LMFDB - Embedded newform 110.4.k.a.7.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [110,4,Mod(7,110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 14])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("110.7"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	110.k (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.49021010063$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.16
Character	$\chi$	$=$	110.7
Dual form			110.4.k.a.63.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.97538 - 0.312869i) q^{2} +(2.68986 + 5.27915i) q^{3} +(3.80423 - 1.23607i) q^{4} +(6.17250 - 9.32203i) q^{5} +(6.96517 + 9.58673i) q^{6} +(12.2499 + 6.24166i) q^{7} +(7.12805 - 3.63192i) q^{8} +(-4.76385 + 6.55687i) q^{9} +(9.27645 - 20.3457i) q^{10} +(-29.8875 - 20.9221i) q^{11} +(16.7582 + 16.7582i) q^{12} +(12.4310 + 78.4862i) q^{13} +(26.1511 + 8.49700i) q^{14} +(65.8155 + 7.51060i) q^{15} +(12.9443 - 9.40456i) q^{16} +(11.4746 - 72.4480i) q^{17} +(-7.35895 + 14.4427i) q^{18} +(-27.1190 + 83.4638i) q^{19} +(11.9589 - 43.0927i) q^{20} +81.4584i q^{21} +(-65.5850 - 31.9782i) q^{22} +(-93.7089 + 93.7089i) q^{23} +(38.3469 + 27.8607i) q^{24} +(-48.8004 - 115.080i) q^{25} +(49.1118 + 151.151i) q^{26} +(110.575 + 17.5133i) q^{27} +(54.3167 + 8.60292i) q^{28} +(-85.0892 - 261.878i) q^{29} +(132.360 - 5.75536i) q^{30} +(-64.2849 - 46.7057i) q^{31} +(22.6274 - 22.6274i) q^{32} +(30.0578 - 214.058i) q^{33} -146.702i q^{34} +(133.798 - 75.6677i) q^{35} +(-10.0180 + 30.8323i) q^{36} +(54.9478 - 107.841i) q^{37} +(-27.4571 + 173.357i) q^{38} +(-380.903 + 276.742i) q^{39} +(10.1410 - 88.8660i) q^{40} +(-205.994 - 66.9316i) q^{41} +(25.4858 + 160.911i) q^{42} +(53.9104 + 53.9104i) q^{43} +(-139.560 - 42.6495i) q^{44} +(31.7185 + 84.8810i) q^{45} +(-155.792 + 214.429i) q^{46} +(47.2118 - 24.0556i) q^{47} +(84.4664 + 43.0378i) q^{48} +(-90.5075 - 124.573i) q^{49} +(-132.404 - 212.059i) q^{50} +(413.329 - 134.299i) q^{51} +(144.305 + 283.214i) q^{52} +(-601.943 + 95.3384i) q^{53} +223.906 q^{54} +(-379.518 + 149.470i) q^{55} +109.987 q^{56} +(-513.564 + 81.3406i) q^{57} +(-250.017 - 490.685i) q^{58} +(-339.420 + 110.284i) q^{59} +(259.661 - 52.7804i) q^{60} +(468.020 + 644.174i) q^{61} +(-141.600 - 72.1486i) q^{62} +(-99.2826 + 50.5870i) q^{63} +(37.6183 - 51.7771i) q^{64} +(808.381 + 368.574i) q^{65} +(-7.59671 - 432.250i) q^{66} +(-284.970 - 284.970i) q^{67} +(-45.8986 - 289.792i) q^{68} +(-746.767 - 242.639i) q^{69} +(240.627 - 191.333i) q^{70} +(484.082 - 351.707i) q^{71} +(-10.1429 + 64.0396i) q^{72} +(166.820 - 327.402i) q^{73} +(74.8024 - 230.218i) q^{74} +(476.261 - 567.175i) q^{75} +351.036i q^{76} +(-235.532 - 442.843i) q^{77} +(-665.842 + 665.842i) q^{78} +(158.768 + 115.352i) q^{79} +(-7.77105 - 178.717i) q^{80} +(272.597 + 838.966i) q^{81} +(-427.857 - 67.7659i) q^{82} +(764.103 + 121.022i) q^{83} +(100.688 + 309.886i) q^{84} +(-604.535 - 554.153i) q^{85} +(123.360 + 89.6264i) q^{86} +(1153.61 - 1153.61i) q^{87} +(-289.027 - 40.5849i) q^{88} +1597.98i q^{89} +(89.2126 + 157.748i) q^{90} +(-337.605 + 1039.04i) q^{91} +(-240.659 + 472.320i) q^{92} +(73.6489 - 465.001i) q^{93} +(85.7349 - 62.2901i) q^{94} +(610.660 + 767.985i) q^{95} +(180.318 + 58.5889i) q^{96} +(-32.3282 - 204.112i) q^{97} +(-217.761 - 217.761i) q^{98} +(279.563 - 96.2988i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 8 q^{3} + 32 q^{5} - 40 q^{7} - 44 q^{11} + 128 q^{12} - 256 q^{15} + 576 q^{16} - 640 q^{17} - 64 q^{20} + 312 q^{22} - 984 q^{23} - 520 q^{25} + 304 q^{26} - 364 q^{27} + 240 q^{28} - 432 q^{31}+ \cdots + 7044 q^{97}+O(q^{100}) $ 144 * q + 8 * q^3 + 32 * q^5 - 40 * q^7 - 44 * q^11 + 128 * q^12 - 256 * q^15 + 576 * q^16 - 640 * q^17 - 64 * q^20 + 312 * q^22 - 984 * q^23 - 520 * q^25 + 304 * q^26 - 364 * q^27 + 240 * q^28 - 432 * q^31 + 2368 * q^33 + 1808 * q^36 - 960 * q^37 + 72 * q^38 + 740 * q^41 + 2440 * q^42 + 2656 * q^45 + 720 * q^46 - 1980 * q^47 - 128 * q^48 - 1360 * q^50 - 3880 * q^51 - 1920 * q^52 - 3060 * q^53 - 3044 * q^55 - 64 * q^56 - 4400 * q^57 - 2016 * q^58 - 1120 * q^60 - 960 * q^61 + 80 * q^62 + 1800 * q^63 + 1552 * q^66 + 10160 * q^67 + 2560 * q^68 + 2304 * q^70 + 1312 * q^71 - 2460 * q^73 + 8644 * q^75 - 1272 * q^77 - 5312 * q^78 + 768 * q^80 + 2116 * q^81 + 1280 * q^82 + 320 * q^85 - 5488 * q^86 + 1248 * q^88 - 8480 * q^90 + 11796 * q^91 - 704 * q^92 + 688 * q^93 - 1280 * q^95 + 7044 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	1.97538	−	0.312869i	0.698401	−	0.110616i
$2$	1.97538	−	0.312869i	0.698401	−	0.110616i
$3$	2.68986	+	5.27915i	0.517664	+	1.01597i	0.990845	+	0.135007i	$0.0431057\pi$
$3$	2.68986	+	5.27915i	0.517664	+	1.01597i	−0.473181	+	0.880965i	$0.656894\pi$
$4$	3.80423	−	1.23607i	0.475528	−	0.154508i
$5$	6.17250	−	9.32203i	0.552085	−	0.833788i
$5$	6.17250	−	9.32203i	0.552085	−	0.833788i
$6$	6.96517	+	9.58673i	0.473920	+	0.652294i
$7$	12.2499	+	6.24166i	0.661435	+	0.337018i	0.752277	−	0.658847i	$-0.228956\pi$
$7$	12.2499	+	6.24166i	0.661435	+	0.337018i	−0.0908417	+	0.995865i	$0.528956\pi$
$8$	7.12805	−	3.63192i	0.315018	−	0.160510i
$9$	−4.76385	+	6.55687i	−0.176439	+	0.242847i
$10$	9.27645	−	20.3457i	0.293347	−	0.643388i
$11$	−29.8875	−	20.9221i	−0.819221	−	0.573478i
$11$	−29.8875	−	20.9221i	−0.819221	−	0.573478i
$12$	16.7582	+	16.7582i	0.403140	+	0.403140i
$13$	12.4310	+	78.4862i	0.265211	+	1.67447i	0.656592	+	0.754246i	$0.271997\pi$
$13$	12.4310	+	78.4862i	0.265211	+	1.67447i	−0.391382	+	0.920228i	$0.628003\pi$
$14$	26.1511	+	8.49700i	0.499226	+	0.162208i
$15$	65.8155	+	7.51060i	1.13290	+	0.129282i
$16$	12.9443	−	9.40456i	0.202254	−	0.146946i
$17$	11.4746	−	72.4480i	0.163706	−	1.03360i	−0.759839	−	0.650112i	$-0.774722\pi$
$17$	11.4746	−	72.4480i	0.163706	−	1.03360i	0.923545	−	0.383490i	$-0.125278\pi$
$18$	−7.35895	+	14.4427i	−0.0963623	+	0.189122i
$19$	−27.1190	+	83.4638i	−0.327449	+	1.00778i	0.642874	+	0.765972i	$0.277742\pi$
$19$	−27.1190	+	83.4638i	−0.327449	+	1.00778i	−0.970323	+	0.241813i	$0.922258\pi$
$20$	11.9589	−	43.0927i	0.133705	−	0.481791i
$21$			81.4584i			0.846461i
$22$	−65.5850	−	31.9782i	−0.635580	−	0.309899i
$23$	−93.7089	+	93.7089i	−0.849550	+	0.849550i	−0.990077	−	0.140527i	$-0.955120\pi$
$23$	−93.7089	+	93.7089i	−0.849550	+	0.849550i	0.140527	+	0.990077i	$0.455120\pi$
$24$	38.3469	+	27.8607i	0.326147	+	0.236960i
$25$	−48.8004	−	115.080i	−0.390403	−	0.920644i
$26$	49.1118	+	151.151i	0.370447	+	1.14012i
$27$	110.575	+	17.5133i	0.788152	+	0.124831i
$28$	54.3167	+	8.60292i	0.366603	+	0.0580642i
$29$	−85.0892	−	261.878i	−0.544851	−	1.67688i	−0.721345	−	0.692576i	$-0.756476\pi$
$29$	−85.0892	−	261.878i	−0.544851	−	1.67688i	0.176494	−	0.984302i	$-0.443524\pi$
$30$	132.360	−	5.75536i	0.805519	−	0.0350260i
$31$	−64.2849	−	46.7057i	−0.372448	−	0.270600i	0.385777	−	0.922592i	$-0.373933\pi$
$31$	−64.2849	−	46.7057i	−0.372448	−	0.270600i	−0.758226	+	0.651992i	$0.773933\pi$
$32$	22.6274	−	22.6274i	0.125000	−	0.125000i
$33$	30.0578	−	214.058i	0.158557	−	1.12917i
$34$		−	146.702i		−	0.739977i
$35$	133.798	−	75.6677i	0.646170	−	0.365433i
$36$	−10.0180	+	30.8323i	−0.0463797	+	0.142742i
$37$	54.9478	−	107.841i	0.244145	−	0.479161i	−0.736120	−	0.676851i	$-0.763344\pi$
$37$	54.9478	−	107.841i	0.244145	−	0.479161i	0.980265	+	0.197690i	$0.0633440\pi$
$38$	−27.4571	+	173.357i	−0.117214	+	0.740059i
$39$	−380.903	+	276.742i	−1.56393	+	1.13626i
$40$	10.1410	−	88.8660i	0.0400859	−	0.351274i
$41$	−205.994	−	66.9316i	−0.784656	−	0.254950i	−0.110829	−	0.993839i	$-0.535351\pi$
$41$	−205.994	−	66.9316i	−0.784656	−	0.254950i	−0.673827	+	0.738889i	$0.735351\pi$
$42$	25.4858	+	160.911i	0.0936321	+	0.591170i
$43$	53.9104	+	53.9104i	0.191192	+	0.191192i	0.796211	−	0.605019i	$-0.206834\pi$
$43$	53.9104	+	53.9104i	0.191192	+	0.191192i	−0.605019	+	0.796211i	$0.706834\pi$
$44$	−139.560	−	42.6495i	−0.478170	−	0.146129i
$45$	31.7185	+	84.8810i	0.105074	+	0.281185i
$46$	−155.792	+	214.429i	−0.499353	+	0.687301i
$47$	47.2118	−	24.0556i	0.146522	−	0.0746569i	−0.379192	−	0.925318i	$-0.623798\pi$
$47$	47.2118	−	24.0556i	0.146522	−	0.0746569i	0.525714	+	0.850661i	$0.323798\pi$
$48$	84.4664	+	43.0378i	0.253993	+	0.129416i
$49$	−90.5075	−	124.573i	−0.263870	−	0.363186i
$50$	−132.404	−	212.059i	−0.374496	−	0.599794i
$51$	413.329	−	134.299i	1.13486	−	0.368737i
$52$	144.305	+	283.214i	0.384836	+	0.755282i
$53$	−601.943	+	95.3384i	−1.56006	+	0.247089i	−0.875991	−	0.482328i	$-0.839791\pi$
$53$	−601.943	+	95.3384i	−1.56006	+	0.247089i	−0.684069	+	0.729417i	$0.739791\pi$
$54$	223.906			0.564255
$55$	−379.518	+	149.470i	−0.930439	+	0.366447i
$56$	109.987			0.262459
$57$	−513.564	+	81.3406i	−1.19339	+	0.189014i
$58$	−250.017	−	490.685i	−0.566014	−	1.11086i
$59$	−339.420	+	110.284i	−0.748961	+	0.243352i	−0.658534	−	0.752551i	$-0.728823\pi$
$59$	−339.420	+	110.284i	−0.748961	+	0.243352i	−0.0904268	+	0.995903i	$0.528823\pi$
$60$	259.661	−	52.7804i	0.558701	−	0.113565i
$61$	468.020	+	644.174i	0.982357	+	1.35210i	0.935550	+	0.353195i	$0.114905\pi$
$61$	468.020	+	644.174i	0.982357	+	1.35210i	0.0468071	+	0.998904i	$0.485095\pi$
$62$	−141.600	−	72.1486i	−0.290051	−	0.147788i
$63$	−99.2826	+	50.5870i	−0.198547	+	0.101165i
$64$	37.6183	−	51.7771i	0.0734732	−	0.101127i
$65$	808.381	+	368.574i	1.54257	+	0.703323i
$66$	−7.59671	−	432.250i	−0.0141680	−	0.806156i
$67$	−284.970	−	284.970i	−0.519621	−	0.519621i	0.397836	−	0.917457i	$-0.369761\pi$
