LMFDB - Embedded newform 69.6.e.a.58.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,6,Mod(4,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.0664835671$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			58.2
Character	$\chi$	$=$	69.58
Dual form			69.6.e.a.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.78439 + 5.00272i) q^{2} +(1.28083 - 8.90839i) q^{3} +(22.2762 - 48.7781i) q^{4} +(101.210 - 29.7181i) q^{5} +(34.5957 + 75.7541i) q^{6} +(-18.4590 - 21.3028i) q^{7} +(28.4763 + 198.057i) q^{8} +(-77.7189 - 22.8203i) q^{9} +O(q^{10})$	\(q+(-7.78439 + 5.00272i) q^{2} +(1.28083 - 8.90839i) q^{3} +(22.2762 - 48.7781i) q^{4} +(101.210 - 29.7181i) q^{5} +(34.5957 + 75.7541i) q^{6} +(-18.4590 - 21.3028i) q^{7} +(28.4763 + 198.057i) q^{8} +(-77.7189 - 22.8203i) q^{9} +(-639.190 + 737.665i) q^{10} +(-421.534 - 270.904i) q^{11} +(-406.002 - 260.922i) q^{12} +(257.044 - 296.645i) q^{13} +(250.264 + 73.4841i) q^{14} +(-135.106 - 939.686i) q^{15} +(-88.7753 - 102.452i) q^{16} +(-92.0613 - 201.586i) q^{17} +(719.158 - 211.164i) q^{18} +(-985.114 + 2157.10i) q^{19} +(804.994 - 5598.86i) q^{20} +(-213.417 + 137.154i) q^{21} +4636.64 q^{22} +(-247.384 - 2524.90i) q^{23} +1800.84 q^{24} +(6731.47 - 4326.05i) q^{25} +(-516.900 + 3595.12i) q^{26} +(-302.838 + 663.122i) q^{27} +(-1450.31 + 425.848i) q^{28} +(-3227.35 - 7066.90i) q^{29} +(5752.71 + 6638.98i) q^{30} +(-341.687 - 2376.49i) q^{31} +(-4940.03 - 1450.52i) q^{32} +(-2953.23 + 3408.21i) q^{33} +(1725.12 + 1108.67i) q^{34} +(-2501.32 - 1607.50i) q^{35} +(-2844.42 + 3282.63i) q^{36} +(-4135.96 - 1214.43i) q^{37} +(-3122.86 - 21719.9i) q^{38} +(-2313.40 - 2669.80i) q^{39} +(8767.97 + 19199.2i) q^{40} +(10541.6 - 3095.31i) q^{41} +(975.172 - 2135.33i) q^{42} +(-1813.54 + 12613.4i) q^{43} +(-22604.3 + 14526.9i) q^{44} -8544.14 q^{45} +(14557.1 + 18417.2i) q^{46} +1317.87 q^{47} +(-1026.39 + 659.621i) q^{48} +(2278.81 - 15849.5i) q^{49} +(-30758.3 + 67351.4i) q^{50} +(-1913.72 + 561.920i) q^{51} +(-8743.79 - 19146.2i) q^{52} +(4777.61 + 5513.66i) q^{53} +(-960.009 - 6677.01i) q^{54} +(-50714.4 - 14891.1i) q^{55} +(3693.52 - 4262.55i) q^{56} +(17954.5 + 11538.7i) q^{57} +(60476.7 + 38866.0i) q^{58} +(21606.1 - 24934.8i) q^{59} +(-48845.8 - 14342.4i) q^{60} +(432.791 + 3010.13i) q^{61} +(14548.7 + 16790.1i) q^{62} +(948.475 + 2076.87i) q^{63} +(49874.0 - 14644.3i) q^{64} +(17199.8 - 37662.4i) q^{65} +(5938.77 - 41305.0i) q^{66} +(-58549.2 + 37627.3i) q^{67} -11883.8 q^{68} +(-22809.7 - 1030.18i) q^{69} +27513.1 q^{70} +(10932.2 - 7025.71i) q^{71} +(2306.58 - 16042.6i) q^{72} +(14881.0 - 32584.9i) q^{73} +(38271.4 - 11237.5i) q^{74} +(-29916.3 - 65507.5i) q^{75} +(83274.5 + 96103.9i) q^{76} +(2010.09 + 13980.5i) q^{77} +(31364.7 + 9209.49i) q^{78} +(40821.4 - 47110.4i) q^{79} +(-12029.7 - 7731.00i) q^{80} +(5519.46 + 3547.14i) q^{81} +(-66575.3 + 76832.0i) q^{82} +(2225.22 + 653.384i) q^{83} +(1936.02 + 13465.3i) q^{84} +(-15308.3 - 17666.7i) q^{85} +(-48984.2 - 107260. i) q^{86} +(-67088.4 + 19698.9i) q^{87} +(41650.6 - 91202.1i) q^{88} +(2187.85 - 15216.8i) q^{89} +(66510.9 - 42744.0i) q^{90} -11064.1 q^{91} +(-128671. - 44178.4i) q^{92} -21608.3 q^{93} +(-10258.8 + 6592.95i) q^{94} +(-35599.0 + 247597. i) q^{95} +(-19249.2 + 42149.8i) q^{96} +(5376.73 - 1578.75i) q^{97} +(61551.4 + 134779. i) q^{98} +(26579.1 + 30673.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 8 q^{2} + 90 q^{3} - 148 q^{4} + 6 q^{5} + 171 q^{6} + 118 q^{7} + 1616 q^{8} - 810 q^{9}+O(q^{10}) $ 100 * q - 8 * q^2 + 90 * q^3 - 148 * q^4 + 6 * q^5 + 171 * q^6 + 118 * q^7 + 1616 * q^8 - 810 * q^9	\( 100 q - 8 q^{2} + 90 q^{3} - 148 q^{4} + 6 q^{5} + 171 q^{6} + 118 q^{7} + 1616 q^{8} - 810 q^{9} - 262 q^{10} + 724 q^{11} + 1332 q^{12} + 2730 q^{13} + 328 q^{14} - 1143 q^{15} - 8596 q^{16} - 5699 q^{17} - 648 q^{18} + 1993 q^{19} + 28263 q^{20} - 1062 q^{21} - 19378 q^{22} + 9084 q^{23} + 1296 q^{24} - 4752 q^{25} - 7828 q^{26} + 7290 q^{27} - 29888 q^{28} - 37644 q^{29} + 2358 q^{30} - 2471 q^{31} + 42352 q^{32} + 1305 q^{33} + 47233 q^{34} + 9062 q^{35} - 21789 q^{36} + 1170 q^{37} - 133648 q^{38} - 24570 q^{39} + 135509 q^{40} - 8556 q^{41} - 17208 q^{42} + 39714 q^{43} + 108207 q^{44} - 44064 q^{45} + 87076 q^{46} + 56898 q^{47} + 60237 q^{48} + 35646 q^{49} + 12207 q^{50} - 48600 q^{51} - 368495 q^{52} + 11912 q^{53} - 34263 q^{54} - 231697 q^{55} + 235302 q^{56} + 4437 q^{57} - 201743 q^{58} + 116756 q^{59} + 209349 q^{60} - 191952 q^{61} - 91633 q^{62} + 9558 q^{63} + 383796 q^{64} + 120963 q^{65} + 92925 q^{66} - 7699 q^{67} - 486648 q^{68} + 9522 q^{69} + 340272 q^{70} + 60029 q^{71} + 130896 q^{72} + 110721 q^{73} - 290458 q^{74} + 48906 q^{75} + 30961 q^{76} - 325750 q^{77} + 51444 q^{78} - 267838 q^{79} - 519366 q^{80} - 65610 q^{81} - 739402 q^{82} - 236288 q^{83} - 382428 q^{84} + 72669 q^{85} + 643772 q^{86} + 62784 q^{87} + 976500 q^{88} + 455688 q^{89} - 21222 q^{90} + 267512 q^{91} + 70711 q^{92} - 12906 q^{93} + 1298755 q^{94} + 1815505 q^{95} + 461520 q^{96} + 271324 q^{97} - 1533115 q^{98} - 11745 q^{99}+O(q^{100}) \) 100 * q - 8 * q^2 + 90 * q^3 - 148 * q^4 + 6 * q^5 + 171 * q^6 + 118 * q^7 + 1616 * q^8 - 810 * q^9 - 262 * q^10 + 724 * q^11 + 1332 * q^12 + 2730 * q^13 + 328 * q^14 - 1143 * q^15 - 8596 * q^16 - 5699 * q^17 - 648 * q^18 + 1993 * q^19 + 28263 * q^20 - 1062 * q^21 - 19378 * q^22 + 9084 * q^23 + 1296 * q^24 - 4752 * q^25 - 7828 * q^26 + 7290 * q^27 - 29888 * q^28 - 37644 * q^29 + 2358 * q^30 - 2471 * q^31 + 42352 * q^32 + 1305 * q^33 + 47233 * q^34 + 9062 * q^35 - 21789 * q^36 + 1170 * q^37 - 133648 * q^38 - 24570 * q^39 + 135509 * q^40 - 8556 * q^41 - 17208 * q^42 + 39714 * q^43 + 108207 * q^44 - 44064 * q^45 + 87076 * q^46 + 56898 * q^47 + 60237 * q^48 + 35646 * q^49 + 12207 * q^50 - 48600 * q^51 - 368495 * q^52 + 11912 * q^53 - 34263 * q^54 - 231697 * q^55 + 235302 * q^56 + 4437 * q^57 - 201743 * q^58 + 116756 * q^59 + 209349 * q^60 - 191952 * q^61 - 91633 * q^62 + 9558 * q^63 + 383796 * q^64 + 120963 * q^65 + 92925 * q^66 - 7699 * q^67 - 486648 * q^68 + 9522 * q^69 + 340272 * q^70 + 60029 * q^71 + 130896 * q^72 + 110721 * q^73 - 290458 * q^74 + 48906 * q^75 + 30961 * q^76 - 325750 * q^77 + 51444 * q^78 - 267838 * q^79 - 519366 * q^80 - 65610 * q^81 - 739402 * q^82 - 236288 * q^83 - 382428 * q^84 + 72669 * q^85 + 643772 * q^86 + 62784 * q^87 + 976500 * q^88 + 455688 * q^89 - 21222 * q^90 + 267512 * q^91 + 70711 * q^92 - 12906 * q^93 + 1298755 * q^94 + 1815505 * q^95 + 461520 * q^96 + 271324 * q^97 - 1533115 * q^98 - 11745 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$1$

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 $

$2$	−7.78439	+	5.00272i	−1.37610	+	0.884365i	−0.999124	−	0.0418584i	$-0.986672\pi$
$2$	−7.78439	+	5.00272i	−1.37610	+	0.884365i	−0.376975	+	0.926223i	$0.623036\pi$
$3$	1.28083	−	8.90839i	0.0821655	−	0.571474i
$3$	1.28083	−	8.90839i	0.0821655	−	0.571474i
$4$	22.2762	−	48.7781i	0.696131	−	1.52432i
$5$	101.210	−	29.7181i	1.81051	−	0.531613i	0.811872	−	0.583836i	$-0.198449\pi$
$5$	101.210	−	29.7181i	1.81051	−	0.531613i	0.998635	+	0.0522229i	$0.0166306\pi$
$6$	34.5957	+	75.7541i	0.392323	+	0.859069i
$7$	−18.4590	−	21.3028i	−0.142384	−	0.164320i	0.680078	−	0.733140i	$-0.261946\pi$
$7$	−18.4590	−	21.3028i	−0.142384	−	0.164320i	−0.822463	+	0.568819i	$0.807400\pi$
$8$	28.4763	+	198.057i	0.157311	+	1.09412i
$9$	−77.7189	−	22.8203i	−0.319831	−	0.0939109i
$10$	−639.190	+	737.665i	−2.02130	+	2.33270i
$11$	−421.534	−	270.904i	−1.05039	−	0.675046i	−0.102856	−	0.994696i	$-0.532798\pi$
$11$	−421.534	−	270.904i	−1.05039	−	0.675046i	−0.947535	+	0.319651i	$0.896434\pi$
$12$	−406.002	−	260.922i	−0.813908	−	0.523067i
$13$	257.044	−	296.645i	0.421841	−	0.486831i	−0.504556	−	0.863379i	$-0.668344\pi$
$13$	257.044	−	296.645i	0.421841	−	0.486831i	0.926397	+	0.376548i	$0.122889\pi$
$14$	250.264	+	73.4841i	0.341254	+	0.100201i
$15$	−135.106	−	939.686i	−0.155042	−	1.07834i
$16$	−88.7753	−	102.452i	−0.0866946	−	0.100051i
$17$	−92.0613	−	201.586i	−0.0772600	−	0.169176i	0.867060	−	0.498203i	$-0.166007\pi$
$17$	−92.0613	−	201.586i	−0.0772600	−	0.169176i	−0.944320	+	0.329027i	$0.893279\pi$
$18$	719.158	−	211.164i	0.523171	−	0.153617i
$19$	−985.114	+	2157.10i	−0.626040	+	1.37084i	0.285003	+	0.958527i	$0.408005\pi$
$19$	−985.114	+	2157.10i	−0.626040	+	1.37084i	−0.911043	+	0.412311i	$0.864722\pi$
$20$	804.994	−	5598.86i	0.450005	−	3.12986i
$21$	−213.417	+	137.154i	−0.105604	+	0.0678675i
$22$	4636.64			2.04243
$23$	−247.384	−	2524.90i	−0.0975108	−	0.995234i
$23$	−247.384	−	2524.90i	−0.0975108	−	0.995234i
$24$	1800.84			0.638187
$25$	6731.47	−	4326.05i	2.15407	−	1.38434i
$26$	−516.900	+	3595.12i	−0.149959	+	1.04299i
$27$	−302.838	+	663.122i	−0.0799467	+	0.175059i
$28$	−1450.31	+	425.848i	−0.349594	+	0.102650i
$29$	−3227.35	−	7066.90i	−0.712608	−	1.56039i	−0.823983	−	0.566615i	$-0.808253\pi$
$29$	−3227.35	−	7066.90i	−0.712608	−	1.56039i	0.111375	−	0.993778i	$-0.464474\pi$
$30$	5752.71	+	6638.98i	1.16700	+	1.34679i
$31$	−341.687	−	2376.49i	−0.0638594	−	0.444152i	−0.996517	−	0.0833891i	$-0.973426\pi$
$31$	−341.687	−	2376.49i	−0.0638594	−	0.444152i	0.932658	−	0.360763i	$-0.117484\pi$
$32$	−4940.03	−	1450.52i	−0.852814	−	0.250409i
$33$	−2953.23	+	3408.21i	−0.472077	+	0.544806i
$34$	1725.12	+	1108.67i	0.255930	+	0.164477i
$35$	−2501.32	−	1607.50i	−0.345143	−	0.221810i
$36$	−2844.42	+	3282.63i	−0.365794	+	0.422149i
$37$	−4135.96	−	1214.43i	−0.496674	−	0.145837i	0.0237954	−	0.999717i	$-0.492425\pi$
$37$	−4135.96	−	1214.43i	−0.496674	−	0.145837i	−0.520470	+	0.853880i	$0.674243\pi$
$38$	−3122.86	−	21719.9i	−0.350827	−	2.44006i
$39$	−2313.40	−	2669.80i	−0.243550	−	0.281072i
$40$	8767.97	+	19199.2i	0.866461	+	1.89728i
$41$	10541.6	−	3095.31i	0.979374	−	0.287570i	0.247408	−	0.968911i	$-0.420421\pi$
$41$	10541.6	−	3095.31i	0.979374	−	0.287570i	0.731966	+	0.681341i	$0.238603\pi$
$42$	975.172	−	2135.33i	0.0853017	−	0.186785i
$43$	−1813.54	+	12613.4i	−0.149574	+	1.04031i	0.767345	+	0.641234i	$0.221577\pi$
$43$	−1813.54	+	12613.4i	−0.149574	+	1.04031i	−0.916919	+	0.399074i	$0.869332\pi$
$44$	−22604.3	+	14526.9i	−1.76019	+	1.13121i
