LMFDB - Embedded newform 74.6.h.a.3.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,6,Mod(3,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("74.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	74.h (of order $18$, 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:	$11.8684026662$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.4
Character	$\chi$	$=$	74.3
Dual form			74.6.h.a.25.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.57115 + 3.06418i) q^{2} +(-4.69686 + 3.94113i) q^{3} +(-2.77837 - 15.7569i) q^{4} +(9.28305 - 25.5050i) q^{5} -24.5252i q^{6} +(77.8232 + 28.3253i) q^{7} +(55.4256 + 32.0000i) q^{8} +(-35.6686 + 202.286i) q^{9} +O(q^{10})$	\(q+(-2.57115 + 3.06418i) q^{2} +(-4.69686 + 3.94113i) q^{3} +(-2.77837 - 15.7569i) q^{4} +(9.28305 - 25.5050i) q^{5} -24.5252i q^{6} +(77.8232 + 28.3253i) q^{7} +(55.4256 + 32.0000i) q^{8} +(-35.6686 + 202.286i) q^{9} +(54.2837 + 94.0221i) q^{10} +(-63.6830 + 110.302i) q^{11} +(75.1497 + 63.0581i) q^{12} +(-616.039 + 108.624i) q^{13} +(-286.889 + 165.636i) q^{14} +(56.9173 + 156.379i) q^{15} +(-240.561 + 87.5572i) q^{16} +(644.300 + 113.607i) q^{17} +(-528.132 - 629.404i) q^{18} +(-1591.21 - 1896.33i) q^{19} +(-427.672 - 75.4101i) q^{20} +(-477.159 + 173.672i) q^{21} +(-174.247 - 478.740i) q^{22} +(-3859.51 + 2228.29i) q^{23} +(-386.442 + 68.1402i) q^{24} +(1829.56 + 1535.18i) q^{25} +(1251.08 - 2166.94i) q^{26} +(-1374.66 - 2380.98i) q^{27} +(230.098 - 1304.95i) q^{28} +(-7388.61 - 4265.82i) q^{29} +(-625.516 - 227.669i) q^{30} +9519.82i q^{31} +(350.229 - 962.245i) q^{32} +(-135.605 - 769.057i) q^{33} +(-2004.71 + 1682.15i) q^{34} +(1444.87 - 1721.93i) q^{35} +3286.51 q^{36} +(-8322.96 + 268.879i) q^{37} +9901.95 q^{38} +(2465.34 - 2938.08i) q^{39} +(1330.68 - 1116.57i) q^{40} +(1075.30 + 6098.32i) q^{41} +(694.686 - 1908.63i) q^{42} +7343.94i q^{43} +(1914.96 + 696.988i) q^{44} +(4828.20 + 2787.56i) q^{45} +(3095.51 - 17555.5i) q^{46} +(7127.96 + 12346.0i) q^{47} +(784.808 - 1359.33i) q^{48} +(-7620.78 - 6394.59i) q^{49} +(-9408.15 + 1658.91i) q^{50} +(-3473.93 + 2005.67i) q^{51} +(3423.17 + 9405.08i) q^{52} +(27157.1 - 9884.39i) q^{53} +(10830.2 + 1909.66i) q^{54} +(2222.08 + 2648.18i) q^{55} +(3406.99 + 4060.29i) q^{56} +(14947.4 + 2635.63i) q^{57} +(32068.5 - 11672.0i) q^{58} +(4937.51 + 13565.7i) q^{59} +(2305.91 - 1331.32i) q^{60} +(-3916.88 + 690.651i) q^{61} +(-29170.4 - 24476.9i) q^{62} +(-8505.67 + 14732.3i) q^{63} +(2048.00 + 3547.24i) q^{64} +(-2948.26 + 16720.4i) q^{65} +(2705.19 + 1561.84i) q^{66} +(21755.7 + 7918.44i) q^{67} -10467.8i q^{68} +(9345.59 - 25676.8i) q^{69} +(1561.32 + 8854.71i) q^{70} +(44704.0 - 37511.1i) q^{71} +(-8450.12 + 10070.5i) q^{72} -77806.6 q^{73} +(20575.7 - 26194.4i) q^{74} -14643.5 q^{75} +(-25459.4 + 30341.3i) q^{76} +(-8080.37 + 6780.23i) q^{77} +(2664.04 + 15108.5i) q^{78} +(-4904.88 + 13476.1i) q^{79} +6948.31i q^{80} +(-31063.4 - 11306.1i) q^{81} +(-21451.1 - 12384.8i) q^{82} +(4865.13 - 27591.5i) q^{83} +(4062.25 + 7036.03i) q^{84} +(8878.63 - 15378.2i) q^{85} +(-22503.2 - 18882.4i) q^{86} +(51515.4 - 9083.56i) q^{87} +(-7059.34 + 4075.71i) q^{88} +(-2391.63 - 6570.96i) q^{89} +(-20955.6 + 7627.22i) q^{90} +(-51018.9 - 8996.02i) q^{91} +(45834.2 + 54623.0i) q^{92} +(-37518.9 - 44713.2i) q^{93} +(-56157.3 - 9902.06i) q^{94} +(-63137.3 + 22980.1i) q^{95} +(2147.36 + 5899.83i) q^{96} +(-57262.6 + 33060.6i) q^{97} +(39188.3 - 6909.96i) q^{98} +(-20041.2 - 16816.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{3} + 90 q^{5} - 228 q^{7} - 186 q^{9}+O(q^{10}) $ 96 * q + 6 * q^3 + 90 * q^5 - 228 * q^7 - 186 * q^9	\( 96 q + 6 q^{3} + 90 q^{5} - 228 q^{7} - 186 q^{9} + 600 q^{10} - 726 q^{11} - 96 q^{12} - 246 q^{13} + 3960 q^{14} - 3960 q^{15} - 1530 q^{17} + 3222 q^{19} + 1440 q^{20} - 16110 q^{21} + 8232 q^{25} + 13632 q^{26} + 2154 q^{27} - 10464 q^{28} - 18378 q^{29} - 25056 q^{30} + 78198 q^{33} + 37296 q^{34} + 82170 q^{35} - 124416 q^{36} - 5586 q^{37} - 39936 q^{38} + 58686 q^{39} - 16128 q^{40} - 59598 q^{41} - 26304 q^{42} + 480 q^{44} - 74646 q^{45} - 22536 q^{46} - 1266 q^{47} + 193320 q^{49} + 18864 q^{50} + 68352 q^{52} - 57432 q^{53} + 101520 q^{54} + 133830 q^{55} - 228936 q^{57} - 79224 q^{58} - 52800 q^{59} + 68664 q^{61} - 72720 q^{62} - 166254 q^{63} + 196608 q^{64} - 122058 q^{65} + 254946 q^{67} - 218094 q^{69} - 25872 q^{70} + 200052 q^{71} - 32244 q^{73} + 124368 q^{74} - 234036 q^{75} + 51552 q^{76} + 397188 q^{77} - 16584 q^{78} + 267462 q^{79} - 371496 q^{81} + 121440 q^{83} + 84672 q^{84} - 337260 q^{85} + 43920 q^{86} - 667500 q^{87} - 135936 q^{88} + 377850 q^{89} - 576408 q^{90} + 875826 q^{91} + 233376 q^{92} + 365868 q^{93} - 80256 q^{94} + 764592 q^{95} - 823212 q^{97} - 342192 q^{98} - 928650 q^{99}+O(q^{100}) \) 96 * q + 6 * q^3 + 90 * q^5 - 228 * q^7 - 186 * q^9 + 600 * q^10 - 726 * q^11 - 96 * q^12 - 246 * q^13 + 3960 * q^14 - 3960 * q^15 - 1530 * q^17 + 3222 * q^19 + 1440 * q^20 - 16110 * q^21 + 8232 * q^25 + 13632 * q^26 + 2154 * q^27 - 10464 * q^28 - 18378 * q^29 - 25056 * q^30 + 78198 * q^33 + 37296 * q^34 + 82170 * q^35 - 124416 * q^36 - 5586 * q^37 - 39936 * q^38 + 58686 * q^39 - 16128 * q^40 - 59598 * q^41 - 26304 * q^42 + 480 * q^44 - 74646 * q^45 - 22536 * q^46 - 1266 * q^47 + 193320 * q^49 + 18864 * q^50 + 68352 * q^52 - 57432 * q^53 + 101520 * q^54 + 133830 * q^55 - 228936 * q^57 - 79224 * q^58 - 52800 * q^59 + 68664 * q^61 - 72720 * q^62 - 166254 * q^63 + 196608 * q^64 - 122058 * q^65 + 254946 * q^67 - 218094 * q^69 - 25872 * q^70 + 200052 * q^71 - 32244 * q^73 + 124368 * q^74 - 234036 * q^75 + 51552 * q^76 + 397188 * q^77 - 16584 * q^78 + 267462 * q^79 - 371496 * q^81 + 121440 * q^83 + 84672 * q^84 - 337260 * q^85 + 43920 * q^86 - 667500 * q^87 - 135936 * q^88 + 377850 * q^89 - 576408 * q^90 + 875826 * q^91 + 233376 * q^92 + 365868 * q^93 - 80256 * q^94 + 764592 * q^95 - 823212 * q^97 - 342192 * q^98 - 928650 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−2.57115	+	3.06418i	−0.454519	+	0.541675i
$2$	−2.57115	+	3.06418i	−0.454519	+	0.541675i
$3$	−4.69686	+	3.94113i	−0.301304	+	0.252824i	−0.780887	−	0.624673i	$-0.785232\pi$
$3$	−4.69686	+	3.94113i	−0.301304	+	0.252824i	0.479583	+	0.877496i	$0.340788\pi$
$4$	−2.77837	−	15.7569i	−0.0868241	−	0.492404i
$5$	9.28305	−	25.5050i	0.166060	−	0.456247i	−0.828552	−	0.559912i	$-0.810835\pi$
$5$	9.28305	−	25.5050i	0.166060	−	0.456247i	0.994612	+	0.103665i	$0.0330571\pi$
$6$		−	24.5252i		−	0.278122i
$7$	77.8232	+	28.3253i	0.600294	+	0.218489i	0.624251	−	0.781224i	$-0.285404\pi$
$7$	77.8232	+	28.3253i	0.600294	+	0.218489i	−0.0239568	+	0.999713i	$0.507626\pi$
$8$	55.4256	+	32.0000i	0.306186	+	0.176777i
$9$	−35.6686	+	202.286i	−0.146784	+	0.832454i
$10$	54.2837	+	94.0221i	0.171660	+	0.297324i
$11$	−63.6830	+	110.302i	−0.158687	+	0.274854i	−0.934396	−	0.356237i	$-0.884059\pi$
$11$	−63.6830	+	110.302i	−0.158687	+	0.274854i	0.775708	+	0.631092i	$0.217393\pi$
$12$	75.1497	+	63.0581i	0.150652	+	0.126412i
$13$	−616.039	+	108.624i	−1.01100	+	0.178266i	−0.654525	−	0.756040i	$-0.727131\pi$
$13$	−616.039	+	108.624i	−1.01100	+	0.178266i	−0.356471	+	0.934306i	$0.616020\pi$
$14$	−286.889	+	165.636i	−0.391196	+	0.225857i
$15$	56.9173	+	156.379i	0.0653155	+	0.179453i
$16$	−240.561	+	87.5572i	−0.234923	+	0.0855050i
$17$	644.300	+	113.607i	0.540712	+	0.0953421i	0.437332	−	0.899300i	$-0.355923\pi$
$17$	644.300	+	113.607i	0.540712	+	0.0953421i	0.103379	+	0.994642i	$0.467034\pi$
$18$	−528.132	−	629.404i	−0.384204	−	0.457876i
$19$	−1591.21	−	1896.33i	−1.01122	−	1.20512i	−0.978625	−	0.205652i	$-0.934068\pi$
$19$	−1591.21	−	1896.33i	−1.01122	−	1.20512i	−0.0325917	−	0.999469i	$-0.510376\pi$
$20$	−427.672	−	75.4101i	−0.239076	−	0.0421555i
$21$	−477.159	+	173.672i	−0.236110	+	0.0859370i
$22$	−174.247	−	478.740i	−0.0767553	−	0.210884i
$23$	−3859.51	+	2228.29i	−1.52129	+	0.878319i	−0.521608	+	0.853185i	$0.674668\pi$
$23$	−3859.51	+	2228.29i	−1.52129	+	0.878319i	−0.999684	+	0.0251337i	$0.991999\pi$
$24$	−386.442	+	68.1402i	−0.136948	+	0.0241477i
$25$	1829.56	+	1535.18i	0.585459	+	0.491259i
$26$	1251.08	−	2166.94i	0.362955	−	0.628657i
$27$	−1374.66	−	2380.98i	−0.362900	−	0.628560i
$28$	230.098	−	1304.95i	0.0554649	−	0.314557i
$29$	−7388.61	−	4265.82i	−1.63143	−	0.941905i	−0.983653	−	0.180074i	$-0.942366\pi$
$29$	−7388.61	−	4265.82i	−1.63143	−	0.941905i	−0.647775	−	0.761832i	$-0.724300\pi$
$30$	−625.516	−	227.669i	−0.126892	−	0.0461850i
$31$			9519.82i			1.77920i	0.456742	+	0.889599i	$0.349016\pi$
$31$			9519.82i			1.77920i	−0.456742	+	0.889599i	$0.650984\pi$
$32$	350.229	−	962.245i	0.0604612	−	0.166116i
$33$	−135.605	−	769.057i	−0.0216767	−	0.122934i
$34$	−2004.71	+	1682.15i	−0.297408	+	0.249555i
$35$	1444.87	−	1721.93i	0.199370	−	0.237600i
$36$	3286.51			0.422648
$37$	−8322.96	+	268.879i	−0.999479	+	0.0322888i
$37$	−8322.96	+	268.879i	−0.999479	+	0.0322888i
$38$	9901.95			1.11240
$39$	2465.34	−	2938.08i	0.259547	−	0.309316i
$40$	1330.68	−	1116.57i	0.131499	−	0.110341i
$41$	1075.30	+	6098.32i	0.0999009	+	0.566566i	0.993135	+	0.116974i	$0.0373195\pi$
$41$	1075.30	+	6098.32i	0.0999009	+	0.566566i	−0.893234	+	0.449592i	$0.851569\pi$
$42$	694.686	−	1908.63i	0.0607667	−	0.166955i
$43$			7343.94i			0.605701i	0.953038	+	0.302850i	$0.0979383\pi$
$43$			7343.94i			0.605701i	−0.953038	+	0.302850i	$0.902062\pi$
$44$	1914.96	+	696.988i	0.149117	+	0.0542742i
$45$	4828.20	+	2787.56i	0.355430	+	0.205207i
$46$	3095.51	−	17555.5i	0.215694	−	1.22326i
$47$	7127.96	+	12346.0i	0.470674	+	0.815232i	0.999437	−	0.0335376i	$-0.0106774\pi$
$47$	7127.96	+	12346.0i	0.470674	+	0.815232i	−0.528763	+	0.848769i	$0.677344\pi$
$48$	784.808	−	1359.33i	0.0491655	−	0.0851571i
$49$	−7620.78	−	6394.59i	−0.453429	−	0.380472i
$50$	−9408.15	+	1658.91i	−0.532205	+	0.0938421i
$51$	−3473.93	+	2005.67i	−0.187023	+	0.107978i
$52$	3423.17	+	9405.08i	0.175558	+	0.482341i
$53$	27157.1	−	9884.39i	1.32799	−	0.483348i	0.421979	−	0.906606i	$-0.361336\pi$
