LMFDB - Embedded newform 175.4.x.a.3.13

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			3.13
Character	$\chi$	$=$	175.3
Dual form			175.4.x.a.117.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.96169 + 3.02073i) q^{2} +(3.41104 - 8.88607i) q^{3} +(-2.02272 - 4.54311i) q^{4} +(-3.76740 - 10.5265i) q^{5} +(20.1510 + 27.7355i) q^{6} +(11.4301 - 14.5724i) q^{7} +(-10.7683 - 1.70553i) q^{8} +(-47.2621 - 42.5550i) q^{9} +(39.1881 + 9.26933i) q^{10} +(4.08483 + 4.53666i) q^{11} +(-47.2699 + 2.47731i) q^{12} +(47.3826 + 24.1427i) q^{13} +(21.5970 + 63.1136i) q^{14} +(-106.390 - 2.42885i) q^{15} +(52.8969 - 58.7480i) q^{16} +(-77.8230 + 96.1034i) q^{17} +(221.261 - 59.2866i) q^{18} +(-114.588 - 51.0180i) q^{19} +(-40.2025 + 38.4078i) q^{20} +(-90.5025 - 151.275i) q^{21} +(-21.7172 + 3.43967i) q^{22} +(-29.0527 - 18.8671i) q^{23} +(-51.8865 + 89.8701i) q^{24} +(-96.6134 + 79.3149i) q^{25} +(-165.878 + 95.7700i) q^{26} +(-310.377 + 158.145i) q^{27} +(-89.3236 - 22.4522i) q^{28} +(64.1803 - 88.3366i) q^{29} +(216.040 - 316.610i) q^{30} +(159.795 - 16.7952i) q^{31} +(51.1205 + 190.784i) q^{32} +(54.2466 - 20.8233i) q^{33} +(-137.638 - 423.608i) q^{34} +(-196.457 - 65.4184i) q^{35} +(-97.7337 + 300.793i) q^{36} +(-11.7411 - 224.034i) q^{37} +(378.898 - 246.059i) q^{38} +(376.157 - 338.694i) q^{39} +(22.6153 + 119.777i) q^{40} +(-27.2715 + 8.86105i) q^{41} +(634.500 + 23.3710i) q^{42} +(102.919 + 102.919i) q^{43} +(12.3481 - 27.7342i) q^{44} +(-269.899 + 657.825i) q^{45} +(113.985 - 50.7493i) q^{46} +(265.897 - 215.319i) q^{47} +(-341.605 - 670.437i) q^{48} +(-81.7069 - 333.126i) q^{49} +(-50.0641 - 447.434i) q^{50} +(588.524 + 1019.35i) q^{51} +(13.8408 - 264.098i) q^{52} +(-552.172 - 211.959i) q^{53} +(131.149 - 1247.80i) q^{54} +(32.3659 - 60.0903i) q^{55} +(-147.936 + 137.425i) q^{56} +(-844.215 + 844.215i) q^{57} +(140.940 + 367.160i) q^{58} +(131.744 + 28.0031i) q^{59} +(204.162 + 488.253i) q^{60} +(-59.0487 - 277.802i) q^{61} +(-262.735 + 515.646i) q^{62} +(-1160.34 + 202.313i) q^{63} +(-75.1191 - 24.4077i) q^{64} +(75.6276 - 589.727i) q^{65} +(-43.5132 + 204.713i) q^{66} +(-218.643 - 177.053i) q^{67} +(594.022 + 159.168i) q^{68} +(-266.754 + 193.808i) q^{69} +(582.999 - 465.114i) q^{70} +(28.4300 + 20.6556i) q^{71} +(436.353 + 538.851i) q^{72} +(-42.2168 - 2.21249i) q^{73} +(699.778 + 404.017i) q^{74} +(375.246 + 1129.06i) q^{75} +623.782i q^{76} +(112.800 - 7.67119i) q^{77} +(285.200 + 1800.68i) q^{78} +(1195.08 + 125.608i) q^{79} +(-817.693 - 335.491i) q^{80} +(167.089 + 1589.74i) q^{81} +(26.7313 - 99.7626i) q^{82} +(20.5434 - 129.706i) q^{83} +(-504.198 + 717.150i) q^{84} +(1304.82 + 457.142i) q^{85} +(-512.786 + 108.996i) q^{86} +(-566.043 - 871.630i) q^{87} +(-36.2492 - 55.8188i) q^{88} +(-699.524 + 148.688i) q^{89} +(-1457.66 - 2105.74i) q^{90} +(893.402 - 414.524i) q^{91} +(-26.9495 + 170.152i) q^{92} +(395.826 - 1477.24i) q^{93} +(128.815 + 1225.59i) q^{94} +(-105.339 + 1398.42i) q^{95} +(1869.70 + 196.513i) q^{96} +(153.435 + 968.747i) q^{97} +(1166.57 + 406.674i) q^{98} -388.242i 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 $

$2$	−1.96169	+	3.02073i	−0.693561	+	1.06799i	0.299917	+	0.953965i	$0.403041\pi$
$2$	−1.96169	+	3.02073i	−0.693561	+	1.06799i	−0.993478	+	0.114025i	$0.963626\pi$
$3$	3.41104	−	8.88607i	0.656455	−	1.71012i	−0.0465268	−	0.998917i	$-0.514815\pi$
$3$	3.41104	−	8.88607i	0.656455	−	1.71012i	0.702982	−	0.711208i	$-0.251851\pi$
$4$	−2.02272	−	4.54311i	−0.252840	−	0.567888i
$5$	−3.76740	−	10.5265i	−0.336967	−	0.941517i
$5$	−3.76740	−	10.5265i	−0.336967	−	0.941517i
$6$	20.1510	+	27.7355i	1.37110	+	1.88716i
$7$	11.4301	−	14.5724i	0.617166	−	0.786833i
$7$	11.4301	−	14.5724i	0.617166	−	0.786833i
$8$	−10.7683	−	1.70553i	−0.475895	−	0.0753744i
$9$	−47.2621	−	42.5550i	−1.75045	−	1.57611i
$10$	39.1881	+	9.26933i	1.23924	+	0.293122i
$11$	4.08483	+	4.53666i	0.111966	+	0.124350i	0.796522	−	0.604609i	$-0.206671\pi$
$11$	4.08483	+	4.53666i	0.111966	+	0.124350i	−0.684557	+	0.728960i	$0.740004\pi$
$12$	−47.2699	+	2.47731i	−1.13714	+	0.0595949i
$13$	47.3826	+	24.1427i	1.01089	+	0.515074i	0.879319	−	0.476232i	$-0.157998\pi$
$13$	47.3826	+	24.1427i	1.01089	+	0.515074i	0.131571	+	0.991307i	$0.457998\pi$
$14$	21.5970	+	63.1136i	0.412288	+	1.20484i
$15$	−106.390	−	2.42885i	−1.83131	−	0.0418084i
$16$	52.8969	−	58.7480i	0.826514	−	0.917937i
$17$	−77.8230	+	96.1034i	−1.11029	+	1.37109i	−0.189104	+	0.981957i	$0.560558\pi$
$17$	−77.8230	+	96.1034i	−1.11029	+	1.37109i	−0.921182	+	0.389132i	$0.872775\pi$
$18$	221.261	−	59.2866i	2.89731	−	0.776333i
$19$	−114.588	−	51.0180i	−1.38360	−	0.616017i	−0.426157	−	0.904649i	$-0.640133\pi$
$19$	−114.588	−	51.0180i	−1.38360	−	0.616017i	−0.957440	+	0.288632i	$0.906800\pi$
$20$	−40.2025	+	38.4078i	−0.449477	+	0.429413i
$21$	−90.5025	−	151.275i	−0.940441	−	1.57195i
$22$	−21.7172	+	3.43967i	−0.210460	+	0.0333336i
$23$	−29.0527	−	18.8671i	−0.263387	−	0.171046i	0.406189	−	0.913789i	$-0.366858\pi$
$23$	−29.0527	−	18.8671i	−0.263387	−	0.171046i	−0.669576	+	0.742743i	$0.733524\pi$
$24$	−51.8865	+	89.8701i	−0.441304	+	0.764360i
$25$	−96.6134	+	79.3149i	−0.772907	+	0.634520i
$26$	−165.878	+	95.7700i	−1.25121	+	0.722386i
$27$	−310.377	+	158.145i	−2.21230	+	1.12722i
$28$	−89.3236	−	22.4522i	−0.602877	−	0.151538i
$29$	64.1803	−	88.3366i	0.410965	−	0.565644i	−0.552489	−	0.833520i	$-0.686322\pi$
$29$	64.1803	−	88.3366i	0.410965	−	0.565644i	0.963453	+	0.267876i	$0.0863218\pi$
$30$	216.040	−	316.610i	1.31478	−	1.92683i
$31$	159.795	−	16.7952i	0.925809	−	0.0973065i	0.370389	−	0.928877i	$-0.379224\pi$
$31$	159.795	−	16.7952i	0.925809	−	0.0973065i	0.555420	+	0.831570i	$0.312558\pi$
$32$	51.1205	+	190.784i	0.282404	+	1.05395i
$33$	54.2466	−	20.8233i	0.286155	−	0.109845i
$34$	−137.638	−	423.608i	−0.694259	−	2.13671i
$35$	−196.457	−	65.4184i	−0.948781	−	0.315935i
$36$	−97.7337	+	300.793i	−0.452471	+	1.39256i
$37$	−11.7411	−	224.034i	−0.0521683	−	0.995430i	−0.891844	−	0.452342i	$-0.850589\pi$
$37$	−11.7411	−	224.034i	−0.0521683	−	0.995430i	0.839676	−	0.543087i	$-0.182745\pi$
$38$	378.898	−	246.059i	1.61751	−	1.05042i
$39$	376.157	−	338.694i	1.54445	−	1.39063i
$40$	22.6153	+	119.777i	0.0893947	+	0.473462i
$41$	−27.2715	+	8.86105i	−0.103880	+	0.0337528i	−0.360496	−	0.932761i	$-0.617393\pi$
$41$	−27.2715	+	8.86105i	−0.103880	+	0.0337528i	0.256616	+	0.966514i	$0.417393\pi$
$42$	634.500	+	23.3710i	2.33108	+	0.0858625i
$43$	102.919	+	102.919i	0.365000	+	0.365000i	0.865650	−	0.500650i	$-0.166906\pi$
$43$	102.919	+	102.919i	0.365000	+	0.365000i	−0.500650	+	0.865650i	$0.666906\pi$
$44$	12.3481	−	27.7342i	0.0423077	−	0.0950247i
$45$	−269.899	+	657.825i	−0.894091	+	2.17917i
$46$	113.985	−	50.7493i	0.365351	−	0.162665i
$47$	265.897	−	215.319i	0.825214	−	0.668245i	−0.120691	−	0.992690i	$-0.538511\pi$
$47$	265.897	−	215.319i	0.825214	−	0.668245i	0.945904	+	0.324445i	$0.105178\pi$
$48$	−341.605	−	670.437i	−1.02722	−	2.01603i
$49$	−81.7069	−	333.126i	−0.238213	−	0.971213i
$50$	−50.0641	−	447.434i	−0.141603	−	1.26554i
$51$	588.524	+	1019.35i	1.61588	+	2.79879i
$52$	13.8408	−	264.098i	0.0369110	−	0.704304i
$53$	−552.172	−	211.959i	−1.43107	−	0.549336i	−0.485350	−	0.874320i	$-0.661308\pi$
$53$	−552.172	−	211.959i	−1.43107	−	0.549336i	−0.945719	+	0.324984i	$0.894641\pi$
$54$	131.149	−	1247.80i	0.330501	−	3.14451i
$55$	32.3659	−	60.0903i	0.0793493	−	0.147319i
$56$	−147.936	+	137.425i	−0.353013	+	0.327932i
$57$	−844.215	+	844.215i	−1.96174	+	1.96174i
$58$	140.940	+	367.160i	0.319074	+	0.831215i
$59$	131.744	+	28.0031i	0.290706	+	0.0617914i	0.350956	−	0.936392i	$-0.385857\pi$
$59$	131.744	+	28.0031i	0.290706	+	0.0617914i	−0.0602504	+	0.998183i	$0.519190\pi$
$60$	204.162	+	488.253i	0.439287	+	1.05055i
$61$	−59.0487	−	277.802i	−0.123941	−	0.583097i	−0.995658	−	0.0930871i	$-0.970326\pi$
$61$	−59.0487	−	277.802i	−0.123941	−	0.583097i	0.871717	−	0.490010i	$-0.163007\pi$
$62$	−262.735	+	515.646i	−0.538183	+	1.05624i
$63$	−1160.34	+	202.313i	−2.32045	+	0.404589i
$64$	−75.1191	−	24.4077i	−0.146717	−	0.0476712i
$65$	75.6276	−	589.727i	0.144315	−	1.12533i
$66$	−43.5132	+	204.713i	−0.0811530	+	0.381795i
$67$	−218.643	−	177.053i	−0.398678	−	0.322843i	0.408926	−	0.912567i	$-0.365903\pi$
$67$	−218.643	−	177.053i	−0.398678	−	0.322843i	−0.807605	+	0.589724i	$0.799237\pi$
$68$	594.022	+	159.168i	1.05935	+	0.283852i
$69$	−266.754	+	193.808i	−0.465412	+	0.338141i
$70$	582.999	−	465.114i	0.995453	−	0.794168i
$71$	28.4300	+	20.6556i	0.0475214	+	0.0345263i	0.611292	−	0.791405i	$-0.290650\pi$
$71$	28.4300	+	20.6556i	0.0475214	+	0.0345263i	−0.563771	+	0.825931i	$0.690650\pi$
$72$	436.353	+	538.851i	0.714232	+	0.882003i
$73$	−42.2168	−	2.21249i	−0.0676863	−	0.00354729i	0.0184628	−	0.999830i	$-0.494123\pi$
$73$	−42.2168	−	2.21249i	−0.0676863	−	0.00354729i	−0.0861490	+	0.996282i	$0.527456\pi$
$74$	699.778	+	404.017i	1.09929	+	0.634676i
$75$	375.246	+	1129.06i	0.577729	+	1.73830i
$76$			623.782i			0.941482i
$77$	112.800	−	7.67119i	0.166944	−	0.0113534i
$78$	285.200	+	1800.68i	0.414007	+	2.61394i
$79$	1195.08	+	125.608i	1.70199	+	0.178886i	0.905089	−	0.425223i	$-0.139804\pi$
$79$	1195.08	+	125.608i	1.70199	+	0.178886i	0.796901	+	0.604109i	$0.206471\pi$
