LMFDB - Embedded newform 168.4.t.a.19.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,4,Mod(19,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("168.19");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	168.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.91232088096$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.22
Character	$\chi$	$=$	168.19
Dual form			168.4.t.a.115.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.300358 + 2.81243i) q^{2} +(2.59808 - 1.50000i) q^{3} +(-7.81957 - 1.68948i) q^{4} +(-7.16825 + 12.4158i) q^{5} +(3.43830 + 7.75746i) q^{6} +(-12.0691 - 14.0477i) q^{7} +(7.10021 - 21.4846i) q^{8} +(4.50000 - 7.79423i) q^{9} +(-32.7655 - 23.8894i) q^{10} +(-8.72655 - 15.1148i) q^{11} +(-22.8501 + 7.33997i) q^{12} +0.0135980 q^{13} +(43.1332 - 29.7241i) q^{14} +43.0095i q^{15} +(58.2913 + 26.4219i) q^{16} +(97.8487 - 56.4930i) q^{17} +(20.5691 + 14.9970i) q^{18} +(-141.172 - 81.5059i) q^{19} +(77.0287 - 84.9754i) q^{20} +(-52.4279 - 18.3934i) q^{21} +(45.1305 - 20.0030i) q^{22} +(-108.849 - 62.8441i) q^{23} +(-13.7800 - 66.4689i) q^{24} +(-40.2675 - 69.7454i) q^{25} +(-0.00408426 + 0.0382434i) q^{26} -27.0000i q^{27} +(70.6417 + 130.237i) q^{28} +79.0227i q^{29} +(-120.961 - 12.9183i) q^{30} +(-57.5343 - 99.6523i) q^{31} +(-91.8183 + 156.005i) q^{32} +(-45.3445 - 26.1796i) q^{33} +(129.493 + 292.161i) q^{34} +(260.927 - 49.1495i) q^{35} +(-48.3562 + 53.3449i) q^{36} +(-34.8737 - 20.1343i) q^{37} +(271.632 - 372.557i) q^{38} +(0.0353286 - 0.0203970i) q^{39} +(215.851 + 242.161i) q^{40} -387.430i q^{41} +(67.4772 - 141.925i) q^{42} +59.4461 q^{43} +(42.7017 + 132.935i) q^{44} +(64.5142 + 111.742i) q^{45} +(209.439 - 287.255i) q^{46} +(-202.646 + 350.993i) q^{47} +(191.078 - 18.7908i) q^{48} +(-51.6750 + 339.085i) q^{49} +(208.249 - 92.3012i) q^{50} +(169.479 - 293.546i) q^{51} +(-0.106330 - 0.0229734i) q^{52} +(96.1083 - 55.4882i) q^{53} +(75.9357 + 8.10967i) q^{54} +250.216 q^{55} +(-387.502 + 159.557i) q^{56} -489.036 q^{57} +(-222.246 - 23.7351i) q^{58} +(-192.766 + 111.294i) q^{59} +(72.6635 - 336.316i) q^{60} +(-314.523 + 544.771i) q^{61} +(297.546 - 131.880i) q^{62} +(-163.802 + 30.8545i) q^{63} +(-411.174 - 305.090i) q^{64} +(-0.0974736 + 0.168829i) q^{65} +(87.2481 - 119.665i) q^{66} +(132.525 + 229.540i) q^{67} +(-860.579 + 276.438i) q^{68} -377.065 q^{69} +(59.8582 + 748.602i) q^{70} -1023.16i q^{71} +(-135.505 - 152.021i) q^{72} +(-952.975 + 550.200i) q^{73} +(67.1010 - 92.0323i) q^{74} +(-209.236 - 120.803i) q^{75} +(966.205 + 875.849i) q^{76} +(-107.007 + 305.010i) q^{77} +(0.0467539 + 0.105486i) q^{78} +(-536.973 - 310.022i) q^{79} +(-745.896 + 534.333i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(1089.62 + 116.368i) q^{82} -57.1755i q^{83} +(378.888 + 232.404i) q^{84} +1619.82i q^{85} +(-17.8551 + 167.188i) q^{86} +(118.534 + 205.307i) q^{87} +(-386.696 + 80.1677i) q^{88} +(-458.297 - 264.598i) q^{89} +(-333.644 + 147.879i) q^{90} +(-0.164115 - 0.191020i) q^{91} +(744.980 + 675.312i) q^{92} +(-298.957 - 172.603i) q^{93} +(-926.278 - 675.352i) q^{94} +(2023.92 - 1168.51i) q^{95} +(-4.54408 + 543.039i) q^{96} +106.812i q^{97} +(-938.133 - 247.180i) q^{98} -157.078 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{2} - 10 q^{4} - 16 q^{8} + 432 q^{9} + 18 q^{10} + 40 q^{11} + 274 q^{14} - 26 q^{16} - 18 q^{18} + 4 q^{22} + 270 q^{24} - 1200 q^{25} + 750 q^{26} + 922 q^{28} + 168 q^{30} - 108 q^{32} + 456 q^{35}+ \cdots + 720 q^{99}+O(q^{100}) $ 96 * q + 2 * q^2 - 10 * q^4 - 16 * q^8 + 432 * q^9 + 18 * q^10 + 40 * q^11 + 274 * q^14 - 26 * q^16 - 18 * q^18 + 4 * q^22 + 270 * q^24 - 1200 * q^25 + 750 * q^26 + 922 * q^28 + 168 * q^30 - 108 * q^32 + 456 * q^35 - 180 * q^36 - 1494 * q^38 + 1170 * q^40 - 564 * q^42 - 1616 * q^43 + 264 * q^44 + 808 * q^46 - 360 * q^49 - 1036 * q^50 - 3564 * q^52 + 176 * q^56 - 336 * q^57 - 394 * q^58 + 4128 * q^59 + 822 * q^60 - 2644 * q^64 + 2052 * q^66 - 1440 * q^67 - 1392 * q^68 + 3234 * q^70 - 72 * q^72 - 648 * q^73 + 850 * q^74 + 1692 * q^78 - 1548 * q^80 - 3888 * q^81 + 4596 * q^82 + 3120 * q^84 - 2522 * q^86 - 1454 * q^88 - 104 * q^91 + 5600 * q^92 - 2052 * q^94 + 3870 * q^96 + 852 * q^98 + 720 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.300358	+	2.81243i	−0.106193	+	0.994346i
$2$	−0.300358	+	2.81243i	−0.106193	+	0.994346i
$3$	2.59808	−	1.50000i	0.500000	−	0.288675i
$3$	2.59808	−	1.50000i	0.500000	−	0.288675i
$4$	−7.81957	−	1.68948i	−0.977446	−	0.211184i
$5$	−7.16825	+	12.4158i	−0.641148	+	1.11050i	0.344029	+	0.938959i	$0.388208\pi$
$5$	−7.16825	+	12.4158i	−0.641148	+	1.11050i	−0.985177	+	0.171541i	$0.945125\pi$
$6$	3.43830	+	7.75746i	0.233947	+	0.527828i
$7$	−12.0691	−	14.0477i	−0.651669	−	0.758504i
$7$	−12.0691	−	14.0477i	−0.651669	−	0.758504i
$8$	7.10021	−	21.4846i	0.313788	−	0.949493i
$9$	4.50000	−	7.79423i	0.166667	−	0.288675i
$10$	−32.7655	−	23.8894i	−1.03614	−	0.755449i
$11$	−8.72655	−	15.1148i	−0.239196	−	0.414299i	0.721288	−	0.692635i	$-0.243550\pi$
$11$	−8.72655	−	15.1148i	−0.239196	−	0.414299i	−0.960484	+	0.278336i	$0.910217\pi$
$12$	−22.8501	+	7.33997i	−0.549687	+	0.176572i
$13$	0.0135980			0.000290108			0.000145054	−	1.00000i	$-0.499954\pi$
$13$	0.0135980			0.000290108			0.000145054		1.00000i	$0.499954\pi$
$14$	43.1332	−	29.7241i	0.823417	−	0.567436i
$15$			43.0095i			0.740333i
$16$	58.2913	+	26.4219i	0.910802	+	0.412843i
$17$	97.8487	−	56.4930i	1.39599	−	0.805974i	0.402019	−	0.915631i	$-0.368309\pi$
$17$	97.8487	−	56.4930i	1.39599	−	0.805974i	0.993970	+	0.109657i	$0.0349752\pi$
$18$	20.5691	+	14.9970i	0.269344	+	0.196379i
$19$	−141.172	−	81.5059i	−1.70459	−	0.984144i	−0.940979	−	0.338465i	$-0.890092\pi$
$19$	−141.172	−	81.5059i	−1.70459	−	0.984144i	−0.763609	−	0.645679i	$-0.776574\pi$
$20$	77.0287	−	84.9754i	0.861208	−	0.950054i
$21$	−52.4279	−	18.3934i	−0.544796	−	0.191131i
$22$	45.1305	−	20.0030i	0.437357	−	0.193848i
$23$	−108.849	−	62.8441i	−0.986810	−	0.569735i	−0.0824906	−	0.996592i	$-0.526287\pi$
$23$	−108.849	−	62.8441i	−0.986810	−	0.569735i	−0.904319	+	0.426857i	$0.859621\pi$
$24$	−13.7800	−	66.4689i	−0.117201	−	0.565329i
$25$	−40.2675	−	69.7454i	−0.322140	−	0.557963i
$26$	−0.00408426	+	0.0382434i	−3.08073e−5	+	0.000288467i
$27$		−	27.0000i		−	0.192450i
$28$	70.6417	+	130.237i	0.476787	+	0.879019i
$29$			79.0227i			0.506005i	0.967466	+	0.253002i	$0.0814181\pi$
$29$			79.0227i			0.506005i	−0.967466	+	0.253002i	$0.918582\pi$
$30$	−120.961	−	12.9183i	−0.736147	−	0.0786180i
$31$	−57.5343	−	99.6523i	−0.333337	−	0.577357i	0.649827	−	0.760082i	$-0.274841\pi$
$31$	−57.5343	−	99.6523i	−0.333337	−	0.577357i	−0.983164	+	0.182725i	$0.941508\pi$
$32$	−91.8183	+	156.005i	−0.507229	+	0.861811i
$33$	−45.3445	−	26.1796i	−0.239196	−	0.138100i
$34$	129.493	+	292.161i	0.653173	+	1.47368i
$35$	260.927	−	49.1495i	1.26013	−	0.237365i
$36$	−48.3562	+	53.3449i	−0.223871	+	0.246967i
$37$	−34.8737	−	20.1343i	−0.154951	−	0.0894611i	0.420520	−	0.907283i	$-0.361848\pi$
$37$	−34.8737	−	20.1343i	−0.154951	−	0.0894611i	−0.575471	+	0.817822i	$0.695181\pi$
$38$	271.632	−	372.557i	1.15959	−	1.59044i
$39$	0.0353286	−	0.0203970i	0.000145054	−	8.37468e-5i
$40$	215.851	+	242.161i	0.853228	+	0.957227i
$41$		−	387.430i		−	1.47577i	−0.674928	−	0.737883i	$-0.735825\pi$
$41$		−	387.430i		−	1.47577i	0.674928	−	0.737883i	$-0.264175\pi$
$42$	67.4772	−	141.925i	0.247904	−	0.521418i
$43$	59.4461			0.210824			0.105412	−	0.994429i	$-0.466384\pi$
$43$	59.4461			0.210824			0.105412	+	0.994429i	$0.466384\pi$
$44$	42.7017	+	132.935i	0.146307	+	0.455469i
$45$	64.5142	+	111.742i	0.213716	+	0.370167i
$46$	209.439	−	287.255i	0.671305	−	0.920728i
$47$	−202.646	+	350.993i	−0.628914	+	1.08931i	0.358856	+	0.933393i	$0.383167\pi$
$47$	−202.646	+	350.993i	−0.628914	+	1.08931i	−0.987770	+	0.155918i	$0.950167\pi$
$48$	191.078	−	18.7908i	0.574579	−	0.0565045i
$49$	−51.6750	+	339.085i	−0.150656	+	0.988586i
$50$	208.249	−	92.3012i	0.589017	−	0.261067i
$51$	169.479	−	293.546i	0.465330	−	0.805974i
$52$	−0.106330	−	0.0229734i	−0.000283565	−	6.12662e-5i
$53$	96.1083	−	55.4882i	0.249085	−	0.143809i	−0.370260	−	0.928928i	$-0.620732\pi$
$53$	96.1083	−	55.4882i	0.249085	−	0.143809i	0.619345	+	0.785119i	$0.287398\pi$
$54$	75.9357	+	8.10967i	0.191362	+	0.0204368i
$55$	250.216			0.613439
$56$	−387.502	+	159.557i	−0.924680	+	0.380746i
$57$	−489.036			−1.13639
$58$	−222.246	−	23.7351i	−0.503144	−	0.0537340i
$59$	−192.766	+	111.294i	−0.425356	+	0.245579i	−0.697366	−	0.716715i	$-0.745645\pi$
$59$	−192.766	+	111.294i	−0.425356	+	0.245579i	0.272010	+	0.962294i	$0.412312\pi$
$60$	72.6635	−	336.316i	0.156347	−	0.723636i
$61$	−314.523	+	544.771i	−0.660174	+	1.14345i	0.320396	+	0.947284i	$0.396184\pi$
$61$	−314.523	+	544.771i	−0.660174	+	1.14345i	−0.980570	+	0.196171i	$0.937149\pi$
$62$	297.546	−	131.880i	0.609491	−	0.270141i
$63$	−163.802	+	30.8545i	−0.327573	+	0.0617032i
$64$	−411.174	−	305.090i	−0.803074	−	0.595879i
$65$	−0.0974736	+	0.168829i	−0.000186002	+	0.000322164i
$66$	87.2481	−	119.665i	0.162720	−	0.223178i
$67$	132.525	+	229.540i	0.241649	+	0.418549i	0.961184	−	0.275907i	$-0.0889783\pi$