$45$	−8544.14			−0.628981
$46$	14557.1	+	18417.2i	1.01434	+	1.28331i
$47$	1317.87			0.0870219			0.0435110	−	0.999053i	$-0.486146\pi$
$47$	1317.87			0.0870219			0.0435110	+	0.999053i	$0.486146\pi$
$48$	−1026.39	+	659.621i	−0.0642998	+	0.0413230i
$49$	2278.81	−	15849.5i	0.135587	−	0.943028i
$50$	−30758.3	+	67351.4i	−1.73995	+	3.80997i
$51$	−1913.72	+	561.920i	−0.103028	+	0.0302516i
$52$	−8743.79	−	19146.2i	−0.448427	−	0.981917i
$53$	4777.61	+	5513.66i	0.233626	+	0.269619i	0.860442	−	0.509549i	$-0.170188\pi$
$53$	4777.61	+	5513.66i	0.233626	+	0.269619i	−0.626816	+	0.779167i	$0.715642\pi$
$54$	−960.009	−	6677.01i	−0.0448013	−	0.311600i
$55$	−50714.4	−	14891.1i	−2.26060	−	0.663773i
$56$	3693.52	−	4262.55i	0.157388	−	0.181635i
$57$	17954.5	+	11538.7i	0.731959	+	0.470401i
$58$	60476.7	+	38866.0i	2.36058	+	1.51705i
$59$	21606.1	−	24934.8i	0.808065	−	0.932556i	−0.190730	−	0.981643i	$-0.561085\pi$
$59$	21606.1	−	24934.8i	0.808065	−	0.932556i	0.998795	+	0.0490863i	$0.0156309\pi$
$60$	−48845.8	−	14342.4i	−1.75166	−	0.514332i
$61$	432.791	+	3010.13i	0.0148920	+	0.103576i	0.995912	−	0.0903318i	$-0.0287928\pi$
$61$	432.791	+	3010.13i	0.0148920	+	0.103576i	−0.981020	+	0.193908i	$0.937884\pi$
$62$	14548.7	+	16790.1i	0.480669	+	0.554722i
$63$	948.475	+	2076.87i	0.0301075	+	0.0659262i
$64$	49874.0	−	14644.3i	1.52203	−	0.446909i
$65$	17199.8	−	37662.4i	0.504941	−	1.10567i
$66$	5938.77	−	41305.0i	0.167817	−	1.16719i
$67$	−58549.2	+	37627.3i	−1.59343	+	1.02404i	−0.623141	+	0.782110i	$0.714144\pi$
$67$	−58549.2	+	37627.3i	−1.59343	+	1.02404i	−0.970294	+	0.241929i	$0.922220\pi$
$68$	−11883.8			−0.311660
$69$	−22809.7	−	1030.18i	−0.576762	−	0.0260491i
$70$	27513.1			0.671112
$71$	10932.2	−	7025.71i	0.257373	−	0.165403i	−0.405592	−	0.914054i	$-0.632934\pi$
$71$	10932.2	−	7025.71i	0.257373	−	0.165403i	0.662964	+	0.748651i	$0.269298\pi$
$72$	2306.58	−	16042.6i	0.0524369	−	0.364707i
$73$	14881.0	−	32584.9i	0.326833	−	0.715664i	−0.672877	−	0.739755i	$-0.734942\pi$
$73$	14881.0	−	32584.9i	0.326833	−	0.715664i	0.999710	+	0.0240902i	$0.00766888\pi$
$74$	38271.4	−	11237.5i	0.812446	−	0.238556i
$75$	−29916.3	−	65507.5i	−0.614122	−	1.34474i
$76$	83274.5	+	96103.9i	1.65378	+	1.90857i
$77$	2010.09	+	13980.5i	0.0386356	+	0.268717i
$78$	31364.7	+	9209.49i	0.583719	+	0.171395i
$79$	40821.4	−	47110.4i	0.735902	−	0.849276i	−0.257221	−	0.966353i	$-0.582807\pi$
$79$	40821.4	−	47110.4i	0.735902	−	0.849276i	0.993123	+	0.117076i	$0.0373523\pi$
$80$	−12029.7	−	7731.00i	−0.210150	−	0.135055i
$81$	5519.46	+	3547.14i	0.0934726	+	0.0600712i
$82$	−66575.3	+	76832.0i	−1.09340	+	1.26185i
$83$	2225.22	+	653.384i	0.0354550	+	0.0104105i	0.299412	−	0.954124i	$-0.403210\pi$
$83$	2225.22	+	653.384i	0.0354550	+	0.0104105i	−0.263957	+	0.964534i	$0.585028\pi$
$84$	1936.02	+	13465.3i	0.0299373	+	0.208218i
$85$	−15308.3	−	17666.7i	−0.229816	−	0.265222i
$86$	−48984.2	−	107260.i	−0.714184	−	1.56384i
$87$	−67088.4	+	19698.9i	−0.950275	+	0.279026i
$88$	41650.6	−	91202.1i	0.573343	−	1.25545i
$89$	2187.85	−	15216.8i	0.0292781	−	0.203634i	−0.969932	−	0.243377i	$-0.921745\pi$
$89$	2187.85	−	15216.8i	0.0292781	−	0.203634i	0.999210	+	0.0397431i	$0.0126540\pi$
$90$	66510.9	−	42744.0i	0.865539	−	0.556248i
$91$	−11064.1			−0.140060
$92$	−128671.	−	44178.4i	−1.58493	−	0.544177i
$93$	−21608.3			−0.259068
$94$	−10258.8	+	6592.95i	−0.119751	+	0.0769591i
$95$	−35599.0	+	247597.i	−0.404696	+	2.81472i
$96$	−19249.2	+	42149.8i	−0.213174	+	0.466786i
$97$	5376.73	−	1578.75i	0.0580215	−	0.0170366i	−0.252593	−	0.967573i	$-0.581283\pi$
$97$	5376.73	−	1578.75i	0.0580215	−	0.0170366i	0.310614	+	0.950536i	$0.399465\pi$
$98$	61551.4	+	134779.i	0.647400	+	1.41761i
$99$	26579.1	+	30673.9i	0.272554	+	0.314544i
$100$	−61065.0	−	424716.i	−0.610650	−	4.24716i
$101$	−108299.	−	31799.4i	−1.05638	−	0.310181i	−0.292988	−	0.956116i	$-0.594650\pi$
$101$	−108299.	−	31799.4i	−1.05638	−	0.310181i	−0.763393	+	0.645935i	$0.776468\pi$
$102$	12086.0	−	13948.0i	0.115023	−	0.132743i
$103$	11394.1	+	7322.56i	0.105825	+	0.0680095i	0.592483	−	0.805583i	$-0.298148\pi$
$103$	11394.1	+	7322.56i	0.105825	+	0.0680095i	−0.486658	+	0.873593i	$0.661784\pi$
$104$	66072.2	+	42462.0i	0.599012	+	0.384961i
$105$	−17524.0	+	20223.8i	−0.155117	+	0.179015i
$106$	−64774.1	−	19019.4i	−0.559934	−	0.164411i
$107$	11075.5	+	77031.5i	0.0935196	+	0.650443i	0.981627	+	0.190808i	$0.0611107\pi$
$107$	11075.5	+	77031.5i	0.0935196	+	0.650443i	−0.888108	+	0.459635i	$0.847980\pi$
$108$	25599.7	+	29543.7i	0.211191	+	0.243728i
$109$	93324.5	+	204352.i	0.752366	+	1.64745i	0.762066	+	0.647499i	$0.224185\pi$
$109$	93324.5	+	204352.i	0.752366	+	1.64745i	−0.00969978	+	0.999953i	$0.503088\pi$
$110$	469277.	−	137792.i	3.69783	−	1.08578i
$111$	−16116.1	+	35289.3i	−0.124151	+	0.271854i
$112$	−543.816	+	3782.32i	−0.00409644	+	0.0284914i
$113$	34114.7	−	21924.2i	0.251331	−	0.161520i	−0.408910	−	0.912575i	$-0.634091\pi$
$113$	34114.7	−	21924.2i	0.251331	−	0.161520i	0.660240	+	0.751055i	$0.270454\pi$
$114$	−197490.			−1.42325
$115$	−100073.	−	248195.i	−0.705624	−	1.75004i
$116$	−416603.			−2.87460
$117$	−26746.7	+	17189.1i	−0.180637	+	0.116088i
$118$	−43448.5	+	302191.i	−0.287257	+	1.99791i
$119$	−2594.99	+	5682.23i	−0.0167984	+	0.0367834i
$120$	182264.	−	53517.6i	1.15544	−	0.339268i
$121$	37399.4	+	81893.2i	0.232221	+	0.508493i
$122$	−18427.8	−	21266.9i	−0.112092	−	0.129361i
$123$	−14072.1	−	97873.7i	−0.0838680	−	0.583315i
$124$	−123532.	−	36272.3i	−0.721482	−	0.211846i
$125$	336868.	−	388766.i	1.92835	−	2.22543i
$126$	−17773.3	−	11422.2i	−0.0997337	−	0.0640950i
$127$	160155.	+	102925.i	0.881110	+	0.566255i	0.901132	−	0.433544i	$-0.142737\pi$
$127$	160155.	+	102925.i	0.881110	+	0.566255i	−0.0200219	+	0.999800i	$0.506374\pi$
$128$	−207086.	+	238990.i	−1.11719	+	1.28930i
$129$	110043.	+	32311.4i	0.582219	+	0.170955i
$130$	54524.3	+	379225.i	0.282964	+	1.96806i
$131$	87808.2	+	101336.i	0.447051	+	0.515924i	0.933886	−	0.357570i	$-0.116395\pi$
$131$	87808.2	+	101336.i	0.447051	+	0.515924i	−0.486836	+	0.873493i	$0.661849\pi$
$132$	100459.	+	219975.i	0.501828	+	1.09885i
$133$	64136.4	−	18832.1i	0.314395	−	0.0923147i
$134$	267531.	−	585811.i	1.28710	−	2.81836i
$135$	−10943.6	+	76114.6i	−0.0516805	+	0.359446i
$136$	37304.0	−	23973.8i	0.172945	−	0.111145i
$137$	−70247.8			−0.319765			−0.159883	−	0.987136i	$-0.551112\pi$
$137$	−70247.8			−0.319765			−0.159883	+	0.987136i	$0.551112\pi$
$138$	182713.	−	106091.i	0.816719	−	0.474222i
$139$	286377.			1.25719			0.628596	−	0.777732i	$-0.283630\pi$
$139$	286377.			1.25719			0.628596	+	0.777732i	$0.283630\pi$
$140$	−134131.	+	86200.5i	−0.578373	+	0.371698i
$141$	1687.98	−	11740.1i	0.00715020	−	0.0497307i
$142$	−49953.0	+	109382.i	−0.207893	+	0.455223i
$143$	−188715.	+	55411.7i	−0.771731	+	0.226601i
$144$	4561.53	+	9988.36i	0.0183318	+	0.0401410i
$145$	−536656.	−	619334.i	−2.11971	−	2.44627i
$146$	47173.6	+	328099.i	0.183154	+	1.27386i
$147$	−138275.	−	40601.1i	−0.527775	−	0.154969i
$148$	−151371.	+	174691.i	−0.568052	+	0.655567i
$149$	−267303.	−	171785.i	−0.986367	−	0.633900i	−0.0551933	−	0.998476i	$-0.517578\pi$
$149$	−267303.	−	171785.i	−0.986367	−	0.633900i	−0.931174	+	0.364576i	$0.881214\pi$
$150$	560596.	+	360273.i	2.03433	+	1.30739i
$151$	−234397.	+	270508.i	−0.836583	+	0.965469i	−0.999777	−	0.0211253i	$-0.993275\pi$
$151$	−234397.	+	270508.i	−0.836583	+	0.965469i	0.163193	+	0.986594i	$0.447821\pi$
$152$	−455281.	−	133682.i	−1.59834	−	0.469316i
$153$	2554.64	+	17767.9i	0.00882270	+	0.0613632i
$154$	−85587.7	−	98773.5i	−0.290810	−	0.335613i
$155$	−105207.	−	230371.i	−0.351735	−	0.770191i
$156$	−181761.	+	53370.0i	−0.597985	+	0.175584i
$157$	−196731.	+	430782.i	−0.636978	+	1.39479i	0.265525	+	0.964104i	$0.414455\pi$
$157$	−196731.	+	430782.i	−0.636978	+	1.39479i	−0.902503	+	0.430684i	$0.858273\pi$
$158$	−82089.3	+	570944.i	−0.261604	+	1.81949i
$159$	55237.2	−	35498.8i	0.173276	−	0.111358i
$160$	−543089.			−1.67715
$161$	−49221.1	+	51877.1i	−0.149653	+	0.157729i
$162$	−60711.0			−0.181752
$163$	384815.	−	247305.i	1.13444	−	0.729062i	0.167960	−	0.985794i	$-0.446282\pi$
$163$	384815.	−	247305.i	1.13444	−	0.729062i	0.966483	+	0.256732i	$0.0826458\pi$
$164$	83844.7	−	583153.i	0.243426	−	1.69306i
$165$	−197612.	+	432711.i	−0.565073	+	1.23734i
$166$	−20590.7	+	6045.97i	−0.0579963	+	0.0170293i
$167$	90845.7	+	198924.i	0.252065	+	0.551946i	0.992791	−	0.119862i	$-0.0382452\pi$
$167$	90845.7	+	198924.i	0.252065	+	0.551946i	−0.740725	+	0.671808i	$0.765518\pi$
$168$	−33241.7	−	38363.0i	−0.0908678	−	0.104867i
$169$	30914.1	+	215012.i	0.0832607	+	0.579091i
$170$	207548.	+	60941.5i	0.550802	+	0.161730i
$171$	125788.	−	145167.i	0.328964	−	0.379644i
$172$	574860.	+	369440.i	1.48163	+	0.952189i
$173$	517432.	+	332533.i	1.31443	+	0.844733i	0.994704	−	0.102776i	$-0.0327726\pi$
$173$	517432.	+	332533.i	1.31443	+	0.844733i	0.319726	+	0.947510i	$0.396409\pi$
$174$	423694.	−	488969.i	1.06091	−	1.22436i
$175$	−216413.	−	63544.6i	−0.534181	−	0.156850i
$176$	9667.17	+	67236.7i	0.0235244	+	0.163616i
$177$	−194455.	−	224413.i	−0.466536	−	0.538412i
$178$	59094.5	+	129399.i	0.139797	+	0.306112i
$179$	682122.	−	200289.i	1.59122	−	0.467224i	0.638132	−	0.769927i	$-0.279707\pi$
$179$	682122.	−	200289.i	1.59122	−	0.467224i	0.953085	+	0.302703i	$0.0978890\pi$
$180$	−190331.	+	416767.i	−0.437853	+	0.958765i
$181$	50345.7	−	350162.i	0.114226	−	0.794462i	−0.849504	−	0.527583i	$-0.823098\pi$
$181$	50345.7	−	350162.i	0.114226	−	0.794462i	0.963730	−	0.266879i	$-0.0859924\pi$
$182$	86127.5	−	55350.8i	0.192736	−	0.123864i
$183$	27369.7			0.0604147
$184$	493030.	−	120896.i	1.07357	−	0.263250i
$185$	−454692.			−0.976761
$186$	168208.	−	108100.i	0.356503	−	0.229111i
$187$	−15803.4	+	109915.i	−0.0330481	+	0.229855i
$188$	29357.2	−	64283.3i	0.0605787	−	0.132649i
$189$	19716.4	−	5789.26i	0.0401489	−	0.0117888i
$190$	−961541.	−	2.10548e6i	−1.93234	−	4.23123i
$191$	176893.	+	204146.i	0.350855	+	0.404909i	0.903555	−	0.428472i	$-0.140948\pi$
$191$	176893.	+	204146.i	0.350855	+	0.404909i	−0.552700	+	0.833380i	$0.686402\pi$
$192$	−66577.1	−	463054.i	−0.130338	−	0.906523i
