LMFDB - Embedded newform 22.6.c.b.15.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,6,Mod(3,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("22.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	22.c (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52844403589$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 329 x^{10} + 1365 x^{9} + 52729 x^{8} + 242031 x^{7} + 7017903 x^{6} + \cdots + 93740681241 $ x^12 - 2x^11 + 329x^10 + 1365x^9 + 52729x^8 + 242031x^7 + 7017903x^6 + 130221686x^5 + 2541092161x^4 + 14394729912x^3 + 45294850764x^2 + 76920871185*x + 93740681241
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			15.2
Root			$-0.669902 - 2.06175i$ of defining polynomial
Character	$\chi$	$=$	22.15
Dual form			22.6.c.b.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.23607 - 2.35114i) q^{2} +(-1.32178 + 4.06802i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-21.5825 + 15.6806i) q^{5} +(13.8418 - 10.0567i) q^{6} +(76.6137 + 235.793i) q^{7} +(19.7771 - 60.8676i) q^{8} +(181.789 + 132.078i) q^{9} +106.710 q^{10} +(-401.306 + 2.06892i) q^{11} -68.4378 q^{12} +(-283.449 - 205.938i) q^{13} +(306.455 - 943.171i) q^{14} +(-35.2616 - 108.524i) q^{15} +(-207.108 + 150.473i) q^{16} +(-257.644 + 187.189i) q^{17} +(-277.750 - 854.825i) q^{18} +(202.192 - 622.284i) q^{19} +(-345.320 - 250.889i) q^{20} -1060.48 q^{21} +(1303.52 + 936.832i) q^{22} +3448.46 q^{23} +(221.470 + 160.907i) q^{24} +(-745.756 + 2295.20i) q^{25} +(433.072 + 1332.86i) q^{26} +(-1618.47 + 1175.89i) q^{27} +(-3209.24 + 2331.65i) q^{28} +(-1270.41 - 3909.92i) q^{29} +(-141.046 + 434.096i) q^{30} +(5668.58 + 4118.46i) q^{31} +1024.00 q^{32} +(522.022 - 1635.26i) q^{33} +1273.86 q^{34} +(-5350.88 - 3887.64i) q^{35} +(-1111.00 + 3419.30i) q^{36} +(-444.060 - 1366.68i) q^{37} +(-2117.38 + 1538.37i) q^{38} +(1212.42 - 880.872i) q^{39} +(527.601 + 1623.79i) q^{40} +(2717.54 - 8363.72i) q^{41} +(3431.77 + 2493.33i) q^{42} +12877.7 q^{43} +(-2015.65 - 6096.41i) q^{44} -5994.52 q^{45} +(-11159.5 - 8107.82i) q^{46} +(6117.54 - 18827.8i) q^{47} +(-338.375 - 1041.41i) q^{48} +(-36131.4 + 26251.0i) q^{49} +(7809.66 - 5674.05i) q^{50} +(-420.941 - 1295.52i) q^{51} +(1732.29 - 5331.43i) q^{52} +(4973.19 + 3613.23i) q^{53} +8002.17 q^{54} +(8628.74 - 6337.37i) q^{55} +15867.3 q^{56} +(2264.21 + 1645.04i) q^{57} +(-5081.64 + 15639.7i) q^{58} +(7700.42 + 23699.4i) q^{59} +(1477.06 - 1073.15i) q^{60} +(-13593.5 + 9876.26i) q^{61} +(-8660.82 - 26655.3i) q^{62} +(-17215.4 + 52983.6i) q^{63} +(-3313.73 - 2407.57i) q^{64} +9346.76 q^{65} +(-5534.01 + 4064.45i) q^{66} +66822.5 q^{67} +(-4122.30 - 2995.03i) q^{68} +(-4558.11 + 14028.4i) q^{69} +(8175.42 + 25161.4i) q^{70} +(-11254.6 + 8176.95i) q^{71} +(11634.5 - 8452.98i) q^{72} +(-17586.7 - 54126.3i) q^{73} +(-1776.24 + 5466.70i) q^{74} +(-8351.19 - 6067.49i) q^{75} +10468.9 q^{76} +(-31233.4 - 94466.6i) q^{77} -5994.52 q^{78} +(-46707.4 - 33934.9i) q^{79} +(2110.41 - 6495.16i) q^{80} +(14229.0 + 43792.4i) q^{81} +(-28458.4 + 20676.2i) q^{82} +(52116.6 - 37865.0i) q^{83} +(-5243.28 - 16137.2i) q^{84} +(2625.36 - 8080.02i) q^{85} +(-41673.2 - 30277.4i) q^{86} +17584.8 q^{87} +(-7810.74 + 24467.5i) q^{88} -44688.3 q^{89} +(19398.7 + 14094.0i) q^{90} +(26842.6 - 82613.0i) q^{91} +(17050.1 + 52474.9i) q^{92} +(-24246.6 + 17616.2i) q^{93} +(-64063.7 + 46545.0i) q^{94} +(5393.96 + 16600.9i) q^{95} +(-1353.50 + 4165.65i) q^{96} +(119204. + 86606.8i) q^{97} +178644. q^{98} +(-73226.5 - 52627.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} - 48 q^{4} + 44 q^{5} - 100 q^{6} - 326 q^{7} - 192 q^{8} - 69 q^{9} + 96 q^{10} + 1011 q^{11} + 800 q^{12} - 246 q^{13} - 1304 q^{14} + 112 q^{15} - 768 q^{16} + 400 q^{17} - 1416 q^{18}+ \cdots - 199487 q^{99}+O(q^{100}) $ 12 * q - 12 * q^2 - 48 * q^4 + 44 * q^5 - 100 * q^6 - 326 * q^7 - 192 * q^8 - 69 * q^9 + 96 * q^10 + 1011 * q^11 + 800 * q^12 - 246 * q^13 - 1304 * q^14 + 112 * q^15 - 768 * q^16 + 400 * q^17 - 1416 * q^18 + 7535 * q^19 + 704 * q^20 - 3368 * q^21 + 484 * q^22 + 15732 * q^23 - 1600 * q^24 - 19283 * q^25 - 984 * q^26 - 27411 * q^27 + 3264 * q^28 - 2504 * q^29 + 448 * q^30 + 15336 * q^31 + 12288 * q^32 + 26213 * q^33 + 24600 * q^34 - 33916 * q^35 - 5664 * q^36 - 116 * q^37 - 34880 * q^38 + 4690 * q^39 - 3584 * q^40 - 38836 * q^41 + 19808 * q^42 + 42230 * q^43 - 4704 * q^44 + 139932 * q^45 - 35232 * q^46 - 57840 * q^47 - 125521 * q^49 + 26268 * q^50 + 16467 * q^51 - 3936 * q^52 + 131934 * q^53 + 60176 * q^54 - 53082 * q^55 + 15616 * q^56 - 90021 * q^57 - 10016 * q^58 + 36585 * q^59 - 37248 * q^60 + 43146 * q^61 - 40016 * q^62 - 52922 * q^63 - 12288 * q^64 - 133772 * q^65 - 211008 * q^66 + 325206 * q^67 + 6400 * q^68 - 103894 * q^69 + 68216 * q^70 - 172806 * q^71 - 4416 * q^72 + 49436 * q^73 - 464 * q^74 + 263915 * q^75 + 37920 * q^76 - 207094 * q^77 + 330000 * q^78 + 58364 * q^79 - 14336 * q^80 + 341038 * q^81 + 82836 * q^82 + 82035 * q^83 - 52288 * q^84 - 317604 * q^85 - 104380 * q^86 - 572732 * q^87 - 38336 * q^88 + 97958 * q^89 - 151672 * q^90 - 22162 * q^91 + 15072 * q^92 - 271316 * q^93 + 153720 * q^94 + 549736 * q^95 + 76403 * q^97 + 198656 * q^98 - 199487 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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
$3$	−1.32178	+	4.06802i	−0.0847921	+	0.260963i	−0.984459	−	0.175613i	$-0.943809\pi$
$3$	−1.32178	+	4.06802i	−0.0847921	+	0.260963i	0.899667	+	0.436577i	$0.143809\pi$
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	−21.5825	+	15.6806i	−0.386079	+	0.280503i	−0.763847	−	0.645398i	$-0.776692\pi$
$5$	−21.5825	+	15.6806i	−0.386079	+	0.280503i	0.377768	+	0.925900i	$0.376692\pi$
$6$	13.8418	−	10.0567i	0.156970	−	0.114045i
$7$	76.6137	+	235.793i	0.590965	+	1.81880i	0.573867	+	0.818948i	$0.305443\pi$
$7$	76.6137	+	235.793i	0.590965	+	1.81880i	0.0170973	+	0.999854i	$0.494557\pi$
$8$	19.7771	−	60.8676i	0.109254	−	0.336249i
$9$	181.789	+	132.078i	0.748105	+	0.543530i
$10$	106.710			0.337445
$11$	−401.306	+	2.06892i	−0.999987	+	0.00515539i
$11$	−401.306	+	2.06892i	−0.999987	+	0.00515539i
$12$	−68.4378			−0.137197
$13$	−283.449	−	205.938i	−0.465176	−	0.337970i	0.330382	−	0.943847i	$-0.392822\pi$
$13$	−283.449	−	205.938i	−0.465176	−	0.337970i	−0.795558	+	0.605877i	$0.792822\pi$
$14$	306.455	−	943.171i	0.417875	−	1.28609i
$15$	−35.2616	−	108.524i	−0.0404645	−	0.124537i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	−257.644	+	187.189i	−0.216221	+	0.157094i	−0.690624	−	0.723214i	$-0.742664\pi$
$17$	−257.644	+	187.189i	−0.216221	+	0.157094i	0.474403	+	0.880308i	$0.342664\pi$
$18$	−277.750	−	854.825i	−0.202056	−	0.621865i
$19$	202.192	−	622.284i	0.128493	−	0.395462i	−0.866028	−	0.499995i	$-0.833335\pi$
$19$	202.192	−	622.284i	0.128493	−	0.395462i	0.994521	+	0.104534i	$0.0333350\pi$
$20$	−345.320	−	250.889i	−0.193039	−	0.140251i
$21$	−1060.48			−0.524750
$22$	1303.52	+	936.832i	0.574197	+	0.412672i
$23$	3448.46			1.35927			0.679635	−	0.733550i	$-0.262138\pi$
$23$	3448.46			1.35927			0.679635	+	0.733550i	$0.262138\pi$
$24$	221.470	+	160.907i	0.0784849	+	0.0570226i
$25$	−745.756	+	2295.20i	−0.238642	+	0.734464i
$26$	433.072	+	1332.86i	0.125640	+	0.386679i
$27$	−1618.47	+	1175.89i	−0.427264	+	0.310425i
$28$	−3209.24	+	2331.65i	−0.773583	+	0.562041i
$29$	−1270.41	−	3909.92i	−0.280510	−	0.863322i	−0.987709	−	0.156307i	$-0.950041\pi$
$29$	−1270.41	−	3909.92i	−0.280510	−	0.863322i	0.707198	−	0.707015i	$-0.249959\pi$
$30$	−141.046	+	434.096i	−0.0286127	+	0.0880609i
$31$	5668.58	+	4118.46i	1.05942	+	0.769717i	0.973982	−	0.226626i	$-0.0727696\pi$
$31$	5668.58	+	4118.46i	1.05942	+	0.769717i	0.0854424	+	0.996343i	$0.472770\pi$
$32$	1024.00			0.176777
$33$	522.022	−	1635.26i	0.0834456	−	0.261397i
$34$	1273.86			0.188984
$35$	−5350.88	−	3887.64i	−0.738338	−	0.536434i
$36$	−1111.00	+	3419.30i	−0.142875	+	0.439725i
$37$	−444.060	−	1366.68i	−0.0533258	−	0.164120i	0.920847	−	0.389924i	$-0.127499\pi$
$37$	−444.060	−	1366.68i	−0.0533258	−	0.164120i	−0.974173	+	0.225805i	$0.927499\pi$
$38$	−2117.38	+	1538.37i	−0.237871	+	0.172823i
$39$	1212.42	−	880.872i	0.127641	−	0.0927366i
$40$	527.601	+	1623.79i	0.0521382	+	0.160465i
$41$	2717.54	−	8363.72i	0.252473	−	0.777033i	−0.741844	−	0.670573i	$-0.766048\pi$
$41$	2717.54	−	8363.72i	0.252473	−	0.777033i	0.994317	−	0.106460i	$-0.0339517\pi$
$42$	3431.77	+	2493.33i	0.300189	+	0.218100i
$43$	12877.7			1.06211			0.531054	−	0.847338i	$-0.321796\pi$
$43$	12877.7			1.06211			0.531054	+	0.847338i	$0.321796\pi$
$44$	−2015.65	−	6096.41i	−0.156958	−	0.474725i
$45$	−5994.52			−0.441289
$46$	−11159.5	−	8107.82i	−0.777586	−	0.564950i
$47$	6117.54	−	18827.8i	0.403954	−	1.24324i	−0.517811	−	0.855495i	$-0.673253\pi$
$47$	6117.54	−	18827.8i	0.403954	−	1.24324i	0.921765	−	0.387748i	$-0.126747\pi$
$48$	−338.375	−	1041.41i	−0.0211980	−	0.0652408i
$49$	−36131.4	+	26251.0i	−2.14978	+	1.56191i
$50$	7809.66	−	5674.05i	0.441781	−	0.320973i
$51$	−420.941	−	1295.52i	−0.0226619	−	0.0697461i
$52$	1732.29	−	5331.43i	0.0888406	−	0.273423i
$53$	4973.19	+	3613.23i	0.243190	+	0.176688i	0.702703	−	0.711483i	$-0.251976\pi$
$53$	4973.19	+	3613.23i	0.243190	+	0.176688i	−0.459513	+	0.888171i	$0.651976\pi$
$54$	8002.17			0.373442
$55$	8628.74	−	6337.37i	0.384628	−	0.282489i
$56$	15867.3			0.676136
$57$	2264.21	+	1645.04i	0.0923058	+	0.0670641i
$58$	−5081.64	+	15639.7i	−0.198351	+	0.610461i
$59$	7700.42	+	23699.4i	0.287995	+	0.886356i	0.985485	+	0.169762i	$0.0542999\pi$
