LMFDB - Embedded newform 40.6.k.a.27.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,6,Mod(3,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

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

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

chi := DirichletCharacter("40.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	40.k (of order $4$, 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:	$6.41535279252$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.5
Character	$\chi$	$=$	40.27
Dual form			40.6.k.a.3.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.60750 + 3.28191i) q^{2} +(-7.52871 + 7.52871i) q^{3} +(10.4581 - 30.2428i) q^{4} +(50.5551 - 23.8576i) q^{5} +(9.97997 - 59.3971i) q^{6} +(51.0903 - 51.0903i) q^{7} +(51.0685 + 173.666i) q^{8} +129.637i q^{9} +O(q^{10})$	\(q+(-4.60750 + 3.28191i) q^{2} +(-7.52871 + 7.52871i) q^{3} +(10.4581 - 30.2428i) q^{4} +(50.5551 - 23.8576i) q^{5} +(9.97997 - 59.3971i) q^{6} +(51.0903 - 51.0903i) q^{7} +(51.0685 + 173.666i) q^{8} +129.637i q^{9} +(-154.634 + 275.841i) q^{10} -209.146 q^{11} +(148.953 + 306.425i) q^{12} +(528.819 + 528.819i) q^{13} +(-67.7247 + 403.073i) q^{14} +(-200.998 + 560.231i) q^{15} +(-805.256 - 632.565i) q^{16} +(1178.43 + 1178.43i) q^{17} +(-425.457 - 597.303i) q^{18} -386.096i q^{19} +(-192.809 - 1778.43i) q^{20} +769.289i q^{21} +(963.642 - 686.400i) q^{22} +(2784.05 + 2784.05i) q^{23} +(-1691.96 - 923.004i) q^{24} +(1986.63 - 2412.24i) q^{25} +(-4172.07 - 700.996i) q^{26} +(-2805.48 - 2805.48i) q^{27} +(-1010.81 - 2079.42i) q^{28} -162.172 q^{29} +(-912.532 - 3240.92i) q^{30} +764.769i q^{31} +(5786.24 + 271.766i) q^{32} +(1574.60 - 1574.60i) q^{33} +(-9297.09 - 1562.11i) q^{34} +(1363.99 - 3801.77i) q^{35} +(3920.59 + 1355.76i) q^{36} +(1723.18 - 1723.18i) q^{37} +(1267.13 + 1778.94i) q^{38} -7962.64 q^{39} +(6725.03 + 7561.35i) q^{40} +13822.2 q^{41} +(-2524.74 - 3544.50i) q^{42} +(-13834.7 + 13834.7i) q^{43} +(-2187.28 + 6325.17i) q^{44} +(3092.82 + 6553.81i) q^{45} +(-21964.5 - 3690.51i) q^{46} +(8464.74 - 8464.74i) q^{47} +(10824.9 - 1300.14i) q^{48} +11586.6i q^{49} +(-1236.64 + 17634.4i) q^{50} -17744.1 q^{51} +(21523.4 - 10462.5i) q^{52} +(-3998.09 - 3998.09i) q^{53} +(22133.6 + 3718.91i) q^{54} +(-10573.4 + 4989.72i) q^{55} +(11481.8 + 6263.57i) q^{56} +(2906.81 + 2906.81i) q^{57} +(747.209 - 532.235i) q^{58} -1240.72i q^{59} +(14840.9 + 11937.7i) q^{60} -50507.3i q^{61} +(-2509.91 - 3523.68i) q^{62} +(6623.20 + 6623.20i) q^{63} +(-27552.0 + 17737.8i) q^{64} +(39350.8 + 14118.1i) q^{65} +(-2087.27 + 12422.7i) q^{66} +(-47228.8 - 47228.8i) q^{67} +(47963.0 - 23314.8i) q^{68} -41920.6 q^{69} +(6192.50 + 21993.1i) q^{70} -26226.6i q^{71} +(-22513.6 + 6620.37i) q^{72} +(-13699.8 + 13699.8i) q^{73} +(-2284.23 + 13594.9i) q^{74} +(3204.29 + 33117.9i) q^{75} +(-11676.6 - 4037.84i) q^{76} +(-10685.4 + 10685.4i) q^{77} +(36687.9 - 26132.7i) q^{78} -41902.4 q^{79} +(-55801.2 - 12767.9i) q^{80} +10741.4 q^{81} +(-63685.8 + 45363.2i) q^{82} +(20497.1 - 20497.1i) q^{83} +(23265.5 + 8045.31i) q^{84} +(87689.8 + 31461.1i) q^{85} +(18339.0 - 109147. i) q^{86} +(1220.95 - 1220.95i) q^{87} +(-10680.8 - 36321.7i) q^{88} -64749.3i q^{89} +(-35759.2 - 20046.3i) q^{90} +54035.1 q^{91} +(113313. - 55081.6i) q^{92} +(-5757.73 - 5757.73i) q^{93} +(-11220.8 + 66781.8i) q^{94} +(-9211.32 - 19519.1i) q^{95} +(-45609.0 + 41516.9i) q^{96} +(-83188.7 - 83188.7i) q^{97} +(-38026.0 - 53385.0i) q^{98} -27113.1i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8}+O(q^{10}) $ 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8	$ 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8} - 570 q^{10} - 8 q^{11} - 308 q^{12} + 456 q^{16} - 408 q^{17} + 3370 q^{18} + 1360 q^{20} - 3148 q^{22} - 3120 q^{25} - 5084 q^{26} + 968 q^{27} - 10020 q^{28} + 21100 q^{30} + 7968 q^{32} - 976 q^{33} - 4780 q^{35} + 23132 q^{36} - 49524 q^{38} - 58980 q^{40} - 8 q^{41} + 42060 q^{42} + 1308 q^{43} + 42416 q^{46} + 93776 q^{48} - 94010 q^{50} + 20872 q^{51} - 67180 q^{52} - 43384 q^{56} + 968 q^{57} + 86100 q^{58} + 118180 q^{60} + 6240 q^{62} + 17680 q^{65} - 41128 q^{66} + 89252 q^{67} - 158164 q^{68} + 116980 q^{70} + 1180 q^{72} - 25184 q^{73} - 127740 q^{75} + 41592 q^{76} - 161440 q^{78} - 167360 q^{80} - 67792 q^{81} + 23412 q^{82} - 126444 q^{83} - 192704 q^{86} + 100176 q^{88} - 82330 q^{90} + 329432 q^{91} + 226020 q^{92} + 358176 q^{96} + 212576 q^{97} + 65834 q^{98}+O(q^{100}) $ 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8 - 570 * q^10 - 8 * q^11 - 308 * q^12 + 456 * q^16 - 408 * q^17 + 3370 * q^18 + 1360 * q^20 - 3148 * q^22 - 3120 * q^25 - 5084 * q^26 + 968 * q^27 - 10020 * q^28 + 21100 * q^30 + 7968 * q^32 - 976 * q^33 - 4780 * q^35 + 23132 * q^36 - 49524 * q^38 - 58980 * q^40 - 8 * q^41 + 42060 * q^42 + 1308 * q^43 + 42416 * q^46 + 93776 * q^48 - 94010 * q^50 + 20872 * q^51 - 67180 * q^52 - 43384 * q^56 + 968 * q^57 + 86100 * q^58 + 118180 * q^60 + 6240 * q^62 + 17680 * q^65 - 41128 * q^66 + 89252 * q^67 - 158164 * q^68 + 116980 * q^70 + 1180 * q^72 - 25184 * q^73 - 127740 * q^75 + 41592 * q^76 - 161440 * q^78 - 167360 * q^80 - 67792 * q^81 + 23412 * q^82 - 126444 * q^83 - 192704 * q^86 + 100176 * q^88 - 82330 * q^90 + 329432 * q^91 + 226020 * q^92 + 358176 * q^96 + 212576 * q^97 + 65834 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

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 $

$2$	−4.60750	+	3.28191i	−0.814499	+	0.580166i
$2$	−4.60750	+	3.28191i	−0.814499	+	0.580166i
$3$	−7.52871	+	7.52871i	−0.482967	+	0.482967i	−0.906078	−	0.423111i	$-0.860938\pi$
$3$	−7.52871	+	7.52871i	−0.482967	+	0.482967i	0.423111	+	0.906078i	$0.360938\pi$
$4$	10.4581	−	30.2428i	0.326816	−	0.945088i
$5$	50.5551	−	23.8576i	0.904357	−	0.426777i
$5$	50.5551	−	23.8576i	0.904357	−	0.426777i
$6$	9.97997	−	59.3971i	0.113175	−	0.673577i
$7$	51.0903	−	51.0903i	0.394088	−	0.394088i	−0.482053	−	0.876142i	$-0.660109\pi$
$7$	51.0903	−	51.0903i	0.394088	−	0.394088i	0.876142	+	0.482053i	$0.160109\pi$
$8$	51.0685	+	173.666i	0.282116	+	0.959380i
$9$			129.637i			0.533486i
$10$	−154.634	+	275.841i	−0.488996	+	0.872286i
$11$	−209.146			−0.521157			−0.260578	−	0.965453i	$-0.583913\pi$
$11$	−209.146			−0.521157			−0.260578	+	0.965453i	$0.583913\pi$
$12$	148.953	+	306.425i	0.298605	+	0.614288i
$13$	528.819	+	528.819i	0.867857	+	0.867857i	0.992235	−	0.124378i	$-0.0396934\pi$
$13$	528.819	+	528.819i	0.867857	+	0.867857i	−0.124378	+	0.992235i	$0.539693\pi$
$14$	−67.7247	+	403.073i	−0.0923480	+	0.549621i
$15$	−200.998	+	560.231i	−0.230655	+	0.642894i
$16$	−805.256	−	632.565i	−0.786383	−	0.617740i
$17$	1178.43	+	1178.43i	0.988963	+	0.988963i	0.999940	−	0.0109768i	$-0.00349409\pi$
$17$	1178.43	+	1178.43i	0.988963	+	0.988963i	−0.0109768	+	0.999940i	$0.503494\pi$
$18$	−425.457	−	597.303i	−0.309510	−	0.434523i
$19$		−	386.096i		−	0.245364i	−0.992446	−	0.122682i	$-0.960850\pi$
$19$		−	386.096i		−	0.245364i	0.992446	−	0.122682i	$-0.0391496\pi$
$20$	−192.809	−	1778.43i	−0.107784	−	0.994174i
$21$			769.289i			0.380663i
$22$	963.642	−	686.400i	0.424482	−	0.302357i
$23$	2784.05	+	2784.05i	1.09738	+	1.09738i	0.994716	+	0.102666i	$0.0327372\pi$
$23$	2784.05	+	2784.05i	1.09738	+	1.09738i	0.102666	+	0.994716i	$0.467263\pi$
$24$	−1691.96	−	923.004i	−0.599602	−	0.327096i
$25$	1986.63	−	2412.24i	0.635723	−	0.771918i
$26$	−4172.07	−	700.996i	−1.21037	−	0.203368i
$27$	−2805.48	−	2805.48i	−0.740623	−	0.740623i
$28$	−1010.81	−	2079.42i	−0.243654	−	0.501243i
$29$	−162.172			−0.0358081			−0.0179041	−	0.999840i	$-0.505699\pi$
$29$	−162.172			−0.0358081			−0.0179041	+	0.999840i	$0.505699\pi$
$30$	−912.532	−	3240.92i	−0.185116	−	0.657454i
$31$			764.769i			0.142931i	0.997443	+	0.0714655i	$0.0227676\pi$
$31$			764.769i			0.142931i	−0.997443	+	0.0714655i	$0.977232\pi$
$32$	5786.24	+	271.766i	0.998899	+	0.0469159i
$33$	1574.60	−	1574.60i	0.251702	−	0.251702i
$34$	−9297.09	−	1562.11i	−1.37927	−	0.231747i
$35$	1363.99	−	3801.77i	0.188209	−	0.524585i
$36$	3920.59	+	1355.76i	0.504191	+	0.174352i
$37$	1723.18	−	1723.18i	0.206932	−	0.206932i	−0.596030	−	0.802962i	$-0.703256\pi$
$37$	1723.18	−	1723.18i	0.206932	−	0.206932i	0.802962	+	0.596030i	$0.203256\pi$
$38$	1267.13	+	1778.94i	0.142352	+	0.199849i
$39$	−7962.64			−0.838293
$40$	6725.03	+	7561.35i	0.664575	+	0.747221i
$41$	13822.2			1.28415			0.642077	−	0.766640i	$-0.278073\pi$
$41$	13822.2			1.28415			0.642077	+	0.766640i	$0.278073\pi$
$42$	−2524.74	−	3544.50i	−0.220848	−	0.310050i
$43$	−13834.7	+	13834.7i	−1.14103	+	1.14103i	−0.152768	+	0.988262i	$0.548819\pi$
$43$	−13834.7	+	13834.7i	−1.14103	+	1.14103i	−0.988262	+	0.152768i	$0.951181\pi$
$44$	−2187.28	+	6325.17i	−0.170322	+	0.492539i
$45$	3092.82	+	6553.81i	0.227680	+	0.482462i
$46$	−21964.5	−	3690.51i	−1.53048	−	0.257153i
$47$	8464.74	−	8464.74i	0.558945	−	0.558945i	−0.370062	−	0.929007i	$-0.620664\pi$
$47$	8464.74	−	8464.74i	0.558945	−	0.558945i	0.929007	+	0.370062i	$0.120664\pi$
$48$	10824.9	−	1300.14i	0.678145	−	0.0814491i
$49$			11586.6i			0.689389i
$50$	−1236.64	+	17634.4i	−0.0699552	+	0.997550i
$51$	−17744.1			−0.955273
$52$	21523.4	−	10462.5i	1.10383	−	0.536572i
$53$	−3998.09	−	3998.09i	−0.195507	−	0.195507i	0.602564	−	0.798071i	$-0.294146\pi$
$53$	−3998.09	−	3998.09i	−0.195507	−	0.195507i	−0.798071	+	0.602564i	$0.794146\pi$
$54$	22133.6	+	3718.91i	1.03292	+	0.173552i
$55$	−10573.4	+	4989.72i	−0.471312	+	0.222418i
$56$	11481.8	+	6263.57i	0.489260	+	0.266902i