$193$	−355045.	−	104251.i	−0.686105	−	0.201459i	−0.0799426	−	0.996799i	$-0.525474\pi$
$193$	−355045.	−	104251.i	−0.686105	−	0.201459i	−0.606163	+	0.795341i	$0.707292\pi$
$194$	−33956.5	+	39187.9i	−0.0647767	+	0.0747562i
$195$	−313481.	−	201462.i	−0.590371	−	0.379408i
$196$	−722344.	−	464222.i	−1.34309	−	0.863149i
$197$	104681.	−	120808.i	0.192176	−	0.221783i	−0.651481	−	0.758665i	$-0.725852\pi$
$197$	104681.	−	120808.i	0.192176	−	0.221783i	0.843658	+	0.536881i	$0.180398\pi$
$198$	−360355.	−	105810.i	−0.653232	−	0.191806i
$199$	−115505.	−	803355.i	−0.206761	−	1.43805i	−0.783636	−	0.621220i	$-0.786637\pi$
$199$	−115505.	−	803355.i	−0.206761	−	1.43805i	0.576875	−	0.816832i	$-0.304272\pi$
$200$	1.04849e6	+	1.21002e6i	1.85349	+	2.13904i
$201$	260207.	+	569774.i	0.454286	+	0.994747i
$202$	1.00212e6	−	294250.i	1.72800	−	0.507386i
$203$	−90971.2	+	199199.i	−0.154940	+	0.339272i
$204$	−15221.1	+	105865.i	−0.0256077	+	0.178106i
$205$	974938.	−	626554.i	1.62029	−	1.04130i
$206$	−125329.			−0.205771
$207$	−38392.7	+	201878.i	−0.0622763	+	0.327464i
$208$	−53211.0			−0.0852792
$209$	999625.	−	642420.i	1.58297	−	1.01731i
$210$	35239.7	−	245098.i	0.0551422	−	0.383523i
$211$	−84850.4	+	185796.i	−0.131204	+	0.287297i	−0.963820	−	0.266554i	$-0.914115\pi$
$211$	−84850.4	+	185796.i	−0.131204	+	0.287297i	0.832616	+	0.553851i	$0.186842\pi$
$212$	375373.	−	110219.i	0.573618	−	0.168430i
$213$	−48585.4	−	106387.i	−0.0733765	−	0.160672i
$214$	−471583.	−	544236.i	−0.703921	−	0.812368i
$215$	191298.	+	1.33051e6i	0.282237	+	1.96300i
$216$	−139960.	−	41095.8i	−0.204112	−	0.0599326i
$217$	−44318.6	+	51146.4i	−0.0638906	+	0.0737337i
$218$	−1.74879e6	−	1.12388e6i	−2.49228	−	1.60169i
$219$	−271219.	−	174302.i	−0.382129	−	0.245579i
$220$	−1.85608e6	+	2.14203e6i	−2.58548	+	2.98380i
$221$	−83463.2	−	24507.0i	−0.114951	−	0.0337528i
$222$	−51088.7	−	355330.i	−0.0695732	−	0.483893i
$223$	90436.3	+	104369.i	0.121781	+	0.140543i	0.813366	−	0.581752i	$-0.197633\pi$
$223$	90436.3	+	104369.i	0.121781	+	0.140543i	−0.691585	+	0.722295i	$0.743087\pi$
$224$	60287.7	+	132012.i	0.0802802	+	0.175789i
$225$	−621885.	+	182602.i	−0.818943	+	0.240463i
$226$	−155881.	+	341333.i	−0.203013	+	0.444536i
$227$	−77130.2	+	536452.i	−0.0993482	+	0.690982i	0.877894	+	0.478855i	$0.158948\pi$
$227$	−77130.2	+	536452.i	−0.0993482	+	0.690982i	−0.977242	+	0.212127i	$0.931961\pi$
$228$	962792.	−	618749.i	1.22658	−	0.788274i
$229$	1.53966e6			1.94016			0.970079	−	0.242791i	$-0.0780629\pi$
$229$	1.53966e6			1.94016			0.970079	+	0.242791i	$0.0780629\pi$
$230$	2.02066e6	+	1.43141e6i	2.51868	+	1.78420i
$231$	127118.			0.156739
$232$	1.30775e6	−	840437.i	1.59516	−	1.02515i
$233$	−221990.	+	1.54397e6i	−0.267881	+	1.86316i	0.200586	+	0.979676i	$0.435715\pi$
$233$	−221990.	+	1.54397e6i	−0.267881	+	1.86316i	−0.468468	+	0.883481i	$0.655194\pi$
$234$	122215.	−	267613.i	0.145910	−	0.319497i
$235$	133382.	−	39164.6i	0.157554	−	0.0462620i
$236$	−734968.	−	1.60936e6i	−0.858990	−	1.88093i
$237$	−367392.	−	423993.i	−0.424873	−	0.490330i
$238$	−8226.24	−	57214.7i	−0.00941367	−	0.0654735i
$239$	−1.34757e6	−	395682.i	−1.52600	−	0.448075i	−0.592180	−	0.805806i	$-0.701732\pi$
$239$	−1.34757e6	−	395682.i	−1.52600	−	0.448075i	−0.933825	+	0.357731i	$0.883551\pi$
$240$	−84278.8	+	97262.9i	−0.0944474	+	0.108998i
$241$	1.13249e6	+	727808.i	1.25601	+	0.807187i	0.987732	−	0.156156i	$-0.0499102\pi$
$241$	1.13249e6	+	727808.i	1.25601	+	0.807187i	0.268275	+	0.963342i	$0.413547\pi$
$242$	−700821.	−	450390.i	−0.769252	−	0.494368i
$243$	38668.9	−	44626.3i	0.0420093	−	0.0484814i
$244$	156469.	+	45943.5i	0.168250	+	0.0494025i
$245$	−240376.	−	1.67185e6i	−0.255845	−	1.77944i
$246$	599178.	+	691488.i	0.631274	+	0.728529i
$247$	386674.	+	846698.i	0.403276	+	0.883052i
$248$	460950.	−	135347.i	0.475910	−	0.139740i
$249$	8670.74	−	18986.3i	0.00886253	−	0.0194062i
$250$	−677421.	+	4.71157e6i	−0.685502	+	4.76777i
$251$	327055.	−	210185.i	0.327670	−	0.210581i	−0.366454	−	0.930436i	$-0.619428\pi$
$251$	327055.	−	210185.i	0.327670	−	0.210581i	0.694124	+	0.719856i	$0.255792\pi$
$252$	122434.			0.121451
$253$	−579725.	+	1.13135e6i	−0.569404	+	1.11121i
$254$	−1.76161e6			−1.71327
$255$	−176990.	+	113744.i	−0.170450	+	0.109542i
$256$	179718.	−	1.24997e6i	0.171393	−	1.19206i
$257$	500992.	−	1.09702e6i	0.473149	−	1.03605i	−0.511142	−	0.859496i	$-0.670777\pi$
$257$	500992.	−	1.09702e6i	0.473149	−	1.03605i	0.984291	−	0.176555i	$-0.0564954\pi$
$258$	−1.01826e6	+	298988.i	−0.952377	+	0.279643i
$259$	50474.9	+	110525.i	0.0467547	+	0.102379i
$260$	−1.45395e6	−	1.67795e6i	−1.33388	−	1.53938i
$261$	89556.8	+	622881.i	0.0813762	+	0.565984i
$262$	−1.19049e6	−	349559.i	−1.07145	−	0.314606i
$263$	−708242.	+	817355.i	−0.631383	+	0.728654i	−0.977827	−	0.209416i	$-0.932844\pi$
$263$	−708242.	+	817355.i	−0.631383	+	0.728654i	0.346444	+	0.938071i	$0.387389\pi$
$264$	−759117.	−	487855.i	−0.670346	−	0.430805i
$265$	647400.	+	416058.i	0.566314	+	0.363948i
$266$	−405051.	+	467454.i	−0.350999	+	0.405074i
$267$	−132755.	−	38980.5i	−0.113966	−	0.0334633i
$268$	531133.	+	3.69411e6i	0.451717	+	3.14176i
$269$	445725.	+	514394.i	0.375566	+	0.433427i	0.911795	−	0.410646i	$-0.134697\pi$
$269$	445725.	+	514394.i	0.375566	+	0.433427i	−0.536228	+	0.844073i	$0.680151\pi$
$270$	−295591.	−	647254.i	−0.246764	−	0.540337i
$271$	−799076.	+	234630.i	−0.660944	+	0.194071i	−0.594967	−	0.803750i	$-0.702835\pi$
$271$	−799076.	+	234630.i	−0.660944	+	0.194071i	−0.0659776	+	0.997821i	$0.521017\pi$
$272$	−12480.2	+	27327.7i	−0.0102282	+	0.0223966i
$273$	−14171.3	+	98563.6i	−0.0115081	+	0.0800405i
$274$	546836.	−	351430.i	0.440028	−	0.282789i
$275$	−4.00949e6			−3.19711
$276$	−558364.	+	1.08966e6i	−0.441209	+	0.861034i
$277$	−256957.			−0.201215			−0.100608	−	0.994926i	$-0.532079\pi$
$277$	−256957.			−0.201215			−0.100608	+	0.994926i	$0.532079\pi$
$278$	−2.22927e6	+	1.43267e6i	−1.73002	+	1.11182i
$279$	−27676.7	+	192495.i	−0.0212865	+	0.148051i
$280$	247148.	−	541179.i	0.188392	−	0.412521i
$281$	2.10704e6	−	618683.i	1.59187	−	0.467414i	0.638599	−	0.769540i	$-0.279514\pi$
$281$	2.10704e6	−	618683.i	1.59187	−	0.467414i	0.953268	+	0.302125i	$0.0976961\pi$
$282$	45592.7	+	99834.2i	0.0341407	+	0.0747578i
$283$	−1.39556e6	−	1.61056e6i	−1.03582	−	1.19540i	−0.980417	−	0.196932i	$-0.936902\pi$
$283$	−1.39556e6	−	1.61056e6i	−1.03582	−	1.19540i	−0.0553998	−	0.998464i	$-0.517643\pi$
$284$	−99172.3	−	689759.i	−0.0729617	−	0.507460i
$285$	2.16009e6	+	634260.i	1.57529	+	0.462546i
$286$	1.19182e6	−	1.37544e6i	0.861581	−	0.994317i
$287$	−260527.	−	167430.i	−0.186701	−	0.119986i
$288$	350832.	+	225466.i	0.249240	+	0.160177i
$289$	897647.	−	1.03594e6i	0.632209	−	0.729609i
$290$	7.27589e6	+	2.13639e6i	5.08032	+	1.49172i
$291$	−7177.43	−	49920.1i	−0.00496863	−	0.0345576i
$292$	−1.25794e6	−	1.45174e6i	−0.863379	−	0.996393i
$293$	511533.	+	1.12010e6i	0.348101	+	0.762234i	0.999992	+	0.00392218i	$0.00124847\pi$
$293$	511533.	+	1.12010e6i	0.348101	+	0.762234i	−0.651892	+	0.758312i	$0.726024\pi$
$294$	1.27950e6	−	375695.i	0.863320	−	0.253494i
$295$	1.44575e6	−	3.16575e6i	0.967248	−	2.11798i
$296$	122749.	−	853738.i	0.0814308	−	0.566363i
$297$	307299.	−	197489.i	0.202148	−	0.129913i
$298$	2.94019e6			1.91794
$299$	−812588.	−	575626.i	−0.525645	−	0.372360i
$300$	−3.86175e6			−2.47732
$301$	302177.	−	194198.i	0.192241	−	0.123546i
$302$	471358.	−	3.27836e6i	0.297395	−	2.06843i
$303$	−421995.	+	924039.i	−0.264059	+	0.578208i
$304$	308453.	−	90570.0i	0.191428	−	0.0562083i
$305$	133258.	+	291794.i	0.0820245	+	0.179609i
$306$	−108774.	−	125532.i	−0.0664084	−	0.0766393i
$307$	130524.	+	907813.i	0.0790394	+	0.549731i	0.990412	+	0.138148i	$0.0441150\pi$
$307$	130524.	+	907813.i	0.0790394	+	0.549731i	−0.911372	+	0.411583i	$0.864976\pi$
$308$	726717.	+	213383.i	0.436504	+	0.128169i
$309$	79826.2	−	92124.4i	0.0475608	−	0.0548881i
$310$	1.97145e6	+	1.26698e6i	1.16515	+	0.748798i
$311$	−999483.	−	642329.i	−0.585969	−	0.376579i	0.213809	−	0.976875i	$-0.431413\pi$
$311$	−999483.	−	642329.i	−0.585969	−	0.376579i	−0.799778	+	0.600296i	$0.795049\pi$
$312$	462896.	−	534210.i	0.269213	−	0.310689i
$313$	2.26214e6	+	664224.i	1.30515	+	0.383225i	0.859110	−	0.511791i	$-0.171018\pi$
$313$	2.26214e6	+	664224.i	1.30515	+	0.383225i	0.446035	+	0.895016i	$0.352836\pi$
$314$	−623648.	−	4.33757e6i	−0.356956	−	2.48269i
$315$	157716.	+	182014.i	0.0895570	+	0.103354i
$316$	−1.38861e6	−	3.04063e6i	−0.782280	−	1.71295i
$317$	−2.08585e6	+	612460.i	−1.16583	+	0.342318i	−0.806694	−	0.590969i	$-0.798746\pi$
$317$	−2.08585e6	+	612460.i	−1.16583	+	0.342318i	−0.359133	+	0.933286i	$0.616927\pi$
$318$	−252397.	+	552673.i	−0.139964	+	0.306479i
$319$	−554012.	+	3.85324e6i	−0.304820	+	2.12007i
$320$	4.61257e6	−	2.96432e6i	2.51807	−	1.61827i
$321$	700413.			0.379395
$322$	123629.	−	650071.i	0.0664478	−	0.349399i
$323$	525532.			0.280280
$324$	295976.	−	190212.i	0.156637	−	0.100664i
$325$	446984.	−	3.10884e6i	0.234738	−	1.63264i
$326$	−1.75835e6	+	3.85024e6i	−0.916348	+	2.00652i
$327$	1.93998e6	−	569630.i	1.00329	−	0.294594i
$328$	913234.	+	1.99970e6i	0.468703	+	1.02632i
$329$	−24326.6	−	28074.4i	−0.0123906	−	0.0142995i
$330$	−626441.	−	4.35699e6i	−0.316661	−	2.20243i
$331$	−321139.	−	94295.1i	−0.161110	−	0.0473063i	0.200183	−	0.979759i	$-0.435846\pi$
$331$	−321139.	−	94295.1i	−0.161110	−	0.0473063i	−0.361293	+	0.932452i	$0.617665\pi$
$332$	81440.3	−	93987.1i	0.0405503	−	0.0467975i
$333$	293729.	+	188768.i	0.145156	+	0.0932862i
$334$	−1.70234e6	−	1.09403e6i	−0.834989	−	0.536615i
$335$	−4.80758e6	+	5.54825e6i	−2.34053	+	2.70112i
$336$	32997.9	+	9689.05i	0.0159455	+	0.00468202i
$337$	221993.	+	1.54400e6i	0.106479	+	0.740579i	0.971190	+	0.238308i	$0.0765929\pi$
$337$	221993.	+	1.54400e6i	0.106479	+	0.740579i	−0.864710	+	0.502271i	$0.832498\pi$
$338$	−1.31630e6	−	1.51909e6i	−0.626703	−	0.723253i
$339$	−151614.	−	331988.i	−0.0716539	−	0.156900i
$340$	−1.20276e6	+	353162.i	−0.564263	+	0.165683i
$341$	−499766.	+	1.09434e6i	−0.232745	+	0.509641i
$342$	−252951.	+	1.75932e6i	−0.116942	+	0.813352i
$343$	−778246.	+	500148.i	−0.357175	+	0.229543i
$344$	−2.54982e6			−1.16175
$345$	−2.33919e6	+	573595.i	−1.05808	+	0.259452i
$346$	−5.69146e6			−2.55584
