LMFDB - Embedded newform 74.6.h.a.21.2

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			21.2
Character	$\chi$	$=$	74.21
Dual form			74.6.h.a.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36808 + 3.75877i) q^{2} +(-17.4563 + 6.35356i) q^{3} +(-12.2567 - 10.2846i) q^{4} +(-104.064 - 18.3493i) q^{5} -74.3062i q^{6} +(19.0842 - 108.232i) q^{7} +(55.4256 - 32.0000i) q^{8} +(78.2045 - 65.6213i) q^{9} +O(q^{10})$	\(q+(-1.36808 + 3.75877i) q^{2} +(-17.4563 + 6.35356i) q^{3} +(-12.2567 - 10.2846i) q^{4} +(-104.064 - 18.3493i) q^{5} -74.3062i q^{6} +(19.0842 - 108.232i) q^{7} +(55.4256 - 32.0000i) q^{8} +(78.2045 - 65.6213i) q^{9} +(211.339 - 366.050i) q^{10} +(189.573 + 328.350i) q^{11} +(279.300 + 101.657i) q^{12} +(-581.568 + 693.085i) q^{13} +(380.710 + 219.803i) q^{14} +(1933.16 - 340.868i) q^{15} +(44.4539 + 252.111i) q^{16} +(-1422.95 - 1695.81i) q^{17} +(139.666 + 383.728i) q^{18} +(376.889 + 1035.50i) q^{19} +(1086.77 + 1295.16i) q^{20} +(354.519 + 2010.58i) q^{21} +(-1493.54 + 263.352i) q^{22} +(223.936 + 129.290i) q^{23} +(-764.210 + 910.750i) q^{24} +(7556.14 + 2750.21i) q^{25} +(-1809.52 - 3134.18i) q^{26} +(1308.82 - 2266.95i) q^{27} +(-1347.03 + 1130.29i) q^{28} +(3481.51 - 2010.05i) q^{29} +(-1363.47 + 7732.63i) q^{30} +2372.38i q^{31} +(-1008.44 - 177.816i) q^{32} +(-5395.43 - 4527.30i) q^{33} +(8320.87 - 3028.55i) q^{34} +(-3971.97 + 10912.9i) q^{35} -1633.42 q^{36} +(7886.04 + 2674.77i) q^{37} -4407.80 q^{38} +(5748.44 - 15793.7i) q^{39} +(-6355.01 + 2313.03i) q^{40} +(-7587.25 - 6366.46i) q^{41} +(-8042.31 - 1418.08i) q^{42} -11440.7i q^{43} +(1053.41 - 5974.18i) q^{44} +(-9342.40 + 5393.84i) q^{45} +(-792.332 + 664.846i) q^{46} +(7271.58 - 12594.8i) q^{47} +(-2377.80 - 4118.47i) q^{48} +(4443.47 + 1617.29i) q^{49} +(-20674.8 + 24639.3i) q^{50} +(35613.8 + 20561.7i) q^{51} +(14256.2 - 2513.76i) q^{52} +(1083.20 + 6143.15i) q^{53} +(6730.37 + 8020.94i) q^{54} +(-13702.8 - 37648.1i) q^{55} +(-2405.67 - 6609.52i) q^{56} +(-13158.2 - 15681.3i) q^{57} +(2792.33 + 15836.1i) q^{58} +(-43505.2 + 7671.14i) q^{59} +(-27199.8 - 15703.8i) q^{60} +(-19511.5 + 23252.9i) q^{61} +(-8917.24 - 3245.61i) q^{62} +(-5609.85 - 9716.55i) q^{63} +(2048.00 - 3547.24i) q^{64} +(73238.1 - 61454.1i) q^{65} +(24398.5 - 14086.5i) q^{66} +(-1036.49 + 5878.22i) q^{67} +35419.5i q^{68} +(-4730.53 - 834.121i) q^{69} +(-35585.1 - 29859.4i) q^{70} +(-40016.3 + 14564.7i) q^{71} +(2234.65 - 6139.65i) q^{72} +19844.5 q^{73} +(-20842.6 + 25982.5i) q^{74} -149375. q^{75} +(6030.23 - 16567.9i) q^{76} +(39155.8 - 14251.6i) q^{77} +(51500.6 + 43214.1i) q^{78} +(-33364.0 - 5882.97i) q^{79} -27051.4i q^{80} +(-12751.8 + 72318.8i) q^{81} +(34310.0 - 19808.9i) q^{82} +(75203.9 - 63103.6i) q^{83} +(16332.7 - 28289.2i) q^{84} +(116962. + 202583. i) q^{85} +(43002.8 + 15651.7i) q^{86} +(-48003.2 + 57208.0i) q^{87} +(21014.4 + 12132.7i) q^{88} +(30940.3 - 5455.60i) q^{89} +(-7493.04 - 42495.1i) q^{90} +(63915.2 + 76171.2i) q^{91} +(-1415.03 - 3887.76i) q^{92} +(-15073.1 - 41412.9i) q^{93} +(37392.7 + 44562.8i) q^{94} +(-20220.1 - 114674. i) q^{95} +(18733.4 - 3303.21i) q^{96} +(128786. + 74354.7i) q^{97} +(-12158.1 + 14489.4i) q^{98} +(36372.2 + 13238.4i) 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 $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−1.36808	+	3.75877i	−0.241845	+	0.664463i
$2$	−1.36808	+	3.75877i	−0.241845	+	0.664463i
$3$	−17.4563	+	6.35356i	−1.11982	+	0.407581i	−0.834586	−	0.550877i	$-0.814293\pi$
$3$	−17.4563	+	6.35356i	−1.11982	+	0.407581i	−0.285233	+	0.958458i	$0.592071\pi$
$4$	−12.2567	−	10.2846i	−0.383022	−	0.321394i
$5$	−104.064	−	18.3493i	−1.86156	−	0.328243i	−0.874053	−	0.485830i	$-0.838517\pi$
$5$	−104.064	−	18.3493i	−1.86156	−	0.328243i	−0.987505	+	0.157587i	$0.949629\pi$
$6$		−	74.3062i		−	0.842650i
$7$	19.0842	−	108.232i	0.147207	−	0.834854i	−0.818361	−	0.574704i	$-0.805117\pi$
$7$	19.0842	−	108.232i	0.147207	−	0.834854i	0.965568	−	0.260149i	$-0.0837718\pi$
$8$	55.4256	−	32.0000i	0.306186	−	0.176777i
$9$	78.2045	−	65.6213i	0.321829	−	0.270047i
$10$	211.339	−	366.050i	0.668313	−	1.15755i
$11$	189.573	+	328.350i	0.472384	+	0.818193i	0.999501	−	0.0316002i	$-0.0100603\pi$
$11$	189.573	+	328.350i	0.472384	+	0.818193i	−0.527117	+	0.849793i	$0.676727\pi$
$12$	279.300	+	101.657i	0.559910	+	0.203790i
$13$	−581.568	+	693.085i	−0.954425	+	1.13744i	0.0359947	+	0.999352i	$0.488540\pi$
$13$	−581.568	+	693.085i	−0.954425	+	1.13744i	−0.990420	+	0.138088i	$0.955904\pi$
$14$	380.710	+	219.803i	0.519128	+	0.299719i
$15$	1933.16	−	340.868i	2.21840	−	0.391163i
$16$	44.4539	+	252.111i	0.0434120	+	0.246202i
$17$	−1422.95	−	1695.81i	−1.19417	−	1.42316i	−0.880771	−	0.473542i	$-0.842975\pi$
$17$	−1422.95	−	1695.81i	−1.19417	−	1.42316i	−0.313404	−	0.949620i	$-0.601469\pi$
$18$	139.666	+	383.728i	0.101603	+	0.279153i
$19$	376.889	+	1035.50i	0.239514	+	0.658058i	0.999962	+	0.00866030i	$0.00275669\pi$
$19$	376.889	+	1035.50i	0.239514	+	0.658058i	−0.760449	+	0.649398i	$0.775021\pi$
$20$	1086.77	+	1295.16i	0.607523	+	0.724018i
$21$	354.519	+	2010.58i	0.175425	+	0.994884i
$22$	−1493.54	+	263.352i	−0.657902	+	0.116006i
$23$	223.936	+	129.290i	0.0882682	+	0.0509617i	0.543484	−	0.839419i	$-0.317105\pi$
$23$	223.936	+	129.290i	0.0882682	+	0.0509617i	−0.455216	+	0.890381i	$0.650438\pi$
$24$	−764.210	+	910.750i	−0.270822	+	0.322754i
$25$	7556.14	+	2750.21i	2.41796	+	0.880067i
$26$	−1809.52	−	3134.18i	−0.524964	−	0.909264i
$27$	1308.82	−	2266.95i	0.345519	−	0.598456i
$28$	−1347.03	+	1130.29i	−0.324700	+	0.272456i
$29$	3481.51	−	2010.05i	0.768728	−	0.443825i	−0.0636925	−	0.997970i	$-0.520288\pi$
$29$	3481.51	−	2010.05i	0.768728	−	0.443825i	0.832421	+	0.554144i	$0.186954\pi$
$30$	−1363.47	+	7732.63i	−0.276594	+	1.56864i
$31$			2372.38i			0.443384i	0.975117	+	0.221692i	$0.0711580\pi$
$31$			2372.38i			0.443384i	−0.975117	+	0.221692i	$0.928842\pi$
$32$	−1008.44	−	177.816i	−0.174091	−	0.0306970i
$33$	−5395.43	−	4527.30i	−0.862464	−	0.723693i
$34$	8320.87	−	3028.55i	1.23444	−	0.449301i
$35$	−3971.97	+	10912.9i	−0.548070	+	1.50581i
$36$	−1633.42			−0.210059
$37$	7886.04	+	2674.77i	0.947010	+	0.321205i
$37$	7886.04	+	2674.77i	0.947010	+	0.321205i
$38$	−4407.80			−0.495180
$39$	5748.44	−	15793.7i	0.605185	−	1.66273i
$40$	−6355.01	+	2313.03i	−0.628009	+	0.228577i
$41$	−7587.25	−	6366.46i	−0.704896	−	0.591478i	0.218266	−	0.975889i	$-0.429960\pi$
$41$	−7587.25	−	6366.46i	−0.704896	−	0.591478i	−0.923162	+	0.384412i	$0.874404\pi$
$42$	−8042.31	−	1418.08i	−0.703489	−	0.124044i
$43$		−	11440.7i		−	0.943582i	−0.881710	−	0.471791i	$-0.843608\pi$
$43$		−	11440.7i		−	0.943582i	0.881710	−	0.471791i	$-0.156392\pi$
$44$	1053.41	−	5974.18i	0.0820286	−	0.465207i
$45$	−9342.40	+	5393.84i	−0.687744	+	0.397069i
$46$	−792.332	+	664.846i	−0.0552094	+	0.0463262i
$47$	7271.58	−	12594.8i	0.480158	−	0.831658i	−0.519583	−	0.854420i	$-0.673913\pi$
$47$	7271.58	−	12594.8i	0.480158	−	0.831658i	0.999741	+	0.0227618i	$0.00724592\pi$
$48$	−2377.80	−	4118.47i	−0.148961	−	0.258008i
$49$	4443.47	+	1617.29i	0.264382	+	0.0962272i
$50$	−20674.8	+	24639.3i	−1.16954	+	1.39381i
$51$	35613.8	+	20561.7i	1.91731	+	1.10696i
$52$	14256.2	−	2513.76i	0.731132	−	0.128918i
$53$	1083.20	+	6143.15i	0.0529688	+	0.300401i	0.999771	−	0.0214161i	$-0.00681748\pi$
$53$	1083.20	+	6143.15i	0.0529688	+	0.300401i	−0.946802	+	0.321817i	$0.895706\pi$
$54$	6730.37	+	8020.94i	0.314090	+	0.374318i
$55$	−13702.8	−	37648.1i	−0.610804	−	1.67817i
$56$	−2405.67	−	6609.52i	−0.102510	−	0.281643i
$57$	−13158.2	−	15681.3i	−0.536424	−	0.639285i
$58$	2792.33	+	15836.1i	0.108993	+	0.618128i
$59$	−43505.2	+	7671.14i	−1.62709	+	0.286899i	−0.911400	−	0.411521i	$-0.864998\pi$
$59$	−43505.2	+	7671.14i	−1.62709	+	0.286899i	−0.715687	+	0.698421i	$0.753886\pi$
$60$	−27199.8	−	15703.8i	−0.975412	−	0.563154i
$61$	−19511.5	+	23252.9i	−0.671376	+	0.800114i	−0.988971	−	0.148112i	$-0.952680\pi$
$61$	−19511.5	+	23252.9i	−0.671376	+	0.800114i	0.317595	+	0.948226i	$0.397125\pi$
$62$	−8917.24	−	3245.61i	−0.294612	−	0.107230i
$63$	−5609.85	−	9716.55i	−0.178074	−	0.308433i
$64$	2048.00	−	3547.24i	0.0625000	−	0.108253i
$65$	73238.1	−	61454.1i	2.15007	−	1.80413i
$66$	24398.5	−	14086.5i	0.689450	−	0.398054i
$67$	−1036.49	+	5878.22i	−0.0282083	+	0.159977i	−0.995658	−	0.0930858i	$-0.970327\pi$
$67$	−1036.49	+	5878.22i	−0.0282083	+	0.159977i	0.967450	+	0.253063i	$0.0814380\pi$
$68$			35419.5i			0.928903i
$69$	−4730.53	−	834.121i	−0.119616	−	0.0210914i
$70$	−35585.1	−	29859.4i	−0.868007	−	0.728344i
$71$	−40016.3	+	14564.7i	−0.942086	+	0.342891i	−0.766989	−	0.641660i	$-0.778246\pi$
$71$	−40016.3	+	14564.7i	−0.942086	+	0.342891i	−0.175097	+	0.984551i	$0.556024\pi$
$72$	2234.65	−	6139.65i	0.0508017	−	0.139576i
$73$	19844.5			0.435847			0.217923	−	0.975966i	$-0.430072\pi$
$73$	19844.5			0.435847			0.217923	+	0.975966i	$0.430072\pi$
$74$	−20842.6	+	25982.5i	−0.442458	+	0.551571i
$75$	−149375.			−3.06638
$76$	6030.23	−	16567.9i	0.119757	−	0.329029i
$77$	39155.8	−	14251.6i	0.752609	−	0.273927i
$78$	51500.6	+	43214.1i	0.958464	+	0.804246i
$79$	−33364.0	−	5882.97i	−0.601465	−	0.106055i	−0.135379	−	0.990794i	$-0.543225\pi$
$79$	−33364.0	−	5882.97i	−0.601465	−	0.106055i	−0.466086	+	0.884739i	$0.654336\pi$
$80$		−	27051.4i		−	0.472569i
$81$	−12751.8	+	72318.8i	−0.215952	+	1.22473i
