LMFDB - Embedded newform 21.6.g.c.5.1

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			5.1
Root			$-8.95007 - 5.16733i$ of defining polynomial
Character	$\chi$	$=$	21.5
Dual form			21.6.g.c.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.95007 - 5.16733i) q^{2} +(14.3022 + 6.20057i) q^{3} +(37.4025 + 64.7831i) q^{4} +(15.8704 - 27.4884i) q^{5} +(-95.9654 - 129.400i) q^{6} +(20.8412 - 127.956i) q^{7} -442.375i q^{8} +(166.106 + 177.364i) q^{9} +O(q^{10})$	\(q+(-8.95007 - 5.16733i) q^{2} +(14.3022 + 6.20057i) 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} +(166.106 + 177.364i) q^{9} +(-284.083 + 164.015i) q^{10} +(392.733 - 226.744i) q^{11} +(133.247 + 1158.46i) 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} +(-570.164 - 2445.74i) q^{18} +(1183.66 + 683.387i) q^{19} +2374.38 q^{20} +(1091.47 - 1700.82i) q^{21} -4686.65 q^{22} +(-2804.16 - 1618.98i) q^{23} +(2742.98 - 6326.94i) 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} +(-5080.00 + 584.305i) q^{30} +(-6122.73 + 3534.96i) q^{31} +(7234.08 - 4176.60i) q^{32} +(7022.89 - 807.777i) 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} +(3421.39 - 7891.76i) q^{39} +(-12160.2 - 7020.68i) q^{40} -1800.47 q^{41} +(-18557.5 + 9582.46i) q^{42} +7882.36 q^{43} +(29378.4 + 16961.6i) q^{44} +(7511.61 - 1751.15i) 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} +(958.600 + 8334.15i) q^{51} +(35746.4 - 20638.2i) q^{52} +(-12278.4 + 7088.96i) q^{53} +(7010.37 - 38514.8i) 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} +(33958.8 + 14722.5i) q^{60} +(-25737.3 - 14859.5i) q^{61} +73065.1 q^{62} +(26156.5 - 17557.7i) q^{63} -16630.3 q^{64} +(-15167.7 - 8757.08i) q^{65} +(-67029.4 - 29059.9i) 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} +(78461.2 - 73481.1i) q^{72} +(8505.52 - 4910.67i) q^{73} +(-17462.2 + 10081.8i) q^{74} +(3771.83 + 32792.6i) 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} +(-3866.66 + 58922.3i) q^{81} +(16114.3 + 9303.61i) q^{82} +79557.4 q^{83} +(151008. + 7094.03i) q^{84} +17081.7 q^{85} +(-70547.7 - 40730.7i) q^{86} +(-9951.18 + 22953.3i) 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} +(-109487. + 12593.3i) q^{93} +(54507.9 - 31470.2i) q^{94} +(37570.4 - 21691.3i) q^{95} +(129361. - 14879.1i) 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 $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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	−0.994543	−	0.104326i	$-0.966731\pi$
$2$	−8.95007	−	5.16733i	−1.58216	−	0.913463i	−0.587621	−	0.809136i	$-0.699935\pi$
$3$	14.3022	+	6.20057i	0.917487	+	0.397767i
$3$	14.3022	+	6.20057i	0.917487	+	0.397767i
$4$	37.4025	+	64.7831i	1.16883	+	2.02447i
$5$	15.8704	−	27.4884i	0.283899	−	0.491727i	−0.688443	−	0.725291i	$-0.741705\pi$
$5$	15.8704	−	27.4884i	0.283899	−	0.491727i	0.972342	+	0.233564i	$0.0750387\pi$
$6$	−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
$9$	166.106	+	177.364i	0.683563	+	0.729891i
$10$	−284.083	+	164.015i	−0.898349	+	0.518662i
$11$	392.733	−	226.744i	0.978623	−	0.565008i	0.0767691	−	0.997049i	$-0.475540\pi$
$11$	392.733	−	226.744i	0.978623	−	0.565008i	0.901854	+	0.432040i	$0.142206\pi$
$12$	133.247	+	1158.46i	0.267118	+	2.32235i
$13$		−	551.786i		−	0.905550i	−0.891625	−	0.452775i	$-0.850434\pi$
$13$		−	551.786i		−	0.905550i	0.891625	−	0.452775i	$-0.149566\pi$
$14$	−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	$-0.0941610\pi$
$17$	269.081	+	466.061i	0.225819	+	0.391129i	−0.730746	+	0.682649i	$0.760828\pi$
$18$	−570.164	−	2445.74i	−0.414781	−	1.77922i
$19$	1183.66	+	683.387i	0.752217	+	0.434293i	0.826494	−	0.562945i	$-0.190332\pi$
$19$	1183.66	+	683.387i	0.752217	+	0.434293i	−0.0742773	+	0.997238i	$0.523665\pi$
$20$	2374.38			1.32732
$21$	1091.47	−	1700.82i	0.540088	−	0.841608i
$22$	−4686.65			−2.06446
$23$	−2804.16	−	1618.98i	−1.10531	−	0.638150i	−0.167698	−	0.985838i	$-0.553633\pi$
$23$	−2804.16	−	1618.98i	−1.10531	−	0.638150i	−0.937610	+	0.347689i	$0.886967\pi$
$24$	2742.98	−	6326.94i	0.972062	−	2.24215i
$25$	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	$0.943302\pi$
$30$	−5080.00	+	584.305i	−1.03053	+	0.118532i
$31$	−6122.73	+	3534.96i	−1.14430	+	0.660663i	−0.947492	−	0.319779i	$-0.896391\pi$
$31$	−6122.73	+	3534.96i	−1.14430	+	0.660663i	−0.196810	+	0.980442i	$0.563058\pi$
$32$	7234.08	−	4176.60i	1.24884	−	0.721021i
$33$	7022.89	−	807.777i	1.12262	−	0.129124i
$34$		−	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	−0.801488	−	0.598011i	$-0.795958\pi$
$37$	975.532	−	1689.67i	0.117149	−	0.202907i	0.918637	+	0.395104i	$0.129291\pi$
$38$	−7062.56	−	12232.7i	−0.793421	−	1.37424i
$39$	3421.39	−	7891.76i	0.360198	−	0.830830i
$40$	−12160.2	−	7020.68i	−1.20168	−	0.693792i
$41$	−1800.47			−0.167273			−0.0836365	−	0.996496i	$-0.526653\pi$
$41$	−1800.47			−0.167273			−0.0836365	+	0.996496i	$0.526653\pi$
$42$	−18557.5	+	9582.46i	−1.62329	+	0.838212i
$43$	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
$45$	7511.61	−	1751.15i	0.552970	−	0.128911i
$46$	16731.6	+	28980.0i	1.16585	+	2.01932i
$47$	−3045.11	+	5274.29i	−0.201075	+	0.348272i	−0.948875	−	0.315652i	$-0.897777\pi$
$47$	−3045.11	+	5274.29i	−0.201075	+	0.348272i	0.747800	+	0.663924i	$0.231110\pi$
$48$	−27271.0	+	20224.7i	−1.70843	+	1.26701i
$49$	−15938.3	−	5333.50i	−0.948312	−	0.317338i
$50$		−	21883.8i		−	1.23794i
$51$	958.600	+	8334.15i	0.0516074	+	0.448679i
$52$	35746.4	−	20638.2i	1.83326	−	1.05843i
$53$	−12278.4	+	7088.96i	−0.600417	+	0.346651i	−0.769206	−	0.639001i	$-0.779348\pi$
$53$	−12278.4	+	7088.96i	−0.600417	+	0.346651i	0.168788	+	0.985652i	$0.446015\pi$
$54$	7010.37	−	38514.8i	0.327157	−	1.79739i
$55$		−	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	$-0.0641986\pi$
$59$	8459.44	+	14652.2i	0.316382	+	0.547990i	−0.663348	+	0.748311i	$0.730865\pi$
$60$	33958.8	+	14722.5i	1.21779	+	0.527962i
$61$	−25737.3	−	14859.5i	−0.885603	−	0.511303i	−0.0131010	−	0.999914i	$-0.504170\pi$
$61$	−25737.3	−	14859.5i	−0.885603	−	0.511303i	−0.872502	+	0.488611i	$0.837504\pi$
$62$	73065.1			2.41396
$63$	26156.5	−	17557.7i	0.830288	−	0.557335i
$64$	−16630.3			−0.507518
$65$	−15167.7	−	8757.08i	−0.445284	−	0.257085i
$66$	−67029.4	−	29059.9i	−1.89411	−	0.821172i
$67$	−6807.13	−	11790.3i	−0.185258	−	0.320876i	0.758405	−	0.651783i	$-0.225979\pi$
$67$	−6807.13	−	11790.3i	−0.185258	−	0.320876i	−0.943663	+	0.330907i	$0.892645\pi$
$68$	−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	$0.879736\pi$
$72$	78461.2	−	73481.1i	1.78371	−	1.67049i
$73$	8505.52	−	4910.67i	0.186807	−	0.107853i	−0.403680	−	0.914900i	$-0.632269\pi$
$73$	8505.52	−	4910.67i	0.186807	−	0.107853i	0.590487	+	0.807047i	$0.298936\pi$
$74$	−17462.2	+	10081.8i	−0.370697	+	0.214022i
$75$	3771.83	+	32792.6i	0.0774282	+	0.673168i
$76$			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	−0.0714791	+	0.997442i	$0.522772\pi$
$79$	−49899.1	+	86427.8i	−0.899550	+	1.55807i	−0.828071	+	0.560624i	$0.810561\pi$