$57$	2906.81	+	2906.81i	0.118503	+	0.118503i
$58$	747.209	−	532.235i	0.0291657	−	0.0207747i
$59$		−	1240.72i		−	0.0464027i	−0.999731	−	0.0232013i	$-0.992614\pi$
$59$		−	1240.72i		−	0.0464027i	0.999731	−	0.0232013i	$-0.00738588\pi$
$60$	14840.9	+	11937.7i	0.532209	+	0.428097i
$61$		−	50507.3i		−	1.73792i	−0.494884	−	0.868959i	$-0.664789\pi$
$61$		−	50507.3i		−	1.73792i	0.494884	−	0.868959i	$-0.335211\pi$
$62$	−2509.91	−	3523.68i	−0.0829236	−	0.116417i
$63$	6623.20	+	6623.20i	0.210241	+	0.210241i
$64$	−27552.0	+	17737.8i	−0.840821	+	0.541314i
$65$	39350.8	+	14118.1i	1.15523	+	0.414471i
$66$	−2087.27	+	12422.7i	−0.0589820	+	0.351039i
$67$	−47228.8	−	47228.8i	−1.28535	−	1.28535i	−0.937583	−	0.347763i	$-0.886942\pi$
$67$	−47228.8	−	47228.8i	−1.28535	−	1.28535i	−0.347763	−	0.937583i	$-0.613058\pi$
$68$	47963.0	−	23314.8i	1.25787	−	0.611448i
$69$	−41920.6			−1.06000
$70$	6192.50	+	21993.1i	0.151050	+	0.536466i
$71$		−	26226.6i		−	0.617443i	−0.951153	−	0.308721i	$-0.900099\pi$
$71$		−	26226.6i		−	0.617443i	0.951153	−	0.308721i	$-0.0999010\pi$
$72$	−22513.6	+	6620.37i	−0.511816	+	0.150505i
$73$	−13699.8	+	13699.8i	−0.300889	+	0.300889i	−0.841362	−	0.540473i	$-0.818245\pi$
$73$	−13699.8	+	13699.8i	−0.300889	+	0.300889i	0.540473	+	0.841362i	$0.318245\pi$
$74$	−2284.23	+	13594.9i	−0.0484909	+	0.288600i
$75$	3204.29	+	33117.9i	0.0657777	+	0.679844i
$76$	−11676.6	−	4037.84i	−0.231891	−	0.0801890i
$77$	−10685.4	+	10685.4i	−0.205382	+	0.205382i
$78$	36687.9	−	26132.7i	0.682788	−	0.486349i
$79$	−41902.4			−0.755390			−0.377695	−	0.925930i	$-0.623283\pi$
$79$	−41902.4			−0.755390			−0.377695	+	0.925930i	$0.623283\pi$
$80$	−55801.2	−	12767.9i	−0.974808	−	0.223047i
$81$	10741.4			0.181907
$82$	−63685.8	+	45363.2i	−1.04594	+	0.745022i
$83$	20497.1	−	20497.1i	0.326586	−	0.326586i	−0.524701	−	0.851287i	$-0.675823\pi$
$83$	20497.1	−	20497.1i	0.326586	−	0.326586i	0.851287	+	0.524701i	$0.175823\pi$
$84$	23265.5	+	8045.31i	0.359760	+	0.124407i
$85$	87689.8	+	31461.1i	1.31644	+	0.472309i
$86$	18339.0	−	109147.i	0.267381	−	1.59135i
$87$	1220.95	−	1220.95i	0.0172942	−	0.0172942i
$88$	−10680.8	−	36321.7i	−0.147027	−	0.499988i
$89$		−	64749.3i		−	0.866483i	−0.901278	−	0.433241i	$-0.857370\pi$
$89$		−	64749.3i		−	0.866483i	0.901278	−	0.433241i	$-0.142630\pi$
$90$	−35759.2	−	20046.3i	−0.465352	−	0.260872i
$91$	54035.1			0.684025
$92$	113313.	−	55081.6i	1.39576	−	0.678480i
$93$	−5757.73	−	5757.73i	−0.0690309	−	0.0690309i
$94$	−11220.8	+	66781.8i	−0.130979	+	0.779540i
$95$	−9211.32	−	19519.1i	−0.104716	−	0.221897i
$96$	−45609.0	+	41516.9i	−0.505094	+	0.459776i
$97$	−83188.7	−	83188.7i	−0.897708	−	0.897708i	0.0975250	−	0.995233i	$-0.468907\pi$
$97$	−83188.7	−	83188.7i	−0.897708	−	0.897708i	−0.995233	+	0.0975250i	$0.968907\pi$
$98$	−38026.0	−	53385.0i	−0.399959	−	0.561506i
$99$		−	27113.1i		−	0.278030i
$100$	−52176.6	−	85308.9i	−0.521766	−	0.853089i
$101$			125685.i			1.22597i	0.790096	+	0.612984i	$0.210031\pi$
$101$			125685.i			1.22597i	−0.790096	+	0.612984i	$0.789969\pi$
$102$	81755.7	−	58234.4i	0.778068	−	0.554216i
$103$	125285.	+	125285.i	1.16361	+	1.16361i	0.983680	+	0.179926i	$0.0575858\pi$
$103$	125285.	+	125285.i	1.16361	+	1.16361i	0.179926	+	0.983680i	$0.442414\pi$
$104$	−64832.0	+	118844.i	−0.587768	+	1.07744i
$105$	18353.4	+	38891.5i	0.162458	+	0.344256i
$106$	31542.6	+	5299.82i	0.272667	+	0.0458138i
$107$	103805.	+	103805.i	0.876512	+	0.876512i	0.993172	−	0.116660i	$-0.0372187\pi$
$107$	103805.	+	103805.i	0.876512	+	0.876512i	−0.116660	+	0.993172i	$0.537219\pi$
$108$	−114185.	+	55505.5i	−0.942001	+	0.457907i
$109$	39926.6			0.321881			0.160941	−	0.986964i	$-0.448547\pi$
$109$	39926.6			0.321881			0.160941	+	0.986964i	$0.448547\pi$
$110$	32341.2	−	57691.1i	0.254844	−	0.454598i
$111$			25946.7i			0.199882i
$112$	−73458.8	+	8822.82i	−0.553348	+	0.0664603i
$113$	−139038.	+	139038.i	−1.02432	+	1.02432i	−0.0246238	+	0.999697i	$0.507839\pi$
$113$	−139038.	+	139038.i	−1.02432	+	1.02432i	−0.999697	+	0.0246238i	$0.992161\pi$
$114$	−22933.0	−	3853.23i	−0.165272	−	0.0277692i
$115$	207169.	+	74327.3i	1.46076	+	0.524087i
$116$	−1696.02	+	4904.55i	−0.0117027	+	0.0338418i
$117$	−68554.5	+	68554.5i	−0.462990	+	0.462990i
$118$	4071.93	+	5716.61i	0.0269212	+	0.0377949i
$119$	120412.			0.779478
$120$	−107558.	−	6296.39i	−0.681851	−	0.0399152i
$121$	−117309.			−0.728395
$122$	165760.	+	232712.i	1.00828	+	1.41553i
$123$	−104063.	+	104063.i	−0.620204	+	0.620204i
$124$	23128.8	+	7998.04i	0.135082	+	0.0467121i
$125$	42884.2	−	169347.i	0.245483	−	0.969401i
$126$	−52253.2	−	8779.64i	−0.293215	−	0.0492663i
$127$	16619.7	−	16619.7i	0.0914356	−	0.0914356i	−0.659910	−	0.751345i	$-0.729405\pi$
$127$	16619.7	−	16619.7i	0.0914356	−	0.0914356i	0.751345	+	0.659910i	$0.229405\pi$
$128$	68732.1	−	172150.i	0.370796	−	0.928714i
$129$		−	208314.i		−	1.10216i
$130$	−227643.	+	64096.5i	−1.18140	+	0.332641i
$131$	155820.			0.793314			0.396657	−	0.917967i	$-0.370170\pi$
$131$	155820.			0.793314			0.396657	+	0.917967i	$0.370170\pi$
$132$	−31153.0	−	64087.8i	−0.155620	−	0.320140i
$133$	−19725.8	−	19725.8i	−0.0966953	−	0.0966953i
$134$	372607.	+	62605.9i	1.79262	+	0.301199i
$135$	−208763.	−	74899.3i	−0.985868	−	0.353707i
$136$	−144472.	+	264833.i	−0.669789	+	1.22779i
$137$	−41457.8	−	41457.8i	−0.188714	−	0.188714i	0.606426	−	0.795140i	$-0.292603\pi$
$137$	−41457.8	−	41457.8i	−0.188714	−	0.188714i	−0.795140	+	0.606426i	$0.792603\pi$
$138$	193149.	−	137580.i	0.863367	−	0.614974i
$139$		−	351852.i		−	1.54462i	−0.635244	−	0.772312i	$-0.719100\pi$
$139$		−	351852.i		−	1.54462i	0.635244	−	0.772312i	$-0.280900\pi$
$140$	−100711.	−	81010.1i	−0.434269	−	0.349316i
$141$			127457.i			0.539904i
$142$	86073.5	+	120839.i	0.358219	+	0.502906i
$143$	−110600.	−	110600.i	−0.452290	−	0.452290i
$144$	82003.9	−	104391.i	0.329555	−	0.419524i
$145$	−8198.64	+	3869.04i	−0.0323833	+	0.0152821i
$146$	18160.3	−	108083.i	0.0705083	−	0.419639i
$147$	−87231.8	−	87231.8i	−0.332952	−	0.332952i
$148$	−34092.7	−	70135.1i	−0.127940	−	0.263197i
$149$	−168103.			−0.620312			−0.310156	−	0.950686i	$-0.600381\pi$
$149$	−168103.			−0.620312			−0.310156	+	0.950686i	$0.600381\pi$
$150$	−123454.	−	142074.i	−0.447998	−	0.515570i
$151$		−	327727.i		−	1.16969i	−0.811146	−	0.584844i	$-0.801156\pi$
$151$		−	327727.i		−	1.16969i	0.811146	−	0.584844i	$-0.198844\pi$
$152$	67051.9	−	19717.4i	0.235398	−	0.0692213i
$153$	−152768.	+	152768.i	−0.527598	+	0.527598i
$154$	14164.4	−	84301.2i	0.0481278	−	0.286439i
$155$	18245.5	+	38663.0i	0.0609997	+	0.129261i
$156$	−83274.2	+	240813.i	−0.273967	+	0.792261i
$157$	143534.	−	143534.i	0.464735	−	0.464735i	−0.435469	−	0.900204i	$-0.643417\pi$
$157$	143534.	−	143534.i	0.464735	−	0.464735i	0.900204	+	0.435469i	$0.143417\pi$
$158$	193065.	−	137520.i	0.615264	−	0.438251i
$159$	60200.9			0.188847
$160$	299008.	−	124306.i	0.923384	−	0.383878i
$161$	284476.			0.864931
$162$	−49491.2	+	35252.4i	−0.148163	+	0.105536i
$163$	−186517.	+	186517.i	−0.549855	+	0.549855i	−0.926399	−	0.376544i	$-0.877113\pi$
$163$	−186517.	+	186517.i	−0.549855	+	0.549855i	0.376544	+	0.926399i	$0.377113\pi$
$164$	144554.	−	418022.i	0.419682	−	1.21364i
$165$	42038.0	−	117170.i	0.120208	−	0.335049i
$166$	−27170.7	+	161710.i	−0.0765299	+	0.455477i
$167$	−433646.	+	433646.i	−1.20322	+	1.20322i	−0.230036	+	0.973182i	$0.573884\pi$
$167$	−433646.	+	433646.i	−1.20322	+	1.20322i	−0.973182	+	0.230036i	$0.926116\pi$
$168$	−133600.	+	39286.4i	−0.365201	+	0.107391i
$169$			188005.i			0.506353i
$170$	−507283.	+	142833.i	−1.34626	+	0.379060i
$171$	50052.4			0.130898
$172$	273715.	+	563083.i	0.705467	+	1.45128i
$173$	−302751.	−	302751.i	−0.769077	−	0.769077i	0.208867	−	0.977944i	$-0.433022\pi$
$173$	−302751.	−	302751.i	−0.769077	−	0.769077i	−0.977944	+	0.208867i	$0.933022\pi$
$174$	−1618.47	+	9632.57i	−0.00405259	+	0.0241195i
$175$	−21744.5	−	224740.i	−0.0536729	−	0.554735i
$176$	168416.	+	132299.i	0.409829	+	0.321939i
$177$	9341.01	+	9341.01i	0.0224110	+	0.0224110i
$178$	212501.	+	298332.i	0.502704	+	0.705749i
$179$			262028.i			0.611245i	0.952153	+	0.305623i	$0.0988646\pi$
$179$			262028.i			0.611245i	−0.952153	+	0.305623i	$0.901135\pi$
$180$	230551.	−	24995.2i	0.530378	−	0.0575011i
$181$			323424.i			0.733798i	0.930261	+	0.366899i	$0.119581\pi$
$181$			323424.i			0.733798i	−0.930261	+	0.366899i	$0.880419\pi$
$182$	−248967.	+	177338.i	−0.557138	+	0.396848i
$183$	380255.	+	380255.i	0.839357	+	0.839357i
$184$	−341319.	+	625674.i	−0.743217	+	1.36240i
$185$	46004.7	−	128227.i	0.0988264	−	0.275454i
$186$	45425.1	+	7632.37i	0.0962750	+	0.0161762i
$187$	−246463.	−	246463.i	−0.515405	−	0.515405i
$188$	−167472.	−	344523.i	−0.345580	−	0.710924i
$189$	−286666.			−0.583742
$190$	106501.	+	59703.7i	0.214028	+	0.119982i
$191$		−	672294.i		−	1.33345i	−0.745305	−	0.666724i	$-0.767696\pi$
$191$		−	672294.i		−	1.33345i	0.745305	−	0.666724i	$-0.232304\pi$
$192$	73888.6	−	340974.i	0.144652	−	0.667525i
$193$	−25987.0	+	25987.0i	−0.0502185	+	0.0502185i	−0.731770	−	0.681552i	$-0.761306\pi$
$193$	−25987.0	+	25987.0i	−0.0502185	+	0.0502185i	0.681552	+	0.731770i	$0.261306\pi$
$194$	656310.	+	110274.i	1.25200	+	0.210363i
$195$	−402552.	+	189969.i	−0.758116	+	0.357764i
$196$	350410.	+	121173.i	0.651533	+	0.225303i
$197$	223666.	−	223666.i	0.410614	−	0.410614i	−0.471338	−	0.881952i	$-0.656229\pi$
$197$	223666.	−	223666.i	0.410614	−	0.410614i	0.881952	+	0.471338i	$0.156229\pi$
$198$	88982.8	+	124924.i	0.161303	+	0.226455i