$82$	34310.0	−	19808.9i	0.563490	−	0.325331i
$83$	75203.9	−	63103.6i	1.19824	−	1.00545i	0.198565	−	0.980088i	$-0.436372\pi$
$83$	75203.9	−	63103.6i	1.19824	−	1.00545i	0.999678	−	0.0253584i	$-0.00807268\pi$
$84$	16332.7	−	28289.2i	0.252558	−	0.437443i
$85$	116962.	+	202583.i	1.75588	+	3.04128i
$86$	43002.8	+	15651.7i	0.626975	+	0.228200i
$87$	−48003.2	+	57208.0i	−0.679942	+	0.810323i
$88$	21014.4	+	12132.7i	0.289275	+	0.167013i
$89$	30940.3	−	5455.60i	0.414046	−	0.0730075i	0.0372552	−	0.999306i	$-0.488139\pi$
$89$	30940.3	−	5455.60i	0.414046	−	0.0730075i	0.376791	+	0.926298i	$0.377027\pi$
$90$	−7493.04	−	42495.1i	−0.0975106	−	0.553010i
$91$	63915.2	+	76171.2i	0.809097	+	0.964245i
$92$	−1415.03	−	3887.76i	−0.0174299	−	0.0478883i
$93$	−15073.1	−	41412.9i	−0.180715	−	0.496510i
$94$	37392.7	+	44562.8i	0.436483	+	0.520180i
$95$	−20220.1	−	114674.i	−0.229865	−	1.30363i
$96$	18733.4	−	3303.21i	0.207462	−	0.0365812i
$97$	128786.	+	74354.7i	1.38976	+	0.802378i	0.993288	−	0.115669i	$-0.0369013\pi$
$97$	128786.	+	74354.7i	1.38976	+	0.802378i	0.396471	+	0.918047i	$0.370235\pi$
$98$	−12158.1	+	14489.4i	−0.127879	+	0.152400i
$99$	36372.2	+	13238.4i	0.372977	+	0.135753i
$100$	−64328.6	−	111420.i	−0.643286	−	1.11420i
$101$	24042.8	−	41643.3i	0.234521	−	0.406202i	−0.724613	−	0.689156i	$-0.757981\pi$
$101$	24042.8	−	41643.3i	0.234521	−	0.406202i	0.959133	+	0.282955i	$0.0913146\pi$
$102$	−126009.	+	105734.i	−1.19923	+	1.00627i
$103$	−62370.0	+	36009.3i	−0.579272	+	0.334443i	−0.760844	−	0.648935i	$-0.775215\pi$
$103$	−62370.0	+	36009.3i	−0.579272	+	0.334443i	0.181572	+	0.983378i	$0.441881\pi$
$104$	−10055.0	+	57024.9i	−0.0911590	+	0.516989i
$105$		−	215734.i		−	1.90962i
$106$	−24572.6	−	4332.81i	−0.212416	−	0.0374546i
$107$	123054.	+	103254.i	1.03905	+	0.871863i	0.991899	−	0.127025i	$-0.0405429\pi$
$107$	123054.	+	103254.i	1.03905	+	0.871863i	0.0471461	+	0.998888i	$0.484987\pi$
$108$	−39356.6	+	14324.6i	−0.324682	+	0.118174i
$109$	48752.0	−	133945.i	0.393030	−	1.07984i	−0.572581	−	0.819848i	$-0.694058\pi$
$109$	48752.0	−	133945.i	0.393030	−	1.07984i	0.965611	−	0.259993i	$-0.0837202\pi$
$110$	160257.			1.26280
$111$	−154655.	+	3412.97i	−1.19140	+	0.0262921i
$112$	28134.8			0.211933
$113$	−5721.14	+	15718.7i	−0.0421490	+	0.115803i	−0.958982	−	0.283469i	$-0.908515\pi$
$113$	−5721.14	+	15718.7i	−0.0421490	+	0.115803i	0.916833	+	0.399272i	$0.130737\pi$
$114$	76943.8	−	28005.2i	0.554513	−	0.201826i
$115$	−20931.4	−	17563.5i	−0.147589	−	0.123842i
$116$	−63344.5	−	11169.3i	−0.437083	−	0.0770695i
$117$			92365.6i			0.623800i
$118$	30684.5	−	174021.i	0.202869	−	1.15052i
$119$	−210697.	+	121646.i	−1.36392	+	0.787461i
$120$	96238.6	−	80753.8i	0.610094	−	0.511929i
$121$	8649.60	−	14981.5i	0.0537072	−	0.0930236i
$122$	−60708.9	−	105151.i	−0.369278	−	0.639608i
$123$	172895.	+	62928.5i	1.03043	+	0.375046i
$124$	24399.0	−	29077.6i	0.142501	−	0.169826i
$125$	−449883.	−	259740.i	−2.57528	−	1.48684i
$126$	44197.0	−	7793.13i	0.248009	−	0.0437306i
$127$	−24683.7	−	139988.i	−0.135800	−	0.770162i	−0.974299	−	0.225258i	$-0.927677\pi$
$127$	−24683.7	−	139988.i	−0.135800	−	0.770162i	0.838499	−	0.544904i	$-0.183434\pi$
$128$	10531.4	+	12550.9i	0.0568149	+	0.0677094i
$129$	72688.9	+	199711.i	0.384586	+	1.05664i
$130$	130796.	+	359359.i	0.678791	+	1.86496i
$131$	157998.	+	188295.i	0.804403	+	0.958650i	0.999756	−	0.0220827i	$-0.00702972\pi$
$131$	157998.	+	188295.i	0.804403	+	0.958650i	−0.195353	+	0.980733i	$0.562585\pi$
$132$	19568.7	+	110980.i	0.0977524	+	0.554381i
$133$	119266.	−	21029.9i	0.584640	−	0.103088i
$134$	−20676.9	−	11937.8i	−0.0994770	−	0.0574331i
$135$	−177799.	+	211892.i	−0.839643	+	1.00065i
$136$	−133134.	−	48456.8i	−0.617222	−	0.224650i
$137$	−55193.6	−	95598.2i	−0.251239	−	0.435159i	0.712628	−	0.701542i	$-0.247505\pi$
$137$	−55193.6	−	95598.2i	−0.251239	−	0.435159i	−0.963867	+	0.266383i	$0.914171\pi$
$138$	9607.02	−	16639.9i	0.0429429	−	0.0743792i
$139$	31032.5	−	26039.4i	0.136232	−	0.114312i	−0.572125	−	0.820166i	$-0.693881\pi$
$139$	31032.5	−	26039.4i	0.136232	−	0.114312i	0.708358	+	0.705854i	$0.249436\pi$
$140$	160918.	−	92906.1i	0.693881	−	0.400612i
$141$	−46913.1	+	266058.i	−0.198722	+	1.12701i
$142$		−	170338.i		−	0.708908i
$143$	−337824.	−	59567.5i	−1.38150	−	0.243596i
$144$	20020.3	+	16799.1i	0.0804573	+	0.0675117i
$145$	−399184.	+	145291.i	−1.57672	+	0.573877i
$146$	−27148.9	+	74591.1i	−0.105407	+	0.289604i
$147$	−87841.9			−0.335281
$148$	−69148.0	−	113889.i	−0.259493	−	0.427392i
$149$	−114653.			−0.423078			−0.211539	−	0.977370i	$-0.567847\pi$
$149$	−114653.			−0.423078			−0.211539	+	0.977370i	$0.567847\pi$
$150$	204358.	−	561468.i	0.741588	−	2.03750i
$151$	278010.	−	101187.i	0.992242	−	0.361146i	0.205654	−	0.978625i	$-0.434068\pi$
$151$	278010.	−	101187.i	0.992242	−	0.361146i	0.786588	+	0.617478i	$0.211846\pi$
$152$	54025.2	+	45332.5i	0.189665	+	0.159148i
$153$	−222562.	−	39243.8i	−0.768640	−	0.135532i
$154$			166675.i			0.566329i
$155$	43531.6	−	246880.i	0.145538	−	0.825386i
$156$	−232889.	+	134458.i	−0.766191	+	0.442361i
$157$	72942.1	−	61205.7i	0.236172	−	0.198172i	−0.517018	−	0.855974i	$-0.672958\pi$
$157$	72942.1	−	61205.7i	0.236172	−	0.198172i	0.753191	+	0.657802i	$0.228514\pi$
$158$	67757.4	−	117359.i	0.215931	−	0.374003i
$159$	−57939.5	−	100354.i	−0.181753	−	0.314806i
$160$	101680.	+	37008.5i	0.314005	+	0.114288i
$161$	18266.9	−	21769.6i	0.0555393	−	0.0661891i
$162$	−254384.	−	146869.i	−0.761558	−	0.439686i
$163$	−41160.3	+	7257.66i	−0.121341	+	0.0213958i	−0.233989	−	0.972239i	$-0.575178\pi$
$163$	−41160.3	+	7257.66i	−0.121341	+	0.0213958i	0.112648	+	0.993635i	$0.464067\pi$
$164$	27518.2	+	156064.i	0.0798934	+	0.453098i
$165$	478398.	+	570133.i	1.36798	+	1.63030i
$166$	134307.	+	369005.i	0.378293	+	1.03935i
$167$	−74482.9	−	204640.i	−0.206664	−	0.567805i	0.792448	−	0.609940i	$-0.208806\pi$
$167$	−74482.9	−	204640.i	−0.206664	−	0.567805i	−0.999112	+	0.0421345i	$0.986584\pi$
$168$	83987.9	+	100093.i	0.229585	+	0.273609i
$169$	−77672.0	−	440500.i	−0.209193	−	1.18639i
$170$	−921477.	+	162481.i	−2.44547	+	0.431202i
$171$	97425.0	+	56248.4i	0.254789	+	0.147102i
$172$	−117663.	+	140225.i	−0.303261	+	0.361413i
$173$	149532.	+	54425.2i	0.379856	+	0.138256i	0.524889	−	0.851171i	$-0.324107\pi$
$173$	149532.	+	54425.2i	0.379856	+	0.138256i	−0.145033	+	0.989427i	$0.546329\pi$
$174$	−149359.	−	258698.i	−0.373990	−	0.647769i
$175$	441863.	−	765330.i	1.09067	−	1.88909i
$176$	−74353.4	+	62389.9i	−0.180933	+	0.151821i
$177$	710699.	−	410322.i	1.70511	−	0.984445i
$178$	−21822.4	+	123761.i	−0.0516241	+	0.292775i
$179$		−	31979.0i		−	0.0745989i	−0.999304	−	0.0372995i	$-0.988124\pi$
$179$		−	31979.0i		−	0.0745989i	0.999304	−	0.0372995i	$-0.0118755\pi$
$180$	169981.	+	29972.2i	0.391037	+	0.0689504i
$181$	499200.	+	418878.i	1.13260	+	0.950367i	0.999172	−	0.0406907i	$-0.0129558\pi$
$181$	499200.	+	418878.i	1.13260	+	0.950367i	0.133432	+	0.991058i	$0.457400\pi$
$182$	−373751.	+	136034.i	−0.836381	+	0.304418i
$183$	192859.	−	529875.i	0.425708	−	1.16962i
$184$	16549.1			0.0360354
$185$	−771575.	−	423051.i	−1.65748	−	0.908790i
$186$	176283.			0.373618
$187$	287066.	−	788706.i	0.600312	−	1.64934i
$188$	−218658.	+	79584.9i	−0.451201	+	0.164224i
$189$	−220378.	−	184919.i	−0.448761	−	0.376555i
$190$	458695.	+	80880.3i	0.921807	+	0.162539i
$191$			842753.i			1.67154i	0.549080	+	0.835770i	$0.314978\pi$
$191$			842753.i			1.67154i	−0.549080	+	0.835770i	$0.685022\pi$
$192$	−13212.8	+	74933.6i	−0.0258668	+	0.146698i
$193$	684621.	−	395266.i	1.32299	−	0.763830i	0.338787	−	0.940863i	$-0.389983\pi$
$193$	684621.	−	395266.i	1.32299	−	0.763830i	0.984205	+	0.177033i	$0.0566501\pi$
$194$	−455672.	+	382354.i	−0.869256	+	0.729393i
$195$	−888011.	+	1.53808e6i	−1.67237	+	2.89663i
$196$	−37829.1	−	65522.0i	−0.0703374	−	0.121828i
$197$	−221750.	−	80710.2i	−0.407096	−	0.148171i	0.130352	−	0.991468i	$-0.458389\pi$
$197$	−221750.	−	80710.2i	−0.407096	−	0.148171i	−0.537448	+	0.843297i	$0.680612\pi$
$198$	−99520.3	+	118604.i	−0.180405	+	0.214998i
$199$	407070.	+	235022.i	0.728678	+	0.420703i	0.817938	−	0.575306i	$-0.195117\pi$
$199$	407070.	+	235022.i	0.728678	+	0.420703i	−0.0892601	+	0.996008i	$0.528450\pi$
$200$	506810.	−	89364.3i	0.895922	−	0.157975i
$201$	−19254.4	−	109197.i	−0.0336155	−	0.190643i
$202$	123635.	+	147343.i	0.213188	+	0.254068i
$203$	−151110.	−	415171.i	−0.257367	−	0.707110i
$204$	−225040.	−	618292.i	−0.378603	−	1.04020i
$205$	672742.	+	801742.i	1.11806	+	1.33245i
$206$	−50023.6	−	283698.i	−0.0821310	−	0.465788i
$207$	25997.0	−	4583.96i	0.0421693	−	0.00743559i
$208$	−200587.	−	115809.i	−0.321473	−	0.185603i
$209$	−268557.	+	320054.i	−0.425276	+	0.506824i
$210$	810896.	+	295142.i	1.26887	+	0.461831i
$211$	5955.77	+	10315.7i	0.00920941	+	0.0159512i	0.870593	−	0.492003i	$-0.163735\pi$
$211$	5955.77	+	10315.7i	0.00920941	+	0.0159512i	−0.861384	+	0.507954i	$0.830402\pi$
$212$	49903.3	−	86435.1i	0.0762588	−	0.132084i
$213$	605996.	−	508491.i	0.915210	−	0.767953i
$214$	−556456.	+	321270.i	−0.830608	+	0.479552i
$215$	−209928.	+	1.19056e6i	−0.309724	+	1.75653i
$216$		−	167529.i		−	0.244319i
$217$	256767.	+	45275.0i	0.370161	+	0.0652694i
$218$	436771.	+	366495.i	0.622462	+	0.522308i
$219$	−346411.	+	126083.i	−0.488070	+	0.177643i
$220$	−219244.	+	602369.i	−0.305402	+	0.839085i
