LMFDB - Embedded newform 21.6.g.c.17.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,6,Mod(5,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("21.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	21.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.36806021607$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 171 x^{14} + 21495 x^{12} - 1128902 x^{10} + 42970860 x^{8} - 655075344 x^{6} + \cdots + 90230547456 $ x^16 - 171x^14 + 21495x^12 - 1128902x^10 + 42970860x^8 - 655075344x^6 + 7244325760x^4 - 29387167488*x^2 + 90230547456
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.8
Root			$8.95007 - 5.16733i$ of defining polynomial
Character	$\chi$	$=$	21.17
Dual form			21.6.g.c.5.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.95007 - 5.16733i) q^{2} +(1.78125 + 15.4864i) q^{3} +(37.4025 - 64.7831i) q^{4} +(-15.8704 - 27.4884i) q^{5} +(95.9654 + 129.400i) q^{6} +(20.8412 + 127.956i) q^{7} -442.375i q^{8} +(-236.654 + 55.1702i) q^{9} +O(q^{10})$	\(q+(8.95007 - 5.16733i) q^{2} +(1.78125 + 15.4864i) q^{3} +(37.4025 - 64.7831i) q^{4} +(-15.8704 - 27.4884i) q^{5} +(95.9654 + 129.400i) q^{6} +(20.8412 + 127.956i) q^{7} -442.375i q^{8} +(-236.654 + 55.1702i) q^{9} +(-284.083 - 164.015i) q^{10} +(-392.733 - 226.744i) q^{11} +(1069.88 + 463.834i) q^{12} +551.786i q^{13} +(847.719 + 1037.52i) q^{14} +(397.426 - 294.739i) q^{15} +(-1089.02 - 1886.23i) q^{16} +(-269.081 + 466.061i) q^{17} +(-1832.99 + 1716.65i) q^{18} +(1183.66 - 683.387i) q^{19} -2374.38 q^{20} +(-1944.44 + 550.676i) q^{21} -4686.65 q^{22} +(2804.16 - 1618.98i) q^{23} +(6850.78 - 787.981i) q^{24} +(1058.76 - 1833.82i) q^{25} +(2851.26 + 4938.53i) q^{26} +(-1275.93 - 3566.64i) q^{27} +(9068.87 + 3435.70i) q^{28} +1604.88i q^{29} +(2033.98 - 4691.56i) q^{30} +(-6122.73 - 3534.96i) q^{31} +(-7234.08 - 4176.60i) q^{32} +(2811.89 - 6485.89i) q^{33} +5561.71i q^{34} +(3186.53 - 2603.60i) q^{35} +(-5277.37 + 17394.7i) q^{36} +(975.532 + 1689.67i) q^{37} +(7062.56 - 12232.7i) q^{38} +(-8545.16 + 982.870i) q^{39} +(-12160.2 + 7020.68i) q^{40} +1800.47 q^{41} +(-14557.4 + 14976.2i) q^{42} +7882.36 q^{43} +(-29378.4 + 16961.6i) q^{44} +(5272.34 + 5629.67i) q^{45} +(16731.6 - 28980.0i) q^{46} +(3045.11 + 5274.29i) q^{47} +(27271.0 - 20224.7i) q^{48} +(-15938.3 + 5333.50i) q^{49} -21883.8i q^{50} +(-7696.89 - 3336.90i) q^{51} +(35746.4 + 20638.2i) q^{52} +(12278.4 + 7088.96i) q^{53} +(-29849.6 - 25328.6i) q^{54} +14394.1i q^{55} +(56604.4 - 9219.64i) q^{56} +(12691.6 + 17113.3i) q^{57} +(8292.95 + 14363.8i) q^{58} +(-8459.44 + 14652.2i) q^{59} +(-4229.36 - 36770.4i) q^{60} +(-25737.3 + 14859.5i) q^{61} -73065.1 q^{62} +(-11991.5 - 29131.4i) q^{63} -16630.3 q^{64} +(15167.7 - 8757.08i) q^{65} +(-8348.10 - 72579.1i) q^{66} +(-6807.13 + 11790.3i) q^{67} +(20128.6 + 34863.7i) q^{68} +(30067.1 + 40542.4i) q^{69} +(15066.0 - 39768.3i) q^{70} +31338.5i q^{71} +(24405.9 + 104690. i) q^{72} +(8505.52 + 4910.67i) q^{73} +(17462.2 + 10081.8i) q^{74} +(30285.2 + 13129.8i) q^{75} -102242. i q^{76} +(20828.2 - 54978.0i) q^{77} +(-71401.0 + 52952.4i) q^{78} +(-49899.1 - 86427.8i) q^{79} +(-34566.3 + 59870.6i) q^{80} +(52961.5 - 26112.5i) q^{81} +(16114.3 - 9303.61i) q^{82} -79557.4 q^{83} +(-37052.6 + 146564. i) q^{84} +17081.7 q^{85} +(70547.7 - 40730.7i) q^{86} +(-24853.8 + 2858.70i) q^{87} +(-100306. + 173735. i) q^{88} +(-476.867 - 825.958i) q^{89} +(76278.2 + 23142.0i) q^{90} +(-70604.2 + 11499.9i) q^{91} -242216. i q^{92} +(43837.5 - 101115. i) q^{93} +(54507.9 + 31470.2i) q^{94} +(-37570.4 - 21691.3i) q^{95} +(51794.6 - 119469. i) q^{96} +115552. i q^{97} +(-115089. + 130094. i) q^{98} +(105451. + 31992.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 18 q^{3} + 86 q^{4} - 616 q^{7} - 606 q^{9}+O(q^{10}) $ 16 * q + 18 * q^3 + 86 * q^4 - 616 * q^7 - 606 * q^9	$ 16 q + 18 q^{3} + 86 q^{4} - 616 q^{7} - 606 q^{9} - 546 q^{10} + 4128 q^{12} + 1188 q^{15} - 2858 q^{16} - 438 q^{18} + 3258 q^{19} + 882 q^{21} - 21900 q^{22} + 10374 q^{24} - 6578 q^{25} + 34006 q^{28} + 450 q^{30} - 9792 q^{31} + 17556 q^{33} - 15132 q^{36} - 10466 q^{37} - 17418 q^{39} - 60774 q^{40} - 56994 q^{42} + 111052 q^{43} - 31374 q^{45} + 81696 q^{46} - 51548 q^{49} + 31596 q^{51} + 126960 q^{52} + 7434 q^{54} - 31368 q^{57} - 41706 q^{58} + 60066 q^{60} - 128580 q^{61} - 123606 q^{63} - 158884 q^{64} - 160314 q^{66} - 102202 q^{67} + 234318 q^{70} + 330864 q^{72} + 345150 q^{73} + 428202 q^{75} - 277512 q^{78} - 251308 q^{79} + 179262 q^{81} - 534576 q^{82} + 106176 q^{84} + 205152 q^{85} - 551922 q^{87} - 359514 q^{88} + 65814 q^{91} + 17676 q^{93} + 276612 q^{94} + 1043910 q^{96} + 215472 q^{99}+O(q^{100}) $ 16 * q + 18 * q^3 + 86 * q^4 - 616 * q^7 - 606 * q^9 - 546 * q^10 + 4128 * q^12 + 1188 * q^15 - 2858 * q^16 - 438 * q^18 + 3258 * q^19 + 882 * q^21 - 21900 * q^22 + 10374 * q^24 - 6578 * q^25 + 34006 * q^28 + 450 * q^30 - 9792 * q^31 + 17556 * q^33 - 15132 * q^36 - 10466 * q^37 - 17418 * q^39 - 60774 * q^40 - 56994 * q^42 + 111052 * q^43 - 31374 * q^45 + 81696 * q^46 - 51548 * q^49 + 31596 * q^51 + 126960 * q^52 + 7434 * q^54 - 31368 * q^57 - 41706 * q^58 + 60066 * q^60 - 128580 * q^61 - 123606 * q^63 - 158884 * q^64 - 160314 * q^66 - 102202 * q^67 + 234318 * q^70 + 330864 * q^72 + 345150 * q^73 + 428202 * q^75 - 277512 * q^78 - 251308 * q^79 + 179262 * q^81 - 534576 * q^82 + 106176 * q^84 + 205152 * q^85 - 551922 * q^87 - 359514 * q^88 + 65814 * q^91 + 17676 * q^93 + 276612 * q^94 + 1043910 * q^96 + 215472 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	8.95007	−	5.16733i	1.58216	−	0.913463i	0.587621	−	0.809136i	$-0.300065\pi$
$2$	8.95007	−	5.16733i	1.58216	−	0.913463i	0.994543	−	0.104326i	$-0.0332687\pi$
$3$	1.78125	+	15.4864i	0.114267	+	0.993450i
$3$	1.78125	+	15.4864i	0.114267	+	0.993450i
$4$	37.4025	−	64.7831i	1.16883	−	2.02447i
$5$	−15.8704	−	27.4884i	−0.283899	−	0.491727i	0.688443	−	0.725291i	$-0.258295\pi$
$5$	−15.8704	−	27.4884i	−0.283899	−	0.491727i	−0.972342	+	0.233564i	$0.924961\pi$
$6$	95.9654	+	129.400i	1.08827	+	1.46742i
$7$	20.8412	+	127.956i	0.160760	+	0.986994i
$7$	20.8412	+	127.956i	0.160760	+	0.986994i
$8$		−	442.375i		−	2.44380i
$9$	−236.654	+	55.1702i	−0.973886	+	0.227038i
$10$	−284.083	−	164.015i	−0.898349	−	0.518662i
$11$	−392.733	−	226.744i	−0.978623	−	0.565008i	−0.0767691	−	0.997049i	$-0.524460\pi$
$11$	−392.733	−	226.744i	−0.978623	−	0.565008i	−0.901854	+	0.432040i	$0.857794\pi$
$12$	1069.88	+	463.834i	2.14477	+	0.929842i
$13$			551.786i			0.905550i	0.891625	+	0.452775i	$0.149566\pi$
$13$			551.786i			0.905550i	−0.891625	+	0.452775i	$0.850434\pi$
$14$	847.719	+	1037.52i	1.15593	+	1.41474i
$15$	397.426	−	294.739i	0.456066	−	0.338228i
$16$	−1089.02	−	1886.23i	−1.06349	−	1.84202i
$17$	−269.081	+	466.061i	−0.225819	+	0.391129i	−0.956565	−	0.291520i	$-0.905839\pi$
$17$	−269.081	+	466.061i	−0.225819	+	0.391129i	0.730746	+	0.682649i	$0.239172\pi$
$18$	−1832.99	+	1716.65i	−1.33346	+	1.24882i
$19$	1183.66	−	683.387i	0.752217	−	0.434293i	−0.0742773	−	0.997238i	$-0.523665\pi$
$19$	1183.66	−	683.387i	0.752217	−	0.434293i	0.826494	+	0.562945i	$0.190332\pi$
$20$	−2374.38			−1.32732
$21$	−1944.44	+	550.676i	−0.962159	+	0.272488i
$22$	−4686.65			−2.06446
$23$	2804.16	−	1618.98i	1.10531	−	0.638150i	0.167698	−	0.985838i	$-0.446367\pi$
$23$	2804.16	−	1618.98i	1.10531	−	0.638150i	0.937610	+	0.347689i	$0.113033\pi$
$24$	6850.78	−	787.981i	2.42779	−	0.279246i
$25$	1058.76	−	1833.82i	0.338803	−	0.586824i
$26$	2851.26	+	4938.53i	0.827186	+	1.43273i
$27$	−1275.93	−	3566.64i	−0.336834	−	0.941564i
$28$	9068.87	+	3435.70i	2.18604	+	0.828172i
$29$			1604.88i			0.354363i	0.984178	+	0.177181i	$0.0566979\pi$
$29$			1604.88i			0.354363i	−0.984178	+	0.177181i	$0.943302\pi$
$30$	2033.98	−	4691.56i	0.412613	−	0.951731i
$31$	−6122.73	−	3534.96i	−1.14430	−	0.660663i	−0.196810	−	0.980442i	$-0.563058\pi$
$31$	−6122.73	−	3534.96i	−1.14430	−	0.660663i	−0.947492	+	0.319779i	$0.896391\pi$
$32$	−7234.08	−	4176.60i	−1.24884	−	0.721021i
$33$	2811.89	−	6485.89i	0.449483	−	1.03678i
$34$			5561.71i			0.825108i
$35$	3186.53	−	2603.60i	0.439692	−	0.359256i
$36$	−5277.37	+	17394.7i	−0.678675	+	2.23697i
$37$	975.532	+	1689.67i	0.117149	+	0.202907i	0.918637	−	0.395104i	$-0.129291\pi$
$37$	975.532	+	1689.67i	0.117149	+	0.202907i	−0.801488	+	0.598011i	$0.795958\pi$
$38$	7062.56	−	12232.7i	0.793421	−	1.37424i
$39$	−8545.16	+	982.870i	−0.899619	+	0.103475i
$40$	−12160.2	+	7020.68i	−1.20168	+	0.693792i
$41$	1800.47			0.167273			0.0836365	−	0.996496i	$-0.473347\pi$
$41$	1800.47			0.167273			0.0836365	+	0.996496i	$0.473347\pi$
$42$	−14557.4	+	14976.2i	−1.27339	+	1.31002i
$43$	7882.36			0.650107			0.325054	−	0.945696i	$-0.394618\pi$
$43$	7882.36			0.650107			0.325054	+	0.945696i	$0.394618\pi$
$44$	−29378.4	+	16961.6i	−2.28769	+	1.32080i
$45$	5272.34	+	5629.67i	0.388126	+	0.414430i
$46$	16731.6	−	28980.0i	1.16585	−	2.01932i
$47$	3045.11	+	5274.29i	0.201075	+	0.348272i	0.948875	−	0.315652i	$-0.102223\pi$
$47$	3045.11	+	5274.29i	0.201075	+	0.348272i	−0.747800	+	0.663924i	$0.768890\pi$
$48$	27271.0	−	20224.7i	1.70843	−	1.26701i
$49$	−15938.3	+	5333.50i	−0.948312	+	0.317338i
$50$		−	21883.8i		−	1.23794i
$51$	−7696.89	−	3336.90i	−0.414371	−	0.179646i
$52$	35746.4	+	20638.2i	1.83326	+	1.05843i
$53$	12278.4	+	7088.96i	0.600417	+	0.346651i	0.769206	−	0.639001i	$-0.220652\pi$
$53$	12278.4	+	7088.96i	0.600417	+	0.346651i	−0.168788	+	0.985652i	$0.553985\pi$
$54$	−29849.6	−	25328.6i	−1.39301	−	1.18202i
$55$			14394.1i			0.641621i
