LMFDB - Embedded newform 69.6.e.a.58.4

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			58.4
Character	$\chi$	$=$	69.58
Dual form			69.6.e.a.25.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.00836 + 2.57601i) q^{2} +(1.28083 - 8.90839i) q^{3} +(-3.86221 + 8.45706i) q^{4} +(16.2258 - 4.76432i) q^{5} +(17.8141 + 39.0075i) q^{6} +(15.8053 + 18.2403i) q^{7} +(-28.0034 - 194.768i) q^{8} +(-77.7189 - 22.8203i) q^{9} +O(q^{10})$	\(q+(-4.00836 + 2.57601i) q^{2} +(1.28083 - 8.90839i) q^{3} +(-3.86221 + 8.45706i) q^{4} +(16.2258 - 4.76432i) q^{5} +(17.8141 + 39.0075i) q^{6} +(15.8053 + 18.2403i) q^{7} +(-28.0034 - 194.768i) q^{8} +(-77.7189 - 22.8203i) q^{9} +(-52.7658 + 60.8950i) q^{10} +(156.880 + 100.820i) q^{11} +(70.3920 + 45.2382i) q^{12} +(-10.9179 + 12.5999i) q^{13} +(-110.341 - 32.3989i) q^{14} +(-21.6599 - 150.648i) q^{15} +(419.144 + 483.718i) q^{16} +(894.150 + 1957.91i) q^{17} +(370.311 - 108.733i) q^{18} +(-240.946 + 527.597i) q^{19} +(-22.3753 + 155.623i) q^{20} +(182.736 - 117.437i) q^{21} -888.544 q^{22} +(-526.923 + 2481.67i) q^{23} -1770.94 q^{24} +(-2388.34 + 1534.89i) q^{25} +(11.3052 - 78.6294i) q^{26} +(-302.838 + 663.122i) q^{27} +(-215.303 + 63.2186i) q^{28} +(2259.77 + 4948.20i) q^{29} +(474.892 + 548.055i) q^{30} +(609.707 + 4240.61i) q^{31} +(3115.46 + 914.782i) q^{32} +(1099.08 - 1268.41i) q^{33} +(-8627.69 - 5544.68i) q^{34} +(343.357 + 220.662i) q^{35} +(493.160 - 569.137i) q^{36} +(-4918.49 - 1444.20i) q^{37} +(-393.302 - 2735.48i) q^{38} +(98.2608 + 113.399i) q^{39} +(-1382.31 - 3026.85i) q^{40} +(16020.4 - 4704.03i) q^{41} +(-429.950 + 941.460i) q^{42} +(677.021 - 4708.79i) q^{43} +(-1458.55 + 937.351i) q^{44} -1369.78 q^{45} +(-4280.73 - 11304.8i) q^{46} +6454.14 q^{47} +(4846.00 - 3114.33i) q^{48} +(2308.98 - 16059.3i) q^{49} +(5619.41 - 12304.8i) q^{50} +(18587.1 - 5457.67i) q^{51} +(-64.3909 - 140.997i) q^{52} +(-1945.57 - 2245.31i) q^{53} +(-494.330 - 3438.14i) q^{54} +(3025.84 + 888.467i) q^{55} +(3110.02 - 3589.16i) q^{56} +(4391.43 + 2822.20i) q^{57} +(-21804.6 - 14012.9i) q^{58} +(-14789.6 + 17068.1i) q^{59} +(1357.70 + 398.655i) q^{60} +(477.780 + 3323.03i) q^{61} +(-13367.8 - 15427.2i) q^{62} +(-812.122 - 1778.30i) q^{63} +(-34496.3 + 10129.0i) q^{64} +(-117.121 + 256.460i) q^{65} +(-1138.08 + 7915.50i) q^{66} +(-26211.0 + 16844.8i) q^{67} -20011.6 q^{68} +(21432.8 + 7872.65i) q^{69} -1944.72 q^{70} +(37066.0 - 23820.9i) q^{71} +(-2268.27 + 15776.2i) q^{72} +(-26317.2 + 57626.7i) q^{73} +(23435.3 - 6881.24i) q^{74} +(10614.4 + 23242.2i) q^{75} +(-3531.34 - 4075.38i) q^{76} +(640.537 + 4455.03i) q^{77} +(-685.982 - 201.422i) q^{78} +(48968.1 - 56512.2i) q^{79} +(9105.53 + 5851.77i) q^{80} +(5519.46 + 3547.14i) q^{81} +(-52098.0 + 60124.3i) q^{82} +(-22307.1 - 6549.95i) q^{83} +(287.409 + 1998.97i) q^{84} +(23836.4 + 27508.7i) q^{85} +(9416.16 + 20618.5i) q^{86} +(46974.9 - 13793.1i) q^{87} +(15243.4 - 33378.4i) q^{88} +(-9422.13 + 65532.4i) q^{89} +(5490.55 - 3528.56i) q^{90} -402.386 q^{91} +(-18952.6 - 14041.0i) q^{92} +38557.9 q^{93} +(-25870.5 + 16625.9i) q^{94} +(-1395.89 + 9708.64i) q^{95} +(12139.6 - 26582.1i) q^{96} +(19245.0 - 5650.84i) q^{97} +(32113.9 + 70319.5i) q^{98} +(-9891.76 - 11415.7i) 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 $

$2$	−4.00836	+	2.57601i	−0.708584	+	0.455379i	−0.844649	−	0.535321i	$-0.820191\pi$
$2$	−4.00836	+	2.57601i	−0.708584	+	0.455379i	0.136065	+	0.990700i	$0.456554\pi$
$3$	1.28083	−	8.90839i	0.0821655	−	0.571474i
$3$	1.28083	−	8.90839i	0.0821655	−	0.571474i
$4$	−3.86221	+	8.45706i	−0.120694	+	0.264283i
$5$	16.2258	−	4.76432i	0.290256	−	0.0852268i	−0.133363	−	0.991067i	$-0.542578\pi$
$5$	16.2258	−	4.76432i	0.290256	−	0.0852268i	0.423619	+	0.905840i	$0.360759\pi$
$6$	17.8141	+	39.0075i	0.202016	+	0.442354i
$7$	15.8053	+	18.2403i	0.121915	+	0.140698i	0.813426	−	0.581669i	$-0.197600\pi$
$7$	15.8053	+	18.2403i	0.121915	+	0.140698i	−0.691511	+	0.722366i	$0.743054\pi$
$8$	−28.0034	−	194.768i	−0.154698	−	1.07595i
$9$	−77.7189	−	22.8203i	−0.319831	−	0.0939109i
$10$	−52.7658	+	60.8950i	−0.166860	+	0.192567i
$11$	156.880	+	100.820i	0.390917	+	0.251227i	0.721304	−	0.692618i	$-0.243543\pi$
$11$	156.880	+	100.820i	0.390917	+	0.251227i	−0.330387	+	0.943846i	$0.607179\pi$
$12$	70.3920	+	45.2382i	0.141114	+	0.0906884i
$13$	−10.9179	+	12.5999i	−0.0179176	+	0.0206780i	−0.764638	−	0.644460i	$-0.777082\pi$
$13$	−10.9179	+	12.5999i	−0.0179176	+	0.0206780i	0.746720	+	0.665138i	$0.231627\pi$
$14$	−110.341	−	32.3989i	−0.150458	−	0.0441785i
$15$	−21.6599	−	150.648i	−0.0248559	−	0.172876i
$16$	419.144	+	483.718i	0.409320	+	0.472380i
$17$	894.150	+	1957.91i	0.750391	+	1.64313i	0.765661	+	0.643245i	$0.222412\pi$
$17$	894.150	+	1957.91i	0.750391	+	1.64313i	−0.0152693	+	0.999883i	$0.504861\pi$
$18$	370.311	−	108.733i	0.269392	−	0.0791007i
$19$	−240.946	+	527.597i	−0.153121	+	0.335289i	−0.970611	−	0.240655i	$-0.922638\pi$
$19$	−240.946	+	527.597i	−0.153121	+	0.335289i	0.817490	+	0.575943i	$0.195365\pi$
$20$	−22.3753	+	155.623i	−0.0125082	+	0.0869961i
$21$	182.736	−	117.437i	0.0904223	−	0.0581109i
$22$	−888.544			−0.391401
$23$	−526.923	+	2481.67i	−0.207696	+	0.978193i
$23$	−526.923	+	2481.67i	−0.207696	+	0.978193i
$24$	−1770.94			−0.627588
$25$	−2388.34	+	1534.89i	−0.764269	+	0.491166i
$26$	11.3052	−	78.6294i	0.00327978	−	0.0228114i
$27$	−302.838	+	663.122i	−0.0799467	+	0.175059i
$28$	−215.303	+	63.2186i	−0.0518985	+	0.0152388i
$29$	2259.77	+	4948.20i	0.498963	+	1.09258i	0.976805	+	0.214131i	$0.0686919\pi$
$29$	2259.77	+	4948.20i	0.498963	+	1.09258i	−0.477842	+	0.878446i	$0.658581\pi$
$30$	474.892	+	548.055i	0.0963368	+	0.111179i
$31$	609.707	+	4240.61i	0.113951	+	0.792545i	0.964012	+	0.265860i	$0.0856560\pi$
$31$	609.707	+	4240.61i	0.113951	+	0.792545i	−0.850061	+	0.526685i	$0.823435\pi$
$32$	3115.46	+	914.782i	0.537833	+	0.157922i
$33$	1099.08	−	1268.41i	0.175690	−	0.202757i
$34$	−8627.69	−	5544.68i	−1.27996	−	0.822581i
$35$	343.357	+	220.662i	0.0473778	+	0.0304479i
$36$	493.160	−	569.137i	0.0634208	−	0.0731915i
$37$	−4918.49	−	1444.20i	−0.590646	−	0.173429i	−0.0272676	−	0.999628i	$-0.508681\pi$
$37$	−4918.49	−	1444.20i	−0.590646	−	0.173429i	−0.563379	+	0.826199i	$0.690499\pi$
$38$	−393.302	−	2735.48i	−0.0441843	−	0.307308i
$39$	98.2608	+	113.399i	0.0103447	+	0.0119384i
$40$	−1382.31	−	3026.85i	−0.136602	−	0.299117i
$41$	16020.4	−	4704.03i	1.48838	−	0.437029i	0.566359	−	0.824159i	$-0.308352\pi$
$41$	16020.4	−	4704.03i	1.48838	−	0.437029i	0.922025	+	0.387130i	$0.126533\pi$
$42$	−429.950	+	941.460i	−0.0376093	+	0.0823528i
$43$	677.021	−	4708.79i	0.0558382	−	0.388363i	−0.942668	−	0.333731i	$-0.891692\pi$
$43$	677.021	−	4708.79i	0.0558382	−	0.388363i	0.998507	−	0.0546321i	$-0.0173986\pi$
$44$	−1458.55	+	937.351i	−0.113577	+	0.0729912i
$45$	−1369.78			−0.100837
$46$	−4280.73	−	11304.8i	−0.298279	−	0.787713i
$47$	6454.14			0.426180			0.213090	−	0.977033i	$-0.431647\pi$
$47$	6454.14			0.426180			0.213090	+	0.977033i	$0.431647\pi$
$48$	4846.00	−	3114.33i	0.303585	−	0.195102i
$49$	2308.98	−	16059.3i	0.137382	−	0.955515i
$50$	5619.41	−	12304.8i	0.317882	−	0.696064i
$51$	18587.1	−	5457.67i	1.00066	−	0.293821i
$52$	−64.3909	−	140.997i	−0.00330230	−	0.00723103i
$53$	−1945.57	−	2245.31i	−0.0951387	−	0.109796i	0.706184	−	0.708029i	$-0.250415\pi$
$53$	−1945.57	−	2245.31i	−0.0951387	−	0.109796i	−0.801322	+	0.598233i	$0.795870\pi$
$54$	−494.330	−	3438.14i	−0.0230692	−	0.160450i
$55$	3025.84	+	888.467i	0.134877	+	0.0396036i
$56$	3110.02	−	3589.16i	0.132524	−	0.152940i
$57$	4391.43	+	2822.20i	0.179027	+	0.115054i
$58$	−21804.6	−	14012.9i	−0.851094	−	0.546965i
$59$	−14789.6	+	17068.1i	−0.553128	+	0.638344i	−0.961609	−	0.274423i	$-0.911513\pi$
$59$	−14789.6	+	17068.1i	−0.553128	+	0.638344i	0.408481	+	0.912767i	$0.366059\pi$
$60$	1357.70	+	398.655i	0.0486883	+	0.0142962i
$61$	477.780	+	3323.03i	0.0164401	+	0.114343i	0.996389	−	0.0849057i	$-0.0270589\pi$
$61$	477.780	+	3323.03i	0.0164401	+	0.114343i	−0.979949	+	0.199249i	$0.936150\pi$
$62$	−13367.8	−	15427.2i	−0.441652	−	0.509694i
$63$	−812.122	−	1778.30i	−0.0257792	−	0.0564487i
$64$	−34496.3	+	10129.0i	−1.05274	+	0.309114i
$65$	−117.121	+	256.460i	−0.00343837	+	0.00752897i
$66$	−1138.08	+	7915.50i	−0.0321597	+	0.223676i
$67$	−26211.0	+	16844.8i	−0.713341	+	0.458436i	−0.846315	−	0.532683i	$-0.821184\pi$
$67$	−26211.0	+	16844.8i	−0.713341	+	0.458436i	0.132974	+	0.991120i	$0.457547\pi$
$68$	−20011.6			−0.524819
$69$	21432.8	+	7872.65i	0.541946	+	0.199066i
$70$	−1944.72			−0.0474365
$71$	37066.0	−	23820.9i	0.872630	−	0.560805i	−0.0259259	−	0.999664i	$-0.508253\pi$
$71$	37066.0	−	23820.9i	0.872630	−	0.560805i	0.898556	+	0.438858i	$0.144617\pi$
$72$	−2268.27	+	15776.2i	−0.0515661	+	0.358650i
$73$	−26317.2	+	57626.7i	−0.578007	+	1.26566i	0.364416	+	0.931236i	$0.381269\pi$
$73$	−26317.2	+	57626.7i	−0.578007	+	1.26566i	−0.942423	+	0.334423i	$0.891459\pi$
$74$	23435.3	−	6881.24i	0.497499	−	0.146079i
$75$	10614.4	+	23242.2i	0.217892	+	0.477116i
$76$	−3531.34	−	4075.38i	−0.0701303	−	0.0809347i
$77$	640.537	+	4455.03i	0.0123117	+	0.0856296i
$78$	−685.982	−	201.422i	−0.0127666	−	0.00374862i
$79$	48968.1	−	56512.2i	0.882765	−	1.01877i	−0.116906	−	0.993143i	$-0.537298\pi$
$79$	48968.1	−	56512.2i	0.882765	−	1.01877i	0.999672	−	0.0256226i	$-0.00815681\pi$
$80$	9105.53	+	5851.77i	0.159067	+	0.102226i