$347$	2.43591e6	−	1.56547e6i	1.08602	−	0.697943i	0.130080	−	0.991504i	$-0.458477\pi$
$347$	2.43591e6	−	1.56547e6i	1.08602	−	0.697943i	0.955940	+	0.293561i	$0.0948403\pi$
$348$	−533599.	+	3.71126e6i	−0.236193	+	1.64276i
$349$	1.28550e6	−	2.81486e6i	0.564950	−	1.23707i	−0.384493	−	0.923128i	$-0.625624\pi$
$349$	1.28550e6	−	2.81486e6i	0.564950	−	1.23707i	0.949443	−	0.313939i	$-0.101649\pi$
$350$	2.00254e6	−	587999.i	0.873798	−	0.256570i
$351$	118869.	+	260287.i	0.0514992	+	0.112767i
$352$	1.68944e6	+	1.94972e6i	0.726752	+	0.838716i
$353$	−94901.3	−	660053.i	−0.0405355	−	0.281931i	−1.00000		0.000101071i	$-0.999968\pi$
$353$	−94901.3	−	660053.i	−0.0405355	−	0.281931i	0.959464	−	0.281830i	$-0.0909413\pi$
$354$	2.63639e6	+	774113.i	1.11815	+	0.328319i
$355$	897664.	−	1.03596e6i	0.378045	−	0.436287i
$356$	−693511.	−	445693.i	−0.290020	−	0.186385i
$357$	47295.8	+	30395.2i	0.0196405	+	0.0126222i
$358$	−4.30791e6	+	4.97160e6i	−1.77648	+	2.05016i
$359$	−2.27647e6	−	668432.i	−0.932237	−	0.273729i	−0.219864	−	0.975531i	$-0.570561\pi$
$359$	−2.27647e6	−	668432.i	−0.932237	−	0.273729i	−0.712373	+	0.701801i	$0.752379\pi$
$360$	−243306.	−	1.69223e6i	−0.0989454	−	0.688181i
$361$	−2.06112e6	−	2.37866e6i	−0.832408	−	0.960650i
$362$	1.35985e6	+	2.97767e6i	0.545407	+	1.19428i
$363$	777440.	−	228277.i	0.309671	−	0.0909275i
$364$	−246467.	+	539687.i	−0.0975001	+	0.213495i
$365$	537755.	−	3.74017e6i	0.211277	−	1.46946i
$366$	−213057.	+	136923.i	−0.0831366	+	0.0534286i
$367$	−131010.			−0.0507738			−0.0253869	−	0.999678i	$-0.508082\pi$
$367$	−131010.			−0.0507738			−0.0253869	+	0.999678i	$0.508082\pi$
$368$	−236720.	+	249494.i	−0.0911205	+	0.0960375i
$369$	−889921.			−0.340240
$370$	3.53950e6	−	2.27470e6i	1.34412	−	0.863814i
$371$	29266.5	−	203553.i	0.0110392	−	0.0767790i
$372$	−481352.	+	1.05401e6i	−0.180345	+	0.394901i
$373$	1.07782e6	−	316477.i	0.401121	−	0.117780i	−0.0749487	−	0.997187i	$-0.523879\pi$
$373$	1.07782e6	−	316477.i	0.401121	−	0.117780i	0.476069	+	0.879408i	$0.342061\pi$
$374$	−426855.	−	934683.i	−0.157798	−	0.345530i
$375$	−3.03181e6	−	3.49890e6i	−1.11333	−	1.28485i
$376$	37528.1	+	261014.i	0.0136895	+	0.0952125i
$377$	−2.92593e6	−	859130.i	−1.06025	−	0.311319i
$378$	−124518.	+	143702.i	−0.0448232	+	0.0517288i
$379$	−1.53727e6	−	987942.i	−0.549733	−	0.353292i	0.236102	−	0.971728i	$-0.424130\pi$
$379$	−1.53727e6	−	987942.i	−0.549733	−	0.353292i	−0.785835	+	0.618437i	$0.787766\pi$
$380$	1.12843e7	+	7.25196e6i	4.00880	+	2.57630i
$381$	1.12203e6	−	1.29489e6i	0.395997	−	0.457005i
$382$	−2.39829e6	−	704202.i	−0.840899	−	0.246910i
$383$	−133198.	−	926411.i	−0.0463981	−	0.322706i	−0.999781	−	0.0209417i	$-0.993334\pi$
$383$	−133198.	−	926411.i	−0.0463981	−	0.322706i	0.953383	−	0.301764i	$-0.0975755\pi$
$384$	1.86377e6	+	2.15091e6i	0.645007	+	0.744378i
$385$	618914.	+	1.35523e6i	0.212803	+	0.465974i
$386$	3.28535e6	−	964666.i	1.12231	−	0.329540i
$387$	428789.	−	938917.i	0.145535	−	0.318676i
$388$	42764.7	−	297435.i	0.0144214	−	0.100303i
$389$	−2.85482e6	+	1.83468e6i	−0.956542	+	0.614732i	−0.923039	−	0.384706i	$-0.874303\pi$
$389$	−2.85482e6	+	1.83468e6i	−0.956542	+	0.614732i	−0.0335031	+	0.999439i	$0.510666\pi$
$390$	3.44812e6			1.14794
$391$	−486211.	+	282315.i	−0.160836	+	0.0933883i
$392$	3.20399e6			1.05312
$393$	1.01521e6	−	652435.i	0.331569	−	0.213086i
$394$	−210506.	+	1.46410e6i	−0.0683163	+	0.475150i
$395$	2.73152e6	−	5.98120e6i	0.880870	−	1.92884i
$396$	2.08830e6	−	613179.i	0.669197	−	0.196494i
$397$	−1.01044e6	−	2.21255e6i	−0.321761	−	0.704558i	0.677767	−	0.735276i	$-0.262948\pi$
$397$	−1.01044e6	−	2.21255e6i	−0.321761	−	0.704558i	−0.999528	+	0.0307187i	$0.990220\pi$
$398$	4.91810e6	+	5.67579e6i	1.55629	+	1.79605i
$399$	−85616.1	−	595473.i	−0.0269230	−	0.187254i
$400$	−1.04080e6	−	305607.i	−0.325251	−	0.0955022i
$401$	−2.22608e6	+	2.56903e6i	−0.691321	+	0.797827i	−0.987553	−	0.157289i	$-0.949724\pi$
$401$	−2.22608e6	+	2.56903e6i	−0.691321	+	0.797827i	0.296232	+	0.955116i	$0.404270\pi$
$402$	−4.87598e6	−	3.13360e6i	−1.50486	−	0.967115i
$403$	−792801.	−	509502.i	−0.243165	−	0.156273i
$404$	−3.96360e6	+	4.57424e6i	−1.20819	+	1.39433i
$405$	664042.	+	194980.i	0.201167	+	0.0590681i
$406$	−288383.	−	2.00575e6i	−0.0868270	−	0.603895i
$407$	1.41446e6	+	1.63237e6i	0.423256	+	0.488464i
$408$	−165788.	−	363025.i	−0.0493063	−	0.107966i
$409$	1.63515e6	−	480122.i	0.483335	−	0.141920i	−0.0309821	−	0.999520i	$-0.509863\pi$
$409$	1.63515e6	−	480122.i	0.483335	−	0.141920i	0.514317	+	0.857600i	$0.328045\pi$
$410$	−4.45482e6	+	9.75469e6i	−1.30879	+	2.86585i
$411$	−89975.7	+	625795.i	−0.0262737	+	0.182737i
$412$	610998.	−	392665.i	0.177336	−	0.113967i
$413$	−930006.			−0.268294
$414$	−711077.	−	1.76357e6i	−0.203899	−	0.505698i
$415$	244633.			0.0697260
$416$	−1.70009e6	+	1.09258e6i	−0.481659	+	0.309543i
$417$	366801.	−	2.55116e6i	0.103298	−	0.718452i
$418$	−4.56762e6	+	1.00017e7i	−1.27864	+	2.79984i
$419$	3.52048e6	−	1.03371e6i	0.979640	−	0.287648i	0.247564	−	0.968872i	$-0.420370\pi$
$419$	3.52048e6	−	1.03371e6i	0.979640	−	0.287648i	0.732076	+	0.681223i	$0.238552\pi$
$420$	596109.	+	1.30530e6i	0.164893	+	0.361066i
$421$	−156519.	−	180633.i	−0.0430390	−	0.0496697i	0.733822	−	0.679342i	$-0.237735\pi$
$421$	−156519.	−	180633.i	−0.0430390	−	0.0496697i	−0.776861	+	0.629672i	$0.783189\pi$
$422$	−268980.	−	1.87079e6i	−0.0735255	−	0.511381i
$423$	−102424.	−	30074.3i	−0.0278323	−	0.00817230i
$424$	−955970.	+	1.10325e6i	−0.258244	+	0.298029i
$425$	−1.49178e6	−	958709.i	−0.400620	−	0.257463i
$426$	910434.	+	585100.i	0.243066	+	0.156209i
$427$	56135.2	−	64783.5i	0.0148993	−	0.0171947i
$428$	4.00417e6	+	1.17573e6i	1.05658	+	0.310240i
$429$	251917.	+	1.75212e6i	0.0660867	+	0.459643i
$430$	−8.14529e6	−	9.40016e6i	−2.12440	−	2.45168i
$431$	−311221.	−	681480.i	−0.0807005	−	0.176710i	0.864981	−	0.501805i	$-0.167331\pi$
$431$	−311221.	−	681480.i	−0.0807005	−	0.176710i	−0.945681	+	0.325096i	$0.894603\pi$
$432$	94822.8	−	27842.5i	0.0244457	−	0.00717792i
$433$	−106591.	+	233402.i	−0.0273212	+	0.0598252i	−0.922801	−	0.385278i	$-0.874106\pi$
$433$	−106591.	+	233402.i	−0.0273212	+	0.0598252i	0.895479	+	0.445103i	$0.146833\pi$
$434$	89122.0	−	619857.i	0.0227123	−	0.157967i
$435$	−6.20463e6	+	3.98748e6i	−1.57215	+	1.01036i
$436$	1.20468e7			3.03498
$437$	5.69017e6	+	1.95369e6i	1.42535	+	0.489386i
$438$	2.98326e6			0.743029
$439$	7186.42	−	4618.43i	0.00177972	−	0.00114376i	−0.539751	−	0.841825i	$-0.681481\pi$
$439$	7186.42	−	4618.43i	0.00177972	−	0.00114376i	0.541530	+	0.840681i	$0.317845\pi$
$440$	1.50513e6	−	1.04684e7i	0.370631	−	2.57779i
$441$	−538797.	+	1.17980e6i	−0.131925	+	0.288877i
$442$	772312.	−	226771.i	0.188034	−	0.0552118i
$443$	104989.	+	229894.i	0.0254177	+	0.0556569i	0.921915	−	0.387392i	$-0.126624\pi$
$443$	104989.	+	229894.i	0.0254177	+	0.0556569i	−0.896497	+	0.443049i	$0.853897\pi$
$444$	1.36234e6	+	1.57222e6i	0.327965	+	0.378492i
$445$	−230782.	−	1.60512e6i	−0.0552460	−	0.384245i
$446$	−1.22612e6	−	360022.i	−0.291874	−	0.0857021i
$447$	−1.87270e6	+	2.16121e6i	−0.443302	+	0.511598i
$448$	−1.23259e6	−	792136.i	−0.290150	−	0.186468i
$449$	1.83821e6	+	1.18135e6i	0.430309	+	0.276543i	0.737814	−	0.675004i	$-0.235858\pi$
$449$	1.83821e6	+	1.18135e6i	0.430309	+	0.276543i	−0.307506	+	0.951546i	$0.599494\pi$
$450$	3.92749e6	−	4.53256e6i	0.914289	−	1.05515i
$451$	−5.28219e6	−	1.55099e6i	−1.22285	−	0.359061i
$452$	−309474.	−	2.15244e6i	−0.0712488	−	0.495546i
$453$	2.10957e6	+	2.43457e6i	0.483002	+	0.557414i
$454$	−2.08331e6	−	4.56182e6i	−0.474367	−	1.03872i
$455$	−1.11980e6	+	328804.i	−0.253579	+	0.0744576i
$456$	−1.77404e6	+	3.88459e6i	−0.399531	+	0.874850i
$457$	692035.	−	4.81321e6i	0.155002	−	1.07806i	−0.752674	−	0.658393i	$-0.771237\pi$
$457$	692035.	−	4.81321e6i	0.155002	−	1.07806i	0.907677	−	0.419670i	$-0.137854\pi$
$458$	−1.19853e7	+	7.70251e6i	−2.66985	+	1.71581i
$459$	161556.			0.0357924
$460$	−1.43357e7	−	647463.i	−3.15882	−	0.142666i
$461$	2.16887e6			0.475314			0.237657	−	0.971349i	$-0.423621\pi$
$461$	2.16887e6			0.475314			0.237657	+	0.971349i	$0.423621\pi$
$462$	−989536.	+	635936.i	−0.215688	+	0.138615i
$463$	557296.	−	3.87608e6i	0.120818	−	0.840311i	−0.835814	−	0.549013i	$-0.815004\pi$
$463$	557296.	−	3.87608e6i	0.120818	−	0.840311i	0.956632	−	0.291298i	$-0.0940871\pi$
$464$	−437511.	+	958015.i	−0.0943395	+	0.206575i
$465$	−2.18699e6	+	642158.i	−0.469044	+	0.137724i
$466$	−5.99601e6	−	1.31294e7i	−1.27908	−	2.80079i
$467$	4.17101e6	+	4.81360e6i	0.885012	+	1.02136i	0.999609	+	0.0279458i	$0.00889658\pi$
$467$	4.17101e6	+	4.81360e6i	0.885012	+	1.02136i	−0.114598	+	0.993412i	$0.536558\pi$
$468$	242635.	+	1.68756e6i	0.0512080	+	0.356160i
$469$	1.88233e6	+	552701.i	0.395151	+	0.116027i
$470$	−842371.	+	972148.i	−0.175897	+	0.202996i
$471$	3.58559e6	+	2.30432e6i	0.744747	+	0.478620i
$472$	5.55376e6	+	3.56919e6i	1.14745	+	0.737419i
$473$	4.18149e6	−	4.82570e6i	0.859367	−	0.991762i
$474$	4.98105e6	+	1.46257e6i	1.01830	+	0.298999i
$475$	2.70046e6	+	1.87821e7i	0.549166	+	3.81953i
$476$	219362.	+	253157.i	0.0443756	+	0.0512121i
$477$	−245487.	−	537542.i	−0.0494007	−	0.108172i
$478$	1.24695e7	−	3.66137e6i	2.49619	−	0.732949i
$479$	3.42827e6	−	7.50686e6i	0.682710	−	1.49493i	−0.177037	−	0.984204i	$-0.556651\pi$
$479$	3.42827e6	−	7.50686e6i	0.682710	−	1.49493i	0.859746	−	0.510721i	$-0.170622\pi$
$480$	−695607.	+	4.83805e6i	−0.137804	+	0.958445i
$481$	−1.42338e6	+	914748.i	−0.280516	+	0.180276i
$482$	−1.24568e7			−2.44224
$483$	399098.	+	504927.i	0.0778416	+	0.0984828i
$484$	4.82771e6			0.936759
$485$	497263.	−	319572.i	0.0959914	−	0.0616899i
$486$	−77760.7	+	540838.i	−0.0149338	+	0.103867i
$487$	−1.82702e6	+	4.00061e6i	−0.349076	+	0.764370i	0.650910	+	0.759155i	$0.274387\pi$
$487$	−1.82702e6	+	4.00061e6i	−0.349076	+	0.764370i	−0.999986	+	0.00521543i	$0.998340\pi$
$488$	−583852.	+	171434.i	−0.110982	+	0.0325873i
$489$	−1.71021e6	−	3.74484e6i	−0.323428	−	0.708208i
$490$	1.02350e7	+	1.18118e7i	1.92574	+	2.22242i
$491$	485280.	+	3.37519e6i	0.0908424	+	0.631822i	0.983476	+	0.181039i	$0.0579461\pi$
$491$	485280.	+	3.37519e6i	0.0908424	+	0.631822i	−0.892634	+	0.450783i	$0.851145\pi$