$59$	7700.42	+	23699.4i	0.287995	+	0.886356i	−0.697491	+	0.716594i	$0.745700\pi$
$60$	1477.06	−	1073.15i	0.0529687	−	0.0384840i
$61$	−13593.5	+	9876.26i	−0.467743	+	0.339835i	−0.796561	−	0.604558i	$-0.793350\pi$
$61$	−13593.5	+	9876.26i	−0.467743	+	0.339835i	0.328818	+	0.944393i	$0.393350\pi$
$62$	−8660.82	−	26655.3i	−0.286141	−	0.880650i
$63$	−17215.4	+	52983.6i	−0.546470	+	1.68186i
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	9346.76			0.274396
$66$	−5534.01	+	4064.45i	−0.156380	+	0.114853i
$67$	66822.5			1.81859			0.909297	−	0.416147i	$-0.136620\pi$
$67$	66822.5			1.81859			0.909297	+	0.416147i	$0.136620\pi$
$68$	−4122.30	−	2995.03i	−0.108110	−	0.0785469i
$69$	−4558.11	+	14028.4i	−0.115255	+	0.354720i
$70$	8175.42	+	25161.4i	0.199418	+	0.613746i
$71$	−11254.6	+	8176.95i	−0.264963	+	0.192507i	−0.712332	−	0.701843i	$-0.752361\pi$
$71$	−11254.6	+	8176.95i	−0.264963	+	0.192507i	0.447369	+	0.894349i	$0.352361\pi$
$72$	11634.5	−	8452.98i	0.264495	−	0.192167i
$73$	−17586.7	−	54126.3i	−0.386258	−	1.18878i	−0.935564	−	0.353158i	$-0.885108\pi$
$73$	−17586.7	−	54126.3i	−0.386258	−	1.18878i	0.549306	−	0.835621i	$-0.314892\pi$
$74$	−1776.24	+	5466.70i	−0.0377070	+	0.116050i
$75$	−8351.19	−	6067.49i	−0.171433	−	0.124554i
$76$	10468.9			0.207906
$77$	−31233.4	−	94466.6i	−0.600333	−	1.81573i
$78$	−5994.52			−0.111562
$79$	−46707.4	−	33934.9i	−0.842012	−	0.611758i	0.0809199	−	0.996721i	$-0.474214\pi$
$79$	−46707.4	−	33934.9i	−0.842012	−	0.611758i	−0.922932	+	0.384963i	$0.874214\pi$
$80$	2110.41	−	6495.16i	0.0368673	−	0.113466i
$81$	14229.0	+	43792.4i	0.240970	+	0.741628i
$82$	−28458.4	+	20676.2i	−0.467386	+	0.339576i
$83$	52116.6	−	37865.0i	0.830388	−	0.603312i	−0.0892810	−	0.996006i	$-0.528457\pi$
$83$	52116.6	−	37865.0i	0.830388	−	0.603312i	0.919669	+	0.392694i	$0.128457\pi$
$84$	−5243.28	−	16137.2i	−0.0810783	−	0.249533i
$85$	2625.36	−	8080.02i	0.0394131	−	0.121301i
$86$	−41673.2	−	30277.4i	−0.607590	−	0.441440i
$87$	17584.8			0.249081
$88$	−7810.74	+	24467.5i	−0.107519	+	0.336808i
$89$	−44688.3			−0.598025			−0.299012	−	0.954249i	$-0.596657\pi$
$89$	−44688.3			−0.598025			−0.299012	+	0.954249i	$0.596657\pi$
$90$	19398.7	+	14094.0i	0.252445	+	0.183412i
$91$	26842.6	−	82613.0i	0.339798	−	1.04579i
$92$	17050.1	+	52474.9i	0.210019	+	0.646372i
$93$	−24246.6	+	17616.2i	−0.290699	+	0.211205i
$94$	−64063.7	+	46545.0i	−0.747812	+	0.543317i
$95$	5393.96	+	16600.9i	0.0613195	+	0.188722i
$96$	−1353.50	+	4165.65i	−0.0149893	+	0.0461322i
$97$	119204.	+	86606.8i	1.28636	+	0.934593i	0.999725	−	0.0234473i	$-0.00746418\pi$
$97$	119204.	+	86606.8i	1.28636	+	0.934593i	0.286632	+	0.958041i	$0.407464\pi$
$98$	178644.			1.87898
$99$	−73226.5	−	52627.5i	−0.750897	−	0.539666i
$100$	−38613.1			−0.386131
$101$	72022.8	+	52327.6i	0.702533	+	0.510420i	0.880756	−	0.473570i	$-0.157035\pi$
$101$	72022.8	+	52327.6i	0.702533	+	0.510420i	−0.178223	+	0.983990i	$0.557035\pi$
$102$	−1683.76	+	5182.09i	−0.0160244	+	0.0493179i
$103$	1714.96	+	5278.09i	0.0159279	+	0.0490212i	0.958705	−	0.284404i	$-0.0917956\pi$
$103$	1714.96	+	5278.09i	0.0159279	+	0.0490212i	−0.942777	+	0.333425i	$0.891796\pi$
$104$	−18140.8	+	13180.0i	−0.164464	+	0.119490i
$105$	22887.7	−	16628.9i	0.202595	−	0.147194i
$106$	−7598.36	−	23385.3i	−0.0656833	−	0.202152i
$107$	−63253.1	+	194673.i	−0.534099	+	1.64379i	0.211488	+	0.977381i	$0.432169\pi$
$107$	−63253.1	+	194673.i	−0.534099	+	1.64379i	−0.745587	+	0.666408i	$0.767831\pi$
$108$	−25895.6	−	18814.2i	−0.213632	−	0.155213i
$109$	−17153.0			−0.138285			−0.0691425	−	0.997607i	$-0.522026\pi$
$109$	−17153.0			−0.138285			−0.0691425	+	0.997607i	$0.522026\pi$
$110$	−42823.2	+	220.773i	−0.337441	+	0.00173966i
$111$	6146.61			0.0473509
$112$	−51347.8	−	37306.4i	−0.386791	−	0.281020i
$113$	−13340.1	+	41056.6i	−0.0982795	+	0.302473i	−0.988094	−	0.153848i	$-0.950833\pi$
$113$	−13340.1	+	41056.6i	−0.0982795	+	0.302473i	0.889815	+	0.456322i	$0.150833\pi$
$114$	−3459.40	−	10646.9i	−0.0249309	−	0.0767295i
$115$	−74426.4	+	54073.9i	−0.524786	+	0.381279i
$116$	53215.6	−	38663.4i	0.367193	−	0.266781i
$117$	−24328.3	−	74874.7i	−0.164303	−	0.505674i
$118$	30801.7	−	94797.8i	0.203643	−	0.626748i
$119$	−63877.0	−	46409.3i	−0.413501	−	0.300426i
$120$	−7302.98			−0.0462963
$121$	161042.	−	1660.54i	0.999947	−	0.0103106i
$122$	67210.0			0.408822
$123$	30431.8	+	22110.0i	0.181369	+	0.131773i
$124$	−34643.3	+	106621.i	−0.202332	+	0.622714i
$125$	−45656.6	−	140517.i	−0.261354	−	0.804364i
$126$	180282.	−	130983.i	1.01164	−	0.735000i
$127$	−27072.1	+	19669.0i	−0.148941	+	0.108212i	−0.659760	−	0.751476i	$-0.729342\pi$
$127$	−27072.1	+	19669.0i	−0.148941	+	0.108212i	0.510819	+	0.859688i	$0.329342\pi$
$128$	5062.93	+	15582.1i	0.0273135	+	0.0840623i
$129$	−17021.5	+	52386.8i	−0.0900583	+	0.277171i
$130$	−30246.8	−	21975.6i	−0.156971	−	0.114046i
$131$	−291258.			−1.48286			−0.741429	−	0.671031i	$-0.765852\pi$
$131$	−291258.			−1.48286			−0.741429	+	0.671031i	$0.765852\pi$
$132$	27464.5	−	141.592i	0.137195	−	0.000707302i
$133$	162221.			0.795201
$134$	−216242.	−	157109.i	−1.04035	−	0.755857i
$135$	16492.0	−	50757.2i	0.0778824	−	0.239697i
$136$	6298.32	+	19384.2i	0.0291996	+	0.0898672i
$137$	7972.17	−	5792.12i	0.0362890	−	0.0263655i	−0.569493	−	0.821996i	$-0.692860\pi$
$137$	7972.17	−	5792.12i	0.0362890	−	0.0263655i	0.605782	+	0.795631i	$0.292860\pi$
$138$	47733.1	−	34680.1i	0.213364	−	0.155018i
$139$	−16414.0	−	50517.1i	−0.0720573	−	0.221769i	0.908542	−	0.417794i	$-0.137197\pi$
$139$	−16414.0	−	50517.1i	−0.0720573	−	0.221769i	−0.980599	+	0.196025i	$0.937197\pi$
$140$	32701.7	−	100645.i	0.141010	−	0.433984i
$141$	68505.9	+	49772.5i	0.290189	+	0.210834i
$142$	55645.8			0.231586
$143$	114176.	+	82057.8i	0.466912	+	0.335567i
$144$	−57524.3			−0.231177
$145$	88728.4	+	64465.0i	0.350464	+	0.254627i
$146$	−70346.8	+	216505.i	−0.273125	+	0.840594i
$147$	−59031.8	−	181681.i	−0.225316	−	0.693453i
$148$	18601.0	−	13514.4i	0.0698043	−	0.0507158i
$149$	−207374.	+	150666.i	−0.765223	+	0.555967i	−0.900508	−	0.434840i	$-0.856805\pi$
$149$	−207374.	+	150666.i	−0.765223	+	0.555967i	0.135285	+	0.990807i	$0.456805\pi$
$150$	12759.5	+	39269.6i	0.0463025	+	0.142505i
$151$	61189.6	−	188322.i	0.218391	−	0.672139i	−0.780504	−	0.625150i	$-0.785038\pi$
$151$	61189.6	−	188322.i	0.218391	−	0.672139i	0.998895	−	0.0469885i	$-0.0149624\pi$
$152$	−33878.1	−	24613.9i	−0.118935	−	0.0864115i
$153$	−71560.5			−0.247141
$154$	−121031.	+	379135.i	−0.411239	+	1.28822i
$155$	−186922.			−0.624929
$156$	19398.7	+	14094.0i	0.0638205	+	0.0463683i
$157$	170781.	−	525610.i	0.552955	−	1.70182i	−0.148327	−	0.988938i	$-0.547389\pi$
$157$	170781.	−	525610.i	0.552955	−	1.70182i	0.701282	−	0.712884i	$-0.252611\pi$
$158$	71362.6	+	219632.i	0.227420	+	0.699926i
$159$	−21272.1	+	15455.1i	−0.0667296	+	0.0484819i
$160$	−22100.5	+	16056.9i	−0.0682498	+	0.0495864i
$161$	264200.	+	813123.i	0.803281	+	2.47224i
$162$	56916.1	−	175170.i	0.170391	−	0.524410i
$163$	116271.	+	84475.8i	0.342770	+	0.249037i	0.745830	−	0.666137i	$-0.232053\pi$
$163$	116271.	+	84475.8i	0.342770	+	0.249037i	−0.403060	+	0.915174i	$0.632053\pi$
$164$	140706.			0.408511
$165$	14375.2	+	43478.5i	0.0411060	+	0.124327i
$166$	−257679.			−0.725786
$167$	357081.	+	259435.i	0.990776	+	0.719841i	0.960091	−	0.279688i	$-0.0902310\pi$
$167$	357081.	+	259435.i	0.990776	+	0.719841i	0.0306854	+	0.999529i	$0.490231\pi$
$168$	−20973.1	+	64548.6i	−0.0573310	+	0.176447i
$169$	−76802.8	−	236375.i	−0.206852	−	0.636626i
$170$	−27493.1	+	19974.9i	−0.0729628	+	0.0530105i
$171$	118946.	−	86419.5i	0.311072	−	0.226007i
$172$	63671.0	+	195959.i	0.164105	+	0.505062i
$173$	161154.	−	495982.i	0.409380	−	1.25994i	−0.507803	−	0.861473i	$-0.669542\pi$
$173$	161154.	−	495982.i	0.409380	−	1.25994i	0.917182	−	0.398468i	$-0.130458\pi$
$174$	−56905.7	−	41344.4i	−0.142489	−	0.103525i
$175$	−598327.			−1.47687
$176$	82802.6	−	60814.3i	0.201494	−	0.147987i
$177$	−106588.			−0.255726
$178$	144615.	+	105069.i	0.342107	+	0.248555i
$179$	−110943.	+	341446.i	−0.258801	+	0.796507i	0.734256	+	0.678872i	$0.237531\pi$
$179$	−110943.	+	341446.i	−0.258801	+	0.796507i	−0.993057	+	0.117634i	$0.962469\pi$
$180$	−29638.6	−	91218.1i	−0.0681829	−	0.209846i
$181$	324312.	−	235627.i	0.735812	−	0.534599i	−0.155585	−	0.987823i	$-0.549726\pi$
$181$	324312.	−	235627.i	0.735812	−	0.534599i	0.891397	+	0.453224i	$0.149726\pi$
$182$	−281099.	+	204231.i	−0.629044	+	0.457027i
$183$	−22209.2	−	68352.9i	−0.0490236	−	0.150879i
$184$	68200.6	−	209900.i	0.148506	−	0.457054i
$185$	31014.2	+	22533.1i	0.0666240	+	0.0484052i
$186$	119882.			0.254080
$187$	103007.	−	75653.3i	0.215408	−	0.158206i
$188$	316748.			0.653611
$189$	−401263.	−	291535.i	−0.817099	−	0.593658i
$190$	21575.8	−	66403.6i	0.0433595	−	0.133447i
$191$	−112279.	−	345560.i	−0.222698	−	0.685394i	−0.998517	−	0.0544387i	$-0.982663\pi$
$191$	−112279.	−	345560.i	−0.222698	−	0.685394i	0.775819	−	0.630955i	$-0.217337\pi$
$192$	14174.0	−	10298.0i	0.0277486	−	0.0201605i
$193$	226270.	−	164395.i	0.437254	−	0.317683i	−0.347289	−	0.937758i	$-0.612898\pi$
$193$	226270.	−	164395.i	0.437254	−	0.317683i	0.784543	+	0.620075i	$0.212898\pi$
$194$	−182128.	−	560531.i	−0.347433	−	1.06929i
$195$	−12354.4	+	38022.8i	−0.0232666	+	0.0716073i
$196$	−578103.	−	420016.i	−1.07489	−	0.780955i
$197$	−983666.			−1.80585			−0.902926	−	0.429796i	$-0.858586\pi$
$197$	−983666.			−1.80585			−0.902926	+	0.429796i	$0.858586\pi$
$198$	113231.	+	342472.i	0.205259	+	0.620815i
$199$	−345412.			−0.618308			−0.309154	−	0.951012i	$-0.600046\pi$
