LMFDB - Embedded newform 82.6.f.b.45.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,6,Mod(23,82)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("82.23"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(82, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([9])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	82.f (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$13.1514732247$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			45.3
Character	$\chi$	$=$	82.45
Dual form			82.6.f.b.31.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.23607 - 2.35114i) q^{2} -13.3586i q^{3} +(4.94427 - 15.2169i) q^{4} +(-5.46557 + 16.8213i) q^{5} +(-31.4079 - 43.2292i) q^{6} +(93.7892 - 129.090i) q^{7} +(-19.7771 - 60.8676i) q^{8} +64.5487 q^{9} +(21.8623 + 67.2851i) q^{10} +(-207.622 + 67.4603i) q^{11} +(-203.276 - 66.0484i) q^{12} +(-646.588 - 889.951i) q^{13} -638.255i q^{14} +(224.708 + 73.0121i) q^{15} +(-207.108 - 150.473i) q^{16} +(-62.7849 + 20.4000i) q^{17} +(208.884 - 151.763i) q^{18} +(-361.673 + 497.800i) q^{19} +(228.945 + 166.338i) q^{20} +(-1724.45 - 1252.89i) q^{21} +(-513.269 + 706.454i) q^{22} +(-3667.21 + 2664.38i) q^{23} +(-813.104 + 264.194i) q^{24} +(2275.10 + 1652.95i) q^{25} +(-4184.80 - 1359.72i) q^{26} -4108.41i q^{27} +(-1500.63 - 2065.44i) q^{28} +(6841.07 + 2222.80i) q^{29} +(898.833 - 292.048i) q^{30} +(-3078.18 - 9473.67i) q^{31} -1024.00 q^{32} +(901.173 + 2773.53i) q^{33} +(-155.213 + 213.632i) q^{34} +(1658.84 + 2283.20i) q^{35} +(319.146 - 982.231i) q^{36} +(797.419 - 2454.20i) q^{37} +2461.26i q^{38} +(-11888.5 + 8637.48i) q^{39} +1131.96 q^{40} +(8219.07 - 6950.04i) q^{41} -8526.17 q^{42} +(14374.2 - 10443.5i) q^{43} +3492.90i q^{44} +(-352.795 + 1085.79i) q^{45} +(-5602.99 + 17244.2i) q^{46} +(3135.70 + 4315.92i) q^{47} +(-2010.10 + 2766.67i) q^{48} +(-2674.11 - 8230.06i) q^{49} +11248.7 q^{50} +(272.515 + 838.716i) q^{51} +(-16739.2 + 5438.90i) q^{52} +(17966.2 + 5837.58i) q^{53} +(-9659.45 - 13295.1i) q^{54} -3861.17i q^{55} +(-9712.27 - 3155.71i) q^{56} +(6649.90 + 4831.44i) q^{57} +(27364.3 - 8891.19i) q^{58} +(-16099.5 + 11697.0i) q^{59} +(2222.04 - 3058.37i) q^{60} +(22943.9 + 16669.7i) q^{61} +(-32235.1 - 23420.2i) q^{62} +(6053.97 - 8332.58i) q^{63} +(-3313.73 + 2407.57i) q^{64} +(18504.1 - 6012.34i) q^{65} +(9437.21 + 6856.54i) q^{66} +(66293.9 + 21540.2i) q^{67} +1056.25i q^{68} +(35592.3 + 48988.6i) q^{69} +(10736.3 + 3488.42i) q^{70} +(-24564.9 + 7981.61i) q^{71} +(-1276.59 - 3928.92i) q^{72} -44002.8 q^{73} +(-3189.68 - 9816.81i) q^{74} +(22081.1 - 30392.0i) q^{75} +(5786.77 + 7964.81i) q^{76} +(-10764.2 + 33128.9i) q^{77} +(-18164.0 + 55903.0i) q^{78} +27331.7i q^{79} +(3663.11 - 2661.41i) q^{80} -39197.1 q^{81} +(10256.9 - 41815.0i) q^{82} +105919. q^{83} +(-27591.3 + 20046.2i) q^{84} -1167.62i q^{85} +(21961.8 - 67591.6i) q^{86} +(29693.4 - 91386.9i) q^{87} +(8212.30 + 11303.3i) q^{88} +(12918.7 - 17781.0i) q^{89} +(1411.18 + 4343.17i) q^{90} -175527. q^{91} +(22412.0 + 68976.9i) q^{92} +(-126555. + 41120.1i) q^{93} +(20294.7 + 6594.14i) q^{94} +(-6396.89 - 8804.57i) q^{95} +13679.2i q^{96} +(51274.0 + 16659.9i) q^{97} +(-28003.6 - 20345.8i) q^{98} +(-13401.7 + 4354.48i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 160 q^{4} + 24 q^{5} - 100 q^{6} + 640 q^{8} - 4576 q^{9} - 96 q^{10} + 20 q^{11} + 400 q^{12} - 275 q^{13} + 1385 q^{15} - 2560 q^{16} - 105 q^{17} - 2476 q^{18} + 4720 q^{19} + 1424 q^{20}+ \cdots - 537690 q^{99}+O(q^{100}) $ 40 * q + 40 * q^2 - 160 * q^4 + 24 * q^5 - 100 * q^6 + 640 * q^8 - 4576 * q^9 - 96 * q^10 + 20 * q^11 + 400 * q^12 - 275 * q^13 + 1385 * q^15 - 2560 * q^16 - 105 * q^17 - 2476 * q^18 + 4720 * q^19 + 1424 * q^20 + 6961 * q^21 - 4140 * q^22 - 1019 * q^23 + 1600 * q^24 - 2006 * q^25 - 8620 * q^26 - 12525 * q^29 + 5540 * q^30 + 8900 * q^31 - 40960 * q^32 + 17684 * q^33 - 13100 * q^34 - 29955 * q^35 + 26704 * q^36 - 31651 * q^37 - 10104 * q^39 + 14464 * q^40 + 35044 * q^41 + 32776 * q^42 - 15615 * q^43 - 39955 * q^45 - 3224 * q^46 + 8330 * q^47 - 6400 * q^48 + 48406 * q^49 - 135016 * q^50 + 120325 * q^51 - 34480 * q^52 + 145425 * q^53 + 72200 * q^54 + 17600 * q^56 + 31992 * q^57 - 50100 * q^58 + 18978 * q^59 + 1680 * q^60 + 52673 * q^61 + 66140 * q^62 - 88455 * q^63 - 40960 * q^64 + 204480 * q^65 - 17556 * q^66 - 149205 * q^67 - 249735 * q^69 - 49100 * q^70 + 151175 * q^71 - 106816 * q^72 - 107670 * q^73 + 126604 * q^74 + 120180 * q^75 - 75520 * q^76 - 207367 * q^77 - 99284 * q^78 + 22784 * q^80 + 1167568 * q^81 + 84204 * q^82 - 281376 * q^83 + 111376 * q^84 - 131400 * q^86 - 141269 * q^87 + 66240 * q^88 - 277775 * q^89 + 159820 * q^90 - 518682 * q^91 + 12896 * q^92 - 172375 * q^93 + 16320 * q^94 + 149585 * q^95 + 330875 * q^97 - 171004 * q^98 - 537690 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	3.23607	−	2.35114i	0.572061	−	0.415627i
$2$	3.23607	−	2.35114i	0.572061	−	0.415627i
$3$		−	13.3586i		−	0.856952i	−0.903553	−	0.428476i	$-0.859051\pi$
$3$		−	13.3586i		−	0.856952i	0.903553	−	0.428476i	$-0.140949\pi$
$4$	4.94427	−	15.2169i	0.154508	−	0.475528i
$5$	−5.46557	+	16.8213i	−0.0977710	+	0.300908i	−0.987966	−	0.154672i	$-0.950568\pi$
$5$	−5.46557	+	16.8213i	−0.0977710	+	0.300908i	0.890195	+	0.455580i	$0.150568\pi$
$6$	−31.4079	−	43.2292i	−0.356173	−	0.490229i
$7$	93.7892	−	129.090i	0.723449	−	0.995742i	−0.275953	−	0.961171i	$-0.588994\pi$
$7$	93.7892	−	129.090i	0.723449	−	0.995742i	0.999402	−	0.0345709i	$-0.0110065\pi$
$8$	−19.7771	−	60.8676i	−0.109254	−	0.336249i
$9$	64.5487			0.265632
$10$	21.8623	+	67.2851i	0.0691345	+	0.212774i
$11$	−207.622	+	67.4603i	−0.517358	+	0.168100i	−0.556046	−	0.831152i	$-0.687682\pi$
$11$	−207.622	+	67.4603i	−0.517358	+	0.168100i	0.0386882	+	0.999251i	$0.487682\pi$
$12$	−203.276	−	66.0484i	−0.407505	−	0.132406i
$13$	−646.588	−	889.951i	−1.06113	−	1.46052i	−0.878743	−	0.477295i	$-0.841617\pi$
$13$	−646.588	−	889.951i	−1.06113	−	1.46052i	−0.182388	−	0.983227i	$-0.558383\pi$
$14$		−	638.255i		−	0.870310i
$15$	224.708	+	73.0121i	0.257864	+	0.0837851i
$16$	−207.108	−	150.473i	−0.202254	−	0.146946i
$17$	−62.7849	+	20.4000i	−0.0526905	+	0.0171202i	−0.335244	−	0.942131i	$-0.608819\pi$
$17$	−62.7849	+	20.4000i	−0.0526905	+	0.0171202i	0.282553	+	0.959252i	$0.408819\pi$
$18$	208.884	−	151.763i	0.151958	−	0.110404i
$19$	−361.673	+	497.800i	−0.229844	+	0.316352i	−0.908325	−	0.418265i	$-0.862638\pi$
$19$	−361.673	+	497.800i	−0.229844	+	0.316352i	0.678482	+	0.734617i	$0.262638\pi$
$20$	228.945	+	166.338i	0.127984	+	0.0929857i
$21$	−1724.45	−	1252.89i	−0.853304	−	0.619961i
$22$	−513.269	+	706.454i	−0.226094	+	0.311191i
$23$	−3667.21	+	2664.38i	−1.44549	+	1.05021i	−0.458633	+	0.888626i	$0.651661\pi$
$23$	−3667.21	+	2664.38i	−1.44549	+	1.05021i	−0.986859	+	0.161585i	$0.948339\pi$
$24$	−813.104	+	264.194i	−0.288150	+	0.0936255i
$25$	2275.10	+	1652.95i	0.728030	+	0.528945i
$26$	−4184.80	−	1359.72i	−1.21406	−	0.394473i
$27$		−	4108.41i		−	1.08459i
$28$	−1500.63	−	2065.44i	−0.361724	−	0.497871i
$29$	6841.07	+	2222.80i	1.51053	+	0.490800i	0.943068	−	0.332600i	$-0.107926\pi$
$29$	6841.07	+	2222.80i	1.51053	+	0.490800i	0.567460	+	0.823401i	$0.307926\pi$
$30$	898.833	−	292.048i	0.182337	−	0.0592450i
$31$	−3078.18	−	9473.67i	−0.575294	−	1.77057i	−0.635176	−	0.772367i	$-0.719072\pi$
$31$	−3078.18	−	9473.67i	−0.575294	−	1.77057i	0.0598820	−	0.998205i	$-0.480928\pi$
$32$	−1024.00			−0.176777
$33$	901.173	+	2773.53i	0.144053	+	0.443351i
$34$	−155.213	+	213.632i	−0.0230266	+	0.0316934i
$35$	1658.84	+	2283.20i	0.228895	+	0.315046i
$36$	319.146	−	982.231i	0.0410425	−	0.126316i
$37$	797.419	−	2454.20i	0.0957596	−	0.294718i	−0.891691	−	0.452644i	$-0.850481\pi$
$37$	797.419	−	2454.20i	0.0957596	−	0.294718i	0.987451	+	0.157926i	$0.0504809\pi$
$38$			2461.26i			0.276502i
$39$	−11888.5	+	8637.48i	−1.25160	+	0.909339i
$40$	1131.96			0.111862
$41$	8219.07	−	6950.04i	0.763595	−	0.645696i
$41$	8219.07	−	6950.04i	0.763595	−	0.645696i
$42$	−8526.17			−0.745815
$43$	14374.2	−	10443.5i	1.18553	−	0.861339i	0.192746	−	0.981249i	$-0.438261\pi$
$43$	14374.2	−	10443.5i	1.18553	−	0.861339i	0.992785	+	0.119910i	$0.0382605\pi$
$44$			3492.90i			0.271991i
$45$	−352.795	+	1085.79i	−0.0259712	+	0.0799310i
$46$	−5602.99	+	17244.2i	−0.390414	+	1.20157i
$47$	3135.70	+	4315.92i	0.207057	+	0.284989i	0.899898	−	0.436101i	$-0.143641\pi$
$47$	3135.70	+	4315.92i	0.207057	+	0.284989i	−0.692841	+	0.721091i	$0.743641\pi$
$48$	−2010.10	+	2766.67i	−0.125926	+	0.173322i
$49$	−2674.11	−	8230.06i	−0.159107	−	0.489680i
$50$	11248.7			0.636322
$51$	272.515	+	838.716i	0.0146712	+	0.0451533i
$52$	−16739.2	+	5438.90i	−0.858473	+	0.278935i
$53$	17966.2	+	5837.58i	0.878551	+	0.285459i	0.713356	−	0.700802i	$-0.247174\pi$
$53$	17966.2	+	5837.58i	0.878551	+	0.285459i	0.165196	+	0.986261i	$0.447174\pi$
$54$	−9659.45	−	13295.1i	−0.450784	−	0.620450i
$55$		−	3861.17i		−	0.172112i
$56$	−9712.27	−	3155.71i	−0.413857	−	0.134470i
$57$	6649.90	+	4831.44i	0.271099	+	0.196965i
$58$	27364.3	−	8891.19i	1.06810	−	0.347048i
$59$	−16099.5	+	11697.0i	−0.602119	+	0.437465i	−0.846630	−	0.532182i	$-0.821372\pi$
$59$	−16099.5	+	11697.0i	−0.602119	+	0.437465i	0.244512	+	0.969646i	$0.421372\pi$
$60$	2222.04	−	3058.37i	0.0796844	−	0.109676i
$61$	22943.9	+	16669.7i	0.789482	+	0.573592i	0.907810	−	0.419382i	$-0.137753\pi$