$53$	27157.1	−	9884.39i	1.32799	−	0.483348i	0.906009	+	0.423257i	$0.139113\pi$
$54$	10830.2	+	1909.66i	0.505421	+	0.0891193i
$55$	2222.08	+	2648.18i	0.0990498	+	0.118043i
$56$	3406.99	+	4060.29i	0.145178	+	0.173016i
$57$	14947.4	+	2635.63i	0.609366	+	0.107448i
$58$	32068.5	−	11672.0i	1.25172	−	0.455590i
$59$	4937.51	+	13565.7i	0.184662	+	0.507356i	0.997135	−	0.0756439i	$-0.0241012\pi$
$59$	4937.51	+	13565.7i	0.184662	+	0.507356i	−0.812473	+	0.582999i	$0.801879\pi$
$60$	2305.91	−	1331.32i	0.0826923	−	0.0477424i
$61$	−3916.88	+	690.651i	−0.134777	+	0.0237648i	−0.240630	−	0.970617i	$-0.577354\pi$
$61$	−3916.88	+	690.651i	−0.134777	+	0.0237648i	0.105853	+	0.994382i	$0.466243\pi$
$62$	−29170.4	−	24476.9i	−0.963748	−	0.808681i
$63$	−8505.67	+	14732.3i	−0.269996	+	0.467647i
$64$	2048.00	+	3547.24i	0.0625000	+	0.108253i
$65$	−2948.26	+	16720.4i	−0.0865531	+	0.490867i
$66$	2705.19	+	1561.84i	0.0764430	+	0.0441344i
$67$	21755.7	+	7918.44i	0.592089	+	0.215503i	0.620648	−	0.784089i	$-0.286870\pi$
$67$	21755.7	+	7918.44i	0.592089	+	0.215503i	−0.0285591	+	0.999592i	$0.509092\pi$
$68$		−	10467.8i		−	0.274527i
$69$	9345.59	−	25676.8i	0.236311	−	0.649259i
$70$	1561.32	+	8854.71i	0.0380845	+	0.215988i
$71$	44704.0	−	37511.1i	1.05245	−	0.883109i	0.0590990	−	0.998252i	$-0.481177\pi$
$71$	44704.0	−	37511.1i	1.05245	−	0.883109i	0.993349	+	0.115143i	$0.0367328\pi$
$72$	−8450.12	+	10070.5i	−0.192102	+	0.228938i
$73$	−77806.6			−1.70887			−0.854435	−	0.519558i	$-0.826097\pi$
$73$	−77806.6			−1.70887			−0.854435	+	0.519558i	$0.826097\pi$
$74$	20575.7	−	26194.4i	0.436792	−	0.556069i
$75$	−14643.5			−0.300603
$76$	−25459.4	+	30341.3i	−0.505608	+	0.602561i
$77$	−8080.37	+	6780.23i	−0.155312	+	0.130322i
$78$	2664.04	+	15108.5i	0.0495797	+	0.281180i
$79$	−4904.88	+	13476.1i	−0.0884221	+	0.242938i	−0.976020	−	0.217682i	$-0.930150\pi$
$79$	−4904.88	+	13476.1i	−0.0884221	+	0.242938i	0.887598	+	0.460619i	$0.152373\pi$
$80$			6948.31i			0.121382i
$81$	−31063.4	−	11306.1i	−0.526061	−	0.191470i
$82$	−21451.1	−	12384.8i	−0.352302	−	0.203402i
$83$	4865.13	−	27591.5i	0.0775173	−	0.439623i	−0.921204	−	0.389079i	$-0.872793\pi$
$83$	4865.13	−	27591.5i	0.0775173	−	0.439623i	0.998722	−	0.0505439i	$-0.0160955\pi$
$84$	4062.25	+	7036.03i	0.0628158	+	0.108800i
$85$	8878.63	−	15378.2i	0.133290	−	0.230866i
$86$	−22503.2	−	18882.4i	−0.328093	−	0.275303i
$87$	51515.4	−	9083.56i	0.729691	−	0.128664i
$88$	−7059.34	+	4075.71i	−0.0971757	+	0.0561044i
$89$	−2391.63	−	6570.96i	−0.0320051	−	0.0879333i	0.922661	−	0.385612i	$-0.126010\pi$
$89$	−2391.63	−	6570.96i	−0.0320051	−	0.0879333i	−0.954666	+	0.297679i	$0.903788\pi$
$90$	−20955.6	+	7627.22i	−0.272706	+	0.0992567i
$91$	−51018.9	−	8996.02i	−0.645844	−	0.113880i
$92$	45834.2	+	54623.0i	0.564572	+	0.672831i
$93$	−37518.9	−	44713.2i	−0.449824	−	0.536079i
$94$	−56157.3	−	9902.06i	−0.655521	−	0.115586i
$95$	−63137.3	+	22980.1i	−0.717756	+	0.261242i
$96$	2147.36	+	5899.83i	0.0237808	+	0.0653373i
$97$	−57262.6	+	33060.6i	−0.617934	+	0.356764i	−0.776064	−	0.630654i	$-0.782787\pi$
$97$	−57262.6	+	33060.6i	−0.617934	+	0.356764i	0.158130	+	0.987418i	$0.449453\pi$
$98$	39188.3	−	6909.96i	0.412184	−	0.0726792i
$99$	−20041.2	−	16816.5i	−0.205511	−	0.172444i
$100$	19106.6	−	33093.5i	0.191066	−	0.330935i
$101$	10274.1	+	17795.3i	0.100217	+	0.173581i	0.911774	−	0.410692i	$-0.134713\pi$
$101$	10274.1	+	17795.3i	0.100217	+	0.173581i	−0.811557	+	0.584273i	$0.801380\pi$
$102$	2786.25	−	15801.6i	0.0265167	−	0.150384i
$103$	100533.	+	58042.7i	0.933717	+	0.539082i	0.887985	−	0.459872i	$-0.152105\pi$
$103$	100533.	+	58042.7i	0.933717	+	0.539082i	0.0457319	+	0.998954i	$0.485438\pi$
$104$	−37620.3	−	13692.7i	−0.341066	−	0.124138i
$105$			13782.1i			0.121995i
$106$	−39537.6	+	108629.i	−0.341779	+	0.939030i
$107$	−18131.0	−	102826.i	−0.153095	−	0.868247i	−0.960506	−	0.278258i	$-0.910243\pi$
$107$	−18131.0	−	102826.i	−0.153095	−	0.868247i	0.807411	−	0.589989i	$-0.200868\pi$
$108$	−33697.7	+	28275.7i	−0.277997	+	0.233267i
$109$	−105810.	+	126099.i	−0.853022	+	1.01659i	0.146602	+	0.989196i	$0.453166\pi$
$109$	−105810.	+	126099.i	−0.853022	+	1.01659i	−0.999625	+	0.0273968i	$0.991278\pi$
$110$	−13827.8			−0.108961
$111$	38032.1	−	34064.8i	0.292983	−	0.262421i
$112$	−21201.3			−0.159705
$113$	100001.	−	119176.i	0.736729	−	0.878000i	−0.259412	−	0.965767i	$-0.583529\pi$
$113$	100001.	−	119176.i	0.736729	−	0.878000i	0.996141	+	0.0877670i	$0.0279731\pi$
$114$	−46508.1	+	39024.9i	−0.335171	+	0.281242i
$115$	21004.4	+	119122.i	0.148104	+	0.839939i
$116$	−46687.9	+	128274.i	−0.322151	+	0.885102i
$117$		−	128491.i		−	0.867775i
$118$	−54262.8	−	19750.1i	−0.358755	−	0.130576i
$119$	46923.5	+	27091.3i	0.303755	+	0.175373i
$120$	−1849.45	+	10488.8i	−0.0117244	+	0.0664922i
$121$	72414.4	+	125426.i	0.449637	+	0.778794i
$122$	7954.60	−	13777.8i	0.0483859	−	0.0838068i
$123$	−29084.8	−	24405.1i	−0.173342	−	0.145451i
$124$	150003.	−	26449.6i	0.876084	−	0.154477i
$125$	129593.	−	74820.8i	0.741836	−	0.428299i
$126$	−23272.9	−	63941.8i	−0.130594	−	0.358805i
$127$	168066.	−	61171.0i	0.924636	−	0.336540i	0.164555	−	0.986368i	$-0.447381\pi$
$127$	168066.	−	61171.0i	0.924636	−	0.336540i	0.760081	+	0.649828i	$0.225159\pi$
$128$	−16135.1	−	2845.05i	−0.0870455	−	0.0153485i
$129$	−28943.5	−	34493.5i	−0.153136	−	0.182500i
$130$	−43653.9	−	52024.7i	−0.226550	−	0.269992i
$131$	−11956.4	−	2108.23i	−0.0608724	−	0.0107334i	0.143129	−	0.989704i	$-0.454284\pi$
$131$	−11956.4	−	2108.23i	−0.0608724	−	0.0107334i	−0.204001	+	0.978971i	$0.565395\pi$
$132$	−11741.2	+	4273.45i	−0.0586514	+	0.0213473i
$133$	−70119.0	−	192650.i	−0.343722	−	0.944367i
$134$	−80200.8	+	46303.9i	−0.385848	+	0.222770i
$135$	−73488.0	+	12957.9i	−0.347042	+	0.0611929i
$136$	32075.3	+	26914.4i	0.148704	+	0.124778i
$137$	174899.	−	302934.i	0.796135	−	1.37895i	−0.125982	−	0.992033i	$-0.540208\pi$
$137$	174899.	−	302934.i	0.796135	−	1.37895i	0.922116	−	0.386913i	$-0.126459\pi$
$138$	54649.4	+	94655.5i	0.244280	+	0.423105i
$139$	−35228.0	+	199788.i	−0.154650	+	0.877066i	0.804454	+	0.594014i	$0.202458\pi$
$139$	−35228.0	+	199788.i	−0.154650	+	0.877066i	−0.959105	+	0.283051i	$0.908653\pi$
$140$	−31146.8	−	17982.6i	−0.134305	−	0.0775412i
$141$	−82136.2	−	29895.1i	−0.347926	−	0.126635i
$142$			233428.i			0.971475i
$143$	27249.7	−	74867.9i	0.111435	−	0.306165i
$144$	−9131.15	−	51785.3i	−0.0366960	−	0.208114i
$145$	−177389.	+	148847.i	−0.700657	+	0.587921i
$146$	200052.	−	238413.i	0.776715	−	0.925653i
$147$	60995.6			0.232812
$148$	27361.0	+	130397.i	0.102678	+	0.489344i
$149$	120696.			0.445376			0.222688	−	0.974890i	$-0.428517\pi$
$149$	120696.			0.445376			0.222688	+	0.974890i	$0.428517\pi$
$150$	37650.7	−	44870.4i	0.136630	−	0.162829i
$151$	342931.	−	287753.i	1.22395	−	1.02702i	0.225342	−	0.974280i	$-0.427650\pi$
$151$	342931.	−	287753.i	1.22395	−	1.02702i	0.998608	−	0.0527365i	$-0.0167943\pi$
$152$	−27511.3	−	156024.i	−0.0965833	−	0.547751i
$153$	−45962.5	+	126281.i	−0.158736	+	0.436123i
$154$		−	42192.7i		−	0.143362i
$155$	242803.	+	88373.0i	0.811754	+	0.295454i
$156$	−53144.8	−	30683.1i	−0.174843	−	0.100946i
$157$	−13083.8	+	74201.7i	−0.0423627	+	0.240251i	−0.998635	−	0.0522261i	$-0.983368\pi$
$157$	−13083.8	+	74201.7i	−0.0423627	+	0.240251i	0.956273	+	0.292477i	$0.0944795\pi$
$158$	−28681.8	−	49678.4i	−0.0914038	−	0.158316i
$159$	−88597.5	+	153455.i	−0.277926	+	0.481381i
$160$	−21290.9	−	17865.1i	−0.0657496	−	0.0551705i
$161$	−363477.	+	64090.8i	−1.10513	+	0.194864i
$162$	114513.	−	66113.9i	0.342820	−	0.197927i
$163$	76891.5	+	211258.i	0.226678	+	0.622793i	0.999936	−	0.0112985i	$-0.00359650\pi$
$163$	76891.5	+	211258.i	0.226678	+	0.622793i	−0.773258	+	0.634091i	$0.781374\pi$
$164$	93103.2	−	33886.8i	0.270306	−	0.0983832i
$165$	−20873.6	−	3680.58i	−0.0596881	−	0.0105246i
$166$	72036.3	+	85849.5i	0.202900	+	0.241806i
$167$	193845.	+	231016.i	0.537853	+	0.640989i	0.964705	−	0.263333i	$-0.0848218\pi$
$167$	193845.	+	231016.i	0.537853	+	0.640989i	−0.426852	+	0.904322i	$0.640377\pi$
$168$	−32004.3	−	5643.22i	−0.0874853	−	0.0154260i
$169$	18803.1	−	6843.75i	0.0506421	−	0.0184322i
$170$	24293.4	+	66745.4i	0.0644711	+	0.177133i
$171$	440359.	−	254241.i	1.15164	−	0.664899i
$172$	115718.	−	20404.2i	0.298249	−	0.0525894i
$173$	−335042.	−	281133.i	−0.851106	−	0.714163i	0.108927	−	0.994050i	$-0.465259\pi$
$173$	−335042.	−	281133.i	−0.851106	−	0.714163i	−0.960033	+	0.279887i	$0.909703\pi$
$174$	−104620.	+	181208.i	−0.261965	+	0.453736i
$175$	98897.7	+	171296.i	0.244113	+	0.422816i
$176$	5661.92	−	32110.4i	0.0137779	−	0.0781382i
$177$	−76655.0	−	44256.8i	−0.183911	−	0.106181i
$178$	26283.8	+	9566.53i	0.0621783	+	0.0226310i
$179$			373149.i			0.870463i	0.900319	+	0.435231i	$0.143333\pi$
$179$			373149.i			0.870463i	−0.900319	+	0.435231i	$0.856667\pi$
$180$	30508.9	−	83822.4i	0.0701851	−	0.192832i
$181$	89677.0	+	508583.i	0.203463	+	1.15389i	0.899841	+	0.436219i	$0.143683\pi$
$181$	89677.0	+	508583.i	0.203463	+	1.15389i	−0.696378	+	0.717675i	$0.745206\pi$
$182$	158743.	−	133201.i	0.355235	−	0.298077i
$183$	15675.1	−	18680.8i	0.0346004	−	0.0412352i
$184$	−285221.			−0.621065
$185$	−70404.7	+	214773.i	−0.151242	+	0.461371i
$186$	233476.			0.494834
$187$	−53562.1	+	63832.8i	−0.112009	+	0.133487i
$188$	174731.	−	146616.i	0.360557	−	0.302544i
$189$	−39538.4	−	224234.i	−0.0805128	−	0.456611i
$190$	91920.3	−	252549.i	0.184726	−	0.507530i
$191$			719618.i			1.42731i	0.700496	+	0.713656i	$0.252962\pi$
$191$			719618.i			1.42731i	−0.700496	+	0.713656i	$0.747038\pi$
$192$	−23599.3	−	8589.44i	−0.0462004	−	0.0168156i
$193$	−557565.	−	321910.i	−1.07746	−	0.622074i	−0.147252	−	0.989099i	$-0.547043\pi$
$193$	−557565.	−	321910.i	−1.07746	−	0.622074i	−0.930211	+	0.367025i	$0.880376\pi$
$194$	45927.3	−	260467.i	0.0876126	−	0.496876i
$195$	−52049.8	−	90152.9i	−0.0980240	−	0.169783i
$196$	−79585.7	+	137847.i	−0.147977	+	0.256304i
$197$	−662390.	−	555811.i	−1.21604	−	1.02038i	−0.999022	−	0.0442115i	$-0.985922\pi$