$80$	34566.3	+	59870.6i	0.603848	+	1.04590i
$81$	−3866.66	+	58922.3i	−0.0654822	+	0.997854i
$82$	16114.3	+	9303.61i	0.264653	+	0.152798i
$83$	79557.4			1.26761			0.633804	−	0.773493i	$-0.281492\pi$
$83$	79557.4			1.26761			0.633804	+	0.773493i	$0.281492\pi$
$84$	151008.	+	7094.03i	2.33508	+	0.109697i
$85$	17081.7			0.256439
$86$	−70547.7	−	40730.7i	−1.02858	−	0.593849i
$87$	−9951.18	+	22953.3i	−0.140954	+	0.325123i
$88$	−100306.	−	173735.i	−1.38077	−	2.39156i
$89$	476.867	−	825.958i	0.00638150	−	0.0110531i	−0.862817	−	0.505516i	$-0.831302\pi$
$89$	476.867	−	825.958i	0.00638150	−	0.0110531i	0.869199	+	0.494463i	$0.164635\pi$
$90$	−76278.2	−	23142.0i	−0.992645	−	0.301159i
$91$	−70604.2	−	11499.9i	−0.893772	−	0.145576i
$92$		−	242216.i		−	2.98355i
$93$	−109487.	+	12593.3i	−1.31267	+	0.150984i
$94$	54507.9	−	31470.2i	0.636268	−	0.367349i
$95$	37570.4	−	21691.3i	0.427107	−	0.246590i
$96$	129361.	−	14879.1i	1.43260	−	0.164778i
$97$		−	115552.i		−	1.24695i	−0.781842	−	0.623476i	$-0.785720\pi$
$97$		−	115552.i		−	1.24695i	0.781842	−	0.623476i	$-0.214280\pi$
$98$	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	$-0.311285\pi$
$101$	−44991.7	−	77927.9i	−0.438863	−	0.760133i	−0.997602	+	0.0692107i	$0.977952\pi$
$102$	34485.7	−	79544.6i	0.328200	−	0.757026i
$103$	135674.	+	78331.5i	1.26010	+	0.727517i	0.973093	−	0.230412i	$-0.0740074\pi$
$103$	135674.	+	78331.5i	1.26010	+	0.727517i	0.287004	+	0.957929i	$0.407341\pi$
$104$	−244096.			−2.21298
$105$	−29430.6	−	56995.6i	−0.260511	−	0.504508i
$106$	146524.			1.26661
$107$	120470.	+	69553.5i	1.01723	+	0.587299i	0.913301	−	0.407286i	$-0.133525\pi$
$107$	120470.	+	69553.5i	1.01723	+	0.587299i	0.103931	+	0.994585i	$0.466858\pi$
$108$	−183335.	+	216060.i	−1.51247	+	1.78244i
$109$	−12113.2	−	20980.7i	−0.0976547	−	0.169143i	0.813059	−	0.582182i	$-0.197801\pi$
$109$	−12113.2	−	20980.7i	−0.0976547	−	0.169143i	−0.910713	+	0.413039i	$0.864467\pi$
$110$	−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	$0.955024\pi$
$114$	−25160.4	−	218747.i	−0.181324	−	1.57645i
$115$	−89006.4	+	51387.9i	−0.627591	+	0.362340i
$116$	−103969.	+	60026.6i	−0.717397	+	0.414189i
$117$	97866.8	−	91654.9i	0.660953	−	0.619001i
$118$		−	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
$123$	−25750.7	−	11163.9i	−0.153471	−	0.0665356i
$124$	−458011.	−	264433.i	−2.67499	−	1.54440i
$125$	166402.			0.952541
$126$	−324829.	+	21983.5i	−1.82276	+	0.123359i
$127$	−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
$129$	112735.	+	48875.1i	0.596465	+	0.258591i
$130$	90501.4	+	156753.i	0.469674	+	0.813500i
$131$	102797.	−	178050.i	0.523364	−	0.906492i	−0.476267	−	0.879301i	$-0.658010\pi$
$131$	102797.	−	178050.i	0.523364	−	0.906492i	0.999630	−	0.0271915i	$-0.00865638\pi$
$132$	315004.	+	424751.i	1.57355	+	2.12178i
$133$	112112.	−	137213.i	0.549571	−	0.672616i
$134$			140699.i			0.676905i
$135$	118291.	+	21531.0i	0.558619	+	0.101679i
$136$	206174.	−	119035.i	0.955842	−	0.551856i
$137$	−355479.	+	205236.i	−1.61813	+	0.934225i	−0.630721	+	0.776010i	$0.717241\pi$
$137$	−355479.	+	205236.i	−1.61813	+	0.934225i	−0.987405	+	0.158216i	$0.949426\pi$
$138$	59606.4	+	518224.i	0.266438	+	2.31643i
$139$			73875.8i			0.324314i	0.986765	+	0.162157i	$0.0518450\pi$
$139$			73875.8i			0.324314i	−0.986765	+	0.162157i	$0.948155\pi$
$140$	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
$144$	−515440.	+	120162.i	−2.07144	+	0.482905i
$145$	44115.6	+	25470.1i	0.174250	+	0.100603i
$146$	−101500.			−0.394080
$147$	−194882.	−	175107.i	−0.743837	−	0.668361i
$148$	145949.			0.547707
$149$	−50205.5	−	28986.1i	−0.185262	−	0.106961i	0.404501	−	0.914538i	$-0.367445\pi$
$149$	−50205.5	−	28986.1i	−0.185262	−	0.106961i	−0.589762	+	0.807577i	$0.700779\pi$
$150$	135692.	−	312987.i	0.492410	−	1.13579i
$151$	86217.4	+	149333.i	0.307718	+	0.532983i	0.977863	−	0.209247i	$-0.0671014\pi$
$151$	86217.4	+	149333.i	0.307718	+	0.532983i	−0.670145	+	0.742230i	$0.733768\pi$
$152$	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
$156$	639221.	−	73523.6i	2.10300	−	0.241888i
$157$	−207228.	+	119643.i	−0.670965	+	0.387382i	−0.796442	−	0.604715i	$-0.793287\pi$
$157$	−207228.	+	119643.i	−0.670965	+	0.387382i	0.125477	+	0.992097i	$0.459954\pi$
$158$	893201.	−	515690.i	2.84647	−	1.64341i
$159$	−219564.	+	25254.4i	−0.688761	+	0.0792218i
$160$		−	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	−0.954414	−	0.298485i	$-0.903519\pi$
$163$	−74189.1	+	128499.i	−0.218711	+	0.378819i	0.735703	+	0.677304i	$0.236852\pi$
$164$	−67342.0	−	116640.i	−0.195513	−	0.338639i
$165$	89251.7	−	205868.i	0.255215	−	0.588679i
$166$	−712044.	−	411099.i	−2.00556	−	1.15791i
$167$	−549931.			−1.52587			−0.762934	−	0.646476i	$-0.776242\pi$
$167$	−549931.			−1.52587			−0.762934	+	0.646476i	$0.776242\pi$
$168$	−752400.	−	482840.i	−2.05672	−	1.31987i
$169$	66825.0			0.179979
$170$	−152882.	−	88266.6i	−0.405728	−	0.234247i
$171$	75405.1	+	323453.i	0.197202	+	0.845903i
$172$	294820.	+	510643.i	0.759864	+	1.31612i
$173$	158136.	−	273900.i	0.401714	−	0.695789i	−0.592219	−	0.805777i	$-0.701748\pi$
$173$	158136.	−	273900.i	0.401714	−	0.695789i	0.993933	+	0.109988i	$0.0350813\pi$
$174$	207671.	−	154013.i	0.520000	−	0.385642i
$175$	256714.	−	97255.1i	0.633657	−	0.240058i
$176$			987713.i			2.40353i
$177$	30136.8	+	262012.i	0.0723042	+	0.628619i
$178$	−8535.99	+	4928.26i	−0.0201931	+	0.0116585i
$179$	−488097.	+	281803.i	−1.13861	+	0.657374i	−0.946085	−	0.323918i	$-0.895000\pi$
$179$	−488097.	+	281803.i	−1.13861	+	0.657374i	−0.192521	+	0.981293i	$0.561666\pi$
$180$	394398.	+	421128.i	0.907305	+	0.968796i
$181$		−	329274.i		−	0.747069i	−0.927616	−	0.373535i	$-0.878146\pi$
$181$		−	329274.i		−	0.747069i	0.927616	−	0.373535i	$-0.121854\pi$
$182$	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
$186$	1.04499e6	+	453045.i	2.21478	+	0.960194i
$187$	211354.	+	122025.i	0.441983	+	0.255179i
$188$	−455579.			−0.940090
$189$	482964.	−	88928.7i	0.983467	−	0.181087i
$190$	−448344.			−0.901004
$191$	697562.	+	402738.i	1.38356	+	0.798801i	0.992580	−	0.121596i	$-0.0388012\pi$
$191$	697562.	+	402738.i	1.38356	+	0.798801i	0.390985	+	0.920397i	$0.372135\pi$
$192$	−237851.	−	103118.i	−0.465641	−	0.201874i
$193$	−317851.	−	550534.i	−0.614228	−	1.06387i	−0.990519	−	0.137373i	$-0.956134\pi$
$193$	−317851.	−	550534.i	−0.614228	−	1.06387i	0.376291	−	0.926502i	$-0.377199\pi$
$194$	−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	$-0.0403417\pi$
$198$	−778480.	−	831241.i	−1.41119	−	1.50683i
$199$	775577.	−	447779.i	1.38833	−	0.801552i	0.395201	−	0.918595i	$-0.370675\pi$
$199$	775577.	−	447779.i	1.38833	−	0.801552i	0.993127	+	0.117043i	$0.0373416\pi$
$200$	811238.	−	468369.i	1.43408	−	0.827967i
$201$	−24250.4	−	210835.i	−0.0423379	−	0.368089i
$202$			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
$207$	−178639.	−	766279.i	−0.289768	−	1.24297i
$208$	1.04080e6	+	600904.i	1.66804	+	0.963045i