$61$	22943.9	+	16669.7i	0.789482	+	0.573592i	−0.118328	+	0.992975i	$0.537753\pi$
$62$	−32235.1	−	23420.2i	−1.06500	−	0.773769i
$63$	6053.97	−	8332.58i	0.192172	−	0.264501i
$64$	−3313.73	+	2407.57i	−0.101127	+	0.0734732i
$65$	18504.1	−	6012.34i	0.543231	−	0.176506i
$66$	9437.21	+	6856.54i	0.266676	+	0.193751i
$67$	66293.9	+	21540.2i	1.80421	+	0.586223i	0.999967	−	0.00808083i	$-0.00257223\pi$
$67$	66293.9	+	21540.2i	1.80421	+	0.586223i	0.804241	+	0.594304i	$0.202572\pi$
$68$			1056.25i			0.0277011i
$69$	35592.3	+	48988.6i	0.899981	+	1.23872i
$70$	10736.3	+	3488.42i	0.261884	+	0.0850911i
$71$	−24564.9	+	7981.61i	−0.578320	+	0.187908i	−0.583548	−	0.812079i	$-0.698336\pi$
$71$	−24564.9	+	7981.61i	−0.578320	+	0.187908i	0.00522767	+	0.999986i	$0.498336\pi$
$72$	−1276.59	−	3928.92i	−0.0290214	−	0.0893187i
$73$	−44002.8			−0.966437			−0.483218	−	0.875500i	$-0.660532\pi$
$73$	−44002.8			−0.966437			−0.483218	+	0.875500i	$0.660532\pi$
$74$	−3189.68	−	9816.81i	−0.0677122	−	0.208397i
$75$	22081.1	−	30392.0i	0.453281	−	0.623887i
$76$	5786.77	+	7964.81i	0.114922	+	0.158176i
$77$	−10764.2	+	33128.9i	−0.206898	+	0.636766i
$78$	−18164.0	+	55903.0i	−0.338045	+	1.04040i
$79$			27331.7i			0.492718i	0.969179	+	0.246359i	$0.0792342\pi$
$79$			27331.7i			0.492718i	−0.969179	+	0.246359i	$0.920766\pi$
$80$	3663.11	−	2661.41i	0.0639920	−	0.0464929i
$81$	−39197.1			−0.663807
$82$	10256.9	−	41815.0i	0.168455	−	0.686748i
$83$	105919.			1.68764			0.843818	−	0.536629i	$-0.180302\pi$
$83$	105919.			1.68764			0.843818	+	0.536629i	$0.180302\pi$
$84$	−27591.3	+	20046.2i	−0.426652	+	0.309981i
$85$		−	1167.62i		−	0.0175289i
$86$	21961.8	−	67591.6i	0.320201	−	0.985477i
$87$	29693.4	−	91386.9i	0.420593	−	1.29445i
$88$	8212.30	+	11303.3i	0.113047	+	0.155596i
$89$	12918.7	−	17781.0i	0.172879	−	0.237948i	−0.713781	−	0.700369i	$-0.753019\pi$
$89$	12918.7	−	17781.0i	0.172879	−	0.237948i	0.886661	+	0.462421i	$0.153019\pi$
$90$	1411.18	+	4343.17i	0.0183644	+	0.0565197i
$91$	−175527.			−2.22198
$92$	22412.0	+	68976.9i	0.276064	+	0.849639i
$93$	−126555.	+	41120.1i	−1.51730	+	0.493000i
$94$	20294.7	+	6594.14i	0.236899	+	0.0769730i
$95$	−6396.89	−	8804.57i	−0.0727210	−	0.100092i
$96$			13679.2i			0.151489i
$97$	51274.0	+	16659.9i	0.553309	+	0.179781i	0.572308	−	0.820039i	$-0.306048\pi$
$97$	51274.0	+	16659.9i	0.553309	+	0.179781i	−0.0189994	+	0.999819i	$0.506048\pi$
$98$	−28003.6	−	20345.8i	−0.294543	−	0.213998i
$99$	−13401.7	+	4354.48i	−0.137427	+	0.0446527i
$100$	36401.5	−	26447.3i	0.364015	−	0.264473i
$101$	50668.7	−	69739.5i	0.494239	−	0.680261i	−0.486924	−	0.873444i	$-0.661881\pi$
$101$	50668.7	−	69739.5i	0.494239	−	0.680261i	0.981163	+	0.193183i	$0.0618811\pi$
$102$	2853.82	+	2073.42i	0.0271597	+	0.0197327i
$103$	−78386.1	−	56950.9i	−0.728025	−	0.528941i	0.160913	−	0.986969i	$-0.448556\pi$
$103$	−78386.1	−	56950.9i	−0.728025	−	0.528941i	−0.888938	+	0.458028i	$0.848556\pi$
$104$	−41381.6	+	56956.9i	−0.375166	+	0.516372i
$105$	30500.3	−	22159.8i	0.269980	−	0.196152i
$106$	71864.9	−	23350.3i	0.621230	−	0.201850i
$107$	−157001.	−	114068.i	−1.32569	−	0.963173i	−0.999842	−	0.0177520i	$-0.994349\pi$
$107$	−157001.	−	114068.i	−1.32569	−	0.963173i	−0.325851	−	0.945421i	$-0.605651\pi$
$108$	−62517.3	−	20313.1i	−0.515752	−	0.167578i
$109$			158765.i			1.27993i	0.768402	+	0.639967i	$0.221052\pi$
$109$			158765.i			1.27993i	−0.768402	+	0.639967i	$0.778948\pi$
$110$	−9078.15	−	12495.0i	−0.0715345	−	0.0984589i
$111$	−32784.6	−	10652.4i	−0.252559	−	0.0820614i
$112$	−38849.1	+	12622.8i	−0.292641	+	0.0950849i
$113$	−31800.8	−	97872.7i	−0.234283	−	0.721050i	−0.997216	−	0.0745717i	$-0.976241\pi$
$113$	−31800.8	−	97872.7i	−0.234283	−	0.721050i	0.762932	−	0.646478i	$-0.223759\pi$
$114$	32878.9			0.236949
$115$	−24774.9	−	76249.4i	−0.174690	−	0.537641i
$116$	67648.2	−	93109.8i	0.466779	−	0.642466i
$117$	−41736.4	−	57445.2i	−0.281871	−	0.387962i
$118$	−24597.8	+	75704.3i	−0.162627	+	0.500513i
$119$	−3255.11	+	10018.2i	−0.0210716	+	0.0648518i
$120$		−	15121.4i		−	0.0958604i
$121$	−91737.2	+	66651.0i	−0.569616	+	0.413850i
$122$	113441.			0.690033
$123$	−92842.6	−	109795.i	−0.553331	−	0.654364i
$124$	−159379.			−0.930845
$125$	−84955.2	+	61723.6i	−0.486312	+	0.353326i
$126$		−	41198.5i		−	0.231183i
$127$	47787.3	−	147074.i	0.262908	−	0.809146i	−0.729261	−	0.684236i	$-0.760136\pi$
$127$	47787.3	−	147074.i	0.262908	−	0.809146i	0.992168	−	0.124910i	$-0.0398642\pi$
$128$	−5062.93	+	15582.1i	−0.0273135	+	0.0840623i
$129$	−139510.	−	192019.i	−0.738126	−	1.01594i
$130$	45744.6	−	62962.1i	0.237401	−	0.326754i
$131$	79753.4	+	245456.i	0.406042	+	1.24967i	0.920022	+	0.391867i	$0.128171\pi$
$131$	79753.4	+	245456.i	0.406042	+	1.24967i	−0.513980	+	0.857802i	$0.671829\pi$
$132$	46660.1			0.233083
$133$	30339.9	+	93376.6i	0.148725	+	0.457730i
$134$	265176.	−	86160.8i	1.27577	−	0.414522i
$135$	69108.7	+	22454.8i	0.326361	+	0.106041i
$136$	2483.40	+	3418.11i	0.0115133	+	0.0158467i
$137$		−	57848.5i		−	0.263324i	−0.991295	−	0.131662i	$-0.957969\pi$
$137$		−	57848.5i		−	0.263324i	0.991295	−	0.131662i	$-0.0420314\pi$
$138$	230358.	+	74847.9i	1.02969	+	0.334566i
$139$	160262.	+	116437.i	0.703547	+	0.511157i	0.881086	−	0.472957i	$-0.156813\pi$
$139$	160262.	+	116437.i	0.703547	+	0.511157i	−0.177538	+	0.984114i	$0.556813\pi$
$140$	42945.1	−	13953.7i	0.185180	−	0.0601685i
$141$	57654.5	−	41888.4i	0.244222	−	0.177438i
$142$	−60727.7	+	83584.5i	−0.252735	+	0.347860i
$143$	194282.	+	141154.i	0.794497	+	0.577236i
$144$	−13368.6	−	9712.84i	−0.0537253	−	0.0390337i
$145$	−74780.6	+	102927.i	−0.295372	+	0.406544i
$146$	−142396.	+	103457.i	−0.552861	+	0.401677i
$147$	−109942.	+	35722.2i	−0.419633	+	0.136347i
$148$	−33402.7	−	24268.5i	−0.125351	−	0.0910728i
$149$	−30714.4	−	9979.71i	−0.113338	−	0.0368258i	0.251799	−	0.967780i	$-0.418978\pi$
$149$	−30714.4	−	9979.71i	−0.113338	−	0.0368258i	−0.365137	+	0.930954i	$0.618978\pi$
$150$		−	150266.i		−	0.545298i
$151$	−34327.8	−	47248.2i	−0.122519	−	0.168633i	0.743352	−	0.668901i	$-0.233235\pi$
$151$	−34327.8	−	47248.2i	−0.122519	−	0.168633i	−0.865871	+	0.500268i	$0.833235\pi$
$152$	37452.8	+	12169.1i	0.131485	+	0.0427219i
$153$	−4052.68	+	1316.80i	−0.0139963	+	0.00454768i
$154$	43056.9	+	132516.i	0.146299	+	0.450262i
$155$	176183.			0.589027
$156$	72655.9	+	223612.i	0.239034	+	0.735670i
$157$	50245.7	−	69157.3i	0.162686	−	0.223918i	−0.719890	−	0.694089i	$-0.755808\pi$
$157$	50245.7	−	69157.3i	0.162686	−	0.223918i	0.882576	+	0.470171i	$0.155808\pi$
$158$	64260.6	+	88447.1i	0.204787	+	0.281865i
$159$	77981.7	−	240003.i	0.244625	−	0.752877i
$160$	5596.74	−	17225.0i	0.0172836	−	0.0531936i
$161$			723289.i			2.19911i
$162$	−126845.	+	92158.0i	−0.379738	+	0.275896i
$163$	−63593.4			−0.187475			−0.0937374	−	0.995597i	$-0.529881\pi$
$163$	−63593.4			−0.187475			−0.0937374	+	0.995597i	$0.529881\pi$
$164$	−65120.9	−	159432.i	−0.189065	−	0.462876i
$165$	−51579.7			−0.147492
$166$	342761.	−	249031.i	0.965432	−	0.701427i
$167$			211125.i			0.585799i	0.956143	+	0.292899i	$0.0946201\pi$
$167$			211125.i			0.585799i	−0.956143	+	0.292899i	$0.905380\pi$
$168$	−42155.7	+	129742.i	−0.115235	+	0.354656i
$169$	−259202.	+	797742.i	−0.698107	+	2.14855i
$170$	−2745.24	−	3778.50i	−0.00728547	−	0.0100276i
$171$	−23345.5	+	32132.4i	−0.0610539	+	0.0840335i
$172$	−87847.4	−	270366.i	−0.226416	−	0.696838i
$173$	65755.1			0.167038			0.0835188	−	0.996506i	$-0.473384\pi$
$173$	65755.1			0.167038			0.0835188	+	0.996506i	$0.473384\pi$
$174$	−118774.	−	365547.i	−0.297404	−	0.915315i
$175$	426759.	−	138662.i	1.05339	−	0.342266i
$176$	53151.1	+	17269.8i	0.129339	+	0.0420249i
$177$	156255.	+	215066.i	0.374887	+	0.515987i
$178$		−	87914.3i		−	0.207974i
$179$	491764.	+	159784.i	1.14716	+	0.372735i	0.820073	−	0.572259i	$-0.193933\pi$
$179$	491764.	+	159784.i	1.14716	+	0.372735i	0.327088	+	0.944994i	$0.393933\pi$
$180$	14778.1	+	10736.9i	0.0339967	+	0.0247000i
$181$	109655.	−	35629.1i	0.248790	−	0.0808368i	−0.181967	−	0.983305i	$-0.558246\pi$
$181$	109655.	−	35629.1i	0.248790	−	0.0808368i	0.430757	+	0.902468i	$0.358246\pi$
$182$	−568016.	+	412688.i	−1.27111	+	0.923513i
$183$	222683.	−	306497.i	0.491541	−	0.676549i
$184$	234701.	+	170520.i	0.511058	+	0.371306i
$185$	36924.5	+	26827.2i	0.0793204	+	0.0576297i
$186$	−312860.	+	430615.i	−0.663083	+	0.912655i
$187$	11659.3	−	8470.98i	0.0243820	−	0.0177145i
$188$	81178.7	−	26376.6i	0.167513	−	0.0544281i
$189$	−530354.	−	385325.i	−1.07997	−	0.784643i
$190$	−41401.6	−	13452.2i	−0.0832018	−	0.0270339i
$191$		−	839963.i		−	1.66601i	−0.553268	−	0.833003i	$-0.686620\pi$
$191$		−	839963.i		−	1.66601i	0.553268	−	0.833003i	$-0.313380\pi$
$192$	32161.7	+	44266.7i	0.0629630	+	0.0866611i
$193$	74370.5	+	24164.4i	0.143717	+	0.0466964i	0.379992	−	0.924990i	$-0.375927\pi$
$193$	74370.5	+	24164.4i	0.143717	+	0.0466964i	−0.236275	+	0.971686i	$0.575927\pi$
$194$	205096.	−	66639.7i	0.391248	−	0.127124i
$195$	−80316.3	−	247188.i	−0.151258	−	0.465523i
$196$	−138457.			−0.257440
$197$	150072.	+	461873.i	0.275507	+	0.847924i	0.989085	+	0.147348i	$0.0470736\pi$
$197$	150072.	+	461873.i	0.275507	+	0.847924i	−0.713578	+	0.700576i	$0.752926\pi$
$198$	−33130.8	+	45600.7i	−0.0600578	+	0.0826625i
$199$	−294954.	−	405970.i	−0.527986	−	0.726710i	0.458836	−	0.888521i	$-0.348267\pi$
$199$	−294954.	−	405970.i	−0.527986	−	0.726710i	−0.986822	+	0.161811i	$0.948267\pi$
$200$	55616.6	−	171170.i	0.0983171	−	0.302589i