$197$	−662390.	−	555811.i	−1.21604	−	1.02038i	−0.217018	−	0.976168i	$-0.569633\pi$
$198$	103058.	−	18171.8i	0.186817	−	0.0329410i
$199$	−677924.	+	391400.i	−1.21352	+	0.700628i	−0.963525	−	0.267618i	$-0.913763\pi$
$199$	−677924.	+	391400.i	−1.21352	+	0.700628i	−0.249999	+	0.968246i	$0.580430\pi$
$200$	52278.6	+	143634.i	0.0924165	+	0.253912i
$201$	−133391.	+	48550.4i	−0.232883	+	0.0847624i
$202$	−80944.2	−	14272.7i	−0.139575	−	0.0246108i
$203$	−454175.	−	541265.i	−0.773541	−	0.921870i
$204$	41255.1	+	49165.9i	0.0694068	+	0.0827158i
$205$	165520.	+	29185.6i	0.275084	+	0.0485047i
$206$	−436339.	+	158814.i	−0.716400	+	0.260748i
$207$	−313090.	−	860207.i	−0.507859	−	1.39533i
$208$	138684.	−	80069.4i	0.222264	−	0.128324i
$209$	310503.	−	54750.1i	0.491700	−	0.0867000i
$210$	−42230.9	−	35435.9i	−0.0660818	−	0.0554492i
$211$	−52329.0	+	90636.4i	−0.0809163	+	0.140151i	−0.903644	−	0.428285i	$-0.859118\pi$
$211$	−52329.0	+	90636.4i	−0.0809163	+	0.140151i	0.822727	+	0.568436i	$0.192451\pi$
$212$	−231200.	−	400450.i	−0.353304	−	0.611940i
$213$	−62132.1	+	352369.i	−0.0938355	+	0.532168i
$214$	361694.	+	208824.i	0.539893	+	0.311707i
$215$	187307.	+	68174.2i	0.276349	+	0.100583i
$216$		−	175957.i		−	0.256609i
$217$	−269652.	+	740863.i	−0.388736	+	1.06804i
$218$	−114338.	−	648441.i	−0.162948	−	0.924122i
$219$	365446.	−	306646.i	0.514889	−	0.432043i
$220$	35553.3	−	42370.8i	0.0495249	−	0.0590215i
$221$	−409254.			−0.563654
$222$	6594.31	+	204123.i	0.00898022	+	0.277977i
$223$	−976573.			−1.31505			−0.657526	−	0.753432i	$-0.728397\pi$
$223$	−976573.			−1.31505			−0.657526	+	0.753432i	$0.728397\pi$
$224$	54511.9	−	64964.7i	0.0725890	−	0.0865082i
$225$	−375804.	+	315337.i	−0.494886	+	0.415259i
$226$	108060.	+	612841.i	0.140733	+	0.798136i
$227$	−157663.	+	433176.i	−0.203080	+	0.557956i	−0.998865	−	0.0476217i	$-0.984836\pi$
$227$	−157663.	+	433176.i	−0.203080	+	0.557956i	0.795786	+	0.605578i	$0.207058\pi$
$228$		−	242848.i		−	0.309383i
$229$	194031.	+	70621.4i	0.244502	+	0.0889913i	0.461364	−	0.887211i	$-0.347360\pi$
$229$	194031.	+	70621.4i	0.244502	+	0.0889913i	−0.216863	+	0.976202i	$0.569582\pi$
$230$	−419017.	−	241920.i	−0.522290	−	0.301544i
$231$	11230.5	−	63691.6i	0.0138475	−	0.0785330i
$232$	−273012.	−	472871.i	−0.333014	−	0.576797i
$233$	−44669.8	+	77370.3i	−0.0539044	+	0.0933651i	−0.891718	−	0.452590i	$-0.850500\pi$
$233$	−44669.8	+	77370.3i	−0.0539044	+	0.0933651i	0.837814	+	0.545956i	$0.183833\pi$
$234$	393718.	+	330369.i	0.470052	+	0.394421i
$235$	381053.	−	67190.0i	0.450107	−	0.0793661i
$236$	200036.	−	115491.i	0.233791	−	0.134979i
$237$	−30073.4	−	82625.9i	−0.0347785	−	0.0955532i
$238$	−203660.	+	74126.2i	−0.233058	+	0.0848261i
$239$	884356.	+	155936.i	1.00146	+	0.176584i	0.650255	−	0.759716i	$-0.274662\pi$
$239$	884356.	+	155936.i	1.00146	+	0.176584i	0.351202	+	0.936300i	$0.385773\pi$
$240$	−27384.2	−	32635.2i	−0.0306882	−	0.0365728i
$241$	−1.00206e6	−	1.19421e6i	−1.11135	−	1.32445i	−0.940746	−	0.339113i	$-0.889873\pi$
$241$	−1.00206e6	−	1.19421e6i	−1.11135	−	1.32445i	−0.170603	−	0.985340i	$-0.554571\pi$
$242$	−570514.	−	100597.i	−0.626222	−	0.110420i
$243$	818254.	−	297820.i	0.888940	−	0.323548i
$244$	21765.1	+	59799.0i	0.0234037	+	0.0643013i
$245$	−233838.	+	135006.i	−0.248886	+	0.143694i
$246$	149563.	−	26372.0i	0.157575	−	0.0277846i
$247$	1.18624e6	+	995370.i	1.23717	+	1.03811i
$248$	−304634.	+	527642.i	−0.314521	+	0.544766i
$249$	85890.9	+	148767.i	0.0877908	+	0.152058i
$250$	−103940.	+	589473.i	−0.105180	+	0.596505i
$251$	740986.	+	427808.i	0.742379	+	0.428613i	0.822934	−	0.568137i	$-0.192336\pi$
$251$	740986.	+	427808.i	0.742379	+	0.428613i	−0.0805547	+	0.996750i	$0.525669\pi$
$252$	255767.	+	93091.6i	0.253713	+	0.0923441i
$253$		−	567617.i		−	0.557512i
$254$	−244684.	+	672264.i	−0.237970	+	0.653816i
$255$	18906.0	+	107221.i	0.0182074	+	0.103260i
$256$	50203.5	−	42125.7i	0.0478778	−	0.0401742i
$257$	1.05620e6	−	1.25873e6i	0.997499	−	1.18877i	0.0155016	−	0.999880i	$-0.495065\pi$
$257$	1.05620e6	−	1.25873e6i	0.997499	−	1.18877i	0.981998	−	0.188893i	$-0.0604901\pi$
$258$	180112.			0.168459
$259$	−655336.	−	214826.i	−0.607036	−	0.198993i
$260$	271654.			0.249220
$261$	1.12646e6	−	1.34246e6i	1.02356	−	1.21983i
$262$	37201.6	−	31215.8i	0.0334817	−	0.0280945i
$263$	39851.1	+	226007.i	0.0355264	+	0.201480i	0.997405	−	0.0719972i	$-0.0229373\pi$
$263$	39851.1	+	226007.i	0.0355264	+	0.201480i	−0.961878	+	0.273477i	$0.911826\pi$
$264$	17093.8	−	46964.8i	0.0150949	−	0.0414728i
$265$		−	784400.i		−	0.686156i
$266$	770602.	+	280476.i	0.667769	+	0.243048i
$267$	37130.2	+	21437.1i	0.0318749	+	0.0184030i
$268$	64324.8	−	364804.i	0.0547068	−	0.310258i
$269$	826326.	+	1.43124e6i	0.696259	+	1.20596i	0.969755	+	0.244082i	$0.0784867\pi$
$269$	826326.	+	1.43124e6i	0.696259	+	1.20596i	−0.273496	+	0.961873i	$0.588180\pi$
$270$	149243.	−	258497.i	0.124591	−	0.215797i
$271$	1.56952e6	+	1.31698e6i	1.29821	+	1.08932i	0.990452	+	0.137858i	$0.0440219\pi$
$271$	1.56952e6	+	1.31698e6i	1.29821	+	1.08932i	0.307754	+	0.951466i	$0.400423\pi$
$272$	−164941.	+	29083.5i	−0.135178	+	0.0238355i
$273$	275083.	−	158819.i	0.223387	−	0.128972i
$274$	478553.	+	1.31481e6i	0.385082	+	1.05800i
$275$	−285846.	+	104039.i	−0.227929	+	0.0829595i
$276$	−430553.	−	75918.1i	−0.340215	−	0.0599891i
$277$	1.14835e6	+	1.36855e6i	0.899241	+	1.07167i	0.997072	+	0.0764711i	$0.0243653\pi$
$277$	1.14835e6	+	1.36855e6i	0.899241	+	1.07167i	−0.0978303	+	0.995203i	$0.531190\pi$
$278$	−521609.	−	621630.i	−0.404793	−	0.482414i
$279$	−1.92573e6	−	339558.i	−1.48110	−	0.261158i
$280$	135185.	−	49203.3i	0.103047	−	0.0375059i
$281$	−103249.	−	283674.i	−0.0780045	−	0.214316i	0.894560	−	0.446947i	$-0.147489\pi$
$281$	−103249.	−	283674.i	−0.0780045	−	0.214316i	−0.972565	+	0.232631i	$0.925266\pi$
$282$	302788.	−	174815.i	0.226734	−	0.130905i
$283$	761203.	−	134221.i	0.564982	−	0.0996216i	0.116140	−	0.993233i	$-0.462948\pi$
$283$	761203.	−	134221.i	0.564982	−	0.0996216i	0.448842	+	0.893611i	$0.351837\pi$
$284$	−715264.	−	600178.i	−0.526224	−	0.441554i
$285$	205979.	−	356766.i	0.150214	−	0.260179i
$286$	159346.	+	275995.i	0.115193	+	0.199520i
$287$	−89053.8	+	505049.i	−0.0638187	+	0.361934i
$288$	182157.	+	105168.i	0.129409	+	0.0747143i
$289$	−932013.	−	339225.i	−0.656414	−	0.238915i
$290$		−	926257.i		−	0.646750i
$291$	138658.	−	380960.i	0.0959872	−	0.263723i
$292$	216175.	+	1.22599e6i	0.148371	+	0.841454i
$293$	−100267.	+	84133.7i	−0.0682319	+	0.0572534i	−0.676266	−	0.736658i	$-0.736403\pi$
$293$	−100267.	+	84133.7i	−0.0682319	+	0.0572534i	0.608034	+	0.793911i	$0.291958\pi$
$294$	−156829.	+	186901.i	−0.105818	+	0.126109i
$295$	391828.			0.262145
$296$	−469909.	−	251432.i	−0.311734	−	0.166798i
$297$	350170.			0.230350
$298$	−310327.	+	369834.i	−0.202432	+	0.241249i
$299$	2.13556e6	−	1.79195e6i	1.38145	−	1.15917i
$300$	40685.2	+	230737.i	0.0260996	+	0.148018i
$301$	−208020.	+	571530.i	−0.132339	+	0.363599i
$302$			1.79066e6i			1.12978i
$303$	−118390.	−	43090.3i	−0.0740810	−	0.0269633i
$304$	548822.	+	316862.i	0.340602	+	0.196647i
$305$	−18745.5	+	106311.i	−0.0115385	+	0.0654379i
$306$	−268771.	−	465524.i	−0.164089	−	0.284210i
$307$	−14897.8	+	25803.8i	−0.00902146	+	0.0156256i	−0.870501	−	0.492167i	$-0.836205\pi$
$307$	−14897.8	+	25803.8i	−0.00902146	+	0.0156256i	0.861479	+	0.507792i	$0.169538\pi$
$308$	129286.	+	108484.i	0.0776559	+	0.0651610i
$309$	−700943.	+	123595.i	−0.417625	+	0.0736386i
$310$	−895073.	+	516771.i	−0.528998	+	0.305417i
$311$	−773503.	−	2.12518e6i	−0.453483	−	1.24593i	−0.930257	−	0.366908i	$-0.880416\pi$
$311$	−773503.	−	2.12518e6i	−0.453483	−	1.24593i	0.476774	−	0.879026i	$-0.341806\pi$
$312$	230662.	−	83954.0i	0.134150	−	0.0488264i
$313$	−1.06915e6	−	188520.i	−0.616847	−	0.108767i	−0.143511	−	0.989649i	$-0.545839\pi$
$313$	−1.06915e6	−	188520.i	−0.616847	−	0.108767i	−0.473336	+	0.880882i	$0.656950\pi$
$314$	−193727.	−	230875.i	−0.110883	−	0.132145i
$315$	296787.	+	353697.i	0.168527	+	0.200842i
$316$	225969.	+	39844.4i	0.127301	+	0.0224465i
$317$	−432441.	+	157396.i	−0.241701	+	0.0879720i	−0.460030	−	0.887903i	$-0.652161\pi$
$317$	−432441.	+	157396.i	−0.241701	+	0.0879720i	0.218329	+	0.975875i	$0.429939\pi$
$318$	−242417.	−	666035.i	−0.134430	−	0.369343i
$319$	941058.	−	543320.i	0.517774	−	0.298937i
$320$	109484.	−	19305.0i	0.0597690	−	0.0105389i
$321$	490409.	+	411502.i	0.265642	+	0.222900i
$322$	738168.	−	1.27854e6i	0.396749	−	0.687189i
$323$	−809781.	−	1.40258e6i	−0.431878	−	0.748035i
$324$	−91844.4	+	520876.i	−0.0486061	+	0.275659i
$325$	−1.29384e6	−	746997.i	−0.679472	−	0.392293i
$326$	−845031.	−	307566.i	−0.440381	−	0.160286i
$327$		−	1.00928e6i		−	0.521967i
$328$	−135547.	+	372413.i	−0.0695674	+	0.191135i
$329$	205017.	+	1.16271e6i	0.104424	+	0.592216i
$330$	64947.2	−	54497.1i	0.0328303	−	0.0275479i
$331$	−1.17122e6	+	1.39581e6i	−0.587584	+	0.700255i	−0.975140	−	0.221591i	$-0.928875\pi$
$331$	−1.17122e6	+	1.39581e6i	−0.587584	+	0.700255i	0.387556	+	0.921846i	$0.373319\pi$
$332$	−448274.			−0.223202
$333$	242477.	−	1.69321e6i	0.119829	−	0.836760i
$334$	−1.20628e6			−0.591673
$335$	403919.	−	481372.i	0.196645	−	0.234352i
$336$	99579.7	−	83557.3i	0.0481197	−	0.0403772i
$337$	−58500.5	−	331773.i	−0.0280598	−	0.159135i	0.967558	−	0.252648i	$-0.0813015\pi$
$337$	−58500.5	−	331773.i	−0.0280598	−	0.159135i	−0.995618	+	0.0935129i	$0.970190\pi$
$338$	−27375.0	+	75212.2i	−0.0130335	+	0.0358094i
$339$			953872.i			0.450807i
$340$	−266982.	−	97173.4i	−0.125252	−	0.0455880i
$341$	−1.05006e6	−	606251.i	−0.489020	−	0.282336i
$342$	−353188.	+	2.00303e6i	−0.163283	+	0.926024i
$343$	−1.10790e6	−	1.91895e6i	−0.508472	−	0.880699i
$344$	−235006.	+	407043.i	−0.107074	+	0.185457i
$345$	−568131.	−	476718.i	−0.256981	−	0.215632i
$346$	1.72289e6	−	303791.i	0.773689	−	0.136422i
$347$	−3.25710e6	+	1.88049e6i	−1.45214	+	0.838391i	−0.998603	−	0.0528478i	$-0.983170\pi$
$347$	−3.25710e6	+	1.88049e6i	−1.45214	+	0.838391i	−0.453534	+	0.891239i	$0.649837\pi$