$81$	5519.46	+	3547.14i	0.0934726	+	0.0600712i
$82$	−52098.0	+	60124.3i	−0.855631	+	0.987451i
$83$	−22307.1	−	6549.95i	−0.355424	−	0.104362i	0.0991458	−	0.995073i	$-0.468389\pi$
$83$	−22307.1	−	6549.95i	−0.355424	−	0.104362i	−0.454570	+	0.890711i	$0.650207\pi$
$84$	287.409	+	1998.97i	0.00444429	+	0.0309107i
$85$	23836.4	+	27508.7i	0.357844	+	0.412974i
$86$	9416.16	+	20618.5i	0.137286	+	0.300615i
$87$	46974.9	−	13793.1i	0.665376	−	0.195372i
$88$	15243.4	−	33378.4i	0.209834	−	0.459472i
$89$	−9422.13	+	65532.4i	−0.126088	+	0.876962i	0.824357	+	0.566070i	$0.191537\pi$
$89$	−9422.13	+	65532.4i	−0.126088	+	0.876962i	−0.950445	+	0.310892i	$0.899372\pi$
$90$	5490.55	−	3528.56i	0.0714512	−	0.0459189i
$91$	−402.386			−0.00509377
$92$	−18952.6	−	14041.0i	−0.233452	−	0.172953i
$93$	38557.9			0.462281
$94$	−25870.5	+	16625.9i	−0.301985	+	0.194074i
$95$	−1395.89	+	9708.64i	−0.0158687	+	0.110370i
$96$	12139.6	−	26582.1i	0.134440	−	0.294382i
$97$	19245.0	−	5650.84i	0.207677	−	0.0609795i	−0.176239	−	0.984347i	$-0.556393\pi$
$97$	19245.0	−	5650.84i	0.207677	−	0.0609795i	0.383916	+	0.923368i	$0.374575\pi$
$98$	32113.9	+	70319.5i	0.337775	+	0.739624i
$99$	−9891.76	−	11415.7i	−0.101435	−	0.117062i
$100$	−3756.41	−	26126.4i	−0.0375641	−	0.261264i
$101$	2228.03	+	654.208i	0.0217329	+	0.00638135i	0.292581	−	0.956241i	$-0.405486\pi$
$101$	2228.03	+	654.208i	0.0217329	+	0.00638135i	−0.270848	+	0.962622i	$0.587304\pi$
$102$	−60444.8	+	69757.0i	−0.575252	+	0.663877i
$103$	−52216.0	−	33557.2i	−0.484965	−	0.311668i	0.275212	−	0.961383i	$-0.411252\pi$
$103$	−52216.0	−	33557.2i	−0.484965	−	0.311668i	−0.760178	+	0.649715i	$0.774888\pi$
$104$	2759.79	+	1773.61i	0.0250203	+	0.0160796i
$105$	2405.53	−	2776.12i	0.0212930	−	0.0245734i
$106$	13582.5	+	3988.18i	0.117413	+	0.0344754i
$107$	−14171.0	−	98561.7i	−0.119658	−	0.832240i	−0.957933	−	0.286992i	$-0.907345\pi$
$107$	−14171.0	−	98561.7i	−0.119658	−	0.832240i	0.838275	−	0.545248i	$-0.183564\pi$
$108$	−4438.44	−	5122.23i	−0.0366160	−	0.0422571i
$109$	45520.7	+	99676.5i	0.366981	+	0.803575i	0.999577	+	0.0290935i	$0.00926207\pi$
$109$	45520.7	+	99676.5i	0.366981	+	0.803575i	−0.632596	+	0.774482i	$0.718011\pi$
$110$	−14417.3	+	4233.31i	−0.113607	+	0.0333579i
$111$	−19165.3	+	41966.1i	−0.147641	+	0.323289i
$112$	−2198.46	+	15290.6i	−0.0165605	+	0.115181i
$113$	52315.8	−	33621.3i	0.385422	−	0.247696i	−0.333553	−	0.942731i	$-0.608248\pi$
$113$	52315.8	−	33621.3i	0.385422	−	0.247696i	0.718976	+	0.695035i	$0.244611\pi$
$114$	−24872.5			−0.179249
$115$	3273.74	+	42777.5i	0.0230834	+	0.301628i
$116$	−50574.9			−0.348971
$117$	1136.06	−	730.101i	0.00767249	−	0.00493081i
$118$	15314.3	−	106513.i	0.101249	−	0.704203i
$119$	−21580.6	+	47255.0i	−0.139700	+	0.305901i
$120$	−28734.9	+	8437.31i	−0.182161	+	0.0534874i
$121$	−52456.5	−	114864.i	−0.325714	−	0.713214i
$122$	−10475.3	−	12089.1i	−0.0637187	−	0.0735353i
$123$	−21385.8	−	148742.i	−0.127457	−	0.886481i
$124$	−38217.9	−	11221.8i	−0.223209	−	0.0655402i
$125$	−66046.9	+	76222.2i	−0.378075	+	0.436322i
$126$	7836.20	+	5036.02i	0.0439723	+	0.0282593i
$127$	106913.	+	68709.0i	0.588196	+	0.378011i	0.800625	−	0.599166i	$-0.204501\pi$
$127$	106913.	+	68709.0i	0.588196	+	0.378011i	−0.212429	+	0.977177i	$0.568137\pi$
$128$	44138.6	−	50938.7i	0.238119	−	0.274804i
$129$	−41080.6	−	12062.3i	−0.217351	−	0.0638201i
$130$	−191.180	−	1329.69i	−0.000992166	−	0.00690067i
$131$	72690.6	+	83889.5i	0.370084	+	0.427100i	0.909993	−	0.414624i	$-0.136087\pi$
$131$	72690.6	+	83889.5i	0.370084	+	0.427100i	−0.539909	+	0.841723i	$0.681541\pi$
$132$	6482.14	+	14193.9i	0.0323805	+	0.0709034i
$133$	−13431.8	+	3943.92i	−0.0658421	+	0.0193330i
$134$	61670.7	−	135040.i	0.296699	−	0.649681i
$135$	−1754.45	+	12202.5i	−0.00828529	+	0.0576254i
$136$	356300.	−	228980.i	1.65184	−	1.06157i
$137$	−43742.5			−0.199114			−0.0995570	−	0.995032i	$-0.531743\pi$
$137$	−43742.5			−0.199114			−0.0995570	+	0.995032i	$0.531743\pi$
$138$	−106190.	+	23654.8i	−0.474665	+	0.105736i
$139$	−83363.6			−0.365965			−0.182982	−	0.983116i	$-0.558575\pi$
$139$	−83363.6			−0.365965			−0.182982	+	0.983116i	$0.558575\pi$
$140$	−3192.27	+	2051.54i	−0.0137651	+	0.00884629i
$141$	8266.67	−	57496.0i	0.0350173	−	0.243551i
$142$	−87210.9	+	190965.i	−0.362953	+	0.794756i
$143$	−2983.12	+	875.923i	−0.0121992	+	0.00358200i
$144$	−21536.8	−	47159.0i	−0.0865516	−	0.189521i
$145$	60241.3	+	69522.2i	0.237944	+	0.274602i
$146$	−42958.4	−	298782.i	−0.166788	−	1.16004i
$147$	−140105.	−	41138.7i	−0.534764	−	0.157021i
$148$	31209.9	−	36018.2i	0.117122	−	0.135166i
$149$	−44523.8	−	28613.7i	−0.164296	−	0.105587i	0.455909	−	0.890026i	$-0.349314\pi$
$149$	−44523.8	−	28613.7i	−0.164296	−	0.105587i	−0.620205	+	0.784440i	$0.712951\pi$
$150$	−102418.	−	65820.3i	−0.371663	−	0.238854i
$151$	−29054.3	+	33530.4i	−0.103697	+	0.119673i	−0.805226	−	0.592968i	$-0.797956\pi$
$151$	−29054.3	+	33530.4i	−0.103697	+	0.119673i	0.701528	+	0.712642i	$0.252501\pi$
$152$	109506.	+	32154.0i	0.384441	+	0.112882i
$153$	−24812.1	−	172572.i	−0.0856909	−	0.595993i
$154$	−14043.7	−	16207.3i	−0.0477178	−	0.0550693i
$155$	30096.6	+	65902.4i	0.100621	+	0.220329i
$156$	−1338.53	+	393.027i	−0.00440368	+	0.00129304i
$157$	179636.	−	393347.i	0.581625	−	1.27358i	−0.358747	−	0.933435i	$-0.616796\pi$
$157$	179636.	−	393347.i	0.581625	−	1.27358i	0.940372	−	0.340147i	$-0.110477\pi$
$158$	−50705.3	+	352663.i	−0.161589	+	1.12387i
$159$	−22494.0	+	14456.0i	−0.0705626	+	0.0453478i
$160$	54909.2			0.169568
$161$	−53594.6	+	29612.4i	−0.162951	+	0.0900344i
$162$	−31261.5			−0.0935884
$163$	385807.	−	247943.i	1.13737	−	0.730943i	0.170284	−	0.985395i	$-0.445531\pi$
$163$	385807.	−	247943.i	1.13737	−	0.730943i	0.967085	+	0.254452i	$0.0818951\pi$
$164$	−22092.1	+	153654.i	−0.0641397	+	0.446102i
$165$	11790.4	−	25817.4i	0.0337147	−	0.0738248i
$166$	106287.	−	31208.8i	0.299372	−	0.0879036i
$167$	−147228.	−	322384.i	−0.408506	−	0.894504i	−0.996337	−	0.0855194i	$-0.972745\pi$
$167$	−147228.	−	322384.i	−0.408506	−	0.894504i	0.587830	−	0.808984i	$-0.299982\pi$
$168$	−27990.2	−	32302.4i	−0.0765126	−	0.0883002i
$169$	52800.9	+	367239.i	0.142208	+	0.989080i
$170$	−166408.	−	48861.7i	−0.441623	−	0.129672i
$171$	30766.0	−	35505.9i	0.0804601	−	0.0928559i
$172$	37207.7	+	23911.9i	0.0958984	+	0.0616302i
$173$	−74309.4	−	47755.7i	−0.188768	−	0.121314i	0.442843	−	0.896599i	$-0.353970\pi$
$173$	−74309.4	−	47755.7i	−0.188768	−	0.121314i	−0.631611	+	0.775285i	$0.717606\pi$
$174$	−152761.	+	176295.i	−0.382507	+	0.441436i
$175$	−65745.4	−	19304.6i	−0.162282	−	0.0476503i
$176$	16986.5	+	118144.i	0.0413354	+	0.287494i
$177$	133106.	+	153613.i	0.319349	+	0.368548i
$178$	−131045.	−	286949.i	−0.310006	−	0.678819i
$179$	394346.	−	115790.i	0.919909	−	0.270110i	0.212703	−	0.977117i	$-0.431773\pi$
$179$	394346.	−	115790.i	0.919909	−	0.270110i	0.707206	+	0.707007i	$0.249955\pi$
$180$	5290.36	−	11584.3i	0.0121704	−	0.0266494i
$181$	−119137.	+	828613.i	−0.270302	+	1.87999i	0.174941	+	0.984579i	$0.444027\pi$
$181$	−119137.	+	828613.i	−0.270302	+	1.87999i	−0.445242	+	0.895410i	$0.646882\pi$
$182$	1612.91	−	1036.55i	0.00360937	−	0.00231960i
$183$	30214.8			0.0666949
$184$	498105.	+	33132.4i	1.08462	+	0.0721454i
$185$	−86687.1			−0.186219
$186$	−154554.	+	99325.8i	−0.327565	+	0.210513i
$187$	−57123.9	+	397306.i	−0.119458	+	0.830846i
$188$	−24927.2	+	54583.0i	−0.0514374	+	0.112632i
$189$	−16882.0	+	4957.00i	−0.0343771	+	0.0100940i
$190$	−19414.4	−	42511.5i	−0.0390157	−	0.0854324i
$191$	−589550.	−	680377.i	−1.16933	−	1.34948i	−0.925082	−	0.379767i	$-0.876004\pi$
$191$	−589550.	−	680377.i	−1.16933	−	1.34948i	−0.244248	−	0.969713i	$-0.578541\pi$
$192$	46049.4	+	320280.i	0.0901510	+	0.627014i
$193$	−130575.	−	38340.3i	−0.252329	−	0.0740905i	0.153122	−	0.988207i	$-0.451067\pi$
$193$	−130575.	−	38340.3i	−0.252329	−	0.0740905i	−0.405451	+	0.914117i	$0.632885\pi$
$194$	−62584.1	+	72225.9i	−0.119388	+	0.137781i
$195$	2134.63	+	1371.84i	0.00402009	+	0.00258356i
$196$	126897.	+	81551.8i	0.235945	+	0.151633i
$197$	−611718.	+	705960.i	−1.12302	+	1.29603i	−0.172618	+	0.984989i	$0.555223\pi$
$197$	−611718.	+	705960.i	−1.12302	+	1.29603i	−0.950397	+	0.311040i	$0.899323\pi$
$198$	69056.7	+	20276.9i	0.125182	+	0.0367568i
$199$	57025.8	+	396623.i	0.102080	+	0.709979i	0.975014	+	0.222142i	$0.0713049\pi$
$199$	57025.8	+	396623.i	0.102080	+	0.709979i	−0.872935	+	0.487837i	$0.837786\pi$
$200$	365829.	+	422189.i	0.646701	+	0.746333i
$201$	116488.	+	255073.i	0.203372	+	0.445323i
$202$	−10616.0	+	3117.13i	−0.0183055	+	0.00537498i
$203$	−54540.3	+	119427.i	−0.0928918	+	0.203405i
$204$	−25631.5	+	178271.i	−0.0431220	+	0.299920i
$205$	237533.	−	152653.i	0.394766	−	0.253701i
$206$	295744.			0.485566
$207$	97584.5	−	180848.i	0.158291	−	0.293352i
$208$	−10670.9			−0.0171019
$209$	−90992.1	+	58477.1i	−0.144091	+	0.0926019i
$210$	−2490.87	+	17324.4i	−0.00389765	+	0.0271087i
$211$	−105631.	+	231300.i	−0.163338	+	0.357659i	−0.973549	−	0.228478i	$-0.926625\pi$
$211$	−105631.	+	231300.i	−0.163338	+	0.357659i	0.810211	+	0.586138i	$0.199352\pi$
$212$	26502.9	−	7781.95i	0.0404999	−	0.0118918i
$213$	−164730.	−	360709.i	−0.248785	−	0.544764i
$214$	310699.	+	358565.i	0.463773	+	0.535222i
$215$	−11449.0	−	79629.4i	−0.0168916	−	0.117484i
$216$	137635.	+	40413.4i	0.200722	+	0.0589373i
$217$	−67713.4	+	78145.4i	−0.0976169	+	0.112656i