$199$	−345412.			−0.618308			−0.309154	+	0.951012i	$0.600046\pi$
$200$	124954.	+	90784.7i	0.220890	+	0.160486i
$201$	−88324.6	+	271835.i	−0.154203	+	0.474587i
$202$	−110041.	−	338672.i	−0.189748	−	0.583983i
$203$	824600.	−	599107.i	1.40444	−	1.02039i
$204$	17632.6	−	12810.8i	0.0296648	−	0.0215527i
$205$	72496.8	+	223122.i	0.120485	+	0.370816i
$206$	6859.82	−	21112.4i	0.0112628	−	0.0346632i
$207$	626894.	+	455465.i	1.01688	+	0.738804i
$208$	89692.8			0.143747
$209$	−79853.5	+	250145.i	−0.126453	+	0.396119i
$210$	−113163.			−0.177074
$211$	487700.	+	354335.i	0.754131	+	0.547908i	0.897105	−	0.441818i	$-0.145666\pi$
$211$	487700.	+	354335.i	0.754131	+	0.547908i	−0.142973	+	0.989727i	$0.545666\pi$
$212$	−30393.4	+	93541.4i	−0.0464451	+	0.142943i
$213$	−18387.9	−	56592.1i	−0.0277704	−	0.0854686i
$214$	662395.	−	481258.i	0.988741	−	0.718362i
$215$	−277933.	+	201930.i	−0.410057	+	0.297924i
$216$	39564.9	+	121768.i	0.0577000	+	0.177582i
$217$	−536813.	+	1.65214e6i	−0.773880	+	2.38176i
$218$	55508.4	+	40329.2i	0.0791075	+	0.0574750i
$219$	243432.			0.342979
$220$	139098.	+	99969.0i	0.193760	+	0.139254i
$221$	111578.			0.153674
$222$	−19890.8	−	14451.5i	−0.0270876	−	0.0196803i
$223$	52180.4	−	160595.i	0.0702660	−	0.216257i	−0.909757	−	0.415142i	$-0.863732\pi$
$223$	52180.4	−	160595.i	0.0702660	−	0.216257i	0.980023	+	0.198885i	$0.0637320\pi$
$224$	78452.5	+	241452.i	0.104469	+	0.321522i
$225$	−438715.	+	318745.i	−0.577732	+	0.419747i
$226$	139699.	−	101498.i	0.181938	−	0.132186i
$227$	76550.7	+	235599.i	0.0986017	+	0.303465i	0.988176	−	0.153326i	$-0.0489986\pi$
$227$	76550.7	+	235599.i	0.0986017	+	0.303465i	−0.889574	+	0.456791i	$0.848999\pi$
$228$	−13837.6	+	42587.7i	−0.0176288	+	0.0542560i
$229$	−1.00001e6	−	726549.i	−1.26013	−	0.915537i	−0.261365	−	0.965240i	$-0.584173\pi$
$229$	−1.00001e6	−	726549.i	−1.26013	−	0.915537i	−0.998764	+	0.0497030i	$0.984173\pi$
$230$	367984.			0.458680
$231$	425575.	−	2194.04i	0.524743	−	0.00270529i
$232$	−263113.			−0.320938
$233$	261056.	+	189668.i	0.315024	+	0.228879i	0.734049	−	0.679096i	$-0.237628\pi$
$233$	261056.	+	189668.i	0.315024	+	0.228879i	−0.419025	+	0.907975i	$0.637628\pi$
$234$	−97313.1	+	299499.i	−0.116180	+	0.357565i
$235$	163200.	+	502278.i	0.192775	+	0.593300i
$236$	−322559.	+	234353.i	−0.376990	+	0.273899i
$237$	199785.	−	145152.i	0.231042	−	0.167862i
$238$	97595.3	+	300367.i	0.111683	+	0.343725i
$239$	214684.	−	660728.i	0.243111	−	0.748218i	−0.752831	−	0.658214i	$-0.771312\pi$
$239$	214684.	−	660728.i	0.243111	−	0.748218i	0.995941	−	0.0900036i	$-0.0286879\pi$
$240$	23632.9	+	17170.3i	0.0264844	+	0.0192420i
$241$	1.18914e6			1.31884			0.659419	−	0.751776i	$-0.270802\pi$
$241$	1.18914e6			1.31884			0.659419	+	0.751776i	$0.270802\pi$
$242$	−525048.	−	373260.i	−0.576316	−	0.409707i
$243$	−683087.			−0.742097
$244$	−217496.	−	158020.i	−0.233871	−	0.169917i
$245$	368174.	−	1.13312e6i	0.391867	−	1.20604i
$246$	−46495.6	−	143099.i	−0.0489862	−	0.150764i
$247$	−185463.	+	134747.i	−0.193426	+	0.140532i
$248$	362789.	−	263582.i	0.374563	−	0.272136i
$249$	85148.6	+	262060.i	0.0870320	+	0.267857i
$250$	−182626.	+	562066.i	−0.184805	+	0.568771i
$251$	−311952.	−	226647.i	−0.312539	−	0.227073i	0.420446	−	0.907317i	$-0.361874\pi$
$251$	−311952.	−	226647.i	−0.312539	−	0.227073i	−0.732985	+	0.680245i	$0.761874\pi$
$252$	−891364.			−0.884207
$253$	−1.38389e6	+	7134.59i	−1.35925	+	0.00700757i
$254$	133852.			0.130179
$255$	29399.5	+	21360.0i	0.0283132	+	0.0205708i
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	−453253.	−	1.39497e6i	−0.428063	−	1.31744i	−0.900030	−	0.435827i	$-0.856456\pi$
$257$	−453253.	−	1.39497e6i	−0.428063	−	1.31744i	0.471967	−	0.881616i	$-0.343544\pi$
$258$	178252.	−	129507.i	0.166719	−	0.121128i
$259$	288231.	−	209412.i	0.266988	−	0.193978i
$260$	46212.9	+	142229.i	0.0423965	+	0.130483i
$261$	285466.	−	878575.i	0.259390	−	0.798321i
$262$	942530.	+	684788.i	0.848286	+	0.616316i
$263$	961837.			0.857456			0.428728	−	0.903434i	$-0.358962\pi$
$263$	961837.			0.857456			0.428728	+	0.903434i	$0.358962\pi$
$264$	−89210.0	−	64114.8i	−0.0787778	−	0.0566172i
$265$	−163991.			−0.143452
$266$	−524957.	−	381404.i	−0.454904	−	0.330507i
$267$	59068.1	−	181793.i	0.0507078	−	0.156063i
$268$	330389.	+	1.01683e6i	0.280988	+	0.864793i
$269$	−113828.	+	82700.9i	−0.0959110	+	0.0696834i	−0.634707	−	0.772753i	$-0.718879\pi$
$269$	−113828.	+	82700.9i	−0.0959110	+	0.0696834i	0.538796	+	0.842436i	$0.318879\pi$
$270$	−172707.	+	125479.i	−0.144178	+	0.104752i
$271$	−479460.	−	1.47563e6i	−0.396578	−	1.22054i	−0.927726	−	0.373263i	$-0.878239\pi$
$271$	−479460.	−	1.47563e6i	−0.396578	−	1.22054i	0.531147	−	0.847280i	$-0.321761\pi$
$272$	25193.3	−	77536.9i	0.0206473	−	0.0635457i
$273$	300591.	+	218392.i	0.244101	+	0.177350i
$274$	−39416.6			−0.0317177
$275$	294528.	−	922621.i	0.234852	−	0.735685i
$276$	−236005.			−0.186487
$277$	240429.	+	174682.i	0.188272	+	0.136788i	0.677929	−	0.735128i	$-0.262878\pi$
$277$	240429.	+	174682.i	0.188272	+	0.136788i	−0.489656	+	0.871915i	$0.662878\pi$
$278$	−65656.0	+	202069.i	−0.0509522	+	0.156815i
$279$	486530.	+	1.49739e6i	0.374196	+	1.15166i
$280$	−342456.	+	248809.i	−0.261042	+	0.189658i
$281$	−357871.	+	260009.i	−0.270372	+	0.196437i	−0.714707	−	0.699424i	$-0.753440\pi$
$281$	−357871.	+	260009.i	−0.270372	+	0.196437i	0.444335	+	0.895861i	$0.353440\pi$
$282$	−104668.	−	322134.i	−0.0783773	−	0.241220i
$283$	−382775.	+	1.17806e6i	−0.284104	+	0.874384i	0.702561	+	0.711623i	$0.252040\pi$
$283$	−382775.	+	1.17806e6i	−0.284104	+	0.874384i	−0.986666	+	0.162760i	$0.947960\pi$
$284$	−180074.	−	130831.i	−0.132481	−	0.0962533i
$285$	−74662.4			−0.0544490
$286$	−176552.	−	533988.i	−0.127631	−	0.386026i
$287$	2.18030e6			1.56247
$288$	186152.	+	135248.i	0.132247	+	0.0960834i
$289$	−407419.	+	1.25391e6i	−0.286944	+	0.883123i
$290$	−135565.	−	417226.i	−0.0946570	−	0.291324i
$291$	−509879.	+	370449.i	−0.352968	+	0.256446i
$292$	736681.	−	535230.i	0.505618	−	0.367353i
$293$	−387305.	−	1.19200e6i	−0.263562	−	0.811162i	−0.992021	−	0.126072i	$-0.959763\pi$
$293$	−387305.	−	1.19200e6i	−0.263562	−	0.811162i	0.728459	−	0.685090i	$-0.240237\pi$
$294$	−236127.	+	726725.i	−0.159323	+	0.490345i
$295$	−537815.	−	390746.i	−0.359814	−	0.261420i
$296$	−91968.5			−0.0610112
$297$	647070.	−	475240.i	0.425657	−	0.312624i
$298$	1.02531e6			0.668829
$299$	−977464.	−	710170.i	−0.632300	−	0.459393i
$300$	51037.9	−	157079.i	0.0327408	−	0.100766i
$301$	986611.	+	3.03648e6i	0.627668	+	1.93176i
$302$	−640786.	+	465558.i	−0.404292	+	0.293735i
$303$	−308068.	+	223824.i	−0.192770	+	0.140056i
$304$	51761.2	+	159305.i	0.0321233	+	0.0988654i
$305$	138516.	−	426308.i	0.0852610	−	0.262406i
$306$	231575.	+	168249.i	0.141380	+	0.102718i
$307$	−1.58831e6			−0.961809			−0.480905	−	0.876773i	$-0.659692\pi$
$307$	−1.58831e6			−0.961809			−0.480905	+	0.876773i	$0.659692\pi$
$308$	1.28306e6	−	942344.i	0.770675	−	0.566021i
$309$	−23738.1			−0.0141433
$310$	604892.	+	439480.i	0.357498	+	0.259737i
$311$	−713092.	+	2.19467e6i	−0.418066	+	1.28667i	0.491414	+	0.870926i	$0.336480\pi$
$311$	−713092.	+	2.19467e6i	−0.418066	+	1.28667i	−0.909480	+	0.415748i	$0.863520\pi$
$312$	−29638.5	−	91218.0i	−0.0172373	−	0.0530510i
$313$	−1.52449e6	+	1.10761e6i	−0.879558	+	0.639036i	−0.933134	−	0.359528i	$-0.882938\pi$
$313$	−1.52449e6	+	1.10761e6i	−0.879558	+	0.639036i	0.0535769	+	0.998564i	$0.482938\pi$
$314$	−1.78844e6	+	1.29938e6i	−1.02365	+	0.743723i
$315$	−459263.	−	1.41347e6i	−0.260786	−	0.802618i
$316$	285450.	−	878526.i	0.160810	−	0.494922i
$317$	1.16948e6	+	849674.i	0.653647	+	0.474902i	0.864511	−	0.502613i	$-0.167628\pi$
$317$	1.16948e6	+	849674.i	0.653647	+	0.474902i	−0.210865	+	0.977515i	$0.567628\pi$
$318$	105175.			0.0583238
$319$	517913.	+	1.56645e6i	0.284957	+	0.861865i
$320$	109271.			0.0596525
$321$	−708326.	−	514629.i	−0.383681	−	0.278761i
$322$	1.05680e6	−	3.25249e6i	0.568005	−	1.74814i
$323$	64391.2	+	198176.i	0.0343416	+	0.105693i
$324$	−596033.	+	433043.i	−0.315433	+	0.229176i
$325$	684053.	−	496993.i	0.359237	−	0.261001i
$326$	−177646.	−	546739.i	−0.0925789	−	0.284929i
$327$	22672.5	−	69778.9i	0.0117255	−	0.0360873i
$328$	−455334.	−	330820.i	−0.233693	−	0.169788i
$329$	4.90816e6			2.49994
$330$	55704.7	−	174497.i	0.0281583	−	0.0882072i
$331$	2.78136e6			1.39536			0.697682	−	0.716407i	$-0.254215\pi$
$331$	2.78136e6			1.39536			0.697682	+	0.716407i	$0.254215\pi$
$332$	833866.	+	605839.i	0.415194	+	0.301656i
$333$	99782.1	−	307098.i	0.0493108	−	0.151763i
$334$	−545571.	−	1.67910e6i	−0.267600	−	0.823587i
$335$	−1.44220e6	+	1.04782e6i	−0.702121	+	0.510121i
$336$	219633.	−	159573.i	0.106133	−	0.0771101i
$337$	240197.	+	739250.i	0.115211	+	0.354582i	0.991991	−	0.126309i	$-0.0403132\pi$
$337$	240197.	+	739250.i	0.115211	+	0.354582i	−0.876780	+	0.480891i	$0.840313\pi$
$338$	−307211.	+	945499.i	−0.146267	+	0.450162i
$339$	−149386.	−	108536.i	−0.0706011	−	0.0512947i
$340$	135933.			0.0637718
$341$	−2.28336e6	−	1.64104e6i	−1.06338	−	0.764245i
$342$	−588103.			−0.271887
$343$	−5.58686e6	−	4.05909e6i	−2.56409	−	1.86292i
$344$	254684.	−	783837.i	0.116039	−	0.357133i
$345$	−121598.	−	374241.i	−0.0550022	−	0.169279i
$346$	−1.68763e6	+	1.22613e6i	−0.757856	+	0.550615i
$347$	−717707.	+	521445.i	−0.319981	+	0.232480i	−0.736167	−	0.676800i	$-0.763366\pi$
$347$	−717707.	+	521445.i	−0.319981	+	0.232480i	0.416187	+	0.909279i	$0.363366\pi$
$348$	86944.2	+	267587.i	0.0384851	+	0.118445i