$348$	−286258.	−	786487.i	−0.126710	−	0.348132i
$349$	2.81548e6	−	1.02475e6i	1.23734	−	0.450355i	0.361235	−	0.932475i	$-0.382355\pi$
$349$	2.81548e6	−	1.02475e6i	1.23734	−	0.450355i	0.876105	+	0.482120i	$0.160133\pi$
$350$	−779162.	−	137387.i	−0.339983	−	0.0599482i
$351$	1.10548e6	+	1.31746e6i	0.478941	+	0.570780i
$352$	83834.2	+	99909.7i	0.0360632	+	0.0429785i
$353$	1.46355e6	+	258064.i	0.625132	+	0.110228i	0.477236	−	0.878775i	$-0.341639\pi$
$353$	1.46355e6	+	258064.i	0.625132	+	0.110228i	0.147896	+	0.989003i	$0.452750\pi$
$354$	332702.	−	121094.i	0.141107	−	0.0513586i
$355$	−541731.	−	1.48839e6i	−0.228146	−	0.626825i
$356$	−96893.2	+	55941.3i	−0.0405199	+	0.0233942i
$357$	−327164.	+	57687.8i	−0.135861	+	0.0239559i
$358$	−1.14340e6	−	959423.i	−0.471508	−	0.395642i
$359$	−2.16936e6	+	3.75744e6i	−0.888372	+	1.53871i	−0.0465728	+	0.998915i	$0.514830\pi$
$359$	−2.16936e6	+	3.75744e6i	−0.888372	+	1.53871i	−0.841799	+	0.539791i	$0.818503\pi$
$360$	178404.	+	309005.i	0.0725518	+	0.125663i
$361$	−634153.	+	3.59646e6i	−0.256110	+	1.45247i
$362$	−1.78896e6	−	1.03286e6i	−0.717513	−	0.414256i
$363$	−834439.	−	303711.i	−0.332375	−	0.120974i
$364$			828896.i			0.327904i
$365$	−722283.	+	1.98445e6i	−0.283776	+	0.779667i
$366$	16938.4	+	96062.3i	0.00660951	+	0.0374844i
$367$	−646460.	+	542444.i	−0.250540	+	0.210228i	−0.759405	−	0.650619i	$-0.774510\pi$
$367$	−646460.	+	542444.i	−0.250540	+	0.210228i	0.508865	+	0.860846i	$0.330065\pi$
$368$	733346.	−	873968.i	0.282286	−	0.336416i
$369$	−1.27196e6			−0.486305
$370$	−477081.	−	767946.i	−0.181171	−	0.291626i
$371$	2.39343e6			0.902790
$372$	−600302.	+	715412.i	−0.224912	+	0.268039i
$373$	1.73486e6	−	1.45572e6i	0.645643	−	0.541759i	−0.260102	−	0.965581i	$-0.583756\pi$
$373$	1.73486e6	−	1.45572e6i	0.645643	−	0.541759i	0.905745	+	0.423822i	$0.139312\pi$
$374$	−57878.9	−	328248.i	−0.0213964	−	0.121345i
$375$	−313803.	+	862168.i	−0.115234	+	0.316602i
$376$			912379.i			0.332817i
$377$	5.01504e6	+	1.82533e6i	1.81728	+	0.661435i
$378$	788751.	+	455386.i	0.283929	+	0.163927i
$379$	314628.	−	1.78434e6i	0.112512	−	0.638087i	−0.875440	−	0.483327i	$-0.839428\pi$
$379$	314628.	−	1.78434e6i	0.112512	−	0.638087i	0.987952	−	0.154760i	$-0.0494605\pi$
$380$	537514.	+	931002.i	0.190955	+	0.330744i
$381$	−548299.	+	949682.i	−0.193511	+	0.335171i
$382$	−2.20504e6	−	1.85025e6i	−0.773140	−	0.648741i
$383$	−2.39541e6	+	422375.i	−0.834415	+	0.147130i	−0.574503	−	0.818502i	$-0.694805\pi$
$383$	−2.39541e6	+	422375.i	−0.834415	+	0.147130i	−0.259912	+	0.965632i	$0.583694\pi$
$384$	86996.9	−	50227.7i	0.0301076	−	0.0173826i
$385$	97919.2	+	269031.i	0.0336679	+	0.0925018i
$386$	2.41997e6	−	880799.i	0.826690	−	0.300890i
$387$	−1.48558e6	−	261948.i	−0.504218	−	0.0889073i
$388$	680030.	+	810428.i	0.229324	+	0.273297i
$389$	−1.24263e6	−	1.48091e6i	−0.416358	−	0.496196i	0.516577	−	0.856241i	$-0.327206\pi$
$389$	−1.24263e6	−	1.48091e6i	−0.416358	−	0.496196i	−0.932935	+	0.360045i	$0.882761\pi$
$390$	410072.	+	72306.8i	0.136521	+	0.0240723i
$391$	−2.73983e6	+	997218.i	−0.906321	+	0.329874i
$392$	−217759.	−	598289.i	−0.0715751	−	0.196651i
$393$	64466.1	−	37219.5i	0.0210547	−	0.0121560i
$394$	3.40621e6	−	600606.i	1.10543	−	0.194917i
$395$	298174.	+	250198.i	0.0961562	+	0.0806846i
$396$	−209295.	+	362510.i	−0.0670689	+	0.116167i
$397$	−371176.	−	642895.i	−0.118196	−	0.204722i	0.800857	−	0.598856i	$-0.204378\pi$
$397$	−371176.	−	642895.i	−0.118196	−	0.204722i	−0.919053	+	0.394134i	$0.871044\pi$
$398$	543727.	−	3.08363e6i	0.172057	−	0.975785i
$399$	1.08860e6	+	628503.i	0.342323	+	0.197640i
$400$	−574538.	−	209115.i	−0.179543	−	0.0653483i
$401$			1.54050e6i			0.478411i	0.970969	+	0.239205i	$0.0768869\pi$
$401$			1.54050e6i			0.478411i	−0.970969	+	0.239205i	$0.923113\pi$
$402$	194202.	−	533565.i	0.0599360	−	0.164673i
$403$	−1.03408e6	−	5.86458e6i	−0.317171	−	1.79876i
$404$	251854.	−	211330.i	0.0767706	−	0.0644182i
$405$	−576726.	+	687315.i	−0.174716	+	0.208218i
$406$	2.82628e6			0.850943
$407$	500373.	−	935164.i	0.149730	−	0.279835i
$408$	−256726.			−0.0763519
$409$	−1.37450e6	+	1.63806e6i	−0.406289	+	0.484196i	−0.929927	−	0.367745i	$-0.880130\pi$
$409$	−1.37450e6	+	1.63806e6i	−0.406289	+	0.484196i	0.523638	+	0.851941i	$0.324575\pi$
$410$	−515006.	+	432141.i	−0.151305	+	0.126960i
$411$	372427.	+	2.11214e6i	0.108752	+	0.616763i
$412$	635257.	−	1.74535e6i	0.184377	−	0.506571i
$413$			1.19558e6i			0.344909i
$414$	3.44083e6	+	1.25236e6i	0.986647	+	0.359110i
$415$	−658558.	−	380218.i	−0.187704	−	0.108371i
$416$	−111231.	+	630824.i	−0.0315133	+	0.178721i
$417$	−621930.	−	1.07721e6i	−0.175146	−	0.303362i
$418$	−630586.	+	1.09221e6i	−0.176524	+	0.305748i
$419$	−3.11492e6	−	2.61373e6i	−0.866786	−	0.727320i	0.0966326	−	0.995320i	$-0.469193\pi$
$419$	−3.11492e6	−	2.61373e6i	−0.866786	−	0.727320i	−0.963419	+	0.268000i	$0.913637\pi$
$420$	217164.	−	38291.8i	0.0600709	−	0.0105921i
$421$	1.98465e6	−	1.14584e6i	0.545732	−	0.315079i	−0.201667	−	0.979454i	$-0.564636\pi$
$421$	1.98465e6	−	1.14584e6i	0.545732	−	0.315079i	0.747399	+	0.664376i	$0.231302\pi$
$422$	−143181.	−	393385.i	−0.0391384	−	0.107532i
$423$	−2.75167e6	+	1.00153e6i	−0.747731	+	0.272152i
$424$	1.82150e6	+	321180.i	0.492056	+	0.0867628i
$425$	1.00438e6	+	1.19697e6i	0.269727	+	0.321448i
$426$	−919970.	−	1.09638e6i	−0.245612	−	0.292709i
$427$	−324387.	−	57198.2i	−0.0860981	−	0.0151814i
$428$	−1.56985e6	+	571377.i	−0.414236	+	0.150769i
$429$	167076.	+	459039.i	0.0438301	+	0.120422i
$430$	−690493.	+	398656.i	−0.180089	+	0.103975i
$431$	6.58895e6	−	1.16181e6i	1.70853	−	0.301260i	0.767869	−	0.640607i	$-0.221317\pi$
$431$	6.58895e6	−	1.16181e6i	1.70853	−	0.301260i	0.940661	+	0.339347i	$0.110206\pi$
$432$	539163.	+	452411.i	0.138999	+	0.116634i
$433$	183458.	−	317759.i	0.0470238	−	0.0814475i	−0.841556	−	0.540171i	$-0.818360\pi$
$433$	183458.	−	317759.i	0.0470238	−	0.0814475i	0.888579	+	0.458723i	$0.151693\pi$
$434$	−1.57682e6	−	2.73113e6i	−0.401844	−	0.696015i
$435$	246544.	−	1.39822e6i	0.0624701	−	0.354285i
$436$	2.28092e6	+	1.31689e6i	0.574637	+	0.331767i
$437$	1.03669e7	+	3.77324e6i	2.59684	+	0.945171i
$438$			1.90823e6i			0.475274i
$439$	−1.81561e6	+	4.98836e6i	−0.449637	+	1.23537i	0.483340	+	0.875433i	$0.339423\pi$
$439$	−1.81561e6	+	4.98836e6i	−0.449637	+	1.23537i	−0.932977	+	0.359935i	$0.882799\pi$
$440$	38418.7	+	217883.i	0.00946044	+	0.0536528i
$441$	1.56536e6	−	1.31349e6i	0.383282	−	0.321612i
$442$	1.05225e6	−	1.25403e6i	0.256192	−	0.305317i
$443$	3.20159e6			0.775098			0.387549	−	0.921849i	$-0.373322\pi$
$443$	3.20159e6			0.775098			0.387549	+	0.921849i	$0.373322\pi$
$444$	−642423.	−	504624.i	−0.154655	−	0.121482i
$445$	−189794.			−0.0454341
$446$	2.51092e6	−	2.99239e6i	0.597716	−	0.712331i
$447$	−566892.	+	475679.i	−0.134193	+	0.112602i
$448$	58905.2	+	334068.i	0.0138662	+	0.0786393i
$449$	−833051.	+	2.28879e6i	−0.195010	+	0.535784i	−0.998202	−	0.0599350i	$-0.980911\pi$
$449$	−833051.	+	2.28879e6i	−0.195010	+	0.535784i	0.803193	+	0.595719i	$0.203133\pi$
$450$		−	1.96231e6i		−	0.456811i
$451$	−741137.	−	269752.i	−0.171576	−	0.0624486i
$452$	−2.15569e6	−	1.24459e6i	−0.496296	−	0.286537i
$453$	−476624.	+	2.70307e6i	−0.109127	+	0.618887i
$454$	−921954.	−	1.59687e6i	−0.209928	−	0.363605i
$455$	−703055.	+	1.21773e6i	−0.159206	+	0.275754i
$456$	744129.	+	624398.i	0.167585	+	0.140621i
$457$	1.43498e6	−	253025.i	0.321406	−	0.0566726i	−0.0106174	−	0.999944i	$-0.503380\pi$
$457$	1.43498e6	−	253025.i	0.321406	−	0.0566726i	0.332024	+	0.943271i	$0.392269\pi$
$458$	−715278.	+	412966.i	−0.159335	+	0.0919922i
$459$	−615197.	−	1.69024e6i	−0.136296	−	0.374470i
$460$	1.81864e6	−	661931.i	0.400730	−	0.145854i
$461$	−3.04502e6	−	536919.i	−0.667325	−	0.117667i	−0.170285	−	0.985395i	$-0.554469\pi$
$461$	−3.04502e6	−	536919.i	−0.667325	−	0.117667i	−0.497040	+	0.867727i	$0.665580\pi$
$462$	166287.	+	198173.i	0.0362454	+	0.0431956i
$463$	−4.82808e6	−	5.75388e6i	−1.04670	−	1.24741i	−0.968117	−	0.250500i	$-0.919405\pi$
$463$	−4.82808e6	−	5.75388e6i	−1.04670	−	1.24741i	−0.0785828	−	0.996908i	$-0.525040\pi$
$464$	2.15092e6	+	379265.i	0.463798	+	0.0817801i
$465$	−1.48870e6	+	541842.i	−0.319282	+	0.116209i
$466$	−122224.	−	335807.i	−0.0260730	−	0.0716349i
$467$	1.67065e6	−	964548.i	0.354480	−	0.204659i	−0.312176	−	0.950024i	$-0.601058\pi$
$467$	1.67065e6	−	964548.i	0.354480	−	0.204659i	0.666657	+	0.745365i	$0.267725\pi$
$468$	−2.02462e6	+	356995.i	−0.427296	+	0.0753438i
$469$	1.46881e6	+	1.23248e6i	0.308342	+	0.258730i
$470$	−773863.	+	1.34037e6i	−0.161592	+	0.279885i
$471$	−230986.	−	400080.i	−0.0479771	−	0.0830987i
$472$	−160438.	+	909888.i	−0.0331476	+	0.187989i
$473$	−810053.	−	467685.i	−0.166480	−	0.0961170i
$474$	330503.	+	120293.i	0.0675663	+	0.0245921i
$475$		−	5.91226e6i		−	1.20232i
$476$	296505.	−	814640.i	0.0599811	−	0.164797i
$477$	1.03082e6	+	5.84608e6i	0.207438	+	1.17644i
$478$	−2.75163e6	+	2.30889e6i	−0.550833	+	0.462203i
$479$	−2.59130e6	+	3.08819e6i	−0.516035	+	0.614986i	−0.959638	−	0.281237i	$-0.909255\pi$
$479$	−2.59130e6	+	3.08819e6i	−0.516035	+	0.614986i	0.443604	+	0.896223i	$0.353700\pi$
$480$	170409.			0.0337590
$481$	5.09806e6	−	1.06971e6i	1.00471	−	0.210817i
$482$	6.23570e6			1.22255
$483$	1.45461e6	−	1.73353e6i	0.283712	−	0.338115i
$484$	1.77513e6	−	1.48951e6i	0.344442	−	0.289021i
$485$	311638.	+	1.76739e6i	0.0601583	+	0.341175i
$486$	−1.19128e6	+	3.27302e6i	−0.228783	+	0.628576i
$487$			68104.8i			0.0130123i	0.999979	+	0.00650617i	$0.00207099\pi$
$487$			68104.8i			0.0130123i	−0.999979	+	0.00650617i	$0.997929\pi$
$488$	−239196.	−	87060.3i	−0.0454679	−	0.0165489i
$489$	−1.19374e6	−	689208.i	−0.225756	−	0.130340i
$490$	187549.	−	1.06364e6i	0.0352878	−	0.200127i
$491$	−1.33662e6	−	2.31510e6i	−0.250210	−	0.433377i	0.713373	−	0.700784i	$-0.247166\pi$
$491$	−1.33662e6	−	2.31510e6i	−0.250210	−	0.433377i	−0.963584	+	0.267407i	$0.913833\pi$
$492$	−303740.	+	526094.i	−0.0565704	+	0.0979829i