$80$	−817.693	−	335.491i	−1.14276	−	0.468862i
$81$	167.089	+	1589.74i	0.229203	+	2.18072i
$82$	26.7313	−	99.7626i	0.0359997	−	0.134353i
$83$	20.5434	−	129.706i	0.0271679	−	0.171531i	−0.970374	−	0.241609i	$-0.922325\pi$
$83$	20.5434	−	129.706i	0.0271679	−	0.171531i	0.997542	+	0.0700779i	$0.0223248\pi$
$84$	−504.198	+	717.150i	−0.654911	+	0.931518i
$85$	1304.82	+	457.142i	1.66503	+	0.583341i
$86$	−512.786	+	108.996i	−0.642967	+	0.136667i
$87$	−566.043	−	871.630i	−0.697542	−	1.07412i
$88$	−36.2492	−	55.8188i	−0.0439111	−	0.0676171i
$89$	−699.524	+	148.688i	−0.833139	+	0.177089i	−0.604684	−	0.796465i	$-0.706701\pi$
$89$	−699.524	+	148.688i	−0.833139	+	0.177089i	−0.228455	+	0.973554i	$0.573367\pi$
$90$	−1457.66	−	2105.74i	−1.70723	−	2.46627i
$91$	893.402	−	414.524i	1.02916	−	0.477516i
$92$	−26.9495	+	170.152i	−0.0305400	+	0.192822i
$93$	395.826	−	1477.24i	0.441346	−	1.64713i
$94$	128.815	+	1225.59i	0.141343	+	1.34479i
$95$	−105.339	+	1398.42i	−0.113764	+	1.51026i
$96$	1869.70	+	196.513i	1.98776	+	0.208922i
$97$	153.435	+	968.747i	0.160607	+	1.01404i	0.927925	+	0.372768i	$0.121591\pi$
$97$	153.435	+	968.747i	0.160607	+	1.01404i	−0.767317	+	0.641267i	$0.778409\pi$
$98$	1166.57	+	406.674i	1.20246	+	0.419187i
$99$		−	388.242i		−	0.394139i
$100$	555.758	+	278.493i	0.555758	+	0.278493i
$101$	−243.123	−	140.367i	−0.239521	−	0.138288i	0.375436	−	0.926849i	$-0.377493\pi$
$101$	−243.123	−	140.367i	−0.239521	−	0.138288i	−0.614957	+	0.788561i	$0.710826\pi$
$102$	−4233.70	−	221.879i	−4.10979	−	0.215385i
$103$	−289.064	−	356.964i	−0.276527	−	0.341483i	0.619894	−	0.784686i	$-0.287176\pi$
$103$	−289.064	−	356.964i	−0.276527	−	0.341483i	−0.896422	+	0.443203i	$0.853842\pi$
$104$	−469.054	−	340.787i	−0.442255	−	0.321317i
$105$	−1251.44	+	1522.59i	−1.16312	+	1.41514i
$106$	1723.46	−	1252.17i	1.57922	−	1.14737i
$107$	499.692	+	133.892i	0.451468	+	0.120971i	0.477386	−	0.878694i	$-0.341584\pi$
$107$	499.692	+	133.892i	0.451468	+	0.120971i	−0.0259181	+	0.999664i	$0.508251\pi$
$108$	1346.27	+	1090.19i	1.19949	+	0.971331i
$109$	270.783	−	1273.93i	0.237948	−	1.11946i	−0.683196	−	0.730235i	$-0.739411\pi$
$109$	270.783	−	1273.93i	0.237948	−	1.11946i	0.921144	−	0.389222i	$-0.127256\pi$
$110$	118.025	+	215.647i	0.102302	+	0.186919i
$111$	−2030.83	−	659.856i	−1.73655	−	0.564241i
$112$	−251.481	−	1442.33i	−0.212167	−	1.21685i
$113$	−403.021	+	790.974i	−0.335514	+	0.658483i	−0.995702	−	0.0926174i	$-0.970477\pi$
$113$	−403.021	+	790.974i	−0.335514	+	0.658483i	0.660188	+	0.751101i	$0.270477\pi$
$114$	−894.062	−	4206.23i	−0.734532	−	3.45570i
$115$	−89.1503	+	376.903i	−0.0722897	+	0.305620i
$116$	−531.141	−	112.898i	−0.425131	−	0.0903644i
$117$	−1212.01	−	3157.40i	−0.957697	−	2.49489i
$118$	−343.031	+	343.031i	−0.267615	+	0.267615i
$119$	510.930	+	2232.53i	0.393588	+	1.71980i
$120$	1141.49	+	207.605i	0.868363	+	0.157931i
$121$	135.232	−	1286.65i	0.101602	−	0.966676i
$122$	955.001	+	366.591i	0.708703	+	0.272046i
$123$	−14.2844	+	272.562i	−0.0104714	+	0.199806i
$124$	−399.524	−	691.995i	−0.289341	−	0.501153i
$125$	1198.89	+	718.187i	0.857855	+	0.513893i
$126$	1665.08	−	3901.94i	1.17728	−	2.75883i
$127$	948.751	+	1862.03i	0.662898	+	1.30101i	0.940330	+	0.340265i	$0.110517\pi$
$127$	948.751	+	1862.03i	0.662898	+	1.30101i	−0.277432	+	0.960745i	$0.589483\pi$
$128$	−1006.89	+	815.365i	−0.695293	+	0.563037i
$129$	1265.61	−	563.484i	0.863802	−	0.384589i
$130$	1633.05	+	1385.31i	1.10175	+	0.934614i
$131$	505.021	−	1134.30i	0.336824	−	0.756519i	−0.663144	−	0.748492i	$-0.730778\pi$
$131$	505.021	−	1134.30i	0.336824	−	0.756519i	0.999968	−	0.00802673i	$-0.00255501\pi$
$132$	−204.328	−	204.328i	−0.134731	−	0.134731i
$133$	−2053.20	+	1086.68i	−1.33861	+	0.708475i
$134$	963.740	−	313.138i	0.621302	−	0.201873i
$135$	2834.02	+	2671.38i	1.80677	+	1.70308i
$136$	1001.93	−	902.140i	0.631725	−	0.568808i
$137$	2071.39	−	1345.17i	1.29176	−	0.838876i	0.298454	−	0.954424i	$-0.403529\pi$
$137$	2071.39	−	1345.17i	1.29176	−	0.838876i	0.993302	+	0.115548i	$0.0368623\pi$
$138$	−62.1548	−	1185.98i	−0.0383403	−	0.731577i
$139$	517.641	−	1593.13i	0.315868	−	0.972143i	−0.659527	−	0.751681i	$-0.729243\pi$
$139$	517.641	−	1593.13i	0.315868	−	0.972143i	0.975396	−	0.220462i	$-0.0707566\pi$
$140$	100.175	+	1024.85i	0.0604739	+	0.618682i
$141$	−1006.35	−	3097.24i	−0.601066	−	1.84989i
$142$	−118.166	+	45.3596i	−0.0698328	+	0.0268063i
$143$	84.0228	+	313.577i	0.0491353	+	0.183375i
$144$	−5000.04	+	525.525i	−2.89354	+	0.304123i
$145$	−1171.67	−	342.793i	−0.671045	−	0.196327i
$146$	89.4994	−	123.185i	0.0507330	−	0.0698280i
$147$	−3238.89	−	410.254i	−1.81727	−	0.230185i
$148$	−994.059	+	506.499i	−0.552103	+	0.281310i
$149$	1588.98	−	917.400i	0.873655	−	0.504405i	0.00509374	−	0.999987i	$-0.498379\pi$
$149$	1588.98	−	917.400i	0.873655	−	0.504405i	0.868561	+	0.495582i	$0.165045\pi$
$150$	−4146.70	−	1081.34i	−2.25718	−	0.588609i
$151$	1488.96	−	2578.95i	0.802447	−	1.38988i	−0.115555	−	0.993301i	$-0.536865\pi$
$151$	1488.96	−	2578.95i	0.802447	−	1.38988i	0.918001	−	0.396577i	$-0.129802\pi$
$152$	1146.91	+	744.810i	0.612016	+	0.397448i
$153$	7767.76	−	1230.29i	4.10448	−	0.650086i
$154$	−198.105	+	355.786i	−0.103661	+	0.186169i
$155$	−778.807	−	1618.81i	−0.403583	−	0.838876i
$156$	−2299.58	−	1023.84i	−1.18022	−	0.525467i
$157$	2233.48	−	598.459i	1.13536	−	0.304218i	0.358275	−	0.933616i	$-0.383365\pi$
$157$	2233.48	−	598.459i	1.13536	−	0.304218i	0.777083	+	0.629398i	$0.216699\pi$
$158$	−2723.81	+	3363.62i	−1.37148	+	1.69364i
$159$	−3766.96	+	4183.64i	−1.87887	+	2.08669i
$160$	1815.70	−	1256.88i	0.897146	−	0.621032i
$161$	−607.012	+	207.715i	−0.297138	+	0.101678i
$162$	−5129.97	−	2613.85i	−2.48795	−	1.26768i
$163$	−3137.29	+	164.418i	−1.50755	+	0.0790076i	−0.788107	−	0.615539i	$-0.788938\pi$
$163$	−3137.29	+	164.418i	−1.50755	+	0.0790076i	−0.719448	+	0.694546i	$0.755605\pi$
$164$	95.4194	+	105.974i	0.0454329	+	0.0504584i
$165$	−423.565	−	492.576i	−0.199845	−	0.232406i
$166$	351.508	+	316.499i	0.164351	+	0.147982i
$167$	−1958.33	−	310.168i	−0.907424	−	0.143722i	−0.314760	−	0.949171i	$-0.601924\pi$
$167$	−1958.33	−	310.168i	−0.907424	−	0.143722i	−0.592664	+	0.805449i	$0.701924\pi$
$168$	716.552	+	1783.33i	0.329067	+	0.818970i
$169$	370.881	+	510.475i	0.168813	+	0.232351i
$170$	−3940.55	+	3044.75i	−1.77780	+	1.37366i
$171$	3244.61	+	7287.52i	1.45100	+	3.25901i
$172$	259.396	−	675.749i	0.114993	−	0.299566i
$173$	−288.754	+	444.642i	−0.126899	+	0.195408i	−0.896410	−	0.443227i	$-0.853834\pi$
$173$	−288.754	+	444.642i	−0.126899	+	0.195408i	0.769510	+	0.638634i	$0.220500\pi$
$174$	3743.36			1.63094
$175$	51.5078	+	2314.46i	0.0222493	+	0.999752i
$176$	482.594			0.206687
$177$	698.223	−	1075.17i	0.296506	−	0.456580i
$178$	923.099	−	2404.76i	0.388703	−	1.01261i
$179$	−311.168	−	698.895i	−0.129932	−	0.291832i	0.836851	−	0.547431i	$-0.184394\pi$
$179$	−311.168	−	698.895i	−0.129932	−	0.291832i	−0.966783	+	0.255599i	$0.917727\pi$
$180$	3534.50	−	104.419i	1.46359	−	0.0432384i
$181$	−349.202	−	480.635i	−0.143403	−	0.197378i	0.731273	−	0.682084i	$-0.238926\pi$
$181$	−349.202	−	480.635i	−0.143403	−	0.197378i	−0.874677	+	0.484707i	$0.838926\pi$
$182$	−500.409	+	3511.90i	−0.203806	+	1.43032i
$183$	−2669.99	−	422.884i	−1.07853	−	0.170822i
$184$	280.670	+	252.716i	0.112452	+	0.101253i
$185$	−2314.05	+	967.617i	−0.919635	+	0.384544i
$186$	3685.87	+	4093.57i	1.45302	+	1.61374i
$187$	−753.882	+	39.5093i	−0.294809	+	0.0154503i
$188$	−1516.05	−	772.467i	−0.588136	−	0.299670i
$189$	−1243.09	+	6330.53i	−0.478419	+	2.43639i
$190$	−4017.60	−	3061.46i	−1.53404	−	1.16895i
$191$	−460.194	+	511.098i	−0.174338	+	0.193622i	−0.823981	−	0.566618i	$-0.808252\pi$
$191$	−460.194	+	511.098i	−0.174338	+	0.193622i	0.649643	+	0.760239i	$0.274918\pi$
$192$	−473.123	+	584.258i	−0.177837	+	0.219610i
$193$	4128.66	−	1106.27i	1.53983	−	0.412596i	0.613619	−	0.789602i	$-0.289713\pi$
$193$	4128.66	−	1106.27i	1.53983	−	0.412596i	0.926211	+	0.377006i	$0.123046\pi$
$194$	−3227.32	−	1436.89i	−1.19437	−	0.531768i
$195$	−4982.39	−	2683.62i	−1.82972	−	0.985527i
$196$	−1348.16	+	1045.02i	−0.491311	+	0.380840i
$197$	−1502.97	+	238.047i	−0.543564	+	0.0860921i	−0.422177	−	0.906513i	$-0.638734\pi$
$197$	−1502.97	+	238.047i	−0.543564	+	0.0860921i	−0.121387	+	0.992605i	$0.538734\pi$
$198$	1172.77	+	761.609i	0.420937	+	0.273360i
$199$	−1078.34	+	1867.74i	−0.384129	+	0.665331i	−0.991648	−	0.128974i	$-0.958831\pi$
$199$	−1078.34	+	1867.74i	−0.384129	+	0.665331i	0.607519	+	0.794305i	$0.292165\pi$
$200$	1175.63	−	689.309i	0.415649	−	0.243708i
$201$	−2319.11	+	1338.94i	−0.813817	+	0.469858i
$202$	900.942	−	459.053i	0.313812	−	0.159895i
$203$	−553.686	−	1944.95i	−0.191434	−	0.672457i
$204$	3440.61	−	4735.60i	1.18084	−	1.62528i
$205$	196.018	+	253.690i	0.0667830	+	0.0864315i
$206$	1645.35	−	172.933i	0.556489	−	0.0584894i
$207$	570.205	+	2128.03i	0.191459	+	0.714534i
$208$	3924.73	−	1506.56i	1.30832	−	0.502217i
$209$	−236.622	−	728.248i	−0.0783133	−	0.241024i
$210$	−2144.40	−	6767.10i	−0.704656	−	2.22369i
$211$	1228.80	−	3781.87i	0.400921	−	1.23391i	−0.523333	−	0.852128i	$-0.675312\pi$
$211$	1228.80	−	3781.87i	0.400921	−	1.23391i	0.924254	−	0.381779i	$-0.124688\pi$