$221$	2.00288e6			2.75851
$222$	198752.	−	585982.i	0.270663	−	0.797998i
$223$	−870147.			−1.17174			−0.585869	−	0.810406i	$-0.699247\pi$
$223$	−870147.			−1.17174			−0.585869	+	0.810406i	$0.699247\pi$
$224$	−38490.7	+	105752.i	−0.0512549	+	0.140822i
$225$	771396.	−	280765.i	1.01583	−	0.369732i
$226$	−51256.1	−	43008.9i	−0.0667535	−	0.0560128i
$227$	713781.	+	125859.i	0.919391	+	0.162113i	0.613265	−	0.789877i	$-0.289856\pi$
$227$	713781.	+	125859.i	0.919391	+	0.162113i	0.306126	+	0.951991i	$0.400967\pi$
$228$			327527.i			0.417264i
$229$	−112450.	+	637733.i	−0.141700	+	0.803619i	0.828258	+	0.560347i	$0.189332\pi$
$229$	−112450.	+	637733.i	−0.141700	+	0.803619i	−0.969958	+	0.243272i	$0.921779\pi$
$230$	94653.0	−	54647.9i	0.117982	−	0.0681168i
$231$	−592966.	+	497558.i	−0.731139	+	0.613498i
$232$	128643.	−	222817.i	0.156916	−	0.271786i
$233$	398738.	+	690635.i	0.481170	+	0.833410i	0.999767	−	0.0216085i	$-0.00687874\pi$
$233$	398738.	+	690635.i	0.481170	+	0.833410i	−0.518597	+	0.855019i	$0.673545\pi$
$234$	−347181.	−	126364.i	−0.414492	−	0.150863i
$235$	−987817.	+	1.17724e6i	−1.16683	+	1.39057i
$236$	612125.	+	353411.i	0.715418	+	0.413047i
$237$	619789.	−	109285.i	0.716758	−	0.126384i
$238$	−168988.	−	958381.i	−0.193381	−	1.09672i
$239$	−704876.	−	840039.i	−0.798212	−	0.951272i	0.201389	−	0.979511i	$-0.435454\pi$
$239$	−704876.	−	840039.i	−0.798212	−	0.951272i	−0.999601	+	0.0282394i	$0.991010\pi$
$240$	171873.	+	472217.i	0.192610	+	0.529192i
$241$	−382286.	−	1.05032e6i	−0.423981	−	1.16488i	−0.949410	−	0.314040i	$-0.898317\pi$
$241$	−382286.	−	1.05032e6i	−0.423981	−	1.16488i	0.525429	−	0.850838i	$-0.323905\pi$
$242$	44478.8	+	53007.8i	0.0488219	+	0.0581837i
$243$	−126428.	−	717010.i	−0.137350	−	0.778950i
$244$	478293.	−	84336.0i	0.514303	−	0.0906856i
$245$	−432730.	−	249837.i	−0.460577	−	0.265914i
$246$	−473068.	+	563780.i	−0.498409	+	0.593980i
$247$	−936874.	−	340994.i	−0.977099	−	0.355635i
$248$	75916.2	+	131491.i	0.0783800	+	0.135758i
$249$	−911847.	+	1.57936e6i	−0.932016	+	1.61430i
$250$	1.59178e6	−	1.33566e6i	1.61077	−	1.35159i
$251$	1.37946e6	−	796429.i	1.38205	−	0.797927i	0.389647	−	0.920964i	$-0.372597\pi$
$251$	1.37946e6	−	796429.i	1.38205	−	0.797927i	0.992402	+	0.123037i	$0.0392635\pi$
$252$	−31172.5	+	176788.i	−0.0309222	+	0.175368i
$253$			98039.3i			0.0962939i
$254$	559953.	+	98734.8i	0.544587	+	0.0960253i
$255$	−3.32884e6	−	2.79322e6i	−3.20584	−	2.69002i
$256$	−61583.7	+	22414.6i	−0.0587308	+	0.0213763i
$257$	189499.	−	520643.i	0.178967	−	0.491708i	−0.817477	−	0.575961i	$-0.804628\pi$
$257$	189499.	−	520643.i	0.178967	−	0.491708i	0.996444	+	0.0842526i	$0.0268503\pi$
$258$	−850112.			−0.795109
$259$	439994.	−	802475.i	0.407565	−	0.743331i
$260$	−1.52969e6			−1.40336
$261$	140367.	−	385656.i	0.127546	−	0.350428i
$262$	−923911.	+	336276.i	−0.831528	+	0.302652i
$263$	−1.39160e6	−	1.16769e6i	−1.24058	−	1.04097i	−0.997478	−	0.0709725i	$-0.977390\pi$
$263$	−1.39160e6	−	1.16769e6i	−1.24058	−	1.04097i	−0.243105	−	0.970000i	$-0.578166\pi$
$264$	−443919.	−	78274.8i	−0.392007	−	0.0691214i
$265$		−	659158.i		−	0.576601i
$266$	−84119.5	+	477065.i	−0.0728941	+	0.413403i
$267$	−505439.	+	291815.i	−0.433901	+	0.250513i
$268$	73159.0	−	61387.7i	0.0622201	−	0.0522089i
$269$	444820.	−	770452.i	0.374804	−	0.649179i	−0.615494	−	0.788142i	$-0.711043\pi$
$269$	444820.	−	770452.i	0.374804	−	0.649179i	0.990298	+	0.138962i	$0.0443767\pi$
$270$	−553212.	−	958191.i	−0.461830	−	0.799913i
$271$	1.57208e6	+	572189.i	1.30032	+	0.473278i	0.897101	−	0.441826i	$-0.145669\pi$
$271$	1.57208e6	+	572189.i	1.30032	+	0.473278i	0.403219	+	0.915104i	$0.367891\pi$
$272$	364276.	−	434127.i	0.298544	−	0.355791i
$273$	−1.59968e6	−	923575.i	−1.29905	−	0.750007i
$274$	434841.	−	76674.2i	0.349908	−	0.0616983i
$275$	529408.	+	3.00242e6i	0.422143	+	2.39409i
$276$	49402.2	+	58875.2i	0.0390367	+	0.0465222i
$277$	−84393.0	−	231868.i	−0.0660856	−	0.181569i	0.902254	−	0.431205i	$-0.141911\pi$
$277$	−84393.0	−	231868.i	−0.0660856	−	0.181569i	−0.968340	+	0.249636i	$0.919689\pi$
$278$	55421.0	+	152268.i	0.0430093	+	0.118167i
$279$	155679.	+	185531.i	0.119734	+	0.142694i
$280$	129064.	+	731957.i	0.0983806	+	0.557944i
$281$	1.10984e6	−	195695.i	0.838487	−	0.147848i	0.262116	−	0.965036i	$-0.415580\pi$
$281$	1.10984e6	−	195695.i	0.838487	−	0.147848i	0.576370	+	0.817189i	$0.304469\pi$
$282$	−935869.	−	540324.i	−0.700797	−	0.404605i
$283$	291814.	−	347770.i	0.216591	−	0.258123i	−0.646799	−	0.762661i	$-0.723893\pi$
$283$	291814.	−	347770.i	0.216591	−	0.258123i	0.863390	+	0.504538i	$0.168337\pi$
$284$	640260.	+	233036.i	0.471043	+	0.171446i
$285$	1.08155e6	+	1.87331e6i	0.788743	+	1.36614i
$286$	686072.	−	1.18831e6i	0.495969	−	0.859043i
$287$	−833851.	+	699684.i	−0.597563	+	0.501415i
$288$	−90533.3	+	52269.4i	−0.0643172	+	0.0371335i
$289$	−604417.	+	3.42782e6i	−0.425689	+	2.41420i
$290$		−	1.69921e6i		−	1.18646i
$291$	−2.72054e6	−	479704.i	−1.88331	−	0.332079i
$292$	−243229.	−	204093.i	−0.166939	−	0.140078i
$293$	−1.51934e6	+	552994.i	−1.03392	+	0.376315i	−0.802571	−	0.596557i	$-0.796535\pi$
$293$	−1.51934e6	+	552994.i	−1.03392	+	0.376315i	−0.231346	+	0.972872i	$0.574313\pi$
$294$	120175.	−	330178.i	0.0810859	−	0.222782i
$295$	4.66810e6			3.12309
$296$	522681.	−	104103.i	0.346743	−	0.0690609i
$297$	992471.			0.652870
$298$	156855.	−	430955.i	0.102319	−	0.281119i
$299$	−219843.	+	80016.2i	−0.142211	+	0.0517607i
$300$	1.83085e6	+	1.53627e6i	1.17449	+	0.985516i
$301$	−1.23824e6	−	218336.i	−0.787753	−	0.138902i
$302$			1.18341e6i			0.746649i
$303$	−155114.	+	879693.i	−0.0970607	+	0.550459i
$304$	−244305.	+	141050.i	−0.151617	+	0.0875363i
$305$	2.45712e6	−	2.06177e6i	1.51244	−	1.26909i
$306$	451992.	−	782872.i	0.275948	−	0.477955i
$307$	−1.06866e6	−	1.85097e6i	−0.647132	−	1.12086i	−0.983805	−	0.179243i	$-0.942635\pi$
$307$	−1.06866e6	−	1.85097e6i	−0.647132	−	1.12086i	0.336673	−	0.941622i	$-0.390698\pi$
$308$	−626493.	−	228025.i	−0.376305	−	0.136964i
$309$	859959.	−	1.02486e6i	0.512368	−	0.610616i
$310$	868411.	+	501377.i	0.513241	+	0.296320i
$311$	−1.52223e6	+	268411.i	−0.892443	+	0.157362i	−0.601022	−	0.799233i	$-0.705239\pi$
$311$	−1.52223e6	+	268411.i	−0.892443	+	0.157362i	−0.291422	+	0.956595i	$0.594128\pi$
$312$	−186788.	−	1.05933e6i	−0.108633	−	0.616089i
$313$	−628739.	−	749302.i	−0.362752	−	0.432311i	0.553540	−	0.832823i	$-0.313277\pi$
$313$	−628739.	−	749302.i	−0.362752	−	0.432311i	−0.916292	+	0.400512i	$0.868832\pi$
$314$	130267.	+	357907.i	0.0745610	+	0.204855i
$315$	405493.	+	1.11408e6i	0.230254	+	0.632617i
$316$	348429.	+	415241.i	0.196289	+	0.233928i
$317$	257953.	+	1.46292e6i	0.144176	+	0.817661i	0.968025	+	0.250853i	$0.0807110\pi$
$317$	257953.	+	1.46292e6i	0.144176	+	0.817661i	−0.823850	+	0.566809i	$0.808178\pi$
$318$	456474.	−	80488.8i	0.253133	−	0.0446342i
$319$	1.32000e6	+	762103.i	0.726269	+	0.419312i
$320$	−278213.	+	331562.i	−0.151881	+	0.181004i
$321$	−2.80409e6	−	1.02060e6i	−1.51890	−	0.552834i
$322$	56836.5	+	98443.7i	0.0305483	+	0.0529113i
$323$	1.21971e6	−	2.11259e6i	0.650502	−	1.12670i
$324$	900065.	−	755244.i	0.476334	−	0.399691i
$325$	−6.30053e6	+	3.63762e6i	−3.30879	+	1.91033i
$326$	29030.7	−	164641.i	0.0151291	−	0.0858013i
$327$			2.64792e6i			1.36942i
$328$	−624255.	−	110073.i	−0.320389	−	0.0564932i
$329$	−1.22438e6	−	1.02738e6i	−0.623630	−	0.523288i
$330$	−2.79749e6	+	1.01820e6i	−1.41411	+	0.514694i
$331$	−545688.	+	1.49927e6i	−0.273763	+	0.752157i	0.724273	+	0.689513i	$0.242175\pi$
$331$	−545688.	+	1.49927e6i	−0.273763	+	0.752157i	−0.998036	+	0.0626440i	$0.980047\pi$
$332$	−1.57075e6			−0.782098
$333$	792245.	−	308314.i	0.391515	−	0.152364i
$334$	871094.			0.427266
$335$	215723.	−	592693.i	0.105023	−	0.288548i
$336$	−491128.	+	178756.i	−0.237327	+	0.0863799i
$337$	2.78976e6	+	2.34089e6i	1.33811	+	1.12281i	0.982107	+	0.188324i	$0.0603054\pi$
$337$	2.78976e6	+	2.34089e6i	1.33811	+	1.12281i	0.356004	+	0.934485i	$0.384139\pi$
$338$	1.76200e6	+	310688.i	0.838908	+	0.147922i
$339$		−	310740.i		−	0.146858i
$340$	649925.	−	3.68591e6i	0.304906	−	1.72921i
$341$	−778972.	+	449740.i	−0.362774	+	0.209447i
$342$	−344710.	+	289246.i	−0.159363	+	0.133722i
$343$	1.18340e6	−	2.04971e6i	0.543121	−	0.940713i
$344$	−366101.	−	634105.i	−0.166803	−	0.288912i
$345$	476974.	+	173604.i	0.215748	+	0.0785259i
$346$	−409144.	+	487598.i	−0.183732	+	0.218964i
$347$	−2.55778e6	−	1.47674e6i	−1.14035	−	0.658384i	−0.193836	−	0.981034i	$-0.562093\pi$
$347$	−2.55778e6	−	1.47674e6i	−1.14035	−	0.658384i	−0.946518	+	0.322650i	$0.895426\pi$
$348$	1.17672e6	−	207488.i	0.520866	−	0.0918427i
$349$	−187183.	−	1.06157e6i	−0.0822627	−	0.466535i	−0.997914	−	0.0645609i	$-0.979435\pi$
$349$	−187183.	−	1.06157e6i	−0.0822627	−	0.466535i	0.915651	−	0.401974i	$-0.131676\pi$
$350$	2.27219e6	+	2.70790e6i	0.991460	+	1.18158i
$351$	810020.	+	2.22551e6i	0.350936	+	0.964189i
$352$	−132788.	−	364832.i	−0.0571218	−	0.156941i
$353$	193842.	+	231012.i	0.0827964	+	0.0986729i	0.805852	−	0.592117i	$-0.201708\pi$
$353$	193842.	+	231012.i	0.0827964	+	0.0986729i	−0.723056	+	0.690790i	$0.757263\pi$
$354$	570013.	+	3.23271e6i	0.241756	+	1.37107i
$355$	4.43152e6	−	781396.i	1.86630	−	0.329079i
$356$	−435334.	−	251340.i	−0.182053	−	0.105108i
$357$	2.90509e6	−	3.46215e6i	1.20639	−	1.43772i
$358$	120202.	+	43749.9i	0.0495682	+	0.0180414i