$209$	619817.			0.981516
$210$	−31108.3	+	662192.i	−0.0486775	+	1.03618i
$211$	−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
$213$	−194317.	+	448210.i	−0.293468	+	0.676912i
$214$	−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
$219$	152097.	−	17494.3i	0.214294	−	0.0246482i
$220$	932495.	−	538376.i	1.29894	−	0.749945i
$221$	257166.	−	148475.i	0.354187	−	0.204490i
$222$	−312260.	+	35916.4i	−0.425240	+	0.0489114i
$223$			1.01457e6i			1.36622i	0.730317	+	0.683109i	$0.239372\pi$
$223$			1.01457e6i			1.36622i	−0.730317	+	0.683109i	$0.760628\pi$
$224$	−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	$-0.231352\pi$
$227$	−156685.	−	271387.i	−0.201820	−	0.349562i	−0.949115	+	0.314930i	$0.898019\pi$
$228$	−633956.	+	1.46228e6i	−0.807647	+	1.86292i
$229$	390355.	+	225372.i	0.491894	+	0.283995i	0.725360	−	0.688370i	$-0.241673\pi$
$229$	390355.	+	225372.i	0.491894	+	0.283995i	−0.233466	+	0.972365i	$0.575007\pi$
$230$	1.06215e6			1.32394
$231$	43006.0	−	915453.i	0.0530272	−	1.12877i
$232$	709960.			0.865992
$233$	116445.	+	67229.3i	0.140517	+	0.0811276i	0.568610	−	0.822607i	$-0.307481\pi$
$233$	116445.	+	67229.3i	0.140517	+	0.0811276i	−0.428093	+	0.903735i	$0.640815\pi$
$234$	−1.34953e6	+	314609.i	−1.61117	+	0.375605i
$235$	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	$-0.253804\pi$
$240$	123142.	+	1.07061e6i	0.138000	+	1.19979i
$241$	421396.	−	243293.i	0.467356	−	0.269828i	−0.247776	−	0.968817i	$-0.579700\pi$
$241$	421396.	−	243293.i	0.467356	−	0.269828i	0.715132	+	0.698989i	$0.246367\pi$
$242$	−399184.	+	230469.i	−0.438162	+	0.252973i
$243$	−420653.	+	818743.i	−0.456992	+	0.889471i
$244$		−	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
$249$	1.13785e6	+	493301.i	1.16301	+	0.504212i
$250$	−1.48931e6	−	859853.i	−1.50708	−	0.870110i
$251$	−453648.			−0.454501			−0.227250	−	0.973836i	$-0.572974\pi$
$251$	−453648.			−0.454501			−0.227250	+	0.973836i	$0.572974\pi$
$252$	2.11576e6	+	1.03780e6i	2.09877	+	1.02946i
$253$	−1.46838e6			−1.44224
$254$	587577.	+	339238.i	0.571453	+	0.329929i
$255$	244306.	+	105916.i	0.235279	+	0.102003i
$256$	759221.	+	1.31501e6i	0.724049	+	1.25409i
$257$	991726.	−	1.71772e6i	0.936610	−	1.62226i	0.164874	−	0.986315i	$-0.447278\pi$
$257$	991726.	−	1.71772e6i	0.936610	−	1.62226i	0.771737	−	0.635942i	$-0.219388\pi$
$258$	−756433.	−	1.01997e6i	−0.707492	−	0.953982i
$259$	−195872.	−	160040.i	−0.181435	−	0.148244i
$260$		−	1.31015e6i		−	1.20195i
$261$	−284647.	+	266580.i	−0.258646	+	0.242229i
$262$	−1.84009e6	+	1.06237e6i	−1.65609	+	0.956146i
$263$	−677452.	+	391127.i	−0.603934	+	0.348681i	−0.770588	−	0.637334i	$-0.780037\pi$
$263$	−677452.	+	391127.i	−0.603934	+	0.348681i	0.166654	+	0.986015i	$0.446704\pi$
$264$	−357341.	−	3.10675e6i	−0.315553	−	2.74345i
$265$			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	0.965211	+	0.261473i	$0.0842081\pi$
$269$	841504.	+	1.45753e6i	0.709047	+	1.22811i	−0.256164	+	0.966633i	$0.582459\pi$
$270$	−947452.	−	803950.i	−0.790948	−	0.671150i
$271$	704628.	+	406817.i	0.582823	+	0.336493i	0.762255	−	0.647277i	$-0.224092\pi$
$271$	704628.	+	406817.i	0.582823	+	0.336493i	−0.179431	+	0.983770i	$0.557426\pi$
$272$	−1.17213e6			−0.960625
$273$	−938489.	−	602260.i	−0.762119	−	0.489077i
$274$	4.24208e6			3.41352
$275$	831619.	+	480136.i	0.663121	+	0.382853i
$276$	1.50188e6	−	3.46422e6i	1.18676	−	2.73737i
$277$	−187762.	−	325214.i	−0.147031	−	0.254665i	0.783098	−	0.621899i	$-0.213638\pi$
$277$	−187762.	−	325214.i	−0.147031	−	0.254665i	−0.930129	+	0.367233i	$0.880305\pi$
$278$	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	$0.968169\pi$
$282$	974716.	−	112112.i	0.729887	−	0.0839520i
$283$	−1.59803e6	+	922626.i	−1.18610	+	0.684793i	−0.957417	−	0.288709i	$-0.906774\pi$
$283$	−1.59803e6	+	922626.i	−1.18610	+	0.684793i	−0.228679	+	0.973502i	$0.573441\pi$
$284$	−2.03020e6	+	1.17214e6i	−1.49363	+	0.862350i
$285$	671838.	−	77275.2i	0.489950	−	0.0563544i
$286$			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
$291$	716491.	−	1.65265e6i	0.495996	−	1.14406i
$292$	636256.	+	367343.i	0.436692	+	0.252124i
$293$	1.96922e6			1.34006			0.670032	−	0.742332i	$-0.266280\pi$
$293$	1.96922e6			1.34006			0.670032	+	0.742332i	$0.266280\pi$
$294$	839370.	+	2.57424e6i	0.566350	+	1.73692i
$295$	537020.			0.359282
$296$	−747468.	−	431551.i	−0.495865	−	0.286288i
$297$	1.30981e6	+	1.11143e6i	0.861625	+	0.731123i
$298$	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
$303$	−160283.	−	1.39351e6i	−0.100295	−	0.871977i
$304$	−2.57805e6	+	1.48844e6i	−1.59995	+	0.923734i
$305$	−816925.	+	471652.i	−0.502843	+	0.290317i
$306$	986444.	−	923832.i	0.602239	−	0.564014i
$307$		−	2.38073e6i		−	1.44166i	−0.693110	−	0.720832i	$-0.743760\pi$
$307$		−	2.38073e6i		−	1.44166i	0.693110	−	0.720832i	$-0.256240\pi$
$308$	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	−0.622727	−	0.782439i	$-0.713975\pi$
$311$	−1.68689e6	−	2.92178e6i	−0.988976	−	1.71296i	−0.366248	−	0.930517i	$-0.619358\pi$
$312$	−3.49112e6	−	1.51354e6i	−2.03038	−	0.880251i
$313$	−2.32670e6	−	1.34332e6i	−1.34239	−	0.775031i	−0.355235	−	0.934777i	$-0.615599\pi$
$313$	−2.32670e6	−	1.34332e6i	−1.34239	−	0.775031i	−0.987158	+	0.159746i	$0.948933\pi$
$314$	2.47294e6			1.41544
$315$	−67518.1	−	997649.i	−0.0383392	−	0.566502i
$316$	−7.46541e6			−4.20568
$317$	−598070.	−	345296.i	−0.334275	−	0.192994i	0.323462	−	0.946241i	$-0.395153\pi$
$317$	−598070.	−	345296.i	−0.334275	−	0.192994i	−0.657738	+	0.753247i	$0.728486\pi$
$318$	2.09561e6	+	908531.i	1.16210	+	0.503816i
$319$	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
$324$	−3.96179e6	+	1.95335e6i	−2.09666	+	1.03375i
$325$	1.01188e6	−	584209.i	0.531398	−	0.306803i
$326$	1.32800e6	−	766718.i	0.692074	−	0.399569i
$327$	−43153.3	−	375179.i	−0.0223175	−	0.194030i
$328$			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	0.100886	+	0.994898i	$0.467832\pi$
$331$	−1.61688e6	+	2.80052e6i	−0.811164	+	1.40498i	−0.912050	+	0.410079i	$0.865501\pi$
$332$	2.97565e6	+	5.15397e6i	1.48162	+	2.56624i
$333$	461728.	−	107641.i	0.228179	−	0.0531943i
$334$	4.92192e6	+	2.84167e6i	2.41417	+	1.39382i
$335$	−432128.			−0.210378
$336$	2.01951e6	+	3.91099e6i	0.975882	+	1.88990i
$337$	−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
$339$	−237053.	+	546785.i	−0.112033	+	0.258415i
$340$	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
$345$	−1.59162e6	+	183069.i	−0.719933	+	0.0828072i
$346$	−2.83067e6	+	1.63429e6i	−1.27115	+	0.733901i
$347$	−1.84192e6	+	1.06343e6i	−0.821196	+	0.474118i	−0.850829	−	0.525443i	$-0.823900\pi$
$347$	−1.84192e6	+	1.06343e6i	−0.821196	+	0.474118i	0.0296326	+	0.999561i	$0.490566\pi$
$348$	−1.85919e6	+	213845.i	−0.822953	+	0.0946566i
$349$		−	1.87399e6i		−	0.823575i	−0.911280	−	0.411787i	$-0.864905\pi$
$349$		−	1.87399e6i		−	0.823575i	0.911280	−	0.411787i	$-0.135095\pi$
$350$	−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	−0.974005	−	0.226526i	$-0.927263\pi$