$349$	964120.	−	2.96726e6i	0.423709	−	1.30404i	−0.480516	−	0.876986i	$-0.659551\pi$
$349$	964120.	−	2.96726e6i	0.423709	−	1.30404i	0.904225	−	0.427056i	$-0.140449\pi$
$350$	1.93623e6	+	1.40675e6i	0.844862	+	0.613828i
$351$	700915.			0.303667
$352$	−410938.	+	2118.57i	−0.176774	+	0.000911353i
$353$	−2.74141e6			−1.17095			−0.585474	−	0.810691i	$-0.699092\pi$
$353$	−2.74141e6			−1.17095			−0.585474	+	0.810691i	$0.699092\pi$
$354$	344926.	+	250603.i	0.146291	+	0.106287i
$355$	114683.	−	352958.i	0.0482978	−	0.148645i
$356$	−220951.	−	680018.i	−0.0923999	−	0.284378i
$357$	273225.	−	198510.i	0.113462	−	0.0824349i
$358$	1.16181e6	−	844101.i	0.479100	−	0.348086i
$359$	23033.4	+	70889.4i	0.00943238	+	0.0290299i	0.955662	−	0.294466i	$-0.0951418\pi$
$359$	23033.4	+	70889.4i	0.00943238	+	0.0290299i	−0.946230	+	0.323496i	$0.895142\pi$
$360$	−118554.	+	364872.i	−0.0482126	+	0.148383i
$361$	1.65685e6	+	1.20377e6i	0.669138	+	0.486157i
$362$	−1.60349e6			−0.643123
$363$	−206107.	+	657318.i	−0.0820969	+	0.261824i
$364$	1.38983e6			0.549805
$365$	1.22830e6	+	892409.i	0.482582	+	0.350616i
$366$	−88836.8	+	273411.i	−0.0346649	+	0.106688i
$367$	−619573.	−	1.90685e6i	−0.240119	−	0.739012i	−0.996401	−	0.0847653i	$-0.972986\pi$
$367$	−619573.	−	1.90685e6i	−0.240119	−	0.739012i	0.756282	−	0.654246i	$-0.227014\pi$
$368$	−714206.	+	518901.i	−0.274918	+	0.199740i
$369$	1.59868e6	−	1.16151e6i	0.611217	−	0.444075i
$370$	−47385.4	−	145837.i	−0.0179945	−	0.0553815i
$371$	−470960.	+	1.44947e6i	−0.177643	+	0.546730i
$372$	−387945.	−	281859.i	−0.145349	−	0.105602i
$373$	1.18585e6			0.441325			0.220662	−	0.975350i	$-0.429178\pi$
$373$	1.18585e6			0.441325			0.220662	+	0.975350i	$0.429178\pi$
$374$	−511209.	+	2635.52i	−0.188982	+	0.000974286i
$375$	631972.			0.232070
$376$	−1.02502e6	−	744720.i	−0.373906	−	0.271659i
$377$	−445104.	+	1.36989e6i	−0.161290	+	0.496401i
$378$	613076.	+	1.88685e6i	0.220691	+	0.679217i
$379$	852348.	−	619267.i	0.304803	−	0.221452i	−0.424860	−	0.905259i	$-0.639677\pi$
$379$	852348.	−	619267.i	0.304803	−	0.221452i	0.729663	+	0.683807i	$0.239677\pi$
$380$	−225945.	+	164159.i	−0.0802683	+	0.0583183i
$381$	−44230.7	−	136128.i	−0.0156103	−	0.0480435i
$382$	−449117.	+	1.38224e6i	−0.157471	+	0.484647i
$383$	−2.59766e6	−	1.88731e6i	−0.904867	−	0.657425i	0.0348442	−	0.999393i	$-0.488907\pi$
$383$	−2.59766e6	−	1.88731e6i	−0.904867	−	0.657425i	−0.939712	+	0.341968i	$0.888907\pi$
$384$	−70080.4			−0.0242532
$385$	2.15539e6	+	1.54907e6i	0.741094	+	0.532621i
$386$	−1.11874e6			−0.382174
$387$	2.34104e6	+	1.70086e6i	0.794567	+	0.577287i
$388$	−728510.	+	2.24212e6i	−0.245672	+	0.756102i
$389$	1.02564e6	+	3.15659e6i	0.343653	+	1.05766i	0.962301	+	0.271987i	$0.0876808\pi$
$389$	1.02564e6	+	3.15659e6i	0.343653	+	1.05766i	−0.618648	+	0.785669i	$0.712319\pi$
$390$	129376.	−	93997.5i	0.0430719	−	0.0312935i
$391$	−888476.	+	645516.i	−0.293903	+	0.213533i
$392$	883263.	+	2.71840e6i	0.290319	+	0.893509i
$393$	384978.	−	1.18484e6i	0.125735	−	0.386972i
$394$	3.18321e6	+	2.31274e6i	1.03306	+	0.750561i
$395$	1.54018e6			0.496683
$396$	438776.	−	1.37449e6i	0.140606	−	0.440456i
$397$	1.28321e6			0.408621			0.204311	−	0.978906i	$-0.434505\pi$
$397$	1.28321e6			0.408621			0.204311	+	0.978906i	$0.434505\pi$
$398$	1.11778e6	+	812113.i	0.353710	+	0.256986i
$399$	−214420.	+	659916.i	−0.0674268	+	0.207518i
$400$	−190913.	−	587571.i	−0.0596605	−	0.183616i
$401$	832356.	−	604742.i	0.258493	−	0.187806i	−0.450990	−	0.892529i	$-0.648929\pi$
$401$	832356.	−	604742.i	0.258493	−	0.187806i	0.709482	+	0.704723i	$0.248929\pi$
$402$	924947.	−	672013.i	0.285464	−	0.207402i
$403$	−758607.	−	2.33475e6i	−0.232677	−	0.716107i
$404$	−440164.	+	1.35469e6i	−0.134172	+	0.412938i
$405$	−993788.	−	722029.i	−0.301062	−	0.218734i
$406$	−4.07705e6			−1.22753
$407$	181032.	+	547537.i	0.0541712	+	0.163843i
$408$	−87180.4			−0.0259280
$409$	−1.65183e6	−	1.20012e6i	−0.488266	−	0.354746i	0.316251	−	0.948675i	$-0.397576\pi$
$409$	−1.65183e6	−	1.20012e6i	−0.488266	−	0.354746i	−0.804517	+	0.593930i	$0.797576\pi$
$410$	289987.	−	892489.i	0.0851960	−	0.262206i
$411$	13025.0	+	40086.8i	0.00380341	+	0.0117057i
$412$	−71837.0	+	52192.6i	−0.0208500	+	0.0151484i
$413$	−4.99820e6	+	3.63141e6i	−1.44191	+	1.04761i
$414$	−957809.	−	2.94783e6i	−0.274649	−	0.845283i
$415$	−531061.	+	1.63444e6i	−0.151365	+	0.465852i
$416$	−290252.	−	210880.i	−0.0822322	−	0.0597452i
$417$	227200.			0.0639836
$418$	846537.	−	621738.i	0.236976	−	0.174047i
$419$	797311.			0.221867			0.110933	−	0.993828i	$-0.464616\pi$
$419$	797311.			0.221867			0.110933	+	0.993828i	$0.464616\pi$
$420$	366203.	+	266062.i	0.101297	+	0.0735969i
$421$	980563.	−	3.01786e6i	0.269631	−	0.829839i	−0.720959	−	0.692978i	$-0.756298\pi$
$421$	980563.	−	3.01786e6i	0.269631	−	0.829839i	0.990590	−	0.136862i	$-0.0437016\pi$
$422$	−745140.	−	2.29330e6i	−0.203684	−	0.626875i
$423$	3.59884e6	−	2.61471e6i	0.977940	−	0.710515i
$424$	318284.	−	231247.i	0.0859806	−	0.0624685i
$425$	−237497.	−	730942.i	−0.0637803	−	0.196296i
$426$	−73551.5	+	226368.i	−0.0196367	+	0.0604354i
$427$	−3.37020e6	−	2.44859e6i	−0.894512	−	0.649901i
$428$	−3.27506e6			−0.864191
$429$	−484728.	+	356008.i	−0.127161	+	0.0933934i
$430$	1.37418e6			0.358403
$431$	5.49188e6	+	3.99008e6i	1.42406	+	1.03464i	0.991085	+	0.133233i	$0.0425358\pi$
$431$	5.49188e6	+	3.99008e6i	1.42406	+	1.03464i	0.432974	+	0.901406i	$0.357464\pi$
$432$	158260.	−	487073.i	0.0408000	−	0.125570i
$433$	−823285.	−	2.53381e6i	−0.211023	−	0.649463i	−0.999412	−	0.0342855i	$-0.989084\pi$
$433$	−823285.	−	2.53381e6i	−0.211023	−	0.649463i	0.788389	−	0.615177i	$-0.210916\pi$
$434$	5.62158e6	−	4.08432e6i	1.43263	−	1.04087i
$435$	−379524.	+	275740.i	−0.0961648	+	0.0698678i
$436$	−84809.3	−	261016.i	−0.0213662	−	0.0657584i
$437$	697252.	−	2.14592e6i	0.174657	−	0.537539i
$438$	−787764.	−	572344.i	−0.196205	−	0.142551i
$439$	−2.51318e6			−0.622390			−0.311195	−	0.950346i	$-0.600729\pi$
$439$	−2.51318e6			−0.622390			−0.311195	+	0.950346i	$0.600729\pi$
$440$	−215089.	−	650546.i	−0.0529647	−	0.160194i
$441$	−1.00355e7			−2.45721
$442$	−361075.	−	262337.i	−0.0879108	−	0.0638709i
$443$	−796545.	+	2.45151e6i	−0.192842	+	0.593505i	0.807153	+	0.590342i	$0.201007\pi$
$443$	−796545.	+	2.45151e6i	−0.192842	+	0.593505i	−0.999995	+	0.00316367i	$0.998993\pi$
$444$	30390.5	+	93532.3i	0.00731611	+	0.0225167i
$445$	964485.	−	700739.i	0.230885	−	0.167748i
$446$	−546440.	+	397012.i	−0.130079	+	0.0945076i
$447$	−338809.	−	1.04275e6i	−0.0802021	−	0.246837i
$448$	313810.	−	965807.i	0.0738706	−	0.227350i
$449$	−1.83008e6	−	1.32963e6i	−0.428405	−	0.311255i	0.352606	−	0.935772i	$-0.385296\pi$
$449$	−1.83008e6	−	1.32963e6i	−0.428405	−	0.311255i	−0.781011	+	0.624517i	$0.785296\pi$
$450$	2.16913e6			0.504957
$451$	−1.07326e6	+	3.36203e6i	−0.248464	+	0.778325i
$452$	−690712.			−0.159020
$453$	685219.	+	497840.i	0.156886	+	0.113984i
$454$	306203.	−	942395.i	0.0697220	−	0.214582i
$455$	716090.	+	2.20390e6i	0.162158	+	0.499072i
$456$	144909.	−	105283.i	0.0326350	−	0.0237107i
$457$	6.57114e6	−	4.77422e6i	1.47181	−	1.06933i	0.491720	−	0.870753i	$-0.336368\pi$
$457$	6.57114e6	−	4.77422e6i	1.47181	−	1.06933i	0.980085	−	0.198576i	$-0.0636318\pi$
$458$	1.52788e6	+	4.70232e6i	0.340349	+	1.04749i
$459$	196876.	−	605921.i	0.0436175	−	0.134241i
$460$	−1.19082e6	−	865183.i	−0.262393	−	0.190640i
$461$	−696701.			−0.152684			−0.0763421	−	0.997082i	$-0.524324\pi$
$461$	−696701.			−0.152684			−0.0763421	+	0.997082i	$0.524324\pi$
$462$	−1.38235e6	−	993488.i	−0.301310	−	0.216550i
$463$	1.94210e6			0.421036			0.210518	−	0.977590i	$-0.432485\pi$
$463$	1.94210e6			0.421036			0.210518	+	0.977590i	$0.432485\pi$
$464$	851450.	+	618615.i	0.183596	+	0.133391i
$465$	247069.	−	760401.i	0.0529891	−	0.163084i
$466$	−398858.	−	1.22756e6i	−0.0850852	−	0.261865i
$467$	1.02824e6	−	747060.i	0.218174	−	0.158512i	−0.473331	−	0.880885i	$-0.656948\pi$
$467$	1.02824e6	−	747060.i	0.218174	−	0.158512i	0.691504	+	0.722372i	$0.256948\pi$
$468$	1.01908e6	−	740402.i	0.215076	−	0.156262i
$469$	5.11952e6	+	1.57563e7i	1.07473	+	3.30766i
$470$	652800.	−	2.00911e6i	0.136312	−	0.419527i
$471$	1.91245e6	+	1.38948e6i	0.397227	+	0.288602i
$472$	1.59482e6			0.329501
$473$	−5.16792e6	+	26643.0i	−1.06209	+	0.00547558i
$474$	−987790.			−0.201938
$475$	1.27748e6	+	928143.i	0.259788	+	0.188747i
$476$	390381.	−	1.20147e6i	0.0789717	−	0.243050i
$477$	426846.	+	1.31370e6i	0.0858964	+	0.264362i
$478$	−2.24820e6	+	1.63341e6i	−0.450054	+	0.326983i
$479$	4.34813e6	−	3.15910e6i	0.865892	−	0.629108i	−0.0635892	−	0.997976i	$-0.520255\pi$
$479$	4.34813e6	−	3.15910e6i	0.865892	−	0.629108i	0.929482	+	0.368868i	$0.120255\pi$
$480$	−36107.9	−	111129.i	−0.00715318	−	0.0220152i
$481$	−155582.	+	478832.i	−0.0306617	+	0.0943671i
$482$	−3.84815e6	−	2.79584e6i	−0.754456	−	0.548145i
$483$	−3.65701e6			−0.713277
$484$	821506.	+	2.44236e6i	0.159403	+	0.473910i
$485$	−3.93076e6			−0.758792
$486$	2.21052e6	+	1.60603e6i	0.424525	+	0.308435i
$487$	−1.27362e6	+	3.91980e6i	−0.243342	+	0.748931i	0.752562	+	0.658521i	$0.228818\pi$
$487$	−1.27362e6	+	3.91980e6i	−0.243342	+	0.748931i	−0.995905	+	0.0904096i	$0.971182\pi$
$488$	332305.	+	1.02273e6i	0.0631665	+	0.194406i
$489$	−497334.	+	361334.i	−0.0940536	+	0.0683340i
$490$	−3.85557e6	+	2.80124e6i	−0.725435	+	0.527059i
$491$	−301095.	−	926675.i	−0.0563637	−	0.173470i	0.918911	−	0.394464i	$-0.129070\pi$
$491$	−301095.	−	926675.i	−0.0563637	−	0.173470i	−0.975275	+	0.220994i	$0.929070\pi$
$492$	−185982.	+	572395.i	−0.0346385	+	0.106606i
