LMFDB - Embedded newform 95.5.q.a.17.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [95,5,Mod(17,95)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("95.17"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([9, 20])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	95.q (of order $36$, degree $12$, 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:	$9.82014649297$
Analytic rank:	$0$
Dimension:	$456$
Relative dimension:	$38$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			17.10
Character	$\chi$	$=$	95.17
Dual form			95.5.q.a.28.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.52270 + 2.46662i) q^{2} +(8.80247 - 0.770116i) q^{3} +(0.852857 - 2.34320i) q^{4} +(-1.44605 - 24.9581i) q^{5} +(-29.1088 + 24.4252i) q^{6} +(-12.6105 + 47.0630i) q^{7} +(-15.0330 - 56.1041i) q^{8} +(-2.87906 + 0.507657i) q^{9} +(66.6562 + 84.3531i) q^{10} +(-41.4630 + 71.8159i) q^{11} +(5.70270 - 21.2828i) q^{12} +(-24.6485 + 281.734i) q^{13} +(-71.6635 - 196.894i) q^{14} +(-31.9495 - 218.580i) q^{15} +(221.907 + 186.202i) q^{16} +(216.706 - 151.739i) q^{17} +(8.88987 - 8.88987i) q^{18} +(-208.018 + 295.042i) q^{19} +(-59.7153 - 17.8973i) q^{20} +(-74.7595 + 423.982i) q^{21} +(-31.0811 - 355.259i) q^{22} +(-602.524 + 280.962i) q^{23} +(-175.535 - 482.277i) q^{24} +(-620.818 + 72.1813i) q^{25} +(-608.101 - 1053.26i) q^{26} +(-716.288 + 191.929i) q^{27} +(99.5233 + 69.6869i) q^{28} +(-504.794 + 89.0088i) q^{29} +(651.701 + 691.182i) q^{30} +(-187.749 - 325.191i) q^{31} +(-315.207 - 27.5770i) q^{32} +(-309.670 + 664.089i) q^{33} +(-389.107 + 1069.06i) q^{34} +(1192.84 + 246.679i) q^{35} +(-1.26589 + 7.17919i) q^{36} +(-331.686 - 331.686i) q^{37} +(5.02829 - 1552.44i) q^{38} +2498.94i q^{39} +(-1378.52 + 456.326i) q^{40} +(1842.87 + 1546.35i) q^{41} +(-782.447 - 1677.96i) q^{42} +(1017.84 - 2182.76i) q^{43} +(132.917 + 158.405i) q^{44} +(16.8334 + 71.1220i) q^{45} +(1429.48 - 2475.94i) q^{46} +(892.625 - 1274.80i) q^{47} +(2096.73 + 1468.15i) q^{48} +(23.4258 + 13.5249i) q^{49} +(2008.91 - 1785.59i) q^{50} +(1790.69 - 1502.57i) q^{51} +(639.139 + 298.035i) q^{52} +(-4363.88 + 2034.91i) q^{53} +(2049.85 - 2442.91i) q^{54} +(1852.35 + 930.989i) q^{55} +2830.00 q^{56} +(-1603.85 + 2757.29i) q^{57} +(1558.69 - 1558.69i) q^{58} +(1539.52 + 271.459i) q^{59} +(-539.425 - 111.553i) q^{60} +(5351.19 + 1947.67i) q^{61} +(1463.50 + 682.443i) q^{62} +(12.4146 - 141.899i) q^{63} +(-2835.52 + 1637.09i) q^{64} +(7067.21 + 207.781i) q^{65} +(-547.181 - 3103.22i) q^{66} +(-424.907 + 606.830i) q^{67} +(-170.737 - 637.200i) q^{68} +(-5087.33 + 2937.17i) q^{69} +(-4810.48 + 2073.31i) q^{70} +(5345.56 - 1945.62i) q^{71} +(71.7627 + 153.896i) q^{72} +(-5742.46 + 502.400i) q^{73} +(1986.57 + 350.286i) q^{74} +(-5409.14 + 1113.48i) q^{75} +(513.934 + 739.056i) q^{76} +(-2857.01 - 2857.01i) q^{77} +(-6163.93 - 8803.00i) q^{78} +(3430.16 - 4087.90i) q^{79} +(4326.38 - 5807.65i) q^{80} +(-5934.77 + 2160.08i) q^{81} +(-10306.1 - 901.669i) q^{82} +(-3795.13 - 1016.90i) q^{83} +(929.717 + 536.773i) q^{84} +(-4100.50 - 5189.17i) q^{85} +(1798.50 + 10199.8i) q^{86} +(-4374.89 + 1172.25i) q^{87} +(4652.48 + 1246.63i) q^{88} +(7457.30 + 8887.26i) q^{89} +(-234.730 - 209.019i) q^{90} +(-12948.4 - 4712.84i) q^{91} +(144.484 + 1651.46i) q^{92} +(-1903.09 - 2717.89i) q^{93} +6692.50i q^{94} +(7664.50 + 4765.09i) q^{95} -2795.84 q^{96} +(-6291.03 + 4405.03i) q^{97} +(-115.883 + 10.1384i) q^{98} +(82.9166 - 227.812i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 456 q - 12 q^{2} - 12 q^{3} - 12 q^{5} + 84 q^{6} - 96 q^{7} - 6 q^{8} - 12 q^{10} - 12 q^{11} - 6 q^{12} - 12 q^{13} - 534 q^{15} + 4092 q^{16} - 1362 q^{17} - 3864 q^{18} - 2364 q^{20} - 4776 q^{21} + 2004 q^{22}+ \cdots + 123726 q^{98}+O(q^{100}) $ 456 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 + 84 * q^6 - 96 * q^7 - 6 * q^8 - 12 * q^10 - 12 * q^11 - 6 * q^12 - 12 * q^13 - 534 * q^15 + 4092 * q^16 - 1362 * q^17 - 3864 * q^18 - 2364 * q^20 - 4776 * q^21 + 2004 * q^22 + 1968 * q^23 + 3252 * q^25 + 7332 * q^26 - 6 * q^27 - 9648 * q^28 - 6 * q^30 - 12 * q^31 + 5922 * q^32 + 16494 * q^33 - 1794 * q^35 + 9048 * q^36 - 24 * q^37 - 15222 * q^38 - 9786 * q^40 - 5640 * q^41 + 7764 * q^42 - 19032 * q^43 - 6144 * q^45 - 12 * q^46 - 4332 * q^47 + 29328 * q^48 + 18426 * q^50 - 10944 * q^51 + 84 * q^52 + 1878 * q^53 + 27018 * q^55 - 48 * q^56 - 14202 * q^57 + 16536 * q^58 - 84108 * q^60 - 14688 * q^61 - 46536 * q^62 - 46098 * q^63 - 13236 * q^65 + 42408 * q^66 + 44748 * q^67 + 20154 * q^68 + 37620 * q^70 - 24 * q^71 + 82680 * q^72 - 10542 * q^73 + 90024 * q^75 - 21600 * q^76 + 20328 * q^77 + 63426 * q^78 - 32688 * q^80 + 41976 * q^81 - 184332 * q^82 - 43476 * q^83 - 51396 * q^85 + 11316 * q^86 - 59286 * q^87 - 1254 * q^88 - 9294 * q^90 - 33312 * q^91 + 163884 * q^92 - 106566 * q^93 - 11424 * q^95 - 200208 * q^96 + 12168 * q^97 + 123726 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−3.52270	+	2.46662i	−0.880674	+	0.616654i	−0.923994	−	0.382407i	$-0.875095\pi$
$2$	−3.52270	+	2.46662i	−0.880674	+	0.616654i	0.0433202	+	0.999061i	$0.486206\pi$
$3$	8.80247	−	0.770116i	0.978052	−	0.0855685i	0.413094	−	0.910688i	$-0.364448\pi$
$3$	8.80247	−	0.770116i	0.978052	−	0.0855685i	0.564958	+	0.825120i	$0.308892\pi$
$4$	0.852857	−	2.34320i	0.0533035	−	0.146450i
$5$	−1.44605	−	24.9581i	−0.0578419	−	0.998326i
$5$	−1.44605	−	24.9581i	−0.0578419	−	0.998326i
$6$	−29.1088	+	24.4252i	−0.808579	+	0.678478i
$7$	−12.6105	+	47.0630i	−0.257357	+	0.960469i	0.709407	+	0.704799i	$0.248963\pi$
$7$	−12.6105	+	47.0630i	−0.257357	+	0.960469i	−0.966764	+	0.255670i	$0.917704\pi$
$8$	−15.0330	−	56.1041i	−0.234891	−	0.876626i
$9$	−2.87906	+	0.507657i	−0.0355440	+	0.00626736i
$10$	66.6562	+	84.3531i	0.666562	+	0.843531i
$11$	−41.4630	+	71.8159i	−0.342669	+	0.593520i	−0.984927	−	0.172968i	$-0.944664\pi$
$11$	−41.4630	+	71.8159i	−0.342669	+	0.593520i	0.642258	+	0.766488i	$0.277998\pi$
$12$	5.70270	−	21.2828i	0.0396021	−	0.147797i
$13$	−24.6485	+	281.734i	−0.145849	+	1.66707i	0.472627	+	0.881263i	$0.343306\pi$
$13$	−24.6485	+	281.734i	−0.145849	+	1.66707i	−0.618476	+	0.785804i	$0.712250\pi$
$14$	−71.6635	−	196.894i	−0.365630	−	1.00456i
$15$	−31.9495	−	218.580i	−0.141998	−	0.971465i
$16$	221.907	+	186.202i	0.866825	+	0.727353i
$17$	216.706	−	151.739i	0.749849	−	0.525050i	−0.135046	−	0.990839i	$-0.543118\pi$
$17$	216.706	−	151.739i	0.749849	−	0.525050i	0.884896	+	0.465789i	$0.154229\pi$
$18$	8.88987	−	8.88987i	0.0274379	−	0.0274379i
$19$	−208.018	+	295.042i	−0.576227	+	0.817290i
$19$	−208.018	+	295.042i	−0.576227	+	0.817290i
$20$	−59.7153	−	17.8973i	−0.149288	−	0.0447433i
$21$	−74.7595	+	423.982i	−0.169523	+	0.961411i
$22$	−31.0811	−	355.259i	−0.0642172	−	0.734006i
$23$	−602.524	+	280.962i	−1.13899	+	0.531118i	−0.898256	−	0.439473i	$-0.855165\pi$
$23$	−602.524	+	280.962i	−1.13899	+	0.531118i	−0.240731	+	0.970592i	$0.577387\pi$
$24$	−175.535	−	482.277i	−0.304747	−	0.837287i
$25$	−620.818	+	72.1813i	−0.993309	+	0.115490i
$26$	−608.101	−	1053.26i	−0.899558	−	1.55808i
$27$	−716.288	+	191.929i	−0.982562	+	0.263277i
$28$	99.5233	+	69.6869i	0.126943	+	0.0888864i
$29$	−504.794	+	89.0088i	−0.600231	+	0.105837i	−0.465504	−	0.885046i	$-0.654127\pi$
$29$	−504.794	+	89.0088i	−0.600231	+	0.105837i	−0.134727	+	0.990883i	$0.543016\pi$
$30$	651.701	+	691.182i	0.724112	+	0.767980i
$31$	−187.749	−	325.191i	−0.195368	−	0.338388i	0.751653	−	0.659559i	$-0.229257\pi$
$31$	−187.749	−	325.191i	−0.195368	−	0.338388i	−0.947021	+	0.321171i	$0.895924\pi$
$32$	−315.207	−	27.5770i	−0.307819	−	0.0269307i
$33$	−309.670	+	664.089i	−0.284362	+	0.609815i