$67$	−284.970	−	284.970i	−0.519621	−	0.519621i	−0.917457	+	0.397836i	$0.869761\pi$
$68$	−45.8986	−	289.792i	−0.0818532	−	0.516801i
$69$	−746.767	−	242.639i	−1.30290	−	0.423338i
$70$	240.627	−	191.333i	0.410863	−	0.326696i
$71$	484.082	−	351.707i	0.809155	−	0.587886i	−0.104430	−	0.994532i	$-0.533302\pi$
$71$	484.082	−	351.707i	0.809155	−	0.587886i	0.913586	+	0.406647i	$0.133302\pi$
$72$	−10.1429	+	64.0396i	−0.0166021	+	0.104821i
$73$	166.820	−	327.402i	0.267462	−	0.524924i	−0.717742	−	0.696309i	$-0.754824\pi$
$73$	166.820	−	327.402i	0.267462	−	0.524924i	0.985204	+	0.171385i	$0.0548242\pi$
$74$	74.8024	−	230.218i	0.117508	−	0.361653i
$75$	476.261	−	567.175i	0.733251	−	0.873223i
$76$			351.036i			0.529824i
$77$	−235.532	−	442.843i	−0.348589	−	0.655411i
$78$	−665.842	+	665.842i	−0.966561	+	0.966561i
$79$	158.768	+	115.352i	0.226111	+	0.164279i	0.695073	−	0.718939i	$-0.255372\pi$
$79$	158.768	+	115.352i	0.226111	+	0.164279i	−0.468962	+	0.883218i	$0.655372\pi$
$80$	−7.77105	−	178.717i	−0.0108604	−	0.249764i
$81$	272.597	+	838.966i	0.373932	+	1.15085i
$82$	−427.857	−	67.7659i	−0.576206	−	0.0912621i
$83$	764.103	+	121.022i	1.01050	+	0.160047i	0.639666	−	0.768653i	$-0.279073\pi$
$83$	764.103	+	121.022i	1.01050	+	0.160047i	0.370831	+	0.928700i	$0.379073\pi$
$84$	100.688	+	309.886i	0.130785	+	0.402516i
$85$	−604.535	−	554.153i	−0.771424	−	0.707133i
$86$	123.360	+	89.6264i	0.154678	+	0.112380i
$87$	1153.61	−	1153.61i	1.42161	−	1.42161i
$88$	−289.027	−	40.5849i	−0.350119	−	0.0491632i
$89$			1597.98i			1.90321i	0.307318	+	0.951607i	$0.400568\pi$
$89$			1597.98i			1.90321i	−0.307318	+	0.951607i	$0.599432\pi$
$90$	89.2126	+	157.748i	0.104487	+	0.184757i
$91$	−337.605	+	1039.04i	−0.388908	+	1.19694i
$92$	−240.659	+	472.320i	−0.272722	+	0.535248i
$93$	73.6489	−	465.001i	0.0821187	−	0.518477i
$94$	85.7349	−	62.2901i	0.0940732	−	0.0683482i
$95$	610.660	+	767.985i	0.659498	+	0.829406i
$96$	180.318	+	58.5889i	0.191705	+	0.0622886i
$97$	−32.3282	−	204.112i	−0.0338395	−	0.213654i	0.964974	−	0.262344i	$-0.0844954\pi$
$97$	−32.3282	−	204.112i	−0.0338395	−	0.213654i	−0.998814	+	0.0486897i	$0.984495\pi$
$98$	−217.761	−	217.761i	−0.224461	−	0.224461i
$99$	279.563	−	96.2988i	0.283810	−	0.0977616i
$100$	−327.895	−	377.472i	−0.327895	−	0.377472i
$101$	492.694	−	678.134i	0.485394	−	0.668088i	−0.494136	−	0.869385i	$-0.664515\pi$
$101$	492.694	−	678.134i	0.485394	−	0.668088i	0.979530	+	0.201297i	$0.0645155\pi$
$102$	774.463	−	394.608i	0.751796	−	0.383059i
$103$	−98.4697	−	50.1728i	−0.0941991	−	0.0479969i	0.406256	−	0.913759i	$-0.366834\pi$
$103$	−98.4697	−	50.1728i	−0.0941991	−	0.0479969i	−0.500455	+	0.865762i	$0.666834\pi$
$104$	373.665	+	514.305i	0.352316	+	0.484921i
$105$	759.358	+	502.803i	0.705769	+	0.467319i
$106$	−1159.24	+	376.658i	−1.06222	+	0.345135i
$107$	60.1784	+	118.107i	0.0543707	+	0.106709i	0.916593	−	0.399822i	$-0.130928\pi$
$107$	60.1784	+	118.107i	0.0543707	+	0.106709i	−0.862222	+	0.506530i	$0.830928\pi$
$108$	442.299	−	70.0532i	0.394076	−	0.0624155i
$109$	1615.92			1.41997			0.709985	−	0.704217i	$-0.248702\pi$
$109$	1615.92			1.41997			0.709985	+	0.704217i	$0.248702\pi$
$110$	−702.926	+	414.000i	−0.609285	+	0.358848i
$111$	717.111			0.613199
$112$	217.267	−	34.4117i	0.183302	−	0.0290321i
$113$	−273.221	−	536.227i	−0.227456	−	0.446407i	0.748869	−	0.662718i	$-0.230597\pi$
$113$	−273.221	−	536.227i	−0.227456	−	0.446407i	−0.976324	+	0.216311i	$0.930597\pi$
$114$	−989.033	+	321.356i	−0.812557	+	0.264016i
$115$	295.138	+	1451.98i	0.239320	+	1.17737i
$116$	−647.397	−	891.066i	−0.518184	−	0.713219i
$117$	−573.843	−	292.388i	−0.453435	−	0.231036i
$118$	−635.977	+	324.047i	−0.496156	+	0.252804i
$119$	592.760	−	815.864i	0.456623	−	0.628488i
$120$	496.414	−	185.501i	0.377635	−	0.141115i
$121$	455.528	+	1250.62i	0.342245	+	0.939611i
$122$	1126.06	+	1126.06i	0.835643	+	0.835643i
$123$	−200.754	−	1267.51i	−0.147166	−	0.929167i
$124$	−302.286	−	98.2185i	−0.218920	−	0.0711313i
$125$	−1374.00	−	255.416i	−0.983157	−	0.182761i
$126$	−180.293	+	130.991i	−0.127475	+	0.0926158i
$127$	−33.9642	+	214.441i	−0.0237310	+	0.149831i	−0.996709	−	0.0810681i	$-0.974167\pi$
$127$	−33.9642	+	214.441i	−0.0237310	+	0.149831i	0.972978	+	0.230900i	$0.0741669\pi$
$128$	58.1108	−	114.049i	0.0401275	−	0.0787546i
$129$	−139.589	+	429.612i	−0.0952726	+	0.293219i
$130$	1712.17	+	475.156i	1.15513	+	0.320569i
$131$			1501.65i			1.00152i	0.865586	+	0.500761i	$0.166946\pi$
$131$			1501.65i			1.00152i	−0.865586	+	0.500761i	$0.833054\pi$
$132$	−150.244	−	851.479i	−0.0990686	−	0.561453i
$133$	−853.159	+	853.159i	−0.556228	+	0.556228i
$134$	−652.081	−	473.765i	−0.420382	−	0.305426i
$135$	845.782	−	922.679i	0.539210	−	0.588234i
$136$	−181.334	−	558.088i	−0.114333	−	0.351880i
$137$	−56.9402	−	9.01844i	−0.0355090	−	0.00562407i	0.138655	−	0.990341i	$-0.455722\pi$
$137$	−56.9402	−	9.01844i	−0.0355090	−	0.00562407i	−0.174164	+	0.984717i	$0.555722\pi$
$138$	−1551.06	−	245.664i	−0.956775	−	0.151538i
$139$	372.434	+	1146.23i	0.227262	+	0.699440i	0.998054	+	0.0623536i	$0.0198606\pi$
$139$	372.434	+	1146.23i	0.227262	+	0.699440i	−0.770792	+	0.637087i	$0.780139\pi$
$140$	415.466	−	453.240i	0.250809	−	0.273613i
$141$	253.986	+	184.532i	0.151699	+	0.110216i
$142$	846.207	−	846.207i	0.500085	−	0.500085i
$143$	1270.57	−	2605.84i	0.743009	−	1.52386i
$144$			129.676i			0.0750439i
$145$	−2966.44	−	823.237i	−1.69896	−	0.471490i
$146$	227.098	−	698.935i	0.128731	−	0.396193i
$147$	414.186	−	812.886i	0.232391	−	0.456093i
$148$	75.7349	−	478.171i	0.0420633	−	0.265577i
$149$	−63.8989	+	46.4253i	−0.0351329	+	0.0255256i	−0.605213	−	0.796063i	$-0.706912\pi$
$149$	−63.8989	+	46.4253i	−0.0351329	+	0.0255256i	0.570080	+	0.821589i	$0.306912\pi$
$150$	763.343	−	1269.39i	0.415511	−	0.690969i
$151$	−1392.90	−	452.580i	−0.750678	−	0.243910i	−0.0914052	−	0.995814i	$-0.529136\pi$
$151$	−1392.90	−	452.580i	−0.750678	−	0.243910i	−0.659273	+	0.751904i	$0.729136\pi$
$152$	109.828	+	693.429i	0.0586069	+	0.370029i
$153$	420.369	+	420.369i	0.222123	+	0.222123i
$154$	−603.816	−	801.091i	−0.315954	−	0.419180i
$155$	−832.190	+	310.974i	−0.431246	+	0.161149i
$156$	−1106.97	+	1523.61i	−0.568131	+	0.781965i
$157$	−3290.07	+	1676.37i	−1.67246	+	0.852161i	−0.679504	+	0.733672i	$0.737805\pi$
$157$	−3290.07	+	1676.37i	−1.67246	+	0.852161i	−0.992955	+	0.118489i	$0.962195\pi$
$158$	349.716	+	178.189i	0.176088	+	0.0897214i
$159$	−2122.45	−	2921.30i	−1.05862	−	1.45707i
$160$	−71.2656	−	350.601i	−0.0352128	−	0.173234i
$161$	−1732.83	+	563.030i	−0.848236	+	0.275609i
$162$	800.967	+	1571.99i	0.388456	+	0.762389i
$163$	1280.25	−	202.772i	0.615196	−	0.0974375i	0.158943	−	0.987288i	$-0.449191\pi$
$163$	1280.25	−	202.772i	0.615196	−	0.0974375i	0.456253	+	0.889850i	$0.349191\pi$
$164$	−866.380			−0.412518
$165$	−1809.93	−	1601.47i	−0.853954	−	0.755604i
$166$	1547.26			0.723436
$167$	4145.99	−	656.661i	1.92112	−	0.304275i	0.924145	−	0.382041i	$-0.124779\pi$
$167$	4145.99	−	656.661i	1.92112	−	0.304275i	0.996972	+	0.0777662i	$0.0247788\pi$
$168$	295.851	+	580.640i	0.135865	+	0.266651i
$169$	−3916.09	+	1272.41i	−1.78247	+	0.579160i
$170$	−1367.56	−	905.520i	−0.616984	−	0.408531i
$171$	−418.070	−	575.425i	−0.186963	−	0.257332i
$172$	271.724	+	138.450i	0.120458	+	0.0613764i
$173$	−691.218	+	352.193i	−0.303771	+	0.154779i	−0.599231	−	0.800576i	$-0.704527\pi$
$173$	−691.218	+	352.193i	−0.303771	+	0.154779i	0.295461	+	0.955355i	$0.404527\pi$
$174$	1917.89	−	2639.75i	0.835603	−	1.15011i
$175$	120.491	−	1714.33i	0.0520472	−	0.740519i
$176$	−583.636	+	10.2573i	−0.249961	+	0.00439302i
$177$	−1495.20	−	1495.20i	−0.634949	−	0.634949i
$178$	499.960	+	3156.62i	0.210526	+	1.32921i
$179$	1449.13	+	470.850i	0.605100	+	0.196609i	0.595514	−	0.803345i	$-0.296949\pi$
$179$	1449.13	+	470.850i	0.605100	+	0.196609i	0.00958642	+	0.999954i	$0.496949\pi$
$180$	225.583	+	283.700i	0.0934109	+	0.117477i
$181$	1088.31	−	790.703i	0.446925	−	0.324710i	−0.341456	−	0.939898i	$-0.610920\pi$
$181$	1088.31	−	790.703i	0.446925	−	0.324710i	0.788380	+	0.615188i	$0.210920\pi$
$182$	−341.813	+	2158.13i	−0.139214	+	0.878961i
$183$	−2141.78	+	4203.48i	−0.865164	+	1.69798i
$184$	−327.618	+	1008.31i	−0.131263	+	0.403985i
$185$	−666.132	−	1177.87i	−0.264730	−	0.468103i
$186$		−	941.595i		−	0.371189i
$187$	−1858.72	+	1925.22i	−0.726860	+	0.752866i
$188$	149.870	−	149.870i	0.0581404	−	0.0581404i
$189$	1245.22	+	904.706i	0.479241	+	0.348189i
$190$	1446.56	+	1326.00i	0.552340	+	0.506307i
$191$	−440.819	−	1356.70i	−0.166998	−	0.513966i	0.832180	−	0.554505i	$-0.187092\pi$
$191$	−440.819	−	1356.70i	−0.166998	−	0.513966i	−0.999178	+	0.0405392i	$0.987092\pi$
$192$	374.527	+	59.3192i	0.140777	+	0.0222968i
$193$	−1016.06	−	160.928i	−0.378951	−	0.0600199i	−0.0359464	−	0.999354i	$-0.511445\pi$
$193$	−1016.06	−	160.928i	−0.378951	−	0.0600199i	−0.343004	+	0.939334i	$0.611445\pi$
$194$	−127.721	−	393.084i	−0.0472671	−	0.145473i
$195$	228.674	+	5258.98i	0.0839777	+	1.93130i
$196$	−498.292	−	362.030i	−0.181593	−	0.131935i
$197$	935.748	−	935.748i	0.338423	−	0.338423i	−0.517351	−	0.855773i	$-0.673082\pi$
$197$	935.748	−	935.748i	0.338423	−	0.338423i	0.855773	+	0.517351i	$0.173082\pi$
$198$	522.114	−	277.693i	0.187399	−	0.0996707i
$199$			2273.10i			0.809727i	0.914377	+	0.404864i	$0.132681\pi$
$199$			2273.10i			0.809727i	−0.914377	+	0.404864i	$0.867319\pi$