$359$	108443.	+	187829.i	0.0444085	+	0.0769178i	0.887375	−	0.461048i	$-0.152526\pi$
$359$	108443.	+	187829.i	0.0444085	+	0.0769178i	−0.842967	+	0.537966i	$0.819193\pi$
$360$	−345206.	+	597914.i	−0.140385	+	0.243154i
$361$	966597.	−	811071.i	0.390371	−	0.327560i
$362$	−2.25741e6	+	1.30332e6i	−0.905398	+	0.522732i
$363$	−55803.5	+	316477.i	−0.0222277	+	0.126060i
$364$		−	1.59095e6i		−	0.629366i
$365$	−2.06511e6	−	364134.i	−0.811354	−	0.143064i
$366$	1.72783e6	+	1.44982e6i	0.674216	+	0.565735i
$367$	4.35443e6	−	1.58488e6i	1.68759	−	0.614232i	0.693269	−	0.720679i	$-0.256170\pi$
$367$	4.35443e6	−	1.58488e6i	1.68759	−	0.614232i	0.994318	+	0.106447i	$0.0339474\pi$
$368$	−22640.5	+	62204.1i	−0.00871496	+	0.0239442i
$369$	−1.01113e6			−0.386583
$370$	2.64573e6	−	2.32140e6i	1.00471	−	0.881549i
$371$	685557.			0.258588
$372$	−241169.	+	662606.i	−0.0903575	+	0.248255i
$373$	−301317.	+	109670.i	−0.112138	+	0.0408147i	−0.397480	−	0.917611i	$-0.630115\pi$
$373$	−301317.	+	109670.i	−0.112138	+	0.0408147i	0.285342	+	0.958426i	$0.407893\pi$
$374$	2.57184e6	+	2.15803e6i	0.950746	+	0.797770i
$375$	9.50354e6	+	1.67573e6i	3.48985	+	0.615355i
$376$		−	930763.i		−	0.339523i
$377$	−631597.	+	3.58197e6i	−0.228869	+	1.29798i
$378$	996565.	−	575367.i	0.358737	−	0.207117i
$379$	−2.17496e6	+	1.82501e6i	−0.777774	+	0.652630i	−0.942687	−	0.333678i	$-0.891710\pi$
$379$	−2.17496e6	+	1.82501e6i	−0.777774	+	0.652630i	0.164913	+	0.986308i	$0.447266\pi$
$380$	−931542.	+	1.61348e6i	−0.330936	+	0.573197i
$381$	1.32031e6	+	2.28684e6i	0.465975	+	0.807093i
$382$	−3.16771e6	−	1.15295e6i	−1.11068	−	0.404253i
$383$	2.28605e6	−	2.72440e6i	0.796321	−	0.949018i	−0.203226	−	0.979132i	$-0.565143\pi$
$383$	2.28605e6	−	2.72440e6i	0.796321	−	0.949018i	0.999546	+	0.0301139i	$0.00958702\pi$
$384$	−263582.	−	152179.i	−0.0912195	−	0.0526656i
$385$	−4.33623e6	+	764594.i	−1.49094	+	0.262893i
$386$	549098.	+	3.11409e6i	0.187578	+	1.06381i
$387$	−750751.	−	894710.i	−0.254811	−	0.303672i
$388$	−813785.	−	2.23586e6i	−0.274429	−	0.753988i
$389$	−816542.	−	2.24343e6i	−0.273593	−	0.751690i	−0.998053	−	0.0623734i	$-0.980133\pi$
$389$	−816542.	−	2.24343e6i	−0.273593	−	0.751690i	0.724460	−	0.689317i	$-0.242089\pi$
$390$	−4.56642e6	−	5.44205e6i	−1.52025	−	1.81176i
$391$	−99400.0	−	563726.i	−0.0328810	−	0.186477i
$392$	298035.	−	52551.7i	0.0979609	−	0.0172731i
$393$	−3.95440e6	−	2.28307e6i	−1.29151	−	0.745656i
$394$	606742.	−	723087.i	0.196908	−	0.234666i
$395$	3.36405e6	+	1.22441e6i	1.08485	+	0.394853i
$396$	−309652.	−	536333.i	−0.0992285	−	0.171869i
$397$	−1.23357e6	+	2.13660e6i	−0.392813	+	0.680372i	−0.992819	−	0.119623i	$-0.961831\pi$
$397$	−1.23357e6	+	2.13660e6i	−0.392813	+	0.680372i	0.600006	+	0.799995i	$0.295165\pi$
$398$	−1.44030e6	+	1.20855e6i	−0.455768	+	0.382435i
$399$	−1.94833e6	+	1.12487e6i	−0.612675	+	0.353728i
$400$	−357457.	+	2.02724e6i	−0.111705	+	0.633513i
$401$		−	2.27817e6i		−	0.707497i	−0.935341	−	0.353748i	$-0.884907\pi$
$401$		−	2.27817e6i		−	0.707497i	0.935341	−	0.353748i	$-0.115093\pi$
$402$	436788.	+	77017.5i	0.134805	+	0.0237697i
$403$	−1.64426e6	−	1.37970e6i	−0.504323	−	0.423177i
$404$	−722970.	+	263140.i	−0.220377	+	0.0802108i
$405$	2.65401e6	−	7.29182e6i	0.804015	−	2.20901i
$406$	1.76726e6			0.532091
$407$	616720.	+	3.09645e6i	0.184545	+	0.926568i
$408$	2.63189e6			0.782740
$409$	−955844.	+	2.62616e6i	−0.282539	+	0.776270i	0.714519	+	0.699616i	$0.246646\pi$
$409$	−955844.	+	2.62616e6i	−0.282539	+	0.776270i	−0.997058	+	0.0766535i	$0.975576\pi$
$410$	−3.93393e6	+	1.43183e6i	−1.15576	+	0.420662i
$411$	1.57086e6	+	1.31811e6i	0.458705	+	0.384900i
$412$	1.13479e6	+	200095.i	0.329362	+	0.0580754i
$413$			4.85505e6i			1.40061i
$414$	−18335.9	+	103988.i	−0.00525776	+	0.0298182i
$415$	−8.98395e6	+	5.18689e6i	−2.56063	+	1.47838i
$416$	709719.	−	595525.i	0.201073	−	0.168720i
$417$	−376269.	+	651717.i	−0.105964	+	0.183535i
$418$	−835601.	−	1.44730e6i	−0.233915	−	0.405153i
$419$	−3.41678e6	−	1.24360e6i	−0.950783	−	0.346057i	−0.180368	−	0.983599i	$-0.557729\pi$
$419$	−3.41678e6	−	1.24360e6i	−0.950783	−	0.346057i	−0.770415	+	0.637543i	$0.779951\pi$
$420$	−2.21874e6	+	2.64419e6i	−0.613739	+	0.731426i
$421$	−365857.	−	211228.i	−0.100602	−	0.0580825i	0.448855	−	0.893605i	$-0.351832\pi$
$421$	−365857.	−	211228.i	−0.100602	−	0.0580825i	−0.549457	+	0.835522i	$0.685165\pi$
$422$	−46922.3	+	8273.67i	−0.0128262	+	0.00226161i
$423$	−257814.	−	1.46214e6i	−0.0700577	−	0.397317i
$424$	256618.	+	305825.i	0.0693222	+	0.0826150i
$425$	−6.08819e6	−	1.67272e7i	−1.63499	−	4.49211i
$426$	1.08225e6	+	2.97346e6i	0.288937	+	0.793849i
$427$	2.14434e6	+	2.55553e6i	0.569147	+	0.678283i
$428$	−446303.	−	2.53111e6i	−0.117766	−	0.667886i
$429$	6.27561e6	−	1.10656e6i	1.64632	−	0.290290i
$430$	−4.18785e6	−	2.41786e6i	−1.09225	−	0.630609i
$431$	492736.	−	587219.i	0.127768	−	0.152267i	−0.698368	−	0.715739i	$-0.746090\pi$
$431$	492736.	−	587219.i	0.127768	−	0.152267i	0.826136	+	0.563471i	$0.190535\pi$
$432$	629705.	+	229194.i	0.162341	+	0.0590872i
$433$	1.55281e6	+	2.68955e6i	0.398014	+	0.689381i	0.993481	−	0.113999i	$-0.0363661\pi$
$433$	1.55281e6	+	2.68955e6i	0.398014	+	0.689381i	−0.595466	+	0.803380i	$0.703033\pi$
$434$	−521457.	+	903190.i	−0.132891	+	0.230173i
$435$	6.04515e6	−	5.07248e6i	1.53173	−	1.28528i
$436$	−1.97511e6	+	1.14033e6i	−0.497594	+	0.287286i
$437$	−49479.6	+	280613.i	−0.0123943	+	0.0702916i
$438$		−	1.47457e6i		−	0.367266i
$439$	636096.	+	112161.i	0.157529	+	0.0277767i	0.251857	−	0.967765i	$-0.418959\pi$
$439$	636096.	+	112161.i	0.157529	+	0.0277767i	−0.0943273	+	0.995541i	$0.530070\pi$
$440$	−1.96422e6	−	1.64818e6i	−0.483681	−	0.405857i
$441$	453628.	−	165107.i	0.111072	−	0.0404268i
$442$	−2.74011e6	+	7.52838e6i	−0.667132	+	1.83293i
$443$	2.17714e6			0.527080			0.263540	−	0.964649i	$-0.415110\pi$
$443$	2.17714e6			0.527080			0.263540	+	0.964649i	$0.415110\pi$
$444$	1.93066e6	+	1.54873e6i	0.464782	+	0.372837i
$445$	−3.31988e6			−0.794736
$446$	1.19043e6	−	3.27068e6i	0.283379	−	0.778576i
$447$	2.00141e6	−	728455.i	0.473771	−	0.172438i
$448$	−344840.	−	289355.i	−0.0811751	−	0.0681140i
$449$	4.00043e6	+	705383.i	0.936463	+	0.165124i	0.620997	−	0.783813i	$-0.286728\pi$
$449$	4.00043e6	+	705383.i	0.936463	+	0.165124i	0.315466	+	0.948937i	$0.397839\pi$
$450$			3.28361e6i			0.764399i
$451$	652090.	−	3.69819e6i	0.150961	−	0.856145i
$452$	231783.	−	133820.i	0.0533624	−	0.0308088i
$453$	−4.21011e6	+	3.53270e6i	−0.963935	+	0.808838i
$454$	−1.44958e6	+	2.51075e6i	−0.330068	+	0.571695i
$455$	−5.25360e6	−	9.09950e6i	−1.18968	−	2.06058i
$456$	−1.23110e6	−	448084.i	−0.277256	−	0.100913i
$457$	2.96262e6	−	3.53071e6i	0.663568	−	0.790809i	−0.324325	−	0.945946i	$-0.605137\pi$
$457$	2.96262e6	−	3.53071e6i	0.663568	−	0.790809i	0.987893	+	0.155136i	$0.0495817\pi$
$458$	−2.24325e6	−	1.29514e6i	−0.499706	−	0.288505i
$459$	−5.70671e6	+	1.00625e6i	−1.26431	+	0.222932i
$460$	75916.1	+	430542.i	0.0167278	+	0.0948682i
$461$	4.81922e6	+	5.74332e6i	1.05615	+	1.25867i	0.964838	+	0.262845i	$0.0846608\pi$
$461$	4.81922e6	+	5.74332e6i	1.05615	+	1.25867i	0.0913095	+	0.995823i	$0.470895\pi$
$462$	−1.05898e6	−	2.90952e6i	−0.230825	−	0.634186i
$463$	−1.19915e6	−	3.29464e6i	−0.259969	−	0.714259i	−0.999168	−	0.0407724i	$-0.987018\pi$
$463$	−1.19915e6	−	3.29464e6i	−0.259969	−	0.714259i	0.739199	−	0.673487i	$-0.235204\pi$
$464$	661523.	+	788372.i	0.142643	+	0.169995i
$465$	808668.	+	4.58618e6i	0.173435	+	0.983601i
$466$	−3.14145e6	+	553922.i	−0.670139	+	0.118164i
$467$	6.02242e6	+	3.47705e6i	1.27785	+	0.737765i	0.976452	−	0.215734i	$-0.0692145\pi$
$467$	6.02242e6	+	3.47705e6i	1.27785	+	0.737765i	0.301395	+	0.953499i	$0.402548\pi$
$468$	949944.	−	1.13210e6i	0.200486	−	0.238929i
$469$	616430.	+	224362.i	0.129405	+	0.0470996i
$470$	−3.07354e6	−	5.32353e6i	−0.641792	−	1.11162i
$471$	−884422.	+	1.53186e6i	−0.183699	+	0.318176i
$472$	−2.16583e6	+	1.81734e6i	−0.447475	+	0.375476i
$473$	3.75654e6	−	2.16884e6i	0.772032	−	0.445733i
$474$	−437142.	+	2.47915e6i	−0.0893668	+	0.506825i
$475$			8.86087e6i			1.80195i
$476$	3.83352e6	+	675954.i	0.775498	+	0.136741i
$477$	487833.	+	409340.i	0.0981692	+	0.0823737i
$478$	4.12184e6	−	1.50023e6i	0.825128	−	0.300322i
$479$	−709885.	+	1.95039e6i	−0.141367	+	0.388403i	−0.990090	−	0.140435i	$-0.955150\pi$
$479$	−709885.	+	1.95039e6i	−0.141367	+	0.388403i	0.848723	+	0.528838i	$0.177372\pi$
$480$	−2.01009e6			−0.398210
$481$	−6.44011e6	+	3.91014e6i	−1.26920	+	0.770601i
$482$	4.47092e6			0.876556
$483$	−180557.	+	496076.i	−0.0352165	+	0.0967566i
$484$	−260095.	+	94666.8i	−0.0504683	+	0.0183689i
$485$	−1.20377e7	−	1.01008e7i	−2.32374	−	1.94985i
$486$	2.86804e6	+	505713.i	0.550801	+	0.0971211i
$487$		−	2.92902e6i		−	0.559629i	−0.960054	−	0.279814i	$-0.909727\pi$
$487$		−	2.92902e6i		−	0.559629i	0.960054	−	0.279814i	$-0.0902730\pi$
$488$	−337344.	+	1.91317e6i	−0.0641244	+	0.363667i
$489$	672392.	−	388206.i	0.127160	−	0.0734158i
$490$	1.53109e6	−	1.28474e6i	0.288078	−	0.241726i
$491$	1.19727e6	−	2.07373e6i	0.224123	−	0.388193i	−0.731933	−	0.681377i	$-0.761381\pi$
$491$	1.19727e6	−	2.07373e6i	0.224123	−	0.388193i	0.956056	+	0.293184i	$0.0947148\pi$
$492$	−1.47193e6	−	2.54945e6i	−0.274140	−	0.474825i
$493$	−8.36269e6	−	3.04377e6i	−1.54963	−	0.564020i
$494$	2.56344e6	−	3.05499e6i	0.472613	−	0.563238i