$34$	−389.107	+	1069.06i	−0.336598	+	0.924796i
$35$	1192.84	+	246.679i	0.973747	+	0.201371i
$36$	−1.26589	+	7.17919i	−0.000976763	+	0.00553950i
$37$	−331.686	−	331.686i	−0.242283	−	0.242283i	0.575511	−	0.817794i	$-0.304803\pi$
$37$	−331.686	−	331.686i	−0.242283	−	0.242283i	−0.817794	+	0.575511i	$0.804803\pi$
$38$	5.02829	−	1552.44i	0.00348219	−	1.07510i
$39$			2498.94i			1.64296i
$40$	−1378.52	+	456.326i	−0.861572	+	0.285204i
$41$	1842.87	+	1546.35i	1.09629	+	0.919900i	0.997170	−	0.0751753i	$-0.0239516\pi$
$41$	1842.87	+	1546.35i	1.09629	+	0.919900i	0.0991236	+	0.995075i	$0.468396\pi$
$42$	−782.447	−	1677.96i	−0.443564	−	0.951226i
$43$	1017.84	−	2182.76i	0.550480	−	1.18051i	−0.412506	−	0.910955i	$-0.635346\pi$
$43$	1017.84	−	2182.76i	0.550480	−	1.18051i	0.962986	−	0.269552i	$-0.0868758\pi$
$44$	132.917	+	158.405i	0.0686557	+	0.0818207i
$45$	16.8334	+	71.1220i	0.00831280	+	0.0351220i
$46$	1429.48	−	2475.94i	0.675559	−	1.17010i
$47$	892.625	−	1274.80i	0.404086	−	0.577094i	−0.564606	−	0.825361i	$-0.690972\pi$
$47$	892.625	−	1274.80i	0.404086	−	0.577094i	0.968692	+	0.248266i	$0.0798608\pi$
$48$	2096.73	+	1468.15i	0.910039	+	0.637216i
$49$	23.4258	+	13.5249i	0.00975668	+	0.00563302i
$50$	2008.91	−	1785.59i	0.803563	−	0.714237i
$51$	1790.69	−	1502.57i	0.688464	−	0.577690i
$52$	639.139	+	298.035i	0.236368	+	0.110220i
$53$	−4363.88	+	2034.91i	−1.55353	+	0.724425i	−0.994502	−	0.104720i	$-0.966605\pi$
$53$	−4363.88	+	2034.91i	−1.55353	+	0.724425i	−0.559033	+	0.829145i	$0.688828\pi$
$54$	2049.85	−	2442.91i	0.702966	−	0.837762i
$55$	1852.35	+	930.989i	0.612347	+	0.307765i
$56$	2830.00			0.902423
$57$	−1603.85	+	2757.29i	−0.493645	+	0.848659i
$58$	1558.69	−	1558.69i	0.463343	−	0.463343i
$59$	1539.52	+	271.459i	0.442263	+	0.0779830i	0.390346	−	0.920668i	$-0.372356\pi$
$59$	1539.52	+	271.459i	0.442263	+	0.0779830i	0.0519178	+	0.998651i	$0.483467\pi$
$60$	−539.425	−	111.553i	−0.149840	−	0.0309869i
$61$	5351.19	+	1947.67i	1.43810	+	0.523427i	0.939243	−	0.343254i	$-0.111529\pi$
$61$	5351.19	+	1947.67i	1.43810	+	0.523427i	0.498862	+	0.866681i	$0.333751\pi$
$62$	1463.50	+	682.443i	0.380724	+	0.177535i
$63$	12.4146	−	141.899i	0.00312788	−	0.0357519i
$64$	−2835.52	+	1637.09i	−0.692265	+	0.399679i
$65$	7067.21	+	207.781i	1.67271	+	0.0491789i
$66$	−547.181	−	3103.22i	−0.125616	−	0.712401i
$67$	−424.907	+	606.830i	−0.0946552	+	0.135182i	−0.863686	−	0.504030i	$-0.831850\pi$
$67$	−424.907	+	606.830i	−0.0946552	+	0.135182i	0.769031	+	0.639211i	$0.220739\pi$
$68$	−170.737	−	637.200i	−0.0369241	−	0.137803i
$69$	−5087.33	+	2937.17i	−1.06854	+	0.616923i
$70$	−4810.48	+	2073.31i	−0.981730	+	0.423124i
$71$	5345.56	−	1945.62i	1.06042	−	0.385960i	0.247832	−	0.968803i	$-0.420282\pi$
$71$	5345.56	−	1945.62i	1.06042	−	0.385960i	0.812585	+	0.582843i	$0.198060\pi$
$72$	71.7627	+	153.896i	0.0138431	+	0.0296866i
$73$	−5742.46	+	502.400i	−1.07759	+	0.0942766i	−0.612102	−	0.790779i	$-0.709676\pi$
$73$	−5742.46	+	502.400i	−1.07759	+	0.0942766i	−0.465485	+	0.885056i	$0.654120\pi$
$74$	1986.57	+	350.286i	0.362778	+	0.0639675i
$75$	−5409.14	+	1113.48i	−0.961625	+	0.197951i
$76$	513.934	+	739.056i	0.0889774	+	0.127953i
$77$	−2857.01	−	2857.01i	−0.481870	−	0.481870i
$78$	−6163.93	−	8803.00i	−1.01314	−	1.44691i
$79$	3430.16	−	4087.90i	0.549617	−	0.655008i	−0.417698	−	0.908586i	$-0.637163\pi$
$79$	3430.16	−	4087.90i	0.549617	−	0.655008i	0.967315	+	0.253578i	$0.0816075\pi$
$80$	4326.38	−	5807.65i	0.675996	−	0.907446i
$81$	−5934.77	+	2160.08i	−0.904553	+	0.329230i
$82$	−10306.1	−	901.669i	−1.53274	−	0.134097i
$83$	−3795.13	−	1016.90i	−0.550897	−	0.147612i	−0.0273760	−	0.999625i	$-0.508715\pi$
$83$	−3795.13	−	1016.90i	−0.550897	−	0.147612i	−0.523521	+	0.852013i	$0.675382\pi$
$84$	929.717	+	536.773i	0.131763	+	0.0760732i
$85$	−4100.50	−	5189.17i	−0.567544	−	0.718224i
$86$	1798.50	+	10199.8i	0.243172	+	1.37910i
$87$	−4374.89	+	1172.25i	−0.578001	+	0.154875i
$88$	4652.48	+	1246.63i	0.600785	+	0.160980i
$89$	7457.30	+	8887.26i	0.941459	+	1.12199i	0.992371	+	0.123284i	$0.0393426\pi$
$89$	7457.30	+	8887.26i	0.941459	+	1.12199i	−0.0509124	+	0.998703i	$0.516213\pi$
$90$	−234.730	−	209.019i	−0.0289790	−	0.0258049i
$91$	−12948.4	−	4712.84i	−1.56363	−	0.569115i
$92$	144.484	+	1651.46i	0.0170704	+	0.195115i
$93$	−1903.09	−	2717.89i	−0.220036	−	0.314243i
$94$			6692.50i			0.757413i
$95$	7664.50	+	4765.09i	0.849252	+	0.527988i
$96$	−2795.84			−0.303368
$97$	−6291.03	+	4405.03i	−0.668619	+	0.468172i	−0.857944	−	0.513743i	$-0.828259\pi$
$97$	−6291.03	+	4405.03i	−0.668619	+	0.468172i	0.189326	+	0.981914i	$0.439370\pi$
$98$	−115.883	+	10.1384i	−0.0120661	+	0.00105565i
$99$	82.9166	−	227.812i	0.00846002	−	0.0232437i
$100$	−360.333	+	1516.26i	−0.0360333	+	0.151626i
$101$	−3907.08	+	3278.43i	−0.383009	+	0.321383i	−0.813883	−	0.581029i	$-0.802650\pi$
$101$	−3907.08	+	3278.43i	−0.383009	+	0.321383i	0.430873	+	0.902413i	$0.358206\pi$
$102$	−2601.80	+	9710.06i	−0.250077	+	0.933301i
$103$	2829.86	+	10561.2i	0.266742	+	0.995494i	0.961176	+	0.275937i	$0.0889883\pi$
$103$	2829.86	+	10561.2i	0.266742	+	0.995494i	−0.694434	+	0.719557i	$0.744345\pi$
$104$	16177.0	−	2852.44i	1.49565	−	0.263724i
$105$	10689.9	+	1252.76i	0.969606	+	0.113629i
$106$	10353.3	−	17932.4i	0.921437	−	1.59598i
$107$	2552.79	−	9527.16i	0.222971	−	0.832139i	−0.760236	−	0.649647i	$-0.774917\pi$
$107$	2552.79	−	9527.16i	0.222971	−	0.832139i	0.983207	−	0.182492i	$-0.0584165\pi$
$108$	−161.163	+	1842.10i	−0.0138171	+	0.157930i
$109$	−5070.81	−	13931.9i	−0.426800	−	1.17262i	−0.947744	−	0.319033i	$-0.896642\pi$
$109$	−5070.81	−	13931.9i	−0.426800	−	1.17262i	0.520944	−	0.853591i	$-0.325580\pi$
$110$	−8821.66	+	1289.45i	−0.729063	+	0.106566i
$111$	−3175.09	−	2664.22i	−0.257698	−	0.216234i
$112$	−11561.6	+	8095.52i	−0.921684	+	0.645370i
$113$	13915.8	−	13915.8i	1.08981	−	1.08981i	0.0942621	−	0.995547i	$-0.469951\pi$
$113$	13915.8	−	13915.8i	1.08981	−	1.08981i	0.995547	−	0.0942621i	$-0.0300492\pi$
$114$	−1151.30	−	13669.2i	−0.0885888	−	1.05180i
$115$	7883.56	+	14631.6i	0.596110	+	1.10636i
$116$	−221.951	+	1258.75i	−0.0164946	+	0.0935454i
$117$	−72.0595	−	823.644i	−0.00526404	−	0.0601683i
$118$	−6092.84	+	2841.14i	−0.437578	+	0.204046i
$119$	4408.54	+	12112.4i	0.311316	+	0.855333i
$120$	−11782.9	+	5078.41i	−0.818258	+	0.352667i
$121$	3882.15	+	6724.08i	0.265156	+	0.459263i
$122$	−23654.8	+	6338.28i	−1.58928	+	0.425845i
$123$	17412.7	+	12192.5i	1.15095	+	0.805902i
$124$	−922.111	+	162.593i	−0.0599708	+	0.0105745i
$125$	2699.24	+	15390.1i	0.172752	+	0.984965i
$126$	306.278	+	530.489i	0.0192919	+	0.0334146i
$127$	4449.24	+	389.258i	0.275853	+	0.0241340i	0.224243	−	0.974533i	$-0.428009\pi$
$127$	4449.24	+	389.258i	0.275853	+	0.0241340i	0.0516103	+	0.998667i	$0.483565\pi$
$128$	8090.13	−	17349.3i	0.493782	−	1.05892i
$129$	7278.50	−	19997.5i	0.437383	−	1.20170i
$130$	−25408.1	+	16700.1i	−1.50344	+	0.988174i
$131$	488.454	−	2770.16i	0.0284630	−	0.161422i	−0.967263	−	0.253775i	$-0.918328\pi$
$131$	488.454	−	2770.16i	0.0284630	−	0.161422i	0.995726	+	0.0923531i	$0.0294389\pi$
$132$	1291.99	+	1291.99i	0.0741501	+	0.0741501i
$133$	−11262.3	−	13510.6i	−0.636686	−	0.763783i
$134$		−	3185.76i		−	0.177420i
$135$	5825.97	+	17599.7i	0.319669	+	0.965689i
$136$	−11771.0	−	9877.01i	−0.636406	−	0.534008i
$137$	−5918.04	−	12691.3i	−0.315309	−	0.676182i	0.683231	−	0.730202i	$-0.260574\pi$
$137$	−5918.04	−	12691.3i	−0.315309	−	0.676182i	−0.998540	+	0.0540201i	$0.982797\pi$
$138$	10676.2	−	22895.2i	0.560608	−	1.20223i
$139$	15576.6	+	18563.4i	0.806198	+	0.960789i	0.999794	−	0.0202920i	$-0.00645958\pi$
$139$	15576.6	+	18563.4i	0.806198	+	0.960789i	−0.193596	+	0.981081i	$0.562015\pi$