$56$	56604.4	−	9219.64i	2.41201	−	0.392865i
$57$	12691.6	+	17113.3i	0.517402	+	0.697665i
$58$	8292.95	+	14363.8i	0.323697	+	0.560660i
$59$	−8459.44	+	14652.2i	−0.316382	+	0.547990i	−0.979730	−	0.200321i	$-0.935801\pi$
$59$	−8459.44	+	14652.2i	−0.316382	+	0.547990i	0.663348	+	0.748311i	$0.269135\pi$
$60$	−4229.36	−	36770.4i	−0.151669	−	1.31862i
$61$	−25737.3	+	14859.5i	−0.885603	+	0.511303i	−0.872502	−	0.488611i	$-0.837504\pi$
$61$	−25737.3	+	14859.5i	−0.885603	+	0.511303i	−0.0131010	+	0.999914i	$0.504170\pi$
$62$	−73065.1			−2.41396
$63$	−11991.5	−	29131.4i	−0.380647	−	0.924721i
$64$	−16630.3			−0.507518
$65$	15167.7	−	8757.08i	0.445284	−	0.257085i
$66$	−8348.10	−	72579.1i	−0.235900	−	2.05093i
$67$	−6807.13	+	11790.3i	−0.185258	+	0.320876i	−0.943663	−	0.330907i	$-0.892645\pi$
$67$	−6807.13	+	11790.3i	−0.185258	+	0.320876i	0.758405	+	0.651783i	$0.225979\pi$
$68$	20128.6	+	34863.7i	0.527887	+	0.914327i
$69$	30067.1	+	40542.4i	0.760271	+	1.02515i
$70$	15066.0	−	39768.3i	0.367497	−	0.970045i
$71$			31338.5i			0.737790i	0.929471	+	0.368895i	$0.120264\pi$
$71$			31338.5i			0.737790i	−0.929471	+	0.368895i	$0.879736\pi$
$72$	24405.9	+	104690.i	0.554835	+	2.37998i
$73$	8505.52	+	4910.67i	0.186807	+	0.107853i	0.590487	−	0.807047i	$-0.298936\pi$
$73$	8505.52	+	4910.67i	0.186807	+	0.107853i	−0.403680	+	0.914900i	$0.632269\pi$
$74$	17462.2	+	10081.8i	0.370697	+	0.214022i
$75$	30285.2	+	13129.8i	0.621694	+	0.269529i
$76$		−	102242.i		−	2.03046i
$77$	20828.2	−	54978.0i	0.400336	−	1.05673i
$78$	−71401.0	+	52952.4i	−1.32882	+	0.985482i
$79$	−49899.1	−	86427.8i	−0.899550	−	1.55807i	−0.828071	−	0.560624i	$-0.810561\pi$
$79$	−49899.1	−	86427.8i	−0.899550	−	1.55807i	−0.0714791	−	0.997442i	$-0.522772\pi$
$80$	−34566.3	+	59870.6i	−0.603848	+	1.04590i
$81$	52961.5	−	26112.5i	0.896908	−	0.442218i
$82$	16114.3	−	9303.61i	0.264653	−	0.152798i
$83$	−79557.4			−1.26761			−0.633804	−	0.773493i	$-0.718508\pi$
$83$	−79557.4			−1.26761			−0.633804	+	0.773493i	$0.718508\pi$
$84$	−37052.6	+	146564.i	−0.572955	+	2.26635i
$85$	17081.7			0.256439
$86$	70547.7	−	40730.7i	1.02858	−	0.593849i
$87$	−24853.8	+	2858.70i	−0.352042	+	0.0404921i
$88$	−100306.	+	173735.i	−1.38077	+	2.39156i
$89$	−476.867	−	825.958i	−0.00638150	−	0.0110531i	0.862817	−	0.505516i	$-0.168698\pi$
$89$	−476.867	−	825.958i	−0.00638150	−	0.0110531i	−0.869199	+	0.494463i	$0.835365\pi$
$90$	76278.2	+	23142.0i	0.992645	+	0.301159i
$91$	−70604.2	+	11499.9i	−0.893772	+	0.145576i
$92$		−	242216.i		−	2.98355i
$93$	43837.5	−	101115.i	0.525579	−	1.21230i
$94$	54507.9	+	31470.2i	0.636268	+	0.367349i
$95$	−37570.4	−	21691.3i	−0.427107	−	0.246590i
$96$	51794.6	−	119469.i	0.573596	−	1.32305i
$97$			115552.i			1.24695i	0.781842	+	0.623476i	$0.214280\pi$
$97$			115552.i			1.24695i	−0.781842	+	0.623476i	$0.785720\pi$
$98$	−115089.	+	130094.i	−1.21051	+	1.36833i
$99$	105451.	+	31992.9i	1.08135	+	0.328069i
$100$	−79200.5	−	137179.i	−0.792005	−	1.37179i
$101$	44991.7	−	77927.9i	0.438863	−	0.760133i	−0.558739	−	0.829343i	$-0.688715\pi$
$101$	44991.7	−	77927.9i	0.438863	−	0.760133i	0.997602	+	0.0692107i	$0.0220481\pi$
$102$	−86130.6	+	9906.79i	−0.819704	+	0.0942828i
$103$	135674.	−	78331.5i	1.26010	−	0.727517i	0.287004	−	0.957929i	$-0.407341\pi$
$103$	135674.	−	78331.5i	1.26010	−	0.727517i	0.973093	+	0.230412i	$0.0740074\pi$
$104$	244096.			2.21298
$105$	45996.3	+	44710.1i	0.407146	+	0.395761i
$106$	146524.			1.26661
$107$	−120470.	+	69553.5i	−1.01723	+	0.587299i	−0.913301	−	0.407286i	$-0.866475\pi$
$107$	−120470.	+	69553.5i	−1.01723	+	0.587299i	−0.103931	+	0.994585i	$0.533142\pi$
$108$	−278781.	−	50743.0i	−2.29987	−	0.418617i
$109$	−12113.2	+	20980.7i	−0.0976547	+	0.169143i	−0.910713	−	0.413039i	$-0.864467\pi$
$109$	−12113.2	+	20980.7i	−0.0976547	+	0.169143i	0.813059	+	0.582182i	$0.197801\pi$
$110$	74379.1	+	128828.i	0.586097	+	1.01515i
$111$	−24429.2	+	18117.2i	−0.188192	+	0.139567i
$112$	218657.	−	178657.i	1.64710	−	1.34578i
$113$			38230.9i			0.281655i	0.990034	+	0.140828i	$0.0449763\pi$
$113$			38230.9i			0.281655i	−0.990034	+	0.140828i	$0.955024\pi$
$114$	202020.	+	87583.8i	1.45591	+	0.631192i
$115$	−89006.4	−	51387.9i	−0.627591	−	0.362340i
$116$	103969.	+	60026.6i	0.717397	+	0.414189i
$117$	−30442.1	−	130583.i	−0.205594	−	0.881903i
$118$			174851.i			1.15601i
$119$	−65243.1	−	24717.1i	−0.422345	−	0.160004i
$120$	−130385.	−	175811.i	−0.826561	−	1.11453i
$121$	22300.6	+	38625.7i	0.138469	+	0.239836i
$122$	−153567.	+	265986.i	−0.934112	+	1.61793i
$123$	3207.09	+	27882.7i	0.0191138	+	0.166177i
$124$	−458011.	+	264433.i	−2.67499	+	1.54440i
$125$	−166402.			−0.952541
$126$	−257856.	−	198764.i	−1.44694	−	1.11535i
$127$	−65650.6			−0.361184			−0.180592	−	0.983558i	$-0.557801\pi$
$127$	−65650.6			−0.361184			−0.180592	+	0.983558i	$0.557801\pi$
$128$	82647.7	−	47716.7i	0.445868	−	0.257422i
$129$	14040.5	+	122069.i	0.0742860	+	0.645849i
$130$	90501.4	−	156753.i	0.469674	−	0.813500i
$131$	−102797.	−	178050.i	−0.523364	−	0.906492i	−0.999630	−	0.0271915i	$-0.991344\pi$
$131$	−102797.	−	178050.i	−0.523364	−	0.906492i	0.476267	−	0.879301i	$-0.341990\pi$
$132$	−315004.	−	424751.i	−1.57355	−	2.12178i
$133$	112112.	+	137213.i	0.549571	+	0.672616i
$134$			140699.i			0.676905i
$135$	−77791.7	+	91677.2i	−0.367366	+	0.432939i
$136$	206174.	+	119035.i	0.955842	+	0.551856i
$137$	355479.	+	205236.i	1.61813	+	0.934225i	0.987405	+	0.158216i	$0.0505742\pi$
$137$	355479.	+	205236.i	1.61813	+	0.934225i	0.630721	+	0.776010i	$0.282759\pi$
$138$	478598.	+	207491.i	2.13931	+	0.927474i
$139$		−	73875.8i		−	0.324314i	−0.986765	−	0.162157i	$-0.948155\pi$
$139$		−	73875.8i		−	0.324314i	0.986765	−	0.162157i	$-0.0518450\pi$
$140$	−49484.9	−	303815.i	−0.213379	−	1.31005i
$141$	−76255.4	+	56552.5i	−0.323015	+	0.239554i
$142$	161936.	+	280482.i	0.673943	+	1.16730i
$143$	125114.	−	216705.i	0.511643	−	0.886192i
$144$	361784.	+	386303.i	1.45393	+	1.55247i
$145$	44115.6	−	25470.1i	0.174250	−	0.100603i
$146$	101500.			0.394080
$147$	−110987.	−	237326.i	−0.423621	−	0.905840i
$148$	145949.			0.547707
$149$	50205.5	−	28986.1i	0.185262	−	0.106961i	−0.404501	−	0.914538i	$-0.632555\pi$
$149$	50205.5	−	28986.1i	0.185262	−	0.106961i	0.589762	+	0.807577i	$0.299221\pi$
$150$	338901.	−	38980.6i	1.22983	−	0.141456i
$151$	86217.4	−	149333.i	0.307718	−	0.532983i	−0.670145	−	0.742230i	$-0.733768\pi$
$151$	86217.4	−	149333.i	0.307718	−	0.532983i	0.977863	+	0.209247i	$0.0671014\pi$
$152$	−302313.	−	523622.i	−1.06132	−	1.83827i
$153$	37966.4	−	125141.i	0.131121	−	0.432185i
$154$	−97675.5	−	599683.i	−0.331882	−	2.03761i
$155$			224405.i			0.750246i
$156$	−255937.	+	590343.i	−0.842019	+	1.94220i
$157$	−207228.	−	119643.i	−0.670965	−	0.387382i	0.125477	−	0.992097i	$-0.459954\pi$
$157$	−207228.	−	119643.i	−0.670965	−	0.387382i	−0.796442	+	0.604715i	$0.793287\pi$
$158$	−893201.	−	515690.i	−2.84647	−	1.64341i
$159$	−87911.1	+	202775.i	−0.275773	+	0.636096i
$160$			265137.i			0.818787i
$161$	265600.	+	325067.i	0.807539	+	0.988343i
$162$	339077.	−	507378.i	1.01511	−	1.51895i
$163$	−74189.1	−	128499.i	−0.218711	−	0.378819i	0.735703	−	0.677304i	$-0.236852\pi$
$163$	−74189.1	−	128499.i	−0.218711	−	0.378819i	−0.954414	+	0.298485i	$0.903519\pi$
$164$	67342.0	−	116640.i	0.195513	−	0.338639i
$165$	−222912.	+	25639.5i	−0.637418	+	0.0733163i
$166$	−712044.	+	411099.i	−2.00556	+	1.15791i
$167$	549931.			1.52587			0.762934	−	0.646476i	$-0.223758\pi$
$167$	549931.			1.52587			0.762934	+	0.646476i	$0.223758\pi$
$168$	243605.	+	860173.i	0.665907	+	2.35132i
$169$	66825.0			0.179979
$170$	152882.	−	88266.6i	0.405728	−	0.234247i
$171$	−242416.	+	227029.i	−0.633973	+	0.593733i
$172$	294820.	−	510643.i	0.759864	−	1.31612i
$173$	−158136.	−	273900.i	−0.401714	−	0.695789i	0.592219	−	0.805777i	$-0.298252\pi$
$173$	−158136.	−	273900.i	−0.401714	−	0.695789i	−0.993933	+	0.109988i	$0.964919\pi$
$174$	−207671.	+	154013.i	−0.520000	+	0.385642i
$175$	256714.	+	97255.1i	0.633657	+	0.240058i
$176$			987713.i			2.40353i
$177$	−241977.	−	104907.i	−0.580552	−	0.251692i
$178$	−8535.99	−	4928.26i	−0.0201931	−	0.0116585i
$179$	488097.	+	281803.i	1.13861	+	0.657374i	0.946085	−	0.323918i	$-0.105000\pi$
$179$	488097.	+	281803.i	1.13861	+	0.657374i	0.192521	+	0.981293i	$0.438334\pi$
$180$	561906.	−	130995.i	1.29265	−	0.301351i
$181$			329274.i			0.747069i	0.927616	+	0.373535i	$0.121854\pi$
$181$			329274.i			0.747069i	−0.927616	+	0.373535i	$0.878146\pi$
$182$	−572488.	+	467760.i	−1.28112	+	1.04675i
$183$	−275963.	−	372109.i	−0.609149	−	0.821377i
$184$	−716198.	−	1.24049e6i	−1.55951	−	2.70115i
$185$	30964.2	−	53631.6i	0.0665167	−	0.115210i
$186$	−130147.	−	1.13151e6i	−0.275837	−	2.39815i
$187$	211354.	−	122025.i	0.441983	−	0.255179i
$188$	455579.			0.940090
$189$	429780.	−	237595.i	0.875168	−	0.483819i
$190$	−448344.			−0.901004
$191$	−697562.	+	402738.i	−1.38356	+	0.798801i	−0.992580	−	0.121596i	$-0.961199\pi$
$191$	−697562.	+	402738.i	−1.38356	+	0.798801i	−0.390985	+	0.920397i	$0.627865\pi$
$192$	−29622.8	−	257543.i	−0.0579927	−	0.504194i
$193$	−317851.	+	550534.i	−0.614228	+	1.06387i	0.376291	+	0.926502i	$0.377199\pi$
$193$	−317851.	+	550534.i	−0.614228	+	1.06387i	−0.990519	+	0.137373i	$0.956134\pi$
$194$	597097.	+	1.03420e6i	1.13904	+	1.97288i
$195$	162633.	+	219294.i	0.306282	+	0.412991i
$196$	−250611.	+	1.23202e6i	−0.465973	+	2.29074i
$197$		−	137701.i		−	0.252796i	−0.991980	−	0.126398i	$-0.959658\pi$
$197$		−	137701.i		−	0.252796i	0.991980	−	0.126398i	$-0.0403417\pi$
$198$	1.10912e6	−	258563.i	2.01055	−	0.468709i