$199$	969198.			1.73492			0.867460	−	0.497506i	$-0.165751\pi$
$199$	969198.			1.73492			0.867460	+	0.497506i	$0.165751\pi$
$200$	520380.	+	221822.i	0.919910	+	0.392129i
$201$	711144.			1.24156
$202$	−412486.	−	579092.i	−0.711264	−	0.998549i
$203$	−8285.44	+	8285.44i	−0.0141116	+	0.0141116i
$204$	−185569.	+	536630.i	−0.312198	+	0.902817i
$205$	698782.	−	329764.i	1.16133	−	0.548048i
$206$	−988425.	−	166076.i	−1.62284	−	0.272671i
$207$	−360916.	+	360916.i	−0.585438	+	0.585438i
$208$	−91322.0	−	760347.i	−0.146358	−	1.21858i
$209$			80750.6i			0.127873i
$210$	−212201.	−	118958.i	−0.332047	−	0.186143i
$211$	−495120.			−0.765604			−0.382802	−	0.923830i	$-0.625041\pi$
$211$	−495120.			−0.765604			−0.382802	+	0.923830i	$0.625041\pi$
$212$	−162726.	+	79101.0i	−0.248666	+	0.120877i
$213$	197453.	+	197453.i	0.298204	+	0.298204i
$214$	−818959.	−	137602.i	−1.22244	−	0.205396i
$215$	−369351.	+	1.02947e6i	−0.544933	+	1.51886i
$216$	343945.	−	630488.i	0.501597	−	0.919481i
$217$	39072.3	+	39072.3i	0.0563274	+	0.0563274i
$218$	−183962.	+	131035.i	−0.262172	+	0.186744i
$219$		−	206283.i		−	0.290639i
$220$	40325.4	+	371953.i	0.0561722	+	0.518121i
$221$			1.24635e6i			1.71656i
$222$	−85154.7	−	119549.i	−0.115965	−	0.162804i
$223$	−5174.56	−	5174.56i	−0.00696804	−	0.00696804i	0.703614	−	0.710582i	$-0.251568\pi$
$223$	−5174.56	−	5174.56i	−0.00696804	−	0.00696804i	−0.710582	+	0.703614i	$0.751568\pi$
$224$	309506.	−	281736.i	0.412144	−	0.375166i
$225$	312716.	+	257541.i	0.411807	+	0.339149i
$226$	184306.	−	1.09692e6i	0.240032	−	1.42858i
$227$	96110.1	+	96110.1i	0.123795	+	0.123795i	0.766290	−	0.642495i	$-0.222101\pi$
$227$	96110.1	+	96110.1i	0.123795	+	0.123795i	−0.642495	+	0.766290i	$0.722101\pi$
$228$	118310.	−	57510.3i	0.150724	−	0.0732671i
$229$	−521668.			−0.657363			−0.328682	−	0.944441i	$-0.606604\pi$
$229$	−521668.			−0.657363			−0.328682	+	0.944441i	$0.606604\pi$
$230$	−1.19847e6	+	337446.i	−1.49385	+	0.420615i
$231$		−	160894.i		−	0.198385i
$232$	−8281.90	−	28163.9i	−0.0101021	−	0.0343536i
$233$	884493.	−	884493.i	1.06734	−	1.06734i	0.0697820	−	0.997562i	$-0.477770\pi$
$233$	884493.	−	884493.i	1.06734	−	1.06734i	0.997562	−	0.0697820i	$-0.0222304\pi$
$234$	90875.0	−	540855.i	0.108494	−	0.645715i
$235$	225988.	−	629884.i	0.266941	−	0.744031i
$236$	−37522.8	−	12975.6i	−0.0438546	−	0.0151651i
$237$	315471.	−	315471.i	0.364829	−	0.364829i
$238$	−554800.	+	395183.i	−0.634884	+	0.452226i
$239$	−258110.			−0.292287			−0.146144	−	0.989263i	$-0.546686\pi$
$239$	−258110.			−0.292287			−0.146144	+	0.989263i	$0.546686\pi$
$240$	516238.	−	323985.i	0.578524	−	0.363076i
$241$	297510.			0.329958			0.164979	−	0.986297i	$-0.447244\pi$
$241$	297510.			0.329958			0.164979	+	0.986297i	$0.447244\pi$
$242$	540500.	−	384997.i	0.593277	−	0.422590i
$243$	600862.	−	600862.i	0.652768	−	0.652768i
$244$	−1.52748e6	−	528211.i	−1.64249	−	0.567979i
$245$	276427.	+	585759.i	0.294215	+	0.623453i
$246$	137945.	−	820998.i	0.145334	−	0.864977i
$247$	204175.	−	204175.i	0.212941	−	0.212941i
$248$	−132815.	+	39055.6i	−0.137125	+	0.0403232i
$249$			308634.i			0.315460i
$250$	358194.	+	921010.i	0.362467	+	0.931997i
$251$	−1.73836e6			−1.74162			−0.870812	−	0.491617i	$-0.836406\pi$
$251$	−1.73836e6			−1.74162			−0.870812	+	0.491617i	$0.836406\pi$
$252$	269570.	−	131038.i	0.267406	−	0.129986i
$253$	−582274.	−	582274.i	−0.571908	−	0.571908i
$254$	−22030.9	+	131120.i	−0.0214264	+	0.127522i
$255$	−897052.	+	423330.i	−0.863908	+	0.407689i
$256$	248298.	+	1.01875e6i	0.236796	+	0.971560i
$257$	217479.	+	217479.i	0.205392	+	0.205392i	0.802306	−	0.596913i	$-0.203606\pi$
$257$	217479.	+	217479.i	0.205392	+	0.205392i	−0.596913	+	0.802306i	$0.703606\pi$
$258$	683669.	+	959808.i	0.639435	+	0.897708i
$259$		−	176076.i		−	0.163099i
$260$	838507.	−	1.04243e6i	0.769261	−	0.956343i
$261$		−	21023.5i		−	0.0191031i
$262$	−717941.	+	511388.i	−0.646153	+	0.460254i
$263$	1.05381e6	+	1.05381e6i	0.939446	+	0.939446i	0.998268	−	0.0588228i	$-0.0187347\pi$
$263$	1.05381e6	+	1.05381e6i	0.939446	+	0.939446i	−0.0588228	+	0.998268i	$0.518735\pi$
$264$	353868.	+	193043.i	0.312487	+	0.170468i
$265$	−297508.	−	106739.i	−0.260246	−	0.0933703i
$266$	155625.	+	26148.3i	0.134857	+	0.0226589i
$267$	487479.	+	487479.i	0.418483	+	0.418483i
$268$	−1.92226e6	+	934408.i	−1.63484	+	0.794693i
$269$	−584734.			−0.492695			−0.246347	−	0.969182i	$-0.579230\pi$
$269$	−584734.			−0.492695			−0.246347	+	0.969182i	$0.579230\pi$
$270$	1.20769e6	−	340043.i	1.00820	−	0.283873i
$271$		−	2.15271e6i		−	1.78059i	−0.455389	−	0.890293i	$-0.650500\pi$
$271$		−	2.15271e6i		−	1.78059i	0.455389	−	0.890293i	$-0.349500\pi$
$272$	−203503.	−	1.69437e6i	−0.166782	−	1.38862i
$273$	−406814.	+	406814.i	−0.330362	+	0.330362i
$274$	327078.	+	54956.0i	0.263193	+	0.0442220i
$275$	−415497.	+	504512.i	−0.331311	+	0.402290i
$276$	−438411.	+	1.26780e6i	−0.346424	+	1.00179i
$277$	1.45027e6	−	1.45027e6i	1.13566	−	1.13566i	0.146441	−	0.989219i	$-0.453218\pi$
$277$	1.45027e6	−	1.45027e6i	1.13566	−	1.13566i	0.989219	−	0.146441i	$-0.0467818\pi$
$278$	1.15475e6	+	1.62116e6i	0.896137	+	1.25809i
$279$	−99142.5			−0.0762516
$280$	729896.	+	42727.7i	0.556373	+	0.0325698i
$281$	−2.60522e6			−1.96825			−0.984123	−	0.177487i	$-0.943203\pi$
$281$	−2.60522e6			−1.96825			−0.984123	+	0.177487i	$0.943203\pi$
$282$	−418303.	−	587259.i	−0.313234	−	0.439751i
$283$	873350.	−	873350.i	0.648220	−	0.648220i	−0.304343	−	0.952563i	$-0.598437\pi$
$283$	873350.	−	873350.i	0.648220	−	0.648220i	0.952563	+	0.304343i	$0.0984368\pi$
$284$	−793167.	−	274281.i	−0.583538	−	0.201790i
$285$	216303.	+	77604.5i	0.157743	+	0.0565946i
$286$	872573.	+	146611.i	0.630793	+	0.105986i
$287$	706181.	−	706181.i	0.506071	−	0.506071i
$288$	−35230.9	+	750111.i	−0.0250290	+	0.532898i
$289$			1.35752e6i			0.956096i
$290$	25077.4	−	44733.8i	0.0175100	−	0.0312349i
$291$	1.25261e6			0.867127
$292$	271046.	+	557594.i	0.186031	+	0.382702i
$293$	−1.34847e6	−	1.34847e6i	−0.917640	−	0.917640i	0.0792171	−	0.996857i	$-0.474758\pi$
$293$	−1.34847e6	−	1.34847e6i	−0.917640	−	0.917640i	−0.996857	+	0.0792171i	$0.974758\pi$
$294$	688208.	+	115633.i	0.464356	+	0.0780216i
$295$	−29600.5	−	62724.6i	−0.0198036	−	0.0419646i
$296$	387259.	+	211259.i	0.256905	+	0.140147i
$297$	586755.	+	586755.i	0.385981	+	0.385981i
$298$	774536.	−	551700.i	0.505244	−	0.359884i
$299$			2.94452e6i			1.90474i
$300$	1.03509e6	+	249443.i	0.664009	+	0.160018i
$301$			1.41363e6i			0.899334i
$302$	1.07557e6	+	1.51000e6i	0.678613	+	0.952709i
$303$	−946244.	−	946244.i	−0.592102	−	0.592102i
$304$	−244231.	+	310906.i	−0.151571	+	0.192950i
$305$	−1.20498e6	−	2.55340e6i	−0.741704	−	1.57170i
$306$	202507.	−	1.20525e6i	0.123634	−	0.735822i
$307$	740904.	+	740904.i	0.448659	+	0.448659i	0.894908	−	0.446250i	$-0.147241\pi$
$307$	740904.	+	740904.i	0.448659	+	0.448659i	−0.446250	+	0.894908i	$0.647241\pi$
$308$	211407.	+	434904.i	0.126982	+	0.261226i
$309$	−1.88647e6			−1.12397
$310$	−210955.	−	118259.i	−0.124677	−	0.0698927i
$311$			984867.i			0.577400i	0.957420	+	0.288700i	$0.0932230\pi$
$311$			984867.i			0.577400i	−0.957420	+	0.288700i	$0.906777\pi$
$312$	−406640.	−	1.38284e6i	−0.236496	−	0.804242i
$313$	−84112.7	+	84112.7i	−0.0485289	+	0.0485289i	−0.730955	−	0.682426i	$-0.760925\pi$
$313$	−84112.7	+	84112.7i	−0.0485289	+	0.0485289i	0.682426	+	0.730955i	$0.260925\pi$
$314$	−190267.	+	1.13240e6i	−0.108903	+	0.648150i
$315$	492850.	+	176823.i	0.279858	+	0.100407i
$316$	−438220.	+	1.26725e6i	−0.246874	+	0.713910i
$317$	−965201.	+	965201.i	−0.539473	+	0.539473i	−0.923374	−	0.383901i	$-0.874580\pi$
$317$	−965201.	+	965201.i	−0.539473	+	0.539473i	0.383901	+	0.923374i	$0.374580\pi$
$318$	−277376.	+	197574.i	−0.153816	+	0.109563i
$319$	33917.7			0.0186617
$320$	−969714.	+	1.55406e6i	−0.529382	+	0.848384i
$321$	−1.56303e6			−0.846653
$322$	−1.31072e6	+	933626.i	−0.704485	+	0.501803i
$323$	454986.	−	454986.i	0.242656	−	0.242656i
$324$	112335.	−	324851.i	0.0594501	−	0.171918i
$325$	2.32621e6	−	225070.i	1.22163	−	0.118198i
$326$	247244.	−	1.47151e6i	0.128849	−	0.766863i
$327$	−300595.	+	300595.i	−0.155458	+	0.155458i
$328$	705879.	+	2.40045e6i	0.362281	+	1.23199i
$329$		−	864933.i		−	0.440548i
$330$	190853.	+	677827.i	0.0964747	+	0.342637i
$331$	1.22036e6			0.612235			0.306117	−	0.951994i	$-0.400970\pi$
$331$	1.22036e6			0.612235			0.306117	+	0.951994i	$0.400970\pi$
$332$	−405529.	−	834251.i	−0.201919	−	0.415386i
$333$	223388.	+	223388.i	0.110395	+	0.110395i
$334$	574836.	−	3.42121e6i	0.281954	−	1.67808i
$335$	−3.51442e6	−	1.26089e6i	−1.71097	−	0.613855i
$336$	486625.	−	619474.i	0.235151	−	0.299347i
$337$	−1.36373e6	−	1.36373e6i	−0.654114	−	0.654114i	0.299867	−	0.953981i	$-0.403058\pi$
$337$	−1.36373e6	−	1.36373e6i	−0.654114	−	0.654114i	−0.953981	+	0.299867i	$0.903058\pi$
$338$	−617017.	−	866235.i	−0.293769	−	0.412424i
$339$		−	2.09355e6i		−	0.989426i
$340$	1.86854e6	−	2.32296e6i	0.876608	−	1.08980i
$341$		−	159949.i		−	0.0744895i
$342$	−230616.	+	164268.i	−0.106617	+	0.0759428i
$343$	1.45064e6	+	1.45064e6i	0.665769	+	0.665769i
$344$	−3.10913e6	−	1.69610e6i	−1.41659	−	0.772778i
$345$	−2.11930e6	+	1.00012e6i	−0.958617	+	0.452383i
$346$	2.38852e6	+	401322.i	1.07260	+	0.180220i
$347$	1.57060e6	+	1.57060e6i	0.700231	+	0.700231i	0.964460	−	0.264229i	$-0.0851174\pi$
$347$	1.57060e6	+	1.57060e6i	0.700231	+	0.700231i	−0.264229	+	0.964460i	$0.585117\pi$
$348$	−24156.1	−	49693.7i	−0.0106925	−	0.0219965i
$349$	1.88122e6			0.826751			0.413376	−	0.910561i	$-0.364350\pi$
