LMFDB - Embedded newform 175.4.x.a.117.47

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			117.47
Character	$\chi$	$=$	175.117
Dual form			175.4.x.a.3.47

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.99423 + 3.07084i) q^{2} +(2.03228 + 5.29426i) q^{3} +(-2.19922 + 4.93952i) q^{4} +(-10.9441 - 2.28640i) q^{5} +(-12.2050 + 16.7988i) q^{6} +(-17.5585 + 5.89045i) q^{7} +(9.37758 - 1.48526i) q^{8} +(-3.83417 + 3.45230i) q^{9} +(-14.8038 - 38.1670i) q^{10} +(-30.8098 + 34.2178i) q^{11} +(-30.6206 - 1.60476i) q^{12} +(-34.9937 + 17.8302i) q^{13} +(-53.1043 - 42.1726i) q^{14} +(-10.1366 - 62.5873i) q^{15} +(52.2058 + 57.9805i) q^{16} +(-35.0386 - 43.2690i) q^{17} +(-18.2476 - 4.88944i) q^{18} +(-26.8797 + 11.9676i) q^{19} +(35.3621 - 49.0301i) q^{20} +(-66.8694 - 80.9886i) q^{21} +(-166.519 - 26.3740i) q^{22} +(16.8829 - 10.9639i) q^{23} +(26.9212 + 46.6289i) q^{24} +(114.545 + 50.0450i) q^{25} +(-124.539 - 71.9027i) q^{26} +(110.357 + 56.2297i) q^{27} +(9.51908 - 99.6853i) q^{28} +(159.008 + 218.856i) q^{29} +(171.981 - 155.941i) q^{30} +(122.378 + 12.8624i) q^{31} +(-54.2796 + 202.574i) q^{32} +(-243.772 - 93.5754i) q^{33} +(62.9974 - 193.886i) q^{34} +(205.630 - 24.3195i) q^{35} +(-8.62054 - 26.5313i) q^{36} +(0.767048 - 14.6361i) q^{37} +(-90.3549 - 58.6771i) q^{38} +(-165.515 - 149.030i) q^{39} +(-106.025 - 5.18611i) q^{40} +(-8.43713 - 2.74139i) q^{41} +(115.350 - 366.855i) q^{42} +(-140.993 + 140.993i) q^{43} +(-101.262 - 227.438i) q^{44} +(49.8547 - 29.0157i) q^{45} +(67.3365 + 29.9801i) q^{46} +(23.9845 + 19.4223i) q^{47} +(-200.867 + 394.224i) q^{48} +(273.605 - 206.855i) q^{49} +(74.7480 + 451.549i) q^{50} +(157.870 - 273.438i) q^{51} +(-11.1139 - 212.065i) q^{52} +(-452.467 + 173.686i) q^{53} +(47.4044 + 451.023i) q^{54} +(415.420 - 304.038i) q^{55} +(-155.908 + 81.3172i) q^{56} +(-117.987 - 117.987i) q^{57} +(-354.973 + 924.736i) q^{58} +(-265.022 + 56.3321i) q^{59} +(331.444 + 87.5734i) q^{60} +(-57.1874 + 269.045i) q^{61} +(204.550 + 401.453i) q^{62} +(46.9868 - 83.2023i) q^{63} +(-136.704 + 44.4177i) q^{64} +(423.741 - 115.125i) q^{65} +(-198.782 - 935.195i) q^{66} +(-276.485 + 223.893i) q^{67} +(290.786 - 77.9158i) q^{68} +(92.3563 + 67.1008i) q^{69} +(484.753 + 582.957i) q^{70} +(562.908 - 408.976i) q^{71} +(-30.8276 + 38.0690i) q^{72} +(-868.150 + 45.4978i) q^{73} +(46.4749 - 26.8323i) q^{74} +(-32.1647 + 708.135i) q^{75} -159.092i q^{76} +(339.418 - 782.298i) q^{77} +(127.574 - 805.469i) q^{78} +(1222.74 - 128.515i) q^{79} +(-438.777 - 753.905i) q^{80} +(-87.9799 + 837.073i) q^{81} +(-8.40718 - 31.3760i) q^{82} +(110.810 + 699.629i) q^{83} +(547.105 - 152.192i) q^{84} +(284.534 + 553.651i) q^{85} +(-714.141 - 151.795i) q^{86} +(-835.532 + 1286.61i) q^{87} +(-238.099 + 366.641i) q^{88} +(-538.578 - 114.478i) q^{89} +(188.524 + 95.2317i) q^{90} +(509.412 - 519.201i) q^{91} +(17.0272 + 107.505i) q^{92} +(180.608 + 674.040i) q^{93} +(-11.8121 + 112.385i) q^{94} +(321.536 - 69.5165i) q^{95} +(-1182.79 + 124.316i) q^{96} +(193.365 - 1220.86i) q^{97} +(1180.85 + 427.681i) q^{98} -237.561i 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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{20}\right)$

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 $

$2$	1.99423	+	3.07084i	0.705065	+	1.08571i	0.991813	+	0.127699i	$0.0407592\pi$
$2$	1.99423	+	3.07084i	0.705065	+	1.08571i	−0.286748	+	0.958006i	$0.592574\pi$
$3$	2.03228	+	5.29426i	0.391112	+	1.01888i	0.977887	+	0.209132i	$0.0670638\pi$
$3$	2.03228	+	5.29426i	0.391112	+	1.01888i	−0.586775	+	0.809750i	$0.699603\pi$
$4$	−2.19922	+	4.93952i	−0.274902	+	0.617441i
$5$	−10.9441	−	2.28640i	−0.978866	−	0.204502i
$5$	−10.9441	−	2.28640i	−0.978866	−	0.204502i
$6$	−12.2050	+	16.7988i	−0.830446	+	1.14301i
$7$	−17.5585	+	5.89045i	−0.948073	+	0.318054i
$7$	−17.5585	+	5.89045i	−0.948073	+	0.318054i
$8$	9.37758	−	1.48526i	0.414435	−	0.0656400i
$9$	−3.83417	+	3.45230i	−0.142006	+	0.127863i
$10$	−14.8038	−	38.1670i	−0.468136	−	1.20695i
$11$	−30.8098	+	34.2178i	−0.844501	+	0.937914i	−0.998743	−	0.0501193i	$-0.984040\pi$
$11$	−30.8098	+	34.2178i	−0.844501	+	0.937914i	0.154242	+	0.988033i	$0.450707\pi$
$12$	−30.6206	−	1.60476i	−0.736616	−	0.0386044i
$13$	−34.9937	+	17.8302i	−0.746578	+	0.380401i	−0.785516	−	0.618841i	$-0.787603\pi$
$13$	−34.9937	+	17.8302i	−0.746578	+	0.380401i	0.0389379	+	0.999242i	$0.487603\pi$
$14$	−53.1043	−	42.1726i	−1.01377	−	0.805078i
$15$	−10.1366	−	62.5873i	−0.174483	−	1.07733i
$16$	52.2058	+	57.9805i	0.815716	+	0.905945i
$17$	−35.0386	−	43.2690i	−0.499888	−	0.617311i	0.463279	−	0.886212i	$-0.346673\pi$
$17$	−35.0386	−	43.2690i	−0.499888	−	0.617311i	−0.963168	+	0.268902i	$0.913339\pi$
$18$	−18.2476	−	4.88944i	−0.238945	−	0.0640251i
$19$	−26.8797	+	11.9676i	−0.324560	+	0.144503i	−0.562548	−	0.826765i	$-0.690179\pi$
$19$	−26.8797	+	11.9676i	−0.324560	+	0.144503i	0.237988	+	0.971268i	$0.423512\pi$
$20$	35.3621	−	49.0301i	0.395360	−	0.548174i
$21$	−66.8694	−	80.9886i	−0.694862	−	0.841579i
$22$	−166.519	−	26.3740i	−1.61373	−	0.255589i
$23$	16.8829	−	10.9639i	0.153057	−	0.0993967i	−0.465838	−	0.884870i	$-0.654247\pi$
$23$	16.8829	−	10.9639i	0.153057	−	0.0993967i	0.618896	+	0.785473i	$0.287580\pi$
$24$	26.9212	+	46.6289i	0.228970	+	0.396587i
$25$	114.545	+	50.0450i	0.916358	+	0.400360i
$26$	−124.539	−	71.9027i	−0.939389	−	0.542357i
$27$	110.357	+	56.2297i	0.786600	+	0.400793i
$28$	9.51908	−	99.6853i	0.0642478	−	0.672812i
$29$	159.008	+	218.856i	1.01817	+	1.40140i	0.913476	+	0.406893i	$0.133388\pi$
$29$	159.008	+	218.856i	1.01817	+	1.40140i	0.104699	+	0.994504i	$0.466612\pi$
$30$	171.981	−	155.941i	1.04664	−	0.949026i
$31$	122.378	+	12.8624i	0.709022	+	0.0745212i	0.452173	−	0.891930i	$-0.350649\pi$
$31$	122.378	+	12.8624i	0.709022	+	0.0745212i	0.256849	+	0.966452i	$0.417316\pi$
$32$	−54.2796	+	202.574i	−0.299855	+	1.11907i
$33$	−243.772	−	93.5754i	−1.28592	−	0.493618i
$34$	62.9974	−	193.886i	0.317764	−	0.977976i
$35$	205.630	−	24.3195i	0.993079	−	0.117450i
$36$	−8.62054	−	26.5313i	−0.0399099	−	0.122830i
$37$	0.767048	−	14.6361i	0.00340816	−	0.0650316i	−0.996396	−	0.0848240i	$-0.972967\pi$
$37$	0.767048	−	14.6361i	0.00340816	−	0.0650316i	0.999804	+	0.0197924i	$0.00630054\pi$
$38$	−90.3549	−	58.6771i	−0.385724	−	0.250492i
$39$	−165.515	−	149.030i	−0.679579	−	0.611896i
$40$	−106.025	−	5.18611i	−0.419099	−	0.0204999i
$41$	−8.43713	−	2.74139i	−0.0321380	−	0.0104423i	0.292904	−	0.956142i	$-0.405378\pi$
$41$	−8.43713	−	2.74139i	−0.0321380	−	0.0104423i	−0.325042	+	0.945700i	$0.605378\pi$
$42$	115.350	−	366.855i	0.423783	−	1.34778i
$43$	−140.993	+	140.993i	−0.500030	+	0.500030i	−0.911447	−	0.411417i	$-0.865034\pi$
$43$	−140.993	+	140.993i	−0.500030	+	0.500030i	0.411417	+	0.911447i	$0.365034\pi$
$44$	−101.262	−	227.438i	−0.346951	−	0.779264i
$45$	49.8547	−	29.0157i	0.165153	−	0.0961201i
$46$	67.3365	+	29.9801i	0.215831	+	0.0960942i
$47$	23.9845	+	19.4223i	0.0744361	+	0.0602772i	0.665816	−	0.746116i	$-0.268083\pi$
$47$	23.9845	+	19.4223i	0.0744361	+	0.0602772i	−0.591380	+	0.806393i	$0.701417\pi$
$48$	−200.867	+	394.224i	−0.604014	+	1.18544i
$49$	273.605	−	206.855i	0.797683	−	0.603077i
$50$	74.7480	+	451.549i	0.211419	+	1.27717i
$51$	157.870	−	273.438i	0.433454	−	0.750765i
$52$	−11.1139	−	212.065i	−0.0296387	−	0.565541i
$53$	−452.467	+	173.686i	−1.17266	+	0.450143i	−0.865205	−	0.501419i	$-0.832812\pi$
$53$	−452.467	+	173.686i	−1.17266	+	0.450143i	−0.307458	+	0.951562i	$0.599478\pi$
$54$	47.4044	+	451.023i	0.119462	+	1.13660i
$55$	415.420	−	304.038i	1.01846	−	0.745390i
$56$	−155.908	+	81.3172i	−0.372037	+	0.194044i
$57$	−117.987	−	117.987i	−0.274171	−	0.274171i
$58$	−354.973	+	924.736i	−0.803625	+	2.09351i
$59$	−265.022	+	56.3321i	−0.584795	+	0.124302i	−0.490802	−	0.871271i	$-0.663296\pi$
$59$	−265.022	+	56.3321i	−0.584795	+	0.124302i	−0.0939924	+	0.995573i	$0.529963\pi$
$60$	331.444	+	87.5734i	0.713154	+	0.188428i
$61$	−57.1874	+	269.045i	−0.120034	+	0.564717i	0.876490	+	0.481419i	$0.159879\pi$
$61$	−57.1874	+	269.045i	−0.120034	+	0.564717i	−0.996525	+	0.0832976i	$0.973455\pi$
$62$	204.550	+	401.453i	0.418999	+	0.822331i
$63$	46.9868	−	83.2023i	0.0939648	−	0.166389i
$64$	−136.704	+	44.4177i	−0.266999	+	0.0867533i
$65$	423.741	−	115.125i	0.808593	−	0.219685i
$66$	−198.782	−	935.195i	−0.370733	−	1.74416i
$67$	−276.485	+	223.893i	−0.504149	+	0.408252i	−0.847370	−	0.531003i	$-0.821815\pi$
$67$	−276.485	+	223.893i	−0.504149	+	0.408252i	0.343221	+	0.939255i	$0.388482\pi$
$68$	290.786	−	77.9158i	0.518573	−	0.138951i
$69$	92.3563	+	67.1008i	0.161136	+	0.117072i
$70$	484.753	+	582.957i	0.827701	+	0.995381i
$71$	562.908	−	408.976i	0.940913	−	0.683613i	−0.00772718	−	0.999970i	$-0.502460\pi$
$71$	562.908	−	408.976i	0.940913	−	0.683613i	0.948640	+	0.316357i	$0.102460\pi$
$72$	−30.8276	+	38.0690i	−0.0504593	+	0.0623121i
$73$	−868.150	+	45.4978i	−1.39191	+	0.0729468i	−0.733487	−	0.679704i	$-0.762108\pi$
$73$	−868.150	+	45.4978i	−1.39191	+	0.0729468i	−0.658420	+	0.752650i	$0.728775\pi$
$74$	46.4749	−	26.8323i	0.0730081	−	0.0421512i
$75$	−32.1647	+	708.135i	−0.0495208	+	1.09025i
$76$		−	159.092i		−	0.240121i
$77$	339.418	−	782.298i	0.502341	−	1.15781i
$78$	127.574	−	805.469i	0.185191	−	1.16925i