$201$	287746.	−	885592.i	0.502365	−	1.54612i
$202$		−	344811.i		−	0.594570i
$203$	928559.	−	674638.i	1.58150	−	1.14903i
$204$	14110.0			0.0237385
$205$	71986.8	+	176241.i	0.119638	+	0.292902i
$206$	−387562.			−0.636317
$207$	−236713.	+	171982.i	−0.383970	+	0.278970i
$208$			281610.i			0.451326i
$209$	41509.4	−	127753.i	0.0657325	−	0.202304i
$210$	46600.4	−	143421.i	0.0729190	−	0.224422i
$211$	−648829.	−	893036.i	−1.00328	−	1.38090i	−0.923289	−	0.384106i	$-0.874510\pi$
$211$	−648829.	−	893036.i	−1.00328	−	1.38090i	−0.0799950	−	0.996795i	$-0.525490\pi$
$212$	177660.	−	244528.i	0.271487	−	0.373670i
$213$	106623.	+	328151.i	0.161028	+	0.495593i
$214$	−776256.			−1.15870
$215$	97109.5	+	298872.i	0.143273	+	0.440950i
$216$	−250069.	+	81252.4i	−0.364692	+	0.118495i
$217$	−1.51165e6	−	491166.i	−2.17923	−	0.708075i
$218$	373278.	+	513773.i	0.531975	+	0.732201i
$219$			587815.i			0.828190i
$220$	−58755.0	−	19090.7i	−0.0818443	−	0.0265928i
$221$	58751.0	+	42685.1i	0.0809160	+	0.0587889i
$222$	−131139.	+	42609.5i	−0.178586	+	0.0580262i
$223$	354297.	−	257412.i	0.477095	−	0.346630i	−0.323105	−	0.946363i	$-0.604727\pi$
$223$	354297.	−	257412.i	0.477095	−	0.346630i	0.800200	+	0.599733i	$0.204727\pi$
$224$	−96040.2	+	132188.i	−0.127889	+	0.176024i
$225$	146854.	+	106696.i	0.193389	+	0.140505i
$226$	−333022.	−	241955.i	−0.433712	−	0.315110i
$227$	−60425.1	+	83168.0i	−0.0778310	+	0.107125i	−0.846157	−	0.532933i	$-0.821090\pi$
$227$	−60425.1	+	83168.0i	−0.0778310	+	0.107125i	0.768326	+	0.640058i	$0.221090\pi$
$228$	106398.	−	77303.0i	0.135550	−	0.0984825i
$229$	−536058.	+	174176.i	−0.675496	+	0.219482i	−0.626622	−	0.779323i	$-0.715563\pi$
$229$	−536058.	+	174176.i	−0.675496	+	0.219482i	−0.0488735	+	0.998805i	$0.515563\pi$
$230$	−259447.	−	188499.i	−0.323391	−	0.234958i
$231$	442554.	+	143795.i	0.545678	+	0.177302i
$232$		−	460360.i		−	0.561536i
$233$	544279.	+	749136.i	0.656798	+	0.904005i	0.999370	−	0.0354865i	$-0.0112981\pi$
$233$	544279.	+	749136.i	0.656798	+	0.904005i	−0.342572	+	0.939492i	$0.611298\pi$
$234$	−270124.	−	87768.5i	−0.322495	−	0.104785i
$235$	−89737.7	+	29157.5i	−0.106000	+	0.0344414i
$236$	98391.3	+	302817.i	0.114994	+	0.353916i
$237$	365112.			0.422236
$238$	13020.4	+	40072.8i	0.0148999	+	0.0458571i
$239$	−612638.	+	843224.i	−0.693760	+	0.954878i	0.306236	+	0.951956i	$0.400930\pi$
$239$	−612638.	+	843224.i	−0.693760	+	0.954878i	−0.999996	+	0.00292257i	$0.999070\pi$
$240$	−35552.6	−	48933.9i	−0.0398422	−	0.0548381i
$241$	−525575.	+	1.61755e6i	−0.582898	+	1.79397i	0.0246567	+	0.999696i	$0.492151\pi$
$241$	−525575.	+	1.61755e6i	−0.582898	+	1.79397i	−0.607554	+	0.794278i	$0.707849\pi$
$242$	−140162.	+	431374.i	−0.153848	+	0.473495i
$243$		−	474726.i		−	0.515736i
$244$	367102.	−	266715.i	0.394741	−	0.286796i
$245$	153056.			0.162905
$246$	−558589.	−	137018.i	−0.588511	−	0.144358i
$247$	676872.			0.705934
$248$	−515762.	+	374723.i	−0.532501	+	0.386884i
$249$		−	1.41493e6i		−	1.44622i
$250$	−129800.	+	399483.i	−0.131348	+	0.404249i
$251$	−178818.	+	550344.i	−0.179154	+	0.551379i	−0.999799	−	0.0200597i	$-0.993614\pi$
$251$	−178818.	+	550344.i	−0.179154	+	0.551379i	0.820645	+	0.571438i	$0.193614\pi$
$252$	−96863.5	−	133321.i	−0.0960858	−	0.132251i
$253$	581651.	−	800574.i	0.571296	−	0.786321i
$254$	−191149.	−	588297.i	−0.185904	−	0.572153i
$255$	−15597.7			−0.0150214
$256$	20251.7	+	62328.4i	0.0193136	+	0.0594410i
$257$	97369.2	−	31637.2i	0.0919579	−	0.0298789i	−0.262677	−	0.964884i	$-0.584605\pi$
$257$	97369.2	−	31637.2i	0.0919579	−	0.0298789i	0.354635	+	0.935005i	$0.384605\pi$
$258$	−902927.	−	293379.i	−0.844507	−	0.274397i
$259$	−242023.	−	333116.i	−0.224186	−	0.308565i
$260$		−	311302.i		−	0.285593i
$261$	441582.	+	143479.i	0.401245	+	0.130373i
$262$	835189.	+	606800.i	0.751677	+	0.546126i
$263$	−829531.	+	269531.i	−0.739508	+	0.240281i	−0.654461	−	0.756096i	$-0.727104\pi$
$263$	−829531.	+	269531.i	−0.739508	+	0.240281i	−0.0850477	+	0.996377i	$0.527104\pi$
$264$	150995.	−	109705.i	0.133338	−	0.0968757i
$265$	−196391.	+	270309.i	−0.171794	+	0.236454i
$266$	317724.	+	230840.i	0.275325	+	0.200035i
$267$	−237529.	−	172575.i	−0.203910	−	0.148149i
$268$	655550.	−	902288.i	0.557531	−	0.767376i
$269$	885940.	−	643673.i	0.746489	−	0.542356i	−0.148247	−	0.988950i	$-0.547363\pi$
$269$	885940.	−	643673.i	0.746489	−	0.542356i	0.894737	+	0.446594i	$0.147363\pi$
$270$	276435.	−	89819.1i	0.230772	−	0.0749824i
$271$	−516026.	−	374915.i	−0.426823	−	0.310105i	0.353554	−	0.935414i	$-0.384973\pi$
$271$	−516026.	−	374915.i	−0.426823	−	0.310105i	−0.780377	+	0.625309i	$0.784973\pi$
$272$	16072.9	+	5222.41i	0.0131726	+	0.00428005i
$273$			2.34478e6i			1.90413i
$274$	−136010.	−	187202.i	−0.109445	−	0.150638i
$275$	−583868.	−	189710.i	−0.465568	−	0.151272i
$276$	921433.	−	299392.i	0.728100	−	0.236574i
$277$	−463067.	−	1.42517e6i	−0.362614	−	1.11601i	−0.951462	−	0.307767i	$-0.900418\pi$
$277$	−463067.	−	1.42517e6i	−0.362614	−	1.11601i	0.588848	−	0.808244i	$-0.299582\pi$
$278$	792379.			0.614923
$279$	−198693.	−	611513.i	−0.152817	−	0.470322i
$280$	106166.	−	146125.i	0.0809265	−	0.111386i
$281$	1.09187e6	+	1.50283e6i	0.824907	+	1.13539i	0.988850	+	0.148917i	$0.0475786\pi$
$281$	1.09187e6	+	1.50283e6i	0.824907	+	1.13539i	−0.163943	+	0.986470i	$0.552421\pi$
$282$	88088.2	−	271108.i	0.0659622	−	0.203011i
$283$	187984.	−	578555.i	0.139526	−	0.429417i	−0.856741	−	0.515748i	$-0.827514\pi$
$283$	187984.	−	578555.i	0.139526	−	0.429417i	0.996267	+	0.0863309i	$0.0275142\pi$
$284$			413264.i			0.304041i
$285$	−117616.	+	85453.3i	−0.0857740	+	0.0623185i
$286$	960583.			0.694416
$287$	−126320.	−	1.71284e6i	−0.0905246	−	1.22747i
$288$	−66097.9			−0.0469576
$289$	−1.14516e6	+	832009.i	−0.806534	+	0.585981i
$290$			508897.i			0.355333i
$291$	222553.	−	684947.i	0.154064	−	0.474159i
$292$	−217562.	+	669587.i	−0.149323	+	0.459568i
$293$	1.42169e6	+	1.95679e6i	0.967466	+	1.33160i	0.943317	+	0.331895i	$0.107688\pi$
$293$	1.42169e6	+	1.95679e6i	0.967466	+	1.33160i	0.0241496	+	0.999708i	$0.492312\pi$
$294$	−271791.	+	374088.i	−0.183386	+	0.252409i
$295$	−108765.	−	334745.i	−0.0727670	−	0.223954i
$296$	−165152.			−0.109561
$297$	277155.	+	852995.i	0.182319	+	0.561119i
$298$	−122858.	+	39918.8i	−0.0801422	+	0.0260398i
$299$	4.74234e6	+	1.54088e6i	3.06771	+	0.996760i
$300$	−353297.	−	486272.i	−0.226640	−	0.311944i
$301$		−	2.83505e6i		−	1.80362i
$302$	−222174.	−	72188.8i	−0.140177	−	0.0455463i
$303$	−931620.	−	676862.i	−0.582952	−	0.423539i
$304$	149811.	−	48676.6i	0.0929737	−	0.0302090i
$305$	−405807.	+	294836.i	−0.249787	+	0.181481i
$306$	−10018.8	+	13789.7i	−0.00611662	+	0.00841880i
$307$	−926019.	−	672792.i	−0.560756	−	0.407413i	0.270980	−	0.962585i	$-0.412652\pi$
$307$	−926019.	−	672792.i	−0.560756	−	0.407413i	−0.831736	+	0.555172i	$0.812652\pi$
$308$	450898.	+	327596.i	0.270833	+	0.196772i
$309$	−760782.	+	1.04713e6i	−0.453277	+	0.623883i
$310$	570141.	−	414231.i	0.336960	−	0.244815i
$311$	−2.30513e6	+	748983.i	−1.35143	+	0.439107i	−0.893174	−	0.449711i	$-0.851527\pi$
$311$	−2.30513e6	+	748983.i	−1.35143	+	0.439107i	−0.458260	+	0.888818i	$0.651527\pi$
$312$	760862.	+	552799.i	0.442507	+	0.321500i
$313$	−27324.9	−	8878.38i	−0.0157651	−	0.00512239i	0.301124	−	0.953585i	$-0.402638\pi$
$313$	−27324.9	−	8878.38i	−0.0157651	−	0.00512239i	−0.316889	+	0.948463i	$0.602638\pi$
$314$		−	341933.i		−	0.195712i
$315$	107076.	+	147378.i	0.0608018	+	0.0836866i
$316$	415903.	+	135135.i	0.234301	+	0.0761291i
$317$	1.20329e6	−	390972.i	0.672545	−	0.218523i	0.0472163	−	0.998885i	$-0.484965\pi$
$317$	1.20329e6	−	390972.i	0.672545	−	0.218523i	0.625329	+	0.780362i	$0.284965\pi$
$318$	−311927.	−	960012.i	−0.172976	−	0.532364i
$319$	−1.57030e6			−0.863987
$320$	−22387.0	−	68900.0i	−0.0122214	−	0.0376135i
$321$	−1.52378e6	+	2.09731e6i	−0.825393	+	1.13606i
$322$	1.70055e6	+	2.34061e6i	0.914010	+	1.25803i
$323$	12552.5	−	38632.5i	0.00669456	−	0.0206037i
$324$	−193801.	+	596459.i	−0.102564	+	0.315659i
$325$		−	3.09350e6i		−	1.62458i
$326$	−205792.	+	149517.i	−0.107247	+	0.0779196i
$327$	2.12087e6			1.09684
$328$	−585582.	−	362823.i	−0.300541	−	0.186213i
$329$	851236.			0.433571
$330$	−166915.	+	121271.i	−0.0843746	+	0.0613017i
$331$			1.71464e6i			0.860209i	0.902779	+	0.430105i	$0.141523\pi$
$331$			1.71464e6i			0.860209i	−0.902779	+	0.430105i	$0.858477\pi$
$332$	523693.	−	1.61176e6i	0.260754	−	0.802519i
$333$	51472.3	−	158416.i	0.0254369	−	0.0782866i
$334$	496384.	+	683215.i	0.243474	+	0.335113i
$335$	−724667.	+	997419.i	−0.352798	+	0.485585i
$336$	168623.	+	518968.i	0.0814832	+	0.250780i
$337$	782140.			0.375154			0.187577	−	0.982250i	$-0.439937\pi$
$337$	782140.			0.375154			0.187577	+	0.982250i	$0.439937\pi$
$338$	1.03681e6	+	3.19097e6i	0.493636	+	1.51926i
$339$	−1.30744e6	+	424813.i	−0.617906	+	0.200770i
$340$	−17767.6	−	5773.03i	−0.00833548	−	0.00270836i
$341$	1.27819e6	+	1.75928e6i	0.595265	+	0.819313i
$342$			158871.i			0.0734480i
$343$	1.23731e6	+	402027.i	0.567864	+	0.184510i
$344$	−919950.	−	668383.i	−0.419149	−	0.304529i
$345$	−1.01858e6	+	330958.i	−0.460732	+	0.149701i
$346$	212788.	−	154599.i	0.0955557	−	0.0694253i
$347$	39849.6	−	54848.3i	0.0177664	−	0.0244534i	−0.800041	−	0.599945i	$-0.795189\pi$
$347$	39849.6	−	54848.3i	0.0177664	−	0.0244534i	0.817808	+	0.575491i	$0.195189\pi$
$348$	−1.24381e6	−	903683.i	−0.550563	−	0.400007i
$349$	−3.24366e6	−	2.35666e6i	−1.42552	−	1.03570i	−0.990830	−	0.135117i	$-0.956859\pi$