$218$	−439231.	−	282277.i	−0.625968	−	0.402285i
$219$	479654.	+	308255.i	0.675799	+	0.434309i
$220$	−19200.2	+	22158.3i	−0.0267455	+	0.0308659i
$221$	−34431.7	−	10110.1i	−0.0474218	−	0.0139243i
$222$	−31284.0	−	217585.i	−0.0426029	−	0.296310i
$223$	−482646.	−	557003.i	−0.649929	−	0.750058i	0.331168	−	0.943572i	$-0.392557\pi$
$223$	−482646.	−	557003.i	−0.649929	−	0.750058i	−0.981098	+	0.193513i	$0.938012\pi$
$224$	32555.0	+	71285.4i	0.0433508	+	0.0949250i
$225$	220646.	−	64787.5i	0.290563	−	0.0853169i
$226$	−123091.	+	269533.i	−0.160309	+	0.351027i
$227$	−60473.8	+	420605.i	−0.0778938	+	0.541763i	0.913088	+	0.407763i	$0.133691\pi$
$227$	−60473.8	+	420605.i	−0.0778938	+	0.541763i	−0.990981	+	0.134000i	$0.957218\pi$
$228$	−40828.2	+	26238.7i	−0.0520143	+	0.0334276i
$229$	−1.28696e6			−1.62172			−0.810860	−	0.585240i	$-0.801000\pi$
$229$	−1.28696e6			−1.62172			−0.810860	+	0.585240i	$0.801000\pi$
$230$	−123318.	−	163034.i	−0.153712	−	0.203217i
$231$	40507.6			0.0499467
$232$	900468.	−	578696.i	1.09837	−	0.705879i
$233$	112088.	−	779590.i	0.135260	−	0.940754i	−0.803284	−	0.595596i	$-0.796916\pi$
$233$	112088.	−	779590.i	0.135260	−	0.940754i	0.938544	−	0.345159i	$-0.112175\pi$
$234$	−2672.98	+	5853.01i	−0.00319121	+	0.00698778i
$235$	104724.	−	30749.6i	0.123701	−	0.0363220i
$236$	−87225.4	−	190997.i	−0.101944	−	0.223227i
$237$	−440713.	−	508610.i	−0.509665	−	0.588185i
$238$	−35226.7	−	245007.i	−0.0403115	−	0.280373i
$239$	29014.4	+	8519.39i	0.0328563	+	0.00964747i	0.298119	−	0.954529i	$-0.403641\pi$
$239$	29014.4	+	8519.39i	0.0328563	+	0.00964747i	−0.265263	+	0.964176i	$0.585459\pi$
$240$	63792.5	−	73620.5i	0.0714894	−	0.0825032i
$241$	−946705.	−	608410.i	−1.04996	−	0.674767i	−0.102528	−	0.994730i	$-0.532693\pi$
$241$	−946705.	−	608410.i	−1.04996	−	0.674767i	−0.947430	+	0.319963i	$0.896330\pi$
$242$	506155.	+	325286.i	0.555578	+	0.357049i
$243$	38668.9	−	44626.3i	0.0420093	−	0.0484814i
$244$	−29948.4	−	8793.64i	−0.0322032	−	0.00945571i
$245$	−39046.8	−	271576.i	−0.0415595	−	0.289053i
$246$	468882.	+	541119.i	0.493999	+	0.570105i
$247$	−4017.06	−	8796.13i	−0.00418953	−	0.00917380i
$248$	808860.	−	237503.i	0.835111	−	0.245211i
$249$	−86921.1	+	190331.i	−0.0888438	+	0.194541i
$250$	68390.1	−	475664.i	0.0692059	−	0.481338i
$251$	1.40516e6	−	903041.i	1.40780	−	0.904738i	0.407835	−	0.913056i	$-0.366284\pi$
$251$	1.40516e6	−	903041.i	1.40780	−	0.904738i	0.999965	+	0.00831737i	$0.00264753\pi$
$252$	18175.8			0.0180298
$253$	−332867.	+	336199.i	−0.326941	+	0.330214i
$254$	−605542.			−0.588925
$255$	275589.	−	177110.i	0.265406	−	0.170566i
$256$	118027.	−	820893.i	0.112559	−	0.782864i
$257$	138137.	−	302478.i	0.130460	−	0.285668i	−0.833118	−	0.553096i	$-0.813446\pi$
$257$	138137.	−	302478.i	0.130460	−	0.285668i	0.963578	+	0.267428i	$0.0861737\pi$
$258$	195738.	−	57474.0i	0.183074	−	0.0537554i
$259$	−51395.6	−	112541.i	−0.0476077	−	0.104246i
$260$	−1716.55	−	1981.00i	−0.00157479	−	0.00181740i
$261$	−62707.1	−	436137.i	−0.0569790	−	0.396298i
$262$	−507470.	−	149007.i	−0.456728	−	0.134107i
$263$	723118.	−	834523.i	0.644644	−	0.743959i	−0.335545	−	0.942024i	$-0.608920\pi$
$263$	723118.	−	834523.i	0.644644	−	0.743959i	0.980189	+	0.198065i	$0.0634658\pi$
$264$	−277824.	−	178547.i	−0.245335	−	0.157667i
$265$	−42265.8	−	27162.6i	−0.0369721	−	0.0237605i
$266$	43679.7	−	50409.0i	0.0378508	−	0.0436822i
$267$	571720.	+	167872.i	0.490801	+	0.144112i
$268$	−41225.0	−	286726.i	−0.0350610	−	0.243854i
$269$	303896.	+	350715.i	0.256061	+	0.295511i	0.869196	−	0.494468i	$-0.164637\pi$
$269$	303896.	+	350715.i	0.256061	+	0.295511i	−0.613134	+	0.789979i	$0.710092\pi$
$270$	−24401.3	−	53431.5i	−0.0203706	−	0.0446054i
$271$	1.42666e6	−	418905.i	1.18004	−	0.346491i	0.367852	−	0.929885i	$-0.380093\pi$
$271$	1.42666e6	−	418905.i	1.18004	−	0.346491i	0.812190	+	0.583393i	$0.198275\pi$
$272$	−572300.	+	1.25316e6i	−0.469031	+	1.02704i
$273$	−515.390	+	3584.61i	−0.000418533	+	0.00291096i
$274$	175335.	−	112681.i	0.141089	−	0.0906724i
$275$	−529430.			−0.422160
$276$	−149357.	+	150853.i	−0.118020	+	0.119201i
$277$	−2.00147e6			−1.56729			−0.783644	−	0.621210i	$-0.786642\pi$
$277$	−2.00147e6			−1.56729			−0.783644	+	0.621210i	$0.786642\pi$
$278$	334151.	−	214746.i	0.259317	−	0.166653i
$279$	49386.3	−	343489.i	0.0379836	−	0.264182i
$280$	33362.7	−	73054.1i	0.0254311	−	0.0556864i
$281$	1.44070e6	−	423026.i	1.08844	−	0.319596i	0.312192	−	0.950019i	$-0.398937\pi$
$281$	1.44070e6	−	423026.i	1.08844	−	0.319596i	0.776252	+	0.630423i	$0.217118\pi$
$282$	114975.	+	251759.i	0.0860953	+	0.188522i
$283$	−1.21521e6	−	1.40243e6i	−0.901956	−	1.04091i	−0.998958	−	0.0456285i	$-0.985471\pi$
$283$	−1.21521e6	−	1.40243e6i	−0.901956	−	1.04091i	0.0970025	−	0.995284i	$-0.469075\pi$
$284$	58297.9	+	405471.i	0.0428901	+	0.298307i
$285$	84700.4	+	24870.3i	0.0617694	+	0.0181371i
$286$	9701.01	−	11195.6i	0.00701297	−	0.00809340i
$287$	339011.	+	217869.i	0.242946	+	0.156132i
$288$	−221255.	−	142192.i	−0.157185	−	0.101017i
$289$	−2.10412e6	+	2.42828e6i	−1.48192	+	1.71023i
$290$	−420559.	−	123487.i	−0.293651	−	0.0862238i
$291$	−25690.3	−	178680.i	−0.0177843	−	0.123692i
$292$	−385710.	−	445133.i	−0.264730	−	0.305515i
$293$	397322.	+	870014.i	0.270379	+	0.592048i	0.995306	−	0.0967779i	$-0.0308537\pi$
$293$	397322.	+	870014.i	0.270379	+	0.592048i	−0.724927	+	0.688826i	$0.758126\pi$
$294$	667567.	−	196015.i	0.450429	−	0.132258i
$295$	−158655.	+	347406.i	−0.106145	+	0.232425i
$296$	−143549.	+	998406.i	−0.0952294	+	0.662335i
$297$	−114365.	+	73498.1i	−0.0752321	+	0.0483487i
$298$	252177.			0.164499
$299$	−25515.9	−	33733.7i	−0.0165057	−	0.0218216i
$300$	−237556.			−0.152392
$301$	96590.2	−	62074.8i	0.0614493	−	0.0394911i
$302$	30085.1	−	209246.i	0.0189816	−	0.132020i
$303$	8681.67	−	19010.2i	0.00543246	−	0.0118954i
$304$	−356199.	+	104589.i	−0.221059	+	0.0649089i
$305$	23584.4	+	51642.6i	0.0145169	+	0.0317876i
$306$	544003.	+	627813.i	0.332122	+	0.383289i
$307$	76544.6	+	532380.i	0.0463520	+	0.322385i	0.999784	+	0.0207777i	$0.00661422\pi$
$307$	76544.6	+	532380.i	0.0463520	+	0.322385i	−0.953432	+	0.301608i	$0.902477\pi$
$308$	−40150.4	−	11789.2i	−0.0241164	−	0.00708122i
$309$	−365821.	+	422180.i	−0.217958	+	0.251537i
$310$	−290403.	−	186631.i	−0.171632	−	0.110301i
$311$	1.92026e6	+	1.23408e6i	1.12579	+	0.723505i	0.964678	−	0.263431i	$-0.0848541\pi$
$311$	1.92026e6	+	1.23408e6i	1.12579	+	0.723505i	0.161117	+	0.986935i	$0.448490\pi$
$312$	19334.8	−	22313.6i	0.0112449	−	0.0129773i
$313$	808833.	+	237495.i	0.466657	+	0.137023i	0.506604	−	0.862179i	$-0.330901\pi$
$313$	808833.	+	237495.i	0.466657	+	0.137023i	−0.0399466	+	0.999202i	$0.512719\pi$
$314$	293224.	+	2.03942e6i	0.167832	+	1.16730i
$315$	−21649.7	−	24985.1i	−0.0122935	−	0.0141875i
$316$	288802.	+	632388.i	0.162698	+	0.356259i
$317$	−857156.	+	251684.i	−0.479084	+	0.140672i	−0.512354	−	0.858775i	$-0.671226\pi$
$317$	−857156.	+	251684.i	−0.479084	+	0.140672i	0.0332693	+	0.999446i	$0.489408\pi$
$318$	52925.1	−	115890.i	0.0293491	−	0.0642655i
$319$	−144368.	+	1.00410e6i	−0.0794318	+	0.552460i
$320$	−511472.	+	328703.i	−0.279221	+	0.179444i
$321$	−896177.			−0.485435
$322$	138545.	−	256757.i	0.0744646	−	0.138001i
$323$	−1.24843e6			−0.665823
$324$	−51315.7	+	32978.6i	−0.0271574	+	0.0174530i
$325$	6736.10	−	46850.6i	0.00353753	−	0.0246040i
$326$	−907748.	+	1.98769e6i	−0.473065	+	1.03587i
$327$	946262.	−	277848.i	0.489375	−	0.143694i
$328$	−1.36482e6	−	2.98854e6i	−0.700472	−	1.53382i
$329$	102010.	+	117725.i	0.0519579	+	0.0599626i
$330$	19245.8	+	133858.i	0.00972862	+	0.0676641i
$331$	−1.10396e6	−	324151.i	−0.553837	−	0.162621i	−0.00717437	−	0.999974i	$-0.502284\pi$
$331$	−1.10396e6	−	324151.i	−0.553837	−	0.162621i	−0.546662	+	0.837353i	$0.684102\pi$
$332$	141548.	−	163355.i	0.0704787	−	0.0813368i
$333$	349303.	+	224483.i	0.172620	+	0.110936i
$334$	1.42061e6	+	912969.i	0.696799	+	0.447806i
$335$	−345041.	+	398198.i	−0.167980	+	0.193860i
$336$	133399.	+	39169.5i	0.0644621	+	0.0189278i
$337$	385751.	+	2.68296e6i	0.185026	+	1.28688i	0.844663	+	0.535299i	$0.179801\pi$
$337$	385751.	+	2.68296e6i	0.185026	+	1.28688i	−0.659637	+	0.751584i	$0.729290\pi$
$338$	−1.15766e6	−	1.33601e6i	−0.551173	−	0.636088i
$339$	−232504.	−	509113.i	−0.109883	−	0.240611i
$340$	−324704.	+	95341.7i	−0.152332	+	0.0447286i
$341$	−331889.	+	726736.i	−0.154564	+	0.338447i
$342$	−31857.5	+	221574.i	−0.0147281	+	0.102436i
$343$	670670.	−	431014.i	0.307804	−	0.197813i
$344$	−936079.			−0.426497
$345$	385272.	+	25627.1i	0.174269	+	0.0115918i
$346$	420878.			0.189002
$347$	3.64484e6	−	2.34240e6i	1.62501	−	1.04433i	0.672370	−	0.740215i	$-0.265276\pi$
$347$	3.64484e6	−	2.34240e6i	1.62501	−	1.04433i	0.952636	−	0.304113i	$-0.0983601\pi$
$348$	−64778.0	+	450541.i	−0.0286734	+	0.199428i
$349$	267270.	−	585239.i	0.117459	−	0.257199i	−0.841766	−	0.539842i	$-0.818484\pi$
$349$	267270.	−	585239.i	0.117459	−	0.257199i	0.959225	+	0.282643i	$0.0912112\pi$
$350$	313260.	−	91981.4i	0.136689	−	0.0401356i
$351$	−5048.92	−	11055.6i	−0.00218741	−	0.00478977i
$352$	396524.	+	457613.i	0.170574	+	0.196853i
$353$	−392741.	−	2.73157e6i	−0.167753	−	1.16674i	−0.883516	−	0.468402i	$-0.844830\pi$
$353$	−392741.	−	2.73157e6i	−0.167753	−	1.16674i	0.715763	−	0.698343i	$-0.246079\pi$
$354$	−929246.	−	272851.i	−0.394115	−	0.115722i
$355$	487936.	−	563108.i	0.205490	−	0.237149i
