	−	0.736325i
$172$	57653.5			0.148595
$173$	583213.	+	212272.i	1.48154	+	0.539235i	0.951206	−	0.308557i	$-0.0998460\pi$
$173$	583213.	+	212272.i	1.48154	+	0.539235i	0.530329	+	0.847792i	$0.322068\pi$
$174$	2357.12	+	13367.9i	0.00590212	+	0.0334726i
$175$	−35516.8	−	29802.1i	−0.0876675	−	0.0735618i
$176$	117033.	−	98202.2i	0.284791	−	0.238968i
$177$	289.309	−	1640.75i	0.000694110	−	0.00393649i
$178$	−179040.	+	310106.i	−0.423545	+	0.733601i
$179$	−102511.	−	177554.i	−0.239132	−	0.414188i	0.721334	−	0.692588i	$-0.243529\pi$
$179$	−102511.	−	177554.i	−0.239132	−	0.414188i	−0.960465	+	0.278400i	$0.910196\pi$
$180$	41511.4	−	15108.9i	0.0954963	−	0.0347578i
$181$	12193.3	−	4437.99i	0.0276646	−	0.0100691i	−0.328151	−	0.944625i	$-0.606425\pi$
$181$	12193.3	−	4437.99i	0.0276646	−	0.0100691i	0.355815	+	0.934556i	$0.384203\pi$
$182$	−31559.1	−	54661.9i	−0.0706230	−	0.122323i
$183$	19700.7	−	34122.7i	0.0434865	−	0.0753208i
$184$	2099.86	−	11908.9i	0.00457243	−	0.0259315i
$185$	33162.8	−	27826.9i	0.0712397	−	0.0597772i
$186$	−16932.8	−	14208.3i	−0.0358877	−	0.0301133i
$187$	26978.4	+	153002.i	0.0564172	+	0.319958i
$188$	−189709.	−	69048.4i	−0.391465	−	0.142482i
$189$	8489.75			0.0172878
$190$	−48338.7	+	53217.6i	−0.0971429	+	0.106948i
$191$	976921.			1.93765			0.968826	−	0.247741i	$-0.0796883\pi$
$191$	976921.			1.93765			0.968826	+	0.247741i	$0.0796883\pi$
$192$	4354.10	+	1584.76i	0.00852404	+	0.00310250i
$193$	−140256.	−	795431.i	−0.271037	−	1.53713i	−0.751276	−	0.659988i	$-0.770561\pi$
$193$	−140256.	−	795431.i	−0.271037	−	1.53713i	0.480240	−	0.877137i	$-0.340550\pi$
$194$	−410926.	−	344808.i	−0.783897	−	0.657768i
$195$	−10087.9	+	8464.73i	−0.0189982	+	0.0159414i
$196$	−46030.1	+	261049.i	−0.0855857	+	0.485381i
$197$	−319195.	+	552862.i	−0.585990	+	1.01496i	0.408761	+	0.912641i	$0.365961\pi$
$197$	−319195.	+	552862.i	−0.585990	+	1.01496i	−0.994751	+	0.102323i	$0.967372\pi$
$198$	288507.	+	499709.i	0.522991	+	0.905846i
$199$	10739.0	−	3908.69i	0.0192235	−	0.00699678i	−0.332391	−	0.943142i	$-0.607855\pi$
$199$	10739.0	−	3908.69i	0.0192235	−	0.00699678i	0.351614	+	0.936145i	$0.385633\pi$
$200$	180092.	−	65548.2i	0.318361	−	0.115874i
$201$	29798.4	+	51612.3i	0.0520238	+	0.0901079i
$202$	−81234.8	+	140703.i	−0.140076	+	0.242619i
$203$	−8065.27	+	45740.4i	−0.0137366	+	0.0779041i
$204$	−3609.59	+	3028.81i	−0.00607272	+	0.00509561i
$205$	−153191.	−	128543.i	−0.254594	−	0.213630i
$206$	93108.4	+	528044.i	0.152870	+	0.866966i
$207$	42918.0	+	15620.9i	0.0696168	+	0.0253384i
$208$	260906.			0.418144
$209$	−794201.	−	501095.i	−1.25766	−	0.793513i
$210$	−800.225			−0.00125217
$211$	579329.	+	210858.i	0.895816	+	0.326050i	0.748575	−	0.663050i	$-0.230738\pi$
$211$	579329.	+	210858.i	0.895816	+	0.326050i	0.147241	+	0.989101i	$0.452961\pi$
$212$	−17900.7	−	101520.i	−0.0273546	−	0.155135i
$213$	2241.53	+	1880.86i	0.00338528	+	0.00284059i
$214$	−219099.	+	183846.i	−0.327044	+	0.274422i
$215$	7147.01	−	40532.7i	0.0105446	−	0.0598011i
$216$	−17546.6	+	30391.7i	−0.0255894	+	0.0443221i
$217$	−37816.5	−	65500.1i	−0.0545170	−	0.0944262i
$218$	−610707.	+	222279.i	−0.870345	+	0.316780i
$219$	24057.7	−	8756.30i	0.0338957	−	0.0123370i
$220$	−54532.1	−	94452.4i	−0.0759619	−	0.131570i
$221$	−132662.	+	229777.i	−0.182711	+	0.316465i
$222$	−2978.05	+	16889.4i	−0.00405555	+	0.0230001i
$223$	692247.	−	580864.i	0.932178	−	0.782190i	−0.0440290	−	0.999030i	$-0.514019\pi$
$223$	692247.	−	580864.i	0.932178	−	0.782190i	0.976207	+	0.216840i	$0.0695750\pi$
$224$	12145.2	+	10191.0i	0.0161728	+	0.0135706i
$225$	125693.	+	712843.i	0.165522	+	0.938723i
$226$	−25860.4	−	9412.42i	−0.0336794	−	0.0122583i
$227$	−88995.6			−0.114631			−0.0573157	−	0.998356i	$-0.518254\pi$
$227$	−88995.6			−0.114631			−0.0573157	+	0.998356i	$0.518254\pi$
$228$	1117.94	−	28459.2i	0.00142424	−	0.0362564i
$229$	588108.			0.741086			0.370543	−	0.928815i	$-0.379172\pi$
$229$	588108.			0.741086			0.370543	+	0.928815i	$0.379172\pi$
$230$	−8112.14	−	2952.58i	−0.0101115	−	0.00368029i
$231$	−1815.05	−	10293.6i	−0.00223799	−	0.0126923i
$232$	−147073.	−	123409.i	−0.179396	−	0.150531i
$233$	−744509.	+	624717.i	−0.898421	+	0.753865i	−0.969881	−	0.243579i	$-0.921679\pi$
$233$	−744509.	+	624717.i	−0.898421	+	0.753865i	0.0714599	+	0.997443i	$0.477234\pi$
$234$	−171115.	+	970439.i	−0.204290	+	1.15859i
$235$	−72061.0	+	124813.i	−0.0851198	+	0.147432i
$236$	11782.3	+	20407.5i	0.0137705	+	0.0238511i
$237$	40967.1	−	14910.8i	0.0473766	−	0.0172437i
$238$	−15150.5	+	5514.34i	−0.0173375	+	0.00631032i
$239$	−149743.	−	259363.i	−0.169571	−	0.293706i	0.768698	−	0.639612i	$-0.220905\pi$
$239$	−149743.	−	259363.i	−0.169571	−	0.293706i	−0.938269	+	0.345906i	$0.887572\pi$
$240$	1653.91	−	2864.65i	0.00185346	−	0.00321029i
$241$	−160914.	+	912588.i	−0.178464	+	1.01212i	0.755605	+	0.655028i	$0.227343\pi$
$241$	−160914.	+	912588.i	−0.178464	+	1.01212i	−0.934069	+	0.357093i	$0.883768\pi$
$242$	597804.	−	501617.i	0.656176	−	0.550597i
$243$	−152435.	−	127908.i	−0.165603	−	0.138958i
$244$	96771.9	+	548821.i	0.104058	+	0.590141i
$245$	177822.	+	64722.0i	0.189265	+	0.0688869i
$246$	79221.6			0.0834653
$247$	−488928.	−	1.52737e6i	−0.509921	−	1.59295i
$248$	312637.			0.322784
$249$	95851.5	+	34887.1i	0.0979717	+	0.0356588i
$250$	−48550.9	−	275346.i	−0.0491301	−	0.278630i
$251$	460466.	+	386377.i	0.461332	+	0.387103i	0.843621	−	0.536939i	$-0.180420\pi$
$251$	460466.	+	386377.i	0.461332	+	0.387103i	−0.382289	+	0.924043i	$0.624864\pi$
$252$	−45870.9	+	38490.3i	−0.0455026	+	0.0381812i
$253$	19580.5	−	111047.i	0.0192320	−	0.109070i
$254$	482862.	−	836342.i	0.469612	−	0.813392i
$255$	1681.91	+	2913.16i	0.00161977	+	0.00280552i
$256$	−61583.7	+	22414.6i	−0.0587308	+	0.0213763i
$257$	−944940.	+	343930.i	−0.892425	+	0.324816i	−0.747213	−	0.664585i	$-0.768609\pi$
$257$	−944940.	+	343930.i	−0.892425	+	0.324816i	−0.145212	+	0.989401i	$0.546386\pi$
$258$	8152.45	+	14120.5i	0.00762499	+	0.0132069i
$259$	−29340.6	+	50819.4i	−0.0271781	+	0.0470739i
$260$	32343.2	−	183427.i	0.0296722	−	0.168279i
$261$	555476.	−	466100.i	0.504736	−	0.423524i
$262$	−636211.	−	533844.i	−0.572595	−	0.480465i
$263$	344305.	+	1.95265e6i	0.306940	+	1.74075i	0.614228	+	0.789129i	$0.289468\pi$
$263$	344305.	+	1.95265e6i	0.306940	+	1.74075i	−0.307288	+	0.951617i	$0.599421\pi$
$264$	40600.6	+	14777.4i	0.0358528	+	0.0130493i
$265$	−73591.5			−0.0643744
$266$	36899.7	−	90196.9i	0.0319756	−	0.0781605i
$267$	−101268.			−0.0869349
$268$	−792092.	−	288298.i	−0.673656	−	0.245191i
$269$	−41582.3	−	235825.i	−0.0350371	−	0.198705i	0.962265	−	0.272115i	$-0.0877231\pi$
$269$	−41582.3	−	235825.i	−0.0350371	−	0.198705i	−0.997302	+	0.0734097i	$0.976612\pi$
$270$	19191.4	+	16103.5i	0.0160213	+	0.0134435i
$271$	664481.	−	557565.i	0.549616	−	0.461182i	−0.325195	−	0.945647i	$-0.605430\pi$
$271$	664481.	−	557565.i	0.549616	−	0.461182i	0.874811	+	0.484465i	$0.160986\pi$
$272$	11572.9	−	65633.1i	0.00948461	−	0.0537899i
$273$	8925.19	−	15458.9i	0.00724788	−	0.0125537i
$274$	13107.9	+	22703.5i	0.0105476	+	0.0182691i
$275$	1.67930e6	−	611216.i	1.33905	−	0.487375i
$276$	3213.66	−	1169.68i	0.00253938	−	0.000924257i
$277$	−749365.	−	1.29794e6i	−0.586805	−	1.01638i	−0.994648	−	0.103324i	$-0.967052\pi$
$277$	−749365.	−	1.29794e6i	−0.586805	−	1.01638i	0.407843	−	0.913052i	$-0.366281\pi$
$278$	587967.	−	1.01839e6i	0.456290	−	0.790317i
$279$	−205043.	+	1.16285e6i	−0.157701	+	0.894365i
$280$	8670.28	−	7275.23i	0.00660904	−	0.00554564i
$281$	−681274.	−	571657.i	−0.514702	−	0.431886i	0.348078	−	0.937466i	$-0.386834\pi$