$493$	1.05921e6	+	769560.i	0.196275	+	0.142602i
$494$	916980.			0.169061
$495$	2.40564e6	−	12402.2i	0.441283	−	0.00227502i
$496$	−1.79373e6			−0.327380
$497$	−2.79032e6	−	2.02729e6i	−0.506715	−	0.368150i
$498$	340594.	−	1.04824e6i	0.0615409	−	0.189404i
$499$	−1.74115e6	−	5.35872e6i	−0.313030	−	0.963406i	−0.976558	−	0.215255i	$-0.930942\pi$
$499$	−1.74115e6	−	5.35872e6i	−0.313030	−	0.963406i	0.663528	−	0.748151i	$-0.269058\pi$
$500$	1.91249e6	−	1.38950e6i	0.342116	−	0.248562i
$501$	−1.52737e6	+	1.10970e6i	−0.271862	+	0.197519i
$502$	476621.	+	1.46689e6i	0.0844138	+	0.259799i
$503$	391597.	−	1.20521e6i	0.0690111	−	0.212394i	−0.910603	−	0.413282i	$-0.864382\pi$
$503$	391597.	−	1.20521e6i	0.0690111	−	0.212394i	0.979614	+	0.200887i	$0.0643825\pi$
$504$	2.88452e6	+	2.09572e6i	0.505821	+	0.367500i
$505$	−2.37496e6			−0.414407
$506$	4.49514e6	+	3.23063e6i	0.780489	+	0.560933i
$507$	1.06309e6			0.183675
$508$	−433154.	−	314705.i	−0.0744703	−	0.0541058i
$509$	567484.	−	1.74654e6i	0.0970865	−	0.298802i	−0.890705	−	0.454581i	$-0.849789\pi$
$509$	567484.	−	1.74654e6i	0.0970865	−	0.298802i	0.987792	+	0.155780i	$0.0497889\pi$
$510$	−44918.4	−	138245.i	−0.00764714	−	0.0235355i
$511$	1.14152e7	−	8.29363e6i	1.93389	−	1.40505i
$512$	−212079.	+	154084.i	−0.0357538	+	0.0259767i
$513$	404494.	+	1.24490e6i	0.0678607	+	0.208854i
$514$	−1.81301e6	+	5.57988e6i	−0.302687	+	0.931573i
$515$	−119777.	−	87022.7i	−0.0199000	−	0.0144582i
$516$	−881324.			−0.145717
$517$	−2.41605e6	+	7.56839e6i	−0.397539	+	1.24531i
$518$	−1.42509e6			−0.233356
$519$	1.80465e6	+	1.31116e6i	0.294086	+	0.213666i
$520$	184852.	−	568915.i	0.0299789	−	0.0922655i
$521$	−3.50060e6	−	1.07738e7i	−0.565000	−	1.73889i	−0.667950	−	0.744206i	$-0.732828\pi$
$521$	−3.50060e6	−	1.07738e7i	−0.565000	−	1.73889i	0.102950	−	0.994687i	$-0.467172\pi$
$522$	−2.98944e6	+	2.17196e6i	−0.480191	+	0.348879i
$523$	−2.61689e6	+	1.90128e6i	−0.418342	+	0.303943i	−0.776970	−	0.629537i	$-0.783244\pi$
$523$	−2.61689e6	+	1.90128e6i	−0.418342	+	0.303943i	0.358629	+	0.933480i	$0.383244\pi$
$524$	−1.44006e6	−	4.43204e6i	−0.229114	−	0.705141i
$525$	790856.	−	2.43400e6i	0.125227	−	0.385410i
$526$	−3.11257e6	−	2.26141e6i	−0.490518	−	0.356382i
$527$	−2.23141e6			−0.349987
$528$	137947.	+	417225.i	0.0215341	+	0.0651307i
$529$	5.45556e6			0.847617
$530$	530687.	+	385567.i	0.0820633	+	0.0596225i
$531$	−1.73032e6	+	5.32536e6i	−0.266311	+	0.819621i
$532$	802063.	+	2.46850e6i	0.122865	+	0.378141i
$533$	−2.49269e6	+	1.81105e6i	−0.380058	+	0.276129i
$534$	−618569.	+	449417.i	−0.0938718	+	0.0682018i
$535$	−1.68743e6	−	5.19337e6i	−0.254883	−	0.784449i
$536$	1.32155e6	−	4.06733e6i	0.198689	−	0.611501i
$537$	−1.24237e6	−	902632.i	−0.185915	−	0.135075i
$538$	562796.			0.0838293
$539$	1.44455e7	−	1.06095e7i	2.14170	−	1.57297i
$540$	853908.			0.126016
$541$	−2.57354e6	−	1.86979e6i	−0.378040	−	0.274662i	0.382497	−	0.923957i	$-0.375064\pi$
$541$	−2.57354e6	−	1.86979e6i	−0.378040	−	0.274662i	−0.760537	+	0.649295i	$0.775064\pi$
$542$	−1.91784e6	+	5.90250e6i	−0.280423	+	0.863054i
$543$	529864.	+	1.63075e6i	0.0771196	+	0.237350i
$544$	−263827.	+	191682.i	−0.0382228	+	0.0277705i
$545$	370205.	−	268970.i	0.0533889	−	0.0387893i
$546$	−459262.	−	1.41346e6i	−0.0659294	−	0.202910i
$547$	−1.70754e6	+	5.25527e6i	−0.244007	+	0.750977i	0.751791	+	0.659402i	$0.229190\pi$
$547$	−1.70754e6	+	5.25527e6i	−0.244007	+	0.750977i	−0.995798	+	0.0915756i	$0.970810\pi$
$548$	127555.	+	92673.9i	0.0181445	+	0.0131828i
$549$	−3.77559e6			−0.534631
$550$	−3.12232e6	+	2.29319e6i	−0.440120	+	0.323246i
$551$	−2.68995e6			−0.377455
$552$	763730.	+	554882.i	0.106682	+	0.0775091i
$553$	4.42318e6	−	1.36132e7i	0.615067	−	1.89298i
$554$	−367342.	−	1.13056e6i	−0.0508506	−	0.156502i
$555$	−132659.	+	96382.4i	−0.0182812	+	0.0132821i
$556$	687559.	−	499541.i	0.0943242	−	0.0685305i
$557$	−692564.	−	2.13149e6i	−0.0945849	−	0.291102i	0.892560	−	0.450928i	$-0.148907\pi$
$557$	−692564.	−	2.13149e6i	−0.0945849	−	0.291102i	−0.987145	+	0.159826i	$0.948907\pi$
$558$	1.94612e6	−	5.98955e6i	0.264597	−	0.814345i
$559$	−3.65018e6	−	2.65201e6i	−0.494066	−	0.358960i
$560$	1.69320e6			0.228159
$561$	171607.	+	519031.i	0.0230211	+	0.0696283i
$562$	1.76941e6			0.236314
$563$	3.52631e6	+	2.56201e6i	0.468867	+	0.340652i	0.797000	−	0.603980i	$-0.206419\pi$
$563$	3.52631e6	+	2.56201e6i	0.468867	+	0.340652i	−0.328133	+	0.944632i	$0.606419\pi$
$564$	−418671.	+	1.28854e6i	−0.0554211	+	0.170569i
$565$	−355879.	−	1.09528e6i	−0.0469009	−	0.144346i
$566$	4.00848e6	−	2.91233e6i	0.525943	−	0.382120i
$567$	−9.23580e6	+	6.71020e6i	−1.20647	+	0.876552i
$568$	275128.	+	846758.i	0.0357820	+	0.110126i
$569$	901504.	−	2.77454e6i	0.116731	−	0.359262i	−0.875573	−	0.483086i	$-0.839516\pi$
$569$	901504.	−	2.77454e6i	0.116731	−	0.359262i	0.992304	+	0.123824i	$0.0395159\pi$
$570$	241613.	+	175542.i	0.0311482	+	0.0226305i
$571$	−4.46777e6			−0.573457			−0.286728	−	0.958012i	$-0.592568\pi$
$571$	−4.46777e6			−0.573457			−0.286728	+	0.958012i	$0.592568\pi$
$572$	−684148.	+	2.14312e6i	−0.0874299	+	0.273878i
$573$	1.55415e6			0.197746
$574$	−7.05561e6	−	5.12620e6i	−0.893830	−	0.649406i
$575$	−2.57171e6	+	7.91491e6i	−0.324379	+	0.998336i
$576$	−284416.	−	875341.i	−0.0357188	−	0.109931i
$577$	−7.50325e6	+	5.45143e6i	−0.938231	+	0.681665i	−0.947994	−	0.318288i	$-0.896892\pi$
$577$	−7.50325e6	+	5.45143e6i	−0.938231	+	0.681665i	0.00976340	+	0.999952i	$0.496892\pi$
$578$	4.26655e6	−	3.09983e6i	0.531199	−	0.385939i
$579$	369682.	+	1.13776e6i	0.0458281	+	0.141044i
$580$	−542260.	+	1.66890e6i	−0.0669326	+	0.205997i
$581$	1.29211e7	+	9.38775e6i	1.58804	+	1.15378i
$582$	2.52098e6			0.308505
$583$	−2.00325e6	−	1.43972e6i	−0.244097	−	0.175432i
$584$	−3.64235e6			−0.441926
$585$	1.69914e6	+	1.23450e6i	0.205277	+	0.149142i
$586$	−1.54922e6	+	4.76800e6i	−0.186367	+	0.573578i
$587$	1.03915e6	+	3.19818e6i	0.124476	+	0.383096i	0.993805	−	0.111136i	$-0.0354491\pi$
$587$	1.03915e6	+	3.19818e6i	0.124476	+	0.383096i	−0.869330	+	0.494233i	$0.835449\pi$
$588$	2.47276e6	−	1.79656e6i	0.294943	−	0.214289i
$589$	3.70899e6	−	2.69474e6i	0.440522	−	0.320058i
$590$	821709.	+	2.52896e6i	0.0971824	+	0.299097i
$591$	1.30019e6	−	4.00157e6i	0.153122	−	0.471261i
$592$	297616.	+	216231.i	0.0349022	+	0.0253579i
$593$	2.54991e6			0.297775			0.148887	−	0.988854i	$-0.452431\pi$
$593$	2.54991e6			0.297775			0.148887	+	0.988854i	$0.452431\pi$
$594$	−3.21132e6	+	16555.8i	−0.373437	+	0.00192524i
$595$	2.10635e6			0.243915
$596$	−3.31798e6	−	2.41065e6i	−0.382611	−	0.277983i
$597$	456559.	−	1.40514e6i	0.0524277	−	0.161356i
$598$	1.49343e6	+	4.59631e6i	0.170778	+	0.525602i
$599$	−9.68867e6	+	7.03923e6i	−1.10331	+	0.801601i	−0.981597	−	0.190964i	$-0.938839\pi$
$599$	−9.68867e6	+	7.03923e6i	−1.10331	+	0.801601i	−0.121712	+	0.992565i	$0.538839\pi$
$600$	−534476.	+	388320.i	−0.0606108	+	0.0440363i
$601$	2.97646e6	+	9.16059e6i	0.336135	+	1.03452i	0.966160	+	0.257942i	$0.0830444\pi$
$601$	2.97646e6	+	9.16059e6i	0.336135	+	1.03452i	−0.630026	+	0.776574i	$0.716956\pi$
$602$	3.94644e6	−	1.21459e7i	0.443828	−	1.36596i
$603$	1.21476e7	+	8.82577e6i	1.36050	+	0.988461i
$604$	3.16822e6			0.353364
$605$	−3.44966e6	+	2.56108e6i	−0.383166	+	0.284469i
$606$	1.52317e6			0.168487
$607$	−1.17375e6	−	852777.i	−0.129301	−	0.0939429i	0.521255	−	0.853401i	$-0.325464\pi$
$607$	−1.17375e6	−	852777.i	−0.129301	−	0.0939429i	−0.650556	+	0.759458i	$0.725464\pi$
$608$	207045.	−	637218.i	0.0227146	−	0.0699084i
$609$	1.34724e6	+	4.14637e6i	0.147198	+	0.453028i
$610$	−1.45056e6	+	1.05389e6i	−0.157838	+	0.114676i
$611$	−5.61138e6	+	4.07691e6i	−0.608088	+	0.441802i
$612$	−353815.	−	1.08893e6i	−0.0381854	−	0.117523i
$613$	−4.04623e6	+	1.24530e7i	−0.434910	+	1.33852i	0.458268	+	0.888814i	$0.348470\pi$
$613$	−4.04623e6	+	1.24530e7i	−0.434910	+	1.33852i	−0.893179	+	0.449702i	$0.851530\pi$
$614$	5.13988e6	+	3.73434e6i	0.550214	+	0.399754i
$615$	−1.00349e6			−0.106986
$616$	−6.36766e6	+	32828.2i	−0.676127	+	0.00348574i
$617$	2.37821e6			0.251500			0.125750	−	0.992062i	$-0.459866\pi$
$617$	2.37821e6			0.251500			0.125750	+	0.992062i	$0.459866\pi$
$618$	76818.3	+	55811.7i	0.00809083	+	0.00587833i
$619$	4.79961e6	−	1.47717e7i	0.503477	−	1.54954i	−0.299840	−	0.953990i	$-0.596933\pi$
$619$	4.79961e6	−	1.47717e7i	0.503477	−	1.54954i	0.803317	−	0.595552i	$-0.203067\pi$
$620$	−924192.	−	2.84437e6i	−0.0965569	−	0.297171i
$621$	−5.58124e6	+	4.05501e6i	−0.580767	+	0.421952i
$622$	7.46760e6	−	5.42553e6i	0.773936	−	0.562297i
$623$	−3.42374e6	−	1.05372e7i	−0.353412	−	1.08769i
$624$	−118554.	+	364872.i	−0.0121886	+	0.0375127i
$625$	−2.91253e6	−	2.11608e6i	−0.298243	−	0.216686i
$626$	7.53750e6			0.768761
$627$	−912044.	−	655481.i	−0.0926503	−	0.0665873i
$628$	8.84254e6			0.894701
$629$	370236.	+	268992.i	0.0373123	+	0.0271090i
$630$	−1.83705e6	+	5.65386e6i	−0.184404	+	0.567536i
$631$	1.62176e6	+	4.99126e6i	0.162149	+	0.499042i	0.998815	−	0.0486710i	$-0.0154986\pi$
$631$	1.62176e6	+	4.99126e6i	0.162149	+	0.499042i	−0.836666	+	0.547713i	$0.815499\pi$
$632$	−2.98928e6	+	2.17184e6i	−0.297696	+	0.216289i
$633$	−2.08607e6	+	1.51562e6i	−0.206928	+	0.150342i
$634$	−1.78680e6	−	5.49920e6i	−0.176544	−	0.543346i
$635$	275861.	−	849013.i	0.0271491	−	0.0835565i
$636$	−340354.	−	247282.i	−0.0333648	−	0.0242409i
$637$	1.56475e7			1.52791
$638$	2.00694e6	−	6.28682e6i	0.195201	−	0.611476i
$639$	−3.12596e6			−0.302853
$640$	−353607.	−	256911.i	−0.0341249	−	0.0247932i
$641$	2.76367e6	−	8.50572e6i	0.265670	−	0.817647i	−0.725869	−	0.687833i	$-0.758562\pi$