$212$	153.938	+	2937.31i	0.0498703	+	0.951581i
$213$	280.523	−	182.174i	0.0902400	−	0.0586025i
$214$	−1384.69	+	1246.78i	−0.442316	+	0.398263i
$215$	695.637	−	1471.11i	0.220661	−	0.466647i
$216$	3611.95	−	1173.59i	1.13779	−	0.369689i
$217$	1581.73	−	2520.56i	0.494814	−	0.788512i
$218$	3317.02	+	3317.02i	1.03054	+	1.03054i
$219$	−163.663	+	367.594i	−0.0504993	+	0.113423i
$220$	−338.463	−	25.4957i	−0.103724	−	0.00781326i
$221$	−6007.65	+	2674.78i	−1.82859	+	0.814141i
$222$	5977.10	−	4840.16i	1.80701	−	1.46329i
$223$	1881.09	+	3691.85i	0.564875	+	1.10863i	0.980024	+	0.198877i	$0.0637295\pi$
$223$	1881.09	+	3691.85i	0.564875	+	1.10863i	−0.415149	+	0.909753i	$0.636271\pi$
$224$	3364.49	+	1435.73i	1.00357	+	0.428254i
$225$	7941.39	+	362.789i	2.35301	+	0.107493i
$226$	−1598.72	−	2769.06i	−0.470554	−	0.815024i
$227$	30.6714	−	585.245i	0.00896797	−	0.171119i	−0.990474	−	0.137703i	$-0.956028\pi$
$227$	30.6714	−	585.245i	0.00896797	−	0.171119i	0.999442	−	0.0334161i	$-0.0106386\pi$
$228$	5542.97	+	2127.75i	1.61005	+	0.618041i
$229$	142.799	−	1358.64i	0.0412071	−	0.392059i	−0.954407	−	0.298507i	$-0.903511\pi$
$229$	142.799	−	1358.64i	0.0412071	−	0.392059i	0.995614	−	0.0935519i	$-0.0298221\pi$
$230$	−963.637	−	1008.66i	−0.276262	−	0.289171i
$231$	316.598	−	1028.51i	0.0901758	−	0.292949i
$232$	−841.772	+	841.772i	−0.238211	+	0.238211i
$233$	141.845	+	369.518i	0.0398822	+	0.103897i	0.952075	−	0.305864i	$-0.0989454\pi$
$233$	141.845	+	369.518i	0.0398822	+	0.103897i	−0.912193	+	0.409761i	$0.865612\pi$
$234$	11915.2	+	2532.66i	3.32874	+	0.707545i
$235$	−3268.29	−	1987.76i	−0.907233	−	0.551776i
$236$	−139.261	−	655.170i	−0.0384115	−	0.180712i
$237$	5192.64	−	10191.1i	1.42320	−	2.79318i
$238$	−7746.18	−	2836.15i	−2.10971	−	0.772438i
$239$	4469.60	+	1452.26i	1.20968	+	0.393050i	0.843315	−	0.537419i	$-0.180601\pi$
$239$	4469.60	+	1452.26i	1.20968	+	0.393050i	0.366369	+	0.930470i	$0.380601\pi$
$240$	−5770.38	+	6121.70i	−1.55198	+	1.64648i
$241$	−1457.09	+	6855.06i	−0.389458	+	1.83225i	0.148031	+	0.988983i	$0.452706\pi$
$241$	−1457.09	+	6855.06i	−0.389458	+	1.83225i	−0.537489	+	0.843271i	$0.680627\pi$
$242$	3621.33	+	2932.50i	0.961934	+	0.778959i
$243$	5611.71	+	1503.65i	1.48145	+	0.396952i
$244$	−1142.65	+	830.180i	−0.299797	+	0.217815i
$245$	−3198.82	+	2115.11i	−0.834143	+	0.551548i
$246$	−795.316	−	577.831i	−0.206128	−	0.149761i
$247$	−4197.78	−	5183.83i	−1.08137	−	1.33538i
$248$	−1749.37	−	91.6804i	−0.447923	−	0.0234746i
$249$	−1082.50	−	624.983i	−0.275505	−	0.159063i
$250$	−4521.29	+	2212.66i	−1.14381	+	0.559765i
$251$			2519.55i			0.633596i	0.948493	+	0.316798i	$0.102608\pi$
$251$			2519.55i			0.633596i	−0.948493	+	0.316798i	$0.897392\pi$
$252$	3266.17	+	4862.30i	0.816465	+	1.21546i
$253$	−33.0819	−	208.871i	−0.00822072	−	0.0519036i
$254$	−7485.84	−	786.794i	−1.84923	−	0.194362i
$255$	8512.99	−	10035.4i	2.09061	−	2.46448i
$256$	−553.843	−	5269.46i	−0.135215	−	1.28649i
$257$	815.288	−	3042.70i	0.197884	−	0.738514i	−0.793617	−	0.608418i	$-0.791805\pi$
$257$	815.288	−	3042.70i	0.197884	−	0.738514i	0.991501	−	0.130097i	$-0.0415288\pi$
$258$	−780.588	+	4928.44i	−0.188362	+	1.18927i
$259$	−3398.90	−	2389.62i	−0.815434	−	0.573298i
$260$	−2832.17	+	849.269i	−0.675552	+	0.202575i
$261$	−6792.45	+	1443.78i	−1.61089	+	0.342405i
$262$	2435.71	+	3750.67i	0.574347	+	0.884416i
$263$	−190.130	−	292.775i	−0.0445776	−	0.0686435i	0.815679	−	0.578505i	$-0.196363\pi$
$263$	−190.130	−	292.775i	−0.0445776	−	0.0686435i	−0.860257	+	0.509861i	$0.829697\pi$
$264$	−619.657	+	131.712i	−0.144459	+	0.0307058i
$265$	−150.926	+	6610.96i	−0.0349862	+	1.53248i
$266$	745.170	−	8333.91i	0.171764	−	1.92100i
$267$	−1064.85	+	6723.20i	−0.244074	+	1.54102i
$268$	−362.119	+	1351.45i	−0.0825371	+	0.308033i
$269$	−342.408	−	3257.80i	−0.0776097	−	0.738407i	−0.962256	−	0.272145i	$-0.912267\pi$
$269$	−342.408	−	3257.80i	−0.0776097	−	0.738407i	0.884647	−	0.466262i	$-0.154400\pi$
$270$	−13629.0	+	3320.42i	−3.07198	+	0.748423i
$271$	−2865.27	−	301.152i	−0.642261	−	0.0675044i	−0.222201	−	0.975001i	$-0.571324\pi$
$271$	−2865.27	−	301.152i	−0.642261	−	0.0675044i	−0.420060	+	0.907496i	$0.637991\pi$
$272$	1529.28	+	9655.52i	0.340906	+	2.15240i
$273$	−636.057	−	9352.79i	−0.141011	−	2.07347i
$274$			8895.92i			1.96140i
$275$	−754.474	−	114.314i	−0.165442	−	0.0250669i
$276$	1420.06	+	819.872i	0.309701	+	0.178806i
$277$	97.7459	+	5.12265i	0.0212021	+	0.00111116i	0.0629341	−	0.998018i	$-0.479954\pi$
$277$	97.7459	+	5.12265i	0.0212021	+	0.00111116i	−0.0417320	+	0.999129i	$0.513288\pi$
$278$	3796.98	+	4688.89i	0.819165	+	1.01159i
$279$	−8266.98	−	6006.31i	−1.77395	−	1.28885i
$280$	2003.93	+	1039.51i	0.427707	+	0.221866i
$281$	−804.570	+	584.555i	−0.170807	+	0.124098i	−0.669904	−	0.742447i	$-0.733665\pi$
$281$	−804.570	+	584.555i	−0.170807	+	0.124098i	0.499098	+	0.866546i	$0.333665\pi$
$282$	11330.1	+	3035.89i	2.39254	+	0.641080i
$283$	−1983.74	−	1606.40i	−0.416683	−	0.337423i	0.397943	−	0.917410i	$-0.369724\pi$
$283$	−1983.74	−	1606.40i	−0.416683	−	0.337423i	−0.814626	+	0.579987i	$0.803058\pi$
$284$	36.3346	−	170.941i	0.00759177	−	0.0357165i
$285$	12067.1	+	5706.11i	2.50805	+	1.18597i
$286$	−1112.06	−	361.330i	−0.229921	−	0.0747060i
$287$	−182.589	+	498.693i	−0.0375536	+	0.102568i
$288$	5702.76	−	11192.3i	1.16680	−	2.28997i
$289$	−2157.98	−	10152.5i	−0.439238	−	2.06645i
$290$	3333.93	−	2866.84i	0.675086	−	0.580505i
$291$	9131.73	+	1941.01i	1.83956	+	0.391010i
$292$	75.3411	+	196.270i	0.0150993	+	0.0393351i
$293$	10.9895	−	10.9895i	0.00219117	−	0.00219117i	−0.706010	−	0.708202i	$-0.749507\pi$
$293$	10.9895	−	10.9895i	0.00219117	−	0.00219117i	0.708202	+	0.706010i	$0.249507\pi$
$294$	7592.95	−	8979.02i	1.50622	−	1.78118i
$295$	−201.560	−	1492.30i	−0.0397805	−	0.294526i
$296$	−255.664	+	2432.48i	−0.0502033	+	0.477653i
$297$	−1985.28	−	762.079i	−0.387872	−	0.148890i
$298$	−345.868	+	6599.55i	−0.0672335	+	1.28289i
$299$	−921.094	−	1595.38i	−0.178155	−	0.308573i
$300$	4370.42	−	3988.55i	0.841087	−	0.767597i
$301$	2676.14	−	323.401i	0.512460	−	0.0619286i
$302$	4869.44	+	9556.82i	0.927831	+	1.82097i
$303$	−2076.61	+	1681.61i	−0.393724	+	0.318831i
$304$	−9058.57	+	4033.13i	−1.70903	+	0.760908i
$305$	−2701.82	+	1668.17i	−0.507231	+	0.313177i
$306$	−11521.5	+	25877.8i	−2.15242	+	4.83443i
$307$	1444.34	+	1444.34i	0.268511	+	0.268511i	0.828500	−	0.559989i	$-0.189195\pi$
$307$	1444.34	+	1444.34i	0.268511	+	0.268511i	−0.559989	+	0.828500i	$0.689195\pi$
$308$	−263.013	−	496.944i	−0.0486577	−	0.0919351i
$309$	−4158.02	+	1351.02i	−0.765506	+	0.248728i
$310$	6417.76	+	823.025i	1.17582	+	0.150789i
$311$	5216.22	−	4696.70i	0.951076	−	0.856353i	−0.0386613	−	0.999252i	$-0.512309\pi$
$311$	5216.22	−	4696.70i	0.951076	−	0.856353i	0.989737	+	0.142900i	$0.0456427\pi$
$312$	−4628.22	+	3005.60i	−0.839812	+	0.545380i
$313$	366.421	+	6991.73i	0.0661704	+	1.26261i	0.806853	+	0.590752i	$0.201169\pi$
$313$	366.421	+	6991.73i	0.0661704	+	1.26261i	−0.740683	+	0.671855i	$0.765498\pi$
$314$	−2573.60	+	7920.74i	−0.462538	+	1.42355i
$315$	6501.10	+	11452.0i	1.16284	+	2.04841i
$316$	−1846.67	−	5683.45i	−0.328744	−	1.01177i
$317$	−1040.21	+	399.300i	−0.184303	+	0.0707473i	−0.448769	−	0.893648i	$-0.648138\pi$
$317$	−1040.21	+	399.300i	−0.184303	+	0.0707473i	0.264466	+	0.964395i	$0.414804\pi$
$318$	−5248.05	−	19586.0i	−0.925459	−	3.45386i
$319$	662.918	−	69.6755i	0.116352	−	0.0122291i
$320$	26.0771	+	882.693i	0.00455549	+	0.154200i
$321$	2894.25	−	3983.59i	0.503243	−	0.692655i
$322$	563.317	−	2241.09i	0.0974921	−	0.387861i
$323$	13820.6	−	7041.95i	2.38080	−	1.21308i
$324$	6884.40	−	3974.71i	1.18045	−	0.681535i
$325$	−6492.67	+	1425.65i	−1.10815	+	0.243325i
$326$	5657.72	−	9799.45i	0.961202	−	1.66485i
$327$	−10396.6	−	6751.64i	−1.75821	−	1.14179i
$328$	308.780	−	48.9060i	0.0519803	−	0.00823287i
$329$	−98.4846	−	6335.86i	−0.0165034	−	1.06172i
$330$	2318.84	−	313.197i	0.386812	−	0.0522453i
$331$	498.500	+	221.947i	0.0827796	+	0.0368559i	0.447709	−	0.894179i	$-0.352240\pi$
$331$	498.500	+	221.947i	0.0827796	+	0.0368559i	−0.364929	+	0.931035i	$0.618907\pi$
$332$	−630.822	+	169.028i	−0.104280	+	0.0279417i
$333$	−8978.84	+	11087.9i	−1.47759	+	1.82467i
$334$	4778.56	−	5307.13i	0.782848	−	0.869441i
$335$	−1040.03	+	2968.57i	−0.169621	+	0.484150i
$336$	−13674.4	−	2685.16i	−2.22024	−	0.435975i
$337$	−996.491	−	507.737i	−0.161075	−	0.0820719i	0.371595	−	0.928395i	$-0.378811\pi$
$337$	−996.491	−	507.737i	−0.161075	−	0.0820719i	−0.532670	+	0.846323i	$0.678811\pi$
$338$	−2269.56	+	118.943i	−0.365230	+	0.0191409i
$339$	5653.93	+	6279.32i	0.905838	+	1.00604i
$340$	−562.446	−	6852.61i	−0.0897144	−	1.09304i
$341$	728.930	+	656.332i	0.115759	+	0.104230i
$342$	−28378.6	−	4494.72i	−4.48695	−	0.710663i
$343$	−5788.35	−	2616.99i	−0.911199	−	0.411966i
$344$	−932.730	−	1283.79i	−0.146190	−	0.201214i
$345$	3045.09	+	2077.83i	0.475194	+	0.324250i
$346$	−776.701	−	1744.50i	−0.120681	−	0.271054i
$347$	1398.94	−	3644.37i	0.216424	−	0.563803i	−0.781790	−	0.623542i	$-0.785693\pi$
$347$	1398.94	−	3644.37i	0.216424	−	0.563803i	0.998214	+	0.0597381i	$0.0190266\pi$
$348$	−2814.96	+	4334.66i	−0.433614	+	0.667707i