$493$	−4.27585e6	−	3.58787e6i	−0.792329	−	0.664843i
$494$	−6.09998e6	+	1.07559e6i	−1.12463	+	0.198303i
$495$	−614948.	+	355041.i	−0.112804	+	0.0651276i
$496$	−833528.	−	2.29010e6i	−0.152130	−	0.417975i
$497$	4.54153e6	−	1.65298e6i	0.824728	−	0.300177i
$498$	−676688.	−	119318.i	−0.122269	−	0.0215593i
$499$	6.32263e6	+	7.53501e6i	1.13670	+	1.35467i	0.926182	+	0.377077i	$0.123071\pi$
$499$	6.32263e6	+	7.53501e6i	1.13670	+	1.35467i	0.210519	+	0.977590i	$0.432485\pi$
$500$	−1.53900e6	−	1.83411e6i	−0.275306	−	0.328096i
$501$	−1.82093e6	−	321079.i	−0.324114	−	0.0571501i
$502$	−3.21607e6	+	1.17055e6i	−0.569595	+	0.207315i
$503$	−923016.	−	2.53596e6i	−0.162663	−	0.446913i	0.831406	−	0.555666i	$-0.187537\pi$
$503$	−923016.	−	2.53596e6i	−0.162663	−	0.446913i	−0.994069	+	0.108753i	$0.965314\pi$
$504$	−942865.	+	544363.i	−0.165338	+	0.0954580i
$505$	549244.	−	96846.5i	0.0958378	−	0.0168988i
$506$	1.73928e6	+	1.45943e6i	0.301990	+	0.253400i
$507$	−61343.1	+	106249.i	−0.0105985	+	0.0183572i
$508$	−1.43082e6	−	2.47825e6i	−0.245994	−	0.426074i
$509$	50660.8	−	287311.i	0.00866717	−	0.0491540i	−0.980167	−	0.198171i	$-0.936500\pi$
$509$	50660.8	−	287311.i	0.00866717	−	0.0491540i	0.988835	+	0.149017i	$0.0476110\pi$
$510$	−377155.	−	217751.i	−0.0642088	−	0.0370710i
$511$	−6.05516e6	−	2.20390e6i	−1.02582	−	0.373370i
$512$			262144.i			0.0441942i
$513$	−2.32776e6	+	6.39547e6i	−0.390521	+	1.07295i
$514$	1.14132e6	+	6.47276e6i	0.190546	+	1.08064i
$515$	2.41363e6	−	2.02528e6i	0.401008	−	0.336486i
$516$	−463095.	+	551895.i	−0.0765678	+	0.0912499i
$517$	−1.81572e6			−0.298760
$518$	2.34323e6	−	1.45572e6i	0.383699	−	0.238370i
$519$	2.68163e6			0.436999
$520$	−698463.	+	832395.i	−0.113275	+	0.134996i
$521$	1.94301e6	−	1.63038e6i	0.313603	−	0.263145i	−0.472376	−	0.881397i	$-0.656604\pi$
$521$	1.94301e6	−	1.63038e6i	0.313603	−	0.263145i	0.785979	+	0.618253i	$0.212159\pi$
$522$	1.21724e6	+	6.90334e6i	0.195525	+	1.10888i
$523$	1.14161e6	−	3.13656e6i	0.182501	−	0.501417i	−0.814380	−	0.580331i	$-0.802923\pi$
$523$	1.14161e6	−	3.13656e6i	0.182501	−	0.501417i	0.996881	+	0.0789141i	$0.0251453\pi$
$524$			194253.i			0.0309057i
$525$	−1.13961e6	−	414783.i	−0.180450	−	0.0656785i
$526$	−794988.	−	458986.i	−0.125284	−	0.0723328i
$527$	−1.08152e6	+	6.13362e6i	−0.169632	+	0.962034i
$528$	99957.9	+	173132.i	0.0156039	+	0.0270267i
$529$	6.71238e6	−	1.16262e7i	1.04289	−	1.80633i
$530$	2.40354e6	+	2.01681e6i	0.371674	+	0.311871i
$531$	−2.92027e6	+	514923.i	−0.449456	+	0.0792512i
$532$	−2.84076e6	+	1.64011e6i	−0.435167	+	0.251244i
$533$	−1.32485e6	−	3.64000e6i	−0.201999	−	0.554988i
$534$	−161154.	+	58655.4i	−0.0244562	+	0.00890133i
$535$	−2.79088e6	−	492108.i	−0.421558	−	0.0743321i
$536$	952435.	+	1.13507e6i	0.143194	+	0.170651i
$537$	−1.47063e6	−	1.75263e6i	−0.220074	−	0.262273i
$538$	−6.51018e6	−	1.14792e6i	−0.969699	−	0.170984i
$539$	1.19065e6	−	433362.i	0.176528	−	0.0642508i
$540$	408354.	+	1.12194e6i	0.0602632	+	0.165572i
$541$	−828296.	+	478217.i	−0.121672	+	0.0702476i	−0.559601	−	0.828762i	$-0.689046\pi$
$541$	−828296.	+	478217.i	−0.121672	+	0.0702476i	0.437929	+	0.899010i	$0.355712\pi$
$542$	−8.07094e6	+	1.42313e6i	−1.18012	+	0.208087i
$543$	−2.42559e6	−	2.03532e6i	−0.353036	−	0.296232i
$544$	334971.	−	580186.i	0.0485299	−	0.0840562i
$545$	2.23392e6	+	3.86927e6i	0.322164	+	0.558004i
$546$	−220630.	+	1.25125e6i	−0.0316725	+	0.179624i
$547$	−2.29433e6	−	1.32463e6i	−0.327859	−	0.189290i	0.327031	−	0.945014i	$-0.393952\pi$
$547$	−2.29433e6	−	1.32463e6i	−0.327859	−	0.189290i	−0.654890	+	0.755724i	$0.727285\pi$
$548$	−5.25925e6	−	1.91421e6i	−0.748122	−	0.272294i
$549$		−	816965.i		−	0.115684i
$550$	416158.	−	1.14338e6i	0.0586612	−	0.161170i
$551$	3.66744e6	+	2.07991e7i	0.514617	+	2.91854i
$552$	1.33964e6	−	1.12409e6i	0.187129	−	0.157020i
$553$	−763428.	+	909817.i	−0.106159	+	0.126515i
$554$	−7.14609e6			−0.989222
$555$	−515767.	−	1.28623e6i	−0.0710757	−	0.177250i
$556$	3.24592e6			0.445298
$557$	−4.50466e6	+	5.36844e6i	−0.615210	+	0.733179i	−0.980239	−	0.197817i	$-0.936615\pi$
$557$	−4.50466e6	+	5.36844e6i	−0.615210	+	0.733179i	0.365028	+	0.930996i	$0.381059\pi$
$558$	5.99181e6	−	5.02772e6i	0.814653	−	0.683575i
$559$	−797730.	−	4.52415e6i	−0.107976	−	0.612361i
$560$	−196813.	+	540740.i	−0.0265207	+	0.0728649i
$561$		−	510909.i		−	0.0685388i
$562$	1.13470e6	+	412996.i	0.151544	+	0.0551575i
$563$	−3.28996e6	−	1.89946e6i	−0.437442	−	0.252557i	0.265070	−	0.964229i	$-0.414605\pi$
$563$	−3.28996e6	−	1.89946e6i	−0.437442	−	0.252557i	−0.702512	+	0.711672i	$0.747938\pi$
$564$	−242850.	+	1.37727e6i	−0.0321470	+	0.182315i
$565$	−2.11128e6	−	3.65684e6i	−0.278243	−	0.481931i
$566$	−1.54589e6	+	2.67756e6i	−0.202833	+	0.351317i
$567$	−2.09720e6	−	1.75976e6i	−0.273957	−	0.229877i
$568$	3.67810e6	−	648549.i	0.478358	−	0.0843474i
$569$	−4.94832e6	+	2.85691e6i	−0.640733	+	0.369927i	−0.784897	−	0.619626i	$-0.787284\pi$
$569$	−4.94832e6	+	2.85691e6i	−0.640733	+	0.369927i	0.144164	+	0.989554i	$0.453951\pi$
$570$	563592.	+	1.54846e6i	0.0726571	+	0.199624i
$571$	4.75126e6	−	1.72932e6i	0.609844	−	0.221965i	−0.0185911	−	0.999827i	$-0.505918\pi$
$571$	4.75126e6	−	1.72932e6i	0.609844	−	0.221965i	0.628435	+	0.777862i	$0.283696\pi$
$572$	−1.25540e6	−	221361.i	−0.160432	−	0.0282885i
$573$	−2.83611e6	−	3.37995e6i	−0.360858	−	0.430054i
$574$	−1.31859e6	−	1.57143e6i	−0.167044	−	0.199075i
$575$	−1.04820e7	−	1.84827e6i	−1.32214	−	0.233128i
$576$	−790608.	+	287758.i	−0.0992898	+	0.0361385i
$577$	−3.57369e6	−	9.81864e6i	−0.446867	−	1.22776i	−0.934894	−	0.354927i	$-0.884506\pi$
$577$	−3.57369e6	−	9.81864e6i	−0.446867	−	1.22776i	0.488027	−	0.872828i	$-0.337717\pi$
$578$	3.43579e6	−	1.98366e6i	0.427767	−	0.246971i
$579$	3.88750e6	−	685470.i	0.481918	−	0.0849752i
$580$	2.83822e6	+	2.38155e6i	0.350329	+	0.293961i
$581$	1.16016e6	−	2.00945e6i	0.142586	−	0.246966i
$582$	810819.	+	1.40438e6i	0.0992239	+	0.171861i
$583$	−639178.	+	3.62496e6i	−0.0778844	+	0.441705i
$584$	−4.31248e6	−	2.48981e6i	−0.523232	−	0.302088i
$585$	−3.27715e6	−	1.19279e6i	−0.395920	−	0.144103i
$586$		−	523556.i		−	0.0629823i
$587$	2.00026e6	−	5.49567e6i	0.239603	−	0.658303i	−0.760359	−	0.649503i	$-0.774977\pi$
$587$	2.00026e6	−	5.49567e6i	0.239603	−	0.658303i	0.999961	−	0.00879937i	$-0.00280096\pi$
$588$	−169468.	−	961104.i	−0.0202137	−	0.114638i
$589$	1.80528e7	−	1.51481e7i	2.14415	−	1.79916i
$590$	−1.00745e6	+	1.20063e6i	−0.119150	+	0.141997i
$591$	5.30167e6			0.624373
$592$	1.97864e6	−	793416.i	0.232040	−	0.0930458i
$593$	−4.43150e6			−0.517504			−0.258752	−	0.965944i	$-0.583311\pi$
$593$	−4.43150e6			−0.517504			−0.258752	+	0.965944i	$0.583311\pi$
$594$	−900341.	+	1.07298e6i	−0.104699	+	0.124775i
$595$	1.12656e6	−	945294.i	0.130455	−	0.109465i
$596$	−335338.	−	1.90180e6i	−0.0386694	−	0.219305i
$597$	1.64155e6	−	4.51014e6i	0.188504	−	0.517909i
$598$			1.11511e7i			1.27516i
$599$	8.88982e6	+	3.23563e6i	1.01234	+	0.368461i	0.794331	−	0.607486i	$-0.207822\pi$
$599$	8.88982e6	+	3.23563e6i	1.01234	+	0.368461i	0.218009	+	0.975947i	$0.430044\pi$
$600$	−811627.	−	468593.i	−0.0920404	−	0.0531396i
$601$	−739086.	+	4.19157e6i	−0.0834659	+	0.473359i	0.914211	+	0.405238i	$0.132811\pi$
$601$	−739086.	+	4.19157e6i	−0.0834659	+	0.473359i	−0.997677	+	0.0681205i	$0.978300\pi$
$602$	−1.21642e6	−	2.10690e6i	−0.136802	−	0.236948i
$603$	−2.37779e6	+	4.11845e6i	−0.266305	+	0.461255i
$604$	−5.48689e6	−	4.60405e6i	−0.611975	−	0.513508i
$605$	3.87120e6	−	682597.i	0.429989	−	0.0758187i
$606$	436434.	−	251975.i	0.0482766	−	0.0278725i
$607$	2.16264e6	+	5.94181e6i	0.238239	+	0.654556i	0.999978	+	0.00667205i	$0.00212379\pi$
$607$	2.16264e6	+	5.94181e6i	0.238239	+	0.654556i	−0.761739	+	0.647884i	$0.775654\pi$
$608$	−2.38203e6	+	866987.i	−0.261329	+	0.0951160i
$609$	4.26639e6	+	752280.i	0.466141	+	0.0821933i
$610$	−277559.	−	330782.i	−0.0302016	−	0.0359929i
$611$	−5.73217e6	−	6.83133e6i	−0.621178	−	0.740291i
$612$	2.11750e6	+	373372.i	0.228531	+	0.0402961i
$613$	−1.21558e7	+	4.42434e6i	−1.30657	+	0.475551i	−0.899130	−	0.437682i	$-0.855800\pi$
$613$	−1.21558e7	+	4.42434e6i	−1.30657	+	0.475551i	−0.407437	+	0.913233i	$0.633577\pi$
$614$	−40762.9	−	111995.i	−0.00436359	−	0.0119889i
$615$	−892447.	+	515254.i	−0.0951469	+	0.0549331i
$616$	−664827.	+	117227.i	−0.0705922	+	0.0124473i
$617$	1.13108e7	+	9.49088e6i	1.19613	+	1.00368i	0.999732	+	0.0231528i	$0.00737041\pi$
$617$	1.13108e7	+	9.49088e6i	1.19613	+	1.00368i	0.196403	+	0.980523i	$0.437074\pi$
$618$	1.42351e6	−	2.46560e6i	0.149931	−	0.259687i
$619$	−4.52881e6	−	7.84412e6i	−0.475069	−	0.822844i	0.524523	−	0.851396i	$-0.324244\pi$
$619$	−4.52881e6	−	7.84412e6i	−0.475069	−	0.822844i	−0.999592	+	0.0285520i	$0.990910\pi$
$620$	717890.	−	4.07136e6i	0.0750030	−	0.425363i
$621$	1.06110e7	+	6.12629e6i	1.10415	+	0.637483i
$622$	8.50073e6	+	3.09401e6i	0.881008	+	0.320661i
$623$		−	579117.i		−	0.0597787i
$624$	−335816.	+	922647.i	−0.0345255	+	0.0948581i
$625$	590743.	+	3.35027e6i	0.0604921	+	0.343068i
$626$	3.32660e6	−	2.79135e6i	0.339285	−	0.284694i
$627$	−1.24261e6	+	1.48089e6i	−0.126231	+	0.150436i
$628$	1.20554e6			0.121979
$629$	−5.39303e6	−	772312.i	−0.543508	−	0.0778334i
$630$	−1.84688e6			−0.185390
$631$	2.56293e6	−	3.05438e6i	0.256250	−	0.305387i	−0.622547	−	0.782582i	$-0.713902\pi$
$631$	2.56293e6	−	3.05438e6i	0.256250	−	0.305387i	0.878797	+	0.477196i	$0.158347\pi$
$632$	−703090.	+	589962.i	−0.0700193	+	0.0587532i
$633$	−111428.	−	631942.i	−0.0110532	−	0.0626856i
$634$	629582.	−	1.72976e6i	0.0622056	−	0.170908i
$635$		−	4.85438e6i		−	0.477748i
$636$	2.66414e6	+	969668.i	0.261165	+	0.0950562i
$637$	5.38930e6	+	3.11151e6i	0.526240	+	0.303825i
$638$	−754773.	+	4.28053e6i	−0.0734116	+	0.416338i
$639$	5.99346e6	+	1.03810e7i	0.580665	+	1.00574i
$640$	−222346.	+	385114.i	−0.0214575	+	0.0371655i
$641$	7.03704e6	+	5.90478e6i	0.676464	+	0.567621i	0.914971	−	0.403520i	$-0.132213\pi$
$641$	7.03704e6	+	5.90478e6i	0.676464	+	0.567621i	−0.238506	+	0.971141i	$0.576658\pi$
$642$	−2.52183e6	+	444667.i	−0.241478	+	0.0425792i