$353$	−1.59945e6	−	2.77034e6i	−0.683180	−	1.18330i	0.290826	−	0.956776i	$-0.406070\pi$
$354$	1.08417e6	−	2.50075e6i	0.459823	−	1.06063i
$355$	861445.	+	497356.i	0.362791	+	0.209458i
$356$	71344.1			0.0298355
$357$	1.08638e6	+	51035.7i	0.451140	+	0.0211935i
$358$	5.82467e6			2.40195
$359$	−213840.	−	123461.i	−0.0875695	−	0.0505583i	0.455576	−	0.890197i	$-0.349433\pi$
$359$	−213840.	−	123461.i	−0.0875695	−	0.0505583i	−0.543145	+	0.839639i	$0.682767\pi$
$360$	−774664.	−	3.32295e6i	−0.315034	−	1.35135i
$361$	−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
$366$	547084.	+	4.75639e6i	0.213477	+	1.85599i
$367$	−393442.	+	227154.i	−0.152481	+	0.0880349i	−0.574299	−	0.818645i	$-0.694725\pi$
$367$	−393442.	+	227154.i	−0.152481	+	0.0880349i	0.421818	+	0.906680i	$0.361392\pi$
$368$	6.10755e6	−	3.52620e6i	2.35097	−	1.35733i
$369$	−299068.	−	319337.i	−0.114342	−	0.122091i
$370$			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	−0.997567	−	0.0697107i	$-0.977792\pi$
$373$	−1.17803e6	+	2.04040e6i	−0.438412	+	0.759353i	0.559155	+	0.829063i	$0.311126\pi$
$374$	−1.26109e6	−	2.18427e6i	−0.466193	−	0.807470i
$375$	2.37991e6	+	1.03179e6i	0.873943	+	0.378889i
$376$	2.33321e6	+	1.34708e6i	0.851108	+	0.491388i
$377$	885551.			0.320893
$378$	−4.78208e6	−	1.69971e6i	−1.72142	−	0.611851i
$379$	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
$381$	−938947.	−	407071.i	−0.331382	−	0.143667i
$382$	−4.16215e6	−	7.20906e6i	−1.45935	−	2.52767i
$383$	2.27893e6	−	3.94722e6i	0.793841	−	1.37497i	−0.129731	−	0.991549i	$-0.541411\pi$
$383$	2.27893e6	−	3.94722e6i	0.793841	−	1.37497i	0.923572	−	0.383424i	$-0.125255\pi$
$384$	−886174.	−	1.19492e6i	−0.306684	−	0.413532i
$385$	−1.84181e6	−	299991.i	−0.633276	−	0.103147i
$386$			6.56975e6i			2.24430i
$387$	1.30931e6	+	1.39804e6i	0.444390	+	0.474508i
$388$	7.48584e6	−	4.32195e6i	2.52442	−	1.45747i
$389$	−1.44441e6	+	833932.i	−0.483969	+	0.279420i	−0.722069	−	0.691821i	$-0.756809\pi$
$389$	−1.44441e6	+	833932.i	−0.483969	+	0.279420i	0.238100	+	0.971241i	$0.423475\pi$
$390$	322411.	+	2.80307e6i	0.107337	+	0.933196i
$391$		−	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
$396$	1.87155e6	+	8.02808e6i	0.599741	+	2.57261i
$397$	1.49251e6	+	861698.i	0.475269	+	0.274397i	0.718443	−	0.695586i	$-0.244855\pi$
$397$	1.49251e6	+	861698.i	0.475269	+	0.274397i	−0.243174	+	0.969983i	$0.578189\pi$
$398$	−9.25529e6			−2.92875
$399$	2.45425e6	−	1.26730e6i	0.771768	−	0.398516i
$400$	−4.61202e6			−1.44126
$401$	−4.90198e6	−	2.83016e6i	−1.52234	−	0.878922i	−0.999652	−	0.0263964i	$-0.991597\pi$
$401$	−4.90198e6	−	2.83016e6i	−1.52234	−	0.878922i	−0.522686	−	0.852525i	$-0.675070\pi$
$402$	−872411.	+	2.01230e6i	−0.269250	+	0.621051i
$403$	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
$408$	3.68682e6	−	424061.i	1.09648	−	0.126118i
$409$	1.94296e6	−	1.12177e6i	0.574322	−	0.331585i	−0.184551	−	0.982823i	$-0.559083\pi$
$409$	1.94296e6	−	1.12177e6i	0.574322	−	0.331585i	0.758874	+	0.651238i	$0.225750\pi$
$410$	511482.	−	295304.i	0.150269	−	0.0867581i
$411$	−6.35671e6	+	731153.i	−1.85621	+	0.213503i
$412$			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
$417$	−458072.	+	1.05659e6i	−0.129001	+	0.297553i
$418$	−5.54740e6	−	3.20279e6i	−1.55292	−	0.896579i
$419$	6.62738e6			1.84419			0.922097	−	0.386959i	$-0.126474\pi$
$419$	6.62738e6			1.84419			0.922097	+	0.386959i	$0.126474\pi$
$420$	2.59157e6	−	4.03838e6i	0.716868	−	1.11708i
$421$	−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
$423$	−1.44128e6	+	335998.i	−0.391649	+	0.0913033i
$424$	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
$429$	−445720.	−	3.87513e6i	−0.116928	−	1.01658i
$430$	−2.23924e6	+	1.29283e6i	−0.584023	+	0.337186i
$431$	3.23887e6	−	1.86996e6i	0.839848	−	0.484886i	−0.0173649	−	0.999849i	$-0.505528\pi$
$431$	3.23887e6	−	1.86996e6i	0.839848	−	0.484886i	0.857212	+	0.514963i	$0.172194\pi$
$432$	−8.11701e6	−	1.47744e6i	−2.09260	−	0.380890i
$433$		−	3.36951e6i		−	0.863668i	−0.901953	−	0.431834i	$-0.857867\pi$
$433$		−	3.36951e6i		−	0.863668i	0.901953	−	0.431834i	$-0.142133\pi$
$434$	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
$438$	−1.45167e6	−	629358.i	−0.361563	−	0.156752i
$439$	1.11009e6	+	640910.i	0.274914	+	0.158722i	0.631119	−	0.775686i	$-0.282596\pi$
$439$	1.11009e6	+	640910.i	0.274914	+	0.158722i	−0.356205	+	0.934408i	$0.615929\pi$
$440$	−6.36760e6			−1.56799
$441$	−1.70147e6	−	3.71280e6i	−0.416609	−	0.909086i
$442$	−3.06887e6			−0.747177
$443$	3.67325e6	+	2.12075e6i	0.889284	+	0.513428i	0.873708	−	0.486450i	$-0.161708\pi$
$443$	3.67325e6	+	2.12075e6i	0.889284	+	0.513428i	0.0155759	+	0.999879i	$0.495042\pi$
$444$	2.08740e6	+	904969.i	0.502514	+	0.217859i
$445$	−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	$0.786973\pi$
$450$	3.88139e6	−	3.63503e6i	0.903558	−	0.846207i
$451$	−707103.	+	408246.i	−0.163697	+	0.0945106i
$452$	−2.47671e6	+	1.42993e6i	−0.570203	+	0.329207i
$453$	307150.	+	2.67039e6i	0.0703241	+	0.611404i
$454$			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	−0.144413	−	0.989517i	$-0.546130\pi$
$457$	3.50362e6	−	6.06844e6i	0.784741	−	1.35921i	0.929154	−	0.369693i	$-0.120537\pi$
$458$	−2.32914e6	−	4.03418e6i	−0.518838	−	0.898653i
$459$	−1.31895e6	+	1.55437e6i	−0.292210	+	0.344368i
$460$	−6.65813e6	−	3.84407e6i	−1.46709	−	0.847027i
$461$	−640032.			−0.140265			−0.0701325	−	0.997538i	$-0.522342\pi$
$461$	−640032.			−0.140265			−0.0701325	+	0.997538i	$0.522342\pi$
$462$	−5.11535e6	+	7.97115e6i	−1.11499	+	1.73746i
$463$	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
$465$	−1.39144e6	+	3.20949e6i	−0.298423	+	0.688340i
$466$	−694791.	−	1.20341e6i	−0.148214	−	0.256714i
$467$	−617824.	+	1.07010e6i	−0.131091	+	0.227056i	−0.924097	−	0.382157i	$-0.875181\pi$
$467$	−617824.	+	1.07010e6i	−0.131091	+	0.227056i	0.793006	+	0.609213i	$0.208515\pi$
$468$	9.59815e6	+	2.91198e6i	2.02569	+	0.614574i
$469$	−1.65050e6	+	625286.i	−0.346485	+	0.131264i
$470$		−	1.99778e6i		−	0.417160i
$471$	−3.70568e6	+	426229.i	−0.769689	+	0.0885301i
$472$	6.48176e6	−	3.74225e6i	1.33918	−	0.773174i
$473$	3.09566e6	−	1.78728e6i	0.636210	−	0.367316i
$474$	1.59723e7	−	1.83715e6i	3.26529	−	0.375576i
$475$			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	$-0.116868\pi$
$479$	782406.	+	1.35517e6i	0.155809	+	0.269870i	−0.777544	+	0.628828i	$0.783535\pi$
$480$	1.64400e6	−	3.79205e6i	0.325686	−	0.751226i
$481$	−932337.	−	538285.i	−0.183743	−	0.106084i
$482$	−5.02870e6			−0.985911
$483$	−5.81426e6	+	3.00230e6i	−1.13404	+	0.585579i
$484$	3.33639e6			0.647387
$485$	−3.17635e6	−	1.83387e6i	−0.613160	−	0.354008i
$486$	7.99559e6	−	5.15415e6i	1.53553	−	0.989844i
$487$	1.44990e6	+	2.51130e6i	0.277023	+	0.479817i	0.970643	−	0.240523i	$-0.0773189\pi$
$487$	1.44990e6	+	2.51130e6i	0.277023	+	0.479817i	−0.693621	+	0.720340i	$0.743986\pi$
$488$	−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	$-0.137165\pi$