$140$	1595.34	−	2584.69i	0.0813950	−	0.131872i
$141$	6875.56	−	11908.8i	0.345836	−	0.599005i
$142$	−14031.7	+	20039.3i	−0.695877	+	0.993815i
$143$	−19211.0	−	13451.7i	−0.939459	−	0.657817i
$144$	−733.412	−	423.436i	−0.0353690	−	0.0204203i
$145$	2951.45	+	12470.0i	0.140378	+	0.593104i
$146$	18989.7	−	15934.3i	0.890866	−	0.747526i
$147$	216.621	+	101.012i	0.0100246	+	0.00467453i
$148$	−1060.09	+	494.328i	−0.0483970	+	0.0225679i
$149$	−9216.40	+	10983.7i	−0.415135	+	0.494738i	−0.932573	−	0.360983i	$-0.882441\pi$
$149$	−9216.40	+	10983.7i	−0.415135	+	0.494738i	0.517438	+	0.855721i	$0.326886\pi$
$150$	16308.2	−	17264.7i	0.724811	−	0.767321i
$151$	−17483.7			−0.766797			−0.383398	−	0.923583i	$-0.625246\pi$
$151$	−17483.7			−0.766797			−0.383398	+	0.923583i	$0.625246\pi$
$152$	19680.2	+	7235.27i	0.851808	+	0.313161i
$153$	−546.880	+	546.880i	−0.0233620	+	0.0233620i
$154$	17111.5	+	3017.22i	0.721517	+	0.127223i
$155$	−7844.66	+	5156.11i	−0.326521	+	0.214614i
$156$	5855.52	+	2131.24i	0.240612	+	0.0875755i
$157$	30430.6	+	14190.0i	1.23456	+	0.575684i	0.926719	−	0.375754i	$-0.122616\pi$
$157$	30430.6	+	14190.0i	1.23456	+	0.575684i	0.307839	+	0.951438i	$0.400394\pi$
$158$	−2000.11	+	22861.3i	−0.0801197	+	0.915772i
$159$	−36845.8	+	21272.9i	−1.45745	+	0.841459i
$160$	−232.467	+	7906.85i	−0.00908075	+	0.308861i
$161$	−5624.77	−	31899.7i	−0.216997	−	1.23065i
$162$	15578.3	−	22248.1i	0.593595	−	0.847741i
$163$	−5337.23	−	19918.8i	−0.200882	−	0.749701i	−0.990665	−	0.136315i	$-0.956474\pi$
$163$	−5337.23	−	19918.8i	−0.200882	−	0.749701i	0.789784	−	0.613385i	$-0.210193\pi$
$164$	5195.12	−	2999.40i	0.193156	−	0.111519i
$165$	17022.2	+	6768.48i	0.625242	+	0.248613i
$166$	15877.4	−	5778.90i	0.576186	−	0.209715i
$167$	−21694.2	−	46523.5i	−0.777878	−	1.66817i	−0.743481	−	0.668757i	$-0.766827\pi$
$167$	−21694.2	−	46523.5i	−0.777878	−	1.66817i	−0.0343969	−	0.999408i	$-0.510951\pi$
$168$	24911.0	−	2179.43i	0.882617	−	0.0772190i
$169$	−50639.5	−	8929.11i	−1.77303	−	0.312633i
$170$	27244.5	+	8165.48i	0.942717	+	0.282543i
$171$	449.117	−	955.045i	0.0153591	−	0.0326612i
$172$	−4246.58	−	4246.58i	−0.143543	−	0.143543i
$173$	20725.7	+	29599.3i	0.692494	+	0.988985i	0.999307	+	0.0372147i	$0.0118485\pi$
$173$	20725.7	+	29599.3i	0.692494	+	0.988985i	−0.306813	+	0.951770i	$0.599263\pi$
$174$	12519.9	−	14920.6i	0.413526	−	0.492821i
$175$	4431.75	−	30127.8i	0.144710	−	0.983765i
$176$	−22573.2	+	8215.98i	−0.728733	+	0.265237i
$177$	13760.6	+	1203.90i	0.439230	+	0.0384276i
$178$	−48191.3	−	12912.8i	−1.52100	−	0.407550i
$179$	980.059	+	565.837i	0.0305877	+	0.0176598i	0.515216	−	0.857060i	$-0.327712\pi$
$179$	980.059	+	565.837i	0.0305877	+	0.0176598i	−0.484628	+	0.874720i	$0.661045\pi$
$180$	181.010	+	21.2127i	0.00558672	+	0.000654713i
$181$	620.162	+	3517.11i	0.0189299	+	0.107357i	0.992809	−	0.119712i	$-0.0381970\pi$
$181$	620.162	+	3517.11i	0.0189299	+	0.107357i	−0.973879	+	0.227068i	$0.927086\pi$
$182$	57238.1	−	15336.9i	1.72800	−	0.463015i
$183$	48603.6	+	13023.3i	1.45133	+	0.388883i
$184$	24820.9	+	29580.3i	0.733130	+	0.873711i
$185$	−7798.63	+	8757.90i	−0.227864	+	0.255892i
$186$	13408.0	+	4880.11i	0.387559	+	0.141060i
$187$	1912.03	+	21854.5i	0.0546777	+	0.624969i
$188$	−2225.84	−	3178.83i	−0.0629764	−	0.0899396i
$189$		−	36131.0i		−	1.01148i
$190$	−38753.4	+	2119.41i	−1.07350	+	0.0587094i
$191$	−16380.2			−0.449007			−0.224503	−	0.974473i	$-0.572076\pi$
$191$	−16380.2			−0.449007			−0.224503	+	0.974473i	$0.572076\pi$
$192$	−23698.8	+	16594.1i	−0.642871	+	0.450143i
$193$	−8560.63	+	748.958i	−0.229822	+	0.0201068i	−0.201485	−	0.979492i	$-0.564577\pi$
$193$	−8560.63	+	748.958i	−0.229822	+	0.0201068i	−0.0283370	+	0.999598i	$0.509021\pi$
$194$	11295.9	−	31035.1i	0.300135	−	0.824613i
$195$	62368.9	−	3613.58i	1.64021	−	0.0950318i
$196$	51.6704	−	43.3566i	0.00134502	−	0.00112861i
$197$	−18747.2	+	69965.5i	−0.483063	+	1.80282i	0.105565	+	0.994412i	$0.466335\pi$
$197$	−18747.2	+	69965.5i	−0.483063	+	1.80282i	−0.588628	+	0.808404i	$0.700332\pi$
$198$	269.834	+	1007.03i	0.00688282	+	0.0256870i
$199$	−20403.4	+	3597.68i	−0.515225	+	0.0908481i	−0.425214	−	0.905093i	$-0.639801\pi$
$199$	−20403.4	+	3597.68i	−0.515225	+	0.0908481i	−0.0900108	+	0.995941i	$0.528690\pi$
$200$	13382.4	+	33745.3i	0.334561	+	0.843633i
$201$	−3272.90	+	5668.83i	−0.0810104	+	0.140314i
$202$	5676.82	−	21186.2i	0.139124	−	0.519218i
$203$	2176.68	−	24879.6i	0.0528205	−	0.603741i
$204$	−1993.63	−	5477.44i	−0.0479053	−	0.131619i
$205$	35929.2	−	48230.7i	0.854948	−	1.14767i
$206$	−36019.2	−	30223.7i	−0.848788	−	0.712218i
$207$	1592.07	−	1114.78i	0.0371554	−	0.0260165i
$208$	−57929.3	+	57929.3i	−1.33897	+	1.33897i
$209$	−12563.7	−	27172.3i	−0.287623	−	0.622062i
$210$	−40747.4	+	21954.8i	−0.923977	+	0.497842i
$211$	2149.95	−	12193.0i	0.0482907	−	0.273870i	−0.951096	−	0.308896i	$-0.900040\pi$
$211$	2149.95	−	12193.0i	0.0482907	−	0.273870i	0.999386	+	0.0350261i	$0.0111514\pi$
$212$	1046.45	+	11960.9i	0.0232834	+	0.266130i
$213$	45555.7	−	21243.0i	1.00412	−	0.468227i
$214$	14507.1	+	39858.0i	0.316778	+	0.870339i
$215$	−55949.4	−	22246.9i	−1.21037	−	0.481275i
$216$	21536.0	+	37301.4i	0.461590	+	0.799498i
$217$	17672.1	−	4735.21i	0.375290	−	0.100559i
$218$	52227.7	+	36570.2i	1.09898	+	0.769511i
$219$	−50160.9	+	8844.72i	−1.04587	+	0.184415i
$220$	3761.29	−	3546.43i	0.0777125	−	0.0732734i
$221$	37408.7	+	64793.8i	0.765928	+	1.32663i
$222$	17756.5	+	1553.49i	0.360289	+	0.0315212i
$223$	−23977.6	+	51420.2i	−0.482166	+	1.03401i	0.503296	+	0.864114i	$0.332120\pi$
$223$	−23977.6	+	51420.2i	−0.482166	+	1.03401i	−0.985462	+	0.169894i	$0.945657\pi$
$224$	5272.77	−	14486.8i	0.105085	−	0.288720i
$225$	1750.73	−	522.977i	0.0345823	−	0.0103304i
$226$	−14696.1	+	83345.9i	−0.287731	+	1.63180i
$227$	−71910.9	−	71910.9i	−1.39554	−	1.39554i	−0.812295	−	0.583247i	$-0.801782\pi$
$227$	−71910.9	−	71910.9i	−1.39554	−	1.39554i	−0.583247	−	0.812295i	$-0.698218\pi$
$228$	5093.04	+	6109.73i	0.0979733	+	0.117531i
$229$			43395.4i			0.827508i	0.910389	+	0.413754i	$0.135783\pi$
$229$			43395.4i			0.827508i	−0.910389	+	0.413754i	$0.864217\pi$
$230$	−63861.9	−	32096.9i	−1.20722	−	0.606747i
$231$	−27348.9	−	22948.5i	−0.512526	−	0.430061i
$232$	12582.3	+	26982.9i	0.233768	+	0.501318i
$233$	−4939.42	+	10592.6i	−0.0909838	+	0.195115i	−0.946534	−	0.322605i	$-0.895441\pi$
$233$	−4939.42	+	10592.6i	−0.0909838	+	0.195115i	0.855550	+	0.517720i	$0.173219\pi$
$234$	2285.46	+	2723.70i	0.0417389	+	0.0497425i
$235$	−33107.5	−	20434.9i	−0.599501	−	0.370029i
$236$	1949.07	−	3375.89i	0.0349948	−	0.0606128i
$237$	27045.7	−	38625.3i	0.481506	−	0.687662i
$238$	−45406.5	−	31794.0i	−0.801612	−	0.561295i
$239$	24072.4	+	13898.2i	0.421429	+	0.243312i	0.695688	−	0.718344i	$-0.255099\pi$
$239$	24072.4	+	13898.2i	0.421429	+	0.243312i	−0.274260	+	0.961656i	$0.588433\pi$
$240$	33610.2	−	54453.5i	0.583511	−	0.945373i
$241$	12087.2	−	10142.4i	0.208110	−	0.174625i	−0.532775	−	0.846257i	$-0.678851\pi$
$241$	12087.2	−	10142.4i	0.208110	−	0.174625i	0.740885	+	0.671632i	$0.234406\pi$
$242$	−30261.3	−	14111.1i	−0.516723	−	0.240952i
$243$	3861.16	−	1800.49i	0.0653891	−	0.0304915i
$244$	9127.59	−	10877.8i	0.153312	−	0.182710i
$245$	303.681	−	604.222i	0.00505925	−	0.0100662i
$246$	−91413.8			−1.51057
$247$	−77996.0	−	65878.1i	−1.27843	−	1.07981i
$248$	−15422.1	+	15422.1i	−0.250749	+	0.250749i
$249$	−34189.6	−	6028.55i	−0.551437	−	0.0972332i
$250$	−47470.1	−	47556.6i	−0.759521	−	0.760905i
$251$	50391.4	+	18341.0i	0.799852	+	0.291122i	0.709425	−	0.704781i	$-0.248955\pi$
$251$	50391.4	+	18341.0i	0.799852	+	0.291122i	0.0904266	+	0.995903i	$0.471177\pi$