$349$	−3.24366e6	−	2.35666e6i	−1.42552	−	1.03570i	−0.434687	−	0.900582i	$-0.643141\pi$
$350$	1.05501e6	−	1.45209e6i	0.460346	−	0.633612i
$351$	−3.65629e6	+	2.65645e6i	−1.58406	+	1.15089i
$352$	212605.	−	69079.4i	0.0914568	−	0.0297161i
$353$	−1.15115e6	−	836360.i	−0.491695	−	0.357237i	0.314141	−	0.949376i	$-0.398284\pi$
$353$	−1.15115e6	−	836360.i	−0.491695	−	0.357237i	−0.805836	+	0.592139i	$0.798284\pi$
$354$	1.01130e6	+	328592.i	0.428916	+	0.139363i
$355$		−	456836.i		−	0.192393i
$356$	−206699.	−	284497.i	−0.0864397	−	0.118974i
$357$	133829.	+	43483.6i	0.0555749	+	0.0180574i
$358$	1.96706e6	−	639135.i	0.811165	−	0.263563i
$359$	−701484.	−	2.15895e6i	−0.287264	−	0.884109i	−0.985711	−	0.168447i	$-0.946125\pi$
$359$	−701484.	−	2.15895e6i	−0.287264	−	0.884109i	0.698446	−	0.715662i	$-0.253875\pi$
$360$	73066.8			0.0297142
$361$	648159.	+	1.99483e6i	0.261766	+	0.805633i
$362$	271083.	−	373113.i	0.108725	−	0.149647i
$363$	890361.	+	1.22548e6i	0.354650	+	0.488134i
$364$	−867851.	+	2.67097e6i	−0.343314	+	1.05661i
$365$	240500.	−	740184.i	0.0944895	−	0.290809i
$366$		−	1.51541e6i		−	0.591325i
$367$	2.45930e6	−	1.78678e6i	0.953117	−	0.692480i	0.00157471	−	0.999999i	$-0.499499\pi$
$367$	2.45930e6	−	1.78678e6i	0.953117	−	0.692480i	0.951542	+	0.307519i	$0.0994988\pi$
$368$	1.16043e6			0.446682
$369$	530530.	−	448616.i	0.202836	−	0.171518i
$370$	182565.			0.0693286
$371$	2.43861e6	−	1.77175e6i	0.919830	−	0.668296i
$372$			2.12908e6i			0.797690i
$373$	−1.32640e6	+	4.08225e6i	−0.493632	+	1.51924i	0.325445	+	0.945561i	$0.394486\pi$
$373$	−1.32640e6	+	4.08225e6i	−0.493632	+	1.51924i	−0.819078	+	0.573683i	$0.805514\pi$
$374$	17813.8	−	54825.3i	0.00658534	−	0.0202676i
$375$	824538.	+	1.13488e6i	0.302784	+	0.416746i
$376$	200685.	−	276219.i	0.0732057	−	0.100759i
$377$	−2.44517e6	−	7.52545e6i	−0.886044	−	2.72696i
$378$	−2.62221e6			−0.943927
$379$	−658191.	−	2.02570e6i	−0.235371	−	0.724399i	−0.997072	−	0.0764695i	$-0.975635\pi$
$379$	−658191.	−	2.02570e6i	−0.235371	−	0.724399i	0.761700	−	0.647929i	$-0.224365\pi$
$380$	−165606.	+	53808.7i	−0.0588325	+	0.0191159i
$381$	−1.96470e6	−	638370.i	−0.693400	−	0.225299i
$382$	−1.97487e6	−	2.71818e6i	−0.692437	−	0.953058i
$383$		−	1.70276e6i		−	0.593138i	−0.955011	−	0.296569i	$-0.904157\pi$
$383$		−	1.70276e6i		−	0.593138i	0.955011	−	0.296569i	$-0.0958425\pi$
$384$	208155.	+	67633.5i	0.0720374	+	0.0234064i
$385$	−498438.	−	362136.i	−0.171380	−	0.124515i
$386$	297482.	−	96657.8i	0.101623	−	0.0330193i
$387$	927837.	−	674113.i	0.314916	−	0.228800i
$388$	507025.	−	697860.i	0.170982	−	0.235336i
$389$	−125725.	−	91344.4i	−0.0421257	−	0.0306061i	0.566523	−	0.824046i	$-0.308288\pi$
$389$	−125725.	−	91344.4i	−0.0421257	−	0.0306061i	−0.608649	+	0.793440i	$0.708288\pi$
$390$	−841083.	−	611083.i	−0.280012	−	0.203441i
$391$	175892.	−	242094.i	0.0581839	−	0.0800833i
$392$	−448058.	+	325533.i	−0.147272	+	0.106999i
$393$	3.27894e6	−	1.06539e6i	1.07091	−	0.347959i
$394$	1.57157e6	+	1.14181e6i	0.510027	+	0.370556i
$395$	−459754.	−	149383.i	−0.148263	−	0.0481735i
$396$			225462.i			0.0722496i
$397$	908347.	+	1.25023e6i	0.289251	+	0.398120i	0.928771	−	0.370655i	$-0.120867\pi$
$397$	908347.	+	1.25023e6i	0.289251	+	0.398120i	−0.639519	+	0.768775i	$0.720867\pi$
$398$	−1.90898e6	−	620267.i	−0.604080	−	0.196278i
$399$	1.24738e6	−	405298.i	0.392253	−	0.127451i
$400$	−222466.	−	684681.i	−0.0695207	−	0.213963i
$401$	−1.48919e6			−0.462476			−0.231238	−	0.972897i	$-0.574278\pi$
$401$	−1.48919e6			−0.462476			−0.231238	+	0.972897i	$0.574278\pi$
$402$	−1.15098e6	−	3.54237e6i	−0.355226	−	1.09327i
$403$	−6.44079e6	+	8.86499e6i	−1.97550	+	2.71904i
$404$	−810700.	−	1.11583e6i	−0.247119	−	0.340131i
$405$	214234.	−	659346.i	0.0649011	−	0.199745i
$406$	1.41871e6	−	4.36635e6i	0.427149	−	1.31463i
$407$			563340.i			0.168572i
$408$	45661.1	−	33174.7i	0.0135799	−	0.00986636i
$409$	−3.66510e6			−1.08337			−0.541686	−	0.840581i	$-0.682214\pi$
$409$	−3.66510e6			−1.08337			−0.541686	+	0.840581i	$0.682214\pi$
$410$	647322.	+	401077.i	0.190178	+	0.117833i
$411$	−772774.			−0.225656
$412$	−1.25418e6	+	911214.i	−0.364012	+	0.264470i
$413$			3.17533e6i			0.916038i
$414$	−361666.	+	1.11309e6i	−0.103707	+	0.319176i
$415$	−578908.	+	1.78169e6i	−0.165002	+	0.507824i
$416$	662106.	+	911310.i	0.187583	+	0.258186i
$417$	1.55543e6	−	2.14087e6i	0.438037	−	0.602907i
$418$	−166037.	−	511011.i	−0.0464799	−	0.143051i
$419$	−3.76412e6			−1.04744			−0.523719	−	0.851891i	$-0.675456\pi$
$419$	−3.76412e6			−1.04744			−0.523719	+	0.851891i	$0.675456\pi$
$420$	−186401.	−	573685.i	−0.0515615	−	0.158690i
$421$	−623649.	+	202636.i	−0.171488	+	0.0557200i	−0.393503	−	0.919323i	$-0.628737\pi$
$421$	−623649.	+	202636.i	−0.171488	+	0.0557200i	0.222014	+	0.975043i	$0.428737\pi$
$422$	−4.19931e6	−	1.36444e6i	−1.14788	−	0.372969i
$423$	202405.	+	278587.i	0.0550010	+	0.0757024i
$424$		−	1.20901e6i		−	0.326600i
$425$	−176562.	−	57368.4i	−0.0474160	−	0.0154064i
$426$	1.11657e6	+	811235.i	0.298100	+	0.216582i
$427$	4.30378e6	−	1.39838e6i	1.14230	−	0.371156i
$428$	−2.51202e6	+	1.82509e6i	−0.662847	+	0.481586i
$429$	1.88562e6	−	2.59533e6i	0.494664	−	0.680846i
$430$	1.01694e6	+	738853.i	0.265232	+	0.192702i
$431$	947269.	+	688231.i	0.245629	+	0.178460i	0.703788	−	0.710411i	$-0.251491\pi$
$431$	947269.	+	688231.i	0.245629	+	0.178460i	−0.458158	+	0.888871i	$0.651491\pi$
$432$	−618205.	+	850886.i	−0.159376	+	0.219362i
$433$	3.23340e6	−	2.34920e6i	0.828781	−	0.602145i	−0.0904331	−	0.995903i	$-0.528825\pi$
$433$	3.23340e6	−	2.34920e6i	0.828781	−	0.602145i	0.919214	+	0.393758i	$0.128825\pi$
$434$	−6.04661e6	+	1.96466e6i	−1.54095	+	0.500684i
$435$	1.37495e6	+	998962.i	0.348389	+	0.253120i
$436$	2.41591e6	+	784976.i	0.608645	+	0.197761i
$437$		−	2.78917e6i		−	0.698669i
$438$	1.38204e6	+	1.90221e6i	0.344218	+	0.473776i
$439$	−43409.3	−	14104.5i	−0.0107503	−	0.00349299i	0.303637	−	0.952788i	$-0.401799\pi$
$439$	−43409.3	−	14104.5i	−0.0107503	−	0.00349299i	−0.314387	+	0.949295i	$0.601799\pi$
$440$	−235020.	+	76362.7i	−0.0578727	+	0.0188040i
$441$	−172610.	−	531239.i	−0.0422639	−	0.130075i
$442$	290481.			0.0707232
$443$	398012.	+	1.22495e6i	0.0963577	+	0.296559i	0.987605	−	0.156959i	$-0.0501690\pi$
$443$	398012.	+	1.22495e6i	0.0963577	+	0.296559i	−0.891247	+	0.453517i	$0.850169\pi$
$444$	−324192.	+	446212.i	−0.0780450	+	0.107420i
$445$	228492.	+	314492.i	0.0546979	+	0.0752852i
$446$	541317.	−	1.66600e6i	0.128859	−	0.396587i
$447$	−133315.	+	410300.i	−0.0315580	+	0.0971254i
$448$			653573.i			0.153851i
$449$	5.37192e6	−	3.90293e6i	1.25752	−	0.913640i	0.258884	−	0.965908i	$-0.416645\pi$
$449$	5.37192e6	−	3.90293e6i	1.25752	−	0.913640i	0.998633	+	0.0522685i	$0.0166452\pi$
$450$	726088.			0.169028
$451$	−1.23760e6	+	1.99744e6i	−0.286510	+	0.462416i
$452$	−1.64655e6			−0.379078
$453$	−631168.	+	458571.i	−0.144511	+	0.104993i
$454$			411205.i			0.0936309i
$455$	959352.	−	2.95258e6i	0.217245	−	0.668611i
$456$	162562.	−	500315.i	0.0366107	−	0.112676i
$457$	1.23140e6	+	1.69488e6i	0.275809	+	0.379618i	0.924340	−	0.381570i	$-0.124616\pi$
$457$	1.23140e6	+	1.69488e6i	0.275809	+	0.379618i	−0.648531	+	0.761188i	$0.724616\pi$
$458$	−1.32521e6	+	1.82399e6i	−0.295203	+	0.406311i
$459$	83811.7	+	257946.i	0.0185683	+	0.0571475i
$460$	−1.28277e6			−0.282654
$461$	722216.	+	2.22275e6i	0.158276	+	0.487123i	0.998478	−	0.0551503i	$-0.0175638\pi$
$461$	722216.	+	2.22275e6i	0.158276	+	0.487123i	−0.840202	+	0.542273i	$0.817564\pi$
$462$	1.77022e6	−	575179.i	0.385853	−	0.125371i
$463$	739090.	+	240145.i	0.160230	+	0.0520620i	0.388034	−	0.921645i	$-0.373154\pi$
$463$	739090.	+	240145.i	0.160230	+	0.0520620i	−0.227803	+	0.973707i	$0.573154\pi$
$464$	−1.08237e6	−	1.48976e6i	−0.233389	−	0.321233i
$465$		−	2.35355e6i		−	0.504768i
$466$	3.52265e6	+	1.14458e6i	0.751458	+	0.244163i
$467$	−752577.	−	546779.i	−0.159683	−	0.116016i	0.505074	−	0.863076i	$-0.331465\pi$
$467$	−752577.	−	546779.i	−0.159683	−	0.116016i	−0.664757	+	0.747059i	$0.731465\pi$
$468$	−1.08049e6	+	351074.i	−0.228038	+	0.0740941i
$469$	8.99827e6	−	6.53763e6i	1.88898	−	1.37242i
$470$	−221844.	+	305342.i	−0.0463236	+	0.0637590i
$471$	−923843.	−	671211.i	−0.191887	−	0.139414i
$472$	1.03037e6	+	748606.i	0.212881	+	0.154667i
$473$	−2.27988e6	+	3.13798e6i	−0.468553	+	0.644908i
$474$	1.18153e6	−	858429.i	0.241545	−	0.175493i
$475$	−1.64568e6	+	534714.i	−0.334666	+	0.108740i
$476$	136352.	+	99065.3i	0.0275831	+	0.0200403i
$477$	1.15970e6	+	376808.i	0.233372	+	0.0758271i
$478$			4.16913e6i			0.834594i
$479$	1.84185e6	+	2.53509e6i	0.366789	+	0.504841i	0.952024	−	0.306022i	$-0.0989981\pi$
$479$	1.84185e6	+	2.53509e6i	0.366789	+	0.504841i	−0.585236	+	0.810863i	$0.698998\pi$
$480$	−230101.	−	74764.4i	−0.0455843	−	0.0148113i
$481$	−2.69972e6	+	877193.i	−0.532055	+	0.172875i
$482$	2.10230e6	+	6.47022e6i	0.412171	+	1.26853i
$483$	9.66210e6			1.88453
$484$	560648.	+	1.72550e6i	0.108787	+	0.334812i
$485$	−560483.	+	771438.i	−0.108195	+	0.148918i
$486$	−1.11615e6	−	1.53625e6i	−0.214354	−	0.295033i
$487$	−879658.	+	2.70731e6i	−0.168070	+	0.517268i	−0.999249	−	0.0387374i	$-0.987666\pi$
$487$	−879658.	+	2.70731e6i	−0.168070	+	0.517268i	0.831179	+	0.556005i	$0.187666\pi$
$488$	560882.	−	1.72622e6i	0.106616	−	0.328130i
$489$			849516.i			0.160657i
$490$	495298.	−	359855.i	0.0931916	−	0.0677076i
$491$	5.41880e6			1.01438			0.507188	−	0.861835i	$-0.330685\pi$