$492$	−5.08756e6	−	1.49384e6i	−0.947539	−	0.278223i
$493$	−1.12747e6	+	1.30118e6i	−0.208925	+	0.241112i
$494$	−7.24582e6	−	4.65660e6i	−1.33589	−	0.858523i
$495$	3.60165e6	+	2.31464e6i	0.660676	+	0.424591i
$496$	−213143.	+	245980.i	−0.0389015	+	0.0448948i
$497$	−351465.	−	103199.i	−0.0638250	−	0.0187407i
$498$	27486.6	+	191174.i	0.00496648	+	0.0345426i
$499$	220480.	+	254448.i	0.0396386	+	0.0457454i	0.775223	−	0.631688i	$-0.217638\pi$
$499$	220480.	+	254448.i	0.0396386	+	0.0457454i	−0.735584	+	0.677433i	$0.763092\pi$
$500$	−1.14591e7	−	2.50920e7i	−2.04987	−	4.48860i
$501$	1.88845e6	−	554500.i	0.336134	−	0.0986978i
$502$	−1.49442e6	+	3.27233e6i	−0.264676	+	0.579559i
$503$	563869.	−	3.92180e6i	0.0993708	−	0.691139i	−0.877853	−	0.478929i	$-0.841025\pi$
$503$	563869.	−	3.92180e6i	0.0993708	−	0.691139i	0.977224	−	0.212209i	$-0.0680659\pi$
$504$	−384330.	+	246994.i	−0.0673950	+	0.0433121i
$505$	−1.19060e7			−2.07748
$506$	−1.14703e6	−	1.17071e7i	−0.199159	−	2.03270i
$507$	1.95501e6			0.337776
$508$	8.58813e6	−	5.51926e6i	1.47652	−	0.948902i
$509$	−585919.	+	4.07516e6i	−0.100241	+	0.697188i	0.876286	+	0.481791i	$0.160014\pi$
$509$	−585919.	+	4.07516e6i	−0.100241	+	0.697188i	−0.976527	+	0.215397i	$0.930895\pi$
$510$	808725.	−	1.77086e6i	0.137681	−	0.301480i
$511$	−968838.	+	284477.i	−0.164134	+	0.0481941i
$512$	650529.	+	1.42446e6i	0.109671	+	0.240146i
$513$	−1.13209e6	−	1.30650e6i	−0.189927	−	0.219188i
$514$	1.58817e6	+	1.10459e7i	0.265148	+	1.84415i
$515$	1.37082e6	+	402508.i	0.227752	+	0.0668739i
$516$	4.02742e6	−	4.64789e6i	0.665890	−	0.768478i
$517$	−555528.	−	357016.i	−0.0914071	−	0.0587438i
$518$	−945840.	−	607854.i	−0.154879	−	0.0995348i
$519$	3.62508e6	−	4.18357e6i	0.590744	−	0.681755i
$520$	7.94908e6	+	2.33406e6i	1.28917	+	0.378533i
$521$	−55637.8	−	386969.i	−0.00897998	−	0.0624571i	0.984839	−	0.173473i	$-0.0554988\pi$
$521$	−55637.8	−	386969.i	−0.00897998	−	0.0624571i	−0.993819	+	0.111015i	$0.964590\pi$
$522$	−3.81325e6	−	4.40072e6i	−0.612518	−	0.706883i
$523$	1.94530e6	+	4.25962e6i	0.310981	+	0.680952i	0.998999	−	0.0447411i	$-0.0142463\pi$
$523$	1.94530e6	+	4.25962e6i	0.310981	+	0.680952i	−0.688018	+	0.725694i	$0.741519\pi$
$524$	6.89901e6	−	2.02573e6i	1.09764	−	0.322295i
$525$	−843270.	+	1.84650e6i	−0.133527	+	0.292383i
$526$	1.42423e6	−	9.90575e6i	0.224448	−	1.56107i
$527$	−447610.	+	287662.i	−0.0702059	+	0.0451186i
$528$	611353.			0.0954348
$529$	−6.31394e6	+	1.24924e6i	−0.980983	+	0.194092i
$530$	−7.12104e6			−1.10117
$531$	−2.24822e6	+	1.44484e6i	−0.346021	+	0.222374i
$532$	510120.	−	3.54796e6i	0.0781435	−	0.543500i
$533$	1.79146e6	−	3.92275e6i	0.273142	−	0.598098i
$534$	1.22843e6	−	360699.i	0.186422	−	0.0547383i
$535$	3.41018e6	+	7.46725e6i	0.515102	+	1.12792i
$536$	−9.11962e6	−	1.05246e7i	−1.37109	−	1.58232i
$537$	−910569.	−	6.33315e6i	−0.136263	−	0.947729i
$538$	−6.04307e6	−	1.77441e6i	−0.900124	−	0.264300i
$539$	−5.25428e6	+	6.06376e6i	−0.779006	+	0.899021i
$540$	3.46894e6	+	2.22935e6i	0.511932	+	0.328999i
$541$	5.44859e6	+	3.50160e6i	0.800370	+	0.514367i	0.875737	−	0.482789i	$-0.160376\pi$
$541$	5.44859e6	+	3.50160e6i	0.800370	+	0.514367i	−0.0753664	+	0.997156i	$0.524013\pi$
$542$	5.04653e6	−	5.82401e6i	0.737895	−	0.851577i
$543$	−3.05490e6	−	896999.i	−0.444629	−	0.130555i
$544$	162380.	+	1.12938e6i	0.0235253	+	0.163622i
$545$	1.55184e7	+	1.79091e7i	2.23797	+	2.58276i
$546$	−382771.	−	838152.i	−0.0549488	−	0.120321i
$547$	−2.25484e6	+	662081.i	−0.322216	+	0.0946112i	−0.438841	−	0.898565i	$-0.644611\pi$
$547$	−2.25484e6	+	662081.i	−0.322216	+	0.0946112i	0.116625	+	0.993176i	$0.462793\pi$
$548$	−1.56485e6	+	3.42655e6i	−0.222599	+	0.487423i
$549$	35056.0	−	243820.i	0.00496400	−	0.0345254i
$550$	3.12114e7	−	2.00584e7i	4.39954	−	2.82741i
$551$	1.84233e7			2.58517
$552$	−445500.	−	4.54696e6i	−0.0622301	−	0.635145i
$553$	−1.75710e6			−0.244334
$554$	2.00025e6	−	1.28548e6i	0.276892	−	0.177948i
$555$	−582385.	+	4.05058e6i	−0.0802561	+	0.558193i
$556$	6.37940e6	−	1.39689e7i	0.875170	−	1.91636i
$557$	2.00224e6	−	587911.i	0.273450	−	0.0802923i	−0.142132	−	0.989848i	$-0.545396\pi$
$557$	2.00224e6	−	587911.i	0.273450	−	0.0802923i	0.415583	+	0.909555i	$0.363578\pi$
$558$	−747556.	−	1.63692e6i	−0.101638	−	0.222557i
$559$	3.27555e6	+	3.78018e6i	0.443358	+	0.511662i
$560$	57363.5	+	398972.i	0.00772975	+	0.0537616i
$561$	958926.	+	281566.i	0.128641	+	0.0377723i
$562$	−1.33069e7	+	1.53570e7i	−1.77720	+	2.05100i
$563$	−5.72921e6	−	3.68194e6i	−0.761770	−	0.489560i	0.101168	−	0.994869i	$-0.467742\pi$
$563$	−5.72921e6	−	3.68194e6i	−0.761770	−	0.489560i	−0.862938	+	0.505309i	$0.831378\pi$
$564$	−535059.	−	343862.i	−0.0708278	−	0.0455183i
$565$	2.80122e6	−	3.23278e6i	0.369170	−	0.426044i
$566$	1.89208e7	+	5.55565e6i	2.48255	+	0.728943i
$567$	−26319.6	−	183057.i	−0.00343812	−	0.0239127i
$568$	1.70280e6	+	1.96514e6i	0.221459	+	0.255577i
$569$	1.78218e6	+	3.90243e6i	0.230766	+	0.505306i	0.989223	−	0.146416i	$-0.0467739\pi$
$569$	1.78218e6	+	3.90243e6i	0.230766	+	0.505306i	−0.758457	+	0.651723i	$0.774047\pi$
$570$	−1.99880e7	+	5.86901e6i	−2.57681	+	0.756620i
$571$	605918.	−	1.32678e6i	0.0777721	−	0.170297i	−0.866752	−	0.498740i	$-0.833796\pi$
$571$	605918.	−	1.32678e6i	0.0777721	−	0.170297i	0.944524	+	0.328442i	$0.106524\pi$
$572$	−1.50098e6	+	1.04395e7i	−0.191815	+	1.33411i
$573$	2.04518e6	−	1.31436e6i	0.260223	−	0.167235i
$574$	2.86565e6			0.363030
$575$	−1.25881e7	−	1.59261e7i	−1.58779	−	2.00882i
$576$	−4.21034e6			−0.528763
$577$	−3.78708e6	+	2.43381e6i	−0.473549	+	0.304331i	−0.755560	−	0.655080i	$-0.772635\pi$
$577$	−3.78708e6	+	2.43381e6i	−0.473549	+	0.304331i	0.282011	+	0.959411i	$0.408999\pi$
$578$	−1.80511e6	+	1.25548e7i	−0.224742	+	1.56312i
$579$	−1.38346e6	+	3.02936e6i	−0.171502	+	0.375538i
$580$	−4.21646e7	+	1.23806e7i	−5.20448	+	1.52817i
$581$	−27156.4	−	59464.2i	−0.00333758	−	0.00730828i
$582$	305608.	+	352691.i	0.0373988	+	0.0431605i
$583$	−520257.	−	3.61847e6i	−0.0633938	−	0.440914i
$584$	6.87743e6	+	2.01939e6i	0.834437	+	0.245013i
$585$	−2.19622e6	+	2.53457e6i	−0.265330	+	0.306207i
$586$	−9.58554e6	−	6.16025e6i	−1.15311	−	0.741062i
$587$	−8.27427e6	−	5.31755e6i	−0.991139	−	0.636966i	−0.0586931	−	0.998276i	$-0.518693\pi$
$587$	−8.27427e6	−	5.31755e6i	−0.991139	−	0.636966i	−0.932446	+	0.361310i	$0.882330\pi$
$588$	−5.06068e6	+	5.84033e6i	−0.603622	+	0.696617i
$589$	5.46292e6	+	1.60406e6i	0.648838	+	0.190516i
$590$	4.58309e6	+	3.18761e7i	0.542036	+	3.76995i
$591$	−942125.	−	1.08727e6i	−0.110953	−	0.128047i
$592$	242750.	+	531549.i	0.0284679	+	0.0623360i
$593$	−1.36341e6	+	400334.i	−0.159217	+	0.0467505i	−0.360370	−	0.932809i	$-0.617350\pi$
$593$	−1.36341e6	+	400334.i	−0.159217	+	0.0467505i	0.201152	+	0.979560i	$0.435531\pi$
$594$	−1.40415e6	+	3.07466e6i	−0.163285	+	0.357545i
$595$	−93775.0	+	652219.i	−0.0108591	+	0.0755268i
$596$	−1.43339e7	+	9.21181e6i	−1.65290	+	1.06226i
$597$	−7.30454e6			−0.838798
$598$	9.20520e6	+	415747.i	1.05264	+	0.0475418i
$599$	−1.33854e7			−1.52428			−0.762142	−	0.647410i	$-0.775852\pi$
$599$	−1.33854e7			−1.52428			−0.762142	+	0.647410i	$0.775852\pi$
$600$	1.21223e7	−	7.79054e6i	1.37470	−	0.883465i
$601$	1.61936e6	−	1.12629e7i	0.182877	−	1.27194i	−0.667041	−	0.745021i	$-0.732440\pi$
$601$	1.61936e6	−	1.12629e7i	0.182877	−	1.27194i	0.849918	−	0.526915i	$-0.176651\pi$
$602$	−1.38075e6	+	3.02342e6i	−0.155283	+	0.340022i
$603$	5.40905e6	−	1.58824e6i	0.605798	−	0.177878i
$604$	7.97341e6	+	1.74593e7i	0.889307	+	1.94731i
$605$	6.21892e6	+	7.17701e6i	0.690759	+	0.797178i
$606$	−1.33774e6	−	9.30420e6i	−0.147976	−	1.02920i
$607$	−2.47711e6	−	727344.i	−0.272881	−	0.0801250i	0.142429	−	0.989805i	$-0.454509\pi$
$607$	−2.47711e6	−	727344.i	−0.272881	−	0.0801250i	−0.415310	+	0.909680i	$0.636327\pi$
$608$	7.99541e6	−	9.22720e6i	0.877166	−	1.01230i
$609$	1.65803e6	+	1.06555e6i	0.181154	+	0.116421i
$610$	−2.49710e6	−	1.60479e6i	−0.271714	−	0.174620i
$611$	338751.	−	390940.i	0.0367094	−	0.0423649i
$612$	923593.	+	271191.i	0.0996786	+	0.0292683i
$613$	1.50263e6	+	1.04510e7i	0.161510	+	1.12333i	0.895788	+	0.444481i	$0.146612\pi$
$613$	1.50263e6	+	1.04510e7i	0.161510	+	1.12333i	−0.734278	+	0.678849i	$0.762479\pi$
$614$	−5.55759e6	−	6.41380e6i	−0.594929	−	0.686585i
$615$	−4.33286e6	−	9.48764e6i	−0.461941	−	1.01151i
$616$	−2.71169e6	+	796223.i	−0.287931	+	0.0845441i
$617$	−4.46326e6	+	9.77317e6i	−0.471997	+	1.03353i	0.512590	+	0.858633i	$0.328686\pi$
$617$	−4.46326e6	+	9.77317e6i	−0.471997	+	1.03353i	−0.984587	+	0.174895i	$0.944041\pi$
$618$	−160526.	+	1.11648e6i	−0.0169073	+	0.117593i
$619$	−5.98292e6	+	3.84499e6i	−0.627605	+	0.403337i	−0.815422	−	0.578867i	$-0.803495\pi$
$619$	−5.98292e6	+	3.84499e6i	−0.627605	+	0.403337i	0.187817	+	0.982204i	$0.439859\pi$
$620$	−1.35807e7			−1.41887
$621$	1.74924e6	+	600590.i	0.182020	+	0.0624955i
$622$	1.09938e7			1.13938
$623$	−364547.	+	234280.i	−0.0376299	+	0.0241833i
$624$	−68154.5	+	474025.i	−0.00700701	+	0.0487348i
$625$	1.21536e7	−	2.66126e7i	1.24453	−	2.72513i
$626$	−2.09323e7	+	6.14628e6i	−2.13492	+	0.626869i
$627$	−4.44258e6	−	9.72789e6i	−0.451301	−	0.988211i
$628$	1.66303e7	+	1.91924e7i	1.68268	+	1.94191i
$629$	135950.	+	945553.i	0.0137010	+	0.0952926i
$630$	−2.13829e6	−	627859.i	−0.214642	−	0.0630247i
$631$	3.86939e6	−	4.46552e6i	0.386874	−	0.446476i	−0.528590	−	0.848878i	$-0.677279\pi$
$631$	3.86939e6	−	4.46552e6i	0.386874	−	0.446476i	0.915463	+	0.402401i	$0.131824\pi$
$632$	1.04930e7	+	6.74343e6i	1.04498	+	0.671565i
$633$	1.54647e6	+	993855.i	0.153402	+	0.0985856i
$634$	1.31731e7	−	1.52025e7i	1.30156	−	1.50208i
$635$	1.92681e7	+	5.65761e6i	1.89629	+	0.556800i
$636$	−501088.	−	3.48514e6i	−0.0491214	−	0.341647i
$637$	−4.11591e6	−	4.75001e6i	−0.401899	−	0.463816i
$638$	−1.49641e7	−	3.27667e7i	−1.45545	−	3.18699i
$639$	−1.00997e6	+	296554.i	−0.0978489	+	0.0287310i
$640$	−1.38569e7	+	3.03424e7i	−1.33726	+	2.92820i
$641$	−677353.	+	4.71110e6i	−0.0651134	+	0.452874i	0.931016	+	0.364978i	$0.118923\pi$
$641$	−677353.	+	4.71110e6i	−0.0651134	+	0.452874i	−0.996130	+	0.0878959i	$0.971986\pi$
$642$	−5.45229e6	+	3.50397e6i	−0.522085	+	0.335524i
$643$	−4.84793e6			−0.462411			−0.231206	−	0.972905i	$-0.574267\pi$