$495$	−3.54213e6	−	2.04505e6i	−0.649759	−	0.375138i
$496$	−598103.	+	105462.i	−0.109162	+	0.0192482i
$497$	812690.	+	4.60899e6i	0.147582	+	0.836980i
$498$	−4.68899e6	−	5.58812e6i	−0.847239	−	1.00970i
$499$	2.26203e6	+	6.21487e6i	0.406674	+	1.11733i	0.958928	+	0.283651i	$0.0915458\pi$
$499$	2.26203e6	+	6.21487e6i	0.406674	+	1.11733i	−0.552254	+	0.833676i	$0.686232\pi$
$500$	2.84276e6	+	7.81042e6i	0.508528	+	1.39717i
$501$	2.60039e6	+	3.09902e6i	0.462853	+	0.551607i
$502$	1.10639e6	+	6.27464e6i	0.195951	+	1.11130i
$503$	−1.40478e6	+	247700.i	−0.247564	+	0.0436522i	−0.296053	−	0.955172i	$-0.595670\pi$
$503$	−1.40478e6	+	247700.i	−0.247564	+	0.0436522i	0.0484892	+	0.998824i	$0.484559\pi$
$504$	−621859.	−	359031.i	−0.109048	−	0.0629586i
$505$	−3.26612e6	+	3.89241e6i	−0.569907	+	0.679188i
$506$	−368507.	−	134126.i	−0.0639837	−	0.0232882i
$507$	4.15461e6	+	7.19599e6i	0.717811	+	1.24328i
$508$	−1.13718e6	+	1.96966e6i	−0.195511	+	0.338635i
$509$	5.21066e6	−	4.37227e6i	0.891453	−	0.748018i	−0.0770479	−	0.997027i	$-0.524549\pi$
$509$	5.21066e6	−	4.37227e6i	0.891453	−	0.748018i	0.968501	+	0.249009i	$0.0801050\pi$
$510$	1.50532e7	−	8.69097e6i	2.56273	−	1.47960i
$511$	378717.	−	2.14781e6i	0.0641598	−	0.363868i
$512$		−	262144.i		−	0.0441942i
$513$	2.84070e6	+	500892.i	0.476575	+	0.0840331i
$514$	1.69773e6	+	1.42456e6i	0.283440	+	0.237834i
$515$	7.15124e6	−	2.60284e6i	1.18813	−	0.432443i
$516$	1.16302e6	−	3.19538e6i	0.192293	−	0.528321i
$517$	5.51399e6			0.907276
$518$	2.41437e6	+	2.75169e6i	0.395348	+	0.450583i
$519$	−2.95606e6			−0.481721
$520$	2.09274e6	−	5.74975e6i	0.339396	−	0.932482i
$521$	6.68195e6	−	2.43203e6i	1.07847	−	0.392532i	0.259133	−	0.965842i	$-0.416563\pi$
$521$	6.68195e6	−	2.43203e6i	1.07847	−	0.392532i	0.819339	+	0.573310i	$0.194341\pi$
$522$	1.25756e6	+	1.05522e6i	0.202001	+	0.169499i
$523$	−1.55977e6	−	275030.i	−0.249348	−	0.0439669i	0.0475768	−	0.998868i	$-0.484850\pi$
$523$	−1.55977e6	−	275030.i	−0.249348	−	0.0439669i	−0.296925	+	0.954901i	$0.595961\pi$
$524$		−	3.93282e6i		−	0.625715i
$525$	−2.85071e6	+	1.61672e7i	−0.451393	+	2.55998i
$526$	6.29291e6	−	3.63322e6i	0.991716	−	0.572568i
$527$	4.02310e6	−	3.37578e6i	0.631008	−	0.529478i
$528$	901534.	−	1.56150e6i	0.140733	−	0.243757i
$529$	−3.18474e6	−	5.51613e6i	−0.494806	−	0.857029i
$530$	2.47763e6	+	901782.i	0.383130	+	0.139448i
$531$	−2.89891e6	+	3.45478e6i	−0.446168	+	0.531722i
$532$	−1.67810e6	−	968849.i	−0.257062	−	0.148415i
$533$	8.82500e6	−	1.55609e6i	1.34554	−	0.237255i
$534$	−405385.	−	2.29905e6i	−0.0615198	−	0.348896i
$535$	−1.09108e7	−	1.30030e7i	−1.64806	−	1.96408i
$536$	130655.	+	358971.i	0.0196433	+	0.0539694i
$537$	203181.	+	558234.i	0.0304051	+	0.0835374i
$538$	2.28740e6	+	2.72602e6i	0.340711	+	0.406044i
$539$	311325.	+	1.76561e6i	0.0461574	+	0.261772i
$540$	4.35846e6	−	768514.i	0.643204	−	0.113414i
$541$	−9.18553e6	−	5.30327e6i	−1.34931	−	0.779024i	−0.361157	−	0.932505i	$-0.617618\pi$
$541$	−9.18553e6	−	5.30327e6i	−1.34931	−	0.779024i	−0.988152	+	0.153481i	$0.950952\pi$
$542$	−4.30145e6	+	5.12627e6i	−0.628951	+	0.749555i
$543$	−1.13755e7	−	4.14035e6i	−1.65566	−	0.602612i
$544$	1.13342e6	+	1.96315e6i	0.164208	+	0.284417i
$545$	−7.53114e6	+	1.30443e7i	−1.08610	+	1.88118i
$546$	5.66000e6	−	4.74930e6i	0.812521	−	0.681786i
$547$	635477.	−	366893.i	0.0908096	−	0.0524289i	−0.453908	−	0.891049i	$-0.649970\pi$
$547$	635477.	−	366893.i	0.0908096	−	0.0524289i	0.544717	+	0.838620i	$0.316637\pi$
$548$	−306697.	+	1.73936e6i	−0.0436273	+	0.247422i
$549$			3.09885e6i			0.438803i
$550$	−1.20097e7	−	2.11763e6i	−1.69288	−	0.298500i
$551$	3.39354e6	+	2.84752e6i	0.476184	+	0.399566i
$552$	−288885.	+	105145.i	−0.0403531	+	0.0146873i
$553$	−1.27345e6	+	3.49878e6i	−0.177080	+	0.486523i
$554$	986995.			0.136628
$555$	1.61567e7	+	2.48265e6i	2.22649	+	0.342123i
$556$	−648161.			−0.0889193
$557$	−2.38461e6	+	6.55165e6i	−0.325671	+	0.894772i	0.663523	+	0.748156i	$0.269061\pi$
$557$	−2.38461e6	+	6.55165e6i	−0.325671	+	0.894772i	−0.989193	+	0.146616i	$0.953162\pi$
$558$	−910349.	+	331340.i	−0.123772	+	0.0450493i
$559$	7.92935e6	+	6.65351e6i	1.07327	+	0.900578i
$560$	−2.92783e6	−	516255.i	−0.394526	−	0.0695656i
$561$			1.55917e7i			2.09164i
$562$	−782782.	+	4.43938e6i	−0.104544	+	0.592900i
$563$	1.52254e6	−	879040.i	0.202441	−	0.116879i	−0.395353	−	0.918529i	$-0.629378\pi$
$563$	1.52254e6	−	879040.i	0.202441	−	0.116879i	0.597794	+	0.801650i	$0.296044\pi$
$564$	3.31130e6	−	2.77851e6i	0.438329	−	0.367802i
$565$	883795.	−	1.53078e6i	0.116474	−	0.201739i
$566$	907963.	+	1.57264e6i	0.119132	+	0.206342i
$567$	7.58385e6	+	2.76029e6i	0.990677	+	0.360577i
$568$	−1.75185e6	+	2.08778e6i	−0.227839	+	0.271527i
$569$	6.94211e6	+	4.00803e6i	0.898899	+	0.518980i	0.876843	−	0.480777i	$-0.159645\pi$
$569$	6.94211e6	+	4.00803e6i	0.898899	+	0.518980i	0.0220563	+	0.999757i	$0.492979\pi$
$570$	−8.52098e6	+	1.50248e6i	−1.09851	+	0.193696i
$571$	−1.87650e6	−	1.06422e7i	−0.240856	−	1.36596i	−0.829922	−	0.557879i	$-0.811615\pi$
$571$	−1.87650e6	−	1.06422e7i	−0.240856	−	1.36596i	0.589066	−	0.808085i	$-0.299496\pi$
$572$	3.52799e6	+	4.20449e6i	0.450855	+	0.537308i
$573$	−5.35448e6	−	1.47113e7i	−0.681288	−	1.87182i
$574$	−1.48918e6	−	4.09148e6i	−0.188654	−	0.518323i
$575$	1.33652e6	+	1.59280e6i	0.168580	+	0.200905i
$576$	−72611.9	−	411802.i	−0.00911909	−	0.0517169i
$577$	−3.18081e6	+	560863.i	−0.397739	+	0.0701322i	−0.368940	−	0.929453i	$-0.620279\pi$
$577$	−3.18081e6	+	560863.i	−0.397739	+	0.0701322i	−0.0287990	+	0.999585i	$0.509168\pi$
$578$	−1.20575e7	−	6.96140e6i	−1.50120	−	0.866717i
$579$	−9.43958e6	+	1.12497e7i	−1.17019	+	1.39458i
$580$	6.38695e6	+	2.32466e6i	0.788358	+	0.286939i
$581$	−5.39461e6	−	9.34375e6i	−0.663010	−	1.14837i
$582$	5.52502e6	−	9.56961e6i	0.676124	−	1.17108i
$583$	−1.81176e6	+	1.52025e6i	−0.220764	+	0.185243i
$584$	1.09990e6	−	635025.i	0.133450	−	0.0770476i
$585$	1.69485e6	−	9.61196e6i	0.204758	−	1.16124i
$586$		−	6.46739e6i		−	0.778009i
$587$	−4.18685e6	−	738255.i	−0.501525	−	0.0884323i	−0.0828378	−	0.996563i	$-0.526398\pi$
$587$	−4.18685e6	−	738255.i	−0.501525	−	0.0884323i	−0.418687	+	0.908131i	$0.637509\pi$
$588$	1.07665e6	+	903419.i	0.128420	+	0.107757i
$589$	−2.45659e6	+	894126.i	−0.291773	+	0.106197i
$590$	−6.38633e6	+	1.75463e7i	−0.755303	+	2.07518i
$591$	4.38371e6			0.516266
$592$	−323772.	+	2.10706e6i	−0.0379696	+	0.247100i
$593$	−5.27773e6			−0.616325			−0.308163	−	0.951334i	$-0.599714\pi$
$593$	−5.27773e6			−0.616325			−0.308163	+	0.951334i	$0.599714\pi$
$594$	−1.35778e6	+	3.73047e6i	−0.157893	+	0.433808i
$595$	2.41581e7	−	8.79283e6i	2.79750	−	1.01821i
$596$	1.40527e6	+	1.17916e6i	0.162048	+	0.135975i
$597$	−8.59914e6	−	1.51626e6i	−0.987459	−	0.174116i
$598$		−	935807.i		−	0.107012i
$599$	1.35977e6	−	7.71162e6i	0.154845	−	0.878170i	−0.804082	−	0.594518i	$-0.797343\pi$
$599$	1.35977e6	−	7.71162e6i	0.154845	−	0.878170i	0.958927	−	0.283652i	$-0.0915460\pi$
$600$	−8.27923e6	+	4.78002e6i	−0.938884	+	0.542065i
$601$	5.81605e6	−	4.88024e6i	0.656813	−	0.551132i	−0.252317	−	0.967645i	$-0.581192\pi$
$601$	5.81605e6	−	4.88024e6i	0.656813	−	0.551132i	0.909130	+	0.416513i	$0.136748\pi$
$602$	2.51469e6	−	4.35557e6i	0.282809	−	0.489840i
$603$	304678.	+	527718.i	0.0341231	+	0.0591029i
$604$	−4.44815e6	−	1.61900e6i	−0.496121	−	0.180573i
$605$	−1.17502e6	+	1.40033e6i	−0.130513	+	0.155540i
$606$	−3.09436e6	−	1.78653e6i	−0.342286	−	0.197619i
$607$	−5.61794e6	+	990595.i	−0.618879	+	0.109125i	−0.474293	−	0.880367i	$-0.657296\pi$
$607$	−5.61794e6	+	990595.i	−0.618879	+	0.109125i	−0.144586	+	0.989492i	$0.546185\pi$
$608$	−195944.	−	1.11126e6i	−0.0214968	−	0.121914i
$609$	5.27563e6	+	6.28725e6i	0.576409	+	0.686938i
$610$	4.38818e6	+	1.20564e7i	0.477485	+	1.31188i
$611$	4.50032e6	+	1.23645e7i	0.487686	+	1.33991i
$612$	2.32428e6	+	2.76996e6i	0.250847	+	0.298948i
$613$	−985589.	−	5.58955e6i	−0.105936	−	0.600795i	−0.990842	−	0.135025i	$-0.956889\pi$
$613$	−985589.	−	5.58955e6i	−0.105936	−	0.600795i	0.884906	−	0.465770i	$-0.154223\pi$
$614$	8.41938e6	−	1.48456e6i	0.901279	−	0.158920i
$615$	−1.68375e7	−	9.72112e6i	−1.79510	−	1.03640i
$616$	1.71419e6	−	2.04289e6i	0.182015	−	0.216917i
$617$	1.18262e7	+	4.30438e6i	1.25064	+	0.455195i	0.880617	−	0.473829i	$-0.157128\pi$
$617$	1.18262e7	+	4.30438e6i	1.25064	+	0.455195i	0.370020	+	0.929024i	$0.379351\pi$
$618$	2.67572e6	+	4.63448e6i	0.281818	+	0.488124i
$619$	−8.64211e6	+	1.49686e7i	−0.906553	+	1.57020i	−0.0877346	+	0.996144i	$0.527963\pi$
$619$	−8.64211e6	+	1.49686e7i	−0.906553	+	1.57020i	−0.818819	+	0.574052i	$0.805371\pi$
$620$	−3.07262e6	+	2.57823e6i	−0.321018	+	0.269366i
$621$	586186.	−	338435.i	0.0609967	−	0.0352165i
$622$	1.07364e6	−	6.08894e6i	0.111272	−	0.631053i
$623$		−	3.45284e6i		−	0.356415i
$624$	4.23730e6	+	747151.i	0.435640	+	0.0768151i
$625$	2.28012e7	+	1.91325e7i	2.33484	+	1.95917i
$626$	3.67662e6	−	1.33818e6i	0.374984	−	0.136483i
$627$	2.65452e6	−	7.29323e6i	0.269660	−	0.740886i
$628$	−1.52351e6			−0.154151
$629$	−6.68556e6	−	1.71793e7i	−0.673769	−	1.73132i
$630$	−4.74233e6			−0.476037
$631$	−4.99679e6	+	1.37286e7i	−0.499594	+	1.37262i	0.392073	+	0.919934i	$0.371758\pi$
$631$	−4.99679e6	+	1.37286e7i	−0.499594	+	1.37262i	−0.891668	+	0.452690i	$0.850464\pi$
$632$	−2.03748e6	+	741581.i	−0.202908	+	0.0738526i
$633$	−169507.	−	142233.i	−0.0168143	−	0.0141089i