$252$	−321.911	−	150.109i	−0.00506914	−	0.00236378i
$253$	4804.91	−	54920.3i	0.0750661	−	0.858010i
$254$	−16633.5	+	9603.33i	−0.257819	+	0.148852i
$255$	−40090.8	−	42519.6i	−0.616545	−	0.653897i
$256$	5198.26	+	29480.8i	0.0793192	+	0.449842i
$257$	22776.3	−	32528.0i	0.344840	−	0.492483i	−0.608845	−	0.793289i	$-0.708367\pi$
$257$	22776.3	−	32528.0i	0.344840	−	0.492483i	0.953685	+	0.300806i	$0.0972558\pi$
$258$	23686.3	+	88398.4i	0.355842	+	1.32802i
$259$	19792.9	−	11427.4i	0.295059	−	0.170352i
$260$	6514.19	−	16382.7i	0.0963637	−	0.242348i
$261$	1408.15	−	512.524i	0.0206713	−	0.00752373i
$262$	5112.25	+	10963.3i	0.0744748	+	0.159712i
$263$	−32553.8	+	2848.09i	−0.470641	+	0.0411758i	−0.320010	−	0.947414i	$-0.603686\pi$
$263$	−32553.8	+	2848.09i	−0.470641	+	0.0411758i	−0.150631	+	0.988590i	$0.548131\pi$
$264$	41913.4	+	7390.46i	0.601374	+	0.106038i
$265$	57098.0	+	105972.i	0.813072	+	1.50903i
$266$	72999.2	+	19813.7i	1.03170	+	0.280029i
$267$	72486.8	+	72486.8i	1.01680	+	1.01680i
$268$	1059.54	+	1513.18i	0.0147519	+	0.0210679i
$269$	1845.03	−	2198.82i	0.0254975	−	0.0303868i	−0.753145	−	0.657855i	$-0.771464\pi$
$269$	1845.03	−	2198.82i	0.0254975	−	0.0303868i	0.778643	+	0.627468i	$0.215909\pi$
$270$	−63934.8	−	47627.8i	−0.877020	−	0.653331i
$271$	−10464.5	+	3808.77i	−0.142488	+	0.0518616i	−0.412280	−	0.911057i	$-0.635267\pi$
$271$	−10464.5	+	3808.77i	−0.142488	+	0.0518616i	0.269791	+	0.962919i	$0.413045\pi$
$272$	76343.0	+	6679.15i	1.03189	+	0.0902783i
$273$	−117608.	−	31512.8i	−1.57801	−	0.422827i
$274$	52151.9	+	30109.9i	0.694655	+	0.401059i
$275$	20557.2	−	47577.5i	0.271830	−	0.629124i
$276$	2543.63	+	14425.6i	0.0333915	+	0.189372i
$277$	45080.0	−	12079.2i	0.587523	−	0.157426i	0.0472020	−	0.998885i	$-0.484970\pi$
$277$	45080.0	−	12079.2i	0.587523	−	0.157426i	0.540321	+	0.841459i	$0.318303\pi$
$278$	−100660.	−	26971.8i	−1.30247	−	0.348996i
$279$	705.626	+	840.933i	0.00906497	+	0.0108032i
$280$	−4092.31	−	70631.5i	−0.0521979	−	0.900913i
$281$	−5600.45	−	2038.40i	−0.0709267	−	0.0258152i	0.306313	−	0.951931i	$-0.400905\pi$
$281$	−5600.45	−	2038.40i	−0.0709267	−	0.0258152i	−0.377240	+	0.926116i	$0.623127\pi$
$282$	5154.00	+	58910.5i	0.0648107	+	0.740789i
$283$	40436.1	+	57748.8i	0.504890	+	0.721058i	0.987992	−	0.154507i	$-0.0493788\pi$
$283$	40436.1	+	57748.8i	0.504890	+	0.721058i	−0.483102	+	0.875564i	$0.660490\pi$
$284$		−	14185.1i		−	0.175871i
$285$	71136.2	+	36042.0i	0.875791	+	0.443731i
$286$	100855.			1.23300
$287$	−96015.4	+	67230.7i	−1.16567	+	0.816214i
$288$	921.500	−	80.6208i	0.0111099	−	0.000971991i
$289$	−4629.05	+	12718.2i	−0.0554238	+	0.152276i
$290$	−41155.8	−	36648.0i	−0.489368	−	0.435766i
$291$	−51984.2	+	43619.9i	−0.613883	+	0.515109i
$292$	−3720.27	+	13884.2i	−0.0436323	+	0.162838i
$293$	26592.9	+	99245.9i	0.309763	+	1.15605i	0.928767	+	0.370664i	$0.120870\pi$
$293$	26592.9	+	99245.9i	0.309763	+	1.15605i	−0.619004	+	0.785388i	$0.712463\pi$
$294$	−1012.25	+	178.486i	−0.0117109	+	0.00206495i
$295$	4548.89	−	38816.1i	0.0522711	−	0.446034i
$296$	−13622.7	+	23595.2i	−0.155482	+	0.269302i
$297$	15915.9	−	59398.8i	0.180434	−	0.673387i
$298$	5374.04	−	61425.5i	0.0605157	−	0.691698i
$299$	−64305.1	−	176677.i	−0.719289	−	1.97623i
$300$	−2004.12	+	13624.4i	−0.0222680	+	0.151382i
$301$	89891.7	+	75428.1i	0.992171	+	0.832531i
$302$	61589.9	−	43125.7i	0.675298	−	0.472849i
$303$	−31867.2	+	31867.2i	−0.347103	+	0.347103i
$304$	−101098.	+	26738.5i	−1.09395	+	0.289328i
$305$	40872.2	−	136372.i	0.439368	−	1.46597i
$306$	577.548	−	3275.44i	0.00616801	−	0.0349805i
$307$	−5634.51	−	64402.8i	−0.0597833	−	0.683326i	−0.965664	−	0.259794i	$-0.916345\pi$
$307$	−5634.51	−	64402.8i	−0.0597833	−	0.683326i	0.905881	−	0.423533i	$-0.139210\pi$
$308$	−9131.16	+	4257.93i	−0.0962553	+	0.0448846i
$309$	33043.1	+	90785.3i	0.346070	+	0.950820i
$310$	14916.2	−	37513.2i	0.155216	−	0.390356i
$311$	30345.1	+	52559.3i	0.313739	+	0.543411i	0.979169	−	0.203049i	$-0.0650851\pi$
$311$	30345.1	+	52559.3i	0.313739	+	0.543411i	−0.665430	+	0.746460i	$0.731752\pi$
$312$	140201.	−	37566.6i	1.44026	−	0.385916i
$313$	40989.1	+	28700.9i	0.418389	+	0.292959i	0.763752	−	0.645510i	$-0.223355\pi$
$313$	40989.1	+	28700.9i	0.418389	+	0.292959i	−0.345363	+	0.938469i	$0.612244\pi$
$314$	−142199.	+	25073.6i	−1.44224	+	0.254306i
$315$	−3559.49	−	104.652i	−0.0358729	−	0.00105469i
$316$	−6653.36	−	11524.0i	−0.0666296	−	0.115406i
$317$	39451.0	+	3451.51i	0.392590	+	0.0343472i	0.281742	−	0.959490i	$-0.409088\pi$
$317$	39451.0	+	3451.51i	0.392590	+	0.0343472i	0.110848	+	0.993837i	$0.464643\pi$
$318$	77324.3	−	165823.i	0.764649	−	1.63979i
$319$	14538.0	−	39942.8i	0.142864	−	0.392516i
$320$	44958.9	+	68401.9i	0.439052	+	0.667987i
$321$	15133.9	−	85828.5i	0.146872	−	0.832955i
$322$	98498.6	+	98498.6i	0.949988	+	0.949988i
$323$	−309.326	+	95502.0i	−0.00296491	+	0.915392i
$324$			15748.6i			0.150021i
$325$	−5033.68	−	176685.i	−0.0476562	−	1.67276i
$326$	67933.5	+	57003.0i	0.639217	+	0.536367i
$327$	−55364.9	−	118730.i	−0.517772	−	1.11037i
$328$	59052.7	−	126639.i	0.548898	−	1.17712i
$329$	48739.5	+	58085.5i	0.450287	+	0.536631i
$330$	−76659.4	+	18144.0i	−0.703943	+	0.166612i
$331$	−44108.5	+	76398.2i	−0.402593	+	0.697312i	−0.994038	−	0.109033i	$-0.965224\pi$
$331$	−44108.5	+	76398.2i	−0.402593	+	0.697312i	0.591445	+	0.806346i	$0.298558\pi$
$332$	−5619.51	+	8025.49i	−0.0509826	+	0.0728107i
$333$	1123.33	+	786.563i	0.0101302	+	0.00709324i
$334$	191178.	+	110377.i	1.71374	+	0.989427i
$335$	15759.8	+	9727.39i	0.140430	+	0.0866776i
$336$	−95536.1	+	80164.3i	−0.846231	+	0.710072i
$337$	123520.	+	57598.5i	1.08762	+	0.507167i	0.881897	−	0.471443i	$-0.156267\pi$
$337$	123520.	+	57598.5i	1.08762	+	0.507167i	0.205726	+	0.978610i	$0.434044\pi$
$338$	200412.	−	93453.8i	1.75425	−	0.818019i
$339$	111776.	−	133210.i	0.972637	−	1.15914i
$340$	−15656.4	+	5182.70i	−0.135436	+	0.0448331i
$341$	31138.5			0.267787
$342$	773.631	+	4472.13i	0.00661426	+	0.0382351i
$343$	−83652.4	+	83652.4i	−0.711034	+	0.711034i
$344$	−137763.	−	24291.3i	−1.16417	−	0.205274i
$345$	80662.8	+	122723.i	0.677696	+	1.03107i
$346$	−146020.	−	53147.1i	−1.21972	−	0.443943i
$347$	52149.3	+	24317.6i	0.433101	+	0.201958i	0.626928	−	0.779077i	$-0.284312\pi$
$347$	52149.3	+	24317.6i	0.433101	+	0.201958i	−0.193827	+	0.981036i	$0.562090\pi$
$348$	−984.336	+	11251.0i	−0.00812802	+	0.0929037i
$349$	−79088.3	+	45661.7i	−0.649324	+	0.374888i	−0.788197	−	0.615423i	$-0.788985\pi$
$349$	−79088.3	+	45661.7i	−0.649324	+	0.374888i	0.138873	+	0.990310i	$0.455652\pi$
$350$	58702.0	+	117062.i	0.479200	+	0.955612i
$351$	−36417.4	−	206533.i	−0.295594	−	1.67639i
$352$	15049.9	−	21493.4i	0.121464	−	0.173469i
$353$	48449.6	+	180817.i	0.388813	+	1.45107i	0.832067	+	0.554675i	$0.187157\pi$
$353$	48449.6	+	180817.i	0.388813	+	1.45107i	−0.443254	+	0.896396i	$0.646176\pi$
$354$	−51444.0	+	29701.2i	−0.410515	+	0.237011i
$355$	−56289.1	−	130602.i	−0.446650	−	1.03632i
$356$	27184.7	−	9894.41i	0.214498	−	0.0780710i
$357$	48134.0	+	103224.i	0.377672	+	0.809921i
$358$	−4848.15	+	424.159i	−0.0378277	+	0.00330950i
$359$	193049.	+	34039.8i	1.49789	+	0.264118i	0.861701	−	0.507417i	$-0.169399\pi$
$359$	193049.	+	34039.8i	1.49789	+	0.264118i	0.636187	+	0.771535i	$0.280511\pi$
$360$	3737.18	−	2013.60i	0.0288362	−	0.0155371i
$361$	−43778.2	−	122748.i	−0.335926	−	0.941888i
$362$	−10860.0	−	10860.0i	−0.0828730	−	0.0828730i
$363$	39350.8	+	56198.8i	0.298635	+	0.426494i
$364$	−22086.3	+	26321.4i	−0.166694	+	0.198658i
$365$	20842.8	+	142595.i	0.156448	+	1.07033i
$366$	−203339.	+	74009.4i	−1.51795	+	0.552490i
$367$	−176631.	−	15453.2i	−1.31140	−	0.114733i	−0.590086	−	0.807340i	$-0.700906\pi$