$200$	−765.815	−	643.060i	−0.270757	−	0.227356i
$201$	737.869	−	2270.93i	0.258932	−	0.796910i
$202$	761.088	−	1493.72i	0.265099	−	0.520286i
$203$	592.213	−	3739.08i	0.204755	−	1.29277i
$204$	1406.39	−	1021.81i	0.482683	−	0.350690i
$205$	−1895.44	+	1507.15i	−0.645771	+	0.513482i
$206$	−210.212	−	68.3021i	−0.0710980	−	0.0231011i
$207$	−168.022	−	1060.85i	−0.0564172	−	0.356204i
$208$	899.039	+	899.039i	0.299698	+	0.299698i
$209$	2556.76	−	1927.14i	0.846196	−	0.637813i
$210$	1657.33	+	755.645i	0.544603	+	0.248307i
$211$	−730.511	+	1005.46i	−0.238343	+	0.328052i	−0.911386	−	0.411552i	$-0.864987\pi$
$211$	−730.511	+	1005.46i	−0.238343	+	0.328052i	0.673043	+	0.739603i	$0.264987\pi$
$212$	−2172.08	+	1106.73i	−0.703675	+	0.358541i
$213$	3158.82	+	1609.50i	1.01615	+	0.517752i
$214$	155.827	+	214.477i	0.0497762	+	0.0685111i
$215$	835.316	−	169.792i	0.264968	−	0.0538592i
$216$	851.789	−	276.763i	0.268319	−	0.0871821i
$217$	−495.965	−	973.386i	−0.155153	−	0.304506i
$218$	3192.04	−	505.570i	0.991709	−	0.157071i
$219$	2177.12			0.671764
$220$	−1259.02	+	1037.73i	−0.385831	+	0.318017i
$221$	5828.81			1.77416
$222$	1416.56	−	224.362i	0.428259	−	0.0678296i
$223$	−202.641	−	397.706i	−0.0608514	−	0.119428i	0.858578	−	0.512684i	$-0.171349\pi$
$223$	−202.641	−	397.706i	−0.0608514	−	0.119428i	−0.919429	+	0.393256i	$0.871349\pi$
$224$	418.417	−	135.952i	0.124807	−	0.0405521i
$225$	987.046	+	228.248i	0.292458	+	0.0676290i
$226$	−707.484	−	973.768i	−0.208235	−	0.286611i
$227$	3680.75	+	1875.44i	1.07621	+	0.548357i	0.899953	−	0.435987i	$-0.143601\pi$
$227$	3680.75	+	1875.44i	1.07621	+	0.548357i	0.176258	+	0.984344i	$0.443601\pi$
$228$	−1853.17	+	944.238i	−0.538286	+	0.274271i
$229$	2538.96	−	3494.58i	0.732661	−	1.00842i	−0.266347	−	0.963877i	$-0.585817\pi$
$229$	2538.96	−	3494.58i	0.732661	−	1.00842i	0.999007	−	0.0445439i	$-0.0141835\pi$
$230$	1037.29	+	2775.86i	0.297377	+	0.795803i
$231$	1704.28	−	2434.59i	0.485427	−	0.693439i
$232$	−1557.64	−	1557.64i	−0.440793	−	0.440793i
$233$	482.487	+	3046.30i	0.135660	+	0.856524i	0.957841	+	0.287298i	$0.0927569\pi$
$233$	482.487	+	3046.30i	0.135660	+	0.856524i	−0.822181	+	0.569226i	$0.807243\pi$
$234$	−1225.04	−	398.038i	−0.342236	−	0.111199i
$235$	67.1680	−	588.594i	0.0186449	−	0.163386i
$236$	−1154.91	+	839.092i	−0.318552	+	0.231442i
$237$	−181.895	+	1148.44i	−0.0498537	+	0.314764i
$238$	915.665	−	1797.09i	0.249386	−	0.489447i
$239$	−155.282	+	477.908i	−0.0420265	+	0.129344i	−0.969868	−	0.243630i	$-0.921662\pi$
$239$	−155.282	+	477.908i	−0.0420265	+	0.129344i	0.927842	+	0.372974i	$0.121662\pi$
$240$	922.568	−	521.747i	0.248131	−	0.140328i
$241$		−	1879.63i		−	0.502398i	−0.967936	−	0.251199i	$-0.919175\pi$
$241$		−	1879.63i		−	0.502398i	0.967936	−	0.251199i	$-0.0808248\pi$
$242$	1291.12	+	2327.93i	0.342960	+	0.618367i
$243$	−1558.38	+	1558.38i	−0.411401	+	0.411401i
$244$	2576.70	+	1872.08i	0.676049	+	0.491179i
$245$	−1719.93	+	74.7869i	−0.448499	+	0.0195019i
$246$	−793.129	−	2441.00i	−0.205561	−	0.632652i
$247$	−6887.87	−	1090.93i	−1.77435	−	0.281030i
$248$	−627.857	−	99.4428i	−0.160762	−	0.0254622i
$249$	1416.44	+	4359.35i	0.360494	+	1.10949i
$250$	−2794.09	−	74.6595i	−0.706854	−	0.0188875i
$251$	−3238.11	−	2352.63i	−0.814295	−	0.591620i	0.100778	−	0.994909i	$-0.467867\pi$
$251$	−3238.11	−	2352.63i	−0.814295	−	0.591620i	−0.915073	+	0.403289i	$0.867867\pi$
$252$	−315.164	+	315.164i	−0.0787837	+	0.0787837i
$253$	4761.32	−	840.136i	1.18317	−	0.208770i
$254$			434.229i			0.107267i
$255$	1299.34	−	4682.02i	0.319089	−	1.14980i
$256$	79.1084	−	243.470i	0.0193136	−	0.0594410i
$257$	1161.70	−	2279.97i	0.281965	−	0.553387i	−0.705973	−	0.708239i	$-0.749490\pi$
$257$	1161.70	−	2279.97i	0.281965	−	0.553387i	0.987938	+	0.154852i	$0.0494900\pi$
$258$	−141.329	+	892.319i	−0.0341038	+	0.215323i
$259$	1346.21	−	978.082i	0.322972	−	0.234653i
$260$	3530.85	+	402.926i	0.842207	+	0.0961093i
$261$	2122.45	+	689.626i	0.503358	+	0.163551i
$262$	469.818	+	2966.32i	0.110784	+	0.699464i
$263$	5685.73	+	5685.73i	1.33307	+	1.33307i	0.902610	+	0.430459i	$0.141648\pi$
$263$	5685.73	+	5685.73i	1.33307	+	1.33307i	0.430459	+	0.902610i	$0.358352\pi$
$264$	−563.190	−	1634.99i	−0.131295	−	0.381161i
$265$	−2826.75	+	6199.80i	−0.655267	+	1.43717i
$266$	−1418.38	+	1952.24i	−0.326942	+	0.449998i
$267$	−8435.99	+	4298.35i	−1.93361	+	0.985225i
$268$	−1436.33	−	731.848i	−0.327380	−	0.166809i
$269$	−591.391	−	813.980i	−0.134044	−	0.184495i	0.736719	−	0.676199i	$-0.236374\pi$
$269$	−591.391	−	813.980i	−0.134044	−	0.184495i	−0.870762	+	0.491704i	$0.836374\pi$
$270$	1382.06	−	2087.26i	0.311517	−	0.470468i
$271$	−5326.15	+	1730.57i	−1.19388	+	0.387914i	−0.837504	−	0.546431i	$-0.815986\pi$
$271$	−5326.15	+	1730.57i	−1.19388	+	0.387914i	−0.356371	+	0.934344i	$0.615986\pi$
$272$	−532.811	−	1045.70i	−0.118774	−	0.233106i
$273$	−6393.37	+	1012.61i	−1.41738	+	0.224491i
$274$	−115.300			−0.0254216
$275$	−949.207	+	4460.48i	−0.208143	+	0.978098i
$276$	−3140.79			−0.684976
$277$	2129.37	−	337.259i	0.461882	−	0.0731549i	0.0788428	−	0.996887i	$-0.474877\pi$
$277$	2129.37	−	337.259i	0.461882	−	0.0731549i	0.383039	+	0.923732i	$0.374877\pi$
$278$	1094.32	+	2147.72i	0.236089	+	0.463351i
$279$	612.486	−	199.009i	0.131429	−	0.0427038i
$280$	678.898	−	1025.31i	0.144900	−	0.218835i
$281$	−3719.72	−	5119.76i	−0.789680	−	1.08690i	−0.994148	−	0.108028i	$-0.965546\pi$
$281$	−3719.72	−	5119.76i	−0.789680	−	1.08690i	0.204468	−	0.978873i	$-0.434454\pi$
$282$	559.453	+	285.056i	0.118138	+	0.0601944i
$283$	3467.27	−	1766.66i	0.728297	−	0.371086i	−0.0501957	−	0.998739i	$-0.515985\pi$
$283$	3467.27	−	1766.66i	0.728297	−	0.371086i	0.778493	+	0.627653i	$0.215985\pi$
$284$	1406.83	−	1936.33i	0.293943	−	0.404578i
$285$	−2411.72	+	5289.53i	−0.501255	+	1.09939i
$286$	1694.56	−	5545.04i	0.350355	−	1.14645i
$287$	−2105.65	−	2105.65i	−0.433076	−	0.433076i
$288$	40.5715	+	256.159i	0.00830104	+	0.0524107i
$289$	−444.511	−	144.430i	−0.0904764	−	0.0293976i
$290$	−6117.41	−	698.094i	−1.23871	−	0.141357i
$291$	990.579	−	719.698i	0.199549	−	0.144981i
$292$	229.928	−	1451.71i	0.0460806	−	0.290942i
$293$	3518.63	−	6905.69i	0.701571	−	1.37691i	−0.214831	−	0.976651i	$-0.568920\pi$
$293$	3518.63	−	6905.69i	0.701571	−	1.37691i	0.916402	−	0.400259i	$-0.131080\pi$
$294$	563.847	−	1735.34i	0.111851	−	0.344242i
$295$	−1067.00	+	3844.81i	−0.210586	+	0.758825i
$296$		−	968.263i		−	0.190132i
$297$	−2938.39	−	2836.89i	−0.574083	−	0.554252i
$298$	−111.699	+	111.699i	−0.0217133	+	0.0217133i
$299$	−8519.75	−	6189.96i	−1.64786	−	1.19724i
$300$	1110.74	−	2746.35i	0.213761	−	0.528536i
$301$	323.909	+	996.890i	0.0620259	+	0.190896i
$302$	−2893.10	−	458.221i	−0.551255	−	0.0873102i
$303$	4905.25	+	776.915i	0.930030	+	0.147302i
$304$	433.904	+	1335.42i	0.0818623	+	0.251946i
$305$	8893.86	−	386.727i	1.66971	−	0.0726031i
$306$	961.908	+	698.867i	0.179701	+	0.130561i
$307$	−582.031	+	582.031i	−0.108203	+	0.108203i	−0.759135	−	0.650933i	$-0.774378\pi$
$307$	−582.031	+	582.031i	−0.108203	+	0.108203i	0.650933	+	0.759135i	$0.274378\pi$
$308$	−1443.40	−	1393.54i	−0.267030	−	0.257806i
$309$		−	654.794i		−	0.120550i
$310$	−1546.60	+	874.658i	−0.283357	+	0.160249i
$311$	3154.97	−	9710.01i	0.575248	−	1.77043i	−0.0600844	−	0.998193i	$-0.519137\pi$
$311$	3154.97	−	9710.01i	0.575248	−	1.77043i	0.635333	−	0.772239i	$-0.280863\pi$
$312$	−1709.99	+	3356.04i	−0.310285	+	0.608969i
$313$	832.266	−	5254.72i	0.150295	−	0.948927i	−0.791116	−	0.611666i	$-0.790500\pi$
$313$	832.266	−	5254.72i	0.150295	−	0.948927i	0.941411	−	0.337261i	$-0.109500\pi$
$314$	−5974.64	+	4340.83i	−1.07379	+	0.780150i
$315$	−141.249	+	1237.76i	−0.0252649	+	0.221397i
$316$	746.571	+	242.576i	0.132905	+	0.0431834i
$317$	26.3516	+	166.377i	0.00466893	+	0.0294785i	0.989913	−	0.141678i	$-0.0452497\pi$
$317$	26.3516	+	166.377i	0.00466893	+	0.0294785i	−0.985244	+	0.171156i	$0.945250\pi$
$318$	−5106.62	−	5106.62i	−0.900518	−	0.900518i
$319$	−2935.93	+	9607.12i	−0.515300	+	1.68619i
$320$	−250.469	−	670.273i	−0.0437551	−	0.117092i
$321$	−461.632	+	635.381i	−0.0802672	+	0.110478i
$322$	−3246.83	+	1654.34i	−0.561922	+	0.286314i
$323$	5735.61	+	2922.44i	0.988043	+	0.503433i
$324$	2074.04	+	2854.67i	0.355631	+	0.489484i
$325$	8425.60	−	5260.73i	1.43806	−	0.897885i
$326$	2465.54	−	801.102i	0.418876	−	0.136101i
$327$	4346.59	+	8530.66i	0.735067	+	1.44265i
$328$	−1711.43	+	271.063i	−0.288103	+	0.0456310i
$329$	728.490			0.122076
$330$	−4076.34	−	2597.25i	−0.679985	−	0.433254i
$331$	3846.66			0.638766			0.319383	−	0.947626i	$-0.396524\pi$
$331$	3846.66			0.638766			0.319383	+	0.947626i	$0.396524\pi$
$332$	3056.41	−	484.088i	0.505248	−	0.0800235i
$333$	445.337	+	874.024i	0.0732863	+	0.143832i
$334$	7984.45	−	2594.30i	1.30805	−	0.425012i
$335$	−4415.47	+	897.520i	−0.720129	+	0.146378i
$336$	766.081	+	1054.42i	0.124384	+	0.171200i
$337$	351.950	+	179.328i	0.0568901	+	0.0289869i	0.482204	−	0.876059i	$-0.339836\pi$
$337$	351.950	+	179.328i	0.0568901	+	0.0289869i	−0.425314	+	0.905046i	$0.639836\pi$
$338$	−7337.65	+	3738.72i	−1.18081	+	0.601655i
$339$	2095.89	−	2884.75i	0.335792	−	0.462177i
$340$	−2984.76	−	1360.88i	−0.476092	−	0.217070i
$341$	944.133	+	2740.89i	0.149934	+	0.435272i
$342$	−1005.88	−	1005.88i	−0.159040	−	0.159040i
$343$	−1068.87	−	6748.58i	−0.168261	−	1.06236i
$344$	580.075	+	188.478i	0.0909172	+	0.0295408i