$79$	1222.74	−	128.515i	1.74137	−	0.183026i	0.820174	−	0.572115i	$-0.193877\pi$
$79$	1222.74	−	128.515i	1.74137	−	0.183026i	0.921200	+	0.389089i	$0.127210\pi$
$80$	−438.777	−	753.905i	−0.613210	−	1.05361i
$81$	−87.9799	+	837.073i	−0.120686	+	1.14825i
$82$	−8.40718	−	31.3760i	−0.0113222	−	0.0422549i
$83$	110.810	+	699.629i	0.146542	+	0.925232i	0.945919	+	0.324402i	$0.105163\pi$
$83$	110.810	+	699.629i	0.146542	+	0.925232i	−0.799377	+	0.600830i	$0.794837\pi$
$84$	547.105	−	152.192i	0.710644	−	0.197684i
$85$	284.534	+	553.651i	0.363083	+	0.706493i
$86$	−714.141	−	151.795i	−0.895440	−	0.190332i
$87$	−835.532	+	1286.61i	−1.02964	+	1.58550i
$88$	−238.099	+	366.641i	−0.288426	+	0.444137i
$89$	−538.578	−	114.478i	−0.641451	−	0.136345i	−0.124308	−	0.992244i	$-0.539671\pi$
$89$	−538.578	−	114.478i	−0.641451	−	0.136345i	−0.517143	+	0.855899i	$0.673004\pi$
$90$	188.524	+	95.2317i	0.220802	+	0.111537i
$91$	509.412	−	519.201i	0.586822	−	0.598100i
$92$	17.0272	+	107.505i	0.0192957	+	0.121828i
$93$	180.608	+	674.040i	0.201379	+	0.751555i
$94$	−11.8121	+	112.385i	−0.0129609	+	0.123315i
$95$	321.536	−	69.5165i	0.347252	−	0.0750763i
$96$	−1182.79	+	124.316i	−1.25748	+	0.132167i
$97$	193.365	−	1220.86i	0.202405	−	1.27793i	−0.651958	−	0.758255i	$-0.726052\pi$
$97$	193.365	−	1220.86i	0.202405	−	1.27793i	0.854362	−	0.519678i	$-0.173948\pi$
$98$	1180.85	+	427.681i	1.21718	+	0.440840i
$99$		−	237.561i		−	0.241170i
$100$	−499.107	+	455.737i	−0.499107	+	0.455737i
$101$	409.809	−	236.603i	0.403738	−	0.233098i	−0.284358	−	0.958718i	$-0.591780\pi$
$101$	409.809	−	236.603i	0.403738	−	0.233098i	0.688096	+	0.725620i	$0.258447\pi$
$102$	1154.51	−	60.5054i	1.12072	−	0.0587346i
$103$	−41.0724	+	50.7201i	−0.0392911	+	0.0485204i	−0.796413	−	0.604753i	$-0.793272\pi$
$103$	−41.0724	+	50.7201i	−0.0392911	+	0.0485204i	0.757122	+	0.653274i	$0.226605\pi$
$104$	−301.674	+	219.179i	−0.284438	+	0.206657i
$105$	546.650	+	1039.23i	0.508072	+	0.965894i
$106$	−1435.68	−	1043.08i	−1.31553	−	0.955785i
$107$	1274.55	−	341.515i	1.15155	−	0.308556i	0.367962	−	0.929841i	$-0.380056\pi$
$107$	1274.55	−	341.515i	1.15155	−	0.308556i	0.783585	+	0.621285i	$0.213389\pi$
$108$	−520.447	+	421.450i	−0.463704	+	0.375500i
$109$	−201.264	−	946.870i	−0.176858	−	0.832053i	−0.973695	−	0.227857i	$-0.926828\pi$
$109$	−201.264	−	946.870i	−0.176858	−	0.832053i	0.796836	−	0.604195i	$-0.206505\pi$
$110$	1762.09	+	669.368i	1.52735	+	0.580198i
$111$	79.0465	−	25.6838i	0.0675924	−	0.0219621i
$112$	−1258.19	−	710.537i	−1.06150	−	0.599459i
$113$	980.457	+	1924.25i	0.816227	+	1.60193i	0.798426	+	0.602093i	$0.205666\pi$
$113$	980.457	+	1924.25i	0.816227	+	1.60193i	0.0178008	+	0.999842i	$0.494334\pi$
$114$	127.026	−	597.611i	0.104360	−	0.490977i
$115$	−209.835	+	81.3881i	−0.170150	+	0.0659955i
$116$	−1430.74	+	304.113i	−1.14518	+	0.243415i
$117$	72.6166	−	189.173i	0.0573796	−	0.149479i
$118$	−701.500	−	701.500i	−0.547274	−	0.547274i
$119$	870.100	+	553.349i	0.670269	+	0.426264i
$120$	−188.015	−	571.862i	−0.143028	−	0.435030i
$121$	−82.4837	−	784.780i	−0.0619713	−	0.589617i
$122$	−940.239	+	360.924i	−0.697748	+	0.267840i
$123$	−2.63295	−	50.2397i	−0.00193012	−	0.0368289i
$124$	−332.669	+	576.200i	−0.240924	+	0.417293i
$125$	−1139.16	−	809.590i	−0.815117	−	0.579296i
$126$	349.203	−	21.6352i	0.246901	−	0.0152970i
$127$	1131.71	−	2221.10i	0.790729	−	1.55189i	−0.0425847	−	0.999093i	$-0.513559\pi$
$127$	1131.71	−	2221.10i	0.790729	−	1.55189i	0.833314	−	0.552800i	$-0.186441\pi$
$128$	894.848	+	724.634i	0.617923	+	0.500384i
$129$	−1032.99	−	459.919i	−0.705040	−	0.313904i
$130$	1198.56	+	1071.65i	0.808624	+	0.723002i
$131$	1167.91	+	2623.17i	0.778938	+	1.74952i	0.652828	+	0.757506i	$0.273583\pi$
$131$	1167.91	+	2623.17i	0.778938	+	1.74952i	0.126110	+	0.992016i	$0.459751\pi$
$132$	998.326	−	998.326i	0.658281	−	0.658281i
$133$	401.474	−	368.468i	0.261746	−	0.240227i
$134$	−1238.91	−	402.547i	−0.798699	−	0.259513i
$135$	−1079.19	−	867.701i	−0.688013	−	0.553184i
$136$	−392.843	−	353.717i	−0.247691	−	0.223022i
$137$	−1920.26	−	1247.03i	−1.19751	−	0.777673i	−0.217392	−	0.976084i	$-0.569755\pi$
$137$	−1920.26	−	1247.03i	−1.19751	−	0.777673i	−0.980119	+	0.198411i	$0.936422\pi$
$138$	−21.8763	+	417.425i	−0.0134945	+	0.257490i
$139$	−425.263	−	1308.83i	−0.259499	−	0.798655i	−0.992910	−	0.118870i	$-0.962073\pi$
$139$	−425.263	−	1308.83i	−0.259499	−	0.798655i	0.733411	−	0.679785i	$-0.237927\pi$
$140$	−332.098	+	1069.20i	−0.200481	+	0.645454i
$141$	−54.0834	+	166.452i	−0.0323025	+	0.0994167i
$142$	2378.46	+	913.007i	1.40561	+	0.539562i
$143$	468.041	−	1746.75i	0.273703	−	1.02148i
$144$	−400.332	−	42.0765i	−0.231673	−	0.0243499i
$145$	−1239.80	−	2758.73i	−0.710068	−	1.58000i
$146$	−1871.00	−	2575.21i	−1.06058	−	1.45977i
$147$	1651.19	+	1028.15i	0.926447	+	0.576874i
$148$	70.6087	+	35.9769i	0.0392162	+	0.0199817i
$149$	693.724	+	400.522i	0.381423	+	0.220215i	0.678437	−	0.734658i	$-0.262658\pi$
$149$	693.724	+	400.522i	0.381423	+	0.220215i	−0.297014	+	0.954873i	$0.595991\pi$
$150$	−2238.71	+	1313.41i	−1.21860	+	0.714929i
$151$	41.3152	+	71.5601i	0.0222661	+	0.0385661i	0.876944	−	0.480593i	$-0.159579\pi$
$151$	41.3152	+	71.5601i	0.0222661	+	0.0385661i	−0.854678	+	0.519159i	$0.826245\pi$
$152$	−234.292	+	152.151i	−0.125023	+	0.0811912i
$153$	283.721	+	44.9370i	0.149918	+	0.0237447i
$154$	3079.19	−	517.782i	1.61122	−	0.270935i
$155$	−1309.90	−	420.571i	−0.678798	−	0.217943i
$156$	1100.14	−	489.815i	0.564627	−	0.251388i
$157$	915.279	+	245.248i	0.465269	+	0.124668i	0.483835	−	0.875159i	$-0.339243\pi$
$157$	915.279	+	245.248i	0.465269	+	0.124668i	−0.0185662	+	0.999828i	$0.505910\pi$
$158$	2833.06	+	3498.54i	1.42649	+	1.76157i
$159$	−1839.08	−	2042.50i	−0.917284	−	1.01875i
$160$	1057.20	−	2092.88i	0.522371	−	1.03410i
$161$	−231.857	+	291.957i	−0.113496	+	0.142916i
$162$	−2745.97	+	1399.14i	−1.33175	+	0.678561i
$163$	−740.169	−	38.7906i	−0.355672	−	0.0186400i	−0.126337	−	0.991987i	$-0.540322\pi$
$163$	−740.169	−	38.7906i	−0.355672	−	0.0186400i	−0.229335	+	0.973347i	$0.573655\pi$
$164$	32.0963	−	35.6465i	0.0152823	−	0.0169727i
$165$	2453.91	+	1581.45i	1.15780	+	0.746158i
$166$	−1927.47	+	1735.50i	−0.901207	+	0.811451i
$167$	2423.98	−	383.921i	1.12319	−	0.177896i	0.432911	−	0.901437i	$-0.357486\pi$
$167$	2423.98	−	383.921i	1.12319	−	0.177896i	0.690282	+	0.723540i	$0.257486\pi$
$168$	−747.363	−	660.158i	−0.343216	−	0.303169i
$169$	−384.718	+	529.519i	−0.175111	+	0.241019i
$170$	−1132.75	+	1977.86i	−0.511046	+	0.892324i
$171$	61.7455	−	138.683i	0.0276128	−	0.0620195i
$172$	−386.365	−	1006.52i	−0.171280	−	0.446198i
$173$	−1973.28	−	3038.58i	−0.867200	−	1.33537i	−0.941108	−	0.338106i	$-0.890214\pi$
$173$	−1973.28	−	3038.58i	−0.867200	−	1.33537i	0.0739076	−	0.997265i	$-0.476453\pi$
$174$	−5617.20			−2.44735
$175$	−2306.03	−	203.998i	−0.996110	−	0.0881189i
$176$	−3592.42			−1.53857
$177$	−836.835	−	1288.61i	−0.355369	−	0.547221i
$178$	−722.502	−	1882.18i	−0.304235	−	0.792559i
$179$	−1360.27	+	3055.22i	−0.567997	+	1.27574i	0.369979	+	0.929040i	$0.379365\pi$
$179$	−1360.27	+	3055.22i	−0.567997	+	1.27574i	−0.937975	+	0.346702i	$0.887302\pi$
$180$	33.6825	+	310.070i	0.0139475	+	0.128396i
$181$	25.4301	−	35.0016i	0.0104431	−	0.0143737i	−0.803764	−	0.594949i	$-0.797172\pi$
$181$	25.4301	−	35.0016i	0.0104431	−	0.0143737i	0.814207	+	0.580575i	$0.197172\pi$
$182$	2610.26	+	528.916i	1.06311	+	0.215417i
$183$	−1540.62	+	244.010i	−0.622326	+	0.0985668i
$184$	142.036	−	127.890i	0.0569079	−	0.0512401i
$185$	−41.8587	+	158.425i	−0.0166352	+	0.0629602i
$186$	−1709.69	+	1898.81i	−0.673982	+	0.748533i
$187$	2560.10	+	134.169i	1.00114	+	0.0524676i
$188$	−148.684	+	75.7582i	−0.0576802	+	0.0293896i
$189$	−2268.93	−	337.260i	−0.873228	−	0.129799i
$190$	854.689	+	848.753i	0.326346	+	0.324079i
$191$	1459.31	+	1620.73i	0.552837	+	0.613987i	0.953189	−	0.302374i	$-0.0977790\pi$
$191$	1459.31	+	1620.73i	0.552837	+	0.613987i	−0.400353	+	0.916361i	$0.631112\pi$
$192$	−512.978	−	633.476i	−0.192818	−	0.238110i
$193$	−500.142	−	134.013i	−0.186534	−	0.0499816i	0.164343	−	0.986403i	$-0.447450\pi$
$193$	−500.142	−	134.013i	−0.186534	−	0.0499816i	−0.350877	+	0.936422i	$0.614116\pi$
$194$	4134.67	−	1840.88i	1.53017	−	0.681274i
$195$	1470.66	+	2009.43i	0.540083	+	0.737939i
$196$	420.049	+	1806.40i	0.153079	+	0.658309i
$197$	3707.49	+	587.209i	1.34085	+	0.212370i	0.785302	−	0.619113i	$-0.212508\pi$
$197$	3707.49	+	587.209i	1.34085	+	0.212370i	0.555550	+	0.831483i	$0.312508\pi$
$198$	729.513	−	473.751i	0.261839	−	0.170040i
$199$	−1644.01	−	2847.51i	−0.585633	−	1.01435i	−0.994796	−	0.101884i	$-0.967513\pi$
$199$	−1644.01	−	2847.51i	−0.585633	−	1.01435i	0.409164	−	0.912461i	$-0.365821\pi$
$200$	1148.48	+	299.172i	0.406050	+	0.105773i
$201$	−1747.24	−	1008.77i	−0.613139	−	0.353996i
$202$	1543.82	+	786.617i	0.537737	+	0.273991i
$203$	−4081.11	−	2906.16i	−1.41102	−	1.00479i
$204$	1003.46	+	1381.15i	0.344395	+	0.474019i
$205$	86.0685	+	49.2926i	0.0293234	+	0.0167939i
$206$	−237.661	−	24.9792i	−0.0803816	−	0.00844845i
$207$	−26.8812	+	100.322i	−0.00902595	+	0.0336853i
$208$	−2860.68	−	1098.11i	−0.953618	−	0.366060i
$209$	418.654	−	1288.49i	0.138559	−	0.426442i
$210$	−2101.17	+	3751.14i	−0.690452	+	1.23263i