$199$	775577.	+	447779.i	1.38833	+	0.801552i	0.993127	−	0.117043i	$-0.0373416\pi$
$199$	775577.	+	447779.i	1.38833	+	0.801552i	0.395201	+	0.918595i	$0.370675\pi$
$200$	−811238.	−	468369.i	−1.43408	−	0.827967i
$201$	−194714.	−	84416.1i	−0.339943	−	0.147379i
$202$		−	929947.i		−	1.60354i
$203$	−205354.	+	33447.7i	−0.349754	+	0.0569674i
$204$	−504058.	+	373819.i	−0.848018	+	0.628907i
$205$	−28574.2	−	49492.0i	−0.0474886	−	0.0822527i
$206$	809529.	−	1.40215e6i	1.32912	−	2.30210i
$207$	−574297.	+	537845.i	−0.931560	+	0.872432i
$208$	1.04080e6	−	600904.i	1.66804	−	0.963045i
$209$	−619817.			−0.981516
$210$	642702.	+	162481.i	1.00568	+	0.254246i
$211$	−392533.			−0.606974			−0.303487	−	0.952836i	$-0.598151\pi$
$211$	−392533.			−0.606974			−0.303487	+	0.952836i	$0.598151\pi$
$212$	918489.	−	530290.i	1.40357	−	0.810352i
$213$	−485319.	+	55821.8i	−0.732957	+	0.0843052i
$214$	−718811.	+	1.24502e6i	−1.07295	+	1.85841i
$215$	−125096.	−	216673.i	−0.184565	−	0.319675i
$216$	−1.57779e6	+	564437.i	−2.30099	+	0.823155i
$217$	324713.	−	857110.i	0.468112	−	1.23563i
$218$			250372.i			0.356816i
$219$	−60897.9	+	140467.i	−0.0858009	+	0.197908i
$220$	932495.	+	538376.i	1.29894	+	0.749945i
$221$	−257166.	−	148475.i	−0.354187	−	0.204490i
$222$	−125026.	+	288383.i	−0.170262	+	0.392724i
$223$		−	1.01457e6i		−	1.36622i	−0.730317	−	0.683109i	$-0.760628\pi$
$223$		−	1.01457e6i		−	1.36622i	0.730317	−	0.683109i	$-0.239372\pi$
$224$	383652.	−	1.01269e6i	0.510878	−	1.34851i
$225$	−149388.	+	492394.i	−0.196724	+	0.648421i
$226$	197551.	+	342169.i	0.257282	+	0.445625i
$227$	156685.	−	271387.i	0.201820	−	0.349562i	−0.747295	−	0.664492i	$-0.768648\pi$
$227$	156685.	−	271387.i	0.201820	−	0.349562i	0.949115	+	0.314930i	$0.101981\pi$
$228$	1.58335e6	−	182118.i	2.01716	−	0.232015i
$229$	390355.	−	225372.i	0.491894	−	0.283995i	−0.233466	−	0.972365i	$-0.575007\pi$
$229$	390355.	−	225372.i	0.491894	−	0.283995i	0.725360	+	0.688370i	$0.241673\pi$
$230$	−1.06215e6			−1.32394
$231$	888509.	+	224623.i	1.09555	+	0.276965i
$232$	709960.			0.865992
$233$	−116445.	+	67229.3i	−0.140517	+	0.0811276i	−0.568610	−	0.822607i	$-0.692519\pi$
$233$	−116445.	+	67229.3i	−0.140517	+	0.0811276i	0.428093	+	0.903735i	$0.359185\pi$
$234$	−947222.	−	1.01142e6i	−1.13087	−	1.20751i
$235$	96654.4	−	167410.i	0.114170	−	0.197748i
$236$	632809.	+	1.09606e6i	0.739592	+	1.28101i
$237$	1.24957e6	−	926705.i	1.44507	−	1.07169i
$238$	−711652.	+	115913.i	−0.814376	+	0.132644i
$239$		−	1.26368e6i		−	1.43101i	−0.698605	−	0.715507i	$-0.746196\pi$
$239$		−	1.26368e6i		−	1.43101i	0.698605	−	0.715507i	$-0.253804\pi$
$240$	−988748.	−	428661.i	−1.10805	−	0.480381i
$241$	421396.	+	243293.i	0.467356	+	0.269828i	0.715132	−	0.698989i	$-0.246367\pi$
$241$	421396.	+	243293.i	0.467356	+	0.269828i	−0.247776	+	0.968817i	$0.579700\pi$
$242$	399184.	+	230469.i	0.438162	+	0.252973i
$243$	498725.	+	773668.i	0.541808	+	0.840502i
$244$			2.22312e6i			2.39050i
$245$	399557.	+	353473.i	0.425269	+	0.376219i
$246$	172783.	+	232980.i	0.182038	+	0.245460i
$247$	377083.	+	653128.i	0.393274	+	0.681170i
$248$	−1.56378e6	+	2.70854e6i	−1.61453	+	2.79644i
$249$	−141712.	−	1.23205e6i	−0.144846	−	1.25931i
$250$	−1.48931e6	+	859853.i	−1.50708	+	0.870110i
$251$	453648.			0.454501			0.227250	−	0.973836i	$-0.427026\pi$
$251$	453648.			0.454501			0.227250	+	0.973836i	$0.427026\pi$
$252$	−2.33574e6	−	312743.i	−2.31698	−	0.310232i
$253$	−1.46838e6			−1.44224
$254$	−587577.	+	339238.i	−0.571453	+	0.329929i
$255$	30426.8	+	264533.i	0.0293025	+	0.254759i
$256$	759221.	−	1.31501e6i	0.724049	−	1.25409i
$257$	−991726.	−	1.71772e6i	−0.936610	−	1.62226i	−0.771737	−	0.635942i	$-0.780612\pi$
$257$	−991726.	−	1.71772e6i	−0.936610	−	1.62226i	−0.164874	−	0.986315i	$-0.552722\pi$
$258$	756433.	+	1.01997e6i	0.707492	+	0.953982i
$259$	−195872.	+	160040.i	−0.181435	+	0.148244i
$260$		−	1.31015e6i		−	1.20195i
$261$	−88541.6	−	379802.i	−0.0804537	−	0.345109i
$262$	−1.84009e6	−	1.06237e6i	−1.65609	−	0.956146i
$263$	677452.	+	391127.i	0.603934	+	0.348681i	0.770588	−	0.637334i	$-0.219963\pi$
$263$	677452.	+	391127.i	0.603934	+	0.348681i	−0.166654	+	0.986015i	$0.553296\pi$
$264$	−2.86920e6	−	1.24391e6i	−2.53367	−	1.09845i
$265$		−	450019.i		−	0.393655i
$266$	1.71244e6	+	648750.i	1.48392	+	0.562177i
$267$	11941.7	−	8856.17i	0.0102515	−	0.00760270i
$268$	509207.	+	881973.i	0.433070	+	0.750099i
$269$	−841504.	+	1.45753e6i	−0.709047	+	1.22811i	0.256164	+	0.966633i	$0.417541\pi$
$269$	−841504.	+	1.45753e6i	−0.709047	+	1.22811i	−0.965211	+	0.261473i	$0.915792\pi$
$270$	−222515.	+	1.22249e6i	−0.185759	+	1.02056i
$271$	704628.	−	406817.i	0.582823	−	0.336493i	−0.179431	−	0.983770i	$-0.557426\pi$
$271$	704628.	−	406817.i	0.582823	−	0.336493i	0.762255	+	0.647277i	$0.224092\pi$
$272$	1.17213e6			0.960625
$273$	−303855.	−	1.07292e6i	−0.246752	−	0.871283i
$274$	4.24208e6			3.41352
$275$	−831619.	+	480136.i	−0.663121	+	0.382853i
$276$	3.75104e6	−	431448.i	2.96401	−	0.340922i
$277$	−187762.	+	325214.i	−0.147031	+	0.254665i	−0.930129	−	0.367233i	$-0.880305\pi$
$277$	−187762.	+	325214.i	−0.147031	+	0.254665i	0.783098	+	0.621899i	$0.213638\pi$
$278$	−381740.	−	661194.i	−0.296248	−	0.513117i
$279$	1.64399e6	+	498771.i	1.26441	+	0.383611i
$280$	−1.15177e6	−	1.40964e6i	−0.877951	−	1.07452i
$281$			264282.i			0.199665i	0.995004	+	0.0998326i	$0.0318307\pi$
$281$			264282.i			0.199665i	−0.995004	+	0.0998326i	$0.968169\pi$
$282$	−390266.	+	900185.i	−0.292239	+	0.674076i
$283$	−1.59803e6	−	922626.i	−1.18610	−	0.684793i	−0.228679	−	0.973502i	$-0.573441\pi$
$283$	−1.59803e6	−	922626.i	−1.18610	−	0.684793i	−0.957417	+	0.288709i	$0.906774\pi$
$284$	2.03020e6	+	1.17214e6i	1.49363	+	0.862350i
$285$	268996.	−	620466.i	0.196171	−	0.452487i
$286$		−	2.58603e6i		−	1.86947i
$287$	37524.0	+	230380.i	0.0268908	+	0.165097i
$288$	1.94240e6	+	589304.i	1.37993	+	0.418657i
$289$	565120.	+	978816.i	0.398012	+	0.689377i
$290$	263225.	−	455919.i	0.183794	−	0.318341i
$291$	−1.78949e6	+	205828.i	−1.23879	+	0.142486i
$292$	636256.	−	367343.i	0.436692	−	0.252124i
$293$	−1.96922e6			−1.34006			−0.670032	−	0.742332i	$-0.733720\pi$
$293$	−1.96922e6			−1.34006			−0.670032	+	0.742332i	$0.733720\pi$
$294$	−2.21968e6	−	1.55058e6i	−1.49769	−	1.04622i
$295$	537020.			0.359282
$296$	747468.	−	431551.i	0.495865	−	0.286288i
$297$	−307618.	+	1.69005e6i	−0.202358	+	1.11175i
$298$	299562.	−	518856.i	0.195409	−	0.338459i
$299$	893333.	+	1.54730e6i	0.577877	+	1.00091i
$300$	1.98333e6	−	1.47088e6i	1.27231	−	0.943569i
$301$	164278.	+	1.00859e6i	0.104511	+	0.641652i
$302$		−	1.78205e6i		−	1.12435i
$303$	1.28696e6	+	557948.i	0.805301	+	0.349130i
$304$	−2.57805e6	−	1.48844e6i	−1.59995	−	0.923734i
$305$	816925.	+	471652.i	0.502843	+	0.290317i
$306$	−306840.	−	1.31620e6i	−0.187331	−	0.803561i
$307$			2.38073e6i			1.44166i	0.693110	+	0.720832i	$0.256240\pi$
$307$			2.38073e6i			1.44166i	−0.693110	+	0.720832i	$0.743760\pi$
$308$	−2.78262e6	−	3.40563e6i	−1.67139	−	2.04560i
$309$	1.45474e6	+	1.96157e6i	0.866740	+	1.16871i
$310$	1.15957e6	+	2.00844e6i	0.685321	+	1.18701i
$311$	1.68689e6	−	2.92178e6i	0.988976	−	1.71296i	0.366248	−	0.930517i	$-0.380642\pi$
$311$	1.68689e6	−	2.92178e6i	0.988976	−	1.71296i	0.622727	−	0.782439i	$-0.286025\pi$
$312$	434797.	+	3.78016e6i	0.252872	+	2.19849i
$313$	−2.32670e6	+	1.34332e6i	−1.34239	+	0.775031i	−0.987158	−	0.159746i	$-0.948933\pi$
$313$	−2.32670e6	+	1.34332e6i	−1.34239	+	0.775031i	−0.355235	+	0.934777i	$0.615599\pi$
$314$	−2.47294e6			−1.41544
$315$	−610466.	+	791955.i	−0.346645	+	0.449701i
$316$	−7.46541e6			−4.20568
$317$	598070.	−	345296.i	0.334275	−	0.192994i	−0.323462	−	0.946241i	$-0.604847\pi$
$317$	598070.	−	345296.i	0.334275	−	0.192994i	0.657738	+	0.753247i	$0.271514\pi$
$318$	260996.	+	2.26912e6i	0.144732	+	1.25832i
$319$	363898.	−	630290.i	0.200218	−	0.346788i
$320$	263931.	+	457141.i	0.144084	+	0.249560i
$321$	−1.29172e6	−	1.74175e6i	−0.699689	−	0.943460i
$322$	4.05687e6	+	1.53693e6i	2.18047	+	0.826063i
$323$			735544.i			0.392286i
$324$	289245.	−	4.40768e6i	0.153075	−	2.33264i
$325$	1.01188e6	+	584209.i	0.531398	+	0.306803i
$326$	−1.32800e6	−	766718.i	−0.692074	−	0.399569i
$327$	−346491.	−	150218.i	−0.179194	−	0.0776875i
$328$		−	796482.i		−	0.408782i
$329$	−611411.	+	499562.i	−0.311418	+	0.254448i
$330$	−1.86259e6	+	1.38134e6i	−0.941528	+	0.698256i
$331$	−1.61688e6	−	2.80052e6i	−0.811164	−	1.40498i	−0.912050	−	0.410079i	$-0.865501\pi$
$331$	−1.61688e6	−	2.80052e6i	−0.811164	−	1.40498i	0.100886	−	0.994898i	$-0.467832\pi$
$332$	−2.97565e6	+	5.15397e6i	−1.48162	+	2.56624i
$333$	−324083.	−	346048.i	−0.160157	−	0.171012i
$334$	4.92192e6	−	2.84167e6i	2.41417	−	1.39382i
$335$	432128.			0.210378
$336$	3.15623e6	+	3.06797e6i	1.52518	+	1.48253i
$337$	−751164.			−0.360296			−0.180148	−	0.983639i	$-0.557658\pi$
$337$	−751164.			−0.360296			−0.180148	+	0.983639i	$0.557658\pi$
$338$	598088.	−	345306.i	0.284756	−	0.164404i
$339$	−592057.	+	68098.7i	−0.279810	+	0.0321840i
$340$	638898.	−	1.10660e6i	0.299733	−	0.519152i
$341$	1.60306e6	+	2.77659e6i	0.746560	+	1.29308i
$342$	−996505.	+	3.28457e6i	−0.460696	+	1.51849i
$343$	−1.01463e6	−	1.92824e6i	−0.465662	−	0.884963i
$344$		−	3.48696e6i		−	1.58873i
$345$	637268.	−	1.46992e6i	0.288253	−	0.664884i
$346$	−2.83067e6	−	1.63429e6i	−1.27115	−	0.733901i
$347$	1.84192e6	+	1.06343e6i	0.821196	+	0.474118i	0.850829	−	0.525443i	$-0.176100\pi$
$347$	1.84192e6	+	1.06343e6i	0.821196	+	0.474118i	−0.0296326	+	0.999561i	$0.509434\pi$
$348$	−744398.	+	1.71703e6i	−0.329501	+	0.760026i
$349$			1.87399e6i			0.823575i	0.911280	+	0.411787i	$0.135095\pi$