$492$	−239906.	−	2.08577e6i	−0.0446816	−	0.388466i
$493$	−747973.	+	431842.i	−0.138602	+	0.0800217i
$494$	−6.74985e6	+	3.89703e6i	−1.24445	+	0.718482i
$495$	2.55299e6	−	2.39095e6i	0.468313	−	0.438589i
$496$		−	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	−0.960673	−	0.277683i	$-0.910433\pi$
$499$	−1.33414e6	+	2.31080e6i	−0.239855	+	0.415442i	0.720817	+	0.693125i	$0.243767\pi$
$500$	6.22385e6	+	1.07800e7i	1.11336	+	1.92839i
$501$	−7.86523e6	−	3.40989e6i	−1.39996	−	0.606940i
$502$	4.06018e6	+	2.34415e6i	0.719095	+	0.415170i
$503$	−6.90952e6			−1.21767			−0.608833	−	0.793299i	$-0.708362\pi$
$503$	−6.90952e6			−1.21767			−0.608833	+	0.793299i	$0.708362\pi$
$504$	−7.76709e6	−	1.15710e7i	−1.36202	−	2.02906i
$505$	−2.85615e6			−0.498370
$506$	1.31421e7	+	7.58761e6i	2.28186	+	1.31743i
$507$	955744.	+	414353.i	0.165128	+	0.0715897i
$508$	−2.45550e6	−	4.25304e6i	−0.422163	−	0.731207i
$509$	−2.28095e6	+	3.95071e6i	−0.390230	+	0.675898i	−0.992480	−	0.122410i	$-0.960938\pi$
$509$	−2.28095e6	+	3.95071e6i	−0.390230	+	0.675898i	0.602250	+	0.798308i	$0.294271\pi$
$510$	−1.63925e6	−	2.21036e6i	−0.279074	−	0.376304i
$511$	−451082.	−	1.19067e6i	−0.0764193	−	0.201716i
$512$		−	1.26387e7i		−	2.13073i
$513$	−927132.	+	5.09364e6i	−0.155542	+	0.854545i
$514$	−1.77520e7	+	1.02491e7i	−2.96374	+	1.71112i
$515$	4.30641e6	−	2.48631e6i	0.715480	−	0.413083i
$516$	1.05030e6	+	9.13137e6i	0.173655	+	1.50977i
$517$			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	$-0.152983\pi$
$521$	266267.	+	461188.i	0.0429758	+	0.0744362i	−0.843737	+	0.536756i	$0.819650\pi$
$522$	3.92512e6	−	915046.i	0.630488	−	0.146983i
$523$	1.14831e6	+	662979.i	0.183572	+	0.105985i	0.588970	−	0.808155i	$-0.299534\pi$
$523$	1.14831e6	+	662979.i	0.183572	+	0.105985i	−0.405398	+	0.914140i	$0.632867\pi$
$524$	1.53795e7			2.44689
$525$	4.27461e6	+	200812.i	0.676859	+	0.0317974i
$526$	8.08433e6			1.27403
$527$	−3.29501e6	−	1.90238e6i	−0.516810	−	0.298380i
$528$	−6.12438e6	+	1.41265e7i	−0.956043	+	2.20520i
$529$	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
$534$	−152641.	+	17556.9i	−0.0231643	+	0.00266437i
$535$	3.82382e6	−	2.20769e6i	0.577582	−	0.333467i
$536$	−5.21573e6	+	3.01130e6i	−0.784157	+	0.452734i
$537$	−8.72820e6	+	1.00392e6i	−1.30614	+	0.150233i
$538$		−	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	−0.0683877	−	0.997659i	$-0.521785\pi$
$541$	5.64896e6	−	9.78429e6i	0.829804	−	1.43726i	0.898192	−	0.439604i	$-0.144881\pi$
$542$	−4.20432e6	−	7.28209e6i	−0.614748	−	1.06477i
$543$	2.04169e6	−	4.70934e6i	0.297159	−	0.685426i
$544$	3.89310e6	+	2.24768e6i	0.564025	+	0.325640i
$545$	−768967.			−0.110896
$546$	5.28747e6	+	1.02397e7i	0.759043	+	1.46997i
$547$	−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
$549$	−1.63960e6	−	7.03311e6i	−0.232170	−	0.995901i
$550$	−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
$555$	−110310.	−	959046.i	−0.0152014	−	0.132162i
$556$	−4.78590e6	+	2.76314e6i	−0.656563	+	0.379067i
$557$	4.74038e6	−	2.73686e6i	0.647404	−	0.373779i	−0.140057	−	0.990143i	$-0.544729\pi$
$557$	4.74038e6	−	2.73686e6i	0.647404	−	0.373779i	0.787461	+	0.616365i	$0.211395\pi$
$558$	1.21365e7	+	1.29591e7i	1.65010	+	1.76193i
$559$		−	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	0.719435	+	0.694560i	$0.244401\pi$
$563$	7.22929e6	+	1.25215e7i	0.961224	+	1.66489i	0.241789	+	0.970329i	$0.422266\pi$
$564$	−6.51579e6	−	2.82485e6i	−0.862520	−	0.373936i
$565$	1.05090e6	+	606740.i	0.138498	+	0.0799616i
$566$	1.90700e7			2.50213
$567$	7.45885e6	+	1.72277e6i	0.974348	+	0.225046i
$568$	1.38634e7			1.80301
$569$	4.06800e6	+	2.34866e6i	0.526745	+	0.304116i	0.739690	−	0.672948i	$-0.234972\pi$
$569$	4.06800e6	+	2.34866e6i	0.526745	+	0.304116i	−0.212945	+	0.977064i	$0.568305\pi$
$570$	−6.41230e6	−	2.77999e6i	−0.826660	−	0.358390i
$571$	−2.53638e6	−	4.39313e6i	−0.325554	−	0.563876i	0.656070	−	0.754700i	$-0.272218\pi$
$571$	−2.53638e6	−	4.39313e6i	−0.325554	−	0.563876i	−0.981624	+	0.190824i	$0.938884\pi$
$572$	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
$576$	−2.76240e6	−	2.94962e6i	−0.346921	−	0.370433i
$577$	6.53049e6	−	3.77038e6i	0.816594	−	0.471461i	−0.0326462	−	0.999467i	$-0.510393\pi$
$577$	6.53049e6	−	3.77038e6i	0.816594	−	0.471461i	0.849241	+	0.528006i	$0.177060\pi$
$578$	−1.01157e7	+	5.84032e6i	−1.25944	+	0.727138i
$579$	−1.13234e6	−	9.84470e6i	−0.140372	−	1.22041i
$580$			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
$585$	−966259.	−	4.14480e6i	−0.116736	−	0.500742i
$586$	−1.76247e7	−	1.01756e7i	−2.12020	−	1.22410i
$587$	−1.49725e7			−1.79349			−0.896743	−	0.442551i	$-0.854074\pi$
$587$	−1.49725e7			−1.79349			−0.896743	+	0.442551i	$0.854074\pi$
$588$	4.05492e6	−	1.91745e7i	0.483658	−	2.28708i
$589$	−9.66297e6			−1.14768
$590$	−4.80636e6	−	2.77496e6i	−0.568443	−	0.328190i
$591$	853822.	−	1.96942e6i	0.100554	−	0.231937i
$592$	2.12474e6	+	3.68016e6i	0.249173	+	0.431581i
$593$	−1.51264e6	+	2.61996e6i	−0.176644	+	0.305956i	−0.940729	−	0.339160i	$-0.889857\pi$
$593$	−1.51264e6	+	2.61996e6i	−0.176644	+	0.305956i	0.764085	+	0.645115i	$0.223191\pi$
$594$	−5.97981e6	−	1.67156e7i	−0.695379	−	1.94382i
$595$	356003.	−	2.18570e6i	0.0412251	−	0.253103i
$596$		−	4.33662e6i		−	0.500075i
$597$	1.38689e7	−	1.59521e6i	1.59260	−	0.183182i
$598$	1.59908e7	−	9.23228e6i	1.82859	−	1.05574i
$599$	5.02690e6	−	2.90228e6i	0.572444	−	0.330501i	−0.185681	−	0.982610i	$-0.559449\pi$
$599$	5.02690e6	−	2.90228e6i	0.572444	−	0.330501i	0.758125	+	0.652110i	$0.226116\pi$
$600$	1.45066e7	−	1.66856e6i	1.64509	−	0.189219i
$601$			8.90296e6i			1.00542i	0.864455	+	0.502711i	$0.167664\pi$
$601$			8.90296e6i			1.00542i	−0.864455	+	0.502711i	$0.832336\pi$
$602$	−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
$606$	−5.76620e6	+	1.33003e7i	−0.637834	+	1.47123i
$607$	−298211.	−	172172.i	−0.0328512	−	0.0189667i	0.483484	−	0.875353i	$-0.339371\pi$
$607$	−298211.	−	172172.i	−0.0328512	−	0.0189667i	−0.516336	+	0.856386i	$0.672704\pi$
$608$	1.14169e7			1.25254
$609$	2.72961e6	+	1.75168e6i	0.298235	+	0.191387i
$610$	9.74871e6			1.06077
$611$	2.91028e6	+	1.68025e6i	0.315378	+	0.182084i
$612$	−9.52703e6	+	2.22099e6i	−1.02820	+	0.239700i
$613$	20098.1	+	34811.0i	0.00216025	+	0.00374167i	0.867104	−	0.498128i	$-0.165979\pi$
$613$	20098.1	+	34811.0i	0.00216025	+	0.00374167i	−0.864943	+	0.501870i	$0.832646\pi$
$614$	−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	$0.931402\pi$
$618$	−2.88395e6	−	2.50733e7i	−0.303750	−	2.64083i
$619$	6.65332e6	−	3.84130e6i	0.697930	−	0.402950i	−0.108646	−	0.994080i	$-0.534652\pi$
$619$	6.65332e6	−	3.84130e6i	0.697930	−	0.402950i	0.806576	+	0.591131i	$0.201318\pi$
$620$	−1.45376e7	+	8.39331e6i	−1.51885	+	0.876909i
$621$	2.19643e6	−	1.20671e7i	0.228554	−	1.25567i
$622$			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
$627$	8.86474e6	+	3.84322e6i	0.900528	+	0.390414i
$628$	−1.55017e7	−	8.94992e6i	−1.56849	−	0.905566i