$356$	−517821.	−	332783.i	−0.216548	−	0.139167i
$357$	393325.	+	252775.i	0.163336	+	0.104969i
$358$	−1.28240e6	+	1.47997e6i	−0.528831	+	0.610303i
$359$	4.24886e6	+	1.24758e6i	1.73995	+	0.510894i	0.988801	−	0.149242i	$-0.0476833\pi$
$359$	4.24886e6	+	1.24758e6i	1.73995	+	0.510894i	0.751146	+	0.660136i	$0.229501\pi$
$360$	38358.3	+	266788.i	0.0155992	+	0.108495i
$361$	1.40120e6	+	1.61707e6i	0.565888	+	0.653070i
$362$	−1.65698e6	−	3.62827e6i	−0.664577	−	1.45522i
$363$	−1.09044e6	+	320182.i	−0.434345	+	0.127535i
$364$	1554.10	−	3403.00i	0.000614788	−	0.00134620i
$365$	−152466.	+	1.06042e6i	−0.0599019	+	0.416627i
$366$	−121112.	+	77833.9i	−0.0472589	+	0.0303715i
$367$	4.70831e6			1.82474			0.912368	−	0.409370i	$-0.134252\pi$
$367$	4.70831e6			1.82474			0.912368	+	0.409370i	$0.134252\pi$
$368$	−1.42128e6	+	785295.i	−0.547093	+	0.302283i
$369$	−1.35244e6			−0.517073
$370$	347473.	−	223307.i	0.131952	−	0.0848005i
$371$	10204.7	−	70975.6i	0.00384917	−	0.0267716i
$372$	−148919.	+	326087.i	−0.0557946	+	0.122173i
$373$	−192366.	+	56483.9i	−0.0715908	+	0.0210210i	−0.317332	−	0.948315i	$-0.602787\pi$
$373$	−192366.	+	56483.9i	−0.0715908	+	0.0210210i	0.245741	+	0.969336i	$0.420969\pi$
$374$	−794492.	−	1.73969e6i	−0.293704	−	0.643123i
$375$	594422.	+	686000.i	0.218282	+	0.251910i
$376$	−180738.	−	1.25706e6i	−0.0659294	−	0.458549i
$377$	−87018.6	−	25551.0i	−0.0315325	−	0.00925878i
$378$	54899.7	−	63357.6i	0.0197624	−	0.0228071i
$379$	2.29952e6	+	1.47781e6i	0.822317	+	0.528471i	0.882828	−	0.469697i	$-0.155637\pi$
$379$	2.29952e6	+	1.47781e6i	0.822317	+	0.528471i	−0.0605113	+	0.998168i	$0.519273\pi$
$380$	−76715.3	−	49301.9i	−0.0272535	−	0.0175148i
$381$	749025.	−	864421.i	0.264353	−	0.305079i
$382$	4.11579e6	+	1.20850e6i	1.44309	+	0.423731i
$383$	−368261.	−	2.56131e6i	−0.128280	−	0.892206i	−0.947734	−	0.319061i	$-0.896632\pi$
$383$	−368261.	−	2.56131e6i	−0.128280	−	0.892206i	0.819454	−	0.573145i	$-0.194277\pi$
$384$	−397248.	−	458448.i	−0.137478	−	0.158658i
$385$	31618.4	+	69234.7i	0.0108715	+	0.0238052i
$386$	622157.	−	182682.i	0.212535	−	0.0624061i
$387$	−160073.	+	350512.i	−0.0543303	+	0.118967i
$388$	−26538.7	+	184581.i	−0.00894954	+	0.0622454i
$389$	−3.34276e6	+	2.14826e6i	−1.12003	+	0.719801i	−0.963457	−	0.267864i	$-0.913682\pi$
$389$	−3.34276e6	+	2.14826e6i	−1.12003	+	0.719801i	−0.156576	+	0.987666i	$0.550046\pi$
$390$	−12090.2			−0.00402507
$391$	−5.33005e6	+	1.18732e6i	−1.76315	+	0.392757i
$392$	−3.19250e6			−1.04934
$393$	840425.	−	540108.i	0.274484	−	0.176400i
$394$	633420.	−	4.40553e6i	0.205566	−	1.42974i
$395$	525304.	−	1.15025e6i	0.169402	−	0.370938i
$396$	134747.	−	39565.4i	0.0431800	−	0.0126788i
$397$	−488622.	−	1.06993e6i	−0.155595	−	0.340706i	0.815740	−	0.578418i	$-0.196330\pi$
$397$	−488622.	−	1.06993e6i	−0.155595	−	0.340706i	−0.971336	+	0.237712i	$0.923603\pi$
$398$	−1.25029e6	−	1.44291e6i	−0.395642	−	0.456595i
$399$	17930.1	+	124707.i	0.00563834	+	0.0392156i
$400$	−1.74351e6	−	511941.i	−0.544847	−	0.159982i
$401$	−2.43207e6	+	2.80676e6i	−0.755292	+	0.871653i	−0.995070	−	0.0991742i	$-0.968380\pi$
$401$	−2.43207e6	+	2.80676e6i	−0.755292	+	0.871653i	0.239778	+	0.970828i	$0.422925\pi$
$402$	−1.12400e6	−	722350.i	−0.346897	−	0.222937i
$403$	−60087.9	−	38616.2i	−0.0184300	−	0.0118442i
$404$	−14137.8	+	16315.9i	−0.00430951	+	0.00497344i
$405$	106457.	+	31258.7i	0.0322507	+	0.00946965i
$406$	−89027.7	−	619201.i	−0.0268046	−	0.186430i
$407$	−626006.	−	722450.i	−0.187324	−	0.216183i
$408$	−1.58348e6	−	3.46734e6i	−0.470937	−	1.03121i
$409$	5.75454e6	−	1.68969e6i	1.70099	−	0.499457i	0.720078	−	0.693893i	$-0.244106\pi$
$409$	5.75454e6	−	1.68969e6i	1.70099	−	0.499457i	0.980915	+	0.194436i	$0.0622877\pi$
$410$	−558880.	+	1.22378e6i	−0.164195	+	0.359536i
$411$	−56026.8	+	389675.i	−0.0163603	+	0.113788i
$412$	485465.	−	311989.i	0.140901	−	0.0905517i
$413$	−545081.			−0.157248
$414$	74714.5	+	976283.i	0.0214242	+	0.279947i
$415$	−393156.			−0.112058
$416$	−45540.4	+	29267.0i	−0.0129022	+	0.00829173i
$417$	−106775.	+	742636.i	−0.0300697	+	0.209139i
$418$	214091.	−	468794.i	0.0599318	−	0.131232i
$419$	1.66080e6	−	487656.i	0.462150	−	0.135699i	−0.0423654	−	0.999102i	$-0.513489\pi$
$419$	1.66080e6	−	487656.i	0.462150	−	0.135699i	0.504515	+	0.863403i	$0.331671\pi$
$420$	14187.2	+	31065.6i	0.00392440	+	0.00859325i
$421$	3.56457e6	+	4.11373e6i	0.980170	+	1.13118i	0.991351	+	0.131239i	$0.0418954\pi$
$421$	3.56457e6	+	4.11373e6i	0.980170	+	1.13118i	−0.0111810	+	0.999937i	$0.503559\pi$
$422$	−172425.	−	1.19924e6i	−0.0471323	−	0.327812i
$423$	−501609.	−	147286.i	−0.136306	−	0.0400230i
$424$	−382831.	+	441811.i	−0.103417	+	0.119350i
$425$	−5.14072e6	−	3.30374e6i	−1.38055	−	0.887225i
$426$	1.58949e6	+	1.02150e6i	0.424360	+	0.272719i
$427$	−53061.7	+	61236.4i	−0.0140835	+	0.0162533i
$428$	888273.	+	260821.i	0.234389	+	0.0688228i
$429$	3982.18	+	27696.7i	0.00104467	+	0.00726582i
$430$	251018.	+	289690.i	0.0654687	+	0.0755549i
$431$	228196.	+	499680.i	0.0591718	+	0.129568i	0.936908	−	0.349576i	$-0.113674\pi$
$431$	228196.	+	499680.i	0.0591718	+	0.129568i	−0.877736	+	0.479144i	$0.840947\pi$
$432$	−447696.	+	131455.i	−0.115418	+	0.0338898i
$433$	−130512.	+	285780.i	−0.0334525	+	0.0732509i	−0.925621	−	0.378453i	$-0.876456\pi$
$433$	−130512.	+	285780.i	−0.0334525	+	0.0732509i	0.892168	+	0.451704i	$0.149184\pi$
$434$	70115.7	−	487665.i	0.0178686	−	0.124279i
$435$	696490.	−	447607.i	0.176478	−	0.113416i
$436$	−1.01878e6			−0.256664
$437$	−1.18236e6	−	875951.i	−0.296174	−	0.219420i
$438$	−2.71669e6			−0.676636
$439$	704230.	−	452581.i	0.174403	−	0.112082i	−0.450527	−	0.892763i	$-0.648764\pi$
$439$	704230.	−	452581.i	0.174403	−	0.112082i	0.624930	+	0.780681i	$0.285128\pi$
$440$	88311.0	−	614216.i	0.0217462	−	0.151248i
$441$	−545931.	+	1.19542e6i	−0.133672	+	0.292702i
$442$	164058.	−	48171.9i	0.0399432	−	0.0117284i
$443$	−1.68980e6	−	3.70014e6i	−0.409097	−	0.895797i	−0.996266	−	0.0863327i	$-0.972485\pi$
$443$	−1.68980e6	−	3.70014e6i	−0.409097	−	0.895797i	0.587170	−	0.809464i	$-0.300242\pi$
$444$	−280889.	−	324163.i	−0.0676204	−	0.0780381i
$445$	159336.	+	1.10821e6i	0.0381429	+	0.265290i
$446$	3.36946e6	+	989363.i	0.802091	+	0.235515i
$447$	−311930.	+	359986.i	−0.0738394	+	0.0852153i
$448$	−729982.	−	469131.i	−0.171837	−	0.110433i
$449$	3.99385e6	+	2.56669e6i	0.934924	+	0.600839i	0.916951	−	0.398999i	$-0.130642\pi$
$449$	3.99385e6	+	2.56669e6i	0.934924	+	0.600839i	0.0179726	+	0.999838i	$0.494279\pi$
$450$	−717534.	+	828078.i	−0.167036	+	0.192770i
$451$	2.98754e6	+	877222.i	0.691629	+	0.203081i
$452$	82283.0	+	572291.i	0.0189437	+	0.131756i
$453$	261489.	+	301774.i	0.0598697	+	0.0690934i
$454$	−841083.	−	1.84171e6i	−0.191513	−	0.419356i
$455$	−6529.04	+	1917.10i	−0.00147850	+	0.000434126i
$456$	426699.	−	934341.i	0.0960970	−	0.210423i
$457$	32731.3	−	227651.i	0.00733116	−	0.0509893i	−0.985827	−	0.167762i	$-0.946346\pi$
$457$	32731.3	−	227651.i	0.00733116	−	0.0509893i	0.993159	+	0.116773i	$0.0372550\pi$
$458$	5.15859e6	−	3.31522e6i	1.14913	−	0.738498i
$459$	−1.56912e6			−0.347635
$460$	−374416.	−	137530.i	−0.0825011	−	0.0303041i
$461$	−965615.			−0.211618			−0.105809	−	0.994386i	$-0.533743\pi$
$461$	−965615.			−0.211618			−0.105809	+	0.994386i	$0.533743\pi$
$462$	−162369.	+	104348.i	−0.0353914	+	0.0227447i
$463$	1.13489e6	−	7.89333e6i	0.246037	−	1.71123i	−0.374648	−	0.927167i	$-0.622236\pi$
$463$	1.13489e6	−	7.89333e6i	0.246037	−	1.71123i	0.620685	−	0.784060i	$-0.286854\pi$
$464$	−1.44636e6	+	3.16709e6i	−0.311876	+	0.682914i
$465$	625633.	−	183703.i	0.134180	−	0.0393988i
$466$	1.55895e6	+	3.41361e6i	0.332557	+	0.728198i
$467$	1.69131e6	+	1.95188e6i	0.358866	+	0.414153i	0.906259	−	0.422722i	$-0.138925\pi$
$467$	1.69131e6	+	1.95188e6i	0.358866	+	0.414153i	−0.547394	+	0.836875i	$0.684380\pi$
$468$	1786.81	+	12427.5i	0.000377106	+	0.00262283i
$469$	−721528.	−	211860.i	−0.151468	−	0.0444750i
$470$	−340558.	+	393025.i	−0.0711125	+	0.0820682i
$471$	−3.27401e6	−	2.10408e6i	−0.680029	−	0.437028i
$472$	3.73847e6	+	2.40257e6i	0.772394	+	0.496388i
$473$	580953.	−	670455.i	0.119396	−	0.137790i
$474$	3.07672e6	+	903406.i	0.628987	+	0.184687i
$475$	−234345.	−	1.62991e6i	−0.0476565	−	0.331458i
$476$	−316290.	−	365018.i	−0.0639834	−	0.0738408i
$477$	99968.9	+	218901.i	0.0201173	+	0.0440507i
$478$	−138246.	+	40592.7i	−0.0276747	+	0.00812602i
$479$	−3.16192e6	+	6.92363e6i	−0.629668	+	1.37878i	0.278606	+	0.960405i	$0.410128\pi$
$479$	−3.16192e6	+	6.92363e6i	−0.629668	+	1.37878i	−0.908274	+	0.418375i	$0.862600\pi$
$480$	70329.5	−	489153.i	0.0139327	−	0.0969039i
$481$	71896.2	−	46204.9i	0.0141691	−	0.00910595i
$482$	5.36200e6			1.05126
$483$	195153.	+	515371.i	0.0380633	+	0.100520i
$484$	1.17401e6			0.227802
$485$	285343.	−	183379.i	0.0550824	−	0.0353993i
$486$	−40040.7	+	278489.i	−0.00768974	+	0.0534833i
$487$	2.25376e6	−	4.93505e6i	0.430611	−	0.942907i	−0.562616	−	0.826718i	$-0.690205\pi$
$487$	2.25376e6	−	4.93505e6i	0.430611	−	0.942907i	0.993227	−	0.116189i	$-0.0370678\pi$
$488$	633841.	−	186112.i	0.120484	−	0.0353774i
$489$	−1.71462e6	−	3.75450e6i	−0.324262	−	0.710035i
$490$	856098.	+	987990.i	0.161077	+	0.185893i
$491$	711832.	+	4.95090e6i	0.133252	+	0.926788i	0.941276	+	0.337638i	$0.109628\pi$
$491$	711832.	+	4.95090e6i	0.133252	+	0.926788i	−0.808024	+	0.589150i	$0.799463\pi$
$492$	1.34051e6	+	393610.i	0.249665	+	0.0733083i
$493$	−7.66758e6	+	8.84886e6i	−1.42083	+	1.63972i