$349$			1.87399e6i			0.823575i	−0.911280	+	0.411787i	$0.864905\pi$
$350$	2.80016e6	−	456086.i	1.22183	−	0.199011i
$351$	1.96802e6	−	704038.i	0.852633	−	0.305020i
$352$	1.89404e6	+	3.28057e6i	0.814765	+	1.41122i
$353$	1.59945e6	−	2.77034e6i	0.683180	−	1.18330i	−0.290826	−	0.956776i	$-0.593930\pi$
$353$	1.59945e6	−	2.77034e6i	0.683180	−	1.18330i	0.974005	−	0.226526i	$-0.0727367\pi$
$354$	−2.70780e6	+	311453.i	−1.14844	+	0.132094i
$355$	861445.	−	497356.i	0.362791	−	0.209458i
$356$	−71344.1			−0.0298355
$357$	266563.	−	1.05441e6i	0.110695	−	0.437862i
$358$	5.82467e6			2.40195
$359$	213840.	−	123461.i	0.0875695	−	0.0505583i	−0.455576	−	0.890197i	$-0.650567\pi$
$359$	213840.	−	123461.i	0.0875695	−	0.0505583i	0.543145	+	0.839639i	$0.317233\pi$
$360$	2.49043e6	−	2.33235e6i	1.01279	−	0.948501i
$361$	−304014.	+	526568.i	−0.122780	+	0.212661i
$362$	1.70147e6	+	2.94702e6i	0.682420	+	1.18199i
$363$	−558449.	+	414157.i	−0.222442	+	0.164967i
$364$	−1.89577e6	+	5.00408e6i	−0.749951	+	1.97957i
$365$		−	311737.i		−	0.122478i
$366$	−4.39270e6	−	1.90441e6i	−1.71407	−	0.743117i
$367$	−393442.	−	227154.i	−0.152481	−	0.0880349i	0.421818	−	0.906680i	$-0.361392\pi$
$367$	−393442.	−	227154.i	−0.152481	−	0.0880349i	−0.574299	+	0.818645i	$0.694725\pi$
$368$	−6.10755e6	−	3.52620e6i	−2.35097	−	1.35733i
$369$	−426089.	+	99332.1i	−0.162905	+	0.0379773i
$370$		−	640009.i		−	0.243042i
$371$	−651174.	+	1.71884e6i	−0.245619	+	0.648336i
$372$	−4.91093e6	−	6.62189e6i	−1.83995	−	2.48099i
$373$	−1.17803e6	−	2.04040e6i	−0.438412	−	0.759353i	0.559155	−	0.829063i	$-0.311126\pi$
$373$	−1.17803e6	−	2.04040e6i	−0.438412	−	0.759353i	−0.997567	+	0.0697107i	$0.977792\pi$
$374$	1.26109e6	−	2.18427e6i	0.466193	−	0.807470i
$375$	−296404.	−	2.57696e6i	−0.108844	−	0.946301i
$376$	2.33321e6	−	1.34708e6i	0.851108	−	0.491388i
$377$	−885551.			−0.320893
$378$	2.61883e6	−	4.34730e6i	0.942709	−	1.56491i
$379$	1.39242e6			0.497935			0.248968	−	0.968512i	$-0.419909\pi$
$379$	1.39242e6			0.497935			0.248968	+	0.968512i	$0.419909\pi$
$380$	−2.81045e6	+	1.62262e6i	−0.998430	+	0.576444i
$381$	−116940.	−	1.01669e6i	−0.0412716	−	0.358819i
$382$	−4.16215e6	+	7.20906e6i	−1.45935	+	2.52767i
$383$	−2.27893e6	−	3.94722e6i	−0.793841	−	1.37497i	−0.923572	−	0.383424i	$-0.874745\pi$
$383$	−2.27893e6	−	3.94722e6i	−0.793841	−	1.37497i	0.129731	−	0.991549i	$-0.458589\pi$
$384$	886174.	+	1.19492e6i	0.306684	+	0.413532i
$385$	−1.84181e6	+	299991.i	−0.633276	+	0.103147i
$386$			6.56975e6i			2.24430i
$387$	−1.86539e6	+	434871.i	−0.633130	+	0.147599i
$388$	7.48584e6	+	4.32195e6i	2.52442	+	1.45747i
$389$	1.44441e6	+	833932.i	0.483969	+	0.279420i	0.722069	−	0.691821i	$-0.243191\pi$
$389$	1.44441e6	+	833932.i	0.483969	+	0.279420i	−0.238100	+	0.971241i	$0.576525\pi$
$390$	2.58874e6	+	1.12232e6i	0.861840	+	0.373642i
$391$			1.74255e6i			0.576425i
$392$	2.35941e6	+	7.05070e6i	0.775511	+	2.31749i
$393$	2.57424e6	−	1.90911e6i	0.840752	−	0.623518i
$394$	−711544.	−	1.23243e6i	−0.230920	−	0.399965i
$395$	−1.58384e6	+	2.74329e6i	−0.510762	+	0.884666i
$396$	6.01675e6	−	5.63485e6i	1.92807	−	1.80570i
$397$	1.49251e6	−	861698.i	0.475269	−	0.274397i	−0.243174	−	0.969983i	$-0.578189\pi$
$397$	1.49251e6	−	861698.i	0.475269	−	0.274397i	0.718443	+	0.695586i	$0.244855\pi$
$398$	9.25529e6			2.92875
$399$	−1.92524e6	+	1.98062e6i	−0.605413	+	0.622829i
$400$	−4.61202e6			−1.44126
$401$	4.90198e6	−	2.83016e6i	1.52234	−	0.878922i	0.522686	−	0.852525i	$-0.324930\pi$
$401$	4.90198e6	−	2.83016e6i	1.52234	−	0.878922i	0.999652	−	0.0263964i	$-0.00840320\pi$
$402$	−2.17891e6	+	250620.i	−0.672471	+	0.0773481i
$403$	1.95054e6	−	3.37844e6i	0.598263	−	1.03622i
$404$	−3.36560e6	−	5.82940e6i	−1.02591	−	1.77693i
$405$	−1.55831e6	−	1.04141e6i	−0.472081	−	0.315489i
$406$	−1.66509e6	+	1.36049e6i	−0.501330	+	0.409619i
$407$		−	884786.i		−	0.264760i
$408$	−1.47616e6	+	3.40491e6i	−0.439020	+	1.01264i
$409$	1.94296e6	+	1.12177e6i	0.574322	+	0.331585i	0.758874	−	0.651238i	$-0.225750\pi$
$409$	1.94296e6	+	1.12177e6i	0.574322	+	0.331585i	−0.184551	+	0.982823i	$0.559083\pi$
$410$	−511482.	−	295304.i	−0.150269	−	0.0867581i
$411$	−2.54516e6	+	5.87065e6i	−0.743207	+	1.71428i
$412$		−	1.17192e7i		−	3.40137i
$413$	−2.05113e6	−	777064.i	−0.591724	−	0.224172i
$414$	−2.36078e6	+	7.78133e6i	−0.676947	+	2.23128i
$415$	1.26261e6	+	2.18690e6i	0.359873	+	0.623317i
$416$	2.30459e6	−	3.99166e6i	0.652920	−	1.13089i
$417$	1.14407e6	−	131591.i	0.322189	−	0.0370584i
$418$	−5.54740e6	+	3.20279e6i	−1.55292	+	0.896579i
$419$	−6.62738e6			−1.84419			−0.922097	−	0.386959i	$-0.873526\pi$
$419$	−6.62738e6			−1.84419			−0.922097	+	0.386959i	$0.873526\pi$
$420$	4.61684e6	−	1.30751e6i	1.27709	−	0.361678i
$421$	−633684.			−0.174248			−0.0871240	−	0.996197i	$-0.527768\pi$
$421$	−633684.			−0.174248			−0.0871240	+	0.996197i	$0.527768\pi$
$422$	−3.51320e6	+	2.02835e6i	−0.960332	+	0.554448i
$423$	−1.01162e6	−	1.08018e6i	−0.274895	−	0.293526i
$424$	3.13598e6	−	5.43167e6i	0.847146	−	1.46730i
$425$	569783.	+	986893.i	0.153016	+	0.265032i
$426$	−4.05519e6	+	3.00741e6i	−1.08265	+	0.802914i
$427$	−2.43775e6	−	2.98355e6i	−0.647022	−	0.791887i
$428$			1.04059e7i			2.74581i
$429$	3.57882e6	+	1.55156e6i	0.938852	+	0.407029i
$430$	−2.23924e6	−	1.29283e6i	−0.584023	−	0.337186i
$431$	−3.23887e6	−	1.86996e6i	−0.839848	−	0.484886i	0.0173649	−	0.999849i	$-0.494472\pi$
$431$	−3.23887e6	−	1.86996e6i	−0.839848	−	0.484886i	−0.857212	+	0.514963i	$0.827806\pi$
$432$	−5.33800e6	+	6.29082e6i	−1.37616	+	1.62180i
$433$			3.36951e6i			0.863668i	0.901953	+	0.431834i	$0.142133\pi$
$433$			3.36951e6i			0.863668i	−0.901953	+	0.431834i	$0.857867\pi$
$434$	−1.52277e6	−	9.34909e6i	−0.388069	−	2.38257i
$435$	473021.	+	637821.i	0.119855	+	0.161613i
$436$	906129.	+	1.56946e6i	0.228283	+	0.395398i
$437$	2.21278e6	−	3.83265e6i	0.554288	−	0.960055i
$438$	180797.	+	1.57187e6i	0.0450304	+	0.391499i
$439$	1.11009e6	−	640910.i	0.274914	−	0.158722i	−0.356205	−	0.934408i	$-0.615929\pi$
$439$	1.11009e6	−	640910.i	0.274914	−	0.158722i	0.631119	+	0.775686i	$0.282596\pi$
$440$	6.36760e6			1.56799
$441$	3.47761e6	−	2.14151e6i	0.851500	−	0.524354i
$442$	−3.06887e6			−0.747177
$443$	−3.67325e6	+	2.12075e6i	−0.889284	+	0.513428i	−0.873708	−	0.486450i	$-0.838292\pi$
$443$	−3.67325e6	+	2.12075e6i	−0.889284	+	0.513428i	−0.0155759	+	0.999879i	$0.504958\pi$
$444$	259972.	+	2.26022e6i	0.0625850	+	0.544119i
$445$	−15136.2	+	26216.6i	−0.00362340	+	0.00627591i
$446$	−5.24261e6	−	9.08047e6i	−1.24799	−	2.16158i
$447$	538318.	+	725868.i	0.127430	+	0.171826i
$448$	−346597.	−	2.12795e6i	−0.0815886	−	0.500917i
$449$			5.30045e6i			1.24079i	0.784291	+	0.620393i	$0.213027\pi$
$449$			5.30045e6i			1.24079i	−0.784291	+	0.620393i	$0.786973\pi$
$450$	1.20733e6	+	5.17890e6i	0.281058	+	1.20561i
$451$	−707103.	−	408246.i	−0.163697	−	0.0945106i
$452$	2.47671e6	+	1.42993e6i	0.570203	+	0.329207i
$453$	2.46620e6	+	1.06919e6i	0.564654	+	0.244800i
$454$		−	3.23857e6i		−	0.737419i
$455$	1.43663e6	+	1.75829e6i	0.325325	+	0.398163i
$456$	7.57050e6	−	5.61443e6i	1.70495	−	1.26443i
$457$	3.50362e6	+	6.06844e6i	0.784741	+	1.35921i	0.929154	+	0.369693i	$0.120537\pi$
$457$	3.50362e6	+	6.06844e6i	0.784741	+	1.35921i	−0.144413	+	0.989517i	$0.546130\pi$
$458$	2.32914e6	−	4.03418e6i	0.518838	−	0.898653i
$459$	2.00560e6	+	365054.i	0.444337	+	0.0808771i
$460$	−6.65813e6	+	3.84407e6i	−1.46709	+	0.847027i
$461$	640032.			0.140265			0.0701325	−	0.997538i	$-0.477658\pi$
$461$	640032.			0.140265			0.0701325	+	0.997538i	$0.477658\pi$
$462$	9.11292e6	−	2.58082e6i	1.98634	−	0.562540i
$463$	3.47378e6			0.753096			0.376548	−	0.926397i	$-0.377111\pi$
$463$	3.47378e6			0.753096			0.376548	+	0.926397i	$0.377111\pi$
$464$	3.02718e6	−	1.74774e6i	0.652744	−	0.376862i
$465$	−3.47522e6	+	399722.i	−0.745332	+	0.0857285i
$466$	−694791.	+	1.20341e6i	−0.148214	+	0.256714i
$467$	617824.	+	1.07010e6i	0.131091	+	0.227056i	0.924097	−	0.382157i	$-0.124819\pi$
$467$	617824.	+	1.07010e6i	0.131091	+	0.227056i	−0.793006	+	0.609213i	$0.791485\pi$
$468$	−9.59815e6	−	2.91198e6i	−2.02569	−	0.614574i
$469$	−1.65050e6	−	625286.i	−0.346485	−	0.131264i
$470$		−	1.99778e6i		−	0.417160i
$471$	1.48371e6	−	3.42232e6i	0.308175	−	0.710835i
$472$	6.48176e6	+	3.74225e6i	1.33918	+	0.773174i
$473$	−3.09566e6	−	1.78728e6i	−0.636210	−	0.367316i
$474$	6.39514e6	−	1.47510e7i	1.30739	−	3.01561i
$475$		−	2.89417e6i		−	0.588559i
$476$	−4.04150e6	+	3.30217e6i	−0.817571	+	0.668008i
$477$	−3.29684e6	−	1.00023e6i	−0.663441	−	0.201281i
$478$	−6.52987e6	−	1.13101e7i	−1.30718	−	2.26410i
$479$	−782406.	+	1.35517e6i	−0.155809	+	0.269870i	−0.933353	−	0.358959i	$-0.883132\pi$
$479$	−782406.	+	1.35517e6i	−0.155809	+	0.269870i	0.777544	+	0.628828i	$0.216465\pi$
$480$	−4.10601e6	+	472276.i	−0.813424	+	0.0935606i
$481$	−932337.	+	538285.i	−0.183743	+	0.106084i
$482$	5.02870e6			0.985911
$483$	−4.56100e6	+	4.69220e6i	−0.889594	+	0.915185i
$484$	3.33639e6			0.647387
$485$	3.17635e6	−	1.83387e6i	0.613160	−	0.354008i
$486$	8.46142e6	+	4.34731e6i	1.62500	+	0.834890i
$487$	1.44990e6	−	2.51130e6i	0.277023	−	0.479817i	−0.693621	−	0.720340i	$-0.743986\pi$
$487$	1.44990e6	−	2.51130e6i	0.277023	−	0.479817i	0.970643	+	0.240523i	$0.0773189\pi$
$488$	6.57345e6	+	1.13856e7i	1.24952	+	2.16424i
$489$	1.85784e6	−	1.37781e6i	0.351346	−	0.260565i
$490$	5.40257e6	+	1.09897e6i	1.01651	+	0.206773i
$491$		−	4.46273e6i		−	0.835405i	−0.908584	−	0.417702i	$-0.862835\pi$
$491$		−	4.46273e6i		−	0.835405i	0.908584	−	0.417702i	$-0.137165\pi$
$492$	1.92628e6	+	835118.i	0.358762	+	0.155537i