$211$	−1271.60	−	3913.60i	−0.414885	−	1.27689i	−0.912353	−	0.409404i	$-0.865737\pi$
$211$	−1271.60	−	3913.60i	−0.414885	−	1.27689i	0.497468	−	0.867482i	$-0.334263\pi$
$212$	137.148	−	2616.94i	0.0444310	−	0.847794i
$213$	3309.21	+	2149.03i	1.06452	+	0.691310i
$214$	3590.48	+	3232.88i	1.14692	+	1.03269i
$215$	1865.41	−	1220.67i	0.591720	−	0.387206i
$216$	1118.40	+	363.389i	0.352302	+	0.114470i
$217$	−2224.54	+	495.014i	−0.695906	+	0.154856i
$218$	2506.32	−	2506.32i	0.778667	−	0.778667i
$219$	−2005.20	−	4503.75i	−0.618716	−	1.38966i
$220$	588.203	+	2720.62i	0.180257	+	0.833747i
$221$	1997.63	+	889.401i	0.608031	+	0.270713i
$222$	236.507	+	191.520i	0.0715014	+	0.0579007i
$223$	−1878.13	+	3686.03i	−0.563985	+	1.10688i	0.416288	+	0.909233i	$0.363331\pi$
$223$	−1878.13	+	3686.03i	−0.563985	+	1.10688i	−0.980273	+	0.197650i	$0.936669\pi$
$224$	−240.181	−	3876.64i	−0.0716419	−	1.15633i
$225$	−611.954	+	203.562i	−0.181320	+	0.0603146i
$226$	−3953.82	+	6848.22i	−1.16374	+	2.01565i
$227$	83.4975	+	1593.23i	0.0244138	+	0.465843i	0.983293	+	0.182029i	$0.0582664\pi$
$227$	83.4975	+	1593.23i	0.0244138	+	0.465843i	−0.958879	+	0.283814i	$0.908400\pi$
$228$	842.277	−	323.320i	0.244654	−	0.0939140i
$229$	−447.984	−	4262.28i	−0.129273	−	1.22995i	−0.846223	−	0.532829i	$-0.821129\pi$
$229$	−447.984	−	4262.28i	−0.129273	−	1.22995i	0.716949	−	0.697125i	$-0.245538\pi$
$230$	−668.388	−	482.063i	−0.191618	−	0.138201i
$231$	4831.49	+	207.121i	1.37614	+	0.0589938i
$232$	1816.17	+	1816.17i	0.513954	+	0.513954i
$233$	−877.699	+	2286.48i	−0.246781	+	0.642886i	−0.999887	−	0.0150124i	$-0.995221\pi$
$233$	−877.699	+	2286.48i	−0.246781	+	0.642886i	0.753106	+	0.657899i	$0.228555\pi$
$234$	725.733	−	154.259i	0.202746	−	0.0430951i
$235$	−218.081	−	267.396i	−0.0605362	−	0.0742256i
$236$	304.587	−	1432.97i	0.0840123	−	0.395247i
$237$	3165.33	+	6212.31i	0.867554	+	1.70267i
$238$	35.9322	+	3775.44i	0.00978630	+	1.02826i
$239$	6163.04	−	2002.49i	1.66801	−	0.541968i	0.685480	−	0.728091i	$-0.259592\pi$
$239$	6163.04	−	2002.49i	1.66801	−	0.541968i	0.982526	+	0.186123i	$0.0595922\pi$
$240$	3099.65	−	3855.15i	0.833674	−	1.03687i
$241$	784.665	+	3691.56i	0.209729	+	0.986698i	0.949482	+	0.313820i	$0.101609\pi$
$241$	784.665	+	3691.56i	0.209729	+	0.986698i	−0.739753	+	0.672878i	$0.765058\pi$
$242$	2245.44	−	1818.32i	0.596457	−	0.483001i
$243$	−1380.31	+	369.853i	−0.364390	+	0.0976381i
$244$	−1203.19	−	874.168i	−0.315681	−	0.229356i
$245$	−3467.31	+	1638.27i	−0.904155	+	0.427204i
$246$	149.027	−	108.275i	0.0386245	−	0.0280623i
$247$	727.237	−	898.063i	0.187340	−	0.231346i
$248$	1166.71	−	61.1447i	0.298735	−	0.0156560i
$249$	−3478.82	+	2008.50i	−0.885387	+	0.511179i
$250$	214.377	−	5112.69i	0.0542335	−	1.29342i
$251$		−	5850.69i		−	1.47128i	−0.677370	−	0.735642i	$-0.736881\pi$
$251$		−	5850.69i		−	1.47128i	0.677370	−	0.735642i	$-0.263119\pi$
$252$	307.645	+	415.072i	0.0769041	+	0.103758i
$253$	−144.999	+	915.489i	−0.0360317	+	0.227495i
$254$	9077.50	−	954.084i	2.24241	−	0.235687i
$255$	−2352.92	+	2631.57i	−0.577826	+	0.646256i
$256$	−560.902	+	5336.63i	−0.136939	+	1.30289i
$257$	1548.55	+	5779.28i	0.375860	+	1.40273i	0.852084	+	0.523405i	$0.175339\pi$
$257$	1548.55	+	5779.28i	0.375860	+	1.40273i	−0.476224	+	0.879324i	$0.657995\pi$
$258$	−647.688	−	4089.34i	−0.156292	−	0.986788i
$259$	72.7452	+	261.508i	0.0174524	+	0.0627386i
$260$	−363.235	+	2346.26i	−0.0866418	+	0.559650i
$261$	−1365.22	−	290.186i	−0.323774	−	0.0688202i
$262$	−5726.25	+	8817.66i	−1.35026	+	2.07922i
$263$	2208.92	−	3401.43i	0.517900	−	0.797496i	−0.478863	−	0.877889i	$-0.658951\pi$
$263$	2208.92	−	3401.43i	0.517900	−	0.797496i	0.996763	+	0.0803938i	$0.0256178\pi$
$264$	−2424.98	−	515.445i	−0.565330	−	0.120165i
$265$	5348.94	−	866.306i	1.23993	−	0.200818i
$266$	1932.13	+	498.055i	0.445364	+	0.114803i
$267$	−488.462	−	3084.03i	−0.111960	−	0.706889i
$268$	−497.875	−	1858.09i	−0.113480	−	0.423512i
$269$	−870.788	+	8284.99i	−0.197371	+	1.87786i	0.229159	+	0.973389i	$0.426402\pi$
$269$	−870.788	+	8284.99i	−0.197371	+	1.87786i	−0.426530	+	0.904473i	$0.640264\pi$
$270$	512.423	−	5044.41i	0.115500	−	1.13701i
$271$	1600.00	−	168.167i	0.358646	−	0.0376953i	0.0765080	−	0.997069i	$-0.475623\pi$
$271$	1600.00	−	168.167i	0.358646	−	0.0376953i	0.282138	+	0.959374i	$0.408956\pi$
$272$	679.540	−	4290.45i	0.151482	−	0.956422i
$273$	3784.05	+	1641.80i	0.838906	+	0.363979i
$274$		−	8383.68i		−	1.84845i
$275$	−5241.53	+	2377.59i	−1.14937	+	0.521360i
$276$	−534.557	+	308.627i	−0.116582	+	0.0673085i
$277$	−5087.94	+	266.648i	−1.10363	+	0.0578387i	−0.595434	−	0.803404i	$-0.703020\pi$
$277$	−5087.94	+	266.648i	−1.10363	+	0.0578387i	−0.508194	+	0.861243i	$0.669687\pi$
$278$	3171.12	−	3916.01i	0.684141	−	0.844843i
$279$	−513.621	+	373.168i	−0.110214	+	0.0800751i
$280$	1892.19	−	533.472i	0.403857	−	0.113861i
$281$	3813.85	+	2770.92i	0.809662	+	0.588254i	0.913733	−	0.406316i	$-0.133187\pi$
$281$	3813.85	+	2770.92i	0.809662	+	0.588254i	−0.104070	+	0.994570i	$0.533187\pi$
$282$	−619.001	+	165.861i	−0.130713	+	0.0350243i
$283$	1154.18	−	934.633i	0.242433	−	0.196319i	−0.500401	−	0.865794i	$-0.666814\pi$
$283$	1154.18	−	934.633i	0.242433	−	0.196319i	0.742835	+	0.669475i	$0.233481\pi$
$284$	782.192	+	3679.92i	0.163431	+	0.768885i
$285$	1021.49	+	1561.02i	0.212308	+	0.324445i
$286$	6297.38	−	2046.14i	1.30200	−	0.423045i
$287$	164.292	−	1.56362i	0.0337904	−	0.000321595i
$288$	−491.229	−	964.092i	−0.100507	−	0.197256i
$289$	376.962	−	1773.47i	0.0767275	−	0.360975i
$290$	5999.16	−	9308.75i	1.21477	−	1.88493i
$291$	6856.52	−	1457.40i	1.38122	−	0.293588i
$292$	1684.51	−	4388.31i	0.337598	−	0.879473i
$293$	1938.99	+	1938.99i	0.386612	+	0.386612i	0.873477	−	0.486865i	$-0.161860\pi$
$293$	1938.99	+	1938.99i	0.386612	+	0.386612i	−0.486865	+	0.873477i	$0.661860\pi$
$294$	135.557	+	7120.90i	0.0268905	+	1.41258i
$295$	3029.21	−	10.5559i	0.597856	−	0.00208335i
$296$	−14.5455	−	138.391i	−0.00285621	−	0.0271750i
$297$	−5324.13	+	2043.74i	−1.04019	+	0.399293i
$298$	153.505	+	2929.04i	0.0298399	+	0.569379i
$299$	−395.307	+	684.692i	−0.0764588	+	0.132431i
$300$	−3427.11	−	1716.22i	−0.659549	−	0.330287i
$301$	1645.13	−	3306.16i	0.315028	−	0.633102i
$302$	−137.358	+	269.579i	−0.0261723	+	0.0513661i
$303$	2085.49	+	1688.79i	0.395406	+	0.320194i
$304$	−2097.17	−	933.719i	−0.395660	−	0.176159i
$305$	1241.01	−	2813.69i	0.232983	−	0.528235i
$306$	427.810	+	960.877i	0.0799224	+	0.179509i
$307$	−4755.07	+	4755.07i	−0.883994	+	0.883994i	−0.993938	−	0.109944i	$-0.964933\pi$
$307$	−4755.07	+	4755.07i	−0.883994	+	0.883994i	0.109944	+	0.993938i	$0.464933\pi$
$308$	3117.73	+	3397.01i	0.576783	+	0.628450i
$309$	−351.996	−	114.371i	−0.0648038	−	0.0210560i
$310$	−1320.73	−	4861.20i	−0.241975	−	0.890638i
$311$	−309.026	−	278.248i	−0.0563448	−	0.0507331i	0.640477	−	0.767977i	$-0.278737\pi$
$311$	−309.026	−	278.248i	−0.0563448	−	0.0507331i	−0.696822	+	0.717244i	$0.745403\pi$
$312$	−1773.48	−	1151.71i	−0.321806	−	0.208983i
$313$	−59.1698	+	1129.03i	−0.0106852	+	0.203886i	0.988070	+	0.154006i	$0.0492174\pi$
$313$	−59.1698	+	1129.03i	−0.0106852	+	0.203886i	−0.998755	+	0.0498805i	$0.984116\pi$
$314$	1072.15	+	3299.75i	0.192692	+	0.593044i
$315$	−704.460	+	803.140i	−0.126006	+	0.143657i
$316$	−2054.26	+	6322.37i	−0.365700	+	1.12551i
$317$	−9651.64	−	3704.92i	−1.71006	−	0.656432i	−0.711151	−	0.703040i	$-0.751826\pi$
$317$	−9651.64	−	3704.92i	−1.71006	−	0.656432i	−0.998913	+	0.0466075i	$0.985159\pi$
$318$	2604.66	−	9720.71i	0.459314	−	1.71418i
$319$	−12387.8	−	1302.01i	−2.17424	−	0.228522i
$320$	1597.65	−	173.550i	0.279098	−	0.0303180i
$321$	4398.31	+	6053.76i	0.764766	+	1.05261i
$322$	−1358.93	−	129.766i	−0.235187	−	0.0224583i
$323$	1459.65	+	743.731i	0.251447	+	0.128119i
$324$	−3941.26	−	2275.49i	−0.675798	−	0.390172i
$325$	−4900.66	+	291.094i	−0.836430	+	0.0496831i
$326$	−1356.94	−	2350.30i	−0.230534	−	0.399297i
$327$	4603.96	−	2989.85i	0.778592	−	0.505623i
$328$	−83.1916	−	13.1763i	−0.0140045	−	0.00221810i
$329$	−535.539	−	199.747i	−0.0897423	−	0.0334724i
$330$	37.2492	+	10689.3i	0.00621364	+	1.78311i
$331$	−8460.22	+	3766.73i	−1.40488	+	0.625493i	−0.962487	−	0.271328i	$-0.912537\pi$
$331$	−8460.22	+	3766.73i	−1.40488	+	0.625493i	−0.442394	+	0.896821i	$0.645871\pi$
$332$	−3699.53	−	991.286i	−0.611561	−	0.163867i
$333$	47.5873	+	58.7655i	0.00783114	+	0.00967066i
$334$	6012.92	+	6678.03i	0.985067	+	1.09403i
$335$	3537.77	−	1818.14i	0.576983	−	0.296525i
$336$	1204.78	−	8105.20i	0.195614	−	1.31600i
$337$	−5739.38	+	2924.36i	−0.927727	+	0.472701i	−0.851479	−	0.524388i	$-0.824294\pi$
$337$	−5739.38	+	2924.36i	−0.927727	+	0.472701i	−0.0762481	+	0.997089i	$0.524294\pi$
$338$	−2393.28	−	125.427i	−0.385140	−	0.0201843i
$339$	−8194.95	+	9101.41i	−1.31295	+	1.45817i
$340$	−3360.52	+	187.862i	−0.536029	+	0.0299655i
$341$	−4210.56	+	3791.20i	−0.668664	+	0.602068i
$342$	549.006	−	86.9541i	0.0868037	−	0.0137484i
$343$	−3585.64	+	5243.74i	−0.564450	+	0.825467i
$344$	−1112.77	+	1531.59i	−0.174408	+	0.240052i
$345$	−857.333	−	945.518i	−0.133789	−	0.147551i
$346$	5395.83	−	12119.2i	0.838387	−	1.88305i
$347$	−2432.32	−	6336.40i	−0.376293	−	0.980276i	−0.982714	−	0.185132i	$-0.940729\pi$
$347$	−2432.32	−	6336.40i	−0.376293	−	0.980276i	0.606421	−	0.795144i	$-0.292605\pi$
