LMFDB - Embedded newform 175.4.x.a.3.40

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$928$
Relative dimension:	$58$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.40
Character	$\chi$	$=$	175.3
Dual form			175.4.x.a.117.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41837 - 2.18410i) q^{2} +(-2.65704 + 6.92183i) q^{3} +(0.495381 + 1.11264i) q^{4} +(10.2470 + 4.47205i) q^{5} +(11.3493 + 15.6209i) q^{6} +(-18.4764 + 1.27366i) q^{7} +(23.7102 + 3.75532i) q^{8} +(-20.7869 - 18.7166i) q^{9} +(24.3014 - 16.0374i) q^{10} +(11.6403 + 12.9278i) q^{11} +(-9.01778 + 0.472602i) q^{12} +(-19.8203 - 10.0990i) q^{13} +(-23.4246 + 42.1608i) q^{14} +(-58.1814 + 59.0454i) q^{15} +(35.3121 - 39.2181i) q^{16} +(-70.3005 + 86.8139i) q^{17} +(-70.3625 + 18.8536i) q^{18} +(-89.9083 - 40.0298i) q^{19} +(0.100358 + 13.6166i) q^{20} +(40.2765 - 131.275i) q^{21} +(44.7458 - 7.08704i) q^{22} +(130.641 + 84.8393i) q^{23} +(-88.9926 + 154.140i) q^{24} +(85.0015 + 91.6502i) q^{25} +(-50.1697 + 28.9655i) q^{26} +(6.41822 - 3.27025i) q^{27} +(-10.5700 - 19.9267i) q^{28} +(-6.80071 + 9.36037i) q^{29} +(46.4382 + 210.822i) q^{30} +(-24.5675 + 2.58214i) q^{31} +(14.1346 + 52.7511i) q^{32} +(-120.413 + 46.2221i) q^{33} +(89.8979 + 276.677i) q^{34} +(-195.023 - 69.5763i) q^{35} +(10.5275 - 32.4003i) q^{36} +(-16.9679 - 323.767i) q^{37} +(-214.952 + 139.592i) q^{38} +(122.567 - 110.360i) q^{39} +(226.164 + 144.514i) q^{40} +(277.574 - 90.1893i) q^{41} +(-229.590 - 274.164i) q^{42} +(245.716 + 245.716i) q^{43} +(-8.61770 + 19.3557i) q^{44} +(-129.301 - 284.749i) q^{45} +(370.595 - 164.999i) q^{46} +(-151.260 + 122.488i) q^{47} +(177.635 + 348.628i) q^{48} +(339.756 - 47.0655i) q^{49} +(320.737 - 55.6577i) q^{50} +(-414.119 - 717.276i) q^{51} +(1.41794 - 27.0558i) q^{52} +(-178.045 - 68.3452i) q^{53} +(1.96087 - 18.6565i) q^{54} +(61.4637 + 184.527i) q^{55} +(-442.862 - 39.1861i) q^{56} +(515.969 - 515.969i) q^{57} +(10.7980 + 28.1299i) q^{58} +(563.953 + 119.872i) q^{59} +(-94.5185 - 35.4852i) q^{60} +(-88.7743 - 417.650i) q^{61} +(-29.2061 + 57.3202i) q^{62} +(407.906 + 319.340i) q^{63} +(536.783 + 174.411i) q^{64} +(-157.936 - 192.122i) q^{65} +(-69.8362 + 328.553i) q^{66} +(70.5206 + 57.1065i) q^{67} +(-131.418 - 35.2135i) q^{68} +(-934.361 + 678.853i) q^{69} +(-428.577 + 327.265i) q^{70} +(518.857 + 376.972i) q^{71} +(-422.574 - 521.836i) q^{72} +(252.580 + 13.2372i) q^{73} +(-731.206 - 422.162i) q^{74} +(-860.239 + 344.847i) q^{75} -119.866i q^{76} +(-231.536 - 224.034i) q^{77} +(-67.1912 - 424.229i) q^{78} +(-1002.33 - 105.349i) q^{79} +(537.228 - 243.949i) q^{80} +(-73.3606 - 697.980i) q^{81} +(196.721 - 734.171i) q^{82} +(-35.9505 + 226.983i) q^{83} +(166.014 - 20.2176i) q^{84} +(-1108.60 + 575.193i) q^{85} +(885.184 - 188.152i) q^{86} +(-46.7211 - 71.9442i) q^{87} +(227.444 + 350.234i) q^{88} +(553.666 - 117.685i) q^{89} +(-805.318 - 121.473i) q^{90} +(379.072 + 161.348i) q^{91} +(-29.6788 + 187.385i) q^{92} +(47.4036 - 176.913i) q^{93} +(52.9831 + 504.101i) q^{94} +(-742.274 - 812.260i) q^{95} +(-402.690 - 42.3245i) q^{96} +(20.7184 + 130.811i) q^{97} +(379.104 - 808.816i) q^{98} -486.596i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) $ 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	1.41837	−	2.18410i	0.501470	−	0.772195i	−0.493776	−	0.869589i	$-0.664384\pi$
$2$	1.41837	−	2.18410i	0.501470	−	0.772195i	0.995246	+	0.0973935i	$0.0310505\pi$
$3$	−2.65704	+	6.92183i	−0.511348	+	1.33211i	0.398502	+	0.917168i	$0.369530\pi$
$3$	−2.65704	+	6.92183i	−0.511348	+	1.33211i	−0.909849	+	0.414939i	$0.863803\pi$
$4$	0.495381	+	1.11264i	0.0619226	+	0.139080i
$5$	10.2470	+	4.47205i	0.916518	+	0.399993i
$5$	10.2470	+	4.47205i	0.916518	+	0.399993i
$6$	11.3493	+	15.6209i	0.772221	+	1.06287i
$7$	−18.4764	+	1.27366i	−0.997632	+	0.0687714i
$7$	−18.4764	+	1.27366i	−0.997632	+	0.0687714i
$8$	23.7102	+	3.75532i	1.04785	+	0.165963i
$9$	−20.7869	−	18.7166i	−0.769886	−	0.693208i
$10$	24.3014	−	16.0374i	0.768479	−	0.507147i
$11$	11.6403	+	12.9278i	0.319061	+	0.354353i	0.881246	−	0.472659i	$-0.156706\pi$
$11$	11.6403	+	12.9278i	0.319061	+	0.354353i	−0.562185	+	0.827012i	$0.690039\pi$
$12$	−9.01778	+	0.472602i	−0.216934	+	0.0113690i
$13$	−19.8203	−	10.0990i	−0.422860	−	0.215458i	0.229594	−	0.973287i	$-0.426260\pi$
$13$	−19.8203	−	10.0990i	−0.422860	−	0.215458i	−0.652453	+	0.757829i	$0.726260\pi$
$14$	−23.4246	+	42.1608i	−0.447177	+	0.804854i
$15$	−58.1814	+	59.0454i	−1.00149	+	1.01636i
$16$	35.3121	−	39.2181i	0.551751	−	0.612782i
$17$	−70.3005	+	86.8139i	−1.00296	+	1.23856i	−0.0319599	+	0.999489i	$0.510175\pi$
$17$	−70.3005	+	86.8139i	−1.00296	+	1.23856i	−0.971003	+	0.239067i	$0.923158\pi$
$18$	−70.3625	+	18.8536i	−0.921366	+	0.246879i
$19$	−89.9083	−	40.0298i	−1.08560	−	0.483340i	−0.215645	−	0.976472i	$-0.569185\pi$
$19$	−89.9083	−	40.0298i	−1.08560	−	0.483340i	−0.869955	+	0.493132i	$0.835852\pi$
$20$	0.100358	+	13.6166i	0.00112204	+	0.152238i
$21$	40.2765	−	131.275i	0.418526	−	1.36412i
$22$	44.7458	−	7.08704i	0.433629	−	0.0686801i
$23$	130.641	+	84.8393i	1.18437	+	0.769140i	0.977851	−	0.209303i	$-0.0671194\pi$
$23$	130.641	+	84.8393i	1.18437	+	0.769140i	0.206520	+	0.978442i	$0.433786\pi$
$24$	−88.9926	+	154.140i	−0.756897	+	1.31098i
$25$	85.0015	+	91.6502i	0.680012	+	0.733201i
$26$	−50.1697	+	28.9655i	−0.378427	+	0.218485i
$27$	6.41822	−	3.27025i	0.0457477	−	0.0233096i
$28$	−10.5700	−	19.9267i	−0.0713408	−	0.134493i
$29$	−6.80071	+	9.36037i	−0.0435469	+	0.0599371i	−0.830235	−	0.557413i	$-0.811794\pi$
$29$	−6.80071	+	9.36037i	−0.0435469	+	0.0599371i	0.786688	+	0.617350i	$0.211794\pi$
$30$	46.4382	+	210.822i	0.282614	+	1.28302i
$31$	−24.5675	+	2.58214i	−0.142337	+	0.0149602i	−0.175429	−	0.984492i	$-0.556131\pi$
$31$	−24.5675	+	2.58214i	−0.142337	+	0.0149602i	0.0330920	+	0.999452i	$0.489465\pi$
$32$	14.1346	+	52.7511i	0.0780835	+	0.291412i
$33$	−120.413	+	46.2221i	−0.635187	+	0.243825i
$34$	89.8979	+	276.677i	0.453452	+	1.39558i
$35$	−195.023	−	69.5763i	−0.941856	−	0.336015i
$36$	10.5275	−	32.4003i	0.0487384	−	0.150001i
$37$	−16.9679	−	323.767i	−0.0753921	−	1.43857i	−0.730439	−	0.682978i	$-0.760684\pi$
$37$	−16.9679	−	323.767i	−0.0753921	−	1.43857i	0.655047	−	0.755588i	$-0.272649\pi$
$38$	−214.952	+	139.592i	−0.917628	+	0.595915i
$39$	122.567	−	110.360i	0.503241	−	0.453120i
$40$	226.164	+	144.514i	0.893991	+	0.571241i
$41$	277.574	−	90.1893i	1.05731	−	0.343542i	0.271778	−	0.962360i	$-0.412388\pi$
$41$	277.574	−	90.1893i	1.05731	−	0.343542i	0.785534	+	0.618818i	$0.212388\pi$
$42$	−229.590	−	274.164i	−0.843488	−	1.00725i
$43$	245.716	+	245.716i	0.871426	+	0.871426i	0.992628	−	0.121202i	$-0.0386749\pi$
$43$	245.716	+	245.716i	0.871426	+	0.871426i	−0.121202	+	0.992628i	$0.538675\pi$
$44$	−8.61770	+	19.3557i	−0.0295265	+	0.0663176i
$45$	−129.301	−	284.749i	−0.428336	−	0.943287i
$46$	370.595	−	164.999i	1.18785	−	0.528866i
$47$	−151.260	+	122.488i	−0.469438	+	0.380143i	−0.834650	−	0.550781i	$-0.814330\pi$
$47$	−151.260	+	122.488i	−0.469438	+	0.380143i	0.365212	+	0.930924i	$0.380997\pi$
$48$	177.635	+	348.628i	0.534154	+	1.04834i
$49$	339.756	−	47.0655i	0.990541	−	0.137217i
$50$	320.737	−	55.6577i	0.907180	−	0.157424i
$51$	−414.119	−	717.276i	−1.13703	−	1.96939i
$52$	1.41794	−	27.0558i	0.00378139	−	0.0721532i
$53$	−178.045	−	68.3452i	−0.461441	−	0.177131i	0.116531	−	0.993187i	$-0.462823\pi$
$53$	−178.045	−	68.3452i	−0.461441	−	0.177131i	−0.577972	+	0.816056i	$0.696156\pi$
$54$	1.96087	−	18.6565i	0.00494150	−	0.0470152i
$55$	61.4637	+	184.527i	0.150687	+	0.452393i
$56$	−442.862	−	39.1861i	−1.05678	−	0.0935082i
$57$	515.969	−	515.969i	1.19898	−	1.19898i
$58$	10.7980	+	28.1299i	0.0244457	+	0.0636833i
$59$	563.953	+	119.872i	1.24441	+	0.264508i	0.782632	−	0.622485i	$-0.213877\pi$
$59$	563.953	+	119.872i	1.24441	+	0.264508i	0.461782	+	0.886993i	$0.347210\pi$
$60$	−94.5185	−	35.4852i	−0.203371	−	0.0763521i
$61$	−88.7743	−	417.650i	−0.186334	−	0.876633i	−0.967610	−	0.252448i	$-0.918764\pi$
$61$	−88.7743	−	417.650i	−0.186334	−	0.876633i	0.781276	−	0.624185i	$-0.214569\pi$
$62$	−29.2061	+	57.3202i	−0.0598255	+	0.117414i
$63$	407.906	+	319.340i	0.815736	+	0.638621i
$64$	536.783	+	174.411i	1.04841	+	0.340647i
$65$	−157.936	−	192.122i	−0.301377	−	0.366612i
$66$	−69.8362	+	328.553i	−0.130246	+	0.612760i
$67$	70.5206	+	57.1065i	0.128589	+	0.104129i	0.691458	−	0.722417i	$-0.256969\pi$
$67$	70.5206	+	57.1065i	0.128589	+	0.104129i	−0.562868	+	0.826546i	$0.690302\pi$
$68$	−131.418	−	35.2135i	−0.234365	−	0.0627979i
$69$	−934.361	+	678.853i	−1.63020	+	1.18441i
$70$	−428.577	+	327.265i	−0.731782	+	0.558796i
$71$	518.857	+	376.972i	0.867281	+	0.630117i	0.929856	−	0.367923i	$-0.119931\pi$
$71$	518.857	+	376.972i	0.867281	+	0.630117i	−0.0625746	+	0.998040i	$0.519931\pi$
$72$	−422.574	−	521.836i	−0.691679	−	0.854152i
$73$	252.580	+	13.2372i	0.404963	+	0.0212232i	0.253730	−	0.967275i	$-0.418342\pi$
$73$	252.580	+	13.2372i	0.404963	+	0.0212232i	0.151233	+	0.988498i	$0.451676\pi$
$74$	−731.206	−	422.162i	−1.14866	−	0.663180i
$75$	−860.239	+	344.847i	−1.32442	+	0.530927i
$76$		−	119.866i		−	0.180915i
$77$	−231.536	−	224.034i	−0.342675	−	0.331572i
$78$	−67.1912	−	424.229i	−0.0975373	−	0.615826i