$345$	−6871.31	+	5463.69i	−1.07229	+	0.852624i
$346$	−1255.22	+	911.974i	−0.195033	+	0.141700i
$347$	−586.169	+	3700.93i	−0.0906836	+	0.572554i	0.899948	+	0.435996i	$0.143604\pi$
$347$	−586.169	+	3700.93i	−0.0906836	+	0.572554i	−0.990632	+	0.136558i	$0.956396\pi$
$348$	2962.66	−	5814.55i	0.456366	−	0.895668i
$349$	483.686	−	1488.63i	0.0741866	−	0.228323i	−0.907087	−	0.420944i	$-0.861699\pi$
$349$	483.686	−	1488.63i	0.0741866	−	0.228323i	0.981273	+	0.192621i	$0.0616989\pi$
$350$	−298.344	−	3424.14i	−0.0455633	−	0.522936i
$351$			8896.30i			1.35285i
$352$	−1149.69	+	202.864i	−0.174087	+	0.0307178i
$353$	−6295.75	+	6295.75i	−0.949261	+	0.949261i	−0.998774	−	0.0495123i	$-0.984233\pi$
$353$	−6295.75	+	6295.75i	−0.949261	+	0.949261i	0.0495123	+	0.998774i	$0.484233\pi$
$354$	−3421.38	−	2485.78i	−0.513684	−	0.373214i
$355$	−290.617	−	6683.54i	−0.0434489	−	0.999227i
$356$	1975.22	+	6079.09i	0.294063	+	0.905032i
$357$	5901.50	+	934.707i	0.874904	+	0.138571i
$358$	3009.89	+	476.720i	0.444351	+	0.0703782i
$359$	−295.886	−	910.643i	−0.0434993	−	0.133877i	0.926948	−	0.375189i	$-0.122422\pi$
$359$	−295.886	−	910.643i	−0.0434993	−	0.133877i	−0.970448	+	0.241312i	$0.922422\pi$
$360$	534.372	+	489.837i	0.0782330	+	0.0717130i
$361$	−681.716	−	495.295i	−0.0993899	−	0.0722110i
$362$	1902.43	−	1902.43i	0.276215	−	0.276215i
$363$	−5376.91	+	5768.80i	−0.777451	+	0.834114i
$364$			4370.05i			0.629267i
$365$	−2022.35	−	3575.99i	−0.290013	−	0.512810i
$366$	−2915.69	+	8973.56i	−0.416408	+	1.28157i
$367$	5813.38	−	11409.4i	0.826856	−	1.62280i	0.0452891	−	0.998974i	$-0.485579\pi$
$367$	5813.38	−	11409.4i	0.826856	−	1.62280i	0.781567	−	0.623822i	$-0.214421\pi$
$368$	−331.702	+	2094.28i	−0.0469869	+	0.296663i
$369$	1420.19	−	1031.83i	0.200358	−	0.145568i
$370$	−1684.38	−	2118.33i	−0.236667	−	0.297640i
$371$	−7968.83	−	2589.23i	−1.11515	−	0.362335i
$372$	−294.596	−	1860.00i	−0.0410593	−	0.259238i
$373$	−767.256	−	767.256i	−0.106507	−	0.106507i	0.651845	−	0.758352i	$-0.273995\pi$
$373$	−767.256	−	767.256i	−0.106507	−	0.106507i	−0.758352	+	0.651845i	$0.773995\pi$
$374$	−3069.32	+	4384.57i	−0.424361	+	0.606205i
$375$	−2347.50	−	7940.60i	−0.323265	−	1.09347i
$376$	249.160	−	342.940i	0.0341741	−	0.0470366i
$377$	19496.0	−	9933.73i	2.66339	−	1.35706i
$378$	2742.84	+	1397.54i	0.373218	+	0.190164i
$379$	−2223.20	−	3059.97i	−0.301314	−	0.414723i	0.631334	−	0.775511i	$-0.282508\pi$
$379$	−2223.20	−	3059.97i	−0.301314	−	0.414723i	−0.932648	+	0.360788i	$0.882508\pi$
$380$	3272.37	+	2166.77i	0.441760	+	0.292508i
$381$	−1223.43	+	397.515i	−0.164509	+	0.0534523i
$382$	−1295.25	−	2542.08i	−0.173484	−	0.340482i
$383$	−6651.87	+	1053.55i	−0.887454	+	0.140559i	−0.583486	−	0.812123i	$-0.698312\pi$
$383$	−6651.87	+	1053.55i	−0.887454	+	0.140559i	−0.303968	+	0.952682i	$0.598312\pi$
$384$	758.390			0.100785
$385$	−5582.01	−	537.816i	−0.738924	−	0.0711938i
$386$	−2057.45			−0.271299
$387$	−610.304	+	96.6627i	−0.0801641	+	0.0126967i
$388$	−375.280	−	736.529i	−0.0491030	−	0.0963700i
$389$	−984.773	+	319.972i	−0.128355	+	0.0417050i	−0.372490	−	0.928036i	$-0.621496\pi$
$389$	−984.773	+	319.972i	−0.128355	+	0.0417050i	0.244135	+	0.969741i	$0.421496\pi$
$390$	2097.09	+	10316.9i	0.272282	+	1.33953i
$391$	5713.75	+	7864.30i	0.739020	+	1.01717i
$392$	−1097.58	−	559.246i	−0.141419	−	0.0720566i
$393$	−7927.41	+	4039.22i	−1.01752	+	0.518452i
$394$	1555.69	−	2141.22i	0.198920	−	0.273790i
$395$	2055.31	−	768.030i	0.261807	−	0.0978324i
$396$	944.490	−	711.902i	0.119855	−	0.0903394i
$397$	7871.19	+	7871.19i	0.995072	+	0.995072i	0.999988	−	0.00491556i	$-0.00156468\pi$
$397$	7871.19	+	7871.19i	0.995072	+	0.995072i	−0.00491556	+	0.999988i	$0.501565\pi$
$398$	711.182	+	4490.23i	0.0895687	+	0.565515i
$399$	−6798.83	−	2209.07i	−0.853051	−	0.277173i
$400$	−1713.97	−	1030.69i	−0.214246	−	0.128836i
$401$	−8049.00	+	5847.94i	−1.00236	+	0.728260i	−0.962594	−	0.270949i	$-0.912663\pi$
$401$	−8049.00	+	5847.94i	−1.00236	+	0.728260i	−0.0397700	+	0.999209i	$0.512663\pi$
$402$	747.066	−	4716.79i	0.0926873	−	0.585204i
$403$	2866.63	−	5626.07i	0.354335	−	0.695421i
$404$	1036.10	−	3188.78i	0.127593	−	0.392692i
$405$	9503.47	+	2637.37i	1.16600	+	0.323585i
$406$		−	7571.39i		−	0.925521i
$407$	−3898.52	+	2073.48i	−0.474797	+	0.252527i
$408$	2458.47	−	2458.47i	0.298314	−	0.298314i
$409$	9412.06	+	6838.26i	1.13789	+	0.826724i	0.986824	−	0.161800i	$-0.0517298\pi$
$409$	9412.06	+	6838.26i	1.13789	+	0.826724i	0.151065	+	0.988524i	$0.451730\pi$
$410$	−3272.66	+	3570.21i	−0.394208	+	0.430049i
$411$	−105.551	−	324.854i	−0.0126678	−	0.0389875i
$412$	−436.618	−	69.1535i	−0.0522103	−	0.00826929i
$413$	−4846.23	−	767.567i	−0.577403	−	0.0914516i
$414$	−663.815	−	2043.01i	−0.0788037	−	0.242533i
$415$	5844.60	−	6375.98i	0.691326	−	0.754180i
$416$	2057.22	+	1494.66i	0.242461	+	0.176158i
$417$	−5049.34	+	5049.34i	−0.592967	+	0.592967i
$418$	4447.63	−	4606.75i	0.520432	−	0.539052i
$419$		−	7496.53i		−	0.874056i	−0.899448	−	0.437028i	$-0.856031\pi$
$419$		−	7496.53i		−	0.874056i	0.899448	−	0.437028i	$-0.143969\pi$
$420$	3510.27	+	974.156i	0.407818	+	0.113176i
$421$	2531.49	−	7791.12i	0.293058	−	0.901938i	−0.690809	−	0.723037i	$-0.742746\pi$
$421$	2531.49	−	7791.12i	0.293058	−	0.901938i	0.983867	−	0.178902i	$-0.0572544\pi$
$422$	−1128.46	+	2214.72i	−0.130172	+	0.255476i
$423$	−67.1802	+	424.159i	−0.00772202	+	0.0487549i
$424$	−3944.42	+	2865.79i	−0.451787	+	0.328243i
$425$	−8897.32	+	2214.99i	−1.01549	+	0.252806i
$426$	6743.43	+	2191.07i	0.766949	+	0.249197i
$427$	1712.50	+	10812.3i	0.194084	+	1.22540i
$428$	374.920	+	374.920i	0.0423422	+	0.0423422i
$429$	17174.3	−	301.835i	1.93282	−	0.0339690i
$430$	1596.94	−	596.748i	0.179096	−	0.0669250i
$431$	−10367.3	+	14269.4i	−1.15865	+	1.59474i	−0.442539	+	0.896749i	$0.645922\pi$
$431$	−10367.3	+	14269.4i	−1.15865	+	1.59474i	−0.716107	+	0.697990i	$0.754078\pi$
$432$	1596.01	−	813.210i	0.177751	−	0.0905684i
$433$	−5861.48	−	2986.57i	−0.650542	−	0.331468i	0.0973871	−	0.995247i	$-0.468952\pi$
$433$	−5861.48	−	2986.57i	−0.650542	−	0.331468i	−0.747929	+	0.663779i	$0.768952\pi$
$434$	−1284.26	−	1767.63i	−0.142043	−	0.195505i
$435$	−3633.33	−	17874.7i	−0.400471	−	1.97017i
$436$	6147.31	−	1997.38i	0.675236	−	0.219397i
$437$	−5280.01	−	10362.6i	−0.577979	−	1.13435i
$438$	4300.64	−	681.154i	0.469161	−	0.0743078i
$439$	200.474			0.0217952			0.0108976	−	0.999941i	$-0.496531\pi$
$439$	200.474			0.0217952			0.0108976	+	0.999941i	$0.496531\pi$
$440$	−2162.36	+	2443.81i	−0.234287	+	0.264782i
$441$	1247.97			0.134756
$442$	11514.1	−	1823.65i	1.23907	−	0.196250i
$443$	7918.08	+	15540.1i	0.849209	+	1.66667i	0.739959	+	0.672652i	$0.234845\pi$
$443$	7918.08	+	15540.1i	0.849209	+	1.66667i	0.109250	+	0.994014i	$0.465155\pi$
$444$	2728.05	−	886.398i	0.291594	−	0.0947445i
$445$	14896.5	+	9863.56i	1.58688	+	1.05074i
$446$	−524.723	−	722.219i	−0.0557093	−	0.0766773i
$447$	−416.965	−	212.454i	−0.0441203	−	0.0224804i
$448$	783.996	−	399.466i	0.0826794	−	0.0421272i
$449$	−9349.20	+	12868.1i	−0.982664	+	1.35252i	−0.0472823	+	0.998882i	$0.515056\pi$
$449$	−9349.20	+	12868.1i	−0.982664	+	1.35252i	−0.935382	+	0.353640i	$0.884944\pi$
$450$	2021.20	+	142.059i	0.211734	+	0.0148817i
$451$	4756.30	+	6310.26i	0.496598	+	0.658843i
$452$	−1702.21	−	1702.21i	−0.177135	−	0.177135i
$453$	−1357.46	−	8570.69i	−0.140793	−	0.888932i
$454$	7857.64	+	2553.10i	0.812284	+	0.263927i
$455$	7602.11	+	9560.65i	0.783280	+	0.985078i
$456$	−3365.29	+	2445.03i	−0.345601	+	0.251094i
$457$	−907.120	+	5727.33i	−0.0928518	+	0.586243i	0.896764	+	0.442508i	$0.145911\pi$
$457$	−907.120	+	5727.33i	−0.0928518	+	0.586243i	−0.989616	+	0.143735i	$0.954089\pi$
$458$	3922.06	−	7697.48i	0.400144	−	0.785326i
$459$	2537.61	−	7809.96i	0.258051	−	0.794200i
$460$	2917.51	+	5158.83i	0.295717	+	0.522895i
$461$		−	1349.04i		−	0.136293i	−0.997675	−	0.0681467i	$-0.978291\pi$
$461$		−	1349.04i		−	0.136293i	0.997675	−	0.0681467i	$-0.0217086\pi$
$462$	2604.90	−	5342.45i	0.262318	−	0.537994i
$463$	10088.3	−	10088.3i	1.01262	−	1.01262i	0.0127001	−	0.999919i	$-0.495957\pi$
$463$	10088.3	−	10088.3i	1.01262	−	1.01262i	0.999919	−	0.0127001i	$-0.00404269\pi$
$464$	−3564.26	−	2589.59i	−0.356609	−	0.259092i
$465$	−3880.15	−	3556.78i	−0.386963	−	0.354713i
$466$	1906.19	+	5866.64i	0.189490	+	0.583191i
$467$	12717.5	+	2014.26i	1.26017	+	0.199591i	0.750551	−	0.660812i	$-0.229788\pi$
$467$	12717.5	+	2014.26i	1.26017	+	0.199591i	0.509614	+	0.860403i	$0.329788\pi$
$468$	−2544.44	−	403.000i	−0.251318	−	0.0398049i
$469$	−1712.18	−	5269.55i	−0.168574	−	0.518817i
$470$	−51.4707	−	1183.71i	−0.00505141	−	0.116171i
$471$	−17699.7	−	12859.5i	−1.73154	−	1.25804i
$472$	−2018.86	+	2018.86i	−0.196876	+	0.196876i
$473$	−483.327	−	2739.17i	−0.0469840	−	0.266273i
$474$			2325.51i			0.225346i
$475$	10928.5	−	952.196i	1.05565	−	0.0919784i
$476$	1246.53	−	3836.42i	0.120031	−	0.369416i
$477$	2242.44	−	4401.04i	0.215250	−	0.422452i
$478$	−157.217	+	992.630i	−0.0150438	+	0.0949829i
$479$	−13764.0	+	10000.1i	−1.31293	+	0.953901i	−0.312940	+	0.949773i	$0.601314\pi$
$479$	−13764.0	+	10000.1i	−1.31293	+	0.953901i	−0.999991	+	0.00412780i	$0.998686\pi$
$480$	1659.18	−	1319.29i	0.157773	−	0.125452i
$481$	9147.09	+	2972.07i	0.867093	+	0.281736i
$482$	−588.079	−	3712.98i	−0.0555731	−	0.350875i
$483$	−7633.38	−	7633.38i	−0.719112	−	0.719112i
$484$	3278.79	+	4194.58i	0.307925	+	0.393932i