$494$	38760.8	+	24910.0i	0.00714620	+	0.00459258i
$495$	−214890.	−	138101.i	−0.0394188	−	0.0253329i
$496$	−1.79570e6	+	2.07235e6i	−0.327740	+	0.378233i
$497$	1.02034e6	+	299599.i	0.185291	+	0.0544063i
$498$	−141884.	−	986823.i	−0.0256365	−	0.178306i
$499$	−4.71974e6	−	5.44688e6i	−0.848530	−	0.979256i	0.151428	−	0.988468i	$-0.451613\pi$
$499$	−4.71974e6	−	5.44688e6i	−0.848530	−	0.979256i	−0.999958	+	0.00921263i	$0.997067\pi$
$500$	−389529.	−	852949.i	−0.0696810	−	0.152580i
$501$	−3.06050e6	+	898643.i	−0.544750	+	0.159953i
$502$	−3.30613e6	+	7.23942e6i	−0.585546	+	1.28217i
$503$	−453518.	+	3.15428e6i	−0.0799234	+	0.555880i	0.910036	+	0.414529i	$0.136054\pi$
$503$	−453518.	+	3.15428e6i	−0.0799234	+	0.555880i	−0.989960	+	0.141351i	$0.954855\pi$
$504$	−323613.	+	207974.i	−0.0567479	+	0.0364697i
$505$	39268.4			0.00685196
$506$	468195.	−	2.20508e6i	0.0812924	−	0.382866i
$507$	3.33914e6			0.576918
$508$	−993998.	+	638803.i	−0.170894	+	0.109827i
$509$	934222.	−	6.49766e6i	0.159829	−	1.11164i	−0.739117	−	0.673577i	$-0.764757\pi$
$509$	934222.	−	6.49766e6i	0.159829	−	1.11164i	0.898946	−	0.438059i	$-0.144334\pi$
$510$	−648420.	+	1.41984e6i	−0.110390	+	0.241721i
$511$	−1.46708e6	+	430774.i	−0.248543	+	0.0729789i
$512$	2.53753e6	+	5.55641e6i	0.427795	+	0.936740i
$513$	−276894.	−	319553.i	−0.0464537	−	0.0536104i
$514$	225485.	+	1.56828e6i	0.0376453	+	0.261829i
$515$	−1.00712e6	−	295718.i	−0.167327	−	0.0491315i
$516$	260674.	−	300834.i	0.0430996	−	0.0497396i
$517$	1.01252e6	+	650709.i	0.166601	+	0.107068i
$518$	495919.	+	318708.i	0.0812056	+	0.0521877i
$519$	−520605.	+	600810.i	−0.0848379	+	0.0979081i
$520$	53229.9	+	15629.7i	0.00863271	+	0.00253479i
$521$	1.38510e6	+	9.63355e6i	0.223555	+	1.55486i	0.724434	+	0.689345i	$0.242101\pi$
$521$	1.38510e6	+	9.63355e6i	0.223555	+	1.55486i	−0.500878	+	0.865518i	$0.666990\pi$
$522$	1.37485e6	+	1.58666e6i	0.220840	+	0.254863i
$523$	−2.61670e6	−	5.72977e6i	−0.418311	−	0.915974i	−0.995081	−	0.0990669i	$-0.968414\pi$
$523$	−2.61670e6	−	5.72977e6i	−0.418311	−	0.915974i	0.576770	−	0.816907i	$-0.304313\pi$
$524$	−990205.	+	290750.i	−0.157542	+	0.0462586i
$525$	−256182.	+	560960.i	−0.0405648	+	0.0888246i
$526$	−748773.	+	5.20783e6i	−0.118001	+	0.820715i
$527$	−7.75758e6	+	4.98549e6i	−1.21674	+	0.781954i
$528$	1.07423e6			0.167692
$529$	−5.88105e6	−	2.61530e6i	−0.913725	−	0.406333i
$530$	239388.			0.0370179
$531$	1.53893e6	−	989010.i	0.236855	−	0.152217i
$532$	18522.3	−	128825.i	0.00283737	−	0.0197343i
$533$	−115639.	+	253214.i	−0.0176314	+	0.0386073i
$534$	−2.72410e6	+	799867.i	−0.413399	+	0.121385i
$535$	−699516.	−	1.53173e6i	−0.105661	−	0.231365i
$536$	4.01482e6	+	4.63335e6i	0.603607	+	0.696600i
$537$	−526415.	−	3.66130e6i	−0.0787758	−	0.547898i
$538$	−2.12157e6	−	622949.i	−0.316010	−	0.0927891i
$539$	1.98134e6	−	2.28659e6i	0.293757	−	0.339013i
$540$	−96421.2	−	61966.1i	−0.0142294	−	0.00914471i
$541$	−1.82708e6	−	1.17419e6i	−0.268389	−	0.172483i	0.399524	−	0.916723i	$-0.369176\pi$
$541$	−1.82708e6	−	1.17419e6i	−0.268389	−	0.172483i	−0.667912	+	0.744240i	$0.732812\pi$
$542$	−4.63946e6	+	5.35422e6i	−0.678373	+	0.782885i
$543$	7.22902e6	+	2.12263e6i	1.05215	+	0.308941i
$544$	994624.	+	6.91776e6i	0.144099	+	1.00223i
$545$	1.21350e6	+	1.40046e6i	0.175004	+	0.201966i
$546$	−7168.15	−	15696.1i	−0.00102902	−	0.00225325i
$547$	2.54428e6	−	747067.i	0.363577	−	0.106756i	−0.0948414	−	0.995492i	$-0.530234\pi$
$547$	2.54428e6	−	747067.i	0.363577	−	0.106756i	0.458418	+	0.888737i	$0.348416\pi$
$548$	168943.	−	369933.i	0.0240319	−	0.0526225i
$549$	38700.2	−	269166.i	0.00548002	−	0.0381144i
$550$	2.12215e6	−	1.36382e6i	0.299136	−	0.192243i
$551$	−3.15514e6			−0.442730
$552$	933147.	−	4.39488e6i	0.130347	−	0.613903i
$553$	1.80475e6			0.250961
$554$	8.02259e6	−	5.15581e6i	1.11056	−	0.713711i
$555$	−111032.	+	772242.i	−0.0153008	+	0.106419i
$556$	321968.	−	705011.i	0.0441698	−	0.0967184i
$557$	6.56053e6	−	1.92634e6i	0.895985	−	0.263085i	0.198854	−	0.980029i	$-0.436278\pi$
$557$	6.56053e6	−	1.92634e6i	0.895985	−	0.263085i	0.697131	+	0.716944i	$0.254460\pi$
$558$	686875.	+	1.50405e6i	0.0933883	+	0.204492i
$559$	51938.6	+	59940.3i	0.00703008	+	0.00811315i
$560$	37177.7	+	258577.i	0.00500971	+	0.0348433i
$561$	3.46619e6	+	1.01776e6i	0.464991	+	0.136534i
$562$	−4.68510e6	+	5.40689e6i	−0.625717	+	0.722116i
$563$	−8.61512e6	−	5.53660e6i	−1.14549	−	0.736160i	−0.176752	−	0.984255i	$-0.556559\pi$
$563$	−8.61512e6	−	5.53660e6i	−1.14549	−	0.736160i	−0.968736	+	0.248095i	$0.920196\pi$
$564$	454319.	+	291973.i	0.0601400	+	0.0386496i
$565$	688683.	−	794783.i	0.0907608	−	0.104744i
$566$	8.48367e6	+	2.49103e6i	1.11312	+	0.326842i
$567$	22535.9	+	156740.i	0.00294386	+	0.0204750i
$568$	−5.67752e6	−	6.55221e6i	−0.738393	−	0.852151i
$569$	−5.70958e6	−	1.25022e7i	−0.739305	−	1.61885i	−0.784694	−	0.619884i	$-0.787180\pi$
$569$	−5.70958e6	−	1.25022e7i	−0.739305	−	1.61885i	0.0453885	−	0.998969i	$-0.485547\pi$
$570$	−403576.	+	118501.i	−0.0520281	+	0.0152768i
$571$	−1.09150e6	+	2.39006e6i	−0.140099	+	0.306774i	−0.966656	−	0.256079i	$-0.917569\pi$
$571$	−1.09150e6	+	2.39006e6i	−0.140099	+	0.306774i	0.826557	+	0.562854i	$0.190296\pi$
$572$	4113.70	−	28611.4i	0.000525705	−	0.00365636i
$573$	−6.81618e6	+	4.38049e6i	−0.867271	+	0.557361i
$574$	−1.92011e6			−0.243247
$575$	−2.55063e6	−	6.73585e6i	−0.321720	−	0.849616i
$576$	2.91217e6			0.365729
$577$	4.49085e6	−	2.88609e6i	0.561550	−	0.360887i	−0.228865	−	0.973458i	$-0.573501\pi$
$577$	4.49085e6	−	2.88609e6i	0.561550	−	0.360887i	0.790415	+	0.612572i	$0.209865\pi$
$578$	2.17877e6	−	1.51536e7i	0.271263	−	1.88668i
$579$	−508795.	+	1.11411e6i	−0.0630735	+	0.138112i
$580$	−820618.	+	240955.i	−0.101291	+	0.0297417i
$581$	−233097.	−	510412.i	−0.0286482	−	0.0627307i
$582$	563257.	+	650034.i	0.0689286	+	0.0795478i
$583$	−78847.5	−	548396.i	−0.00960763	−	0.0668226i
$584$	1.19608e7	+	3.51201e6i	1.45120	+	0.426112i
$585$	14955.0	−	17259.0i	0.00180675	−	0.00208510i
$586$	−3.83377e6	−	2.46382e6i	−0.461193	−	0.296391i
$587$	−6.67945e6	−	4.29262e6i	−0.800103	−	0.514195i	0.0755467	−	0.997142i	$-0.475930\pi$
$587$	−6.67945e6	−	4.29262e6i	−0.800103	−	0.514195i	−0.875649	+	0.482948i	$0.839566\pi$
$588$	889029.	−	1.02599e6i	0.106041	−	0.122378i
$589$	−2.38424e6	−	700076.i	−0.283179	−	0.0831490i
$590$	−258977.	−	1.80122e6i	−0.0306289	−	0.213028i
$591$	5.50546e6	+	6.35364e6i	0.648373	+	0.748262i
$592$	−1.36297e6	−	2.98449e6i	−0.159839	−	0.349998i
$593$	−2.20900e6	+	648621.i	−0.257964	+	0.0757451i	−0.408157	−	0.912912i	$-0.633829\pi$
$593$	−2.20900e6	+	648621.i	−0.257964	+	0.0757451i	0.150193	+	0.988657i	$0.452010\pi$
$594$	269085.	−	589213.i	0.0312912	−	0.0685183i
$595$	−125025.	+	869568.i	−0.0144779	+	0.100696i
$596$	413949.	−	266029.i	0.0477343	−	0.0306770i
$597$	3.60632e6			0.414122
$598$	189176.	+	69487.5i	0.0216328	+	0.00794609i
$599$	1.33154e7			1.51631			0.758154	−	0.652075i	$-0.226101\pi$
$599$	1.33154e7			1.51631			0.758154	+	0.652075i	$0.226101\pi$
$600$	4.22960e6	−	2.71820e6i	0.479646	−	0.308250i
$601$	1.95184e6	−	1.35754e7i	0.220424	−	1.53308i	−0.516016	−	0.856579i	$-0.672586\pi$
$601$	1.95184e6	−	1.35754e7i	0.220424	−	1.53308i	0.736440	−	0.676503i	$-0.236505\pi$
$602$	−227263.	+	497636.i	−0.0255586	+	0.0559655i
$603$	2.42150e6	−	711016.i	0.271201	−	0.0796317i
$604$	−171355.	−	375216.i	−0.0191119	−	0.0418493i
$605$	−1.39840e6	−	1.61384e6i	−0.155325	−	0.179255i
$606$	14171.3	+	98563.8i	0.00156758	+	0.0109027i
$607$	−6.04637e6	−	1.77537e6i	−0.666075	−	0.195577i	−0.0688203	−	0.997629i	$-0.521923\pi$
$607$	−6.04637e6	−	1.77537e6i	−0.666075	−	0.195577i	−0.597254	+	0.802052i	$0.703742\pi$
$608$	−1.23329e6	+	1.42330e6i	−0.135303	+	0.156148i
$609$	994042.	+	638832.i	0.108608	+	0.0697981i
$610$	−227567.	−	146248.i	−0.0247619	−	0.0159135i
$611$	−70465.4	+	81321.4i	−0.00763612	+	0.00881256i
$612$	1.55528e6	+	456671.i	0.167853	+	0.0492862i
$613$	360331.	+	2.50616e6i	0.0387303	+	0.269375i	0.999980	−	0.00630353i	$-0.00200649\pi$
$613$	360331.	+	2.50616e6i	0.0387303	+	0.269375i	−0.961250	+	0.275679i	$0.911097\pi$
$614$	−1.67824e6	−	1.93679e6i	−0.179652	−	0.207329i
$615$	−1.05565e6	−	2.31156e6i	−0.112547	−	0.246444i
$616$	849760.	−	249512.i	0.0902286	−	0.0264935i
$617$	−5.94279e6	+	1.30129e7i	−0.628460	+	1.37613i	0.280744	+	0.959783i	$0.409419\pi$
$617$	−5.94279e6	+	1.30129e7i	−0.628460	+	1.37613i	−0.909204	+	0.416352i	$0.863308\pi$
$618$	378799.	−	2.63461e6i	0.0398968	−	0.277488i
$619$	1.11882e7	−	7.19023e6i	1.17364	−	0.754251i	0.199432	−	0.979912i	$-0.436090\pi$
$619$	1.11882e7	−	7.19023e6i	1.17364	−	0.754251i	0.974206	+	0.225660i	$0.0724539\pi$
$620$	−673580.			−0.0703736
$621$	−1.48608e6	−	1.10096e6i	−0.154637	−	0.114562i
$622$	−1.08761e7			−1.12719
$623$	−1.34425e6	+	863897.i	−0.138759	+	0.0891748i
$624$	−13667.7	+	95061.0i	−0.00140519	+	0.00977329i
$625$	2.97703e6	−	6.51878e6i	0.304847	−	0.667523i
$626$	−3.85388e6	+	1.13160e6i	−0.393063	+	0.115414i
$627$	404391.	+	885493.i	0.0410802	+	0.0899531i
$628$	2.63277e6	+	3.03838e6i	0.266387	+	0.307427i
$629$	−1.57025e6	−	1.09213e7i	−0.158249	−	1.10065i
$630$	151142.	+	44379.3i	0.0151717	+	0.00445480i
$631$	−1.95414e6	+	2.25520e6i	−0.195381	+	0.225482i	−0.844984	−	0.534792i	$-0.820390\pi$
$631$	−1.95414e6	+	2.25520e6i	−0.195381	+	0.225482i	0.649603	+	0.760274i	$0.274935\pi$
$632$	−1.23780e7	−	7.95487e6i	−1.23270	−	0.792210i