$281$	−681274.	−	571657.i	−0.514702	−	0.431886i	−0.862780	+	0.505579i	$0.831279\pi$
$282$	−9914.36	−	56227.1i	−0.00742407	−	0.0421040i
$283$	−1.31760e6	−	479569.i	−0.977955	−	0.355947i	−0.196910	−	0.980421i	$-0.563091\pi$
$283$	−1.31760e6	−	479569.i	−0.977955	−	0.355947i	−0.781045	+	0.624475i	$0.785313\pi$
$284$	−41386.4			−0.0304482
$285$	−19869.3	−	4313.90i	−0.0144901	−	0.00314599i
$286$	2.43286e6			1.75874
$287$	254722.	+	92711.4i	0.182542	+	0.0664398i
$288$	−42981.7	−	243761.i	−0.0305353	−	0.173174i
$289$	−1.03576e6	−	869102.i	−0.729479	−	0.612105i
$290$	−104993.	+	88099.7i	−0.0733104	+	0.0615148i
$291$	26343.5	−	149401.i	0.0182364	−	0.103424i
$292$	−181053.	+	313593.i	−0.124265	+	0.215233i
$293$	578159.	+	1.00140e6i	0.393440	+	0.681458i	0.992901	−	0.118946i	$-0.0379516\pi$
$293$	578159.	+	1.00140e6i	0.393440	+	0.681458i	−0.599461	+	0.800404i	$0.704618\pi$
$294$	−70445.0	+	25639.9i	−0.0475315	+	0.0173001i
$295$	15807.8	−	5753.59i	0.0105759	−	0.00384932i
$296$	−121283.	−	210068.i	−0.0804580	−	0.139357i
$297$	−163617.	+	283393.i	−0.107631	+	0.186422i
$298$	297723.	−	1.68847e6i	0.194210	−	1.10142i
$299$	147516.	−	123781.i	0.0954247	−	0.0800708i
$300$	41519.9	+	34839.3i	0.0266350	+	0.0223494i
$301$	9687.82	+	54942.4i	0.00616325	+	0.0349535i
$302$	−1.82741e6	−	665122.i	−1.15297	−	0.419647i
$303$	−45947.8			−0.0287514
$304$	246623.	+	318513.i	0.153056	+	0.197671i
$305$	397840.			0.244883
$306$	236532.	+	86090.7i	0.144407	+	0.0525597i
$307$	−89080.6	−	505201.i	−0.0539432	−	0.305927i	0.945884	−	0.324504i	$-0.105198\pi$
$307$	−89080.6	−	505201.i	−0.0539432	−	0.305927i	−0.999827	+	0.0185771i	$0.994086\pi$
$308$	113250.	+	95028.0i	0.0680239	+	0.0570788i
$309$	−116162.	+	97471.8i	−0.0692101	+	0.0580742i
$310$	38756.1	−	219797.i	0.0229053	−	0.129902i
$311$	−690771.	+	1.19645e6i	−0.404980	+	0.701445i	−0.994319	−	0.106440i	$-0.966055\pi$
$311$	−690771.	+	1.19645e6i	−0.404980	+	0.701445i	0.589339	+	0.807886i	$0.299388\pi$
$312$	36893.2	+	63901.0i	0.0214566	+	0.0371639i
$313$	245509.	−	89358.0i	0.141647	−	0.0515552i	−0.270224	−	0.962797i	$-0.587098\pi$
$313$	245509.	−	89358.0i	0.141647	−	0.0515552i	0.411871	+	0.911242i	$0.364876\pi$
$314$	−156620.	+	57005.1i	−0.0896445	+	0.0326279i
$315$	21373.8	+	37020.6i	0.0121369	+	0.0210216i
$316$	−308309.	+	534007.i	−0.173687	+	0.300835i
$317$	−505030.	+	2.86417e6i	−0.282273	+	1.60085i	0.432595	+	0.901588i	$0.357598\pi$
$317$	−505030.	+	2.86417e6i	−0.282273	+	1.60085i	−0.714868	+	0.699260i	$0.753513\pi$
$318$	22333.0	−	18739.6i	0.0123845	−	0.0103918i
$319$	−1.37141e6	−	1.15075e6i	−0.754552	−	0.633144i
$320$	8124.17	+	46074.4i	0.00443511	+	0.0251527i
$321$	−76009.0	−	27665.0i	−0.0411720	−	0.0149854i
$322$	11701.8			0.00628944
$323$	−405910.	+	55245.2i	−0.216483	+	0.0294637i
$324$	929884.			0.492115
$325$	2.86787e6	+	1.04382e6i	1.50609	+	0.548171i
$326$	310252.	+	1.75953e6i	0.161685	+	0.916963i
$327$	−140797.	−	118143.i	−0.0728156	−	0.0610995i
$328$	−858350.	+	720242.i	−0.440535	+	0.369652i
$329$	33923.6	−	192391.i	0.0172788	−	0.0979928i
$330$	15422.2	−	26712.0i	0.00779580	−	0.0135027i
$331$	688597.	+	1.19269e6i	0.345458	+	0.598351i	0.985437	−	0.170042i	$-0.0543902\pi$
$331$	688597.	+	1.19269e6i	0.345458	+	0.598351i	−0.639979	+	0.768393i	$0.721057\pi$
$332$	−1.35571e6	+	493437.i	−0.675027	+	0.245690i
$333$	860890.	−	313338.i	0.425439	−	0.154847i
$334$	696044.	+	1.20558e6i	0.341405	+	0.591331i
$335$	−300877.	+	521133.i	−0.146479	+	0.253710i
$336$	−778.599	+	4415.65i	−0.000376241	+	0.00213377i
$337$	−1.96245e6	+	1.64669e6i	−0.941290	+	0.789836i	−0.977809	−	0.209497i	$-0.932817\pi$
$337$	−1.96245e6	+	1.64669e6i	−0.941290	+	0.789836i	0.0365192	+	0.999333i	$0.488373\pi$
$338$	2.04504e6	+	1.71599e6i	0.973664	+	0.817001i
$339$	−1351.49	−	7664.68i	−0.000638724	−	0.00362239i
$340$	−44708.1	−	16272.4i	−0.0209744	−	0.00763404i
$341$	2.91524e6			1.35765
$342$	−1.34646e6	+	708419.i	−0.622483	+	0.327510i
$343$	−516729.			−0.237152
$344$	−216706.	−	78874.6i	−0.0987359	−	0.0359369i
$345$	−423.948	−	2404.33i	−0.000191763	−	0.00108754i
$346$	−1.90176e6	−	1.59576e6i	−0.854014	−	0.716603i
$347$	−400345.	+	335930.i	−0.178489	+	0.149770i	−0.727655	−	0.685943i	$-0.759390\pi$
$347$	−400345.	+	335930.i	−0.178489	+	0.149770i	0.549166	+	0.835713i	$0.314945\pi$
$348$	9428.47	−	53471.5i	0.00417343	−	0.0236687i
$349$	343066.	−	594207.i	0.150770	−	0.261140i	−0.780741	−	0.624855i	$-0.785158\pi$
$349$	343066.	−	594207.i	0.150770	−	0.261140i	0.931511	+	0.363714i	$0.118492\pi$
$350$	92727.8	+	160609.i	0.0404613	+	0.0700810i
$351$	−525138.	+	191135.i	−0.227513	+	0.0828079i
$352$	−574248.	+	209009.i	−0.247026	+	0.0899101i
$353$	−759987.	−	1.31634e6i	−0.324616	−	0.562251i	0.656819	−	0.754049i	$-0.271902\pi$
$353$	−759987.	−	1.31634e6i	−0.324616	−	0.562251i	−0.981435	+	0.191797i	$0.938568\pi$
$354$	−3332.12	+	5771.41i	−0.00141323	+	0.00244779i
$355$	−5130.46	+	29096.3i	−0.00216065	+	0.0122537i
$356$	1.09722e6	−	920676.i	0.458848	−	0.385019i
$357$	−3492.92	−	2930.91i	−0.00145050	−	0.00121712i
$358$	142406.	+	807627.i	0.0587249	+	0.333045i
$359$	1.61275e6	+	586993.i	0.660436	+	0.240379i	0.650425	−	0.759571i	$-0.274591\pi$
$359$	1.61275e6	+	586993.i	0.660436	+	0.240379i	0.0100115	+	0.999950i	$0.496813\pi$
$360$	−176702.			−0.0718597
$361$	1.40245e6	−	2.04064e6i	0.566393	−	0.824135i
$362$	−51903.3			−0.0208173
$363$	207388.	+	75483.1i	0.0826070	+	0.0300665i
$364$	43841.4	+	248637.i	0.0173433	+	0.0983586i
$365$	198024.	+	166162.i	0.0778012	+	0.0652830i
$366$	−120733.	+	101307.i	−0.0471111	+	0.0395309i
$367$	−36297.8	+	205855.i	−0.0140675	+	0.0797805i	−0.991033	−	0.133615i	$-0.957341\pi$
$367$	−36297.8	+	205855.i	−0.0140675	+	0.0797805i	0.976966	+	0.213396i	$0.0684524\pi$
$368$	−24185.3	+	41890.1i	−0.00930961	+	0.0161247i
$369$	−2.11599e6	−	3.66500e6i	−0.808999	−	1.40123i
$370$	−162721.	+	59225.5i	−0.0617929	+	0.0224908i
$371$	93738.0	−	34117.8i	0.0353574	−	0.0128691i
$372$	44208.3	+	76571.0i	0.0165633	+	0.0286884i
$373$	1.48399e6	−	2.57035e6i	0.552281	−	0.956578i	−0.445829	−	0.895118i	$-0.647091\pi$
$373$	1.48399e6	−	2.57035e6i	0.552281	−	0.956578i	0.998110	−	0.0614598i	$-0.0195756\pi$
$374$	107913.	−	612007.i	0.0398930	−	0.226244i
$375$	60572.3	−	50826.2i	0.0222431	−	0.0186642i
$376$	618608.	+	519074.i	0.225656	+	0.189347i
$377$	−530899.	−	3.01088e6i	−0.192380	−	1.09104i
$378$	−31911.0	−	11614.7i	−0.0114871	−	0.00418097i
$379$	−4.32371e6			−1.54617			−0.773087	−	0.634300i	$-0.781288\pi$
$379$	−4.32371e6			−1.54617			−0.773087	+	0.634300i	$0.781288\pi$
$380$	254500.	−	133902.i	0.0904126	−	0.0475693i
$381$	273115.			0.0963904
$382$	−3.67202e6	−	1.33651e6i	−1.28750	−	0.468611i
$383$	−768680.	−	4.35940e6i	−0.267762	−	1.51855i	−0.761053	−	0.648689i	$-0.775317\pi$
$383$	−768680.	−	4.35940e6i	−0.267762	−	1.51855i	0.493291	−	0.869864i	$-0.335794\pi$
$384$	−14198.0	−	11913.5i	−0.00491359	−	0.00412299i
$385$	80847.6	−	67839.2i	0.0277981	−	0.0233254i
$386$	−561024.	+	3.18172e6i	−0.191652	+	1.08691i
$387$	435500.	−	754309.i	0.147812	−	0.256019i
$388$	1.07285e6	+	1.85823e6i	0.361793	+	0.626644i
$389$	2.51940e6	−	916987.i	0.844158	−	0.307248i	0.116502	−	0.993190i	$-0.462832\pi$
$389$	2.51940e6	−	916987.i	0.844158	−	0.307248i	0.727656	+	0.685942i	$0.240610\pi$
$390$	49498.4	−	18015.9i	0.0164790	−	0.00599785i
$391$	−24594.8	−	42599.4i	−0.00813581	−	0.0140916i
$392$	530153.	−	918252.i	0.174255	−	0.301819i
$393$	40785.9	−	231308.i	0.0133208	−	0.0755458i
$394$	1.95614e6	−	1.64140e6i	0.634833	−	0.532688i
$395$	337209.	+	282952.i	0.108744	+	0.0912472i