$485$	−2102.28	−	958.518i	−0.196824	−	0.0897404i
$486$	−2590.83	+	3565.97i	−0.241815	+	0.332830i
$487$	−13347.1	+	6800.69i	−1.24192	+	0.632789i	−0.946539	−	0.322590i	$-0.895446\pi$
$487$	−13347.1	+	6800.69i	−1.24192	+	0.632789i	−0.295380	+	0.955380i	$0.595446\pi$
$488$	5675.66	+	2891.89i	0.526486	+	0.268258i
$489$	4514.16	+	6213.21i	0.417459	+	0.574583i
$490$	−3374.11	+	685.845i	−0.311075	+	0.0632313i
$491$	−1961.46	+	637.318i	−0.180284	+	0.0585779i	−0.397768	−	0.917486i	$-0.630215\pi$
$491$	−1961.46	+	637.318i	−0.180284	+	0.0585779i	0.217484	+	0.976064i	$0.430215\pi$
$492$	−2330.44	−	4573.75i	−0.213546	−	0.419107i
$493$	−19948.9	+	3159.59i	−1.82242	+	0.288643i
$494$	−13947.5			−1.27030
$495$	827.905	−	3200.50i	0.0751749	−	0.290610i
$496$	−1271.37			−0.115093
$497$	8125.22	−	1286.91i	0.733331	−	0.116148i
$498$	4161.90	+	8168.19i	0.374497	+	0.734991i
$499$	−12345.0	+	4011.14i	−1.10749	+	0.359847i	−0.804982	−	0.593299i	$-0.797825\pi$
$499$	−12345.0	+	4011.14i	−1.10749	+	0.359847i	−0.302512	+	0.953146i	$0.597825\pi$
$500$	−5542.73	+	726.703i	−0.495757	+	0.0649983i
$501$	14618.7	+	20121.0i	1.30363	+	1.79429i
$502$	−7132.56	−	3634.22i	−0.634147	−	0.323114i
$503$	−15023.3	+	7654.74i	−1.33172	+	0.678544i	−0.967524	−	0.252779i	$-0.918656\pi$
$503$	−15023.3	+	7654.74i	−1.33172	+	0.678544i	−0.364194	+	0.931323i	$0.618656\pi$
$504$	−523.963	+	721.174i	−0.0463079	+	0.0637374i
$505$	−3280.44	−	8778.69i	−0.289064	−	0.773558i
$506$	9142.54	−	3149.25i	0.803232	−	0.276683i
$507$	−17251.0	−	17251.0i	−1.51113	−	1.51113i
$508$	135.857	+	857.765i	0.0118655	+	0.0749157i
$509$	−1217.20	−	395.491i	−0.105995	−	0.0344398i	0.255539	−	0.966799i	$-0.417747\pi$
$509$	−1217.20	−	395.491i	−0.105995	−	0.0344398i	−0.361534	+	0.932359i	$0.617747\pi$
$510$	1101.82	−	9655.28i	0.0956657	−	0.838320i
$511$	4087.06	−	2969.42i	0.353818	−	0.257064i
$512$	80.0944	−	505.696i	0.00691349	−	0.0436501i
$513$	−4460.41	+	8754.04i	−0.383882	+	0.753412i
$514$	1581.47	−	4867.26i	0.135711	−	0.417676i
$515$	−1075.52	+	608.246i	−0.0920252	+	0.0520437i
$516$			1806.88i			0.154154i
$517$	−1914.34	−	268.809i	−0.162848	−	0.0228670i
$518$	2353.27	−	2353.27i	0.199608	−	0.199608i
$519$	−3718.56	−	2701.69i	−0.314502	−	0.228499i
$520$	7100.82	−	308.761i	0.598830	−	0.0260386i
$521$	−2430.97	−	7481.76i	−0.204420	−	0.629140i	−0.999737	−	0.0229456i	$-0.992696\pi$
$521$	−2430.97	−	7481.76i	−0.204420	−	0.629140i	0.795317	−	0.606194i	$-0.207304\pi$
$522$	4408.40	+	698.222i	0.369637	+	0.0585447i
$523$	−15937.3	−	2524.22i	−1.33249	−	0.211045i	−0.550758	−	0.834665i	$-0.685661\pi$
$523$	−15937.3	−	2524.22i	−1.33249	−	0.211045i	−0.781728	+	0.623620i	$0.785661\pi$
$524$	1856.14	+	5712.60i	0.154744	+	0.476252i
$525$	9374.28	−	3975.21i	0.779290	−	0.330461i
$526$	13010.3	+	9452.57i	1.07848	+	0.783558i
$527$	−4121.38	+	4121.38i	−0.340665	+	0.340665i
$528$	−1624.05	−	3053.51i	−0.133859	−	0.251680i
$529$		−	5395.71i		−	0.443471i
$530$	−3644.16	+	13131.3i	−0.298665	+	1.07621i
$531$	893.824	−	2750.91i	0.0730483	−	0.224820i
$532$	−2191.05	+	4300.17i	−0.178560	+	0.350444i
$533$	2692.49	−	16999.7i	0.218808	−	1.38150i
$534$	−15319.4	+	11130.2i	−1.24146	+	0.901970i
$535$	1472.45	+	168.030i	0.118990	+	0.0135786i
$536$	−3066.27	−	996.291i	−0.247094	−	0.0802859i
$537$	1412.26	+	8916.68i	0.113489	+	0.716542i
$538$	−1422.89	−	1422.89i	−0.114024	−	0.114024i
$539$	98.7139	+	5616.79i	0.00788852	+	0.448854i
$540$	2077.05	−	4555.52i	0.165522	−	0.363034i
$541$	−2344.37	+	3226.76i	−0.186308	+	0.256431i	−0.891946	−	0.452141i	$-0.850660\pi$
$541$	−2344.37	+	3226.76i	−0.186308	+	0.256431i	0.705638	+	0.708572i	$0.250660\pi$
$542$	−9979.70	+	5084.91i	−0.790895	+	0.402981i
$543$	7101.64	+	3618.46i	0.561253	+	0.285973i
$544$	−1379.67	−	1898.95i	−0.108737	−	0.149664i
$545$	9974.25	−	15063.6i	0.783945	−	1.18395i
$546$	−12312.5	+	4000.57i	−0.965066	+	0.313569i
$547$	−6840.41	−	13425.1i	−0.534689	−	1.04939i	−0.987476	−	0.157767i	$-0.949570\pi$
$547$	−6840.41	−	13425.1i	−0.534689	−	1.04939i	0.452787	−	0.891618i	$-0.350430\pi$
$548$	−227.761	+	36.0738i	−0.0177545	+	0.00281203i
$549$	−6453.34			−0.501679
$550$	−479.495	+	9108.11i	−0.0371741	+	0.706129i
$551$	24164.8			1.86834
$552$	−6204.24	+	982.655i	−0.478388	+	0.0757692i
$553$	1224.91	+	2404.03i	0.0941927	+	0.184864i
$554$	4100.78	−	1332.43i	0.314487	−	0.102183i
$555$	4426.37	−	6684.93i	0.338538	−	0.511278i
$556$	2833.64	+	3900.17i	0.216139	+	0.297490i
$557$	1572.22	+	801.085i	0.119600	+	0.0609391i	0.512767	−	0.858528i	$-0.328621\pi$
$557$	1572.22	+	801.085i	0.119600	+	0.0609391i	−0.393167	+	0.919467i	$0.628621\pi$
$558$	1147.63	−	584.745i	0.0870662	−	0.0443625i
$559$	−3561.06	+	4901.38i	−0.269440	+	0.370852i
$560$	1020.29	−	2237.77i	0.0769915	−	0.168863i
$561$	−15163.2	−	4633.87i	−1.14116	−	0.348738i
$562$	−8949.67	−	8949.67i	−0.671742	−	0.671742i
$563$	−1623.06	−	10247.6i	−0.121499	−	0.767114i	−0.970921	−	0.239400i	$-0.923049\pi$
$563$	−1623.06	−	10247.6i	−0.121499	−	0.767114i	0.849422	−	0.527714i	$-0.176951\pi$
$564$	1194.32	+	388.057i	0.0891663	+	0.0289719i
$565$	−6685.18	−	762.886i	−0.497784	−	0.0568051i
$566$	6296.44	−	4574.63i	0.467596	−	0.339728i
$567$	−1897.25	+	11978.7i	−0.140524	+	0.887231i
$568$	2173.19	−	4265.13i	0.160537	−	0.315072i
$569$	2890.59	−	8896.31i	0.212970	−	0.655453i	−0.786322	−	0.617817i	$-0.788017\pi$
$569$	2890.59	−	8896.31i	0.212970	−	0.655453i	0.999292	−	0.0376361i	$-0.0119828\pi$
$570$	−3109.12	+	11203.4i	−0.228468	+	0.823259i
$571$		−	10591.2i		−	0.776233i	−0.921610	−	0.388116i	$-0.873126\pi$
$571$		−	10591.2i		−	0.776233i	0.921610	−	0.388116i	$-0.126874\pi$
$572$	1612.53	−	11483.7i	0.117873	−	0.839438i
$573$	5976.49	−	5976.49i	0.435727	−	0.435727i
$574$	−4818.25	−	3500.66i	−0.350366	−	0.254556i
$575$	15357.1	+	6211.03i	1.11380	+	0.450466i
$576$	160.288	+	493.316i	0.0115949	+	0.0356855i
$577$	−829.757	−	131.421i	−0.0598670	−	0.00948200i	0.126429	−	0.991976i	$-0.459648\pi$
$577$	−829.757	−	131.421i	−0.0598670	−	0.00948200i	−0.186296	+	0.982494i	$0.559648\pi$
$578$	−923.264	−	146.231i	−0.0664407	−	0.0105232i
$579$	−1883.49	−	5796.79i	−0.135190	−	0.416073i
$580$	−12302.6	+	534.948i	−0.880755	+	0.0382974i
$581$	8604.85	+	6251.79i	0.614439	+	0.446416i
$582$	1731.60	−	1731.60i	0.123328	−	0.123328i
$583$	19985.3	+	9744.50i	1.41973	+	0.692240i
$584$		−	2939.61i		−	0.208291i
$585$	−6267.70	+	3544.62i	−0.442970	+	0.250516i
$586$	4790.04	−	14742.2i	0.337670	−	1.03924i
$587$	−7176.50	+	14084.7i	−0.504610	+	0.990353i	0.488433	+	0.872601i	$0.337569\pi$
$587$	−7176.50	+	14084.7i	−0.504610	+	0.990353i	−0.993043	+	0.117751i	$0.962431\pi$
$588$	570.875	−	3604.36i	0.0400383	−	0.252792i
$589$	5641.58	−	4098.85i	0.394664	−	0.286740i
$590$	−904.800	+	7928.78i	−0.0631357	+	0.553259i
$591$	7456.98	+	2422.92i	0.519017	+	0.168639i
$592$	−302.939	−	1912.68i	−0.0210316	−	0.132789i
$593$	−12051.8	−	12051.8i	−0.834585	−	0.834585i	0.153555	−	0.988140i	$-0.450928\pi$
$593$	−12051.8	−	12051.8i	−0.834585	−	0.834585i	−0.988140	+	0.153555i	$0.950928\pi$
$594$	−6692.00	−	4684.59i	−0.462249	−	0.323588i
$595$	−3946.69	−	10561.6i	−0.271930	−	0.727706i
$596$	−185.701	+	255.596i	−0.0127628	+	0.0175665i
$597$	−12000.0	+	6114.32i	−0.822661	+	0.419167i
$598$	−18766.4	−	9561.94i	−1.28330	−	0.653874i
$599$	−2648.71	−	3645.64i	−0.180673	−	0.248676i	0.709068	−	0.705140i	$-0.249116\pi$
$599$	−2648.71	−	3645.64i	−0.180673	−	0.248676i	−0.889742	+	0.456464i	$0.849116\pi$
$600$	1334.87	−	5772.59i	0.0908267	−	0.392775i
$601$	−20616.5	+	6698.71i	−1.39928	+	0.454652i	−0.908957	−	0.416891i	$-0.863120\pi$
$601$	−20616.5	+	6698.71i	−1.39928	+	0.454652i	−0.490319	+	0.871543i	$0.663120\pi$
$602$	951.738	+	1867.89i	0.0644351	+	0.126461i
$603$	3226.06	−	510.958i	0.217870	−	0.0345072i
$604$	−5858.32			−0.394655
$605$	14470.1	+	3473.02i	0.972384	+	0.233386i
$606$	9932.79			0.665828
$607$	−7801.60	+	1235.65i	−0.521676	+	0.0826254i	−0.411719	−	0.911311i	$-0.635071\pi$
$607$	−7801.60	+	1235.65i	−0.521676	+	0.0826254i	−0.109957	+	0.993936i	$0.535071\pi$
$608$	1274.94	+	2502.20i	0.0850419	+	0.166904i
$609$	21332.1	−	6931.23i	1.41941	−	0.461195i
$610$	17447.7	−	3546.54i	1.15809	−	0.235402i
$611$	2474.93	+	3406.44i	0.163870	+	0.225548i
$612$	2118.78	+	1079.57i	0.139946	+	0.0713059i
$613$	16433.6	−	8373.34i	1.08278	−	0.551706i	0.180820	−	0.983516i	$-0.442125\pi$
$613$	16433.6	−	8373.34i	1.08278	−	0.551706i	0.901965	+	0.431810i	$0.142125\pi$
$614$	−967.631	+	1331.83i	−0.0636000	+	0.0875380i
$615$	−13054.9	−	5952.28i	−0.855976	−	0.390275i
$616$	−3287.25	−	2301.17i	−0.215012	−	0.150514i
$617$	3611.69	+	3611.69i	0.235658	+	0.235658i	0.815050	−	0.579391i	$-0.196710\pi$
$617$	3611.69	+	3611.69i	0.235658	+	0.235658i	−0.579391	+	0.815050i	$0.696710\pi$
$618$	−204.865	−	1293.46i	−0.0133347	−	0.0841922i
$619$	15030.0	+	4883.54i	0.975940	+	0.317102i	0.753212	−	0.657778i	$-0.228504\pi$
$619$	15030.0	+	4883.54i	0.975940	+	0.317102i	0.222728	+	0.974881i	$0.428504\pi$
$620$	−2781.45	+	2211.66i	−0.180171	+	0.143262i
$621$	−12003.0	+	8720.68i	−0.775625	+	0.563525i
$622$	3194.30	−	20168.0i	0.205916	−	1.30010i
$623$	−9974.07	+	19575.2i	−0.641417	+	1.25885i
$624$	−2327.87	+	7164.45i	−0.149342	+	0.459627i
$625$	−10862.0	+	11231.9i	−0.695171	+	0.718845i
$626$		−	10640.4i		−	0.679357i
$627$	17051.0	+	8313.79i	1.08605	+	0.529539i
$628$	−10444.1	+	10444.1i	−0.663636	+	0.663636i
$629$	−7182.37	−	5218.30i	−0.455294	−	0.330790i