$643$	−4.84793e6			−0.462411			−0.231206	+	0.972905i	$0.574267\pi$
$644$	1.43401e6	+	3.55653e6i	0.136250	+	0.337919i
$645$	1.20977e7			1.14499
$646$	−4.09094e6	+	2.62909e6i	−0.385693	+	0.247870i
$647$	479019.	−	3.33165e6i	0.0449875	−	0.312895i	−0.954886	−	0.296973i	$-0.904023\pi$
$647$	479019.	−	3.33165e6i	0.0449875	−	0.312895i	0.999873	−	0.0159215i	$-0.00506819\pi$
$648$	−545363.	+	1.19418e6i	−0.0510209	+	0.111720i
$649$	−1.58626e7	+	4.65769e6i	−1.47830	+	0.434069i
$650$	1.20732e7	+	2.64366e7i	1.12083	+	2.45427i
$651$	398868.	+	460318.i	0.0368872	+	0.0425702i
$652$	−3.49087e6	−	2.42795e7i	−0.321599	−	2.23677i
$653$	3.88411e6	+	1.14048e6i	0.356458	+	0.104666i	0.455059	−	0.890462i	$-0.349618\pi$
$653$	3.88411e6	+	1.14048e6i	0.356458	+	0.104666i	−0.0986002	+	0.995127i	$0.531436\pi$
$654$	−1.22519e7	+	1.41394e7i	−1.12010	+	1.29267i
$655$	1.18986e7	+	7.64677e6i	1.08366	+	0.696426i
$656$	−1.25296e6	−	805227.i	−0.113678	−	0.0730565i
$657$	−1.90014e6	+	2.19287e6i	−0.171740	+	0.198198i
$658$	329816.	+	96842.7i	0.0296966	+	0.00871971i
$659$	−1.20448e6	−	8.37735e6i	−0.108040	−	0.751438i	−0.969761	−	0.244055i	$-0.921522\pi$
$659$	−1.20448e6	−	8.37735e6i	−0.108040	−	0.751438i	0.861721	−	0.507383i	$-0.169387\pi$
$660$	1.67048e7	+	1.92783e7i	1.49273	+	1.72270i
$661$	4.96356e6	+	1.08687e7i	0.441865	+	0.967548i	0.991252	+	0.131981i	$0.0421338\pi$
$661$	4.96356e6	+	1.08687e7i	0.441865	+	0.967548i	−0.549388	+	0.835568i	$0.685139\pi$
$662$	2.97161e6	−	872543.i	0.263540	−	0.0773823i
$663$	−325220.	+	712134.i	−0.0287339	+	0.0629184i
$664$	−66041.2	+	459326.i	−0.00581292	+	0.0404298i
$665$	5.93162e6	−	3.81202e6i	0.520139	−	0.334273i
$666$	−3.23085e6			−0.282248
$667$	−1.70449e7	+	9.89698e6i	−1.48347	+	0.861367i
$668$	1.17268e7			1.01681
$669$	1.04559e6	−	671963.i	0.0903229	−	0.0580470i
$670$	9.66776e6	−	6.72407e7i	0.832030	−	5.78689i
$671$	633018.	−	1.38612e6i	0.0542762	−	0.118848i
$672$	1.25323e6	−	367981.i	0.107055	−	0.0314342i
$673$	−2.27876e6	−	4.98978e6i	−0.193937	−	0.424662i	0.787535	−	0.616270i	$-0.211357\pi$
$673$	−2.27876e6	−	4.98978e6i	−0.193937	−	0.424662i	−0.981472	+	0.191608i	$0.938630\pi$
$674$	−9.45227e6	−	1.09085e7i	−0.801469	−	0.924944i
$675$	830158.	+	5.77388e6i	0.0701296	+	0.487762i
$676$	1.11765e7	+	3.28173e6i	0.940677	+	0.276208i
$677$	751189.	−	866918.i	0.0629909	−	0.0726953i	−0.723380	−	0.690451i	$-0.757412\pi$
$677$	751189.	−	866918.i	0.0629909	−	0.0726953i	0.786370	+	0.617755i	$0.211958\pi$
$678$	2.84107e6	+	1.82584e6i	0.237360	+	0.152542i
$679$	−132881.	−	85397.2i	−0.0110608	−	0.00710836i
$680$	3.06309e6	−	3.53500e6i	0.254032	−	0.293168i
$681$	4.68014e6	+	1.37421e6i	0.386715	+	0.113550i
$682$	−1.58428e6	−	1.10189e7i	−0.130428	−	0.907148i
$683$	−6.90136e6	−	7.96460e6i	−0.566087	−	0.653299i	0.398468	−	0.917182i	$-0.369542\pi$
$683$	−6.90136e6	−	7.96460e6i	−0.566087	−	0.653299i	−0.964555	+	0.263883i	$0.914997\pi$
$684$	−4.27888e6	−	9.36945e6i	−0.349696	−	0.765727i
$685$	−7.10981e6	+	2.08763e6i	−0.578937	+	0.169991i
$686$	3.55607e6	−	7.78670e6i	0.288509	−	0.631747i
$687$	1.97205e6	−	1.37159e7i	0.159414	−	1.10875i
$688$	1.45327e6	−	933960.i	0.117051	−	0.0752241i
$689$	2.86365e6			0.229812
$690$	1.53397e7	−	1.61674e7i	1.22657	−	1.29276i
$691$	1.82197e7			1.45160			0.725798	−	0.687908i	$-0.241471\pi$
$691$	1.82197e7			1.45160			0.725798	+	0.687908i	$0.241471\pi$
$692$	2.77467e7	−	1.78318e7i	2.20266	−	1.41556i
$693$	162817.	−	1.13242e6i	0.0128785	−	0.0895722i
$694$	−1.11305e7	+	2.43724e7i	−0.877235	+	1.92088i
$695$	2.89844e7	−	8.51057e6i	2.27615	−	0.668339i
$696$	−5.81194e6	−	1.27264e7i	−0.454777	−	0.995822i
$697$	−1.59445e6	−	1.84009e6i	−0.124316	−	0.143469i
$698$	4.07511e6	+	2.83430e7i	0.316592	+	2.20195i
$699$	1.34700e7	+	3.95514e6i	1.04273	+	0.306174i
$700$	−7.92045e6	+	9.14068e6i	−0.610948	+	0.705072i
$701$	−1.72257e7	−	1.10703e7i	−1.32398	−	0.850871i	−0.328379	−	0.944546i	$-0.606502\pi$
$701$	−1.72257e7	−	1.10703e7i	−1.32398	−	0.850871i	−0.995603	+	0.0936748i	$0.970139\pi$
$702$	−2.22746e6	−	1.43150e6i	−0.170596	−	0.109635i
$703$	6.69403e6	−	7.72532e6i	0.510857	−	0.589560i
$704$	−2.49908e7	−	7.33796e6i	−1.90042	−	0.558012i
$705$	−178053.	−	1.23839e6i	−0.0134920	−	0.0938390i
$706$	4.04081e6	+	4.66335e6i	0.305110	+	0.352116i
$707$	1.32167e6	+	2.89405e6i	0.0994431	+	0.217750i
$708$	−1.52781e7	+	4.48607e6i	−1.14548	+	0.336343i
$709$	1.07069e6	−	2.34448e6i	0.0799922	−	0.175158i	−0.865410	−	0.501064i	$-0.832942\pi$
$709$	1.07069e6	−	2.34448e6i	0.0799922	−	0.175158i	0.945402	+	0.325906i	$0.105669\pi$
$710$	−1.80515e6	+	1.25551e7i	−0.134390	+	0.934703i
$711$	−4.24767e6	+	2.72981e6i	−0.315121	+	0.202516i
$712$	3.07610e6			0.227405
$713$	−5.91588e6	+	1.45063e6i	−0.435808	+	0.106865i
$714$	−520228.			−0.0381899
$715$	−1.74532e7	+	1.12165e7i	−1.27676	+	0.820525i
$716$	5.42537e6	−	3.77343e7i	0.395500	−	2.75077i
$717$	−5.25090e6	+	1.14979e7i	−0.381448	+	0.835255i
$718$	2.10649e7	−	6.18522e6i	1.52493	−	0.447759i
$719$	−6.49530e6	−	1.42227e7i	−0.468573	−	1.02603i	−0.985449	−	0.169971i	$-0.945633\pi$
$719$	−6.49530e6	−	1.42227e7i	−0.468573	−	1.02603i	0.516876	−	0.856060i	$-0.327095\pi$
$720$	758509.	+	875366.i	0.0545292	+	0.0629301i
$721$	−54332.9	−	377894.i	−0.00389247	−	0.0270727i
$722$	2.79444e7	+	8.20521e6i	1.99504	+	0.585797i
$723$	7.93413e6	−	9.15647e6i	0.564486	−	0.651452i
$724$	−1.59587e7	−	1.02561e7i	−1.13149	−	0.727167i
$725$	−5.22966e7	−	3.36090e7i	−3.69512	−	2.37471i
$726$	−4.90989e6	+	5.66631e6i	−0.345724	+	0.398987i
$727$	−1.25667e7	−	3.68991e6i	−0.881830	−	0.258929i	−0.190690	−	0.981650i	$-0.561073\pi$
$727$	−1.25667e7	−	3.68991e6i	−0.881830	−	0.258929i	−0.691139	+	0.722722i	$0.742891\pi$
$728$	−315065.	−	2.19133e6i	−0.0220329	−	0.153242i
$729$	−348020.	−	401636.i	−0.0242541	−	0.0279907i
$730$	1.45249e7	+	3.18052e7i	1.00880	+	2.20897i
$731$	2.70965e6	−	795624.i	0.187551	−	0.0550699i
$732$	609693.	−	1.33504e6i	0.0420566	−	0.0920910i
$733$	−711839.	+	4.95095e6i	−0.0489353	+	0.340352i	0.950615	+	0.310372i	$0.100454\pi$
$733$	−711839.	+	4.95095e6i	−0.0489353	+	0.340352i	−0.999550	+	0.0299804i	$0.990456\pi$
$734$	1.01983e6	−	655407.i	0.0698698	−	0.0449026i
$735$	−1.52014e7			−1.03792
$736$	−2.44035e6	+	1.28319e7i	−0.166057	+	0.873168i
$737$	3.48739e7			2.36500
$738$	6.92749e6	−	4.45203e6i	0.468204	−	0.300897i
$739$	−1.72990e6	+	1.20317e7i	−0.116522	+	0.810431i	0.844815	+	0.535058i	$0.179710\pi$
$739$	−1.72990e6	+	1.20317e7i	−0.116522	+	0.810431i	−0.961338	+	0.275373i	$0.911199\pi$
$740$	−1.01288e7	+	2.21790e7i	−0.679954	+	1.48889i
$741$	8.03798e6	−	2.36016e6i	0.537776	−	0.157905i
$742$	790498.	+	1.73095e6i	0.0527097	+	0.115418i
$743$	−722477.	−	833782.i	−0.0480122	−	0.0554090i	0.731235	−	0.682125i	$-0.238944\pi$
$743$	−722477.	−	833782.i	−0.0480122	−	0.0554090i	−0.779248	+	0.626716i	$0.784399\pi$
$744$	−615325.	−	4.27968e6i	−0.0407542	−	0.283452i
$745$	−3.21590e7	−	9.44273e6i	−2.12281	−	0.623314i
$746$	−6.80694e6	+	7.85563e6i	−0.447822	+	0.516814i
$747$	−158031.	−	101561.i	−0.0103620	−	0.00665922i
$748$	5.00941e6	+	3.21935e6i	0.327365	+	0.210385i
$749$	1.43655e6	−	1.65786e6i	0.0935653	−	0.107980i
$750$	4.11048e7	+	1.20695e7i	2.66833	+	0.783493i
$751$	−1.60184e6	−	1.11410e7i	−0.103638	−	0.720818i	−0.973693	−	0.227863i	$-0.926826\pi$
$751$	−1.60184e6	−	1.11410e7i	−0.103638	−	0.720818i	0.870055	−	0.492954i	$-0.164083\pi$
$752$	−116995.	−	135019.i	−0.00754433	−	0.00870663i
$753$	−1.45351e6	−	3.18275e6i	−0.0934181	−	0.204557i
$754$	2.70745e7	−	7.94980e6i	1.73433	−	0.509247i
$755$	−1.56844e7	+	3.43441e7i	−1.00138	+	2.19273i
$756$	156818.	−	1.09069e6i	0.00997909	−	0.0694061i
$757$	1.32090e7	−	8.48894e6i	0.837783	−	0.538411i	−0.0499592	−	0.998751i	$-0.515909\pi$
$757$	1.32090e7	−	8.48894e6i	0.837783	−	0.538411i	0.887742	+	0.460341i	$0.152273\pi$
$758$	1.69091e7			1.06893
$759$	9.33599e6	+	6.61349e6i	0.588242	+	0.416703i
$760$	−5.00519e7			−3.14331
$761$	1.23684e7	−	7.94870e6i	0.774199	−	0.497547i	−0.0929051	−	0.995675i	$-0.529615\pi$
$761$	1.23684e7	−	7.94870e6i	0.774199	−	0.497547i	0.867104	+	0.498128i	$0.165979\pi$
$762$	−2.25633e6	+	1.56931e7i	−0.140772	+	0.979089i
$763$	2.63060e6	−	5.76020e6i	0.163585	−	0.358201i
$764$	1.38984e7	−	4.08092e6i	0.861450	−	0.252944i
$765$	786585.	+	1.72238e6i	0.0485950	+	0.106408i
$766$	5.67144e6	+	6.54519e6i	0.349238	+	0.403042i
$767$	−1.84304e6	−	1.28187e7i	−0.113122	−	0.786781i
$768$	−1.09050e7	−	3.20200e6i	−0.667149	−	0.195893i
$769$	−9.49998e6	+	1.09636e7i	−0.579304	+	0.668553i	−0.967455	−	0.253043i	$-0.918569\pi$
$769$	−9.49998e6	+	1.09636e7i	−0.579304	+	0.668553i	0.388151	+	0.921596i	$0.373114\pi$
$770$	−1.15977e7	−	7.45340e6i	−0.704930	−	0.453031i
$771$	−9.13099e6	−	5.86813e6i	−0.553200	−	0.355520i
$772$	−1.29942e7	+	1.49961e7i	−0.784706	+	0.905599i
$773$	−1.61311e7	−	4.73652e6i	−0.970992	−	0.285109i	−0.242491	−	0.970154i	$-0.577964\pi$
$773$	−1.61311e7	−	4.73652e6i	−0.970992	−	0.285109i	−0.728501	+	0.685045i	$0.759783\pi$
$774$	1.35928e6	+	9.45401e6i	0.0815562	+	0.567236i
$775$	−1.25809e7	−	1.45191e7i	−0.752413	−	0.868331i
$776$	465792.	+	1.01994e6i	0.0277675	+	0.0608024i
$777$	1.04925e6	−	308086.i	0.0623483	−	0.0183071i
$778$	1.30446e7	−	2.85637e7i	0.772649	−	1.69186i
$779$	−3.70784e6	+	2.57886e7i	−0.218916	+	1.52259i
$780$	−1.68101e7	+	1.08032e7i	−0.989313	+	0.635793i
$781$	−6.51160e6			−0.381997
$782$	2.37251e6	−	4.63003e6i	0.138737	−	0.270749i
$783$	5.66358e6			0.330131
$784$	−1.82611e6	+	1.17357e6i	−0.106106	+	0.0681899i
$785$	−7.10927e6	+	4.94461e7i	−0.411766	+	2.86390i
$786$	−4.63883e6	+	1.01576e7i	−0.267826	+	0.586456i
$787$	2.55452e7	−	7.50073e6i	1.47018	−	0.431685i	0.554025	−	0.832500i	$-0.313091\pi$
$787$	2.55452e7	−	7.50073e6i	1.47018	−	0.431685i	0.916159	+	0.400815i	$0.131273\pi$
$788$	−3.56089e6	−	7.79725e6i	−0.204288	−	0.447328i
$789$	6.37418e6	+	7.35620e6i	0.364529	+	0.420689i
$790$	8.65905e6	+	6.02250e7i	0.493631	+	3.43328i
$791$	−1.09677e6	−	322040.i	−0.0623267	−	0.0183008i
$792$	−5.31831e6	+	6.13765e6i	−0.301273	+	0.347688i
$793$	1.00418e6	+	645350.i	0.0567061	+	0.0364428i
$794$	1.89344e7	+	1.21684e7i	1.06586	+	0.684987i
$795$	4.53562e6	−	5.23439e6i	0.254518	−	0.293730i
$796$	−4.17591e7	−	1.22616e7i	−2.33598	−	0.685905i