$67$	132.525	+	229.540i	0.241649	+	0.418549i	−0.719535	+	0.694456i	$0.755645\pi$
$68$	−860.579	+	276.438i	−1.53471	+	0.492986i
$69$	−377.065			−0.657873
$70$	59.8582	+	748.602i	0.102206	+	1.27822i
$71$		−	1023.16i		−	1.71023i	−0.518440	−	0.855114i	$-0.673487\pi$
$71$		−	1023.16i		−	1.71023i	0.518440	−	0.855114i	$-0.326513\pi$
$72$	−135.505	−	152.021i	−0.221797	−	0.248832i
$73$	−952.975	+	550.200i	−1.52791	+	0.882138i	−0.528459	+	0.848959i	$0.677230\pi$
$73$	−952.975	+	550.200i	−1.52791	+	0.882138i	−0.999449	+	0.0331792i	$0.989437\pi$
$74$	67.1010	−	92.0323i	0.105410	−	0.144575i
$75$	−209.236	−	120.803i	−0.322140	−	0.185988i
$76$	966.205	+	875.849i	1.45831	+	1.32193i
$77$	−107.007	+	305.010i	−0.158371	+	0.451417i
$78$	0.0467539	+	0.105486i	6.78696e−5	+	0.000153127i
$79$	−536.973	−	310.022i	−0.764737	−	0.441521i	0.0662572	−	0.997803i	$-0.478894\pi$
$79$	−536.973	−	310.022i	−0.764737	−	0.441521i	−0.830994	+	0.556282i	$0.812228\pi$
$80$	−745.896	+	534.333i	−1.04242	+	0.746753i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	1089.62	+	116.368i	1.46742	+	0.156716i
$83$		−	57.1755i		−	0.0756124i	−0.999285	−	0.0378062i	$-0.987963\pi$
$83$		−	57.1755i		−	0.0756124i	0.999285	−	0.0378062i	$-0.0120370\pi$
$84$	378.888	+	232.404i	0.492144	+	0.301873i
$85$			1619.82i			2.06699i
$86$	−17.8551	+	167.188i	−0.0223880	+	0.209632i
$87$	118.534	+	205.307i	0.146071	+	0.253002i
$88$	−386.696	+	80.1677i	−0.468431	+	0.0971126i
$89$	−458.297	−	264.598i	−0.545835	−	0.315138i	0.201605	−	0.979467i	$-0.435384\pi$
$89$	−458.297	−	264.598i	−0.545835	−	0.315138i	−0.747441	+	0.664329i	$0.768718\pi$
$90$	−333.644	+	147.879i	−0.390769	+	0.173198i
$91$	−0.164115	−	0.191020i	−0.000189054	−	0.000220048i
$92$	744.980	+	675.312i	0.844234	+	0.765284i
$93$	−298.957	−	172.603i	−0.333337	−	0.192452i
$94$	−926.278	−	675.352i	−1.01637	−	0.741034i
$95$	2023.92	−	1168.51i	2.18578	−	1.26196i
$96$	−4.54408	+	543.039i	−0.00483102	+	0.577330i
$97$			106.812i			0.111805i	0.998436	+	0.0559026i	$0.0178036\pi$
$97$			106.812i			0.111805i	−0.998436	+	0.0559026i	$0.982196\pi$
$98$	−938.133	−	247.180i	−0.966998	−	0.254785i
$99$	−157.078			−0.159464
$100$	197.042	+	613.410i	0.197042	+	0.613410i
$101$	144.912	+	250.995i	0.142765	+	0.247277i	0.928537	−	0.371240i	$-0.121067\pi$
$101$	144.912	+	250.995i	0.142765	+	0.247277i	−0.785772	+	0.618517i	$0.787734\pi$
$102$	774.675	+	564.818i	0.752002	+	0.548287i
$103$	69.8537	−	120.990i	0.0668241	−	0.115743i	−0.830678	−	0.556754i	$-0.812047\pi$
$103$	69.8537	−	120.990i	0.0668241	−	0.115743i	0.897502	+	0.441011i	$0.145380\pi$
$104$	0.0965484	−	0.292147i	9.10322e−5	−	0.000275455i
$105$	604.184	−	519.085i	0.561546	−	0.482452i
$106$	127.190	+	286.965i	0.116545	+	0.262948i
$107$	−514.157	+	890.546i	−0.464537	+	0.804602i	−0.999181	−	0.0404761i	$-0.987113\pi$
$107$	−514.157	+	890.546i	−0.464537	+	0.804602i	0.534644	+	0.845078i	$0.320446\pi$
$108$	−45.6158	+	211.128i	−0.0406425	+	0.188110i
$109$	1136.39	−	656.098i	0.998595	−	0.576539i	0.0907629	−	0.995873i	$-0.471069\pi$
$109$	1136.39	−	656.098i	0.998595	−	0.576539i	0.907832	+	0.419333i	$0.137736\pi$
$110$	−75.1545	+	703.716i	−0.0651427	+	0.609970i
$111$	−120.806			−0.103301
$112$	−332.355	−	1137.75i	−0.280398	−	0.959884i
$113$	763.883			0.635929			0.317965	−	0.948103i	$-0.397001\pi$
$113$	763.883			0.635929			0.317965	+	0.948103i	$0.397001\pi$
$114$	146.886	−	1375.38i	0.120677	−	1.12997i
$115$	1560.52	−	900.964i	1.26538	−	0.730568i
$116$	133.507	−	617.923i	0.106860	−	0.494593i
$117$	0.0611909	−	0.105986i	4.83513e−5	−	8.37468e-5i
$118$	−255.107	−	575.570i	−0.199021	−	0.449030i
$119$	−1974.54	−	692.730i	−1.52106	−	0.533634i
$120$	924.041	+	305.376i	0.702941	+	0.232308i
$121$	513.195	−	888.879i	0.385571	−	0.667828i
$122$	−1437.66	−	1048.20i	−1.06688	−	0.777867i
$123$	−581.145	−	1006.57i	−0.426017	−	0.737883i
$124$	281.533	+	876.441i	0.203891	+	0.634731i
$125$	−637.471			−0.456137
$126$	−37.5771	−	469.949i	−0.0265685	−	0.332273i
$127$		−	2297.90i		−	1.60555i	−0.596279	−	0.802777i	$-0.703355\pi$
$127$		−	2297.90i		−	1.60555i	0.596279	−	0.802777i	$-0.296645\pi$
$128$	981.545	−	1064.76i	0.677790	−	0.735255i
$129$	154.445	−	89.1691i	0.105412	−	0.0608597i
$130$	−0.445544	−	0.324847i	−0.000300591	−	0.000219161i
$131$	2206.31	+	1273.81i	1.47150	+	0.849570i	0.999487	−	0.0320218i	$-0.0101946\pi$
$131$	2206.31	+	1273.81i	1.47150	+	0.849570i	0.472012	+	0.881592i	$0.343528\pi$
$132$	310.344	+	281.322i	0.204636	+	0.185499i
$133$	558.850	+	2966.85i	0.364349	+	1.93427i
$134$	−685.371	+	303.774i	−0.441844	+	0.195836i
$135$	335.226	+	193.543i	0.213716	+	0.123389i
$136$	−518.981	−	2503.35i	−0.327223	−	1.57839i
$137$	985.764	+	1707.39i	0.614741	+	1.06476i	0.990430	+	0.138016i	$0.0440726\pi$
$137$	985.764	+	1707.39i	0.614741	+	1.06476i	−0.375689	+	0.926746i	$0.622594\pi$
$138$	113.254	−	1060.47i	0.0698613	−	0.654153i
$139$			2423.81i			1.47903i	0.673141	+	0.739514i	$0.264944\pi$
$139$			2423.81i			1.47903i	−0.673141	+	0.739514i	$0.735056\pi$
$140$	−2123.37	−	56.5016i	−1.28184	−	0.0341090i
$141$			1215.88i			0.726207i
$142$	2877.56	+	307.313i	1.70056	+	0.181614i
$143$	−0.118663	−	0.205531i	−6.93925e−5	−	0.000120191i
$144$	468.250	−	335.437i	0.270978	−	0.194119i
$145$	−981.127	−	566.454i	−0.561919	−	0.324424i
$146$	−1261.17	−	2845.44i	−0.714898	−	1.61295i
$147$	374.372	+	958.481i	0.210052	+	0.537784i
$148$	238.681	+	216.360i	0.132564	+	0.120167i
$149$	517.719	+	298.905i	0.284652	+	0.164344i	0.635528	−	0.772078i	$-0.280783\pi$
$149$	517.719	+	298.905i	0.284652	+	0.164344i	−0.350875	+	0.936422i	$0.614116\pi$
$150$	402.595	−	552.179i	0.219145	−	0.300568i
$151$	687.580	−	396.974i	0.370559	−	0.213943i	−0.303143	−	0.952945i	$-0.598036\pi$
$151$	687.580	−	396.974i	0.370559	−	0.213943i	0.673703	+	0.739002i	$0.264703\pi$
$152$	−2753.47	+	2454.32i	−1.46932	+	1.30968i
$153$		−	1016.87i		−	0.537316i
$154$	−825.679	−	392.562i	−0.432046	−	0.205413i
$155$	1649.68			0.854874
$156$	−0.310714	+	0.0998087i	−0.000159468	+	5.12249e-5i
$157$	−1088.93	−	1886.09i	−0.553544	−	0.958766i	−0.998015	−	0.0629729i	$-0.979942\pi$
$157$	−1088.93	−	1886.09i	−0.553544	−	0.958766i	0.444472	−	0.895793i	$-0.353391\pi$
$158$	1033.20	−	1417.08i	0.520234	−	0.713526i
$159$	166.465	−	288.325i	0.0830283	−	0.143809i
$160$	−1278.74	−	2258.27i	−0.631833	−	1.11583i
$161$	430.894	+	2287.55i	0.210927	+	1.11978i
$162$	209.451	−	92.8340i	0.101581	−	0.0450230i
$163$	698.201	−	1209.32i	0.335505	−	0.581112i	−0.648077	−	0.761575i	$-0.724426\pi$
$163$	698.201	−	1209.32i	0.335505	−	0.581112i	0.983582	+	0.180463i	$0.0577597\pi$
$164$	−654.554	+	3029.54i	−0.311659	+	1.44248i
$165$	650.081	−	375.324i	0.306719	−	0.177085i
$166$	160.802	+	17.1731i	0.0751849	+	0.00802949i
$167$	2709.12			1.25532			0.627658	−	0.778490i	$-0.284014\pi$
$167$	2709.12			1.25532			0.627658	+	0.778490i	$0.284014\pi$
$168$	−767.423	+	995.795i	−0.352428	+	0.457305i
$169$	−2197.00			−1.00000
$170$	−4555.65	−	486.527i	−2.05531	−	0.219500i
$171$	−1270.55	+	733.553i	−0.568196	+	0.328048i
$172$	−464.843	−	100.433i	−0.206069	−	0.0445228i
$173$	2134.57	−	3697.18i	0.938081	−	1.62480i	0.169036	−	0.985610i	$-0.445935\pi$
$173$	2134.57	−	3697.18i	0.938081	−	1.62480i	0.769045	−	0.639194i	$-0.220732\pi$
$174$	−613.015	+	271.703i	−0.267084	+	0.118378i
$175$	−493.770	+	1407.43i	−0.213289	+	0.607952i
$176$	−109.319	−	1111.64i	−0.0468195	−	0.476095i
$177$	−333.881	+	578.298i	−0.141785	+	0.245579i
$178$	881.817	−	1209.45i	0.371320	−	0.509283i
$179$	−1236.00	−	2140.81i	−0.516104	−	0.893918i	−0.999825	−	0.0186963i	$-0.994048\pi$
$179$	−1236.00	−	2140.81i	−0.516104	−	0.893918i	0.483721	−	0.875222i	$-0.339285\pi$
$180$	−315.688	−	982.769i	−0.130722	−	0.406952i
$181$	−1085.09			−0.445601			−0.222801	−	0.974864i	$-0.571520\pi$
$181$	−1085.09			−0.445601			−0.222801	+	0.974864i	$0.571520\pi$
$182$	0.586524	−	0.404188i	0.000238880	−	0.000164618i
$183$			1887.14i			0.762303i
$184$	−2123.03	+	1892.37i	−0.850608	+	0.758193i
$185$	499.966	−	288.656i	0.198693	−	0.114716i
$186$	575.228	−	788.954i	0.226762	−	0.311016i
$187$	−1707.76	−	985.977i	−0.667829	−	0.385571i
$188$	2177.60	−	2402.25i	0.844775	−	0.931926i
$189$	−379.288	+	325.865i	−0.145974	+	0.125414i
$190$	2678.45	+	6043.11i	1.02271	+	2.30744i
$191$	3251.48	+	1877.25i	1.23178	+	0.711166i	0.967400	−	0.253254i	$-0.0815007\pi$
$191$	3251.48	+	1877.25i	1.23178	+	0.711166i	0.264376	+	0.964420i	$0.414834\pi$
$192$	−1525.90	−	175.886i	−0.573553	−	0.0661119i
$193$	−258.194	−	447.204i	−0.0962963	−	0.166790i	0.813853	−	0.581071i	$-0.197366\pi$
$193$	−258.194	−	447.204i	−0.0962963	−	0.166790i	−0.910149	+	0.414281i	$0.864033\pi$
$194$	−300.401	−	32.0818i	−0.111173	−	0.0118729i
$195$			0.584842i			0.000214776i
$196$	976.952	−	2564.20i	0.356032	−	0.934474i
$197$		−	2723.54i		−	0.984995i	−0.870314	−	0.492497i	$-0.836084\pi$
$197$		−	2723.54i		−	0.984995i	0.870314	−	0.492497i	$-0.163916\pi$
$198$	47.1796	−	441.771i	0.0169339	−	0.158562i
$199$	−2259.07	−	3912.82i	−0.804729	−	1.39383i	−0.916474	−	0.400095i	$-0.868977\pi$
$199$	−2259.07	−	3912.82i	−0.804729	−	1.39383i	0.111744	−	0.993737i	$-0.464356\pi$
$200$	−1784.36	+	369.924i	−0.630866	+	0.130788i