$396$	−400790.	−	2.27299e6i	−0.128434	−	0.728384i
$397$	5.05560e6	+	1.84009e6i	1.60989	+	0.585952i	0.981418	−	0.191881i	$-0.0614587\pi$
$397$	5.05560e6	+	1.84009e6i	1.60989	+	0.585952i	0.628471	+	0.777833i	$0.283681\pi$
$398$	−45712.9			−0.0144654
$399$	27308.8	−	3716.77i	0.00858756	−	0.00116878i
$400$	−766601.			−0.239563
$401$	−1.58753e6	−	577812.i	−0.493015	−	0.179443i	0.0835349	−	0.996505i	$-0.473379\pi$
$401$	−1.58753e6	−	577812.i	−0.493015	−	0.179443i	−0.576550	+	0.817062i	$0.695601\pi$
$402$	−41395.5	−	234765.i	−0.0127758	−	0.0724551i
$403$	3.81381e6	+	3.20016e6i	1.16976	+	0.981543i
$404$	497836.	−	417734.i	0.151751	−	0.127334i
$405$	115273.	−	653746.i	0.0349213	−	0.198048i
$406$	92892.1	−	160894.i	0.0279682	−	0.0484423i
$407$	−1.13092e6	−	1.95881e6i	−0.338412	−	0.586148i
$408$	17711.3	−	6446.38i	0.00526744	−	0.00191719i
$409$	−3.10067e6	+	1.12855e6i	−0.916532	+	0.333590i	−0.756858	−	0.653579i	$-0.773267\pi$
$409$	−3.10067e6	+	1.12855e6i	−0.916532	+	0.333590i	−0.159674	+	0.987170i	$0.551044\pi$
$410$	399953.	+	692740.i	0.117503	+	0.203522i
$411$	−3707.02	+	6420.74i	−0.00108248	+	0.00187491i
$412$	372434.	−	2.11218e6i	0.108095	−	0.613038i
$413$	−17468.0	+	14657.4i	−0.00503927	+	0.00422845i
$414$	−139948.	−	117431.i	−0.0401298	−	0.0336729i
$415$	178846.	+	1.01429e6i	0.0509752	+	0.289095i
$416$	−980685.	−	356940.i	−0.277841	−	0.101126i
$417$	332564.			0.0936560
$418$	2.29968e6	+	2.97003e6i	0.643764	+	0.831420i
$419$	−6.35878e6			−1.76945			−0.884726	−	0.466112i	$-0.845654\pi$
$419$	−6.35878e6			−1.76945			−0.884726	+	0.466112i	$0.845654\pi$
$420$	3007.86	+	1094.77i	0.000832022	+	0.000302831i
$421$	957000.	+	5.42742e6i	0.263152	+	1.49241i	0.774246	+	0.632884i	$0.218129\pi$
$421$	957000.	+	5.42742e6i	0.263152	+	1.49241i	−0.511094	+	0.859525i	$0.670760\pi$
$422$	−1.88909e6	−	1.58514e6i	−0.516383	−	0.433297i
$423$	−2.33641e6	+	1.96048e6i	−0.634889	+	0.532735i
$424$	−71602.7	+	406079.i	−0.0193426	+	0.109697i
$425$	389790.	−	675136.i	0.104679	−	0.181309i
$426$	−5852.21	−	10136.3i	−0.00156241	−	0.00270618i
$427$	−506752.	+	184443.i	−0.134501	+	0.0489544i
$428$	1.07506e6	−	391289.i	0.283676	−	0.103250i
$429$	344017.	+	595856.i	0.0902479	+	0.156314i
$430$	−82316.0	+	142575.i	−0.0214691	+	0.0371855i
$431$	−128666.	+	729700.i	−0.0333634	+	0.189213i	−0.996935	−	0.0782385i	$-0.975070\pi$
$431$	−128666.	+	729700.i	−0.0333634	+	0.189213i	0.963571	+	0.267452i	$0.0861816\pi$
$432$	107532.	−	90230.1i	0.0277223	−	0.0232617i
$433$	1.90445e6	+	1.59802e6i	0.488145	+	0.409602i	0.853361	−	0.521321i	$-0.174560\pi$
$433$	1.90445e6	+	1.59802e6i	0.488145	+	0.409602i	−0.365216	+	0.930923i	$0.619005\pi$
$434$	52534.1	+	297936.i	0.0133880	+	0.0759274i
$435$	−36423.8	−	13257.2i	−0.00922917	−	0.00335914i
$436$	2.59960e6			0.654923
$437$	290551.	+	63082.5i	0.0727812	+	0.0158018i
$438$	−102407.			−0.0255061
$439$	4.12968e6	+	1.50308e6i	1.02272	+	0.372239i	0.798303	−	0.602256i	$-0.205731\pi$
$439$	4.12968e6	+	1.50308e6i	1.02272	+	0.372239i	0.224414	+	0.974494i	$0.427953\pi$
$440$	75755.2	+	429629.i	0.0186544	+	0.105794i
$441$	3.06774e6	+	2.57414e6i	0.751142	+	0.630283i
$442$	812998.	−	682186.i	0.197940	−	0.166091i
$443$	1.00942e6	−	5.72471e6i	0.244379	−	1.38594i	−0.577553	−	0.816354i	$-0.695992\pi$
$443$	1.00942e6	−	5.72471e6i	0.244379	−	1.38594i	0.821931	−	0.569587i	$-0.192897\pi$
$444$	34299.8	−	59409.0i	0.00825723	−	0.0143019i
$445$	−511256.	−	885521.i	−0.122388	−	0.211982i
$446$	−3.39667e6	+	1.23629e6i	−0.808567	+	0.294294i
$447$	455639.	−	165839.i	0.107858	−	0.0392571i
$448$	−31708.9	−	54921.4i	−0.00746424	−	0.0129284i
$449$	−3.74499e6	+	6.48652e6i	−0.876668	+	1.51843i	−0.0216932	+	0.999765i	$0.506906\pi$
$449$	−3.74499e6	+	6.48652e6i	−0.876668	+	1.51843i	−0.854975	+	0.518669i	$0.826428\pi$
$450$	502774.	−	2.85137e6i	0.117042	−	0.663778i
$451$	−8.00384e6	+	6.71602e6i	−1.85292	+	1.55479i
$452$	84326.4	+	70758.2i	0.0194141	+	0.0162904i
$453$	−95502.0	−	541619.i	−0.0218659	−	0.124008i
$454$	334514.	+	121753.i	0.0761683	+	0.0277230i
$455$	180237.			0.0408145
$456$	−43136.5	+	105442.i	−0.00971478	+	0.0237466i
$457$	−3.32838e6			−0.745491			−0.372745	−	0.927934i	$-0.621584\pi$
$457$	−3.32838e6			−0.745491			−0.372745	+	0.927934i	$0.621584\pi$
$458$	−2.21056e6	−	804580.i	−0.492424	−	0.179228i
$459$	24788.3	+	140581.i	0.00549179	+	0.0311455i
$460$	26452.3	+	22196.1i	0.00582866	+	0.00489083i
$461$	6.10122e6	−	5.11953e6i	1.33710	−	1.12196i	0.354741	−	0.934965i	$-0.384569\pi$
$461$	6.10122e6	−	5.11953e6i	1.33710	−	1.12196i	0.982361	−	0.186996i	$-0.0598753\pi$
$462$	−7260.18	+	41174.5i	−0.00158250	+	0.00897478i
$463$	−3.15816e6	+	5.47009e6i	−0.684670	+	1.18588i	0.288870	+	0.957368i	$0.406720\pi$
$463$	−3.15816e6	+	5.47009e6i	−0.684670	+	1.18588i	−0.973540	+	0.228515i	$0.926613\pi$
$464$	383980.	+	665072.i	0.0827967	+	0.143408i
$465$	59312.8	−	21588.1i	0.0127208	−	0.00463001i
$466$	3.65310e6	−	1.32962e6i	0.779286	−	0.283637i
$467$	3.09823e6	+	5.36629e6i	0.657387	+	1.13863i	0.981290	+	0.192538i	$0.0616718\pi$
$467$	3.09823e6	+	5.36629e6i	0.657387	+	1.13863i	−0.323902	+	0.946091i	$0.604995\pi$
$468$	1.97082e6	−	3.41356e6i	0.415942	−	0.720432i
$469$	141641.	−	803289.i	0.0297343	−	0.168632i
$470$	441615.	−	370559.i	0.0922146	−	0.0773772i
$471$	−36108.4	−	30298.6i	−0.00749992	−	0.00629318i
$472$	−16367.7	−	92826.0i	−0.00338169	−	0.0191785i
$473$	−2.02071e6	−	735480.i	−0.415291	−	0.151153i
$474$	−174385.			−0.0356503
$475$	1.43658e6	+	4.48776e6i	0.292144	+	0.912632i
$476$	64491.5			0.0130462
$477$	−1.46345e6	−	532653.i	−0.294498	−	0.107188i
$478$	208021.	+	1.17975e6i	0.0416426	+	0.236167i
$479$	−2.38916e6	−	2.00475e6i	−0.475781	−	0.399228i	0.373117	−	0.927784i	$-0.378289\pi$
$479$	−2.38916e6	−	2.00475e6i	−0.475781	−	0.399228i	−0.848898	+	0.528557i	$0.822733\pi$
$480$	−10135.7	+	8504.90i	−0.00200795	+	0.00168487i
$481$	670753.	−	3.80403e6i	0.132190	−	0.749689i
$482$	1.85333e6	−	3.21007e6i	0.363359	−	0.629356i
$483$	1654.68	+	2865.99i	0.000322735	+	0.000558994i
$484$	−2.93326e6	+	1.06762e6i	−0.569164	+	0.207159i
$485$	1.43941e6	−	523902.i	0.277862	−	0.101134i
$486$	397979.	+	689320.i	0.0764311	+	0.132382i
$487$	−1.90422e6	+	3.29820e6i	−0.363827	+	0.630166i	−0.988587	−	0.150650i	$-0.951863\pi$
$487$	−1.90422e6	+	3.29820e6i	−0.363827	+	0.630166i	0.624760	+	0.780816i	$0.285197\pi$
$488$	387088.	−	2.19528e6i	0.0735800	−	0.417293i
$489$	−387071.	+	324791.i	−0.0732013	+	0.0614232i
$490$	−579848.	−	486550.i	−0.109100	−	0.0915456i
$491$	−1.80155e6	−	1.02171e7i	−0.337242	−	1.91260i	−0.403868	−	0.914817i	$-0.632335\pi$
$491$	−1.80155e6	−	1.02171e7i	−0.337242	−	1.91260i	0.0666263	−	0.997778i	$-0.478776\pi$
$492$	−297776.	−	108382.i	−0.0554596	−	0.0201856i
$493$	−780962.			−0.144715
$494$	−251797.	+	6.40993e6i	−0.0464230	+	1.18178i
$495$	−1.64769e6			−0.302247
$496$	−1.17513e6	−	427713.i	−0.214478	−	0.0780635i
$497$	−6954.37	−	39440.2i	−0.00126289	−	0.00716223i
$498$	−312556.	−	262265.i	−0.0564747	−	0.0473879i
$499$	5.77506e6	−	4.84585e6i	1.03826	−	0.871201i	0.0464469	−	0.998921i	$-0.485210\pi$
$499$	5.77506e6	−	4.84585e6i	1.03826	−	0.871201i	0.991810	+	0.127720i	$0.0407657\pi$
$500$	−194204.	+	1.10138e6i	−0.0347402	+	0.197021i
$501$	−196847.	+	340949.i	−0.0350377	+	0.0606870i
$502$	−1.20219e6	−	2.08226e6i	−0.212919	−	0.368787i
$503$	5.41426e6	−	1.97063e6i	0.954155	−	0.347284i	0.182415	−	0.983222i	$-0.441609\pi$
$503$	5.41426e6	−	1.97063e6i	0.954155	−	0.347284i	0.771740	+	0.635938i	$0.219386\pi$
$504$	225076.	−	81921.0i	0.0394687	−	0.0143654i
$505$	−231969.	−	401783.i	−0.0404764	−	0.0701072i