$367$	−176631.	−	15453.2i	−1.31140	−	0.114733i	−0.721315	+	0.692607i	$0.756462\pi$
$368$	−186020.	−	49844.0i	−1.37361	−	0.368059i
$369$	−6090.75	−	3516.50i	−0.0447320	−	0.0258260i
$370$	5869.82	−	50087.7i	0.0428767	−	0.365870i
$371$	−40738.3	−	231038.i	−0.295975	−	1.67856i
$372$	−7991.64	+	2141.35i	−0.0577497	+	0.0154740i
$373$	93994.0	+	25185.6i	0.675589	+	0.181024i	0.580271	−	0.814423i	$-0.302947\pi$
$373$	93994.0	+	25185.6i	0.675589	+	0.181024i	0.0953178	+	0.995447i	$0.469613\pi$
$374$	−60642.3	−	72270.7i	−0.433543	−	0.516677i
$375$	35612.2	+	133392.i	0.253242	+	0.948565i
$376$	−84940.4	−	30915.8i	−0.600812	−	0.218678i
$377$	−12634.4	−	144412.i	−0.0888938	−	1.01606i
$378$	89121.3	+	127278.i	0.623732	+	0.890781i
$379$		−	52173.3i		−	0.363220i	−0.983371	−	0.181610i	$-0.941869\pi$
$379$		−	52173.3i		−	0.363220i	0.983371	−	0.181610i	$-0.0581309\pi$
$380$	17702.3	−	13895.5i	0.122592	−	0.0962295i
$381$	39464.0			0.271864
$382$	57702.5	−	40403.7i	0.395428	−	0.276882i
$383$	−196202.	+	17165.5i	−1.33754	+	0.117019i	−0.733366	−	0.679834i	$-0.762052\pi$
$383$	−196202.	+	17165.5i	−1.33754	+	0.117019i	−0.604172	+	0.796854i	$0.706496\pi$
$384$	57852.1	−	158947.i	0.392335	−	1.07793i
$385$	−67174.2	+	75436.9i	−0.453191	+	0.508935i
$386$	28309.1	−	23754.2i	0.189999	−	0.159428i
$387$	−1822.33	+	6801.01i	−0.0121676	+	0.0454100i
$388$	4956.53	+	18498.0i	0.0329241	+	0.122875i
$389$	−201273.	+	35489.9i	−1.33011	+	0.234534i	−0.793124	−	0.609060i	$-0.791547\pi$
$389$	−201273.	+	35489.9i	−1.33011	+	0.234534i	−0.536982	+	0.843594i	$0.680436\pi$
$390$	−210793.	+	166570.i	−1.38589	+	1.09513i
$391$	−87937.9	+	152313.i	−0.575205	+	0.996284i
$392$	406.641	−	1517.60i	0.00264630	−	0.00987611i
$393$	2166.26	−	24760.4i	0.0140257	−	0.160314i
$394$	−106537.	−	292709.i	−0.686294	−	1.88558i
$395$	−106987.	−	79699.1i	−0.685702	−	0.510810i
$396$	−463.093	−	388.581i	−0.00295310	−	0.00247794i
$397$	−237364.	+	166204.i	−1.50603	+	1.05454i	−0.527231	+	0.849722i	$0.676770\pi$
$397$	−237364.	+	166204.i	−1.50603	+	1.05454i	−0.978801	+	0.204813i	$0.934341\pi$
$398$	63001.0	−	63001.0i	0.397723	−	0.397723i
$399$	−109541.	−	110253.i	−0.688068	−	0.692540i
$400$	−151204.	−	99580.2i	−0.945027	−	0.622376i
$401$	26010.3	−	147512.i	0.161755	−	0.917357i	−0.790593	−	0.612342i	$-0.790227\pi$
$401$	26010.3	−	147512.i	0.161755	−	0.917357i	0.952348	−	0.305015i	$-0.0986615\pi$
$402$	−2453.41	−	28042.6i	−0.0151816	−	0.173526i
$403$	96245.1	−	44879.8i	0.592609	−	0.276338i
$404$	4349.85	+	11951.1i	0.0266509	+	0.0732227i
$405$	62493.5	+	144997.i	0.381000	+	0.883995i
$406$	53700.6	+	93012.2i	0.325782	+	0.564271i
$407$	37573.0	−	10067.7i	0.226823	−	0.0607771i
$408$	−111220.	−	77877.1i	−0.668132	−	0.467831i
$409$	−91592.1	+	16150.2i	−0.547534	+	0.0965450i	−0.440571	−	0.897718i	$-0.645224\pi$
$409$	−91592.1	+	16150.2i	−0.547534	+	0.0965450i	−0.106963	+	0.994263i	$0.534113\pi$
$410$	−7600.85	+	258526.i	−0.0452162	+	1.53793i
$411$	−61867.1	−	107157.i	−0.366249	−	0.634361i
$412$	27160.5	+	2376.24i	0.160009	+	0.0139989i
$413$	−32189.8	+	69031.2i	−0.188720	+	0.404711i
$414$	−2858.65	+	7854.07i	−0.0166786	+	0.0458241i
$415$	−19892.0	+	96189.9i	−0.115500	+	0.558513i
$416$	15538.8	−	88124.8i	0.0897905	−	0.509227i
$417$	151408.	+	151408.i	0.870717	+	0.870717i
$418$	111282.	+	64730.0i	0.636900	+	0.370470i
$419$			72891.5i			0.415192i	0.978215	+	0.207596i	$0.0665639\pi$
$419$			72891.5i			0.415192i	−0.978215	+	0.207596i	$0.933436\pi$
$420$	12052.4	−	23980.2i	0.0683245	−	0.135942i
$421$	182183.	+	152870.i	1.02788	+	0.862498i	0.990598	−	0.136807i	$-0.0436840\pi$
$421$	182183.	+	152870.i	1.02788	+	0.862498i	0.0372870	+	0.999305i	$0.488128\pi$
$422$	22501.8	+	48255.3i	0.126355	+	0.270969i
$423$	−1922.76	+	4123.38i	−0.0107460	+	0.0230448i
$424$	179769.	+	214241.i	0.999962	+	1.19171i
$425$	−123582.	+	109845.i	−0.684194	+	0.608137i
$426$	−108081.	+	187201.i	−0.595565	+	1.03155i
$427$	−159144.	+	227282.i	−0.872842	+	1.24655i
$428$	−20146.9	−	14107.0i	−0.109982	−	0.0770101i
$429$	−179464.	−	103613.i	−0.975129	−	0.562991i
$430$	251967.	−	59636.6i	1.36272	−	0.322535i
$431$	−74577.9	+	62578.3i	−0.401472	+	0.336875i	−0.821062	−	0.570838i	$-0.806618\pi$
$431$	−74577.9	+	62578.3i	−0.401472	+	0.336875i	0.419590	+	0.907714i	$0.362174\pi$
$432$	−194687.	−	90784.1i	−1.04320	−	0.486454i
$433$	281004.	−	131035.i	1.49878	−	0.698892i	0.511705	−	0.859161i	$-0.329014\pi$
$433$	281004.	−	131035.i	1.49878	−	0.698892i	0.987073	+	0.160270i	$0.0512364\pi$
$434$	−50573.3	+	60270.9i	−0.268498	+	0.319984i
$435$	35583.4	+	107494.i	0.188048	+	0.568075i
$436$	−36970.1			−0.194481
$437$	42440.4	−	236215.i	0.222237	−	1.23693i
$438$	154885.	−	154885.i	0.807349	−	0.807349i
$439$	301919.	+	53236.5i	1.56661	+	0.276236i	0.888554	−	0.458773i	$-0.151711\pi$
$439$	301919.	+	53236.5i	1.56661	+	0.276236i	0.678058	+	0.735009i	$0.262822\pi$
$440$	24385.8	−	117920.i	0.125960	−	0.609091i
$441$	−74.3104	−	27.0468i	−0.000382096	−	0.000139071i
$442$	−291601.	−	135976.i	−1.49260	−	0.696012i
$443$	−11110.5	+	126993.i	−0.0566142	+	0.647103i	0.913881	+	0.405982i	$0.133071\pi$
$443$	−11110.5	+	126993.i	−0.0566142	+	0.647103i	−0.970495	+	0.241121i	$0.922485\pi$
$444$	−8950.71	+	5167.69i	−0.0454037	+	0.0262139i
$445$	211026.	−	198972.i	1.06565	−	1.00478i
$446$	−42368.1	−	240281.i	−0.212995	−	1.20795i
$447$	−72668.4	+	103781.i	−0.363689	+	0.519402i
$448$	−41288.9	−	154092.i	−0.205720	−	0.767759i
$449$	161126.	−	93025.9i	0.799230	−	0.461436i	−0.0439718	−	0.999033i	$-0.514001\pi$
$449$	161126.	−	93025.9i	0.799230	−	0.461436i	0.843202	+	0.537597i	$0.180668\pi$
$450$	−4877.31	+	6160.67i	−0.0240855	+	0.0304231i
$451$	−187464.	+	68231.1i	−0.921645	+	0.335451i
$452$	−20739.3	−	44475.7i	−0.101512	−	0.217694i
$453$	−153900.	+	13464.5i	−0.749967	+	0.0656136i
$454$	430697.	+	75943.5i	2.08958	+	0.368450i
$455$	−98899.7	+	329984.i	−0.477719	+	1.59393i
$456$	178806.	+	48532.2i	0.859910	+	0.233400i
$457$	−165530.	−	165530.i	−0.792580	−	0.792580i	0.189333	−	0.981913i	$-0.439368\pi$
$457$	−165530.	−	165530.i	−0.792580	−	0.792580i	−0.981913	+	0.189333i	$0.939368\pi$
$458$	−107040.	−	152869.i	−0.510287	−	0.728765i
$459$	−126101.	+	150281.i	−0.598540	+	0.713312i
$460$	41008.4	−	5994.13i	0.193801	−	0.0283277i
$461$	90929.5	−	33095.6i	0.427861	−	0.155729i	−0.119108	−	0.992881i	$-0.538004\pi$
$461$	90929.5	−	33095.6i	0.427861	−	0.155729i	0.546970	+	0.837153i	$0.315781\pi$
$462$	152947.	+	13381.1i	0.716568	+	0.0626915i
$463$	143729.	+	38511.9i	0.670472	+	0.179653i	0.577968	−	0.816060i	$-0.303846\pi$
$463$	143729.	+	38511.9i	0.670472	+	0.179653i	0.0925048	+	0.995712i	$0.470513\pi$
$464$	−128591.	−	74242.1i	−0.597276	−	0.344838i
$465$	−65081.6	+	51427.8i	−0.300990	+	0.237844i
$466$	−8727.87	−	49498.2i	−0.0401917	−	0.227939i
$467$	229824.	−	61581.0i	1.05381	−	0.282367i	0.309983	−	0.950742i	$-0.399677\pi$
$467$	229824.	−	61581.0i	1.05381	−	0.282367i	0.743824	+	0.668376i	$0.233010\pi$
$468$	−1991.42	−	533.600i	−0.00909225	−	0.00243626i
$469$	−23201.0	−	27649.8i	−0.105478	−	0.125703i
$470$	167032.	−	9677.67i	0.756145	−	0.0438102i
$471$	278793.	+	101472.i	1.25672	+	0.457410i
$472$	−7913.71	−	90454.1i	−0.0355219	−	0.406017i
$473$	114554.	+	163601.i	0.512023	+	0.731244i
$474$			202776.i			0.902528i
$475$	107845.	−	198182.i	0.477982	−	0.878370i
$476$	32141.6			0.141858
$477$	11530.8	−	8073.99i	0.0506786	−	0.0354855i
$478$	−119081.	+	10418.3i	−0.521180	+	0.0455974i
$479$	−93248.0	+	256197.i	−0.406414	+	1.11661i	0.552647	+	0.833415i	$0.313618\pi$
$479$	−93248.0	+	256197.i	−0.406414	+	1.11661i	−0.959061	+	0.283198i	$0.908605\pi$
$480$	4042.91	+	69778.9i	0.0175474	+	0.302860i
$481$	101623.	−	85271.7i	0.439239	−	0.368566i