$348$	−4517.71	−	6956.66i	−0.695904	−	1.07160i
$349$	5857.65			0.898433			0.449216	−	0.893423i	$-0.351703\pi$
$349$	5857.65			0.898433			0.449216	+	0.893423i	$0.351703\pi$
$350$	−3972.29	−	7488.25i	−0.606651	−	1.14361i
$351$	−4864.39			−0.739721
$352$	−5259.29	−	8098.60i	−0.796367	−	1.22630i
$353$	1924.03	+	5012.28i	0.290102	+	0.755741i	0.998741	+	0.0501696i	$0.0159762\pi$
$353$	1924.03	+	5012.28i	0.290102	+	0.755741i	−0.708639	+	0.705571i	$0.750690\pi$
$354$	2288.28	−	5139.57i	0.343562	−	0.771652i
$355$	−7095.58	+	3188.83i	−1.06083	+	0.476748i
$356$	1749.92	−	2408.56i	0.260521	−	0.358576i
$357$	−1161.29	+	5731.10i	−0.172162	+	0.849641i
$358$	−12094.8	+	1915.62i	−1.78555	+	0.282804i
$359$	−2462.37	+	2217.12i	−0.362002	+	0.325948i	−0.829981	−	0.557791i	$-0.811649\pi$
$359$	−2462.37	+	2217.12i	−0.362002	+	0.325948i	0.467979	+	0.883740i	$0.344982\pi$
$360$	424.420	−	346.144i	0.0621359	−	0.0506762i
$361$	−4010.27	+	4453.86i	−0.584673	+	0.649345i
$362$	158.198	+	8.29078i	0.0229687	+	0.00120374i
$363$	3987.20	−	2031.58i	0.576512	−	0.293748i
$364$	1444.30	+	3658.09i	0.207972	+	0.526747i
$365$	9605.11	+	1487.01i	1.37741	+	0.213243i
$366$	−3821.65	−	4244.38i	−0.545795	−	0.606167i
$367$	−469.562	−	579.861i	−0.0667873	−	0.0824755i	0.742657	−	0.669672i	$-0.233565\pi$
$367$	−469.562	−	579.861i	−0.0667873	−	0.0824755i	−0.809445	+	0.587196i	$0.800232\pi$
$368$	1517.07	+	406.499i	0.214899	+	0.0575821i
$369$	41.8135	−	18.6166i	0.00589897	−	0.00262639i
$370$	−569.973	+	187.394i	−0.0800851	+	0.0263301i
$371$	6921.57	−	5714.90i	0.968599	−	0.799738i
$372$	−3726.63	−	590.240i	−0.519400	−	0.0822649i
$373$	−3955.81	+	2568.93i	−0.549126	+	0.356607i	−0.789189	−	0.614151i	$-0.789499\pi$
$373$	−3955.81	+	2568.93i	−0.549126	+	0.356607i	0.240063	+	0.970757i	$0.422832\pi$
$374$	4693.41	+	8129.23i	0.648905	+	1.12394i
$375$	1971.09	−	7676.33i	0.271432	−	1.05708i
$376$	253.764	+	146.511i	0.0348055	+	0.0200950i
$377$	−9466.53	−	4823.44i	−1.29324	−	0.658938i
$378$	−3489.08	−	7640.08i	−0.474759	−	1.03959i
$379$	−3441.45	−	4736.75i	−0.466426	−	0.641980i	0.509400	−	0.860530i	$-0.329867\pi$
$379$	−3441.45	−	4736.75i	−0.466426	−	0.641980i	−0.975826	+	0.218550i	$0.929867\pi$
$380$	−363.749	+	1741.12i	−0.0491051	+	0.235046i
$381$	14059.0	+	1477.66i	1.89046	+	0.198695i
$382$	−2066.80	+	7713.39i	−0.276823	+	1.03312i
$383$	−10233.7	−	3928.36i	−1.36532	−	0.524099i	−0.438208	−	0.898874i	$-0.644387\pi$
$383$	−10233.7	−	3928.36i	−1.36532	−	0.524099i	−0.927116	+	0.374775i	$0.877720\pi$
$384$	−2017.82	+	6210.22i	−0.268155	+	0.825297i
$385$	−5503.26	+	7785.47i	−0.728499	+	1.03061i
$386$	−585.865	−	1803.11i	−0.0772532	−	0.237761i
$387$	53.8408	−	1027.34i	0.00707205	−	0.134943i
$388$	5605.21	+	3640.07i	0.733406	+	0.476279i
$389$	8236.23	+	7415.93i	1.07350	+	0.966588i	0.999529	−	0.0306723i	$-0.00976483\pi$
$389$	8236.23	+	7415.93i	1.07350	+	0.966588i	0.0739750	+	0.997260i	$0.476431\pi$
$390$	−3237.80	+	8523.41i	−0.420391	+	1.10667i
$391$	−1065.95	−	346.347i	−0.137870	−	0.0447968i
$392$	2258.52	−	2346.18i	0.291001	−	0.302296i
$393$	−11514.2	+	11514.2i	−1.47790	+	1.47790i
$394$	5590.35	+	12556.1i	0.714817	+	1.60550i
$395$	−13675.5	−	1389.19i	−1.74200	−	0.176957i
$396$	1173.44	+	522.449i	0.148908	+	0.0662981i
$397$	5939.11	+	4809.40i	0.750820	+	0.608002i	0.926434	−	0.376457i	$-0.122858\pi$
$397$	5939.11	+	4809.40i	0.750820	+	0.608002i	−0.175614	+	0.984459i	$0.556191\pi$
$398$	5465.72	−	10727.1i	0.688371	−	1.35100i
$399$	2766.67	+	1376.68i	0.347135	+	0.172733i
$400$	3078.27	+	9254.00i	0.384784	+	1.15675i
$401$	1018.51	−	1764.12i	0.126838	−	0.219691i	−0.795612	−	0.605807i	$-0.792850\pi$
$401$	1018.51	−	1764.12i	0.126838	−	0.219691i	0.922450	+	0.386116i	$0.126184\pi$
$402$	−386.623	−	7377.22i	−0.0479677	−	0.915279i
$403$	−4511.79	+	1731.91i	−0.557688	+	0.214076i
$404$	267.449	+	2544.60i	0.0329358	+	0.313363i
$405$	2876.74	−	8959.82i	0.352954	−	1.09930i
$406$	785.702	−	18328.0i	0.0960437	−	2.24040i
$407$	477.184	+	477.184i	0.0581158	+	0.0581158i
$408$	1074.31	−	2798.67i	0.130358	−	0.339595i
$409$	12372.4	−	2629.83i	1.49578	−	0.317938i	0.613890	−	0.789391i	$-0.289604\pi$
$409$	12372.4	−	2629.83i	1.49578	−	0.317938i	0.881891	+	0.471453i	$0.156270\pi$
$410$	20.2705	+	362.603i	0.00244168	+	0.0436773i
$411$	2699.61	−	12700.7i	0.323996	−	1.52428i
$412$	−160.206	−	314.423i	−0.0191573	−	0.0375983i
$413$	4321.58	−	2550.21i	0.514893	−	0.303844i
$414$	−361.680	+	117.517i	−0.0429362	+	0.0139508i
$415$	386.917	−	7910.14i	0.0457663	−	0.935647i
$416$	−1712.49	−	8056.64i	−0.201831	−	0.949542i
$417$	6065.01	−	4911.35i	0.712242	−	0.576762i
$418$	4791.62	−	1283.91i	0.560684	−	0.150235i
$419$	713.589	+	518.453i	0.0832007	+	0.0604489i	0.628608	−	0.777722i	$-0.283625\pi$
$419$	713.589	+	518.453i	0.0832007	+	0.0604489i	−0.545407	+	0.838171i	$0.683625\pi$
$420$	−6335.52	+	414.691i	−0.736052	+	0.0481782i
$421$	8896.35	−	6463.57i	1.02988	−	0.748255i	0.0615990	−	0.998101i	$-0.480380\pi$
$421$	8896.35	−	6463.57i	1.02988	−	0.748255i	0.968286	+	0.249846i	$0.0803800\pi$
$422$	9482.15	−	11709.5i	1.09380	−	1.35073i
$423$	−159.012	+	8.33346i	−0.0182776	+	0.000957889i
$424$	−3985.08	+	2300.78i	−0.456444	+	0.263528i
$425$	−1848.09	−	6709.75i	−0.210930	−	0.765813i
$426$			14447.7i			1.64318i
$427$	−580.670	−	5060.90i	−0.0658093	−	0.573570i
$428$	−1116.09	+	7046.74i	−0.126048	+	0.795835i
$429$	10199.0	−	1071.95i	1.14781	−	0.120640i
$430$	7468.53	+	3294.07i	0.837592	+	0.369428i
$431$	272.592	−	2593.54i	0.0304647	−	0.289852i	−0.968673	−	0.248339i	$-0.920115\pi$
$431$	272.592	−	2593.54i	0.0304647	−	0.289852i	0.999138	−	0.0415134i	$-0.0132179\pi$
$432$	2501.05	+	9334.06i	0.278546	+	1.03955i
$433$	830.931	+	5246.29i	0.0922217	+	0.582265i	0.989917	+	0.141648i	$0.0452401\pi$
$433$	830.931	+	5246.29i	0.0922217	+	0.582265i	−0.897695	+	0.440617i	$0.854760\pi$
$434$	−5956.34	−	5844.03i	−0.658787	−	0.646365i
$435$	12085.8	−	12170.3i	1.33212	−	1.34143i
$436$	5119.71	+	1088.23i	0.562362	+	0.119534i
$437$	−322.596	+	496.754i	−0.0353131	+	0.0543774i
$438$	9831.47	−	15139.1i	1.07252	−	1.65154i
$439$	10993.6	+	2336.75i	1.19520	+	0.254048i	0.762198	−	0.647344i	$-0.224120\pi$
$439$	10993.6	+	2336.75i	1.19520	+	0.254048i	0.433004	+	0.901392i	$0.357454\pi$
$440$	3444.06	−	3468.15i	0.373157	−	0.375767i
$441$	−334.922	+	1737.68i	−0.0361647	+	0.187635i
$442$	1252.51	+	7908.05i	0.134787	+	0.851013i
$443$	2680.14	+	10002.4i	0.287443	+	1.07275i	0.947036	+	0.321128i	$0.104062\pi$
$443$	2680.14	+	10002.4i	0.287443	+	1.07275i	−0.659593	+	0.751623i	$0.729271\pi$
$444$	−46.9749	+	446.936i	−0.00502101	+	0.0477717i
$445$	5632.48	+	2484.26i	0.600012	+	0.264641i
$446$	−15064.6	+	1583.35i	−1.59939	+	0.168103i
$447$	−710.628	+	4486.73i	−0.0751936	+	0.474754i
$448$	2138.68	−	1585.15i	0.225542	−	0.167169i
$449$		−	18171.0i		−	1.90989i	−0.296776	−	0.954947i	$-0.595912\pi$
$449$		−	18171.0i		−	1.90989i	0.296776	−	0.954947i	$-0.404088\pi$
$450$	−1845.48	−	1473.26i	−0.193326	−	0.154334i
$451$	353.751	−	204.238i	0.0369346	−	0.0213242i
$452$	−11661.1	+	611.134i	−1.21348	+	0.0635959i
$453$	−294.894	+	364.164i	−0.0305857	+	0.0377702i
$454$	−4726.03	+	3433.66i	−0.488554	+	0.354956i
$455$	−6762.13	+	4517.45i	−0.696733	+	0.465453i
$456$	−1281.67	−	931.190i	−0.131622	−	0.0956293i
$457$	6578.13	−	1762.60i	0.673330	−	0.180418i	0.0940755	−	0.995565i	$-0.470010\pi$
$457$	6578.13	−	1762.60i	0.673330	−	0.180418i	0.579254	+	0.815147i	$0.303344\pi$
$458$	12195.4	−	9875.64i	1.24422	−	1.00755i
$459$	−1433.75	−	6745.25i	−0.145799	−	0.685928i
$460$	59.4539	−	1215.47i	0.00602620	−	0.123200i
$461$	−13753.8	+	4468.88i	−1.38954	+	0.451489i	−0.905793	−	0.423720i	$-0.860724\pi$
$461$	−13753.8	+	4468.88i	−1.38954	+	0.451489i	−0.483746	+	0.875208i	$0.660724\pi$
$462$	8999.04	+	15249.8i	0.906219	+	1.53568i
$463$	−2411.22	−	4732.28i	−0.242028	−	0.475006i	0.737755	−	0.675068i	$-0.235886\pi$
$463$	−2411.22	−	4732.28i	−0.242028	−	0.475006i	−0.979783	+	0.200062i	$0.935886\pi$
$464$	−4388.21	+	20644.9i	−0.439047	+	2.06555i
$465$	−435.464	−	7789.67i	−0.0434283	−	0.776854i
$466$	−8771.75	+	1864.49i	−0.871982	+	0.185345i
$467$	664.968	−	1732.30i	0.0658909	−	0.171652i	−0.896682	−	0.442676i	$-0.854029\pi$
$467$	664.968	−	1732.30i	0.0658909	−	0.171652i	0.962572	+	0.271025i	$0.0873625\pi$
$468$	774.724	+	774.724i	0.0765206	+	0.0765206i
$469$	3535.84	−	5559.86i	0.348124	−	0.547399i
$470$	386.229	−	1202.94i	0.0379052	−	0.118058i
$471$	561.692	+	5344.14i	0.0549499	+	0.522813i
$472$	−2401.60	+	921.886i	−0.234200	+	0.0899009i
$473$	−480.499	−	9168.47i	−0.0467090	−	0.891262i
$474$	−12764.6	+	22109.0i	−1.23692	+	2.14240i
$475$	−3677.85	+	25.6328i	−0.355266	+	0.00247603i
$476$	−4646.82	+	3080.95i	−0.447451	+	0.296670i
$477$	1135.22	−	2227.99i	0.108969	−	0.213863i
$478$	18439.8	+	14932.3i	1.76447	+	1.42884i
$479$	15738.2	+	7007.12i	1.50125	+	0.668400i	0.982455	−	0.186499i	$-0.0597142\pi$
$479$	15738.2	+	7007.12i	1.50125	+	0.668400i	0.518795	+	0.854899i	$0.326381\pi$
$480$	13228.8	+	1343.81i	1.25793	+	0.127784i
$481$	234.124	+	525.850i	0.0221936	+	0.0498476i
$482$	−9771.38	+	9771.38i	−0.923391	+	0.923391i
$483$	−2016.90	−	634.172i	−0.190004	−	0.0597430i
$484$	4057.84	+	1318.47i	0.381090	+	0.123823i
$485$	−4907.57	+	12919.0i	−0.459467	+	1.20953i