$506$	−225520.	+	390612.i	−0.0391569	+	0.0678217i
$507$	−131102.	+	743517.i	−0.0226511	+	0.128461i
$508$	−2.95915e6	+	2.48302e6i	−0.508754	+	0.426896i
$509$	−41122.5	−	34505.9i	−0.00703534	−	0.00590335i	0.639263	−	0.768988i	$-0.279239\pi$
$509$	−41122.5	−	34505.9i	−0.00703534	−	0.00590335i	−0.646299	+	0.763085i	$0.723684\pi$
$510$	−2336.49	−	13250.9i	−0.000397775	−	0.00225590i
$511$	−329270.	−	119845.i	−0.0557828	−	0.0203033i
$512$	262144.			0.0441942
$513$	−729728.	−	460416.i	−0.122424	−	0.0772426i
$514$	4.02234e6			0.671538
$515$	−1.43878e6	−	523672.i	−0.239043	−	0.0870044i
$516$	−11325.3	−	64228.8i	−0.00187251	−	0.0106195i
$517$	5.76832e6	+	4.84019e6i	0.949124	+	0.796410i
$518$	179810.	−	150878.i	0.0294435	−	0.0247060i
$519$	121917.	−	691426.i	0.0198676	−	0.112675i
$520$	−372514.	+	645213.i	−0.0604135	+	0.104639i
$521$	−139887.	−	242291.i	−0.0225779	−	0.0391060i	0.854516	−	0.519426i	$-0.173854\pi$
$521$	−139887.	−	242291.i	−0.0225779	−	0.0391060i	−0.877094	+	0.480320i	$0.840521\pi$
$522$	−2.72557e6	+	992026.i	−0.437805	+	0.159348i
$523$	5.54069e6	−	2.01665e6i	0.885747	−	0.322385i	0.141220	−	0.989978i	$-0.454898\pi$
$523$	5.54069e6	−	2.01665e6i	0.885747	−	0.322385i	0.744527	+	0.667593i	$0.232675\pi$
$524$	1.66103e6	+	2.87699e6i	0.264271	+	0.457730i
$525$	−26224.2	+	45421.7i	−0.00415245	+	0.00719226i
$526$	1.37722e6	−	7.81060e6i	0.217040	−	1.23089i
$527$	974196.	−	817447.i	0.152799	−	0.128213i
$528$	−132392.	−	111090.i	−0.0206669	−	0.0173416i
$529$	−1.11146e6	−	6.30340e6i	−0.172685	−	0.979345i
$530$	276614.	+	100679.i	0.0427744	+	0.0155686i
$531$	356001.			0.0547917
$532$	−262094.	+	288548.i	−0.0401493	+	0.0442016i
$533$	−1.78433e7			−2.72055
$534$	380643.	+	138543.i	0.0577651	+	0.0210248i
$535$	−141822.	−	804315.i	−0.0214220	−	0.121490i
$536$	2.58288e6	+	2.16729e6i	0.388322	+	0.325841i
$537$	−177667.	+	149080.i	−0.0265871	+	0.0223092i
$538$	−166329.	+	943300.i	−0.0247750	+	0.140506i
$539$	4.94350e6	−	8.56240e6i	0.732931	−	1.26947i
$540$	−50105.2	−	86784.8i	−0.00739432	−	0.0128073i
$541$	1.31836e6	−	479845.i	0.193661	−	0.0704868i	−0.243369	−	0.969934i	$-0.578253\pi$
$541$	1.31836e6	−	479845.i	0.193661	−	0.0704868i	0.437030	+	0.899447i	$0.356030\pi$
$542$	−3.26042e6	+	1.18670e6i	−0.476734	+	0.173517i
$543$	−7339.35	−	12712.1i	−0.00106821	−	0.00185020i
$544$	−133291.	+	230867.i	−0.0193110	+	0.0334476i
$545$	322259.	−	1.82762e6i	0.0464745	−	0.263570i
$546$	−54696.7	+	45896.0i	−0.00785199	+	0.00658860i
$547$	3.65234e6	+	3.06468e6i	0.521919	+	0.437942i	0.865300	−	0.501254i	$-0.167128\pi$
$547$	3.65234e6	+	3.06468e6i	0.521919	+	0.437942i	−0.343381	+	0.939196i	$0.611572\pi$
$548$	−18209.2	−	103270.i	−0.00259024	−	0.0146900i
$549$	7.91149e6	+	2.87955e6i	1.12028	+	0.407749i
$550$	−7.14830e6			−1.00762
$551$	3.17384e6	−	3.49418e6i	0.445354	−	0.490305i
$552$	−13679.6			−0.00191085
$553$	−560702.	−	204079.i	−0.0779686	−	0.0283782i
$554$	1.04101e6	+	5.90384e6i	0.144105	+	0.817260i
$555$	−37514.9	−	31478.8i	−0.00516978	−	0.00433796i
$556$	−3.60327e6	+	3.02350e6i	−0.494322	+	0.414785i
$557$	−363259.	+	2.06015e6i	−0.0496111	+	0.281359i	−0.999514	−	0.0311880i	$-0.990071\pi$
$557$	−363259.	+	2.06015e6i	−0.0496111	+	0.281359i	0.949902	+	0.312547i	$0.101182\pi$
$558$	2.36159e6	−	4.09039e6i	0.321084	−	0.556133i
$559$	−1.83620e6	−	3.18039e6i	−0.248536	−	0.430477i
$560$	−42542.7	+	15484.3i	−0.00573264	+	0.00208651i
$561$	165152.	−	60110.4i	0.0221553	−	0.00806385i
$562$	1.77868e6	+	3.08076e6i	0.237551	+	0.411450i
$563$	3.56651e6	−	6.17738e6i	0.474212	−	0.821360i	−0.525352	−	0.850885i	$-0.676066\pi$
$563$	3.56651e6	−	6.17738e6i	0.474212	−	0.821360i	0.999564	+	0.0295254i	$0.00939960\pi$
$564$	−39657.5	+	224909.i	−0.00524961	+	0.0297720i
$565$	60199.4	−	50513.3i	0.00793361	−	0.00665709i
$566$	4.29648e6	+	3.60518e6i	0.563731	+	0.473027i
$567$	156253.	+	886157.i	0.0204114	+	0.115759i
$568$	155562.	+	56619.9i	0.0202317	+	0.00736373i
$569$	−1.17282e7			−1.51863			−0.759314	−	0.650725i	$-0.774465\pi$
$569$	−1.17282e7			−1.51863			−0.759314	+	0.650725i	$0.774465\pi$
$570$	68782.6	+	43397.8i	0.00886730	+	0.00559475i
$571$	−7.62656e6			−0.978900			−0.489450	−	0.872031i	$-0.662802\pi$
$571$	−7.62656e6			−0.978900			−0.489450	+	0.872031i	$0.662802\pi$
$572$	−9.14457e6	−	3.32835e6i	−1.16862	−	0.425343i
$573$	−191903.	−	1.08834e6i	−0.0244172	−	0.138477i
$574$	−830606.	−	696962.i	−0.105224	−	0.0882936i
$575$	−433435.	+	363695.i	−0.0546707	+	0.0458742i
$576$	−171927.	+	975045.i	−0.0215917	+	0.122453i
$577$	3.40972e6	−	5.90580e6i	0.426362	−	0.738481i	−0.570184	−	0.821517i	$-0.693128\pi$
$577$	3.40972e6	−	5.90580e6i	0.426362	−	0.738481i	0.996547	+	0.0830359i	$0.0264616\pi$
$578$	2.70417e6	+	4.68375e6i	0.336677	+	0.583142i
$579$	−858598.	+	312504.i	−0.106437	+	0.0387400i
$580$	515173.	−	187507.i	0.0635891	−	0.0231445i
$581$	−698041.	−	1.20904e6i	−0.0857908	−	0.148594i
$582$	−303412.	+	525525.i	−0.0371300	+	0.0643111i
$583$	−667672.	+	3.78656e6i	−0.0813564	+	0.461395i
$584$	1.10956e6	−	931030.i	0.134623	−	0.112962i
$585$	−2.15556e6	−	1.80873e6i	−0.260417	−	0.218516i
$586$	−803170.	−	4.55501e6i	−0.0966193	−	0.547955i
$587$	1.46078e7	+	5.31681e6i	1.74981	+	0.636877i	0.999701	−	0.0244425i	$-0.00778107\pi$
$587$	1.46078e7	+	5.31681e6i	1.74981	+	0.636877i	0.750104	+	0.661320i	$0.230003\pi$
$588$	299864.			0.0357669
$589$	−301722.	+	7.68086e6i	−0.0358360	+	0.912266i
$590$	−67289.4			−0.00795824
$591$	678617.	+	246996.i	0.0799201	+	0.0290885i
$592$	168484.	+	955521.i	0.0197585	+	0.112056i
$593$	8.10680e6	+	6.80242e6i	0.946701	+	0.794377i	0.978739	−	0.205110i	$-0.0657552\pi$
$593$	8.10680e6	+	6.80242e6i	0.946701	+	0.794377i	−0.0320376	+	0.999487i	$0.510200\pi$
$594$	1.00270e6	−	841367.i	0.116602	−	0.0978406i
$595$	7994.68	−	45340.1i	0.000925782	−	0.00525037i
$596$	−3.42904e6	+	5.93927e6i	−0.395418	+	0.684885i
$597$	−6464.01	−	11196.0i	−0.000742277	−	0.00128566i
$598$	−723820.	+	263449.i	−0.0827709	+	0.0301261i
$599$	1.99607e6	−	726509.i	0.227305	−	0.0827321i	−0.225857	−	0.974160i	$-0.572518\pi$
$599$	1.99607e6	−	726509.i	0.227305	−	0.0827321i	0.453162	+	0.891428i	$0.350296\pi$
$600$	−108401.	−	187756.i	−0.0122929	−	0.0212919i
$601$	−4.92964e6	+	8.53839e6i	−0.556710	+	0.964251i	0.441058	+	0.897479i	$0.354603\pi$
$601$	−4.92964e6	+	8.53839e6i	−0.556710	+	0.964251i	−0.997768	+	0.0667720i	$0.978730\pi$
$602$	38751.3	−	219770.i	0.00435808	−	0.0247159i
$603$	−9.75521e6	+	8.18559e6i	−1.09256	+	0.916763i
$604$	5.95886e6	+	5.00008e6i	0.664616	+	0.557679i
$605$	386958.	+	2.19455e6i	0.0429809	+	0.243757i
$606$	172707.	+	62860.3i	0.0191042	+	0.00695336i
$607$	5.07793e6			0.559390			0.279695	−	0.960089i	$-0.409767\pi$
$607$	5.07793e6			0.559390			0.279695	+	0.960089i	$0.409767\pi$
$608$	−491248.	−	1.53462e6i	−0.0538942	−	0.168361i
$609$	52541.4			0.00574062
$610$	−1.49539e6	−	544277.i	−0.162716	−	0.0592236i
$611$	2.23304e6	+	1.26642e7i	0.241987	+	1.37238i
$612$	−771292.	−	647191.i	−0.0832415	−	0.0698479i
$613$	−7.49756e6	+	6.29120e6i	−0.805877	+	0.676211i	−0.949620	−	0.313404i	$-0.898531\pi$
$613$	−7.49756e6	+	6.29120e6i	−0.805877	+	0.676211i	0.143743	+	0.989615i	$0.454086\pi$
$614$	−356322.	+	2.02080e6i	−0.0381436	+	0.216323i
$615$	−113110.	+	195913.i	−0.0120591	+	0.0208870i
$616$	−295675.	−	512124.i	−0.0313951	−	0.0543780i
$617$	2.20526e6	−	802648.i	0.233210	−	0.0848814i	−0.222772	−	0.974871i	$-0.571511\pi$
$617$	2.20526e6	−	802648.i	0.233210	−	0.0848814i	0.455982	+	0.889989i	$0.349288\pi$
$618$	569977.	−	207455.i	0.0600325	−	0.0218500i