$491$	5.41880e6			1.01438			0.507188	+	0.861835i	$0.330685\pi$
$492$	−2.12978e6	+	869921.i	−0.396663	+	0.162019i
$493$	−474861.			−0.0879932
$494$	2.19040e6	−	1.59142e6i	0.403837	−	0.293405i
$495$		−	249233.i		−	0.0457186i
$496$	−788014.	+	2.42526e6i	−0.143824	+	0.442643i
$497$	−1.27358e6	+	3.91966e6i	−0.231278	+	0.711799i
$498$	−3.32669e6	−	4.57880e6i	−0.601090	−	0.827329i
$499$	−3.56664e6	+	4.90906e6i	−0.641222	+	0.882566i	−0.998680	−	0.0513633i	$-0.983643\pi$
$499$	−3.56664e6	+	4.90906e6i	−0.641222	+	0.882566i	0.357458	+	0.933929i	$0.383643\pi$
$500$	519200.	+	1.59793e6i	0.0928773	+	0.285847i
$501$	2.82033e6			0.502002
$502$	715271.	+	2.20138e6i	0.126681	+	0.389884i
$503$	−1.93057e6	+	627280.i	−0.340224	+	0.110546i	−0.474146	−	0.880446i	$-0.657243\pi$
$503$	−1.93057e6	+	627280.i	−0.340224	+	0.110546i	0.133921	+	0.990992i	$0.457243\pi$
$504$	−626914.	−	203697.i	−0.109934	−	0.0357197i
$505$	896175.	+	1.23348e6i	0.156374	+	0.215230i
$506$		−	3.95825e6i		−	0.687270i
$507$	1.06567e7	+	3.46257e6i	1.84121	+	0.598244i
$508$	−2.00174e6	−	1.45435e6i	−0.344150	−	0.250040i
$509$	791443.	−	257156.i	0.135402	−	0.0439948i	−0.240532	−	0.970641i	$-0.577322\pi$
$509$	791443.	−	257156.i	0.135402	−	0.0439948i	0.375934	+	0.926646i	$0.377322\pi$
$510$	−50475.3	+	36672.4i	−0.00859317	+	0.00624330i
$511$	−4.12699e6	+	5.68032e6i	−0.699168	+	0.962322i
$512$	212079.	+	154084.i	0.0357538	+	0.0259767i
$513$	2.04517e6	+	1.48590e6i	0.343112	+	0.249285i
$514$	240710.	−	331309.i	0.0401871	−	0.0553128i
$515$	1.38641e6	−	1.00729e6i	0.230342	−	0.167354i
$516$	−3.61171e6	+	1.17352e6i	−0.597157	+	0.194028i
$517$	−942192.	−	684543.i	−0.155029	−	0.112635i
$518$	−1.56641e6	−	508957.i	−0.256496	−	0.0833405i
$519$		−	878394.i		−	0.143143i
$520$	−731914.	−	1.00739e6i	−0.118700	−	0.163377i
$521$	−2.01116e6	−	653465.i	−0.324603	−	0.105470i	0.142183	−	0.989840i	$-0.454588\pi$
$521$	−2.01116e6	−	653465.i	−0.324603	−	0.105470i	−0.466785	+	0.884371i	$0.654588\pi$
$522$	1.76633e6	−	573915.i	0.283723	−	0.0921873i
$523$	3.20154e6	+	9.85334e6i	0.511806	+	1.57518i	0.789019	+	0.614368i	$0.210589\pi$
$523$	3.20154e6	+	9.85334e6i	0.511806	+	1.57518i	−0.277213	+	0.960808i	$0.589411\pi$
$524$	4.12940e6			0.656990
$525$	−1.85233e6	−	5.70089e6i	−0.293305	−	0.902701i
$526$	−2.05071e6	+	2.82256e6i	−0.323177	+	0.444815i
$527$	386526.	+	532008.i	0.0606251	+	0.0834433i
$528$	230700.	−	710023.i	0.0360134	−	0.110838i
$529$	4.36053e6	−	1.34203e7i	0.677486	−	2.08509i
$530$			1.33648e6i			0.206668i
$531$	−1.03920e6	+	755024.i	−0.159942	+	0.116205i
$532$	1.57091e6			0.240643
$533$	−1.14995e7	−	2.82076e6i	−1.75333	−	0.430079i
$534$	−1.17441e6			−0.178224
$535$	2.77687e6	−	2.01751e6i	0.419441	−	0.304742i
$536$		−	4.46115e6i		−	0.670711i
$537$	2.13448e6	−	6.56926e6i	0.319416	−	0.983062i
$538$	1.35360e6	−	4.16594e6i	0.201620	−	0.620522i
$539$	1.11040e6	+	1.52834e6i	0.164630	+	0.226594i
$540$	683385.	−	940598.i	0.100851	−	0.138810i
$541$	3.86143e6	+	1.18843e7i	0.567225	+	1.74574i	0.661248	+	0.750168i	$0.270027\pi$
$541$	3.86143e6	+	1.18843e7i	0.567225	+	1.74574i	−0.0940229	+	0.995570i	$0.529973\pi$
$542$	−2.55137e6			−0.373057
$543$	−475954.	−	1.46484e6i	−0.0692733	−	0.213201i
$544$	64291.7	−	20889.6i	0.00931446	−	0.00302645i
$545$	−2.67063e6	−	867739.i	−0.385143	−	0.125140i
$546$	5.51292e6	+	7.58788e6i	0.791407	+	1.08928i
$547$		−	4.39112e6i		−	0.627490i	−0.949507	−	0.313745i	$-0.898416\pi$
$547$		−	4.39112e6i		−	0.627490i	0.949507	−	0.313745i	$-0.101584\pi$
$548$	−880276.	−	286019.i	−0.125218	−	0.0406858i
$549$	1.48100e6	+	1.07601e6i	0.209712	+	0.152365i
$550$	−2.33547e6	+	758840.i	−0.329206	+	0.106965i
$551$	−3.58074e6	+	2.60156e6i	−0.502451	+	0.365052i
$552$	2.27791e6	−	3.13527e6i	0.318191	−	0.437953i
$553$	3.52824e6	+	2.56342e6i	0.490620	+	0.356456i
$554$	−4.84930e6	−	3.52322e6i	−0.671281	−	0.487715i
$555$	358373.	−	493258.i	0.0493859	−	0.0679739i
$556$	2.56419e6	−	1.86299e6i	0.351774	−	0.255579i
$557$	−1.12296e7	+	3.64871e6i	−1.53365	+	0.498312i	−0.949615	−	0.313420i	$-0.898525\pi$
$557$	−1.12296e7	+	3.64871e6i	−1.53365	+	0.498312i	−0.584031	+	0.811732i	$0.698525\pi$
$558$	−2.08074e6	−	1.51174e6i	−0.282899	−	0.205538i
$559$	−1.85884e7	−	6.03973e6i	−2.51601	−	0.817500i
$560$		−	722482.i		−	0.0973547i
$561$	−113160.	−	155752.i	−0.0151805	−	0.0208942i
$562$	7.06673e6	+	2.29612e6i	0.943794	+	0.306657i
$563$	−3.11769e6	+	1.01300e6i	−0.414536	+	0.134691i	−0.508857	−	0.860851i	$-0.669932\pi$
$563$	−3.11769e6	+	1.01300e6i	−0.414536	+	0.134691i	0.0943211	+	0.995542i	$0.469932\pi$
$564$	−352353.	−	1.08443e6i	−0.0466423	−	0.143550i
$565$	1.82015e6			0.239876
$566$	−751936.	−	2.31422e6i	−0.0986597	−	0.303643i
$567$	−3.67627e6	+	5.05995e6i	−0.480230	+	0.660980i
$568$	971643.	+	1.33735e6i	0.126368	+	0.173930i
$569$	1.22378e6	−	3.76642e6i	0.158462	−	0.487695i	−0.840034	−	0.542534i	$-0.817465\pi$
$569$	1.22378e6	−	3.76642e6i	0.158462	−	0.487695i	0.998495	+	0.0548398i	$0.0174648\pi$
$570$	−179702.	+	553065.i	−0.0231668	+	0.0713000i
$571$		−	5.69100e6i		−	0.730463i	−0.930917	−	0.365232i	$-0.880990\pi$
$571$		−	5.69100e6i		−	0.730463i	0.930917	−	0.365232i	$-0.119010\pi$
$572$	3.10851e6	−	2.25847e6i	0.397249	−	0.288618i
$573$	−1.12207e7			−1.42769
$574$	−4.43590e6	−	5.24586e6i	−0.561956	−	0.664564i
$575$	−1.27473e7			−1.60787
$576$	−213897.	+	155405.i	−0.0268626	+	0.0195169i
$577$			7.69889e6i			0.962694i	0.876530	+	0.481347i	$0.159852\pi$
$577$			7.69889e6i			0.962694i	−0.876530	+	0.481347i	$0.840148\pi$
$578$	−1.74965e6	+	5.38488e6i	−0.217837	+	0.670434i
$579$	322802.	−	993483.i	0.0400166	−	0.123158i
$580$	1.19649e6	+	1.64683e6i	0.147686	+	0.203272i
$581$	9.93407e6	−	1.36731e7i	1.22092	−	1.68045i
$582$	−890211.	−	2.73979e6i	−0.108940	−	0.335281i
$583$	−4.12398e6			−0.502511
$584$	870248.	+	2.67835e6i	0.105587	+	0.324964i
$585$	1.19441e6	−	388089.i	0.144300	−	0.0468858i
$586$	9.20137e6	+	2.98971e6i	1.10690	+	0.359654i
$587$	1.18643e6	+	1.63299e6i	0.142118	+	0.195608i	0.874142	−	0.485670i	$-0.161424\pi$
$587$	1.18643e6	+	1.63299e6i	0.142118	+	0.195608i	−0.732025	+	0.681278i	$0.761424\pi$
$588$			1.84959e6i			0.220614i
$589$	5.82929e6	+	1.89405e6i	0.692353	+	0.224959i
$590$	−1.13900e6	−	827534.i	−0.134708	−	0.0978714i
$591$	6.16996e6	−	2.00474e6i	0.726630	−	0.236097i
$592$	−534443.	+	388296.i	−0.0626755	+	0.0455364i
$593$	3.82152e6	−	5.25987e6i	0.446272	−	0.614240i	−0.525320	−	0.850905i	$-0.676054\pi$
$593$	3.82152e6	−	5.25987e6i	0.446272	−	0.614240i	0.971591	+	0.236665i	$0.0760542\pi$
$594$	2.90240e6	+	2.10872e6i	0.337514	+	0.245218i
$595$	−150728.	−	109510.i	−0.0174542	−	0.0126812i
$596$	−303721.	+	418036.i	−0.0350234	+	0.0482056i
$597$	−5.42318e6	+	3.94017e6i	−0.622756	+	0.452459i
$598$	1.89694e7	−	6.16352e6i	2.16920	−	0.704816i
$599$	−1.34201e7	−	9.75030e6i	−1.52823	−	1.11033i	−0.957211	−	0.289392i	$-0.906547\pi$
$599$	−1.34201e7	−	9.75030e6i	−1.52823	−	1.11033i	−0.571023	−	0.820934i	$-0.693453\pi$
$600$	−2.28659e6	−	742958.i	−0.259304	−	0.0842531i
$601$		−	9.80120e6i		−	1.10686i	−0.832895	−	0.553430i	$-0.813318\pi$
$601$		−	9.80120e6i		−	1.10686i	0.832895	−	0.553430i	$-0.186682\pi$
$602$	−6.66560e6	−	9.17442e6i	−0.749632	−	1.03178i
$603$	4.27919e6	+	1.39039e6i	0.479256	+	0.155720i
$604$	−888698.	+	288755.i	−0.0991201	+	0.0322061i
$605$	−619759.	−	1.90742e6i	−0.0688390	−	0.211865i
$606$	−4.60618e6			−0.509518
$607$	−1.09556e6	−	3.37179e6i	−0.120688	−	0.371440i	0.872403	−	0.488788i	$-0.162561\pi$
$607$	−1.09556e6	−	3.37179e6i	−0.120688	−	0.371440i	−0.993091	+	0.117348i	$0.962561\pi$
$608$	370353.	−	509748.i	0.0406310	−	0.0559237i
$609$	−9.01219e6	−	1.24042e7i	−0.984662	−	1.35527i
$610$	−620018.	+	1.90822e6i	−0.0674652	+	0.207636i
$611$	1.81345e6	−	5.58124e6i	0.196519	−	0.604822i
$612$			68179.9i			0.00735830i
$613$	−9.72116e6	+	7.06284e6i	−1.04488	+	0.759151i	−0.971232	−	0.238134i	$-0.923464\pi$
$613$	−9.72116e6	+	7.06284e6i	−1.04488	+	0.759151i	−0.0736488	+	0.997284i	$0.523464\pi$
$614$	−4.57849e6			−0.490119
$615$	2.35433e6	−	961640.i	0.251003	−	0.102524i
$616$	2.22936e6			0.236717
$617$	2.05176e6	−	1.49069e6i	0.216977	−	0.157643i	−0.473988	−	0.880532i	$-0.657186\pi$
$617$	2.05176e6	−	1.49069e6i	0.216977	−	0.157643i	0.690965	+	0.722888i	$0.257186\pi$
$618$			5.17728e6i			0.545293i
$619$	1.38811e6	−	4.27218e6i	0.145612	−	0.448149i	−0.851477	−	0.524392i	$-0.824293\pi$
$619$	1.38811e6	−	4.27218e6i	0.145612	−	0.448149i	0.997089	+	0.0762432i	$0.0242925\pi$
$620$	871098.	−	2.68096e6i	0.0910097	−	0.280099i
$621$	1.09464e7	+	1.50664e7i	1.13905	+	1.56776i
$622$	−5.69860e6	+	7.84345e6i	−0.590598	+	0.812889i
$623$	−1.08372e6	−	3.33534e6i	−0.111865	−	0.344286i
$624$	3.76191e6			0.386765
$625$	2.14171e6	+	6.59151e6i	0.219311	+	0.674971i
$626$	−109299.	+	35513.5i	−0.0111476	+	0.00362208i
$627$	−1.70659e6	−	554506.i	−0.173365	−	0.0563297i
$628$	−803932.	−	1.10652e6i	−0.0813430	−	0.111959i
$629$			170354.i			0.0171683i
$630$	693012.	+	225173.i	0.0695648	+	0.0226030i
$631$	−3.41446e6	−	2.48075e6i	−0.341388	−	0.248033i	0.403859	−	0.914821i	$-0.367669\pi$
$631$	−3.41446e6	−	2.48075e6i	−0.341388	−	0.248033i	−0.745247	+	0.666788i	$0.767669\pi$
$632$	1.66361e6	−	540541.i	0.165676	−	0.0538314i
$633$	−1.19297e7	+	8.66742e6i	−1.18337	+	0.859767i
$634$	2.97469e6	−	4.09431e6i	0.293913	−	0.404536i
$635$	2.21279e6	+	1.60769e6i	0.217774	+	0.158222i
$636$	−3.26654e6	−	2.37328e6i	−0.320218	−	0.232652i