$201$	688.620	+	397.575i	0.241649	+	0.139516i
$202$	−749.432	+	332.167i	−0.261039	+	0.115699i
$203$	1110.09	−	953.730i	0.383807	−	0.329748i
$204$	−1821.19	+	2009.07i	−0.625044	+	0.689526i
$205$	4810.24	+	2777.20i	1.63884	+	0.946184i
$206$	319.295	+	232.799i	0.107992	+	0.0787373i
$207$	−979.643	+	565.597i	−0.328937	+	0.189912i
$208$	0.792644	+	0.359285i	0.000264231	+	0.000119769i
$209$			2845.06i			0.941612i
$210$	1278.42	+	1855.14i	0.420092	+	0.609603i
$211$	693.490			0.226265			0.113132	−	0.993580i	$-0.463912\pi$
$211$	693.490			0.226265			0.113132	+	0.993580i	$0.463912\pi$
$212$	−845.272	+	271.521i	−0.273837	+	0.0879629i
$213$	−1534.73	−	2658.24i	−0.493700	−	0.855114i
$214$	−2350.17	−	1713.52i	−0.750722	−	0.547353i
$215$	−426.124	+	738.069i	−0.135169	+	0.234120i
$216$	−580.084	−	191.706i	−0.182730	−	0.0603885i
$217$	−705.499	+	2010.93i	−0.220702	+	0.629083i
$218$	1503.91	+	3393.10i	0.467236	+	1.05417i
$219$	−1650.60	+	2858.93i	−0.509303	+	0.882138i
$220$	−1956.58	−	422.734i	−0.599604	−	0.129549i
$221$	1.33054	−	0.768190i	0.000404987	−	0.000233819i
$222$	36.2850	−	339.759i	0.0109698	−	0.102717i
$223$	−3875.20			−1.16369			−0.581844	−	0.813300i	$-0.697669\pi$
$223$	−3875.20			−1.16369			−0.581844	+	0.813300i	$0.697669\pi$
$224$	3299.66	−	592.996i	0.984232	−	0.176880i
$225$	−724.816			−0.214760
$226$	−229.438	+	2148.37i	−0.0675310	+	0.632334i
$227$	1611.42	−	930.351i	0.471160	−	0.272024i	−0.245565	−	0.969380i	$-0.578973\pi$
$227$	1611.42	−	930.351i	0.471160	−	0.272024i	0.716725	+	0.697356i	$0.245640\pi$
$228$	3824.05	+	826.214i	1.11076	+	0.239988i
$229$	−665.716	+	1153.05i	−0.192104	+	0.332733i	−0.945947	−	0.324321i	$-0.894864\pi$
$229$	−665.716	+	1153.05i	−0.192104	+	0.332733i	0.753844	+	0.657054i	$0.228198\pi$
$230$	2065.19	+	4659.46i	0.592063	+	1.33581i
$231$	179.502	+	952.949i	0.0511272	+	0.271426i
$232$	1697.77	+	561.078i	0.480448	+	0.158778i
$233$	1454.66	−	2519.54i	0.409004	−	0.708415i	−0.585775	−	0.810474i	$-0.699210\pi$
$233$	1454.66	−	2519.54i	0.409004	−	0.708415i	0.994778	+	0.102059i	$0.0325430\pi$
$234$	0.279699	+	0.203929i	7.81387e−5	+	5.69712e-5i
$235$	−2905.23	−	5032.01i	−0.806453	−	1.39682i
$236$	1695.38	−	544.594i	0.467625	−	0.150212i
$237$	−1860.13			−0.509824
$238$	2541.33	−	5345.19i	0.692142	−	1.45579i
$239$			2878.18i			0.778971i	0.921033	+	0.389486i	$0.127347\pi$
$239$			2878.18i			0.778971i	−0.921033	+	0.389486i	$0.872653\pi$
$240$	−1136.39	+	2507.08i	−0.305641	+	0.674297i
$241$	2620.03	−	1512.68i	0.700296	−	0.404316i	−0.107162	−	0.994242i	$-0.534176\pi$
$241$	2620.03	−	1512.68i	0.700296	−	0.404316i	0.807458	+	0.589926i	$0.200843\pi$
$242$	2345.77	+	1710.31i	0.623107	+	0.454309i
$243$	−210.444	−	121.500i	−0.0555556	−	0.0320750i
$244$	3379.81	−	3728.49i	0.886764	−	0.978247i
$245$	−3839.58	−	3072.23i	−1.00123	−	0.801133i
$246$	3005.47	−	1332.10i	0.778951	−	0.345250i
$247$	−1.91966	−	1.10831i	−0.000494514	−	0.000285508i
$248$	−2549.49	+	528.547i	−0.652794	+	0.135334i
$249$	−85.7633	−	148.546i	−0.0218274	−	0.0378062i
$250$	191.470	−	1792.85i	0.0484384	−	0.453558i
$251$			6545.00i			1.64588i	0.568126	+	0.822942i	$0.307669\pi$
$251$			6545.00i			1.64588i	−0.568126	+	0.822942i	$0.692331\pi$
$252$	1332.99	+	35.4699i	0.333215	+	0.00886665i
$253$			2193.65i			0.545112i
$254$	6462.69	+	690.193i	1.59648	+	0.170498i
$255$	2429.73	+	4208.42i	0.596690	+	1.03350i
$256$	2699.76	+	3080.34i	0.659122	+	0.752036i
$257$	1072.74	+	619.345i	0.260372	+	0.150326i	0.624504	−	0.781022i	$-0.285301\pi$
$257$	1072.74	+	619.345i	0.260372	+	0.150326i	−0.364132	+	0.931347i	$0.618634\pi$
$258$	204.393	+	461.150i	0.0493216	+	0.111279i
$259$	138.052	+	732.897i	0.0331202	+	0.175830i
$260$	1.04743	−	1.15549i	0.000249843	−	0.000275618i
$261$	615.921	+	355.602i	0.146071	+	0.0843342i
$262$	−4245.20	+	5822.51i	−1.00103	+	1.37296i
$263$	809.679	−	467.468i	0.189836	−	0.109602i	−0.402070	−	0.915609i	$-0.631709\pi$
$263$	809.679	−	467.468i	0.189836	−	0.109602i	0.591906	+	0.806007i	$0.298376\pi$
$264$	−884.414	+	788.326i	−0.206181	+	0.183781i
$265$			1591.01i			0.368812i
$266$	−8511.92	+	680.612i	−1.96203	+	0.156884i
$267$	−1587.59			−0.363890
$268$	−648.487	−	2018.80i	−0.147808	−	0.460142i
$269$	556.221	+	963.402i	0.126072	+	0.218363i	0.922151	−	0.386829i	$-0.126430\pi$
$269$	556.221	+	963.402i	0.126072	+	0.218363i	−0.796079	+	0.605192i	$0.793096\pi$
$270$	−645.014	+	884.668i	−0.145386	+	0.199404i
$271$	−2696.04	+	4669.69i	−0.604329	+	1.04673i	0.387829	+	0.921731i	$0.373225\pi$
$271$	−2696.04	+	4669.69i	−0.604329	+	1.04673i	−0.992157	+	0.124996i	$0.960108\pi$
$272$	7196.39	−	707.699i	1.60421	−	0.157759i
$273$	−0.712913	−	0.250112i	−0.000158049	−	5.54486e-5i
$274$	−5098.01	+	2259.57i	−1.12402	+	0.498195i
$275$	−702.793	+	1217.27i	−0.154109	+	0.266925i
$276$	2948.48	+	637.041i	0.643036	+	0.138933i
$277$	−1478.86	+	853.823i	−0.320781	+	0.185203i	−0.651741	−	0.758442i	$-0.725961\pi$
$277$	−1478.86	+	853.823i	−0.320781	+	0.185203i	0.330960	+	0.943645i	$0.392628\pi$
$278$	−6816.80	−	728.011i	−1.47066	−	0.157062i
$279$	−1035.62			−0.222225
$280$	796.680	−	5954.88i	0.170038	−	1.27097i
$281$	214.055			0.0454429			0.0227214	−	0.999742i	$-0.492767\pi$
$281$	214.055			0.0454429			0.0227214	+	0.999742i	$0.492767\pi$
$282$	−3419.57	−	365.198i	−0.722101	−	0.0771179i
$283$	−3145.91	+	1816.29i	−0.660795	+	0.381510i	−0.792580	−	0.609768i	$-0.791262\pi$
$283$	−3145.91	+	1816.29i	−0.660795	+	0.381510i	0.131785	+	0.991278i	$0.457929\pi$
$284$	−1728.60	+	8000.64i	−0.361174	+	1.67166i
$285$	3505.53	−	6071.75i	0.728595	−	1.26196i
$286$	0.613683	−	0.272000i	0.000126881	−	5.62367e-5i
$287$	−5442.50	+	4675.92i	−1.11937	+	0.961711i
$288$	802.753	+	1417.67i	0.164245	+	0.290060i
$289$	3926.42	−	6800.76i	0.799189	−	1.38424i
$290$	1887.80	−	2589.22i	0.382261	−	0.524290i
$291$	160.218	+	277.505i	0.0322754	+	0.0559026i
$292$	8381.41	−	2692.30i	1.67974	−	0.539572i
$293$	−620.515			−0.123723			−0.0618615	−	0.998085i	$-0.519704\pi$
$293$	−620.515			−0.123723			−0.0618615	+	0.998085i	$0.519704\pi$
$294$	−2808.11	+	765.009i	−0.557049	+	0.151756i
$295$		−	3191.12i		−	0.629811i
$296$	−680.188	+	606.288i	−0.133565	+	0.119053i
$297$	−408.100	+	235.617i	−0.0797319	+	0.0460332i
$298$	−996.152	+	1366.27i	−0.193643	+	0.265590i
$299$	−1.48013	−	0.854552i	−0.000286281	−	0.000165284i
$300$	1432.04	+	1298.12i	0.275597	+	0.249824i
$301$	−717.459	−	835.080i	−0.137388	−	0.159911i
$302$	909.944	+	2053.01i	0.173382	+	0.391183i
$303$	752.985	+	434.736i	0.142765	+	0.0824255i
$304$	−6075.58	−	8481.14i	−1.14625	−	1.60009i
$305$	−4509.16	−	7810.10i	−0.846538	−	1.46625i
$306$	2859.89	+	305.427i	0.534278	+	0.0570591i
$307$		−	5779.18i		−	1.07438i	−0.843461	−	0.537191i	$-0.819486\pi$
$307$		−	5779.18i		−	1.07438i	0.843461	−	0.537191i	$-0.180514\pi$
$308$	1352.05	−	2204.26i	0.250131	−	0.407790i
$309$		−	419.122i		−	0.0771619i
$310$	−495.495	+	4639.61i	−0.0907814	+	0.850040i
$311$	1260.47	+	2183.20i	0.229823	+	0.398065i	0.957755	−	0.287584i	$-0.0928520\pi$
$311$	1260.47	+	2183.20i	0.229823	+	0.398065i	−0.727933	+	0.685649i	$0.759519\pi$
$312$	−0.187380	−	0.903842i	−3.40009e−5	−	0.000164006i
$313$	−6168.58	−	3561.43i	−1.11396	−	0.643144i	−0.174106	−	0.984727i	$-0.555703\pi$
$313$	−6168.58	−	3561.43i	−1.11396	−	0.643144i	−0.939851	+	0.341583i	$0.889037\pi$
$314$	5631.57	−	2496.05i	1.01213	−	0.448600i
$315$	791.089	−	2254.90i	0.141501	−	0.403330i
$316$	3675.12	+	3331.44i	0.654247	+	0.593063i
$317$	−1901.44	−	1097.79i	−0.336894	−	0.194506i	0.322004	−	0.946738i	$-0.395644\pi$
$317$	−1901.44	−	1097.79i	−0.336894	−	0.194506i	−0.658898	+	0.752233i	$0.728977\pi$
$318$	760.896	+	554.771i	0.134179	+	0.0978303i
$319$	1194.41	−	689.595i	0.209637	−	0.121034i
$320$	6735.32	−	2918.08i	1.17661	−	0.509768i
$321$			3084.94i			0.536401i
$322$	−6563.00	+	524.778i	−1.13584	+	0.0908221i
$323$	−18418.1			−3.17278
$324$	198.179	+	616.951i	0.0339813	+	0.105787i
$325$	−0.547557	−	0.948396i	−9.34553e−5	−	0.000161869i
$326$	3191.42	+	2326.87i	0.542198	+	0.395318i
$327$	1968.29	−	3409.18i	0.332865	−	0.576539i
$328$	−8323.77	−	2750.84i	−1.40123	−	0.463078i
$329$	7376.39	−	1389.45i	1.23609	−	0.232836i
$330$	860.318	+	1941.04i	0.143512	+	0.323790i
$331$	3370.28	−	5837.50i	0.559660	−	0.969360i	−0.437864	−	0.899041i	$-0.644265\pi$
$331$	3370.28	−	5837.50i	0.559660	−	0.969360i	0.997525	−	0.0703191i	$-0.0224018\pi$
$332$	−96.5967	+	447.088i	−0.0159682	+	0.0739071i
$333$	−313.863	+	181.209i	−0.0516504	+	0.0298204i
$334$	−813.705	+	7619.21i	−0.133305	+	1.24822i
$335$	−3799.89			−0.619732
$336$	−2570.10	−	2457.42i	−0.417294	−	0.398998i
$337$	−3202.38			−0.517641			−0.258820	−	0.965925i	$-0.583334\pi$
$337$	−3202.38			−0.517641			−0.258820	+	0.965925i	$0.583334\pi$
$338$	659.887	−	6178.92i	0.106193	−	0.994345i
$339$	1984.63	−	1145.82i	0.317965	−	0.183577i
$340$	2736.65	−	12666.3i	0.436517	−	2.02038i
$341$	−1004.15	+	1739.24i	−0.159466	+	0.276203i
$342$	−1681.45	−	3793.67i	−0.265855	−	0.599819i
$343$	5387.03	−	3366.53i	0.848024	−	0.529958i
$344$	422.080	−	1277.17i	0.0661541	−	0.200176i
$345$	2702.89	−	4681.55i	0.421794	−	0.730568i
$346$	9756.93	+	7113.80i	1.51600	+	1.10532i