$619$	−3.83994e6	−	6.65096e6i	−0.402807	−	0.697683i	0.591256	−	0.806484i	$-0.298632\pi$
$619$	−3.83994e6	−	6.65096e6i	−0.402807	−	0.697683i	−0.994064	+	0.108801i	$0.965299\pi$
$620$	−446375.	+	773143.i	−0.0466359	+	0.0807757i
$621$	17991.0	−	102032.i	0.00187209	−	0.0106171i
$622$	4.23329e6	−	3.55215e6i	0.438735	−	0.368142i
$623$	1.06175e6	+	890918.i	0.109598	+	0.0919639i
$624$	−51251.5	−	290662.i	−0.00526921	−	0.0298832i
$625$	−8.04332e6	−	2.92753e6i	−0.823636	−	0.299779i
$626$	−1.04506e6			−0.106587
$627$	−402234.	+	983213.i	−0.0408611	+	0.0998800i
$628$	666687.			0.0674563
$629$	−927184.	−	337467.i	−0.0934414	−	0.0340099i
$630$	−29692.2	−	168393.i	−0.00298051	−	0.0169033i
$631$	−4.19466e6	−	3.51974e6i	−0.419395	−	0.351915i	0.408538	−	0.912741i	$-0.366039\pi$
$631$	−4.19466e6	−	3.51974e6i	−0.419395	−	0.351915i	−0.827933	+	0.560827i	$0.810483\pi$
$632$	1.88943e6	−	1.58542e6i	0.188164	−	0.157889i
$633$	121105.	−	686821.i	0.0120130	−	0.0681294i
$634$	5.81670e6	−	1.00748e7i	0.574717	−	0.995438i
$635$	1.37883e6	+	2.38821e6i	0.135699	+	0.235038i
$636$	−109582.	+	39884.5i	−0.0107422	+	0.00390986i
$637$	1.58665e7	−	5.77493e6i	1.54929	−	0.563895i
$638$	3.58049e6	+	6.20158e6i	0.348249	+	0.603185i
$639$	−312623.	+	541478.i	−0.0302878	+	0.0524601i
$640$	32496.7	−	184298.i	0.00313609	−	0.0177857i
$641$	−9.47679e6	+	7.95197e6i	−0.910995	+	0.764416i	−0.972308	−	0.233703i	$-0.924916\pi$
$641$	−9.47679e6	+	7.95197e6i	−0.910995	+	0.764416i	0.0613128	+	0.998119i	$0.480471\pi$
$642$	247852.	+	207973.i	0.0237332	+	0.0199145i
$643$	−3.21402e6	−	1.82276e7i	−0.306564	−	1.73861i	−0.616051	−	0.787706i	$-0.711269\pi$
$643$	−3.21402e6	−	1.82276e7i	−0.306564	−	1.73861i	0.309487	−	0.950904i	$-0.399843\pi$
$644$	−43984.3	−	16009.0i	−0.00417910	−	0.00152107i
$645$	−46559.4			−0.00440664
$646$	1.60130e6	+	347664.i	0.150971	+	0.0327777i
$647$	1.28259e7			1.20456			0.602278	−	0.798286i	$-0.294260\pi$
$647$	1.28259e7			1.20456			0.602278	+	0.798286i	$0.294260\pi$
$648$	−3.49522e6	−	1.27216e6i	−0.326992	−	0.119015i
$649$	−152624.	−	865572.i	−0.0142236	−	0.0806662i
$650$	−9.35162e6	−	7.84694e6i	−0.868168	−	0.728479i
$651$	−65541.8	+	54996.1i	−0.00606130	+	0.00508603i
$652$	1.24101e6	−	7.03810e6i	0.114329	−	0.648390i
$653$	−6.75662e6	+	1.17028e7i	−0.620079	+	1.07401i	0.369392	+	0.929274i	$0.379566\pi$
$653$	−6.75662e6	+	1.17028e7i	−0.620079	+	1.07401i	−0.989471	+	0.144734i	$0.953767\pi$
$654$	367595.	+	636693.i	0.0336067	+	0.0582084i
$655$	2.22855e6	−	811125.i	0.202964	−	0.0738728i
$656$	4.21169e6	−	1.53293e6i	0.382117	−	0.139079i
$657$	2.73526e6	+	4.73762e6i	0.247221	+	0.428200i
$658$	−390717.	+	676742.i	−0.0351801	+	0.0609338i
$659$	−1.37795e6	+	7.81476e6i	−0.123601	+	0.700974i	0.858528	+	0.512766i	$0.171379\pi$
$659$	−1.37795e6	+	7.81476e6i	−0.123601	+	0.700974i	−0.982129	+	0.188208i	$0.939732\pi$
$660$	−94512.5	+	79305.4i	−0.00844558	+	0.00708668i
$661$	−1.35246e7	−	1.13485e7i	−1.20399	−	1.01027i	−0.999507	−	0.0313953i	$-0.990005\pi$
$661$	−1.35246e7	−	1.13485e7i	−1.20399	−	1.01027i	−0.204481	−	0.978871i	$-0.565551\pi$
$662$	−956589.	−	5.42509e6i	−0.0848361	−	0.481129i
$663$	282042.	+	102655.i	0.0249190	+	0.00906977i
$664$	5.77086e6			0.507949
$665$	170370.	+	220032.i	0.0149396	+	0.0192945i
$666$	−3.66456e6			−0.320137
$667$	532629.	+	193861.i	0.0463565	+	0.0168724i
$668$	−966934.	−	5.48375e6i	−0.0838408	−	0.475485i
$669$	−783094.	−	657094.i	−0.0676470	−	0.0567626i
$670$	1.84388e6	−	1.54720e6i	0.158688	−	0.133155i
$671$	3.60947e6	−	2.04703e7i	0.309483	−	1.75517i
$672$	8967.54	−	15532.2i	0.000766038	−	0.00132682i
$673$	193313.	+	334829.i	0.0164522	+	0.0284961i	0.874134	−	0.485684i	$-0.161430\pi$
$673$	193313.	+	334829.i	0.0164522	+	0.0284961i	−0.857682	+	0.514180i	$0.828096\pi$
$674$	9.62920e6	−	3.50474e6i	0.816470	−	0.297171i
$675$	1.54298e6	−	561597.i	0.130347	−	0.0474423i
$676$	−5.33921e6	−	9.24778e6i	−0.449376	−	0.778342i
$677$	5.67362e6	−	9.82699e6i	0.475760	−	0.824041i	−0.523854	−	0.851808i	$-0.675506\pi$
$677$	5.67362e6	−	9.82699e6i	0.475760	−	0.824041i	0.999614	+	0.0277669i	$0.00883961\pi$
$678$	−5405.96	+	30658.7i	−0.000451646	+	0.00256141i
$679$	−1.59058e6	+	1.33465e6i	−0.132397	+	0.111095i
$680$	145785.	+	122329.i	0.0120904	+	0.0101451i
$681$	17482.0	+	99145.4i	0.00144452	+	0.00819228i
$682$	−1.09577e7	−	3.98828e6i	−0.902110	−	0.328341i
$683$	−5.48388e6			−0.449817			−0.224909	−	0.974380i	$-0.572208\pi$
$683$	−5.48388e6			−0.449817			−0.224909	+	0.974380i	$0.572208\pi$
$684$	6.03020e6	−	820721.i	0.492823	−	0.0670742i
$685$	−74860.1			−0.00609571
$686$	1.94226e6	+	706926.i	0.157579	+	0.0573540i
$687$	−115526.	−	655182.i	−0.00933875	−	0.0529627i
$688$	706642.	+	592943.i	0.0569152	+	0.0477575i
$689$	−5.03010e6	+	4.22076e6i	−0.403672	+	0.338721i
$690$	−1695.79	+	9617.32i	−0.000135597	+	0.000769009i
$691$	4.67254e6	−	8.09308e6i	0.372270	−	0.644791i	−0.617644	−	0.786458i	$-0.711913\pi$
$691$	4.67254e6	−	8.09308e6i	0.372270	−	0.644791i	0.989914	+	0.141667i	$0.0452462\pi$
$692$	4.96514e6	+	8.59987e6i	0.394154	+	0.682695i
$693$	2.09876e6	−	763887.i	0.166008	−	0.0604221i
$694$	1.96439e6	−	714978.i	0.154820	−	0.0563500i
$695$	1.67896e6	+	2.90805e6i	0.131850	+	0.228370i
$696$	−108593.	+	188088.i	−0.00849724	+	0.0147177i
$697$	−791466.	+	4.48863e6i	−0.0617093	+	0.349971i
$698$	−2.10243e6	+	1.76415e6i	−0.163336	+	0.137055i
$699$	842215.	+	706702.i	0.0651973	+	0.0547071i
$700$	−128816.	−	730552.i	−0.00993631	−	0.0563516i
$701$	−1.53506e7	−	5.58716e6i	−1.17986	−	0.429434i	−0.323707	−	0.946157i	$-0.604929\pi$
$701$	−1.53506e7	−	5.58716e6i	−1.17986	−	0.429434i	−0.856152	+	0.516723i	$0.827152\pi$
$702$	2.23536e6			0.171201
$703$	5.27798e6	−	2.77693e6i	0.402791	−	0.211923i
$704$	2.44441e6			0.185884
$705$	153204.	+	55761.6i	0.0116090	+	0.00422534i
$706$	1.05576e6	+	5.98753e6i	0.0797177	+	0.452102i
$707$	481744.	+	404231.i	0.0362467	+	0.0304146i
$708$	20420.4	−	17134.8i	0.00153102	−	0.00128468i
$709$	884422.	−	5.01581e6i	0.0660760	−	0.374736i	−0.933781	−	0.357844i	$-0.883512\pi$
$709$	884422.	−	5.01581e6i	0.0660760	−	0.374736i	0.999857	−	0.0168916i	$-0.00537701\pi$
$710$	59090.3	−	102347.i	0.00439916	−	0.00761957i
$711$	4.65778e6	+	8.06751e6i	0.345545	+	0.598502i
$712$	−5.38376e6	+	1.95953e6i	−0.398002	+	0.144861i
$713$	−867336.	+	315685.i	−0.0638945	+	0.0232557i
$714$	9119.38	+	15795.2i	0.000669452	+	0.00115953i
$715$	−3.47357e6	+	6.01640e6i	−0.254104	+	0.440121i
$716$	569626.	−	3.23051e6i	0.0415248	−	0.235499i
$717$	−259528.	+	217770.i	−0.0188533	+	0.0158198i
$718$	−5.25890e6	−	4.41274e6i	−0.380701	−	0.319446i
$719$	2.91449e6	+	1.65289e7i	0.210252	+	1.19240i	0.888958	+	0.457989i	$0.151430\pi$
$719$	2.91449e6	+	1.65289e7i	0.210252	+	1.19240i	−0.678706	+	0.734411i	$0.737459\pi$
$720$	664183.	+	241743.i	0.0477481	+	0.0173789i
$721$	2.07544e6			0.148686
$722$	−8.06323e6	+	5.75164e6i	−0.575660	+	0.410628i
$723$	1.04828e6			0.0745814
$724$	195093.	+	71007.9i	0.0138323	+	0.00503454i
$725$	1.55990e6	+	8.84665e6i	0.110218	+	0.625078i
$726$	−676257.	−	567447.i	−0.0476179	−	0.0399562i
$727$	−885411.	+	742948.i	−0.0621310	+	0.0521341i	−0.673324	−	0.739347i	$-0.735134\pi$
$727$	−885411.	+	742948.i	−0.0621310	+	0.0521341i	0.611193	+	0.791481i	$0.290690\pi$
$728$	175366.	−	994548.i	0.0122635	−	0.0695500i
$729$	6.94875e6	−	1.20356e7i	0.484271	−	0.838781i
$730$	−517005.	−	895479.i	−0.0359077	−	0.0621940i
$731$	−881501.	+	320840.i	−0.0610140	+	0.0222073i
$732$	592404.	−	215617.i	0.0408639	−	0.0148733i
$733$	−8.76801e6	−	1.51866e7i	−0.602756	−	1.04400i	−0.992402	−	0.123039i	$-0.960736\pi$