$349$	1.88122e6			0.826751			0.413376	+	0.910561i	$0.364350\pi$
$350$	837765.	+	964126.i	0.365554	+	0.420692i
$351$		−	2.96718e6i		−	1.28551i
$352$	−1.21017e6	−	56838.8i	−0.520583	−	0.0244505i
$353$	1.85407e6	−	1.85407e6i	0.791936	−	0.791936i	−0.189873	−	0.981809i	$-0.560808\pi$
$353$	1.85407e6	−	1.85407e6i	0.791936	−	0.791936i	0.981809	+	0.189873i	$0.0608077\pi$
$354$	−73695.0	−	12382.3i	−0.0312558	−	0.00525163i
$355$	−625703.	−	1.32589e6i	−0.263510	−	0.558388i
$356$	−1.95820e6	−	677155.i	−0.818903	−	0.283180i
$357$	−906550.	+	906550.i	−0.376462	+	0.376462i
$358$	−859953.	−	1.20729e6i	−0.354623	−	0.497858i
$359$	4.03875e6			1.65390			0.826952	−	0.562272i	$-0.190073\pi$
$359$	4.03875e6			1.65390			0.826952	+	0.562272i	$0.190073\pi$
$360$	−980231.	+	871813.i	−0.398632	+	0.354542i
$361$	2.32703e6			0.939796
$362$	−1.06145e6	−	1.49018e6i	−0.425724	−	0.597677i
$363$	883184.	−	883184.i	0.351791	−	0.351791i
$364$	565105.	−	1.63417e6i	0.223550	−	0.646464i
$365$	−365750.	+	1.01944e6i	−0.143699	+	0.400524i
$366$	−2.99999e6	−	504061.i	−1.17062	−	0.196689i
$367$	−699570.	+	699570.i	−0.271123	+	0.271123i	−0.829552	−	0.558429i	$-0.811404\pi$
$367$	−699570.	+	699570.i	−0.271123	+	0.271123i	0.558429	+	0.829552i	$0.311404\pi$
$368$	−480779.	−	4.00297e6i	−0.185066	−	1.54086i
$369$			1.79187e6i			0.685078i
$370$	208862.	+	741787.i	0.0793149	+	0.281692i
$371$	−408528.			−0.154094
$372$	−234345.	+	113915.i	−0.0878007	+	0.0426799i
$373$	−1.43587e6	−	1.43587e6i	−0.534373	−	0.534373i	0.387498	−	0.921871i	$-0.373339\pi$
$373$	−1.43587e6	−	1.43587e6i	−0.534373	−	0.534373i	−0.921871	+	0.387498i	$0.873339\pi$
$374$	1.94445e6	+	326709.i	0.718817	+	0.120776i
$375$	952105.	+	1.59783e6i	0.349628	+	0.586749i
$376$	1.90232e6	+	1.03776e6i	0.693928	+	0.378553i
$377$	−85759.8	−	85759.8i	−0.0310764	−	0.0310764i
$378$	1.32081e6	−	940811.i	0.475457	−	0.338667i
$379$		−	196527.i		−	0.0702789i	−0.999382	−	0.0351395i	$-0.988812\pi$
$379$		−	196527.i		−	0.0702789i	0.999382	−	0.0351395i	$-0.0111875\pi$
$380$	−686647.	+	74443.0i	−0.243935	+	0.0264463i
$381$			250251.i			0.0883207i
$382$	2.20641e6	+	3.09760e6i	0.773620	+	1.08609i
$383$	14751.8	+	14751.8i	0.00513865	+	0.00513865i	0.709671	−	0.704533i	$-0.248843\pi$
$383$	14751.8	+	14751.8i	0.00513865	+	0.00513865i	−0.704533	+	0.709671i	$0.748843\pi$
$384$	778604.	+	1.81353e6i	0.269456	+	0.627620i
$385$	−285273.	+	795126.i	−0.0980863	+	0.273391i
$386$	34448.1	−	205022.i	0.0117678	−	0.0700379i
$387$	−1.79348e6	−	1.79348e6i	−0.608723	−	0.608723i
$388$	−3.38586e6	+	1.64586e6i	−1.14180	+	0.555028i
$389$	3.21899e6			1.07856			0.539282	−	0.842125i	$-0.318696\pi$
$389$	3.21899e6			1.07856			0.539282	+	0.842125i	$0.318696\pi$
$390$	1.23130e6	−	2.19642e6i	0.409922	−	0.731231i
$391$			6.56160e6i			2.17054i
$392$	−2.01219e6	+	591708.i	−0.661386	+	0.194488i
$393$	−1.17312e6	+	1.17312e6i	−0.383145	+	0.383145i
$394$	−296489.	+	1.76459e6i	−0.0962205	+	0.572669i
$395$	−2.11838e6	+	999690.i	−0.683143	+	0.322383i
$396$	−819977.	−	283552.i	−0.262763	−	0.0908646i
$397$	−1.36965e6	+	1.36965e6i	−0.436147	+	0.436147i	−0.890713	−	0.454566i	$-0.849794\pi$
$397$	−1.36965e6	+	1.36965e6i	−0.436147	+	0.436147i	0.454566	+	0.890713i	$0.349794\pi$
$398$	−4.46558e6	+	3.18082e6i	−1.41309	+	1.00654i
$399$	297020.			0.0934013
$400$	−3.12565e6	+	685797.i	−0.976765	+	0.214312i
$401$	4.21327e6			1.30845			0.654227	−	0.756298i	$-0.272994\pi$
$401$	4.21327e6			1.30845			0.654227	+	0.756298i	$0.272994\pi$
$402$	−3.27659e6	+	2.33391e6i	−1.01125	+	0.720310i
$403$	−404424.	+	404424.i	−0.124044	+	0.124044i
$404$	3.80106e6	+	1.31442e6i	1.15865	+	0.400666i
$405$	543034.	−	256264.i	0.164509	−	0.0776338i
$406$	10983.1	−	65367.3i	0.00330681	−	0.0196809i
$407$	−360397.	+	360397.i	−0.107844	+	0.107844i
$408$	−906163.	−	3.08155e6i	−0.269498	−	0.916470i
$409$		−	87415.5i		−	0.0258393i	−0.999917	−	0.0129196i	$-0.995887\pi$
$409$		−	87415.5i		−	0.0258393i	0.999917	−	0.0129196i	$-0.00411256\pi$
$410$	−2.13738e6	+	3.81273e6i	−0.627947	+	1.12015i
$411$	624248.			0.182286
$412$	5.09922e6	−	2.47873e6i	1.48000	−	0.719425i
$413$	−63388.7	−	63388.7i	−0.0182868	−	0.0182868i
$414$	478426.	−	2.84742e6i	0.137187	−	0.816489i
$415$	547222.	−	1.52524e6i	0.155971	−	0.434729i
$416$	2.91616e6	+	3.20359e6i	0.826185	+	0.907618i
$417$	2.64899e6	+	2.64899e6i	0.746002	+	0.746002i
$418$	−265016.	−	372059.i	−0.0741877	−	0.104153i
$419$			3.03985e6i			0.845897i	0.906154	+	0.422948i	$0.139005\pi$
$419$			3.03985e6i			0.845897i	−0.906154	+	0.422948i	$0.860995\pi$
$420$	1.36813e6	−	148326.i	0.378446	−	0.0410293i
$421$			2.59517e6i			0.713608i	0.934179	+	0.356804i	$0.116134\pi$
$421$			2.59517e6i			0.713608i	−0.934179	+	0.356804i	$0.883866\pi$
$422$	2.28126e6	−	1.62494e6i	0.623583	−	0.444177i
$423$	1.09734e6	+	1.09734e6i	0.298189	+	0.298189i
$424$	490157.	−	898510.i	0.132410	−	0.242722i
$425$	5.18375e6	−	501549.i	1.39210	−	0.134692i
$426$	−1.55779e6	−	261741.i	−0.415895	−	0.0698791i
$427$	−2.58043e6	−	2.58043e6i	−0.684894	−	0.684894i
$428$	4.22495e6	−	2.05375e6i	1.11484	−	0.541923i
$429$	1.66536e6			0.436882
$430$	−1.67686e6	−	5.95547e6i	−0.437345	−	1.55326i
$431$		−	3.24379e6i		−	0.841122i	−0.907264	−	0.420561i	$-0.861833\pi$
$431$		−	3.24379e6i		−	0.841122i	0.907264	−	0.420561i	$-0.138167\pi$
$432$	484479.	+	4.03377e6i	0.124901	+	1.03993i
$433$	−2.83919e6	+	2.83919e6i	−0.727738	+	0.727738i	−0.970169	−	0.242431i	$-0.922055\pi$
$433$	−2.83919e6	+	2.83919e6i	−0.727738	+	0.727738i	0.242431	+	0.970169i	$0.422055\pi$
$434$	−308258.	−	51793.8i	−0.0785579	−	0.0131994i
$435$	32596.3	−	90854.0i	0.00825934	−	0.0230208i
$436$	417556.	−	1.20749e6i	0.105196	−	0.304206i
$437$	1.07491e6	−	1.07491e6i	0.269258	−	0.269258i
$438$	677004.	+	950451.i	0.168619	+	0.236725i
$439$	−4.72246e6			−1.16952			−0.584759	−	0.811207i	$-0.698811\pi$
$439$	−4.72246e6			−1.16952			−0.584759	+	0.811207i	$0.698811\pi$
$440$	−1.40652e6	−	1.58143e6i	−0.346348	−	0.389420i
$441$	−1.50205e6			−0.367779
$442$	−4.09040e6	−	5.74255e6i	−0.995888	−	1.39813i
$443$	−3.54476e6	+	3.54476e6i	−0.858178	+	0.858178i	−0.991123	−	0.132945i	$-0.957556\pi$
$443$	−3.54476e6	+	3.54476e6i	−0.858178	+	0.858178i	0.132945	+	0.991123i	$0.457556\pi$
$444$	784701.	+	271353.i	0.188906	+	0.0653247i
$445$	−1.54476e6	−	3.27341e6i	−0.369795	−	0.783610i
$446$	40824.2	+	6859.33i	0.00971808	+	0.00163284i
$447$	1.26560e6	−	1.26560e6i	0.299590	−	0.299590i
$448$	−501413.	+	2.31387e6i	−0.118032	+	0.544683i
$449$		−	5.55787e6i		−	1.30105i	−0.759487	−	0.650523i	$-0.774550\pi$
$449$		−	5.55787e6i		−	1.30105i	0.759487	−	0.650523i	$-0.225450\pi$
$450$	−2.28607e6	−	160315.i	−0.532179	−	0.0373201i
$451$	−2.89086e6			−0.669246
$452$	2.75082e6	+	5.65896e6i	0.633309	+	1.30284i
$453$	2.46736e6	+	2.46736e6i	0.564921	+	0.564921i
$454$	−758252.	−	127402.i	−0.172653	−	0.0290093i
$455$	2.73175e6	−	1.28914e6i	0.618603	−	0.291926i
$456$	−356368.	+	653261.i	−0.0802578	+	0.147121i
$457$	827241.	+	827241.i	0.185286	+	0.185286i	0.793654	−	0.608369i	$-0.208176\pi$
$457$	827241.	+	827241.i	0.185286	+	0.185286i	−0.608369	+	0.793654i	$0.708176\pi$
$458$	2.40358e6	−	1.71207e6i	0.535421	−	0.381379i
$459$		−	6.61209e6i		−	1.46490i
$460$	4.41446e6	−	5.48804e6i	0.972709	−	1.20927i
$461$		−	5.22863e6i		−	1.14587i	−0.819600	−	0.572936i	$-0.805804\pi$
$461$		−	5.22863e6i		−	1.14587i	0.819600	−	0.572936i	$-0.194196\pi$
$462$	528040.	+	741319.i	0.115096	+	0.161585i
$463$	−5.71441e6	−	5.71441e6i	−1.23885	−	1.23885i	−0.960471	−	0.278380i	$-0.910203\pi$
$463$	−5.71441e6	−	5.71441e6i	−1.23885	−	1.23885i	−0.278380	−	0.960471i	$-0.589797\pi$
$464$	130590.	+	102585.i	0.0281589	+	0.0221201i
$465$	−428448.	−	153717.i	−0.0918894	−	0.0329678i
$466$	−1.17247e6	+	6.97813e6i	−0.250114	+	1.48859i
$467$	1.68851e6	+	1.68851e6i	0.358271	+	0.358271i	0.863175	−	0.504904i	$-0.168472\pi$
$467$	1.68851e6	+	1.68851e6i	0.358271	+	0.358271i	−0.504904	+	0.863175i	$0.668472\pi$
$468$	1.35633e6	+	2.79023e6i	0.286254	+	0.588878i
$469$	−4.82587e6			−1.01308
$470$	1.02599e6	+	3.64386e6i	0.214238	+	0.760882i
$471$			2.16125e6i			0.448904i
$472$	215471.	−	63361.6i	0.0445178	−	0.0130910i
$473$	2.89347e6	−	2.89347e6i	0.594656	−	0.594656i
$474$	−418185.	+	2.48888e6i	−0.0854914	+	0.508813i
$475$	−931358.	−	767032.i	−0.189401	−	0.155984i
$476$	1.25929e6	−	3.64161e6i	0.254746	−	0.736675i
$477$	518301.	−	518301.i	0.104300	−	0.104300i
$478$	1.18924e6	−	847094.i	0.238068	−	0.169575i
$479$	−2.52841e6			−0.503510			−0.251755	−	0.967791i	$-0.581008\pi$
$479$	−2.52841e6			−0.503510			−0.251755	+	0.967791i	$0.581008\pi$
$480$	−1.31527e6	+	3.18701e6i	−0.260563	+	0.631364i
$481$	1.82250e6			0.359174
$482$	−1.37078e6	+	976402.i	−0.268751	+	0.191430i
$483$	−2.14174e6	+	2.14174e6i	−0.417733	+	0.417733i
$484$	−1.22683e6	+	3.54775e6i	−0.238051	+	0.688398i
$485$	−6.19029e6	−	2.22093e6i	−1.19497	−	0.428727i
$486$	−796495.	+	4.74044e6i	−0.152965	+	0.910392i
$487$	−618270.	+	618270.i	−0.118129	+	0.118129i	−0.763700	−	0.645571i	$-0.776619\pi$
$487$	−618270.	+	618270.i	−0.118129	+	0.118129i	0.645571	+	0.763700i	$0.276619\pi$
$488$	8.77142e6	−	2.57933e6i	1.66732	−	0.490295i
$489$		−	2.80846e6i		−	0.531124i
$490$	−3.19605e6	−	1.79168e6i	−0.601344	−	0.337108i
$491$	−3.42336e6			−0.640839			−0.320420	−	0.947276i	$-0.603824\pi$
$491$	−3.42336e6			−0.640839			−0.320420	+	0.947276i	$0.603824\pi$
$492$	2.05886e6	+	4.23547e6i	0.383455	+	0.788840i
$493$	−191108.	−	191108.i	−0.0354129	−	0.0354129i
$494$	−270652.	+	1.61082e6i	−0.0498992	+	0.296982i