$79$	−1002.33	−	105.349i	−1.42747	−	0.150034i	−0.640945	−	0.767587i	$-0.721457\pi$
$79$	−1002.33	−	105.349i	−1.42747	−	0.150034i	−0.786529	+	0.617553i	$0.788124\pi$
$80$	537.228	−	243.949i	0.750799	−	0.340929i
$81$	−73.3606	−	697.980i	−0.100632	−	0.957448i
$82$	196.721	−	734.171i	0.264929	−	0.988727i
$83$	−35.9505	+	226.983i	−0.0475431	+	0.300176i	−0.999990	−	0.00452998i	$-0.998558\pi$
$83$	−35.9505	+	226.983i	−0.0475431	+	0.300176i	0.952447	+	0.304706i	$0.0985581\pi$
$84$	166.014	−	20.2176i	0.215638	−	0.0262610i
$85$	−1108.60	+	575.193i	−1.41465	+	0.733982i
$86$	885.184	−	188.152i	1.10990	−	0.235918i
$87$	−46.7211	−	71.9442i	−0.0575750	−	0.0886578i
$88$	227.444	+	350.234i	0.275519	+	0.424262i
$89$	553.666	−	117.685i	0.659422	−	0.140164i	0.133967	−	0.990986i	$-0.457228\pi$
$89$	553.666	−	117.685i	0.659422	−	0.140164i	0.525455	+	0.850821i	$0.323895\pi$
$90$	−805.318	−	121.473i	−0.943199	−	0.142270i
$91$	379.072	+	161.348i	0.436676	+	0.185867i
$92$	−29.6788	+	187.385i	−0.0336329	+	0.212350i
$93$	47.4036	−	176.913i	0.0528551	−	0.197258i
$94$	52.9831	+	504.101i	0.0581361	+	0.553128i
$95$	−742.274	−	812.260i	−0.801639	−	0.877222i
$96$	−402.690	−	42.3245i	−0.428119	−	0.0449971i
$97$	20.7184	+	130.811i	0.0216869	+	0.136926i	0.996156	−	0.0875953i	$-0.0279182\pi$
$97$	20.7184	+	130.811i	0.0216869	+	0.136926i	−0.974469	+	0.224521i	$0.927918\pi$
$98$	379.104	−	808.816i	0.390768	−	0.833701i
$99$		−	486.596i		−	0.493987i
$100$	−59.8659	+	139.978i	−0.0598659	+	0.139978i
$101$	562.645	+	324.843i	0.554309	+	0.320031i	0.750858	−	0.660463i	$-0.229640\pi$
$101$	562.645	+	324.843i	0.554309	+	0.320031i	−0.196549	+	0.980494i	$0.562973\pi$
$102$	−2153.98	−	112.885i	−2.09093	−	0.109581i
$103$	673.852	+	832.138i	0.644627	+	0.796048i	0.989796	−	0.142493i	$-0.0455117\pi$
$103$	673.852	+	832.138i	0.644627	+	0.796048i	−0.345169	+	0.938541i	$0.612178\pi$
$104$	−432.019	−	313.880i	−0.407336	−	0.295947i
$105$	999.780	−	1165.05i	0.929224	−	1.08283i
$106$	−401.807	+	291.930i	−0.368178	+	0.267497i
$107$	1525.83	+	408.845i	1.37858	+	0.369388i	0.870604	−	0.491985i	$-0.163728\pi$
$107$	1525.83	+	408.845i	1.37858	+	0.369388i	0.507973	+	0.861373i	$0.330395\pi$
$108$	6.81809	+	5.52118i	0.00607473	+	0.00491922i
$109$	360.082	−	1694.05i	0.316419	−	1.48863i	−0.476429	−	0.879213i	$-0.658069\pi$
$109$	360.082	−	1694.05i	0.316419	−	1.48863i	0.792848	−	0.609420i	$-0.208598\pi$
$110$	490.204	+	127.485i	0.424901	+	0.110502i
$111$	2286.14	+	742.813i	1.95487	+	0.635177i
$112$	−602.490	+	769.585i	−0.508303	+	0.649276i
$113$	316.002	−	620.189i	0.263070	−	0.516305i	−0.721254	−	0.692670i	$-0.756434\pi$
$113$	316.002	−	620.189i	0.263070	−	0.516305i	0.984325	+	0.176366i	$0.0564341\pi$
$114$	−395.092	−	1858.76i	−0.324595	−	1.52710i
$115$	959.271	+	1453.58i	0.777848	+	1.17867i
$116$	−13.7837	−	2.92982i	−0.0110326	−	0.00234506i
$117$	222.985	+	580.896i	0.176197	+	0.459008i
$118$	1061.71	−	1061.71i	0.828288	−	0.828288i
$119$	1188.33	−	1693.55i	0.915411	−	1.30460i
$120$	−1601.23	+	1181.49i	−1.21809	+	0.898788i
$121$	107.495	−	1022.74i	0.0807622	−	0.768401i
$122$	−1038.10	−	398.491i	−0.770373	−	0.295719i
$123$	−113.251	+	2160.96i	−0.0830203	+	1.58412i
$124$	−15.0433	−	26.0557i	−0.0108946	−	0.0188699i
$125$	461.144	+	1319.27i	0.329968	+	0.943992i
$126$	1276.03	−	437.964i	0.902207	−	0.309659i
$127$	1291.70	+	2535.11i	0.902521	+	1.77130i	0.548824	+	0.835938i	$0.315076\pi$
$127$	1291.70	+	2535.11i	0.902521	+	1.77130i	0.353697	+	0.935360i	$0.384924\pi$
$128$	802.757	−	650.060i	0.554331	−	0.448889i
$129$	−2353.68	+	1047.93i	−1.60643	+	0.715230i
$130$	−643.624	+	72.4474i	−0.434227	+	0.0488774i
$131$	−42.4848	+	95.4224i	−0.0283352	+	0.0636420i	−0.927159	−	0.374669i	$-0.877756\pi$
$131$	−42.4848	+	95.4224i	−0.0283352	+	0.0636420i	0.898823	+	0.438311i	$0.144423\pi$
$132$	−111.079	−	111.079i	−0.0732438	−	0.0732438i
$133$	1712.17	+	625.094i	1.11627	+	0.407537i
$134$	224.750	−	73.0259i	0.144892	−	0.0470782i
$135$	80.3922	−	4.80755i	0.0512523	−	0.00306495i
$136$	−1992.85	+	1794.37i	−1.25651	+	1.13137i
$137$	913.055	−	592.945i	0.569398	−	0.369771i	−0.227599	−	0.973755i	$-0.573087\pi$
$137$	913.055	−	592.945i	0.569398	−	0.369771i	0.796997	+	0.603984i	$0.206421\pi$
$138$	157.412	+	3003.60i	0.0971001	+	1.85278i
$139$	772.143	−	2376.41i	0.471168	−	1.45011i	−0.379889	−	0.925032i	$-0.624038\pi$
$139$	772.143	−	2376.41i	0.471168	−	1.45011i	0.851057	−	0.525074i	$-0.175962\pi$
$140$	−19.1972	−	251.458i	−0.0115890	−	0.151801i
$141$	−445.937	−	1372.45i	−0.266345	−	0.819727i
$142$	1559.27	−	598.549i	0.921489	−	0.353726i
$143$	−100.156	−	373.789i	−0.0585699	−	0.218586i
$144$	−1468.06	+	154.299i	−0.849571	+	0.0892935i
$145$	−111.547	+	65.5024i	−0.0638859	+	0.0375150i
$146$	387.164	−	532.885i	0.219465	−	0.302068i
$147$	−576.965	+	2476.78i	−0.323723	+	1.38967i
$148$	351.832	−	179.267i	0.195408	−	0.0995654i
$149$	1918.87	−	1107.86i	1.05503	−	0.609123i	0.130978	−	0.991385i	$-0.458188\pi$
$149$	1918.87	−	1107.86i	1.05503	−	0.609123i	0.924054	+	0.382262i	$0.124855\pi$
$150$	−466.957	+	2367.97i	−0.254179	+	1.28896i
$151$	−560.666	+	971.102i	−0.302161	+	0.523359i	−0.976625	−	0.214949i	$-0.931041\pi$
$151$	−560.666	+	971.102i	−0.302161	+	0.523359i	0.674464	+	0.738308i	$0.264375\pi$
$152$	−1981.42	−	1286.75i	−1.05733	−	0.686638i
$153$	3086.19	−	488.805i	1.63074	−	0.258284i
$154$	−817.716	+	187.934i	−0.427879	+	0.0983388i
$155$	−263.290	−	83.4078i	−0.136438	−	0.0432224i
$156$	183.508	+	81.7031i	0.0941822	+	0.0419326i
$157$	175.853	−	47.1196i	0.0893923	−	0.0239526i	−0.213846	−	0.976867i	$-0.568599\pi$
$157$	175.853	−	47.1196i	0.0893923	−	0.0239526i	0.303238	+	0.952915i	$0.401932\pi$
$158$	−1651.76	+	2039.75i	−0.831690	+	1.02705i
$159$	946.147	−	1050.80i	0.471914	−	0.524114i
$160$	−91.0686	+	603.751i	−0.0449976	+	0.298317i
$161$	−2521.83	−	1401.13i	−1.23446	−	0.685868i
$162$	−1628.51	−	829.767i	−0.789801	−	0.402424i
$163$	−3733.90	+	195.686i	−1.79424	+	0.0940324i	−0.920112	−	0.391655i	$-0.871903\pi$
$163$	−3733.90	+	195.686i	−1.79424	+	0.0940324i	−0.874133	+	0.485687i	$0.838569\pi$
$164$	237.854	+	264.163i	0.113251	+	0.125779i
$165$	−1440.58	−	64.8549i	−0.679689	−	0.0305997i
$166$	444.761	+	400.465i	0.207953	+	0.187242i
$167$	−2753.75	−	436.150i	−1.27600	−	0.202098i	−0.518579	−	0.855030i	$-0.673539\pi$
$167$	−2753.75	−	436.150i	−1.27600	−	0.202098i	−0.757417	+	0.652932i	$0.773539\pi$
$168$	1447.94	−	2961.29i	0.664947	−	1.35993i
$169$	−1000.51	−	1377.08i	−0.455397	−	0.626800i
$170$	−316.133	+	3237.14i	−0.142625	+	1.46045i
$171$	1119.69	+	2514.88i	0.500732	+	1.12466i
$172$	−151.671	+	395.117i	−0.0672374	+	0.175159i
$173$	−1618.09	+	2491.63i	−0.711103	+	1.09500i	0.279752	+	0.960072i	$0.409748\pi$
$173$	−1618.09	+	2491.63i	−0.711103	+	1.09500i	−0.990855	+	0.134930i	$0.956919\pi$
$174$	−223.401			−0.0973332
$175$	−1687.25	−	1585.10i	−0.728825	−	0.684700i
$176$	918.046			0.393184
$177$	−2328.18	+	3585.08i	−0.988681	+	1.52244i
$178$	528.267	−	1376.18i	0.222446	−	0.579491i
$179$	219.278	+	492.507i	0.0915622	+	0.205652i	0.953521	−	0.301326i	$-0.0974292\pi$
$179$	219.278	+	492.507i	0.0915622	+	0.205652i	−0.861959	+	0.506978i	$0.830763\pi$
$180$	252.771	−	284.926i	0.104669	−	0.117984i
$181$	1409.09	+	1939.45i	0.578657	+	0.796453i	0.993547	−	0.113419i	$-0.0361801\pi$
$181$	1409.09	+	1939.45i	0.578657	+	0.796453i	−0.414891	+	0.909871i	$0.636180\pi$
$182$	890.064	−	599.078i	0.362505	−	0.243992i
$183$	3126.78	+	495.233i	1.26305	+	0.200048i
$184$	2778.92	+	2502.15i	1.11340	+	1.00251i
$185$	1274.03	−	3393.52i	0.506318	−	1.34863i
$186$	−319.159	−	354.462i	−0.125816	−	0.139733i
$187$	−1940.63	+	101.704i	−0.758893	+	0.0397719i
$188$	−211.217	−	107.621i	−0.0819394	−	0.0417502i
$189$	−114.421	+	68.5971i	−0.0440364	+	0.0264006i
$190$	−2826.87	+	469.115i	−1.07938	+	0.179122i
$191$	−53.3995	+	59.3062i	−0.0202296	+	0.0224673i	−0.753175	−	0.657821i	$-0.771479\pi$
$191$	−53.3995	+	59.3062i	−0.0202296	+	0.0224673i	0.732945	+	0.680288i	$0.238145\pi$
$192$	−2633.50	+	3252.10i	−0.989878	+	1.22240i
$193$	−656.097	+	175.801i	−0.244699	+	0.0655669i	−0.379084	−	0.925362i	$-0.623761\pi$
$193$	−656.097	+	175.801i	−0.244699	+	0.0655669i	0.134385	+	0.990929i	$0.457094\pi$
$194$	315.090	+	140.287i	0.116609	+	0.0519176i
$195$	1749.47	−	582.728i	0.642474	−	0.214000i
$196$	220.676	+	354.712i	0.0804211	+	0.129268i
$197$	−270.475	+	42.8390i	−0.0978200	+	0.0154932i	−0.205153	−	0.978730i	$-0.565769\pi$
$197$	−270.475	+	42.8390i	−0.0978200	+	0.0154932i	0.107333	+	0.994223i	$0.465769\pi$
$198$	−1062.77	−	690.173i	−0.381455	−	0.247719i
$199$	−1477.49	+	2559.08i	−0.526312	+	0.911600i	0.473218	+	0.880945i	$0.343092\pi$
$199$	−1477.49	+	2559.08i	−0.526312	+	0.911600i	−0.999530	+	0.0306541i	$0.990241\pi$
$200$	1671.22	+	2492.25i	0.590867	+	0.881143i
$201$	−582.657	+	336.397i	−0.204465	+	0.118048i
$202$	1507.53	−	768.124i	0.525095	−	0.267549i
$203$	113.731	−	181.608i	0.0393218	−	0.0627900i
$204$	592.926	−	816.092i	0.203496	−	0.280088i
$205$	3247.63	+	317.158i	1.10646	+	0.108055i
$206$	2773.24	−	291.479i	0.937965	−	0.0985841i
$207$	−1127.72	−	4208.71i	−0.378657	−	1.41317i
$208$	−1095.96	+	420.700i	−0.365342	+	0.140242i
$209$	−529.059	−	1628.28i	−0.175099	−	0.538901i
$210$	−1126.53	−	3836.09i	−0.370180	−	1.26055i
$211$	−1370.92	+	4219.25i	−0.447289	+	1.37661i	0.432665	+	0.901555i	$0.357573\pi$