$486$	−3888.40	−	3501.13i	−0.362925	−	0.326779i
$487$	−6416.87	−	4167.16i	−0.597076	−	0.387746i	0.210427	−	0.977610i	$-0.432515\pi$
$487$	−6416.87	−	4167.16i	−0.597076	−	0.387746i	−0.807503	+	0.589864i	$0.799181\pi$
$488$	−136.676	+	2607.93i	−0.0126783	+	0.241917i
$489$	−1298.86	−	3997.48i	−0.120116	−	0.369678i
$490$	−11945.4	−	7380.47i	−1.10131	−	0.680440i
$491$	−2772.50	+	8532.86i	−0.254829	+	0.784282i	0.739035	+	0.673668i	$0.235282\pi$
$491$	−2772.50	+	8532.86i	−0.254829	+	0.784282i	−0.993863	+	0.110615i	$0.964718\pi$
$492$	253.951	+	97.4825i	0.0232703	+	0.00893262i
$493$	3898.26	−	14548.5i	0.356124	−	1.32907i
$494$	4208.08	+	442.287i	0.383260	+	0.0402823i
$495$	−543.161	+	2599.89i	−0.0493197	+	0.236073i
$496$	5643.06	+	7767.01i	0.510848	+	0.703123i
$497$	−7474.79	+	10496.8i	−0.674628	+	0.947376i
$498$	−13105.3	−	6677.50i	−1.17925	−	0.600855i
$499$	−14142.1	−	8164.94i	−1.26871	−	0.732490i	−0.293967	−	0.955816i	$-0.594975\pi$
$499$	−14142.1	−	8164.94i	−1.26871	−	0.732490i	−0.974744	+	0.223325i	$0.928309\pi$
$500$	6504.26	−	3846.45i	0.581758	−	0.344037i
$501$	6958.78	+	12053.0i	0.620550	+	1.07482i
$502$	17966.5	−	11667.6i	1.59738	−	1.03735i
$503$	4695.86	+	743.751i	0.416259	+	0.0659289i	0.361051	−	0.932546i	$-0.382418\pi$
$503$	4695.86	+	743.751i	0.416259	+	0.0659289i	0.0552075	+	0.998475i	$0.482418\pi$
$504$	317.045	−	850.024i	0.0280205	−	0.0751252i
$505$	−5025.94	+	1652.41i	−0.442874	+	0.145607i
$506$	−3100.48	+	1380.42i	−0.272398	+	0.121279i
$507$	−3585.27	−	960.669i	−0.314058	−	0.0841515i
$508$	8482.29	+	10474.8i	0.740829	+	0.914847i
$509$	8032.16	+	8920.62i	0.699448	+	0.776816i	0.983288	−	0.182055i	$-0.0582750\pi$
$509$	8032.16	+	8920.62i	0.699448	+	0.776816i	−0.283840	+	0.958872i	$0.591608\pi$
$510$	−12773.4	−	1977.50i	−1.10905	−	0.171697i
$511$	14975.4	−	5912.66i	1.29643	−	0.511861i
$512$	−9298.85	+	4738.00i	−0.802647	+	0.408969i
$513$	−3639.30	−	190.728i	−0.313214	−	0.0164149i
$514$	−14659.1	+	16280.5i	−1.25794	+	1.39709i
$515$	565.465	−	461.176i	0.0483832	−	0.0394599i
$516$	4543.56	−	4091.04i	0.387634	−	0.349027i
$517$	−1403.55	+	222.300i	−0.119396	+	0.0189105i
$518$	−657.978	+	744.894i	−0.0558106	+	0.0631829i
$519$	12076.8	−	16622.3i	1.02141	−	1.40585i
$520$	3802.67	−	1708.96i	0.320689	−	0.144121i
$521$	2123.06	−	4768.47i	0.178528	−	0.400980i	−0.802010	−	0.597311i	$-0.796236\pi$
$521$	2123.06	−	4768.47i	0.178528	−	0.400980i	0.980538	+	0.196331i	$0.0629027\pi$
$522$	−1831.44	−	4771.06i	−0.153563	−	0.400045i
$523$	12438.6	+	19153.8i	1.03997	+	1.60141i	0.769466	+	0.638688i	$0.220522\pi$
$523$	12438.6	+	19153.8i	1.03997	+	1.60141i	0.270500	+	0.962720i	$0.412811\pi$
$524$	−15525.7			−1.29436
$525$	−3606.47	−	12623.3i	−0.299808	−	1.04938i
$526$	14850.3			1.23100
$527$	−3731.39	−	5745.84i	−0.308429	−	0.474939i
$528$	−7300.79	−	19019.2i	−0.601754	−	1.56762i
$529$	−4783.94	+	10744.9i	−0.393190	+	0.883119i
$530$	13327.3	+	14698.1i	1.09226	+	1.20461i
$531$	821.662	−	1130.92i	0.0671508	−	0.0924252i
$532$	937.125	+	2793.43i	0.0763713	+	0.227652i
$533$	344.126	−	54.5043i	0.0279658	−	0.00442935i
$534$	8496.44	−	7650.23i	0.688534	−	0.619958i
$535$	−14729.6	+	823.425i	−1.19031	+	0.0665416i
$536$	−2260.22	+	2510.23i	−0.182139	+	0.202286i
$537$	−18939.6	−	992.581i	−1.52198	−	0.0797636i
$538$	−27178.4	+	13848.1i	−2.17796	+	1.10973i
$539$	−1351.60	+	15735.3i	−0.108010	+	1.25746i
$540$	6659.40	−	3422.42i	0.530695	−	0.272736i
$541$	6225.28	+	6913.87i	0.494724	+	0.549446i	0.937863	−	0.347007i	$-0.112802\pi$
$541$	6225.28	+	6913.87i	0.494724	+	0.549446i	−0.443139	+	0.896453i	$0.646135\pi$
$542$	3707.18	+	4577.98i	0.293795	+	0.362807i
$543$	236.989	+	63.5009i	0.0187296	+	0.00501857i
$544$	10667.1	−	4749.28i	0.840711	−	0.374309i
$545$	37.7142	+	10822.8i	0.00296422	+	0.850636i
$546$	2504.56	+	14894.3i	0.196310	+	1.16743i
$547$	4362.44	+	690.942i	0.340995	+	0.0540083i	0.324584	−	0.945857i	$-0.394776\pi$
$547$	4362.44	+	690.942i	0.340995	+	0.0540083i	0.0164116	+	0.999865i	$0.494776\pi$
$548$	10382.8	−	6742.68i	0.809365	−	0.525608i
$549$	−709.559	−	1228.99i	−0.0551607	−	0.0955412i
$550$	−17754.0	−	11354.5i	−1.37642	−	0.880283i
$551$	−6893.28	−	3979.84i	−0.532965	−	0.307707i
$552$	965.741	+	492.070i	0.0744650	+	0.0379418i
$553$	−20712.5	+	9458.99i	−1.59274	+	0.727373i
$554$	−10965.3	−	15092.5i	−0.840925	−	1.15743i
$555$	−923.812	+	100.353i	−0.0706552	+	0.00767519i
$556$	7400.22	+	777.794i	0.564459	+	0.0593270i
$557$	3019.87	−	11270.3i	0.229724	−	0.857341i	−0.750733	−	0.660606i	$-0.770299\pi$
$557$	3019.87	−	11270.3i	0.229724	−	0.857341i	0.980457	−	0.196735i	$-0.0630338\pi$
$558$	−2170.21	−	833.067i	−0.164646	−	0.0632017i
$559$	2419.95	−	7447.83i	0.183100	−	0.563524i
$560$	12145.1	+	10652.9i	0.916474	+	0.803869i
$561$	4492.51	+	13826.5i	0.338100	+	1.04056i
$562$	−903.382	+	17237.6i	−0.0678058	+	1.29381i
$563$	7998.06	+	5194.00i	0.598718	+	0.388812i	0.808120	−	0.589018i	$-0.200485\pi$
$563$	7998.06	+	5194.00i	0.598718	+	0.388812i	−0.209403	+	0.977830i	$0.567152\pi$
$564$	−703.251	−	633.210i	−0.0525039	−	0.0472747i
$565$	−6330.56	−	23300.9i	−0.471378	−	1.73500i
$566$	5171.79	+	1680.42i	0.384076	+	0.124794i
$567$	−3385.93	−	15216.0i	−0.250786	−	1.12701i
$568$	4671.27	−	4671.27i	0.345074	−	0.345074i
$569$	3496.78	+	7853.89i	0.257632	+	0.578651i	0.995335	−	0.0964741i	$-0.0307565\pi$
$569$	3496.78	+	7853.89i	0.257632	+	0.578651i	−0.737704	+	0.675125i	$0.764090\pi$
$570$	−2756.56	+	6249.85i	−0.202561	+	0.459259i
$571$	−3693.62	−	1644.50i	−0.270706	−	0.120526i	0.266895	−	0.963726i	$-0.414002\pi$
$571$	−3693.62	−	1644.50i	−0.270706	−	0.120526i	−0.537600	+	0.843200i	$0.680669\pi$
$572$	7598.81	+	6153.40i	0.555458	+	0.449801i
$573$	−5614.83	+	11019.7i	−0.409359	+	0.803413i
$574$	332.437	+	501.395i	0.0241736	+	0.0364596i
$575$	2482.53	−	410.950i	0.180050	−	0.0298049i
$576$	370.801	−	642.246i	0.0268230	−	0.0464588i
$577$	−81.4162	−	1553.51i	−0.00587418	−	0.112086i	−0.999993	−	0.00378954i	$-0.998794\pi$
$577$	−81.4162	−	1553.51i	−0.00587418	−	0.112086i	0.994119	−	0.108296i	$-0.0345396\pi$
$578$	6197.78	−	2379.11i	0.446010	−	0.171207i
$579$	−306.929	−	2920.23i	−0.0220303	−	0.209604i
$580$	16353.4	−	56.9868i	1.17075	−	0.00407974i
$581$	−6066.80	−	11631.7i	−0.433207	−	0.830579i
$582$	18148.9	+	18148.9i	1.29260	+	1.29260i
$583$	7997.29	−	20833.6i	0.568120	−	1.48000i
$584$	−8073.57	+	1716.09i	−0.572066	+	0.121596i
$585$	−1227.25	+	1904.29i	−0.0867356	+	0.134586i
$586$	−2087.55	+	9821.13i	−0.147160	+	0.692333i
$587$	7022.00	+	13781.5i	0.493746	+	0.969032i	0.994628	+	0.103516i	$0.0330093\pi$
$587$	7022.00	+	13781.5i	0.493746	+	0.969032i	−0.500881	+	0.865516i	$0.666991\pi$
$588$	−8709.90	+	5894.96i	−0.610868	+	0.413442i
$589$	−3443.41	+	1118.83i	−0.240888	+	0.0782694i
$590$	6073.35	+	9281.17i	0.423789	+	0.647626i
$591$	4425.81	+	20821.8i	0.308043	+	1.44923i
$592$	888.655	−	719.618i	0.0616951	−	0.0499597i
$593$	3854.22	−	1032.73i	0.266903	−	0.0715166i	−0.122885	−	0.992421i	$-0.539215\pi$
$593$	3854.22	−	1032.73i	0.266903	−	0.0715166i	0.389789	+	0.920904i	$0.372548\pi$
$594$	−16893.5	−	12273.9i	−1.16692	−	0.847816i
$595$	−8257.25	−	8045.28i	−0.568932	−	0.554326i
$596$	−3504.04	+	2545.83i	−0.240824	+	0.174969i
$597$	11734.4	−	14490.8i	0.804450	−	0.993413i
$598$	−2890.91	+	151.506i	−0.197689	+	0.0103604i
$599$	−343.689	+	198.429i	−0.0234437	+	0.0135352i	−0.511676	−	0.859178i	$-0.670975\pi$
$599$	−343.689	+	198.429i	−0.0234437	+	0.0135352i	0.488232	+	0.872714i	$0.337642\pi$
$600$	750.140	+	6688.37i	0.0510406	+	0.455086i
$601$		−	8246.41i		−	0.559697i	−0.960044	−	0.279849i	$-0.909716\pi$
$601$		−	8246.41i		−	0.559697i	0.960044	−	0.279849i	$-0.0902843\pi$
$602$	13433.4	−	1541.30i	0.909477	−	0.104350i
$603$	287.143	−	1812.95i	0.0193920	−	0.122436i
$604$	−444.334	+	46.7014i	−0.0299333	+	0.00314611i
$605$	−891.616	+	8777.27i	−0.0599162	+	0.589829i
$606$	−1027.08	+	9772.02i	−0.0688487	+	0.655052i
$607$	−6376.99	−	23799.2i	−0.426415	−	1.59140i	−0.760813	−	0.648971i	$-0.775200\pi$
$607$	−6376.99	−	23799.2i	−0.426415	−	1.59140i	0.334398	−	0.942432i	$-0.391467\pi$
$608$	−965.311	−	6094.73i	−0.0643890	−	0.406536i
$609$	7092.05	−	27512.6i	0.471895	−	1.83065i
$610$	11115.2	−	1800.21i	0.737776	−	0.119489i
$611$	−1185.61	−	252.009i	−0.0785019	−	0.0166861i
$612$	−845.932	+	1302.62i	−0.0558738	+	0.0860382i
$613$	9800.15	−	15090.9i	0.645717	−	0.994317i	−0.352569	−	0.935786i	$-0.614692\pi$
$613$	9800.15	−	15090.9i	0.645717	−	0.994317i	0.998286	−	0.0585308i	$-0.0186416\pi$
$614$	−24084.7	−	5119.37i	−1.58303	−	0.336484i
$615$	−86.0529	+	555.846i	−0.00564225	+	0.0364453i
$616$	2021.00	−	7840.19i	0.132189	−	0.512809i
$617$	2634.93	+	16636.3i	0.171926	+	1.08550i	0.911161	+	0.412051i	$0.135187\pi$
$617$	2634.93	+	16636.3i	0.171926	+	1.08550i	−0.739235	+	0.673448i	$0.764813\pi$
$618$	−350.747	−	1309.00i	−0.0228303	−	0.0852037i
$619$	2755.07	−	26212.7i	0.178894	−	1.70206i	−0.425157	−	0.905119i	$-0.639781\pi$
$619$	2755.07	−	26212.7i	0.178894	−	1.70206i	0.604052	−	0.796945i	$-0.293552\pi$
$620$	4958.18	−	5545.35i	0.321170	−	0.359204i
$621$	2479.64	−	260.620i	0.160233	−	0.0168411i
$622$	238.188	−	1503.86i	0.0153544	−	0.0969440i
$623$	10131.0	−	1162.39i	0.651507	−	0.0747516i
$624$		−	17376.9i		−	1.11479i