$495$	−646853.	−	1.37071e6i	−0.118657	−	0.251438i
$496$	483767.	−	615835.i	0.0882941	−	0.112398i
$497$	−1.33993e6	−	1.33993e6i	−0.243327	−	0.243327i
$498$	−1.01291e6	−	1.42203e6i	−0.183019	−	0.256942i
$499$		−	116929.i		−	0.0210218i	−0.999945	−	0.0105109i	$-0.996654\pi$
$499$		−	116929.i		−	0.0210218i	0.999945	−	0.0105109i	$-0.00334578\pi$
$500$	−4.67305e6	−	3.06799e6i	−0.835941	−	0.548819i
$501$		−	6.52959e6i		−	1.16223i
$502$	8.00947e6	−	5.70513e6i	1.41855	−	1.01043i
$503$	2.68560e6	+	2.68560e6i	0.473284	+	0.473284i	0.902976	−	0.429692i	$-0.141378\pi$
$503$	2.68560e6	+	2.68560e6i	0.473284	+	0.473284i	−0.429692	+	0.902976i	$0.641378\pi$
$504$	−811990.	+	1.48846e6i	−0.142388	+	0.261013i
$505$	2.99853e6	+	6.35400e6i	0.523215	+	1.10871i
$506$	4.59380e6	+	771856.i	0.797620	+	0.134017i
$507$	−1.41544e6	−	1.41544e6i	−0.244552	−	0.244552i
$508$	−328817.	−	676439.i	−0.0565321	−	0.116297i
$509$	−4.09184e6			−0.700043			−0.350021	−	0.936742i	$-0.613826\pi$
$509$	−4.09184e6			−0.700043			−0.350021	+	0.936742i	$0.613826\pi$
$510$	2.74384e6	−	4.89454e6i	0.467125	−	0.833271i
$511$			1.39985e6i			0.237154i
$512$	−4.48749e6	−	3.87902e6i	−0.756535	−	0.653953i
$513$	−1.08318e6	+	1.08318e6i	−0.181723	+	0.181723i
$514$	−1.71578e6	−	288287.i	−0.286453	−	0.0481302i
$515$	9.32279e6	+	3.34480e6i	1.54892	+	0.555715i
$516$	−6.30001e6	−	2.17857e6i	−1.04164	−	0.360203i
$517$	−1.77037e6	+	1.77037e6i	−0.291298	+	0.291298i
$518$	577866.	+	811270.i	0.0946243	+	0.132844i
$519$	4.55864e6			0.742877
$520$	−442260.	+	7.55490e6i	−0.0717248	+	1.22524i
$521$	−5.55983e6			−0.897360			−0.448680	−	0.893692i	$-0.648106\pi$
$521$	−5.55983e6			−0.897360			−0.448680	+	0.893692i	$0.648106\pi$
$522$	68997.4	+	96866.0i	0.0110830	+	0.0155595i
$523$	1.22502e6	−	1.22502e6i	0.195835	−	0.195835i	−0.602377	−	0.798212i	$-0.705780\pi$
$523$	1.22502e6	−	1.22502e6i	0.195835	−	0.195835i	0.798212	+	0.602377i	$0.205780\pi$
$524$	1.62958e6	−	4.71244e6i	0.259268	−	0.749752i
$525$	1.85571e6	+	1.52829e6i	0.293841	+	0.241996i
$526$	−8.31392e6	−	1.39691e6i	−1.31021	−	0.220143i
$527$	−901224.	+	901224.i	−0.141353	+	0.141353i
$528$	−2.26400e6	+	271919.i	−0.353420	+	0.0424477i
$529$			9.06554e6i			1.40849i
$530$	1.72108e6	−	484596.i	0.266140	−	0.0749360i
$531$	160843.			0.0247552
$532$	−802858.	+	390269.i	−0.122987	+	0.0597840i
$533$	7.30944e6	+	7.30944e6i	1.11446	+	1.11446i
$534$	−3.84592e6	−	646196.i	−0.583643	−	0.0980643i
$535$	7.72439e6	+	2.77133e6i	1.16676	+	0.418604i
$536$	5.79015e6	−	1.06140e7i	0.870518	−	1.59575i
$537$	−1.97273e6	−	1.97273e6i	−0.295211	−	0.295211i
$538$	2.69416e6	−	1.91905e6i	0.401299	−	0.285844i
$539$		−	2.42328e6i		−	0.359280i
$540$	−4.44843e6	+	5.53027e6i	−0.656481	+	0.816136i
$541$			3.09831e6i			0.455126i	0.973763	+	0.227563i	$0.0730758\pi$
$541$			3.09831e6i			0.455126i	−0.973763	+	0.227563i	$0.926924\pi$
$542$	7.06501e6	+	9.91862e6i	1.03303	+	1.45028i
$543$	−2.43497e6	−	2.43497e6i	−0.354400	−	0.354400i
$544$	6.49840e6	+	7.13891e6i	0.941476	+	1.03427i
$545$	2.01849e6	−	952550.i	0.291095	−	0.137372i
$546$	539268.	−	3.20953e6i	0.0774146	−	0.460743i
$547$	−3.00330e6	−	3.00330e6i	−0.429171	−	0.429171i	0.459175	−	0.888346i	$-0.348145\pi$
$547$	−3.00330e6	−	3.00330e6i	−0.429171	−	0.429171i	−0.888346	+	0.459175i	$0.848145\pi$
$548$	−1.68737e6	+	820231.i	−0.240027	+	0.116677i
$549$	6.54761e6			0.927155
$550$	258640.	−	3.68816e6i	0.0364576	−	0.519880i
$551$			62614.1i			0.00878605i
$552$	−2.14082e6	−	7.28020e6i	−0.299043	−	1.01694i
$553$	−2.14081e6	+	2.14081e6i	−0.297691	+	0.297691i
$554$	−1.92246e6	+	1.14418e7i	−0.266123	+	1.58386i
$555$	619025.	+	1.31174e6i	0.0853052	+	0.180765i
$556$	−1.06410e7	−	3.67970e6i	−1.45980	−	0.504807i
$557$	7.17930e6	−	7.17930e6i	0.980492	−	0.980492i	−0.0193214	−	0.999813i	$-0.506151\pi$
$557$	7.17930e6	−	7.17930e6i	0.980492	−	0.980492i	0.999813	+	0.0193214i	$0.00615057\pi$
$558$	456799.	−	325377.i	0.0621068	−	0.0442386i
$559$	−1.46320e7			−1.98050
$560$	−3.50322e6	+	2.19859e6i	−0.472061	+	0.296260i
$561$	3.71110e6			0.497847
$562$	1.20036e7	−	8.55012e6i	1.60313	−	1.14191i
$563$	−6.92226e6	+	6.92226e6i	−0.920400	+	0.920400i	−0.997057	−	0.0766573i	$-0.975575\pi$
$563$	−6.92226e6	+	6.92226e6i	−0.920400	+	0.920400i	0.0766573	+	0.997057i	$0.475575\pi$
$564$	3.85466e6	+	1.33296e6i	0.510257	+	0.176449i
$565$	−3.71196e6	+	1.03462e7i	−0.489195	+	1.36351i
$566$	−1.15770e6	+	6.89022e6i	−0.151899	+	0.904049i
$567$	548784.	−	548784.i	0.0716875	−	0.0716875i
$568$	4.55468e6	−	1.33936e6i	0.592362	−	0.174191i
$569$		−	9.05668e6i		−	1.17270i	−0.810057	−	0.586352i	$-0.800564\pi$
$569$		−	9.05668e6i		−	1.17270i	0.810057	−	0.586352i	$-0.199436\pi$
$570$	−1.25131e6	+	352325.i	−0.161316	+	0.0454210i
$571$	1.49702e7			1.92149			0.960745	−	0.277435i	$-0.0894842\pi$
$571$	1.49702e7			1.92149			0.960745	+	0.277435i	$0.0894842\pi$
$572$	−4.50154e6	+	2.18820e6i	−0.575269	+	0.279638i
$573$	5.06151e6	+	5.06151e6i	0.644011	+	0.644011i
$574$	−936105.	+	5.57135e6i	−0.118589	+	0.705799i
$575$	1.22467e7	−	1.18492e6i	1.54472	−	0.149458i
$576$	−2.29947e6	−	3.57176e6i	−0.288783	−	0.448566i
$577$	−7.13017e6	−	7.13017e6i	−0.891580	−	0.891580i	0.103092	−	0.994672i	$-0.467126\pi$
$577$	−7.13017e6	−	7.13017e6i	−0.891580	−	0.891580i	−0.994672	+	0.103092i	$0.967126\pi$
$578$	−4.45526e6	−	6.25477e6i	−0.554694	−	0.778738i
$579$		−	391298.i		−	0.0485077i
$580$	31268.4	+	288413.i	0.00385954	+	0.0355995i
$581$		−	2.09441e6i		−	0.257407i
$582$	−5.77139e6	+	4.11095e6i	−0.706274	+	0.503077i
$583$	836186.	+	836186.i	0.101890	+	0.101890i
$584$	−3.07882e6	−	1.67956e6i	−0.373553	−	0.203781i
$585$	−1.83023e6	+	5.10132e6i	−0.221114	+	0.616301i
$586$	1.06386e7	+	1.78752e6i	1.27980	+	0.215033i
$587$	1.85509e6	+	1.85509e6i	0.222213	+	0.222213i	0.809430	−	0.587217i	$-0.199776\pi$
$587$	1.85509e6	+	1.85509e6i	0.222213	+	0.222213i	−0.587217	+	0.809430i	$0.699776\pi$
$588$	−3.55042e6	+	1.72586e6i	−0.423483	+	0.205855i
$589$	295275.			0.0350702
$590$	342241.	+	191857.i	0.0404764	+	0.0226907i
$591$			3.36783e6i			0.396626i
$592$	−2.47763e6	+	297577.i	−0.290557	+	0.0348976i
$593$	−4.16864e6	+	4.16864e6i	−0.486808	+	0.486808i	−0.907298	−	0.420489i	$-0.861858\pi$
$593$	−4.16864e6	+	4.16864e6i	−0.486808	+	0.486808i	0.420489	+	0.907298i	$0.361858\pi$
$594$	−4.62915e6	−	777795.i	−0.538314	−	0.0904481i
$595$	6.08746e6	−	2.87275e6i	0.704926	−	0.332663i
$596$	−1.75804e6	+	5.08392e6i	−0.202728	+	0.586250i
$597$	−7.29681e6	+	7.29681e6i	−0.837910	+	0.837910i
$598$	−9.66364e6	−	1.35669e7i	−1.10507	−	1.55141i
$599$	−199615.			−0.0227314			−0.0113657	−	0.999935i	$-0.503618\pi$
$599$	−199615.			−0.0227314			−0.0113657	+	0.999935i	$0.503618\pi$
$600$	−5.58782e6	+	2.24776e6i	−0.633672	+	0.254901i
$601$	−4.47068e6			−0.504880			−0.252440	−	0.967613i	$-0.581233\pi$
$601$	−4.47068e6			−0.504880			−0.252440	+	0.967613i	$0.581233\pi$
$602$	−4.63942e6	−	6.51332e6i	−0.521762	−	0.732506i
$603$	6.12260e6	−	6.12260e6i	0.685713	−	0.685713i
$604$	−9.91139e6	−	3.42741e6i	−1.10546	−	0.382273i
$605$	−5.93056e6	+	2.79870e6i	−0.658729	+	0.310863i
$606$	7.46530e6	+	1.25433e6i	0.825783	+	0.138749i
$607$	4.55140e6	−	4.55140e6i	0.501387	−	0.501387i	−0.410481	−	0.911869i	$-0.634639\pi$
$607$	4.55140e6	−	4.55140e6i	0.501387	−	0.501387i	0.911869	+	0.410481i	$0.134639\pi$
$608$	104928.	−	2.23405e6i	0.0115115	−	0.245094i
$609$		−	124757.i		−	0.0136309i
$610$	1.39320e7	+	7.81015e6i	1.51596	+	0.849835i
$611$	8.95263e6			0.970169
$612$	3.02246e6	+	6.21779e6i	0.326199	+	0.671054i
$613$	256784.	+	256784.i	0.0276005	+	0.0276005i	0.720772	−	0.693172i	$-0.243787\pi$
$613$	256784.	+	256784.i	0.0276005	+	0.0276005i	−0.693172	+	0.720772i	$0.743787\pi$
$614$	−5.84530e6	−	982133.i	−0.625728	−	0.105136i
$615$	−2.77823e6	+	7.74363e6i	−0.296197	+	0.825575i
$616$	−2.40137e6	−	1.31000e6i	−0.254981	−	0.139098i
$617$	−3.63901e6	−	3.63901e6i	−0.384831	−	0.384831i	0.488008	−	0.872839i	$-0.337724\pi$
$617$	−3.63901e6	−	3.63901e6i	−0.384831	−	0.384831i	−0.872839	+	0.488008i	$0.837724\pi$
$618$	8.69190e6	−	6.19122e6i	0.915469	−	0.652087i
$619$			1.22111e7i			1.28094i	0.767983	+	0.640470i	$0.221261\pi$
$619$			1.22111e7i			1.28094i	−0.767983	+	0.640470i	$0.778739\pi$
$620$	1.36009e6	−	147455.i	0.142098	−	0.0154056i
$621$		−	1.56212e7i		−	1.62549i
$622$	−3.23225e6	−	4.53778e6i	−0.334988	−	0.470291i
$623$	−3.30806e6	−	3.30806e6i	−0.341471	−	0.341471i
$624$	6.41197e6	+	5.03689e6i	0.659219	+	0.517847i
$625$	−1.87220e6	−	9.58448e6i	−0.191714	−	0.981451i
$626$	111499.	−	663600.i	0.0113719	−	0.0676816i
$627$	−607948.	−	607948.i	−0.0617586	−	0.0617586i
$628$	−2.83978e6	−	5.84197e6i	−0.287333	−	0.591099i
$629$	4.06129e6			0.409296
$630$	−2.85112e6	+	802778.i	−0.286197	+	0.0805831i
$631$			5.51289e6i			0.551196i	0.961273	+	0.275598i	$0.0888759\pi$
$631$			5.51289e6i			0.551196i	−0.961273	+	0.275598i	$0.911124\pi$
$632$	−2.13990e6	−	7.27704e6i	−0.213108	−	0.724707i
$633$	3.72761e6	−	3.72761e6i	0.369761	−	0.369761i
$634$	1.27946e6	−	7.61486e6i	0.126416	−	0.752383i
$635$	443706.	−	1.23672e6i	0.0436678	−	0.121713i
$636$	629588.	−	1.82065e6i	0.0617182	−	0.178477i
$637$	−6.12719e6	+	6.12719e6i	−0.598291	+	0.598291i
$638$	−156276.	+	111315.i	−0.0151999	+	0.0108269i
$639$	3.39994e6			0.329397
$640$	−632324.	−	1.03428e7i	−0.0610225	−	0.998136i
$641$	−5.49557e6			−0.528285			−0.264142	−	0.964484i	$-0.585089\pi$
$641$	−5.49557e6			−0.528285			−0.264142	+	0.964484i	$0.585089\pi$
$642$	7.20167e6	−	5.12973e6i	0.689598	−	0.491199i
$643$	3.73494e6	−	3.73494e6i	0.356252	−	0.356252i	−0.506178	−	0.862429i	$-0.668942\pi$