$637$	−5.59531e6	+	7.70128e6i	−0.546355	+	0.751994i
$638$	−5.08161e6	+	3.69201e6i	−0.494253	+	0.359096i
$639$	−1.58563e6	+	515202.i	−0.153621	+	0.0499144i
$640$	−234439.	−	170330.i	−0.0226246	−	0.0164377i
$641$	1.29024e7	+	4.19226e6i	1.24030	+	0.402998i	0.854435	−	0.519558i	$-0.173903\pi$
$641$	1.29024e7	+	4.19226e6i	1.24030	+	0.402998i	0.385865	+	0.922555i	$0.373903\pi$
$642$			1.03697e7i			0.992950i
$643$	1.58444e6	+	2.18080e6i	0.151130	+	0.208012i	0.877868	−	0.478902i	$-0.158965\pi$
$643$	1.58444e6	+	2.18080e6i	0.151130	+	0.208012i	−0.726739	+	0.686914i	$0.758965\pi$
$644$	1.10062e7	+	3.57614e6i	1.04574	+	0.339781i
$645$	3.99250e6	−	1.29724e6i	0.377873	−	0.122778i
$646$	−50209.8	−	154530.i	−0.00473377	−	0.0145691i
$647$	9.45495e6			0.887970			0.443985	−	0.896034i	$-0.353564\pi$
$647$	9.45495e6			0.887970			0.443985	+	0.896034i	$0.353564\pi$
$648$	775205.	+	2.38584e6i	0.0725236	+	0.223205i
$649$	2.55352e6	−	3.51462e6i	0.237973	−	0.327542i
$650$	−7.27326e6	−	1.00108e7i	−0.675221	−	0.929362i
$651$	−6.56127e6	+	2.01935e7i	−0.606786	+	1.86750i
$652$	−314423.	+	967694.i	−0.0289664	+	0.0891495i
$653$			7.68648e6i			0.705415i	0.935734	+	0.352707i	$0.114739\pi$
$653$			7.68648e6i			0.705415i	−0.935734	+	0.352707i	$0.885261\pi$
$654$	6.86328e6	−	4.98646e6i	0.627462	−	0.455878i
$655$	−4.56478e6			−0.415735
$656$	−2.74803e6	+	202664.i	−0.249323	+	0.0183873i
$657$	−2.84032e6			−0.256717
$658$	2.75466e6	−	2.00138e6i	0.248029	−	0.180204i
$659$			6.42427e6i			0.576249i	0.957593	+	0.288125i	$0.0930318\pi$
$659$			6.42427e6i			0.576249i	−0.957593	+	0.288125i	$0.906968\pi$
$660$	−255024.	+	784883.i	−0.0227888	+	0.0701367i
$661$	3.05614e6	−	9.40583e6i	0.272063	−	0.837324i	−0.717919	−	0.696127i	$-0.754905\pi$
$661$	3.05614e6	−	9.40583e6i	0.272063	−	0.837324i	0.989982	−	0.141197i	$-0.0450950\pi$
$662$	4.03137e6	+	5.54871e6i	0.357526	+	0.492093i
$663$	570211.	−	784829.i	0.0503793	−	0.0693411i
$664$	−2.09477e6	−	6.44704e6i	−0.184381	−	0.567467i
$665$	−1.73654e6			−0.152276
$666$	−205889.	−	633662.i	−0.0179866	−	0.0553570i
$667$	−3.10100e7	+	1.00758e7i	−2.69890	+	0.876926i
$668$	3.21267e6	+	1.04386e6i	0.278564	+	0.0905109i
$669$	−3.43865e6	−	4.73290e6i	−0.297045	−	0.408848i
$670$			4.93151e6i			0.424417i
$671$	−5.88819e6	−	1.91319e6i	−0.504865	−	0.164041i
$672$	1.76584e6	+	1.28296e6i	0.150844	+	0.109595i
$673$	2.10163e7	−	6.82862e6i	1.78862	−	0.581159i	0.789170	−	0.614175i	$-0.210511\pi$
$673$	2.10163e7	−	6.82862e6i	1.78862	−	0.581159i	0.999455	+	0.0330156i	$0.0105111\pi$
$674$	2.53106e6	−	1.83892e6i	0.214611	−	0.155924i
$675$	6.79101e6	−	9.34702e6i	0.573687	−	0.789612i
$676$	1.08576e7	+	7.88851e6i	0.913834	+	0.663939i
$677$	−2.93159e6	−	2.12992e6i	−0.245828	−	0.178604i	0.458048	−	0.888928i	$-0.348549\pi$
$677$	−2.93159e6	−	2.12992e6i	−0.245828	−	0.178604i	−0.703876	+	0.710323i	$0.748549\pi$
$678$	−3.23217e6	+	4.44870e6i	−0.270035	+	0.371671i
$679$	6.95957e6	−	5.05643e6i	0.579306	−	0.420891i
$680$	−71070.2	+	23092.1i	−0.00589407	+	0.00191510i
$681$	1.11101e6	+	807193.i	0.0918012	+	0.0666975i
$682$	8.27264e6	+	2.68794e6i	0.681057	+	0.221289i
$683$			1.42508e7i			1.16893i	0.811420	+	0.584464i	$0.198695\pi$
$683$			1.42508e7i			1.16893i	−0.811420	+	0.584464i	$0.801305\pi$
$684$	373528.	+	514118.i	0.0305270	+	0.0420167i
$685$	973086.	+	316175.i	0.0792364	+	0.0257455i
$686$	4.94925e6	−	1.60811e6i	0.401541	−	0.130468i
$687$	2.32674e6	+	7.16096e6i	0.188086	+	0.578868i
$688$	−4.54848e6			−0.366349
$689$	−6.42157e6	−	1.97636e7i	−0.515340	−	1.58605i
$690$	−2.51808e6	+	3.46583e6i	−0.201347	+	0.277131i
$691$	2.66231e6	+	3.66436e6i	0.212111	+	0.291946i	0.901795	−	0.432165i	$-0.142250\pi$
$691$	2.66231e6	+	3.66436e6i	0.212111	+	0.291946i	−0.689683	+	0.724111i	$0.742250\pi$
$692$	325111.	−	1.00059e6i	0.0258087	−	0.0794311i
$693$	−694817.	+	2.13843e6i	−0.0549588	+	0.169146i
$694$		−	271185.i		−	0.0213731i
$695$	−2.83454e6	+	2.05942e6i	−0.222598	+	0.161727i
$696$	−6.14975e6			−0.481210
$697$	−374252.	+	604027.i	−0.0291798	+	0.0470950i
$698$	−1.60376e7			−1.24595
$699$	1.00074e7	−	7.27079e6i	0.774689	−	0.562845i
$700$		−	7.17953e6i		−	0.553798i
$701$	7.55062e6	−	2.32384e7i	0.580347	−	1.78612i	−0.0368582	−	0.999321i	$-0.511735\pi$
$701$	7.55062e6	−	2.32384e7i	0.580347	−	1.78612i	0.617205	−	0.786803i	$-0.288265\pi$
$702$	−5.58631e6	+	1.71929e7i	−0.427841	+	1.31676i
$703$	933298.	+	1.28457e6i	0.0712249	+	0.0980327i
$704$	525587.	−	723409.i	0.0399681	−	0.0550113i
$705$	389503.	+	1.19877e6i	0.0295147	+	0.0908368i
$706$	−5.69161e6			−0.429757
$707$	−4.25048e6	−	1.30816e7i	−0.319808	−	0.984268i
$708$	4.04521e6	−	1.31437e6i	0.303290	−	0.0985448i
$709$	−1.76941e6	−	574916.i	−0.132194	−	0.0429525i	0.242173	−	0.970233i	$-0.422140\pi$
$709$	−1.76941e6	−	574916.i	−0.132194	−	0.0429525i	−0.374367	+	0.927281i	$0.622140\pi$
$710$	−1.07409e6	−	1.47835e6i	−0.0799638	−	0.110061i
$711$			1.76422e6i			0.130882i
$712$	−1.33778e6	−	434672.i	−0.0988976	−	0.0321338i
$713$	3.65298e7	+	2.65404e7i	2.69106	+	1.95517i
$714$	535315.	−	173934.i	0.0392974	−	0.0127685i
$715$	−3.43625e6	+	2.49658e6i	−0.251374	+	0.182634i
$716$	4.86283e6	−	6.69311e6i	0.354492	−	0.487917i
$717$	1.12643e7	+	8.18396e6i	0.818285	+	0.594519i
$718$	−7.34604e6	−	5.33721e6i	−0.531792	−	0.386370i
$719$	6.77397e6	−	9.32358e6i	0.488676	−	0.672605i	−0.491467	−	0.870896i	$-0.663539\pi$
$719$	6.77397e6	−	9.32358e6i	0.488676	−	0.672605i	0.980143	+	0.198291i	$0.0635391\pi$
$720$	236449.	−	171790.i	0.0169983	−	0.0123500i
$721$	−1.47035e7	+	4.77747e6i	−1.05338	+	0.342263i
$722$	6.78761e6	+	4.93149e6i	0.484589	+	0.352075i
$723$	2.16082e7	+	7.02093e6i	1.53735	+	0.499515i
$724$		−	1.84477e6i		−	0.130797i
$725$	1.18899e7	+	1.63650e7i	0.840104	+	1.15630i
$726$	5.76254e6	+	1.87236e6i	0.405763	+	0.131840i
$727$	7.65466e6	−	2.48715e6i	0.537143	−	0.174528i	−0.0278683	−	0.999612i	$-0.508872\pi$
$727$	7.65466e6	−	2.48715e6i	0.537143	−	0.174528i	0.565011	+	0.825083i	$0.308872\pi$
$728$	3.47140e6	+	1.06839e7i	0.242760	+	0.747138i
$729$	−1.58666e7			−1.10577
$730$	−962001.	−	2.96074e6i	−0.0668142	−	0.205633i
$731$	−689436.	+	948927.i	−0.0477200	+	0.0656809i
$732$	−3.56293e6	−	4.90396e6i	−0.245771	−	0.338274i
$733$	3.07720e6	−	9.47066e6i	0.211542	−	0.651059i	−0.787839	−	0.615881i	$-0.788800\pi$
$733$	3.07720e6	−	9.47066e6i	0.211542	−	0.651059i	0.999381	−	0.0351778i	$-0.0111997\pi$
$734$	3.75747e6	−	1.15643e7i	0.257428	−	0.792282i
$735$		−	2.04460e6i		−	0.139602i
$736$	3.75522e6	−	2.72833e6i	0.255529	−	0.185653i
$737$	−1.52172e7			−1.03196
$738$	662071.	−	2.69910e6i	0.0447470	−	0.182423i
$739$	1.11034e7			0.747901			0.373950	−	0.927449i	$-0.378003\pi$
$739$	1.11034e7			0.747901			0.373950	+	0.927449i	$0.378003\pi$
$740$	590792.	−	429235.i	0.0396602	−	0.0288148i
$741$		−	9.04203e6i		−	0.604952i
$742$	3.72587e6	−	1.14670e7i	0.248438	−	0.764612i
$743$	867563.	−	2.67008e6i	0.0576539	−	0.177441i	−0.918082	−	0.396390i	$-0.870263\pi$
$743$	867563.	−	2.67008e6i	0.0576539	−	0.177441i	0.975736	+	0.218949i	$0.0702629\pi$
$744$	5.00576e6	+	6.88984e6i	0.331542	+	0.456328i
$745$	335743.	−	462111.i	0.0221624	−	0.0305039i
$746$	5.30561e6	+	1.63290e7i	0.349051	+	1.07427i
$747$	6.83694e6			0.448291
$748$	−71255.3	−	219301.i	−0.00465654	−	0.0143314i
$749$	−2.94500e7	+	9.56889e6i	−1.91814	+	0.623243i
$750$	5.33652e6	+	1.73394e6i	0.346422	+	0.112559i
$751$	−3.26150e6	−	4.48907e6i	−0.211017	−	0.290440i	0.690368	−	0.723458i	$-0.257449\pi$
$751$	−3.26150e6	−	4.48907e6i	−0.211017	−	0.290440i	−0.901385	+	0.433018i	$0.857449\pi$
$752$		−	1.36570e6i		−	0.0880666i
$753$	7.35181e6	+	2.38875e6i	0.472505	+	0.153526i
$754$	−2.56061e7	−	1.86039e7i	−1.64027	−	1.19173i
$755$	982396.	−	319200.i	0.0627219	−	0.0203796i
$756$	−8.48566e6	+	6.16519e6i	−0.539984	+	0.392322i
$757$	−3.42778e6	+	4.71794e6i	−0.217407	+	0.299235i	−0.903765	−	0.428029i	$-0.859208\pi$
$757$	−3.42778e6	+	4.71794e6i	−0.217407	+	0.299235i	0.686358	+	0.727264i	$0.259208\pi$
$758$	−6.89266e6	−	5.00781e6i	−0.435727	−	0.316574i
$759$	−1.06945e7	−	7.77002e6i	−0.673840	−	0.489573i
$760$	−409401.	+	563492.i	−0.0257108	+	0.0353878i
$761$	−2.19111e7	+	1.59194e7i	−1.37152	+	0.996471i	−0.373908	+	0.927466i	$0.621982\pi$
$761$	−2.19111e7	+	1.59194e7i	−1.37152	+	0.996471i	−0.997616	+	0.0690047i	$0.978018\pi$
$762$	−7.85880e6	+	2.55348e6i	−0.490308	+	0.159311i
$763$	2.04949e7	+	1.48904e7i	1.27448	+	0.925967i
$764$	−1.27816e7	−	4.15300e6i	−0.792233	−	0.257412i
$765$		−	75368.3i		−	0.00465624i
$766$	−4.00342e6	−	5.51024e6i	−0.246524	−	0.339312i
$767$	2.08195e7	+	6.76465e6i	1.27785	+	0.415200i
$768$	832619.	−	270534.i	0.0509381	−	0.0165508i
$769$	5.99977e6	+	1.84654e7i	0.365863	+	1.12601i	0.949439	+	0.313952i	$0.101653\pi$
$769$	5.99977e6	+	1.84654e7i	0.365863	+	1.12601i	−0.583576	+	0.812059i	$0.698347\pi$
$770$	−2.46441e6			−0.149791
$771$	−422627.	−	1.30071e6i	−0.0256048	−	0.0788035i
$772$	735416.	−	1.01221e6i	0.0444109	−	0.0611264i
$773$	1.49260e7	+	2.05439e7i	0.898451	+	1.23661i	0.970959	+	0.239244i	$0.0768997\pi$
$773$	1.49260e7	+	2.05439e7i	0.898451	+	1.23661i	−0.0725081	+	0.997368i	$0.523100\pi$
$774$	1.41761e6	−	4.36295e6i	0.0850558	−	0.261775i
$775$	8.65637e6	−	2.66416e7i	0.517704	−	1.59333i
$776$		−	3.45041e6i		−	0.205692i
$777$	−4.44996e6	+	3.23308e6i	−0.264426	+	0.192116i
$778$	−621617.			−0.0368192
$779$	487119.	+	6.60510e6i	0.0287601	+	0.389974i
$780$	−4.15854e6			−0.244740