$633$	1.92522e6	+	1.23726e6i	0.190972	+	0.122730i
$634$	2.78745e6	−	3.21689e6i	0.275412	−	0.317843i
$635$	2.06211e6	+	605489.i	0.202944	+	0.0595898i
$636$	−35378.9	−	246066.i	−0.00346818	−	0.0241217i
$637$	177137.	+	204427.i	0.0172966	+	0.0199613i
$638$	−2.00790e6	−	4.39669e6i	−0.195295	−	0.427636i
$639$	−3.42433e6	+	1.00548e6i	−0.331760	+	0.0974135i
$640$	473496.	−	1.03681e6i	0.0456948	−	0.100058i
$641$	−283398.	+	1.97108e6i	−0.0272428	+	0.189478i	−0.998899	−	0.0469224i	$-0.985059\pi$
$641$	−283398.	+	1.97108e6i	−0.0272428	+	0.189478i	0.971656	+	0.236400i	$0.0759677\pi$
$642$	3.59220e6	−	2.30856e6i	0.343971	−	0.221057i
$643$	−8.56278e6			−0.816746			−0.408373	−	0.912815i	$-0.633904\pi$
$643$	−8.56278e6			−0.816746			−0.408373	+	0.912815i	$0.633904\pi$
$644$	−43439.8	−	567622.i	−0.00412737	−	0.0539318i
$645$	−724034.			−0.0685267
$646$	5.00416e6	−	3.21598e6i	0.471791	−	0.303202i
$647$	−1.53175e6	+	1.06536e7i	−0.143856	+	1.00054i	0.782165	+	0.623071i	$0.214115\pi$
$647$	−1.53175e6	+	1.06536e7i	−0.143856	+	1.00054i	−0.926022	+	0.377471i	$0.876794\pi$
$648$	536306.	−	1.17435e6i	0.0501736	−	0.109865i
$649$	−4.04100e6	+	1.18654e6i	−0.376597	+	0.110579i
$650$	93687.1	+	205146.i	0.00869754	+	0.0190450i
$651$	609420.	+	703308.i	0.0563591	+	0.0650419i
$652$	606803.	+	4.22041e6i	0.0559022	+	0.388808i
$653$	5.14325e6	+	1.51019e6i	0.472014	+	0.138596i	0.509084	−	0.860717i	$-0.329984\pi$
$653$	5.14325e6	+	1.51019e6i	0.472014	+	0.138596i	−0.0370702	+	0.999313i	$0.511803\pi$
$654$	−3.07722e6	+	3.55130e6i	−0.281328	+	0.324670i
$655$	1.57914e6	+	1.01485e6i	0.143819	+	0.0924271i
$656$	8.99029e6	+	5.77771e6i	0.815669	+	0.524199i
$657$	3.36041e6	−	3.87812e6i	0.303724	−	0.350516i
$658$	−712153.	−	209107.i	−0.0641223	−	0.0188280i
$659$	305256.	+	2.12310e6i	0.0273811	+	0.190440i	0.998921	−	0.0464350i	$-0.0147860\pi$
$659$	305256.	+	2.12310e6i	0.0273811	+	0.190440i	−0.971540	+	0.236875i	$0.923877\pi$
$660$	172802.	+	199424.i	0.0154415	+	0.0178204i
$661$	5.40870e6	+	1.18434e7i	0.481492	+	1.05432i	0.982050	+	0.188618i	$0.0604009\pi$
$661$	5.40870e6	+	1.18434e7i	0.481492	+	1.05432i	−0.500558	+	0.865703i	$0.666872\pi$
$662$	5.26007e6	−	1.54449e6i	0.466494	−	0.136975i
$663$	−134166.	+	293782.i	−0.0118538	+	0.0259562i
$664$	−651045.	+	4.52812e6i	−0.0573048	+	0.398564i
$665$	−199151.	+	127987.i	−0.0174634	+	0.0112230i
$666$	−1.97840e6			−0.172834
$667$	−1.34705e7	+	3.00068e6i	−1.17238	+	0.261159i
$668$	3.29504e6			0.285706
$669$	−5.58019e6	+	3.58617e6i	−0.482040	+	0.309789i
$670$	357282.	−	2.48495e6i	0.0307485	−	0.213861i
$671$	−260076.	+	569486.i	−0.0222994	+	0.0488289i
$672$	676736.	−	198708.i	0.0578091	−	0.0169743i
$673$	2.33853e6	+	5.12067e6i	0.199024	+	0.435802i	0.982660	−	0.185419i	$-0.0593642\pi$
$673$	2.33853e6	+	5.12067e6i	0.199024	+	0.435802i	−0.783635	+	0.621221i	$0.786637\pi$
$674$	−8.45756e6	−	9.76055e6i	−0.717126	−	0.827608i
$675$	−294542.	−	2.04858e6i	−0.0248821	−	0.173059i
$676$	−3.30969e6	−	971812.i	−0.278561	−	0.0817929i
$677$	−4.35542e6	+	5.02643e6i	−0.365223	+	0.421490i	−0.908383	−	0.418139i	$-0.862682\pi$
$677$	−4.35542e6	+	5.02643e6i	−0.365223	+	0.421490i	0.543160	+	0.839630i	$0.317228\pi$
$678$	2.24344e6	+	1.44177e6i	0.187431	+	0.120454i
$679$	407246.	+	261721.i	0.0338987	+	0.0217853i
$680$	4.69031e6	−	5.41291e6i	0.388982	−	0.448909i
$681$	3.66945e6	+	1.07745e6i	0.303203	+	0.0890285i
$682$	−541752.	−	3.76797e6i	−0.0446005	−	0.310203i
$683$	1.01942e7	+	1.17647e7i	0.836182	+	0.965005i	0.999768	−	0.0215236i	$-0.00685169\pi$
$683$	1.01942e7	+	1.17647e7i	0.836182	+	0.965005i	−0.163586	+	0.986529i	$0.552306\pi$
$684$	181450.	+	397321.i	0.0148292	+	0.0324714i
$685$	−709756.	+	208403.i	−0.0577940	+	0.0169699i
$686$	−1.57799e6	+	3.45531e6i	−0.128025	+	0.280335i
$687$	−1.64838e6	+	1.14647e7i	−0.133250	+	0.926771i
$688$	2.56149e6	−	1.64617e6i	0.206311	−	0.132588i
$689$	49532.1			0.00397502
$690$	−1.61032e6	+	889744.i	−0.128763	+	0.0711447i
$691$	4.02267e6			0.320493			0.160247	−	0.987077i	$-0.448771\pi$
$691$	4.02267e6			0.320493			0.160247	+	0.987077i	$0.448771\pi$
$692$	690872.	−	443996.i	0.0548444	−	0.0352463i
$693$	51883.5	−	360858.i	0.00410389	−	0.0285432i
$694$	−8.57578e6	+	1.87783e7i	−0.675888	+	1.47999i
$695$	−1.35264e6	+	397171.i	−0.106223	+	0.0311900i
$696$	−4.00190e6	−	8.76294e6i	−0.313143	−	0.685688i
$697$	2.35348e7	+	2.71606e7i	1.83497	+	2.11766i
$698$	436272.	+	3.03434e6i	0.0338937	+	0.235736i
$699$	−6.80133e6	−	1.99705e6i	−0.526503	−	0.154595i
$700$	417182.	−	481454.i	0.0321796	−	0.0371373i
$701$	7.42705e6	+	4.77307e6i	0.570849	+	0.366862i	0.793996	−	0.607922i	$-0.207997\pi$
$701$	7.42705e6	+	4.77307e6i	0.570849	+	0.366862i	−0.223148	+	0.974785i	$0.571633\pi$
$702$	48717.3	+	31308.7i	0.00373113	+	0.00239785i
$703$	1.94704e6	−	2.24701e6i	0.148589	−	0.171481i
$704$	−6.43299e6	−	1.88890e6i	−0.489194	−	0.143640i
$705$	−139796.	−	972303.i	−0.0105931	−	0.0736765i
$706$	8.61081e6	+	9.93741e6i	0.650178	+	0.750345i
$707$	23281.7	+	50979.8i	0.00175173	+	0.00383575i
$708$	−1.81320e6	+	532403.i	−0.135945	+	0.0399169i
$709$	4.63658e6	−	1.01527e7i	0.346403	−	0.758517i	−0.653595	−	0.756844i	$-0.726740\pi$
$709$	4.63658e6	−	1.01527e7i	0.346403	−	0.758517i	0.999999	−	0.00167321i	$-0.000532598\pi$
$710$	−505246.	+	3.51407e6i	−0.0376147	+	0.261616i
$711$	−5.09537e6	+	3.27460e6i	−0.378009	+	0.242932i
$712$	1.30275e7			0.963074
$713$	−1.08451e7	−	721380.i	−0.798929	−	0.0531423i
$714$	−2.22774e6			−0.163538
$715$	−44230.3	+	28425.1i	−0.00323560	+	0.00207939i
$716$	−543801.	+	3.78222e6i	−0.0396421	+	0.275717i
$717$	113057.	−	247559.i	0.00821293	−	0.0179838i
$718$	−2.02447e7	+	5.94438e6i	−1.46555	+	0.430324i
$719$	7.82417e6	+	1.71325e7i	0.564438	+	1.23595i	0.949706	+	0.313142i	$0.101382\pi$
$719$	7.82417e6	+	1.71325e7i	0.564438	+	1.23595i	−0.385268	+	0.922805i	$0.625891\pi$
$720$	−574133.	−	662584.i	−0.0412744	−	0.0476332i
$721$	−213197.	−	1.48282e6i	−0.0152737	−	0.106231i
$722$	−9.78208e6	−	2.87228e6i	−0.698374	−	0.205061i
$723$	−6.63253e6	+	7.65435e6i	−0.471882	+	0.544581i
$724$	−6.54750e6	−	4.20782e6i	−0.464226	−	0.298340i
$725$	−1.29920e7	−	8.34948e6i	−0.917978	−	0.589949i
$726$	3.54608e6	−	4.09239e6i	0.249693	−	0.288161i
$727$	8.18969e6	+	2.40471e6i	0.574687	+	0.168743i	0.556146	−	0.831085i	$-0.312280\pi$
$727$	8.18969e6	+	2.40471e6i	0.574687	+	0.168743i	0.0185414	+	0.999828i	$0.494098\pi$
$728$	11268.2	+	78371.9i	0.000787998	+	0.00548065i
$729$	−348020.	−	401636.i	−0.0242541	−	0.0279907i
$730$	−2.12053e6	−	4.64331e6i	−0.147278	−	0.322493i
$731$	9.82476e6	−	2.88481e6i	0.680031	−	0.199675i
$732$	−116696.	+	255529.i	−0.00804968	+	0.0176263i
$733$	1.31455e6	−	9.14289e6i	0.0903685	−	0.628526i	−0.893424	−	0.449215i	$-0.851704\pi$
$733$	1.31455e6	−	9.14289e6i	0.0903685	−	0.628526i	0.983792	−	0.179312i	$-0.0573871\pi$
$734$	−1.88726e7	+	1.21287e7i	−1.29298	+	0.830947i
$735$	−2.46932e6			−0.168601
$736$	−3.91180e6	+	7.24953e6i	−0.266184	+	0.493305i
$737$	−5.81028e6			−0.394029
$738$	5.42106e6	−	3.48390e6i	0.366390	−	0.235464i
$739$	3.36458e6	−	2.34012e7i	0.226631	−	1.57626i	−0.485517	−	0.874227i	$-0.661369\pi$
$739$	3.36458e6	−	2.34012e7i	0.226631	−	1.57626i	0.712149	−	0.702029i	$-0.247722\pi$
$740$	334804.	−	733118.i	0.0224756	−	0.0492147i
$741$	−83504.6	+	24519.2i	−0.00558682	+	0.00164044i
$742$	141930.	+	310783.i	0.00946376	+	0.0207228i
$743$	6.50807e6	+	7.51072e6i	0.432494	+	0.499125i	0.929603	−	0.368563i	$-0.120150\pi$
$743$	6.50807e6	+	7.51072e6i	0.432494	+	0.499125i	−0.497108	+	0.867689i	$0.665605\pi$
$744$	−1.07975e6	−	7.50984e6i	−0.0715141	−	0.497392i
$745$	−858760.	−	252155.i	−0.0566867	−	0.0166447i
$746$	625570.	−	721946.i	0.0411556	−	0.0474961i
$747$	1.58421e6	+	1.01811e6i	0.103875	+	0.0667564i
$748$	−3.13941e6	−	2.01758e6i	−0.205161	−	0.131849i
$749$	1.57382e6	−	1.81628e6i	0.102506	−	0.118298i
$750$	−4.14980e6	−	1.21849e6i	−0.269386	−	0.0790987i
$751$	3.52976e6	+	2.45500e7i	0.228373	+	1.58837i	0.704961	+	0.709246i	$0.250964\pi$
$751$	3.52976e6	+	2.45500e7i	0.228373	+	1.58837i	−0.476588	+	0.879127i	$0.658127\pi$
$752$	2.70521e6	+	3.12198e6i	0.174444	+	0.201319i
$753$	−6.24487e6	−	1.36744e7i	−0.401362	−	0.878859i
$754$	414621.	−	121744.i	0.0265597	−	0.00779863i
$755$	−311679.	+	682482.i	−0.0198994	+	0.0435737i
$756$	23280.1	−	161917.i	0.00148143	−	0.0103036i
$757$	1.83442e7	−	1.17891e7i	1.16348	−	0.747724i	0.191203	−	0.981551i	$-0.438761\pi$
$757$	1.83442e7	−	1.17891e7i	1.16348	−	0.747724i	0.972278	+	0.233827i	$0.0751249\pi$
$758$	−1.30242e7			−0.823335
$759$	2.56865e6	+	3.39592e6i	0.161845	+	0.213970i
$760$	1.93002e6			0.121207
$761$	1.02853e7	−	6.60997e6i	0.643808	−	0.413750i	−0.177591	−	0.984104i	$-0.556830\pi$
$761$	1.02853e7	−	6.60997e6i	0.643808	−	0.413750i	0.821399	+	0.570354i	$0.193194\pi$
$762$	−775598.	+	5.39440e6i	−0.0483893	+	0.336555i
$763$	−1.09866e6	+	2.40573e6i	−0.0683207	+	0.149601i
$764$	8.03096e6	−	2.35810e6i	0.497776	−	0.146160i
$765$	−1.22478e6	−	2.68190e6i	−0.0756669	−	0.165687i
$766$	8.07409e6	+	9.31799e6i	0.497189	+	0.573787i
$767$	−53585.3	−	372694.i	−0.00328895	−	0.0228752i
$768$	−7.16166e6	−	2.10285e6i	−0.438138	−	0.128649i
$769$	9.79420e6	−	1.13031e7i	0.597246	−	0.689258i	−0.373975	−	0.927439i	$-0.622006\pi$
$769$	9.79420e6	−	1.13031e7i	0.597246	−	0.689258i	0.971221	+	0.238181i	$0.0765510\pi$
$770$	−305088.	−	196068.i	−0.0185438	−	0.0119174i