$347$	−2395.49	−	4149.10i	−0.370595	−	0.641889i	0.619062	−	0.785342i	$-0.287513\pi$
$347$	−2395.49	−	4149.10i	−0.370595	−	0.641889i	−0.989657	+	0.143453i	$0.954179\pi$
$348$	−580.024	−	1805.67i	−0.0893464	−	0.278144i
$349$	−2226.98			−0.341568			−0.170784	−	0.985308i	$-0.554630\pi$
$349$	−2226.98			−0.341568			−0.170784	+	0.985308i	$0.554630\pi$
$350$	−3809.99	−	1811.43i	−0.581865	−	0.276643i
$351$		−	0.367145i		−	5.58312e-5i
$352$	3159.24	+	26.4361i	0.478375	+	0.00400297i
$353$	−2615.57	+	1510.10i	−0.394371	+	0.227690i	−0.684052	−	0.729433i	$-0.739784\pi$
$353$	−2615.57	+	1510.10i	−0.394371	+	0.227690i	0.289682	+	0.957123i	$0.406451\pi$
$354$	−1526.14	−	1112.71i	−0.229134	−	0.167062i
$355$	12703.3	+	7334.23i	1.89921	+	1.09651i
$356$	3136.65	+	2843.32i	0.466972	+	0.423302i
$357$	−6169.10	+	1162.04i	−0.914575	+	0.172274i
$358$	6392.12	−	2833.15i	0.943670	−	0.418258i
$359$	3403.84	+	1965.21i	0.500411	+	0.288913i	0.728883	−	0.684638i	$-0.240040\pi$
$359$	3403.84	+	1965.21i	0.500411	+	0.288913i	−0.228472	+	0.973550i	$0.573373\pi$
$360$	2858.79	−	592.670i	0.418532	−	0.0867679i
$361$	9856.93	+	17072.7i	1.43708	+	2.48910i
$362$	325.915	−	3051.73i	0.0473196	−	0.443082i
$363$		−	3079.17i		−	0.445219i
$364$	0.960584	+	1.77096i	0.000138319	+	0.000255010i
$365$		−	15775.9i		−	2.26232i
$366$	−5307.46	−	566.818i	−0.757993	−	0.0809510i
$367$	695.065	+	1203.89i	0.0988613	+	0.171233i	0.911214	−	0.411934i	$-0.135147\pi$
$367$	695.065	+	1203.89i	0.0988613	+	0.171233i	−0.812352	+	0.583167i	$0.801813\pi$
$368$	−4684.50	−	6539.27i	−0.663578	−	0.926313i
$369$	−3019.72	−	1743.44i	−0.426017	−	0.245961i
$370$	661.656	+	1492.82i	0.0929671	+	0.209752i
$371$	−1939.42	−	680.409i	−0.271401	−	0.0952158i
$372$	2046.11	+	1854.76i	0.285176	+	0.258508i
$373$	10511.1	+	6068.57i	1.45910	+	0.842409i	0.998967	−	0.0454434i	$-0.0144701\pi$
$373$	10511.1	+	6068.57i	1.45910	+	0.842409i	0.460128	+	0.887852i	$0.347803\pi$
$374$	3285.94	−	4506.82i	0.454310	−	0.623108i
$375$	−1656.20	+	956.206i	−0.228069	+	0.131675i
$376$	6102.11	+	6845.89i	0.836947	+	0.938962i
$377$			1.07455i			0.000146796i
$378$	−802.552	−	1164.60i	−0.109203	−	0.158467i
$379$	321.051			0.0435127			0.0217563	−	0.999763i	$-0.493074\pi$
$379$	321.051			0.0435127			0.0217563	+	0.999763i	$0.493074\pi$
$380$	−17800.3	+	5717.88i	−2.40299	+	0.771898i
$381$	−3446.85	−	5970.11i	−0.463484	−	0.802777i
$382$	−6256.24	+	8580.74i	−0.837950	+	1.14929i
$383$	−5584.09	+	9671.92i	−0.744996	+	1.29037i	0.205200	+	0.978720i	$0.434215\pi$
$383$	−5584.09	+	9671.92i	−0.744996	+	1.29037i	−0.950197	+	0.311651i	$0.899118\pi$
$384$	952.984	−	4238.65i	0.126645	−	0.563289i
$385$	−3019.88	−	3514.96i	−0.399759	−	0.465296i
$386$	1335.28	−	591.831i	0.176073	−	0.0780399i
$387$	267.507	−	463.336i	0.0351374	−	0.0608597i
$388$	180.456	−	835.223i	0.0236115	−	0.109284i
$389$	−5487.56	+	3168.25i	−0.715246	+	0.412947i	−0.813000	−	0.582263i	$-0.802167\pi$
$389$	−5487.56	+	3168.25i	−0.715246	+	0.412947i	0.0977547	+	0.995211i	$0.468834\pi$
$390$	−1.64483	−	0.175662i	−0.000213562	−	2.28077e-5i
$391$	−14201.0			−1.83677
$392$	6918.20	+	3517.79i	0.891382	+	0.453253i
$393$	7642.89			0.980999
$394$	7659.77	+	818.037i	0.979425	+	0.104599i
$395$	7698.31	−	4444.62i	0.980618	−	0.566160i
$396$	1228.28	+	265.379i	0.155867	+	0.0336763i
$397$	−2394.19	+	4146.85i	−0.302672	+	0.524243i	−0.976740	−	0.214426i	$-0.931212\pi$
$397$	−2394.19	+	4146.85i	−0.302672	+	0.524243i	0.674068	+	0.738669i	$0.264545\pi$
$398$	11683.1	−	5178.23i	1.47141	−	0.652164i
$399$	5902.21	+	6869.82i	0.740551	+	0.861958i
$400$	−504.439	−	5129.50i	−0.0630549	−	0.641188i
$401$	4608.04	−	7981.36i	0.573852	−	0.993940i	−0.422314	−	0.906450i	$-0.638782\pi$
$401$	4608.04	−	7981.36i	0.573852	−	0.993940i	0.996165	−	0.0874903i	$-0.0278847\pi$
$402$	−1324.99	+	1817.28i	−0.164389	+	0.225467i
$403$	−0.782349	−	1.35507i	−9.67037e−5	−	0.000167496i
$404$	−709.100	−	2207.50i	−0.0873243	−	0.271849i
$405$	1161.26			0.142477
$406$	2348.88	+	3408.50i	0.287126	+	0.416653i
$407$			702.812i			0.0855948i
$408$	−5103.38	−	5725.42i	−0.619252	−	0.694732i
$409$	−10106.2	+	5834.81i	−1.22181	+	0.705411i	−0.965303	−	0.261132i	$-0.915904\pi$
$409$	−10106.2	+	5834.81i	−1.22181	+	0.705411i	−0.256504	+	0.966543i	$0.582571\pi$
$410$	−9255.48	+	12694.3i	−1.11487	+	1.52909i
$411$	5122.18	+	2957.29i	0.614741	+	0.354921i
$412$	−750.635	+	828.074i	−0.0897601	+	0.0990201i
$413$	3889.92	+	1364.71i	0.463464	+	0.162598i
$414$	−1296.46	−	2925.06i	−0.153907	−	0.347244i
$415$	709.878	+	409.848i	0.0839676	+	0.0484787i
$416$	−1.24854	+	2.12134i	−0.000147151	+	0.000250018i
$417$	3635.71	+	6297.24i	0.426958	+	0.739514i
$418$	−8001.55	−	854.537i	−0.936288	−	0.0999923i
$419$			1594.55i			0.185916i	0.995670	+	0.0929582i	$0.0296323\pi$
$419$			1594.55i			0.185916i	−0.995670	+	0.0929582i	$0.970368\pi$
$420$	−5601.44	+	3038.26i	−0.650767	+	0.352981i
$421$		−	14519.0i		−	1.68079i	−0.541975	−	0.840394i	$-0.682323\pi$
$421$		−	14519.0i		−	1.68079i	0.541975	−	0.840394i	$-0.317677\pi$
$422$	−208.295	+	1950.39i	−0.0240276	+	0.224985i
$423$	1823.81	+	3158.94i	0.209638	+	0.363104i
$424$	−509.750	−	2458.82i	−0.0583860	−	0.281630i
$425$	−7880.26	−	4549.67i	−0.899409	−	0.519274i
$426$	7937.08	−	3517.91i	0.902706	−	0.400102i
$427$	11448.8	−	2156.55i	1.29753	−	0.244409i
$428$	5525.04	−	6095.03i	0.623979	−	0.688352i
$429$	−0.616593	−	0.355990i	−6.93925e−5	−	4.00638e-5i
$430$	−1947.78	−	1420.13i	−0.218443	−	0.159267i
$431$	8079.55	−	4664.73i	0.902966	−	0.521328i	0.0248046	−	0.999692i	$-0.492104\pi$
$431$	8079.55	−	4664.73i	0.902966	−	0.521328i	0.878161	+	0.478365i	$0.158770\pi$
$432$	713.392	−	1573.87i	0.0794516	−	0.175284i
$433$			7452.02i			0.827069i	0.910488	+	0.413535i	$0.135706\pi$
$433$			7452.02i			0.827069i	−0.910488	+	0.413535i	$0.864294\pi$
$434$	−5443.72	−	2588.17i	−0.602089	−	0.286258i
$435$	−3398.72			−0.374612
$436$	−9994.58	+	3210.49i	−1.09783	+	0.352648i
$437$	10244.3	+	17743.7i	1.12140	+	1.94233i
$438$	−7544.77	−	5500.91i	−0.823066	−	0.600100i
$439$	4973.45	−	8614.28i	0.540706	−	0.936531i	−0.458157	−	0.888871i	$-0.651490\pi$
$439$	4973.45	−	8614.28i	0.540706	−	0.936531i	0.998864	−	0.0476596i	$-0.0151763\pi$
$440$	1776.59	−	5375.79i	0.192490	−	0.582456i
$441$	2410.37	+	1928.65i	0.260271	+	0.208255i
$442$	1.76084	+	3.97280i	0.000189490	+	0.000427527i
$443$	−3025.34	+	5240.04i	−0.324466	+	0.561991i	−0.981404	−	0.191953i	$-0.938518\pi$
$443$	−3025.34	+	5240.04i	−0.324466	+	0.561991i	0.656939	+	0.753944i	$0.271851\pi$
$444$	944.650	+	204.099i	0.100971	+	0.0218155i
$445$	6570.37	−	3793.40i	0.699922	−	0.404100i
$446$	1163.95	−	10898.7i	0.123575	−	1.15711i
$447$	1793.43			0.189768
$448$	676.680	+	9458.20i	0.0713618	+	0.997450i
$449$	4126.16			0.433687			0.216844	−	0.976206i	$-0.430424\pi$
$449$	4126.16			0.433687			0.216844	+	0.976206i	$0.430424\pi$
$450$	217.704	−	2038.50i	0.0228060	−	0.213546i
$451$	−5855.94	+	3380.93i	−0.611409	+	0.352997i
$452$	−5973.23	−	1290.56i	−0.621587	−	0.134298i
$453$	1190.92	−	2062.74i	0.123520	−	0.213943i
$454$	2132.55	+	4811.44i	0.220453	+	0.497383i
$455$	3.54808	−	0.668334i	0.000365574	−	6.88615e-5i
$456$	−3472.26	+	10506.7i	−0.356586	+	1.07900i
$457$	−55.1701	+	95.5574i	−0.00564715	+	0.00978116i	−0.868835	−	0.495101i	$-0.835131\pi$
$457$	−55.1701	+	95.5574i	−0.00564715	+	0.00978116i	0.863188	+	0.504883i	$0.168464\pi$
$458$	−3042.93	−	2218.61i	−0.310452	−	0.226351i
$459$	−1525.31	−	2641.92i	−0.155110	−	0.268658i
$460$	−13724.7	+	4408.70i	−1.39113	+	0.446862i
$461$	−9429.10			−0.952618			−0.476309	−	0.879278i	$-0.658026\pi$
$461$	−9429.10			−0.952618			−0.476309	+	0.879278i	$0.658026\pi$
$462$	−2734.02	+	218.612i	−0.275321	+	0.0220146i
$463$		−	9382.12i		−	0.941737i	−0.882203	−	0.470868i	$-0.843941\pi$
$463$		−	9382.12i		−	0.941737i	0.882203	−	0.470868i	$-0.156059\pi$
$464$	−2087.93	+	4606.34i	−0.208901	+	0.460870i
$465$	4285.99	−	2474.52i	0.427437	−	0.246781i
$466$	6649.13	+	4847.90i	0.660976	+	0.481920i
$467$	−6270.05	−	3620.01i	−0.621292	−	0.358703i	0.156080	−	0.987744i	$-0.450114\pi$
$467$	−6270.05	−	3620.01i	−0.621292	−	0.358703i	−0.777372	+	0.629042i	$0.783448\pi$
$468$	−0.657546	+	0.725382i	−6.49468e−5	+	7.16470e-5i
$469$	1625.05	−	4632.01i	0.159996	−	0.456047i
$470$	15024.8	−	6659.37i	1.47456	−	0.653561i
$471$	−5658.27	−	3266.80i	−0.553544	−	0.319589i
$472$	1022.41	+	4931.71i	0.0997044	+	0.480933i
$473$	−518.759	−	898.517i	−0.0504283	−	0.0873443i
$474$	558.705	−	5231.49i	0.0541396	−	0.506942i
$475$			13128.2i			1.26813i
$476$	14269.7	+	8752.79i	1.37406	+	0.842822i
$477$		−	998.787i		−	0.0958728i
$478$	−8094.70	−	864.486i	−0.774567	−	0.0827211i
$479$	4352.19	+	7538.22i	0.415150	+	0.719060i	0.995444	−	0.0953464i	$-0.0303959\pi$
$479$	4352.19	+	7538.22i	0.415150	+	0.719060i	−0.580294	+	0.814407i	$0.697063\pi$
$480$	−6709.67	−	3949.06i	−0.638028	−	0.375519i
$481$	−0.474211	−	0.273786i	−4.49525e−5	−	2.59533e-5i
$482$	3467.36	+	7823.02i	0.327663	+	0.739271i
$483$	4550.82	+	5296.89i	0.428715	+	0.498999i
$484$	−5514.70	+	6083.62i	−0.517910	+	0.571340i
$485$	−1326.15	−	765.654i	−0.124160	−	0.0716836i
$486$	404.919	−	555.367i	0.0377932	−	0.0518353i