$493$	−747973.	−	431842.i	−0.138602	−	0.0800217i
$494$	6.74985e6	+	3.89703e6i	1.24445	+	0.718482i
$495$	−794126.	−	3.40643e6i	−0.145672	−	0.624866i
$496$			1.53985e7i			2.81044i
$497$	−4.00994e6	+	653133.i	−0.728194	+	0.118607i
$498$	−7.63475e6	−	1.02947e7i	−1.37950	−	1.86012i
$499$	−1.33414e6	−	2.31080e6i	−0.239855	−	0.415442i	0.720817	−	0.693125i	$-0.243767\pi$
$499$	−1.33414e6	−	2.31080e6i	−0.239855	−	0.415442i	−0.960673	+	0.277683i	$0.910433\pi$
$500$	−6.22385e6	+	1.07800e7i	−1.11336	+	1.92839i
$501$	979565.	+	8.51643e6i	0.174357	+	1.51587i
$502$	4.06018e6	−	2.34415e6i	0.719095	−	0.415170i
$503$	6.90952e6			1.21767			0.608833	−	0.793299i	$-0.291638\pi$
$503$	6.90952e6			1.21767			0.608833	+	0.793299i	$0.291638\pi$
$504$	−1.28870e7	+	5.30474e6i	−2.25983	+	0.930224i
$505$	−2.85615e6			−0.498370
$506$	−1.31421e7	+	7.58761e6i	−2.28186	+	1.31743i
$507$	119032.	+	1.03488e6i	0.0205657	+	0.178800i
$508$	−2.45550e6	+	4.25304e6i	−0.422163	+	0.731207i
$509$	2.28095e6	+	3.95071e6i	0.390230	+	0.675898i	0.992480	−	0.122410i	$-0.0390622\pi$
$509$	2.28095e6	+	3.95071e6i	0.390230	+	0.675898i	−0.602250	+	0.798308i	$0.705729\pi$
$510$	1.63925e6	+	2.21036e6i	0.279074	+	0.376304i
$511$	−451082.	+	1.19067e6i	−0.0764193	+	0.201716i
$512$		−	1.26387e7i		−	2.13073i
$513$	−3.94766e6	−	3.34974e6i	−0.662287	−	0.561976i
$514$	−1.77520e7	−	1.02491e7i	−2.96374	−	1.71112i
$515$	−4.30641e6	−	2.48631e6i	−0.715480	−	0.413083i
$516$	8.43315e6	+	3.65610e6i	1.39433	+	0.604497i
$517$		−	2.76185e6i		−	0.454437i
$518$	−926088.	+	2.44450e6i	−0.151645	+	0.400281i
$519$	3.96004e6	−	2.93684e6i	0.645329	−	0.478589i
$520$	−3.87391e6	−	6.70982e6i	−0.628263	−	1.08818i
$521$	−266267.	+	461188.i	−0.0429758	+	0.0744362i	−0.886713	−	0.462320i	$-0.847017\pi$
$521$	−266267.	+	461188.i	−0.0429758	+	0.0744362i	0.843737	+	0.536756i	$0.180350\pi$
$522$	−2.75501e6	−	2.94173e6i	−0.442535	−	0.472527i
$523$	1.14831e6	−	662979.i	0.183572	−	0.105985i	−0.405398	−	0.914140i	$-0.632867\pi$
$523$	1.14831e6	−	662979.i	0.183572	−	0.105985i	0.588970	+	0.808155i	$0.299534\pi$
$524$	−1.53795e7			−2.44689
$525$	−1.04885e6	+	4.14880e6i	−0.166080	+	0.656938i
$526$	8.08433e6			1.27403
$527$	3.29501e6	−	1.90238e6i	0.516810	−	0.298380i
$528$	−1.52961e7	+	1.75936e6i	−2.38778	+	0.274645i
$529$	2.02404e6	−	3.50574e6i	0.314471	−	0.544679i
$530$	−2.32540e6	−	4.02770e6i	−0.359590	−	0.622827i
$531$	1.19360e6	−	3.93421e6i	0.183706	−	0.605510i
$532$	1.30824e7	−	2.13084e6i	2.00405	−	0.326416i
$533$			993473.i			0.151474i
$534$	61116.0	−	140970.i	0.00927474	−	0.0213931i
$535$	3.82382e6	+	2.20769e6i	0.577582	+	0.333467i
$536$	5.21573e6	+	3.01130e6i	0.784157	+	0.452734i
$537$	−3.49468e6	+	8.06080e6i	−0.522963	+	1.20626i
$538$			1.73933e7i			2.59075i
$539$	7.46883e6	+	1.51928e6i	1.10734	+	0.225250i
$540$	3.02952e6	+	8.46854e6i	0.447085	+	1.24975i
$541$	5.64896e6	+	9.78429e6i	0.829804	+	1.43726i	0.898192	+	0.439604i	$0.144881\pi$
$541$	5.64896e6	+	9.78429e6i	0.829804	+	1.43726i	−0.0683877	+	0.997659i	$0.521785\pi$
$542$	4.20432e6	−	7.28209e6i	0.614748	−	1.06477i
$543$	−5.09925e6	+	586519.i	−0.742176	+	0.0853656i
$544$	3.89310e6	−	2.24768e6i	0.564025	−	0.325640i
$545$	768967.			0.110896
$546$	−8.26364e6	−	8.03256e6i	−1.18629	−	1.15311i
$547$	−1.17217e7			−1.67503			−0.837516	−	0.546413i	$-0.815993\pi$
$547$	−1.17217e7			−1.67503			−0.837516	+	0.546413i	$0.815993\pi$
$548$	2.65916e7	−	1.53527e7i	3.78262	−	2.18390i
$549$	5.27105e6	−	4.93649e6i	0.746391	−	0.699016i
$550$	−4.96203e6	+	8.59450e6i	−0.699444	+	1.21147i
$551$	1.09675e6	+	1.89964e6i	0.153897	+	0.266558i
$552$	1.79350e7	−	1.33009e7i	2.50526	−	1.85795i
$553$	1.00190e7	−	8.18614e6i	1.39319	−	1.13832i
$554$			3.88091e6i			0.537229i
$555$	885713.	+	383991.i	0.122056	+	0.0529163i
$556$	−4.78590e6	−	2.76314e6i	−0.656563	−	0.379067i
$557$	−4.74038e6	−	2.73686e6i	−0.647404	−	0.373779i	0.140057	−	0.990143i	$-0.455271\pi$
$557$	−4.74038e6	−	2.73686e6i	−0.647404	−	0.373779i	−0.787461	+	0.616365i	$0.788605\pi$
$558$	1.72912e7	−	4.03101e6i	2.35093	−	0.548061i
$559$			4.34938e6i			0.588705i
$560$	−8.38118e6	−	3.17517e6i	−1.12937	−	0.427856i
$561$	2.26620e6	+	3.05574e6i	0.304012	+	0.409929i
$562$	1.36563e6	+	2.36535e6i	0.182387	+	0.315903i
$563$	−7.22929e6	+	1.25215e7i	−0.961224	+	1.66489i	−0.241789	+	0.970329i	$0.577734\pi$
$563$	−7.22929e6	+	1.25215e7i	−0.961224	+	1.66489i	−0.719435	+	0.694560i	$0.755599\pi$
$564$	811501.	+	7.05526e6i	0.107421	+	0.933932i
$565$	1.05090e6	−	606740.i	0.138498	−	0.0799616i
$566$	−1.90700e7			−2.50213
$567$	4.44503e6	+	6.23251e6i	0.580653	+	0.814151i
$568$	1.38634e7			1.80301
$569$	−4.06800e6	+	2.34866e6i	−0.526745	+	0.304116i	−0.739690	−	0.672948i	$-0.765028\pi$
$569$	−4.06800e6	+	2.34866e6i	−0.526745	+	0.304116i	0.212945	+	0.977064i	$0.431695\pi$
$570$	−798612.	−	6.94321e6i	−0.102955	−	0.895103i
$571$	−2.53638e6	+	4.39313e6i	−0.325554	+	0.563876i	−0.981624	−	0.190824i	$-0.938884\pi$
$571$	−2.53638e6	+	4.39313e6i	−0.325554	+	0.563876i	0.656070	+	0.754700i	$0.272218\pi$
$572$	−9.35919e6	−	1.62106e7i	−1.19605	−	2.07161i
$573$	−7.47947e6	−	1.00853e7i	−0.951665	−	1.28323i
$574$	1.52629e6	+	1.86802e6i	0.193356	+	0.236647i
$575$		−	6.85645e6i		−	0.864828i
$576$	3.93564e6	−	917499.i	0.494265	−	0.115226i
$577$	6.53049e6	+	3.77038e6i	0.816594	+	0.471461i	0.849241	−	0.528006i	$-0.177060\pi$
$577$	6.53049e6	+	3.77038e6i	0.816594	+	0.471461i	−0.0326462	+	0.999467i	$0.510393\pi$
$578$	1.01157e7	+	5.84032e6i	1.25944	+	0.727138i
$579$	−9.09193e6	−	3.94171e6i	−1.12709	−	0.488639i
$580$		−	3.81059e6i		−	0.470351i
$581$	−1.65807e6	−	1.01798e7i	−0.203781	−	1.25112i
$582$	−1.49525e7	+	1.10890e7i	−1.82981	+	1.35702i
$583$	−3.21476e6	−	5.56813e6i	−0.391722	−	0.678482i
$584$	2.17236e6	−	3.76263e6i	0.263572	−	0.456520i
$585$	−3.10637e6	+	2.90921e6i	−0.375287	+	0.351467i
$586$	−1.76247e7	+	1.01756e7i	−2.12020	+	1.22410i
$587$	1.49725e7			1.79349			0.896743	−	0.442551i	$-0.145926\pi$
$587$	1.49725e7			1.79349			0.896743	+	0.442551i	$0.145926\pi$
$588$	−1.95259e7	−	1.68652e6i	−2.32899	−	0.201163i
$589$	−9.66297e6			−1.14768
$590$	4.80636e6	−	2.77496e6i	0.568443	−	0.328190i
$591$	2.13248e6	−	245279.i	0.251140	−	0.0288863i
$592$	2.12474e6	−	3.68016e6i	0.249173	−	0.431581i
$593$	1.51264e6	+	2.61996e6i	0.176644	+	0.305956i	0.940729	−	0.339160i	$-0.110143\pi$
$593$	1.51264e6	+	2.61996e6i	0.176644	+	0.305956i	−0.764085	+	0.645115i	$0.776809\pi$
$594$	5.97981e6	+	1.67156e7i	0.695379	+	1.94382i
$595$	356003.	+	2.18570e6i	0.0412251	+	0.253103i
$596$		−	4.33662e6i		−	0.500075i
$597$	−5.55297e6	+	1.28085e7i	−0.637661	+	1.47083i
$598$	1.59908e7	+	9.23228e6i	1.82859	+	1.05574i
$599$	−5.02690e6	−	2.90228e6i	−0.572444	−	0.330501i	0.185681	−	0.982610i	$-0.440551\pi$
$599$	−5.02690e6	−	2.90228e6i	−0.572444	−	0.330501i	−0.758125	+	0.652110i	$0.773884\pi$
$600$	5.80830e6	−	1.33974e7i	0.658675	−	1.51930i
$601$		−	8.90296e6i		−	1.00542i	−0.864455	−	0.502711i	$-0.832336\pi$
$601$		−	8.90296e6i		−	1.00542i	0.864455	−	0.502711i	$-0.167664\pi$
$602$	6.68202e6	+	8.17809e6i	0.751479	+	0.919731i
$603$	960464.	−	3.16577e6i	0.107569	−	0.354557i
$604$	−6.44949e6	−	1.11709e7i	−0.719339	−	1.24593i
$605$	707840.	−	1.22601e6i	0.0786224	−	0.136178i
$606$	1.44015e7	−	1.65647e6i	1.59304	−	0.183232i
$607$	−298211.	+	172172.i	−0.0328512	+	0.0189667i	−0.516336	−	0.856386i	$-0.672704\pi$
$607$	−298211.	+	172172.i	−0.0328512	+	0.0189667i	0.483484	+	0.875353i	$0.339371\pi$
$608$	−1.14169e7			−1.25254
$609$	−883769.	−	3.12060e6i	−0.0965596	−	0.340953i
$610$	9.74871e6			1.06077
$611$	−2.91028e6	+	1.68025e6i	−0.315378	+	0.182084i
$612$	−6.68695e6	−	7.14015e6i	−0.721688	−	0.770600i
$613$	20098.1	−	34811.0i	0.00216025	−	0.00374167i	−0.864943	−	0.501870i	$-0.832646\pi$
$613$	20098.1	−	34811.0i	0.00216025	−	0.00374167i	0.867104	+	0.498128i	$0.165979\pi$
$614$	1.23020e7	+	2.13077e7i	1.31691	+	2.28095i
$615$	715552.	−	530668.i	0.0762875	−	0.0565763i
$616$	−2.43209e7	−	9.21387e6i	−2.58243	−	0.978341i
$617$			4.04424e6i			0.427685i	0.976868	+	0.213843i	$0.0685980\pi$
$617$			4.04424e6i			0.427685i	−0.976868	+	0.213843i	$0.931402\pi$
$618$	2.31561e7	+	1.00391e7i	2.43890	+	1.05736i
$619$	6.65332e6	+	3.84130e6i	0.697930	+	0.402950i	0.806576	−	0.591131i	$-0.201318\pi$
$619$	6.65332e6	+	3.84130e6i	0.697930	+	0.402950i	−0.108646	+	0.994080i	$0.534652\pi$
$620$	1.45376e7	+	8.39331e6i	1.51885	+	0.876909i
$621$	−9.35223e6	−	7.93573e6i	−0.973164	−	0.825768i
$622$		−	3.48668e7i		−	3.61357i
$623$	95747.5	−	78231.8i	0.00988342	−	0.00807539i
$624$	1.11597e7	+	1.50478e7i	1.14734	+	1.54707i
$625$	−667753.	−	1.15658e6i	−0.0683779	−	0.118434i
$626$	−1.38828e7	+	2.40456e7i	−1.41592	+	2.45245i
$627$	−1.10405e6	−	9.59870e6i	−0.112155	−	0.975087i
$628$	−1.55017e7	+	8.94992e6i	−1.56849	+	0.905566i
$629$	−1.04999e6			−0.105817
$630$	−1.37142e6	+	1.02425e7i	−0.137664	+	1.02815i
$631$	1.42740e7			1.42716			0.713582	−	0.700572i	$-0.247072\pi$
$631$	1.42740e7			1.42716			0.713582	+	0.700572i	$0.247072\pi$
$632$	−3.82335e7	+	2.20741e7i	−3.80760	+	2.19832i
$633$	−699199.	−	6.07890e6i	−0.0693572	−	0.602998i
$634$	3.56851e6	−	6.18085e6i	0.352585	−	0.610696i
$635$	1.04190e6	+	1.80463e6i	0.102540	+	0.177604i
$636$	9.84831e6	+	1.32795e7i	0.965426	+	1.30178i
$637$	−2.94295e6	−	8.79453e6i	−0.287366	−	0.858744i
$638$		−	7.52152e6i		−	0.731566i
$639$	−1.72895e6	−	7.41639e6i	−0.167506	−	0.718523i
$640$	−2.62331e6	−	1.51457e6i	−0.253163	−	0.146163i
$641$	6.69847e6	+	3.86736e6i	0.643918	+	0.371766i	0.786122	−	0.618071i	$-0.212086\pi$
$641$	6.69847e6	+	3.86736e6i	0.643918	+	0.371766i	−0.142204	+	0.989837i	$0.545419\pi$