$634$	−5.85169e6	−	1.03181e6i	−0.578174	−	0.101948i
$635$			1.50207e7i			1.47828i
$636$	−321955.	+	1.82590e6i	−0.0315611	+	0.178992i
$637$	−3.70510e6	+	2.13914e6i	−0.361786	+	0.208877i
$638$	−4.67044e6	+	3.91896e6i	−0.454262	+	0.381171i
$639$	−2.17369e6	+	3.76495e6i	−0.210594	+	0.364760i
$640$	−865646.	−	1.49934e6i	−0.0835392	−	0.144694i
$641$	9.98039e6	+	3.63257e6i	0.959406	+	0.349195i	0.773801	−	0.633429i	$-0.218353\pi$
$641$	9.98039e6	+	3.63257e6i	0.959406	+	0.349195i	0.185606	+	0.982624i	$0.440575\pi$
$642$	7.67243e6	−	9.14365e6i	0.734675	−	0.875552i
$643$	−1.06466e7	−	6.14682e6i	−1.01551	−	0.586304i	−0.102709	−	0.994711i	$-0.532751\pi$
$643$	−1.06466e7	−	6.14682e6i	−1.01551	−	0.586304i	−0.912800	+	0.408407i	$0.866084\pi$
$644$	−447784.	+	78956.4i	−0.0425456	+	0.00750193i
$645$	−3.89975e6	−	2.21166e7i	−0.369094	−	2.09324i
$646$	6.27209e6	+	7.47479e6i	0.591332	+	0.704722i
$647$	−2.45611e6	−	6.74811e6i	−0.230668	−	0.633755i	0.769319	−	0.638865i	$-0.220596\pi$
$647$	−2.45611e6	−	6.74811e6i	−0.230668	−	0.633755i	−0.999987	+	0.00511001i	$0.998373\pi$
$648$	1.60743e6	+	4.41637e6i	0.150381	+	0.413169i
$649$	−1.07662e7	−	1.28307e7i	−1.00335	−	1.19574i
$650$	−5.05332e6	−	2.86588e7i	−0.469130	−	2.66057i
$651$	−4.76986e6	+	841054.i	−0.441116	+	0.0777806i
$652$	579132.	+	334362.i	0.0533529	+	0.0308033i
$653$	−2.75274e6	+	3.28059e6i	−0.252628	+	0.301071i	−0.877422	−	0.479719i	$-0.840739\pi$
$653$	−2.75274e6	+	3.28059e6i	−0.252628	+	0.301071i	0.624794	+	0.780790i	$0.285183\pi$
$654$	−9.95294e6	−	3.62257e6i	−0.909928	−	0.331187i
$655$	−1.29869e7	−	2.24939e7i	−1.18277	−	2.04862i
$656$	1.26777e6	−	2.19584e6i	0.115022	−	0.199224i
$657$	1.55193e6	−	1.30223e6i	0.140268	−	0.117699i
$658$	5.53673e6	−	3.19663e6i	0.498527	−	0.287825i
$659$	845732.	−	4.79638e6i	0.0758611	−	0.430230i	−0.923096	−	0.384570i	$-0.874350\pi$
$659$	845732.	−	4.79638e6i	0.0758611	−	0.430230i	0.998957	−	0.0456600i	$-0.0145391\pi$
$660$		−	1.19081e7i		−	1.06410i
$661$	1.57163e6	+	277122.i	0.139910	+	0.0246699i	0.243164	−	0.969985i	$-0.421815\pi$
$661$	1.57163e6	+	277122.i	0.139910	+	0.0246699i	−0.103255	+	0.994655i	$0.532926\pi$
$662$	−4.88885e6	−	4.10223e6i	−0.433573	−	0.363811i
$663$	−3.49628e7	+	1.27254e7i	−3.08904	+	1.12432i
$664$	2.14891e6	−	5.90408e6i	0.189146	−	0.519675i
$665$	−1.27972e7			−1.12218
$666$	75024.7	+	3.39967e6i	0.00655418	+	0.296996i
$667$	1.03951e6			0.0904724
$668$	−1.19173e6	+	3.27424e6i	−0.103332	+	0.283903i
$669$	1.51895e7	−	5.52853e6i	1.31213	−	0.477578i
$670$	1.93267e6	+	1.62170e6i	0.166330	+	0.139568i
$671$	−1.13339e7	−	1.99848e6i	−0.971794	−	0.171354i
$672$		−	2.09059e6i		−	0.178585i
$673$	3.68976e6	−	2.09257e7i	0.314022	−	1.78091i	−0.263628	−	0.964624i	$-0.584919\pi$
$673$	3.68976e6	−	2.09257e7i	0.314022	−	1.78091i	0.577650	−	0.816284i	$-0.303970\pi$
$674$	−1.26155e7	+	7.28355e6i	−1.06968	+	0.617580i
$675$	1.61242e7	−	1.35298e7i	1.36213	−	1.14297i
$676$	−3.57836e6	+	6.19791e6i	−0.301174	+	0.521649i
$677$	2.30474e6	+	3.99193e6i	0.193264	+	0.334743i	0.946330	−	0.323202i	$-0.104759\pi$
$677$	2.30474e6	+	3.99193e6i	0.193264	+	0.334743i	−0.753066	+	0.657945i	$0.771426\pi$
$678$	1.16800e6	+	425117.i	0.0975816	+	0.0355168i
$679$	1.05053e7	−	1.25198e7i	0.874450	−	1.04213i
$680$	1.29653e7	+	7.48554e6i	1.07525	+	0.620799i
$681$	−1.32596e7	+	2.33802e6i	−1.09563	+	0.193189i
$682$	−624772.	−	3.54326e6i	−0.0514352	−	0.291703i
$683$	9.54697e6	+	1.13776e7i	0.783094	+	0.933255i	0.999069	−	0.0431441i	$-0.0137375\pi$
$683$	9.54697e6	+	1.13776e7i	0.783094	+	0.933255i	−0.215975	+	0.976399i	$0.569293\pi$
$684$	−615618.	−	1.69140e6i	−0.0503120	−	0.138231i
$685$	3.98952e6	+	1.09611e7i	0.324859	+	0.892542i
$686$	6.08540e6	+	7.25230e6i	0.493718	+	0.588390i
$687$	−2.08893e6	−	1.18469e7i	−0.168862	−	0.957662i
$688$	2.88431e6	−	508582.i	0.232312	−	0.0409628i
$689$	−4.88768e6	−	2.82191e6i	−0.392243	−	0.226461i
$690$	−1.30508e6	+	1.55533e6i	−0.104355	+	0.124366i
$691$	1.53172e7	+	5.57501e6i	1.22035	+	0.444172i	0.870283	−	0.492553i	$-0.163936\pi$
$691$	1.53172e7	+	5.57501e6i	1.22035	+	0.444172i	0.350069	+	0.936724i	$0.386158\pi$
$692$	−1.27303e6	−	2.20495e6i	−0.101059	−	0.175039i
$693$	2.12695e6	−	3.68399e6i	0.168238	−	0.291397i
$694$	9.04996e6	−	7.59382e6i	0.713260	−	0.598496i
$695$	−3.70718e6	+	2.14034e6i	−0.291126	+	0.168082i
$696$	−829952.	+	4.70689e6i	−0.0649426	+	0.368308i
$697$			2.19257e7i			1.70951i
$698$	4.24627e6	+	748732.i	0.329890	+	0.0581685i
$699$	−1.13485e7	−	9.52250e6i	−0.878506	−	0.737154i
$700$	−1.32869e7	+	4.83604e6i	−1.02489	+	0.373031i
$701$	−8.11322e6	+	2.22909e7i	−0.623588	+	1.71330i	0.0744405	+	0.997225i	$0.476283\pi$
$701$	−8.11322e6	+	2.22909e7i	−0.623588	+	1.71330i	−0.698029	+	0.716070i	$0.745939\pi$
$702$	−9.47336e6			−0.725540
$703$	202455.	+	9.17405e6i	0.0154504	+	0.700120i
$704$	1.55298e6			0.118096
$705$	9.76397e6	−	2.68263e7i	0.739867	−	2.03277i
$706$	−1.13351e6	+	412565.i	−0.0855883	+	0.0311516i
$707$	−4.04830e6	−	3.39692e6i	−0.304596	−	0.255586i
$708$	−1.29308e7	−	2.28005e6i	−0.969490	−	0.170947i
$709$			5.19058e6i			0.387793i	0.981022	+	0.193896i	$0.0621126\pi$
$709$			5.19058e6i			0.387793i	−0.981022	+	0.193896i	$0.937887\pi$
$710$	−3.12558e6	+	1.77261e7i	−0.232694	+	1.31967i
$711$	−2.99526e6	+	1.72932e6i	−0.222209	+	0.128292i
$712$	1.54030e6	−	1.29247e6i	0.113869	−	0.0955476i
$713$	−306724.	+	531262.i	−0.0225956	+	0.0391367i
$714$	9.03903e6	+	1.56561e7i	0.663554	+	1.14931i
$715$	3.40624e7	+	1.23977e7i	2.49178	+	0.906935i
$716$	−328892.	+	391958.i	−0.0239756	+	0.0285731i
$717$	1.76417e7	+	1.01855e7i	1.28157	+	0.739917i
$718$	−854366.	+	150648.i	−0.0618490	+	0.0109056i
$719$	−3.19945e6	−	1.81450e7i	−0.230809	−	1.30898i	−0.851263	−	0.524740i	$-0.824163\pi$
$719$	−3.19945e6	−	1.81450e7i	−0.230809	−	1.30898i	0.620454	−	0.784243i	$-0.286948\pi$
$720$	−1.77515e6	−	2.11554e6i	−0.127616	−	0.152086i
$721$	2.70708e6	+	7.43763e6i	0.193938	+	0.532840i
$722$	1.72625e6	+	4.74283e6i	0.123242	+	0.338606i
$723$	1.33466e7	+	1.59058e7i	0.949564	+	1.13165i
$724$	−1.81055e6	−	1.02681e7i	−0.128370	−	0.728024i
$725$	3.18348e7	−	5.61334e6i	2.24935	−	0.396622i
$726$	−1.11322e6	−	642719.i	−0.0783863	−	0.0452564i
$727$	−1.25643e7	+	1.49736e7i	−0.881663	+	1.05072i	0.116680	+	0.993170i	$0.462775\pi$
$727$	−1.25643e7	+	1.49736e7i	−0.881663	+	1.05072i	−0.998342	+	0.0575549i	$0.981670\pi$
$728$	5.98002e6	+	2.17655e6i	0.418190	+	0.152209i
$729$	−2.15976e6	−	3.74081e6i	−0.150517	−	0.260703i
$730$	4.19393e6	−	7.26410e6i	0.291282	−	0.504516i
$731$	−1.94012e7	+	1.62795e7i	−1.34287	+	1.12680i
$732$	−7.81337e6	+	4.51105e6i	−0.538965	+	0.311172i
$733$	1.11192e6	−	6.30602e6i	0.0764388	−	0.433506i	−0.922439	−	0.386143i	$-0.873807\pi$
$733$	1.11192e6	−	6.30602e6i	0.0764388	−	0.433506i	0.998878	−	0.0473630i	$-0.0150818\pi$
$734$			1.85356e7i			1.26989i
$735$	9.14121e6	+	1.61184e6i	0.624145	+	0.110054i
$736$	−202837.	−	170201.i	−0.0138023	−	0.0115815i
$737$	−2.12660e6	+	774020.i	−0.144217	+	0.0524909i
$738$	1.38331e6	−	3.80062e6i	0.0934930	−	0.256870i
$739$	1.69750e7			1.14340			0.571700	−	0.820463i	$-0.306284\pi$
$739$	1.69750e7			1.14340			0.571700	+	0.820463i	$0.306284\pi$
$740$	5.10605e6	+	1.31206e7i	0.342772	+	0.880791i
$741$	1.85208e7			1.23912
$742$	−937897.	+	2.57685e6i	−0.0625382	+	0.171822i
$743$	1.85808e7	−	6.76285e6i	1.23479	−	0.449425i	0.359552	−	0.933125i	$-0.382929\pi$
$743$	1.85808e7	−	6.76285e6i	1.23479	−	0.449425i	0.875234	+	0.483700i	$0.160707\pi$
$744$	−2.16065e6	−	1.81300e6i	−0.143104	−	0.120078i
$745$	1.19313e7	+	2.10381e6i	0.787584	+	0.138872i
$746$		−	1.28262e6i		−	0.0843821i
$747$	1.74034e6	−	9.86996e6i	0.114112	−	0.647163i
$748$	−1.16300e7	+	6.71459e6i	−0.760022	+	0.438799i
$749$	1.35238e7	−	1.13478e7i	0.880833	−	0.739106i
$750$	−1.93003e7	+	3.34291e7i	−1.25288	+	2.17006i
$751$	−3.37976e6	−	5.85392e6i	−0.218668	−	0.378745i	0.735733	−	0.677272i	$-0.236838\pi$
$751$	−3.37976e6	−	5.85392e6i	−0.218668	−	0.378745i	−0.954401	+	0.298527i	$0.903505\pi$
$752$	3.49852e6	+	1.27336e6i	0.225601	+	0.0821119i
$753$	−1.90200e7	+	2.26671e7i	−1.22243	+	1.45683i
$754$	−1.25997e7	−	7.27445e6i	−0.807109	−	0.465985i
$755$	−3.07876e7	+	5.42868e6i	−1.96566	+	0.346599i
$756$	799292.	+	4.53301e6i	0.0508629	+	0.288458i
$757$	−3.58000e6	−	4.26648e6i	−0.227061	−	0.270601i	0.640470	−	0.767983i	$-0.278739\pi$
$757$	−3.58000e6	−	4.26648e6i	−0.227061	−	0.270601i	−0.867532	+	0.497381i	$0.834295\pi$
$758$	−3.88427e6	−	1.06719e7i	−0.245548	−	0.674637i
$759$	−622898.	−	1.71140e6i	−0.0392476	−	0.107832i
$760$	−4.79027e6	−	5.70882e6i	−0.300833	−	0.358519i
$761$	4.30772e6	+	2.44303e7i	0.269641	+	1.52921i	0.755486	+	0.655165i	$0.227401\pi$
$761$	4.30772e6	+	2.44303e7i	0.269641	+	1.52921i	−0.485845	+	0.874045i	$0.661488\pi$
$762$	−1.04020e7	+	1.83415e6i	−0.648977	+	0.114432i
$763$	−1.35667e7	−	7.83275e6i	−0.843652	−	0.487083i
$764$	8.66737e6	−	1.03294e7i	0.537222	−	0.640237i
$765$	2.24407e7	+	8.16775e6i	1.38638	+	0.504602i
$766$	7.11291e6	+	1.23199e7i	0.438001	+	0.758641i
$767$	1.99845e7	−	3.46141e7i	1.22660	−	2.12454i
$768$	932608.	−	782551.i	0.0570553	−	0.0478751i
$769$	1.78198e7	−	1.02883e7i	1.08664	−	0.627374i	0.153963	−	0.988077i	$-0.450796\pi$
$769$	1.78198e7	−	1.02883e7i	1.08664	−	0.627374i	0.932681	+	0.360702i	$0.117463\pi$
$770$	3.05838e6	−	1.73449e7i	0.185894	−	1.05425i