$797$	−84658.7	−	588814.i	−0.00472091	−	0.0328347i	0.987325	−	0.158713i	$-0.0507343\pi$
$797$	−84658.7	−	588814.i	−0.00472091	−	0.0328347i	−0.992046	+	0.125878i	$0.959825\pi$
$798$	3.64546e6	+	4.20708e6i	0.202649	+	0.233870i
$799$	−121325.	−	265665.i	−0.00672331	−	0.0147220i
$800$	−3.95287e7	+	1.16067e7i	−2.18367	+	0.641184i
$801$	−517291.	+	1.13271e6i	−0.0284874	+	0.0623788i
$802$	4.47651e6	−	3.11348e7i	0.245756	−	1.70927i
$803$	−1.51002e7	+	9.70433e6i	−0.826409	+	0.531101i
$804$	3.35889e7			1.83255
$805$	−3.44000e6	+	6.71326e6i	−0.187098	+	0.365127i
$806$	8.72037e6			0.472821
$807$	5.15333e6	−	3.31184e6i	0.278550	−	0.179014i
$808$	3.21415e6	−	2.23549e7i	0.173196	−	1.20460i
$809$	−546352.	+	1.19634e6i	−0.0293495	+	0.0642665i	−0.923739	−	0.383022i	$-0.874883\pi$
$809$	−546352.	+	1.19634e6i	−0.0293495	+	0.0642665i	0.894389	+	0.447289i	$0.147610\pi$
$810$	−6.14459e6	+	1.80421e6i	−0.329064	+	0.0966219i
$811$	9.70217e6	+	2.12448e7i	0.517984	+	1.13423i	0.970197	+	0.242317i	$0.0779075\pi$
$811$	9.70217e6	+	2.12448e7i	0.517984	+	1.13423i	−0.452213	+	0.891910i	$0.649365\pi$
$812$	7.69006e6	+	8.87480e6i	0.409298	+	0.472355i
$813$	1.06669e6	+	7.41901e6i	0.0565995	+	0.393658i
$814$	−1.91770e7	−	5.63086e6i	−1.01442	−	0.297861i
$815$	3.15978e7	−	3.64658e7i	1.66634	−	1.92306i
$816$	227461.	+	146180.i	0.0119586	+	0.00768535i
$817$	−2.54219e7	−	1.63376e7i	−1.33245	−	0.856316i
$818$	−1.03267e7	+	1.19176e7i	−0.539608	+	0.622741i
$819$	859892.	+	252487.i	0.0447955	+	0.0131531i
$820$	−8.84421e6	−	6.15129e7i	−0.459330	−	3.19471i
$821$	−2.28830e7	−	2.64084e7i	−1.18483	−	1.36737i	−0.914494	−	0.404600i	$-0.867411\pi$
$821$	−2.28830e7	−	2.64084e7i	−1.18483	−	1.36737i	−0.270336	−	0.962766i	$-0.587135\pi$
$822$	−2.43027e6	−	5.32155e6i	−0.125451	−	0.274700i
$823$	3.31186e7	−	9.72450e6i	1.70440	−	0.500458i	0.722747	−	0.691113i	$-0.242879\pi$
$823$	3.31186e7	−	9.72450e6i	1.70440	−	0.500458i	0.981657	+	0.190655i	$0.0610611\pi$
$824$	−1.12582e6	+	2.46521e6i	−0.0577632	+	0.126484i
$825$	−5.13549e6	+	3.57181e7i	−0.262692	+	1.82706i
$826$	7.23953e6	−	4.65256e6i	0.369199	−	0.237270i
$827$	2.48675e7			1.26435			0.632177	−	0.774824i	$-0.282161\pi$
$827$	2.48675e7			1.26435			0.632177	+	0.774824i	$0.282161\pi$
$828$	8.99199e6	+	6.36981e6i	0.455806	+	0.322887i
$829$	2.00159e7			1.01155			0.505776	−	0.862665i	$-0.331206\pi$
$829$	2.00159e7			1.01155			0.505776	+	0.862665i	$0.331206\pi$
$830$	−1.90432e6	+	1.22383e6i	−0.0959498	+	0.0616632i
$831$	−329119.	+	2.28907e6i	−0.0165329	+	0.114989i
$832$	8.47565e6	−	1.85591e7i	0.424487	−	0.929497i
$833$	−3.40482e6	+	999746.i	−0.170013	+	0.0499203i
$834$	9.90742e6	+	2.16942e7i	0.493226	+	1.08001i
$835$	1.51062e7	+	1.74335e7i	0.749788	+	0.865301i
$836$	−9.06817e6	−	6.30705e7i	−0.448749	−	3.12112i
$837$	1.67938e6	+	493109.i	0.0828580	+	0.0243293i
$838$	−2.22334e7	+	2.56587e7i	−1.09370	+	1.26219i
$839$	−1.62462e7	−	1.04408e7i	−0.796798	−	0.512071i	0.0777715	−	0.996971i	$-0.475220\pi$
$839$	−1.62462e7	−	1.04408e7i	−0.796798	−	0.512071i	−0.874569	+	0.484900i	$0.838856\pi$
$840$	−4.50448e6	−	2.89485e6i	−0.220266	−	0.141556i
$841$	−2.60934e7	+	3.01134e7i	−1.27216	+	1.46815i
$842$	2.12206e6	+	623094.i	0.103152	+	0.0302882i
$843$	−2.81270e6	−	1.95628e7i	−0.136318	−	0.948115i
$844$	7.17265e6	+	8.27768e6i	0.346596	+	0.399993i
$845$	9.51858e6	+	2.08428e7i	0.458596	+	1.00419i
$846$	947759.	−	278287.i	0.0455273	−	0.0133680i
$847$	1.05420e6	−	2.30838e6i	0.0504911	−	0.110560i
$848$	140752.	−	978953.i	0.00672149	−	0.0467490i
$849$	−1.61350e7	+	1.03693e7i	−0.768246	+	0.493722i
$850$	1.64088e7			0.778983
$851$	−2.04314e6	+	1.07433e7i	−0.0967106	+	0.508528i
$852$	−6.27167e6			−0.295995
$853$	−1.91746e7	+	1.23227e7i	−0.902304	+	0.579876i	−0.907473	−	0.420111i	$-0.861991\pi$
$853$	−1.91746e7	+	1.23227e7i	−0.902304	+	0.579876i	0.00516863	+	0.999987i	$0.498355\pi$
$854$	−112884.	+	785129.i	−0.00529651	+	0.0368380i
$855$	8.41695e6	−	1.84306e7i	0.393767	−	0.862230i
$856$	−1.49412e7	+	4.38714e6i	−0.696951	+	0.204643i
$857$	1.38053e6	+	3.02293e6i	0.0642086	+	0.140597i	0.939016	−	0.343874i	$-0.111739\pi$
$857$	1.38053e6	+	3.02293e6i	0.0642086	+	0.140597i	−0.874807	+	0.484471i	$0.839012\pi$
$858$	−1.07264e7	−	1.23789e7i	−0.497434	−	0.574069i
$859$	278390.	+	1.93625e6i	0.0128728	+	0.0895320i	0.995245	−	0.0974032i	$-0.0310536\pi$
$859$	278390.	+	1.93625e6i	0.0128728	+	0.0895320i	−0.982372	+	0.186935i	$0.940145\pi$
$860$	6.91609e7	+	2.03075e7i	3.18871	+	0.936289i
$861$	−1.82523e6	+	2.10642e6i	−0.0839090	+	0.0968362i
$862$	5.83193e6	+	3.74795e6i	0.267328	+	0.171801i
$863$	2.95988e7	+	1.90220e7i	1.35284	+	0.869419i	0.997856	−	0.0654518i	$-0.0208489\pi$
$863$	2.95988e7	+	1.90220e7i	1.35284	+	0.869419i	0.354987	+	0.934871i	$0.384485\pi$
$864$	2.45790e6	−	2.83657e6i	0.112016	−	0.129273i
$865$	6.22517e7	+	1.82788e7i	2.82886	+	0.830628i
$866$	−337898.	−	2.35013e6i	−0.0153106	−	0.106487i
$867$	−8.07882e6	−	9.32346e6i	−0.365006	−	0.421240i
$868$	1.50757e6	+	3.30113e6i	0.0679171	+	0.148718i
$869$	−2.99700e7	+	8.79998e6i	−1.34629	+	0.395305i
$870$	2.83510e7	−	6.20801e7i	1.26990	−	2.78070i
$871$	−3.88779e6	+	2.70402e7i	−0.173643	+	1.20771i
$872$	−3.78158e7	+	2.43028e7i	−1.68416	+	1.08234i
$873$	−453901.			−0.0201570
$874$	−5.40683e7	+	1.32581e7i	−2.39422	+	0.587087i
$875$	−1.45000e7			−0.640250
$876$	−1.45438e7	+	9.34676e6i	−0.640352	+	0.411529i
$877$	1.38310e6	−	9.61970e6i	0.0607234	−	0.422340i	−0.936672	−	0.350209i	$-0.886111\pi$
$877$	1.38310e6	−	9.61970e6i	0.0607234	−	0.422340i	0.997395	−	0.0721318i	$-0.0229802\pi$
$878$	−32837.2	+	71903.4i	−0.00143757	+	0.00314784i
$879$	1.06335e7	−	3.12228e6i	0.464199	−	0.136301i
$880$	2.97656e6	+	6.51776e6i	0.129571	+	0.283721i
$881$	−1.95760e6	−	2.25919e6i	−0.0849735	−	0.0980646i	0.711671	−	0.702513i	$-0.247939\pi$
$881$	−1.95760e6	−	2.25919e6i	−0.0849735	−	0.0980646i	−0.796644	+	0.604449i	$0.793393\pi$
$882$	−1.70801e6	−	1.18795e7i	−0.0739298	−	0.514193i
$883$	−6.51195e6	−	1.91208e6i	−0.281067	−	0.0825287i	0.138161	−	0.990410i	$-0.455881\pi$
$883$	−6.51195e6	−	1.91208e6i	−0.281067	−	0.0825287i	−0.419228	+	0.907881i	$0.637699\pi$
$884$	−3.05465e6	+	3.52525e6i	−0.131471	+	0.151726i
$885$	−2.63500e7	−	1.69341e7i	−1.13089	−	0.726781i
$886$	−1.96738e6	−	1.26436e6i	−0.0841982	−	0.0541109i
$887$	−138642.	+	160001.i	−0.00591678	+	0.00682832i	−0.758700	−	0.651440i	$-0.774165\pi$
$887$	−138642.	+	160001.i	−0.00591678	+	0.00682832i	0.752783	+	0.658268i	$0.228711\pi$
$888$	−7.44821e6	−	2.18699e6i	−0.316971	−	0.0930711i
$889$	−763698.	−	5.31163e6i	−0.0324091	−	0.225410i
$890$	9.82647e6	+	1.13404e7i	0.415837	+	0.479901i
$891$	−1.36571e6	−	2.99049e6i	−0.0576320	−	0.126197i
$892$	7.10550e6	−	2.08636e6i	0.299008	−	0.0877966i
$893$	−1.29825e6	+	2.84278e6i	−0.0544792	+	0.119293i
$894$	3.76589e6	−	2.61923e7i	0.157588	−	1.09605i
$895$	6.30857e7	−	4.05427e7i	2.63253	−	1.69182i
$896$	8.91374e6			0.370928
$897$	−6.16870e6	+	6.50157e6i	−0.255984	+	0.269797i
$898$	−2.02193e7			−0.836712
$899$	−1.56917e7	+	1.00844e7i	−0.647544	+	0.416152i
$900$	−4.94626e6	+	3.44020e7i	−0.203550	+	1.41572i
$901$	671644.	−	1.47069e6i	0.0275630	−	0.0603546i
$902$	4.88778e7	−	1.43518e7i	2.00030	−	0.587342i
$903$	−1.34295e6	−	2.94065e6i	−0.0548075	−	0.120012i
$904$	5.31370e6	+	6.13233e6i	0.216260	+	0.249577i
$905$	−5.31063e6	−	3.69363e7i	−0.215538	−	1.49910i
$906$	−2.86012e7	−	8.39808e6i	−1.15762	−	0.339906i
$907$	1.07518e7	−	1.24082e7i	0.433973	−	0.500831i	−0.496070	−	0.868283i	$-0.665224\pi$
$907$	1.07518e7	−	1.24082e7i	0.433973	−	0.500831i	0.930043	+	0.367451i	$0.119769\pi$
$908$	2.44490e7	+	1.57124e7i	0.984115	+	0.632452i
$909$	7.69120e6	+	4.94283e6i	0.308734	+	0.198411i
$910$	7.07208e6	−	8.16162e6i	0.283103	−	0.326718i
$911$	1.30854e7	+	3.84222e6i	0.522386	+	0.153386i	0.532286	−	0.846565i	$-0.321333\pi$
$911$	1.30854e7	+	3.84222e6i	0.522386	+	0.153386i	−0.00990003	+	0.999951i	$0.503151\pi$
$912$	−411756.	−	2.86383e6i	−0.0163928	−	0.114014i
$913$	−761003.	−	878244.i	−0.0302141	−	0.0348689i
$914$	1.86921e7	+	4.09300e7i	0.740103	+	1.62060i
$915$	2.77010e6	−	813375.i	0.109381	−	0.0321172i
$916$	3.42978e7	−	7.51018e7i	1.35060	−	2.95741i
$917$	537892.	−	3.74112e6i	0.0211238	−	0.146919i
$918$	−1.25761e6	+	808219.i	−0.0492538	+	0.0316535i
$919$	−3.22705e7			−1.26042			−0.630212	−	0.776423i	$-0.717032\pi$
$919$	−3.22705e7			−1.26042			−0.630212	+	0.776423i	$0.717032\pi$
$920$	4.63070e7	−	2.68879e7i	1.80375	−	1.04734i
$921$	8.25433e6			0.320651
$922$	−1.68833e7	+	1.08502e7i	−0.654079	+	0.420351i
$923$	725922.	−	5.04890e6i	0.0280470	−	0.195071i
$924$	2.83171e6	−	6.20057e6i	0.109111	−	0.238920i
$925$	−3.30948e7	+	9.71750e6i	−1.27176	+	0.373422i
$926$	1.50527e7	+	3.29609e7i	0.576883	+	1.26320i
$927$	−718436.	−	829119.i	−0.0274593	−	0.0316897i
$928$	5.69247e6	+	3.95920e7i	0.216986	+	1.50917i
$929$	−2.08540e7	−	6.12330e6i	−0.792777	−	0.232780i	−0.139821	−	0.990177i	$-0.544653\pi$
$929$	−2.08540e7	−	6.12330e6i	−0.792777	−	0.232780i	−0.652955	+	0.757397i	$0.726471\pi$
$930$	1.38118e7	−	1.59397e7i	0.523653	−	0.604328i
$931$	3.19440e7	+	2.05292e7i	1.20786	+	0.776241i
$932$	7.03669e7	+	4.52220e7i	2.65356	+	1.70534i
$933$	−7.00229e6	+	8.08107e6i	−0.263352	+	0.303924i
$934$	−5.65499e7	−	1.66045e7i	−2.12112	−	0.622816i
$935$	1.66700e6	+	1.15942e7i	0.0623599	+	0.433723i
$936$	−4.16606e6	−	4.80789e6i	−0.155430	−	0.179376i
$937$	−2.01450e7	−	4.41114e7i	−0.749581	−	1.64135i	−0.767117	−	0.641508i	$-0.778309\pi$
$937$	−2.01450e7	−	4.41114e7i	−0.749581	−	1.64135i	0.0175354	−	0.999846i	$-0.494418\pi$
$938$	−1.74178e7	+	5.11432e6i	−0.646376	+	0.189793i
$939$	8.81460e6	−	1.93013e7i	0.326241	−	0.714368i
$940$	1.06088e6	−	7.37858e6i	0.0391603	−	0.272366i
$941$	−1.32562e7	+	8.51927e6i	−0.488030	+	0.313638i	−0.761413	−	0.648268i	$-0.775494\pi$
$941$	−1.32562e7	+	8.51927e6i	−0.488030	+	0.313638i	0.273383	+	0.961905i	$0.411857\pi$
$942$	−3.94395e7			−1.44812
$943$	−1.04232e7	−	2.58509e7i	−0.381699	−	0.946666i
$944$	−4.47271e6			−0.163358
$945$	1.82346e6	−	1.17187e6i	0.0664228	−	0.0426873i
$946$	−8.40873e6	+	5.84840e7i	−0.305494	+	2.12476i
$947$	−1.07067e7	+	2.34443e7i	−0.387953	+	0.849499i	0.610398	+	0.792095i	$0.291010\pi$