$211$	−1370.92	+	4219.25i	−0.447289	+	1.37661i	−0.879954	+	0.475059i	$0.842427\pi$
$212$	−12.1564	−	231.958i	−0.00393823	−	0.0751459i
$213$	−3987.96	+	2589.81i	−1.28286	+	0.833102i
$214$	3057.15	−	2752.67i	0.976554	−	0.879293i
$215$	1418.99	+	3616.70i	0.450114	+	1.14724i
$216$	164.458	−	53.4356i	0.0518053	−	0.0168326i
$217$	450.630	−	78.9995i	0.140971	−	0.0247135i
$218$	−3189.25	−	3189.25i	−0.990841	−	0.990841i
$219$	−762.742	+	1713.15i	−0.235348	+	0.528601i
$220$	−174.865	+	159.798i	−0.0535882	+	0.0489709i
$221$	2270.11	−	1010.72i	0.690969	−	0.307639i
$222$	4864.97	−	3939.58i	1.47079	−	1.19102i
$223$	−2036.07	−	3996.00i	−0.611413	−	1.19996i	−0.964428	−	0.264347i	$-0.914844\pi$
$223$	−2036.07	−	3996.00i	−0.611413	−	1.19996i	0.353015	−	0.935618i	$-0.385156\pi$
$224$	−328.344	−	956.649i	−0.0979394	−	0.285352i
$225$	−51.5366	−	3496.06i	−0.0152701	−	1.03587i
$226$	−906.346	−	1569.84i	−0.266766	−	0.462053i
$227$	124.319	−	2372.14i	0.0363494	−	0.693588i	−0.918305	−	0.395873i	$-0.870442\pi$
$227$	124.319	−	2372.14i	0.0363494	−	0.693588i	0.954655	−	0.297715i	$-0.0962245\pi$
$228$	829.691	+	318.489i	0.240998	+	0.0925106i
$229$	317.104	−	3017.04i	0.0915056	−	0.870618i	−0.848439	−	0.529292i	$-0.822457\pi$
$229$	317.104	−	3017.04i	0.0915056	−	0.870618i	0.939945	−	0.341326i	$-0.110876\pi$
$230$	4535.37	−	33.4268i	1.30023	−	0.00958305i
$231$	2165.92	−	1007.38i	0.616915	−	0.286931i
$232$	−196.397	+	196.397i	−0.0555780	+	0.0555780i
$233$	737.550	+	1921.38i	0.207375	+	0.540232i	0.997337	−	0.0729242i	$-0.0232331\pi$
$233$	737.550	+	1921.38i	0.207375	+	0.540232i	−0.789962	+	0.613156i	$0.789900\pi$
$234$	1585.01	+	336.904i	0.442801	+	0.0941202i
$235$	−2097.74	+	578.690i	−0.582303	+	0.160637i
$236$	145.997	+	686.861i	0.0402694	+	0.189453i
$237$	3392.42	−	6658.01i	0.929796	−	1.82483i
$238$	−2013.38	−	4997.50i	−0.548354	−	1.36109i
$239$	−5428.29	−	1763.76i	−1.46915	−	0.477356i	−0.538299	−	0.842754i	$-0.680933\pi$
$239$	−5428.29	−	1763.76i	−1.46915	−	0.477356i	−0.930852	+	0.365398i	$0.880933\pi$
$240$	261.139	+	4366.78i	0.0702351	+	1.17448i
$241$	436.450	−	2053.33i	0.116656	−	0.548825i	−0.880538	−	0.473975i	$-0.842819\pi$
$241$	436.450	−	2053.33i	0.116656	−	0.548825i	0.997195	−	0.0748504i	$-0.0238479\pi$
$242$	−2081.30	−	1685.41i	−0.552856	−	0.447694i
$243$	5214.08	+	1397.11i	1.37647	+	0.368825i
$244$	420.719	−	305.670i	0.110384	−	0.0801989i
$245$	3691.95	+	1037.13i	0.962735	+	0.270447i
$246$	4559.11	+	3312.39i	1.18162	+	0.858497i
$247$	1377.76	+	1701.39i	0.354917	+	0.438286i
$248$	−592.196	−	31.0357i	−0.151631	−	0.00794664i
$249$	−1475.61	−	851.945i	−0.375555	−	0.216827i
$250$	3535.49	+	864.027i	0.894415	+	0.218584i
$251$		−	4623.99i		−	1.16280i	−0.813617	−	0.581402i	$-0.802504\pi$
$251$		−	4623.99i		−	1.16280i	0.813617	−	0.581402i	$-0.197496\pi$
$252$	−153.243	+	612.050i	−0.0383072	+	0.152998i
$253$	423.909	+	2676.46i	0.105340	+	0.665088i
$254$	7369.05	+	774.518i	1.82038	+	0.191329i
$255$	−1035.78	−	9201.88i	−0.254365	−	2.25978i
$256$	190.785	+	1815.20i	0.0465784	+	0.443163i
$257$	274.575	−	1024.73i	0.0666440	−	0.248719i	−0.924565	−	0.381025i	$-0.875571\pi$
$257$	274.575	−	1024.73i	0.0666440	−	0.248719i	0.991209	+	0.132306i	$0.0422380\pi$
$258$	−1049.62	+	6627.01i	−0.253280	+	1.59915i
$259$	725.876	+	5960.44i	0.174146	+	1.42998i
$260$	135.525	−	270.900i	0.0323265	−	0.0646172i
$261$	316.560	−	67.2869i	0.0750750	−	0.0159577i
$262$	148.153	+	228.135i	0.0349348	+	0.0537948i
$263$	−4067.05	−	6262.71i	−0.953556	−	1.46835i	−0.882188	−	0.470897i	$-0.843930\pi$
$263$	−4067.05	−	6262.71i	−0.953556	−	1.46835i	−0.0713677	−	0.997450i	$-0.522736\pi$
$264$	−3028.59	+	643.746i	−0.706048	+	0.150075i
$265$	−1518.78	−	1496.56i	−0.352068	−	0.346917i
$266$	3793.75	−	2852.93i	0.874474	−	0.657610i
$267$	−656.516	+	4145.08i	−0.150480	+	0.950092i
$268$	−28.6046	+	106.754i	−0.00651979	+	0.0243322i
$269$	597.063	+	5680.68i	0.135329	+	1.28757i	0.825697	+	0.564114i	$0.190782\pi$
$269$	597.063	+	5680.68i	0.135329	+	1.28757i	−0.690368	+	0.723458i	$0.742551\pi$
$270$	103.526	−	182.403i	0.0233347	−	0.0411138i
$271$	−7633.37	−	802.299i	−1.71105	−	0.179838i	−0.802226	−	0.597021i	$-0.796351\pi$
$271$	−7633.37	−	802.299i	−1.71105	−	0.179838i	−0.908823	+	0.417182i	$0.863018\pi$
$272$	922.214	+	5822.63i	0.205579	+	1.29797i
$273$	−2124.03	+	2195.16i	−0.470888	+	0.486656i
$274$		−	2835.22i		−	0.625116i
$275$	−195.398	+	2165.72i	−0.0428470	+	0.474900i
$276$	−1218.19	−	703.320i	−0.265675	−	0.153387i
$277$	−3209.40	−	168.198i	−0.696152	−	0.0364838i	−0.299022	−	0.954246i	$-0.596660\pi$
$277$	−3209.40	−	168.198i	−0.696152	−	0.0364838i	−0.397130	+	0.917762i	$0.629994\pi$
$278$	−4095.14	−	5057.07i	−0.883489	−	1.09102i
$279$	559.011	+	406.145i	0.119954	+	0.0871515i
$280$	−4362.76	−	2382.04i	−0.931159	−	0.508408i
$281$	2679.55	−	1946.81i	0.568857	−	0.413299i	−0.265833	−	0.964019i	$-0.585647\pi$
$281$	2679.55	−	1946.81i	0.568857	−	0.413299i	0.834690	+	0.550720i	$0.185647\pi$
$282$	−3630.08	−	972.677i	−0.766553	−	0.205397i
$283$	3572.02	+	2892.56i	0.750298	+	0.607579i	0.926290	−	0.376812i	$-0.122980\pi$
$283$	3572.02	+	2892.56i	0.750298	+	0.607579i	−0.175992	+	0.984392i	$0.556313\pi$
$284$	−162.403	+	764.047i	−0.0339326	+	0.159640i
$285$	7594.57	−	2979.69i	1.57847	−	0.619303i
$286$	−958.450	−	311.419i	−0.198162	−	0.0643867i
$287$	−5013.70	+	2019.91i	−1.03118	+	0.415441i
$288$	693.508	−	1361.09i	0.141894	−	0.278482i
$289$	−1573.02	−	7400.47i	−0.320175	−	1.50630i
$290$	−15.1509	+	336.536i	−0.00306790	+	0.0681451i
$291$	−960.498	−	204.160i	−0.193489	−	0.0411274i
$292$	110.395	+	287.589i	0.0221246	+	0.0576366i
$293$	−2162.03	+	2162.03i	−0.431082	+	0.431082i	−0.888996	−	0.457914i	$-0.848597\pi$
$293$	−2162.03	+	2162.03i	−0.431082	+	0.431082i	0.457914	+	0.888996i	$0.348597\pi$
$294$	4591.19	+	4773.15i	0.910761	+	0.946855i
$295$	5242.74	+	3750.35i	1.03473	+	0.740183i
$296$	813.537	−	7740.29i	0.159750	−	1.51992i
$297$	116.987	+	44.9071i	0.0228561	+	0.00877365i
$298$	301.992	−	5762.35i	0.0587044	−	1.12015i
$299$	−1732.56	−	3000.88i	−0.335106	−	0.580420i
$300$	−809.838	−	786.309i	−0.155853	−	0.151325i
$301$	−4852.91	−	4226.99i	−0.929292	−	0.809434i
$302$	1325.75	+	2601.93i	0.252611	+	0.495776i
$303$	−3743.48	+	3031.41i	−0.709759	+	0.574752i
$304$	−4744.74	+	2112.50i	−0.895163	+	0.398552i
$305$	958.086	−	4676.66i	0.179868	−	0.877983i
$306$	3309.76	−	7433.85i	0.618322	−	1.38877i
$307$	−2087.93	−	2087.93i	−0.388158	−	0.388158i	0.485872	−	0.874030i	$-0.338502\pi$
$307$	−2087.93	−	2087.93i	−0.388158	−	0.388158i	−0.874030	+	0.485872i	$0.838502\pi$
$308$	134.571	−	368.599i	0.0248959	−	0.0681912i
$309$	−7550.36	+	2453.26i	−1.39005	+	0.451654i
$310$	−555.614	+	456.748i	−0.101796	+	0.0836824i
$311$	−1789.52	+	1611.29i	−0.326285	+	0.293788i	−0.815950	−	0.578122i	$-0.803786\pi$
$311$	−1789.52	+	1611.29i	−0.326285	+	0.293788i	0.489665	+	0.871911i	$0.337119\pi$
$312$	3320.52	−	2156.37i	0.602523	−	0.391283i
$313$	396.110	+	7558.23i	0.0715318	+	1.36491i	0.764818	+	0.644246i	$0.222829\pi$
$313$	396.110	+	7558.23i	0.0715318	+	1.36491i	−0.693286	+	0.720662i	$0.743838\pi$
$314$	146.511	−	450.913i	0.0263314	−	0.0810398i
$315$	2751.70	+	5096.46i	0.492193	+	0.911596i
$316$	−379.317	−	1167.42i	−0.0675262	−	0.207824i
$317$	373.373	−	143.325i	0.0661538	−	0.0253940i	−0.325066	−	0.945691i	$-0.605387\pi$
$317$	373.373	−	143.325i	0.0661538	−	0.0253940i	0.391220	+	0.920297i	$0.372053\pi$
$318$	−953.070	−	3556.90i	−0.168068	−	0.627237i
$319$	−200.171	+	21.0388i	−0.0351330	+	0.00369263i
$320$	4720.43	+	4187.72i	0.824626	+	0.731564i
$321$	−6884.15	+	9475.22i	−1.19700	+	1.64752i
$322$	−6637.11	+	3520.61i	−1.14867	+	0.609304i
$323$	9795.74	−	4991.18i	1.68746	−	0.859804i
$324$	740.261	−	427.390i	0.126931	−	0.0732836i
$325$	−759.186	−	2674.97i	−0.129576	−	0.456555i
$326$	−4868.66	+	8432.77i	−0.827148	+	1.43266i
$327$	10769.2	+	6993.60i	1.82122	+	1.18271i
$328$	6920.02	−	1096.02i	1.16492	−	0.184505i
$329$	2638.74	−	2455.80i	0.442184	−	0.411527i
$330$	−2184.92	+	3054.37i	−0.364472	+	0.509508i
$331$	3741.59	+	1665.87i	0.621319	+	0.276629i	0.693156	−	0.720787i	$-0.256220\pi$
$331$	3741.59	+	1665.87i	0.621319	+	0.276629i	−0.0718372	+	0.997416i	$0.522886\pi$
$332$	−270.360	+	72.4427i	−0.0446926	+	0.0119753i
$333$	−5707.11	+	7047.70i	−0.939183	+	1.15979i
$334$	−4858.43	+	5395.83i	−0.795932	+	0.883972i
$335$	467.241	+	900.541i	0.0762032	+	0.146871i
$336$	−3726.09	−	6215.15i	−0.604985	−	1.00912i
$337$	−10624.3	−	5413.37i	−1.71734	−	0.875029i	−0.979866	−	0.199655i	$-0.936018\pi$
$337$	−10624.3	−	5413.37i	−1.71734	−	0.875029i	−0.737475	−	0.675374i	$-0.763982\pi$
$338$	−4426.77	+	231.997i	−0.712380	+	0.0373343i
$339$	3453.21	+	3835.18i	0.553252	+	0.614449i
$340$	−1189.17	−	948.542i	−0.189681	−	0.151300i
$341$	−319.353	−	287.547i	−0.0507154	−	0.0456643i
$342$	7080.88	+	1121.50i	1.11956	+	0.177321i
$343$	−6217.52	+	1302.34i	−0.978759	+	0.205013i
$344$	4903.22	+	6748.71i	0.768500	+	1.05775i
$345$	−12610.3	+	2777.69i	−1.96786	+	0.433465i
$346$	3146.93	+	7068.12i	0.488960	+	1.09822i
$347$	3804.53	−	9911.15i	0.588582	−	1.53331i	−0.238450	−	0.971155i	$-0.576639\pi$
$347$	3804.53	−	9911.15i	0.588582	−	1.53331i	0.827032	−	0.562155i	$-0.190028\pi$