$771$			1.02925e7i			0.623568i
$772$	−1.24564e7	−	2.19639e6i	−0.752225	−	0.132638i
$773$	−2.02191e7	−	1.69658e7i	−1.21706	−	1.02124i	−0.998973	−	0.0453064i	$-0.985574\pi$
$773$	−2.02191e7	−	1.69658e7i	−1.21706	−	1.02124i	−0.218088	−	0.975929i	$-0.569982\pi$
$774$	4.39010e6	−	1.59786e6i	0.263404	−	0.0958711i
$775$	−6.52454e6	+	1.79260e7i	−0.390208	+	1.07209i
$776$	9.51740e6			0.567367
$777$	−2.58208e6	+	1.68037e7i	−0.153432	+	0.998512i
$778$	9.54964e6			0.565637
$779$	3.73288e6	−	1.02560e7i	0.220395	−	0.605529i
$780$	2.67026e7	−	9.71897e6i	1.57151	−	0.571984i
$781$	−1.23683e7	−	1.03783e7i	−0.725577	−	0.608832i
$782$	2.25490e6	+	397600.i	0.131859	+	0.0232504i
$783$		−	1.05232e7i		−	0.613400i
$784$	−210207.	+	1.19214e6i	−0.0122140	+	0.0692688i
$785$	−8.71375e6	+	5.03089e6i	−0.504697	+	0.291387i
$786$	1.39915e7	−	1.17402e7i	0.807807	−	0.677830i
$787$	−3.40150e6	+	5.89157e6i	−0.195764	+	0.339074i	−0.947151	−	0.320789i	$-0.896052\pi$
$787$	−3.40150e6	+	5.89157e6i	−0.195764	+	0.339074i	0.751386	+	0.659862i	$0.229385\pi$
$788$	1.88785e6	+	3.26985e6i	0.108306	+	0.187591i
$789$	3.17112e7	+	1.15419e7i	1.81351	+	0.660063i
$790$	−9.20459e6	+	1.09696e7i	−0.524731	+	0.625350i
$791$	1.59208e6	+	919190.i	0.0904742	+	0.0522353i
$792$	2.43958e6	−	430164.i	0.138198	−	0.0243681i
$793$	−4.76898e6	−	2.70462e7i	−0.269304	−	1.52730i
$794$	−6.34336e6	−	7.55973e6i	−0.357082	−	0.425554i
$795$	4.18800e6	+	1.15064e7i	0.235011	+	0.645689i
$796$	−2.57223e6	−	7.06714e6i	−0.143889	−	0.395331i
$797$	−9.00608e6	−	1.07330e7i	−0.502215	−	0.598517i	0.454065	−	0.890969i	$-0.349973\pi$
$797$	−9.00608e6	−	1.07330e7i	−0.502215	−	0.598517i	−0.956280	+	0.292452i	$0.905529\pi$
$798$	−1.56265e6	−	8.86223e6i	−0.0868670	−	0.492647i
$799$	−3.17054e7	+	5.59052e6i	−1.75698	+	0.309803i
$800$	−7.13090e6	−	4.11703e6i	−0.393930	−	0.227436i
$801$	2.06166e6	−	2.45699e6i	0.113537	−	0.135308i
$802$	8.56310e6	+	3.11671e6i	0.470105	+	0.171104i
$803$	3.76199e6	+	6.51596e6i	0.205887	+	0.356607i
$804$	−887053.	+	1.53642e6i	−0.0483960	+	0.0838243i
$805$	−2.30039e6	+	1.93026e6i	−0.125116	+	0.104985i
$806$	7.43546e6	−	4.29287e6i	0.403153	−	0.232761i
$807$	−2.86979e6	+	1.62754e7i	−0.155120	+	0.879727i
$808$		−	3.07747e6i		−	0.165831i
$809$	8.25511e6	+	1.45560e6i	0.443457	+	0.0781935i	0.390918	−	0.920425i	$-0.372158\pi$
$809$	8.25511e6	+	1.45560e6i	0.443457	+	0.0781935i	0.0525390	+	0.998619i	$0.483269\pi$
$810$	2.37774e7	+	1.99516e7i	1.27336	+	1.06848i
$811$	1.29612e7	−	4.71749e6i	0.691980	−	0.251860i	0.0279970	−	0.999608i	$-0.491087\pi$
$811$	1.29612e7	−	4.71749e6i	0.691980	−	0.251860i	0.663983	+	0.747748i	$0.268865\pi$
$812$	−2.41776e6	+	6.64274e6i	−0.128683	+	0.353555i
$813$	−3.10780e7			−1.64902
$814$	−1.24826e7	−	1.91808e6i	−0.660302	−	0.101462i
$815$	4.41649e6			0.232907
$816$	−3.60064e6	+	9.89268e6i	−0.189302	+	0.520102i
$817$	1.18467e7	−	4.31186e6i	0.620932	−	0.226001i
$818$	−8.56346e6	−	7.18559e6i	−0.447472	−	0.375474i
$819$	9.99691e6	+	1.76272e6i	0.520782	+	0.0918279i
$820$		−	1.67456e7i		−	0.869693i
$821$	−1.41032e6	+	7.99833e6i	−0.0730231	+	0.414135i	0.926281	+	0.376834i	$0.122987\pi$
$821$	−1.41032e6	+	7.99833e6i	−0.0730231	+	0.414135i	−0.999304	+	0.0373010i	$0.988124\pi$
$822$	−7.10354e6	+	4.10123e6i	−0.366687	+	0.211707i
$823$	−8.53523e6	+	7.16191e6i	−0.439254	+	0.368578i	−0.835430	−	0.549597i	$-0.814781\pi$
$823$	−8.53523e6	+	7.16191e6i	−0.439254	+	0.368578i	0.396176	+	0.918175i	$0.370337\pi$
$824$	−2.30460e6	+	3.99168e6i	−0.118243	+	0.204804i
$825$	−2.83176e7	−	4.90475e7i	−1.44851	−	2.50889i
$826$	−1.82490e7	−	6.64210e6i	−0.930656	−	0.338731i
$827$	1.01355e7	−	1.20791e7i	0.515327	−	0.614143i	−0.444142	−	0.895956i	$-0.646492\pi$
$827$	1.01355e7	−	1.20791e7i	0.515327	−	0.614143i	0.959469	+	0.281814i	$0.0909360\pi$
$828$	−365781.	−	211184.i	−0.0185415	−	0.0107050i
$829$	−3.69679e6	+	651845.i	−0.186827	+	0.0329426i	−0.266279	−	0.963896i	$-0.585794\pi$
$829$	−3.69679e6	+	651845.i	−0.186827	+	0.0329426i	0.0794519	+	0.996839i	$0.474683\pi$
$830$	−7.20555e6	−	4.08647e7i	−0.363054	−	2.05898i
$831$	2.94637e6	+	3.51135e6i	0.148008	+	0.176389i
$832$	1.26749e6	+	3.48240e6i	0.0634799	+	0.174410i
$833$	−3.58023e6	−	9.83660e6i	−0.178772	−	0.491171i
$834$	−1.93489e6	−	2.30591e6i	−0.0963253	−	0.114796i
$835$	3.99600e6	+	2.26624e7i	0.198339	+	1.12484i
$836$	6.58325e6	−	1.16080e6i	0.325780	−	0.0574438i
$837$	5.37807e6	+	3.10503e6i	0.265346	+	0.153198i
$838$	9.34885e6	−	1.11415e7i	0.459884	−	0.548068i
$839$	7.39770e6	+	2.69254e6i	0.362821	+	0.132056i	0.516996	−	0.855988i	$-0.327050\pi$
$839$	7.39770e6	+	2.69254e6i	0.362821	+	0.132056i	−0.154176	+	0.988043i	$0.549272\pi$
$840$	−6.90350e6	−	1.19572e7i	−0.337576	−	0.584698i
$841$	−2.17496e6	+	3.76714e6i	−0.106038	+	0.183663i
$842$	1.29448e6	−	1.08620e6i	0.0629237	−	0.0527993i
$843$	−1.81304e7	+	1.04676e7i	−0.878694	+	0.507314i
$844$	33094.7	−	187689.i	0.00159920	−	0.00906950i
$845$			4.72655e7i			2.27721i
$846$	5.84855e6	+	1.03126e6i	0.280946	+	0.0495383i
$847$	−1.45641e6	−	1.22207e6i	−0.0697550	−	0.0585314i
$848$	−1.50060e6	+	546174.i	−0.0716598	+	0.0260820i
$849$	−2.88440e6	+	7.92482e6i	−0.137337	+	0.377329i
$850$	7.12027e7			3.38025
$851$	1.42015e6	+	1.61856e6i	0.0672218	+	0.0766134i
$852$	−1.26572e7			−0.597361
$853$	−452645.	+	1.24363e6i	−0.0213003	+	0.0585220i	−0.949887	−	0.312593i	$-0.898802\pi$
$853$	−452645.	+	1.24363e6i	−0.0213003	+	0.0585220i	0.928587	+	0.371115i	$0.121025\pi$
$854$	−1.25393e7	+	4.56392e6i	−0.588339	+	0.214138i
$855$	−9.10634e6	−	7.64113e6i	−0.426019	−	0.357472i
$856$	1.01245e7	+	1.78521e6i	0.472266	+	0.0832733i
$857$			7.00346e6i			0.325732i	0.986648	+	0.162866i	$0.0520739\pi$
$857$			7.00346e6i			0.325732i	−0.986648	+	0.162866i	$0.947926\pi$
$858$	−4.42624e6	+	2.51025e7i	−0.205266	+	1.16412i
$859$	6.80286e6	−	3.92763e6i	0.314564	−	0.181613i	−0.334403	−	0.942430i	$-0.608535\pi$
$859$	6.80286e6	−	3.92763e6i	0.314564	−	0.181613i	0.648967	+	0.760817i	$0.275201\pi$
$860$	1.48175e7	−	1.24334e7i	0.683170	−	0.573248i
$861$	1.01104e7	−	1.75118e7i	0.464796	−	0.805050i
$862$	1.53312e6	+	2.65544e6i	0.0702762	+	0.121722i
$863$	−1.07994e7	−	3.93066e6i	−0.493597	−	0.179655i	0.0832149	−	0.996532i	$-0.473481\pi$
$863$	−1.07994e7	−	3.93066e6i	−0.493597	−	0.179655i	−0.576812	+	0.816877i	$0.695703\pi$
$864$	−1.72297e6	+	2.05336e6i	−0.0785225	+	0.0935795i
$865$	−1.45623e7	−	8.40753e6i	−0.661742	−	0.382057i
$866$	−1.22338e7	+	2.15714e6i	−0.554326	+	0.0977426i
$867$	−1.12280e7	−	6.36771e7i	−0.507288	−	2.87697i
$868$	−2.68149e6	−	3.19567e6i	−0.120803	−	0.143967i
$869$	−4.39324e6	−	1.20703e7i	−0.197349	−	0.542213i
$870$	1.07960e7	+	2.96619e7i	0.483578	+	1.32862i
$871$	−3.47132e6	−	4.13695e6i	−0.155042	−	0.184772i
$872$	−1.58413e6	−	8.98404e6i	−0.0705504	−	0.400111i
$873$	1.49509e7	−	2.63625e6i	0.663944	−	0.117071i
$874$	−987067.	−	569883.i	−0.0437087	−	0.0252352i
$875$	−3.66978e7	+	4.37347e7i	−1.62039	+	1.93111i
$876$	5.54258e6	+	2.01733e6i	0.244035	+	0.0888214i
$877$	−3.44081e6	−	5.95965e6i	−0.151064	−	0.261651i	0.780555	−	0.625087i	$-0.214937\pi$
$877$	−3.44081e6	−	5.95965e6i	−0.151064	−	0.261651i	−0.931619	+	0.363437i	$0.881603\pi$
$878$	−1.29182e6	+	2.23749e6i	−0.0565542	+	0.0979547i
$879$	2.30085e7	−	1.93064e7i	1.00442	−	0.842810i
$880$	8.88234e6	−	5.12822e6i	0.386652	−	0.223234i
$881$	−4.68415e6	+	2.65652e7i	−0.203325	+	1.15311i	0.696728	+	0.717335i	$0.254638\pi$
$881$	−4.68415e6	+	2.65652e7i	−0.203325	+	1.15311i	−0.900053	+	0.435780i	$0.856473\pi$
$882$			1.93096e6i			0.0835800i
$883$	3.96838e6	+	699732.i	0.171282	+	0.0302016i	0.258631	−	0.965976i	$-0.416729\pi$
$883$	3.96838e6	+	699732.i	0.171282	+	0.0302016i	−0.0873495	+	0.996178i	$0.527840\pi$
$884$	−2.45488e7	−	2.05989e7i	−1.05657	−	0.886569i
$885$	−8.14875e7	+	2.96590e7i	−3.49730	+	1.27291i
$886$	−2.97850e6	+	8.18336e6i	−0.127471	+	0.350225i
$887$	−1.04611e7			−0.446444			−0.223222	−	0.974768i	$-0.571658\pi$
$887$	−1.04611e7			−0.446444			−0.223222	+	0.974768i	$0.571658\pi$
$888$	−8.46263e6	+	5.13813e6i	−0.360142	+	0.218661i
$889$	−1.56223e7			−0.662963
$890$	4.54187e6	−	1.24787e7i	0.192203	−	0.528072i
$891$	−2.61633e7	+	9.52266e6i	−1.10407	+	0.401850i
$892$	1.06651e7	+	8.94911e6i	0.448802	+	0.376589i
$893$	1.57824e7	+	2.78286e6i	0.662284	+	0.116779i
$894$			8.51944e6i			0.356506i
$895$	−586794.	+	3.32787e6i	−0.0244866	+	0.138870i
$896$	1.55939e6	−	900314.i	0.0648910	−	0.0374648i
$897$	3.32924e6	−	2.79357e6i	0.138154	−	0.115925i
$898$	−8.12428e6	+	1.40717e7i	−0.336197	+	0.582311i
$899$	4.76861e6	+	8.25947e6i	0.196785	+	0.340842i
$900$	−1.23423e7	−	4.49224e6i	−0.507915	−	0.184866i
$901$	8.87626e6	−	1.05783e7i	0.364265	−	0.434115i
$902$	1.30085e7	+	7.51047e6i	0.532367	+	0.307362i
$903$	2.30023e7	−	4.05593e6i	0.938755	−	0.165528i
$904$	185901.	+	1.05430e6i	0.00756590	+	0.0429083i
$905$	−4.42627e7	−	5.27503e7i	−1.79646	−	2.14093i
$906$	−7.51884e6	−	2.06579e7i	−0.304320	−	0.836112i
$907$	−3.45701e6	−	9.49804e6i	−0.139535	−	0.383368i	0.850167	−	0.526513i	$-0.176501\pi$
$907$	−3.45701e6	−	9.49804e6i	−0.139535	−	0.383368i	−0.989702	+	0.143145i	$0.954279\pi$
$908$	−7.45420e6	−	8.88357e6i	−0.300045	−	0.357580i
$909$	−852437.	−	4.83441e6i	−0.0342178	−	0.194059i
$910$	4.13903e7	−	7.29822e6i	1.65689	−	0.292155i
$911$	−2.00778e7	−	1.15919e7i	−0.801532	−	0.462765i	0.0424746	−	0.999098i	$-0.486476\pi$