$630$	108.239	+	2489.24i	0.00684496	+	0.157419i
$631$	−3738.04	−	11504.5i	−0.235830	−	0.725811i	−0.997010	−	0.0772703i	$-0.975380\pi$
$631$	−3738.04	−	11504.5i	−0.235830	−	0.725811i	0.761180	−	0.648541i	$-0.224620\pi$
$632$	1550.65	+	245.599i	0.0975976	+	0.0154579i
$633$	−7272.96	−	1151.92i	−0.456673	−	0.0723299i
$634$	104.108	+	320.413i	0.00652157	+	0.0200713i
$635$	1789.38	+	1640.25i	0.111826	+	0.102506i
$636$	−11685.2	−	8489.79i	−0.728534	−	0.529311i
$637$	8652.16	−	8652.16i	0.538165	−	0.538165i
$638$	−2793.81	+	19896.3i	−0.173367	+	1.23464i
$639$			4849.54i			0.300227i
$640$	−704.477	−	1245.68i	−0.0435108	−	0.0769371i
$641$	−5169.01	+	15908.6i	−0.318508	+	0.980266i	0.655779	+	0.754953i	$0.272340\pi$
$641$	−5169.01	+	15908.6i	−0.318508	+	0.980266i	−0.974286	+	0.225313i	$0.927660\pi$
$642$	−713.105	+	1399.55i	−0.0438380	+	0.0860370i
$643$	−4338.91	+	27394.8i	−0.266112	+	1.68016i	0.386359	+	0.922349i	$0.373733\pi$
$643$	−4338.91	+	27394.8i	−0.266112	+	1.68016i	−0.652470	+	0.757814i	$0.726267\pi$
$644$	−5896.13	+	4283.79i	−0.360776	+	0.262119i
$645$	3143.24	+	3953.04i	0.191884	+	0.241319i
$646$	12244.3	+	3978.42i	0.745738	+	0.242305i
$647$	−738.967	−	4665.65i	−0.0449023	−	0.283502i	0.955012	−	0.296566i	$-0.0958415\pi$
$647$	−738.967	−	4665.65i	−0.0449023	−	0.283502i	−0.999915	+	0.0130641i	$0.995841\pi$
$648$	4990.14	+	4990.14i	0.302518	+	0.302518i
$649$	12451.8	+	3805.27i	0.753121	+	0.230154i
$650$	14997.8	−	13028.0i	0.905019	−	0.786155i
$651$	3804.57	−	5236.55i	0.229052	−	0.315263i
$652$	4619.72	−	2353.87i	0.277488	−	0.141387i
$653$	19296.7	+	9832.15i	1.15641	+	0.589222i	0.923622	−	0.383305i	$-0.125214\pi$
$653$	19296.7	+	9832.15i	1.15641	+	0.589222i	0.232791	+	0.972527i	$0.425214\pi$
$654$	11255.1	+	15491.4i	0.672952	+	0.926239i
$655$	13998.4	+	9268.91i	0.835057	+	0.552926i
$656$	−3295.91	+	1070.90i	−0.196164	+	0.0637375i
$657$	1352.03	+	2653.51i	0.0802856	+	0.157569i
$658$	1439.04	−	227.922i	0.0852579	−	0.0135035i
$659$	17480.7			1.03331			0.516655	−	0.856193i	$-0.327177\pi$
$659$	17480.7			1.03331			0.516655	+	0.856193i	$0.327177\pi$
$660$	−8864.90	−	3855.18i	−0.522827	−	0.227368i
$661$	−9491.73			−0.558525			−0.279263	−	0.960215i	$-0.590090\pi$
$661$	−9491.73			−0.558525			−0.279263	+	0.960215i	$0.590090\pi$
$662$	7598.61	−	1203.50i	0.446115	−	0.0706577i
$663$	15678.7	+	30771.2i	0.918416	+	1.80249i
$664$	5886.11	−	1912.51i	0.344014	−	0.111777i
$665$	2687.05	+	13219.3i	0.156690	+	0.770861i
$666$	1153.16	+	1587.19i	0.0670934	+	0.0923461i
$667$	32513.9	+	16566.7i	1.88747	+	0.961714i
$668$	14960.6	−	7622.81i	0.866532	−	0.441520i
$669$	1554.47	−	2139.55i	0.0898346	−	0.123647i
$670$	−8441.42	+	3154.40i	−0.486747	+	0.181888i
$671$	−510.456	−	29044.7i	−0.0293680	−	1.67103i
$672$	1843.19	+	1843.19i	0.105808	+	0.105808i
$673$	−1035.12	−	6535.48i	−0.0592881	−	0.374330i	−0.999437	−	0.0335650i	$-0.989314\pi$
$673$	−1035.12	−	6535.48i	−0.0592881	−	0.374330i	0.940148	−	0.340765i	$-0.110686\pi$
$674$	751.341	+	244.125i	0.0429385	+	0.0139516i
$675$	−3380.65	−	13579.6i	−0.192772	−	0.774342i
$676$	−13324.9	+	9681.10i	−0.758130	+	0.550814i
$677$	3034.99	−	19162.2i	0.172296	−	1.08783i	−0.738282	−	0.674493i	$-0.764362\pi$
$677$	3034.99	−	19162.2i	0.172296	−	1.08783i	0.910577	−	0.413339i	$-0.135638\pi$
$678$	3237.63	−	6354.21i	0.183393	−	0.359929i
$679$	877.980	−	2702.14i	0.0496226	−	0.152723i
$680$	−6321.80	−	1754.40i	−0.356515	−	0.0989386i
$681$			24475.9i			1.37727i
$682$	2722.56	+	5118.91i	0.152862	+	0.287409i
$683$	−11543.9	+	11543.9i	−0.646730	+	0.646730i	−0.952201	−	0.305471i	$-0.901186\pi$
$683$	−11543.9	+	11543.9i	−0.646730	+	0.646730i	0.305471	+	0.952201i	$0.401186\pi$
$684$	−2301.70	−	1672.28i	−0.128666	−	0.0934814i
$685$	−435.534	+	475.132i	−0.0242933	+	0.0265020i
$686$	−4222.84	−	12996.6i	−0.235028	−	0.723341i
$687$	25277.9	+	4003.62i	1.40380	+	0.222340i
$688$	1204.83	+	190.827i	0.0667644	+	0.0105744i
$689$	−14965.5	−	46059.1i	−0.827489	−	2.54675i
$690$	−11864.0	+	12942.7i	−0.654573	+	0.714085i
$691$	10105.8	+	7342.27i	0.556355	+	0.404216i	0.830123	−	0.557580i	$-0.188270\pi$
$691$	10105.8	+	7342.27i	0.556355	+	0.404216i	−0.273768	+	0.961796i	$0.588270\pi$
$692$	−2194.21	+	2194.21i	−0.120537	+	0.120537i
$693$	4025.70	+	565.284i	0.220669	+	0.0309861i
$694$			7494.12i			0.409903i
$695$	12984.1	+	3603.29i	0.708652	+	0.196663i
$696$	4033.18	−	12412.8i	0.219651	−	0.676017i
$697$	−7212.77	+	14155.9i	−0.391970	+	0.769285i
$698$	489.715	−	3091.94i	0.0265559	−	0.167667i
$699$	−14784.1	+	10741.3i	−0.799978	+	0.581218i
$700$	−1660.65	−	6670.62i	−0.0896666	−	0.360179i
$701$	−168.874	−	54.8706i	−0.00909885	−	0.00295640i	0.304464	−	0.952524i	$-0.401523\pi$
$701$	−168.874	−	54.8706i	−0.00909885	−	0.00295640i	−0.313563	+	0.949567i	$0.601523\pi$
$702$	2783.38	+	17573.5i	0.149646	+	0.944830i
$703$	7510.70	+	7510.70i	0.402946	+	0.402946i
$704$	−2207.60	+	760.435i	−0.118185	+	0.0407102i
$705$	3287.94	−	1228.64i	0.175647	−	0.0656361i
$706$	−10466.7	+	14406.2i	−0.557962	+	0.767968i
$707$	10268.2	−	5231.88i	0.546214	−	0.278310i
$708$	−7536.24	−	3839.90i	−0.400041	−	0.203831i
$709$	−8231.59	−	11329.8i	−0.436028	−	0.600141i	0.533296	−	0.845929i	$-0.320953\pi$
$709$	−8231.59	−	11329.8i	−0.436028	−	0.600141i	−0.969324	+	0.245788i	$0.920953\pi$
$710$	−2665.15	−	13111.6i	−0.140875	−	0.693055i
$711$	−1512.69	+	491.503i	−0.0797895	+	0.0259252i
$712$	5803.76	+	11390.5i	0.305485	+	0.599547i
$713$	10400.8	−	1647.33i	0.546302	−	0.0865257i
$714$	11950.1			0.626362
$715$	−16449.1	−	27928.8i	−0.860368	−	1.46081i
$716$	6094.82			0.318120
$717$	−2940.63	+	465.750i	−0.153166	+	0.0242591i
$718$	−869.398	−	1706.29i	−0.0451889	−	0.0886882i
$719$	−18856.2	+	6126.75i	−0.978049	+	0.317787i	−0.754061	−	0.656804i	$-0.771908\pi$
$719$	−18856.2	+	6126.75i	−0.978049	+	0.317787i	−0.223988	+	0.974592i	$0.571908\pi$
$720$	1208.84	+	800.424i	0.0625706	+	0.0414306i
$721$	−893.087	−	1229.23i	−0.0461308	−	0.0634936i
$722$	−1501.61	−	765.107i	−0.0774017	−	0.0394382i
$723$	9922.86	−	5055.95i	0.510422	−	0.260073i
$724$	3162.81	−	4353.24i	0.162355	−	0.223462i
$725$	−25984.6	+	22571.8i	−1.33110	+	1.15627i
$726$	−8816.54	+	13077.8i	−0.450706	+	0.668544i
$727$	−20143.2	−	20143.2i	−1.02761	−	1.02761i	−0.999608	−	0.0279999i	$-0.991086\pi$
$727$	−20143.2	−	20143.2i	−1.02761	−	1.02761i	−0.0279999	−	0.999608i	$-0.508914\pi$
$728$	1367.25	+	8632.50i	0.0696069	+	0.439480i
$729$	10233.3	+	3325.00i	0.519906	+	0.168928i
$730$	−5113.73	−	6431.19i	−0.259271	−	0.326067i
$731$	4524.30	−	3287.10i	0.228916	−	0.166317i
$732$	−2952.03	+	18638.4i	−0.149058	+	0.941113i
$733$	12402.7	−	24341.6i	0.624969	−	1.22657i	−0.333869	−	0.942619i	$-0.608354\pi$
$733$	12402.7	−	24341.6i	0.624969	−	1.22657i	0.958839	−	0.283952i	$-0.0916456\pi$
$734$	7913.97	−	24356.7i	0.397970	−	1.22483i
$735$	−5021.18	−	8878.60i	−0.251985	−	0.445567i
$736$			4240.78i			0.212388i
$737$	2554.86	+	14479.2i	0.127693	+	0.723676i
$738$	2482.58	−	2482.58i	0.123828	−	0.123828i
$739$	18117.4	+	13163.1i	0.901840	+	0.655225i	0.938938	−	0.344086i	$-0.111811\pi$
$739$	18117.4	+	13163.1i	0.901840	+	0.655225i	−0.0370976	+	0.999312i	$0.511811\pi$
$740$	−3990.05	−	3657.51i	−0.198212	−	0.181693i
$741$	−12768.2	−	39296.6i	−0.632999	−	1.94817i
$742$	−16551.5	−	2621.51i	−0.818903	−	0.129702i
$743$	6836.98	+	1082.87i	0.337583	+	0.0534679i	0.322925	−	0.946425i	$-0.395334\pi$
$743$	6836.98	+	1082.87i	0.337583	+	0.0534679i	0.0146584	+	0.999893i	$0.495334\pi$
$744$	−1163.87	−	3582.04i	−0.0573518	−	0.176511i
$745$	38.3615	+	882.228i	0.00188652	+	0.0433857i
$746$	−1755.67	−	1275.57i	−0.0861657	−	0.0626031i
$747$	−4433.60	+	4433.60i	−0.217158	+	0.217158i
$748$	−4691.28	+	9621.47i	−0.229318	+	0.470315i
$749$			1822.41i			0.0889047i
$750$	−7121.57	−	14951.2i	−0.346724	−	0.727922i
$751$	5746.86	−	17687.0i	0.279235	−	0.859398i	−0.708832	−	0.705377i	$-0.750778\pi$
$751$	5746.86	−	17687.0i	0.279235	−	0.859398i	0.988068	−	0.154021i	$-0.0492223\pi$
$752$	384.890	−	755.390i	0.0186642	−	0.0366306i
$753$	3709.79	−	23422.7i	0.179538	−	1.13356i
$754$	35404.1	−	25722.6i	1.71000	−	1.24239i
$755$	−12816.6	+	10191.1i	−0.617808	+	0.491247i
$756$	5855.38	+	1902.53i	0.281691	+	0.0915269i
$757$	−4825.55	−	30467.3i	−0.231688	−	1.46282i	−0.779598	−	0.626281i	$-0.784576\pi$
$757$	−4825.55	−	30467.3i	−0.231688	−	1.46282i	0.547910	−	0.836537i	$-0.315424\pi$
$758$	−5349.02	−	5349.02i	−0.256313	−	0.256313i
$759$	17242.5	+	22875.8i	0.824588	+	1.09399i
$760$	7142.08	+	3256.37i	0.340882	+	0.155422i
$761$	8591.54	−	11825.2i	0.409255	−	0.563291i	−0.553781	−	0.832662i	$-0.686816\pi$
$761$	8591.54	−	11825.2i	0.409255	−	0.563291i	0.963037	+	0.269371i	$0.0868157\pi$
$762$	−2292.36	+	1168.01i	−0.108981	+	0.0555285i
$763$	19794.9	+	10086.0i	0.939218	+	0.478555i
$764$	−3353.95	−	4616.32i	−0.158824	−	0.218603i
$765$	6513.42	−	1323.96i	0.307834	−	0.0625725i
$766$	−12810.3	+	4162.33i	−0.604251	+	0.196333i
$767$	−12875.1	−	25268.8i	−0.606119	−	1.18958i
$768$	1498.11	−	237.277i	0.0703884	−	0.0111484i
$769$	−30864.2			−1.44732			−0.723662	−	0.690154i	$-0.757543\pi$
$769$	−30864.2			−1.44732			−0.723662	+	0.690154i	$0.757543\pi$
$770$	−11194.8	+	684.050i	−0.523940	+	0.0320149i
$771$	15161.1			0.708189
$772$	−4064.23	+	643.711i	−0.189475	+	0.0300099i
$773$	−5587.52	−	10966.1i	−0.259986	−	0.510251i	0.723707	−	0.690107i	$-0.242437\pi$
$773$	−5587.52	−	10966.1i	−0.259986	−	0.510251i	−0.983693	+	0.179856i	$0.942437\pi$