$733$	−8.76801e6	−	1.51866e7i	−0.602756	−	1.04400i	0.389646	−	0.920965i	$-0.372597\pi$
$734$	418062.	−	724105.i	0.0286418	−	0.0496091i
$735$	37172.6	−	210816.i	0.00253808	−	0.0143941i
$736$	148216.	−	124368.i	0.0100856	−	0.00846280i
$737$	2.40845e7	+	2.02093e7i	1.63331	+	1.37051i
$738$	2.93950e6	+	1.66708e7i	0.198670	+	1.12672i
$739$	5.57775e6	+	2.03014e6i	0.375706	+	0.136746i	0.522969	−	0.852352i	$-0.324824\pi$
$739$	5.57775e6	+	2.03014e6i	0.375706	+	0.136746i	−0.147263	+	0.989097i	$0.547046\pi$
$740$	692656.			0.0464984
$741$	−1.60552e6	+	844722.i	−0.107416	+	0.0565156i
$742$	−399016.			−0.0266060
$743$	−1.67676e7	−	6.10291e6i	−1.11429	−	0.405569i	−0.281726	−	0.959495i	$-0.590907\pi$
$743$	−1.67676e7	−	6.10291e6i	−1.11429	−	0.405569i	−0.832566	+	0.553926i	$0.813129\pi$
$744$	−61413.5	−	348293.i	−0.00406754	−	0.0230681i
$745$	3.75046e6	+	3.14701e6i	0.247568	+	0.207734i
$746$	−9.09444e6	+	7.63114e6i	−0.598313	+	0.502045i
$747$	−3.78481e6	+	2.14647e7i	−0.248166	+	1.40742i
$748$	−1.24290e6	+	2.15276e6i	−0.0812234	+	0.140683i
$749$	553537.	+	958755.i	0.0360531	+	0.0624457i
$750$	−297212.	+	108176.i	−0.0192936	+	0.00702229i
$751$	−1.93811e7	+	7.05414e6i	−1.25395	+	0.456399i	−0.881733	−	0.471749i	$-0.843623\pi$
$751$	−1.93811e7	+	7.05414e6i	−1.25395	+	0.456399i	−0.372212	+	0.928148i	$0.621401\pi$
$752$	−1.61507e6	−	2.79738e6i	−0.104147	−	0.180388i
$753$	339990.	−	588881.i	0.0218514	−	0.0378477i
$754$	−2.12360e6	+	1.20435e7i	−0.136033	+	0.771481i
$755$	4.25395e6	−	3.56949e6i	0.271597	−	0.227897i
$756$	104056.	+	87313.7i	0.00662162	+	0.00555620i
$757$	390824.	+	2.21647e6i	0.0247880	+	0.140580i	0.994690	−	0.102915i	$-0.0328171\pi$
$757$	390824.	+	2.21647e6i	0.0247880	+	0.140580i	−0.969902	+	0.243495i	$0.921706\pi$
$758$	1.62518e7	+	5.91518e6i	1.02738	+	0.373934i
$759$	−127558.			−0.00803717
$760$	−1.13980e6	+	155128.i	−0.0715802	+	0.00974221i
$761$	1.20169e7			0.752198			0.376099	−	0.926579i	$-0.377265\pi$
$761$	1.20169e7			0.752198			0.376099	+	0.926579i	$0.377265\pi$
$762$	−1.02658e6	−	373644.i	−0.0640479	−	0.0233115i
$763$	436825.	+	2.47736e6i	0.0271642	+	0.154056i
$764$	1.19738e7	+	1.00472e7i	0.742164	+	0.622750i
$765$	−550614.	+	462020.i	−0.0340168	+	0.0285435i
$766$	−3.07472e6	+	1.74376e7i	−0.189336	+	1.07378i
$767$	750502.	−	1.29991e6i	0.0460642	−	0.0797856i
$768$	37068.3	+	64204.2i	0.00226777	+	0.00392790i
$769$	1.21275e7	−	4.41403e6i	0.739527	−	0.269166i	0.0553348	−	0.998468i	$-0.482377\pi$
$769$	1.21275e7	−	4.41403e6i	0.739527	−	0.269166i	0.684192	+	0.729302i	$0.260155\pi$
$770$	−396697.	+	144386.i	−0.0241119	+	0.00877603i
$771$	568776.	+	985150.i	0.0344592	+	0.0596851i
$772$	6.46161e6	−	1.11918e7i	0.390209	−	0.675863i
$773$	−1.88170e6	+	1.06717e7i	−0.113267	+	0.642368i	0.874327	+	0.485337i	$0.161303\pi$
$773$	−1.88170e6	+	1.06717e7i	−0.113267	+	0.642368i	−0.987594	+	0.157030i	$0.949808\pi$
$774$	−2.66890e6	+	2.23947e6i	−0.160133	+	0.134367i
$775$	−1.12058e7	−	9.40281e6i	−0.670177	−	0.562345i
$776$	−1.49039e6	−	8.45242e6i	−0.0888476	−	0.503880i
$777$	62378.9	+	22704.1i	0.00370668	+	0.00134912i
$778$	−1.07244e7			−0.635218
$779$	−1.68665e7	−	2.17830e7i	−0.995820	−	1.28610i
$780$	−210700.			−0.0124002
$781$	1.45056e6	+	527962.i	0.0850960	+	0.0309724i
$782$	34166.7	+	193769.i	0.00199796	+	0.0113310i
$783$	−1.26007e6	−	1.05733e6i	−0.0734500	−	0.0616319i
$784$	−3.24897e6	+	2.72621e6i	−0.188780	+	0.158405i
$785$	82645.8	−	468708.i	0.00478682	−	0.0271474i
$786$	−469754.	+	813637.i	−0.0271215	+	0.0469758i
$787$	6.27288e6	+	1.08650e7i	0.361019	+	0.625304i	0.988129	−	0.153627i	$-0.0490955\pi$
$787$	6.27288e6	+	1.08650e7i	0.361019	+	0.625304i	−0.627110	+	0.778931i	$0.715762\pi$
$788$	−9.59824e6	+	3.49347e6i	−0.550651	+	0.200420i
$789$	2.10772e6	−	767146.i	0.120537	−	0.0438718i
$790$	−880389.	−	1.52488e6i	−0.0501888	−	0.0869296i
$791$	−53261.1	+	92250.9i	−0.00302670	+	0.00524239i
$792$	−1.60316e6	+	9.09198e6i	−0.0908164	+	0.515045i
$793$	2.71930e7	−	2.28176e7i	1.53559	−	1.28851i
$794$	−1.64854e7	−	1.38329e7i	−0.928003	−	0.778687i
$795$	14456.1	+	81984.6i	0.000811210	+	0.00460060i
$796$	171824.	+	62539.0i	0.00961174	+	0.00349839i
$797$	−5.82290e6			−0.324708			−0.162354	−	0.986733i	$-0.551909\pi$
$797$	−5.82290e6			−0.324708			−0.162354	+	0.986733i	$0.551909\pi$
$798$	−107732.	−	23390.1i	−0.00598878	−	0.00130024i
$799$	3.28483e6			0.182031
$800$	2.88148e6	+	1.04877e6i	0.159181	+	0.0579370i
$801$	−3.75753e6	−	2.13100e7i	−0.206929	−	1.17355i
$802$	5.17665e6	+	4.34373e6i	0.284193	+	0.238466i
$803$	1.03463e7	−	8.68155e6i	0.566233	−	0.475126i
$804$	−165582.	+	939061.i	−0.00903384	+	0.0512335i
$805$	−16707.5	+	28938.2i	−0.000908700	+	0.00157391i
$806$	−9.95714e6	−	1.72463e7i	−0.539880	−	0.935099i
$807$	−254552.	+	92649.5i	−0.0137592	+	0.00500794i
$808$	−2.44274e6	+	889086.i	−0.131628	+	0.0479088i
$809$	4.98973e6	+	8.64246e6i	0.268044	+	0.464265i	0.968357	−	0.249571i	$-0.0802896\pi$
$809$	4.98973e6	+	8.64246e6i	0.268044	+	0.464265i	−0.700313	+	0.713836i	$0.746956\pi$
$810$	−1.32766e6	+	2.29958e6i	−0.0711009	+	0.123150i
$811$	3.38527e6	−	1.91988e7i	0.180735	−	1.02500i	−0.750579	−	0.660780i	$-0.770225\pi$
$811$	3.38527e6	−	1.91988e7i	0.180735	−	1.02500i	0.931314	−	0.364217i	$-0.118663\pi$
$812$	−569276.	+	477679.i	−0.0302993	+	0.0254241i
$813$	−751684.	−	630738.i	−0.0398849	−	0.0334674i
$814$	1.57106e6	+	8.90992e6i	0.0831058	+	0.471317i
$815$	−4.79423e6	−	1.74496e6i	−0.252828	−	0.0920218i
$816$	−75391.9			−0.00396368
$817$	2.14693e6	−	5.24791e6i	0.112528	−	0.275062i
$818$	1.31987e7			0.689679
$819$	3.58421e6	+	1.30455e6i	0.186717	+	0.0679594i
$820$	−555609.	−	3.15102e6i	−0.0288559	−	0.163650i
$821$	−2.25173e7	−	1.88943e7i	−1.16589	−	0.978301i	−0.165924	−	0.986138i	$-0.553061\pi$
$821$	−2.25173e7	−	1.88943e7i	−1.16589	−	0.978301i	−0.999969	+	0.00783751i	$0.997505\pi$
$822$	22717.9	−	19062.6i	0.00117271	−	0.000984017i
$823$	−2.30058e6	+	1.30472e7i	−0.118396	+	0.671458i	0.866616	+	0.498975i	$0.166290\pi$
$823$	−2.30058e6	+	1.30472e7i	−0.118396	+	0.671458i	−0.985012	+	0.172483i	$0.944821\pi$
$824$	−4.28952e6	+	7.42967e6i	−0.220085	+	0.381199i
$825$	−1.01080e6	−	1.75076e6i	−0.0517048	−	0.0895554i
$826$	85710.6	−	31196.1i	0.00437104	−	0.00159093i
$827$	575420.	−	209436.i	0.0292564	−	0.0106485i	−0.327350	−	0.944903i	$-0.606156\pi$
$827$	575420.	−	209436.i	0.0292564	−	0.0106485i	0.356607	+	0.934255i	$0.383934\pi$
$828$	365379.	+	632856.i	0.0185212	+	0.0320796i
$829$	−1.75161e6	+	3.03388e6i	−0.0885221	+	0.153325i	−0.906887	−	0.421375i	$-0.861548\pi$
$829$	−1.75161e6	+	3.03388e6i	−0.0885221	+	0.153325i	0.818365	+	0.574699i	$0.194881\pi$
$830$	715384.	−	4.05714e6i	0.0360449	−	0.204421i
$831$	−1.29876e6	+	1.08979e6i	−0.0652421	+	0.0547446i
$832$	3.19785e6	+	2.68331e6i	0.160158	+	0.134389i
$833$	−748950.	−	4.24751e6i	−0.0373973	−	0.212091i
$834$	−1.25003e6	−	454975.i	−0.0622309	−	0.0226502i
$835$	−3.97516e6			−0.197305
$836$	−4.58073e6	−	1.43098e7i	−0.226683	−	0.708139i
$837$	2.67858e6			0.132157
$838$	2.39012e7	+	8.69932e6i	1.17573	+	0.427933i
$839$	−541714.	−	3.07221e6i	−0.0265684	−	0.150677i	0.968638	−	0.248478i	$-0.0799303\pi$
$839$	−541714.	−	3.07221e6i	−0.0265684	−	0.150677i	−0.995206	+	0.0978009i	$0.968819\pi$
$840$	−9808.13	−	8230.00i	−0.000479610	−	0.000402440i
$841$	−8.81878e6	+	7.39984e6i	−0.429951	+	0.360771i
$842$	3.82800e6	−	2.17097e7i	0.186077	−	1.05529i
$843$	−503026.	+	871267.i	−0.0243793	+	0.0422262i
$844$	4.93207e6	+	8.54259e6i	0.238327	+	0.412794i
$845$	−7.16343e6	+	2.60728e6i	−0.345127	+	0.125616i
$846$	1.14641e7	−	4.17260e6i	0.550699	−	0.200438i