$911$	−2.00778e7	−	1.15919e7i	−0.801532	−	0.462765i	−0.844007	+	0.536333i	$0.819809\pi$
$912$	3.36849e6	−	4.01441e6i	0.134106	−	0.159821i
$913$	3.49767e7	+	1.27305e7i	1.38868	+	0.505438i
$914$	9.21803e6	+	1.59661e7i	0.364983	+	0.632169i
$915$	−2.97926e7	+	5.16023e7i	−1.17640	+	2.03759i
$916$	7.93709e6	−	6.66001e6i	0.312552	−	0.262263i
$917$	2.33948e7	−	1.35070e7i	0.918746	−	0.530439i
$918$	4.02498e6	−	2.28268e7i	0.157637	−	0.894003i
$919$		−	2.28372e7i		−	0.891977i	−0.895039	−	0.445988i	$-0.852852\pi$
$919$		−	2.28372e7i		−	0.891977i	0.895039	−	0.445988i	$-0.147148\pi$
$920$	−1.72217e6	−	303664.i	−0.0670819	−	0.0118284i
$921$	3.04150e7	+	2.55212e7i	1.18151	+	0.991408i
$922$	−2.81809e7	+	1.02570e7i	−1.09176	+	0.397369i
$923$	1.31776e7	−	3.62051e7i	0.509133	−	1.39883i
$924$	1.23850e7			0.477217
$925$	5.22318e7	+	4.18992e7i	2.00715	+	1.61009i
$926$	1.40243e7			0.537471
$927$	−2.51463e6	+	6.90889e6i	−0.0961114	+	0.264064i
$928$	−3.86833e6	+	1.40796e6i	−0.147453	+	0.0536684i
$929$	7.45691e6	+	6.25709e6i	0.283478	+	0.237867i	0.773428	−	0.633884i	$-0.218540\pi$
$929$	7.45691e6	+	6.25709e6i	0.283478	+	0.237867i	−0.489950	+	0.871751i	$0.662985\pi$
$930$	−1.83447e7	−	3.23467e6i	−0.695511	−	0.122637i
$931$			5.21073e6i			0.197026i
$932$	2.21569e6	−	1.25658e7i	0.0835542	−	0.473860i
$933$	2.48672e7	−	1.43571e7i	0.935238	−	0.539960i
$934$	−2.13086e7	+	1.78800e7i	−0.799258	+	0.670657i
$935$	−4.43455e7	+	7.68087e7i	−1.65890	+	2.87330i
$936$	2.95570e6	+	5.11942e6i	0.110273	+	0.190999i
$937$	−1.08403e7	−	3.94554e6i	−0.403358	−	0.146810i	0.132371	−	0.991200i	$-0.457741\pi$
$937$	−1.08403e7	−	3.94554e6i	−0.403358	−	0.146810i	−0.535729	+	0.844390i	$0.679963\pi$
$938$	−1.68665e6	+	2.01007e6i	−0.0625919	+	0.0745942i
$939$	1.57362e7	+	9.08528e6i	0.582418	+	0.336259i
$940$	2.42148e7	−	4.26972e6i	0.893843	−	0.157609i
$941$	3.10253e6	+	1.75953e7i	0.114220	+	0.647773i	0.987134	+	0.159898i	$0.0511166\pi$
$941$	3.10253e6	+	1.75953e7i	0.114220	+	0.647773i	−0.872914	+	0.487875i	$0.837772\pi$
$942$	−4.54796e6	−	5.42005e6i	−0.166990	−	0.199011i
$943$	−875943.	−	2.40663e6i	−0.0320772	−	0.0881314i
$944$	−3.86795e6	−	1.06271e7i	−0.141270	−	0.388137i
$945$	1.95404e7	+	2.32873e7i	0.711792	+	0.848281i
$946$	3.01292e6	+	1.70871e7i	0.109461	+	0.620785i
$947$	−3.60464e7	+	6.35595e6i	−1.30613	+	0.230306i	−0.783040	−	0.621971i	$-0.786332\pi$
$947$	−3.60464e7	+	6.35595e6i	−1.30613	+	0.230306i	−0.523090	+	0.852277i	$0.675221\pi$
$948$	−8.72053e6	−	5.03480e6i	−0.315153	−	0.181954i
$949$	−1.15409e7	+	1.37540e7i	−0.415983	+	0.495749i
$950$	−3.33060e7	−	1.21224e7i	−1.19733	−	0.435792i
$951$	−1.37977e7	−	2.38983e7i	−0.494714	−	0.856870i
$952$	−7.78532e6	+	1.34846e7i	−0.278410	+	0.482220i
$953$	3.44893e7	−	2.89400e7i	1.23013	−	1.03220i	0.231903	−	0.972739i	$-0.425505\pi$
$953$	3.44893e7	−	2.89400e7i	1.23013	−	1.03220i	0.998230	−	0.0594655i	$-0.0189396\pi$
$954$	−2.20601e6	+	1.27364e6i	−0.0784760	+	0.0453081i
$955$	1.54640e7	−	8.77004e7i	0.548671	−	3.11167i
$956$			1.75455e7i			0.620899i
$957$	−2.78844e7	−	4.91677e6i	−0.984194	−	0.173540i
$958$	−6.35990e6	−	5.33659e6i	−0.223891	−	0.187867i
$959$	−1.14001e7	+	4.14930e6i	−0.400279	+	0.145689i
$960$	2.74997e6	−	7.55547e6i	0.0963051	−	0.264596i
$961$	2.30010e7			0.803410
$962$	−5.88673e6	−	2.95563e7i	−0.205086	−	1.02970i
$963$	1.63990e7			0.569839
$964$	−6.11658e6	+	1.68052e7i	−0.211990	+	0.582439i
$965$	−7.84975e7	+	2.85708e7i	−2.71355	+	0.987651i
$966$	−1.61762e6	−	1.35734e6i	−0.0557743	−	0.0468002i
$967$	−4.25356e7	−	7.50017e6i	−1.46280	−	0.257932i	−0.615120	−	0.788434i	$-0.710892\pi$
$967$	−4.25356e7	−	7.50017e6i	−1.46280	−	0.257932i	−0.847684	+	0.530502i	$0.822003\pi$
$968$		−	1.10715e6i		−	0.0379767i
$969$	−7.86902e6	+	4.46274e7i	−0.269222	+	1.52684i
$970$	5.44351e7	−	3.14281e7i	1.85759	−	1.07248i
$971$	−6.64220e6	+	5.57346e6i	−0.226081	+	0.189704i	−0.748791	−	0.662806i	$-0.769365\pi$
$971$	−6.64220e6	+	5.57346e6i	−0.226081	+	0.189704i	0.522710	+	0.852510i	$0.324921\pi$
$972$	−5.82457e6	+	1.00884e7i	−0.197742	+	0.342499i
$973$	−2.22606e6	−	3.85565e6i	−0.0753798	−	0.130562i
$974$	1.10095e7	+	4.00714e6i	0.371853	+	0.135343i
$975$	8.68720e7	−	1.03530e8i	2.92663	−	3.48782i
$976$	−6.72966e6	−	3.88537e6i	−0.226135	−	0.130559i
$977$	1.11935e7	−	1.97372e6i	0.375171	−	0.0661528i	0.0171168	−	0.999853i	$-0.494551\pi$
$977$	1.11935e7	−	1.97372e6i	0.375171	−	0.0661528i	0.358055	+	0.933701i	$0.383440\pi$
$978$	539290.	+	3.05846e6i	0.0180291	+	0.102248i
$979$	7.65679e6	+	9.12500e6i	0.255323	+	0.304282i
$980$	2.73438e6	+	7.51264e6i	0.0909480	+	0.249878i
$981$	−4.97702e6	−	1.36743e7i	−0.165119	−	0.453661i
$982$	6.15670e6	+	7.33727e6i	0.203737	+	0.242804i
$983$	7.35428e6	+	4.17082e7i	0.242748	+	1.37669i	0.825664	+	0.564162i	$0.190801\pi$
$983$	7.35428e6	+	4.17082e7i	0.242748	+	1.37669i	−0.582916	+	0.812532i	$0.698088\pi$
$984$	1.15965e7	−	2.04478e6i	0.381803	−	0.0673222i
$985$	2.15952e7	+	1.24680e7i	0.709197	+	0.409455i
$986$	2.28817e7	−	2.72693e7i	0.749541	−	0.893268i
$987$	2.79006e7	+	1.01550e7i	0.911635	+	0.331808i
$988$	7.97600e6	+	1.38148e7i	0.259952	+	0.450250i
$989$	1.47916e6	−	2.56197e6i	0.0480865	−	0.0832883i
$990$	1.25328e7	−	1.05163e7i	0.406406	−	0.341015i
$991$	−3.03009e7	+	1.74942e7i	−0.980103	+	0.565863i	−0.902301	−	0.431106i	$-0.858123\pi$
$991$	−3.03009e7	+	1.74942e7i	−0.980103	+	0.565863i	−0.0778018	+	0.996969i	$0.524790\pi$
$992$	421847.	−	2.39241e6i	0.0136105	−	0.0771892i
$993$		−	2.96386e7i		−	0.953861i
$994$	−1.84360e7	−	3.25076e6i	−0.591834	−	0.104356i
$995$	−3.80489e7	−	3.19268e7i	−1.21838	−	1.02235i
$996$	2.74194e7	−	9.97984e6i	0.875809	−	0.318768i
$997$	2.82388e6	−	7.75856e6i	0.0899723	−	0.247197i	−0.886542	−	0.462647i	$-0.846900\pi$
$997$	2.82388e6	−	7.75856e6i	0.0899723	−	0.247197i	0.976515	+	0.215450i	$0.0691219\pi$
$998$	−2.64549e7			−0.840775
$999$	1.63850e7	−	1.43764e7i	0.519437	−	0.455762i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.h.a.21.2	✓	96
37.30	even	18	inner	74.6.h.a.67.2	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.h.a.21.2	✓	96	1.1	even	1	trivial
74.6.h.a.67.2	yes	96	37.30	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)

\(f(q)\)	\(=\)	\(q+(-1.36808 + 3.75877i) q^{2} +(-17.4563 + 6.35356i) q^{3} +(-12.2567 - 10.2846i) q^{4} +(-104.064 - 18.3493i) q^{5} -74.3062i q^{6} +(19.0842 - 108.232i) q^{7} +(55.4256 - 32.0000i) q^{8} +(78.2045 - 65.6213i) q^{9} +O(q^{10})\)	\(q+(-1.36808 + 3.75877i) q^{2} +(-17.4563 + 6.35356i) q^{3} +(-12.2567 - 10.2846i) q^{4} +(-104.064 - 18.3493i) q^{5} -74.3062i q^{6} +(19.0842 - 108.232i) q^{7} +(55.4256 - 32.0000i) q^{8} +(78.2045 - 65.6213i) q^{9} +(211.339 - 366.050i) q^{10} +(189.573 + 328.350i) q^{11} +(279.300 + 101.657i) q^{12} +(-581.568 + 693.085i) q^{13} +(380.710 + 219.803i) q^{14} +(1933.16 - 340.868i) q^{15} +(44.4539 + 252.111i) q^{16} +(-1422.95 - 1695.81i) q^{17} +(139.666 + 383.728i) q^{18} +(376.889 + 1035.50i) q^{19} +(1086.77 + 1295.16i) q^{20} +(354.519 + 2010.58i) q^{21} +(-1493.54 + 263.352i) q^{22} +(223.936 + 129.290i) q^{23} +(-764.210 + 910.750i) q^{24} +(7556.14 + 2750.21i) q^{25} +(-1809.52 - 3134.18i) q^{26} +(1308.82 - 2266.95i) q^{27} +(-1347.03 + 1130.29i) q^{28} +(3481.51 - 2010.05i) q^{29} +(-1363.47 + 7732.63i) q^{30} +2372.38i q^{31} +(-1008.44 - 177.816i) q^{32} +(-5395.43 - 4527.30i) q^{33} +(8320.87 - 3028.55i) q^{34} +(-3971.97 + 10912.9i) q^{35} -1633.42 q^{36} +(7886.04 + 2674.77i) q^{37} -4407.80 q^{38} +(5748.44 - 15793.7i) q^{39} +(-6355.01 + 2313.03i) q^{40} +(-7587.25 - 6366.46i) q^{41} +(-8042.31 - 1418.08i) q^{42} -11440.7i q^{43} +(1053.41 - 5974.18i) q^{44} +(-9342.40 + 5393.84i) q^{45} +(-792.332 + 664.846i) q^{46} +(7271.58 - 12594.8i) q^{47} +(-2377.80 - 4118.47i) q^{48} +(4443.47 + 1617.29i) q^{49} +(-20674.8 + 24639.3i) q^{50} +(35613.8 + 20561.7i) q^{51} +(14256.2 - 2513.76i) q^{52} +(1083.20 + 6143.15i) q^{53} +(6730.37 + 8020.94i) q^{54} +(-13702.8 - 37648.1i) q^{55} +(-2405.67 - 6609.52i) q^{56} +(-13158.2 - 15681.3i) q^{57} +(2792.33 + 15836.1i) q^{58} +(-43505.2 + 7671.14i) q^{59} +(-27199.8 - 15703.8i) q^{60} +(-19511.5 + 23252.9i) q^{61} +(-8917.24 - 3245.61i) q^{62} +(-5609.85 - 9716.55i) q^{63} +(2048.00 - 3547.24i) q^{64} +(73238.1 - 61454.1i) q^{65} +(24398.5 - 14086.5i) q^{66} +(-1036.49 + 5878.22i) q^{67} +35419.5i q^{68} +(-4730.53 - 834.121i) q^{69} +(-35585.1 - 29859.4i) q^{70} +(-40016.3 + 14564.7i) q^{71} +(2234.65 - 6139.65i) q^{72} +19844.5 q^{73} +(-20842.6 + 25982.5i) q^{74} -149375. q^{75} +(6030.23 - 16567.9i) q^{76} +(39155.8 - 14251.6i) q^{77} +(51500.6 + 43214.1i) q^{78} +(-33364.0 - 5882.97i) q^{79} -27051.4i q^{80} +(-12751.8 + 72318.8i) q^{81} +(34310.0 - 19808.9i) q^{82} +(75203.9 - 63103.6i) q^{83} +(16332.7 - 28289.2i) q^{84} +(116962. + 202583. i) q^{85} +(43002.8 + 15651.7i) q^{86} +(-48003.2 + 57208.0i) q^{87} +(21014.4 + 12132.7i) q^{88} +(30940.3 - 5455.60i) q^{89} +(-7493.04 - 42495.1i) q^{90} +(63915.2 + 76171.2i) q^{91} +(-1415.03 - 3887.76i) q^{92} +(-15073.1 - 41412.9i) q^{93} +(37392.7 + 44562.8i) q^{94} +(-20220.1 - 114674. i) q^{95} +(18733.4 - 3303.21i) q^{96} +(128786. + 74354.7i) q^{97} +(-12158.1 + 14489.4i) q^{98} +(36372.2 + 13238.4i) 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

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