$629$	1.04999e6			0.105817
$630$	−4.55088e6	+	9.27791e6i	−0.456819	+	0.931320i
$631$	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
$633$	−5.61408e6	−	2.43393e6i	−0.556890	−	0.241434i
$634$	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
$639$	−5.55831e6	+	5.20551e6i	−0.538506	+	0.504326i
$640$	−2.62331e6	+	1.51457e6i	−0.253163	+	0.146163i
$641$	−6.69847e6	+	3.86736e6i	−0.643918	+	0.371766i	−0.786122	−	0.618071i	$-0.787914\pi$
$641$	−6.69847e6	+	3.86736e6i	−0.643918	+	0.371766i	0.142204	+	0.989837i	$0.454581\pi$
$642$	−2.56076e6	−	2.22635e7i	−0.245207	−	2.13185i
$643$		−	1.41911e7i		−	1.35360i	−0.736168	−	0.676799i	$-0.763367\pi$
$643$		−	1.41911e7i		−	1.35360i	0.736168	−	0.676799i	$-0.236633\pi$
$644$	−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	$-0.176817\pi$
$647$	−339476.	−	587989.i	−0.0318822	−	0.0552216i	−0.881526	+	0.472135i	$0.843483\pi$
$648$	2.60657e7	+	1.71051e6i	2.43856	+	0.160025i
$649$	6.64460e6	+	3.83626e6i	0.619237	+	0.357517i
$650$	−1.20752e7			−1.12101
$651$	−670465.	+	1.42720e7i	−0.0620046	+	1.31987i
$652$	−1.10994e7			−1.02254
$653$	2.29785e6	+	1.32666e6i	0.210881	+	0.121752i	0.601721	−	0.798706i	$-0.294482\pi$
$653$	2.29785e6	+	1.32666e6i	0.210881	+	0.121752i	−0.390840	+	0.920459i	$0.627815\pi$
$654$	−1.55245e6	+	3.58087e6i	−0.141929	+	0.327374i
$655$	−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	$-0.160844\pi$
$660$	1.66750e7	−	1.91797e6i	1.49007	−	0.171388i
$661$	−1.78194e7	+	1.02881e7i	−1.58632	+	0.915861i	−0.592411	+	0.805636i	$0.701824\pi$
$661$	−1.78194e7	+	1.02881e7i	−1.58632	+	0.915861i	−0.993907	+	0.110225i	$0.964843\pi$
$662$	2.89424e7	−	1.67099e7i	2.56679	−	1.48194i
$663$	4.59867e6	−	528942.i	0.406301	−	0.0467331i
$664$		−	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
$669$	−6.29091e6	+	1.45106e7i	−0.543436	+	1.25349i
$670$	3.86758e6	+	2.23295e6i	0.332853	+	0.192173i
$671$	−1.34772e7			−1.15556
$672$	792163.	−	1.68625e7i	0.0676693	−	1.44045i
$673$	−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
$675$	−5.18970e6	+	6.11604e6i	−0.438412	+	0.516667i
$676$	2.49942e6	+	4.32913e6i	0.210365	+	0.364362i
$677$	−1.07332e6	+	1.85904e6i	−0.0900031	+	0.155890i	−0.907512	−	0.420026i	$-0.862021\pi$
$677$	−1.07332e6	+	1.85904e6i	−0.0900031	+	0.155890i	0.817509	+	0.575916i	$0.195354\pi$
$678$	4.94706e6	−	3.66884e6i	0.413307	−	0.306517i
$679$	−1.47856e7	−	2.40826e6i	−1.23073	−	0.200460i
$680$		−	7.55651e6i		−	0.626685i
$681$	−558191.	−	4.85296e6i	−0.0461228	−	0.400995i
$682$	2.86951e7	−	1.65671e7i	2.36236	−	1.36391i
$683$	−2.25952e6	+	1.30453e6i	−0.185338	+	0.107005i	−0.589798	−	0.807551i	$-0.700793\pi$
$683$	−2.25952e6	+	1.30453e6i	−0.185338	+	0.107005i	0.404460	+	0.914556i	$0.367459\pi$
$684$	−1.81339e7	+	1.69829e7i	−1.48201	+	1.38794i
$685$			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
$690$	1.51911e7	+	6.58595e6i	1.21469	+	0.526618i
$691$	7.26513e6	+	4.19452e6i	0.578826	+	0.334185i	0.760667	−	0.649143i	$-0.224872\pi$
$691$	7.26513e6	+	4.19452e6i	0.578826	+	0.334185i	−0.181841	+	0.983328i	$0.558206\pi$
$692$	2.36588e7			1.87814
$693$	6.29141e6	−	1.28263e7i	0.497640	−	1.01454i
$694$	2.19804e7			1.73236
$695$	2.03073e6	+	1.17244e6i	0.159474	+	0.0920722i
$696$	1.01540e7	+	4.40215e6i	0.794536	+	0.344463i
$697$	−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	$0.987066\pi$
$702$	−2.12519e7	−	3.86823e6i	−1.62763	−	0.296257i
$703$	2.30940e6	−	1.33333e6i	0.176242	−	0.101754i
$704$	−6.53128e6	+	3.77084e6i	−0.496669	+	0.286752i
$705$	344331.	+	2.99365e6i	0.0260918	+	0.226844i
$706$			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	−0.981603	−	0.190933i	$-0.938849\pi$
$709$	−4.35611e6	+	7.54500e6i	−0.325449	+	0.563694i	0.656154	+	0.754627i	$0.272182\pi$
$710$	−5.14000e6	−	8.90273e6i	−0.382663	−	0.662792i
$711$	−2.36177e7	+	5.50588e6i	−1.75212	+	0.408463i
$712$	−365383.	−	210954.i	−0.0270115	−	0.0155951i
$713$	2.28921e7			1.68641
$714$	−9.45946e6	−	6.07045e6i	−0.694418	−	0.445631i
$715$	−7.94248e6			−0.581020
$716$	−3.65121e7	−	2.10803e7i	−2.66167	−	1.53672i
$717$	7.83556e6	−	1.80735e7i	0.569210	−	1.31294i
$718$	1.27592e6	+	2.20996e6i	0.0923662	+	0.159983i
$719$	1.17047e7	−	2.02731e7i	0.844380	−	1.46251i	−0.0417778	−	0.999127i	$-0.513302\pi$
$719$	1.17047e7	−	2.02731e7i	0.844380	−	1.46251i	0.886158	−	0.463383i	$-0.153365\pi$
$720$	−4.87719e6	+	1.60757e7i	−0.350621	+	1.15568i
$721$	1.28506e7	−	1.57277e7i	0.920628	−	1.12675i
$722$			6.28377e6i			0.448618i
$723$	7.53544e6	−	866732.i	0.536121	−	0.0616650i
$724$	2.13314e7	−	1.23157e7i	1.51242	−	0.873196i
$725$	−2.94307e6	+	1.69918e6i	−0.207949	+	0.120059i
$726$	−7.13824e6	+	821045.i	−0.502632	+	0.0578130i
$727$		−	1.80153e7i		−	1.26417i	−0.774899	−	0.632085i	$-0.782199\pi$
$727$		−	1.80153e7i		−	1.26417i	0.774899	−	0.632085i	$-0.217801\pi$
$728$	−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
$732$	1.37846e7	−	3.17956e7i	0.950862	−	2.19325i
$733$	6.08790e6	+	3.51485e6i	0.418512	+	0.241628i	0.694440	−	0.719550i	$-0.255652\pi$
$733$	6.08790e6	+	3.51485e6i	0.418512	+	0.241628i	−0.275929	+	0.961178i	$0.588985\pi$
$734$	4.69511e6			0.321667
$735$	−7.90627e6	+	2.57796e6i	−0.539826	+	0.176018i
$736$	−2.70474e7			−1.84048
$737$	−5.34677e6	−	3.08696e6i	−0.362596	−	0.209345i
$738$	1.02656e6	+	4.40348e6i	0.0693816	+	0.297615i
$739$	−7.98435e6	−	1.38293e7i	−0.537810	−	0.931514i	−0.999022	−	0.0442238i	$-0.985919\pi$
$739$	−7.98435e6	−	1.38293e7i	−0.537810	−	0.931514i	0.461212	−	0.887290i	$-0.347415\pi$
$740$	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	$0.686534\pi$
$744$	5.57096e6	+	4.84344e7i	0.368976	+	3.20791i
$745$	−1.59356e6	+	920044.i	−0.105191	+	0.0607321i
$746$	2.10868e7	−	1.21745e7i	1.38728	−	0.800947i
$747$	1.32149e7	+	1.41106e7i	0.866491	+	0.925216i
$748$			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	−0.828443	−	0.560073i	$-0.810773\pi$
$751$	1.09454e6	−	1.89580e6i	0.0708159	−	0.122657i	0.899259	+	0.437416i	$0.144106\pi$
$752$	−6.63235e6	−	1.14876e7i	−0.427684	−	0.740770i
$753$	−6.48817e6	−	2.81288e6i	−0.416999	−	0.180785i
$754$	−7.92575e6	−	4.57593e6i	−0.507706	−	0.293124i
$755$	5.47323e6			0.349443
$756$	2.38251e7	+	2.79617e7i	1.51611	+	1.77934i
$757$	−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
$759$	−2.10011e7	−	9.10480e6i	−1.32324	−	0.573675i
$760$	−9.59568e6	−	1.66202e7i	−0.602618	−	1.04376i
$761$	−682367.	+	1.18189e6i	−0.0427126	+	0.0739805i	−0.886591	−	0.462553i	$-0.846933\pi$
$761$	−682367.	+	1.18189e6i	−0.0427126	+	0.0739805i	0.843879	+	0.536534i	$0.180267\pi$
$762$	6.30018e6	+	8.49516e6i	0.393066	+	0.530010i
$763$	−2.93705e6	+	1.11269e6i	−0.182642	+	0.0691931i
$764$			6.02536e7i			3.73465i
$765$	2.83737e6	+	3.02967e6i	0.175292	+	0.187172i
$766$	−4.07931e7	+	2.35519e7i	−2.51197	+	1.45029i
$767$	8.08487e6	−	4.66780e6i	0.496232	−	0.286500i
$768$	2.70473e6	+	2.35151e7i	0.165470	+	1.43861i
$769$		−	1.59541e7i		−	0.972875i	−0.873715	−	0.486437i	$-0.838296\pi$