$349$	1688.35			0.258955			0.129478	−	0.991582i	$-0.458670\pi$
$349$	1688.35			0.258955			0.129478	+	0.991582i	$0.458670\pi$
$350$	−7092.41	−	4384.65i	−1.08316	−	0.669627i
$351$	−18524.5			−2.81699
$352$	−656.706	+	1011.24i	−0.0994390	+	0.153123i
$353$	−3759.82	+	9794.66i	−0.566898	+	1.47682i	0.287798	+	0.957691i	$0.407077\pi$
$353$	−3759.82	+	9794.66i	−0.566898	+	1.47682i	−0.854696	+	0.519129i	$0.826257\pi$
$354$	1878.10	+	4218.29i	0.281978	+	0.633332i
$355$	110.323	−	377.086i	0.0164940	−	0.0563764i
$356$	2090.45	+	2877.26i	0.311218	+	0.428355i
$357$	21581.3	+	3075.10i	3.19944	+	0.455887i
$358$	2721.59	+	431.058i	0.401789	+	0.0636372i
$359$	2572.04	+	2315.87i	0.378125	+	0.340465i	0.836177	−	0.548460i	$-0.184786\pi$
$359$	2572.04	+	2315.87i	0.378125	+	0.340465i	−0.458052	+	0.888926i	$0.651453\pi$
$360$	4028.28	−	6623.33i	0.589748	−	0.969666i
$361$	5938.07	+	6594.89i	0.865734	+	0.961495i
$362$	2136.90	−	111.990i	0.310256	−	0.0162598i
$363$	−10971.9	−	5590.48i	−1.58644	−	0.808331i
$364$	−3690.33	−	3220.35i	−0.531390	−	0.463715i
$365$	135.758	+	452.729i	0.0194682	+	0.0649230i
$366$	6515.10	−	7235.75i	0.930463	−	1.03338i
$367$	−5787.63	+	7147.12i	−0.823192	+	1.01656i	0.176288	+	0.984339i	$0.443591\pi$
$367$	−5787.63	+	7147.12i	−0.823192	+	1.01656i	−0.999481	+	0.0322194i	$0.989742\pi$
$368$	−2645.20	+	708.779i	−0.374703	+	0.100401i
$369$	1665.99	+	741.747i	0.235035	+	0.104644i
$370$	1616.53	−	8888.29i	0.227133	−	1.24887i
$371$	−9400.11	+	5623.74i	−1.31544	+	0.786981i
$372$	−7511.91	+	1189.77i	−1.04697	+	0.165824i
$373$	1787.30	+	1160.68i	0.248104	+	0.161121i	0.662700	−	0.748885i	$-0.269410\pi$
$373$	1787.30	+	1160.68i	0.248104	+	0.161121i	−0.414596	+	0.910006i	$0.636077\pi$
$374$	1359.53	−	2354.78i	0.187968	−	0.325569i
$375$	10471.3	−	8203.64i	1.44196	−	1.12969i
$376$	−3230.49	+	1865.12i	−0.443084	+	0.255815i
$377$	5173.71	−	2636.14i	0.706789	−	0.360127i
$378$	−16684.3	−	16173.5i	−2.27023	−	2.20073i
$379$	−8200.75	+	11287.4i	−1.11146	+	1.52980i	−0.292219	+	0.956351i	$0.594394\pi$
$379$	−8200.75	+	11287.4i	−1.11146	+	1.52980i	−0.819243	+	0.573446i	$0.805606\pi$
$380$	6566.22	−	2350.04i	0.886421	−	0.317248i
$381$	19782.3	−	2079.21i	2.66005	−	0.279583i
$382$	−641.132	−	2392.74i	−0.0858722	−	0.320479i
$383$	2934.21	−	1126.34i	0.391466	−	0.150270i	−0.154670	−	0.987966i	$-0.549432\pi$
$383$	2934.21	−	1126.34i	0.391466	−	0.150270i	0.546136	+	0.837697i	$0.316098\pi$
$384$	3810.84	+	11728.6i	0.506435	+	1.55865i
$385$	−505.712	−	1158.48i	−0.0669441	−	0.153355i
$386$	−4757.38	+	14641.7i	−0.627317	+	1.93068i
$387$	−484.452	−	9243.89i	−0.0636332	−	1.21419i
$388$	4090.77	−	2656.57i	0.535251	−	0.347596i
$389$	3610.60	−	3251.00i	0.470603	−	0.423733i	−0.399402	−	0.916776i	$-0.630782\pi$
$389$	3610.60	−	3251.00i	0.470603	−	0.423733i	0.870005	+	0.493043i	$0.164116\pi$
$390$	17880.4	−	9786.05i	2.32156	−	1.27060i
$391$	4074.16	−	1323.78i	0.526954	−	0.171218i
$392$	311.687	+	3726.55i	0.0401596	+	0.480151i
$393$	−8356.79	−	8356.79i	−1.07263	−	1.07263i
$394$	2229.28	−	5007.04i	0.285049	−	0.640231i
$395$	−3180.14	−	13053.2i	−0.405090	−	1.66273i
$396$	−1763.82	+	785.305i	−0.223827	+	0.0996542i
$397$	8642.20	−	6998.31i	1.09254	−	0.884723i	0.0986550	−	0.995122i	$-0.468546\pi$
$397$	8642.20	−	6998.31i	1.09254	−	0.884723i	0.993887	+	0.110398i	$0.0352126\pi$
$398$	−3526.58	−	6921.31i	−0.444150	−	0.871693i
$399$	2652.76	+	21951.6i	0.332842	+	2.75428i
$400$	−450.956	+	9871.35i	−0.0563694	+	1.23392i
$401$	621.039	+	1075.67i	0.0773396	+	0.133956i	0.902101	−	0.431524i	$-0.142024\pi$
$401$	621.039	+	1075.67i	0.0773396	+	0.133956i	−0.824762	+	0.565481i	$0.808691\pi$
$402$	504.791	−	9631.98i	0.0626286	−	1.19502i
$403$	7977.00	+	3062.08i	0.986012	+	0.378495i
$404$	−145.933	+	1388.46i	−0.0179713	+	0.170986i
$405$	16104.9	−	7748.06i	1.97595	−	0.950628i
$406$	6961.34	+	2142.85i	0.850949	+	0.261940i
$407$	968.404	−	968.404i	0.117941	−	0.117941i
$408$	−4598.86	−	11980.4i	−0.558033	−	1.45373i
$409$	−3405.40	−	723.841i	−0.411703	−	0.0875101i	−0.00259589	−	0.999997i	$-0.500826\pi$
$409$	−3405.40	−	723.841i	−0.411703	−	0.0875101i	−0.409107	+	0.912487i	$0.634160\pi$
$410$	−1150.86	+	94.4595i	−0.138626	+	0.0113781i
$411$	−4887.73	−	22994.9i	−0.586603	−	2.75975i
$412$	−1037.03	+	2035.29i	−0.124007	+	0.243377i
$413$	1913.92	−	1599.75i	0.228033	−	0.190601i
$414$	−7546.79	−	2452.10i	−0.895905	−	0.291097i
$415$	−1442.74	+	272.405i	−0.170654	+	0.0322213i
$416$	−2183.82	+	10274.1i	−0.257381	+	1.21088i
$417$	−12391.0	−	10034.0i	−1.45513	−	1.17834i
$418$	2664.02	+	713.822i	0.311726	+	0.0835268i
$419$	−1530.90	+	1112.27i	−0.178495	+	0.129684i	−0.673445	−	0.739237i	$-0.735186\pi$
$419$	−1530.90	+	1112.27i	−0.178495	+	0.129684i	0.494950	+	0.868921i	$0.335186\pi$
$420$	9448.58	+	2605.64i	1.09772	+	0.302719i
$421$	10091.5	+	7331.94i	1.16825	+	0.848781i	0.990798	−	0.135349i	$-0.0432156\pi$
$421$	10091.5	+	7331.94i	1.16825	+	0.848781i	0.177449	+	0.984130i	$0.443216\pi$
$422$	9013.48	+	11130.7i	1.03974	+	1.28397i
$423$	−21729.7	−	1138.81i	−2.49772	−	0.130900i
$424$	5584.44	+	3224.18i	0.639633	+	0.369292i
$425$	−103.695	−	15457.4i	−0.0118352	−	1.76422i
$426$			1204.75i			0.137020i
$427$	−4723.16	−	2314.82i	−0.535292	−	0.262347i
$428$	−402.452	−	2540.98i	−0.0454515	−	0.286970i
$429$	3073.08	+	322.993i	0.345850	+	0.0363503i
$430$	3079.22	+	4987.20i	0.345332	+	0.559312i
$431$	1152.10	+	10961.5i	0.128757	+	1.22505i	0.847890	+	0.530172i	$0.177873\pi$
$431$	1152.10	+	10961.5i	0.128757	+	1.22505i	−0.719132	+	0.694873i	$0.755461\pi$
$432$	−7127.28	+	26599.4i	−0.793776	+	2.96241i
$433$	−1615.55	+	10200.2i	−0.179303	+	1.13208i	0.719749	+	0.694234i	$0.244257\pi$
$433$	−1615.55	+	10200.2i	−0.179303	+	1.13208i	−0.899052	+	0.437841i	$0.855743\pi$
$434$	4511.10	+	9722.53i	0.498939	+	1.07534i
$435$	−7042.68	+	9242.22i	−0.776254	+	1.01869i
$436$	−6335.34	+	1346.62i	−0.695889	+	0.147916i
$437$	2366.54	+	3644.16i	0.259055	+	0.398910i
$438$	−789.347	−	1215.49i	−0.0861107	−	0.132599i
$439$	−11295.5	+	2400.93i	−1.22803	+	0.261026i	−0.775860	−	0.630906i	$-0.782683\pi$
$439$	−11295.5	+	2400.93i	−1.22803	+	0.261026i	−0.452171	+	0.891932i	$0.649350\pi$
$440$	−451.010	+	591.868i	−0.0488661	+	0.0641277i
$441$	−10314.5	+	19221.3i	−1.11376	+	2.07551i
$442$	3705.34	−	23394.6i	0.398744	−	2.51757i
$443$	−1634.94	+	6101.69i	−0.175346	+	0.654402i	0.821146	+	0.570718i	$0.193335\pi$
$443$	−1634.94	+	6101.69i	−0.175346	+	0.654402i	−0.996492	+	0.0836836i	$0.973331\pi$
$444$	1110.00	+	10561.0i	0.118645	+	1.12883i
$445$	4200.55	+	6803.35i	0.447473	+	0.724741i
$446$	−14842.2	−	1559.98i	−1.57578	−	0.165621i
$447$	−2731.99	−	17249.1i	−0.289080	−	1.82518i
$448$	−1214.29	+	815.680i	−0.128058	+	0.0860207i
$449$		−	10170.1i		−	1.06895i	−0.845185	−	0.534475i	$-0.820509\pi$
$449$		−	10170.1i		−	1.06895i	0.845185	−	0.534475i	$-0.179491\pi$
$450$	−16674.4	+	23277.2i	−1.74675	+	2.43843i
$451$	−151.599	−	87.5257i	−0.0158282	−	0.00913842i
$452$	4408.68	+	231.049i	0.458776	+	0.0240434i
$453$	−17837.8	−	22027.8i	−1.85009	−	2.28468i
$454$	1707.70	+	1240.72i	0.176534	+	0.128259i
$455$	−7729.28	−	7842.70i	−0.796383	−	0.808069i
$456$	10530.6	−	7650.91i	1.08145	−	0.785716i
$457$	11719.4	+	3140.20i	1.19958	+	0.321427i	0.802667	−	0.596427i	$-0.203414\pi$
$457$	11719.4	+	3140.20i	1.19958	+	0.321427i	0.396916	+	0.917855i	$0.370080\pi$
$458$	3823.97	+	3096.59i	0.390136	+	0.315926i
$459$	8956.19	−	42135.6i	0.910761	−	4.28479i
$460$	1892.63	−	357.349i	0.191836	−	0.0362207i
$461$	9435.99	+	3065.94i	0.953314	+	0.309751i	0.744062	−	0.668111i	$-0.232897\pi$
$461$	9435.99	+	3065.94i	0.953314	+	0.309751i	0.209253	+	0.977862i	$0.432897\pi$
$462$	2485.80	+	2973.98i	0.250324	+	0.299485i
$463$	−2451.91	+	4812.14i	−0.246112	+	0.483022i	−0.980707	−	0.195484i	$-0.937372\pi$
$463$	−2451.91	+	4812.14i	−0.246112	+	0.483022i	0.734595	+	0.678506i	$0.237372\pi$
$464$	−1794.66	−	8443.19i	−0.179558	−	0.844753i
$465$	−17041.4	+	1398.71i	−1.69952	+	0.139492i
$466$	−1394.47	−	296.404i	−0.138621	−	0.0294649i
$467$	3031.17	+	7896.47i	0.300355	+	0.782452i	0.997830	+	0.0658427i	$0.0209736\pi$
$467$	3031.17	+	7896.47i	0.300355	+	0.782452i	−0.697475	+	0.716609i	$0.745693\pi$
$468$	−11892.8	+	11892.8i	−1.17467	+	1.17467i
$469$	−5079.19	+	1162.41i	−0.500075	+	0.114445i
$470$	12415.9	−	5973.27i	1.21851	−	0.586226i
$471$	2300.55	−	21888.2i	0.225061	−	2.14131i
$472$	−1370.90	−	526.239i	−0.133688	−	0.0513180i
$473$	−46.5022	+	887.315i	−0.00452045	+	0.0862554i
$474$	20598.3	+	35677.4i	1.99602	+	3.45721i
$475$	15117.2	−	4159.54i	1.46027	−	0.401796i
$476$	9109.17	−	6837.00i	0.877139	−	0.658348i
$477$	17076.9	+	33515.3i	1.63920	+	3.21711i
$478$	−13154.9	+	10652.6i	−1.25876	+	1.01933i
$479$	2156.42	−	960.101i	0.205698	−	0.0915827i	−0.301302	−	0.953529i	$-0.597421\pi$
$479$	2156.42	−	960.101i	0.205698	−	0.0915827i	0.507000	+	0.861946i	$0.330754\pi$
$480$	−4975.31	−	20421.7i	−0.473106	−	1.94191i
$481$	4852.44	−	10898.8i	0.459984	−	1.03314i
$482$	−17849.0	−	17849.0i	−1.68672	−	1.68672i
$483$	−224.777	+	6102.48i	−0.0211754	+	0.574891i
$484$	−6118.90	+	1988.15i	−0.574653	+	0.186716i
$485$	9619.45	−	5264.79i	0.900611	−	0.492911i
$486$	−15550.6	+	14001.8i	−1.45141	+	1.30686i