$348$	56.9035	−	87.6237i	0.00876537	−	0.0134975i
$349$	105.304			0.0161513			0.00807563	−	0.999967i	$-0.497429\pi$
$349$	105.304			0.0161513			0.00807563	+	0.999967i	$0.497429\pi$
$350$	−5855.17	+	1436.87i	−0.894206	+	0.219439i
$351$	−160.238			−0.0243671
$352$	−517.426	+	796.767i	−0.0783492	+	0.120647i
$353$	2883.93	−	7512.88i	0.434833	−	1.13278i	−0.524727	−	0.851271i	$-0.675832\pi$
$353$	2883.93	−	7512.88i	0.434833	−	1.13278i	0.959559	−	0.281507i	$-0.0908342\pi$
$354$	4527.95	+	10169.9i	0.679824	+	1.52691i
$355$	3630.88	+	6183.18i	0.542837	+	0.924420i
$356$	405.218	+	557.734i	0.0603272	+	0.0830333i
$357$	8565.01	+	12725.2i	1.26977	+	1.88653i
$358$	1386.70	+	219.632i	0.204719	+	0.0324243i
$359$	4151.54	+	3738.06i	0.610334	+	0.549547i	0.915278	−	0.402823i	$-0.131971\pi$
$359$	4151.54	+	3738.06i	0.610334	+	0.549547i	−0.304944	+	0.952370i	$0.598638\pi$
$360$	−1996.43	−	7237.02i	−0.292282	−	1.05951i
$361$	1891.56	+	2100.79i	0.275778	+	0.306282i
$362$	6234.55	−	326.739i	0.905196	−	0.0474393i
$363$	6793.63	+	3461.53i	0.982295	+	0.500504i
$364$	8.26166	+	501.701i	0.00118964	+	0.0722425i
$365$	2528.99	+	1265.19i	0.362667	+	0.181434i
$366$	5516.57	−	6126.77i	0.787857	−	0.875004i
$367$	5881.11	−	7262.57i	0.836489	−	1.03298i	−0.162440	−	0.986718i	$-0.551937\pi$
$367$	5881.11	−	7262.57i	0.836489	−	1.03298i	0.998929	−	0.0462596i	$-0.0147302\pi$
$368$	7940.44	−	2127.63i	1.12479	−	0.301388i
$369$	−7457.95	−	3320.49i	−1.05216	−	0.468450i
$370$	−5604.72	−	7595.88i	−0.787502	−	1.06727i
$371$	3376.69	+	1036.00i	0.472530	+	0.144977i
$372$	220.324	−	34.8958i	0.0307076	−	0.00486361i
$373$	1895.19	+	1230.75i	0.263081	+	0.170847i	0.669439	−	0.742867i	$-0.266535\pi$
$373$	1895.19	+	1230.75i	0.263081	+	0.170847i	−0.406358	+	0.913714i	$0.633201\pi$
$374$	−2530.40	+	4382.78i	−0.349850	+	0.605958i
$375$	−10357.0	−	313.390i	−1.42623	−	0.0431558i
$376$	−4046.39	+	2336.18i	−0.554991	+	0.320424i
$377$	229.322	−	116.846i	0.0313281	−	0.0159625i
$378$	−12.4678	+	347.202i	−0.00169650	+	0.0472438i
$379$	1996.22	−	2747.55i	0.270551	−	0.372381i	−0.652025	−	0.758198i	$-0.726080\pi$
$379$	1996.22	−	2747.55i	0.270551	−	0.372381i	0.922575	+	0.385817i	$0.126080\pi$
$380$	536.047	−	1228.26i	0.0723648	−	0.165812i
$381$	−20979.7	+	2205.06i	−2.82106	+	0.296505i
$382$	53.7903	+	200.748i	0.00720458	+	0.0268879i
$383$	10894.0	−	4181.81i	1.45341	−	0.557912i	0.501736	−	0.865021i	$-0.332695\pi$
$383$	10894.0	−	4181.81i	1.45341	−	0.557912i	0.951675	+	0.307108i	$0.0993614\pi$
$384$	2366.65	+	7283.78i	0.314511	+	0.967966i
$385$	−1370.65	−	3331.11i	−0.181442	−	0.440959i
$386$	−546.622	+	1682.33i	−0.0720786	+	0.221835i
$387$	−508.704	−	9706.64i	−0.0668188	−	1.27498i
$388$	−135.282	+	87.8532i	−0.0177008	+	0.0114950i
$389$	1434.29	−	1291.44i	0.186944	−	0.168325i	−0.570345	−	0.821406i	$-0.693190\pi$
$389$	1434.29	−	1291.44i	0.186944	−	0.168325i	0.757289	+	0.653080i	$0.226524\pi$
$390$	1208.67	−	4647.55i	0.156931	−	0.603430i
$391$	−16549.4	+	5377.21i	−2.14050	+	0.695492i
$392$	8232.41	+	159.961i	1.06071	+	0.0206103i
$393$	−547.614	−	547.614i	−0.0702887	−	0.0702887i
$394$	−290.069	+	651.505i	−0.0370900	+	0.0833055i
$395$	−9799.69	−	5561.96i	−1.24829	−	0.708488i
$396$	541.408	−	241.050i	0.0687040	−	0.0305890i
$397$	884.674	−	716.395i	0.111840	−	0.0905663i	−0.571769	−	0.820415i	$-0.693743\pi$
$397$	884.674	−	716.395i	0.111840	−	0.0905663i	0.683609	+	0.729848i	$0.260409\pi$
$398$	3493.66	+	6856.69i	0.440003	+	0.863555i
$399$	−8876.09	+	10190.4i	−1.11368	+	1.27860i
$400$	6595.92	−	97.2327i	0.824490	−	0.0121541i
$401$	−1958.71	−	3392.58i	−0.243923	−	0.422488i	0.717905	−	0.696141i	$-0.245101\pi$
$401$	−1958.71	−	3392.58i	−0.243923	−	0.422488i	−0.961828	+	0.273653i	$0.911768\pi$
$402$	−91.6988	+	1749.72i	−0.0113769	+	0.217084i
$403$	513.013	+	196.927i	0.0634119	+	0.0243415i
$404$	−82.7112	+	786.944i	−0.0101857	+	0.0969107i
$405$	2369.68	−	7480.26i	0.290741	−	0.917771i
$406$	−235.337	−	505.986i	−0.0287675	−	0.0618514i
$407$	3988.09	−	3988.09i	0.485706	−	0.485706i
$408$	−7125.24	−	18561.9i	−0.864588	−	2.25233i
$409$	5520.42	+	1173.40i	0.667401	+	0.141860i	0.529139	−	0.848535i	$-0.322515\pi$
$409$	5520.42	+	1173.40i	0.667401	+	0.141860i	0.138262	+	0.990396i	$0.455848\pi$
$410$	5299.05	−	6643.30i	0.638296	−	0.800217i
$411$	1678.24	+	7895.49i	0.201414	+	0.947581i
$412$	−592.059	+	1161.98i	−0.0707978	+	0.138948i
$413$	−10572.5	−	1496.52i	−1.25966	−	0.178302i
$414$	−10791.8	−	3506.45i	−1.28112	−	0.416263i
$415$	−1383.46	+	2165.11i	−0.163642	+	0.256100i
$416$	252.579	−	1188.29i	0.0297685	−	0.140050i
$417$	14397.5	+	11658.9i	1.69076	+	1.36915i
$418$	−4306.72	−	1153.98i	−0.503944	−	0.135031i
$419$	3601.32	−	2616.51i	0.419894	−	0.305071i	−0.357701	−	0.933836i	$-0.616439\pi$
$419$	3601.32	−	2616.51i	0.419894	−	0.305071i	0.777595	+	0.628765i	$0.216439\pi$
$420$	1791.56	+	535.255i	0.208141	+	0.0621852i
$421$	2152.87	+	1564.15i	0.249227	+	0.181074i	0.705384	−	0.708825i	$-0.250774\pi$
$421$	2152.87	+	1564.15i	0.249227	+	0.181074i	−0.456157	+	0.889899i	$0.650774\pi$
$422$	7270.79	+	8978.68i	0.838713	+	1.03572i
$423$	5436.80	+	284.931i	0.624932	+	0.0327513i
$424$	−3964.82	−	2289.09i	−0.454125	−	0.262189i
$425$	−13932.1	+	936.255i	−1.59014	+	0.106859i
$426$			12383.4i			1.40840i
$427$	2172.18	+	7603.61i	0.246180	+	0.861743i
$428$	300.969	+	1900.24i	0.0339903	+	0.214607i
$429$	2853.42	+	299.906i	0.321129	+	0.0337520i
$430$	9911.89	+	2030.60i	1.11161	+	0.227731i
$431$	1515.71	+	14421.1i	0.169395	+	1.61169i	0.667526	+	0.744587i	$0.267353\pi$
$431$	1515.71	+	14421.1i	0.169395	+	1.61169i	−0.498130	+	0.867102i	$0.665980\pi$
$432$	98.3882	−	367.190i	0.0109576	−	0.0408945i
$433$	−715.165	+	4515.38i	−0.0793733	+	0.501143i	0.915689	+	0.401888i	$0.131646\pi$
$433$	−715.165	+	4515.38i	−0.0793733	+	0.501143i	−0.995062	+	0.0992551i	$0.968354\pi$
$434$	466.617	−	1096.27i	0.0516091	−	0.121250i
$435$	−157.012	−	946.150i	−0.0173061	−	0.104286i
$436$	2063.26	−	438.559i	0.226633	−	0.0481724i
$437$	−8349.62	−	12857.3i	−0.913997	−	1.40743i
$438$	2659.83	+	4095.78i	0.290163	+	0.446812i
$439$	10275.5	−	2184.12i	1.11713	−	0.237454i	0.387888	−	0.921707i	$-0.373205\pi$
$439$	10275.5	−	2184.12i	1.11713	−	0.237454i	0.729245	+	0.684253i	$0.239872\pi$
$440$	764.356	+	4605.98i	0.0828164	+	0.499049i
$441$	−7943.38	−	5380.73i	−0.857723	−	0.581010i
$442$	1012.35	−	6391.72i	0.108942	−	0.687835i
$443$	−1544.61	+	5764.55i	−0.165658	+	0.618244i	0.832297	+	0.554329i	$0.187025\pi$
$443$	−1544.61	+	5764.55i	−0.165658	+	0.618244i	−0.997955	+	0.0639147i	$0.979641\pi$
$444$	306.026	+	2911.64i	0.0327102	+	0.311217i
$445$	6199.71	+	1270.11i	0.660437	+	0.135301i
$446$	−11615.6	−	1220.84i	−1.23321	−	0.129616i
$447$	2569.90	+	16225.7i	0.271928	+	1.71689i
$448$	−10140.0	−	2538.82i	−1.06935	−	0.267741i
$449$			9420.69i			0.990177i	0.868842	+	0.495089i	$0.164864\pi$
$449$			9420.69i			0.990177i	−0.868842	+	0.495089i	$0.835136\pi$
$450$	−7708.85	−	4846.15i	−0.807552	−	0.507666i
$451$	4396.99	+	2538.60i	0.459082	+	0.265051i
$452$	846.591	+	44.3679i	0.0880979	+	0.00461702i
$453$	−5232.09	−	6461.09i	−0.542660	−	0.670129i
$454$	−5004.66	−	3636.09i	−0.517357	−	0.375882i
$455$	3162.78	+	3348.56i	0.325876	+	0.345018i
$456$	14171.3	−	10296.1i	1.45534	−	1.05736i
$457$	5295.53	+	1418.93i	0.542044	+	0.145240i	0.519444	−	0.854504i	$-0.326139\pi$
$457$	5295.53	+	1418.93i	0.542044	+	0.145240i	0.0225999	+	0.999745i	$0.492806\pi$
$458$	−6139.74	−	4971.86i	−0.626400	−	0.507249i
$459$	−167.301	+	787.091i	−0.0170130	+	0.0800398i
$460$	−1142.11	+	1787.40i	−0.115764	+	0.181170i
$461$	−12462.2	−	4049.21i	−1.25905	−	0.409090i	−0.397893	−	0.917432i	$-0.630259\pi$
$461$	−12462.2	−	4049.21i	−1.25905	−	0.409090i	−0.861155	+	0.508342i	$0.830259\pi$
$462$	871.856	−	6159.44i	0.0877974	−	0.620266i
$463$	7427.76	−	14577.8i	0.745566	−	1.46326i	−0.135757	−	0.990742i	$-0.543347\pi$
$463$	7427.76	−	14577.8i	0.745566	−	1.46326i	0.881323	−	0.472514i	$-0.156653\pi$
$464$	126.948	+	597.245i	0.0127013	+	0.0597551i
$465$	1276.91	−	1600.83i	0.127344	−	0.159649i
$466$	5242.61	+	1114.35i	0.521157	+	0.110775i
$467$	219.057	+	570.662i	0.0217061	+	0.0565462i	0.944005	−	0.329930i	$-0.107025\pi$
$467$	219.057	+	570.662i	0.0217061	+	0.0565462i	−0.922299	+	0.386477i	$0.873692\pi$
$468$	−535.868	+	535.868i	−0.0529284	+	0.0529284i
$469$	−1375.70	−	965.303i	−0.135446	−	0.0950396i
$470$	−1711.45	+	5402.46i	−0.167964	+	0.530206i
$471$	−141.094	+	1342.42i	−0.0138031	+	0.131328i
$472$	12921.3	+	4960.01i	1.26006	+	0.483692i
$473$	−316.374	+	6036.77i	−0.0307545	+	0.586831i
$474$	−9730.03	−	16852.9i	−0.942859	−	1.63308i
$475$	−3973.61	−	11642.7i	−0.383835	−	1.12464i
$476$	2472.99	+	483.235i	0.238129	+	0.0465316i
$477$	2421.82	+	4753.09i	0.232469	+	0.456245i
$478$	−11551.6	+	9354.26i	−1.10535	+	0.895092i
$479$	4350.70	−	1937.05i	0.415007	−	0.184773i	−0.188602	−	0.982054i	$-0.560396\pi$
$479$	4350.70	−	1937.05i	0.415007	−	0.184773i	0.603609	+	0.797281i	$0.293729\pi$
$480$	−3937.09	−	2234.55i	−0.374380	−	0.212485i
$481$	−2933.40	+	6588.53i	−0.278070	+	0.624556i
$482$	−3865.64	−	3865.64i	−0.365301	−	0.365301i
$483$	16399.0	−	13732.8i	1.54489	−	1.29372i
$484$	1191.20	−	387.044i	0.111871	−	0.0363490i
$485$	−372.691	+	1433.07i	−0.0348929	+	0.134170i
$486$	10446.9	−	9406.45i	0.975065	−	0.877953i