$643$	−7.97570e6	+	4.60477e6i	−0.760749	+	0.439218i	−0.829564	−	0.558411i	$-0.811411\pi$
$643$	−7.97570e6	+	4.60477e6i	−0.760749	+	0.439218i	0.0688158	+	0.997629i	$0.478078\pi$
$644$	2.01975e6	+	5.54921e6i	0.191903	+	0.527250i
$645$	−1.14844e6	+	417998.i	−0.108695	+	0.0395617i
$646$	6.37983e6	+	1.12494e6i	0.601489	+	0.106059i
$647$	4.06100e6	+	4.83972e6i	0.381393	+	0.454526i	0.922253	−	0.386586i	$-0.126346\pi$
$647$	4.06100e6	+	4.83972e6i	0.381393	+	0.454526i	−0.540860	+	0.841112i	$0.681901\pi$
$648$	−1.35991e6	−	1.62068e6i	−0.127225	−	0.151621i
$649$	−1.81076e6	−	319286.i	−0.168752	−	0.0297556i
$650$	5.61558e6	−	2.04391e6i	0.521329	−	0.189748i
$651$	−1.65332e6	−	4.54246e6i	−0.152899	−	0.420087i
$652$	3.11514e6	−	1.79853e6i	0.286985	−	0.165691i
$653$	7.75553e6	−	1.36751e6i	0.711751	−	0.125501i	0.193962	−	0.981009i	$-0.437866\pi$
$653$	7.75553e6	−	1.36751e6i	0.711751	−	0.125501i	0.517789	+	0.855508i	$0.326755\pi$
$654$	3.09262e6	+	2.59502e6i	0.282737	+	0.237244i
$655$	−164762.	+	285376.i	−0.0150056	+	0.0259905i
$656$	−792627.	−	1.37287e6i	−0.0719133	−	0.124558i
$657$	2.77525e6	−	1.57392e7i	0.250835	−	1.42256i
$658$	−4.08987e6	−	2.36129e6i	−0.368251	−	0.212610i
$659$	1.67341e6	+	609070.i	0.150102	+	0.0546328i	0.415979	−	0.909374i	$-0.363439\pi$
$659$	1.67341e6	+	609070.i	0.150102	+	0.0546328i	−0.265876	+	0.964007i	$0.585661\pi$
$660$			339130.i			0.0303045i
$661$	−6.71648e6	+	1.84534e7i	−0.597913	+	1.64275i	0.157512	+	0.987517i	$0.449653\pi$
$661$	−6.71648e6	+	1.84534e7i	−0.597913	+	1.64275i	−0.755425	+	0.655236i	$0.772569\pi$
$662$	−1.26562e6	−	7.17767e6i	−0.112243	−	0.636559i
$663$	1.92221e6	−	1.61292e6i	0.169831	−	0.142505i
$664$	1.15258e6	−	1.37359e6i	0.101450	−	0.120903i
$665$	−5.56447e6			−0.487943
$666$	4.56486e6	+	5.09650e6i	0.398788	+	0.445232i
$667$	3.80219e7			3.30917
$668$	3.10152e6	−	3.69625e6i	0.268927	−	0.320494i
$669$	4.58683e6	−	3.84880e6i	0.396230	−	0.332476i
$670$	436473.	+	2.47536e6i	0.0375639	+	0.213035i
$671$	173258.	−	476023.i	0.0148555	−	0.0408152i
$672$			519968.i			0.0444175i
$673$	4.61907e6	+	1.68120e6i	0.393113	+	0.143081i	0.531011	−	0.847365i	$-0.321812\pi$
$673$	4.61907e6	+	1.68120e6i	0.393113	+	0.143081i	−0.137898	+	0.990446i	$0.544035\pi$
$674$	1.16702e6	+	673782.i	0.0989533	+	0.0571307i
$675$	1.14022e6	−	6.46651e6i	0.0963228	−	0.546274i
$676$	−160078.	−	277264.i	−0.0134730	−	0.0233360i
$677$	−7.62745e6	+	1.32111e7i	−0.639599	+	1.10782i	0.345922	+	0.938263i	$0.387566\pi$
$677$	−7.62745e6	+	1.32111e7i	−0.639599	+	1.10782i	−0.985521	+	0.169554i	$0.945767\pi$
$678$	−2.92283e6	−	2.45255e6i	−0.244191	−	0.204901i
$679$	−5.39281e6	+	950899.i	−0.448891	+	0.0791516i
$680$	984207.	−	568232.i	0.0816233	−	0.0471252i
$681$	−966683.	−	2.65594e6i	−0.0798760	−	0.219458i
$682$	4.55752e6	−	1.65880e6i	0.375204	−	0.136563i
$683$	−9.75034e6	−	1.71925e6i	−0.799775	−	0.141022i	−0.241200	−	0.970476i	$-0.577541\pi$
$683$	−9.75034e6	−	1.71925e6i	−0.799775	−	0.141022i	−0.558576	+	0.829454i	$0.688652\pi$
$684$	−5.22954e6	−	6.23232e6i	−0.427389	−	0.509342i
$685$	−6.10274e6	−	7.27296e6i	−0.496933	−	0.592222i
$686$	8.72858e6	+	1.53908e6i	0.708163	+	0.124868i
$687$	−1.18966e6	+	433002.i	−0.0961683	+	0.0350024i
$688$	−643015.	−	1.76667e6i	−0.0517905	−	0.142293i
$689$	−1.56562e7	+	9.03909e6i	−1.25643	+	0.725398i
$690$	2.92150e6	−	515139.i	0.233606	−	0.0411910i
$691$	1.64419e6	+	1.37964e6i	0.130995	+	0.109918i	0.705931	−	0.708280i	$-0.250529\pi$
$691$	1.64419e6	+	1.37964e6i	0.130995	+	0.109918i	−0.574936	+	0.818198i	$0.694973\pi$
$692$	−3.49893e6	+	6.06032e6i	−0.277760	+	0.481094i
$693$	−1.08333e6	−	1.87639e6i	−0.0856898	−	0.148419i
$694$	2.61235e6	−	1.48153e7i	0.205888	−	1.16765i
$695$	4.76856e6	+	2.75313e6i	0.374477	+	0.216205i
$696$	3.14595e6	+	1.14503e6i	0.246166	+	0.0895972i
$697$			4.05131e6i			0.315874i
$698$	−4.09901e6	+	1.12619e7i	−0.318449	+	0.874932i
$699$	−95119.0	−	539447.i	−0.00736333	−	0.0417595i
$700$	2.42432e6	−	2.03425e6i	0.187001	−	0.156913i
$701$	−1.05911e7	+	1.26219e7i	−0.814038	+	0.970133i	−0.999923	−	0.0124385i	$-0.996041\pi$
$701$	−1.05911e7	+	1.26219e7i	−0.814038	+	0.970133i	0.185884	+	0.982572i	$0.440485\pi$
$702$	−6.87927e6			−0.526865
$703$	1.37535e7	+	1.53553e7i	1.04960	+	1.17184i
$704$	−521691.			−0.0396718
$705$	−1.52495e6	+	1.81736e6i	−0.115553	+	0.137711i
$706$	−4.55377e6	+	3.82107e6i	−0.343843	+	0.288518i
$707$	295507.	+	1.67590e6i	0.0222341	+	0.126096i
$708$	−484375.	+	1.33081e6i	−0.0363160	+	0.0997775i
$709$			1.11072e7i			0.829832i	0.909860	+	0.414916i	$0.136189\pi$
$709$			1.11072e7i			0.829832i	−0.909860	+	0.414916i	$0.863811\pi$
$710$	5.95357e6	+	2.16692e6i	0.443233	+	0.161323i
$711$	−2.55107e6	−	1.47286e6i	−0.189256	−	0.109267i
$712$	77712.9	−	440732.i	0.00574504	−	0.0325817i
$713$	−2.12129e7	−	3.67419e7i	−1.56270	−	2.70668i
$714$	664421.	−	1.15081e6i	0.0487751	−	0.0844809i
$715$	−1.65655e6	−	1.39001e6i	−0.121182	−	0.101684i
$716$	5.87969e6	−	1.03675e6i	0.428619	−	0.0755771i
$717$	−4.76826e6	+	2.75295e6i	−0.346387	+	0.199987i
$718$	−5.93571e6	−	1.63082e7i	−0.429696	−	1.18058i
$719$	−1.67351e7	+	6.09108e6i	−1.20727	+	0.439412i	−0.865757	−	0.500464i	$-0.833163\pi$
$719$	−1.67351e7	+	6.09108e6i	−1.20727	+	0.439412i	−0.341517	+	0.939876i	$0.610941\pi$
$720$	−1.40555e6	−	247836.i	−0.101045	−	0.0178170i
$721$	6.17972e6	+	7.36470e6i	0.442722	+	0.527615i
$722$	−9.38969e6	−	1.11902e7i	−0.670360	−	0.798904i
$723$	9.41304e6	+	1.65977e6i	0.669706	+	0.118087i
$724$	7.76455e6	−	2.82607e6i	0.550516	−	0.200372i
$725$	−6.96910e6	−	1.91474e7i	−0.492415	−	1.35290i
$726$	3.07609e6	−	1.77598e6i	0.216600	−	0.125054i
$727$	5.20442e6	−	917680.i	0.365205	−	0.0643954i	0.0119653	−	0.999928i	$-0.496191\pi$
$727$	5.20442e6	−	917680.i	0.365205	−	0.0643954i	0.353239	+	0.935533i	$0.385080\pi$
$728$	−2.53988e6	−	2.13122e6i	−0.177617	−	0.149039i
$729$	1.34694e6	−	2.33297e6i	0.0938708	−	0.162589i
$730$	−4.22363e6	−	7.31553e6i	−0.293345	−	0.508088i
$731$	−834327.	+	4.73170e6i	−0.0577488	+	0.327510i
$732$	−337903.	−	195089.i	−0.0233085	−	0.0134572i
$733$	−9.30734e6	−	3.38760e6i	−0.639832	−	0.232880i	0.00167321	−	0.999999i	$-0.499467\pi$
$733$	−9.30734e6	−	3.38760e6i	−0.639832	−	0.232880i	−0.641505	+	0.767119i	$0.721690\pi$
$734$		−	3.37558e6i		−	0.231264i
$735$	566226.	−	1.55569e6i	0.0386608	−	0.106220i
$736$	792450.	+	4.49421e6i	0.0539234	+	0.305815i
$737$	−2.25889e6	+	1.89544e6i	−0.153189	+	0.128541i
$738$	3.27041e6	−	3.89752e6i	0.221035	−	0.263419i
$739$	−2.38085e7			−1.60369			−0.801846	−	0.597530i	$-0.796149\pi$
$739$	−2.38085e7			−1.60369			−0.801846	+	0.597530i	$0.796149\pi$
$740$	3.57977e6	+	512643.i	0.240312	+	0.0344141i
$741$	−9.49447e6			−0.635221
$742$	−6.15388e6	+	7.33391e6i	−0.410336	+	0.489019i
$743$	9.06556e6	−	7.60691e6i	0.602452	−	0.505517i	−0.289781	−	0.957093i	$-0.593582\pi$
$743$	9.06556e6	−	7.60691e6i	0.602452	−	0.505517i	0.892233	+	0.451576i	$0.149138\pi$
$744$	−648683.	−	3.67886e6i	−0.0429635	−	0.243658i
$745$	1.12043e6	−	3.07835e6i	0.0739593	−	0.203202i
$746$			9.05880e6i			0.595969i
$747$	5.40785e6	+	1.96830e6i	0.354588	+	0.129059i
$748$	1.15462e6	+	666623.i	0.0754548	+	0.0435638i
$749$	1.50157e6	−	8.51581e6i	0.0978003	−	0.554653i
$750$	−1.83500e6	−	3.17831e6i	−0.119119	−	0.206321i
$751$	446886.	−	774029.i	0.0289132	−	0.0500792i	−0.851207	−	0.524831i	$-0.824129\pi$
$751$	446886.	−	774029.i	0.0289132	−	0.0500792i	0.880120	+	0.474751i	$0.157462\pi$
$752$	−2.79569e6	−	2.34586e6i	−0.180279	−	0.151272i
$753$	−5.16635e6	+	910968.i	−0.332045	+	0.0585485i
$754$	−1.84876e7	+	1.06738e7i	−1.18427	+	0.683739i
$755$	−4.15569e6	−	1.14177e7i	−0.265323	−	0.728970i
$756$	−3.42338e6	+	1.24601e6i	−0.217847	+	0.0792896i
$757$	−1.05432e7	−	1.85906e6i	−0.668704	−	0.117911i	−0.171018	−	0.985268i	$-0.554706\pi$
$757$	−1.05432e7	−	1.85906e6i	−0.668704	−	0.117911i	−0.497686	+	0.867357i	$0.665817\pi$
$758$	4.65858e6	+	5.55188e6i	0.294497	+	0.350968i
$759$	2.23705e6	+	2.66602e6i	0.140952	+	0.167980i
$760$	−4.23479e6	−	746707.i	−0.265948	−	0.0468939i
$761$	6.02006e6	−	2.19112e6i	0.376825	−	0.137153i	−0.146662	−	0.989187i	$-0.546853\pi$
$761$	6.02006e6	−	2.19112e6i	0.376825	−	0.137153i	0.523487	+	0.852034i	$0.324631\pi$
$762$	−1.50023e6	−	4.12186e6i	−0.0935991	−	0.257162i
$763$	−1.18063e7	+	6.81636e6i	−0.734179	+	0.423878i
$764$	1.13390e7	−	1.99937e6i	0.702814	−	0.123925i
$765$	2.79412e6	+	2.34454e6i	0.172620	+	0.144845i
$766$	4.86472e6	−	8.42594e6i	0.299561	−	0.518855i
$767$	−4.51526e6	−	7.82067e6i	−0.277137	−	0.480016i
$768$	−69775.6	+	395717.i	−0.00426875	+	0.0242093i
$769$	−2.15535e7	−	1.24439e7i	−1.31432	−	0.758825i	−0.331514	−	0.943450i	$-0.607559\pi$
$769$	−2.15535e7	−	1.24439e7i	−1.31432	−	0.758825i	−0.982809	+	0.184626i	$0.940893\pi$
$770$	−1.07612e6	−	391677.i	−0.0654087	−	0.0238068i
$771$			1.00747e7i			0.610373i
$772$	−3.52319e6	+	9.67990e6i	−0.212762	+	0.584558i
$773$	5.42310e6	+	3.07559e7i	0.326436	+	1.85131i	0.499383	+	0.866381i	$0.333560\pi$
$773$	5.42310e6	+	3.07559e7i	0.326436	+	1.85131i	−0.172947	+	0.984931i	$0.555329\pi$
$774$	4.62231e6	−	3.87857e6i	0.277336	−	0.232713i
$775$	−1.46147e7	+	1.74171e7i	−0.874047	+	1.04165i
$776$	−4.23175e6			−0.252270
$777$	3.92468e6	−	1.57376e6i	0.233212	−	0.0935159i
$778$	7.73274e6			0.458020
$779$	9.85342e6	−	1.17429e7i	0.581760	−	0.693314i
$780$	−1.27592e6	+	1.07062e6i	−0.0750908	+	0.0630086i
$781$	1.29067e6	+	7.31977e6i	0.0757162	+	0.429408i
$782$	3.98887e6	−	1.09593e7i	0.233256	−	0.640866i
$783$			2.34562e7i			1.36727i
$784$	2.39316e6	+	871038.i	0.139053	+	0.0506112i
$785$	1.77106e6	+	1.02252e6i	0.102579	+	0.0592240i
$786$	−51704.8	+	293233.i	−0.00298521	+	0.0169300i
$787$	−8.90300e6	−	1.54205e7i	−0.512389	−	0.887483i	−0.999897	−	0.0143649i	$-0.995427\pi$
$787$	−8.90300e6	−	1.54205e7i	−0.512389	−	0.887483i	0.487508	−	0.873119i	$-0.337906\pi$
$788$	−6.91751e6	+	1.19815e7i	−0.396857	+	0.687376i
$789$	−1.07790e6	−	904463.i	−0.0616431	−	0.0517247i
$790$	−1.53330e6	+	270362.i	−0.0874097	+	0.0154127i