$774$	−1175.34	+	381.891i	−0.0545822	+	0.0177348i
$775$	−2237.79	+	9677.19i	−0.103721	+	0.448535i
$776$	−971.757	−	1337.51i	−0.0449536	−	0.0618734i
$777$	8784.57	+	4475.96i	0.405591	+	0.206659i
$778$	−1845.19	+	940.171i	−0.0850299	+	0.0433249i
$779$	11172.7	−	15377.9i	0.513870	−	0.707281i
$780$	7370.38	+	19723.7i	0.338336	+	0.905412i
$781$	−21826.5	+	383.596i	−1.00002	+	0.0175751i
$782$	13747.3	+	13747.3i	0.628648	+	0.628648i
$783$	−4822.37	−	30447.2i	−0.220099	−	1.38965i
$784$	−2343.11	−	761.322i	−0.106738	−	0.0346812i
$785$	−4680.76	+	41017.5i	−0.212820	+	1.86494i
$786$	−14395.9	+	10459.2i	−0.653287	+	0.474641i
$787$	−3310.86	+	20904.0i	−0.149961	+	0.946819i	0.791860	+	0.610703i	$0.209113\pi$
$787$	−3310.86	+	20904.0i	−0.149961	+	0.946819i	−0.941821	+	0.336115i	$0.890887\pi$
$788$	2403.15	−	4716.44i	0.108640	−	0.213219i
$789$	−14722.0	+	45309.6i	−0.664280	+	2.04444i
$790$	3819.71	−	2160.19i	0.172024	−	0.0972862i
$791$		−	8274.10i		−	0.371926i
$792$	1642.99	−	1701.78i	0.0737136	−	0.0763510i
$793$	−44740.8	+	44740.8i	−2.00352	+	2.00352i
$794$	18011.2	+	13085.9i	0.805030	+	0.584889i
$795$	−40333.2	+	1753.79i	−1.79934	+	0.0782397i
$796$	2809.71	+	8647.38i	0.125110	+	0.385048i
$797$	3251.48	+	514.983i	0.144508	+	0.0228879i	0.228269	−	0.973598i	$-0.426693\pi$
$797$	3251.48	+	514.983i	0.144508	+	0.0228879i	−0.0837611	+	0.996486i	$0.526693\pi$
$798$	−14121.4	−	2236.61i	−0.626431	−	0.0992170i
$799$	−1201.04	−	3696.44i	−0.0531789	−	0.163668i
$800$	−3708.20	−	1499.75i	−0.163881	−	0.0662801i
$801$	−10477.8	−	7612.55i	−0.462190	−	0.335801i
$802$	−14070.2	+	14070.2i	−0.619495	+	0.619495i
$803$	−11835.8	+	6295.01i	−0.520143	+	0.276645i
$804$		−	9551.17i		−	0.418960i
$805$	−5447.30	+	19628.8i	−0.238500	+	0.859408i
$806$	3902.45	−	12010.5i	0.170543	−	0.524878i
$807$	2706.36	−	5311.53i	0.118053	−	0.231691i
$808$	1049.01	−	6623.20i	0.0456734	−	0.288371i
$809$	−2471.08	+	1795.35i	−0.107390	+	0.0780235i	−0.640184	−	0.768221i	$-0.721142\pi$
$809$	−2471.08	+	1795.35i	−0.107390	+	0.0780235i	0.532794	+	0.846245i	$0.321142\pi$
$810$	19598.1	+	2236.45i	0.850131	+	0.0970136i
$811$	−30536.5	−	9921.90i	−1.32217	−	0.429599i	−0.438931	−	0.898521i	$-0.644643\pi$
$811$	−30536.5	−	9921.90i	−1.32217	−	0.429599i	−0.883240	+	0.468921i	$0.844643\pi$
$812$	−2368.85	−	14956.3i	−0.102377	−	0.646385i
$813$	−23462.5	−	23462.5i	−1.01214	−	1.01214i
$814$	−7052.32	+	5315.63i	−0.303665	+	0.228885i
$815$	6012.11	−	13186.1i	0.258399	−	0.566737i
$816$	4087.22	−	5625.58i	0.175345	−	0.241341i
$817$	−5961.56	+	3037.57i	−0.255286	+	0.130075i
$818$	20731.8	+	10563.4i	0.886151	+	0.451517i
$819$	−5204.57	−	7163.47i	−0.222054	−	0.305631i
$820$	−5347.74	+	8076.42i	−0.227745	+	0.343952i
$821$	30566.2	−	9931.56i	1.29935	−	0.422185i	0.423996	−	0.905664i	$-0.360627\pi$
$821$	30566.2	−	9931.56i	1.29935	−	0.422185i	0.875356	+	0.483479i	$0.160627\pi$
$822$	−310.141	−	608.685i	−0.0131598	−	0.0258277i
$823$	25744.1	−	4077.47i	1.09038	−	0.172699i	0.414747	−	0.909937i	$-0.363870\pi$
$823$	25744.1	−	4077.47i	1.09038	−	0.172699i	0.675634	+	0.737237i	$0.263870\pi$
$824$	−884.121			−0.0373784
$825$	−26100.8	+	6987.06i	−1.10147	+	0.294859i
$826$	−9813.28			−0.413375
$827$	−29610.3	+	4689.81i	−1.24504	+	0.197196i	−0.743973	−	0.668210i	$-0.767061\pi$
$827$	−29610.3	+	4689.81i	−1.24504	+	0.197196i	−0.501072	+	0.865406i	$0.667061\pi$
$828$	−1950.48	−	3828.03i	−0.0818646	−	0.160668i
$829$	31663.5	−	10288.1i	1.32656	−	0.431025i	0.441817	−	0.897105i	$-0.354334\pi$
$829$	31663.5	−	10288.1i	1.32656	−	0.431025i	0.884743	+	0.466080i	$0.154334\pi$
$830$	9550.44	−	14423.6i	0.399398	−	0.603192i
$831$	7508.13	+	10334.1i	0.313423	+	0.431389i
$832$	4531.42	+	2308.87i	0.188821	+	0.0962089i
$833$	−10063.6	+	5127.66i	−0.418587	+	0.213281i
$834$	−8394.56	+	11554.1i	−0.348537	+	0.479720i
$835$	19469.7	−	42702.3i	0.806920	−	1.76979i
$836$	7344.43	−	10491.6i	0.303842	−	0.434043i
$837$	−6290.31	−	6290.31i	−0.259767	−	0.259767i
$838$	−2345.43	−	14808.5i	−0.0966845	−	0.610442i
$839$	−38878.2	−	12632.3i	−1.59979	−	0.519803i	−0.632734	−	0.774370i	$-0.718067\pi$
$839$	−38878.2	−	12632.3i	−1.59979	−	0.519803i	−0.967055	+	0.254567i	$0.918067\pi$
$840$	7238.88	+	826.072i	0.297340	+	0.0339312i
$841$	−41608.6	+	30230.4i	−1.70604	+	1.23951i
$842$	2563.04	−	16182.4i	0.104903	−	0.662332i
$843$	17022.4	−	33408.4i	0.695473	−	1.36494i
$844$	−1536.21	+	4727.97i	−0.0626523	+	0.192824i
$845$	−12310.6	+	44359.8i	−0.501180	+	1.80595i
$846$			858.893i			0.0349047i
$847$	−2225.76	+	18163.3i	−0.0902928	+	0.736834i
$848$	−6895.09	+	6895.09i	−0.279220	+	0.279220i
$849$	18653.0	+	13552.2i	0.754026	+	0.547832i
$850$	−16882.6	+	7159.13i	−0.681256	+	0.288890i
$851$	4956.57	+	15254.8i	0.199658	+	0.614485i
$852$	14006.3	+	2218.39i	0.563203	+	0.0892026i
$853$	−2851.49	−	451.631i	−0.114458	−	0.0181284i	0.0989424	−	0.995093i	$-0.468454\pi$
$853$	−2851.49	−	451.631i	−0.114458	−	0.0181284i	−0.213401	+	0.976965i	$0.568454\pi$
$854$	6765.67	+	20822.6i	0.271097	+	0.834350i
$855$	−7944.67	+	345.454i	−0.317780	+	0.0138179i
$856$	857.910	+	623.308i	0.0342556	+	0.0248881i
$857$	14394.5	−	14394.5i	0.573755	−	0.573755i	−0.359420	−	0.933176i	$-0.617026\pi$
$857$	14394.5	−	14394.5i	0.573755	−	0.573755i	0.933176	+	0.359420i	$0.117026\pi$
$858$	33831.2	−	5969.53i	1.34613	−	0.237525i
$859$			12482.9i			0.495822i	0.968783	+	0.247911i	$0.0797440\pi$
$859$			12482.9i			0.495822i	−0.968783	+	0.247911i	$0.920256\pi$
$860$	2967.86	−	1678.44i	0.117678	−	0.0665514i
$861$	5452.14	−	16780.0i	0.215805	−	0.664181i
$862$	−16014.9	+	31431.1i	−0.632796	+	1.24193i
$863$	661.134	−	4174.24i	0.0260779	−	0.164650i	−0.971212	−	0.238215i	$-0.923438\pi$
$863$	661.134	−	4174.24i	0.0260779	−	0.164650i	0.997290	+	0.0735653i	$0.0234377\pi$
$864$	2898.30	−	2105.74i	0.114123	−	0.0829151i
$865$	−983.390	+	8617.46i	−0.0386547	+	0.338731i
$866$	−12513.0	−	4065.73i	−0.491005	−	0.159537i
$867$	−433.203	−	2735.14i	−0.0169692	−	0.107140i
$868$	−3089.93	−	3089.93i	−0.120829	−	0.120829i
$869$	−2331.78	−	6769.34i	−0.0910243	−	0.264251i
$870$	−12769.6	−	34172.5i	−0.497622	−	1.33167i
$871$	18823.7	−	25908.7i	0.732283	−	1.00790i
$872$	11518.3	−	5868.89i	0.447317	−	0.227919i
$873$	1492.34	+	760.387i	0.0578559	+	0.0294790i
$874$	−13672.1	−	18818.1i	−0.529138	−	0.728296i
$875$	−15237.3	−	11704.9i	−0.588701	−	0.452226i
$876$	8282.27	−	2691.07i	0.319443	−	0.103793i
$877$	11783.2	+	23125.8i	0.453694	+	0.890424i	0.998649	+	0.0519591i	$0.0165465\pi$
$877$	11783.2	+	23125.8i	0.453694	+	0.890424i	−0.544956	+	0.838465i	$0.683453\pi$
$878$	396.012	−	62.7221i	0.0152218	−	0.00241090i
$879$	45920.8			1.76208
$880$	−3506.88	+	5503.98i	−0.134337	+	0.210840i
$881$	42597.1			1.62898			0.814491	−	0.580177i	$-0.197017\pi$
$881$	42597.1			1.62898			0.814491	+	0.580177i	$0.197017\pi$
$882$	2465.22	−	390.452i	0.0941135	−	0.0149061i
$883$	−3557.66	−	6982.29i	−0.135588	−	0.266107i	0.813222	−	0.581954i	$-0.197712\pi$
$883$	−3557.66	−	6982.29i	−0.135588	−	0.266107i	−0.948810	+	0.315846i	$0.897712\pi$
$884$	22174.1	−	7204.81i	0.843661	−	0.274122i
$885$	−23167.4	+	4709.16i	−0.879958	+	0.178866i
$886$	20503.2	+	28220.3i	0.777448	+	1.07007i
$887$	2066.81	+	1053.09i	0.0782376	+	0.0398641i	0.492672	−	0.870215i	$-0.336020\pi$
$887$	2066.81	+	1053.09i	0.0782376	+	0.0398641i	−0.414434	+	0.910079i	$0.636020\pi$
$888$	5111.60	−	2604.49i	0.193169	−	0.0984246i
$889$	−1754.53	+	2414.90i	−0.0661923	+	0.0911059i
$890$	32512.1	+	14823.6i	1.22450	+	0.558302i
$891$	9405.73	−	30777.9i	0.353652	−	1.15724i
$892$	−1262.48	−	1262.48i	−0.0473891	−	0.0473891i
$893$	727.435	+	4592.85i	0.0272595	+	0.172109i
$894$	−890.134	−	289.222i	−0.0333004	−	0.0108199i
$895$	13334.0	−	10602.5i	0.497997	−	0.395980i
$896$	1423.71	−	1034.38i	0.0530834	−	0.0385674i
$897$	9760.78	−	61627.2i	0.363326	−	2.29395i
$898$	−14442.2	+	28344.4i	−0.536683	+	1.05330i
$899$	−6761.23	+	20808.9i	−0.250834	+	0.771987i
$900$	4037.07	−	351.749i	0.149521	−	0.0130278i
$901$			44703.5i			1.65293i
$902$	11369.8	+	10977.0i	0.419703	+	0.405205i
$903$	−4391.46	+	4391.46i	−0.161837	+	0.161837i
$904$	−3895.07	−	2829.93i	−0.143305	−	0.104118i
$905$	−653.363	−	15025.9i	−0.0239984	−	0.551908i
$906$	−5363.00	−	16505.6i	−0.196660	−	0.605257i
$907$	−32569.9	−	5158.57i	−1.19236	−	0.188851i	−0.471456	−	0.881890i	$-0.656271\pi$
$907$	−32569.9	−	5158.57i	−1.19236	−	0.188851i	−0.720900	+	0.693039i	$0.756271\pi$
$908$	16320.6	+	2584.93i	0.596495	+	0.0944755i
$909$	2099.32	+	6461.06i	0.0766009	+	0.235753i
$910$	18008.3	+	16507.4i	0.656009	+	0.601336i
$911$	−42928.0	−	31189.0i	−1.56122	−	1.13429i	−0.935004	−	0.354638i	$-0.884604\pi$
$911$	−42928.0	−	31189.0i	−1.56122	−	1.13429i	−0.626213	−	0.779652i	$-0.715396\pi$
$912$	−5882.74	+	5882.74i	−0.213593	+	0.213593i
$913$	−20305.1	−	19603.7i	−0.736037	−	0.710612i
$914$			11597.4i			0.419704i
$915$	25964.8	+	45911.7i	0.938110	+	1.65879i
$916$	5339.25	−	16432.5i	0.192591	−	0.592735i
$917$	−9372.76	+	18395.1i	−0.337531	+	0.662442i
$918$	2569.24	−	16221.6i	0.0923721	−	0.583215i
$919$	−35507.6	+	25797.8i	−1.27453	+	0.925997i	−0.999373	−	0.0354036i	$-0.988728\pi$
$919$	−35507.6	+	25797.8i	−1.27453	+	0.925997i	−0.275152	+	0.961401i	$0.588728\pi$
$920$	7377.23	+	9277.84i	0.264370	+	0.332480i
$921$	−4638.21	−	1507.05i	−0.165944	−	0.0539184i
$922$	−422.074	−	2664.87i	−0.0150762	−	0.0951874i