$487$	−5936.13	+	3854.97i	−0.552344	+	0.358697i	−0.790435	−	0.612546i	$-0.790145\pi$
$487$	−5936.13	+	3854.97i	−0.552344	+	0.358697i	0.238090	+	0.971243i	$0.423479\pi$
$488$	162.053	+	3092.16i	0.0150324	+	0.286835i
$489$	−9240.39	+	28439.0i	−0.854529	+	2.62997i
$490$	−114.086	−	13812.0i	−0.0105181	−	1.27339i
$491$	−4063.14	−	12505.1i	−0.373456	−	1.14938i	−0.944514	−	0.328470i	$-0.893467\pi$
$491$	−4063.14	−	12505.1i	−0.373456	−	1.14938i	0.571058	−	0.820909i	$-0.306533\pi$
$492$	1267.17	−	486.421i	0.116115	−	0.0445723i
$493$	3494.74	+	13042.6i	0.319260	+	1.19150i
$494$	23893.7	−	2511.33i	2.17617	−	0.228725i
$495$	−4086.82	+	1462.66i	−0.371088	+	0.132812i
$496$	7466.00	−	10276.1i	0.675873	−	0.930260i
$497$	625.957	−	178.197i	0.0564950	−	0.0160829i
$498$	4011.44	−	2043.93i	0.360958	−	0.183917i
$499$	5785.42	−	3340.22i	0.519020	−	0.299657i	−0.217513	−	0.976057i	$-0.569795\pi$
$499$	5785.42	−	3340.22i	0.519020	−	0.299657i	0.736534	+	0.676401i	$0.236461\pi$
$500$	837.782	−	6899.37i	0.0749335	−	0.617098i
$501$	−9436.11	+	16343.8i	−0.841466	+	1.45746i
$502$	−7610.89	−	4942.57i	−0.676674	−	0.439437i
$503$	−2322.47	+	367.844i	−0.205873	+	0.0326070i	−0.258519	−	0.966006i	$-0.583234\pi$
$503$	−2322.47	+	367.844i	−0.205873	+	0.0326070i	0.0526462	+	0.998613i	$0.483234\pi$
$504$	12839.9	−	199.583i	1.13479	−	0.0176392i
$505$	−561.628	+	3088.05i	−0.0494894	+	0.272111i
$506$	695.840	+	309.808i	0.0611341	+	0.0272187i
$507$	5801.20	−	1554.43i	0.508167	−	0.136163i
$508$	6540.33	−	8076.64i	0.571221	−	0.705399i
$509$	−2933.07	+	3257.51i	−0.255415	+	0.283667i	−0.857192	−	0.514997i	$-0.827793\pi$
$509$	−2933.07	+	3257.51i	−0.255415	+	0.283667i	0.601777	+	0.798664i	$0.294460\pi$
$510$	13614.4	+	45401.8i	1.18207	+	3.94201i
$511$	−514.782	+	589.908i	−0.0445648	+	0.0510685i
$512$	7768.80	+	3958.40i	0.670578	+	0.341676i
$513$	43633.8	−	2286.75i	3.75532	−	0.196808i
$514$	7591.83	+	8431.59i	0.651481	+	0.723543i
$515$	−2668.56	+	4387.65i	−0.228331	+	0.375424i
$516$	−5119.94	−	4610.01i	−0.436808	−	0.393303i
$517$	2062.97	+	326.743i	0.175492	+	0.0277952i
$518$	13886.0	−	5579.47i	1.17783	−	0.473258i
$519$	2966.17	+	4082.58i	0.250868	+	0.345290i
$520$	−1820.18	+	6221.36i	−0.153500	+	0.524663i
$521$	−8102.58	−	18198.7i	−0.681344	−	1.53032i	−0.839763	−	0.542952i	$-0.817306\pi$
$521$	−8102.58	−	18198.7i	−0.681344	−	1.53032i	0.158419	−	0.987372i	$-0.449360\pi$
$522$	8963.39	−	23350.4i	0.751565	−	1.95789i
$523$	−7595.72	+	11696.4i	−0.635063	+	0.977911i	0.363858	+	0.931455i	$0.381459\pi$
$523$	−7595.72	+	11696.4i	−0.635063	+	0.977911i	−0.998920	+	0.0464563i	$0.985207\pi$
$524$	−6174.74			−0.514780
$525$	20742.1	+	7437.02i	1.72431	+	0.618244i
$526$	1257.37			0.104228
$527$	−10821.7	+	16663.9i	−0.894497	+	1.37740i
$528$	1646.15	−	4288.37i	0.135681	−	0.353460i
$529$	−4460.67	−	10018.8i	−0.366620	−	0.823443i
$530$	−19673.9	−	13424.5i	−1.61241	−	1.10024i
$531$	−5034.84	−	6929.86i	−0.411475	−	0.566347i
$532$	9089.97	+	7129.87i	0.740790	+	0.581051i
$533$	−1506.13	−	238.547i	−0.122397	−	0.0193858i
$534$	−18220.1	−	16405.4i	−1.47652	−	1.32946i
$535$	−473.130	−	5764.43i	−0.0382340	−	0.465828i
$536$	2052.44	+	2279.46i	0.165395	+	0.183690i
$537$	−7271.84	+	381.101i	−0.584363	+	0.0306252i
$538$	10512.6	+	5356.45i	0.842438	+	0.429244i
$539$	1177.52	−	1731.44i	0.0940991	−	0.138364i
$540$	6403.91	−	18278.7i	0.510334	−	1.45665i
$541$	773.128	−	858.646i	0.0614406	−	0.0682367i	−0.711641	−	0.702543i	$-0.752048\pi$
$541$	773.128	−	858.646i	0.0614406	−	0.0682367i	0.773082	+	0.634307i	$0.218714\pi$
$542$	6530.46	−	8064.45i	0.517541	−	0.639110i
$543$	−5462.10	+	1463.57i	−0.431678	+	0.115668i
$544$	−22313.4	−	9934.56i	−1.75860	−	0.782980i
$545$	−14430.2	+	1949.03i	−1.13417	+	0.153188i
$546$	29500.0	+	16425.9i	2.31224	+	1.28748i
$547$	214.476	−	33.9697i	0.0167648	−	0.00265528i	−0.148046	−	0.988980i	$-0.547299\pi$
$547$	214.476	−	33.9697i	0.0167648	−	0.00265528i	0.164811	+	0.986325i	$0.447299\pi$
$548$	−10301.1	−	6689.62i	−0.802996	−	0.521472i
$549$	−9031.10	+	15642.3i	−0.702073	+	1.21603i
$550$	1825.35	−	2054.82i	0.141515	−	0.159305i
$551$	−11861.1	+	6847.98i	−0.917056	+	0.529463i
$552$	3203.03	−	1632.02i	0.246975	−	0.125840i
$553$	15490.3	−	15979.4i	1.19116	−	1.22878i
$554$	−207.221	+	285.215i	−0.0158917	+	0.0218730i
$555$	704.989	+	23863.4i	0.0539192	+	1.82513i
$556$	−8284.82	+	870.770i	−0.631933	+	0.0664188i
$557$	2268.22	+	8465.13i	0.172545	+	0.643948i	0.996957	+	0.0779568i	$0.0248396\pi$
$557$	2268.22	+	8465.13i	0.172545	+	0.643948i	−0.824411	+	0.565991i	$0.808494\pi$
$558$	34360.7	−	13189.8i	2.60682	−	1.00066i
$559$	2391.84	+	7361.31i	0.180973	+	0.556978i
$560$	−14235.2	+	8081.03i	−1.07419	+	0.609796i
$561$	−2220.44	+	6833.82i	−0.167107	+	0.514303i
$562$	−187.468	−	3577.11i	−0.0140709	−	0.268490i
$563$	125.269	−	81.3505i	0.00937736	−	0.00608973i	−0.539942	−	0.841702i	$-0.681554\pi$
$563$	125.269	−	81.3505i	0.00937736	−	0.00608973i	0.549319	+	0.835613i	$0.314887\pi$
$564$	−12035.5	+	10836.8i	−0.898558	+	0.809065i
$565$	9844.51	+	1262.48i	0.733030	+	0.0940050i
$566$	8744.00	−	2841.10i	0.649360	−	0.210990i
$567$	25076.1	+	15736.0i	1.85732	+	1.16552i
$568$	−270.913	−	270.913i	−0.0200128	−	0.0200128i
$569$	−9761.49	+	21924.7i	−0.719197	+	1.61534i	0.0672878	+	0.997734i	$0.478565\pi$
$569$	−9761.49	+	21924.7i	−0.719197	+	1.61534i	−0.786485	+	0.617610i	$0.788101\pi$
$570$	−40908.5	+	25257.9i	−3.00609	+	1.85603i
$571$	−10407.6	+	4633.76i	−0.762775	+	0.339609i	−0.750983	−	0.660321i	$-0.770420\pi$
$571$	−10407.6	+	4633.76i	−0.762775	+	0.339609i	−0.0117919	+	0.999930i	$0.503754\pi$
$572$	1254.66	−	1016.00i	0.0917133	−	0.0742680i
$573$	2971.91	+	5832.69i	0.216672	+	0.425243i
$574$	−1148.24	−	1529.83i	−0.0834955	−	0.111244i
$575$	4303.32	−	481.505i	0.312106	−	0.0349220i
$576$	2511.62	+	4350.25i	0.181685	+	0.314688i
$577$	49.4221	−	943.031i	0.00356581	−	0.0680396i	−0.996267	−	0.0863254i	$-0.972488\pi$
$577$	49.4221	−	943.031i	0.00356581	−	0.0680396i	0.999833	+	0.0182858i	$0.00582086\pi$
$578$	34901.2	+	13397.3i	2.51159	+	0.964110i
$579$	4252.63	−	40461.1i	0.305239	−	2.90415i
$580$	812.609	+	6016.37i	0.0581755	+	0.430718i
$581$	−1655.31	−	1781.92i	−0.118199	−	0.127240i
$582$	−23776.9	+	23776.9i	−1.69344	+	1.69344i
$583$	−1293.94	−	3370.83i	−0.0919204	−	0.239461i
$584$	450.828	+	95.8266i	0.0319442	+	0.00678995i
$585$	−28670.1	+	24653.4i	−2.02626	+	1.74238i
$586$	11.6384	+	54.7542i	0.000820437	+	0.00385985i
$587$	6215.09	−	12197.8i	0.437009	−	0.857678i	−0.562514	−	0.826788i	$-0.690166\pi$
$587$	6215.09	−	12197.8i	0.437009	−	0.857678i	0.999523	−	0.0308904i	$-0.00983428\pi$
$588$	4687.54	+	15544.4i	0.328760	+	1.09021i
$589$	−19167.5	−	6227.91i	−1.34089	−	0.435682i
$590$	4903.24	+	2318.57i	0.342141	+	0.161787i
$591$	−3011.39	+	14167.5i	−0.209597	+	0.986078i
$592$	−13782.6	−	11160.9i	−0.956859	−	0.774850i
$593$	2287.07	+	612.819i	0.158379	+	0.0424376i	0.337137	−	0.941455i	$-0.390541\pi$
$593$	2287.07	+	612.819i	0.158379	+	0.0424376i	−0.178758	+	0.983893i	$0.557208\pi$
$594$	6196.55	−	4502.05i	0.428026	−	0.310979i
$595$	21575.8	−	13789.2i	1.48659	−	0.950084i
$596$	−7381.91	−	5363.27i	−0.507340	−	0.368604i
$597$	12918.6	+	15953.2i	0.885635	+	1.09367i
$598$	6626.12	+	347.260i	0.453114	+	0.0237467i
$599$	−23533.1	−	13586.8i	−1.60523	−	0.926783i	−0.990416	−	0.138114i	$-0.955896\pi$
$599$	−23533.1	−	13586.8i	−1.60523	−	0.926783i	−0.614818	−	0.788669i	$-0.710771\pi$
$600$	−2115.11	−	12798.0i	−0.143915	−	0.870795i
$601$		−	6266.76i		−	0.425335i	−0.977125	−	0.212668i	$-0.931785\pi$
$601$		−	6266.76i		−	0.425335i	0.977125	−	0.212668i	$-0.0682151\pi$
$602$	−4272.85	+	8718.33i	−0.289283	+	0.590254i
$603$	2799.01	+	17672.2i	0.189029	+	1.19348i
$604$	−14728.2	−	1547.99i	−0.992186	−	0.104283i
$605$	−14053.3	+	3423.80i	−0.944378	+	0.230078i
$606$	−1006.02	−	9571.68i	−0.0674372	−	0.641622i
$607$	−44.1788	+	164.878i	−0.00295414	+	0.0110250i	−0.967387	−	0.253302i	$-0.918483\pi$
$607$	−44.1788	+	164.878i	−0.00295414	+	0.0110250i	0.964433	+	0.264327i	$0.0851499\pi$
$608$	3875.62	−	24469.7i	0.258515	−	1.63220i
$609$	−19171.6	−	1714.21i	−1.27565	−	0.114061i
$610$	261.033	−	11433.9i	0.0173261	−	0.758926i
$611$	17797.3	−	3782.93i	1.17840	−	0.250476i
$612$	−21301.4	−	32801.2i	−1.40695	−	2.16652i
$613$	−7950.55	−	12242.8i	−0.523850	−	0.806658i	0.473394	−	0.880851i	$-0.343029\pi$
$613$	−7950.55	−	12242.8i	−0.523850	−	0.806658i	−0.997244	+	0.0741929i	$0.976362\pi$
$614$	−7196.33	+	1529.63i	−0.472997	+	0.100539i
$615$	2922.93	−	876.487i	0.191649	−	0.0574689i
$616$	−1227.74	−	109.778i	−0.0803038	−	0.00718030i
$617$	455.999	−	2879.07i	0.0297534	−	0.187856i	−0.968335	−	0.249653i	$-0.919683\pi$
$617$	455.999	−	2879.07i	0.0297534	−	0.187856i	0.998089	+	0.0617977i	$0.0196834\pi$
$618$	4075.66	−	15210.6i	0.265286	−	0.990062i
$619$	756.187	+	7194.64i	0.0491013	+	0.467168i	0.991252	+	0.131980i	$0.0421333\pi$
$619$	756.187	+	7194.64i	0.0491013	+	0.467168i	−0.942151	+	0.335188i	$0.891200\pi$
$620$	−5779.10	+	6812.60i	−0.374346	+	0.441291i
$621$	12001.0	+	1261.36i	0.775498	+	0.0815081i
$622$	3954.90	+	24970.3i	0.254947	+	1.60967i
$623$	−5828.87	+	11893.2i	−0.374845	+	0.764835i
$624$		−	40014.3i		−	2.56708i
$625$	3043.28	−	15325.8i	0.194770	−	0.980849i