$641$	2.76367e6	−	8.50572e6i	0.265670	−	0.817647i	0.991538	−	0.129814i	$-0.0414379\pi$
$642$	1.08223e6	+	3.33075e6i	0.103629	+	0.318937i
$643$	−2.41405e6	+	1.75391e6i	−0.230260	+	0.167294i	−0.696933	−	0.717136i	$-0.745453\pi$
$643$	−2.41405e6	+	1.75391e6i	−0.230260	+	0.167294i	0.466673	+	0.884430i	$0.345453\pi$
$644$	−1.10669e7	+	8.04060e6i	−1.05151	+	0.763966i
$645$	−454090.	−	1.39754e6i	−0.0429776	−	0.132272i
$646$	257565.	−	792703.i	0.0242832	−	0.0747359i
$647$	−7.28511e6	−	5.29294e6i	−0.684188	−	0.497092i	0.190556	−	0.981676i	$-0.438971\pi$
$647$	−7.28511e6	−	5.29294e6i	−0.684188	−	0.497092i	−0.874745	+	0.484584i	$0.838971\pi$
$648$	2.94695e6			0.275699
$649$	−3.13926e6	−	9.49481e6i	−0.292560	−	0.884860i
$650$	−3.38214e6			−0.313985
$651$	−6.01139e6	−	4.36753e6i	−0.555933	−	0.403909i
$652$	−710585.	+	2.18696e6i	−0.0654632	+	0.201475i
$653$	593661.	+	1.82710e6i	0.0544823	+	0.167679i	0.974595	−	0.223974i	$-0.0719032\pi$
$653$	593661.	+	1.82710e6i	0.0544823	+	0.167679i	−0.920113	+	0.391654i	$0.871903\pi$
$654$	−237430.	+	172503.i	−0.0217066	+	0.0157707i
$655$	6.28607e6	−	4.56709e6i	0.572500	−	0.415946i
$656$	695689.	+	2.14111e6i	0.0631184	+	0.194258i
$657$	3.95180e6	−	1.21624e7i	0.357176	−	1.09927i
$658$	−1.58831e7	−	1.15398e7i	−1.43012	−	1.03904i
$659$	−1.90140e7			−1.70554			−0.852768	−	0.522290i	$-0.825078\pi$
$659$	−1.90140e7			−1.70554			−0.852768	+	0.522290i	$0.825078\pi$
$660$	−590532.	+	433716.i	−0.0527696	+	0.0387566i
$661$	4.96738e6			0.442205			0.221103	−	0.975251i	$-0.429034\pi$
$661$	4.96738e6			0.442205			0.221103	+	0.975251i	$0.429034\pi$
$662$	−9.00068e6	−	6.53938e6i	−0.798234	−	0.579951i
$663$	−147482.	+	453903.i	−0.0130303	+	0.0401032i
$664$	−1.27403e6	−	3.92107e6i	−0.112140	−	0.345132i
$665$	−3.50112e6	+	2.54371e6i	−0.307011	+	0.223056i
$666$	−1.04493e6	+	759187.i	−0.0912856	+	0.0663229i
$667$	−4.38096e6	−	1.34832e7i	−0.381290	−	1.17349i
$668$	−2.18229e6	+	6.71638e6i	−0.189221	+	0.582364i
$669$	584331.	+	424542.i	0.0504770	+	0.0366737i
$670$	7.13061e6			0.613676
$671$	5.43473e6	−	3.99153e6i	0.465985	−	0.342242i
$672$	−1.08593e6			−0.0927635
$673$	2.18225e6	+	1.58550e6i	0.185724	+	0.134936i	0.676762	−	0.736202i	$-0.263383\pi$
$673$	2.18225e6	+	1.58550e6i	0.185724	+	0.134936i	−0.491038	+	0.871138i	$0.663383\pi$
$674$	960788.	−	2.95700e6i	0.0814662	−	0.250727i
$675$	−1.49192e6	−	4.59164e6i	−0.126033	−	0.387890i
$676$	3.21716e6	−	2.33740e6i	0.270773	−	0.196728i
$677$	1.58486e7	−	1.15147e7i	1.32898	−	0.965562i	0.329209	−	0.944257i	$-0.393218\pi$
$677$	1.58486e7	−	1.15147e7i	1.32898	−	0.965562i	0.999773	−	0.0213049i	$-0.00678209\pi$
$678$	228242.	+	702457.i	0.0190687	+	0.0586875i
$679$	−1.12886e7	+	3.47427e7i	−0.939649	+	2.89194i
$680$	−439889.	−	319598.i	−0.0364814	−	0.0265053i
$681$	−1.05960e6			−0.0875539
$682$	3.53079e6	+	1.06790e7i	0.290677	+	0.879164i
$683$	1.93523e7			1.58738			0.793689	−	0.608324i	$-0.208158\pi$
$683$	1.93523e7			1.58738			0.793689	+	0.608324i	$0.208158\pi$
$684$	1.90314e6	+	1.38271e6i	0.155536	+	0.113003i
$685$	−81235.3	+	250016.i	−0.00661482	+	0.0203583i
$686$	8.53597e6	+	2.62710e7i	0.692536	+	2.13141i
$687$	4.27740e6	−	3.10771e6i	0.345771	−	0.251217i
$688$	−2.66709e6	+	1.93775e6i	−0.214816	+	0.156073i
$689$	−665545.	−	2.04834e6i	−0.0534108	−	0.164382i
$690$	−486394.	+	1.49697e6i	−0.0388924	+	0.119699i
$691$	−6.10065e6	−	4.43238e6i	−0.486050	−	0.353136i	0.317613	−	0.948220i	$-0.397119\pi$
$691$	−6.10065e6	−	4.43238e6i	−0.486050	−	0.353136i	−0.803663	+	0.595084i	$0.797119\pi$
$692$	8.34409e6			0.662390
$693$	6.79904e6	−	2.12983e7i	0.537792	−	1.68466i
$694$	3.54854e6			0.279673
$695$	1.14639e6	+	832903.i	0.0900267	+	0.0654083i
$696$	347777.	−	1.07035e6i	0.0272131	−	0.0837532i
$697$	865441.	+	2.66355e6i	0.0674770	+	0.207673i
$698$	−1.00964e7	+	7.33546e6i	−0.784382	+	0.569887i
$699$	−1.11663e6	+	811281.i	−0.0864405	+	0.0628027i
$700$	−2.95829e6	−	9.10468e6i	−0.228190	−	0.702295i
$701$	−1.27831e6	+	3.93422e6i	−0.0982517	+	0.302388i	−0.988087	−	0.153893i	$-0.950819\pi$
$701$	−1.27831e6	+	3.93422e6i	−0.0982517	+	0.302388i	0.889836	+	0.456281i	$0.150819\pi$
$702$	−2.26821e6	−	1.64795e6i	−0.173716	−	0.126212i
$703$	−940245.			−0.0717551
$704$	1.33480e6	+	959316.i	0.101505	+	0.0729508i
$705$	−2.25899e6			−0.171175
$706$	8.87140e6	+	6.44545e6i	0.669855	+	0.486678i
$707$	−6.82054e6	+	2.09915e7i	−0.513181	+	1.57941i
$708$	−527000.	−	1.62194e6i	−0.0395119	−	0.121605i
$709$	−6.87829e6	+	4.99737e6i	−0.513884	+	0.373358i	−0.814295	−	0.580451i	$-0.802876\pi$
$709$	−6.87829e6	+	4.99737e6i	−0.513884	+	0.373358i	0.300411	+	0.953810i	$0.402876\pi$
$710$	−1.20097e6	+	872559.i	−0.0894104	+	0.0649605i
$711$	−4.00887e6	−	1.23380e7i	−0.297405	−	0.915318i
$712$	−883805.	+	2.72007e6i	−0.0653366	+	0.201085i
$713$	1.95479e7	+	1.42024e7i	1.44004	+	1.04625i
$714$	−1.35090e6			−0.0991693
$715$	−3.75091e6	+	19337.7i	−0.274392	+	0.00141462i
$716$	−5.74428e6			−0.418748
$717$	2.40409e6	+	1.74667e6i	0.174644	+	0.126886i
$718$	92133.4	−	283558.i	0.00666970	−	0.0205272i
$719$	756187.	+	2.32730e6i	0.0545516	+	0.167892i	0.974620	−	0.223865i	$-0.0718674\pi$
$719$	756187.	+	2.32730e6i	0.0545516	+	0.167892i	−0.920069	+	0.391757i	$0.871867\pi$
$720$	1.24152e6	−	902014.i	0.0892526	−	0.0648458i
$721$	−1.11315e6	+	808748.i	−0.0797470	+	0.0579396i
$722$	−2.53144e6	−	7.79098e6i	−0.180728	−	0.556223i
$723$	−1.57178e6	+	4.83745e6i	−0.111827	+	0.344168i
$724$	5.18899e6	+	3.77003e6i	0.367906	+	0.267299i
$725$	9.92147e6			0.701021
$726$	2.21242e6	−	1.64254e6i	0.155785	−	0.115658i
$727$	1.95778e7			1.37381			0.686907	−	0.726745i	$-0.258968\pi$
$727$	1.95778e7			1.37381			0.686907	+	0.726745i	$0.258968\pi$
$728$	−4.49759e6	−	3.26769e6i	−0.314522	−	0.228514i
$729$	−2.55476e6	+	7.86274e6i	−0.178046	+	0.547968i
$730$	−1.87667e6	−	5.77579e6i	−0.130341	−	0.401148i
$731$	−3.31787e6	+	2.41057e6i	−0.229650	+	0.166850i
$732$	930311.	−	675910.i	0.0641727	−	0.0466242i
$733$	6.86146e6	+	2.11174e7i	0.471690	+	1.45171i	0.850371	+	0.526184i	$0.176378\pi$
$733$	6.86146e6	+	2.11174e7i	0.471690	+	1.45171i	−0.378681	+	0.925527i	$0.623622\pi$
$734$	−2.47829e6	+	7.62740e6i	−0.169790	+	0.522560i
$735$	4.12292e6	+	2.99548e6i	0.281505	+	0.204526i
$736$	3.53123e6			0.240287
$737$	−2.68163e7	+	138250.i	−1.81857	+	0.00937556i
$738$	−7.90431e6			−0.534224
$739$	−1.63436e7	−	1.18743e7i	−1.10087	−	0.799828i	−0.119667	−	0.992814i	$-0.538183\pi$
$739$	−1.63436e7	−	1.18743e7i	−1.10087	−	0.799828i	−0.981201	+	0.192986i	$0.938183\pi$
$740$	−189542.	+	583350.i	−0.0127241	+	0.0391606i
$741$	−303011.	−	932572.i	−0.0202728	−	0.0623931i
$742$	4.93196e6	−	3.58328e6i	0.328859	−	0.238930i
$743$	1.08677e7	−	7.89582e6i	0.722211	−	0.524717i	−0.164879	−	0.986314i	$-0.552723\pi$
$743$	1.08677e7	−	7.89582e6i	0.722211	−	0.524717i	0.887090	+	0.461597i	$0.152723\pi$
$744$	592728.	+	1.82423e6i	0.0392575	+	0.120822i
$745$	2.11311e6	−	6.50348e6i	0.139486	−	0.429294i
$746$	−3.83750e6	−	2.78810e6i	−0.252465	−	0.183426i
$747$	1.44754e7			0.949136
$748$	1.66050e6	+	1.19340e6i	0.108514	+	0.0779885i
$749$	−5.07485e7			−3.30536
$750$	−2.04510e6	−	1.48585e6i	−0.132758	−	0.0964546i
$751$	5.07534e6	−	1.56203e7i	0.328371	−	1.01062i	−0.641525	−	0.767102i	$-0.721698\pi$
$751$	5.07534e6	−	1.56203e7i	0.328371	−	1.01062i	0.969896	−	0.243520i	$-0.0783022\pi$
$752$	1.56609e6	+	4.81993e6i	0.100989	+	0.310811i
$753$	1.33433e6	−	969450.i	0.0857585	−	0.0623072i
$754$	4.66119e6	−	3.38655e6i	0.298585	−	0.216935i
$755$	1.63238e6	+	5.02395e6i	0.104221	+	0.320758i
$756$	2.45230e6	−	7.54741e6i	0.156052	−	0.480279i
$757$	−9.57374e6	−	6.95573e6i	−0.607214	−	0.441167i	0.241218	−	0.970471i	$-0.422453\pi$
$757$	−9.57374e6	−	6.95573e6i	−0.607214	−	0.441167i	−0.848432	+	0.529304i	$0.822453\pi$
$758$	−4.21424e6			−0.266407
$759$	1.80017e6	−	5.63912e6i	0.113425	−	0.355309i
$760$	1.11713e6			0.0701571
$761$	1.99372e7	+	1.44852e7i	1.24797	+	0.906701i	0.998102	−	0.0615795i	$-0.0196138\pi$
$761$	1.99372e7	+	1.44852e7i	1.24797	+	0.906701i	0.249865	+	0.968281i	$0.419614\pi$
$762$	−176923.	+	544512.i	−0.0110381	+	0.0339719i
$763$	−1.31416e6	−	4.04456e6i	−0.0817215	−	0.251513i
$764$	4.70322e6	−	3.41709e6i	0.291516	−	0.211798i
$765$	1.54445e6	−	1.12211e6i	0.0954160	−	0.0693238i
$766$	3.96887e6	+	1.22149e7i	0.244396	+	0.752175i
$767$	2.69794e6	−	8.30340e6i	0.165594	−	0.509645i
$768$	226785.	+	164769.i	0.0138743	+	0.0100803i
$769$	3.87154e6			0.236085			0.118042	−	0.993009i	$-0.462338\pi$
$769$	3.87154e6			0.236085			0.118042	+	0.993009i	$0.462338\pi$
$770$	−3.33290e6	−	1.00805e7i	−0.202580	−	0.612710i
$771$	6.27386e6			0.380101
$772$	3.62032e6	+	2.63032e6i	0.218627	+	0.158842i
$773$	3.88671e6	−	1.19621e7i	0.233956	−	0.720041i	−0.763303	−	0.646041i	$-0.776423\pi$
$773$	3.88671e6	−	1.19621e7i	0.233956	−	0.720041i	0.997258	−	0.0740003i	$-0.0235766\pi$
$774$	−3.57679e6	−	1.10082e7i	−0.214605	−	0.660487i
$775$	−1.36801e7	+	9.93915e6i	−0.818152	+	0.594422i
$776$	7.62906e6	−	5.54284e6i	0.454796	−	0.330429i
$777$	470914.	+	1.44933e6i	0.0279827	+	0.0861219i
$778$	4.10255e6	−	1.26264e7i	0.242999	−	0.747876i
$779$	−4.65514e6	−	3.38216e6i	−0.274846	−	0.199687i
$780$	−639672.			−0.0376462
$781$	4.49963e6	−	3.30475e6i	0.263967	−	0.193870i
$782$	4.39287e6			0.256880
$783$	6.65376e6	+	4.83424e6i	0.387849	+	0.281789i
$784$	3.53305e6	−	1.08736e7i	0.205286	−	0.631806i
$785$	4.55599e6	+	1.40219e7i	0.263881	+	0.812143i
$786$	−4.03155e6	+	2.92909e6i	−0.232764	+	0.169113i