$769$		−	1.59541e7i		−	0.972875i	0.873715	−	0.486437i	$-0.161704\pi$
$770$	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	0.999732	+	0.0231692i	$0.00737565\pi$
$773$	8.63763e6	+	1.49608e7i	0.519931	+	0.900547i	−0.479801	+	0.877378i	$0.659291\pi$
$774$	−4.49424e6	−	1.92782e7i	−0.269652	−	1.15668i
$775$	−1.29650e7	−	7.48534e6i	−0.775386	−	0.447669i
$776$	−5.11175e7			−3.04730
$777$	−1.80906e6	−	3.50343e6i	−0.107498	−	0.208181i
$778$	1.72368e7			1.02096
$779$	−2.13114e6	−	1.23042e6i	−0.125826	−	0.0726454i
$780$	8.12366e6	−	1.87380e7i	0.478096	−	1.10277i
$781$	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
$786$	−3.29046e7	+	3.78471e6i	−1.89977	+	0.218513i
$787$	−5.46964e6	+	3.15790e6i	−0.314791	+	0.181744i	−0.649068	−	0.760730i	$-0.724841\pi$
$787$	−5.46964e6	+	3.15790e6i	−0.314791	+	0.181744i	0.334278	+	0.942475i	$0.391508\pi$
$788$	8.92067e6	−	5.15035e6i	0.511778	−	0.295475i
$789$	−1.21143e7	+	1.39339e6i	−0.692795	+	0.0796857i
$790$		−	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
$795$	−2.79037e6	+	6.43626e6i	−0.156583	+	0.361174i
$796$	5.80170e7	+	3.34962e7i	3.24543	+	1.87375i
$797$	−8.89295e6			−0.495907			−0.247953	−	0.968772i	$-0.579758\pi$
$797$	−8.89295e6			−0.495907			−0.247953	+	0.968772i	$0.579758\pi$
$798$	−2.85143e7	−	1.33954e6i	−1.58509	−	0.0744641i
$799$	−3.27752e6			−0.181626
$800$	1.53183e7	+	8.84402e6i	0.846224	+	0.488568i
$801$	225705.	−	52617.7i	0.0124297	−	0.00289768i
$802$	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
$807$	2.99786e6	+	2.60636e7i	0.162042	+	1.40881i
$808$	−3.44733e7	+	1.99032e7i	−1.85761	+	1.07249i
$809$	−239245.	+	138128.i	−0.0128520	+	0.00742013i	−0.506412	−	0.862291i	$-0.669029\pi$
$809$	−239245.	+	138128.i	−0.0128520	+	0.00742013i	0.493560	+	0.869712i	$0.335695\pi$
$810$	−8.56570e6	−	1.73730e7i	−0.458723	−	0.930384i
$811$		−	1.88633e7i		−	1.00708i	−0.863971	−	0.503542i	$-0.832030\pi$
$811$		−	1.88633e7i		−	1.00708i	0.863971	−	0.503542i	$-0.167970\pi$
$812$	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
$816$	−1.67641e7	−	7.26788e6i	−0.881361	−	0.382105i
$817$	9.33004e6	+	5.38670e6i	0.489022	+	0.282337i
$818$	−2.31862e7			−1.21156
$819$	−9.68810e6	−	1.44328e7i	−0.504695	−	0.751867i
$820$	−4.27499e6			−0.222024
$821$	−6.00902e6	−	3.46931e6i	−0.311133	−	0.179633i	0.336300	−	0.941755i	$-0.390824\pi$
$821$	−6.00902e6	−	3.46931e6i	−0.311133	−	0.179633i	−0.647433	+	0.762122i	$0.724158\pi$
$822$	6.06711e7	+	2.63033e7i	3.13186	+	1.35778i
$823$	1.49084e7	+	2.58220e7i	0.767238	+	1.32890i	0.939055	+	0.343766i	$0.111703\pi$
$823$	1.49084e7	+	2.58220e7i	0.767238	+	1.32890i	−0.171817	+	0.985129i	$0.554964\pi$
$824$	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	$-0.225982\pi$
$828$	4.29603e7	−	4.02335e7i	2.17767	−	2.03945i
$829$	3.53011e6	−	2.03811e6i	0.178403	−	0.103001i	−0.408139	−	0.912920i	$-0.633822\pi$
$829$	3.53011e6	−	2.03811e6i	0.178403	−	0.103001i	0.586542	+	0.809919i	$0.300489\pi$
$830$	−2.26009e7	+	1.30486e7i	−1.13875	+	0.657460i
$831$	−668903.	−	5.81550e6i	−0.0336017	−	0.292136i
$832$			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
$837$	−2.04201e7	−	1.73272e7i	−1.00750	−	0.854900i
$838$	−5.93155e7	−	3.42458e7i	−2.91782	−	1.68460i
$839$	−2.71420e7			−1.33118			−0.665591	−	0.746317i	$-0.731820\pi$
$839$	−2.71420e7			−1.33118			−0.665591	+	0.746317i	$0.731820\pi$
$840$	−2.52134e7	+	1.30194e7i	−1.23292	+	0.636637i
$841$	1.79355e7			0.874427
$842$	5.67152e6	+	3.27445e6i	0.275689	+	0.159169i
$843$	−1.63870e6	+	3.77982e6i	−0.0794202	+	0.183190i
$844$	−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
$849$	−2.85762e7	+	3.28685e6i	−1.36062	+	0.156499i
$850$	1.01992e7	−	5.88851e6i	0.484193	−	0.279549i
$851$	−5.47110e6	+	3.15874e6i	−0.258971	+	0.149517i
$852$	−3.63043e7	+	4.17575e6i	−1.71340	+	0.197077i
$853$			2.48053e6i			0.116727i	0.998295	+	0.0583637i	$0.0185883\pi$
$853$			2.48053e6i			0.116727i	−0.998295	+	0.0583637i	$0.981412\pi$
$854$	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	−0.868558	−	0.495588i	$-0.834953\pi$
$857$	−1.85652e7	−	3.21559e7i	−0.863471	−	1.49558i	0.00508680	−	0.999987i	$-0.498381\pi$
$858$	−1.60348e7	+	3.69859e7i	−0.743612	+	1.71521i
$859$	3.60500e6	+	2.08135e6i	0.166695	+	0.0962414i	0.581027	−	0.813885i	$-0.302651\pi$
$859$	3.60500e6	+	2.08135e6i	0.166695	+	0.0962414i	−0.414332	+	0.910126i	$0.635985\pi$
$860$	1.87157e7			0.862898
$861$	−1.96516e6	+	3.06227e6i	−0.0903422	+	0.140778i
$862$	−3.86508e7			−1.77170
$863$	2.00534e7	+	1.15779e7i	0.916562	+	0.529177i	0.882537	−	0.470244i	$-0.155834\pi$
$863$	2.00534e7	+	1.15779e7i	0.916562	+	0.529177i	0.0340252	+	0.999421i	$0.489167\pi$
$864$	2.41266e7	+	2.04723e7i	1.09954	+	0.933003i
$865$	−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
$870$	−937740.	−	8.15279e6i	−0.0420034	−	0.365181i
$871$	−6.50572e6	+	3.75608e6i	−0.290570	+	0.167760i
$872$	−9.28134e6	+	5.35858e6i	−0.413351	+	0.238648i
$873$	2.04948e7	−	1.91939e7i	0.910140	−	0.852371i
$874$			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	−0.778641	−	0.627469i	$-0.784091\pi$
$877$	3.50958e6	−	6.07877e6i	0.154084	−	0.266881i	0.932725	+	0.360589i	$0.117424\pi$
$878$	−6.62359e6	−	1.14724e7i	−0.289973	−	0.502247i
$879$	2.81642e7	+	1.22103e7i	1.22949	+	0.533033i
$880$	2.71506e7	+	1.56754e7i	1.18188	+	0.682359i
$881$	1.66384e7			0.722224			0.361112	−	0.932523i	$-0.382397\pi$
$881$	1.66384e7			0.722224			0.361112	+	0.932523i	$0.382397\pi$
$882$	−3.95692e6	+	4.20219e7i	−0.171272	+	1.81888i
$883$	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
$885$	7.68056e6	+	3.32983e6i	0.329636	+	0.142910i
$886$	−2.19172e7	−	3.79617e7i	−0.937996	−	1.62466i
$887$	−207256.	+	358978.i	−0.00884501	+	0.0153200i	−0.870414	−	0.492320i	$-0.836149\pi$
$887$	−207256.	+	358978.i	−0.00884501	+	0.0153200i	0.861569	+	0.507640i	$0.169482\pi$
$888$	−8.01458e6	−	1.08069e7i	−0.341074	−	0.459904i
$889$	−1.36824e6	+	8.40036e6i	−0.0580640	+	0.356487i
$890$			312854.i			0.0132394i
$891$	1.18417e7	+	2.40175e7i	0.499713	+	1.01352i
$892$	−6.57269e7	+	3.79475e7i	−2.76587	+	1.59687i
$893$	−7.20876e6	+	4.16198e6i	−0.302504	+	0.174651i
$894$	1.06719e6	+	9.27823e6i	0.0446578	+	0.388259i
$895$			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
$900$	−3.74863e7	+	8.73901e6i	−1.54265	+	0.359630i
$901$	−6.60777e6	−	3.81500e6i	−0.271171	−	0.156561i
$902$	8.43816e6			0.345328
$903$	8.60338e6	−	1.34065e7i	0.351115	−	0.547136i
$904$	1.69124e7			0.688309
$905$	−9.05121e6	−	5.22572e6i	−0.367354	−	0.212092i
$906$	1.10497e7	−	2.54873e7i	0.447231	−	1.03158i
$907$	−1.69139e6	−	2.92957e6i	−0.0682693	−	0.118246i	0.829870	−	0.557956i	$-0.188414\pi$
$907$	−1.69139e6	−	2.92957e6i	−0.0682693	−	0.118246i	−0.898140	+	0.439711i	$0.855081\pi$
$908$	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	$0.850497\pi$
$912$	−4.61010e7	+	5.30256e6i	−1.83537	+	0.211105i
$913$	3.12448e7	−	1.80392e7i	1.24051	−	0.716210i