$771$	−2.51766e6	−	1.61800e6i	−0.152532	−	0.0980266i
$772$	828555.	−	956203.i	0.0500355	−	0.0577440i
$773$	2.10388e7	+	6.17754e6i	1.26640	+	0.371849i	0.844874	−	0.534966i	$-0.179675\pi$
$773$	2.10388e7	+	6.17754e6i	1.26640	+	0.371849i	0.421529	+	0.906815i	$0.361494\pi$
$774$	−261292.	−	1.81733e6i	−0.0156774	−	0.109039i
$775$	−7.96506e6	−	9.19217e6i	−0.476360	−	0.549748i
$776$	−1.63953e6	−	3.59006e6i	−0.0977382	−	0.214017i
$777$	−1.06839e6	+	313707.i	−0.0634857	+	0.0186411i
$778$	7.86501e6	−	1.72220e7i	0.465855	−	1.02008i
$779$	−1.37822e6	+	9.58576e6i	−0.0813723	+	0.565956i
$780$	−19846.2	+	12754.3i	−0.00116799	+	0.000750623i
$781$	8.21654e6			0.482016
$782$	1.83062e7	−	1.84895e7i	1.07049	−	1.08120i
$783$	−3.96560e6			−0.231156
$784$	8.73598e6	−	5.61427e6i	0.507600	−	0.326215i
$785$	1.04070e6	−	7.23821e6i	0.0602768	−	0.419235i
$786$	−1.97740e6	+	4.32989e6i	−0.114166	+	0.249989i
$787$	−8.95476e6	+	2.62935e6i	−0.515367	+	0.151326i	−0.529066	−	0.848581i	$-0.677458\pi$
$787$	−8.95476e6	+	2.62935e6i	−0.515367	+	0.151326i	0.0136987	+	0.999906i	$0.495639\pi$
$788$	−3.60776e6	−	7.89990e6i	−0.206977	−	0.453217i
$789$	−6.50807e6	−	7.51071e6i	−0.372185	−	0.429525i
$790$	857468.	+	5.96382e6i	0.0488821	+	0.339983i
$791$	1.44013e6	+	422861.i	0.0818391	+	0.0240301i
$792$	−1.94641e6	+	2.24628e6i	−0.110261	+	0.127248i
$793$	−47086.2	−	30260.5i	−0.00265895	−	0.00170881i
$794$	4.71473e6	+	3.02997e6i	0.265403	+	0.170564i
$795$	−296110.	+	341730.i	−0.0166164	+	0.0191763i
$796$	−3.57451e6	−	1.04957e6i	−0.199956	−	0.0587123i
$797$	−2.25477e6	−	1.56823e7i	−0.125735	−	0.874506i	−0.950874	−	0.309577i	$-0.899813\pi$
$797$	−2.25477e6	−	1.56823e7i	−0.125735	−	0.874506i	0.825139	−	0.564929i	$-0.191096\pi$
$798$	−393117.	−	453681.i	−0.0218532	−	0.0252199i
$799$	5.77096e6	+	1.26366e7i	0.319802	+	0.700269i
$800$	−8.84487e6	+	2.59709e6i	−0.488615	+	0.143470i
$801$	2.22775e6	−	4.87809e6i	0.122683	−	0.268639i
$802$	2.51835e6	−	1.75155e7i	0.138255	−	0.961584i
$803$	−9.93859e6	+	6.38715e6i	−0.543921	+	0.349557i
$804$	−2.60707e6			−0.142237
$805$	−728533.	+	735827.i	−0.0396241	+	0.0400208i
$806$	340329.			0.0184528
$807$	3.51354e6	−	2.25802e6i	0.189916	−	0.122052i
$808$	65026.3	−	452268.i	0.00350397	−	0.0243707i
$809$	2.69569e6	−	5.90273e6i	0.144810	−	0.317089i	−0.823304	−	0.567601i	$-0.807872\pi$
$809$	2.69569e6	−	5.90273e6i	0.144810	−	0.317089i	0.968114	+	0.250512i	$0.0805989\pi$
$810$	−507242.	+	148940.i	−0.0271646	+	0.00797624i
$811$	−1.02323e7	−	2.24057e7i	−0.546289	−	1.19621i	−0.958493	−	0.285115i	$-0.907968\pi$
$811$	−1.02323e7	−	2.24057e7i	−0.546289	−	1.19621i	0.412204	−	0.911092i	$-0.364759\pi$
$812$	−799352.	−	922501.i	−0.0425449	−	0.0490995i
$813$	−1.90446e6	−	1.32458e7i	−0.101052	−	0.702832i
$814$	4.37030e6	+	1.28323e6i	0.231180	+	0.0678805i
$815$	5.07875e6	−	5.86119e6i	0.267832	−	0.309095i
$816$	1.04306e7	+	6.70337e6i	0.548385	+	0.352426i
$817$	2.32122e6	+	1.49176e6i	0.121664	+	0.0781885i
$818$	−1.87136e7	+	2.15967e7i	−0.977854	+	1.12850i
$819$	31273.0	+	9182.59i	0.00162915	+	0.000478361i
$820$	373595.	+	2.59841e6i	0.0194029	+	0.134950i
$821$	−1.35303e7	−	1.56148e7i	−0.700567	−	0.808497i	0.288262	−	0.957551i	$-0.406922\pi$
$821$	−1.35303e7	−	1.56148e7i	−0.700567	−	0.808497i	−0.988829	+	0.149055i	$0.952377\pi$
$822$	−779233.	−	1.70628e6i	−0.0402242	−	0.0880788i
$823$	−3.13483e6	+	920469.i	−0.161330	+	0.0473707i	−0.361400	−	0.932411i	$-0.617701\pi$
$823$	−3.13483e6	+	920469.i	−0.161330	+	0.0473707i	0.200070	+	0.979782i	$0.435883\pi$
$824$	−5.07364e6	+	1.11097e7i	−0.260316	+	0.570013i
$825$	−678112.	+	4.71637e6i	−0.0346870	+	0.241253i
$826$	2.18488e6	−	1.40414e6i	0.111424	−	0.0716076i
$827$	−2.71147e7			−1.37861			−0.689304	−	0.724472i	$-0.742084\pi$
$827$	−2.71147e7			−1.37861			−0.689304	+	0.724472i	$0.742084\pi$
$828$	1.15255e6	+	1.52375e6i	0.0584232	+	0.0772393i
$829$	2.67166e7			1.35019			0.675095	−	0.737731i	$-0.264103\pi$
$829$	2.67166e7			1.35019			0.675095	+	0.737731i	$0.264103\pi$
$830$	1.57591e6	−	1.01278e6i	0.0794028	−	0.0510291i
$831$	−2.56355e6	+	1.78299e7i	−0.128777	+	0.895664i
$832$	249002.	−	545237.i	0.0124708	−	0.0273072i
$833$	3.35074e7	−	9.83866e6i	1.67312	−	0.491274i
$834$	−1.48505e6	−	3.25180e6i	−0.0739308	−	0.161886i
$835$	−3.92483e6	−	4.52950e6i	−0.194807	−	0.224819i
$836$	−143114.	−	995376.i	−0.00708215	−	0.0492574i
$837$	−2.99668e6	−	879905.i	−0.147852	−	0.0434132i
$838$	−5.40088e6	+	6.23295e6i	−0.265677	+	0.306608i
$839$	4.70122e6	+	3.02129e6i	0.230572	+	0.148179i	0.650826	−	0.759227i	$-0.274423\pi$
$839$	4.70122e6	+	3.02129e6i	0.230572	+	0.148179i	−0.420254	+	0.907406i	$0.638059\pi$
$840$	−608063.	−	390778.i	−0.0297338	−	0.0191087i
$841$	−5.94616e6	+	6.86223e6i	−0.289899	+	0.334561i
$842$	−2.48851e7	−	7.30691e6i	−1.20965	−	0.355184i
$843$	−1.92319e6	−	1.33761e7i	−0.0932082	−	0.648277i
$844$	−1.54815e6	−	1.78666e6i	−0.0748094	−	0.0863347i
$845$	2.60638e6	+	5.70718e6i	0.125573	+	0.274967i
$846$	2.39004e6	−	701778.i	0.114810	−	0.0337112i
$847$	1.26606e6	−	2.77228e6i	0.0606381	−	0.132779i
$848$	270621.	−	1.88221e6i	0.0129233	−	0.0898833i
$849$	−1.40499e7	+	9.02929e6i	−0.668964	+	0.429917i
$850$	2.91163e7			1.38226
$851$	6.17569e6	−	1.14451e7i	0.292322	−	0.541746i
$852$	3.68677e6			0.173999
$853$	−2.10861e7	+	1.35512e7i	−0.992254	+	0.637683i	−0.932742	−	0.360545i	$-0.882591\pi$
$853$	−2.10861e7	+	1.35512e7i	−0.992254	+	0.637683i	−0.0595118	+	0.998228i	$0.518954\pi$
$854$	54944.2	−	382145.i	0.00257796	−	0.0179301i
$855$	330041.	−	722690.i	0.0154402	−	0.0338093i
$856$	−1.87998e7	+	5.52012e6i	−0.876938	+	0.257492i
$857$	618038.	+	1.35331e6i	0.0287451	+	0.0629429i	0.923460	−	0.383695i	$-0.125349\pi$
$857$	618038.	+	1.35331e6i	0.0287451	+	0.0629429i	−0.894715	+	0.446638i	$0.852621\pi$
$858$	−87309.1	−	100760.i	−0.00404894	−	0.00467273i
$859$	−1.29067e6	−	8.97681e6i	−0.0596805	−	0.415087i	−0.997659	−	0.0683922i	$-0.978213\pi$
$859$	−1.29067e6	−	8.97681e6i	−0.0596805	−	0.415087i	0.937978	−	0.346695i	$-0.112696\pi$
$860$	717649.	+	210721.i	0.0330876	+	0.00971541i
$861$	2.37508e6	−	2.74099e6i	0.109187	−	0.126008i
$862$	−2.20187e6	−	1.41506e6i	−0.100931	−	0.0648643i
$863$	591278.	+	379991.i	0.0270249	+	0.0173679i	0.554084	−	0.832461i	$-0.313069\pi$
$863$	591278.	+	379991.i	0.0270249	+	0.0173679i	−0.527059	+	0.849829i	$0.676705\pi$
$864$	−1.55009e6	+	1.78890e6i	−0.0706436	+	0.0815271i
$865$	−1.43325e6	−	420841.i	−0.0651302	−	0.0191240i
$866$	−213038.	−	1.48171e6i	−0.00965298	−	0.0671380i
$867$	1.89371e7	+	2.18545e7i	0.855588	+	0.987401i
$868$	−399357.	−	874470.i	−0.0179913	−	0.0393954i
$869$	1.33797e7	−	3.92863e6i	0.601030	−	0.176478i
$870$	−1.63874e6	+	3.58834e6i	−0.0734026	+	0.160729i
$871$	73925.8	−	514165.i	0.00330180	−	0.0229645i
$872$	1.81390e7	−	1.16573e7i	0.807836	−	0.519165i
$873$	−1.62465e6			−0.0721482
$874$	6.99580e6	+	465339.i	0.309784	+	0.0206059i
$875$	−2.43421e6			−0.107483
$876$	−4.45945e6	+	2.86591e6i	−0.196346	+	0.126184i
$877$	−4.92299e6	+	3.42402e7i	−0.216137	+	1.50327i	0.535975	+	0.844234i	$0.319944\pi$
$877$	−4.92299e6	+	3.42402e7i	−0.216137	+	1.50327i	−0.752112	+	0.659035i	$0.770965\pi$
$878$	−1.65695e6	+	3.62821e6i	−0.0725392	+	0.158839i
$879$	8.25933e6	−	2.42516e6i	0.360556	−	0.105869i
$880$	838494.	+	1.83605e6i	0.0365001	+	0.0799240i
$881$	−2.54971e7	−	2.94253e7i	−1.10676	−	1.27726i	−0.957490	−	0.288467i	$-0.906855\pi$
$881$	−2.54971e7	−	2.94253e7i	−1.10676	−	1.27726i	−0.149266	−	0.988797i	$-0.547691\pi$
$882$	−891139.	−	6.19801e6i	−0.0385722	−	0.268275i
$883$	−1.43215e7	−	4.20517e6i	−0.618140	−	0.181502i	−0.0423538	−	0.999103i	$-0.513486\pi$
$883$	−1.43215e7	−	4.20517e6i	−0.618140	−	0.181502i	−0.575786	+	0.817600i	$0.695304\pi$
$884$	218484.	−	252144.i	0.00940349	−	0.0108522i
$885$	2.89162e6	+	1.85833e6i	0.124103	+	0.0797562i
$886$	1.63049e7	+	1.04785e7i	0.697806	+	0.448453i
$887$	−1.38692e6	+	1.60059e6i	−0.0591890	+	0.0683078i	−0.784572	−	0.620038i	$-0.787117\pi$
$887$	−1.38692e6	+	1.60059e6i	−0.0591890	+	0.0683078i	0.725383	+	0.688346i	$0.241663\pi$
$888$	8.71033e6	+	2.55758e6i	0.370683	+	0.108842i
$889$	436525.	+	3.03610e6i	0.0185249	+	0.128843i
$890$	−3.49343e6	−	4.03163e6i	−0.147835	−	0.170610i
$891$	508267.	+	1.11295e6i	0.0214485	+	0.0469657i
$892$	6.57468e6	−	1.93050e6i	0.276670	−	0.0812378i
$893$	−1.55510e6	+	3.40519e6i	−0.0652572	+	0.142893i
$894$	322997.	−	2.24649e6i	0.0135162	−	0.0940071i
$895$	5.84692e6	−	3.75759e6i	0.243989	−	0.156802i
$896$	1.62676e6			0.0676946
$897$	−333195.	+	184099.i	−0.0138267	+	0.00763958i
$898$	−2.26206e7			−0.936082
$899$	−1.96056e7	+	1.25997e7i	−0.809059	+	0.519950i
$900$	−304269.	+	2.11624e6i	−0.0125214	+	0.0870880i
$901$	2.65649e6	−	5.81690e6i	0.109017	−	0.238715i
$902$	−1.42349e7	+	4.17974e6i	−0.582556	+	0.171054i
$903$	−429270.	−	939971.i	−0.0175191	−	0.0383615i
$904$	−8.01337e6	−	9.24793e6i	−0.326133	−	0.376377i
$905$	2.01470e6	+	1.40125e7i	0.0817689	+	0.568715i
$906$	−1.82551e6	−	536019.i	−0.0738864	−	0.0216950i
$907$	7.60927e6	−	8.78156e6i	0.307132	−	0.354449i	−0.581110	−	0.813825i	$-0.697381\pi$
$907$	7.60927e6	−	8.78156e6i	0.307132	−	0.354449i	0.888242	+	0.459376i	$0.151927\pi$
$908$	−3.32352e6	−	2.13589e6i	−0.133778	−	0.0859736i
$909$	−158231.	−	101689.i	−0.00635157	−	0.00408190i
$910$	21232.2	−	24503.3i	0.000849948	−	0.000980892i
$911$	−3.01551e7	−	8.85434e6i	−1.20383	−	0.353476i	−0.382514	−	0.923950i	$-0.624941\pi$