$787$	−1.07082e7	+	7.77996e6i	−0.616282	+	0.447755i	−0.851621	−	0.524158i	$-0.824380\pi$
$787$	−1.07082e7	+	7.77996e6i	−0.616282	+	0.447755i	0.235339	+	0.971913i	$0.424380\pi$
$788$	−4.86351e6	−	1.49684e7i	−0.279020	−	0.858734i
$789$	−1.27133e6	+	3.91277e6i	−0.0727055	+	0.223765i
$790$	−4.98413e6	−	3.62118e6i	−0.284133	−	0.206435i
$791$	−1.07029e7			−0.608219
$792$	−4.65152e6	+	3.41630e6i	−0.263501	+	0.193528i
$793$	5.88697e6			0.332437
$794$	−4.15255e6	−	3.01701e6i	−0.233757	−	0.169834i
$795$	216760.	−	667119.i	0.0121636	−	0.0374357i
$796$	−1.70781e6	−	5.25611e6i	−0.0955339	−	0.294023i
$797$	8.07740e6	−	5.86857e6i	0.450428	−	0.327255i	−0.339337	−	0.940665i	$-0.610203\pi$
$797$	8.07740e6	−	5.86857e6i	0.450428	−	0.327255i	0.789765	+	0.613410i	$0.210203\pi$
$798$	2.24543e6	−	1.63140e6i	0.124823	−	0.0906889i
$799$	1.94822e6	+	5.99602e6i	0.107962	+	0.332274i
$800$	−763654.	+	2.35028e6i	−0.0421863	+	0.129836i
$801$	−8.12387e6	−	5.90234e6i	−0.447385	−	0.325044i
$802$	−4.11539e6			−0.225931
$803$	7.16963e6	+	2.16848e7i	0.392381	+	1.18677i
$804$	−4.57319e6			−0.249505
$805$	−1.84523e7	−	1.34064e7i	−1.00360	−	0.729159i
$806$	−3.03443e6	+	9.33900e6i	−0.164528	+	0.506364i
$807$	−185973.	−	572366.i	−0.0100523	−	0.0309379i
$808$	4.60946e6	−	3.34897e6i	0.248383	−	0.180461i
$809$	−2.04173e7	+	1.48340e7i	−1.09680	+	0.796870i	−0.980534	−	0.196348i	$-0.937092\pi$
$809$	−2.04173e7	+	1.48340e7i	−1.09680	+	0.796870i	−0.116263	+	0.993218i	$0.537092\pi$
$810$	1.51837e6	+	4.67307e6i	0.0813141	+	0.250259i
$811$	927407.	−	2.85427e6i	0.0495129	−	0.152385i	−0.923243	−	0.384216i	$-0.874472\pi$
$811$	927407.	−	2.85427e6i	0.0495129	−	0.152385i	0.972756	+	0.231831i	$0.0744717\pi$
$812$	1.31936e7	+	9.58572e6i	0.702220	+	0.510193i
$813$	6.63661e6			0.352144
$814$	701506.	−	2.19750e6i	0.0371082	−	0.116243i
$815$	−3.83405e6			−0.202192
$816$	282122.	+	204973.i	0.0148324	+	0.0107764i
$817$	2.60378e6	−	8.01360e6i	0.136474	−	0.420023i
$818$	2.52377e6	+	7.76736e6i	0.131876	+	0.405873i
$819$	1.57910e7	−	1.14729e7i	0.822623	−	0.597671i
$820$	−3.03679e6	+	2.20635e6i	−0.157717	+	0.114588i
$821$	−5.01417e6	−	1.54320e7i	−0.259622	−	0.799033i	−0.992884	−	0.119087i	$-0.962003\pi$
$821$	−5.01417e6	−	1.54320e7i	−0.259622	−	0.799033i	0.733262	−	0.679946i	$-0.237997\pi$
$822$	52100.0	−	160347.i	0.00268942	−	0.00827717i
$823$	3.05087e6	+	2.21658e6i	0.157009	+	0.114073i	0.663516	−	0.748162i	$-0.269064\pi$
$823$	3.05087e6	+	2.21658e6i	0.157009	+	0.114073i	−0.506507	+	0.862236i	$0.669064\pi$
$824$	355182.			0.0182235
$825$	3.36394e6	+	2.41764e6i	0.172073	+	0.123668i
$826$	2.47125e7			1.26028
$827$	2.45796e7	+	1.78581e7i	1.24972	+	0.907972i	0.998205	−	0.0598821i	$-0.0190725\pi$
$827$	2.45796e7	+	1.78581e7i	1.24972	+	0.907972i	0.251511	+	0.967854i	$0.419072\pi$
$828$	−3.83124e6	+	1.17913e7i	−0.194206	+	0.597705i
$829$	−6.08855e6	−	1.87386e7i	−0.307700	−	0.947004i	−0.978656	−	0.205506i	$-0.934116\pi$
$829$	−6.08855e6	−	1.87386e7i	−0.307700	−	0.947004i	0.670956	−	0.741497i	$-0.265884\pi$
$830$	5.56135e6	−	4.04055e6i	0.280211	−	0.203585i
$831$	−1.02840e6	+	747177.i	−0.0516606	+	0.0375336i
$832$	443466.	+	1.36485e6i	0.0222102	+	0.0683558i
$833$	4.39514e6	−	1.35268e7i	0.219462	−	0.675435i
$834$	−735235.	−	534180.i	−0.0366025	−	0.0265933i
$835$	−1.17748e7			−0.584435
$836$	−4.20124e6	+	21659.3i	−0.207904	+	0.00107184i
$837$	−1.40173e7			−0.691593
$838$	−2.58015e6	−	1.87459e6i	−0.126921	−	0.0922138i
$839$	−905404.	+	2.78655e6i	−0.0444056	+	0.136666i	−0.970801	−	0.239885i	$-0.922890\pi$
$839$	−905404.	+	2.78655e6i	−0.0444056	+	0.136666i	0.926396	+	0.376551i	$0.122890\pi$
$840$	−559508.	−	1.72199e6i	−0.0273595	−	0.0842039i
$841$	2.92033e6	−	2.12174e6i	0.142378	−	0.103443i
$842$	−1.02686e7	+	7.46056e6i	−0.499149	+	0.362653i
$843$	−584693.	−	1.79950e6i	−0.0283374	−	0.0872134i
$844$	−2.98056e6	+	9.17322e6i	−0.144026	+	0.443267i
$845$	5.36409e6	+	3.89724e6i	0.258437	+	0.187765i
$846$	−1.77937e7			−0.854751
$847$	1.27296e7	+	3.78454e7i	0.609686	+	1.81261i
$848$	−1.57368e6			−0.0751498
$849$	−4.28643e6	−	3.11427e6i	−0.204092	−	0.148282i
$850$	−949990.	+	2.92377e6i	−0.0450995	+	0.138802i
$851$	−1.53132e6	−	4.71293e6i	−0.0724842	−	0.223083i
$852$	770241.	−	559613.i	0.0363520	−	0.0264112i
$853$	−2.17005e7	+	1.57663e7i	−1.02117	+	0.741921i	−0.966522	−	0.256585i	$-0.917403\pi$
$853$	−2.17005e7	+	1.57663e7i	−1.02117	+	0.741921i	−0.0546451	+	0.998506i	$0.517403\pi$
$854$	5.14921e6	+	1.58476e7i	0.241599	+	0.743567i
$855$	−1.21205e6	+	3.73029e6i	−0.0567027	+	0.174513i
$856$	1.05983e7	+	7.70013e6i	0.494370	+	0.359181i
$857$	−2.33342e7			−1.08528			−0.542639	−	0.839966i	$-0.682575\pi$
$857$	−2.33342e7			−1.08528			−0.542639	+	0.839966i	$0.682575\pi$
$858$	2.40564e6	−	12402.2i	0.111561	−	0.000575147i
$859$	2.92630e7			1.35312			0.676559	−	0.736389i	$-0.263471\pi$
$859$	2.92630e7			1.35312			0.676559	+	0.736389i	$0.263471\pi$
$860$	−4.44693e6	−	3.23089e6i	−0.205029	−	0.148962i
$861$	−2.88188e6	+	8.86951e6i	−0.132485	+	0.407748i
$862$	−8.39085e6	−	2.58244e7i	−0.384625	−	1.18375i
$863$	2.81459e7	−	2.04492e7i	1.28644	−	0.934650i	0.286709	−	0.958018i	$-0.407439\pi$
$863$	2.81459e7	−	2.04492e7i	1.28644	−	0.934650i	0.999727	+	0.0233677i	$0.00743883\pi$
$864$	−1.65732e6	+	1.20411e6i	−0.0755302	+	0.0548759i
$865$	4.29918e6	+	1.32315e7i	0.195364	+	0.601269i
$866$	−3.29314e6	+	1.01352e7i	−0.149216	+	0.459240i
$867$	−4.56240e6	−	3.31478e6i	−0.206132	−	0.149764i
$868$	−2.77946e7			−1.25216
$869$	1.88142e7	+	1.35217e7i	0.845155	+	0.607409i
$870$	1.87647e6			0.0840511
$871$	−1.89408e7	−	1.37613e7i	−0.845966	−	0.614630i
$872$	−339237.	+	1.04406e6i	−0.0151082	+	0.0464982i
$873$	1.02312e7	+	3.14884e7i	0.454351	+	1.39835i
$874$	−7.30172e6	+	5.30501e6i	−0.323330	+	0.234913i
$875$	2.96349e7	−	2.15310e7i	1.30853	−	0.950701i
$876$	1.20360e6	+	3.70429e6i	0.0529932	+	0.163096i
$877$	7.02553e6	−	2.16224e7i	0.308447	−	0.949302i	−0.669922	−	0.742432i	$-0.733672\pi$
$877$	7.02553e6	−	2.16224e7i	0.308447	−	0.949302i	0.978368	−	0.206870i	$-0.0663277\pi$
$878$	8.13282e6	+	5.90884e6i	0.356045	+	0.258682i
$879$	5.36101e6			0.234032
$880$	−833481.	+	2.61091e6i	−0.0362818	+	0.113654i
$881$	−1.22248e6			−0.0530642			−0.0265321	−	0.999648i	$-0.508446\pi$
$881$	−1.22248e6			−0.0530642			−0.0265321	+	0.999648i	$0.508446\pi$
$882$	3.24755e7	+	2.35949e7i	1.40567	+	1.02128i
$883$	−3.32947e6	+	1.02471e7i	−0.143705	+	0.442280i	−0.996842	−	0.0794073i	$-0.974697\pi$
$883$	−3.32947e6	+	1.02471e7i	−0.143705	+	0.442280i	0.853137	+	0.521687i	$0.174697\pi$
$884$	551674.	+	1.69788e6i	0.0237439	+	0.0730762i
$885$	2.30043e6	−	1.67136e6i	0.0987305	−	0.0717319i
$886$	8.34152e6	−	6.06047e6i	0.356994	−	0.259371i
$887$	−2.16403e6	−	6.66018e6i	−0.0923535	−	0.284235i	0.894201	−	0.447665i	$-0.147744\pi$
$887$	−2.16403e6	−	6.66018e6i	−0.0923535	−	0.284235i	−0.986555	+	0.163430i	$0.947744\pi$
$888$	121562.	−	374129.i	0.00517327	−	0.0159217i
$889$	−6.71192e6	−	4.87649e6i	−0.284834	−	0.206944i
$890$	−4.76868e6			−0.201801
$891$	−5.80080e6	−	1.75447e7i	−0.244790	−	0.740376i
$892$	2.70175e6			0.113693
$893$	−1.04793e7	−	7.61368e6i	−0.439749	−	0.319497i
$894$	−1.35523e6	+	4.17098e6i	−0.0567114	+	0.174540i
$895$	−2.95966e6	−	9.10889e6i	−0.123505	−	0.380109i
$896$	−3.28626e6	+	2.38761e6i	−0.136751	+	0.0993557i
$897$	4.18097e6	−	3.03765e6i	0.173499	−	0.126054i
$898$	2.79612e6	+	8.60557e6i	0.115708	+	0.356114i
$899$	8.90145e6	−	2.73958e7i	0.367334	−	1.13054i
$900$	−7.01945e6	−	5.09993e6i	−0.288866	−	0.209874i
$901$	−1.95767e6			−0.0803393
$902$	1.13778e7	−	8.35638e6i	0.465629	−	0.341981i
$903$	−1.36565e7			−0.557341
$904$	2.23519e6	+	1.62396e6i	0.0909690	+	0.0660928i
$905$	−3.30470e6	+	1.01708e7i	−0.134125	+	0.412795i
$906$	−1.04692e6	−	3.22209e6i	−0.0423734	−	0.130412i
$907$	−584594.	+	424732.i	−0.0235959	+	0.0171434i	−0.599521	−	0.800359i	$-0.704642\pi$
$907$	−584594.	+	424732.i	−0.0235959	+	0.0171434i	0.575925	+	0.817503i	$0.304642\pi$
$908$	−3.20660e6	+	2.32973e6i	−0.129071	+	0.0937758i
$909$	6.18167e6	+	1.90252e7i	0.248140	+	0.763695i
$910$	2.86436e6	−	8.81560e6i	0.114663	−	0.352897i
$911$	−1.07649e7	−	7.82115e6i	−0.429748	−	0.312230i	0.351800	−	0.936075i	$-0.385570\pi$
$911$	−1.07649e7	−	7.82115e6i	−0.429748	−	0.312230i	−0.781548	+	0.623845i	$0.785570\pi$
$912$	−716470.			−0.0285240
$913$	−2.08364e7	+	1.53033e7i	−0.827267	+	0.607585i
$914$	−3.24895e7			−1.28641
$915$	1.55114e6	+	1.12697e6i	0.0612490	+	0.0445000i
$916$	6.11151e6	−	1.88093e7i	0.240663	−	0.740685i
$917$	−2.23144e7	−	6.86765e7i	−0.876316	−	2.69702i
$918$	−2.06171e6	+	1.49792e6i	−0.0807460	+	0.0586654i
$919$	−3.87440e6	+	2.81491e6i	−0.151327	+	0.109945i	−0.660872	−	0.750498i	$-0.729813\pi$
$919$	−3.87440e6	+	2.81491e6i	−0.151327	+	0.109945i	0.509546	+	0.860444i	$0.329813\pi$
$920$	1.81941e6	+	5.59958e6i	0.0708699	+	0.218115i
$921$	2.09939e6	−	6.46127e6i	0.0815539	−	0.250997i
$922$	2.25457e6	+	1.63804e6i	0.0873447	+	0.0634596i
$923$	4.87406e6			0.188316
$924$	2.13755e6	+	6.46509e6i	0.0823637	+	0.249112i
$925$	3.46795e6			0.133266
$926$	−6.28477e6	−	4.56615e6i	−0.240858	−	0.174994i
$927$	−385358.	+	1.18601e6i	−0.0147287	+	0.0453303i
$928$	−1.30090e6	−	4.00376e6i	−0.0495877	−	0.152615i
$929$	1.48761e7	−	1.08081e7i	0.565522	−	0.410876i	−0.267954	−	0.963432i	$-0.586347\pi$
$929$	1.48761e7	−	1.08081e7i	0.565522	−	0.410876i	0.833476	+	0.552556i	$0.186347\pi$
$930$	−2.58734e6	+	1.87981e6i	−0.0980949	+	0.0712702i
$931$	9.03009e6	+	2.77917e7i	0.341443	+	1.05085i
$932$	−1.59543e6	+	4.91024e6i	−0.0601643	+	0.185167i