$482$	−17562.2	+	65543.1i	−0.0755936	+	0.282119i
$483$	−74078.3	−	276464.i	−0.317539	−	1.18507i
$484$	19066.8	−	3361.99i	0.0813930	−	0.0143518i
$485$	119038.	+	150643.i	0.506062	+	0.640419i
$486$	−9160.58	+	15866.6i	−0.0387838	+	0.0671755i
$487$	−40644.3	+	151686.i	−0.171373	+	0.639571i	0.825769	+	0.564009i	$0.190742\pi$
$487$	−40644.3	+	151686.i	−0.171373	+	0.639571i	−0.997141	+	0.0755620i	$0.975925\pi$
$488$	28827.8	−	329503.i	0.121052	−	1.38363i
$489$	−62320.5	−	171224.i	−0.260623	−	0.716057i
$490$	420.608	+	2877.56i	0.00175180	+	0.0119848i
$491$	62258.3	+	52240.9i	0.258246	+	0.216694i	0.762714	−	0.646736i	$-0.223867\pi$
$491$	62258.3	+	52240.9i	0.258246	+	0.216694i	−0.504467	+	0.863431i	$0.668311\pi$
$492$	43420.0	−	30403.0i	0.179374	−	0.125599i
$493$	−95886.0	+	95886.0i	−0.394513	+	0.394513i
$494$	437252.	+	39682.1i	1.79175	+	0.162608i
$495$	−5805.66	−	1740.02i	−0.0236941	−	0.00710139i
$496$	18888.4	−	107121.i	0.0767771	−	0.435425i
$497$	24156.8	+	276113.i	0.0977972	+	1.11783i
$498$	135310.	−	63096.0i	0.545595	−	0.254415i
$499$	−43803.3	−	120349.i	−0.175916	−	0.483326i	0.820128	−	0.572179i	$-0.193902\pi$
$499$	−43803.3	−	120349.i	−0.175916	−	0.483326i	−0.996045	+	0.0888535i	$0.971680\pi$
$500$	38364.2	+	6800.66i	0.153457	+	0.0272026i
$501$	−226791.	−	392814.i	−0.903548	−	1.56499i
$502$	−222754.	+	59686.7i	−0.883930	+	0.236848i
$503$	−69587.6	−	48725.8i	−0.275040	−	0.192585i	0.427916	−	0.903819i	$-0.359248\pi$
$503$	−69587.6	−	48725.8i	−0.275040	−	0.192585i	−0.702956	+	0.711233i	$0.748137\pi$
$504$	−8147.75	+	1436.67i	−0.0320757	+	0.00565582i
$505$	87473.3	+	92772.7i	0.342999	+	0.363779i
$506$	118541.	+	205319.i	0.462987	+	0.801916i
$507$	−452629.	−	39599.9i	−1.76087	−	0.154056i
$508$	4706.67	−	10093.5i	0.0182384	−	0.0391123i
$509$	77338.5	−	212486.i	0.298511	−	0.820152i	−0.696238	−	0.717811i	$-0.745144\pi$
$509$	77338.5	−	212486.i	0.298511	−	0.820152i	0.994749	−	0.102341i	$-0.0326334\pi$
$510$	246107.	+	50895.0i	0.946203	+	0.195675i
$511$	48770.8	−	276593.i	0.186775	−	1.05925i
$512$	125547.	+	125547.i	0.478924	+	0.478924i
$513$	92373.6	−	251259.i	0.351005	−	0.954745i
$514$			170767.i			0.646364i
$515$	259496.	−	85900.1i	0.978399	−	0.323877i
$516$	−40650.7	−	34110.0i	−0.152675	−	0.128110i
$517$	54540.2	+	116962.i	0.204049	+	0.437585i
$518$	−41537.2	+	89076.7i	−0.154802	+	0.331975i
$519$	205232.	+	244586.i	0.761921	+	0.908023i
$520$	−94584.2	−	399623.i	−0.349794	−	1.47789i
$521$	−13273.0	+	22989.6i	−0.0488984	+	0.0846945i	−0.889439	−	0.457055i	$-0.848904\pi$
$521$	−13273.0	+	22989.6i	−0.0488984	+	0.0846945i	0.840540	+	0.541749i	$0.182238\pi$
$522$	−3696.28	+	5278.83i	−0.0135651	+	0.0193730i
$523$	−359904.	−	252007.i	−1.31578	−	0.921319i	−0.316155	−	0.948707i	$-0.602392\pi$
$523$	−359904.	−	252007.i	−1.31578	−	0.921319i	−0.999625	+	0.0273884i	$0.991281\pi$
$524$	−6074.47	−	3507.10i	−0.0221231	−	0.0127728i
$525$	15808.4	−	268612.i	0.0573549	−	0.974556i
$526$	107652.	−	90330.7i	0.389090	−	0.326486i
$527$	−90030.7	−	41982.0i	−0.324167	−	0.151162i
$528$	−192373.	+	89704.9i	−0.690043	+	0.321772i
$529$	104217.	−	124202.i	0.372417	−	0.443829i
$530$	−462531.	−	232467.i	−1.64660	−	0.827580i
$531$	−4570.18			−0.0162086
$532$	−41263.2	+	14867.4i	−0.145794	+	0.0525305i
$533$	−481084.	+	481084.i	−1.69343	+	1.69343i
$534$	−434146.	−	76551.7i	−1.52249	−	0.268456i
$535$	−241472.	−	49936.3i	−0.843643	−	0.174465i
$536$	40433.3	+	14716.5i	0.140737	+	0.0512242i
$537$	9062.70	+	4226.01i	0.0314274	+	0.0146549i
$538$	−1075.83	+	12296.7i	−0.00371687	+	0.0424840i
$539$	−1942.61	+	1121.56i	−0.00668663	+	0.00386053i
$540$	46208.3	+	1358.56i	0.158465	+	0.00465898i
$541$	69971.6	+	396829.i	0.239071	+	1.35584i	0.833868	+	0.551965i	$0.186122\pi$
$541$	69971.6	+	396829.i	0.239071	+	1.35584i	−0.594796	+	0.803877i	$0.702767\pi$
$542$	27468.5	−	39229.0i	0.0935052	−	0.133539i
$543$	8167.54	+	30481.7i	0.0277007	+	0.103381i
$544$	−72491.9	+	41853.2i	−0.244958	+	0.141427i
$545$	−340383.	+	146704.i	−1.14597	+	0.493912i
$546$	492026.	−	179083.i	1.65045	−	0.600715i
$547$	115479.	+	247646.i	0.385949	+	0.827670i	0.999284	+	0.0378470i	$0.0120500\pi$
$547$	115479.	+	247646.i	0.385949	+	0.827670i	−0.613335	+	0.789823i	$0.710172\pi$
$548$	−34785.5	+	3043.33i	−0.115834	+	0.0101342i
$549$	−16395.2	−	2890.91i	−0.0543965	−	0.00959157i
$550$	44938.8	+	218308.i	0.148558	+	0.721678i
$551$	78744.9	−	167451.i	0.259370	−	0.551549i
$552$	241265.	+	241265.i	0.791802	+	0.791802i
$553$	149133.	+	212984.i	0.487667	+	0.696461i
$554$	−129009.	+	153746.i	−0.420338	+	0.500940i
$555$	−61902.6	+	83097.0i	−0.200966	+	0.269774i
$556$	56782.4	−	20667.1i	0.183681	−	0.0668544i
$557$	29614.4	+	2590.92i	0.0954535	+	0.00835110i	0.134782	−	0.990875i	$-0.456966\pi$
$557$	29614.4	+	2590.92i	0.0954535	+	0.00835110i	−0.0393289	+	0.999226i	$0.512522\pi$
$558$	−4559.97	−	1221.84i	−0.0146451	−	0.00392415i
$559$	589869.	+	340561.i	1.88770	+	1.08986i
$560$	218768.	+	276850.i	0.697601	+	0.882811i
$561$	33661.1	+	190901.i	0.106955	+	0.606574i
$562$	24756.6	−	6633.51i	0.0783824	−	0.0210025i
$563$	74836.9	+	20052.5i	0.236102	+	0.0632633i	0.374930	−	0.927053i	$-0.377667\pi$
$563$	74836.9	+	20052.5i	0.236102	+	0.0632633i	−0.138828	+	0.990317i	$0.544334\pi$
$564$	−22040.9	−	26267.4i	−0.0692902	−	0.0825768i
$565$	−367435.	−	327189.i	−1.15102	−	1.02495i
$566$	−284888.	−	103691.i	−0.889287	−	0.323674i
$567$	−26819.5	−	306548.i	−0.0834226	−	0.953525i
$568$	−189517.	−	270659.i	−0.587425	−	0.838930i
$569$		−	350882.i		−	1.08377i	−0.840453	−	0.541884i	$-0.817711\pi$
$569$		−	350882.i		−	1.08377i	0.840453	−	0.541884i	$-0.182289\pi$
$570$	−339493.	+	48500.6i	−1.04492	+	0.149279i
$571$	295959.			0.907737			0.453868	−	0.891069i	$-0.350044\pi$
$571$	295959.			0.907737			0.453868	+	0.891069i	$0.350044\pi$
$572$	−47904.3	+	33542.9i	−0.146414	+	0.102520i
$573$	−144186.	+	12614.7i	−0.439152	+	0.0384208i
$574$	172401.	−	473667.i	0.523257	−	1.43764i
$575$	353778.	−	217917.i	1.07003	−	0.659106i
$576$	7332.55	−	6152.74i	0.0221009	−	0.0185449i
$577$	−22750.5	+	84906.2i	−0.0683345	+	0.255028i	−0.991639	−	0.129040i	$-0.958810\pi$
$577$	−22750.5	+	84906.2i	−0.0683345	+	0.255028i	0.923305	+	0.384068i	$0.125477\pi$
$578$	−15064.2	−	56220.5i	−0.0450911	−	0.168282i
$579$	−74777.9	+	13185.4i	−0.223057	+	0.0393310i
$580$	31737.0	+	3719.28i	0.0943429	+	0.0110561i
$581$	95716.9	−	165786.i	0.283554	−	0.491130i
$582$	75530.9	−	281885.i	0.222986	−	0.832197i
$583$	34800.3	−	397770.i	0.102387	−	1.17029i
$584$	114513.	+	314623.i	0.335761	+	0.922496i
$585$	−20452.4	+	2989.50i	−0.0597631	+	0.00873548i
$586$	−338480.	−	284019.i	−0.985685	−	0.827088i
$587$	37888.2	−	26529.6i	0.109958	−	0.0769935i	−0.517304	−	0.855802i	$-0.673064\pi$
$587$	37888.2	−	26529.6i	0.109958	−	0.0769935i	0.627262	+	0.778808i	$0.284175\pi$
$588$	421.438	−	421.438i	0.00121893	−	0.00121893i
$589$	135000.	+	12251.7i	0.389137	+	0.0353155i
$590$	79720.1	+	147958.i	0.229015	+	0.425043i
$591$	−111140.	+	630307.i	−0.318197	+	1.80458i
$592$	−11842.8	−	135364.i	−0.0337919	−	0.386243i
$593$	254816.	−	118823.i	0.724632	−	0.337901i	−0.0250622	−	0.999686i	$-0.507978\pi$
$593$	254816.	−	118823.i	0.724632	−	0.337901i	0.749694	+	0.661784i	$0.230201\pi$
$594$	90447.4	+	248502.i	0.256344	+	0.704300i
$595$	295927.	−	127544.i	0.835894	−	0.360268i
$596$	17876.7	+	30963.4i	0.0503264	+	0.0871679i
$597$	−176830.	+	47381.4i	−0.496143	+	0.132941i
$598$	662322.	+	463763.i	1.85211	+	1.29686i
$599$	1111.61	−	196.006i	0.00309811	−	0.000546281i	−0.172099	−	0.985080i	$-0.555055\pi$
$599$	1111.61	−	196.006i	0.00309811	−	0.000546281i	0.175197	+	0.984533i	$0.443944\pi$
$600$	143786.	+	286736.i	0.399407	+	0.796489i