$487$	8626.15	−	5601.89i	0.802645	−	0.521244i	−0.0769114	−	0.997038i	$-0.524506\pi$
$487$	8626.15	−	5601.89i	0.802645	−	0.521244i	0.879557	+	0.475794i	$0.157839\pi$
$488$	−536.443	−	10235.9i	−0.0497615	−	0.949506i
$489$	8566.63	−	26365.4i	0.792222	−	2.43821i
$490$	7501.74	−	6592.55i	0.691620	−	0.607798i
$491$	−512.088	−	1576.04i	−0.0470676	−	0.144859i	0.924761	−	0.380549i	$-0.124265\pi$
$491$	−512.088	−	1576.04i	−0.0470676	−	0.144859i	−0.971828	+	0.235690i	$0.924265\pi$
$492$	−2460.48	+	944.489i	−0.225461	+	0.0865464i
$493$	−334.517	−	1248.43i	−0.0305596	−	0.114050i
$494$	5670.16	−	595.958i	0.516422	−	0.0542782i
$495$	2176.08	−	4986.14i	0.197591	−	0.452748i
$496$	−766.262	+	1054.67i	−0.0693673	+	0.0954759i
$497$	−10066.7	−	6304.23i	−0.908562	−	0.568981i
$498$	−3953.70	+	2014.51i	−0.355762	+	0.181270i
$499$	3145.47	−	1816.04i	0.282185	−	0.162920i	−0.352227	−	0.935915i	$-0.614576\pi$
$499$	3145.47	−	1816.04i	0.282185	−	0.162920i	0.634412	+	0.772995i	$0.281242\pi$
$500$	−1239.43	+	1166.63i	−0.110858	+	0.104347i
$501$	10335.8	−	17902.1i	0.921693	−	1.59642i
$502$	−10099.2	−	6558.53i	−0.897911	−	0.583110i
$503$	−13850.8	+	2193.75i	−1.22778	+	0.194462i	−0.736440	−	0.676503i	$-0.763495\pi$
$503$	−13850.8	+	2193.75i	−1.22778	+	0.194462i	−0.491345	+	0.870965i	$0.663495\pi$
$504$	8472.30	+	9103.43i	0.748782	+	0.804562i
$505$	4312.70	+	5844.84i	0.380025	+	0.515033i
$506$	6446.90	+	2870.35i	0.566403	+	0.252179i
$507$	12190.3	−	3266.38i	1.06783	−	0.286124i
$508$	−2180.79	+	2693.05i	−0.190466	+	0.235207i
$509$	−6826.46	+	7581.55i	−0.594455	+	0.660209i	−0.963032	−	0.269389i	$-0.913178\pi$
$509$	−6826.46	+	7581.55i	−0.594455	+	0.660209i	0.368577	+	0.929597i	$0.379845\pi$
$510$	−21566.9	−	10789.4i	−1.87255	−	0.936792i
$511$	−4683.64	+	77.1270i	−0.405464	+	0.00667690i
$512$	11598.1	+	5909.55i	1.00111	+	0.510093i
$513$	−707.959	+	37.1026i	−0.0609301	+	0.00319321i
$514$	−1848.66	−	2053.14i	−0.158640	−	0.176187i
$515$	3183.58	+	11540.4i	0.272399	+	0.987439i
$516$	−2331.94	−	2099.68i	−0.198949	−	0.179135i
$517$	−3344.22	−	529.672i	−0.284484	−	0.0450579i
$518$	14047.7	+	6868.72i	1.19155	+	0.582615i
$519$	−12947.3	−	17820.5i	−1.09504	−	1.50719i
$520$	−3023.20	−	5148.34i	−0.254954	−	0.434172i
$521$	1473.57	+	3309.70i	0.123913	+	0.278312i	0.964841	−	0.262834i	$-0.0846572\pi$
$521$	1473.57	+	3309.70i	0.123913	+	0.278312i	−0.840928	+	0.541146i	$0.817991\pi$
$522$	302.038	−	786.836i	0.0253254	−	0.0659749i
$523$	1140.67	−	1756.47i	0.0953687	−	0.146855i	−0.787766	−	0.615975i	$-0.788762\pi$
$523$	1140.67	−	1756.47i	0.0953687	−	0.146855i	0.883134	+	0.469120i	$0.155429\pi$
$524$	−127.217			−0.0106059
$525$	15454.9	−	7467.19i	1.28478	−	0.620752i
$526$	−19447.0			−1.61203
$527$	1502.94	−	2314.32i	0.124230	−	0.191297i
$528$	−2439.29	+	6354.56i	−0.201054	+	0.523762i
$529$	4920.61	+	11051.9i	0.404423	+	0.908349i
$530$	−5422.83	+	1194.50i	−0.444439	+	0.0978975i
$531$	−9479.24	−	13047.1i	−0.774697	−	1.06628i
$532$	152.669	+	2214.69i	0.0124418	+	0.180487i
$533$	−6412.44	−	1015.63i	−0.521113	−	0.0825363i
$534$	8122.08	+	7313.15i	0.658196	+	0.592642i
$535$	13806.8	+	11013.0i	1.11574	+	0.889972i
$536$	1457.60	+	1618.83i	0.117461	+	0.130453i
$537$	−3991.68	+	209.195i	−0.320770	+	0.0168109i
$538$	13254.0	+	6753.26i	1.06212	+	0.541178i
$539$	4563.30	+	3844.44i	0.364666	+	0.307221i
$540$	45.1738	+	87.0663i	0.00359995	+	0.00693840i
$541$	−7318.93	+	8128.49i	−0.581636	+	0.645973i	−0.960104	−	0.279642i	$-0.909784\pi$
$541$	−7318.93	+	8128.49i	−0.581636	+	0.645973i	0.378468	+	0.925614i	$0.376451\pi$
$542$	−12579.2	+	15534.1i	−0.996909	+	1.23108i
$543$	−17168.5	+	4600.29i	−1.35685	+	0.363568i
$544$	−5573.20	−	2481.35i	−0.439244	−	0.195564i
$545$	11265.7	−	15748.6i	0.885446	−	1.23779i
$546$	1781.78	+	7752.65i	0.139658	+	0.607661i
$547$	−18193.9	+	2881.64i	−1.42215	+	0.225247i	−0.819647	−	0.572869i	$-0.805830\pi$
$547$	−18193.9	+	2881.64i	−1.42215	+	0.225247i	−0.602505	+	0.798115i	$0.705830\pi$
$548$	1112.05	+	722.171i	0.0866866	+	0.0562949i
$549$	−5971.66	+	10343.2i	−0.464233	+	0.804076i
$550$	4452.99	+	3498.55i	0.345229	+	0.271234i
$551$	986.134	−	569.344i	0.0762445	−	0.0440198i
$552$	−24703.2	+	12586.9i	−1.90478	+	0.970532i
$553$	18653.6	+	669.839i	1.43441	+	0.0515090i
$554$	−4919.48	+	6771.08i	−0.377272	+	0.519270i
$555$	20104.2	+	17835.4i	1.53761	+	1.36409i
$556$	3026.61	−	318.109i	0.230857	−	0.0242641i
$557$	−5320.06	−	19854.7i	−0.404700	−	1.51036i	−0.804608	−	0.593806i	$-0.797625\pi$
$557$	−5320.06	−	19854.7i	−0.404700	−	1.51036i	0.399908	−	0.916555i	$-0.369042\pi$
$558$	1679.95	−	644.871i	0.127451	−	0.0489239i
$559$	−2388.70	−	7351.65i	−0.180735	−	0.556246i
$560$	−9615.33	+	5191.55i	−0.725575	+	0.391756i
$561$	4452.35	−	13702.9i	0.335078	−	1.03126i
$562$	−451.425	−	8613.71i	−0.0338830	−	0.646526i
$563$	19374.2	−	12581.7i	1.45031	−	0.941841i	0.451538	−	0.892252i	$-0.350875\pi$
$563$	19374.2	−	12581.7i	1.45031	−	0.941841i	0.998770	−	0.0495894i	$-0.0157913\pi$
$564$	1306.14	−	1176.06i	0.0975152	−	0.0878031i
$565$	6011.59	−	4941.89i	0.447627	−	0.367977i
$566$	11384.1	−	3698.91i	0.845421	−	0.274694i
$567$	2244.43	+	12802.7i	0.166239	+	0.948261i
$568$	10886.5	+	10886.5i	0.804206	+	0.804206i
$569$	−5347.93	+	12011.6i	−0.394019	+	0.884981i	0.602220	+	0.798330i	$0.294283\pi$
$569$	−5347.93	+	12011.6i	−0.394019	+	0.884981i	−0.996239	+	0.0866505i	$0.972384\pi$
$570$	4263.98	−	20813.6i	0.313331	−	1.52945i
$571$	3390.49	−	1509.54i	0.248489	−	0.110635i	−0.278713	−	0.960375i	$-0.589908\pi$
$571$	3390.49	−	1509.54i	0.248489	−	0.110635i	0.527202	+	0.849740i	$0.323241\pi$
$572$	366.278	−	296.606i	0.0267742	−	0.0216813i
$573$	−268.622	−	527.201i	−0.0195844	−	0.0384366i
$574$	−2699.60	+	13815.4i	−0.196305	+	1.00461i
$575$	3329.15	+	19184.7i	0.241452	+	1.39141i
$576$	−7893.68	−	13672.2i	−0.571012	−	0.989023i
$577$	−502.301	+	9584.48i	−0.0362410	+	0.691520i	0.918742	+	0.394859i	$0.129207\pi$
$577$	−502.301	+	9584.48i	−0.0362410	+	0.691520i	−0.954983	+	0.296661i	$0.904127\pi$
$578$	−18394.5	−	7060.98i	−1.32372	−	0.508128i
$579$	526.414	−	5008.50i	0.0377842	−	0.359492i
$580$	−128.139	−	91.6632i	−0.00917359	−	0.00656225i
$581$	375.137	−	4239.61i	0.0267871	−	0.302735i
$582$	−1808.25	+	1808.25i	−0.128787	+	0.128787i
$583$	−1188.94	−	3097.29i	−0.0844611	−	0.220029i
$584$	5939.01	+	1262.38i	0.420819	+	0.0894478i
$585$	−312.874	+	6949.64i	−0.0221124	+	0.491166i
$586$	1655.53	+	7788.64i	0.116705	+	0.549054i
$587$	2647.77	−	5196.54i	0.186176	−	0.365390i	−0.778987	−	0.627040i	$-0.784266\pi$
$587$	2647.77	−	5196.54i	0.186176	−	0.365390i	0.965163	+	0.261649i	$0.0842664\pi$
$588$	−3041.60	+	584.995i	−0.213322	+	0.0410285i
$589$	2312.18	+	751.274i	0.161752	+	0.0525564i
$590$	15627.3	−	6131.28i	1.09045	−	0.427832i
$591$	422.138	−	1986.00i	0.0293815	−	0.138229i
$592$	−13296.7	−	10767.4i	−0.923125	−	0.747532i
$593$	−11237.8	−	3011.17i	−0.778218	−	0.208523i	−0.152219	−	0.988347i	$-0.548642\pi$
$593$	−11237.8	−	3011.17i	−0.778218	−	0.208523i	−0.625999	+	0.779824i	$0.715309\pi$
$594$	264.012	−	191.816i	0.0182366	−	0.0132497i
$595$	19750.4	−	12039.5i	1.36082	−	0.829531i
$596$	2183.22	+	1586.20i	0.150047	+	0.109016i
$597$	−13787.8	−	17026.5i	−0.945219	−	1.16725i
$598$	−9011.64	−	472.280i	−0.616243	−	0.0322959i
$599$	−17579.1	−	10149.3i	−1.19910	−	0.692301i	−0.238746	−	0.971082i	$-0.576736\pi$
$599$	−17579.1	−	10149.3i	−1.19910	−	0.692301i	−0.960355	+	0.278781i	$0.910070\pi$
$600$	−21691.4	+	4945.91i	−1.47591	+	0.336527i
$601$			14153.7i			0.960637i	0.877094	+	0.480318i	$0.159479\pi$
$601$			14153.7i			0.960637i	−0.877094	+	0.480318i	$0.840521\pi$
$602$	−16115.4	+	4603.79i	−1.09105	+	0.311689i
$603$	−397.066	−	2506.97i	−0.0268155	−	0.169307i
$604$	−1358.23	−	142.756i	−0.0914996	−	0.00961700i
$605$	5675.25	−	9999.30i	0.381375	−	0.671950i
$606$	1311.26	+	12475.8i	0.0878980	+	0.836293i
$607$	4208.00	−	15704.5i	0.281380	−	1.05012i	−0.670065	−	0.742303i	$-0.733734\pi$
$607$	4208.00	−	15704.5i	0.281380	−	1.05012i	0.951444	−	0.307821i	$-0.0995997\pi$
$608$	840.795	−	5308.57i	0.0560835	−	0.354097i
$609$	954.871	+	1269.76i	0.0635358	+	0.0844884i
$610$	−8855.37	−	8725.79i	−0.587776	−	0.579175i
$611$	4235.04	−	900.185i	0.280411	−	0.0596032i
$612$	2072.71	+	3191.69i	0.136902	+	0.210811i
$613$	6898.76	+	10623.2i	0.454549	+	0.699944i	0.989434	−	0.144981i	$-0.0463120\pi$
$613$	6898.76	+	10623.2i	0.454549	+	0.699944i	−0.534886	+	0.844924i	$0.679645\pi$
$614$	−7521.70	+	1598.79i	−0.494383	+	0.105084i
$615$	−10824.4	+	21636.8i	−0.709727	+	1.41867i
$616$	−4648.44	−	6181.37i	−0.304044	−	0.404310i
$617$	1.16761	−	7.37199i	7.61850e−5	−	0.000481013i	−0.987650	−	0.156675i	$-0.949922\pi$
$617$	1.16761	−	7.37199i	7.61850e−5	−	0.000481013i	0.987726	+	0.156194i	$0.0499225\pi$
$618$	−5351.04	+	19970.4i	−0.348302	+	1.29988i
$619$	−1251.11	−	11903.5i	−0.0812378	−	0.772926i	−0.956981	−	0.290149i	$-0.906295\pi$
$619$	−1251.11	−	11903.5i	−0.0812378	−	0.772926i	0.875744	−	0.482777i	$-0.160372\pi$
$620$	−37.6256	−	334.267i	−0.00243723	−	0.0216524i
$621$	1115.93	+	117.289i	0.0721106	+	0.00757913i
$622$	981.019	+	6193.91i	0.0632400	+	0.399282i
$623$	−10079.9	+	2879.59i	−0.648221	+	0.185182i
$624$		−	8703.86i		−	0.558387i
$625$	−1174.50	+	15580.8i	−0.0751683	+	0.997171i