$933$	−7.98541e6	−	5.80174e6i	−0.300326	−	0.218200i
$934$	−5.08390e6			−0.190691
$935$	−1.03686e6	+	3.24799e6i	−0.0387873	+	0.121503i
$936$	−5.03859e6			−0.187983
$937$	1.20080e7	+	8.72431e6i	0.446808	+	0.324625i	0.788334	−	0.615247i	$-0.210944\pi$
$937$	1.20080e7	+	8.72431e6i	0.446808	+	0.324625i	−0.341526	+	0.939872i	$0.610944\pi$
$938$	2.04781e7	−	6.30251e7i	0.759945	−	2.33887i
$939$	−2.49073e6	−	7.66567e6i	−0.0921854	−	0.283718i
$940$	−6.83621e6	+	4.96680e6i	−0.252346	+	0.183340i
$941$	9.28589e6	−	6.74660e6i	0.341861	−	0.248377i	−0.403586	−	0.914942i	$-0.632236\pi$
$941$	9.28589e6	−	6.74660e6i	0.341861	−	0.248377i	0.745447	+	0.666565i	$0.232236\pi$
$942$	−2.92197e6	−	8.99290e6i	−0.107287	−	0.330196i
$943$	9.37132e6	−	2.88420e7i	0.343180	−	1.05620i
$944$	−5.16095e6	−	3.74965e6i	−0.188495	−	0.136950i
$945$	1.32317e7			0.481988
$946$	1.67864e7	+	1.20643e7i	0.609858	+	0.438302i
$947$	−4.57615e7			−1.65816			−0.829078	−	0.559133i	$-0.811134\pi$
$947$	−4.57615e7			−1.65816			−0.829078	+	0.559133i	$0.811134\pi$
$948$	3.19656e6	+	2.32243e6i	0.115521	+	0.0839310i
$949$	−6.16172e6	+	1.89638e7i	−0.222094	+	0.683534i
$950$	−1.95181e6	−	6.00707e6i	−0.0701665	−	0.215950i
$951$	−5.00227e6	+	3.63436e6i	−0.179356	+	0.130310i
$952$	−4.08813e6	+	2.97020e6i	−0.146195	+	0.106217i
$953$	3.04751e6	+	9.37927e6i	0.108696	+	0.334531i	0.990580	−	0.136935i	$-0.0437250\pi$
$953$	3.04751e6	+	9.37927e6i	0.108696	+	0.334531i	−0.881884	+	0.471466i	$0.843725\pi$
$954$	1.70738e6	−	5.25478e6i	0.0607379	−	0.186932i
$955$	7.84185e6	+	5.69744e6i	0.278234	+	0.202149i
$956$	1.11157e7			0.393361
$957$	−7.05690e6	+	36381.5i	−0.249077	+	0.00128411i
$958$	−2.14983e7			−0.756818
$959$	1.97652e6	+	1.43602e6i	0.0693991	+	0.0504214i
$960$	−144432.	+	444515.i	−0.00505806	+	0.0155671i
$961$	6.32415e6	+	1.94637e7i	0.220899	+	0.679857i
$962$	1.62928e6	−	1.18374e6i	0.0567619	−	0.0412399i
$963$	−3.72107e7	+	2.70352e7i	−1.29301	+	0.939427i
$964$	5.87945e6	+	1.80951e7i	0.203772	+	0.627145i
$965$	−2.30566e6	+	7.09609e6i	−0.0797034	+	0.245302i
$966$	1.18343e7	+	8.59815e6i	0.408038	+	0.296457i
$967$	−1.16954e7			−0.402206			−0.201103	−	0.979570i	$-0.564453\pi$
$967$	−1.16954e7			−0.402206			−0.201103	+	0.979570i	$0.564453\pi$
$968$	3.08388e6	−	9.83511e6i	0.105781	−	0.337358i
$969$	−891293.			−0.0304938
$970$	1.27202e7	+	9.24178e6i	0.434075	+	0.315374i
$971$	−1.03326e7	+	3.18005e7i	−0.351691	+	1.08239i	0.606212	+	0.795303i	$0.292688\pi$
$971$	−1.03326e7	+	3.18005e7i	−0.351691	+	1.08239i	−0.957903	+	0.287091i	$0.907312\pi$
$972$	−3.37737e6	−	1.03945e7i	−0.114660	−	0.352888i
$973$	1.06540e7	−	7.74061e6i	0.360771	−	0.262116i
$974$	1.33375e7	−	9.69028e6i	0.450482	−	0.327295i
$975$	1.11761e6	+	3.43965e6i	0.0376512	+	0.115879i
$976$	1.32922e6	−	4.09091e6i	0.0446655	−	0.137466i
$977$	9.59962e6	+	6.97453e6i	0.321749	+	0.233765i	0.736922	−	0.675978i	$-0.236279\pi$
$977$	9.59962e6	+	6.97453e6i	0.321749	+	0.233765i	−0.415172	+	0.909743i	$0.636279\pi$
$978$	2.45895e6			0.0822059
$979$	1.79337e7	−	92456.5i	0.598017	−	0.00308305i
$980$	1.90630e7			0.634054
$981$	−3.11824e6	−	2.26554e6i	−0.103452	−	0.0751620i
$982$	−1.20438e6	+	3.70670e6i	−0.0398552	+	0.122662i
$983$	1.57967e7	+	4.86174e7i	0.521415	+	1.60475i	0.771297	+	0.636475i	$0.219608\pi$
$983$	1.57967e7	+	4.86174e7i	0.521415	+	1.60475i	−0.249882	+	0.968276i	$0.580392\pi$
$984$	1.94763e6	−	1.41504e6i	0.0641238	−	0.0465887i
$985$	2.12300e7	−	1.54245e7i	0.697202	−	0.506547i
$986$	−1.61833e6	−	4.98070e6i	−0.0530120	−	0.163154i
$987$	−6.48750e6	+	1.99665e7i	−0.211975	+	0.652391i
$988$	−2.96741e6	−	2.15595e6i	−0.0967130	−	0.0702661i
$989$	4.44084e7			1.44369
$990$	−7.81397e6	−	5.61586e6i	−0.253387	−	0.182108i
$991$	−9.95092e6			−0.321869			−0.160934	−	0.986965i	$-0.551451\pi$
$991$	−9.95092e6			−0.321869			−0.160934	+	0.986965i	$0.551451\pi$
$992$	5.80462e6	+	4.21731e6i	0.187282	+	0.136068i
$993$	−3.67635e6	+	1.13146e7i	−0.118316	+	0.364139i
$994$	4.26324e6	+	1.31209e7i	0.136859	+	0.421209i
$995$	7.45485e6	−	5.41627e6i	0.238716	−	0.173437i
$996$	−3.56675e6	+	2.59140e6i	−0.113926	+	0.0827724i
$997$	1.73606e6	+	5.34306e6i	0.0553131	+	0.170236i	0.974896	−	0.222659i	$-0.0714736\pi$
$997$	1.73606e6	+	5.34306e6i	0.0553131	+	0.170236i	−0.919583	+	0.392895i	$0.871474\pi$
$998$	−6.96461e6	+	2.14349e7i	−0.221345	+	0.681231i
$999$	2.32576e6	+	1.68976e6i	0.0737311	+	0.0535688i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.6.c.b.15.2	yes	12
3.2	odd	2		198.6.f.e.37.2		12
11.3	even	5	inner	22.6.c.b.3.2	✓	12
11.5	even	5		242.6.a.p.1.3		6
11.6	odd	10		242.6.a.o.1.3		6
33.14	odd	10		198.6.f.e.91.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.6.c.b.3.2	✓	12	11.3	even	5	inner
22.6.c.b.15.2	yes	12	1.1	even	1	trivial
198.6.f.e.37.2		12	3.2	odd	2
198.6.f.e.91.2		12	33.14	odd	10
242.6.a.o.1.3		6	11.6	odd	10
242.6.a.p.1.3		6	11.5	even	5

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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	22.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23607 - 2.35114i) q^{2} +(-1.32178 + 4.06802i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-21.5825 + 15.6806i) q^{5} +(13.8418 - 10.0567i) q^{6} +(76.6137 + 235.793i) q^{7} +(19.7771 - 60.8676i) q^{8} +(181.789 + 132.078i) q^{9} +106.710 q^{10} +(-401.306 + 2.06892i) q^{11} -68.4378 q^{12} +(-283.449 - 205.938i) q^{13} +(306.455 - 943.171i) q^{14} +(-35.2616 - 108.524i) q^{15} +(-207.108 + 150.473i) q^{16} +(-257.644 + 187.189i) q^{17} +(-277.750 - 854.825i) q^{18} +(202.192 - 622.284i) q^{19} +(-345.320 - 250.889i) q^{20} -1060.48 q^{21} +(1303.52 + 936.832i) q^{22} +3448.46 q^{23} +(221.470 + 160.907i) q^{24} +(-745.756 + 2295.20i) q^{25} +(433.072 + 1332.86i) q^{26} +(-1618.47 + 1175.89i) q^{27} +(-3209.24 + 2331.65i) q^{28} +(-1270.41 - 3909.92i) q^{29} +(-141.046 + 434.096i) q^{30} +(5668.58 + 4118.46i) q^{31} +1024.00 q^{32} +(522.022 - 1635.26i) q^{33} +1273.86 q^{34} +(-5350.88 - 3887.64i) q^{35} +(-1111.00 + 3419.30i) q^{36} +(-444.060 - 1366.68i) q^{37} +(-2117.38 + 1538.37i) q^{38} +(1212.42 - 880.872i) q^{39} +(527.601 + 1623.79i) q^{40} +(2717.54 - 8363.72i) q^{41} +(3431.77 + 2493.33i) q^{42} +12877.7 q^{43} +(-2015.65 - 6096.41i) q^{44} -5994.52 q^{45} +(-11159.5 - 8107.82i) q^{46} +(6117.54 - 18827.8i) q^{47} +(-338.375 - 1041.41i) q^{48} +(-36131.4 + 26251.0i) q^{49} +(7809.66 - 5674.05i) q^{50} +(-420.941 - 1295.52i) q^{51} +(1732.29 - 5331.43i) q^{52} +(4973.19 + 3613.23i) q^{53} +8002.17 q^{54} +(8628.74 - 6337.37i) q^{55} +15867.3 q^{56} +(2264.21 + 1645.04i) q^{57} +(-5081.64 + 15639.7i) q^{58} +(7700.42 + 23699.4i) q^{59} +(1477.06 - 1073.15i) q^{60} +(-13593.5 + 9876.26i) q^{61} +(-8660.82 - 26655.3i) q^{62} +(-17215.4 + 52983.6i) q^{63} +(-3313.73 - 2407.57i) q^{64} +9346.76 q^{65} +(-5534.01 + 4064.45i) q^{66} +66822.5 q^{67} +(-4122.30 - 2995.03i) q^{68} +(-4558.11 + 14028.4i) q^{69} +(8175.42 + 25161.4i) q^{70} +(-11254.6 + 8176.95i) q^{71} +(11634.5 - 8452.98i) q^{72} +(-17586.7 - 54126.3i) q^{73} +(-1776.24 + 5466.70i) q^{74} +(-8351.19 - 6067.49i) q^{75} +10468.9 q^{76} +(-31233.4 - 94466.6i) q^{77} -5994.52 q^{78} +(-46707.4 - 33934.9i) q^{79} +(2110.41 - 6495.16i) q^{80} +(14229.0 + 43792.4i) q^{81} +(-28458.4 + 20676.2i) q^{82} +(52116.6 - 37865.0i) q^{83} +(-5243.28 - 16137.2i) q^{84} +(2625.36 - 8080.02i) q^{85} +(-41673.2 - 30277.4i) q^{86} +17584.8 q^{87} +(-7810.74 + 24467.5i) q^{88} -44688.3 q^{89} +(19398.7 + 14094.0i) q^{90} +(26842.6 - 82613.0i) q^{91} +(17050.1 + 52474.9i) q^{92} +(-24246.6 + 17616.2i) q^{93} +(-64063.7 + 46545.0i) q^{94} +(5393.96 + 16600.9i) q^{95} +(-1353.50 + 4165.65i) q^{96} +(119204. + 86606.8i) q^{97} +178644. q^{98} +(-73226.5 - 52627.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} - 48 q^{4} + 44 q^{5} - 100 q^{6} - 326 q^{7} - 192 q^{8} - 69 q^{9} + 96 q^{10} + 1011 q^{11} + 800 q^{12} - 246 q^{13} - 1304 q^{14} + 112 q^{15} - 768 q^{16} + 400 q^{17} - 1416 q^{18}+ \cdots - 199487 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 48 * q^4 + 44 * q^5 - 100 * q^6 - 326 * q^7 - 192 * q^8 - 69 * q^9 + 96 * q^10 + 1011 * q^11 + 800 * q^12 - 246 * q^13 - 1304 * q^14 + 112 * q^15 - 768 * q^16 + 400 * q^17 - 1416 * q^18 + 7535 * q^19 + 704 * q^20 - 3368 * q^21 + 484 * q^22 + 15732 * q^23 - 1600 * q^24 - 19283 * q^25 - 984 * q^26 - 27411 * q^27 + 3264 * q^28 - 2504 * q^29 + 448 * q^30 + 15336 * q^31 + 12288 * q^32 + 26213 * q^33 + 24600 * q^34 - 33916 * q^35 - 5664 * q^36 - 116 * q^37 - 34880 * q^38 + 4690 * q^39 - 3584 * q^40 - 38836 * q^41 + 19808 * q^42 + 42230 * q^43 - 4704 * q^44 + 139932 * q^45 - 35232 * q^46 - 57840 * q^47 - 125521 * q^49 + 26268 * q^50 + 16467 * q^51 - 3936 * q^52 + 131934 * q^53 + 60176 * q^54 - 53082 * q^55 + 15616 * q^56 - 90021 * q^57 - 10016 * q^58 + 36585 * q^59 - 37248 * q^60 + 43146 * q^61 - 40016 * q^62 - 52922 * q^63 - 12288 * q^64 - 133772 * q^65 - 211008 * q^66 + 325206 * q^67 + 6400 * q^68 - 103894 * q^69 + 68216 * q^70 - 172806 * q^71 - 4416 * q^72 + 49436 * q^73 - 464 * q^74 + 263915 * q^75 + 37920 * q^76 - 207094 * q^77 + 330000 * q^78 + 58364 * q^79 - 14336 * q^80 + 341038 * q^81 + 82836 * q^82 + 82035 * q^83 - 52288 * q^84 - 317604 * q^85 - 104380 * q^86 - 572732 * q^87 - 38336 * q^88 + 97958 * q^89 - 151672 * q^90 - 22162 * q^91 + 15072 * q^92 - 271316 * q^93 + 153720 * q^94 + 549736 * q^95 + 76403 * q^97 + 198656 * q^98 - 199487 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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