$914$	−6.27152e7	+	3.62087e7i	−2.48318	+	1.43366i
$915$	−1.46083e7	+	1.68026e6i	−0.576830	+	0.0663474i
$916$			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	−0.961920	−	0.273329i	$-0.911875\pi$
$919$	−6.25350e6	+	1.08314e7i	−0.244250	+	0.423053i	0.717670	+	0.696383i	$0.245208\pi$
$920$	2.27327e7	+	3.93742e7i	0.885486	+	1.53371i
$921$	1.47619e7	−	3.40496e7i	0.573446	−	1.32271i
$922$	5.72833e6	+	3.30725e6i	0.221922	+	0.128127i
$923$	1.72922e7			0.668105
$924$	6.09144e7	−	3.14542e7i	2.34715	−	1.21199i
$925$	4.13141e6			0.158761
$926$	−3.10906e7	−	1.79502e7i	−1.19152	−	0.687925i
$927$	8.64312e6	+	3.70750e7i	0.330348	+	1.41704i
$928$	6.70294e6	+	1.16098e7i	0.255503	+	0.442544i
$929$	2.72778e6	−	4.72466e6i	0.103698	−	0.179610i	−0.809507	−	0.587110i	$-0.800266\pi$
$929$	2.72778e6	−	4.72466e6i	0.103698	−	0.179610i	0.913206	+	0.407499i	$0.133599\pi$
$930$	2.90379e7	−	2.15351e7i	1.10093	−	0.816469i
$931$	−1.52207e7	−	1.72051e7i	−0.575519	−	0.650552i
$932$			1.00582e7i			0.379297i
$933$	−6.00955e6	−	5.22475e7i	−0.226015	−	1.96500i
$934$	1.10591e7	−	6.38499e6i	0.414815	−	0.239493i
$935$	6.70854e6	−	3.87318e6i	0.250957	−	0.144890i
$936$	−4.05459e7	−	4.32938e7i	−1.51271	−	1.61524i
$937$		−	2.63266e6i		−	0.0979595i	−0.998800	−	0.0489797i	$-0.984403\pi$
$937$		−	2.63266e6i		−	0.0979595i	0.998800	−	0.0489797i	$-0.0155970\pi$
$938$	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	$-0.0882529\pi$
$941$	6.62391e6	+	1.14730e7i	0.243860	+	0.422378i	−0.717950	+	0.696094i	$0.754920\pi$
$942$	3.53685e7	+	1.53337e7i	1.29864	+	0.563013i
$943$	5.04880e6	+	2.91493e6i	0.184888	+	0.106745i
$944$	−3.68499e7			−1.34588
$945$	5.22033e6	−	1.46872e7i	0.190160	−	0.535008i
$946$	−3.69419e7			−1.34212
$947$	5.21057e6	+	3.00832e6i	0.188804	+	0.109006i	0.591422	−	0.806362i	$-0.298567\pi$
$947$	5.21057e6	+	3.00832e6i	0.188804	+	0.109006i	−0.402619	+	0.915368i	$0.631900\pi$
$948$	−1.06772e8	−	4.62898e7i	−3.85865	−	1.67288i
$949$	−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	$-0.155699\pi$
$954$	2.43385e7	+	2.59880e7i	0.865810	+	0.924489i
$955$	2.21412e7	−	1.27832e7i	0.785584	−	0.453557i
$956$	8.18654e7	−	4.72650e7i	2.89705	−	1.67261i
$957$	1.29639e6	+	1.12709e7i	0.0457567	+	0.397813i
$958$		−	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
$963$	7.67455e6	+	3.29202e7i	0.266678	+	1.14392i
$964$	3.15225e7	+	1.81995e7i	1.09252	+	0.630765i
$965$	−2.01777e7			−0.697515
$966$	6.75519e7	+	3.17344e6i	2.32914	+	0.109418i
$967$	−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
$969$	−4.56079e6	+	1.05199e7i	−0.156038	+	0.359917i
$970$	1.89524e7	+	3.28265e7i	0.646747	+	1.12020i
$971$	−1.76368e7	+	3.05478e7i	−0.600303	+	1.03976i	0.392471	+	0.919764i	$0.371620\pi$
$971$	−1.76368e7	+	3.05478e7i	−0.600303	+	1.03976i	−0.992775	+	0.119992i	$0.961713\pi$
$972$	−6.87741e7	+	3.37183e6i	−2.33485	+	0.114472i
$973$	9.45282e6	+	1.53966e6i	0.320095	+	0.0521367i
$974$		−	2.99684e7i		−	1.01220i
$975$	1.80945e7	−	2.08124e6i	0.609587	−	0.0701151i
$976$	5.60567e7	−	3.23644e7i	1.88366	−	1.08753i
$977$	−2.54762e7	+	1.47087e7i	−0.853884	+	0.492990i	−0.861959	−	0.506978i	$-0.830763\pi$
$977$	−2.54762e7	+	1.47087e7i	−0.853884	+	0.492990i	0.00807575	+	0.999967i	$0.497429\pi$
$978$	2.37473e7	−	2.73144e6i	0.793904	−	0.0913154i
$979$		−	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	$-0.0535806\pi$
$983$	1.05382e7	+	1.82528e7i	0.347844	+	0.602483i	−0.638022	+	0.770018i	$0.720247\pi$
$984$	−4.93864e6	+	1.13914e7i	−0.162600	+	0.375052i
$985$	−3.78517e6	−	2.18537e6i	−0.124307	−	0.0717685i
$986$	8.92588e6			0.292387
$987$	5.64695e6	+	1.09359e7i	0.184511	+	0.357324i
$988$	5.64155e7			1.83868
$989$	−2.21034e7	−	1.27614e7i	−0.718569	−	0.414866i
$990$	−3.52043e7	+	8.20702e6i	−1.14158	+	0.266132i
$991$	−1.45076e7	−	2.51279e7i	−0.469257	−	0.812778i	0.530125	−	0.847920i	$-0.322145\pi$
$991$	−1.45076e7	−	2.51279e7i	−0.469257	−	0.812778i	−0.999382	+	0.0351419i	$0.988812\pi$
$992$	−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
$996$	1.06007e7	+	9.21638e7i	0.338601	+	2.94383i
$997$	−3.54751e7	+	2.04816e7i	−1.13028	+	0.652568i	−0.944005	−	0.329930i	$-0.892975\pi$
$997$	−3.54751e7	+	2.04816e7i	−1.13028	+	0.652568i	−0.186275	+	0.982498i	$0.559641\pi$
$998$	2.38813e7	−	1.37879e7i	0.758981	−	0.438198i
$999$	7.27115e6	+	1.32348e6i	0.230510	+	0.0419569i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.g.c.5.1	✓	16	1.1	even	1	trivial
21.6.g.c.5.8	yes	16	3.2	odd	2	inner
21.6.g.c.17.1	yes	16	21.17	even	6	inner
21.6.g.c.17.8	yes	16	7.3	odd	6	inner
147.6.c.c.146.1		16	21.5	even	6
147.6.c.c.146.2		16	21.2	odd	6
147.6.c.c.146.15		16	7.2	even	3
147.6.c.c.146.16		16	7.5	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-8.95007 - 5.16733i) q^{2} +(14.3022 + 6.20057i) q^{3} +(37.4025 + 64.7831i) q^{4} +(15.8704 - 27.4884i) q^{5} +(-95.9654 - 129.400i) q^{6} +(20.8412 - 127.956i) q^{7} -442.375i q^{8} +(166.106 + 177.364i) q^{9} +O(q^{10})\)	\(q+(-8.95007 - 5.16733i) q^{2} +(14.3022 + 6.20057i) 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} +(166.106 + 177.364i) q^{9} +(-284.083 + 164.015i) q^{10} +(392.733 - 226.744i) q^{11} +(133.247 + 1158.46i) 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} +(-570.164 - 2445.74i) q^{18} +(1183.66 + 683.387i) q^{19} +2374.38 q^{20} +(1091.47 - 1700.82i) q^{21} -4686.65 q^{22} +(-2804.16 - 1618.98i) q^{23} +(2742.98 - 6326.94i) 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} +(-5080.00 + 584.305i) q^{30} +(-6122.73 + 3534.96i) q^{31} +(7234.08 - 4176.60i) q^{32} +(7022.89 - 807.777i) 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} +(3421.39 - 7891.76i) q^{39} +(-12160.2 - 7020.68i) q^{40} -1800.47 q^{41} +(-18557.5 + 9582.46i) q^{42} +7882.36 q^{43} +(29378.4 + 16961.6i) q^{44} +(7511.61 - 1751.15i) 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} +(958.600 + 8334.15i) q^{51} +(35746.4 - 20638.2i) q^{52} +(-12278.4 + 7088.96i) q^{53} +(7010.37 - 38514.8i) 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} +(33958.8 + 14722.5i) q^{60} +(-25737.3 - 14859.5i) q^{61} +73065.1 q^{62} +(26156.5 - 17557.7i) q^{63} -16630.3 q^{64} +(-15167.7 - 8757.08i) q^{65} +(-67029.4 - 29059.9i) 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} +(78461.2 - 73481.1i) q^{72} +(8505.52 - 4910.67i) q^{73} +(-17462.2 + 10081.8i) q^{74} +(3771.83 + 32792.6i) 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} +(-3866.66 + 58922.3i) q^{81} +(16114.3 + 9303.61i) q^{82} +79557.4 q^{83} +(151008. + 7094.03i) q^{84} +17081.7 q^{85} +(-70547.7 - 40730.7i) q^{86} +(-9951.18 + 22953.3i) 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} +(-109487. + 12593.3i) q^{93} +(54507.9 - 31470.2i) q^{94} +(37570.4 - 21691.3i) q^{95} +(129361. - 14879.1i) 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

Varieties

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Database

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