$642$	−2.05612e7	−	8.91407e6i	−1.96884	−	0.853569i
$643$			1.41911e7i			1.35360i	0.736168	+	0.676799i	$0.236633\pi$
$643$			1.41911e7i			1.35360i	−0.736168	+	0.676799i	$0.763367\pi$
$644$	3.09929e7	−	5.04808e6i	2.94475	−	0.479636i
$645$	3.13265e6	−	2.32324e6i	0.296492	−	0.219884i
$646$	3.80080e6	+	6.58317e6i	0.358338	+	0.620660i
$647$	339476.	−	587989.i	0.0318822	−	0.0552216i	−0.849644	−	0.527357i	$-0.823183\pi$
$647$	339476.	−	587989.i	0.0318822	−	0.0552216i	0.881526	+	0.472135i	$0.156517\pi$
$648$	−1.15515e7	−	2.34289e7i	−1.08069	−	2.19186i
$649$	6.64460e6	−	3.83626e6i	0.619237	−	0.357517i
$650$	1.20752e7			1.12101
$651$	1.38519e7	+	3.50189e6i	1.28102	+	0.323854i
$652$	−1.10994e7			−1.02254
$653$	−2.29785e6	+	1.32666e6i	−0.210881	+	0.121752i	−0.601721	−	0.798706i	$-0.705518\pi$
$653$	−2.29785e6	+	1.32666e6i	−0.210881	+	0.121752i	0.390840	+	0.920459i	$0.372185\pi$
$654$	−3.87734e6	+	445975.i	−0.354478	+	0.0407724i
$655$	−3.26287e6	+	5.65146e6i	−0.297165	+	0.514704i
$656$	−1.96074e6	−	3.39610e6i	−0.177893	−	0.308121i
$657$	−2.28379e6	−	692879.i	−0.206416	−	0.0626245i
$658$	−2.89077e6	+	7.63047e6i	−0.260285	+	0.687047i
$659$		−	1.07933e7i		−	0.968149i	−0.875027	−	0.484074i	$-0.839156\pi$
$659$		−	1.07933e7i		−	0.968149i	0.875027	−	0.484074i	$-0.160844\pi$
$660$	−6.67648e6	+	1.53999e7i	−0.596606	+	1.37613i
$661$	−1.78194e7	−	1.02881e7i	−1.58632	−	0.915861i	−0.993907	−	0.110225i	$-0.964843\pi$
$661$	−1.78194e7	−	1.02881e7i	−1.58632	−	0.915861i	−0.592411	−	0.805636i	$-0.701824\pi$
$662$	−2.89424e7	−	1.67099e7i	−2.56679	−	1.48194i
$663$	1.84126e6	−	4.24704e6i	0.162679	−	0.375234i
$664$			3.51942e7i			3.09778i
$665$	1.99251e6	−	5.25942e6i	0.174721	−	0.461194i
$666$	−4.68871e6	−	1.42251e6i	−0.409607	−	0.124271i
$667$	2.59828e6	+	4.50035e6i	0.226137	+	0.391680i
$668$	2.05688e7	−	3.56262e7i	1.78348	−	3.08908i
$669$	1.57120e7	−	1.80720e6i	1.35727	−	0.156114i
$670$	3.86758e6	−	2.23295e6i	0.332853	−	0.192173i
$671$	1.34772e7			1.15556
$672$	1.63662e7	+	4.13752e6i	1.39806	+	0.353441i
$673$	−1.73039e7			−1.47268			−0.736338	−	0.676614i	$-0.763447\pi$
$673$	−1.73039e7			−1.47268			−0.736338	+	0.676614i	$0.763447\pi$
$674$	−6.72297e6	+	3.88151e6i	−0.570048	+	0.329117i
$675$	−7.89149e6	−	1.43639e6i	−0.666653	−	0.121343i
$676$	2.49942e6	−	4.32913e6i	0.210365	−	0.364362i
$677$	1.07332e6	+	1.85904e6i	0.0900031	+	0.155890i	0.907512	−	0.420026i	$-0.137979\pi$
$677$	1.07332e6	+	1.85904e6i	0.0900031	+	0.155890i	−0.817509	+	0.575916i	$0.804646\pi$
$678$	−4.94706e6	+	3.66884e6i	−0.413307	+	0.306517i
$679$	−1.47856e7	+	2.40826e6i	−1.23073	+	0.200460i
$680$		−	7.55651e6i		−	0.626685i
$681$	4.48189e6	+	1.94307e6i	0.370334	+	0.160554i
$682$	2.86951e7	+	1.65671e7i	2.36236	+	1.36391i
$683$	2.25952e6	+	1.30453e6i	0.185338	+	0.107005i	0.589798	−	0.807551i	$-0.299207\pi$
$683$	2.25952e6	+	1.30453e6i	0.185338	+	0.107005i	−0.404460	+	0.914556i	$0.632541\pi$
$684$	5.64068e6	+	2.41959e7i	0.460990	+	1.97743i
$685$		−	1.30287e7i		−	1.06090i
$686$	−1.90448e7	−	1.20150e7i	−1.54513	−	0.974792i
$687$	4.18550e6	+	5.64373e6i	0.338342	+	0.456220i
$688$	−8.58401e6	−	1.48679e7i	−0.691384	−	1.19751i
$689$	−3.91159e6	+	6.77507e6i	−0.313910	+	0.543708i
$690$	−1.89196e6	−	1.64489e7i	−0.151283	−	1.31526i
$691$	7.26513e6	−	4.19452e6i	0.578826	−	0.334185i	−0.181841	−	0.983328i	$-0.558206\pi$
$691$	7.26513e6	−	4.19452e6i	0.578826	−	0.334185i	0.760667	+	0.649143i	$0.224872\pi$
$692$	−2.36588e7			−1.87814
$693$	−1.89594e6	+	1.41599e7i	−0.149965	+	1.12002i
$694$	2.19804e7			1.73236
$695$	−2.03073e6	+	1.17244e6i	−0.159474	+	0.0920722i
$696$	1.26462e6	+	1.09947e7i	0.0989545	+	0.860319i
$697$	−484471.	+	839128.i	−0.0377734	+	0.0654254i
$698$	9.68350e6	+	1.67723e7i	0.752305	+	1.30303i
$699$	−1.24855e6	−	1.68355e6i	−0.0966527	−	0.130327i
$700$	1.59022e7	−	1.29931e7i	1.22663	−	1.00223i
$701$			1.05701e6i			0.0812425i	0.999175	+	0.0406213i	$0.0129337\pi$
$701$			1.05701e6i			0.0812425i	−0.999175	+	0.0406213i	$0.987066\pi$
$702$	1.39760e7	−	1.64706e7i	1.07038	−	1.26144i
$703$	2.30940e6	+	1.33333e6i	0.176242	+	0.101754i
$704$	6.53128e6	+	3.77084e6i	0.496669	+	0.286752i
$705$	2.76474e6	+	1.19862e6i	0.209499	+	0.0908260i
$706$		−	3.30596e7i		−	2.49624i
$707$	1.09090e7	+	4.13283e6i	0.820798	+	0.310956i
$708$	−1.58467e7	+	1.17523e7i	−1.18811	+	0.881126i
$709$	−4.35611e6	−	7.54500e6i	−0.325449	−	0.563694i	0.656154	−	0.754627i	$-0.272182\pi$
$709$	−4.35611e6	−	7.54500e6i	−0.325449	−	0.563694i	−0.981603	+	0.190933i	$0.938849\pi$
$710$	5.14000e6	−	8.90273e6i	0.382663	−	0.662792i
$711$	1.65771e7	+	1.77006e7i	1.22980	+	1.31315i
$712$	−365383.	+	210954.i	−0.0270115	+	0.0155951i
$713$	−2.28921e7			−1.68641
$714$	−3.06270e6	−	1.08144e7i	−0.224832	−	0.793885i
$715$	−7.94248e6			−0.581020
$716$	3.65121e7	−	2.10803e7i	2.66167	−	1.53672i
$717$	1.95699e7	−	2.25094e6i	1.42164	−	0.163518i
$718$	1.27592e6	−	2.20996e6i	0.0923662	−	0.159983i
$719$	−1.17047e7	−	2.02731e7i	−0.844380	−	1.46251i	−0.886158	−	0.463383i	$-0.846635\pi$
$719$	−1.17047e7	−	2.02731e7i	−0.844380	−	1.46251i	0.0417778	−	0.999127i	$-0.486698\pi$
$720$	4.87719e6	−	1.60757e7i	0.350621	−	1.15568i
$721$	1.28506e7	+	1.57277e7i	0.920628	+	1.12675i
$722$			6.28377e6i			0.448618i
$723$	−3.01711e6	+	6.95925e6i	−0.214657	+	0.495127i
$724$	2.13314e7	+	1.23157e7i	1.51242	+	0.873196i
$725$	2.94307e6	+	1.69918e6i	0.207949	+	0.120059i
$726$	−2.85808e6	+	6.59242e6i	−0.201248	+	0.464198i
$727$			1.80153e7i			1.26417i	0.774899	+	0.632085i	$0.217801\pi$
$727$			1.80153e7i			1.26417i	−0.774899	+	0.632085i	$0.782199\pi$
$728$	5.08727e6	+	3.12335e7i	0.355759	+	2.18420i
$729$	−1.10929e7	+	9.10153e6i	−0.773086	+	0.634301i
$730$	−1.61085e6	−	2.79007e6i	−0.111879	−	0.193780i
$731$	−2.12099e6	+	3.67366e6i	−0.146806	+	0.254276i
$732$	−3.44281e7	+	3.95994e6i	−2.37484	+	0.273156i
$733$	6.08790e6	−	3.51485e6i	0.418512	−	0.241628i	−0.275929	−	0.961178i	$-0.588985\pi$
$733$	6.08790e6	−	3.51485e6i	0.418512	−	0.241628i	0.694440	+	0.719550i	$0.255652\pi$
$734$	−4.69511e6			−0.321667
$735$	−4.76229e6	+	6.81730e6i	−0.325160	+	0.465473i
$736$	−2.70474e7			−1.84048
$737$	5.34677e6	−	3.08696e6i	0.362596	−	0.209345i
$738$	−3.30024e6	+	3.09077e6i	−0.223051	+	0.208894i
$739$	−7.98435e6	+	1.38293e7i	−0.537810	+	0.931514i	0.461212	+	0.887290i	$0.347415\pi$
$739$	−7.98435e6	+	1.38293e7i	−0.537810	+	0.931514i	−0.999022	+	0.0442238i	$0.985919\pi$
$740$	−2.31628e6	−	4.01191e6i	−0.155493	−	0.269322i
$741$	−9.44289e6	+	7.00303e6i	−0.631770	+	0.468533i
$742$	3.05374e6	+	1.87485e7i	0.203621	+	1.25014i
$743$			2.50742e7i			1.66630i	0.553044	+	0.833152i	$0.313466\pi$
$743$			2.50742e7i			1.66630i	−0.553044	+	0.833152i	$0.686534\pi$
$744$	−4.47309e7	−	1.93926e7i	−2.96262	−	1.28441i
$745$	−1.59356e6	−	920044.i	−0.105191	−	0.0607321i
$746$	−2.10868e7	−	1.21745e7i	−1.38728	−	0.800947i
$747$	1.88276e7	−	4.38919e6i	1.23451	−	0.287795i
$748$		−	1.82562e7i		−	1.19304i
$749$	−1.14105e7	−	1.39653e7i	−0.743191	−	0.909587i
$750$	−1.59688e7	−	2.15324e7i	−1.03662	−	1.39778i
$751$	1.09454e6	+	1.89580e6i	0.0708159	+	0.122657i	0.899259	−	0.437416i	$-0.144106\pi$
$751$	1.09454e6	+	1.89580e6i	0.0708159	+	0.122657i	−0.828443	+	0.560073i	$0.810773\pi$
$752$	6.63235e6	−	1.14876e7i	0.427684	−	0.740770i
$753$	808061.	+	7.02535e6i	0.0519346	+	0.451524i
$754$	−7.92575e6	+	4.57593e6i	−0.507706	+	0.293124i
$755$	−5.47323e6			−0.349443
$756$	682719.	−	3.67291e7i	0.0434448	−	2.33725i
$757$	−1.44147e6			−0.0914251			−0.0457126	−	0.998955i	$-0.514556\pi$
$757$	−1.44147e6			−0.0914251			−0.0457126	+	0.998955i	$0.514556\pi$
$758$	1.24623e7	−	7.19510e6i	0.787815	−	0.454845i
$759$	−2.61556e6	−	2.27399e7i	−0.164801	−	1.43279i
$760$	−9.59568e6	+	1.66202e7i	−0.602618	+	1.04376i
$761$	682367.	+	1.18189e6i	0.0427126	+	0.0739805i	0.886591	−	0.462553i	$-0.153067\pi$
$761$	682367.	+	1.18189e6i	0.0427126	+	0.0739805i	−0.843879	+	0.536534i	$0.819733\pi$
$762$	−6.30018e6	−	8.49516e6i	−0.393066	−	0.530010i
$763$	−2.93705e6	−	1.11269e6i	−0.182642	−	0.0691931i
$764$			6.02536e7i			3.73465i
$765$	−4.04245e6	+	942399.i	−0.249742	+	0.0582212i
$766$	−4.07931e7	−	2.35519e7i	−2.51197	−	1.45029i
$767$	−8.08487e6	−	4.66780e6i	−0.496232	−	0.286500i
$768$	2.17171e7	+	9.41520e6i	1.32861	+	0.576005i
$769$			1.59541e7i			0.972875i	0.873715	+	0.486437i	$0.161704\pi$
$769$			1.59541e7i			0.972875i	−0.873715	+	0.486437i	$0.838296\pi$
$770$	−1.49342e7	+	1.22022e7i	−0.907725	+	0.741669i
$771$	2.48347e7	−	1.84179e7i	1.50461	−	1.11585i
$772$	2.37768e7	+	4.11827e7i	1.43586	+	2.48697i
$773$	−8.63763e6	+	1.49608e7i	−0.519931	+	0.900547i	0.479801	+	0.877378i	$0.340709\pi$
$773$	−8.63763e6	+	1.49608e7i	−0.519931	+	0.900547i	−0.999732	+	0.0231692i	$0.992624\pi$
$774$	−1.44483e7	+	1.35312e7i	−0.866890	+	0.811867i
$775$	−1.29650e7	+	7.48534e6i	−0.775386	+	0.447669i
$776$	5.11175e7			3.04730
$777$	−2.82733e6	−	2.74827e6i	−0.168005	−	0.163308i
$778$	1.72368e7			1.02096
$779$	2.13114e6	−	1.23042e6i	0.125826	−	0.0726454i
$780$	2.02894e7	−	2.33370e6i	1.19408	−	0.137344i
$781$	7.10583e6	−	1.23077e7i	0.416857	−	0.722018i
$782$	9.00431e6	+	1.55959e7i	0.526543	+	0.911998i
$783$	5.72403e6	−	2.04771e6i	0.333655	−	0.119361i
$784$	2.74173e7	+	2.42550e7i	1.59307	+	1.40933i
$785$			7.59516e6i			0.439909i
$786$	1.31747e7	−	3.03886e7i	0.760646	−	1.75450i
$787$	−5.46964e6	−	3.15790e6i	−0.314791	−	0.181744i	0.334278	−	0.942475i	$-0.391508\pi$
$787$	−5.46964e6	−	3.15790e6i	−0.314791	−	0.181744i	−0.649068	+	0.760730i	$0.724841\pi$
$788$	−8.92067e6	−	5.15035e6i	−0.511778	−	0.295475i