$643$	3.73494e6	−	3.73494e6i	0.356252	−	0.356252i	0.862429	+	0.506178i	$0.168942\pi$
$644$	2.97508e6	−	8.60337e6i	0.282673	−	0.817436i
$645$	−4.96987e6	−	1.05313e7i	−0.470377	−	0.996746i
$646$	−603124.	+	3.58957e6i	−0.0568624	+	0.338424i
$647$	1.39016e6	−	1.39016e6i	0.130558	−	0.130558i	−0.638808	−	0.769366i	$-0.720572\pi$
$647$	1.39016e6	−	1.39016e6i	0.130558	−	0.130558i	0.769366	+	0.638808i	$0.220572\pi$
$648$	548549.	+	1.86543e6i	0.0513190	+	0.174518i
$649$			259492.i			0.0241831i
$650$	−9.97934e6	+	8.67142e6i	−0.926442	+	0.805020i
$651$	−588329.			−0.0544086
$652$	3.69018e6	+	7.59140e6i	0.339960	+	0.699363i
$653$	4.89294e6	+	4.89294e6i	0.449042	+	0.449042i	0.895036	−	0.445994i	$-0.147150\pi$
$653$	4.89294e6	+	4.89294e6i	0.449042	+	0.449042i	−0.445994	+	0.895036i	$0.647150\pi$
$654$	398466.	−	2.37152e6i	0.0364289	−	0.216812i
$655$	7.87750e6	−	3.71749e6i	0.717439	−	0.338568i
$656$	−1.11304e7	−	8.74344e6i	−1.00984	−	0.793273i
$657$	−1.77600e6	−	1.77600e6i	−0.160520	−	0.160520i
$658$	2.83863e6	+	3.98518e6i	0.255590	+	0.358825i
$659$		−	5.27341e6i		−	0.473019i	−0.971629	−	0.236509i	$-0.923997\pi$
$659$		−	5.27341e6i		−	0.473019i	0.971629	−	0.236509i	$-0.0760034\pi$
$660$	−3.10392e6	−	2.49673e6i	−0.277365	−	0.223106i
$661$		−	1.94657e6i		−	0.173287i	−0.996239	−	0.0866434i	$-0.972386\pi$
$661$		−	1.94657e6i		−	0.173287i	0.996239	−	0.0866434i	$-0.0276141\pi$
$662$	−5.62281e6	+	4.00511e6i	−0.498664	+	0.355198i
$663$	−9.38339e6	−	9.38339e6i	−0.829041	−	0.829041i
$664$	4.60641e6	+	2.51290e6i	0.405455	+	0.221185i
$665$	−1.46785e6	−	526630.i	−0.128714	−	0.0461797i
$666$	−1.76240e6	−	296121.i	−0.153964	−	0.0258692i
$667$	−451496.	−	451496.i	−0.0392952	−	0.0392952i
$668$	8.57956e6	+	1.76498e7i	0.743916	+	1.53038i
$669$	77915.5			0.00673067
$670$	2.03308e7	−	5.72446e6i	1.74972	−	0.492660i
$671$			1.05634e7i			0.905728i
$672$	−209066.	+	4.45129e6i	−0.0178592	+	0.380244i
$673$	−3.79903e6	+	3.79903e6i	−0.323322	+	0.323322i	−0.850040	−	0.526718i	$-0.823422\pi$
$673$	−3.79903e6	+	3.79903e6i	−0.323322	+	0.323322i	0.526718	+	0.850040i	$0.323422\pi$
$674$	1.07590e7	+	1.80774e6i	0.912269	+	0.153281i
$675$	−1.23409e7	+	1.19404e6i	−1.04253	+	0.100869i
$676$	5.68581e6	+	1.96618e6i	0.478548	+	0.165484i
$677$	−5.44238e6	+	5.44238e6i	−0.456370	+	0.456370i	−0.897462	−	0.441092i	$-0.854591\pi$
$677$	−5.44238e6	+	5.44238e6i	−0.456370	+	0.456370i	0.441092	+	0.897462i	$0.354591\pi$
$678$	6.87083e6	+	9.64601e6i	0.574031	+	0.805886i
$679$	−8.50028e6			−0.707553
$680$	−985538.	+	1.68354e7i	−0.0817337	+	1.39621i
$681$	−1.44717e6			−0.119578
$682$	524938.	+	736964.i	0.0432162	+	0.0606716i
$683$	−4.04342e6	+	4.04342e6i	−0.331663	+	0.331663i	−0.853218	−	0.521555i	$-0.825352\pi$
$683$	−4.04342e6	+	4.04342e6i	−0.331663	+	0.331663i	0.521555	+	0.853218i	$0.325352\pi$
$684$	523453.	−	1.51373e6i	0.0427797	−	0.123711i
$685$	−3.08499e6	−	1.10682e6i	−0.251204	−	0.0901262i
$686$	−1.14447e7	−	1.92295e6i	−0.928524	−	0.156012i
$687$	3.92749e6	−	3.92749e6i	0.317485	−	0.317485i
$688$	1.98918e7	−	2.38911e6i	1.60215	−	0.192427i
$689$		−	4.22853e6i		−	0.339345i
$690$	6.48236e6	−	1.15634e7i	0.518335	−	0.924622i
$691$	−1.81841e6			−0.144876			−0.0724382	−	0.997373i	$-0.523078\pi$
$691$	−1.81841e6			−0.144876			−0.0724382	+	0.997373i	$0.523078\pi$
$692$	−1.23222e7	+	5.98983e6i	−0.978192	+	0.475499i
$693$	−1.38522e6	−	1.38522e6i	−0.109568	−	0.109568i
$694$	−1.23911e7	−	2.08197e6i	−0.976587	−	0.164087i
$695$	−8.39432e6	−	1.77879e7i	−0.659210	−	1.39689i
$696$	274390.	+	149686.i	0.0214706	+	0.0117127i
$697$	1.62884e7	+	1.62884e7i	1.26998	+	1.26998i
$698$	−8.66770e6	+	6.17398e6i	−0.673388	+	0.479653i
$699$			1.33182e7i			1.03098i
$700$	−7.02418e6	−	1.69274e6i	−0.541814	−	0.130571i
$701$		−	8.48609e6i		−	0.652248i	−0.945327	−	0.326124i	$-0.894257\pi$
$701$		−	8.48609e6i		−	0.652248i	0.945327	−	0.326124i	$-0.105743\pi$
$702$	9.73801e6	+	1.36713e7i	0.745809	+	1.04705i
$703$	−665315.	−	665315.i	−0.0507737	−	0.0507737i
$704$	5.76240e6	−	3.70979e6i	0.438200	−	0.282109i
$705$	3.04082e6	+	6.44361e6i	0.230419	+	0.488266i
$706$	−2.45774e6	+	1.46275e7i	−0.185577	+	1.10448i
$707$	6.42127e6	+	6.42127e6i	0.483140	+	0.483140i
$708$	380188.	−	184809.i	0.0285046	−	0.0138561i
$709$	1.68500e7			1.25888			0.629440	−	0.777049i	$-0.283284\pi$
$709$	1.68500e7			1.25888			0.629440	+	0.777049i	$0.283284\pi$
$710$	7.23438e6	+	4.05553e6i	0.538587	+	0.301927i
$711$		−	5.43211e6i		−	0.402990i
$712$	1.12448e7	−	3.30665e6i	0.831287	−	0.244449i
$713$	−2.12916e6	+	2.12916e6i	−0.156850	+	0.156850i
$714$	1.20171e6	−	7.15215e6i	0.0882175	−	0.525038i
$715$	−8.23007e6	−	2.95276e6i	−0.602058	−	0.216004i
$716$	7.92447e6	+	2.74032e6i	0.577680	+	0.199765i
$717$	1.94324e6	−	1.94324e6i	0.141165	−	0.141165i
$718$	−1.86085e7	+	1.32548e7i	−1.34710	+	0.959538i
$719$	−5.25706e6			−0.379245			−0.189623	−	0.981857i	$-0.560726\pi$
$719$	−5.25706e6			−0.379245			−0.189623	+	0.981857i	$0.560726\pi$
$720$	1.65520e6	−	7.23391e6i	0.118992	−	0.520046i
$721$	1.28017e7			0.917128
$722$	−1.07218e7	+	7.63710e6i	−0.765463	+	0.545237i
$723$	−2.23987e6	+	2.23987e6i	−0.159359	+	0.159359i
$724$	9.78127e6	+	3.38241e6i	0.693504	+	0.239817i
$725$	−322177.	+	391199.i	−0.0227640	+	0.0276409i
$726$	−1.17074e6	+	6.96780e6i	−0.0824363	+	0.490630i
$727$	351685.	−	351685.i	0.0246784	−	0.0246784i	−0.694660	−	0.719338i	$-0.744445\pi$
$727$	351685.	−	351685.i	0.0246784	−	0.0246784i	0.719338	+	0.694660i	$0.244445\pi$
$728$	2.75949e6	+	9.38407e6i	0.192975	+	0.656240i
$729$			1.16576e7i			0.812438i
$730$	−1.66051e6	−	5.89742e6i	−0.115328	−	0.409595i
$731$	−3.26062e7			−2.25687
$732$	1.54767e7	−	7.52323e6i	1.06758	−	0.518951i
$733$	−1.15656e7	−	1.15656e7i	−0.795076	−	0.795076i	0.187239	−	0.982314i	$-0.440046\pi$
$733$	−1.15656e7	−	1.15656e7i	−0.795076	−	0.795076i	−0.982314	+	0.187239i	$0.940046\pi$
$734$	927342.	−	5.51920e6i	0.0635331	−	0.378125i
$735$	−6.49115e6	−	2.32887e6i	−0.443204	−	0.159011i
$736$	1.53526e7	+	1.68658e7i	1.04469	+	1.14766i
$737$	9.87773e6	+	9.87773e6i	0.669867	+	0.669867i
$738$	−5.88076e6	−	8.25603e6i	−0.397459	−	0.557995i
$739$		−	1.72691e7i		−	1.16321i	−0.813470	−	0.581606i	$-0.802424\pi$
$739$		−	1.72691e7i		−	1.16321i	0.813470	−	0.581606i	$-0.197576\pi$
$740$	−3.39681e6	−	2.73232e6i	−0.228030	−	0.183422i
$741$			3.07435e6i			0.205687i
$742$	1.88229e6	−	1.34075e6i	0.125510	−	0.0894002i
$743$	6.71067e6	+	6.71067e6i	0.445958	+	0.445958i	0.894008	−	0.448050i	$-0.147881\pi$
$743$	6.71067e6	+	6.71067e6i	0.445958	+	0.445958i	−0.448050	+	0.894008i	$0.647881\pi$
$744$	705885.	−	1.29396e6i	0.0467522	−	0.0857017i
$745$	−8.49847e6	+	4.01053e6i	−0.560984	+	0.264735i
$746$	1.13282e7	+	1.90338e6i	0.745271	+	0.125221i
$747$	2.65718e6	+	2.65718e6i	0.174229	+	0.174229i
$748$	−1.00313e7	+	4.87621e6i	−0.655546	+	0.318660i
$749$	1.06068e7			0.690847
$750$	−9.63076e6	−	4.23728e6i	−0.625183	−	0.275064i
$751$			1.91770e7i			1.24074i	0.784310	+	0.620369i	$0.213017\pi$
$751$			1.91770e7i			1.24074i	−0.784310	+	0.620369i	$0.786983\pi$
$752$	−1.21708e7	+	1.46178e6i	−0.784827	+	0.0942622i
$753$	1.30876e7	−	1.30876e7i	0.841147	−	0.841147i
$754$	676594.	+	113682.i	0.0433411	+	0.00728222i
$755$	−7.81877e6	−	1.65683e7i	−0.499196	−	1.05782i
$756$	−2.99798e6	+	8.66957e6i	−0.190776	+	0.551688i
$757$	9.28826e6	−	9.28826e6i	0.589107	−	0.589107i	−0.348282	−	0.937390i	$-0.613235\pi$
$757$	9.28826e6	−	9.28826e6i	0.589107	−	0.589107i	0.937390	+	0.348282i	$0.113235\pi$
$758$	644986.	+	905500.i	0.0407734	+	0.0572421i
$759$	8.76755e6			0.552425
$760$	2.91941e6	−	2.59651e6i	0.183342	−	0.163063i
$761$	−1.51980e6			−0.0951315			−0.0475657	−	0.998868i	$-0.515146\pi$
$761$	−1.51980e6			−0.0951315			−0.0475657	+	0.998868i	$0.515146\pi$
$762$	−821300.	−	1.15303e6i	−0.0512406	−	0.0719371i
$763$	2.03986e6	−	2.03986e6i	0.126850	−	0.126850i
$764$	−2.03321e7	−	7.03093e6i	−1.26023	−	0.435792i
$765$	−4.07852e6	+	1.13678e7i	−0.251970	+	0.702303i
$766$	−116383.	−	19554.9i	−0.00716670	−	0.00120416i
$767$	656115.	−	656115.i	0.0402709	−	0.0402709i
$768$	−9.53927e6	−	5.80054e6i	−0.583596	−	0.354867i
$769$			3.15675e6i			0.192497i	0.995357	+	0.0962485i	$0.0306843\pi$
$769$			3.15675e6i			0.192497i	−0.995357	+	0.0962485i	$0.969316\pi$
$770$	−1.29514e6	−	4.59978e6i	−0.0787208	−	0.279583i
$771$	−3.27467e6			−0.198395
$772$	514146.	+	1.05770e6i	0.0310487	+	0.0638731i
$773$	−1.10811e7	−	1.10811e7i	−0.667012	−	0.667012i	0.290011	−	0.957023i	$-0.406341\pi$
$773$	−1.10811e7	−	1.10811e7i	−0.667012	−	0.667012i	−0.957023	+	0.290011i	$0.906341\pi$
$774$	1.41495e7	+	2.37742e6i	0.848965	+	0.142644i
$775$	1.84481e6	+	1.51932e6i	0.110331	+	0.0908644i
$776$	1.01988e7	−	1.86954e7i	0.607985	−	1.11450i
$777$	1.32563e6	+	1.32563e6i	0.0787713	+	0.0787713i
$778$	−1.48315e7	+	1.05645e7i	−0.878490	+	0.625746i
$779$		−	5.33670e6i		−	0.315086i
$780$	1.53527e6	+	1.41610e7i	0.0903543	+	0.833409i
$781$			5.48520e6i			0.321784i
$782$	−2.15346e7	−	3.02326e7i	−1.25927	−	1.76790i
$783$	454971.	+	454971.i	0.0265203	+	0.0265203i
$784$	7.32925e6	−	9.33014e6i	0.425863	−	0.542123i
$785$	3.83200e6	−	1.06807e7i	0.221948	−	0.618625i
$786$	1.55508e6	−	9.25526e6i	0.0897835	−	0.534358i
$787$	−8.62335e6	−	8.62335e6i	−0.496294	−	0.496294i	0.413988	−	0.910282i	$-0.364135\pi$
$787$	−8.62335e6	−	8.62335e6i	−0.496294	−	0.496294i	−0.910282	+	0.413988i	$0.864135\pi$
$788$	−4.42516e6	−	9.10340e6i	−0.253871	−	0.522262i
$789$	−1.58676e7			−0.907442
$790$	6.47955e6	−	1.15584e7i	0.369383	−	0.658917i