$791$	1.11581e7	−	6.44214e6i	0.634088	−	0.366091i
$792$	−572665.	−	1.57338e6i	−0.0324405	−	0.0891296i
$793$	2.33792e6	−	850935.i	0.132022	−	0.0480522i
$794$	2.92429e6	+	515632.i	0.164615	+	0.0290261i
$795$	3.09142e6	+	3.68421e6i	0.173476	+	0.206741i
$796$	8.05078e6	+	9.59454e6i	0.450355	+	0.536712i
$797$	−2.63219e6	−	464126.i	−0.146782	−	0.0258816i	0.0997745	−	0.995010i	$-0.468188\pi$
$797$	−2.63219e6	−	464126.i	−0.146782	−	0.0258816i	−0.246556	+	0.969129i	$0.579299\pi$
$798$	−4.72480e6	+	1.71969e6i	−0.262649	+	0.0955965i
$799$	3.18995e6	+	8.76431e6i	0.176773	+	0.485680i
$800$	2.11799e6	−	1.22282e6i	0.117003	−	0.0675519i
$801$	1.41452e6	−	249418.i	0.0778983	−	0.0137356i
$802$	−4.72037e6	−	3.96086e6i	−0.259143	−	0.217447i
$803$	4.95496e6	−	8.58224e6i	0.271176	−	0.469690i
$804$	1.13562e6	+	1.96694e6i	0.0619571	+	0.107313i
$805$	−1.73954e6	+	9.86543e6i	−0.0946117	+	0.536570i
$806$	2.06289e7	+	1.19101e7i	1.11851	+	0.645770i
$807$	−9.52183e6	−	3.46566e6i	−0.514679	−	0.187328i
$808$			1.31509e6i			0.0708641i
$809$	3.14125e6	−	8.63050e6i	0.168745	−	0.463623i	−0.826279	−	0.563261i	$-0.809546\pi$
$809$	3.14125e6	−	8.63050e6i	0.168745	−	0.463623i	0.995024	+	0.0996385i	$0.0317686\pi$
$810$	−623207.	−	3.53438e6i	−0.0333749	−	0.189278i
$811$	−4.30423e6	+	3.61168e6i	−0.229797	+	0.192822i	−0.750414	−	0.660968i	$-0.770146\pi$
$811$	−4.30423e6	+	3.61168e6i	−0.229797	+	0.192822i	0.520618	+	0.853790i	$0.325702\pi$
$812$	−7.26680e6	+	8.66024e6i	−0.386770	+	0.460935i
$813$	−1.25622e7			−0.666561
$814$	1.57897e6	+	3.93768e6i	0.0835245	+	0.208295i
$815$	6.10191e6			0.321790
$816$	660081.	−	786654.i	0.0347034	−	0.0413579i
$817$	1.39266e7	−	1.16858e7i	0.729943	−	0.612495i
$818$	−1.48527e6	−	8.42340e6i	−0.0776109	−	0.440153i
$819$	3.63954e6	−	9.99956e6i	0.189599	−	0.520920i
$820$		−	2.68917e6i		−	0.139664i
$821$	−9.73702e6	−	3.54398e6i	−0.504160	−	0.183499i	0.0774043	−	0.997000i	$-0.475337\pi$
$821$	−9.73702e6	−	3.54398e6i	−0.504160	−	0.183499i	−0.581564	+	0.813501i	$0.697559\pi$
$822$	−7.42954e6	−	4.28945e6i	−0.383515	−	0.221423i
$823$	−4.72628e6	+	2.68041e7i	−0.243232	+	1.37943i	0.581332	+	0.813666i	$0.302532\pi$
$823$	−4.72628e6	+	2.68041e7i	−0.243232	+	1.37943i	−0.824564	+	0.565769i	$0.808579\pi$
$824$	3.71473e6	+	6.43411e6i	0.190594	+	0.330119i
$825$	932545.	−	1.61522e6i	0.0477018	−	0.0826220i
$826$	−3.66348e6	−	3.07403e6i	−0.186829	−	0.156768i
$827$	2.10178e7	−	3.70600e6i	1.06862	−	0.188426i	0.388441	−	0.921474i	$-0.373014\pi$
$827$	2.10178e7	−	3.70600e6i	1.06862	−	0.188426i	0.680178	+	0.733047i	$0.261903\pi$
$828$	−1.26843e7	+	7.32330e6i	−0.642972	+	0.371220i
$829$	−9.72292e6	−	2.67135e7i	−0.491372	−	1.35003i	−0.899425	−	0.437075i	$-0.856014\pi$
$829$	−9.72292e6	−	2.67135e7i	−0.491372	−	1.35003i	0.408053	−	0.912958i	$-0.366208\pi$
$830$	2.85831e6	−	1.04034e6i	0.144017	−	0.0524179i
$831$	−1.07873e7	−	1.90209e6i	−0.541889	−	0.0955497i
$832$	−1.64696e6	−	1.96277e6i	−0.0824851	−	0.0983019i
$833$	−4.18359e6	−	4.98581e6i	−0.208899	−	0.248956i
$834$	4.89985e6	+	863975.i	0.243931	+	0.0430117i
$835$	7.69153e6	−	2.79949e6i	0.381765	−	0.138951i
$836$	−1.72539e6	−	4.74046e6i	−0.0853828	−	0.234587i
$837$	2.26665e7	−	1.30865e7i	1.11833	−	0.645670i
$838$	1.60179e7	−	2.82438e6i	0.787942	−	0.138936i
$839$	2.29820e7	+	1.92842e7i	1.12715	+	0.945794i	0.998944	−	0.0459532i	$-0.0146325\pi$
$839$	2.29820e7	+	1.92842e7i	1.12715	+	0.945794i	0.128210	+	0.991747i	$0.459077\pi$
$840$	−441028.	+	763883.i	−0.0215659	+	0.0373533i
$841$	2.61388e7	+	4.52738e7i	1.27437	+	2.20728i
$842$	−1.59179e6	+	9.02746e6i	−0.0773756	+	0.438819i
$843$	1.60294e6	+	925459.i	0.0776871	+	0.0448527i
$844$	1.57354e6	+	572722.i	0.0760365	+	0.0276750i
$845$		−	543102.i		−	0.0261662i
$846$	4.00610e6	−	1.10067e7i	0.192440	−	0.528726i
$847$	2.08281e6	+	1.18122e7i	0.0997563	+	0.565746i
$848$	−5.66751e6	+	4.75560e6i	−0.270647	+	0.227099i
$849$	−3.04628e6	+	3.63042e6i	−0.145044	+	0.172857i
$850$	−6.25013e6			−0.296717
$851$	3.15234e7	−	1.95837e7i	1.49214	−	0.926981i
$852$	5.72487e6			0.270189
$853$	2.67702e7	−	3.19035e7i	1.25973	−	1.50129i	0.477046	−	0.878878i	$-0.341707\pi$
$853$	2.67702e7	−	3.19035e7i	1.25973	−	1.50129i	0.782688	−	0.622415i	$-0.213848\pi$
$854$	1.00931e6	−	846914.i	0.0473567	−	0.0397370i
$855$	−2.39654e6	−	1.35915e7i	−0.112117	−	0.635845i
$856$	2.28551e6	−	6.27938e6i	0.106610	−	0.292909i
$857$			9.69844e6i			0.451076i	0.974234	+	0.225538i	$0.0724140\pi$
$857$			9.69844e6i			0.451076i	−0.974234	+	0.225538i	$0.927586\pi$
$858$	−1.83616e6	−	668306.i	−0.0851513	−	0.0309925i
$859$	1.37588e7	+	7.94363e6i	0.636205	+	0.367313i	0.783151	−	0.621831i	$-0.213611\pi$
$859$	1.37588e7	+	7.94363e6i	0.636205	+	0.367313i	−0.146946	+	0.989144i	$0.546944\pi$
$860$	553807.	−	3.14080e6i	0.0255336	−	0.144808i
$861$	−1.57219e6	−	2.72312e6i	−0.0722766	−	0.125187i
$862$	−1.33812e7	+	2.31769e7i	−0.613375	+	1.06240i
$863$	1.05698e7	+	8.86915e6i	0.483105	+	0.405373i	0.851548	−	0.524277i	$-0.175664\pi$
$863$	1.05698e7	+	8.86915e6i	0.483105	+	0.405373i	−0.368443	+	0.929650i	$0.620109\pi$
$864$	−2.77254e6	+	488873.i	−0.126355	+	0.0222798i
$865$	−1.02805e7	+	5.93546e6i	−0.467170	+	0.269720i
$866$	501971.	+	1.37915e6i	0.0227449	+	0.0624911i
$867$	5.71447e6	−	2.07990e6i	0.258183	−	0.0939710i
$868$	1.24229e7	+	2.19050e6i	0.559660	+	0.0986832i
$869$	−1.17408e6	−	1.39921e6i	−0.0527410	−	0.0628543i
$870$	3.65050e6	+	4.35050e6i	0.163514	+	0.194868i
$871$	−1.42625e7	−	2.51487e6i	−0.637016	−	0.112323i
$872$	−9.89977e6	+	3.60322e6i	−0.440893	+	0.160472i
$873$	−4.64523e6	−	1.27627e7i	−0.206287	−	0.566769i
$874$	−3.82167e7	+	2.20644e7i	−1.69229	+	0.977043i
$875$	1.22047e7	−	2.15202e6i	0.538899	−	0.0950224i
$876$	−5.84714e6	−	4.90633e6i	−0.257444	−	0.216021i
$877$	5.57957e6	−	9.66410e6i	0.244964	−	0.424290i	−0.717158	−	0.696911i	$-0.754557\pi$
$877$	5.57957e6	−	9.66410e6i	0.244964	−	0.424290i	0.962121	+	0.272621i	$0.0878906\pi$
$878$	−1.06170e7	−	1.83892e7i	−0.464799	−	0.805056i
$879$	139356.	−	790328.i	0.00608351	−	0.0345013i
$880$	−766414.	−	442489.i	−0.0333624	−	0.0192618i
$881$	−4.17227e7	−	1.51858e7i	−1.81106	−	0.659171i	−0.996913	−	0.0785097i	$-0.974984\pi$
$881$	−4.17227e7	−	1.51858e7i	−1.81106	−	0.659171i	−0.814145	−	0.580662i	$-0.802794\pi$
$882$			8.17374e6i			0.353793i
$883$	−2.37922e6	+	6.53686e6i	−0.102691	+	0.282142i	−0.980389	−	0.197073i	$-0.936856\pi$
$883$	−2.37922e6	+	6.53686e6i	−0.102691	+	0.282142i	0.877698	+	0.479215i	$0.159079\pi$
$884$	1.13706e6	+	6.44859e6i	0.0489387	+	0.277545i
$885$	−1.84036e6	+	1.54425e6i	−0.0789851	+	0.0662764i
$886$	−8.23177e6	+	9.81025e6i	−0.352297	+	0.419851i
$887$	−1.93423e6			−0.0825465			−0.0412733	−	0.999148i	$-0.513141\pi$
$887$	−1.93423e6			−0.0825465			−0.0412733	+	0.999148i	$0.513141\pi$
$888$	3.19802e6	−	671035.i	0.136097	−	0.0285570i
$889$	1.48121e7			0.628584
$890$	487988.	−	581562.i	0.0206507	−	0.0246105i
$891$	3.22530e6	−	2.70635e6i	0.136106	−	0.114206i
$892$	2.71328e6	+	1.53878e7i	0.114178	+	0.647536i
$893$	1.20700e7	−	3.31621e7i	0.506499	−	1.39160i
$894$		−	2.96010e6i		−	0.123869i
$895$	9.51717e6	+	3.46397e6i	0.397146	+	0.144549i
$896$	−1.17510e6	−	678443.i	−0.0488995	−	0.0282321i
$897$	−2.96812e6	+	1.68331e7i	−0.123169	+	0.698525i
$898$	−4.87136e6	−	8.43744e6i	−0.201585	−	0.349156i
$899$	4.06098e7	−	7.03383e7i	1.67584	−	2.90263i
$900$	6.01287e6	+	5.04540e6i	0.247443	+	0.207630i
$901$	1.86203e7	−	3.28326e6i	0.764142	−	0.134739i
$902$	2.73214e6	−	1.57740e6i	0.111812	−	0.0645545i
$903$	−1.27543e6	−	3.50423e6i	−0.0520521	−	0.143012i
$904$	9.35626e6	−	3.40540e6i	0.380786	−	0.138595i
$905$	1.38039e7	+	2.43400e6i	0.560248	+	0.0987868i
$906$	−7.05721e6	−	8.41046e6i	−0.285636	−	0.340407i
$907$	−5.33947e6	−	6.36333e6i	−0.215516	−	0.256842i	0.647445	−	0.762112i	$-0.275837\pi$
$907$	−5.33947e6	−	6.36333e6i	−0.215516	−	0.256842i	−0.862961	+	0.505270i	$0.831393\pi$
$908$	7.26358e6	+	1.28076e6i	0.292372	+	0.0515531i
$909$	−3.96621e6	+	1.44358e6i	−0.159208	+	0.0579471i
$910$	−1.92367e6	−	5.28524e6i	−0.0770065	−	0.211574i
$911$	−2.85649e7	+	1.64920e7i	−1.14035	+	0.658379i	−0.946516	−	0.322656i	$-0.895424\pi$
$911$	−2.85649e7	+	1.64920e7i	−1.14035	+	0.658379i	−0.193830	+	0.981035i	$0.562091\pi$
$912$	−3.82653e6	+	674721.i	−0.152342	+	0.0268619i
$913$	2.73358e6	+	2.29374e6i	0.108531	+	0.0910685i
$914$	−2.91423e6	+	5.04759e6i	−0.115387	+	0.199857i
$915$	−330941.	−	573207.i	−0.0130677	−	0.0226339i
$916$	573687.	−	3.25354e6i	0.0225910	−	0.128120i
$917$	−870766.	−	502737.i	−0.0341962	−	0.0197432i
$918$	6.76096e6	+	2.46079e6i	0.264790	+	0.0963757i
$919$			3.98096e6i			0.155489i	0.996973	+	0.0777444i	$0.0247718\pi$
$919$			3.98096e6i			0.155489i	−0.996973	+	0.0777444i	$0.975228\pi$
$920$	−2.64772e6	+	7.27456e6i	−0.103134	+	0.283359i
$921$	−31723.2	−	179911.i	−0.00123233	−	0.00698890i
$922$	9.47442e6	−	7.94998e6i	0.367050	−	0.307991i
$923$	−2.34648e7	+	2.79642e7i	−0.906593	+	1.08044i
$924$	−1.03479e6			−0.0398722
$925$	−1.56401e7	−	1.22853e7i	−0.601016	−	0.472099i
$926$	3.00446e7			1.15144
$927$	−1.53271e7	+	1.82662e7i	−0.585816	+	0.698148i
$928$	−6.69247e6	+	5.61565e6i	−0.255103	+	0.214057i
$929$	5.33183e6	+	3.02383e7i	0.202692	+	1.14953i	0.901030	+	0.433757i	$0.142812\pi$
$929$	5.33183e6	+	3.02383e7i	0.202692	+	1.14953i	−0.698338	+	0.715768i	$0.746077\pi$
$930$	2.16737e6	−	5.95480e6i	0.0821723	−	0.225767i
$931$			2.46267e7i			0.931176i
$932$	1.34323e6	+	488895.i	0.0506535	+	0.0184364i
$933$	1.20087e7	+	6.93320e6i	0.451638	+	0.260753i
$934$	−1.33994e6	+	7.59915e6i	−0.0502593	+	0.285035i
$935$	1.13084e6	+	1.95866e6i	0.0423029	+	0.0732708i
$936$	4.11170e6	−	7.12168e6i	0.153402	−	0.265701i
$937$	1.49700e7	+	1.25613e7i	0.557023	+	0.467398i	0.877311	−	0.479922i	$-0.159335\pi$
$937$	1.49700e7	+	1.25613e7i	0.557023	+	0.467398i	−0.320288	+	0.947320i	$0.603780\pi$
$938$	−7.55306e6	+	1.33181e6i	−0.280295	+	0.0494236i
$939$	5.76462e6	−	3.32821e6i	0.213357	−	0.123182i
$940$	−2.11742e6	−	5.81755e6i	−0.0781603	−	0.214744i