$847$	−1.51031e6	−	2.61593e6i	−0.0723364	−	0.125290i
$848$	824687.	−	1.42840e6i	0.0393822	−	0.0682119i
$849$	−275437.	+	1.56208e6i	−0.0131145	+	0.0743763i
$850$	−2.38877e6	+	2.00442e6i	−0.113404	+	0.0951570i
$851$	548585.	+	460317.i	0.0259669	+	0.0217888i
$852$	8129.81	+	46106.4i	0.000383691	+	0.00217602i
$853$	4.11830e6	+	1.49894e6i	0.193796	+	0.0705361i	0.437095	−	0.899415i	$-0.356007\pi$
$853$	4.11830e6	+	1.49894e6i	0.193796	+	0.0705361i	−0.243299	+	0.969951i	$0.578230\pi$
$854$	2.15710e6			0.101210
$855$	170533.	−	4.34121e6i	0.00797799	−	0.203093i
$856$	−4.57621e6			−0.213463
$857$	2.68079e7	+	9.75727e6i	1.24684	+	0.453812i	0.879332	−	0.476209i	$-0.157989\pi$
$857$	2.68079e7	+	9.75727e6i	1.24684	+	0.453812i	0.367507	+	0.930021i	$0.380212\pi$
$858$	−477904.	−	2.71033e6i	−0.0221627	−	0.125691i
$859$	−4.99058e6	−	4.18760e6i	−0.230764	−	0.193634i	0.520072	−	0.854122i	$-0.325905\pi$
$859$	−4.99058e6	−	4.18760e6i	−0.230764	−	0.193634i	−0.750837	+	0.660488i	$0.770349\pi$
$860$	504462.	−	423293.i	0.0232585	−	0.0195162i
$861$	53248.1	−	301985.i	0.00244792	−	0.0138828i
$862$	1.48191e6	−	2.56675e6i	0.0679289	−	0.117656i
$863$	−1.79283e6	−	3.10527e6i	−0.0819429	−	0.141929i	0.822142	−	0.569283i	$-0.192779\pi$
$863$	−1.79283e6	−	3.10527e6i	−0.0819429	−	0.141929i	−0.904084	+	0.427354i	$0.859446\pi$
$864$	−527631.	+	192042.i	−0.0240462	+	0.00875208i
$865$	6.66156e6	−	2.42461e6i	0.302716	−	0.110180i
$866$	−4.97215e6	−	8.61202e6i	−0.225294	−	0.390221i
$867$	−764762.	+	1.32461e6i	−0.0345524	+	0.0598466i
$868$	210137.	−	1.19174e6i	0.00946678	−	0.0536888i
$869$	1.76183e7	−	1.47835e7i	0.791433	−	0.664091i
$870$	118772.	+	99661.5i	0.00532005	+	0.00446405i
$871$	9.32360e6	+	5.28768e7i	0.416426	+	2.36167i
$872$	−9.77130e6	−	3.55646e6i	−0.435172	−	0.158390i
$873$	3.24162e7			1.43955
$874$	−1.00581e6	−	634610.i	−0.0445389	−	0.0281014i
$875$	−1.08223e6			−0.0477857
$876$	384924.	+	140101.i	0.0169478	+	0.00616851i
$877$	−4.22766e6	−	2.39762e7i	−0.185610	−	1.05264i	−0.925170	−	0.379554i	$-0.876077\pi$
$877$	−4.22766e6	−	2.39762e7i	−0.185610	−	1.05264i	0.739560	−	0.673091i	$-0.235034\pi$
$878$	−1.34662e7	−	1.12995e7i	−0.589534	−	0.494677i
$879$	1.00204e6	−	840810.i	0.0437434	−	0.0367050i
$880$	303021.	−	1.71852e6i	0.0131906	−	0.0748078i
$881$	−1.53334e7	+	2.65582e7i	−0.665578	+	1.15281i	0.313551	+	0.949571i	$0.398481\pi$
$881$	−1.53334e7	+	2.65582e7i	−0.665578	+	1.15281i	−0.979128	+	0.203243i	$0.934852\pi$
$882$	−8.00930e6	−	1.38725e7i	−0.346675	−	0.600459i
$883$	−3.19403e7	+	1.16253e7i	−1.37860	+	0.501768i	−0.921752	−	0.387779i	$-0.873242\pi$
$883$	−3.19403e7	+	1.16253e7i	−1.37860	+	0.501768i	−0.456844	+	0.889547i	$0.651020\pi$
$884$	−3.98916e6	+	1.45193e6i	−0.171692	+	0.0624908i
$885$	−9515.02	−	16480.5i	−0.000408368	−	0.000707314i
$886$	−1.16261e7	+	2.01369e7i	−0.497563	+	0.861804i
$887$	3.44719e6	−	1.95500e7i	0.147115	−	0.834329i	−0.818530	−	0.574464i	$-0.805211\pi$
$887$	3.44719e6	−	1.95500e7i	0.147115	−	0.834329i	0.965645	−	0.259865i	$-0.0836782\pi$
$888$	−210201.	+	176380.i	−0.00894547	+	0.00750614i
$889$	−2.86351e6	−	2.40277e6i	−0.121519	−	0.101966i
$890$	710229.	+	4.02791e6i	0.0300555	+	0.170453i
$891$	−3.25918e7	−	1.18624e7i	−1.37535	−	0.500587i
$892$	1.44586e7			0.608436
$893$	−1.33496e7	+	1.46970e7i	−0.560195	+	0.616737i
$894$	−1.93952e6			−0.0811618
$895$	−2.20056e6	−	800940.i	−0.0918283	−	0.0334228i
$896$	44049.5	+	249817.i	0.00183304	+	0.0103957i
$897$	−166875.	−	140025.i	−0.00692485	−	0.00581064i
$898$	2.29507e7	−	1.92579e7i	0.949739	−	0.796926i
$899$	−2.54466e6	+	1.44315e7i	−0.105010	+	0.595540i
$900$	−5.79072e6	+	1.00298e7i	−0.238301	+	0.412750i
$901$	838650.	+	1.45258e6i	0.0344167	+	0.0596114i
$902$	3.92727e7	−	1.42941e7i	1.60721	−	0.584978i
$903$	59305.5	−	21585.4i	0.00242033	−	0.000880930i
$904$	−220161.	−	381329.i	−0.00896021	−	0.0155195i
$905$	74106.0	−	128355.i	0.00300768	−	0.00520946i
$906$	−382008.	+	2.16648e6i	−0.0154615	+	0.0876866i
$907$	−9.32979e6	+	7.82863e6i	−0.376577	+	0.315986i	−0.811357	−	0.584551i	$-0.801271\pi$
$907$	−9.32979e6	+	7.82863e6i	−0.376577	+	0.315986i	0.434780	+	0.900537i	$0.356826\pi$
$908$	−1.09079e6	−	915284.i	−0.0439064	−	0.0368418i
$909$	−1.70489e6	−	9.66889e6i	−0.0684362	−	0.388121i
$910$	−677468.	−	246578.i	−0.0271197	−	0.00987078i
$911$	−7.83360e6			−0.312727			−0.156363	−	0.987700i	$-0.549977\pi$
$911$	−7.83360e6			−0.312727			−0.156363	+	0.987700i	$0.549977\pi$
$912$	306393.	−	337318.i	0.0121981	−	0.0134293i
$913$	5.38114e7			2.13647
$914$	1.25106e7	+	4.55349e6i	0.495351	+	0.180293i
$915$	−78150.4	−	443213.i	−0.00308588	−	0.0175009i
$916$	7.20828e6	+	6.04846e6i	0.283852	+	0.238180i
$917$	−2.46259e6	+	2.06636e6i	−0.0967093	+	0.0811488i
$918$	99153.0	−	562325.i	0.00388328	−	0.0220232i
$919$	−1.61037e7	+	2.78925e7i	−0.628981	+	1.08943i	0.358776	+	0.933424i	$0.383194\pi$
$919$	−1.61037e7	+	2.78925e7i	−0.628981	+	1.08943i	−0.987757	+	0.156003i	$0.950139\pi$
$920$	−69062.1	−	119619.i	−0.00269011	−	0.00465941i
$921$	−545320.	+	198480.i	−0.0211837	+	0.00771025i
$922$	−2.99370e7	+	1.08962e7i	−1.15979	+	0.422131i
$923$	1.31811e6	+	2.28303e6i	0.0509268	+	0.0882079i
$924$	83619.4	−	144833.i	0.00322201	−	0.00558069i
$925$	−1.97083e6	+	1.11771e7i	−0.0757345	+	0.429512i
$926$	1.93543e7	−	1.62402e7i	0.741738	−	0.622392i
$927$	−2.48214e7	−	2.08276e7i	−0.948695	−	0.796049i
$928$	−533419.	−	3.02517e6i	−0.0203329	−	0.115313i
$929$	−2.21347e7	−	8.05638e6i	−0.841462	−	0.306267i	−0.114908	−	0.993376i	$-0.536657\pi$
$929$	−2.21347e7	−	8.05638e6i	−0.841462	−	0.306267i	−0.726554	+	0.687109i	$0.758879\pi$
$930$	−252477.			−0.00957227
$931$	2.20479e7	+	1.39110e7i	0.833669	+	0.525997i
$932$	−1.55502e7			−0.586403
$933$	1.46860e6	+	534526.i	0.0552330	+	0.0201032i
$934$	−4.30402e6	−	2.44093e7i	−0.161438	−	0.915562i
$935$	1.35940e6	+	1.14067e6i	0.0508533	+	0.0426710i
$936$	−1.20779e7	+	1.01345e7i	−0.450610	+	0.378107i
$937$	−2.47386e6	+	1.40299e7i	−0.0920504	+	0.522044i	0.903561	+	0.428460i	$0.140944\pi$
$937$	−2.47386e6	+	1.40299e7i	−0.0920504	+	0.522044i	−0.995611	+	0.0935842i	$0.970168\pi$
$938$	−1.63136e6	+	2.82560e6i	−0.0605401	+	0.104859i
$939$	−147776.	−	255956.i	−0.00546941	−	0.00947330i
$940$	−2.16689e6	+	788682.i	−0.0799865	+	0.0291127i
$941$	−3.93434e7	+	1.43198e7i	−1.44843	+	0.527186i	−0.942152	−	0.335185i	$-0.891201\pi$
$941$	−3.93434e7	+	1.43198e7i	−1.44843	+	0.527186i	−0.506278	+	0.862370i	$0.668979\pi$
$942$	94272.5	+	163285.i	0.00346145	+	0.00599540i
$943$	1.65402e6	−	2.86485e6i	0.0605707	−	0.104911i
$944$	−65470.9	+	371304.i	−0.00239121	+	0.0135612i
$945$	74284.4	−	62332.0i	0.00270594	−	0.00227055i
$946$	6.58921e6	+	5.52900e6i	0.239390	+	0.200872i
$947$	8.81639e6	+	5.00002e7i	0.319459	+	1.81174i	0.546048	+	0.837754i	$0.316132\pi$
$947$	8.81639e6	+	5.00002e7i	0.319459	+	1.81174i	−0.226589	+	0.973991i	$0.572757\pi$
$948$	655473.	+	238573.i	0.0236883	+	0.00862184i
$949$	2.30653e7			0.831370
$950$	739837.	−	1.88338e7i	0.0265966	−	0.677064i
$951$	3.29003e6			0.117964
$952$	−242409.	−	88229.5i	−0.00866873	−	0.00315516i
$953$	7.25996e6	+	4.11733e7i	0.258942	+	1.46853i	0.785749	+	0.618546i	$0.212278\pi$
$953$	7.25996e6	+	4.11733e7i	0.258942	+	1.46853i	−0.526807	+	0.849985i	$0.676611\pi$
$954$	4.77206e6	+	4.00424e6i	0.169760	+	0.142446i
$955$	8.54795e6	−	7.17258e6i	0.303287	−	0.254488i
$956$	832085.	−	4.71899e6i	0.0294458	−	0.166995i
$957$	−1.01259e6	+	1.75386e6i	−0.0357400	+	0.0619036i
$958$	6.23766e6	+	1.08040e7i	0.219588	+	0.380337i
$959$	95353.8	−	34706.0i	0.00334805	−	0.00121859i