$791$			1.42069e7i			0.807346i
$792$	4.70864e6	−	1.38463e6i	0.266736	−	0.0784368i
$793$	2.67092e7	−	2.67092e7i	1.50827	−	1.50827i
$794$	1.81559e6	−	1.08057e7i	0.102204	−	0.608278i
$795$	3.04346e6	−	1.43625e6i	0.170785	−	0.0805956i
$796$	1.01360e7	−	2.93113e7i	0.567000	−	1.63965i
$797$	−1.59570e7	+	1.59570e7i	−0.889825	+	0.889825i	−0.994506	−	0.104681i	$-0.966618\pi$
$797$	−1.59570e7	+	1.59570e7i	−0.889825	+	0.889825i	0.104681	+	0.994506i	$0.466618\pi$
$798$	−1.36852e6	+	974792.i	−0.0760752	+	0.0541882i
$799$	1.99501e7			1.10555
$800$	1.21507e7	−	1.34179e7i	0.671238	−	0.741242i
$801$	8.39391e6			0.462256
$802$	−1.94127e7	+	1.38276e7i	−1.06573	+	0.759120i
$803$	2.86526e6	−	2.86526e6i	0.156810	−	0.156810i
$804$	7.43722e6	−	2.15070e7i	0.405761	−	1.17338i
$805$	1.43817e7	−	6.78691e6i	0.782206	−	0.369133i
$806$	536100.	−	3.19067e6i	0.0290675	−	0.172999i
$807$	4.40230e6	−	4.40230e6i	0.237955	−	0.237955i
$808$	−2.18272e7	+	6.41853e6i	−1.17617	+	0.345865i
$809$		−	8.86014e6i		−	0.475959i	−0.971270	−	0.237979i	$-0.923515\pi$
$809$		−	8.86014e6i		−	0.475959i	0.971270	−	0.237979i	$-0.0764851\pi$
$810$	−1.66099e6	+	2.96293e6i	−0.0889519	+	0.158675i
$811$	7.70669e6			0.411449			0.205724	−	0.978610i	$-0.434045\pi$
$811$	7.70669e6			0.411449			0.205724	+	0.978610i	$0.434045\pi$
$812$	163925.	+	337225.i	0.00872479	+	0.0179486i
$813$	1.62071e7	+	1.62071e7i	0.859964	+	0.859964i
$814$	477738.	−	2.84332e6i	0.0252714	−	0.150406i
$815$	−4.97953e6	+	1.38792e7i	−0.262600	+	0.731931i
$816$	1.42885e7	+	1.12243e7i	0.751210	+	0.590110i
$817$	5.34151e6	+	5.34151e6i	0.279968	+	0.279968i
$818$	286890.	+	402767.i	0.0149911	+	0.0210460i
$819$			7.00494e6i			0.364918i
$820$	−2.66505e6	−	2.45819e7i	−0.138411	−	1.27667i
$821$			7.43845e6i			0.385145i	0.981283	+	0.192573i	$0.0616831\pi$
$821$			7.43845e6i			0.385145i	−0.981283	+	0.192573i	$0.938317\pi$
$822$	−2.87622e6	+	2.04873e6i	−0.148471	+	0.105756i
$823$	−1.58115e7	−	1.58115e7i	−0.813719	−	0.813719i	0.171471	−	0.985189i	$-0.445148\pi$
$823$	−1.58115e7	−	1.58115e7i	−0.813719	−	0.813719i	−0.985189	+	0.171471i	$0.945148\pi$
$824$	−1.53597e7	+	2.81559e7i	−0.788068	+	1.44461i
$825$	−670165.	−	6.92648e6i	−0.0342805	−	0.354305i
$826$	500100.	+	84027.3i	0.0255039	+	0.00428519i
$827$	6.62472e6	+	6.62472e6i	0.336824	+	0.336824i	0.855171	−	0.518346i	$-0.173452\pi$
$827$	6.62472e6	+	6.62472e6i	0.336824	+	0.336824i	−0.518346	+	0.855171i	$0.673452\pi$
$828$	7.14062e6	+	1.46896e7i	0.361960	+	0.744620i
$829$	9.68299e6			0.489354			0.244677	−	0.969605i	$-0.421318\pi$
$829$	9.68299e6			0.489354			0.244677	+	0.969605i	$0.421318\pi$
$830$	2.48439e6	+	8.82349e6i	0.125177	+	0.444575i
$831$			2.18373e7i			1.09697i
$832$	−2.39501e7	−	5.18995e6i	−1.19950	−	0.259929i
$833$	−1.36539e7	+	1.36539e7i	−0.681780	+	0.681780i
$834$	−2.08990e7	−	3.51147e6i	−1.04042	−	0.174813i
$835$	−1.15773e7	+	3.22688e7i	−0.574632	+	1.60164i
$836$	2.44213e6	+	844499.i	0.120852	+	0.0417911i
$837$	2.14554e6	−	2.14554e6i	0.105858	−	0.105858i
$838$	−9.97653e6	−	1.40061e7i	−0.490760	−	0.688982i
$839$	−1.12154e7			−0.550061			−0.275031	−	0.961435i	$-0.588688\pi$
$839$	−1.12154e7			−0.550061			−0.275031	+	0.961435i	$0.588688\pi$
$840$	−5.81686e6	+	5.17349e6i	−0.284440	+	0.252980i
$841$	−2.04848e7			−0.998718
$842$	−8.51711e6	−	1.19572e7i	−0.414011	−	0.581233i
$843$	1.96140e7	−	1.96140e7i	0.950598	−	0.950598i
$844$	−5.17802e6	+	1.49738e7i	−0.250211	+	0.723563i
$845$	4.48535e6	+	9.50463e6i	0.216100	+	0.457924i
$846$	−8.65740e6	−	1.45463e6i	−0.415874	−	0.0698756i
$847$	−5.99335e6	+	5.99335e6i	−0.287052	+	0.287052i
$848$	690432.	+	5.74854e6i	0.0329709	+	0.274516i
$849$			1.31504e7i			0.626138i
$850$	−2.22381e7	+	1.93235e7i	−1.05572	+	0.917357i
$851$	9.59486e6			0.454166
$852$	8.03651e6	−	3.90654e6i	0.379287	−	0.184371i
$853$	−5.42137e6	−	5.42137e6i	−0.255115	−	0.255115i	0.567949	−	0.823064i	$-0.307737\pi$
$853$	−5.42137e6	−	5.42137e6i	−0.255115	−	0.255115i	−0.823064	+	0.567949i	$0.807737\pi$
$854$	2.03581e7	+	3.42059e6i	0.955197	+	0.160493i
$855$	2.53040e6	−	1.19413e6i	0.118379	−	0.0558645i
$856$	−1.27262e7	+	2.33286e7i	−0.593630	+	1.08819i
$857$	1.56889e7	+	1.56889e7i	0.729692	+	0.729692i	0.970558	−	0.240866i	$-0.0774316\pi$
$857$	1.56889e7	+	1.56889e7i	0.729692	+	0.729692i	−0.240866	+	0.970558i	$0.577432\pi$
$858$	−7.67314e6	+	5.46556e6i	−0.355840	+	0.253464i
$859$			2.32917e7i			1.07701i	0.842624	+	0.538503i	$0.181010\pi$
$859$			2.32917e7i			1.07701i	−0.842624	+	0.538503i	$0.818990\pi$
$860$	2.72715e7	+	2.19366e7i	1.25737	+	1.01140i
$861$			1.06333e7i			0.488831i
$862$	1.06458e7	+	1.49457e7i	0.487990	+	0.685093i
$863$	1.82269e7	+	1.82269e7i	0.833080	+	0.833080i	0.987937	−	0.154857i	$-0.0494917\pi$
$863$	1.82269e7	+	1.82269e7i	0.833080	+	0.833080i	−0.154857	+	0.987937i	$0.549492\pi$
$864$	−1.54707e7	−	1.69956e7i	−0.705060	−	0.774554i
$865$	−2.25285e7	−	8.08269e6i	−1.02374	−	0.367295i
$866$	3.76360e6	−	2.23996e7i	0.170533	−	1.01495i
$867$	−1.02204e7	−	1.02204e7i	−0.461763	−	0.461763i
$868$	1.59028e6	−	773035.i	0.0716431	−	0.0348257i
$869$	8.76374e6			0.393677
$870$	147987.	+	525588.i	0.00662868	+	0.0235422i
$871$		−	4.99509e7i		−	2.23099i
$872$	2.03899e6	+	6.93390e6i	0.0908080	+	0.308806i
$873$	1.07843e7	−	1.07843e7i	0.478915	−	0.478915i
$874$	−1.42489e6	+	8.48042e6i	−0.0630962	+	0.375525i
$875$	−6.46105e6	−	1.08430e7i	−0.285288	−	0.478772i
$876$	−6.23859e6	−	2.15733e6i	−0.274679	−	0.0949855i
$877$	9.59239e6	−	9.59239e6i	0.421141	−	0.421141i	−0.464455	−	0.885597i	$-0.653750\pi$
$877$	9.59239e6	−	9.59239e6i	0.421141	−	0.421141i	0.885597	+	0.464455i	$0.153750\pi$
$878$	2.17587e7	−	1.54987e7i	0.952570	−	0.678514i
$879$	2.03045e7			0.886380
$880$	1.16706e7	+	2.67037e6i	0.508028	+	0.116242i
$881$	−6.57569e6			−0.285431			−0.142716	−	0.989764i	$-0.545583\pi$
$881$	−6.57569e6			−0.285431			−0.142716	+	0.989764i	$0.545583\pi$
$882$	6.92068e6	−	4.92958e6i	0.299555	−	0.213373i
$883$	−4.41888e6	+	4.41888e6i	−0.190726	+	0.190726i	−0.796010	−	0.605284i	$-0.793060\pi$
$883$	−4.41888e6	+	4.41888e6i	−0.190726	+	0.190726i	0.605284	+	0.796010i	$0.293060\pi$
$884$	3.76931e7	+	1.30344e7i	1.62230	+	0.560998i
$885$	695089.	+	249382.i	0.0298320	+	0.0107030i
$886$	4.69889e6	−	2.79661e7i	0.201099	−	1.19687i
$887$	301239.	−	301239.i	0.0128559	−	0.0128559i	−0.700650	−	0.713505i	$-0.747106\pi$
$887$	301239.	−	301239.i	0.0128559	−	0.0128559i	0.713505	+	0.700650i	$0.247106\pi$
$888$	−4.50607e6	+	1.32506e6i	−0.191763	+	0.0563901i
$889$		−	1.69822e6i		−	0.0720674i
$890$	1.78605e7	+	1.00124e7i	0.755821	+	0.423707i
$891$	−2.24653e6			−0.0948022
$892$	−210609.	+	102377.i	−0.00886268	+	0.00430815i
$893$	−3.26821e6	−	3.26821e6i	−0.137145	−	0.137145i
$894$	−1.67767e6	+	9.98485e6i	−0.0702039	+	0.417828i
$895$	6.25135e6	+	1.32469e7i	0.260865	+	0.552784i
$896$	−5.28366e6	−	1.23068e7i	−0.219869	−	0.512122i
$897$	−2.21684e7	−	2.21684e7i	−0.919927	−	0.919927i
$898$	1.82404e7	+	2.56079e7i	0.754822	+	1.05970i
$899$		−	124024.i		−	0.00511809i
$900$	1.10592e7	−	6.76402e6i	0.455111	−	0.278355i
$901$		−	9.42291e6i		−	0.386699i
$902$	1.33196e7	−	9.48755e6i	0.545100	−	0.388274i
$903$	−1.06428e7	−	1.06428e7i	−0.434348	−	0.434348i
$904$	−3.12466e7	−	1.70457e7i	−1.27169	−	0.693735i
$905$	7.71612e6	+	1.63508e7i	0.313168	+	0.663615i
$906$	−1.94660e7	−	3.27071e6i	−0.787875	−	0.132380i
$907$	8.72829e6	+	8.72829e6i	0.352298	+	0.352298i	0.860964	−	0.508666i	$-0.169861\pi$
$907$	8.72829e6	+	8.72829e6i	0.352298	+	0.352298i	−0.508666	+	0.860964i	$0.669861\pi$
$908$	3.91177e6	−	1.90151e6i	0.157456	−	0.0765392i
$909$	−1.62934e7			−0.654036
$910$	−8.35566e6	+	1.49051e7i	−0.334486	+	0.596666i
$911$		−	3.87384e7i		−	1.54649i	−0.634110	−	0.773243i	$-0.718633\pi$
$911$		−	3.87384e7i		−	1.54649i	0.634110	−	0.773243i	$-0.281367\pi$
$912$	−501978.	−	4.17947e6i	−0.0199847	−	0.166393i
$913$	−4.28689e6	+	4.28689e6i	−0.170202	+	0.170202i
$914$	−6.52645e6	−	1.09658e6i	−0.258411	−	0.0434185i
$915$	2.82958e7	+	1.01519e7i	1.11730	+	0.400860i
$916$	−5.45566e6	+	1.57767e7i	−0.214837	+	0.621266i
$917$	7.96090e6	−	7.96090e6i	0.312636	−	0.312636i
$918$	2.17003e7	+	3.04652e7i	0.849883	+	1.19316i
$919$	−2.08867e7			−0.815794			−0.407897	−	0.913028i	$-0.633738\pi$
$919$	−2.08867e7			−0.815794			−0.407897	+	0.913028i	$0.633738\pi$
$920$	−2.32835e6	+	3.97740e7i	−0.0906940	+	1.54928i
$921$	−1.11561e7			−0.433375
$922$	1.71599e7	+	2.40909e7i	0.664795	+	0.933311i
$923$	1.38691e7	−	1.38691e7i	0.535852	−	0.535852i
$924$	−4.86589e6	−	1.68265e6i	−0.187492	−	0.0648355i
$925$	−733403.	−	7.58007e6i	−0.0281831	−	0.291285i
$926$	4.50833e7	+	7.57495e6i	1.72778	+	0.290304i
$927$	−1.62416e7	+	1.62416e7i	−0.620767	+	0.620767i
$928$	−938368.	−	44072.9i	−0.0357687	−	0.00167997i
$929$			2.74270e7i			1.04265i	0.853358	+	0.521326i	$0.174562\pi$
$929$			2.74270e7i			1.04265i	−0.853358	+	0.521326i	$0.825438\pi$
$930$	2.47856e6	−	697877.i	0.0939706	−	0.0264589i
$931$	4.47353e6			0.169151
$932$	−1.74994e7	−	3.59997e7i	−0.659909	−	1.35756i
$933$	−7.41478e6	−	7.41478e6i	−0.278865	−	0.278865i
$934$	−1.33214e7	−	2.23827e6i	−0.499668	−	0.0839548i
$935$	−1.83400e7	−	6.57996e6i	−0.686073	−	0.246147i
$936$	−1.54066e7	−	8.40463e6i	−0.574800	−	0.313566i
$937$	−3.37108e7	−	3.37108e7i	−1.25435	−	1.25435i	−0.953749	−	0.300603i	$-0.902812\pi$
$937$	−3.37108e7	−	3.37108e7i	−1.25435	−	1.25435i	−0.300603	−	0.953749i	$-0.597188\pi$
$938$	2.22352e7	−	1.58381e7i	0.825152	−	0.587754i
$939$		−	1.26652e6i		−	0.0468757i
$940$	−1.66861e7	−	1.34219e7i	−0.615934	−	0.495444i