$626$	17069.7	+	9855.22i	1.08985	+	0.629224i
$627$	12676.4	+	664.341i	0.807409	+	0.0423145i
$628$	139.542	+	172.319i	0.00886674	+	0.0109495i
$629$	29300.3	+	21287.9i	1.85736	+	1.34945i
$630$	15034.1	+	1218.67i	0.950750	+	0.0770684i
$631$	4506.50	−	3274.16i	0.284312	−	0.206565i	−0.436484	−	0.899712i	$-0.643776\pi$
$631$	4506.50	−	3274.16i	0.284312	−	0.206565i	0.720796	+	0.693147i	$0.243776\pi$
$632$	−23369.7	−	6261.89i	−1.47088	−	0.394121i
$633$	−25562.4	−	20700.0i	−1.60507	−	1.29976i
$634$	216.547	−	1018.77i	0.0135649	−	0.0638180i
$635$	1898.92	+	31753.8i	0.118671	+	1.98443i
$636$	1637.87	+	532.177i	0.102116	+	0.0331795i
$637$	−7209.39	−	2498.33i	−0.448424	−	0.155396i
$638$	−237.966	+	467.034i	−0.0147667	+	0.0289813i
$639$	−3729.80	−	17547.3i	−0.230905	−	1.08632i
$640$	11132.9	−	3071.18i	0.687607	−	0.189686i
$641$	22324.6	+	4745.24i	1.37561	+	0.292396i	0.835636	−	0.549283i	$-0.185099\pi$
$641$	22324.6	+	4745.24i	1.37561	+	0.292396i	0.539978	+	0.841679i	$0.318432\pi$
$642$	10930.5	+	28475.0i	0.671953	+	1.75050i
$643$	10194.5	−	10194.5i	0.625246	−	0.625246i	−0.321622	−	0.946868i	$-0.604228\pi$
$643$	10194.5	−	10194.5i	0.625246	−	0.625246i	0.946868	+	0.321622i	$0.104228\pi$
$644$	309.693	−	3500.00i	0.0189497	−	0.214160i
$645$	−28804.5	+	212.297i	−1.75841	+	0.0129600i
$646$	2992.76	−	28474.2i	0.182273	−	1.73421i
$647$	−6072.63	−	2331.06i	−0.368995	−	0.141644i	0.166803	−	0.985990i	$-0.446656\pi$
$647$	−6072.63	−	2331.06i	−0.368995	−	0.141644i	−0.535798	+	0.844346i	$0.679989\pi$
$648$	881.745	−	16824.7i	0.0534541	−	1.01996i
$649$	5014.88	+	8686.02i	0.303315	+	0.525356i
$650$	−6919.19	−	2135.95i	−0.417528	−	0.128891i
$651$	−650.521	+	3329.09i	−0.0391643	+	0.200426i
$652$	−2067.43	−	4057.57i	−0.124182	−	0.243722i
$653$	−17047.6	+	13804.9i	−1.02163	+	0.827299i	−0.985091	−	0.172033i	$-0.944966\pi$
$653$	−17047.6	+	13804.9i	−1.02163	+	0.827299i	−0.0365379	+	0.999332i	$0.511633\pi$
$654$	30549.4	−	13601.5i	1.82657	−	0.813241i
$655$	−862.076	+	787.798i	−0.0514261	+	0.0469951i
$656$	6264.68	−	14070.7i	0.372857	−	0.837452i
$657$	−5002.61	−	5002.61i	−0.297063	−	0.297063i
$658$	−1620.99	−	9246.49i	−0.0960379	−	0.547821i
$659$	2179.68	−	708.221i	0.128844	−	0.0418640i	−0.243885	−	0.969804i	$-0.578422\pi$
$659$	2179.68	−	708.221i	0.128844	−	0.0418640i	0.372729	+	0.927940i	$0.378422\pi$
$660$	−641.474	−	1634.98i	−0.0378323	−	0.0964263i
$661$	−9784.35	+	8809.87i	−0.575745	+	0.518403i	−0.904760	−	0.425922i	$-0.859950\pi$
$661$	−9784.35	+	8809.87i	−0.575745	+	0.518403i	0.329015	+	0.944325i	$0.393283\pi$
$662$	8945.38	−	5809.20i	0.525184	−	0.341059i
$663$	964.242	+	18398.8i	0.0564827	+	1.07775i
$664$	−1704.79	+	5246.79i	−0.0996363	+	0.306649i
$665$	14749.1	+	14062.2i	0.860069	+	0.820015i
$666$	7298.07	+	22461.1i	0.424616	+	1.30683i
$667$	−1682.58	+	645.881i	−0.0976757	+	0.0374942i
$668$	−878.873	−	3280.00i	−0.0509051	−	0.189980i
$669$	33069.5	−	3475.75i	1.91113	−	0.200867i
$670$	2629.59	+	256.801i	0.151627	+	0.0148076i
$671$	4365.95	−	6009.22i	0.251186	−	0.345728i
$672$	7494.18	+	269.112i	0.430200	+	0.0154483i
$673$	8654.75	−	4409.81i	0.495715	−	0.252579i	−0.188214	−	0.982128i	$-0.560270\pi$
$673$	8654.75	−	4409.81i	0.495715	−	0.252579i	0.683929	+	0.729549i	$0.260270\pi$
$674$	−26892.6	+	15526.4i	−1.53689	+	0.887323i
$675$	845.277	+	310.255i	0.0481996	+	0.0176915i
$676$	1036.57	−	1795.39i	0.0589763	−	0.102150i
$677$	−25562.3	−	16600.3i	−1.45116	−	0.942397i	−0.998719	−	0.0506047i	$-0.983885\pi$
$677$	−25562.3	−	16600.3i	−1.45116	−	0.942397i	−0.452445	−	0.891792i	$-0.649448\pi$
$678$	13274.3	−	2102.45i	0.751914	−	0.119091i
$679$	−549.410	−	2390.52i	−0.0310522	−	0.135110i
$680$	−28445.2	+	9474.75i	−1.60415	+	0.534324i
$681$	16089.2	+	7163.38i	0.905345	+	0.403086i
$682$	−1080.99	+	289.651i	−0.0606940	+	0.0162629i
$683$	−19134.7	+	23629.4i	−1.07199	+	1.32380i	−0.128752	+	0.991677i	$0.541097\pi$
$683$	−19134.7	+	23629.4i	−1.07199	+	1.32380i	−0.943237	+	0.332120i	$0.892236\pi$
$684$	−2243.49	+	2491.64i	−0.125412	+	0.139284i
$685$	12007.7	−	1992.67i	0.669770	−	0.111147i
$686$	−5974.31	+	15426.9i	−0.332508	+	0.858601i
$687$	20040.9	+	10211.3i	1.11296	+	0.567084i
$688$	18313.2	−	959.756i	1.01480	−	0.0531837i
$689$	2838.70	+	3152.70i	0.156961	+	0.174323i
$690$	−11819.3	+	31481.8i	−0.652104	+	1.73695i
$691$	22838.0	+	20563.4i	1.25731	+	1.13208i	0.985490	+	0.169734i	$0.0542909\pi$
$691$	22838.0	+	20563.4i	1.25731	+	1.13208i	0.271816	+	0.962349i	$0.412376\pi$
$692$	−3573.87	−	566.046i	−0.196327	−	0.0310951i
$693$	619.760	+	8990.55i	0.0339722	+	0.492818i
$694$	−16250.7	−	22367.2i	−0.888859	−	1.22341i
$695$	18539.6	−	20898.0i	1.01187	−	1.14059i
$696$	−837.592	−	1881.26i	−0.0456161	−	0.102456i
$697$	−11683.9	+	30437.6i	−0.634950	+	1.65410i
$698$	149.360	−	229.994i	0.00809936	−	0.0124719i
$699$	−15259.2			−0.825687
$700$	927.822	−	2662.54i	0.0500977	−	0.143764i
$701$	10261.1			0.552865			0.276432	−	0.961033i	$-0.410848\pi$
$701$	10261.1			0.552865			0.276432	+	0.961033i	$0.410848\pi$
$702$	−227.276	+	349.975i	−0.0122194	+	0.0188162i
$703$	−11434.8	+	29788.6i	−0.613471	+	1.59815i
$704$	3993.54	+	8969.64i	0.213796	+	0.480193i
$705$	1568.17	−	16057.8i	0.0837743	−	0.857831i
$706$	−12318.4	−	16954.8i	−0.656670	−	0.903829i
$707$	−10809.4	−	5285.31i	−0.575006	−	0.281152i
$708$	−5142.25	−	814.453i	−0.272963	−	0.0432331i
$709$	1559.19	+	1403.90i	0.0825905	+	0.0743648i	0.709392	−	0.704814i	$-0.248970\pi$
$709$	1559.19	+	1403.90i	0.0825905	+	0.0743648i	−0.626801	+	0.779179i	$0.715636\pi$
$710$	18654.6	+	839.833i	0.986049	+	0.0443921i
$711$	18863.5	+	20950.0i	0.994987	+	1.10505i
$712$	13569.5	−	711.146i	0.714238	−	0.0374316i
$713$	−3428.59	−	1746.95i	−0.180086	−	0.0917586i
$714$	39941.5	−	657.730i	2.09352	−	0.0344747i
$715$	645.302	−	4278.11i	0.0337524	−	0.223765i
$716$	−439.359	+	487.957i	−0.0229324	+	0.0254690i
$717$	26631.6	−	32887.3i	1.38714	−	1.71297i
$718$	14052.7	−	3765.41i	0.730422	−	0.195716i
$719$	−18024.2	−	8024.90i	−0.934895	−	0.416242i	−0.117990	−	0.993015i	$-0.537645\pi$
$719$	−18024.2	−	8024.90i	−0.934895	−	0.416242i	−0.816905	+	0.576773i	$0.804312\pi$
$720$	−15733.2	−	4984.14i	−0.814364	−	0.257983i
$721$	−13510.2	−	14516.7i	−0.697846	−	0.749831i
$722$	7271.27	−	1151.66i	0.374804	−	0.0593631i
$723$	13053.2	+	8476.82i	0.671442	+	0.436039i
$724$	−1459.88	+	2528.58i	−0.0749391	+	0.129798i
$725$	−1435.95	+	172.359i	−0.0735584	+	0.00882932i
$726$	17196.2	−	9928.23i	0.879078	−	0.507536i
$727$	5743.34	−	2926.38i	0.292997	−	0.149289i	−0.301313	−	0.953525i	$-0.597425\pi$
$727$	5743.34	−	2926.38i	0.292997	−	0.149289i	0.594310	+	0.804236i	$0.297425\pi$
$728$	8381.94	+	5249.13i	0.426724	+	0.267233i
$729$	−12386.5	+	17048.5i	−0.629298	+	0.866154i
$730$	6350.35	−	3729.05i	0.321969	−	0.189066i
$731$	−38605.5	+	4057.60i	−1.95332	+	0.205302i
$732$	997.929	+	3724.32i	0.0503887	+	0.188053i
$733$	20238.7	−	7768.89i	1.01983	−	0.391474i	0.209722	−	0.977761i	$-0.432744\pi$
$733$	20238.7	−	7768.89i	1.01983	−	0.391474i	0.810103	+	0.586287i	$0.199411\pi$
$734$	−7520.57	−	23145.9i	−0.378187	−	1.16394i
$735$	−16988.5	+	22799.4i	−0.852557	+	1.14417i
$736$	−2628.81	+	8090.63i	−0.131656	+	0.405197i
$737$	82.6163	+	1576.41i	0.00412918	+	0.0787895i
$738$	−17830.4	+	11579.2i	−0.889359	+	0.577556i
$739$	−2220.33	+	1999.19i	−0.110522	+	0.0995148i	−0.722539	−	0.691330i	$-0.757025\pi$
$739$	−2220.33	+	1999.19i	−0.110522	+	0.0995148i	0.612017	+	0.790845i	$0.290358\pi$
$740$	4406.91	−	263.538i	0.218920	−	0.0130917i
$741$	−15437.4	+	5015.93i	−0.765329	+	0.248670i
$742$	7052.12	−	5905.58i	0.348911	−	0.292184i
$743$	−21852.7	−	21852.7i	−1.07900	−	1.07900i	−0.996599	−	0.0824042i	$-0.973740\pi$
$743$	−21852.7	−	21852.7i	−1.07900	−	1.07900i	−0.0824042	−	0.996599i	$-0.526260\pi$
$744$	1788.31	−	4016.61i	0.0881219	−	0.197925i
$745$	24617.0	−	2770.93i	1.21060	−	0.136267i
$746$	5376.17	−	2393.62i	0.263855	−	0.117476i
$747$	4995.65	−	4045.39i	0.244687	−	0.198144i
$748$	−1074.51	−	2108.85i	−0.0525241	−	0.103084i
$749$	−28712.6	−	5610.60i	−1.40072	−	0.273707i
$750$	−15374.6	+	22176.3i	−0.748534	+	1.07968i
$751$	14877.0	+	25767.8i	0.722864	+	1.25204i	0.959847	+	0.280524i	$0.0905081\pi$
$751$	14877.0	+	25767.8i	0.722864	+	1.25204i	−0.236983	+	0.971514i	$0.576159\pi$
$752$	−537.570	+	10257.4i	−0.0260680	+	0.497408i
$753$	32006.5	+	12286.1i	1.54898	+	0.594597i
$754$	70.0618	−	666.593i	0.00338395	−	0.0321961i
$755$	−10088.0	+	7443.54i	−0.486276	+	0.358806i
$756$	−133.006	−	93.3276i	−0.00639865	−	0.00448981i
$757$	23735.0	−	23735.0i	1.13958	−	1.13958i	0.151056	−	0.988525i	$-0.451733\pi$
$757$	23735.0	−	23735.0i	1.13958	−	1.13958i	0.988525	−	0.151056i	$-0.0482674\pi$
$758$	−3169.56	−	8256.98i	−0.151878	−	0.395656i
$759$	−19652.3	−	4177.23i	−0.939833	−	0.199768i
$760$	−14549.2	−	22046.3i	−0.694412	−	1.05224i
$761$	−7338.91	−	34526.9i	−0.349586	−	1.64468i	−0.704448	−	0.709756i	$-0.748805\pi$
$761$	−7338.91	−	34526.9i	−0.349586	−	1.64468i	0.354861	−	0.934919i	$-0.384528\pi$
$762$	−24940.9	+	48949.4i	−1.18572	+	2.32710i
$763$	−4495.37	+	31758.7i	−0.213294	+	1.50687i
$764$	−92.4398	−	30.0355i	−0.00437743	−	0.00142231i
$765$	33810.1	+	8792.84i	1.59792	+	0.415563i
$766$	6318.22	−	29724.9i	0.298024	−	1.40209i
$767$	−9967.16	−	8071.25i	−0.469222	−	0.379968i
$768$	−13071.4	−	3502.47i	−0.614158	−	0.164563i