$626$	−21839.0	−	12608.7i	−1.39435	−	0.805026i
$627$	−7278.39	−	381.444i	−0.463590	−	0.0242957i
$628$	−7236.57	−	8936.42i	−0.459826	−	0.567838i
$629$	22444.1	+	16306.6i	1.42274	+	1.03368i
$630$	−47346.7	−	2827.25i	−2.99419	−	0.178794i
$631$	−3973.07	+	2886.61i	−0.250658	+	0.182114i	−0.706019	−	0.708193i	$-0.749511\pi$
$631$	−3973.07	+	2886.61i	−0.250658	+	0.182114i	0.455360	+	0.890307i	$0.349511\pi$
$632$	−12654.8	−	3390.83i	−0.796486	−	0.213418i
$633$	−29414.4	−	23819.3i	−1.84695	−	1.49563i
$634$	834.391	−	3925.50i	0.0522680	−	0.245902i
$635$	16026.3	−	17002.0i	1.00155	−	1.06253i
$636$	26626.2	+	8651.38i	1.66006	+	0.539386i
$637$	4171.06	−	17757.0i	0.259440	−	1.10449i
$638$	−1089.97	+	2139.18i	−0.0676367	+	0.132744i
$639$	−464.662	−	2186.06i	−0.0287664	−	0.135335i
$640$	12376.3	+	7527.21i	0.764400	+	0.464905i
$641$	25263.6	+	5369.95i	1.55671	+	0.330890i	0.904274	−	0.426952i	$-0.140413\pi$
$641$	25263.6	+	5369.95i	1.55671	+	0.330890i	0.652439	+	0.757842i	$0.273746\pi$
$642$	6355.75	+	16557.3i	0.390719	+	1.01786i
$643$	−12804.6	+	12804.6i	−0.785326	+	0.785326i	−0.980724	−	0.195398i	$-0.937400\pi$
$643$	−12804.6	+	12804.6i	−0.785326	+	0.785326i	0.195398	+	0.980724i	$0.437400\pi$
$644$	2171.49	+	2337.57i	0.132870	+	0.143033i
$645$	−10699.6	−	11199.5i	−0.653170	−	0.683690i
$646$	−5839.85	+	55562.5i	−0.355675	+	3.38402i
$647$	−955.813	−	366.902i	−0.0580787	−	0.0222943i	0.329155	−	0.944276i	$-0.393236\pi$
$647$	−955.813	−	366.902i	−0.0580787	−	0.0222943i	−0.387234	+	0.921982i	$0.626569\pi$
$648$	912.094	−	17403.8i	0.0552939	−	1.05507i
$649$	411.112	+	712.067i	0.0248653	+	0.0430679i
$650$	8430.08	−	22409.3i	0.508700	−	1.35225i
$651$	−17002.6	−	22653.1i	−1.02363	−	1.36382i
$652$	7092.83	+	13920.5i	0.426038	+	0.836146i
$653$	−13396.6	+	10848.3i	−0.802832	+	0.650121i	−0.940285	−	0.340388i	$-0.889442\pi$
$653$	−13396.6	+	10848.3i	−0.802832	+	0.650121i	0.137453	+	0.990508i	$0.456108\pi$
$654$	40789.8	−	18160.8i	2.43885	−	1.08585i
$655$	−13842.8	−	1042.74i	−0.825773	−	0.0622035i
$656$	−922.010	+	2070.87i	−0.0548757	+	0.123253i
$657$	1901.10	+	1901.10i	0.112890	+	0.112890i
$658$	19332.1	+	12131.5i	1.14536	+	0.718745i
$659$	18448.3	−	5994.22i	1.09051	−	0.354327i	0.292065	−	0.956399i	$-0.405658\pi$
$659$	18448.3	−	5994.22i	1.09051	−	0.354327i	0.798442	+	0.602071i	$0.205658\pi$
$660$	−1381.07	+	2920.64i	−0.0814516	+	0.172251i
$661$	−10775.2	+	9702.04i	−0.634050	+	0.570901i	−0.922214	−	0.386680i	$-0.873622\pi$
$661$	−10775.2	+	9702.04i	−0.634050	+	0.570901i	0.288164	+	0.957581i	$0.406955\pi$
$662$	−1648.34	+	1070.45i	−0.0967744	+	0.0628460i
$663$	3275.92	+	62508.2i	0.191894	+	3.66156i
$664$	−442.435	+	1361.67i	−0.0258581	+	0.0795832i
$665$	19174.2	+	17519.0i	1.11811	+	1.02159i
$666$	−15880.0	−	48873.7i	−0.923933	−	2.84357i
$667$	−3531.26	+	1355.52i	−0.204994	+	0.0786898i
$668$	2552.02	+	9524.27i	0.147815	+	0.551654i
$669$	39222.5	−	4122.45i	2.26671	−	0.238241i
$670$	−6927.04	−	8965.06i	−0.399425	−	0.516941i
$671$	1019.09	−	1402.66i	0.0586312	−	0.0806989i
$672$	24234.4	−	24999.7i	1.39117	−	1.43510i
$673$	26256.8	−	13378.5i	1.50390	−	0.766275i	0.508407	−	0.861117i	$-0.330235\pi$
$673$	26256.8	−	13378.5i	1.50390	−	0.766275i	0.995492	+	0.0948417i	$0.0302345\pi$
$674$	3488.54	−	2014.11i	0.199367	−	0.115105i
$675$	17443.3	−	39896.4i	0.994655	−	2.27498i
$676$	1568.95	−	2717.50i	0.0892666	−	0.154614i
$677$	12489.2	+	8110.58i	0.709008	+	0.460435i	0.848095	−	0.529845i	$-0.177750\pi$
$677$	12489.2	+	8110.58i	0.709008	+	0.460435i	−0.139086	+	0.990280i	$0.544417\pi$
$678$	−30059.4	+	4760.94i	−1.70269	+	0.269680i
$679$	15870.7	+	8836.95i	0.896998	+	0.499457i
$680$	−13271.0	−	7148.04i	−0.748412	−	0.403110i
$681$	−5095.90	−	2268.84i	−0.286748	−	0.127668i
$682$	−3412.54	+	914.387i	−0.191602	+	0.0513397i
$683$	21216.4	−	26200.1i	1.18862	−	1.46782i	0.338703	−	0.940893i	$-0.390012\pi$
$683$	21216.4	−	26200.1i	1.18862	−	1.46782i	0.849912	−	0.526924i	$-0.176655\pi$
$684$	26545.0	−	29481.2i	1.48388	−	1.64802i
$685$	−21963.7	−	16736.6i	−1.22509	−	0.933536i
$686$	19260.2	−	12351.3i	1.07195	−	0.687429i
$687$	−11585.9	−	5903.31i	−0.643420	−	0.327839i
$688$	11490.4	−	602.185i	0.636725	−	0.0333693i
$689$	−21046.1	−	23374.1i	−1.16371	−	1.29243i
$690$	−12250.1	+	5122.35i	−0.675873	+	0.282615i
$691$	9252.78	+	8331.24i	0.509396	+	0.458662i	0.883302	−	0.468805i	$-0.155315\pi$
$691$	9252.78	+	8331.24i	0.509396	+	0.458662i	−0.373906	+	0.927467i	$0.621982\pi$
$692$	2604.13	+	412.453i	0.143055	+	0.0226577i
$693$	−5657.60	−	4437.63i	−0.310122	−	0.243249i
$694$	8264.37	+	11374.9i	0.452034	+	0.622171i
$695$	−18720.2	+	553.047i	−1.02173	+	0.0301845i
$696$	4608.72	+	10351.4i	0.250996	+	0.563746i
$697$	1270.77	−	3310.48i	0.0690589	−	0.179904i
$698$	−3312.02	+	5100.06i	−0.179601	+	0.276562i
$699$	3767.40			0.203857
$700$	10410.6	−	4915.51i	0.562122	−	0.265413i
$701$	12600.6			0.678916			0.339458	−	0.940621i	$-0.389756\pi$
$701$	12600.6			0.678916			0.339458	+	0.940621i	$0.389756\pi$
$702$	36339.3	−	55957.6i	1.95376	−	3.00852i
$703$	−10084.4	+	26270.6i	−0.541022	+	1.40941i
$704$	−196.119	−	440.491i	−0.0104993	−	0.0235819i
$705$	−28811.7	+	22261.9i	−1.53916	+	1.18927i
$706$	−22211.5	−	30571.5i	−1.18405	−	1.62971i
$707$	−4824.39	+	1938.47i	−0.256633	+	0.103117i
$708$	−6296.91	−	997.333i	−0.334255	−	0.0529408i
$709$	−2248.90	−	2024.92i	−0.119124	−	0.107260i	0.607416	−	0.794384i	$-0.292206\pi$
$709$	−2248.90	−	2024.92i	−0.119124	−	0.107260i	−0.726540	+	0.687124i	$0.758873\pi$
$710$	922.655	+	1072.98i	0.0487699	+	0.0567159i
$711$	−51136.8	−	56793.2i	−2.69730	−	2.99566i
$712$	7786.26	−	408.061i	0.409835	−	0.0214785i
$713$	−4959.37	−	2526.92i	−0.260490	−	0.132727i
$714$	−51624.7	+	59158.8i	−2.70589	+	3.10079i
$715$	2984.32	−	2065.84i	0.156094	−	0.108053i
$716$	−2545.75	+	2827.34i	−0.132876	+	0.147574i
$717$	28150.9	−	34763.5i	1.46627	−	1.81069i
$718$	−12041.2	+	3226.42i	−0.625866	+	0.167700i
$719$	−28654.0	−	12757.6i	−1.48625	−	0.661721i	−0.506553	−	0.862209i	$-0.669080\pi$
$719$	−28654.0	−	12757.6i	−1.48625	−	0.661721i	−0.979696	+	0.200488i	$0.935747\pi$
$720$	24369.1	+	50652.9i	1.26136	+	2.62184i
$721$	−8505.84	+	132.215i	−0.439353	+	0.00682932i
$722$	−31570.1	+	5000.21i	−1.62731	+	0.257740i
$723$	55944.3	+	36330.7i	2.87772	+	1.86881i
$724$	−1477.24	+	2558.65i	−0.0758303	+	0.131342i
$725$	805.739	+	13624.9i	0.0412750	+	0.697955i
$726$	38410.9	−	22176.5i	1.96358	−	1.13368i
$727$	24402.0	−	12433.4i	1.24487	−	0.634293i	0.297588	−	0.954694i	$-0.403818\pi$
$727$	24402.0	−	12433.4i	1.24487	−	0.634293i	0.947282	+	0.320401i	$0.103818\pi$
$728$	−10327.4	+	2939.99i	−0.525767	+	0.149675i
$729$	7134.81	−	9820.23i	0.362486	−	0.498919i
$730$	−1633.89	−	478.024i	−0.0828396	−	0.0242363i
$731$	−17900.3	+	1881.40i	−0.905702	+	0.0951931i
$732$	3479.43	+	12985.4i	0.175688	+	0.655675i
$733$	2751.62	−	1056.25i	0.138654	−	0.0532242i	−0.288052	−	0.957615i	$-0.593007\pi$
$733$	2751.62	−	1056.25i	0.138654	−	0.0532242i	0.426705	+	0.904391i	$0.359674\pi$
$734$	−10236.0	−	31503.3i	−0.514740	−	1.58421i
$735$	7883.66	+	35639.7i	0.395637	+	1.78856i
$736$	2114.35	−	6507.30i	0.105891	−	0.325900i
$737$	−89.8867	−	1715.14i	−0.00449256	−	0.0857232i
$738$	−5508.77	+	3577.44i	−0.274771	+	0.178438i
$739$	−8035.08	+	7234.82i	−0.399967	+	0.360132i	−0.844430	−	0.535665i	$-0.820061\pi$
$739$	−8035.08	+	7234.82i	−0.399967	+	0.360132i	0.444464	+	0.895797i	$0.353394\pi$
$740$	9076.67	+	8555.76i	0.450899	+	0.425021i
$741$	−60382.7	+	19619.5i	−2.99354	+	0.972660i
$742$	1452.25	−	39427.2i	0.0718516	−	1.95070i
$743$	20148.5	+	20148.5i	0.994853	+	0.994853i	0.999987	−	0.00513408i	$-0.00163423\pi$
$743$	20148.5	+	20148.5i	0.994853	+	0.994853i	−0.00513408	+	0.999987i	$0.501634\pi$
$744$	−6781.84	+	15232.3i	−0.334186	+	0.750594i
$745$	−15643.3	−	13270.2i	−0.769298	−	0.652593i
$746$	−7012.24	+	3122.05i	−0.344150	+	0.153226i
$747$	−6490.57	+	5255.96i	−0.317908	+	0.257437i
$748$	1704.39	+	3345.05i	0.0833137	+	0.163512i
$749$	7662.64	−	5751.30i	0.373814	−	0.280571i
$750$	4239.56	+	47724.0i	0.206409	+	2.32351i
$751$	20178.3	+	34949.8i	0.980447	+	1.69818i	0.660643	+	0.750700i	$0.270284\pi$
$751$	20178.3	+	34949.8i	0.980447	+	1.69818i	0.319803	+	0.947484i	$0.396383\pi$
$752$	1415.57	−	27010.6i	0.0686441	−	1.30981i
$753$	22388.9	+	8594.29i	1.08353	+	0.415927i
$754$	−2186.13	+	20799.7i	−0.105589	+	1.00461i
$755$	−32756.7	−	5957.52i	−1.57899	−	0.287174i
$756$	31274.7	−	7157.42i	1.50456	−	0.344329i
$757$	−4202.56	+	4202.56i	−0.201776	+	0.201776i	−0.800761	−	0.598984i	$-0.795571\pi$
$757$	−4202.56	+	4202.56i	−0.201776	+	0.201776i	0.598984	+	0.800761i	$0.295571\pi$
$758$	−18008.8	−	46914.6i	−0.862942	−	2.24804i
$759$	−1968.89	−	418.500i	−0.0941582	−	0.0200139i
$760$	3519.36	−	14878.9i	0.167975	−	0.710150i
$761$	4373.75	+	20576.9i	0.208342	+	0.980172i	0.950687	+	0.310153i	$0.100380\pi$
$761$	4373.75	+	20576.9i	0.208342	+	0.980172i	−0.742345	+	0.670018i	$0.766286\pi$
$762$	−32526.0	+	63835.9i	−1.54632	+	3.03482i
$763$	−15469.2	−	18507.1i	−0.733972	−	0.878116i
$764$	3252.82	+	1056.90i	0.154035	+	0.0500490i
$765$	−42214.9	−	77132.1i	−1.99514	−	3.64538i
$766$	−2353.64	+	11073.0i	−0.111019	+	0.522303i
$767$	5566.32	+	4507.52i	0.262045	+	0.212199i