$923$	33621.7	+	33621.7i	1.19900	+	1.19900i
$924$	3474.16	−	11368.3i	0.123692	−	0.404752i
$925$	−15091.9	−	1060.73i	−0.536452	−	0.0377044i
$926$	16771.9	−	23084.5i	0.595203	−	0.819226i
$927$	798.071	−	406.638i	0.0282763	−	0.0144075i
$928$	−7850.96	−	4000.27i	−0.277716	−	0.141503i
$929$	−23537.1	−	32396.1i	−0.831246	−	1.14411i	−0.987690	−	0.156426i	$-0.950003\pi$
$929$	−23537.1	−	32396.1i	−0.831246	−	1.14411i	0.156443	−	0.987687i	$-0.449997\pi$
$930$	−8777.57	−	5812.00i	−0.309492	−	0.204928i
$931$	12851.8	−	4175.80i	0.452418	−	0.146999i
$932$	5600.93	+	10992.4i	0.196850	+	0.386341i
$933$	59747.0	−	9463.00i	2.09649	−	0.332052i
$934$	25752.1			0.902179
$935$	6474.01	+	29210.4i	0.226441	+	1.02169i
$936$	−5152.32			−0.179924
$937$	−16736.5	+	2650.79i	−0.583518	+	0.0924202i	−0.441213	−	0.897403i	$-0.645452\pi$
$937$	−16736.5	+	2650.79i	−0.583518	+	0.0924202i	−0.142305	+	0.989823i	$0.545452\pi$
$938$	−5030.88	−	9873.66i	−0.175122	−	0.343695i
$939$	29979.1	−	9740.80i	1.04189	−	0.338529i
$940$	−472.020	−	2322.17i	−0.0163783	−	0.0805753i
$941$	7548.75	+	10390.0i	0.261511	+	0.359940i	0.919501	−	0.393087i	$-0.128593\pi$
$941$	7548.75	+	10390.0i	0.261511	+	0.359940i	−0.657990	+	0.753027i	$0.728593\pi$
$942$	−38986.8	−	19864.8i	−1.34847	−	0.687080i
$943$	25575.6	−	13031.4i	0.883197	−	0.450012i
$944$	−3356.37	+	4619.64i	−0.115721	+	0.159276i
$945$	16119.8	−	6023.69i	0.554898	−	0.207355i
$946$	−1811.75	−	5259.67i	−0.0622677	−	0.180768i
$947$	12989.0	+	12989.0i	0.445709	+	0.445709i	0.893925	−	0.448216i	$-0.147941\pi$
$947$	12989.0	+	12989.0i	0.445709	+	0.445709i	−0.448216	+	0.893925i	$0.647941\pi$
$948$	727.579	+	4593.75i	0.0249269	+	0.157382i
$949$	27770.3	+	9023.11i	0.949906	+	0.308643i
$950$	21289.9	−	5300.13i	0.727091	−	0.181009i
$951$	−807.447	+	586.645i	−0.0275324	+	0.0200034i
$952$	1262.07	−	7968.38i	0.0429662	−	0.271278i
$953$	−4273.36	+	8386.95i	−0.145255	+	0.285079i	−0.952159	−	0.305604i	$-0.901142\pi$
$953$	−4273.36	+	8386.95i	−0.145255	+	0.285079i	0.806904	+	0.590683i	$0.201142\pi$
$954$	3052.72	−	9395.30i	0.103601	−	0.318851i
$955$	−15368.2	−	4264.92i	−0.520735	−	0.144513i
$956$			2010.01i			0.0680003i
$957$	−58614.7	+	10342.6i	−1.97988	+	0.349350i
$958$	−24060.4	+	24060.4i	−0.811436	+	0.811436i
$959$	−641.224	−	465.877i	−0.0215915	−	0.0156871i
$960$	2864.74	−	3125.20i	0.0963116	−	0.105068i
$961$	−7254.80	−	22328.0i	−0.243523	−	0.749488i
$962$	18998.8	+	3009.12i	0.636743	+	0.100850i
$963$	−1061.09	−	168.060i	−0.0355070	−	0.00562375i
$964$	−2323.35	−	7150.55i	−0.0776247	−	0.238904i
$965$	−7771.80	+	8478.40i	−0.259257	+	0.282828i
$966$	−17467.1	−	12690.6i	−0.581773	−	0.422683i
$967$	−487.730	+	487.730i	−0.0162196	+	0.0162196i	−0.715170	−	0.698950i	$-0.753651\pi$
$967$	−487.730	+	487.730i	−0.0162196	+	0.0162196i	0.698950	+	0.715170i	$0.253651\pi$
$968$	7789.19	+	7260.05i	0.258630	+	0.241061i
$969$			38140.1i			1.26443i
$970$	−4452.69	−	1235.70i	−0.147389	−	0.0409029i
$971$	−10100.4	+	31085.8i	−0.333818	+	1.02739i	0.633483	+	0.773756i	$0.281625\pi$
$971$	−10100.4	+	31085.8i	−0.333818	+	1.02739i	−0.967301	+	0.253630i	$0.918375\pi$
$972$	−4002.18	+	7854.72i	−0.132068	+	0.259198i
$973$	−2592.10	+	16365.9i	−0.0854049	+	0.539225i
$974$	−24237.8	+	17609.8i	−0.797361	+	0.579317i
$975$	50435.8	+	30329.3i	1.65666	+	0.996222i
$976$	12116.3	+	3936.84i	0.397372	+	0.129114i
$977$	−2237.29	−	14125.7i	−0.0732623	−	0.462560i	−0.996859	−	0.0791947i	$-0.974765\pi$
$977$	−2237.29	−	14125.7i	−0.0732623	−	0.462560i	0.923597	−	0.383365i	$-0.125235\pi$
$978$	10861.1	+	10861.1i	0.355112	+	0.355112i
$979$	33433.3	−	47759.8i	1.09145	−	1.55915i
$980$	−6450.56	+	2410.46i	−0.210261	+	0.0785706i
$981$	−7697.98	+	10595.4i	−0.250538	+	0.344836i
$982$	−3675.23	+	1872.62i	−0.119431	+	0.0608532i
$983$	−18784.3	−	9571.09i	−0.609488	−	0.310550i	0.121867	−	0.992546i	$-0.461112\pi$
$983$	−18784.3	−	9571.09i	−0.609488	−	0.310550i	−0.731355	+	0.681997i	$0.761112\pi$
$984$	−6034.48	−	8305.75i	−0.195500	−	0.269083i
$985$	−2947.16	−	14499.0i	−0.0953344	−	0.469011i
$986$	−38418.0	+	12482.8i	−1.24085	+	0.403177i
$987$	1959.53	+	3845.80i	0.0631942	+	0.124026i
$988$	−27551.5	+	4363.73i	−0.887176	+	0.140515i
$989$	−10103.8			−0.324854
$990$	634.087	−	6581.22i	0.0203562	−	0.211278i
$991$	−491.219			−0.0157458			−0.00787291	−	0.999969i	$-0.502506\pi$
$991$	−491.219			−0.0157458			−0.00787291	+	0.999969i	$0.502506\pi$
$992$	−2511.43	+	397.771i	−0.0803810	+	0.0127311i
$993$	10347.0	+	20307.1i	0.330666	+	0.648969i
$994$	15647.7	−	5084.25i	0.499312	−	0.162236i
$995$	21189.9	+	14030.7i	0.675141	+	0.447039i
$996$	10776.9	+	14833.1i	0.342850	+	0.471893i
$997$	10236.0	+	5215.50i	0.325152	+	0.165673i	0.608945	−	0.793212i	$-0.291593\pi$
$997$	10236.0	+	5215.50i	0.325152	+	0.165673i	−0.283793	+	0.958886i	$0.591593\pi$
$998$	−23131.1	+	11785.9i	−0.733670	+	0.373824i
$999$	7964.49	−	10962.2i	0.252237	−	0.347175i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.4.k.a.7.16	✓	144
5.3	odd	4	inner	110.4.k.a.73.3	yes	144
11.8	odd	10	inner	110.4.k.a.107.3	yes	144
55.8	even	20	inner	110.4.k.a.63.16	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.4.k.a.7.16	✓	144	1.1	even	1	trivial
110.4.k.a.63.16	yes	144	55.8	even	20	inner
110.4.k.a.73.3	yes	144	5.3	odd	4	inner
110.4.k.a.107.3	yes	144	11.8	odd	10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	110.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.97538 - 0.312869i) q^{2} +(2.68986 + 5.27915i) q^{3} +(3.80423 - 1.23607i) q^{4} +(6.17250 - 9.32203i) q^{5} +(6.96517 + 9.58673i) q^{6} +(12.2499 + 6.24166i) q^{7} +(7.12805 - 3.63192i) q^{8} +(-4.76385 + 6.55687i) q^{9} +(9.27645 - 20.3457i) q^{10} +(-29.8875 - 20.9221i) q^{11} +(16.7582 + 16.7582i) q^{12} +(12.4310 + 78.4862i) q^{13} +(26.1511 + 8.49700i) q^{14} +(65.8155 + 7.51060i) q^{15} +(12.9443 - 9.40456i) q^{16} +(11.4746 - 72.4480i) q^{17} +(-7.35895 + 14.4427i) q^{18} +(-27.1190 + 83.4638i) q^{19} +(11.9589 - 43.0927i) q^{20} +81.4584i q^{21} +(-65.5850 - 31.9782i) q^{22} +(-93.7089 + 93.7089i) q^{23} +(38.3469 + 27.8607i) q^{24} +(-48.8004 - 115.080i) q^{25} +(49.1118 + 151.151i) q^{26} +(110.575 + 17.5133i) q^{27} +(54.3167 + 8.60292i) q^{28} +(-85.0892 - 261.878i) q^{29} +(132.360 - 5.75536i) q^{30} +(-64.2849 - 46.7057i) q^{31} +(22.6274 - 22.6274i) q^{32} +(30.0578 - 214.058i) q^{33} -146.702i q^{34} +(133.798 - 75.6677i) q^{35} +(-10.0180 + 30.8323i) q^{36} +(54.9478 - 107.841i) q^{37} +(-27.4571 + 173.357i) q^{38} +(-380.903 + 276.742i) q^{39} +(10.1410 - 88.8660i) q^{40} +(-205.994 - 66.9316i) q^{41} +(25.4858 + 160.911i) q^{42} +(53.9104 + 53.9104i) q^{43} +(-139.560 - 42.6495i) q^{44} +(31.7185 + 84.8810i) q^{45} +(-155.792 + 214.429i) q^{46} +(47.2118 - 24.0556i) q^{47} +(84.4664 + 43.0378i) q^{48} +(-90.5075 - 124.573i) q^{49} +(-132.404 - 212.059i) q^{50} +(413.329 - 134.299i) q^{51} +(144.305 + 283.214i) q^{52} +(-601.943 + 95.3384i) q^{53} +223.906 q^{54} +(-379.518 + 149.470i) q^{55} +109.987 q^{56} +(-513.564 + 81.3406i) q^{57} +(-250.017 - 490.685i) q^{58} +(-339.420 + 110.284i) q^{59} +(259.661 - 52.7804i) q^{60} +(468.020 + 644.174i) q^{61} +(-141.600 - 72.1486i) q^{62} +(-99.2826 + 50.5870i) q^{63} +(37.6183 - 51.7771i) q^{64} +(808.381 + 368.574i) q^{65} +(-7.59671 - 432.250i) q^{66} +(-284.970 - 284.970i) q^{67} +(-45.8986 - 289.792i) q^{68} +(-746.767 - 242.639i) q^{69} +(240.627 - 191.333i) q^{70} +(484.082 - 351.707i) q^{71} +(-10.1429 + 64.0396i) q^{72} +(166.820 - 327.402i) q^{73} +(74.8024 - 230.218i) q^{74} +(476.261 - 567.175i) q^{75} +351.036i q^{76} +(-235.532 - 442.843i) q^{77} +(-665.842 + 665.842i) q^{78} +(158.768 + 115.352i) q^{79} +(-7.77105 - 178.717i) q^{80} +(272.597 + 838.966i) q^{81} +(-427.857 - 67.7659i) q^{82} +(764.103 + 121.022i) q^{83} +(100.688 + 309.886i) q^{84} +(-604.535 - 554.153i) q^{85} +(123.360 + 89.6264i) q^{86} +(1153.61 - 1153.61i) q^{87} +(-289.027 - 40.5849i) q^{88} +1597.98i q^{89} +(89.2126 + 157.748i) q^{90} +(-337.605 + 1039.04i) q^{91} +(-240.659 + 472.320i) q^{92} +(73.6489 - 465.001i) q^{93} +(85.7349 - 62.2901i) q^{94} +(610.660 + 767.985i) q^{95} +(180.318 + 58.5889i) q^{96} +(-32.3282 - 204.112i) q^{97} +(-217.761 - 217.761i) q^{98} +(279.563 - 96.2988i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 8 q^{3} + 32 q^{5} - 40 q^{7} - 44 q^{11} + 128 q^{12} - 256 q^{15} + 576 q^{16} - 640 q^{17} - 64 q^{20} + 312 q^{22} - 984 q^{23} - 520 q^{25} + 304 q^{26} - 364 q^{27} + 240 q^{28} - 432 q^{31}+ \cdots + 7044 q^{97}+O(q^{100}) \) 144 * q + 8 * q^3 + 32 * q^5 - 40 * q^7 - 44 * q^11 + 128 * q^12 - 256 * q^15 + 576 * q^16 - 640 * q^17 - 64 * q^20 + 312 * q^22 - 984 * q^23 - 520 * q^25 + 304 * q^26 - 364 * q^27 + 240 * q^28 - 432 * q^31 + 2368 * q^33 + 1808 * q^36 - 960 * q^37 + 72 * q^38 + 740 * q^41 + 2440 * q^42 + 2656 * q^45 + 720 * q^46 - 1980 * q^47 - 128 * q^48 - 1360 * q^50 - 3880 * q^51 - 1920 * q^52 - 3060 * q^53 - 3044 * q^55 - 64 * q^56 - 4400 * q^57 - 2016 * q^58 - 1120 * q^60 - 960 * q^61 + 80 * q^62 + 1800 * q^63 + 1552 * q^66 + 10160 * q^67 + 2560 * q^68 + 2304 * q^70 + 1312 * q^71 - 2460 * q^73 + 8644 * q^75 - 1272 * q^77 - 5312 * q^78 + 768 * q^80 + 2116 * q^81 + 1280 * q^82 + 320 * q^85 - 5488 * q^86 + 1248 * q^88 - 8480 * q^90 + 11796 * q^91 - 704 * q^92 + 688 * q^93 - 1280 * q^95 + 7044 * q^97

Introduction

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