$487$	5116.57	−	2954.05i	0.476086	−	0.274868i	−0.242698	−	0.970102i	$-0.578032\pi$
$487$	5116.57	−	2954.05i	0.476086	−	0.274868i	0.718784	+	0.695234i	$0.244699\pi$
$488$	9470.98	+	10625.4i	0.878548	+	0.985633i
$489$		−	4189.21i		−	0.387408i
$490$	9793.70	−	9875.80i	0.902927	−	0.910497i
$491$	2879.70			0.264682			0.132341	−	0.991204i	$-0.457751\pi$
$491$	2879.70			0.264682			0.132341	+	0.991204i	$0.457751\pi$
$492$	2843.73	+	8852.80i	0.260579	+	0.811210i
$493$	4464.23	+	7732.27i	0.407827	+	0.706377i
$494$	3.69365	−	5.06602i	0.000336407	−	0.000461399i
$495$	1125.97	−	1950.24i	0.102240	−	0.177085i
$496$	−720.743	−	7329.03i	−0.0652466	−	0.663474i
$497$	−14373.0	+	12348.5i	−1.29721	+	1.11450i
$498$	443.537	−	196.587i	0.0399104	−	0.0176893i
$499$	−10301.7	+	17843.1i	−0.924186	+	1.60074i	−0.131320	+	0.991340i	$0.541922\pi$
$499$	−10301.7	+	17843.1i	−0.924186	+	1.60074i	−0.792865	+	0.609397i	$0.791412\pi$
$500$	4984.75	+	1076.99i	0.445849	+	0.0963291i
$501$	7038.49	−	4063.67i	0.627658	−	0.362378i
$502$	−18407.4	−	1965.84i	−1.63658	−	0.174781i
$503$	−10122.2			−0.897274			−0.448637	−	0.893714i	$-0.648090\pi$
$503$	−10122.2			−0.897274			−0.448637	+	0.893714i	$0.648090\pi$
$504$	−500.130	+	3738.28i	−0.0442015	+	0.330390i
$505$	−4155.06			−0.366134
$506$	−6169.49	−	658.880i	−0.542030	−	0.0578870i
$507$	−5707.97	+	3295.50i	−0.500000	+	0.288675i
$508$	−3882.24	+	17968.6i	−0.339068	+	1.56934i
$509$	452.319	−	783.440i	0.0393884	−	0.0682227i	−0.845659	−	0.533723i	$-0.820792\pi$
$509$	452.319	−	783.440i	0.0393884	−	0.0682227i	0.885048	+	0.465501i	$0.154126\pi$
$510$	−12565.7	+	5569.43i	−1.09102	+	0.483566i
$511$	19230.6	+	6746.69i	1.66479	+	0.584062i
$512$	−9474.15	+	6667.70i	−0.817778	+	0.575534i
$513$	−2200.66	+	3811.65i	−0.189399	+	0.328048i
$514$	−2064.07	+	2830.98i	−0.177125	+	0.242936i
$515$	1001.46	+	1734.57i	0.0856883	+	0.148416i
$516$	−1358.35	+	436.332i	−0.115887	+	0.0372257i
$517$	7073.60			0.601734
$518$	−2102.69	+	168.131i	−0.178353	+	0.0142611i
$519$		−	12807.4i		−	1.08320i
$520$	2.93514	+	3.29290i	0.000247528	+	0.000277699i
$521$	10554.3	−	6093.53i	0.887510	−	0.512404i	0.0143826	−	0.999897i	$-0.495422\pi$
$521$	10554.3	−	6093.53i	0.887510	−	0.512404i	0.873127	+	0.487493i	$0.162088\pi$
$522$	−1185.10	+	1625.43i	−0.0993690	+	0.136289i
$523$	4054.18	+	2340.68i	0.338962	+	0.195700i	0.659813	−	0.751430i	$-0.270636\pi$
$523$	4054.18	+	2340.68i	0.338962	+	0.195700i	−0.320851	+	0.947130i	$0.603969\pi$
$524$	−15100.3	−	13688.2i	−1.25890	−	1.14117i
$525$	828.290	+	4397.26i	0.0688563	+	0.365547i
$526$	1071.53	+	2417.58i	0.0888230	+	0.200402i
$527$	−11259.3	−	6500.57i	−0.930671	−	0.537323i
$528$	−1951.47	−	2724.14i	−0.160846	−	0.224532i
$529$	1815.26	+	3144.13i	0.149196	+	0.258414i
$530$	−4474.62	−	477.874i	−0.366726	−	0.0391651i
$531$			2003.28i			0.163720i
$532$	642.446	−	24143.6i	0.0523564	−	1.96759i
$533$		−	5.26826i		−	0.000428131i
$534$	476.845	−	4464.98i	0.0386425	−	0.361833i
$535$	−7371.21	−	12767.3i	−0.595673	−	1.03174i
$536$	5872.53	−	1217.46i	0.473236	−	0.0981088i
$537$	−6422.42	−	3707.99i	−0.516104	−	0.297973i
$538$	−2876.57	+	1274.97i	−0.230516	+	0.102171i
$539$	5576.15	−	2177.98i	0.445607	−	0.174049i
$540$	−2294.34	−	2079.78i	−0.182838	−	0.165739i
$541$	11836.3	+	6833.70i	0.940634	+	0.543075i	0.890159	−	0.455650i	$-0.150593\pi$
$541$	11836.3	+	6833.70i	0.940634	+	0.543075i	0.0504750	+	0.998725i	$0.483926\pi$
$542$	−12323.4	−	8985.03i	−0.976634	−	0.712066i
$543$	−2819.14	+	1627.63i	−0.222801	+	0.128634i
$544$	−171.139	+	20451.9i	−0.0134881	+	1.61189i
$545$			18812.3i			1.47859i
$546$	0.917553	−	1.92990i	7.19188e−5	−	0.000151267i
$547$	−14251.9			−1.11402			−0.557009	−	0.830506i	$-0.688051\pi$
$547$	−14251.9			−1.11402			−0.557009	+	0.830506i	$0.688051\pi$
$548$	−4823.65	−	15016.5i	−0.376015	−	1.17057i
$549$	2830.71	+	4902.94i	0.220058	+	0.381151i
$550$	−3212.41	−	2342.18i	−0.249050	−	0.181583i
$551$	6440.82	−	11155.8i	0.497982	−	0.862530i
$552$	−2677.24	+	8101.07i	−0.206433	+	0.624646i
$553$	2125.68	+	11284.9i	0.163460	+	0.867781i
$554$	−1957.13	−	4415.66i	−0.150091	−	0.338635i
$555$	865.967	−	1499.90i	0.0662310	−	0.114716i
$556$	4094.97	−	18953.1i	0.312348	−	1.44567i
$557$	−9512.61	+	5492.11i	−0.723631	+	0.417788i	−0.816088	−	0.577928i	$-0.803861\pi$
$557$	−9512.61	+	5492.11i	−0.723631	+	0.417788i	0.0924567	+	0.995717i	$0.470528\pi$
$558$	311.056	−	2912.60i	0.0235987	−	0.220968i
$559$	0.808346			6.11617e−5
$560$	16508.4	+	4029.21i	1.24573	+	0.304045i
$561$	−5915.86			−0.445219
$562$	−64.2932	+	602.015i	−0.00482570	+	0.0451859i
$563$	1766.78	−	1020.05i	0.132257	−	0.0763588i	−0.432412	−	0.901676i	$-0.642337\pi$
$563$	1766.78	−	1020.05i	0.132257	−	0.0763588i	0.564669	+	0.825318i	$0.309004\pi$
$564$	2054.19	−	9507.62i	0.153364	−	0.709828i
$565$	−5475.70	+	9484.19i	−0.407725	+	0.706200i
$566$	−4163.30	−	9393.20i	−0.309181	−	0.697572i
$567$	−496.621	+	1415.55i	−0.0367832	+	0.104846i
$568$	−21982.1	−	7264.62i	−1.62385	−	0.536649i
$569$	910.229	−	1576.56i	0.0670629	−	0.116156i	−0.830544	−	0.556953i	$-0.811971\pi$
$569$	910.229	−	1576.56i	0.0670629	−	0.116156i	0.897607	+	0.440796i	$0.145304\pi$
$570$	16023.5	+	11682.8i	1.17746	+	0.858486i
$571$	632.042	+	1094.73i	0.0463225	+	0.0802329i	0.888257	−	0.459347i	$-0.151916\pi$
$571$	632.042	+	1094.73i	0.0463225	+	0.0802329i	−0.841935	+	0.539580i	$0.818583\pi$
$572$	0.580657	+	1.80764i	4.24449e−5	+	0.000132135i
$573$	11263.5			0.821184
$574$	−11516.0	−	16711.1i	−0.837404	−	1.21517i
$575$			10122.3i			0.734138i
$576$	−4228.22	+	1831.88i	−0.305861	+	0.132514i
$577$	19613.3	−	11323.7i	1.41510	−	0.817008i	0.419236	−	0.907877i	$-0.362298\pi$
$577$	19613.3	−	11323.7i	1.41510	−	0.817008i	0.995863	+	0.0908695i	$0.0289646\pi$
$578$	17947.3	+	13085.5i	1.29154	+	0.941666i
$579$	−1341.61	−	774.581i	−0.0962963	−	0.0555967i
$580$	6714.98	+	6087.02i	0.480732	+	0.435775i
$581$	−803.184	+	690.056i	−0.0573523	+	0.0492742i
$582$	−828.588	+	367.251i	−0.0590139	+	0.0261564i
$583$	−1677.39	−	968.440i	−0.119160	−	0.0687971i
$584$	5054.50	+	24380.8i	0.358145	+	1.72754i
$585$	0.877262	+	1.51946i	6.20006e−5	+	0.000107388i
$586$	186.377	−	1745.16i	0.0131385	−	0.123023i
$587$		−	22223.9i		−	1.56265i	−0.624122	−	0.781327i	$-0.714543\pi$
$587$		−	22223.9i		−	1.56265i	0.624122	−	0.781327i	$-0.285457\pi$
$588$	−1308.10	−	8127.40i	−0.0917433	−	0.570014i
$589$			18757.5i			1.31221i
$590$	8974.81	+	958.479i	0.626249	+	0.0668813i
$591$	−4085.31	−	7075.96i	−0.284344	−	0.492497i
$592$	−1500.84	−	2095.09i	−0.104197	−	0.145452i
$593$	−15704.3	−	9066.88i	−1.08752	−	0.627879i	−0.154603	−	0.987977i	$-0.549410\pi$
$593$	−15704.3	−	9066.88i	−1.08752	−	0.627879i	−0.932915	+	0.360098i	$0.882743\pi$
$594$	−540.080	−	1218.52i	−0.0373060	−	0.0841694i
$595$	22754.8	−	19549.8i	1.56782	−	1.34700i
$596$	−3543.35	−	3211.98i	−0.243525	−	0.220752i
$597$	−11738.5	−	6777.21i	−0.804729	−	0.464611i
$598$	2.84794	−	3.90609i	0.000194751	−	0.000267110i
$599$	23274.1	−	13437.3i	1.58757	−	0.916584i	0.593864	−	0.804566i	$-0.297602\pi$
$599$	23274.1	−	13437.3i	1.58757	−	0.916584i	0.993706	−	0.112018i	$-0.0357316\pi$
$600$	−4081.02	+	3637.63i	−0.277678	+	0.247509i
$601$			2069.10i			0.140433i	0.997532	+	0.0702167i	$0.0223691\pi$
$601$			2069.10i			0.140433i	−0.997532	+	0.0702167i	$0.977631\pi$
$602$	2564.10	−	1766.98i	0.173596	−	0.119629i
$603$	2385.45			0.161100
$604$	−6047.26	+	1942.52i	−0.407383	+	0.130861i
$605$	7357.41	+	12743.4i	0.494416	+	0.856353i
$606$	−1448.83	+	1987.14i	−0.0971201	+	0.133205i
$607$	−3262.04	+	5650.02i	−0.218126	+	0.377804i	−0.954235	−	0.299058i	$-0.903328\pi$
$607$	−3262.04	+	5650.02i	−0.218126	+	0.377804i	0.736109	+	0.676863i	$0.236661\pi$
$608$	25677.5	−	14539.8i	1.71276	−	0.969847i
$609$	1453.49	−	4142.99i	0.0967134	−	0.275669i
$610$	23319.8	−	10335.9i	1.54785	−	0.686046i
$611$	−2.75557	+	4.77279i	−0.000182453	+	0.000316017i
$612$	−1717.98	+	7951.52i	−0.113473	+	0.525198i
$613$	−24391.0	+	14082.2i	−1.60709	+	0.927852i	−0.617069	+	0.786909i	$0.711680\pi$
$613$	−24391.0	+	14082.2i	−1.60709	+	0.927852i	−0.990018	+	0.140943i	$0.954987\pi$
$614$	16253.6	+	1735.82i	1.06831	+	0.114091i
$615$	16663.2			1.09256
$616$	5793.23	+	4464.63i	0.378922	+	0.292021i
$617$	2680.20			0.174880			0.0874398	−	0.996170i	$-0.472131\pi$
$617$	2680.20			0.174880			0.0874398	+	0.996170i	$0.472131\pi$
$618$	1178.75	+	125.887i	0.0767256	+	0.00819402i
$619$	3985.34	−	2300.94i	0.258780	−	0.149406i	−0.364998	−	0.931008i	$-0.618930\pi$
$619$	3985.34	−	2300.94i	0.258780	−	0.149406i	0.623778	+	0.781602i	$0.285597\pi$
$620$	−12899.8	−	2787.09i	−0.835593	−	0.180536i
$621$	−1696.79	+	2938.93i	−0.109646	+	0.189912i
$622$	−6518.71	+	2889.26i	−0.420219	+	0.186252i
$623$	1814.23	+	9631.45i	0.116670	+	0.619384i
$624$	2.59828	−	0.255517i	0.000166690	−	1.63924e-5i
$625$	9602.99	−	16632.9i	0.614592	−	1.06450i
$626$	11869.1	−	16279.0i	0.757801	−	1.03936i
$627$	4267.59	+	7391.68i	0.271820	+	0.470806i
$628$	5328.49	+	16588.1i	0.338583	+	1.05404i
$629$	−4549.79			−0.288413
$630$	6104.14	+	2902.16i	0.386023	+	0.183532i
$631$		−	28417.5i		−	1.79284i	−0.443206	−	0.896420i	$-0.646159\pi$