$941$	−4.08220e6	+	1.48580e6i	−0.150286	+	0.0546998i	−0.416068	−	0.909333i	$-0.636592\pi$
$941$	−4.08220e6	+	1.48580e6i	−0.150286	+	0.0546998i	0.265782	+	0.964033i	$0.414370\pi$
$942$	1.81982e6	+	320883.i	0.0668190	+	0.0117820i
$943$	−1.77390e7	−	2.11405e7i	−0.649604	−	0.774168i
$944$	−2.37555e6	−	2.83107e6i	−0.0867629	−	0.103400i
$945$	−6.08611e6	−	1.07315e6i	−0.221697	−	0.0390912i
$946$	3.51584e6	−	1.27966e6i	0.127732	−	0.0464908i
$947$	−1.16237e7	−	3.19358e7i	−0.421181	−	1.15718i	−0.951032	−	0.309094i	$-0.899974\pi$
$947$	−1.16237e7	−	3.19358e7i	−0.421181	−	1.15718i	0.529851	−	0.848091i	$-0.322248\pi$
$948$	−1.21837e6	+	703429.i	−0.0440311	+	0.0254214i
$949$	4.79318e7	−	8.45168e6i	1.72766	−	0.304633i
$950$	1.81162e7	+	1.52013e7i	0.651266	+	0.546477i
$951$	1.41080e6	−	2.44357e6i	0.0505840	−	0.0876140i
$952$	1.73384e6	+	3.00311e6i	0.0620037	+	0.107394i
$953$	7.90066e6	−	4.48069e7i	0.281793	−	1.59813i	−0.434726	−	0.900563i	$-0.643155\pi$
$953$	7.90066e6	−	4.48069e7i	0.281793	−	1.59813i	0.716519	−	0.697567i	$-0.245734\pi$
$954$	−2.05638e7	−	1.18725e7i	−0.731532	−	0.422350i
$955$	1.83539e7	+	6.68026e6i	0.651207	+	0.237020i
$956$		−	1.43680e7i		−	0.508453i
$957$	−2.27872e6	+	6.26073e6i	−0.0804287	+	0.220976i
$958$	−2.80014e6	−	1.58804e7i	−0.0985750	−	0.559046i
$959$	2.21919e7	−	1.86213e7i	0.779200	−	0.653826i
$960$	−438147.	+	522164.i	−0.0153441	+	0.0182864i
$961$	−6.19978e7			−2.16555
$962$	−9.83008e6	+	1.83718e7i	−0.342467	+	0.640049i
$963$	2.14470e7			0.745248
$964$	−1.60329e7	+	1.91073e7i	−0.555674	+	0.662227i
$965$	−1.33862e7	+	1.12324e7i	−0.462743	+	0.388288i
$966$	1.57184e6	+	8.91436e6i	0.0541959	+	0.307360i
$967$	−9.12626e6	+	2.50742e7i	−0.313853	+	0.862304i	0.678017	+	0.735047i	$0.262840\pi$
$967$	−9.12626e6	+	2.50742e7i	−0.313853	+	0.862304i	−0.991870	+	0.127258i	$0.959382\pi$
$968$			9.26905e6i			0.317941i
$969$	9.33118e6	+	3.39627e6i	0.319247	+	0.116196i
$970$	−6.21685e6	−	3.58930e6i	−0.212149	−	0.122484i
$971$	−3.04649e6	+	1.72775e7i	−0.103693	+	0.588074i	0.888041	+	0.459765i	$0.152066\pi$
$971$	−3.04649e6	+	1.72775e7i	−0.103693	+	0.588074i	−0.991734	+	0.128310i	$0.959045\pi$
$972$	−6.96614e6	−	1.20657e7i	−0.236498	−	0.409626i
$973$	−8.40062e6	+	1.45503e7i	−0.284465	+	0.492708i
$974$	−208685.	−	175108.i	−0.00704846	−	0.00591436i
$975$	9.02099e6	−	1.59064e6i	0.303908	−	0.0535872i
$976$	881777.	−	509094.i	0.0296302	−	0.0171070i
$977$	−4.76280e6	−	1.30857e7i	−0.159634	−	0.438591i	0.833929	−	0.551872i	$-0.186086\pi$
$977$	−4.76280e6	−	1.30857e7i	−0.159634	−	0.438591i	−0.993563	+	0.113281i	$0.963864\pi$
$978$	5.18115e6	−	1.88578e6i	0.173212	−	0.0630442i
$979$	877097.	+	154656.i	0.0292477	+	0.00515715i
$980$	2.77698e6	+	3.30947e6i	0.0923649	+	0.110076i
$981$	−2.17341e7	−	2.59017e7i	−0.721057	−	0.859322i
$982$	1.05305e7	+	1.85682e6i	0.348475	+	0.0614456i
$983$	−1.76687e7	+	6.43088e6i	−0.583204	+	0.212269i	−0.616738	−	0.787169i	$-0.711546\pi$
$983$	−1.76687e7	+	6.43088e6i	−0.583204	+	0.212269i	0.0335338	+	0.999438i	$0.489324\pi$
$984$	−831082.	−	2.28338e6i	−0.0273625	−	0.0751779i
$985$	−2.03249e7	+	1.17346e7i	−0.667481	+	0.385370i
$986$	2.19877e7	−	3.87703e6i	0.720258	−	0.127001i
$987$	−5.54531e6	−	4.65307e6i	−0.181190	−	0.152036i
$988$	1.23882e7	−	2.14569e7i	0.403752	−	0.699319i
$989$	−1.63644e7	−	2.83440e7i	−0.531998	−	0.921448i
$990$	493217.	−	2.79717e6i	0.0159938	−	0.0907051i
$991$	1.73809e7	+	1.00348e7i	0.562195	+	0.324584i	0.754026	−	0.656844i	$-0.228109\pi$
$991$	1.73809e7	+	1.00348e7i	0.562195	+	0.324584i	−0.191831	+	0.981428i	$0.561443\pi$
$992$	9.16040e6	+	3.33411e6i	0.295553	+	0.107572i
$993$		−	1.11719e7i		−	0.359544i
$994$	−6.61192e6	+	1.81661e7i	−0.212257	+	0.583171i
$995$	3.68943e6	+	2.09238e7i	0.118141	+	0.670013i
$996$	2.10548e6	−	1.76671e6i	0.0672516	−	0.0564308i
$997$	−3.41902e7	+	4.07463e7i	−1.08934	+	1.29823i	−0.137883	+	0.990448i	$0.544030\pi$
$997$	−3.41902e7	+	4.07463e7i	−1.08934	+	1.29823i	−0.951458	+	0.307778i	$0.900415\pi$
$998$	−3.93450e7			−1.25044
$999$	1.20814e7	+	1.94472e7i	0.383006	+	0.616515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.h.a.3.4	✓	96
37.25	even	18	inner	74.6.h.a.25.4	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.h.a.3.4	✓	96	1.1	even	1	trivial
74.6.h.a.25.4	yes	96	37.25	even	18	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	74.h (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.57115 + 3.06418i) q^{2} +(-4.69686 + 3.94113i) q^{3} +(-2.77837 - 15.7569i) q^{4} +(9.28305 - 25.5050i) q^{5} -24.5252i q^{6} +(77.8232 + 28.3253i) q^{7} +(55.4256 + 32.0000i) q^{8} +(-35.6686 + 202.286i) q^{9} +O(q^{10})\)	\(q+(-2.57115 + 3.06418i) q^{2} +(-4.69686 + 3.94113i) q^{3} +(-2.77837 - 15.7569i) q^{4} +(9.28305 - 25.5050i) q^{5} -24.5252i q^{6} +(77.8232 + 28.3253i) q^{7} +(55.4256 + 32.0000i) q^{8} +(-35.6686 + 202.286i) q^{9} +(54.2837 + 94.0221i) q^{10} +(-63.6830 + 110.302i) q^{11} +(75.1497 + 63.0581i) q^{12} +(-616.039 + 108.624i) q^{13} +(-286.889 + 165.636i) q^{14} +(56.9173 + 156.379i) q^{15} +(-240.561 + 87.5572i) q^{16} +(644.300 + 113.607i) q^{17} +(-528.132 - 629.404i) q^{18} +(-1591.21 - 1896.33i) q^{19} +(-427.672 - 75.4101i) q^{20} +(-477.159 + 173.672i) q^{21} +(-174.247 - 478.740i) q^{22} +(-3859.51 + 2228.29i) q^{23} +(-386.442 + 68.1402i) q^{24} +(1829.56 + 1535.18i) q^{25} +(1251.08 - 2166.94i) q^{26} +(-1374.66 - 2380.98i) q^{27} +(230.098 - 1304.95i) q^{28} +(-7388.61 - 4265.82i) q^{29} +(-625.516 - 227.669i) q^{30} +9519.82i q^{31} +(350.229 - 962.245i) q^{32} +(-135.605 - 769.057i) q^{33} +(-2004.71 + 1682.15i) q^{34} +(1444.87 - 1721.93i) q^{35} +3286.51 q^{36} +(-8322.96 + 268.879i) q^{37} +9901.95 q^{38} +(2465.34 - 2938.08i) q^{39} +(1330.68 - 1116.57i) q^{40} +(1075.30 + 6098.32i) q^{41} +(694.686 - 1908.63i) q^{42} +7343.94i q^{43} +(1914.96 + 696.988i) q^{44} +(4828.20 + 2787.56i) q^{45} +(3095.51 - 17555.5i) q^{46} +(7127.96 + 12346.0i) q^{47} +(784.808 - 1359.33i) q^{48} +(-7620.78 - 6394.59i) q^{49} +(-9408.15 + 1658.91i) q^{50} +(-3473.93 + 2005.67i) q^{51} +(3423.17 + 9405.08i) q^{52} +(27157.1 - 9884.39i) q^{53} +(10830.2 + 1909.66i) q^{54} +(2222.08 + 2648.18i) q^{55} +(3406.99 + 4060.29i) q^{56} +(14947.4 + 2635.63i) q^{57} +(32068.5 - 11672.0i) q^{58} +(4937.51 + 13565.7i) q^{59} +(2305.91 - 1331.32i) q^{60} +(-3916.88 + 690.651i) q^{61} +(-29170.4 - 24476.9i) q^{62} +(-8505.67 + 14732.3i) q^{63} +(2048.00 + 3547.24i) q^{64} +(-2948.26 + 16720.4i) q^{65} +(2705.19 + 1561.84i) q^{66} +(21755.7 + 7918.44i) q^{67} -10467.8i q^{68} +(9345.59 - 25676.8i) q^{69} +(1561.32 + 8854.71i) q^{70} +(44704.0 - 37511.1i) q^{71} +(-8450.12 + 10070.5i) q^{72} -77806.6 q^{73} +(20575.7 - 26194.4i) q^{74} -14643.5 q^{75} +(-25459.4 + 30341.3i) q^{76} +(-8080.37 + 6780.23i) q^{77} +(2664.04 + 15108.5i) q^{78} +(-4904.88 + 13476.1i) q^{79} +6948.31i q^{80} +(-31063.4 - 11306.1i) q^{81} +(-21451.1 - 12384.8i) q^{82} +(4865.13 - 27591.5i) q^{83} +(4062.25 + 7036.03i) q^{84} +(8878.63 - 15378.2i) q^{85} +(-22503.2 - 18882.4i) q^{86} +(51515.4 - 9083.56i) q^{87} +(-7059.34 + 4075.71i) q^{88} +(-2391.63 - 6570.96i) q^{89} +(-20955.6 + 7627.22i) q^{90} +(-51018.9 - 8996.02i) q^{91} +(45834.2 + 54623.0i) q^{92} +(-37518.9 - 44713.2i) q^{93} +(-56157.3 - 9902.06i) q^{94} +(-63137.3 + 22980.1i) q^{95} +(2147.36 + 5899.83i) q^{96} +(-57262.6 + 33060.6i) q^{97} +(39188.3 - 6909.96i) q^{98} +(-20041.2 - 16816.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{3} + 90 q^{5} - 228 q^{7} - 186 q^{9}+O(q^{10}) \) 96 * q + 6 * q^3 + 90 * q^5 - 228 * q^7 - 186 * q^9	\( 96 q + 6 q^{3} + 90 q^{5} - 228 q^{7} - 186 q^{9} + 600 q^{10} - 726 q^{11} - 96 q^{12} - 246 q^{13} + 3960 q^{14} - 3960 q^{15} - 1530 q^{17} + 3222 q^{19} + 1440 q^{20} - 16110 q^{21} + 8232 q^{25} + 13632 q^{26} + 2154 q^{27} - 10464 q^{28} - 18378 q^{29} - 25056 q^{30} + 78198 q^{33} + 37296 q^{34} + 82170 q^{35} - 124416 q^{36} - 5586 q^{37} - 39936 q^{38} + 58686 q^{39} - 16128 q^{40} - 59598 q^{41} - 26304 q^{42} + 480 q^{44} - 74646 q^{45} - 22536 q^{46} - 1266 q^{47} + 193320 q^{49} + 18864 q^{50} + 68352 q^{52} - 57432 q^{53} + 101520 q^{54} + 133830 q^{55} - 228936 q^{57} - 79224 q^{58} - 52800 q^{59} + 68664 q^{61} - 72720 q^{62} - 166254 q^{63} + 196608 q^{64} - 122058 q^{65} + 254946 q^{67} - 218094 q^{69} - 25872 q^{70} + 200052 q^{71} - 32244 q^{73} + 124368 q^{74} - 234036 q^{75} + 51552 q^{76} + 397188 q^{77} - 16584 q^{78} + 267462 q^{79} - 371496 q^{81} + 121440 q^{83} + 84672 q^{84} - 337260 q^{85} + 43920 q^{86} - 667500 q^{87} - 135936 q^{88} + 377850 q^{89} - 576408 q^{90} + 875826 q^{91} + 233376 q^{92} + 365868 q^{93} - 80256 q^{94} + 764592 q^{95} - 823212 q^{97} - 342192 q^{98} - 928650 q^{99}+O(q^{100}) \) 96 * q + 6 * q^3 + 90 * q^5 - 228 * q^7 - 186 * q^9 + 600 * q^10 - 726 * q^11 - 96 * q^12 - 246 * q^13 + 3960 * q^14 - 3960 * q^15 - 1530 * q^17 + 3222 * q^19 + 1440 * q^20 - 16110 * q^21 + 8232 * q^25 + 13632 * q^26 + 2154 * q^27 - 10464 * q^28 - 18378 * q^29 - 25056 * q^30 + 78198 * q^33 + 37296 * q^34 + 82170 * q^35 - 124416 * q^36 - 5586 * q^37 - 39936 * q^38 + 58686 * q^39 - 16128 * q^40 - 59598 * q^41 - 26304 * q^42 + 480 * q^44 - 74646 * q^45 - 22536 * q^46 - 1266 * q^47 + 193320 * q^49 + 18864 * q^50 + 68352 * q^52 - 57432 * q^53 + 101520 * q^54 + 133830 * q^55 - 228936 * q^57 - 79224 * q^58 - 52800 * q^59 + 68664 * q^61 - 72720 * q^62 - 166254 * q^63 + 196608 * q^64 - 122058 * q^65 + 254946 * q^67 - 218094 * q^69 - 25872 * q^70 + 200052 * q^71 - 32244 * q^73 + 124368 * q^74 - 234036 * q^75 + 51552 * q^76 + 397188 * q^77 - 16584 * q^78 + 267462 * q^79 - 371496 * q^81 + 121440 * q^83 + 84672 * q^84 - 337260 * q^85 + 43920 * q^86 - 667500 * q^87 - 135936 * q^88 + 377850 * q^89 - 576408 * q^90 + 875826 * q^91 + 233376 * q^92 + 365868 * q^93 - 80256 * q^94 + 764592 * q^95 - 823212 * q^97 - 342192 * q^98 - 928650 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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