$768$	−48714.0	−	13052.9i	−2.28882	−	0.613288i
$769$	26645.1	−	19358.8i	1.24947	−	0.907796i	0.251283	−	0.967914i	$-0.419148\pi$
$769$	26645.1	−	19358.8i	1.24947	−	0.907796i	0.998191	+	0.0601174i	$0.0191475\pi$
$770$	4491.52	+	744.958i	0.210212	+	0.0348655i
$771$	−24256.6	−	17623.5i	−1.13305	−	0.823208i
$772$	−13377.0	−	16519.2i	−0.623639	−	0.770130i
$773$	29405.3	+	1541.06i	1.36822	+	0.0717053i	0.722236	−	0.691647i	$-0.243114\pi$
$773$	29405.3	+	1541.06i	1.36822	+	0.0717053i	0.645983	+	0.763352i	$0.276448\pi$
$774$	28873.7	+	16670.2i	1.34088	+	0.774158i
$775$	−14106.3	+	14296.8i	−0.653821	+	0.662653i
$776$		−	10693.4i		−	0.494680i
$777$	−32828.2	+	22051.7i	−1.51571	+	1.01815i
$778$	2737.53	+	17284.1i	0.126151	+	0.796484i
$779$	3577.07	+	375.965i	0.164521	+	0.0172918i
$780$	−2113.97	+	28063.7i	−0.0970415	+	1.28826i
$781$	22.4242	+	213.352i	0.00102740	+	0.00977507i
$782$	−3993.46	+	14903.8i	−0.182616	+	0.681532i
$783$	−5950.09	+	37567.4i	−0.271569	+	1.71462i
$784$	−23892.5	−	12821.2i	−1.08840	−	0.584057i
$785$	−14714.1	−	21256.0i	−0.669004	−	0.966446i
$786$	41637.0	−	8850.22i	1.88950	−	0.401625i
$787$	8830.13	+	13597.2i	0.399949	+	0.615868i	0.980068	−	0.198664i	$-0.0636603\pi$
$787$	8830.13	+	13597.2i	0.399949	+	0.615868i	−0.580118	+	0.814532i	$0.696994\pi$
$788$	4121.56	+	6346.64i	0.186325	+	0.286916i
$789$	−3250.16	+	690.842i	−0.146652	+	0.0311719i
$790$	45668.7	+	16000.0i	2.05674	+	0.720574i
$791$	6919.79	+	14913.9i	0.311049	+	0.670387i
$792$	−662.157	+	4180.70i	−0.0297080	+	0.187569i
$793$	3909.00	−	14588.6i	0.175047	−	0.653286i
$794$	4186.75	+	39834.3i	0.187131	+	1.78043i
$795$	58230.6	+	23891.4i	2.59777	+	1.06584i
$796$	10666.5	+	1121.10i	0.474957	+	0.0499199i
$797$	−3657.89	−	23095.0i	−0.162571	−	1.02643i	−0.925167	−	0.379559i	$-0.876076\pi$
$797$	−3657.89	−	23095.0i	−0.162571	−	1.02643i	0.762596	−	0.646875i	$-0.223924\pi$
$798$	−71513.9	−	35048.9i	−3.17239	−	1.55479i
$799$			42310.4i			1.87338i
$800$	−20071.0	−	14377.7i	−0.887020	−	0.635411i
$801$	39388.4	+	22740.9i	1.73748	+	1.00313i
$802$	−4467.60	−	234.137i	−0.196704	−	0.0103088i
$803$	−162.411	−	200.561i	−0.00713743	−	0.00881399i
$804$	10773.8	+	7827.65i	0.472592	+	0.343358i
$805$	4473.36	+	5607.15i	0.195858	+	0.245498i
$806$	−24898.1	+	18089.5i	−1.08809	+	0.790542i
$807$	−30117.0	−	8069.82i	−1.31371	−	0.352009i
$808$	2378.62	+	1926.16i	0.103564	+	0.0838642i
$809$	5621.00	−	26444.7i	0.244281	−	1.14925i	−0.669425	−	0.742880i	$-0.733459\pi$
$809$	5621.00	−	26444.7i	0.244281	−	1.14925i	0.913707	−	0.406375i	$-0.133207\pi$
$810$	−8187.96	+	63847.9i	−0.355180	+	2.76961i
$811$	38631.1	+	12552.0i	1.67265	+	0.543478i	0.983464	−	0.181105i	$-0.0579673\pi$
$811$	38631.1	+	12552.0i	1.67265	+	0.543478i	0.689188	+	0.724582i	$0.257967\pi$
$812$	−7716.16	+	6449.55i	−0.333478	+	0.278737i
$813$	−12449.6	+	24433.7i	−0.537057	+	1.05403i
$814$	1025.58	+	4825.00i	0.0441606	+	0.207759i
$815$	13550.2	+	32405.2i	0.582383	+	1.39276i
$816$	91016.1	+	19346.1i	3.90466	+	0.829960i
$817$	−6542.59	−	17044.0i	−0.280167	−	0.729860i
$818$	8866.87	−	8866.87i	0.379001	−	0.379001i
$819$	−59864.1	−	18427.4i	−2.55412	−	0.786211i
$820$	756.049	−	1403.68i	0.0321980	−	0.0597787i
$821$	−1056.74	+	10054.2i	−0.0449214	+	0.427399i	0.948830	+	0.315786i	$0.102268\pi$
$821$	−1056.74	+	10054.2i	−0.0449214	+	0.427399i	−0.993752	+	0.111613i	$0.964398\pi$
$822$	79049.8	+	30344.4i	3.35423	+	1.28757i
$823$	−885.626	+	16898.8i	−0.0375103	+	0.715739i	0.913549	+	0.406730i	$0.133331\pi$
$823$	−885.626	+	16898.8i	−0.0375103	+	0.715739i	−0.951059	+	0.309010i	$0.900002\pi$
$824$	2503.91	+	4336.90i	0.105859	+	0.183353i
$825$	−3589.34	+	6314.38i	−0.151473	+	0.266471i
$826$	1077.90	+	8919.64i	0.0454055	+	0.375731i
$827$	4257.28	+	8355.39i	0.179009	+	0.351324i	0.963023	−	0.269418i	$-0.0868313\pi$
$827$	4257.28	+	8355.39i	0.179009	+	0.351324i	−0.784015	+	0.620742i	$0.786831\pi$
$828$	8514.52	−	6894.92i	0.357367	−	0.289390i
$829$	−7995.56	+	3559.85i	−0.334979	+	0.149142i	−0.567332	−	0.823489i	$-0.692024\pi$
$829$	−7995.56	+	3559.85i	−0.334979	+	0.149142i	0.232353	+	0.972632i	$0.425358\pi$
$830$	2007.35	−	4892.52i	0.0839471	−	0.204605i
$831$	378.936	−	851.103i	0.0158184	−	0.0355288i
$832$	−2970.07	−	2970.07i	−0.123761	−	0.123761i
$833$	38373.2	+	18072.6i	1.59610	+	0.751713i
$834$	54617.4	−	17746.3i	2.26768	−	0.736815i
$835$	4112.82	+	21782.8i	0.170455	+	0.902784i
$836$	−2829.89	+	2548.04i	−0.117074	+	0.105414i
$837$	−46940.7	+	30483.6i	−1.93848	+	1.25886i
$838$	−356.706	−	6806.36i	−0.0147043	−	0.280575i
$839$	2292.63	−	7055.99i	0.0943389	−	0.290345i	−0.892742	−	0.450568i	$-0.851221\pi$
$839$	2292.63	−	7055.99i	0.0943389	−	0.290345i	0.987081	+	0.160223i	$0.0512214\pi$
$840$	16072.6	−	14261.3i	0.660189	−	0.585787i
$841$	3852.38	+	11856.4i	0.157955	+	0.486137i
$842$	−41944.3	+	16100.9i	−1.71674	+	0.658995i
$843$	2449.97	+	9143.41i	0.100097	+	0.373565i
$844$	−19666.9	+	2067.08i	−0.802090	+	0.0843031i
$845$	3976.24	−	5827.24i	0.161878	−	0.237234i
$846$	46067.0	−	63405.8i	1.87212	−	2.57676i
$847$	−17203.7	−	16677.1i	−0.697907	−	0.676543i
$848$	−41660.3	+	21227.0i	−1.68705	+	0.859597i
$849$	−21041.2	+	12148.2i	−0.850570	+	0.491077i
$850$	46896.1	+	30009.4i	1.89238	+	1.21096i
$851$	−3885.74	+	6730.31i	−0.156524	+	0.271107i
$852$	−1395.05	−	905.959i	−0.0560960	−	0.0364291i
$853$	−904.656	+	143.283i	−0.0363128	+	0.00575138i	−0.174564	−	0.984646i	$-0.555852\pi$
$853$	−904.656	+	143.283i	−0.0363128	+	0.00575138i	0.138252	+	0.990397i	$0.455852\pi$
$854$	16257.8	−	9726.46i	0.651442	−	0.389734i
$855$	64488.1	−	61609.3i	2.57947	−	2.46432i
$856$	−5152.47	−	2294.03i	−0.205734	−	0.0915985i
$857$	−1602.78	+	429.465i	−0.0638857	+	0.0171181i	−0.290620	−	0.956838i	$-0.593862\pi$
$857$	−1602.78	+	429.465i	−0.0638857	+	0.0171181i	0.226735	+	0.973957i	$0.427195\pi$
$858$	−7004.09	+	8649.33i	−0.278690	+	0.344153i
$859$	−25117.2	+	27895.5i	−0.997658	+	1.10801i	−0.00350900	+	0.999994i	$0.501117\pi$
$859$	−25117.2	+	27895.5i	−0.997658	+	1.10801i	−0.994149	+	0.108018i	$0.965550\pi$
$860$	−8090.50	−	184.704i	−0.320795	−	0.00732366i
$861$	3808.60	+	3323.56i	0.150751	+	0.131552i
$862$	−35371.7	−	18022.8i	−1.39764	−	0.712132i
$863$	27233.3	−	1427.24i	1.07420	−	0.0562964i	0.492978	−	0.870042i	$-0.335908\pi$
$863$	27233.3	−	1427.24i	1.07420	−	0.0562964i	0.581221	+	0.813745i	$0.302575\pi$
$864$	−46038.2	−	51130.6i	−1.81279	−	2.01331i
$865$	5768.37	+	1364.42i	0.226740	+	0.0536318i
$866$	−27642.8	−	24889.7i	−1.08469	−	0.976658i
$867$	−97576.6	−	15454.6i	−3.82223	−	0.605382i
$868$	−14650.6	−	2087.56i	−0.572895	−	0.0816316i
$869$	4311.86	+	5934.77i	0.168320	+	0.231672i
$870$	−14102.7	−	39404.4i	−0.549572	−	1.53556i
$871$	−6085.33	−	13667.9i	−0.236732	−	0.531709i
$872$	−5088.60	+	13256.3i	−0.197617	+	0.514809i
$873$	33973.4	−	52314.4i	1.31710	−	2.02815i
$874$	−15650.4			−0.605702
$875$	24169.0	−	9261.70i	0.933786	−	0.357831i
$876$	2001.06			0.0771800
$877$	2983.19	−	4593.71i	0.114863	−	0.176874i	−0.776563	−	0.630040i	$-0.783039\pi$
$877$	2983.19	−	4593.71i	0.114863	−	0.176874i	0.891426	+	0.453165i	$0.149705\pi$
$878$	14905.7	−	38830.6i	0.572941	−	1.49256i
$879$	−60.1676	−	135.139i	−0.00230876	−	0.00518557i
$880$	−1818.13	−	5080.02i	−0.0696466	−	0.194599i
$881$	−22140.6	−	30473.9i	−0.846691	−	1.16537i	−0.984582	−	0.174923i	$-0.944032\pi$
$881$	−22140.6	−	30473.9i	−0.846691	−	1.16537i	0.137891	−	0.990447i	$-0.455968\pi$
$882$	−37828.4	−	68863.6i	−1.44416	−	2.62898i
$883$	−11137.3	−	1763.97i	−0.424461	−	0.0672281i	−0.0594503	−	0.998231i	$-0.518935\pi$
$883$	−11137.3	−	1763.97i	−0.424461	−	0.0672281i	−0.365011	+	0.931003i	$0.618935\pi$
$884$	24303.6	+	21883.1i	0.924682	+	0.832587i
$885$	−13948.2	−	3299.23i	−0.529790	−	0.125313i
$886$	−15224.3	−	16908.3i	−0.577282	−	0.641136i
$887$	−20579.9	+	1078.55i	−0.779037	+	0.0408276i	−0.437709	−	0.899117i	$-0.644210\pi$
$887$	−20579.9	+	1078.55i	−0.779037	+	0.0408276i	−0.341328	+	0.939944i	$0.610877\pi$
$888$	20743.1	+	10569.1i	0.783889	+	0.399411i
$889$	37978.4	+	7457.59i	1.43280	+	0.281349i
$890$	−28791.3	−	657.297i	−1.08437	−	0.0247558i
$891$	−6529.60	+	7251.85i	−0.245510	+	0.272667i
$892$	12967.5	−	16013.6i	0.486755	−	0.601092i
$893$	−41453.8	+	11107.5i	−1.55341	+	0.416236i
$894$	57464.2	+	25584.7i	2.14977	+	0.957138i
$895$	−6184.61	+	5908.52i	−0.230982	+	0.220671i
$896$	372.939	+	23992.5i	0.0139052	+	0.894567i
$897$	−17318.6	+	2742.99i	−0.644648	+	0.102102i
$898$	30721.3	+	19950.6i	1.14163	+	0.741382i
$899$	8772.08	−	15193.7i	0.325434	−	0.563668i
$900$	−14415.0	−	36812.4i	−0.533890	−	1.36342i
$901$	63341.7	−	36570.3i	2.34208	−	1.35220i
$902$	561.782	−	286.242i	0.0207376	−	0.0105663i
$903$	6254.68	−	24883.5i	0.230501	−	0.917024i
$904$	5688.88	−	7830.07i	0.209302	−	0.288080i
$905$	−3743.81	+	5486.61i	−0.137512	+	0.201526i
$906$	101532.	−	10671.5i	3.72317	−	0.391321i
$907$	−7414.90	−	27672.8i	−0.271453	−	1.01308i	−0.958181	−	0.286161i	$-0.907621\pi$
$907$	−7414.90	−	27672.8i	−0.271453	−	1.01308i	0.686729	−	0.726914i	$-0.259046\pi$
$908$	−2720.87	+	1044.44i	−0.0994440	+	0.0381730i
$909$	5517.18	+	16980.1i	0.201313	+	0.619577i
$910$	38853.1	−	7963.19i	1.41535	−	0.290085i