$631$		−	28417.5i		−	1.79284i	0.443206	−	0.896420i	$-0.353841\pi$
$632$	−10473.3	+	9335.42i	−0.659186	+	0.587568i
$633$	1801.74	−	1040.23i	0.113132	−	0.0653169i
$634$	3658.59	−	5017.93i	0.229181	−	0.314334i
$635$	28530.2	+	16471.9i	1.78297	+	1.02940i
$636$	−1788.80	+	1973.34i	−0.111526	+	0.123031i
$637$	−0.702675	+	4.61087i	−4.37064e−5	+	0.000286796i
$638$	1580.69	+	3566.34i	0.0980879	+	0.221305i
$639$	−7974.71	−	4604.20i	−0.493700	−	0.285038i
$640$	6183.90	+	19819.1i	0.381938	+	1.22409i
$641$	857.499	+	1485.23i	0.0528380	+	0.0915181i	0.891235	−	0.453543i	$-0.149840\pi$
$641$	857.499	+	1485.23i	0.0528380	+	0.0915181i	−0.838397	+	0.545061i	$0.816507\pi$
$642$	−8676.20	−	926.588i	−0.533368	−	0.0569619i
$643$		−	5665.36i		−	0.347465i	−0.984793	−	0.173733i	$-0.944417\pi$
$643$		−	5665.36i		−	0.347465i	0.984793	−	0.173733i	$-0.0555828\pi$
$644$	495.350	−	18615.6i	0.0303098	−	1.13907i
$645$			2556.75i			0.156080i
$646$	5532.02	−	51799.6i	0.336926	−	3.15484i
$647$	−5809.92	−	10063.1i	−0.353032	−	0.611469i	0.633747	−	0.773540i	$-0.281516\pi$
$647$	−5809.92	−	10063.1i	−0.353032	−	0.611469i	−0.986779	+	0.162071i	$0.948183\pi$
$648$	−1794.66	+	372.059i	−0.108798	+	0.0225554i
$649$	3364.36	+	1942.42i	0.203487	+	0.117483i
$650$	2.83176	−	1.25511i	0.000170878	−	7.57376e-5i
$651$	1183.46	+	6282.81i	0.0712496	+	0.378253i
$652$	−7502.75	+	8276.77i	−0.450660	+	0.497152i
$653$	−16057.9	−	9271.01i	−0.962317	−	0.555594i	−0.0654313	−	0.997857i	$-0.520842\pi$
$653$	−16057.9	−	9271.01i	−0.962317	−	0.555594i	−0.896885	+	0.442263i	$0.854176\pi$
$654$	8996.91	+	6559.67i	0.537931	+	0.392207i
$655$	−31630.8	+	18262.0i	−1.88690	+	1.08940i
$656$	10236.7	−	22583.8i	0.609260	−	1.34413i
$657$			9903.61i			0.588092i
$658$	1692.19	+	21162.9i	0.100256	+	1.25383i
$659$	7570.77			0.447519			0.223760	−	0.974644i	$-0.428167\pi$
$659$	7570.77			0.447519			0.223760	+	0.974644i	$0.428167\pi$
$660$	−5717.45	+	1836.58i	−0.337199	+	0.108316i
$661$	−9925.25	−	17191.0i	−0.584036	−	1.01158i	−0.994995	−	0.0999258i	$-0.968139\pi$
$661$	−9925.25	−	17191.0i	−0.584036	−	1.01158i	0.410959	−	0.911654i	$-0.365194\pi$
$662$	15405.3	+	11232.0i	0.904447	+	0.659435i
$663$	2.30457	−	3.99163i	0.000134996	−	0.000233819i
$664$	−1228.39	−	405.958i	−0.0717935	−	0.0237263i
$665$	−40841.7	−	14328.5i	−2.38161	−	0.835544i
$666$	−415.367	−	937.146i	−0.0241669	−	0.0545250i
$667$	4966.11	−	8601.55i	0.288289	−	0.499331i
$668$	−21184.1	−	4576.98i	−1.22700	−	0.265103i
$669$	−10068.1	+	5812.80i	−0.581844	+	0.335928i
$670$	1141.33	−	10686.9i	0.0658110	−	0.616228i
$671$	10978.8			0.631643
$672$	7683.28	−	6490.14i	0.441055	−	0.372564i
$673$	−6328.13			−0.362454			−0.181227	−	0.983441i	$-0.558007\pi$
$673$	−6328.13			−0.362454			−0.181227	+	0.983441i	$0.558007\pi$
$674$	961.862	−	9006.49i	0.0549697	−	0.514714i
$675$	−1883.13	+	1087.22i	−0.107380	+	0.0619959i
$676$	17179.6	+	3711.78i	0.977446	+	0.211184i
$677$	7175.39	−	12428.1i	0.407345	−	0.705542i	−0.587246	−	0.809408i	$-0.699788\pi$
$677$	7175.39	−	12428.1i	0.407345	−	0.705542i	0.994591	+	0.103866i	$0.0331213\pi$
$678$	2626.46	+	5925.78i	0.148773	+	0.335661i
$679$	1500.46	−	1289.12i	0.0848046	−	0.0728599i
$680$	34801.2	+	11501.1i	1.96260	+	0.648598i
$681$	2791.05	−	4834.25i	0.157053	−	0.272024i
$682$	−4589.89	−	3346.50i	−0.257707	−	0.187895i
$683$	−14738.8	−	25528.3i	−0.825716	−	1.43018i	−0.901371	−	0.433048i	$-0.857438\pi$
$683$	−14738.8	−	25528.3i	−0.825716	−	1.43018i	0.0756553	−	0.997134i	$-0.475895\pi$
$684$	11174.5	−	3589.51i	0.624660	−	0.200655i
$685$	−28264.8			−1.57656
$686$	7850.10	+	16161.8i	0.436907	+	0.899507i
$687$			3994.30i			0.221822i
$688$	3465.19	+	1570.68i	0.192019	+	0.0870373i
$689$	1.30688	−	0.754527i	7.22614e−5	−	4.17201e-5i
$690$	12354.7	+	9007.85i	0.681646	+	0.496990i
$691$	−1274.09	−	735.599i	−0.0701430	−	0.0404971i	0.464518	−	0.885564i	$-0.346227\pi$
$691$	−1274.09	−	735.599i	−0.0701430	−	0.0404971i	−0.534661	+	0.845066i	$0.679561\pi$
$692$	−22937.7	+	25304.0i	−1.26006	+	1.39005i
$693$	1895.78	+	2206.58i	0.103918	+	0.120954i
$694$	12388.6	−	5490.93i	0.677614	−	0.300335i
$695$	−30093.5	−	17374.5i	−1.64246	−	0.948275i
$696$	5252.55	−	1088.93i	0.286059	−	0.0593043i
$697$	−21887.1	−	37909.6i	−1.18943	−	2.06015i
$698$	668.891	−	6263.23i	0.0362721	−	0.339637i
$699$		−	8727.95i		−	0.472277i
$700$	6238.89	−	10171.3i	0.336868	−	0.549197i
$701$			36181.3i			1.94943i	0.223460	+	0.974713i	$0.428265\pi$
$701$			36181.3i			1.94943i	−0.223460	+	0.974713i	$0.571735\pi$
$702$	1.03257	+	0.110275i	5.55155e−5	+	5.92887e-6i
$703$	3282.13	+	5684.82i	0.176085	+	0.304989i
$704$	−1023.25	+	8877.20i	−0.0547802	+	0.475245i
$705$	−15096.0	−	8715.70i	−0.806453	−	0.465606i
$706$	−3461.45	−	7809.69i	−0.184523	−	0.416320i
$707$	1776.95	−	5064.96i	0.0945246	−	0.269430i
$708$	3587.82	−	3957.96i	0.190450	−	0.210098i
$709$	13668.1	+	7891.26i	0.723998	+	0.418001i	0.816223	−	0.577738i	$-0.196064\pi$
$709$	13668.1	+	7891.26i	0.723998	+	0.418001i	−0.0922242	+	0.995738i	$0.529398\pi$
$710$	−24442.6	+	33524.2i	−1.29199	+	1.77203i
$711$	−4832.76	+	2790.19i	−0.254912	+	0.147174i
$712$	−8938.77	+	7967.61i	−0.470498	+	0.419380i
$713$			14462.8i			0.759656i
$714$	−1415.23	−	17699.2i	−0.0741787	−	0.927698i
$715$	3.40243			0.000177963
$716$	6048.11	+	18828.4i	0.315682	+	0.982750i
$717$	4317.27	+	7477.74i	0.224870	+	0.389486i
$718$	−6549.38	+	8982.80i	−0.340419	+	0.466901i
$719$	−7498.23	+	12987.3i	−0.388925	+	0.673638i	−0.992305	−	0.123816i	$-0.960487\pi$
$719$	−7498.23	+	12987.3i	−0.388925	+	0.673638i	0.603380	+	0.797454i	$0.293820\pi$
$720$	808.182	+	8218.18i	0.0418322	+	0.425380i
$721$	−2542.70	+	478.956i	−0.131339	+	0.0247396i
$722$	−50976.5	+	22594.0i	−2.62763	+	1.16463i
$723$	4538.03	−	7860.10i	0.233432	−	0.404316i
$724$	8484.91	+	1833.23i	0.435551	+	0.0941041i
$725$	5511.47	−	3182.05i	0.282332	−	0.163005i
$726$	8659.96	+	924.854i	0.442701	+	0.0472790i
$727$	23460.4			1.19684			0.598418	−	0.801184i	$-0.295796\pi$
$727$	23460.4			1.19684			0.598418	+	0.801184i	$0.295796\pi$
$728$	−5.26923	+	2.16966i	−0.000268257	+	0.000110457i
$729$	−729.000			−0.0370370
$730$	44368.7	+	4738.42i	2.24953	+	0.240242i
$731$	5816.73	−	3358.29i	0.294308	−	0.169919i
$732$	3188.28	−	14756.6i	0.160987	−	0.745110i
$733$	15323.6	−	26541.3i	0.772157	−	1.33742i	−0.164221	−	0.986424i	$-0.552511\pi$
$733$	15323.6	−	26541.3i	0.772157	−	1.33742i	0.936378	−	0.350992i	$-0.114156\pi$
$734$	−3594.62	+	1593.23i	−0.180763	+	0.0801186i
$735$	−14583.9	−	2222.51i	−0.731883	−	0.111536i
$736$	19798.3	−	11210.7i	0.991542	−	0.561458i
$737$	2312.97	−	4006.18i	0.115603	−	0.200230i
$738$	5810.30	−	7969.11i	0.289810	−	0.397489i
$739$	−12993.6	−	22505.6i	−0.646791	−	1.12028i	−0.983885	−	0.178804i	$-0.942777\pi$
$739$	−12993.6	−	22505.6i	−0.646791	−	1.12028i	0.337093	−	0.941471i	$-0.390556\pi$
$740$	−4397.20	+	1412.48i	−0.218438	+	0.0701674i
$741$	−6.64989			−0.000329676
$742$	2496.13	−	5250.12i	0.123498	−	0.259755i
$743$		−	31662.8i		−	1.56339i	−0.623664	−	0.781693i	$-0.714357\pi$
$743$		−	31662.8i		−	1.56339i	0.623664	−	0.781693i	$-0.285643\pi$
$744$	−5830.95	+	5197.44i	−0.287330	+	0.256112i
$745$	−7422.27	+	4285.25i	−0.365008	+	0.210738i
$746$	−20224.5	+	27738.9i	−0.992591	+	1.36139i
$747$	−445.639	−	257.290i	−0.0218274	−	0.0126021i
$748$	11688.2	+	10595.1i	0.571340	+	0.517910i
$749$	18715.5	−	3525.35i	0.913017	−	0.171981i
$750$	−2191.81	−	4945.15i	−0.106712	−	0.240762i
$751$	20071.7	+	11588.4i	0.975267	+	0.563070i	0.900838	−	0.434156i	$-0.142953\pi$
$751$	20071.7	+	11588.4i	0.975267	+	0.563070i	0.0744288	+	0.997226i	$0.476287\pi$
$752$	−21086.4	+	15105.6i	−1.02253	+	0.732504i
$753$	9817.50	+	17004.4i	0.475125	+	0.822942i
$754$	−3.02210	−	0.322749i	−0.000145966	−	1.55886e-5i
$755$			11382.4i			0.548675i
$756$	3516.41	−	1907.33i	0.169167	−	0.0917577i
$757$		−	21080.0i		−	1.01211i	−0.862501	−	0.506055i	$-0.831103\pi$
$757$		−	21080.0i		−	1.01211i	0.862501	−	0.506055i	$-0.168897\pi$
$758$	−96.4304	+	902.935i	−0.00462073	+	0.0432666i
$759$	3290.47	+	5699.26i	0.157360	+	0.272556i
$760$	−10734.7	−	51779.7i	−0.512353	−	2.47138i
$761$	−5731.49	−	3309.08i	−0.273017	−	0.157627i	0.357241	−	0.934012i	$-0.383718\pi$
$761$	−5731.49	−	3309.08i	−0.273017	−	0.157627i	−0.630258	+	0.776386i	$0.717051\pi$
$762$	17825.8	−	7900.86i	0.847457	−	0.375614i
$763$	−22931.9	−	8045.23i	−1.08806	−	0.381726i
$764$	−22253.7	−	20172.6i	−1.05381	−	0.955258i
$765$	12625.3	+	7289.20i	0.596690	+	0.344499i
$766$	−25524.4	−	18609.9i	−1.20396	−	0.877812i
$767$	−2.62123	+	1.51337i	−0.000123399	+	7.12444e-5i
$768$	11634.7	+	3953.32i	0.546655	+	0.185746i
$769$		−	30464.7i		−	1.42859i	−0.699844	−	0.714296i	$-0.746747\pi$
$769$		−	30464.7i		−	1.42859i	0.699844	−	0.714296i	$-0.253253\pi$
$770$	10792.6	−	7437.46i	0.505116	−	0.348087i
$771$	3716.07			0.173581
$772$	1263.42	+	3933.16i	0.0589010	+	0.183365i
$773$	13374.8	+	23165.8i	0.622325	+	1.07790i	0.989052	+	0.147570i	$0.0471451\pi$
$773$	13374.8	+	23165.8i	0.622325	+	1.07790i	−0.366727	+	0.930329i	$0.619522\pi$
$774$	1222.76	+	891.514i	0.0567843	+	0.0414016i
$775$	−4633.53	+	8025.51i	−0.214763	+	0.371980i
$776$	2294.81	+	758.387i	0.106158	+	0.0350831i