$625$	10616.0	+	11464.8i	0.679424	+	0.733746i
$626$	−3585.06	+	2069.83i	−0.228894	+	0.132152i
$627$	7672.40	−	402.094i	0.488686	−	0.0256110i
$628$	−3224.31	+	3981.69i	−0.204879	+	0.253004i
$629$	−660.168	+	479.640i	−0.0418484	+	0.0304046i
$630$	−3871.16	−	561.641i	−0.244811	−	0.0355179i
$631$	−5818.38	−	4227.30i	−0.367078	−	0.266698i	0.388920	−	0.921271i	$-0.372848\pi$
$631$	−5818.38	−	4227.30i	−0.367078	−	0.266698i	−0.755998	+	0.654574i	$0.772848\pi$
$632$	11275.4	−	3021.24i	0.709672	−	0.190156i
$633$	18135.4	−	14685.7i	1.13873	−	0.922125i
$634$	−7870.35	−	37027.1i	−0.493015	−	2.31945i
$635$	−17463.8	+	21720.3i	−1.09138	+	1.35739i
$636$	14133.5	−	4592.26i	0.881180	−	0.286313i
$637$	−5886.20	+	12117.1i	−0.366122	+	0.753683i
$638$	−20705.8	−	40637.4i	−1.28487	−	2.52171i
$639$	−746.373	+	3511.41i	−0.0462066	+	0.217385i
$640$	−8136.47	−	9976.41i	−0.502534	−	0.616176i
$641$	−3299.38	+	701.305i	−0.203304	+	0.0432135i	−0.308438	−	0.951245i	$-0.599806\pi$
$641$	−3299.38	+	701.305i	−0.203304	+	0.0432135i	0.105134	+	0.994458i	$0.466473\pi$
$642$	−9818.88	+	25579.1i	−0.603614	+	1.57247i
$643$	6544.77	+	6544.77i	0.401401	+	0.401401i	0.878726	−	0.477326i	$-0.158394\pi$
$643$	6544.77	+	6544.77i	0.401401	+	0.401401i	−0.477326	+	0.878726i	$0.658394\pi$
$644$	−932.226	−	1787.34i	−0.0570417	−	0.109365i
$645$	10253.6	+	7395.22i	0.625945	+	0.451452i
$646$	627.003	+	5965.53i	0.0381874	+	0.363329i
$647$	3671.85	−	1409.49i	0.223115	−	0.0856458i	−0.244243	−	0.969714i	$-0.578539\pi$
$647$	3671.85	−	1409.49i	0.223115	−	0.0856458i	0.467358	+	0.884068i	$0.345206\pi$
$648$	418.235	+	7980.40i	0.0253547	+	0.483796i
$649$	6237.72	−	10804.0i	0.377275	−	0.653460i
$650$	−10666.9	−	14468.6i	−0.643679	−	0.873087i
$651$	−7141.61	−	10771.3i	−0.429957	−	0.648480i
$652$	1819.40	−	3570.78i	0.109284	−	0.214482i
$653$	13400.4	+	10851.4i	0.803061	+	0.650306i	0.940344	−	0.340226i	$-0.110504\pi$
$653$	13400.4	+	10851.4i	0.803061	+	0.650306i	−0.137283	+	0.990532i	$0.543837\pi$
$654$	18362.7	+	8175.58i	1.09792	+	0.488824i
$655$	−6784.06	−	31378.4i	−0.404695	−	1.87184i
$656$	−281.521	−	632.305i	−0.0167554	−	0.0376332i
$657$	3171.56	−	3171.56i	0.188332	−	0.188332i
$658$	−454.593	−	2042.89i	−0.0269330	−	0.121034i
$659$	6615.94	+	2149.65i	0.391078	+	0.127069i	0.497954	−	0.867203i	$-0.334085\pi$
$659$	6615.94	+	2149.65i	0.391078	+	0.127069i	−0.106876	+	0.994272i	$0.534085\pi$
$660$	−13208.3	+	8643.16i	−0.778989	+	0.509749i
$661$	12828.8	+	11551.1i	0.754889	+	0.679705i	0.953844	−	0.300303i	$-0.0970879\pi$
$661$	12828.8	+	11551.1i	0.754889	+	0.679705i	−0.198954	+	0.980009i	$0.563755\pi$
$662$	−28438.6	−	18468.2i	−1.66963	−	1.08427i
$663$	−648.990	+	12383.5i	−0.0380161	+	0.725391i
$664$	2078.27	+	6396.25i	0.121464	+	0.373829i
$665$	−5236.22	+	3114.60i	−0.305341	+	0.181623i
$666$	−85.5594	+	263.325i	−0.00497802	+	0.0153208i
$667$	5084.02	+	1951.57i	0.295133	+	0.113291i
$668$	−3434.48	+	12817.6i	−0.198928	+	0.742409i
$669$	−23331.7	−	2452.26i	−1.34836	−	0.141719i
$670$	12638.3	+	7238.15i	0.728749	+	0.417364i
$671$	−7444.20	−	10246.1i	−0.428287	−	0.589486i
$672$	20035.8	−	9149.99i	1.15015	−	0.525251i
$673$	491.355	+	250.358i	0.0281431	+	0.0143397i	0.468005	−	0.883726i	$-0.344973\pi$
$673$	491.355	+	250.358i	0.0281431	+	0.0143397i	−0.439862	+	0.898065i	$0.644973\pi$
$674$	−20425.9	−	11792.9i	−1.16732	−	0.673954i
$675$	9826.80	+	11963.6i	0.560346	+	0.682193i
$676$	−1769.49	−	3064.85i	−0.100677	−	0.174377i
$677$	−21188.2	+	13759.8i	−1.20285	+	0.781138i	−0.981012	−	0.193947i	$-0.937871\pi$
$677$	−21188.2	+	13759.8i	−1.20285	+	0.781138i	−0.221834	+	0.975084i	$0.571204\pi$
$678$	−44291.6	−	7015.09i	−2.50886	−	0.397364i
$679$	3796.19	+	22575.5i	0.214557	+	1.27595i
$680$	3490.56	+	4769.30i	0.196848	+	0.268962i
$681$	−8265.28	+	3679.94i	−0.465090	+	0.207071i
$682$	−20039.0	−	5369.43i	−1.12512	−	0.301475i
$683$	8775.71	+	10837.1i	0.491645	+	0.607131i	0.961227	−	0.275758i	$-0.0889289\pi$
$683$	8775.71	+	10837.1i	0.491645	+	0.607131i	−0.469582	+	0.882889i	$0.655596\pi$
$684$	549.235	+	609.987i	0.0307025	+	0.0340986i
$685$	18164.2	+	18038.1i	1.01317	+	1.00613i
$686$	−23253.2	−	553.733i	−1.29419	−	0.0308187i
$687$	21655.2	−	11033.9i	1.20262	−	0.612764i
$688$	−15535.5	−	814.184i	−0.860883	−	0.0451169i
$689$	12736.7	−	14145.5i	0.704250	−	0.782148i
$690$	1193.82	−	4518.31i	0.0658664	−	0.249288i
$691$	2775.74	−	2499.29i	0.152814	−	0.137594i	−0.589178	−	0.808003i	$-0.700548\pi$
$691$	2775.74	−	2499.29i	0.152814	−	0.137594i	0.741991	+	0.670409i	$0.233882\pi$
$692$	19348.8	−	3064.55i	1.06291	−	0.168348i
$693$	1399.34	+	4171.23i	0.0767051	+	0.228647i
$694$	14607.5	−	20105.5i	0.798980	−	1.09970i
$695$	1661.60	+	15296.2i	0.0906881	+	0.834845i
$696$	−5924.32	+	13306.2i	−0.322645	+	0.724672i
$697$	177.008	+	461.121i	0.00961929	+	0.0250591i
$698$	11681.5	+	17987.9i	0.633454	+	0.975433i
$699$	−13889.0			−0.751544
$700$	6079.11	−	10942.0i	0.328241	−	0.590815i
$701$	−19010.7			−1.02429			−0.512143	−	0.858900i	$-0.671148\pi$
$701$	−19010.7			−1.02429			−0.512143	+	0.858900i	$0.671148\pi$
$702$	−9700.69	−	14937.8i	−0.521551	−	0.803119i
$703$	154.542	+	402.595i	0.00829112	+	0.0215991i
$704$	2691.94	−	6046.19i	0.144114	−	0.323685i
$705$	972.467	−	1698.00i	0.0519507	−	0.0907098i
$706$	−11554.9	+	15904.0i	−0.615971	+	0.847812i
$707$	−5801.95	+	6568.37i	−0.308635	+	0.349404i
$708$	8205.51	−	1299.63i	0.435568	−	0.0689872i
$709$	5387.87	−	4851.26i	0.285396	−	0.256972i	−0.513981	−	0.857802i	$-0.671830\pi$
$709$	5387.87	−	4851.26i	0.285396	−	0.256972i	0.799377	+	0.600830i	$0.205163\pi$
$710$	−23942.5	−	15430.1i	−1.26556	−	0.815609i
$711$	−4244.50	+	4714.00i	−0.223884	+	0.248648i
$712$	−5220.59	−	273.600i	−0.274789	−	0.0144011i
$713$	2207.11	−	1124.58i	0.115928	−	0.0590684i
$714$	−19915.1	+	7862.97i	−1.04385	+	0.412135i
$715$	−9116.05	+	18046.4i	−0.476813	+	0.943915i
$716$	−12099.8	−	13438.2i	−0.631551	−	0.701409i
$717$	23126.7	+	28559.1i	1.20458	+	1.48753i
$718$	−11718.9	−	3140.08i	−0.609119	−	0.163213i
$719$	23924.2	−	10651.8i	1.24092	−	0.552494i	0.321928	−	0.946764i	$-0.395669\pi$
$719$	23924.2	−	10651.8i	1.24092	−	0.552494i	0.918995	+	0.394270i	$0.129003\pi$
$720$	4285.05	+	1375.81i	0.221798	+	0.0712129i
$721$	422.407	−	1132.51i	0.0218187	−	0.0584976i
$722$	−21674.5	−	3432.90i	−1.11723	−	0.176952i
$723$	−17949.4	+	11656.5i	−0.923301	+	0.599599i
$724$	116.965	+	202.589i	0.00600409	+	0.0103994i
$725$	7260.90	+	33026.3i	0.371949	+	1.69182i
$726$	14190.0	+	8192.63i	0.725402	+	0.418811i
$727$	16650.6	+	8483.88i	0.849429	+	0.432806i	0.823810	−	0.566866i	$-0.191844\pi$
$727$	16650.6	+	8483.88i	0.849429	+	0.432806i	0.0256190	+	0.999672i	$0.491844\pi$
$728$	4005.90	−	5625.46i	0.203940	−	0.286392i
$729$	8594.43	+	11829.2i	0.436642	+	0.600986i
$730$	14588.4	+	32461.2i	0.739645	+	1.64581i
$731$	11040.9	+	1160.44i	0.558633	+	0.0587147i
$732$	2182.86	−	8146.55i	0.110220	−	0.411346i
$733$	−24691.7	−	9478.25i	−1.24421	−	0.477609i	−0.354899	−	0.934905i	$-0.615485\pi$
$733$	−24691.7	−	9478.25i	−1.24421	−	0.477609i	−0.889315	+	0.457296i	$0.848818\pi$
$734$	844.246	−	2598.32i	0.0424546	−	0.130662i
$735$	−15719.9	−	15027.4i	−0.788896	−	0.754143i
$736$	1304.60	+	4015.15i	0.0653372	+	0.201087i
$737$	857.329	−	16358.8i	0.0428495	−	0.817618i
$738$	140.554	+	91.2768i	0.00701065	+	0.00455277i
$739$	78.0944	+	70.3165i	0.00388734	+	0.00350018i	0.671072	−	0.741392i	$-0.265834\pi$
$739$	78.0944	+	70.3165i	0.00388734	+	0.00350018i	−0.667185	+	0.744892i	$0.732501\pi$
$740$	−690.488	−	555.173i	−0.0343011	−	0.0275792i
$741$	6232.53	+	2025.07i	0.308985	+	0.100395i
$742$	31352.7	+	9858.23i	1.55121	+	0.487745i
$743$	−1133.40	+	1133.40i	−0.0559631	+	0.0559631i	−0.734534	−	0.678571i	$-0.762599\pi$
$743$	−1133.40	+	1133.40i	−0.0559631	+	0.0559631i	0.678571	+	0.734534i	$0.262599\pi$
$744$	2694.80	+	6052.61i	0.132790	+	0.298252i
$745$	−6676.40	−	5969.46i	−0.328328	−	0.293563i
$746$	−15777.6	−	7024.62i	−0.774340	−	0.344758i
$747$	−2840.19	−	2299.94i	−0.139113	−	0.112651i
$748$	−6292.96	+	12350.6i	−0.307611	+	0.603721i
$749$	−20367.6	+	13504.2i	−0.993613	+	0.658788i
$750$	27503.6	−	9255.43i	1.33905	−	0.450614i
$751$	819.087	−	1418.70i	0.0397988	−	0.0689336i	−0.845440	−	0.534071i	$-0.820662\pi$
$751$	819.087	−	1418.70i	0.0397988	−	0.0689336i	0.885239	+	0.465137i	$0.153995\pi$
$752$	126.019	+	2404.59i	0.00611096	+	0.116604i
$753$	30975.1	−	11890.2i	1.49906	−	0.575437i
$754$	−4066.40	−	38689.2i	−0.196405	−	1.86867i
$755$	−288.541	−	877.621i	−0.0139087	−	0.0423045i
$756$	6655.77	−	10465.7i	0.320196	−	0.503484i
$757$	−26296.9	−	26296.9i	−1.26258	−	1.26258i	−0.949836	−	0.312748i	$-0.898750\pi$
$757$	−26296.9	−	26296.9i	−1.26258	−	1.26258i	−0.312748	−	0.949836i	$-0.601250\pi$
$758$	7682.76	−	20014.3i	0.368140	−	0.959039i
$759$	−5141.52	+	1092.86i	−0.245883	+	0.0522641i
$760$	2911.98	−	1129.46i	0.138985	−	0.0539078i
$761$	−15.7664	+	74.1751i	−0.000751028	+	0.00353331i	−0.978522	−	0.206145i	$-0.933908\pi$
$761$	−15.7664	+	74.1751i	−0.000751028	+	0.00353331i	0.977770	+	0.209678i	$0.0672416\pi$
$762$	23499.2	+	46119.7i	1.11717	+	2.19257i
$763$	9111.38	+	15440.1i	0.432312	+	0.732596i
$764$	−11215.0	+	3643.96i	−0.531077	+	0.172557i
$765$	−3002.32	−	1140.49i	−0.141894	−	0.0539015i
$766$	−8345.00	−	39260.1i	−0.393626	−	1.85186i