$911$	6751.87	−	20780.1i	0.245554	−	0.755737i	−0.749991	−	0.661448i	$-0.769942\pi$
$911$	6751.87	−	20780.1i	0.245554	−	0.755737i	0.995545	−	0.0942889i	$-0.0300577\pi$
$912$	4939.55	+	94252.2i	0.179347	+	3.42215i
$913$	672.349	−	436.628i	0.0243719	−	0.0158273i
$914$	−32475.5	+	29241.0i	−1.17527	+	1.05821i
$915$	5607.43	+	29698.7i	0.202597	+	1.07302i
$916$	−6461.29	+	2099.40i	−0.233065	+	0.0757273i
$917$	−10756.9	−	20324.4i	−0.387378	−	0.731921i
$918$	109711.	+	109711.i	3.94445	+	3.94445i
$919$	15507.7	−	34830.8i	0.556638	−	1.25023i	−0.387862	−	0.921718i	$-0.626786\pi$
$919$	15507.7	−	34830.8i	0.556638	−	1.25023i	0.944500	−	0.328512i	$-0.106547\pi$
$920$	1602.81	−	3906.55i	0.0574383	−	0.139995i
$921$	17761.2	−	7907.82i	0.635454	−	0.282922i
$922$	−27771.9	+	22489.2i	−0.991993	+	0.803300i
$923$	848.407	+	1665.09i	0.0302553	+	0.0593794i
$924$	−5313.03	+	642.057i	−0.189162	+	0.0228594i
$925$	18903.6	+	20713.4i	0.671941	+	0.736273i
$926$	−9726.32	−	16846.5i	−0.345169	−	0.597850i
$927$	−1528.84	+	29172.0i	−0.0541679	+	1.03359i
$928$	20134.2	+	7728.78i	0.712216	+	0.273394i
$929$	5162.54	−	49118.3i	0.182322	−	1.73468i	−0.395454	−	0.918486i	$-0.629413\pi$
$929$	5162.54	−	49118.3i	0.182322	−	1.73468i	0.577776	−	0.816195i	$-0.303921\pi$
$930$	29204.7	−	54221.3i	1.02974	−	1.91181i
$931$	−7632.77	+	42340.9i	−0.268694	+	1.49051i
$932$	1391.85	−	1391.85i	0.0489179	−	0.0489179i
$933$	−23942.5	−	62372.3i	−0.840131	−	2.18862i
$934$	−29799.3	−	6334.05i	−1.04397	−	0.221902i
$935$	3256.07	+	7786.88i	0.113888	+	0.272362i
$936$	7666.25	+	36066.9i	0.267713	+	1.25949i
$937$	3982.69	−	7816.47i	0.138857	−	0.272522i	−0.811097	−	0.584911i	$-0.801129\pi$
$937$	3982.69	−	7816.47i	0.138857	−	0.272522i	0.949954	+	0.312389i	$0.101129\pi$
$938$	6452.46	−	17623.1i	0.224606	−	0.613450i
$939$	63378.9	+	20593.0i	2.20265	+	0.715685i
$940$	−2419.78	+	18868.9i	−0.0839622	+	0.654718i
$941$	−2278.09	+	10717.6i	−0.0789201	+	0.371290i	−0.999829	−	0.0184879i	$-0.994115\pi$
$941$	−2278.09	+	10717.6i	−0.0789201	+	0.371290i	0.920909	+	0.389778i	$0.127448\pi$
$942$	61605.6	+	49887.2i	2.13080	+	1.72549i
$943$	959.494	+	257.096i	0.0331341	+	0.00887825i
$944$	8613.99	−	6258.43i	0.296993	−	0.215778i
$945$	71321.3	−	10764.3i	2.45511	−	0.370544i
$946$	−2589.12	−	1881.11i	−0.0889847	−	0.0646512i
$947$	11442.5	+	14130.3i	0.392642	+	0.484872i	0.934684	−	0.355479i	$-0.115682\pi$
$947$	11442.5	+	14130.3i	0.392642	+	0.484872i	−0.542043	+	0.840351i	$0.682349\pi$
$948$	−56802.6	−	2976.90i	−1.94606	−	0.101989i
$949$	−1946.93	−	1124.06i	−0.0665963	−	0.0384494i
$950$	−17090.4	+	53824.9i	−0.583670	+	1.83822i
$951$			10605.4i			0.361624i
$952$	−1694.19	−	24912.0i	−0.0576776	−	0.848111i
$953$	−3268.12	−	20634.1i	−0.111086	−	0.701368i	−0.978879	−	0.204442i	$-0.934462\pi$
$953$	−3268.12	−	20634.1i	−0.111086	−	0.701368i	0.867793	−	0.496926i	$-0.165538\pi$
$954$	−134740.	−	14161.8i	−4.57272	−	0.480613i
$955$	7113.79	+	2918.71i	0.241044	+	0.0988978i
$956$	−2442.98	−	23243.4i	−0.0826481	−	0.786344i
$957$	1642.10	−	6128.40i	0.0554666	−	0.207004i
$958$	−1330.02	+	8397.39i	−0.0448548	+	0.283202i
$959$	4073.75	−	45560.4i	0.137172	−	1.53412i
$960$	7932.62	+	2779.18i	0.266692	+	0.0934350i
$961$	−3887.52	+	826.318i	−0.130493	+	0.0277372i
$962$	23403.3	+	36037.9i	0.784358	+	1.20781i
$963$	−17918.7	−	27592.4i	−0.599608	−	0.923316i
$964$	34090.5	−	7246.17i	1.13899	−	0.242099i
$965$	−27199.4	−	39292.4i	−0.907338	−	1.31074i
$966$	−17993.0	−	12650.1i	−0.599292	−	0.421337i
$967$	−177.621	+	1121.45i	−0.00590682	+	0.0372942i	−0.990466	−	0.137759i	$-0.956010\pi$
$967$	−177.621	+	1121.45i	−0.00590682	+	0.0372942i	0.984559	+	0.175054i	$0.0560099\pi$
$968$	−3650.63	+	13624.3i	−0.121214	+	0.452378i
$969$	−15432.6	−	146831.i	−0.511627	−	4.86780i
$970$	−2966.83	+	39385.6i	−0.0982052	+	1.30371i
$971$	39114.0	+	4111.04i	1.29272	+	0.135870i	0.725800	−	0.687906i	$-0.241470\pi$
$971$	39114.0	+	4111.04i	1.29272	+	0.135870i	0.566916	+	0.823776i	$0.308137\pi$
$972$	−4519.67	−	28536.1i	−0.149144	−	0.941661i
$973$	−17299.0	−	25752.9i	−0.569971	−	0.848509i
$974$		−	25493.7i		−	0.838677i
$975$	−9478.36	+	62557.2i	−0.311334	+	2.05480i
$976$	−19443.8	−	11225.9i	−0.637685	−	0.368168i
$977$	29590.3	+	1550.76i	0.968963	+	0.0507812i	0.530246	−	0.847844i	$-0.322100\pi$
$977$	29590.3	+	1550.76i	0.968963	+	0.0507812i	0.438717	+	0.898625i	$0.355433\pi$
$978$	−67779.9	−	83701.2i	−2.21612	−	2.73668i
$979$	−3531.98	−	2566.14i	−0.115304	−	0.0837733i
$980$	16079.5	+	10254.3i	0.524122	+	0.334247i
$981$	−67010.0	+	48685.6i	−2.18090	+	1.58452i
$982$	45745.1	+	12257.4i	1.48654	+	0.398317i
$983$	−10272.2	−	8318.29i	−0.333300	−	0.269901i	0.448031	−	0.894018i	$-0.352125\pi$
$983$	−10272.2	−	8318.29i	−0.333300	−	0.269901i	−0.781331	+	0.624117i	$0.785459\pi$
$984$	618.680	−	2910.66i	0.0200435	−	0.0942973i
$985$	8168.09	+	14924.1i	0.264220	+	0.482764i
$986$	−46253.7	−	15028.7i	−1.49393	−	0.485408i
$987$	−56636.8	−	20736.7i	−1.82651	−	0.668751i
$988$	−15059.7	+	29556.4i	−0.484934	+	0.951736i
$989$	−1048.30	−	4931.86i	−0.0337047	−	0.158568i
$990$	3598.74	−	15214.5i	0.115531	−	0.488432i
$991$	−45860.6	−	9747.98i	−1.47004	−	0.312467i	−0.597841	−	0.801615i	$-0.703975\pi$
$991$	−45860.6	−	9747.98i	−1.47004	−	0.312467i	−0.872201	+	0.489148i	$0.837308\pi$
$992$	11373.1	+	29627.9i	0.364008	+	0.948272i
$993$	3672.64	−	3672.64i	0.117369	−	0.117369i
$994$	−689.648	+	2240.42i	−0.0220063	+	0.0714907i
$995$	23723.3	+	4314.60i	0.755858	+	0.137469i
$996$	−649.764	+	6182.09i	−0.0206712	+	0.196674i
$997$	−47204.1	−	18119.9i	−1.49947	−	0.575591i	−0.536189	−	0.844098i	$-0.680136\pi$
$997$	−47204.1	−	18119.9i	−1.49947	−	0.575591i	−0.963278	+	0.268507i	$0.913470\pi$
$998$	−1259.29	+	24028.7i	−0.0399420	+	0.762139i
$999$	39073.9	+	67678.0i	1.23748	+	2.14338i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.x.a.3.13	✓	928
7.5	odd	6	inner	175.4.x.a.103.46	yes	928
25.17	odd	20	inner	175.4.x.a.17.46	yes	928
175.117	even	60	inner	175.4.x.a.117.13	yes	928

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.4.x.a.3.13	✓	928	1.1	even	1	trivial
175.4.x.a.17.46	yes	928	25.17	odd	20	inner
175.4.x.a.103.46	yes	928	7.5	odd	6	inner
175.4.x.a.117.13	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+(-1.96169 + 3.02073i) q^{2} +(3.41104 - 8.88607i) q^{3} +(-2.02272 - 4.54311i) q^{4} +(-3.76740 - 10.5265i) q^{5} +(20.1510 + 27.7355i) q^{6} +(11.4301 - 14.5724i) q^{7} +(-10.7683 - 1.70553i) q^{8} +(-47.2621 - 42.5550i) q^{9} +(39.1881 + 9.26933i) q^{10} +(4.08483 + 4.53666i) q^{11} +(-47.2699 + 2.47731i) q^{12} +(47.3826 + 24.1427i) q^{13} +(21.5970 + 63.1136i) q^{14} +(-106.390 - 2.42885i) q^{15} +(52.8969 - 58.7480i) q^{16} +(-77.8230 + 96.1034i) q^{17} +(221.261 - 59.2866i) q^{18} +(-114.588 - 51.0180i) q^{19} +(-40.2025 + 38.4078i) q^{20} +(-90.5025 - 151.275i) q^{21} +(-21.7172 + 3.43967i) q^{22} +(-29.0527 - 18.8671i) q^{23} +(-51.8865 + 89.8701i) q^{24} +(-96.6134 + 79.3149i) q^{25} +(-165.878 + 95.7700i) q^{26} +(-310.377 + 158.145i) q^{27} +(-89.3236 - 22.4522i) q^{28} +(64.1803 - 88.3366i) q^{29} +(216.040 - 316.610i) q^{30} +(159.795 - 16.7952i) q^{31} +(51.1205 + 190.784i) q^{32} +(54.2466 - 20.8233i) q^{33} +(-137.638 - 423.608i) q^{34} +(-196.457 - 65.4184i) q^{35} +(-97.7337 + 300.793i) q^{36} +(-11.7411 - 224.034i) q^{37} +(378.898 - 246.059i) q^{38} +(376.157 - 338.694i) q^{39} +(22.6153 + 119.777i) q^{40} +(-27.2715 + 8.86105i) q^{41} +(634.500 + 23.3710i) q^{42} +(102.919 + 102.919i) q^{43} +(12.3481 - 27.7342i) q^{44} +(-269.899 + 657.825i) q^{45} +(113.985 - 50.7493i) q^{46} +(265.897 - 215.319i) q^{47} +(-341.605 - 670.437i) q^{48} +(-81.7069 - 333.126i) q^{49} +(-50.0641 - 447.434i) q^{50} +(588.524 + 1019.35i) q^{51} +(13.8408 - 264.098i) q^{52} +(-552.172 - 211.959i) q^{53} +(131.149 - 1247.80i) q^{54} +(32.3659 - 60.0903i) q^{55} +(-147.936 + 137.425i) q^{56} +(-844.215 + 844.215i) q^{57} +(140.940 + 367.160i) q^{58} +(131.744 + 28.0031i) q^{59} +(204.162 + 488.253i) q^{60} +(-59.0487 - 277.802i) q^{61} +(-262.735 + 515.646i) q^{62} +(-1160.34 + 202.313i) q^{63} +(-75.1191 - 24.4077i) q^{64} +(75.6276 - 589.727i) q^{65} +(-43.5132 + 204.713i) q^{66} +(-218.643 - 177.053i) q^{67} +(594.022 + 159.168i) q^{68} +(-266.754 + 193.808i) q^{69} +(582.999 - 465.114i) q^{70} +(28.4300 + 20.6556i) q^{71} +(436.353 + 538.851i) q^{72} +(-42.2168 - 2.21249i) q^{73} +(699.778 + 404.017i) q^{74} +(375.246 + 1129.06i) q^{75} +623.782i q^{76} +(112.800 - 7.67119i) q^{77} +(285.200 + 1800.68i) q^{78} +(1195.08 + 125.608i) q^{79} +(-817.693 - 335.491i) q^{80} +(167.089 + 1589.74i) q^{81} +(26.7313 - 99.7626i) q^{82} +(20.5434 - 129.706i) q^{83} +(-504.198 + 717.150i) q^{84} +(1304.82 + 457.142i) q^{85} +(-512.786 + 108.996i) q^{86} +(-566.043 - 871.630i) q^{87} +(-36.2492 - 55.8188i) q^{88} +(-699.524 + 148.688i) q^{89} +(-1457.66 - 2105.74i) q^{90} +(893.402 - 414.524i) q^{91} +(-26.9495 + 170.152i) q^{92} +(395.826 - 1477.24i) q^{93} +(128.815 + 1225.59i) q^{94} +(-105.339 + 1398.42i) q^{95} +(1869.70 + 196.513i) q^{96} +(153.435 + 968.747i) q^{97} +(1166.57 + 406.674i) q^{98} -388.242i 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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