$777$	1458.01	+	1697.04i	0.0673179	+	0.0783540i
$778$	−7262.25	−	16385.0i	−0.334658	−	0.755053i
$779$	−31577.9	+	54694.5i	−1.45237	+	2.51557i
$780$	0.988076	−	4.57321i	4.53574e−5	−	0.000209932i
$781$	−15464.8	+	8928.61i	−0.708546	+	0.409079i
$782$	4265.39	−	39939.4i	0.195051	−	1.82638i
$783$	2133.61			0.0973807
$784$	−11971.5	+	18400.4i	−0.545349	+	0.838209i
$785$	31223.0			1.41961
$786$	−2295.60	+	21495.1i	−0.104175	+	0.975452i
$787$	−19932.1	+	11507.8i	−0.902798	+	0.521231i	−0.878107	−	0.478464i	$-0.841194\pi$
$787$	−19932.1	+	11507.8i	−0.902798	+	0.521231i	−0.0246914	+	0.999695i	$0.507860\pi$
$788$	−4601.35	+	21296.9i	−0.208016	+	0.962780i
$789$	1402.40	−	2429.04i	0.0632787	−	0.109602i
$790$	10188.0	+	22986.0i	0.458824	+	1.03520i
$791$	−9219.35	−	10730.8i	−0.414415	−	0.482355i
$792$	−1115.29	+	3374.75i	−0.0500378	+	0.151410i
$793$	−4.27688	+	7.40777i	−0.000191521	+	0.000331725i
$794$	−10943.6	−	7979.03i	−0.489137	−	0.356631i
$795$	2386.52	+	4133.57i	0.106467	+	0.184406i
$796$	11054.3	+	34413.2i	0.492224	+	1.53234i
$797$	−36331.6			−1.61472			−0.807359	−	0.590060i	$-0.799104\pi$
$797$	−36331.6			−1.61472			−0.807359	+	0.590060i	$0.799104\pi$
$798$	−21093.7	+	14536.2i	−0.935725	+	0.644830i
$799$			45792.3i			2.02755i
$800$	14577.9	+	121.986i	0.644258	+	0.00539106i
$801$	−4124.67	+	2381.38i	−0.181945	+	0.105046i
$802$	21063.0	+	15357.1i	0.927381	+	0.676156i
$803$	16632.4	+	9602.70i	0.730938	+	0.422007i
$804$	−4713.02	−	4272.27i	−0.206736	−	0.187402i
$805$	−31490.4	−	11047.8i	−1.37875	−	0.483708i
$806$	4.04603	−	1.79330i	0.000176818	−	7.83701e-5i
$807$	2890.21	+	1668.66i	0.126072	+	0.0727877i
$808$	6421.43	−	1331.26i	0.279585	−	0.0579622i
$809$	16290.8	+	28216.4i	0.707976	+	1.22625i	0.965607	+	0.260007i	$0.0837250\pi$
$809$	16290.8	+	28216.4i	0.707976	+	1.22625i	−0.257630	+	0.966244i	$0.582942\pi$
$810$	−348.793	+	3265.96i	−0.0151300	+	0.141672i
$811$		−	13370.1i		−	0.578898i	−0.957193	−	0.289449i	$-0.906528\pi$
$811$		−	13370.1i		−	0.578898i	0.957193	−	0.289449i	$-0.0934720\pi$
$812$	−10291.7	+	5582.30i	−0.444788	+	0.241257i
$813$			16176.3i			0.697818i
$814$	−1976.61	−	211.095i	−0.0851109	−	0.00908955i
$815$	10009.8	+	17337.4i	0.430216	+	0.745157i
$816$	17635.2	−	12633.2i	0.756564	−	0.541975i
$817$	−8392.15	−	4845.21i	−0.359369	−	0.207482i
$818$	−13374.6	−	30175.5i	−0.571675	−	1.28981i
$819$	−2.22737	+	0.419559i	−9.50313e−5	+	1.79006e-5i
$820$	−32922.0	−	29843.3i	−1.40206	−	1.27094i
$821$	22344.3	+	12900.5i	0.949845	+	0.548393i	0.893033	−	0.449992i	$-0.148573\pi$
$821$	22344.3	+	12900.5i	0.949845	+	0.548393i	0.0568122	+	0.998385i	$0.481906\pi$
$822$	−9855.67	+	13517.5i	−0.418195	+	0.573575i
$823$	−15322.0	+	8846.18i	−0.648958	+	0.374676i	−0.788057	−	0.615602i	$-0.788913\pi$
$823$	−15322.0	+	8846.18i	−0.648958	+	0.374676i	0.139099	+	0.990279i	$0.455579\pi$
$824$	−2103.44	−	2359.83i	−0.0889284	−	0.0997677i
$825$			4216.76i			0.177950i
$826$	−5006.52	+	10530.3i	−0.210895	+	0.443577i
$827$	−32331.0			−1.35944			−0.679722	−	0.733470i	$-0.737900\pi$
$827$	−32331.0			−1.35944			−0.679722	+	0.733470i	$0.737900\pi$
$828$	8615.95	−	2767.64i	0.361624	−	0.116162i
$829$	−17484.5	−	30284.1i	−0.732524	−	1.26877i	−0.955801	−	0.294014i	$-0.905009\pi$
$829$	−17484.5	−	30284.1i	−0.732524	−	1.26877i	0.223277	−	0.974755i	$-0.428324\pi$
$830$	−1365.89	+	1873.38i	−0.0571214	+	0.0783447i
$831$	−2561.47	+	4436.59i	−0.106927	+	0.185203i
$832$	−5.59113	−	4.14860i	−0.000232978	−	0.000172869i
$833$	14099.6	+	36098.3i	0.586461	+	1.50148i
$834$	−18802.6	+	8333.78i	−0.780672	+	0.346013i
$835$	−19419.6	+	33635.7i	−0.804842	+	1.39403i
$836$	4806.66	−	22247.2i	0.198854	−	0.920375i
$837$	−2690.61	+	1553.43i	−0.111112	+	0.0641508i
$838$	−4484.57	−	478.937i	−0.184865	−	0.0197430i
$839$	−620.863			−0.0255478			−0.0127739	−	0.999918i	$-0.504066\pi$
$839$	−620.863			−0.0255478			−0.0127739	+	0.999918i	$0.504066\pi$
$840$	−6862.48	−	16666.2i	−0.281879	−	0.684571i
$841$	18144.4			0.743959
$842$	40833.7	+	4360.90i	1.67129	+	0.178487i
$843$	556.131	−	321.082i	0.0227214	−	0.0131182i
$844$	−5422.79	−	1171.63i	−0.221161	−	0.0477835i
$845$	15748.6	−	27277.4i	0.641147	−	1.11050i
$846$	−9432.10	+	4180.54i	−0.383312	+	0.169894i
$847$	−18680.5	+	3518.75i	−0.757815	+	0.142746i
$848$	7068.39	−	695.111i	0.286238	−	0.0281488i
$849$	−5448.87	+	9437.73i	−0.220265	+	0.381510i
$850$	15162.5	−	20796.2i	0.611848	−	0.839180i
$851$	2530.65	+	4383.21i	0.101938	+	0.176562i
$852$	7509.93	+	23379.2i	0.301979	+	0.940090i
$853$	48976.5			1.96591			0.982955	−	0.183844i	$-0.0588542\pi$
$853$	48976.5			1.96591			0.982955	+	0.183844i	$0.0588542\pi$
$854$	2626.42	+	32846.7i	0.105239	+	1.31615i
$855$		−	21033.2i		−	0.841309i
$856$	15482.4	+	17369.5i	0.618198	+	0.693549i
$857$	41178.0	−	23774.1i	1.64132	−	0.947618i	0.660959	−	0.750422i	$-0.270150\pi$
$857$	41178.0	−	23774.1i	1.64132	−	0.947618i	0.980364	−	0.197196i	$-0.0631836\pi$
$858$	1.18640	−	1.62720i	4.72062e−5	−	6.47456e-5i
$859$	−5907.86	−	3410.90i	−0.234661	−	0.135481i	0.378060	−	0.925781i	$-0.376591\pi$
$859$	−5907.86	−	3410.90i	−0.234661	−	0.135481i	−0.612720	+	0.790300i	$0.709925\pi$
$860$	4579.06	−	5051.46i	0.181563	−	0.200294i
$861$	−7126.14	+	20312.2i	−0.282065	+	0.803991i
$862$	10692.5	+	24124.3i	0.422491	+	0.953221i
$863$	3901.64	+	2252.61i	0.153897	+	0.0888526i	0.574971	−	0.818174i	$-0.305013\pi$
$863$	3901.64	+	2252.61i	0.153897	+	0.0888526i	−0.421074	+	0.907026i	$0.638347\pi$
$864$	4212.12	+	2479.09i	0.165856	+	0.0976163i
$865$	30602.2	+	53004.6i	1.20290	+	2.08348i
$866$	−20958.3	−	2238.27i	−0.822393	−	0.0878287i
$867$		−	23558.5i		−	0.922825i
$868$	8914.12	−	14532.7i	0.348577	−	0.568286i
$869$			10821.7i			0.422440i
$870$	1020.84	−	9558.69i	0.0397811	−	0.372494i
$871$	1.80207	+	3.12128i	7.01043e−5	+	0.000121424i
$872$	−6027.34	−	29073.4i	−0.234073	−	1.12907i
$873$	832.516	+	480.653i	0.0322754	+	0.0186342i
$874$	−52980.0	+	23482.0i	−2.05043	+	0.908801i
$875$	7693.68	+	8954.99i	0.297250	+	0.345982i
$876$	17737.1	−	19566.9i	0.684110	−	0.754686i
$877$	−19331.7	−	11161.2i	−0.744339	−	0.429745i	0.0793055	−	0.996850i	$-0.474730\pi$
$877$	−19331.7	−	11161.2i	−0.744339	−	0.429745i	−0.823645	+	0.567106i	$0.808063\pi$
$878$	22733.3	+	16574.9i	0.873816	+	0.637102i
$879$	−1612.14	+	930.772i	−0.0618615	+	0.0357158i
$880$	14585.4	+	6611.20i	0.558722	+	0.253254i
$881$		−	10311.4i		−	0.394325i	−0.980371	−	0.197162i	$-0.936827\pi$
$881$		−	10311.4i		−	0.394325i	0.980371	−	0.197162i	$-0.0631726\pi$
$882$	−6148.17	+	6199.72i	−0.234716	+	0.236684i
$883$	30437.2			1.16002			0.580008	−	0.814611i	$-0.303049\pi$
$883$	30437.2			1.16002			0.580008	+	0.814611i	$0.303049\pi$
$884$	−11.7021	+	3.75899i	−0.000445232	+	0.000143019i
$885$	−4786.68	−	8290.77i	−0.181811	−	0.314905i
$886$	−13828.6	−	10082.5i	−0.524357	−	0.382310i
$887$	76.5737	−	132.629i	0.00289864	−	0.00502059i	−0.864572	−	0.502508i	$-0.832411\pi$
$887$	76.5737	−	132.629i	0.00289864	−	0.00502059i	0.867471	+	0.497488i	$0.165744\pi$
$888$	−857.747	+	2595.46i	−0.0324145	+	0.0980834i
$889$	−32280.1	+	27733.5i	−1.21782	+	1.04629i
$890$	8695.23	+	19618.1i	0.327489	+	0.738877i
$891$	−706.850	+	1224.30i	−0.0265773	+	0.0460332i
$892$	30302.4	+	6547.05i	1.13744	+	0.245753i
$893$	57216.0	−	33033.7i	2.14408	−	1.23788i
$894$	−538.672	+	5043.90i	−0.0201520	+	0.188695i
$895$	35439.7			1.32360
$896$	−26803.8	−	937.731i	−0.999389	−	0.0349636i
$897$	−5.12731			−0.000190854
$898$	−1239.33	+	11604.6i	−0.0460544	+	0.431235i
$899$	7874.79	−	4546.51i	0.292146	−	0.168670i
$900$	5667.75	+	1224.56i	0.209917	+	0.0453540i
$901$	6269.39	−	10858.9i	0.231813	−	0.401512i
$902$	−7749.76	−	17484.9i	−0.286074	−	0.645437i
$903$	−3116.63	−	1093.41i	−0.114856	−	0.0402951i
$904$	5423.73	−	16411.7i	0.199547	−	0.603811i
$905$	7778.17	−	13472.2i	0.285696	−	0.494840i
$906$	5443.62	+	3968.95i	0.199616	+	0.145540i
$907$	8377.82	+	14510.8i	0.306705	+	0.531228i	0.977639	−	0.210288i	$-0.0674403\pi$
$907$	8377.82	+	14510.8i	0.306705	+	0.531228i	−0.670935	+	0.741516i	$0.734107\pi$
$908$	−14172.4	+	4552.50i	−0.517981	+	0.166388i
$909$	2608.42			0.0951768
$910$	0.813950	+	10.1795i	2.96507e−5	+	0.000370820i
$911$			30395.6i			1.10543i	0.833369	+	0.552717i	$0.186409\pi$
$911$			30395.6i			1.10543i	−0.833369	+	0.552717i	$0.813591\pi$
$912$	−28506.5	−	12921.3i	−1.03503	−	0.469151i
$913$	−864.198	+	498.945i	−0.0313262	+	0.0180862i
$914$	−252.178	−	183.864i	−0.00912616	−	0.00665391i
$915$	−23430.3	−	13527.5i	−0.846538	−	0.488749i
$916$	7153.67	−	7891.67i	0.258039	−	0.284660i
$917$	−8733.99	−	46367.3i	−0.314527	−	1.66978i
$918$	7888.35	−	3496.32i	0.283611	−	0.125703i
$919$	22204.2	+	12819.6i	0.797005	+	0.460151i	0.842423	−	0.538817i	$-0.181129\pi$
$919$	22204.2	+	12819.6i	0.797005	+	0.460151i	−0.0454180	+	0.998968i	$0.514462\pi$
$920$	−8276.84	−	39924.1i	−0.296608	−	1.43071i
$921$	−8668.77	−	15014.7i	−0.310147	−	0.537191i
$922$	2832.11	−	26518.7i	0.101161	−	0.947231i
$923$		−	13.9128i		−	0.000496150i
$924$	206.353	−	7754.91i	0.00734689	−	0.276102i
$925$			3243.04i			0.115276i
$926$	26386.6	+	2818.00i	0.936412	+	0.100006i
$927$	−628.683	−	1088.91i	−0.0222747	−	0.0385809i