$769$	25251.2	−	18346.1i	1.18411	−	0.860306i	0.191481	−	0.981496i	$-0.438671\pi$
$769$	25251.2	−	18346.1i	1.18411	−	0.860306i	0.992629	+	0.121190i	$0.0386710\pi$
$770$	−9219.58	−	1731.11i	−0.431494	−	0.0810193i
$771$	6363.43	+	4623.30i	0.297242	+	0.215959i
$772$	−520.621	−	642.914i	−0.0242715	−	0.0299728i
$773$	−24813.7	−	1300.43i	−1.15458	−	0.0605088i	−0.534583	−	0.845116i	$-0.679531\pi$
$773$	−24813.7	−	1300.43i	−1.15458	−	0.0605088i	−0.619993	+	0.784607i	$0.712865\pi$
$774$	−21921.8	−	12656.6i	−1.01804	−	0.587765i
$775$	−2324.92	−	2032.13i	−0.107760	−	0.0941886i
$776$			3179.35i			0.147077i
$777$	−43185.8	−	10812.7i	−1.99393	−	0.499234i
$778$	−786.277	−	4964.36i	−0.0362332	−	0.228767i
$779$	−28566.5	−	3002.46i	−1.31386	−	0.138093i
$780$	1515.03	+	1657.87i	0.0695469	+	0.0761042i
$781$	1166.21	+	11095.7i	0.0534318	+	0.508370i
$782$	−11728.8	+	43772.3i	−0.536342	+	2.00165i
$783$	−13.0377	+	82.3169i	−0.000595058	+	0.00375705i
$784$	10151.7	−	14986.5i	0.462448	−	0.682696i
$785$	2012.68	+	303.589i	0.0915105	+	0.0138033i
$786$	−1972.76	+	419.323i	−0.0895242	+	0.0190290i
$787$	−12943.6	−	19931.3i	−0.586262	−	0.902765i	0.413709	−	0.910409i	$-0.364233\pi$
$787$	−12943.6	−	19931.3i	−0.586262	−	0.902765i	−0.999971	+	0.00764473i	$0.997567\pi$
$788$	−181.653	−	279.721i	−0.00821206	−	0.0126455i
$789$	54155.7	−	11511.2i	2.44359	−	0.519402i
$790$	−26047.5	+	13514.6i	−1.17307	+	0.608642i
$791$	−5048.67	+	11861.3i	−0.226941	+	0.533174i
$792$	1827.32	−	11537.3i	0.0819837	−	0.517625i
$793$	−2458.30	+	9174.50i	−0.110084	+	0.410840i
$794$	−309.882	−	2948.33i	−0.0138505	−	0.131779i
$795$	14394.4	−	6536.34i	0.642159	−	0.291598i
$796$	−3579.26	−	376.196i	−0.159376	−	0.0167511i
$797$	5272.20	+	33287.4i	0.234317	+	1.47942i	0.771648	+	0.636050i	$0.219433\pi$
$797$	5272.20	+	33287.4i	0.234317	+	1.47942i	−0.537330	+	0.843372i	$0.680567\pi$
$798$	9667.33	+	33840.1i	0.428847	+	1.50116i
$799$		−	21742.5i		−	0.962695i
$800$	−3633.19	+	5779.36i	−0.160566	+	0.255414i
$801$	−13711.7	−	7916.45i	−0.604842	−	0.349206i
$802$	−10187.9	−	533.926i	−0.448563	−	0.0235082i
$803$	2768.97	+	3419.40i	0.121687	+	0.150271i
$804$	−662.928	−	481.645i	−0.0290792	−	0.0211273i
$805$	−19575.3	−	25635.2i	−0.857065	−	1.12239i
$806$	1157.75	−	841.155i	0.0505955	−	0.0367598i
$807$	−40907.1	−	10961.0i	−1.78438	−	0.478124i
$808$	12120.5	+	9814.99i	0.527720	+	0.427339i
$809$	1667.24	−	7843.77i	0.0724564	−	0.340880i	−0.926956	−	0.375171i	$-0.877584\pi$
$809$	1667.24	−	7843.77i	0.0724564	−	0.340880i	0.999412	+	0.0342908i	$0.0109172\pi$
$810$	−12976.5	−	15785.4i	−0.562900	−	0.684743i
$811$	11348.0	+	3687.18i	0.491346	+	0.159648i	0.544202	−	0.838954i	$-0.316832\pi$
$811$	11348.0	+	3687.18i	0.491346	+	0.159648i	−0.0528561	+	0.998602i	$0.516832\pi$
$812$	258.405	+	36.5767i	0.0111678	+	0.00158078i
$813$	25835.5	−	50705.1i	1.11450	−	2.18734i
$814$	−3053.79	−	14367.0i	−0.131493	−	0.618627i
$815$	−39136.4	−	14693.0i	−1.68207	−	0.631502i
$816$	−42753.6	−	9087.55i	−1.83416	−	0.389863i
$817$	−12256.0	−	31927.9i	−0.524824	−	1.36721i
$818$	10392.8	−	10392.8i	0.444225	−	0.444225i
$819$	−4859.83	−	10448.9i	−0.207346	−	0.445804i
$820$	1255.93	+	3770.57i	0.0534866	+	0.160578i
$821$	−87.3599	+	831.174i	−0.00371362	+	0.0353327i	−0.996222	−	0.0868456i	$-0.972321\pi$
$821$	−87.3599	+	831.174i	−0.00371362	+	0.0353327i	0.992508	+	0.122178i	$0.0389880\pi$
$822$	19624.9	+	7533.29i	0.832721	+	0.319651i
$823$	935.127	−	17843.3i	0.0396069	−	0.755745i	−0.904574	−	0.426317i	$-0.859811\pi$
$823$	935.127	−	17843.3i	0.0396069	−	0.755745i	0.944181	−	0.329428i	$-0.106856\pi$
$824$	12852.2	+	22260.7i	0.543358	+	0.941124i
$825$	−14471.5	−	7106.90i	−0.610708	−	0.299916i
$826$	−18264.3	+	20968.8i	−0.769364	+	0.883289i
$827$	15212.4	+	29856.1i	0.639647	+	1.25538i	0.952199	+	0.305477i	$0.0988159\pi$
$827$	15212.4	+	29856.1i	0.639647	+	1.25538i	−0.312553	+	0.949900i	$0.601184\pi$
$828$	4124.14	−	3339.66i	0.173096	−	0.140171i
$829$	8149.56	−	3628.42i	0.341431	−	0.152015i	−0.228856	−	0.973460i	$-0.573499\pi$
$829$	8149.56	−	3628.42i	0.341431	−	0.152015i	0.570287	+	0.821445i	$0.306832\pi$
$830$	2766.56	+	6092.55i	0.115697	+	0.254790i
$831$	9691.74	−	21768.0i	0.404576	−	0.908693i
$832$	−8877.86	−	8877.86i	−0.369933	−	0.369933i
$833$	−19799.0	+	32804.2i	−0.823525	+	1.36446i
$834$	45885.1	−	14909.0i	1.90512	−	0.619012i
$835$	−26267.1	−	16784.1i	−1.08864	−	0.695615i
$836$	1549.61	−	1395.27i	0.0641079	−	0.0577230i
$837$	−149.235	+	96.9145i	−0.00616287	+	0.00400222i
$838$	−606.715	−	11576.8i	−0.0250103	−	0.477224i
$839$	−730.724	+	2248.94i	−0.0300684	+	0.0925411i	−0.964964	−	0.262381i	$-0.915492\pi$
$839$	−730.724	+	2248.94i	−0.0300684	+	0.0925411i	0.934896	+	0.354922i	$0.115492\pi$
$840$	28080.1	−	23869.1i	1.15340	−	0.980430i
$841$	7495.25	+	23068.0i	0.307321	+	0.945836i
$842$	6469.84	−	2483.54i	0.264804	−	0.101649i
$843$	6355.80	+	23720.2i	0.259674	+	0.969117i
$844$	−5373.65	+	564.794i	−0.219157	+	0.0230344i
$845$	−4093.81	−	18585.2i	−0.166664	−	0.756629i
$846$	8333.71	−	11470.4i	0.338675	−	0.466146i
$847$	−683.484	+	19033.5i	−0.0277270	+	0.772136i
$848$	−8967.51	+	4569.18i	−0.363144	+	0.185031i
$849$	−29512.8	+	17039.2i	−1.19302	+	0.688792i
$850$	−17716.1	+	31757.1i	−0.714890	+	1.28148i
$851$	25251.5	−	43736.8i	1.01717	−	1.76178i
$852$	−4857.09	−	3154.23i	−0.195307	−	0.126834i
$853$	21283.2	−	3370.93i	0.854307	−	0.135309i	0.286105	−	0.958198i	$-0.407639\pi$
$853$	21283.2	−	3370.93i	0.854307	−	0.135309i	0.568202	+	0.822889i	$0.307639\pi$
$854$	19688.0	+	6040.48i	0.788886	+	0.242039i
$855$	226.836	+	30777.2i	0.00907326	+	1.23106i
$856$	34642.4	+	15423.8i	1.38324	+	0.615857i
$857$	−21911.3	+	5871.10i	−0.873366	+	0.234018i	−0.667543	−	0.744572i	$-0.732654\pi$
$857$	−21911.3	+	5871.10i	−0.873366	+	0.234018i	−0.205823	+	0.978589i	$0.565987\pi$
$858$	4702.23	−	5806.77i	0.187100	−	0.231049i
$859$	−20912.0	+	23225.2i	−0.830628	+	0.922506i	−0.997989	−	0.0633898i	$-0.979809\pi$
$859$	−20912.0	+	23225.2i	−0.830628	+	0.922506i	0.167361	+	0.985896i	$0.446476\pi$
$860$	−3321.16	+	3370.48i	−0.131687	+	0.133642i
$861$	−659.862	−	40071.0i	−0.0261185	−	1.58608i
$862$	33646.9	+	17143.9i	1.32949	+	0.677407i
$863$	42327.7	−	2218.30i	1.66959	−	0.0874993i	0.806070	−	0.591820i	$-0.201590\pi$
$863$	42327.7	−	2218.30i	1.66959	−	0.0874993i	0.863516	+	0.504321i	$0.168257\pi$
$864$	263.229	+	292.345i	0.0103648	+	0.0115113i
$865$	−27723.2	+	18295.6i	−1.08973	+	0.719154i
$866$	8847.66	+	7966.46i	0.347177	+	0.312600i
$867$	55404.4	+	8775.19i	2.17028	+	0.343738i
$868$	311.132	+	462.256i	0.0121665	+	0.0180760i
$869$	−10305.4	−	14184.2i	−0.402286	−	0.553700i
$870$	−2289.19	−	999.061i	−0.0892077	−	0.0389326i
$871$	−821.027	−	1844.06i	−0.0319396	−	0.0717376i
$872$	14899.3	−	38814.1i	0.578618	−	1.50735i
$873$	2017.66	−	3106.93i	0.0782216	−	0.120451i
$874$	−39924.4			−1.54515
$875$	−10200.6	−	23788.0i	−0.394106	−	0.919065i
$876$	−2283.97			−0.0880915
$877$	9471.98	−	14585.6i	0.364705	−	0.561596i	−0.607914	−	0.794003i	$-0.707993\pi$
$877$	9471.98	−	14585.6i	0.364705	−	0.561596i	0.972619	+	0.232407i	$0.0746601\pi$
$878$	9804.08	−	25540.5i	0.376847	−	0.981720i
$879$	−9220.59	−	20709.8i	−0.353814	−	0.794680i
$880$	9407.21	+	4105.55i	0.360360	+	0.157271i
$881$	14772.2	+	20332.2i	0.564912	+	0.777535i	0.991941	−	0.126703i	$-0.0404395\pi$
$881$	14772.2	+	20332.2i	0.564912	+	0.777535i	−0.427028	+	0.904238i	$0.640440\pi$
$882$	−23018.7	+	9717.25i	−0.878775	+	0.370971i
$883$	23668.9	+	3748.78i	0.902062	+	0.142873i	0.590202	−	0.807256i	$-0.299048\pi$
$883$	23668.9	+	3748.78i	0.902062	+	0.142873i	0.311860	+	0.950128i	$0.399048\pi$
$884$	2249.14	+	2025.13i	0.0855732	+	0.0770505i
$885$	−39889.5	+	26324.5i	−1.51511	+	0.999875i
$886$	10399.5	+	11549.8i	0.394333	+	0.437951i
$887$	−16896.4	+	885.501i	−0.639599	+	0.0335200i	−0.369379	−	0.929279i	$-0.620430\pi$
$887$	−16896.4	+	885.501i	−0.639599	+	0.0335200i	−0.270220	+	0.962799i	$0.587096\pi$
$888$	51415.3	+	26197.4i	1.94300	+	0.990009i
$889$	−27094.9	−	45194.6i	−1.02220	−	1.70504i
$890$	11567.5	−	11739.3i	0.435667	−	0.442137i
$891$	8169.42	−	9073.06i	0.307167	−	0.341144i
$892$	3437.50	−	4244.96i	0.129031	−	0.159341i
$893$	18502.7	−	4957.79i	0.693360	−	0.185785i
$894$	39083.6	+	17401.1i	1.46214	+	0.650985i
$895$	44.4231	+	6027.34i	0.00165911	+	0.225108i
$896$	−14004.1	+	13033.2i	−0.522148	+	0.485948i
$897$	25375.1	−	4019.02i	0.944537	−	0.149600i
$898$	20575.7	+	13362.0i	0.764611	+	0.496544i
$899$	142.906	−	247.521i	0.00530166	−	0.00918274i
$900$	3864.34	−	1789.23i	0.143124	−	0.0662676i
$901$	18450.0	−	10652.1i	0.682195	−	0.393865i
$902$	11781.1	−	6002.78i	0.434887	−	0.221586i
$903$	42152.8	−	22359.7i	1.55344	−	0.824014i
$904$	9821.47	−	13518.1i	0.361346	−	0.497351i
$905$	5765.62	+	26175.0i	0.211774	+	0.961422i
$906$	−21532.7	+	2263.18i	−0.789598	+	0.0829901i
$907$	−2091.68	−	7806.25i	−0.0765744	−	0.285780i	0.917011	−	0.398861i	$-0.130595\pi$
$907$	−2091.68	−	7806.25i	−0.0765744	−	0.285780i	−0.993586	+	0.113082i	$0.963928\pi$
$908$	2700.93	−	1036.79i	0.0987153	−	0.0378933i
$909$	−5615.68	−	17283.3i	−0.204907	−	0.630639i
$910$	11799.6	−	2158.33i	0.429838	−	0.0786241i
$911$	−3684.97	+	11341.2i	−0.134016	+	0.412458i	−0.995436	−	0.0954354i	$-0.969576\pi$