$767$	8269.69	−	6696.66i	0.389311	−	0.315258i
$768$	−29393.4	+	7875.94i	−1.38105	+	0.370050i
$769$	−17086.5	−	12414.1i	−0.801244	−	0.582138i	0.110035	−	0.993928i	$-0.464904\pi$
$769$	−17086.5	−	12414.1i	−0.801244	−	0.582138i	−0.911279	+	0.411790i	$0.864904\pi$
$770$	−34882.7	−	1373.63i	−1.63258	−	0.0642883i
$771$	−27449.9	+	19943.5i	−1.28221	+	0.931581i
$772$	1761.88	−	2175.74i	0.0821392	−	0.101433i
$773$	−8713.28	+	456.643i	−0.405427	+	0.0212475i	−0.253960	−	0.967215i	$-0.581733\pi$
$773$	−8713.28	+	456.643i	−0.405427	+	0.0212475i	−0.151467	+	0.988462i	$0.548400\pi$
$774$	3262.18	−	1883.42i	0.151494	−	0.0874652i
$775$	13374.0	+	7597.71i	0.619882	+	0.352152i
$776$		−	11735.9i		−	0.542905i
$777$	−1236.65	+	916.588i	−0.0570974	+	0.0423197i
$778$	−6348.23	+	40081.2i	−0.292539	+	1.84702i
$779$	259.596	−	27.2846i	0.0119396	−	0.00125491i
$780$	−13159.9	+	2845.19i	−0.604104	+	0.130608i
$781$	−3348.83	+	31861.9i	−0.153432	+	1.45981i
$782$	−1062.16	−	3964.05i	−0.0485715	−	0.181271i
$783$	5241.45	+	33093.2i	0.239226	+	1.51042i
$784$	26277.4	+	5064.70i	1.19704	+	0.230717i
$785$	−9456.13	−	4776.71i	−0.429941	−	0.217182i
$786$	−58320.3	−	12396.4i	−2.64659	−	0.562550i
$787$	18885.8	−	29081.5i	0.855406	−	1.31721i	−0.0915352	−	0.995802i	$-0.529177\pi$
$787$	18885.8	−	29081.5i	0.855406	−	1.31721i	0.946941	−	0.321408i	$-0.104156\pi$
$788$	−11054.1	+	17021.8i	−0.499729	+	0.769515i
$789$	22497.2	+	4781.93i	1.01511	+	0.215768i
$790$	−23006.1	−	44765.7i	−1.03610	−	2.01607i
$791$	−28550.1	−	28011.8i	−1.28334	−	1.25915i
$792$	−352.841	−	2227.75i	−0.0158304	−	0.0999491i
$793$	−2795.93	−	10434.6i	−0.125204	−	0.467266i
$794$	−2924.95	+	27829.1i	−0.130734	+	1.24385i
$795$	15457.0	+	26558.1i	0.689563	+	1.18480i
$796$	17680.9	−	1858.34i	0.787290	−	0.0827475i
$797$	3692.63	−	23314.4i	0.164115	−	1.03618i	−0.758841	−	0.651276i	$-0.774234\pi$
$797$	3692.63	−	23314.4i	0.164115	−	1.03618i	0.922956	−	0.384906i	$-0.125766\pi$
$798$	1289.80	+	11241.4i	0.0572160	+	0.498674i
$799$		−	1718.31i		−	0.0760821i
$800$	−16355.3	+	20487.4i	−0.722807	+	0.905423i
$801$	2460.21	−	1420.40i	0.108523	−	0.0626560i
$802$	7448.47	−	390.358i	0.327948	−	0.0171871i
$803$	25190.7	−	31107.9i	1.10705	−	1.36709i
$804$	8825.42	−	6412.04i	0.387125	−	0.281263i
$805$	3204.98	−	2665.08i	0.140324	−	0.116685i
$806$	−14316.0	−	10401.2i	−0.625631	−	0.454547i
$807$	−45632.6	+	12227.2i	−1.99051	+	0.533356i
$808$	3491.60	−	2827.44i	0.152022	−	0.123105i
$809$	−215.401	−	1013.38i	−0.00936105	−	0.0440403i	0.973219	−	0.229879i	$-0.0738331\pi$
$809$	−215.401	−	1013.38i	−0.00936105	−	0.0440403i	−0.982580	+	0.185839i	$0.940500\pi$
$810$	33251.0	−	9033.89i	1.44237	−	0.391875i
$811$	35331.9	−	11480.0i	1.52980	−	0.497063i	0.581263	−	0.813716i	$-0.302559\pi$
$811$	35331.9	−	11480.0i	1.52980	−	0.497063i	0.948542	+	0.316653i	$0.102559\pi$
$812$	23330.3	−	13767.5i	1.00829	−	0.595004i
$813$	4141.97	+	8129.07i	0.178678	+	0.350675i
$814$	−513.742	+	2416.97i	−0.0221212	+	0.104072i
$815$	8011.76	+	2116.85i	0.344343	+	0.0909816i
$816$	24095.8	−	5121.72i	1.03373	−	0.219725i
$817$	2102.51	−	5477.22i	0.0900336	−	0.234546i
$818$	32749.1	+	32749.1i	1.39981	+	1.39981i
$819$	−160.731	+	3749.34i	−0.00685762	+	0.159967i
$820$	−432.765	+	316.732i	−0.0184303	+	0.0134888i
$821$	−3099.47	−	29489.5i	−0.131757	−	1.25358i	−0.838022	−	0.545636i	$-0.816288\pi$
$821$	−3099.47	−	29489.5i	−0.131757	−	1.25358i	0.706265	−	0.707947i	$-0.250379\pi$
$822$	44385.4	−	17038.0i	1.88336	−	0.722953i
$823$	−1238.04	−	23623.3i	−0.0524368	−	1.00055i	−0.890501	−	0.454982i	$-0.849646\pi$
$823$	−1238.04	−	23623.3i	−0.0524368	−	1.00055i	0.838064	−	0.545572i	$-0.183688\pi$
$824$	−309.827	+	536.636i	−0.0130987	+	0.0226876i
$825$	−23239.8	−	22918.1i	−0.980736	−	0.967160i
$826$	16449.5	+	8185.17i	0.692918	+	0.344793i
$827$	−10328.3	+	20270.4i	−0.434279	+	0.852321i	0.565344	+	0.824856i	$0.308744\pi$
$827$	−10328.3	+	20270.4i	−0.434279	+	0.852321i	−0.999623	+	0.0274654i	$0.991256\pi$
$828$	−436.425	−	353.410i	−0.0183174	−	0.0148332i
$829$	6492.25	+	2890.54i	0.271997	+	0.121101i	0.538203	−	0.842815i	$-0.319103\pi$
$829$	6492.25	+	2890.54i	0.271997	+	0.121101i	−0.266206	+	0.963916i	$0.585770\pi$
$830$	25062.3	−	14586.4i	1.04810	−	0.610003i
$831$	−11751.8	−	26395.0i	−0.490573	−	1.10184i
$832$	3991.79	−	3991.79i	0.166335	−	0.166335i
$833$	−18537.2	−	4590.72i	−0.771038	−	0.190947i
$834$	27177.0	+	8830.33i	1.12837	+	0.366630i
$835$	−27406.0	−	1340.54i	−1.13584	−	0.0555584i
$836$	5443.79	+	4901.61i	0.225212	+	0.202782i
$837$	12782.0	+	8300.71i	0.527849	+	0.342789i
$838$	−169.027	+	3225.23i	−0.00696771	+	0.132952i
$839$	−4127.35	−	12702.7i	−0.169835	−	0.522699i	0.829525	−	0.558470i	$-0.188611\pi$
$839$	−4127.35	−	12702.7i	−0.169835	−	0.522699i	−0.999360	+	0.0357707i	$0.988611\pi$
$840$	6669.79	+	8933.58i	0.273964	+	0.366950i
$841$	−15077.7	+	46404.4i	−0.618217	+	1.90268i
$842$	37589.9	+	14429.4i	1.53852	+	0.590583i
$843$	−6919.20	+	25822.8i	−0.282693	+	1.05502i
$844$	22127.8	+	2325.73i	0.902454	+	0.0948518i
$845$	5421.07	−	4915.47i	0.220699	−	0.200115i
$846$	−342.696	−	471.681i	−0.0139269	−	0.0191687i
$847$	6071.00	+	13293.7i	0.246283	+	0.539290i
$848$	−33691.8	−	17166.8i	−1.36436	−	0.695178i
$849$	7293.80	+	4211.08i	0.294844	+	0.170228i
$850$	16919.0	−	19055.9i	0.682727	−	0.768956i
$851$	−147.519	−	255.510i	−0.00594228	−	0.0102923i
$852$	−17892.9	+	11619.8i	−0.719482	+	0.467237i
$853$	23658.6	+	3747.16i	0.949656	+	0.150411i	0.611999	−	0.790859i	$-0.290366\pi$
$853$	23658.6	+	3747.16i	0.949656	+	0.150411i	0.337657	+	0.941269i	$0.390366\pi$
$854$	14383.2	−	11875.7i	0.576328	−	0.475854i
$855$	−992.830	+	1376.58i	−0.0397124	+	0.0550619i
$856$	11445.0	−	5095.63i	0.456987	−	0.203464i
$857$	−16882.3	−	4523.61i	−0.672917	−	0.180308i	−0.0938486	−	0.995586i	$-0.529917\pi$
$857$	−16882.3	−	4523.61i	−0.672917	−	0.180308i	−0.579069	+	0.815279i	$0.696584\pi$
$858$	23630.8	+	29181.7i	0.940261	+	1.16113i
$859$	−17526.5	−	19465.2i	−0.696155	−	0.773159i	0.286604	−	0.958049i	$-0.407474\pi$
$859$	−17526.5	−	19465.2i	−0.696155	−	0.773159i	−0.982759	+	0.184890i	$0.940807\pi$
$860$	1927.11	+	11898.8i	0.0764113	+	0.471796i
$861$	342.165	+	866.626i	0.0135435	+	0.0343026i
$862$	8507.94	−	4335.01i	0.336174	−	0.171289i
$863$	−47564.2	−	2492.73i	−1.87613	−	0.0983240i	−0.920119	−	0.391639i	$-0.871908\pi$
$863$	−47564.2	−	2492.73i	−1.87613	−	0.0983240i	−0.956016	+	0.293315i	$0.905241\pi$
$864$	−17380.8	+	19303.3i	−0.684383	+	0.760084i
$865$	14648.3	+	37766.1i	0.575787	+	1.48449i
$866$	−14453.4	+	13013.9i	−0.567145	+	0.510660i
$867$	10155.3	−	1608.44i	0.397800	−	0.0630053i
$868$	2447.12	−	12076.8i	0.0956918	−	0.472251i
$869$	−33274.8	+	45798.8i	−1.29893	+	1.78782i
$870$	61474.9	+	12843.2i	2.39563	+	0.500488i
$871$	5683.18	−	12764.6i	0.221088	−	0.496571i
$872$	−3293.72	−	8580.43i	−0.127912	−	0.333222i
$873$	3473.38	+	5348.53i	0.134657	+	0.207354i
$874$	−2168.78			−0.0839359
$875$	24770.9	+	7505.07i	0.957038	+	0.289963i
$876$	26656.2			1.02812
$877$	−11639.9	−	17923.9i	−0.448177	−	0.690132i	0.540305	−	0.841469i	$-0.318309\pi$
$877$	−11639.9	−	17923.9i	−0.448177	−	0.690132i	−0.988482	+	0.151337i	$0.951642\pi$
$878$	14747.8	+	38419.4i	0.566874	+	1.47676i
$879$	−6324.97	+	14206.1i	−0.242703	+	0.545120i
$880$	39315.6	+	8213.70i	1.50606	+	0.314641i
$881$	−4337.67	+	5970.29i	−0.165879	+	0.228313i	−0.883862	−	0.467747i	$-0.845066\pi$
$881$	−4337.67	+	5970.29i	−0.165879	+	0.228313i	0.717983	+	0.696061i	$0.245066\pi$
$882$	−6004.06	+	2436.84i	−0.229214	+	0.0930304i
$883$	22451.1	−	3555.91i	0.855652	−	0.135522i	0.286829	−	0.957982i	$-0.407399\pi$
$883$	22451.1	−	3555.91i	0.855652	−	0.135522i	0.568823	+	0.822460i	$0.307399\pi$
$884$	−8786.43	+	7911.34i	−0.334298	+	0.301004i
$885$	6212.08	+	16016.0i	0.235951	+	0.608329i
$886$	−25371.0	+	28177.3i	−0.962026	+	1.06844i
$887$	37223.0	+	1950.78i	1.40905	+	0.0738451i	0.741616	−	0.670825i	$-0.234060\pi$
$887$	37223.0	+	1950.78i	1.40905	+	0.0738451i	0.667433	+	0.744670i	$0.267393\pi$
$888$	703.118	−	358.256i	0.0265710	−	0.0135386i
$889$	−6787.85	+	45665.5i	−0.256082	+	1.72280i
$890$	3603.68	+	22250.6i	0.135725	+	0.838026i
$891$	−25932.1	−	28800.6i	−0.975039	−	1.08289i
$892$	−14076.8	−	17383.4i	−0.528394	−	0.652512i
$893$	−877.135	−	235.028i	−0.0328692	−	0.00880728i
$894$	−15195.2	+	6765.32i	−0.568459	+	0.253094i
$895$	21872.3	−	30326.4i	0.816885	−	1.13262i
$896$	−19980.7	−	7452.46i	−0.744985	−	0.277868i
$897$	−4428.31	−	701.376i	−0.164835	−	0.0261073i
$898$	55800.2	−	36237.1i	2.07358	−	1.34660i
$899$	16644.0	+	28828.3i	0.617474	+	1.06950i
$900$	340.321	−	3470.44i	0.0126045	−	0.128535i
$901$	23369.0	+	13492.1i	0.864078	+	0.498876i
$902$	1332.64	+	679.015i	0.0491930	+	0.0250651i
$903$	20847.0	+	1990.71i	0.768267	+	0.0733629i
$904$	12052.3	+	16588.6i	0.443423	+	0.610320i
$905$	−358.336	+	324.916i	−0.0131619	+	0.0119343i
$906$	−1706.37	−	179.347i	−0.0625722	−	0.00657661i
$907$	−446.773	+	1667.38i	−0.0163559	+	0.0610412i	−0.973621	−	0.228169i	$-0.926726\pi$
$907$	−446.773	+	1667.38i	−0.0163559	+	0.0610412i	0.957266	+	0.289210i	$0.0933927\pi$
$908$	−8053.42	−	3091.42i	−0.294341	−	0.112987i
$909$	−754.450	+	2321.96i	−0.0275286	+	0.0847244i
$910$	−27357.6	−	11756.6i	−0.996587	−	0.428272i