$947$	−1.07067e7	+	2.34443e7i	−0.387953	+	0.849499i	−0.998351	+	0.0574038i	$0.981718\pi$
$948$	−2.88657e7	+	8.47573e6i	−1.04318	+	0.306307i
$949$	−5.84106e6	−	1.27901e7i	−0.210536	−	0.461009i
$950$	−1.14983e8	−	1.32698e8i	−4.13357	−	4.77039i
$951$	2.78441e6	+	1.93660e7i	0.0998348	+	0.694366i
$952$	−1.19930e6	−	352147.i	−0.0428880	−	0.0125931i
$953$	−9.18001e6	+	1.05943e7i	−0.327424	+	0.377868i	−0.895464	−	0.445133i	$-0.853156\pi$
$953$	−9.18001e6	+	1.05943e7i	−0.327424	+	0.377868i	0.568040	+	0.823001i	$0.307702\pi$
$954$	4.60015e6	+	2.95633e6i	0.163644	+	0.105168i
$955$	2.39703e7	+	1.54048e7i	0.850481	+	0.546571i
$956$	−4.93193e7	+	5.69175e7i	−1.74531	+	2.01419i
$957$	3.36166e7	+	9.87072e6i	1.18652	+	0.348393i
$958$	1.08678e7	+	7.55870e7i	0.382584	+	2.66093i
$959$	1.29670e6	+	1.49647e6i	0.0455296	+	0.0525439i
$960$	−2.04994e7	−	4.48874e7i	−0.717897	−	1.57198i
$961$	2.19385e7	−	6.44173e6i	0.766300	−	0.225006i
$962$	6.50388e6	−	1.42415e7i	0.226587	−	0.496156i
$963$	897112.	−	6.23955e6i	0.0311732	−	0.216814i
$964$	6.07287e7	−	3.90279e7i	2.10475	−	1.35264i
$965$	−3.90324e7			−1.34930
$966$	−5.63274e6	−	1.93397e6i	−0.194212	−	0.0666817i
$967$	−3.93238e7			−1.35235			−0.676176	−	0.736740i	$-0.736364\pi$
$967$	−3.93238e7			−1.35235			−0.676176	+	0.736740i	$0.736364\pi$
$968$	−1.51545e7	+	9.73923e6i	−0.519821	+	0.334069i
$969$	673119.	−	4.68164e6i	0.0230294	−	0.160173i
$970$	−2.27216e6	+	4.97534e6i	−0.0775372	+	0.169783i
$971$	3.58119e7	−	1.05153e7i	1.21893	−	0.357910i	0.391868	−	0.920021i	$-0.371829\pi$
$971$	3.58119e7	−	1.05153e7i	1.21893	−	0.357910i	0.827062	+	0.562111i	$0.190011\pi$
$972$	−1.31539e6	−	2.88030e6i	−0.0446569	−	0.0977849i
$973$	−5.28623e6	−	6.10063e6i	−0.179004	−	0.206582i
$974$	−5.79173e6	−	4.02824e7i	−0.195619	−	1.36056i
$975$	−2.71223e7	−	7.96381e6i	−0.913722	−	0.268293i
$976$	269973.	−	311565.i	0.00907184	−	0.0104695i
$977$	4.04505e7	+	2.59959e7i	1.35577	+	0.871302i	0.998044	−	0.0625228i	$-0.0199146\pi$
$977$	4.04505e7	+	2.59959e7i	1.35577	+	0.871302i	0.357730	+	0.933825i	$0.383551\pi$
$978$	3.20473e7	+	2.05956e7i	1.07138	+	0.688536i
$979$	−5.04455e6	+	5.82172e6i	−0.168215	+	0.194131i
$980$	−8.69045e7	−	2.55175e7i	−2.89053	−	0.848735i
$981$	−2.58969e6	−	1.80117e7i	−0.0859164	−	0.597562i
$982$	−2.06628e7	−	2.38461e7i	−0.683770	−	0.789112i
$983$	4.36947e6	+	9.56780e6i	0.144226	+	0.315812i	0.967935	−	0.251202i	$-0.0808259\pi$
$983$	4.36947e6	+	9.56780e6i	0.144226	+	0.315812i	−0.823708	+	0.567014i	$0.808099\pi$
$984$	1.89838e7	−	5.57416e6i	0.625023	−	0.183523i
$985$	7.00459e6	−	1.53379e7i	0.230034	−	0.503704i
$986$	2.26728e6	−	1.57693e7i	0.0742700	−	0.516559i
$987$	−281256.	+	180752.i	−0.00918985	+	0.00590596i
$988$	4.99139e7			1.62678
$989$	3.22963e7	+	1.45864e6i	1.04994	+	0.0474196i
$990$	−3.96161e7			−1.28465
$991$	−3.27634e7	+	2.10557e7i	−1.05975	+	0.681061i	−0.949794	−	0.312875i	$-0.898708\pi$
$991$	−3.27634e7	+	2.10557e7i	−1.05975	+	0.681061i	−0.109958	+	0.993936i	$0.535072\pi$
$992$	−1.75921e6	+	1.22355e7i	−0.0567593	+	0.394770i
$993$	−1.25134e6	+	2.74006e6i	−0.0402720	+	0.0881834i
$994$	3.25222e6	−	954937.i	0.104403	−	0.0306555i
$995$	−3.55645e7	−	7.78753e7i	−1.13883	−	2.49369i
$996$	−732962.	−	845884.i	−0.0234117	−	0.0270186i
$997$	−4.39296e6	−	3.05537e7i	−0.139965	−	0.973478i	−0.931859	−	0.362820i	$-0.881814\pi$
$997$	−4.39296e6	−	3.05537e7i	−0.139965	−	0.973478i	0.791894	−	0.610658i	$-0.209095\pi$
$998$	−2.98924e6	−	877719.i	−0.0950022	−	0.0278952i
$999$	2.05784e6	−	2.37487e6i	0.0652375	−	0.0752880i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.6.e.a.58.2	yes	100
23.2	even	11	inner	69.6.e.a.25.2	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.6.e.a.25.2	✓	100	23.2	even	11	inner
69.6.e.a.58.2	yes	100	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.78439 + 5.00272i) q^{2} +(1.28083 - 8.90839i) q^{3} +(22.2762 - 48.7781i) q^{4} +(101.210 - 29.7181i) q^{5} +(34.5957 + 75.7541i) q^{6} +(-18.4590 - 21.3028i) q^{7} +(28.4763 + 198.057i) q^{8} +(-77.7189 - 22.8203i) q^{9} +O(q^{10})\)	\(q+(-7.78439 + 5.00272i) q^{2} +(1.28083 - 8.90839i) q^{3} +(22.2762 - 48.7781i) q^{4} +(101.210 - 29.7181i) q^{5} +(34.5957 + 75.7541i) q^{6} +(-18.4590 - 21.3028i) q^{7} +(28.4763 + 198.057i) q^{8} +(-77.7189 - 22.8203i) q^{9} +(-639.190 + 737.665i) q^{10} +(-421.534 - 270.904i) q^{11} +(-406.002 - 260.922i) q^{12} +(257.044 - 296.645i) q^{13} +(250.264 + 73.4841i) q^{14} +(-135.106 - 939.686i) q^{15} +(-88.7753 - 102.452i) q^{16} +(-92.0613 - 201.586i) q^{17} +(719.158 - 211.164i) q^{18} +(-985.114 + 2157.10i) q^{19} +(804.994 - 5598.86i) q^{20} +(-213.417 + 137.154i) q^{21} +4636.64 q^{22} +(-247.384 - 2524.90i) q^{23} +1800.84 q^{24} +(6731.47 - 4326.05i) q^{25} +(-516.900 + 3595.12i) q^{26} +(-302.838 + 663.122i) q^{27} +(-1450.31 + 425.848i) q^{28} +(-3227.35 - 7066.90i) q^{29} +(5752.71 + 6638.98i) q^{30} +(-341.687 - 2376.49i) q^{31} +(-4940.03 - 1450.52i) q^{32} +(-2953.23 + 3408.21i) q^{33} +(1725.12 + 1108.67i) q^{34} +(-2501.32 - 1607.50i) q^{35} +(-2844.42 + 3282.63i) q^{36} +(-4135.96 - 1214.43i) q^{37} +(-3122.86 - 21719.9i) q^{38} +(-2313.40 - 2669.80i) q^{39} +(8767.97 + 19199.2i) q^{40} +(10541.6 - 3095.31i) q^{41} +(975.172 - 2135.33i) q^{42} +(-1813.54 + 12613.4i) q^{43} +(-22604.3 + 14526.9i) q^{44} -8544.14 q^{45} +(14557.1 + 18417.2i) q^{46} +1317.87 q^{47} +(-1026.39 + 659.621i) q^{48} +(2278.81 - 15849.5i) q^{49} +(-30758.3 + 67351.4i) q^{50} +(-1913.72 + 561.920i) q^{51} +(-8743.79 - 19146.2i) q^{52} +(4777.61 + 5513.66i) q^{53} +(-960.009 - 6677.01i) q^{54} +(-50714.4 - 14891.1i) q^{55} +(3693.52 - 4262.55i) q^{56} +(17954.5 + 11538.7i) q^{57} +(60476.7 + 38866.0i) q^{58} +(21606.1 - 24934.8i) q^{59} +(-48845.8 - 14342.4i) q^{60} +(432.791 + 3010.13i) q^{61} +(14548.7 + 16790.1i) q^{62} +(948.475 + 2076.87i) q^{63} +(49874.0 - 14644.3i) q^{64} +(17199.8 - 37662.4i) q^{65} +(5938.77 - 41305.0i) q^{66} +(-58549.2 + 37627.3i) q^{67} -11883.8 q^{68} +(-22809.7 - 1030.18i) q^{69} +27513.1 q^{70} +(10932.2 - 7025.71i) q^{71} +(2306.58 - 16042.6i) q^{72} +(14881.0 - 32584.9i) q^{73} +(38271.4 - 11237.5i) q^{74} +(-29916.3 - 65507.5i) q^{75} +(83274.5 + 96103.9i) q^{76} +(2010.09 + 13980.5i) q^{77} +(31364.7 + 9209.49i) q^{78} +(40821.4 - 47110.4i) q^{79} +(-12029.7 - 7731.00i) q^{80} +(5519.46 + 3547.14i) q^{81} +(-66575.3 + 76832.0i) q^{82} +(2225.22 + 653.384i) q^{83} +(1936.02 + 13465.3i) q^{84} +(-15308.3 - 17666.7i) q^{85} +(-48984.2 - 107260. i) q^{86} +(-67088.4 + 19698.9i) q^{87} +(41650.6 - 91202.1i) q^{88} +(2187.85 - 15216.8i) q^{89} +(66510.9 - 42744.0i) q^{90} -11064.1 q^{91} +(-128671. - 44178.4i) q^{92} -21608.3 q^{93} +(-10258.8 + 6592.95i) q^{94} +(-35599.0 + 247597. i) q^{95} +(-19249.2 + 42149.8i) q^{96} +(5376.73 - 1578.75i) q^{97} +(61551.4 + 134779. i) q^{98} +(26579.1 + 30673.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 8 q^{2} + 90 q^{3} - 148 q^{4} + 6 q^{5} + 171 q^{6} + 118 q^{7} + 1616 q^{8} - 810 q^{9}+O(q^{10}) \) 100 * q - 8 * q^2 + 90 * q^3 - 148 * q^4 + 6 * q^5 + 171 * q^6 + 118 * q^7 + 1616 * q^8 - 810 * q^9	\( 100 q - 8 q^{2} + 90 q^{3} - 148 q^{4} + 6 q^{5} + 171 q^{6} + 118 q^{7} + 1616 q^{8} - 810 q^{9} - 262 q^{10} + 724 q^{11} + 1332 q^{12} + 2730 q^{13} + 328 q^{14} - 1143 q^{15} - 8596 q^{16} - 5699 q^{17} - 648 q^{18} + 1993 q^{19} + 28263 q^{20} - 1062 q^{21} - 19378 q^{22} + 9084 q^{23} + 1296 q^{24} - 4752 q^{25} - 7828 q^{26} + 7290 q^{27} - 29888 q^{28} - 37644 q^{29} + 2358 q^{30} - 2471 q^{31} + 42352 q^{32} + 1305 q^{33} + 47233 q^{34} + 9062 q^{35} - 21789 q^{36} + 1170 q^{37} - 133648 q^{38} - 24570 q^{39} + 135509 q^{40} - 8556 q^{41} - 17208 q^{42} + 39714 q^{43} + 108207 q^{44} - 44064 q^{45} + 87076 q^{46} + 56898 q^{47} + 60237 q^{48} + 35646 q^{49} + 12207 q^{50} - 48600 q^{51} - 368495 q^{52} + 11912 q^{53} - 34263 q^{54} - 231697 q^{55} + 235302 q^{56} + 4437 q^{57} - 201743 q^{58} + 116756 q^{59} + 209349 q^{60} - 191952 q^{61} - 91633 q^{62} + 9558 q^{63} + 383796 q^{64} + 120963 q^{65} + 92925 q^{66} - 7699 q^{67} - 486648 q^{68} + 9522 q^{69} + 340272 q^{70} + 60029 q^{71} + 130896 q^{72} + 110721 q^{73} - 290458 q^{74} + 48906 q^{75} + 30961 q^{76} - 325750 q^{77} + 51444 q^{78} - 267838 q^{79} - 519366 q^{80} - 65610 q^{81} - 739402 q^{82} - 236288 q^{83} - 382428 q^{84} + 72669 q^{85} + 643772 q^{86} + 62784 q^{87} + 976500 q^{88} + 455688 q^{89} - 21222 q^{90} + 267512 q^{91} + 70711 q^{92} - 12906 q^{93} + 1298755 q^{94} + 1815505 q^{95} + 461520 q^{96} + 271324 q^{97} - 1533115 q^{98} - 11745 q^{99}+O(q^{100}) \) 100 * q - 8 * q^2 + 90 * q^3 - 148 * q^4 + 6 * q^5 + 171 * q^6 + 118 * q^7 + 1616 * q^8 - 810 * q^9 - 262 * q^10 + 724 * q^11 + 1332 * q^12 + 2730 * q^13 + 328 * q^14 - 1143 * q^15 - 8596 * q^16 - 5699 * q^17 - 648 * q^18 + 1993 * q^19 + 28263 * q^20 - 1062 * q^21 - 19378 * q^22 + 9084 * q^23 + 1296 * q^24 - 4752 * q^25 - 7828 * q^26 + 7290 * q^27 - 29888 * q^28 - 37644 * q^29 + 2358 * q^30 - 2471 * q^31 + 42352 * q^32 + 1305 * q^33 + 47233 * q^34 + 9062 * q^35 - 21789 * q^36 + 1170 * q^37 - 133648 * q^38 - 24570 * q^39 + 135509 * q^40 - 8556 * q^41 - 17208 * q^42 + 39714 * q^43 + 108207 * q^44 - 44064 * q^45 + 87076 * q^46 + 56898 * q^47 + 60237 * q^48 + 35646 * q^49 + 12207 * q^50 - 48600 * q^51 - 368495 * q^52 + 11912 * q^53 - 34263 * q^54 - 231697 * q^55 + 235302 * q^56 + 4437 * q^57 - 201743 * q^58 + 116756 * q^59 + 209349 * q^60 - 191952 * q^61 - 91633 * q^62 + 9558 * q^63 + 383796 * q^64 + 120963 * q^65 + 92925 * q^66 - 7699 * q^67 - 486648 * q^68 + 9522 * q^69 + 340272 * q^70 + 60029 * q^71 + 130896 * q^72 + 110721 * q^73 - 290458 * q^74 + 48906 * q^75 + 30961 * q^76 - 325750 * q^77 + 51444 * q^78 - 267838 * q^79 - 519366 * q^80 - 65610 * q^81 - 739402 * q^82 - 236288 * q^83 - 382428 * q^84 + 72669 * q^85 + 643772 * q^86 + 62784 * q^87 + 976500 * q^88 + 455688 * q^89 - 21222 * q^90 + 267512 * q^91 + 70711 * q^92 - 12906 * q^93 + 1298755 * q^94 + 1815505 * q^95 + 461520 * q^96 + 271324 * q^97 - 1533115 * q^98 - 11745 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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