$601$	218046.	+	377667.i	0.603669	+	1.04559i	0.992260	+	0.124175i	$0.0396285\pi$
$601$	218046.	+	377667.i	0.603669	+	1.04559i	−0.388591	+	0.921410i	$0.627038\pi$
$602$	−502713.	−	43981.7i	−1.38716	−	0.121361i
$603$	915.273	−	1962.81i	0.00251719	−	0.00539813i
$604$	−14911.1	+	40968.0i	−0.0408730	+	0.112298i
$605$	162207.	−	106615.i	0.443157	−	0.291277i
$606$	33654.2	−	190862.i	0.0916419	−	0.519727i
$607$	−171750.	−	171750.i	−0.466143	−	0.466143i	0.434520	−	0.900662i	$-0.356918\pi$
$607$	−171750.	−	171750.i	−0.466143	−	0.466143i	−0.900662	+	0.434520i	$0.856918\pi$
$608$	73705.0	−	87262.6i	0.199384	−	0.236059i
$609$		−	220678.i		−	0.595010i
$610$	192398.	+	581214.i	0.517059	+	1.56198i
$611$	337153.	+	282905.i	0.903119	+	0.757807i
$612$	815.041	+	1747.86i	0.00217609	+	0.00466664i
$613$	−20425.9	+	43803.4i	−0.0543575	+	0.116570i	−0.931610	−	0.363458i	$-0.881596\pi$
$613$	−20425.9	+	43803.4i	−0.0543575	+	0.116570i	0.877253	+	0.480028i	$0.159374\pi$
$614$	178706.	+	212973.i	0.474026	+	0.564922i
$615$	279122.	−	452219.i	0.737979	−	1.19563i
$616$	−117340.	+	203239.i	−0.309233	+	0.535607i
$617$	−227064.	+	324281.i	−0.596455	+	0.851826i	−0.997948	−	0.0640362i	$-0.979603\pi$
$617$	−227064.	+	324281.i	−0.596455	+	0.851826i	0.401492	+	0.915862i	$0.368492\pi$
$618$	−340333.	−	238304.i	−0.891103	−	0.623957i
$619$	−448318.	−	258837.i	−1.17005	−	0.675529i	−0.216359	−	0.976314i	$-0.569418\pi$
$619$	−448318.	−	258837.i	−1.17005	−	0.675529i	−0.953692	+	0.300784i	$0.902752\pi$
$620$	5391.44	+	22779.1i	0.0140256	+	0.0592587i
$621$	377656.	−	316891.i	0.979294	−	0.821725i
$622$	−236540.	−	110301.i	−0.611398	−	0.285100i
$623$	−512301.	+	238890.i	−1.31993	+	0.615491i
$624$	−465308.	+	554533.i	−1.19501	+	1.42416i
$625$	380205.	−	89622.9i	0.973324	−	0.229435i
$626$	−215186.			−0.549119
$627$	−131517.	−	229508.i	−0.334539	−	0.583798i
$628$	59203.1	−	59203.1i	0.150115	−	0.150115i
$629$	−122208.	−	21548.6i	−0.308887	−	0.0544651i
$630$	12797.1	−	8411.25i	0.0322427	−	0.0211924i
$631$	−386373.	−	140628.i	−0.970394	−	0.353195i	−0.192296	−	0.981337i	$-0.561593\pi$
$631$	−386373.	−	140628.i	−0.970394	−	0.353195i	−0.778098	+	0.628142i	$0.783815\pi$
$632$	−280914.	−	130992.i	−0.703297	−	0.327953i
$633$	9534.87	−	108984.i	0.0237962	−	0.271992i
$634$	−147487.	+	85151.8i	−0.366924	+	0.211844i
$635$	3281.34	−	111608.i	0.00813775	−	0.276787i
$636$	18422.6	+	104480.i	0.0455447	+	0.258297i
$637$	−4387.84	+	6266.48i	−0.0108136	+	0.0154435i
$638$	47310.8	+	176566.i	0.116230	+	0.433777i
$639$	−14402.5	+	8315.28i	−0.0352725	+	0.0203646i
$640$	−444706.	−	176827.i	−1.08571	−	0.431706i
$641$	195256.	−	71067.4i	0.475213	−	0.172964i	−0.0932991	−	0.995638i	$-0.529741\pi$
$641$	195256.	−	71067.4i	0.475213	−	0.172964i	0.568513	+	0.822675i	$0.307519\pi$
$642$	158394.	+	339677.i	0.384298	+	0.824131i
$643$	447954.	−	39190.9i	1.08346	−	0.0947902i	0.468586	−	0.883418i	$-0.344764\pi$
$643$	447954.	−	39190.9i	1.08346	−	0.0947902i	0.614871	+	0.788628i	$0.289208\pi$
$644$	−79544.5	−	14025.8i	−0.191796	−	0.0338187i
$645$	−509626.	−	152740.i	−1.22499	−	0.367143i
$646$	−234477.	−	337187.i	−0.561870	−	0.807990i
$647$	−551265.	−	551265.i	−1.31690	−	1.31690i	−0.916219	−	0.400678i	$-0.868774\pi$
$647$	−551265.	−	551265.i	−1.31690	−	1.31690i	−0.400678	−	0.916219i	$-0.631226\pi$
$648$	210407.	+	300492.i	0.501083	+	0.715621i
$649$	−83328.1	+	99306.5i	−0.197834	+	0.235770i
$650$	453546.	+	609991.i	1.07348	+	1.44376i
$651$	151911.	−	55291.1i	0.358449	−	0.130465i
$652$	−51225.7	−	4481.67i	−0.120502	−	0.0105425i
$653$	−719093.	−	192680.i	−1.68639	−	0.451868i	−0.716938	−	0.697137i	$-0.754457\pi$
$653$	−719093.	−	192680.i	−1.68639	−	0.451868i	−0.969455	+	0.245269i	$0.921124\pi$
$654$	487896.	+	281687.i	1.14070	+	0.658584i
$655$	−69844.4	−	8185.12i	−0.162798	−	0.0190784i
$656$	121012.	+	686293.i	0.281204	+	1.59478i
$657$	16277.9	−	4361.64i	0.0377109	−	0.0101046i
$658$	−314969.	−	84395.7i	−0.727472	−	0.194926i
$659$	−56797.0	−	67688.0i	−0.130784	−	0.155862i	0.696678	−	0.717384i	$-0.254661\pi$
$659$	−56797.0	−	67688.0i	−0.130784	−	0.155862i	−0.827462	+	0.561522i	$0.810216\pi$
$660$	30377.4	−	34114.0i	0.0697370	−	0.0783150i
$661$	589596.	+	214596.i	1.34943	+	0.491154i	0.912771	−	0.408471i	$-0.133938\pi$
$661$	589596.	+	214596.i	1.34943	+	0.491154i	0.436663	+	0.899625i	$0.356160\pi$
$662$	−33064.3	−	377926.i	−0.0754472	−	0.862365i
$663$	379188.	+	541536.i	0.862635	+	1.23197i
$664$			228209.i			0.517603i
$665$	−320913.	+	300624.i	−0.725677	+	0.679799i
$666$	−5897.29			−0.0132955
$667$	279143.	−	195458.i	0.627443	−	0.439340i
$668$	−127516.	+	11156.2i	−0.285767	+	0.0250014i
$669$	−171463.	+	471090.i	−0.383105	+	1.05257i
$670$	−79510.7	+	4606.76i	−0.177123	+	0.0102623i
$671$	−361750.	+	303544.i	−0.803459	+	0.674182i
$672$	35256.9	−	131580.i	0.0780737	−	0.291375i
$673$	−29735.8	−	110976.i	−0.0656523	−	0.245018i	0.925299	−	0.379238i	$-0.123814\pi$
$673$	−29735.8	−	110976.i	−0.0656523	−	0.245018i	−0.990952	+	0.134220i	$0.957147\pi$
$674$	−577198.	+	101776.i	−1.27059	+	0.224039i
$675$	430831.	−	170855.i	0.945581	−	0.374991i
$676$	−64111.0	+	111043.i	−0.140294	+	0.242996i
$677$	84441.0	−	315138.i	0.184237	−	0.687580i	−0.810556	−	0.585661i	$-0.800835\pi$
$677$	84441.0	−	315138.i	0.184237	−	0.687580i	0.994793	−	0.101919i	$-0.0324983\pi$
$678$	−65176.2	+	744968.i	−0.141785	+	1.62061i
$679$	−127981.	−	351624.i	−0.277591	−	0.762675i
$680$	−229490.	+	308064.i	−0.496303	+	0.666228i
$681$	−688373.	−	577613.i	−1.48433	−	1.24550i
$682$	−109691.	+	76806.8i	−0.235833	+	0.165132i
$683$	47082.9	−	47082.9i	0.100930	−	0.100930i	−0.654838	−	0.755769i	$-0.727263\pi$
$683$	47082.9	−	47082.9i	0.100930	−	0.100930i	0.755769	+	0.654838i	$0.227263\pi$
$684$	−1854.83	−	1866.89i	−0.00396454	−	0.00399031i
$685$	−308193.	+	166055.i	−0.656812	+	0.353893i
$686$	88343.4	−	501020.i	0.187727	−	1.06465i
$687$	33419.5	+	381986.i	0.0708086	+	0.809346i
$688$	632300.	−	294846.i	1.33582	−	0.622901i
$689$	−465741.	−	1.27961e6i	−0.981083	−	2.69550i
$690$	−586861.	−	233351.i	−1.23264	−	0.490131i
$691$	188388.	+	326298.i	0.394546	+	0.683373i	0.993043	−	0.117752i	$-0.0375687\pi$
$691$	188388.	+	326298.i	0.394546	+	0.683373i	−0.598497	+	0.801125i	$0.704235\pi$
$692$	87033.3	−	23320.5i	0.181749	−	0.0486996i
$693$	9675.88	+	6775.12i	0.0201476	+	0.0141075i
$694$	−243688.	+	42968.8i	−0.505959	+	0.0892143i
$695$	440784.	−	415605.i	0.912549	−	0.860422i
$696$	131536.	+	227827.i	0.271535	+	0.470312i
$697$	634004.	+	55468.2i	1.30505	+	0.114177i
$698$	165974.	−	355933.i	0.340667	−	0.730562i
$699$	−35321.5	+	97045.1i	−0.0722912	+	0.198618i
$700$	−66815.9	−	36079.2i	−0.136359	−	0.0736310i
$701$	17099.2	−	96974.4i	0.0347968	−	0.197343i	−0.962454	−	0.271446i	$-0.912498\pi$
$701$	17099.2	−	96974.4i	0.0347968	−	0.197343i	0.997251	+	0.0741031i	$0.0236094\pi$
$702$	637727.	+	637727.i	1.29408	+	1.29408i
$703$	166858.	−	28864.6i	0.337626	−	0.0584057i
$704$		−	271514.i		−	0.547831i
$705$	−307164.	−	154381.i	−0.618006	−	0.310609i
$706$	−616679.	−	517455.i	−1.23723	−	1.03816i
$707$	−105022.	−	225221.i	−0.210108	−	0.450579i
$708$	14556.8	−	31217.2i	0.0290402	−	0.0622770i
$709$	−15103.5	−	17999.7i	−0.0300459	−	0.0358073i	0.750812	−	0.660516i	$-0.229662\pi$
$709$	−15103.5	−	17999.7i	−0.0300459	−	0.0358073i	−0.780858	+	0.624708i	$0.785218\pi$
$710$	520434.	+	321226.i	1.03240	+	0.637228i
$711$	−7800.39	+	13510.7i	−0.0154304	+	0.0267262i
$712$	386506.	−	551987.i	0.762423	−	1.08885i
$713$	204489.	+	143185.i	0.402246	+	0.281656i
$714$	−424175.	−	244897.i	−0.832048	−	0.480383i
$715$	−307949.	+	498923.i	−0.602375	+	0.975936i
$716$	2161.72	−	1813.90i	0.00421671	−	0.00353824i