$941$			1.48625e7i			0.547165i	0.961849	+	0.273582i	$0.0882086\pi$
$941$			1.48625e7i			0.547165i	−0.961849	+	0.273582i	$0.911791\pi$
$942$	−7.09304e6	−	9.95797e6i	−0.260438	−	0.365631i
$943$	3.84817e7	+	3.84817e7i	1.40921	+	1.40921i
$944$	−784835.	+	999096.i	−0.0286648	+	0.0364903i
$945$	−1.44924e7	+	6.83914e6i	−0.527911	+	0.249128i
$946$	−3.83554e6	+	2.28277e7i	−0.139348	+	0.829345i
$947$	2.08076e7	+	2.08076e7i	0.753957	+	0.753957i	0.975215	−	0.221258i	$-0.0710163\pi$
$947$	2.08076e7	+	2.08076e7i	0.753957	+	0.753957i	−0.221258	+	0.975215i	$0.571016\pi$
$948$	−6.24151e6	−	1.28400e7i	−0.225563	−	0.464027i
$949$	−1.44894e7			−0.522258
$950$	6.80856e6	+	477464.i	0.244763	+	0.0171645i
$951$		−	1.45334e7i		−	0.521095i
$952$	6.14928e6	+	2.09116e7i	0.219903	+	0.747816i
$953$	−2.11871e7	+	2.11871e7i	−0.755681	+	0.755681i	−0.975533	−	0.219852i	$-0.929443\pi$
$953$	−2.11871e7	+	2.11871e7i	−0.755681	+	0.755681i	0.219852	+	0.975533i	$0.429443\pi$
$954$	−687053.	+	4.08909e6i	−0.0244410	+	0.145464i
$955$	−1.60393e7	−	3.39879e7i	−0.569085	−	1.20591i
$956$	−2.69934e6	+	7.80597e6i	−0.0955242	+	0.276237i
$957$	−255357.	+	255357.i	−0.00901297	+	0.00901297i
$958$	1.16496e7	−	8.29801e6i	0.410108	−	0.292119i
$959$	−4.23619e6			−0.148740
$960$	−4.39936e6	−	1.90008e7i	−0.154068	−	0.665415i
$961$	2.80443e7			0.979571
$962$	−8.39718e6	+	5.98129e6i	−0.292547	+	0.208381i
$963$	−1.34569e7	+	1.34569e7i	−0.467607	+	0.467607i
$964$	3.11139e6	−	8.99754e6i	0.107836	−	0.311840i
$965$	−693789.	+	1.93376e6i	−0.0239833	+	0.0668475i
$966$	2.83906e6	−	1.68971e7i	0.0978887	−	0.582597i
$967$	1.10939e7	−	1.10939e7i	0.381521	−	0.381521i	−0.490129	−	0.871650i	$-0.663050\pi$
$967$	1.10939e7	−	1.10939e7i	0.381521	−	0.381521i	0.871650	+	0.490129i	$0.163050\pi$
$968$	−5.99079e6	−	2.03726e7i	−0.205492	−	0.698808i
$969$			6.85092e6i			0.234390i
$970$	3.58107e7	−	1.00831e7i	1.22203	−	0.344083i
$971$	−5.51613e6			−0.187753			−0.0938765	−	0.995584i	$-0.529926\pi$
$971$	−5.51613e6			−0.187753			−0.0938765	+	0.995584i	$0.529926\pi$
$972$	−1.18879e7	−	2.44556e7i	−0.403588	−	0.830258i
$973$	−1.79762e7	−	1.79762e7i	−0.608718	−	0.608718i
$974$	819571.	−	4.87778e6i	0.0276815	−	0.164750i
$975$	−1.58189e7	+	1.92078e7i	−0.532922	+	0.647093i
$976$	−3.19492e7	+	4.06713e7i	−1.07358	+	1.36667i
$977$	7.17940e6	+	7.17940e6i	0.240631	+	0.240631i	0.817111	−	0.576480i	$-0.195574\pi$
$977$	7.17940e6	+	7.17940e6i	0.240631	+	0.240631i	−0.576480	+	0.817111i	$0.695574\pi$
$978$	9.21711e6	+	1.29400e7i	0.308140	+	0.432600i
$979$			1.35421e7i			0.451574i
$980$	2.06059e7	−	2.23400e6i	0.685372	−	0.0743049i
$981$			5.17596e6i			0.171719i
$982$	1.57731e7	−	1.12352e7i	0.521963	−	0.371793i
$983$	−2.42340e7	−	2.42340e7i	−0.799911	−	0.799911i	0.183170	−	0.983081i	$-0.441364\pi$
$983$	−2.42340e7	−	2.42340e7i	−0.799911	−	0.799911i	−0.983081	+	0.183170i	$0.941364\pi$
$984$	−2.33867e7	−	1.27579e7i	−0.769982	−	0.420042i
$985$	5.97132e6	−	1.66436e7i	0.196101	−	0.546582i
$986$	1.50773e6	+	253331.i	0.0493891	+	0.00829842i
$987$	6.51183e6	+	6.51183e6i	0.212770	+	0.212770i
$988$	−4.03954e6	−	8.31011e6i	−0.131656	−	0.270841i
$989$	−7.70328e7			−2.50429
$990$	7.47891e6	+	4.19261e6i	0.242522	+	0.135955i
$991$		−	3.29661e7i		−	1.06631i	−0.846017	−	0.533156i	$-0.821006\pi$
$991$		−	3.29661e7i		−	1.06631i	0.846017	−	0.533156i	$-0.178994\pi$
$992$	−207838.	+	4.42514e6i	−0.00670573	+	0.142774i
$993$	−9.18774e6	+	9.18774e6i	−0.295689	+	0.295689i
$994$	1.05712e7	+	1.77619e6i	0.339359	+	0.0570196i
$995$	4.89979e7	−	2.31227e7i	1.56899	−	0.740425i
$996$	9.33395e6	+	3.22772e6i	0.298138	+	0.103097i
$997$	1.80740e7	−	1.80740e7i	0.575859	−	0.575859i	−0.357901	−	0.933760i	$-0.616507\pi$
$997$	1.80740e7	−	1.80740e7i	0.575859	−	0.575859i	0.933760	+	0.357901i	$0.116507\pi$
$998$	383750.	+	538749.i	0.0121961	+	0.0171222i
$999$	−9.66870e6			−0.306517

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.k.a.27.5	yes	56
4.3	odd	2		160.6.o.a.47.19		56
5.3	odd	4	inner	40.6.k.a.3.20	yes	56
8.3	odd	2	inner	40.6.k.a.27.20	yes	56
8.5	even	2		160.6.o.a.47.20		56
20.3	even	4		160.6.o.a.143.20		56
40.3	even	4	inner	40.6.k.a.3.5	✓	56
40.13	odd	4		160.6.o.a.143.19		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.5	✓	56	40.3	even	4	inner
40.6.k.a.3.20	yes	56	5.3	odd	4	inner
40.6.k.a.27.5	yes	56	1.1	even	1	trivial
40.6.k.a.27.20	yes	56	8.3	odd	2	inner
160.6.o.a.47.19		56	4.3	odd	2
160.6.o.a.47.20		56	8.5	even	2
160.6.o.a.143.19		56	40.13	odd	4
160.6.o.a.143.20		56	20.3	even	4

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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	40.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.60750 + 3.28191i) q^{2} +(-7.52871 + 7.52871i) q^{3} +(10.4581 - 30.2428i) q^{4} +(50.5551 - 23.8576i) q^{5} +(9.97997 - 59.3971i) q^{6} +(51.0903 - 51.0903i) q^{7} +(51.0685 + 173.666i) q^{8} +129.637i q^{9} +O(q^{10})\)	\(q+(-4.60750 + 3.28191i) q^{2} +(-7.52871 + 7.52871i) q^{3} +(10.4581 - 30.2428i) q^{4} +(50.5551 - 23.8576i) q^{5} +(9.97997 - 59.3971i) q^{6} +(51.0903 - 51.0903i) q^{7} +(51.0685 + 173.666i) q^{8} +129.637i q^{9} +(-154.634 + 275.841i) q^{10} -209.146 q^{11} +(148.953 + 306.425i) q^{12} +(528.819 + 528.819i) q^{13} +(-67.7247 + 403.073i) q^{14} +(-200.998 + 560.231i) q^{15} +(-805.256 - 632.565i) q^{16} +(1178.43 + 1178.43i) q^{17} +(-425.457 - 597.303i) q^{18} -386.096i q^{19} +(-192.809 - 1778.43i) q^{20} +769.289i q^{21} +(963.642 - 686.400i) q^{22} +(2784.05 + 2784.05i) q^{23} +(-1691.96 - 923.004i) q^{24} +(1986.63 - 2412.24i) q^{25} +(-4172.07 - 700.996i) q^{26} +(-2805.48 - 2805.48i) q^{27} +(-1010.81 - 2079.42i) q^{28} -162.172 q^{29} +(-912.532 - 3240.92i) q^{30} +764.769i q^{31} +(5786.24 + 271.766i) q^{32} +(1574.60 - 1574.60i) q^{33} +(-9297.09 - 1562.11i) q^{34} +(1363.99 - 3801.77i) q^{35} +(3920.59 + 1355.76i) q^{36} +(1723.18 - 1723.18i) q^{37} +(1267.13 + 1778.94i) q^{38} -7962.64 q^{39} +(6725.03 + 7561.35i) q^{40} +13822.2 q^{41} +(-2524.74 - 3544.50i) q^{42} +(-13834.7 + 13834.7i) q^{43} +(-2187.28 + 6325.17i) q^{44} +(3092.82 + 6553.81i) q^{45} +(-21964.5 - 3690.51i) q^{46} +(8464.74 - 8464.74i) q^{47} +(10824.9 - 1300.14i) q^{48} +11586.6i q^{49} +(-1236.64 + 17634.4i) q^{50} -17744.1 q^{51} +(21523.4 - 10462.5i) q^{52} +(-3998.09 - 3998.09i) q^{53} +(22133.6 + 3718.91i) q^{54} +(-10573.4 + 4989.72i) q^{55} +(11481.8 + 6263.57i) q^{56} +(2906.81 + 2906.81i) q^{57} +(747.209 - 532.235i) q^{58} -1240.72i q^{59} +(14840.9 + 11937.7i) q^{60} -50507.3i q^{61} +(-2509.91 - 3523.68i) q^{62} +(6623.20 + 6623.20i) q^{63} +(-27552.0 + 17737.8i) q^{64} +(39350.8 + 14118.1i) q^{65} +(-2087.27 + 12422.7i) q^{66} +(-47228.8 - 47228.8i) q^{67} +(47963.0 - 23314.8i) q^{68} -41920.6 q^{69} +(6192.50 + 21993.1i) q^{70} -26226.6i q^{71} +(-22513.6 + 6620.37i) q^{72} +(-13699.8 + 13699.8i) q^{73} +(-2284.23 + 13594.9i) q^{74} +(3204.29 + 33117.9i) q^{75} +(-11676.6 - 4037.84i) q^{76} +(-10685.4 + 10685.4i) q^{77} +(36687.9 - 26132.7i) q^{78} -41902.4 q^{79} +(-55801.2 - 12767.9i) q^{80} +10741.4 q^{81} +(-63685.8 + 45363.2i) q^{82} +(20497.1 - 20497.1i) q^{83} +(23265.5 + 8045.31i) q^{84} +(87689.8 + 31461.1i) q^{85} +(18339.0 - 109147. i) q^{86} +(1220.95 - 1220.95i) q^{87} +(-10680.8 - 36321.7i) q^{88} -64749.3i q^{89} +(-35759.2 - 20046.3i) q^{90} +54035.1 q^{91} +(113313. - 55081.6i) q^{92} +(-5757.73 - 5757.73i) q^{93} +(-11220.8 + 66781.8i) q^{94} +(-9211.32 - 19519.1i) q^{95} +(-45609.0 + 41516.9i) q^{96} +(-83188.7 - 83188.7i) q^{97} +(-38026.0 - 53385.0i) q^{98} -27113.1i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8}+O(q^{10}) \) 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8	\( 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8} - 570 q^{10} - 8 q^{11} - 308 q^{12} + 456 q^{16} - 408 q^{17} + 3370 q^{18} + 1360 q^{20} - 3148 q^{22} - 3120 q^{25} - 5084 q^{26} + 968 q^{27} - 10020 q^{28} + 21100 q^{30} + 7968 q^{32} - 976 q^{33} - 4780 q^{35} + 23132 q^{36} - 49524 q^{38} - 58980 q^{40} - 8 q^{41} + 42060 q^{42} + 1308 q^{43} + 42416 q^{46} + 93776 q^{48} - 94010 q^{50} + 20872 q^{51} - 67180 q^{52} - 43384 q^{56} + 968 q^{57} + 86100 q^{58} + 118180 q^{60} + 6240 q^{62} + 17680 q^{65} - 41128 q^{66} + 89252 q^{67} - 158164 q^{68} + 116980 q^{70} + 1180 q^{72} - 25184 q^{73} - 127740 q^{75} + 41592 q^{76} - 161440 q^{78} - 167360 q^{80} - 67792 q^{81} + 23412 q^{82} - 126444 q^{83} - 192704 q^{86} + 100176 q^{88} - 82330 q^{90} + 329432 q^{91} + 226020 q^{92} + 358176 q^{96} + 212576 q^{97} + 65834 q^{98}+O(q^{100}) \) 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8 - 570 * q^10 - 8 * q^11 - 308 * q^12 + 456 * q^16 - 408 * q^17 + 3370 * q^18 + 1360 * q^20 - 3148 * q^22 - 3120 * q^25 - 5084 * q^26 + 968 * q^27 - 10020 * q^28 + 21100 * q^30 + 7968 * q^32 - 976 * q^33 - 4780 * q^35 + 23132 * q^36 - 49524 * q^38 - 58980 * q^40 - 8 * q^41 + 42060 * q^42 + 1308 * q^43 + 42416 * q^46 + 93776 * q^48 - 94010 * q^50 + 20872 * q^51 - 67180 * q^52 - 43384 * q^56 + 968 * q^57 + 86100 * q^58 + 118180 * q^60 + 6240 * q^62 + 17680 * q^65 - 41128 * q^66 + 89252 * q^67 - 158164 * q^68 + 116980 * q^70 + 1180 * q^72 - 25184 * q^73 - 127740 * q^75 + 41592 * q^76 - 161440 * q^78 - 167360 * q^80 - 67792 * q^81 + 23412 * q^82 - 126444 * q^83 - 192704 * q^86 + 100176 * q^88 - 82330 * q^90 + 329432 * q^91 + 226020 * q^92 + 358176 * q^96 + 212576 * q^97 + 65834 * q^98

Introduction

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