$789$	−4.85042e6	+	1.11880e7i	−0.277388	+	0.639821i
$790$			3.27369e7i			1.86625i
$791$	−4.89185e6	+	796778.i	−0.277992	+	0.0452789i
$792$	1.41529e7	−	4.66491e7i	0.801736	−	2.64259i
$793$	−8.19924e6	−	1.42015e7i	−0.463010	−	0.801957i
$794$	8.90535e6	−	1.54245e7i	0.501302	−	0.868281i
$795$	6.96915e6	−	801597.i	0.391077	−	0.0449819i
$796$	5.80170e7	−	3.34962e7i	3.24543	−	1.87375i
$797$	8.89295e6			0.495907			0.247953	−	0.968772i	$-0.420242\pi$
$797$	8.89295e6			0.495907			0.247953	+	0.968772i	$0.420242\pi$
$798$	−6.99649e6	+	2.76750e7i	−0.388931	+	1.53844i
$799$	−3.27752e6			−0.181626
$800$	−1.53183e7	+	8.84402e6i	−0.846224	+	0.488568i
$801$	158421.	+	169158.i	0.00872431	+	0.00931560i
$802$	2.92487e7	−	5.06603e7i	1.60572	−	2.78120i
$803$	−2.22693e6	−	3.85716e6i	−0.121876	−	0.211095i
$804$	−1.27515e7	+	9.45678e6i	−0.695700	+	0.515945i
$805$	4.72037e6	−	1.24599e7i	0.256736	−	0.677678i
$806$		−	4.03163e7i		−	2.18597i
$807$	−2.40707e7	−	1.04356e7i	−1.30108	−	0.564071i
$808$	−3.44733e7	−	1.99032e7i	−1.85761	−	1.07249i
$809$	239245.	+	138128.i	0.0128520	+	0.00742013i	0.506412	−	0.862291i	$-0.330971\pi$
$809$	239245.	+	138128.i	0.0128520	+	0.00742013i	−0.493560	+	0.869712i	$0.664305\pi$
$810$	−1.93283e7	−	1.26838e6i	−1.03510	−	0.0679262i
$811$			1.88633e7i			1.00708i	0.863971	+	0.503542i	$0.167970\pi$
$811$			1.88633e7i			1.00708i	−0.863971	+	0.503542i	$0.832030\pi$
$812$	−5.51390e6	+	1.45545e7i	−0.293473	+	0.774651i
$813$	7.55524e6	+	1.01875e7i	0.400887	+	0.540556i
$814$	−4.57198e6	−	7.91890e6i	−0.241848	−	0.418894i
$815$	−2.35482e6	+	4.07868e6i	−0.124184	+	0.215092i
$816$	2.08786e6	+	1.81520e7i	0.109768	+	0.954333i
$817$	9.33004e6	−	5.38670e6i	0.489022	−	0.282337i
$818$	2.31862e7			1.21156
$819$	1.60743e7	−	6.61674e6i	0.837381	−	0.344695i
$820$	−4.27499e6			−0.222024
$821$	6.00902e6	−	3.46931e6i	0.311133	−	0.179633i	−0.336300	−	0.941755i	$-0.609176\pi$
$821$	6.00902e6	−	3.46931e6i	0.311133	−	0.179633i	0.647433	+	0.762122i	$0.275842\pi$
$822$	7.55621e6	+	6.56944e7i	0.390054	+	3.39116i
$823$	1.49084e7	−	2.58220e7i	0.767238	−	1.32890i	−0.171817	−	0.985129i	$-0.554964\pi$
$823$	1.49084e7	−	2.58220e7i	0.767238	−	1.32890i	0.939055	−	0.343766i	$-0.111703\pi$
$824$	−3.46519e7	−	6.00189e7i	−1.77791	−	3.07943i
$825$	−8.91687e6	−	1.20235e7i	−0.456118	−	0.615030i
$826$	−2.23731e7	+	3.64410e6i	−1.14098	+	0.185841i
$827$		−	2.56391e7i		−	1.30358i	−0.758398	−	0.651792i	$-0.774018\pi$
$827$		−	2.56391e7i		−	1.30358i	0.758398	−	0.651792i	$-0.225982\pi$
$828$	1.33631e7	+	5.73215e7i	0.677379	+	2.90564i
$829$	3.53011e6	+	2.03811e6i	0.178403	+	0.103001i	0.586542	−	0.809919i	$-0.300489\pi$
$829$	3.53011e6	+	2.03811e6i	0.178403	+	0.103001i	−0.408139	+	0.912920i	$0.633822\pi$
$830$	2.26009e7	+	1.30486e7i	1.13875	+	0.657460i
$831$	−5.37083e6	−	2.32847e6i	−0.269798	−	0.116968i
$832$		−	9.17640e6i		−	0.459583i
$833$	1.80294e6	−	8.86336e6i	0.0900263	−	0.442574i
$834$	9.55950e6	−	7.08952e6i	0.475905	−	0.352941i
$835$	−8.72764e6	−	1.51167e7i	−0.433192	−	0.750311i
$836$	−2.31827e7	+	4.01536e7i	−1.14722	+	1.98705i
$837$	−4.79578e6	+	2.63479e7i	−0.236617	+	1.29997i
$838$	−5.93155e7	+	3.42458e7i	−2.91782	+	1.68460i
$839$	2.71420e7			1.33118			0.665591	−	0.746317i	$-0.268180\pi$
$839$	2.71420e7			1.33118			0.665591	+	0.746317i	$0.268180\pi$
$840$	1.97786e7	−	2.03476e7i	0.967160	−	0.994982i
$841$	1.79355e7			0.874427
$842$	−5.67152e6	+	3.27445e6i	−0.275689	+	0.159169i
$843$	−4.09277e6	+	470753.i	−0.198357	+	0.0228152i
$844$	−1.46817e7	+	2.54295e7i	−0.709448	+	1.22880i
$845$	−1.06054e6	−	1.83691e6i	−0.0510958	−	0.0885006i
$846$	−1.46357e7	−	4.44034e6i	−0.703054	−	0.213300i
$847$	−4.47761e6	+	3.65849e6i	−0.214456	+	0.175224i
$848$		−	3.08799e7i		−	1.47464i
$849$	1.14416e7	−	2.63912e7i	0.544776	−	1.25658i
$850$	1.01992e7	+	5.88851e6i	0.484193	+	0.279549i
$851$	5.47110e6	+	3.15874e6i	0.258971	+	0.149517i
$852$	−1.45359e7	+	3.35283e7i	−0.686028	+	1.58239i
$853$		−	2.48053e6i		−	0.116727i	−0.998295	−	0.0583637i	$-0.981412\pi$
$853$		−	2.48053e6i		−	0.116727i	0.998295	−	0.0583637i	$-0.0185883\pi$
$854$	−3.72350e7	−	1.41063e7i	−1.74705	−	0.661864i
$855$	1.00879e7	+	3.06057e6i	0.471939	+	0.143182i
$856$	3.07687e7	+	5.32930e7i	1.43524	+	2.48591i
$857$	1.85652e7	−	3.21559e7i	0.863471	−	1.49558i	−0.00508680	−	0.999987i	$-0.501619\pi$
$857$	1.85652e7	−	3.21559e7i	0.863471	−	1.49558i	0.868558	−	0.495588i	$-0.165047\pi$
$858$	4.00482e7	−	4.60637e6i	1.85722	−	0.213619i
$859$	3.60500e6	−	2.08135e6i	0.166695	−	0.0962414i	−0.414332	−	0.910126i	$-0.635985\pi$
$859$	3.60500e6	−	2.08135e6i	0.166695	−	0.0962414i	0.581027	+	0.813885i	$0.302651\pi$
$860$	−1.87157e7			−0.862898
$861$	−3.50091e6	+	991474.i	−0.160943	+	0.0455799i
$862$	−3.86508e7			−1.77170
$863$	−2.00534e7	+	1.15779e7i	−0.916562	+	0.529177i	−0.882537	−	0.470244i	$-0.844166\pi$
$863$	−2.00534e7	+	1.15779e7i	−0.916562	+	0.529177i	−0.0340252	+	0.999421i	$0.510833\pi$
$864$	−5.66628e6	+	3.11304e7i	−0.258234	+	1.41873i
$865$	−5.01939e6	+	8.69383e6i	−0.228092	+	0.395067i
$866$	1.74114e7	+	3.01573e7i	0.788929	+	1.36646i
$867$	−1.41517e7	+	1.04952e7i	−0.639382	+	0.474178i
$868$	−4.33811e7	−	5.30939e7i	−1.95435	−	2.39191i
$869$			4.52574e7i			2.03301i
$870$	7.52940e6	+	3.26429e6i	0.337258	+	0.146215i
$871$	−6.50572e6	−	3.75608e6i	−0.290570	−	0.167760i
$872$	9.28134e6	+	5.35858e6i	0.413351	+	0.238648i
$873$	−6.37505e6	−	2.73460e7i	−0.283105	−	1.21439i
$874$		−	4.57367e7i		−	2.02529i
$875$	−3.46802e6	−	2.12921e7i	−0.153130	−	0.940151i
$876$	6.82213e6	+	9.19896e6i	0.300372	+	0.405022i
$877$	3.50958e6	+	6.07877e6i	0.154084	+	0.266881i	0.932725	−	0.360589i	$-0.117424\pi$
$877$	3.50958e6	+	6.07877e6i	0.154084	+	0.266881i	−0.778641	+	0.627469i	$0.784091\pi$
$878$	6.62359e6	−	1.14724e7i	0.289973	−	0.502247i
$879$	−3.50768e6	−	3.04961e7i	−0.153125	−	1.33129i
$880$	2.71506e7	−	1.56754e7i	1.18188	−	0.682359i
$881$	−1.66384e7			−0.722224			−0.361112	−	0.932523i	$-0.617603\pi$
$881$	−1.66384e7			−0.722224			−0.361112	+	0.932523i	$0.617603\pi$
$882$	2.00590e7	−	3.71367e7i	0.868235	−	1.60743i
$883$	3.49413e7			1.50812			0.754062	−	0.656803i	$-0.228092\pi$
$883$	3.49413e7			1.50812			0.754062	+	0.656803i	$0.228092\pi$
$884$	−1.92373e7	+	1.11067e7i	−0.827969	+	0.478028i
$885$	956567.	+	8.31648e6i	0.0410541	+	0.356928i
$886$	−2.19172e7	+	3.79617e7i	−0.937996	+	1.62466i
$887$	207256.	+	358978.i	0.00884501	+	0.0153200i	0.870414	−	0.492320i	$-0.163851\pi$
$887$	207256.	+	358978.i	0.00884501	+	0.0153200i	−0.861569	+	0.507640i	$0.830518\pi$
$888$	8.01458e6	+	1.08069e7i	0.341074	+	0.459904i
$889$	−1.36824e6	−	8.40036e6i	−0.0580640	−	0.356487i
$890$			312854.i			0.0132394i
$891$	−2.67206e7	−	1.75349e6i	−1.12759	−	0.0739960i
$892$	−6.57269e7	−	3.79475e7i	−2.76587	−	1.59687i
$893$	7.20876e6	+	4.16198e6i	0.302504	+	0.174651i
$894$	8.56878e6	+	3.71490e6i	0.358571	+	0.155455i
$895$		−	1.78893e7i		−	0.746511i
$896$	7.82810e6	+	9.58077e6i	0.325751	+	0.398685i
$897$	−2.23707e7	+	1.65906e7i	−0.928323	+	0.688463i
$898$	2.73892e7	+	4.74394e7i	1.13341	+	1.96313i
$899$	5.67319e6	−	9.82625e6i	0.234114	−	0.405498i
$900$	2.63113e7	+	2.80946e7i	1.08277	+	1.15616i
$901$	−6.60777e6	+	3.81500e6i	−0.271171	+	0.156561i
$902$	−8.43816e6			−0.345328
$903$	−1.53268e7	+	4.34062e6i	−0.625507	+	0.177147i
$904$	1.69124e7			0.688309
$905$	9.05121e6	−	5.22572e6i	0.367354	−	0.212092i
$906$	2.75975e7	−	3.17428e6i	1.11699	−	0.128477i
$907$	−1.69139e6	+	2.92957e6i	−0.0682693	+	0.118246i	−0.898140	−	0.439711i	$-0.855081\pi$
$907$	−1.69139e6	+	2.92957e6i	−0.0682693	+	0.118246i	0.829870	+	0.557956i	$0.188414\pi$
$908$	−1.17208e7	−	2.03011e7i	−0.471785	−	0.817156i
$909$	−6.34818e6	+	2.09242e7i	−0.254824	+	0.839921i
$910$	2.19436e7	+	8.31324e6i	0.878424	+	0.332787i
$911$			2.26746e7i			0.905197i	0.891714	+	0.452598i	$0.149503\pi$
$911$			2.26746e7i			0.905197i	−0.891714	+	0.452598i	$0.850497\pi$
$912$	1.84583e7	−	4.25759e7i	0.734861	−	1.69503i
$913$	3.12448e7	+	1.80392e7i	1.24051	+	0.716210i
$914$	6.27152e7	+	3.62087e7i	2.48318	+	1.43366i
$915$	−5.84902e6	+	1.34913e7i	−0.230956	+	0.532723i
$916$		−	3.37179e7i		−	1.32777i
$917$	2.06401e7	−	1.68643e7i	0.810566	−	0.662284i
$918$	1.98366e7	−	7.09632e6i	0.776892	−	0.277924i
$919$	−6.25350e6	−	1.08314e7i	−0.244250	−	0.423053i	0.717670	−	0.696383i	$-0.245208\pi$
$919$	−6.25350e6	−	1.08314e7i	−0.244250	−	0.423053i	−0.961920	+	0.273329i	$0.911875\pi$
$920$	−2.27327e7	+	3.93742e7i	−0.885486	+	1.53371i
$921$	−3.68688e7	+	4.24067e6i	−1.43222	+	0.164735i
$922$	5.72833e6	−	3.30725e6i	0.221922	−	0.128127i
$923$	−1.72922e7			−0.668105
$924$	4.77843e7	−	4.91589e7i	1.84122	−	1.89418i
$925$	4.13141e6			0.158761
$926$	3.10906e7	−	1.79502e7i	1.19152	−	0.687925i
$927$	−2.77863e7	+	2.60227e7i	−1.06202	+	0.994609i
$928$	6.70294e6	−	1.16098e7i	0.255503	−	0.442544i
$929$	−2.72778e6	−	4.72466e6i	−0.103698	−	0.179610i	0.809507	−	0.587110i	$-0.199734\pi$
$929$	−2.72778e6	−	4.72466e6i	−0.103698	−	0.179610i	−0.913206	+	0.407499i	$0.866401\pi$
$930$	−2.90379e7	+	2.15351e7i	−1.10093	+	0.816469i
$931$	−1.52207e7	+	1.72051e7i	−0.575519	+	0.650552i
$932$			1.00582e7i			0.379297i
$933$	4.82525e7	+	2.09193e7i	1.81474	+	0.786763i
$934$	1.10591e7	+	6.38499e6i	0.414815	+	0.239493i
$935$	−6.70854e6	−	3.87318e6i	−0.250957	−	0.144890i
$936$	−5.77665e7	+	1.34668e7i	−2.15519	+	0.502431i
$937$			2.63266e6i			0.0979595i	0.998800	+	0.0489797i	$0.0155970\pi$
$937$			2.63266e6i			0.0979595i	−0.998800	+	0.0489797i	$0.984403\pi$
$938$	−1.80032e7	+	2.93233e6i	−0.668101	+	0.108819i
$939$	−2.49476e7	−	3.36393e7i	−0.923346	−	1.24504i