$928$	−12327.9	−	7255.73i	−0.436081	−	0.256660i
$929$	4081.79	+	2356.63i	0.144154	+	0.0832275i	0.570342	−	0.821407i	$-0.306811\pi$
$929$	4081.79	+	2356.63i	0.144154	+	0.0832275i	−0.426188	+	0.904635i	$0.640144\pi$
$930$	5672.09	+	12797.3i	0.199995	+	0.451226i
$931$	34932.5	−	43657.6i	1.22972	−	1.53686i
$932$	−15631.5	+	17244.1i	−0.549385	+	0.606063i
$933$	6549.61	+	3781.42i	0.229823	+	0.132688i
$934$	12064.3	−	16546.8i	0.422651	−	0.579687i
$935$	24483.3	−	14135.5i	0.856354	−	0.494416i
$936$	−1.84259	−	2.06718i	−6.43450e−5	−	7.21879e-5i
$937$		−	36696.5i		−	1.27943i	−0.768614	−	0.639713i	$-0.779053\pi$
$937$		−	36696.5i		−	1.27943i	0.768614	−	0.639713i	$-0.220947\pi$
$938$	12539.1	+	5961.62i	0.436478	+	0.207520i
$939$	−21368.6			−0.742638
$940$	14216.2	+	44256.5i	0.493278	+	1.53562i
$941$	−22166.4	−	38393.3i	−0.767910	−	1.33006i	−0.938694	−	0.344751i	$-0.887963\pi$
$941$	−22166.4	−	38393.3i	−0.767910	−	1.33006i	0.170784	−	0.985309i	$-0.445370\pi$
$942$	10887.2	−	14932.3i	0.376564	−	0.516476i
$943$	−24347.7	+	42171.5i	−0.840796	+	1.45630i
$944$	−14177.2	+	1394.20i	−0.488801	+	0.0480691i
$945$	−1327.04	−	7045.03i	−0.0456810	−	0.242513i
$946$	2682.83	−	1189.10i	0.0922055	−	0.0408678i
$947$	4439.42	−	7689.30i	0.152335	−	0.263853i	−0.779750	−	0.626091i	$-0.784654\pi$
$947$	4439.42	−	7689.30i	0.152335	−	0.263853i	0.932086	+	0.362238i	$0.117987\pi$
$948$	14545.4	+	3142.64i	0.498326	+	0.107667i
$949$	−12.9585	+	7.48161i	−0.000443258	+	0.000255915i
$950$	−36922.1	−	3943.16i	−1.26096	−	0.134666i
$951$	−6586.77			−0.224596
$952$	−28902.7	+	37503.6i	−0.983971	+	1.27678i
$953$	9873.81			0.335618			0.167809	−	0.985820i	$-0.446331\pi$
$953$	9873.81			0.335618			0.167809	+	0.985820i	$0.446331\pi$
$954$	2809.02	+	299.994i	0.0953307	+	0.0101810i
$955$	−46614.9	+	26913.1i	−1.57950	+	0.911925i
$956$	4862.62	−	22506.2i	0.164507	−	0.761403i
$957$	2068.79	−	3583.24i	0.0698791	−	0.121034i
$958$	−22508.0	+	9976.09i	−0.759080	+	0.336443i
$959$	12087.7	−	34454.3i	0.407019	−	1.16016i
$960$	13121.8	−	17684.4i	0.441149	−	0.594543i
$961$	8275.12	−	14332.9i	0.277772	−	0.481116i
$962$	0.912438	−	1.25145i	3.05802e−5	−	4.19423e-5i
$963$	4627.41	+	8014.92i	0.154846	+	0.268201i
$964$	−23043.2	+	7402.00i	−0.769887	+	0.247305i
$965$	7403.18			0.246960
$966$	−16264.0	+	11207.9i	−0.541704	+	0.373301i
$967$			37987.8i			1.26329i	0.775256	+	0.631647i	$0.217621\pi$
$967$			37987.8i			1.26329i	−0.775256	+	0.631647i	$0.782379\pi$
$968$	−15453.4	−	17337.0i	−0.513111	−	0.575653i
$969$	−47851.5	+	27627.1i	−1.58639	+	0.915903i
$970$	2551.67	−	3499.74i	0.0844631	−	0.115845i
$971$	15678.8	+	9052.15i	0.518184	+	0.299173i	0.736191	−	0.676774i	$-0.236622\pi$
$971$	15678.8	+	9052.15i	0.518184	+	0.299173i	−0.218008	+	0.975947i	$0.569956\pi$
$972$	1440.31	+	1305.62i	0.0475288	+	0.0430841i
$973$	34048.9	−	29253.1i	1.12185	−	0.963836i
$974$	6771.27	+	15277.3i	0.222757	+	0.502583i
$975$	−2.84519	−	1.64267i	−9.34553e−5	−	5.39565e-5i
$976$	−32727.9	+	23445.1i	−1.07335	+	0.768913i
$977$	−17975.5	−	31134.4i	−0.588624	−	1.01953i	−0.994413	−	0.105560i	$-0.966336\pi$
$977$	−17975.5	−	31134.4i	−0.588624	−	1.01953i	0.405789	−	0.913967i	$-0.366997\pi$
$978$	11781.9	+	1258.26i	0.385217	+	0.0411399i
$979$			9236.09i			0.301519i
$980$	24833.4	+	30510.4i	0.809464	+	0.994509i
$981$		−	11809.8i		−	0.384359i
$982$	−864.942	+	8098.97i	−0.0281073	+	0.263186i
$983$	−8106.45	−	14040.8i	−0.263027	−	0.455576i	0.704018	−	0.710182i	$-0.251387\pi$
$983$	−8106.45	−	14040.8i	−0.263027	−	0.455576i	−0.967045	+	0.254606i	$0.918054\pi$
$984$	−25752.1	+	5338.78i	−0.834294	+	0.172961i
$985$	33814.8	+	19523.0i	1.09384	+	0.631527i
$986$	−23087.4	+	10232.9i	−0.745691	+	0.330509i
$987$	17080.2	−	14674.5i	0.550831	−	0.473246i
$988$	13.1384	+	11.9098i	0.000423066	+	0.000383502i
$989$	−6470.66	−	3735.84i	−0.208043	−	0.120114i
$990$	5146.73	+	3752.50i	0.165226	+	0.120467i
$991$	15142.2	−	8742.34i	0.485375	−	0.280232i	−0.237278	−	0.971442i	$-0.576255\pi$
$991$	15142.2	−	8742.34i	0.485375	−	0.280232i	0.722654	+	0.691210i	$0.242922\pi$
$992$	20828.9	+	174.293i	0.666652	+	0.00557845i
$993$		−	20221.7i		−	0.646240i
$994$	−30412.4	−	44132.0i	−0.970446	−	1.40823i
$995$	64774.3			2.06380
$996$	419.667	+	1306.46i	0.0133511	+	0.0415632i
$997$	−12042.3	−	20857.9i	−0.382531	−	0.662562i	0.608893	−	0.793253i	$-0.291614\pi$
$997$	−12042.3	−	20857.9i	−0.382531	−	0.662562i	−0.991423	+	0.130690i	$0.958281\pi$
$998$	−47088.4	−	34332.3i	−1.49354	−	1.08895i
$999$	−543.627	+	941.589i	−0.0172168	+	0.0298204i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.t.a.19.22	yes	96
4.3	odd	2		672.4.bb.a.271.17		96
7.3	odd	6	inner	168.4.t.a.115.10	yes	96
8.3	odd	2	inner	168.4.t.a.19.10	✓	96
8.5	even	2		672.4.bb.a.271.18		96
28.3	even	6		672.4.bb.a.367.18		96
56.3	even	6	inner	168.4.t.a.115.22	yes	96
56.45	odd	6		672.4.bb.a.367.17		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.t.a.19.10	✓	96	8.3	odd	2	inner
168.4.t.a.19.22	yes	96	1.1	even	1	trivial
168.4.t.a.115.10	yes	96	7.3	odd	6	inner
168.4.t.a.115.22	yes	96	56.3	even	6	inner
672.4.bb.a.271.17		96	4.3	odd	2
672.4.bb.a.271.18		96	8.5	even	2
672.4.bb.a.367.17		96	56.45	odd	6
672.4.bb.a.367.18		96	28.3	even	6

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	168.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.300358 + 2.81243i) q^{2} +(2.59808 - 1.50000i) q^{3} +(-7.81957 - 1.68948i) q^{4} +(-7.16825 + 12.4158i) q^{5} +(3.43830 + 7.75746i) q^{6} +(-12.0691 - 14.0477i) q^{7} +(7.10021 - 21.4846i) q^{8} +(4.50000 - 7.79423i) q^{9} +(-32.7655 - 23.8894i) q^{10} +(-8.72655 - 15.1148i) q^{11} +(-22.8501 + 7.33997i) q^{12} +0.0135980 q^{13} +(43.1332 - 29.7241i) q^{14} +43.0095i q^{15} +(58.2913 + 26.4219i) q^{16} +(97.8487 - 56.4930i) q^{17} +(20.5691 + 14.9970i) q^{18} +(-141.172 - 81.5059i) q^{19} +(77.0287 - 84.9754i) q^{20} +(-52.4279 - 18.3934i) q^{21} +(45.1305 - 20.0030i) q^{22} +(-108.849 - 62.8441i) q^{23} +(-13.7800 - 66.4689i) q^{24} +(-40.2675 - 69.7454i) q^{25} +(-0.00408426 + 0.0382434i) q^{26} -27.0000i q^{27} +(70.6417 + 130.237i) q^{28} +79.0227i q^{29} +(-120.961 - 12.9183i) q^{30} +(-57.5343 - 99.6523i) q^{31} +(-91.8183 + 156.005i) q^{32} +(-45.3445 - 26.1796i) q^{33} +(129.493 + 292.161i) q^{34} +(260.927 - 49.1495i) q^{35} +(-48.3562 + 53.3449i) q^{36} +(-34.8737 - 20.1343i) q^{37} +(271.632 - 372.557i) q^{38} +(0.0353286 - 0.0203970i) q^{39} +(215.851 + 242.161i) q^{40} -387.430i q^{41} +(67.4772 - 141.925i) q^{42} +59.4461 q^{43} +(42.7017 + 132.935i) q^{44} +(64.5142 + 111.742i) q^{45} +(209.439 - 287.255i) q^{46} +(-202.646 + 350.993i) q^{47} +(191.078 - 18.7908i) q^{48} +(-51.6750 + 339.085i) q^{49} +(208.249 - 92.3012i) q^{50} +(169.479 - 293.546i) q^{51} +(-0.106330 - 0.0229734i) q^{52} +(96.1083 - 55.4882i) q^{53} +(75.9357 + 8.10967i) q^{54} +250.216 q^{55} +(-387.502 + 159.557i) q^{56} -489.036 q^{57} +(-222.246 - 23.7351i) q^{58} +(-192.766 + 111.294i) q^{59} +(72.6635 - 336.316i) q^{60} +(-314.523 + 544.771i) q^{61} +(297.546 - 131.880i) q^{62} +(-163.802 + 30.8545i) q^{63} +(-411.174 - 305.090i) q^{64} +(-0.0974736 + 0.168829i) q^{65} +(87.2481 - 119.665i) q^{66} +(132.525 + 229.540i) q^{67} +(-860.579 + 276.438i) q^{68} -377.065 q^{69} +(59.8582 + 748.602i) q^{70} -1023.16i q^{71} +(-135.505 - 152.021i) q^{72} +(-952.975 + 550.200i) q^{73} +(67.1010 - 92.0323i) q^{74} +(-209.236 - 120.803i) q^{75} +(966.205 + 875.849i) q^{76} +(-107.007 + 305.010i) q^{77} +(0.0467539 + 0.105486i) q^{78} +(-536.973 - 310.022i) q^{79} +(-745.896 + 534.333i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(1089.62 + 116.368i) q^{82} -57.1755i q^{83} +(378.888 + 232.404i) q^{84} +1619.82i q^{85} +(-17.8551 + 167.188i) q^{86} +(118.534 + 205.307i) q^{87} +(-386.696 + 80.1677i) q^{88} +(-458.297 - 264.598i) q^{89} +(-333.644 + 147.879i) q^{90} +(-0.164115 - 0.191020i) q^{91} +(744.980 + 675.312i) q^{92} +(-298.957 - 172.603i) q^{93} +(-926.278 - 675.352i) q^{94} +(2023.92 - 1168.51i) q^{95} +(-4.54408 + 543.039i) q^{96} +106.812i q^{97} +(-938.133 - 247.180i) q^{98} -157.078 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{2} - 10 q^{4} - 16 q^{8} + 432 q^{9} + 18 q^{10} + 40 q^{11} + 274 q^{14} - 26 q^{16} - 18 q^{18} + 4 q^{22} + 270 q^{24} - 1200 q^{25} + 750 q^{26} + 922 q^{28} + 168 q^{30} - 108 q^{32} + 456 q^{35}+ \cdots + 720 q^{99}+O(q^{100}) \) 96 * q + 2 * q^2 - 10 * q^4 - 16 * q^8 + 432 * q^9 + 18 * q^10 + 40 * q^11 + 274 * q^14 - 26 * q^16 - 18 * q^18 + 4 * q^22 + 270 * q^24 - 1200 * q^25 + 750 * q^26 + 922 * q^28 + 168 * q^30 - 108 * q^32 + 456 * q^35 - 180 * q^36 - 1494 * q^38 + 1170 * q^40 - 564 * q^42 - 1616 * q^43 + 264 * q^44 + 808 * q^46 - 360 * q^49 - 1036 * q^50 - 3564 * q^52 + 176 * q^56 - 336 * q^57 - 394 * q^58 + 4128 * q^59 + 822 * q^60 - 2644 * q^64 + 2052 * q^66 - 1440 * q^67 - 1392 * q^68 + 3234 * q^70 - 72 * q^72 - 648 * q^73 + 850 * q^74 + 1692 * q^78 - 1548 * q^80 - 3888 * q^81 + 4596 * q^82 + 3120 * q^84 - 2522 * q^86 - 1454 * q^88 - 104 * q^91 + 5600 * q^92 - 2052 * q^94 + 3870 * q^96 + 852 * q^98 + 720 * q^99

Introduction

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