$960$	49733.3	−	18101.4i	0.00174168	−	0.000633921i
$961$	2.38317e6	+	4.12778e6i	0.0832429	+	0.144181i
$962$	−7.72543e6	+	1.33808e7i	−0.269144	+	0.466171i
$963$	3.00130e6	−	1.70212e7i	0.104290	−	0.591460i
$964$	−1.13579e7	+	9.53040e6i	−0.393645	+	0.330307i
$965$	−7.06730e6	−	5.93017e6i	−0.244307	−	0.204998i
$966$	−2298.66	−	13036.3i	−7.92560e−5	−	0.000449483i
$967$	3.69567e7	+	1.34511e7i	1.27095	+	0.462587i	0.887428	−	0.460946i	$-0.152490\pi$
$967$	3.69567e7	+	1.34511e7i	1.27095	+	0.462587i	0.383519	+	0.923533i	$0.374712\pi$
$968$	1.24860e7			0.428289
$969$	141282.	+	441352.i	0.00483366	+	0.0150999i
$970$	−6.12715e6			−0.209088
$971$	1.58428e7	+	5.76629e6i	0.539241	+	0.196268i	0.597260	−	0.802048i	$-0.296256\pi$
$971$	1.58428e7	+	5.76629e6i	0.539241	+	0.196268i	−0.0580190	+	0.998315i	$0.518478\pi$
$972$	−552867.	−	3.13547e6i	−0.0187696	−	0.106448i
$973$	−3.48680e6	−	2.92577e6i	−0.118072	−	0.0990738i
$974$	1.16697e7	−	9.79207e6i	0.394152	−	0.330733i
$975$	599510.	−	3.39999e6i	0.0201969	−	0.114542i
$976$	−4.45830e6	+	7.72200e6i	−0.149811	+	0.259481i
$977$	−1.66312e7	−	2.88060e7i	−0.557425	−	0.965489i	−0.997710	−	0.0676309i	$-0.978456\pi$
$977$	−1.66312e7	−	2.88060e7i	−0.557425	−	0.965489i	0.440285	−	0.897858i	$-0.354877\pi$
$978$	1.89925e6	−	691272.i	0.0634945	−	0.0231101i
$979$	−5.02018e7	+	1.82720e7i	−1.67403	+	0.609296i
$980$	1.51387e6	+	2.62211e6i	0.0503529	+	0.0872138i
$981$	1.96368e7	−	3.40119e7i	0.651474	−	1.12839i
$982$	−7.20619e6	+	4.08683e7i	−0.238466	+	1.35241i
$983$	3.84112e7	−	3.22309e7i	1.26787	−	1.06387i	0.273072	−	0.961994i	$-0.411960\pi$
$983$	3.84112e7	−	3.22309e7i	1.26787	−	1.06387i	0.994797	−	0.101875i	$-0.0324842\pi$
$984$	970996.	+	814763.i	0.0319691	+	0.0268252i
$985$	1.26621e6	+	7.18102e6i	0.0415829	+	0.235828i
$986$	2.93546e6	+	1.06842e6i	0.0961575	+	0.0349985i
$987$	−220996.			−0.00722092
$988$	9.71574e6	−	2.37490e7i	0.316653	−	0.774020i
$989$	680842.			0.0221338
$990$	6.19329e6	+	2.25417e6i	0.200832	+	0.0730969i
$991$	−6.12702e6	−	3.47481e7i	−0.198182	−	1.12395i	−0.907813	−	0.419375i	$-0.862249\pi$
$991$	−6.12702e6	−	3.47481e7i	−0.198182	−	1.12395i	0.709631	−	0.704574i	$-0.248862\pi$
$992$	3.83190e6	+	3.21535e6i	0.123633	+	0.103741i
$993$	1.19344e6	−	1.00142e6i	0.0384087	−	0.0322287i
$994$	−27817.5	+	157761.i	−0.000893001	+	0.00506446i
$995$	65267.6	−	113047.i	0.00208997	−	0.00361993i
$996$	816025.	+	1.41340e6i	0.0260648	+	0.0451456i
$997$	−5.18988e7	+	1.88896e7i	−1.65356	+	0.601846i	−0.989331	−	0.145684i	$-0.953462\pi$
$997$	−5.18988e7	+	1.88896e7i	−1.65356	+	0.601846i	−0.664228	+	0.747530i	$0.731240\pi$
$998$	−2.83366e7	+	1.03137e7i	−0.900579	+	0.327784i
$999$	−1.03911e6	−	1.79980e6i	−0.0329419	−	0.0570571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.e.b.23.3	yes	30
19.5	even	9	inner	38.6.e.b.5.3	✓	30
19.9	even	9		722.6.a.r.1.7		15
19.10	odd	18		722.6.a.q.1.9		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.b.5.3	✓	30	19.5	even	9	inner
38.6.e.b.23.3	yes	30	1.1	even	1	trivial
722.6.a.q.1.9		15	19.10	odd	18
722.6.a.r.1.7		15	19.9	even	9

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.75877 - 1.36808i) q^{2} +(-0.196437 - 1.11405i) q^{3} +(12.2567 + 10.2846i) q^{4} +(8.74989 - 7.34203i) q^{5} +(-0.785748 + 4.45620i) q^{6} +(-7.74142 + 13.4085i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(227.143 - 82.6732i) q^{9} +(-42.9333 + 15.6265i) q^{10} +(-298.390 - 516.826i) q^{11} +(9.04988 - 15.6749i) q^{12} +(176.976 - 1003.68i) q^{13} +(47.4422 - 39.8087i) q^{14} +(-9.89819 - 8.30556i) q^{15} +(44.4539 + 252.111i) q^{16} +(-244.634 - 89.0396i) q^{17} -966.881 q^{18} +(1392.58 - 732.684i) q^{19} +182.755 q^{20} +(16.4585 + 5.99039i) q^{21} +(414.519 + 2350.85i) q^{22} +(144.742 + 121.453i) q^{23} +(-55.4609 + 46.5372i) q^{24} +(-519.995 + 2949.04i) q^{25} +(-2038.33 + 3530.49i) q^{26} +(-274.166 - 474.870i) q^{27} +(-232.786 + 84.7271i) q^{28} +(2818.93 - 1026.01i) q^{29} +(25.8423 + 44.7602i) q^{30} +(-2442.48 + 4230.50i) q^{31} +(177.816 - 1008.44i) q^{32} +(-517.155 + 433.944i) q^{33} +(797.711 + 669.359i) q^{34} +(30.7093 + 174.161i) q^{35} +(3634.28 + 1322.77i) q^{36} +3790.08 q^{37} +(-6236.75 + 848.834i) q^{38} -1152.91 q^{39} +(-686.933 - 250.023i) q^{40} +(-3040.19 - 17241.8i) q^{41} +(-53.6683 - 45.0330i) q^{42} +(2760.32 - 2316.18i) q^{43} +(1658.07 - 9403.41i) q^{44} +(1380.49 - 2391.07i) q^{45} +(-377.895 - 654.533i) q^{46} +(-11856.8 + 4315.52i) q^{47} +(272.131 - 99.0477i) q^{48} +(8283.64 + 14347.7i) q^{49} +(5989.07 - 10373.4i) q^{50} +(-51.1393 + 290.025i) q^{51} +(12491.6 - 10481.7i) q^{52} +(-4935.52 - 4141.40i) q^{53} +(380.868 + 2160.01i) q^{54} +(-6405.43 - 2331.39i) q^{55} +990.902 q^{56} +(-1089.80 - 1407.47i) q^{57} -11999.4 q^{58} +(1383.96 + 503.721i) q^{59} +(-35.8998 - 203.598i) q^{60} +(26681.7 + 22388.6i) q^{61} +(14968.4 - 12560.0i) q^{62} +(-649.881 + 3685.66i) q^{63} +(-2048.00 + 3547.24i) q^{64} +(-5820.53 - 10081.5i) q^{65} +(2537.54 - 923.588i) q^{66} +(-49505.7 + 18018.6i) q^{67} +(-2082.68 - 3607.30i) q^{68} +(106.872 - 185.108i) q^{69} +(122.837 - 696.644i) q^{70} +(-1981.49 + 1662.66i) q^{71} +(-11850.8 - 9943.99i) q^{72} +(3929.94 + 22287.8i) q^{73} +(-14246.0 - 5185.14i) q^{74} +3387.52 q^{75} +(24603.8 + 5341.81i) q^{76} +9239.84 q^{77} +(4333.54 + 1577.28i) q^{78} +(6692.16 + 37953.1i) q^{79} +(2239.97 + 1879.56i) q^{80} +(44520.8 - 37357.4i) q^{81} +(-12160.8 + 68967.1i) q^{82} +(-45084.8 + 78089.2i) q^{83} +(140.118 + 242.691i) q^{84} +(-2794.26 + 1017.03i) q^{85} +(-13544.1 + 4929.66i) q^{86} +(-1696.76 - 2938.88i) q^{87} +(-19096.9 + 33076.9i) q^{88} +(15545.0 - 88159.9i) q^{89} +(-8460.11 + 7098.87i) q^{90} +(12087.8 + 10142.9i) q^{91} +(524.966 + 2977.23i) q^{92} +(5192.77 + 1890.02i) q^{93} +50471.0 q^{94} +(6805.51 - 16635.3i) q^{95} -1158.38 q^{96} +(126019. + 45867.1i) q^{97} +(-11507.5 - 65262.3i) q^{98} +(-110505. - 92724.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9} - 126 q^{11} - 2610 q^{13} - 864 q^{14} - 5160 q^{15} + 1902 q^{17} + 17016 q^{18} - 2400 q^{19} + 3456 q^{20} - 6426 q^{21} + 216 q^{22} - 3306 q^{23}+ \cdots - 1068531 q^{99}+O(q^{100}) \) 30 * q + 15 * q^3 + 60 * q^6 - 84 * q^7 - 960 * q^8 - 345 * q^9 - 126 * q^11 - 2610 * q^13 - 864 * q^14 - 5160 * q^15 + 1902 * q^17 + 17016 * q^18 - 2400 * q^19 + 3456 * q^20 - 6426 * q^21 + 216 * q^22 - 3306 * q^23 + 960 * q^24 - 18060 * q^25 + 456 * q^26 + 13017 * q^27 + 6048 * q^28 + 5988 * q^29 - 6840 * q^31 + 51867 * q^33 - 10752 * q^34 + 24408 * q^35 - 5520 * q^36 - 8556 * q^37 + 2772 * q^38 + 9912 * q^39 - 40527 * q^41 + 27432 * q^42 + 3678 * q^43 + 864 * q^44 - 31770 * q^45 - 15744 * q^46 - 133740 * q^47 - 7680 * q^48 - 63777 * q^49 - 107580 * q^50 + 45657 * q^51 + 5760 * q^52 - 64626 * q^53 + 1476 * q^54 + 142056 * q^55 + 10752 * q^56 + 232824 * q^57 + 117264 * q^58 + 169041 * q^59 - 56640 * q^60 + 61698 * q^61 - 101616 * q^62 - 188064 * q^63 - 61440 * q^64 - 80646 * q^65 - 173772 * q^66 - 72129 * q^67 - 65904 * q^68 - 124224 * q^69 + 97632 * q^70 + 417828 * q^71 + 44160 * q^72 + 239082 * q^73 - 116112 * q^74 - 174960 * q^75 + 6912 * q^76 + 242436 * q^77 + 336624 * q^78 - 145740 * q^79 + 14781 * q^81 - 162108 * q^82 - 201630 * q^83 - 54528 * q^84 - 46512 * q^85 - 75720 * q^86 - 376512 * q^87 - 8064 * q^88 + 416928 * q^89 + 560640 * q^90 - 380316 * q^91 + 269376 * q^92 - 205146 * q^93 + 5616 * q^94 + 708168 * q^95 + 858363 * q^97 + 308328 * q^98 - 1068531 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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