$911$	−3684.97	+	11341.2i	−0.134016	+	0.412458i	0.861420	+	0.507894i	$0.169576\pi$
$912$	−2015.36	−	38455.3i	−0.0731744	−	1.39625i
$913$	−3352.86	+	2177.37i	−0.121537	+	0.0789273i
$914$	10610.1	−	9553.38i	0.383973	−	0.345730i
$915$	29825.4	+	19057.8i	1.07759	+	0.688558i
$916$	3513.98	−	1141.76i	0.126752	−	0.0411843i
$917$	663.431	−	1817.18i	0.0238914	−	0.0654399i
$918$	1481.79	+	1481.79i	0.0532749	+	0.0532749i
$919$	−19978.9	+	44873.4i	−0.717131	+	1.61070i	0.0726816	+	0.997355i	$0.476844\pi$
$919$	−19978.9	+	44873.4i	−0.717131	+	1.61070i	−0.789813	+	0.613348i	$0.789822\pi$
$920$	17285.8	+	38067.0i	0.619453	+	1.36417i
$921$	20000.0	−	8904.57i	0.715551	−	0.318584i
$922$	−26519.8	+	21475.3i	−0.947272	+	0.767086i
$923$	−6476.90	−	12711.6i	−0.230975	−	0.453314i
$924$	2193.82	+	1910.86i	0.0781075	+	0.0680333i
$925$	28231.0	−	29075.8i	1.00349	−	1.03352i
$926$	−21304.0	−	36899.7i	−0.756041	−	1.30950i
$927$	1567.51	−	29909.8i	0.0555379	−	1.05973i
$928$	−589.895	−	226.440i	−0.0208667	−	0.00800996i
$929$	637.618	−	6066.53i	0.0225184	−	0.214248i	−0.977477	−	0.211044i	$-0.932314\pi$
$929$	637.618	−	6066.53i	0.0225184	−	0.214248i	0.999995	−	0.00320363i	$-0.00101975\pi$
$930$	−1685.24	−	5059.46i	−0.0594208	−	0.178394i
$931$	−32430.9	−	9368.76i	−1.14165	−	0.329805i
$932$	−1772.45	+	1772.45i	−0.0622944	+	0.0622944i
$933$	−6398.27	−	16668.1i	−0.224512	−	0.584874i
$934$	1557.08	+	330.969i	0.0545496	+	0.0115949i
$935$	−20340.4	−	7636.44i	−0.711447	−	0.267100i
$936$	3105.56	+	14610.5i	0.108449	+	0.510214i
$937$	4584.79	−	8998.15i	0.159849	−	0.313721i	−0.797166	−	0.603760i	$-0.793668\pi$
$937$	4584.79	−	8998.15i	0.159849	−	0.313721i	0.957015	+	0.290039i	$0.0936684\pi$
$938$	−4059.57	+	1635.51i	−0.141311	+	0.0569311i
$939$	−53369.2	−	17340.7i	−1.85478	−	0.602655i
$940$	−1683.05	−	2047.36i	−0.0583991	−	0.0710400i
$941$	10826.2	−	50933.3i	0.375053	−	1.76448i	−0.234874	−	0.972026i	$-0.575468\pi$
$941$	10826.2	−	50933.3i	0.375053	−	1.76448i	0.609927	−	0.792458i	$-0.291199\pi$
$942$	2731.86	+	2212.21i	0.0944891	+	0.0765158i
$943$	43914.2	+	11766.8i	1.51648	+	0.406340i
$944$	24615.5	−	17884.2i	0.848693	−	0.616612i
$945$	−1479.24	+	191.219i	−0.0509202	+	0.00658238i
$946$	12736.2	+	9253.36i	0.437725	+	0.318026i
$947$	606.455	+	748.909i	0.0208101	+	0.0256983i	0.787445	−	0.616385i	$-0.211404\pi$
$947$	606.455	+	748.909i	0.0208101	+	0.0256983i	−0.766635	+	0.642084i	$0.778070\pi$
$948$	9088.53	+	476.310i	0.311373	+	0.0163184i
$949$	−4872.55	−	2813.17i	−0.166670	−	0.0962268i
$950$	−31064.9	−	7834.92i	−1.06092	−	0.267577i
$951$			2965.25i			0.101109i
$952$	34535.3	−	35691.7i	1.17573	−	1.21510i
$953$	4191.39	+	26463.4i	0.142468	+	0.899509i	0.950580	+	0.310480i	$0.100490\pi$
$953$	4191.39	+	26463.4i	0.142468	+	0.899509i	−0.808112	+	0.589029i	$0.799510\pi$
$954$	13816.3	+	1452.15i	0.468886	+	0.0492820i
$955$	−812.405	+	368.904i	−0.0275275	+	0.0125000i
$956$	−726.637	−	6913.49i	−0.0245828	−	0.233889i
$957$	386.236	−	1441.45i	0.0130462	−	0.0486891i
$958$	1940.18	−	12249.8i	0.0654325	−	0.413125i
$959$	−16114.8	+	12118.4i	−0.542620	+	0.408054i
$960$	−41529.0	+	21547.1i	−1.39619	+	0.724406i
$961$	−28543.1	+	6067.02i	−0.958112	+	0.203653i
$962$	10229.4	+	15751.8i	0.342835	+	0.527920i
$963$	−24065.1	−	37057.0i	−0.805283	−	1.24003i
$964$	2500.84	−	531.570i	0.0835546	−	0.0177601i
$965$	−7509.21	−	1132.67i	−0.250497	−	0.0377845i
$966$	−6733.99	−	55295.3i	−0.224288	−	1.84172i
$967$	465.201	−	2937.17i	0.0154704	−	0.0976762i	−0.978745	−	0.205081i	$-0.934254\pi$
$967$	465.201	−	2937.17i	0.0154704	−	0.0976762i	0.994215	+	0.107405i	$0.0342541\pi$
$968$	6389.44	−	23845.7i	0.212153	−	0.791767i
$969$	8520.40	+	81066.2i	0.282471	+	2.68753i
$970$	2601.35	+	2846.62i	0.0861075	+	0.0942261i
$971$	33282.4	+	3498.12i	1.09998	+	0.115613i	0.637081	−	0.770797i	$-0.280142\pi$
$971$	33282.4	+	3498.12i	1.09998	+	0.115613i	0.462901	+	0.886410i	$0.346809\pi$
$972$	1028.47	+	6493.51i	0.0339385	+	0.214279i
$973$	−11239.7	+	44891.0i	−0.370327	+	1.47908i
$974$		−	26785.9i		−	0.881187i
$975$	20532.8	+	1852.54i	0.674438	+	0.0608499i
$976$	−19514.2	−	11266.6i	−0.639995	−	0.369502i
$977$	−3009.20	−	157.706i	−0.0985393	−	0.00516423i	0.00300255	−	0.999995i	$-0.499044\pi$
$977$	−3009.20	−	157.706i	−0.0985393	−	0.00516423i	−0.101542	+	0.994831i	$0.532378\pi$
$978$	−45433.9	−	56106.2i	−1.48550	−	1.83444i
$979$	7966.24	+	5787.81i	0.260063	+	0.188947i
$980$	674.970	+	4621.60i	0.0220011	+	0.150644i
$981$	−39192.0	+	28474.6i	−1.27554	+	0.926733i
$982$	−4168.57	−	1116.96i	−0.135463	−	0.0362971i
$983$	−15103.6	−	12230.7i	−0.490062	−	0.396844i	0.352190	−	0.935928i	$-0.385437\pi$
$983$	−15103.6	−	12230.7i	−0.490062	−	0.396844i	−0.842252	+	0.539084i	$0.818770\pi$
$984$	−10800.3	+	50811.4i	−0.349899	+	1.64615i
$985$	−2963.13	−	770.607i	−0.0958509	−	0.0249275i
$986$	−3201.17	−	1040.12i	−0.103394	−	0.0335946i
$987$	9987.36	+	24790.0i	0.322088	+	0.799469i
$988$	−1210.52	+	2375.78i	−0.0389796	+	0.0765018i
$989$	11254.2	+	52946.9i	0.361844	+	1.70234i
$990$	−7803.73	−	11825.0i	−0.250524	−	0.379619i
$991$	−47476.7	−	10091.5i	−1.52184	−	0.323478i	−0.630278	−	0.776370i	$-0.717059\pi$
$991$	−47476.7	−	10091.5i	−1.52184	−	0.323478i	−0.891565	+	0.452892i	$0.850392\pi$
$992$	−483.463	−	1259.46i	−0.0154738	−	0.0403105i
$993$	−21472.4	+	21472.4i	−0.686209	+	0.686209i
$994$	−28047.4	+	13045.0i	−0.894981	+	0.416261i
$995$	−26584.1	+	19615.5i	−0.847008	+	0.624977i
$996$	216.921	−	2063.87i	0.00690102	−	0.0656588i
$997$	40339.8	+	15485.0i	1.28142	+	0.491891i	0.901360	−	0.433071i	$-0.142570\pi$
$997$	40339.8	+	15485.0i	1.28142	+	0.491891i	0.380060	+	0.924962i	$0.375903\pi$
$998$	495.034	−	9445.82i	0.0157014	−	0.299601i
$999$	−1167.70	−	2022.52i	−0.0369814	−	0.0640537i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.x.a.3.40	✓	928
7.5	odd	6	inner	175.4.x.a.103.19	yes	928
25.17	odd	20	inner	175.4.x.a.17.19	yes	928
175.117	even	60	inner	175.4.x.a.117.40	yes	928

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.4.x.a.3.40	✓	928	1.1	even	1	trivial
175.4.x.a.17.19	yes	928	25.17	odd	20	inner
175.4.x.a.103.19	yes	928	7.5	odd	6	inner
175.4.x.a.117.40	yes	928	175.117	even	60	inner

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41837 - 2.18410i) q^{2} +(-2.65704 + 6.92183i) q^{3} +(0.495381 + 1.11264i) q^{4} +(10.2470 + 4.47205i) q^{5} +(11.3493 + 15.6209i) q^{6} +(-18.4764 + 1.27366i) q^{7} +(23.7102 + 3.75532i) q^{8} +(-20.7869 - 18.7166i) q^{9} +(24.3014 - 16.0374i) q^{10} +(11.6403 + 12.9278i) q^{11} +(-9.01778 + 0.472602i) q^{12} +(-19.8203 - 10.0990i) q^{13} +(-23.4246 + 42.1608i) q^{14} +(-58.1814 + 59.0454i) q^{15} +(35.3121 - 39.2181i) q^{16} +(-70.3005 + 86.8139i) q^{17} +(-70.3625 + 18.8536i) q^{18} +(-89.9083 - 40.0298i) q^{19} +(0.100358 + 13.6166i) q^{20} +(40.2765 - 131.275i) q^{21} +(44.7458 - 7.08704i) q^{22} +(130.641 + 84.8393i) q^{23} +(-88.9926 + 154.140i) q^{24} +(85.0015 + 91.6502i) q^{25} +(-50.1697 + 28.9655i) q^{26} +(6.41822 - 3.27025i) q^{27} +(-10.5700 - 19.9267i) q^{28} +(-6.80071 + 9.36037i) q^{29} +(46.4382 + 210.822i) q^{30} +(-24.5675 + 2.58214i) q^{31} +(14.1346 + 52.7511i) q^{32} +(-120.413 + 46.2221i) q^{33} +(89.8979 + 276.677i) q^{34} +(-195.023 - 69.5763i) q^{35} +(10.5275 - 32.4003i) q^{36} +(-16.9679 - 323.767i) q^{37} +(-214.952 + 139.592i) q^{38} +(122.567 - 110.360i) q^{39} +(226.164 + 144.514i) q^{40} +(277.574 - 90.1893i) q^{41} +(-229.590 - 274.164i) q^{42} +(245.716 + 245.716i) q^{43} +(-8.61770 + 19.3557i) q^{44} +(-129.301 - 284.749i) q^{45} +(370.595 - 164.999i) q^{46} +(-151.260 + 122.488i) q^{47} +(177.635 + 348.628i) q^{48} +(339.756 - 47.0655i) q^{49} +(320.737 - 55.6577i) q^{50} +(-414.119 - 717.276i) q^{51} +(1.41794 - 27.0558i) q^{52} +(-178.045 - 68.3452i) q^{53} +(1.96087 - 18.6565i) q^{54} +(61.4637 + 184.527i) q^{55} +(-442.862 - 39.1861i) q^{56} +(515.969 - 515.969i) q^{57} +(10.7980 + 28.1299i) q^{58} +(563.953 + 119.872i) q^{59} +(-94.5185 - 35.4852i) q^{60} +(-88.7743 - 417.650i) q^{61} +(-29.2061 + 57.3202i) q^{62} +(407.906 + 319.340i) q^{63} +(536.783 + 174.411i) q^{64} +(-157.936 - 192.122i) q^{65} +(-69.8362 + 328.553i) q^{66} +(70.5206 + 57.1065i) q^{67} +(-131.418 - 35.2135i) q^{68} +(-934.361 + 678.853i) q^{69} +(-428.577 + 327.265i) q^{70} +(518.857 + 376.972i) q^{71} +(-422.574 - 521.836i) q^{72} +(252.580 + 13.2372i) q^{73} +(-731.206 - 422.162i) q^{74} +(-860.239 + 344.847i) q^{75} -119.866i q^{76} +(-231.536 - 224.034i) q^{77} +(-67.1912 - 424.229i) q^{78} +(-1002.33 - 105.349i) q^{79} +(537.228 - 243.949i) q^{80} +(-73.3606 - 697.980i) q^{81} +(196.721 - 734.171i) q^{82} +(-35.9505 + 226.983i) q^{83} +(166.014 - 20.2176i) q^{84} +(-1108.60 + 575.193i) q^{85} +(885.184 - 188.152i) q^{86} +(-46.7211 - 71.9442i) q^{87} +(227.444 + 350.234i) q^{88} +(553.666 - 117.685i) q^{89} +(-805.318 - 121.473i) q^{90} +(379.072 + 161.348i) q^{91} +(-29.6788 + 187.385i) q^{92} +(47.4036 - 176.913i) q^{93} +(52.9831 + 504.101i) q^{94} +(-742.274 - 812.260i) q^{95} +(-402.690 - 42.3245i) q^{96} +(20.7184 + 130.811i) q^{97} +(379.104 - 808.816i) q^{98} -486.596i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) \) 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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