$940$	−7.23024e6	−	1.25231e7i	−0.266890	−	0.462268i
$941$	−6.62391e6	+	1.14730e7i	−0.243860	+	0.422378i	−0.961810	−	0.273716i	$-0.911747\pi$
$941$	−6.62391e6	+	1.14730e7i	−0.243860	+	0.422378i	0.717950	+	0.696094i	$0.245080\pi$
$942$	−4.40493e6	−	3.82969e7i	−0.161738	−	1.40616i
$943$	5.04880e6	−	2.91493e6i	0.184888	−	0.106745i
$944$	3.68499e7			1.34588
$945$	−1.33519e7	−	8.04322e6i	−0.486366	−	0.292988i
$946$	−3.69419e7			−1.34212
$947$	−5.21057e6	+	3.00832e6i	−0.188804	+	0.109006i	−0.591422	−	0.806362i	$-0.701433\pi$
$947$	−5.21057e6	+	3.00832e6i	−0.188804	+	0.109006i	0.402619	+	0.915368i	$0.368100\pi$
$948$	−1.32978e7	−	1.15612e8i	−0.480571	−	4.17813i
$949$	−2.70964e6	+	4.69323e6i	−0.0976665	+	0.169163i
$950$	−1.49551e7	−	2.59030e7i	−0.537626	−	0.931196i
$951$	6.41269e6	+	8.64687e6i	0.229926	+	0.310033i
$952$	−1.09342e7	+	2.88619e7i	−0.391017	+	1.03213i
$953$		−	2.63475e7i		−	0.939739i	−0.882736	−	0.469870i	$-0.844301\pi$
$953$		−	2.63475e7i		−	0.939739i	0.882736	−	0.469870i	$-0.155699\pi$
$954$	−3.46755e7	+	8.08374e6i	−1.23354	+	0.287569i
$955$	2.21412e7	+	1.27832e7i	0.785584	+	0.453557i
$956$	−8.18654e7	−	4.72650e7i	−2.89705	−	1.67261i
$957$	1.04091e7	+	4.51275e6i	0.367395	+	0.159280i
$958$			1.61718e7i			0.569304i
$959$	−1.88525e7	+	4.97629e7i	−0.661944	+	1.74727i
$960$	−6.60933e6	+	4.90161e6i	−0.231462	+	0.171657i
$961$	1.06773e7	+	1.84936e7i	0.372951	+	0.645970i
$962$	−5.56299e6	+	9.63538e6i	−0.193807	+	0.335684i
$963$	2.46725e7	−	2.31065e7i	0.857329	−	0.802912i
$964$	3.15225e7	−	1.81995e7i	1.09252	−	0.630765i
$965$	2.01777e7			0.697515
$966$	−1.65751e7	+	6.55637e7i	−0.571496	+	2.26058i
$967$	−1.11608e7			−0.383822			−0.191911	−	0.981412i	$-0.561468\pi$
$967$	−1.11608e7			−0.383822			−0.191911	+	0.981412i	$0.561468\pi$
$968$	1.70871e7	−	9.86522e6i	0.586110	−	0.338391i
$969$	−1.13909e7	+	1.31019e6i	−0.389716	+	0.0448254i
$970$	1.89524e7	−	3.28265e7i	0.646747	−	1.12020i
$971$	1.76368e7	+	3.05478e7i	0.600303	+	1.03976i	0.992775	+	0.119992i	$0.0382869\pi$
$971$	1.76368e7	+	3.05478e7i	0.600303	+	1.03976i	−0.392471	+	0.919764i	$0.628380\pi$
$972$	6.87741e7	−	3.37183e6i	2.33485	−	0.114472i
$973$	9.45282e6	−	1.53966e6i	0.320095	−	0.0521367i
$974$		−	2.99684e7i		−	1.01220i
$975$	−7.24485e6	+	1.67109e7i	−0.244072	+	0.562975i
$976$	5.60567e7	+	3.23644e7i	1.88366	+	1.08753i
$977$	2.54762e7	+	1.47087e7i	0.853884	+	0.492990i	0.861959	−	0.506978i	$-0.169237\pi$
$977$	2.54762e7	+	1.47087e7i	0.853884	+	0.492990i	−0.00807575	+	0.999967i	$0.502571\pi$
$978$	9.50818e6	−	2.19315e7i	0.317871	−	0.733199i
$979$			432508.i			0.0144224i
$980$	3.78435e7	−	1.26637e7i	1.25871	−	0.421208i
$981$	1.70913e6	−	5.63346e6i	0.0567027	−	0.186897i
$982$	−2.30604e7	−	3.99418e7i	−0.763111	−	1.32175i
$983$	−1.05382e7	+	1.82528e7i	−0.347844	+	0.602483i	−0.985866	−	0.167534i	$-0.946419\pi$
$983$	−1.05382e7	+	1.82528e7i	−0.347844	+	0.602483i	0.638022	+	0.770018i	$0.279753\pi$
$984$	1.23346e7	−	1.41873e6i	0.406104	−	0.0467104i
$985$	−3.78517e6	+	2.18537e6i	−0.124307	+	0.0717685i
$986$	−8.92588e6			−0.292387
$987$	−8.82546e6	−	8.57868e6i	−0.288366	−	0.280303i
$988$	5.64155e7			1.83868
$989$	2.21034e7	−	1.27614e7i	0.718569	−	0.414866i
$990$	−2.47096e7	−	2.63843e7i	−0.801269	−	0.855574i
$991$	−1.45076e7	+	2.51279e7i	−0.469257	+	0.812778i	−0.999382	−	0.0351419i	$-0.988812\pi$
$991$	−1.45076e7	+	2.51279e7i	−0.469257	+	0.812778i	0.530125	+	0.847920i	$0.322145\pi$
$992$	2.95282e7	+	5.11443e7i	0.952703	+	1.65013i
$993$	4.04898e7	−	3.00281e7i	1.30308	−	0.966394i
$994$	−3.25143e7	+	2.65663e7i	−1.04378	+	0.852834i
$995$		−	2.84258e7i		−	0.910238i
$996$	−8.51166e7	−	3.69014e7i	−2.71873	−	1.17868i
$997$	−3.54751e7	−	2.04816e7i	−1.13028	−	0.652568i	−0.186275	−	0.982498i	$-0.559641\pi$
$997$	−3.54751e7	−	2.04816e7i	−1.13028	−	0.652568i	−0.944005	+	0.329930i	$0.892975\pi$
$998$	−2.38813e7	−	1.37879e7i	−0.758981	−	0.438198i
$999$	4.78174e6	−	5.63527e6i	0.151591	−	0.178649i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.6.g.c.17.8	yes	16
3.2	odd	2	inner	21.6.g.c.17.1	yes	16
7.3	odd	6		147.6.c.c.146.15		16
7.4	even	3		147.6.c.c.146.16		16
7.5	odd	6	inner	21.6.g.c.5.1	✓	16
21.5	even	6	inner	21.6.g.c.5.8	yes	16
21.11	odd	6		147.6.c.c.146.1		16
21.17	even	6		147.6.c.c.146.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.g.c.5.1	✓	16	7.5	odd	6	inner
21.6.g.c.5.8	yes	16	21.5	even	6	inner
21.6.g.c.17.1	yes	16	3.2	odd	2	inner
21.6.g.c.17.8	yes	16	1.1	even	1	trivial
147.6.c.c.146.1		16	21.11	odd	6
147.6.c.c.146.2		16	21.17	even	6
147.6.c.c.146.15		16	7.3	odd	6
147.6.c.c.146.16		16	7.4	even	3

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	21.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(8.95007 - 5.16733i) q^{2} +(1.78125 + 15.4864i) q^{3} +(37.4025 - 64.7831i) q^{4} +(-15.8704 - 27.4884i) q^{5} +(95.9654 + 129.400i) q^{6} +(20.8412 + 127.956i) q^{7} -442.375i q^{8} +(-236.654 + 55.1702i) q^{9} +O(q^{10})\)	\(q+(8.95007 - 5.16733i) q^{2} +(1.78125 + 15.4864i) q^{3} +(37.4025 - 64.7831i) q^{4} +(-15.8704 - 27.4884i) q^{5} +(95.9654 + 129.400i) q^{6} +(20.8412 + 127.956i) q^{7} -442.375i q^{8} +(-236.654 + 55.1702i) q^{9} +(-284.083 - 164.015i) q^{10} +(-392.733 - 226.744i) q^{11} +(1069.88 + 463.834i) q^{12} +551.786i q^{13} +(847.719 + 1037.52i) q^{14} +(397.426 - 294.739i) q^{15} +(-1089.02 - 1886.23i) q^{16} +(-269.081 + 466.061i) q^{17} +(-1832.99 + 1716.65i) q^{18} +(1183.66 - 683.387i) q^{19} -2374.38 q^{20} +(-1944.44 + 550.676i) q^{21} -4686.65 q^{22} +(2804.16 - 1618.98i) q^{23} +(6850.78 - 787.981i) q^{24} +(1058.76 - 1833.82i) q^{25} +(2851.26 + 4938.53i) q^{26} +(-1275.93 - 3566.64i) q^{27} +(9068.87 + 3435.70i) q^{28} +1604.88i q^{29} +(2033.98 - 4691.56i) q^{30} +(-6122.73 - 3534.96i) q^{31} +(-7234.08 - 4176.60i) q^{32} +(2811.89 - 6485.89i) q^{33} +5561.71i q^{34} +(3186.53 - 2603.60i) q^{35} +(-5277.37 + 17394.7i) q^{36} +(975.532 + 1689.67i) q^{37} +(7062.56 - 12232.7i) q^{38} +(-8545.16 + 982.870i) q^{39} +(-12160.2 + 7020.68i) q^{40} +1800.47 q^{41} +(-14557.4 + 14976.2i) q^{42} +7882.36 q^{43} +(-29378.4 + 16961.6i) q^{44} +(5272.34 + 5629.67i) q^{45} +(16731.6 - 28980.0i) q^{46} +(3045.11 + 5274.29i) q^{47} +(27271.0 - 20224.7i) q^{48} +(-15938.3 + 5333.50i) q^{49} -21883.8i q^{50} +(-7696.89 - 3336.90i) q^{51} +(35746.4 + 20638.2i) q^{52} +(12278.4 + 7088.96i) q^{53} +(-29849.6 - 25328.6i) q^{54} +14394.1i q^{55} +(56604.4 - 9219.64i) q^{56} +(12691.6 + 17113.3i) q^{57} +(8292.95 + 14363.8i) q^{58} +(-8459.44 + 14652.2i) q^{59} +(-4229.36 - 36770.4i) q^{60} +(-25737.3 + 14859.5i) q^{61} -73065.1 q^{62} +(-11991.5 - 29131.4i) q^{63} -16630.3 q^{64} +(15167.7 - 8757.08i) q^{65} +(-8348.10 - 72579.1i) q^{66} +(-6807.13 + 11790.3i) q^{67} +(20128.6 + 34863.7i) q^{68} +(30067.1 + 40542.4i) q^{69} +(15066.0 - 39768.3i) q^{70} +31338.5i q^{71} +(24405.9 + 104690. i) q^{72} +(8505.52 + 4910.67i) q^{73} +(17462.2 + 10081.8i) q^{74} +(30285.2 + 13129.8i) q^{75} -102242. i q^{76} +(20828.2 - 54978.0i) q^{77} +(-71401.0 + 52952.4i) q^{78} +(-49899.1 - 86427.8i) q^{79} +(-34566.3 + 59870.6i) q^{80} +(52961.5 - 26112.5i) q^{81} +(16114.3 - 9303.61i) q^{82} -79557.4 q^{83} +(-37052.6 + 146564. i) q^{84} +17081.7 q^{85} +(70547.7 - 40730.7i) q^{86} +(-24853.8 + 2858.70i) q^{87} +(-100306. + 173735. i) q^{88} +(-476.867 - 825.958i) q^{89} +(76278.2 + 23142.0i) q^{90} +(-70604.2 + 11499.9i) q^{91} -242216. i q^{92} +(43837.5 - 101115. i) q^{93} +(54507.9 + 31470.2i) q^{94} +(-37570.4 - 21691.3i) q^{95} +(51794.6 - 119469. i) q^{96} +115552. i q^{97} +(-115089. + 130094. i) q^{98} +(105451. + 31992.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 18 q^{3} + 86 q^{4} - 616 q^{7} - 606 q^{9}+O(q^{10}) \) 16 * q + 18 * q^3 + 86 * q^4 - 616 * q^7 - 606 * q^9	\( 16 q + 18 q^{3} + 86 q^{4} - 616 q^{7} - 606 q^{9} - 546 q^{10} + 4128 q^{12} + 1188 q^{15} - 2858 q^{16} - 438 q^{18} + 3258 q^{19} + 882 q^{21} - 21900 q^{22} + 10374 q^{24} - 6578 q^{25} + 34006 q^{28} + 450 q^{30} - 9792 q^{31} + 17556 q^{33} - 15132 q^{36} - 10466 q^{37} - 17418 q^{39} - 60774 q^{40} - 56994 q^{42} + 111052 q^{43} - 31374 q^{45} + 81696 q^{46} - 51548 q^{49} + 31596 q^{51} + 126960 q^{52} + 7434 q^{54} - 31368 q^{57} - 41706 q^{58} + 60066 q^{60} - 128580 q^{61} - 123606 q^{63} - 158884 q^{64} - 160314 q^{66} - 102202 q^{67} + 234318 q^{70} + 330864 q^{72} + 345150 q^{73} + 428202 q^{75} - 277512 q^{78} - 251308 q^{79} + 179262 q^{81} - 534576 q^{82} + 106176 q^{84} + 205152 q^{85} - 551922 q^{87} - 359514 q^{88} + 65814 q^{91} + 17676 q^{93} + 276612 q^{94} + 1043910 q^{96} + 215472 q^{99}+O(q^{100}) \) 16 * q + 18 * q^3 + 86 * q^4 - 616 * q^7 - 606 * q^9 - 546 * q^10 + 4128 * q^12 + 1188 * q^15 - 2858 * q^16 - 438 * q^18 + 3258 * q^19 + 882 * q^21 - 21900 * q^22 + 10374 * q^24 - 6578 * q^25 + 34006 * q^28 + 450 * q^30 - 9792 * q^31 + 17556 * q^33 - 15132 * q^36 - 10466 * q^37 - 17418 * q^39 - 60774 * q^40 - 56994 * q^42 + 111052 * q^43 - 31374 * q^45 + 81696 * q^46 - 51548 * q^49 + 31596 * q^51 + 126960 * q^52 + 7434 * q^54 - 31368 * q^57 - 41706 * q^58 + 60066 * q^60 - 128580 * q^61 - 123606 * q^63 - 158884 * q^64 - 160314 * q^66 - 102202 * q^67 + 234318 * q^70 + 330864 * q^72 + 345150 * q^73 + 428202 * q^75 - 277512 * q^78 - 251308 * q^79 + 179262 * q^81 - 534576 * q^82 + 106176 * q^84 + 205152 * q^85 - 551922 * q^87 - 359514 * q^88 + 65814 * q^91 + 17676 * q^93 + 276612 * q^94 + 1043910 * q^96 + 215472 * q^99

Introduction

L-functions

Modular forms

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