$781$	4.56175e6	−	3.31431e6i	0.267611	−	0.194431i
$782$		−	1.19698e6i		−	0.0699954i
$783$	9.13216e6	−	2.81059e7i	0.532316	−	1.63830i
$784$	−684572.	+	2.10689e6i	−0.0397767	+	0.122420i
$785$	888694.	+	1.22318e6i	0.0514728	+	0.0708462i
$786$	8.10598e6	−	1.11569e7i	0.468004	−	0.644152i
$787$	−515661.	−	1.58704e6i	−0.0296775	−	0.0913379i	0.935121	−	0.354329i	$-0.115291\pi$
$787$	−515661.	−	1.58704e6i	−0.0296775	−	0.0913379i	−0.964798	+	0.262992i	$0.915291\pi$
$788$	7.77027e6			0.445780
$789$	3.60055e6	+	1.10813e7i	0.205909	+	0.633724i
$790$	−1.83901e6	+	597532.i	−0.104838	+	0.0340638i
$791$	−1.56169e7	−	5.07425e6i	−0.887472	−	0.288357i
$792$	530093.	+	729611.i	0.0300289	+	0.0413312i
$793$		−	3.11974e7i		−	1.76171i
$794$	5.87894e6	+	1.91018e6i	0.330939	+	0.107529i
$795$	3.61094e6	+	2.62350e6i	0.202630	+	0.147219i
$796$	−7.63594e6	+	2.48107e6i	−0.427149	+	0.138789i
$797$	1.54273e7	−	1.12086e7i	0.860289	−	0.625036i	−0.0676746	−	0.997707i	$-0.521558\pi$
$797$	1.54273e7	−	1.12086e7i	0.860289	−	0.625036i	0.927964	+	0.372671i	$0.121558\pi$
$798$	3.08369e6	−	4.24433e6i	0.171421	−	0.235940i
$799$	−284919.	−	207006.i	−0.0157890	−	0.0114714i
$800$	−2.32970e6	−	1.69262e6i	−0.128699	−	0.0935052i
$801$	833884.	−	1.14774e6i	0.0459224	−	0.0632067i
$802$	−4.81912e6	+	3.50130e6i	−0.264565	+	0.192218i
$803$	9.13594e6	−	2.96845e6i	0.499993	−	0.162458i
$804$	−1.20533e7	−	8.75721e6i	−0.657604	−	0.477778i
$805$	−1.21666e7	−	3.95318e6i	−0.661730	−	0.215009i
$806$			4.38309e7i			2.37653i
$807$	−8.59855e6	−	1.18349e7i	−0.464774	−	0.639706i
$808$	−5.24696e6	−	1.70484e6i	−0.282735	−	0.0918661i
$809$	−7.83107e6	+	2.54447e6i	−0.420678	+	0.136687i	−0.511704	−	0.859162i	$-0.670985\pi$
$809$	−7.83107e6	+	2.54447e6i	−0.420678	+	0.136687i	0.0910258	+	0.995849i	$0.470985\pi$
$810$	−856938.	−	2.63738e6i	−0.0458920	−	0.141241i
$811$	6.20272e6			0.331154			0.165577	−	0.986197i	$-0.447051\pi$
$811$	6.20272e6			0.331154			0.165577	+	0.986197i	$0.447051\pi$
$812$	−5.67485e6	−	1.74654e7i	−0.302040	−	0.929583i
$813$	−5.00832e6	+	6.89336e6i	−0.265746	+	0.365767i
$814$	1.32449e6	+	1.82301e6i	0.0700629	+	0.0964333i
$815$	347574.	−	1.06972e6i	0.0183296	−	0.0564127i
$816$	69763.9	−	214711.i	0.00366780	−	0.0112883i
$817$			1.09326e7i			0.573019i
$818$	−1.18605e7	+	8.61717e6i	−0.619755	+	0.450279i
$819$	−1.13300e7			−0.590229
$820$	3.03777e6	−	224032.i	0.157768	−	0.0116352i
$821$	−2.25766e7			−1.16896			−0.584481	−	0.811408i	$-0.698702\pi$
$821$	−2.25766e7			−1.16896			−0.584481	+	0.811408i	$0.698702\pi$
$822$	−2.50075e6	+	1.81690e6i	−0.129089	+	0.0937889i
$823$			1.72012e7i			0.885235i	0.896711	+	0.442617i	$0.145950\pi$
$823$			1.72012e7i			0.885235i	−0.896711	+	0.442617i	$0.854050\pi$
$824$	−1.91621e6	+	5.89750e6i	−0.0983164	+	0.302587i
$825$	−2.53426e6	+	7.79963e6i	−0.129633	+	0.398969i
$826$	7.46565e6	+	1.02756e7i	0.380730	+	0.524030i
$827$	1.49402e7	−	2.05634e7i	0.759613	−	1.04552i	−0.237634	−	0.971355i	$-0.576372\pi$
$827$	1.49402e7	−	2.05634e7i	0.759613	−	1.04552i	0.997246	−	0.0741622i	$-0.0236283\pi$
$828$	1.44666e6	+	4.45237e6i	0.0733317	+	0.225692i
$829$	1.17874e7			0.595705			0.297853	−	0.954612i	$-0.403730\pi$
$829$	1.17874e7			0.595705			0.297853	+	0.954612i	$0.403730\pi$
$830$	2.31563e6	+	7.12678e6i	0.116674	+	0.359086i
$831$	−1.90383e7	+	6.18591e6i	−0.956368	+	0.310743i
$832$	4.28524e6	+	1.39236e6i	0.214618	+	0.0697337i
$833$	335787.	+	462171.i	0.0167668	+	0.0230776i
$834$		−	1.05850e7i		−	0.526960i
$835$	−3.55139e6	−	1.15392e6i	−0.176272	−	0.0572741i
$836$	−1.73877e6	−	1.26329e6i	−0.0860450	−	0.0625154i
$837$	−3.89217e7	+	1.26464e7i	−1.92034	+	0.623956i
$838$	−1.21809e7	+	8.84997e6i	−0.599198	+	0.435343i
$839$	−7.77948e6	+	1.07075e7i	−0.381545	+	0.525152i	−0.955993	−	0.293389i	$-0.905217\pi$
$839$	−7.77948e6	+	1.07075e7i	−0.381545	+	0.525152i	0.574448	+	0.818541i	$0.305217\pi$
$840$	−1.95202e6	−	1.41823e6i	−0.0954523	−	0.0693501i
$841$	2.52655e7	+	1.83565e7i	1.23179	+	0.894951i
$842$	−1.54174e6	+	2.12203e6i	−0.0749432	+	0.103150i
$843$	2.00756e7	−	1.45858e7i	0.972972	−	0.706906i
$844$	−1.67972e7	+	5.45775e6i	−0.811674	+	0.263729i
$845$	−1.20024e7	−	8.72023e6i	−0.578262	−	0.420132i
$846$	1.30999e6	+	425643.i	0.0629279	+	0.0204465i
$847$			1.80935e7i			0.866590i
$848$	−2.84256e6	−	3.91244e6i	−0.135744	−	0.186835i
$849$	−7.72867e6	−	2.51120e6i	−0.367990	−	0.119567i
$850$	−706247.	+	229474.i	−0.0335281	+	0.0108940i
$851$	3.61463e6	+	1.11247e7i	0.171096	+	0.526580i
$852$	5.52062e6			0.260549
$853$	−1.15402e7	−	3.55171e7i	−0.543052	−	1.67134i	−0.725577	−	0.688141i	$-0.758427\pi$
$853$	−1.15402e7	−	3.55171e7i	−0.543052	−	1.67134i	0.182525	−	0.983201i	$-0.441573\pi$
$854$	1.06395e7	−	1.46440e7i	0.499203	−	0.687094i
$855$	−412911.	−	568323.i	−0.0193171	−	0.0265877i
$856$	−3.83802e6	+	1.18122e7i	−0.179029	+	0.550994i
$857$	−7.05937e6	+	2.17265e7i	−0.328333	+	1.01050i	0.641581	+	0.767055i	$0.278279\pi$
$857$	−7.05937e6	+	2.17265e7i	−0.328333	+	1.01050i	−0.969914	+	0.243449i	$0.921721\pi$
$858$		−	1.28320e7i		−	0.595082i
$859$	2.16092e7	−	1.57000e7i	0.999206	−	0.725965i	0.0372879	−	0.999305i	$-0.488128\pi$
$859$	2.16092e7	−	1.57000e7i	0.999206	−	0.725965i	0.961918	+	0.273339i	$0.0881281\pi$
$860$	5.02805e6			0.231821
$861$	−2.28810e7	+	1.68745e6i	−1.05188	+	0.0775753i
$862$	4.68355e6			0.214688
$863$	6.81499e6	−	4.95138e6i	0.311486	−	0.226308i	−0.421048	−	0.907038i	$-0.638338\pi$
$863$	6.81499e6	−	4.95138e6i	0.311486	−	0.226308i	0.732534	+	0.680731i	$0.238338\pi$
$864$			4.20701e6i			0.191730i
$865$	−359389.	+	1.10608e6i	−0.0163314	+	0.0502630i
$866$	4.94020e6	−	1.52044e7i	0.223846	−	0.688927i
$867$	1.11145e7	+	1.52977e7i	0.502158	+	0.691161i
$868$	−1.49481e7	+	2.05742e7i	−0.673419	+	0.926882i
$869$	−1.84380e6	−	5.67464e6i	−0.0828257	−	0.254911i
$870$	6.79814e6			0.304503
$871$	−2.36951e7	−	7.29260e7i	−1.05831	−	3.25714i
$872$	9.66363e6	−	3.13990e6i	0.430377	−	0.139838i
$873$	3.30967e6	+	1.07538e6i	0.146977	+	0.0477557i
$874$	−6.55773e6	−	9.02595e6i	−0.290386	−	0.399682i
$875$			1.67559e7i			0.739855i
$876$	8.94472e6	+	2.90632e6i	0.393828	+	0.127962i
$877$	−2.11886e7	−	1.53944e7i	−0.930259	−	0.675873i	0.0157970	−	0.999875i	$-0.494971\pi$
$877$	−2.11886e7	−	1.53944e7i	−0.930259	−	0.675873i	−0.946056	+	0.324002i	$0.894971\pi$
$878$	−173637.	+	56418.1i	−0.00760163	+	0.00246992i
$879$	2.61399e7	−	1.89917e7i	1.14112	−	0.829072i
$880$	−581002.	+	799680.i	−0.0252913	+	0.0348105i
$881$	3.01203e7	+	2.18836e7i	1.30743	+	0.949905i	0.999999	−	0.00166523i	$-0.000530061\pi$
$881$	3.01203e7	+	2.18836e7i	1.30743	+	0.949905i	0.307433	+	0.951570i	$0.400530\pi$
$882$	−1.80760e6	−	1.31330e6i	−0.0782402	−	0.0568449i
$883$	−2.10627e7	+	2.89903e7i	−0.909100	+	1.25127i	0.0583733	+	0.998295i	$0.481409\pi$
$883$	−2.10627e7	+	2.89903e7i	−0.909100	+	1.25127i	−0.967473	+	0.252974i	$0.918591\pi$
$884$	940015.	−	682961.i	0.0404580	−	0.0293944i
$885$	−4.47171e6	+	1.45295e6i	−0.191918	+	0.0623579i
$886$	4.16803e6	+	3.02825e6i	0.178380	+	0.129601i
$887$	3.99761e6	+	1.29890e6i	0.170605	+	0.0554329i	0.393074	−	0.919507i	$-0.371412\pi$
$887$	3.99761e6	+	1.29890e6i	0.170605	+	0.0554329i	−0.222469	+	0.974940i	$0.571412\pi$
$888$			2.20620e6i			0.0938883i
$889$	−1.45038e7	−	1.99628e7i	−0.615501	−	0.847164i
$890$	1.47883e6	+	480501.i	0.0625811	+	0.0203338i
$891$	8.13817e6	−	2.64425e6i	0.343426	−	0.111586i
$892$	−2.16527e6	−	6.66401e6i	−0.0911171	−	0.280430i
$893$	−3.28256e6			−0.137748
$894$	533259.	+	1.64120e6i	0.0223149	+	0.0686781i
$895$	−5.37554e6	+	7.39879e6i	−0.224318	+	0.308747i
$896$	1.53664e6	+	2.11501e6i	0.0639445	+	0.0880120i
$897$	2.05839e7	−	6.33508e7i	0.854176	−	2.62888i
$898$	8.20757e6	−	2.52603e7i	0.339644	−	1.04532i
$899$		−	7.16522e7i		−	2.95686i
$900$	2.34967e6	−	1.70714e6i	0.0966943	−	0.0702525i
$901$	−1.24709e6			−0.0511785
$902$	691295.	+	9.37363e6i	0.0282909	+	0.383612i
$903$	−3.78722e7			−1.54561
$904$	−5.32835e6	+	3.87127e6i	−0.216856	+	0.157555i
$905$			2.03927e6i			0.0827665i
$906$	−964339.	+	2.96793e6i	−0.0390310	+	0.120125i
$907$	−7.98343e6	+	2.45705e7i	−0.322234	+	0.991734i	0.650440	+	0.759558i	$0.274585\pi$
$907$	−7.98343e6	+	2.45705e7i	−0.322234	+	0.991734i	−0.972674	+	0.232176i	$0.925415\pi$
$908$	966801.	+	1.33069e6i	0.0389155	+	0.0535626i
$909$	3.27060e6	−	4.50160e6i	0.131286	−	0.180699i
$910$	−3.83741e6	−	1.18103e7i	−0.153615	−	0.472779i
$911$	−1.83761e7			−0.733599			−0.366799	−	0.930300i	$-0.619546\pi$
$911$	−1.83761e7			−0.733599			−0.366799	+	0.930300i	$0.619546\pi$
$912$	−650249.	−	2.00126e6i	−0.0258877	−	0.0796740i
$913$	−2.19911e7	+	7.14534e6i	−0.873112	+	0.283691i
$914$	7.96978e6	+	2.58954e6i	0.315559	+	0.102531i
$915$	3.93859e6	+	5.42100e6i	0.155521	+	0.214056i
$916$			9.01831e6i			0.355129i
$917$	3.91659e7	+	1.27258e7i	1.53810	+	0.499759i
$918$	877688.	+	637677.i	0.0343743	+	0.0249744i
$919$	3.32254e7	−	1.07956e7i	1.29772	−	0.421655i	0.422932	−	0.906161i	$-0.361001\pi$
$919$	3.32254e7	−	1.07956e7i	1.29772	−	0.421655i	0.874788	+	0.484507i	$0.161001\pi$
$920$	−4.15114e6	+	3.01598e6i	−0.161696	+	0.117479i
$921$	−8.98754e6	+	1.23703e7i	−0.349134	+	0.480541i
$922$	7.56314e6	+	5.49494e6i	0.293005	+	0.212880i
$923$	2.29866e7	+	1.67007e7i	0.888117	+	0.645255i
$924$	4.37622e6	−	6.02335e6i	0.168624	−	0.232091i
$925$	5.87089e6	−	4.26545e6i	0.225605	−	0.163912i
$926$	2.95636e6	−	960580.i	0.113300	−	0.0368134i
$927$	−5.05972e6	−	3.67610e6i	−0.193387	−	0.140504i