$911$	−3.01551e7	−	8.85434e6i	−1.20383	−	0.353476i	−0.821316	+	0.570474i	$0.806760\pi$
$912$	475492.	+	3.30712e6i	0.0189303	+	0.131663i
$913$	−2.83916e6	−	3.27656e6i	−0.112723	−	0.130089i
$914$	455234.	+	996823.i	0.0180247	+	0.0394687i
$915$	490260.	−	143953.i	0.0193586	−	0.00568420i
$916$	4.97051e6	−	1.08839e7i	0.195732	−	0.428593i
$917$	−381271.	+	2.65180e6i	−0.0149731	+	0.104140i
$918$	6.28958e6	−	4.04207e6i	0.246329	−	0.158306i
$919$	−3.34875e7			−1.30796			−0.653979	−	0.756512i	$-0.726902\pi$
$919$	−3.34875e7			−1.30796			−0.653979	+	0.756512i	$0.726902\pi$
$920$	8.24001e6	−	1.83554e6i	0.320965	−	0.0714979i
$921$	4.84069e6			0.188043
$922$	3.87053e6	−	2.48744e6i	0.149949	−	0.0963662i
$923$	−104541.	+	727102.i	−0.00403910	+	0.0280925i
$924$	−156449.	+	342575.i	−0.00602827	+	0.0132001i
$925$	1.39637e7	−	4.10012e6i	0.536595	−	0.157558i
$926$	1.57843e7	+	3.45628e7i	0.604919	+	1.32459i
$927$	3.29239e6	+	3.79962e6i	0.125838	+	0.145225i
$928$	2.51369e6	+	1.74831e7i	0.0958169	+	0.666421i
$929$	4.17870e7	+	1.22698e7i	1.58856	+	0.466442i	0.952332	−	0.305063i	$-0.0986776\pi$
$929$	4.17870e7	+	1.22698e7i	1.58856	+	0.466442i	0.636223	+	0.771505i	$0.280496\pi$
$930$	−2.03454e6	+	2.34799e6i	−0.0771363	+	0.0890201i
$931$	7.91653e6	+	5.08764e6i	0.299337	+	0.192372i
$932$	6.16013e6	+	3.95887e6i	0.232300	+	0.149290i
$933$	1.34532e7	−	1.55258e7i	0.505965	−	0.583915i
$934$	−1.18075e7	−	3.46698e6i	−0.442883	−	0.130042i
$935$	966011.	+	6.71876e6i	0.0361371	+	0.251339i
$936$	−174014.	−	200822.i	−0.00649223	−	0.00749243i
$937$	1.54395e7	+	3.38078e7i	0.574493	+	1.25797i	0.944370	+	0.328884i	$0.106673\pi$
$937$	1.54395e7	+	3.38078e7i	0.574493	+	1.25797i	−0.369877	+	0.929081i	$0.620600\pi$
$938$	3.43789e6	−	1.00946e6i	0.127581	−	0.0374611i
$939$	3.15168e6	−	6.90121e6i	0.116648	−	0.255424i
$940$	−144413.	+	1.00441e6i	−0.00533073	+	0.0370760i
$941$	−1.66906e7	+	1.07264e7i	−0.614467	+	0.394894i	−0.810530	−	0.585697i	$-0.800821\pi$
$941$	−1.66906e7	+	1.07264e7i	−0.614467	+	0.394894i	0.196063	+	0.980591i	$0.437184\pi$
$942$	1.85435e7			0.680871
$943$	3.23231e6	+	4.22362e7i	0.118368	+	1.54670i
$944$	−1.44551e7			−0.527948
$945$	−250307.	+	160863.i	−0.00911787	+	0.00585970i
$946$	−601563.	+	4.18397e6i	−0.0218551	+	0.152006i
$947$	4.51447e6	−	9.88532e6i	0.163581	−	0.358192i	−0.810036	−	0.586380i	$-0.800553\pi$
$947$	4.51447e6	−	9.88532e6i	0.163581	−	0.358192i	0.973617	+	0.228188i	$0.0732800\pi$
$948$	6.00347e6	−	1.76278e6i	0.216961	−	0.0637054i
$949$	−438762.	−	960756.i	−0.0158148	−	0.0346296i
$950$	5.13800e6	+	5.92957e6i	0.184708	+	0.213164i
$951$	1.14422e6	+	7.95825e6i	0.0410260	+	0.285342i
$952$	9.80809e6	+	2.87991e6i	0.350745	+	0.102988i
$953$	3.39512e7	−	3.91818e7i	1.21094	−	1.39750i	0.317539	−	0.948245i	$-0.397144\pi$
$953$	3.39512e7	−	3.91818e7i	1.21094	−	1.39750i	0.893403	−	0.449256i	$-0.148311\pi$
$954$	−964604.	−	619914.i	−0.0343146	−	0.0220526i
$955$	−1.28075e7	−	8.23086e6i	−0.454417	−	0.292036i
$956$	−184109.	+	212473.i	−0.00651522	+	0.00751897i
$957$	8.76002e6	+	2.57217e6i	0.309190	+	0.0907864i
$958$	−5.16129e6	−	3.58975e7i	−0.181695	−	1.26372i
$959$	−691363.	−	797876.i	−0.0242750	−	0.0280149i
$960$	2.27311e6	+	4.97741e6i	0.0796053	+	0.174311i
$961$	9.85846e6	−	2.89471e6i	0.344350	−	0.101110i
$962$	−169161.	+	370411.i	−0.00589336	+	0.0129047i
$963$	−1.14785e6	+	7.98349e6i	−0.0398860	+	0.277413i
$964$	8.80174e6	−	5.65653e6i	0.305053	−	0.196046i
$965$	−2.30135e6			−0.0795545
$966$	−2.10984e6	−	1.56307e6i	−0.0727457	−	0.0538935i
$967$	−4.53370e7			−1.55914			−0.779572	−	0.626313i	$-0.784563\pi$
$967$	−4.53370e7			−1.55914			−0.779572	+	0.626313i	$0.784563\pi$
$968$	−2.09028e7	+	1.34334e7i	−0.716995	+	0.460785i
$969$	−1.59903e6	+	1.11215e7i	−0.0547077	+	0.380500i
$970$	−671370.	+	1.47009e6i	−0.0229104	+	0.0501668i
$971$	3.42613e7	−	1.00600e7i	1.16615	−	0.342414i	0.359333	−	0.933209i	$-0.383004\pi$
$971$	3.42613e7	−	1.00600e7i	1.16615	−	0.342414i	0.806821	+	0.590796i	$0.201186\pi$
$972$	228060.	+	499381.i	0.00774253	+	0.0169538i
$973$	−1.31759e6	−	1.52058e6i	−0.0446167	−	0.0514904i
$974$	3.67888e6	+	2.55872e7i	0.124256	+	0.864220i
$975$	−408736.	−	120016.i	−0.0137699	−	0.00404321i
$976$	−1.40715e6	+	1.62394e6i	−0.0472842	+	0.0545689i
$977$	−3.84914e7	−	2.47369e7i	−1.29011	−	0.829104i	−0.298012	−	0.954562i	$-0.596324\pi$
$977$	−3.84914e7	−	2.47369e7i	−1.29011	−	0.829104i	−0.992099	+	0.125458i	$0.959960\pi$
$978$	1.65445e7	+	1.06325e7i	0.553102	+	0.355457i
$979$	−8.08514e6	+	9.33075e6i	−0.269607	+	0.311143i
$980$	2.44754e6	+	718664.i	0.0814077	+	0.0239035i
$981$	−1.26317e6	−	8.78555e6i	−0.0419073	−	0.291472i
$982$	−1.56069e7	−	1.80113e7i	−0.516460	−	0.596027i
$983$	1.92659e7	+	4.21864e7i	0.635924	+	1.39248i	0.903351	+	0.428902i	$0.141099\pi$
$983$	1.92659e7	+	4.21864e7i	0.635924	+	1.39248i	−0.267427	+	0.963578i	$0.586173\pi$
$984$	−2.83712e7	+	8.33053e6i	−0.934092	+	0.274274i
$985$	−6.56219e6	+	1.43692e7i	−0.215505	+	0.471891i
$986$	7.93960e6	−	5.52211e7i	0.260080	−	1.80889i
$987$	1.17940e6	−	757955.i	0.0385362	−	0.0247657i
$988$	89904.1			0.00293013
$989$	1.13289e7	+	4.16131e6i	0.368297	+	0.135282i
$990$	1.21711e6			0.0394676
$991$	−2.28984e7	+	1.47159e7i	−0.740664	+	0.475996i	−0.855770	−	0.517357i	$-0.826916\pi$
$991$	−2.28984e7	+	1.47159e7i	−0.740664	+	0.475996i	0.115105	+	0.993353i	$0.463280\pi$
$992$	−1.97971e6	+	1.37692e7i	−0.0638738	+	0.444252i
$993$	−4.30165e6	+	9.41929e6i	−0.138440	+	0.303141i
$994$	−4.86166e6	+	1.42751e6i	−0.156070	+	0.0458262i
$995$	2.81493e6	+	6.16384e6i	0.0901385	+	0.197376i
$996$	−1.27393e6	−	1.47019e6i	−0.0406909	−	0.0469598i
$997$	−467564.	−	3.25198e6i	−0.0148972	−	0.103612i	0.981016	−	0.193926i	$-0.0621221\pi$
$997$	−467564.	−	3.25198e6i	−0.0148972	−	0.103612i	−0.995913	+	0.0903138i	$0.971213\pi$
$998$	3.29496e7	+	9.67489e6i	1.04719	+	0.307482i
$999$	2.44718e6	−	2.82420e6i	0.0775805	−	0.0895327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.6.e.a.58.4	yes	100
23.2	even	11	inner	69.6.e.a.25.4	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.6.e.a.25.4	✓	100	23.2	even	11	inner
69.6.e.a.58.4	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)

\(f(q)\)	\(=\)	\(q+(-4.00836 + 2.57601i) q^{2} +(1.28083 - 8.90839i) q^{3} +(-3.86221 + 8.45706i) q^{4} +(16.2258 - 4.76432i) q^{5} +(17.8141 + 39.0075i) q^{6} +(15.8053 + 18.2403i) q^{7} +(-28.0034 - 194.768i) q^{8} +(-77.7189 - 22.8203i) q^{9} +O(q^{10})\)	\(q+(-4.00836 + 2.57601i) q^{2} +(1.28083 - 8.90839i) q^{3} +(-3.86221 + 8.45706i) q^{4} +(16.2258 - 4.76432i) q^{5} +(17.8141 + 39.0075i) q^{6} +(15.8053 + 18.2403i) q^{7} +(-28.0034 - 194.768i) q^{8} +(-77.7189 - 22.8203i) q^{9} +(-52.7658 + 60.8950i) q^{10} +(156.880 + 100.820i) q^{11} +(70.3920 + 45.2382i) q^{12} +(-10.9179 + 12.5999i) q^{13} +(-110.341 - 32.3989i) q^{14} +(-21.6599 - 150.648i) q^{15} +(419.144 + 483.718i) q^{16} +(894.150 + 1957.91i) q^{17} +(370.311 - 108.733i) q^{18} +(-240.946 + 527.597i) q^{19} +(-22.3753 + 155.623i) q^{20} +(182.736 - 117.437i) q^{21} -888.544 q^{22} +(-526.923 + 2481.67i) q^{23} -1770.94 q^{24} +(-2388.34 + 1534.89i) q^{25} +(11.3052 - 78.6294i) q^{26} +(-302.838 + 663.122i) q^{27} +(-215.303 + 63.2186i) q^{28} +(2259.77 + 4948.20i) q^{29} +(474.892 + 548.055i) q^{30} +(609.707 + 4240.61i) q^{31} +(3115.46 + 914.782i) q^{32} +(1099.08 - 1268.41i) q^{33} +(-8627.69 - 5544.68i) q^{34} +(343.357 + 220.662i) q^{35} +(493.160 - 569.137i) q^{36} +(-4918.49 - 1444.20i) q^{37} +(-393.302 - 2735.48i) q^{38} +(98.2608 + 113.399i) q^{39} +(-1382.31 - 3026.85i) q^{40} +(16020.4 - 4704.03i) q^{41} +(-429.950 + 941.460i) q^{42} +(677.021 - 4708.79i) q^{43} +(-1458.55 + 937.351i) q^{44} -1369.78 q^{45} +(-4280.73 - 11304.8i) q^{46} +6454.14 q^{47} +(4846.00 - 3114.33i) q^{48} +(2308.98 - 16059.3i) q^{49} +(5619.41 - 12304.8i) q^{50} +(18587.1 - 5457.67i) q^{51} +(-64.3909 - 140.997i) q^{52} +(-1945.57 - 2245.31i) q^{53} +(-494.330 - 3438.14i) q^{54} +(3025.84 + 888.467i) q^{55} +(3110.02 - 3589.16i) q^{56} +(4391.43 + 2822.20i) q^{57} +(-21804.6 - 14012.9i) q^{58} +(-14789.6 + 17068.1i) q^{59} +(1357.70 + 398.655i) q^{60} +(477.780 + 3323.03i) q^{61} +(-13367.8 - 15427.2i) q^{62} +(-812.122 - 1778.30i) q^{63} +(-34496.3 + 10129.0i) q^{64} +(-117.121 + 256.460i) q^{65} +(-1138.08 + 7915.50i) q^{66} +(-26211.0 + 16844.8i) q^{67} -20011.6 q^{68} +(21432.8 + 7872.65i) q^{69} -1944.72 q^{70} +(37066.0 - 23820.9i) q^{71} +(-2268.27 + 15776.2i) q^{72} +(-26317.2 + 57626.7i) q^{73} +(23435.3 - 6881.24i) q^{74} +(10614.4 + 23242.2i) q^{75} +(-3531.34 - 4075.38i) q^{76} +(640.537 + 4455.03i) q^{77} +(-685.982 - 201.422i) q^{78} +(48968.1 - 56512.2i) q^{79} +(9105.53 + 5851.77i) q^{80} +(5519.46 + 3547.14i) q^{81} +(-52098.0 + 60124.3i) q^{82} +(-22307.1 - 6549.95i) q^{83} +(287.409 + 1998.97i) q^{84} +(23836.4 + 27508.7i) q^{85} +(9416.16 + 20618.5i) q^{86} +(46974.9 - 13793.1i) q^{87} +(15243.4 - 33378.4i) q^{88} +(-9422.13 + 65532.4i) q^{89} +(5490.55 - 3528.56i) q^{90} -402.386 q^{91} +(-18952.6 - 14041.0i) q^{92} +38557.9 q^{93} +(-25870.5 + 16625.9i) q^{94} +(-1395.89 + 9708.64i) q^{95} +(12139.6 - 26582.1i) q^{96} +(19245.0 - 5650.84i) q^{97} +(32113.9 + 70319.5i) q^{98} +(-9891.76 - 11415.7i) 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

Fields

Representations

Groups

Database

Properties

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