$911$	9474.19	+	29158.6i	0.344560	+	1.06045i	0.961819	+	0.273686i	$0.0882429\pi$
$911$	9474.19	+	29158.6i	0.344560	+	1.06045i	−0.617259	+	0.786760i	$0.711757\pi$
$912$	681.329	−	13000.5i	0.0247380	−	0.472029i
$913$	−27353.8	−	17763.8i	−0.991543	−	0.643916i
$914$	18530.9	+	16685.3i	0.670622	+	0.603831i
$915$	17418.5	+	852.011i	0.629331	+	0.0307832i
$916$	22038.9	+	7160.86i	0.794962	+	0.258299i
$917$	−35958.5	−	39179.6i	−1.29493	−	1.41093i
$918$	17854.3	−	17854.3i	0.641919	−	0.641919i
$919$	2358.44	+	5297.13i	0.0846546	+	0.190137i	0.950913	−	0.309460i	$-0.100148\pi$
$919$	2358.44	+	5297.13i	0.0846546	+	0.190137i	−0.866258	+	0.499597i	$0.833481\pi$
$920$	−1846.86	+	1074.88i	−0.0661839	+	0.0385194i
$921$	−34838.2	−	15511.0i	−1.24643	−	0.554945i
$922$	−41151.4	−	33323.7i	−1.46990	−	1.19030i
$923$	−12406.1	+	24348.4i	−0.442418	+	0.868295i
$924$	−11648.6	+	23409.7i	−0.414729	+	0.833467i
$925$	820.327	−	1638.11i	0.0291591	−	0.0582277i
$926$	9723.57	−	16841.7i	0.345071	−	0.597681i
$927$	−17.6228	−	336.263i	−0.000624390	−	0.0119141i
$928$	−52965.4	+	20331.5i	−1.87357	+	0.719197i
$929$	−3321.04	−	31597.6i	−0.117287	−	1.11591i	−0.881904	−	0.471428i	$-0.843739\pi$
$929$	−3321.04	−	31597.6i	−0.117287	−	1.11591i	0.764617	−	0.644485i	$-0.222928\pi$
$930$	23052.4	−	16871.6i	0.812815	−	0.594883i
$931$	−4878.87	+	8834.62i	−0.171749	+	0.311002i
$932$	−9363.89	−	9363.89i	−0.329103	−	0.329103i
$933$	845.092	−	2201.54i	0.0296539	−	0.0772510i
$934$	6645.71	−	1412.59i	0.232820	−	0.0494875i
$935$	−27711.2	−	7321.78i	−0.969253	−	0.256094i
$936$	399.997	−	1881.84i	0.0139683	−	0.0657156i
$937$	12643.4	+	24814.1i	0.440814	+	0.865146i	0.999363	+	0.0356751i	$0.0113581\pi$
$937$	12643.4	+	24814.1i	0.440814	+	0.865146i	−0.558549	+	0.829471i	$0.688642\pi$
$938$	24124.7	−	229.603i	0.839764	−	0.00799234i
$939$	−6097.61	+	1981.23i	−0.211915	+	0.0688553i
$940$	1800.42	−	489.151i	0.0624715	−	0.0169727i
$941$	−3204.16	−	15074.4i	−0.111002	−	0.522221i	−0.998153	−	0.0607437i	$-0.980653\pi$
$941$	−3204.16	−	15074.4i	−0.111002	−	0.522221i	0.887152	−	0.461478i	$-0.152681\pi$
$942$	−15290.8	+	12382.3i	−0.528878	+	0.428277i
$943$	−172.499	+	46.2210i	−0.00595689	+	0.00159614i
$944$	−17101.8	−	12425.2i	−0.589637	−	0.428397i
$945$	24060.1	+	8878.67i	0.828229	+	0.305633i
$946$	27196.7	−	19759.5i	0.934715	−	0.679110i
$947$	13795.2	−	17035.6i	0.473372	−	0.584565i	−0.483402	−	0.875398i	$-0.660599\pi$
$947$	13795.2	−	17035.6i	0.473372	−	0.584565i	0.956774	+	0.290833i	$0.0939325\pi$
$948$	−37647.1	+	1973.00i	−1.28979	+	0.0675950i
$949$	29568.6	−	17071.4i	1.01142	−	0.583943i
$950$	−7413.18	−	11243.0i	−0.253174	−	0.383968i
$951$		−	58627.8i		−	1.99909i
$952$	8981.31	+	3896.74i	0.305762	+	0.132662i
$953$	3789.18	−	23924.0i	0.128797	−	0.813193i	−0.835717	−	0.549161i	$-0.814947\pi$
$953$	3789.18	−	23924.0i	0.128797	−	0.813193i	0.964514	−	0.264032i	$-0.0850526\pi$
$954$	9105.68	−	957.045i	0.309022	−	0.0324795i
$955$	−12265.1	−	21073.9i	−0.415592	−	0.714068i
$956$	−3662.50	+	34846.4i	−0.123906	+	1.17888i
$957$	−18282.2	−	68230.2i	−0.617534	−	2.30467i
$958$	9867.88	+	62303.4i	0.332794	+	2.10118i
$959$	41062.6	+	10584.9i	1.38267	+	0.356417i
$960$	4165.69	+	8105.67i	0.140049	+	0.272510i
$961$	−14329.1	−	3045.75i	−0.480989	−	0.102237i
$962$	−1147.91	+	1767.62i	−0.0384719	+	0.0592415i
$963$	−3707.83	+	5709.56i	−0.124074	+	0.191057i
$964$	−19960.2	−	4242.67i	−0.666882	−	0.141750i
$965$	5167.18	+	2610.17i	0.172370	+	0.0870718i
$966$	−2074.70	−	7458.24i	−0.0691020	−	0.248411i
$967$	−4246.69	−	26812.5i	−0.141225	−	0.891658i	−0.951955	−	0.306238i	$-0.900930\pi$
$967$	−4246.69	−	26812.5i	−0.141225	−	0.891658i	0.810730	−	0.585420i	$-0.199070\pi$
$968$	−1939.10	−	7236.83i	−0.0643855	−	0.240290i
$969$	−971.086	+	9239.27i	−0.0321938	+	0.306303i
$970$	−49459.1	+	10693.1i	−1.63715	+	0.353954i
$971$	36307.2	−	3816.04i	1.19995	−	0.126120i	0.516612	−	0.856220i	$-0.327193\pi$
$971$	36307.2	−	3816.04i	1.19995	−	0.126120i	0.683341	+	0.730099i	$0.260526\pi$
$972$	1208.70	−	7631.45i	0.0398860	−	0.251830i
$973$	15176.6	+	20476.1i	0.500039	+	0.674649i
$974$		−	28015.4i		−	0.921635i
$975$	−11500.6	−	25353.8i	−0.377759	−	0.832792i
$976$	−18584.9	+	10730.0i	−0.609516	+	0.351904i
$977$	−32481.2	+	1702.27i	−1.06363	+	0.0557424i	−0.576111	−	0.817371i	$-0.695431\pi$
$977$	−32481.2	+	1702.27i	−1.06363	+	0.0557424i	−0.487517	+	0.873114i	$0.662097\pi$
$978$	9685.41	−	11960.5i	0.316672	−	0.391057i
$979$	20510.7	−	14901.9i	0.669586	−	0.486483i
$980$	−466.889	−	20729.7i	−0.0152186	−	0.675701i
$981$	4040.56	+	2935.64i	0.131504	+	0.0955430i
$982$	−31732.0	+	8502.57i	−1.03117	+	0.276301i
$983$	−21133.8	+	17113.8i	−0.685722	+	0.555287i	−0.907625	−	0.419782i	$-0.862107\pi$
$983$	−21133.8	+	17113.8i	−0.685722	+	0.555287i	0.221903	+	0.975069i	$0.428773\pi$
$984$	−99.3098	−	467.216i	−0.00321736	−	0.0151365i
$985$	−39232.4	−	14903.3i	−1.26908	−	0.482088i
$986$	52450.2	−	17042.1i	1.69407	−	0.550437i
$987$	−30.8479	−	3241.23i	−0.000994832	−	0.104528i
$988$	2836.65	+	5567.24i	0.0913420	+	0.179269i
$989$	−834.541	+	3926.21i	−0.0268320	+	0.126235i
$990$	−9067.01	+	3516.80i	−0.291079	+	0.112900i
$991$	23965.2	−	5093.96i	0.768193	−	0.163285i	0.192885	−	0.981221i	$-0.438215\pi$
$991$	23965.2	−	5093.96i	0.768193	−	0.163285i	0.575308	+	0.817937i	$0.304882\pi$
$992$	−9248.20	+	24092.4i	−0.295999	+	0.771103i
$993$	−37135.6	−	37135.6i	−1.18677	−	1.18677i
$994$	−47140.4	−	2020.86i	−1.50423	−	0.0644848i
$995$	11481.6	+	34922.2i	0.365820	+	1.11267i
$996$	−2270.34	−	21600.9i	−0.0722274	−	0.687198i
$997$	−23654.4	+	9080.06i	−0.751395	+	0.288434i	−0.703766	−	0.710432i	$-0.748500\pi$
$997$	−23654.4	+	9080.06i	−0.751395	+	0.288434i	−0.0476288	+	0.998865i	$0.515166\pi$
$998$	−3129.31	−	59710.8i	−0.0992551	−	1.89390i
$999$	907.635	−	1572.07i	0.0287450	−	0.0497879i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.x.a.117.47	yes	928
7.3	odd	6	inner	175.4.x.a.17.12	yes	928
25.3	odd	20	inner	175.4.x.a.103.12	yes	928
175.3	even	60	inner	175.4.x.a.3.47	✓	928

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.4.x.a.3.47	✓	928	175.3	even	60	inner
175.4.x.a.17.12	yes	928	7.3	odd	6	inner
175.4.x.a.103.12	yes	928	25.3	odd	20	inner
175.4.x.a.117.47	yes	928	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.99423 + 3.07084i) q^{2} +(2.03228 + 5.29426i) q^{3} +(-2.19922 + 4.93952i) q^{4} +(-10.9441 - 2.28640i) q^{5} +(-12.2050 + 16.7988i) q^{6} +(-17.5585 + 5.89045i) q^{7} +(9.37758 - 1.48526i) q^{8} +(-3.83417 + 3.45230i) q^{9} +(-14.8038 - 38.1670i) q^{10} +(-30.8098 + 34.2178i) q^{11} +(-30.6206 - 1.60476i) q^{12} +(-34.9937 + 17.8302i) q^{13} +(-53.1043 - 42.1726i) q^{14} +(-10.1366 - 62.5873i) q^{15} +(52.2058 + 57.9805i) q^{16} +(-35.0386 - 43.2690i) q^{17} +(-18.2476 - 4.88944i) q^{18} +(-26.8797 + 11.9676i) q^{19} +(35.3621 - 49.0301i) q^{20} +(-66.8694 - 80.9886i) q^{21} +(-166.519 - 26.3740i) q^{22} +(16.8829 - 10.9639i) q^{23} +(26.9212 + 46.6289i) q^{24} +(114.545 + 50.0450i) q^{25} +(-124.539 - 71.9027i) q^{26} +(110.357 + 56.2297i) q^{27} +(9.51908 - 99.6853i) q^{28} +(159.008 + 218.856i) q^{29} +(171.981 - 155.941i) q^{30} +(122.378 + 12.8624i) q^{31} +(-54.2796 + 202.574i) q^{32} +(-243.772 - 93.5754i) q^{33} +(62.9974 - 193.886i) q^{34} +(205.630 - 24.3195i) q^{35} +(-8.62054 - 26.5313i) q^{36} +(0.767048 - 14.6361i) q^{37} +(-90.3549 - 58.6771i) q^{38} +(-165.515 - 149.030i) q^{39} +(-106.025 - 5.18611i) q^{40} +(-8.43713 - 2.74139i) q^{41} +(115.350 - 366.855i) q^{42} +(-140.993 + 140.993i) q^{43} +(-101.262 - 227.438i) q^{44} +(49.8547 - 29.0157i) q^{45} +(67.3365 + 29.9801i) q^{46} +(23.9845 + 19.4223i) q^{47} +(-200.867 + 394.224i) q^{48} +(273.605 - 206.855i) q^{49} +(74.7480 + 451.549i) q^{50} +(157.870 - 273.438i) q^{51} +(-11.1139 - 212.065i) q^{52} +(-452.467 + 173.686i) q^{53} +(47.4044 + 451.023i) q^{54} +(415.420 - 304.038i) q^{55} +(-155.908 + 81.3172i) q^{56} +(-117.987 - 117.987i) q^{57} +(-354.973 + 924.736i) q^{58} +(-265.022 + 56.3321i) q^{59} +(331.444 + 87.5734i) q^{60} +(-57.1874 + 269.045i) q^{61} +(204.550 + 401.453i) q^{62} +(46.9868 - 83.2023i) q^{63} +(-136.704 + 44.4177i) q^{64} +(423.741 - 115.125i) q^{65} +(-198.782 - 935.195i) q^{66} +(-276.485 + 223.893i) q^{67} +(290.786 - 77.9158i) q^{68} +(92.3563 + 67.1008i) q^{69} +(484.753 + 582.957i) q^{70} +(562.908 - 408.976i) q^{71} +(-30.8276 + 38.0690i) q^{72} +(-868.150 + 45.4978i) q^{73} +(46.4749 - 26.8323i) q^{74} +(-32.1647 + 708.135i) q^{75} -159.092i q^{76} +(339.418 - 782.298i) q^{77} +(127.574 - 805.469i) q^{78} +(1222.74 - 128.515i) q^{79} +(-438.777 - 753.905i) q^{80} +(-87.9799 + 837.073i) q^{81} +(-8.40718 - 31.3760i) q^{82} +(110.810 + 699.629i) q^{83} +(547.105 - 152.192i) q^{84} +(284.534 + 553.651i) q^{85} +(-714.141 - 151.795i) q^{86} +(-835.532 + 1286.61i) q^{87} +(-238.099 + 366.641i) q^{88} +(-538.578 - 114.478i) q^{89} +(188.524 + 95.2317i) q^{90} +(509.412 - 519.201i) q^{91} +(17.0272 + 107.505i) q^{92} +(180.608 + 674.040i) q^{93} +(-11.8121 + 112.385i) q^{94} +(321.536 - 69.5165i) q^{95} +(-1182.79 + 124.316i) q^{96} +(193.365 - 1220.86i) q^{97} +(1180.85 + 427.681i) q^{98} -237.561i 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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