$928$	−7.00525e6	−	2.27614e6i	−0.267026	−	0.0867621i
$929$			2.71459e7i			1.03196i	0.856599	+	0.515982i	$0.172573\pi$
$929$			2.71459e7i			1.03196i	−0.856599	+	0.515982i	$0.827427\pi$
$930$	−5.53354e6	−	7.61626e6i	−0.209795	−	0.288758i
$931$	5.06408e6	+	1.64542e6i	0.191481	+	0.0622160i
$932$	1.40906e7	−	4.57831e6i	0.531361	−	0.172650i
$933$	1.00053e7	+	3.07933e7i	0.376294	+	1.15811i
$934$	−3.72094e6			−0.139568
$935$	78768.0	+	242423.i	0.00294660	+	0.00906870i
$936$	−2.67113e6	+	3.67649e6i	−0.0996564	+	0.137165i
$937$	−1.07946e7	−	1.48575e7i	−0.401660	−	0.552838i	0.559499	−	0.828831i	$-0.310993\pi$
$937$	−1.07946e7	−	1.48575e7i	−0.401660	−	0.552838i	−0.961160	+	0.275993i	$0.910993\pi$
$938$	1.37481e7	−	4.23124e7i	0.510196	−	1.57022i
$939$	−118602.	+	365021.i	−0.00438965	+	0.0135099i
$940$			1.50969e6i			0.0557274i
$941$	3.04304e7	−	2.21090e7i	1.12030	−	0.813944i	0.136044	−	0.990703i	$-0.456561\pi$
$941$	3.04304e7	−	2.21090e7i	1.12030	−	0.813944i	0.984254	+	0.176759i	$0.0565612\pi$
$942$	−4.56773e6			−0.167716
$943$	−1.16234e7	+	4.73860e7i	−0.425653	+	1.73528i
$944$	5.09442e6			0.186065
$945$	9.38034e6	−	6.81521e6i	0.341695	−	0.248256i
$946$			1.55150e7i			0.563670i
$947$	−4.88602e6	+	1.50376e7i	−0.177044	+	0.544884i	−0.999721	−	0.0236246i	$-0.992479\pi$
$947$	−4.88602e6	+	1.50376e7i	−0.177044	+	0.544884i	0.822677	+	0.568509i	$0.192479\pi$
$948$	1.80521e6	−	5.55587e6i	0.0652390	−	0.200785i
$949$	2.84517e7	+	3.91604e7i	1.02552	+	1.41150i
$950$	−4.06835e6	+	5.59960e6i	−0.146254	+	0.201302i
$951$	−5.22282e6	−	1.60742e7i	−0.187264	−	0.576339i
$952$	674160.			0.0241085
$953$	−4.46518e6	−	1.37424e7i	−0.159260	−	0.490152i	0.839307	−	0.543657i	$-0.182961\pi$
$953$	−4.46518e6	−	1.37424e7i	−0.159260	−	0.490152i	−0.998568	+	0.0535048i	$0.982961\pi$
$954$	4.63879e6	−	1.50723e6i	0.165019	−	0.0536178i
$955$	1.41293e7	+	4.59087e6i	0.501315	+	0.162887i
$956$	9.80220e6	+	1.34916e7i	0.346880	+	0.477439i
$957$			2.09770e7i			0.740395i
$958$	1.19207e7	+	3.87328e6i	0.419651	+	0.136353i
$959$	−7.46766e6	−	5.42557e6i	−0.262203	−	0.190502i
$960$	−920405.	+	299058.i	−0.0322330	+	0.0104731i
$961$	−5.71137e7	+	4.14955e7i	−1.99495	+	1.44941i
$962$	−6.67408e6	+	9.18608e6i	−0.232517	+	0.320032i
$963$	−1.01342e7	−	7.36294e6i	−0.352147	−	0.255850i
$964$	2.20156e7	+	1.59953e7i	0.763023	+	0.554368i
$965$	−812954.	+	1.11893e6i	−0.0281027	+	0.0386800i
$966$	3.12672e7	−	2.27170e7i	1.07807	−	0.783263i
$967$	−1.01119e7	+	3.28556e6i	−0.347750	+	0.112991i	−0.477684	−	0.878532i	$-0.658524\pi$
$967$	−1.01119e7	+	3.28556e6i	−0.347750	+	0.112991i	0.129934	+	0.991523i	$0.458524\pi$
$968$	5.87118e6	+	4.26566e6i	0.201390	+	0.146318i
$969$	−516075.	−	167683.i	−0.0176564	−	0.00573692i
$970$			3.81420e6i			0.130159i
$971$	−9.14851e6	−	1.25918e7i	−0.311388	−	0.428589i	0.624425	−	0.781084i	$-0.285333\pi$
$971$	−9.14851e6	−	1.25918e7i	−0.311388	−	0.428589i	−0.935814	+	0.352495i	$0.885333\pi$
$972$	−7.22386e6	−	2.34717e6i	−0.245247	−	0.0796856i
$973$	3.00617e7	−	9.76763e6i	1.01796	−	0.330756i
$974$	3.51863e6	+	1.08292e7i	0.118844	+	0.365763i
$975$	−4.13248e7			−1.39219
$976$	−2.24353e6	−	6.90487e6i	−0.0753888	−	0.232023i
$977$	−5.77747e6	+	7.95201e6i	−0.193643	+	0.266527i	−0.894787	−	0.446493i	$-0.852673\pi$
$977$	−5.77747e6	+	7.95201e6i	−0.193643	+	0.266527i	0.701144	+	0.713019i	$0.252673\pi$
$978$	1.99733e6	+	2.74909e6i	0.0667734	+	0.0919056i
$979$	−1.48268e6	+	4.56323e6i	−0.0494415	+	0.152165i
$980$	756748.	−	2.32903e6i	0.0251702	−	0.0774659i
$981$			1.02481e7i			0.339992i
$982$	1.75356e7	−	1.27404e7i	0.580285	−	0.421602i
$983$	−1.83308e7			−0.605060			−0.302530	−	0.953140i	$-0.597831\pi$
$983$	−1.83308e7			−0.605060			−0.302530	+	0.953140i	$0.597831\pi$
$984$	−4.84680e6	+	7.82253e6i	−0.159576	+	0.257549i
$985$	−8.58952e6			−0.282084
$986$	−1.53668e6	+	1.11646e6i	−0.0503375	+	0.0365723i
$987$		−	1.13713e7i		−	0.371550i
$988$	3.34664e6	−	1.02999e7i	0.109073	−	0.335691i
$989$	−2.48878e7	+	7.65968e7i	−0.809088	+	2.49012i
$990$	−585983.	−	806536.i	−0.0190019	−	0.0261539i
$991$	−1.97827e7	+	2.72285e7i	−0.639883	+	0.880723i	−0.998609	−	0.0527193i	$-0.983211\pi$
$991$	−1.97827e7	+	2.72285e7i	−0.639883	+	0.880723i	0.358726	+	0.933443i	$0.383211\pi$
$992$	3.15206e6	+	9.70103e6i	0.101699	+	0.312996i
$993$	2.29052e7			0.737158
$994$	5.09430e6	+	1.56786e7i	0.163538	+	0.503318i
$995$	8.44103e6	−	2.74266e6i	0.270295	−	0.0878241i
$996$	−2.15308e7	−	6.99578e6i	−0.687721	−	0.223454i
$997$	9.22940e6	+	1.27032e7i	0.294060	+	0.404738i	0.930327	−	0.366730i	$-0.119523\pi$
$997$	9.22940e6	+	1.27032e7i	0.294060	+	0.404738i	−0.636268	+	0.771468i	$0.719523\pi$
$998$			2.42717e7i			0.771391i
$999$	−1.00829e7	−	3.27612e6i	−0.319647	−	0.103860i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.6.f.b.45.3	yes	40
41.31	even	10	inner	82.6.f.b.31.8	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.6.f.b.31.8	✓	40	41.31	even	10	inner
82.6.f.b.45.3	yes	40	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	82.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.23607 - 2.35114i) q^{2} -13.3586i q^{3} +(4.94427 - 15.2169i) q^{4} +(-5.46557 + 16.8213i) q^{5} +(-31.4079 - 43.2292i) q^{6} +(93.7892 - 129.090i) q^{7} +(-19.7771 - 60.8676i) q^{8} +64.5487 q^{9} +(21.8623 + 67.2851i) q^{10} +(-207.622 + 67.4603i) q^{11} +(-203.276 - 66.0484i) q^{12} +(-646.588 - 889.951i) q^{13} -638.255i q^{14} +(224.708 + 73.0121i) q^{15} +(-207.108 - 150.473i) q^{16} +(-62.7849 + 20.4000i) q^{17} +(208.884 - 151.763i) q^{18} +(-361.673 + 497.800i) q^{19} +(228.945 + 166.338i) q^{20} +(-1724.45 - 1252.89i) q^{21} +(-513.269 + 706.454i) q^{22} +(-3667.21 + 2664.38i) q^{23} +(-813.104 + 264.194i) q^{24} +(2275.10 + 1652.95i) q^{25} +(-4184.80 - 1359.72i) q^{26} -4108.41i q^{27} +(-1500.63 - 2065.44i) q^{28} +(6841.07 + 2222.80i) q^{29} +(898.833 - 292.048i) q^{30} +(-3078.18 - 9473.67i) q^{31} -1024.00 q^{32} +(901.173 + 2773.53i) q^{33} +(-155.213 + 213.632i) q^{34} +(1658.84 + 2283.20i) q^{35} +(319.146 - 982.231i) q^{36} +(797.419 - 2454.20i) q^{37} +2461.26i q^{38} +(-11888.5 + 8637.48i) q^{39} +1131.96 q^{40} +(8219.07 - 6950.04i) q^{41} -8526.17 q^{42} +(14374.2 - 10443.5i) q^{43} +3492.90i q^{44} +(-352.795 + 1085.79i) q^{45} +(-5602.99 + 17244.2i) q^{46} +(3135.70 + 4315.92i) q^{47} +(-2010.10 + 2766.67i) q^{48} +(-2674.11 - 8230.06i) q^{49} +11248.7 q^{50} +(272.515 + 838.716i) q^{51} +(-16739.2 + 5438.90i) q^{52} +(17966.2 + 5837.58i) q^{53} +(-9659.45 - 13295.1i) q^{54} -3861.17i q^{55} +(-9712.27 - 3155.71i) q^{56} +(6649.90 + 4831.44i) q^{57} +(27364.3 - 8891.19i) q^{58} +(-16099.5 + 11697.0i) q^{59} +(2222.04 - 3058.37i) q^{60} +(22943.9 + 16669.7i) q^{61} +(-32235.1 - 23420.2i) q^{62} +(6053.97 - 8332.58i) q^{63} +(-3313.73 + 2407.57i) q^{64} +(18504.1 - 6012.34i) q^{65} +(9437.21 + 6856.54i) q^{66} +(66293.9 + 21540.2i) q^{67} +1056.25i q^{68} +(35592.3 + 48988.6i) q^{69} +(10736.3 + 3488.42i) q^{70} +(-24564.9 + 7981.61i) q^{71} +(-1276.59 - 3928.92i) q^{72} -44002.8 q^{73} +(-3189.68 - 9816.81i) q^{74} +(22081.1 - 30392.0i) q^{75} +(5786.77 + 7964.81i) q^{76} +(-10764.2 + 33128.9i) q^{77} +(-18164.0 + 55903.0i) q^{78} +27331.7i q^{79} +(3663.11 - 2661.41i) q^{80} -39197.1 q^{81} +(10256.9 - 41815.0i) q^{82} +105919. q^{83} +(-27591.3 + 20046.2i) q^{84} -1167.62i q^{85} +(21961.8 - 67591.6i) q^{86} +(29693.4 - 91386.9i) q^{87} +(8212.30 + 11303.3i) q^{88} +(12918.7 - 17781.0i) q^{89} +(1411.18 + 4343.17i) q^{90} -175527. q^{91} +(22412.0 + 68976.9i) q^{92} +(-126555. + 41120.1i) q^{93} +(20294.7 + 6594.14i) q^{94} +(-6396.89 - 8804.57i) q^{95} +13679.2i q^{96} +(51274.0 + 16659.9i) q^{97} +(-28003.6 - 20345.8i) q^{98} +(-13401.7 + 4354.48i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 160 q^{4} + 24 q^{5} - 100 q^{6} + 640 q^{8} - 4576 q^{9} - 96 q^{10} + 20 q^{11} + 400 q^{12} - 275 q^{13} + 1385 q^{15} - 2560 q^{16} - 105 q^{17} - 2476 q^{18} + 4720 q^{19} + 1424 q^{20}+ \cdots - 537690 q^{99}+O(q^{100}) \) 40 * q + 40 * q^2 - 160 * q^4 + 24 * q^5 - 100 * q^6 + 640 * q^8 - 4576 * q^9 - 96 * q^10 + 20 * q^11 + 400 * q^12 - 275 * q^13 + 1385 * q^15 - 2560 * q^16 - 105 * q^17 - 2476 * q^18 + 4720 * q^19 + 1424 * q^20 + 6961 * q^21 - 4140 * q^22 - 1019 * q^23 + 1600 * q^24 - 2006 * q^25 - 8620 * q^26 - 12525 * q^29 + 5540 * q^30 + 8900 * q^31 - 40960 * q^32 + 17684 * q^33 - 13100 * q^34 - 29955 * q^35 + 26704 * q^36 - 31651 * q^37 - 10104 * q^39 + 14464 * q^40 + 35044 * q^41 + 32776 * q^42 - 15615 * q^43 - 39955 * q^45 - 3224 * q^46 + 8330 * q^47 - 6400 * q^48 + 48406 * q^49 - 135016 * q^50 + 120325 * q^51 - 34480 * q^52 + 145425 * q^53 + 72200 * q^54 + 17600 * q^56 + 31992 * q^57 - 50100 * q^58 + 18978 * q^59 + 1680 * q^60 + 52673 * q^61 + 66140 * q^62 - 88455 * q^63 - 40960 * q^64 + 204480 * q^65 - 17556 * q^66 - 149205 * q^67 - 249735 * q^69 - 49100 * q^70 + 151175 * q^71 - 106816 * q^72 - 107670 * q^73 + 126604 * q^74 + 120180 * q^75 - 75520 * q^76 - 207367 * q^77 - 99284 * q^78 + 22784 * q^80 + 1167568 * q^81 + 84204 * q^82 - 281376 * q^83 + 111376 * q^84 - 131400 * q^86 - 141269 * q^87 + 66240 * q^88 - 277775 * q^89 + 159820 * q^90 - 518682 * q^91 + 12896 * q^92 - 172375 * q^93 + 16320 * q^94 + 149585 * q^95 + 330875 * q^97 - 171004 * q^98 - 537690 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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