$717$	222600.	+	103800.i	0.432999	+	0.201911i
$718$	−764017.	+	356267.i	−1.48202	+	0.691078i
$719$	−269509.	+	321188.i	−0.521333	+	0.621301i	−0.960895	−	0.276911i	$-0.910689\pi$
$719$	−269509.	+	321188.i	−0.521333	+	0.621301i	0.439562	+	0.898212i	$0.355134\pi$
$720$	−9507.62	+	18916.9i	−0.0183403	+	0.0364910i
$721$	−532728.			−1.02479
$722$	456989.	+	324419.i	0.876661	+	0.622346i
$723$	98586.5	−	98586.5i	0.188600	−	0.188600i
$724$	8770.22	+	1546.43i	0.0167314	+	0.00295020i
$725$	306960.	−	91695.0i	0.583991	−	0.174449i
$726$	−277242.	−	100908.i	−0.525999	−	0.191448i
$727$	745839.	+	347790.i	1.41116	+	0.658035i	0.970823	−	0.239798i	$-0.0770811\pi$
$727$	745839.	+	347790.i	1.41116	+	0.658035i	0.440337	+	0.897832i	$0.354859\pi$
$728$	−69755.4	+	797308.i	−0.131618	+	1.50440i
$729$	475632.	−	274606.i	0.894985	−	0.516720i
$730$	−425149.	−	450906.i	−0.797803	−	0.846136i
$731$	−110639.	−	627464.i	−0.207049	−	1.17423i
$732$	71968.1	−	102781.i	0.134313	−	0.191819i
$733$	−216629.	−	808469.i	−0.403188	−	1.50472i	−0.807373	−	0.590041i	$-0.799111\pi$
$733$	−216629.	−	808469.i	−0.403188	−	1.50472i	0.404185	−	0.914677i	$-0.367555\pi$
$734$	660336.	−	381245.i	1.22567	−	0.707639i
$735$	2207.82	−	5552.52i	0.00408686	−	0.0102782i
$736$	197668.	−	71945.2i	0.364905	−	0.132815i
$737$	−25962.2	−	55676.1i	−0.0477976	−	0.102502i
$738$	30129.7	−	2636.01i	0.0553200	−	0.00483988i
$739$	671907.	+	118475.i	1.23033	+	0.216940i	0.750765	−	0.660569i	$-0.229685\pi$
$739$	671907.	+	118475.i	1.23033	+	0.216940i	0.479561	+	0.877509i	$0.340796\pi$
$740$	13870.4	+	25743.0i	0.0253295	+	0.0470106i
$741$	−737291.	−	519824.i	−1.34277	−	0.946716i
$742$	713392.	+	713392.i	1.29575	+	1.29575i
$743$	−536933.	−	766820.i	−0.972619	−	1.38904i	−0.920648	−	0.390395i	$-0.872338\pi$
$743$	−536933.	−	766820.i	−0.972619	−	1.38904i	−0.0519712	−	0.998649i	$-0.516550\pi$
$744$	−123876.	+	147629.i	−0.223790	+	0.266702i
$745$	287460.	+	214141.i	0.517922	+	0.385823i
$746$	−393236.	+	143126.i	−0.706602	+	0.257182i
$747$	11442.7	+	1001.10i	0.0205062	+	0.00179406i
$748$	52840.4	+	14158.5i	0.0944414	+	0.0253055i
$749$	416185.	+	240284.i	0.741861	+	0.428314i
$750$	−454478.	−	382058.i	−0.807961	−	0.679214i
$751$	119129.	+	675614.i	0.211221	+	1.19789i	0.887345	+	0.461107i	$0.152547\pi$
$751$	119129.	+	675614.i	0.211221	+	1.19789i	−0.676124	+	0.736788i	$0.736341\pi$
$752$	435451.	−	116679.i	0.770023	−	0.206327i
$753$	457694.	+	122639.i	0.807207	+	0.216291i
$754$	400716.	+	477554.i	0.704845	+	0.840001i
$755$	25282.3	+	436361.i	0.0443530	+	0.765513i
$756$	−84662.2	−	30814.5i	−0.148131	−	0.0539153i
$757$	−23963.5	−	273904.i	−0.0418175	−	0.477977i	−0.988012	−	0.154378i	$-0.950663\pi$
$757$	−23963.5	−	273904.i	−0.0418175	−	0.477977i	0.946194	−	0.323599i	$-0.104893\pi$
$758$	128692.	+	183791.i	0.223981	+	0.319878i
$759$		−	487135.i		−	0.845601i
$760$	152121.	−	501643.i	0.263367	−	0.868496i
$761$	−60826.0			−0.105032			−0.0525158	−	0.998620i	$-0.516724\pi$
$761$	−60826.0			−0.105032			−0.0525158	+	0.998620i	$0.516724\pi$
$762$	−139020.	+	97342.7i	−0.239423	+	0.167646i
$763$	719624.	−	62959.0i	1.23611	−	0.108146i
$764$	−13970.0	+	38382.2i	−0.0239336	+	0.0657572i
$765$	14439.9	+	12858.3i	0.0246741	+	0.0219715i
$766$	648820.	−	544424.i	1.10577	−	0.927855i
$767$	−114426.	+	427044.i	−0.194507	+	0.725909i
$768$	68461.2	+	255501.i	0.116071	+	0.433181i
$769$	411246.	−	72513.7i	0.695422	−	0.122622i	0.185247	−	0.982692i	$-0.440692\pi$
$769$	411246.	−	72513.7i	0.695422	−	0.122622i	0.510176	+	0.860070i	$0.329580\pi$
$770$	50560.2	−	431434.i	0.0852760	−	0.727668i
$771$	175438.	−	303867.i	0.295131	−	0.511181i
$772$	−5546.03	+	20698.1i	−0.00930567	+	0.0347292i
$773$	−46400.8	+	530363.i	−0.0776544	+	0.887594i	0.853052	+	0.521826i	$0.174749\pi$
$773$	−46400.8	+	530363.i	−0.0776544	+	0.887594i	−0.930706	+	0.365768i	$0.880806\pi$
$774$	−10356.0	−	28452.9i	−0.0172866	−	0.0474946i
$775$	140031.	+	188332.i	0.233141	+	0.313560i
$776$	341713.	+	286732.i	0.567464	+	0.476159i
$777$	165426.	−	115832.i	0.274006	−	0.191861i
$778$	621484.	−	621484.i	1.02676	−	1.02676i
$779$	−839588.	+	222055.i	−1.38354	+	0.365919i
$780$	44724.3	−	149225.i	0.0735114	−	0.245274i
$781$	−81915.8	+	464568.i	−0.134297	+	0.761635i
$782$	−65919.3	−	753461.i	−0.107795	−	1.23210i
$783$	344494.	−	160640.i	0.561900	−	0.262018i
$784$	2679.99	+	7363.21i	0.00436015	+	0.0119794i
$785$	310153.	−	780012.i	0.503311	−	1.26579i
$786$	53443.4	+	92566.7i	0.0865066	+	0.149834i
$787$	−763984.	+	204709.i	−1.23349	+	0.330512i	−0.815937	−	0.578141i	$-0.803778\pi$
$787$	−763984.	+	204709.i	−1.23349	+	0.330512i	−0.417551	+	0.908653i	$0.637112\pi$
$788$	147955.	+	103599.i	0.238274	+	0.166841i
$789$	−284360.	+	50140.4i	−0.456788	+	0.0805441i
$790$	573469.	+	16860.4i	0.918873	+	0.0270155i
$791$	479433.	+	830403.i	0.766259	+	1.32720i
$792$	−14027.6	−	1227.26i	−0.0223632	−	0.00195653i
$793$	−680625.	+	1.45961e6i	−1.08233	+	2.32107i
$794$	426200.	−	1.17097e6i	0.676039	−	1.85740i
$795$	584214.	+	888841.i	0.924352	+	1.40634i
$796$	−8971.11	+	50877.7i	−0.0141586	+	0.0802974i
$797$	555867.	+	555867.i	0.875092	+	0.875092i	0.993022	−	0.117929i	$-0.0376257\pi$
$797$	555867.	+	555867.i	0.875092	+	0.875092i	−0.117929	+	0.993022i	$0.537626\pi$
$798$	657832.	+	118192.i	1.03302	+	0.185601i
$799$		−	411704.i		−	0.644899i
$800$	197677.	−	5631.73i	0.308870	−	0.00879958i
$801$	−25981.7	−	21801.2i	−0.0404951	−	0.0339794i
$802$	272229.	+	583797.i	0.423239	+	0.907639i
$803$	202019.	−	433231.i	0.313301	−	0.671875i
$804$	10491.9	+	12503.8i	0.0162309	+	0.0193432i
$805$	−788022.	+	186512.i	−1.21604	+	0.287816i
$806$	−228341.	+	395498.i	−0.351490	+	0.608799i
$807$	14547.4	−	20775.9i	0.0223378	−	0.0319016i
$808$	242668.	+	169918.i	0.371698	+	0.260266i
$809$	−266895.	−	154092.i	−0.407797	−	0.235442i	0.282046	−	0.959401i	$-0.408987\pi$
$809$	−266895.	−	154092.i	−0.407797	−	0.235442i	−0.689843	+	0.723959i	$0.742320\pi$
$810$	−577799.	−	356634.i	−0.880656	−	0.543566i
$811$	−367191.	+	308110.i	−0.558277	+	0.468450i	−0.877732	−	0.479151i	$-0.840945\pi$
$811$	−367191.	+	308110.i	−0.558277	+	0.468450i	0.319455	+	0.947601i	$0.396500\pi$
$812$	−56441.5	−	26319.1i	−0.0856025	−	0.0399171i
$813$	−89180.2	+	41585.4i	−0.134923	+	0.0629158i
$814$	−107525.	+	128144.i	−0.162279	+	0.193396i
$815$	−489418.	+	162011.i	−0.736826	+	0.243909i
$816$	677150.			1.01696
$817$	432276.	+	754357.i	0.647616	+	1.13014i
$818$	282815.	−	282815.i	0.422664	−	0.422664i
$819$	39671.8	+	6995.22i	0.0591445	+	0.0104288i
$820$	−82372.0	−	125323.i	−0.122504	−	0.186382i
$821$	−955347.	−	347718.i	−1.41734	−	0.515870i	−0.484067	−	0.875031i	$-0.660841\pi$
$821$	−955347.	−	347718.i	−1.41734	−	0.515870i	−0.933276	+	0.359161i	$0.883063\pi$
$822$	482254.	+	224879.i	0.713727	+	0.332816i
$823$	4390.89	−	50188.1i	0.00648265	−	0.0740970i	−0.992264	−	0.124144i	$-0.960382\pi$
$823$	4390.89	−	50188.1i	0.00648265	−	0.0740970i	0.998747	+	0.0500469i	$0.0159371\pi$
$824$	549985.	−	317534.i	0.810021	−	0.467666i
$825$	144314.	−	434631.i	0.212031	−	0.638576i
$826$	−56878.8	−	322576.i	−0.0833662	−	0.472793i
$827$	455030.	−	649850.i	0.665318	−	0.950172i	−0.334651	−	0.942342i	$-0.608619\pi$
$827$	455030.	−	649850.i	0.665318	−	0.950172i	0.999969	−	0.00783046i	$-0.00249254\pi$
$828$	−1254.35	−	4681.30i	−0.00182961	−	0.00682819i
$829$	−500171.	+	288774.i	−0.727795	+	0.420193i	−0.817615	−	0.575765i	$-0.804704\pi$
$829$	−500171.	+	288774.i	−0.727795	+	0.420193i	0.0898198	+	0.995958i	$0.471371\pi$
$830$	−167190.	−	387914.i	−0.242691	−	0.563091i
$831$	387513.	−	141043.i	0.561157	−	0.204245i
$832$	−391332.	−	839214.i	−0.565325	−	1.21234i
$833$	7128.78	−	623.688i	0.0102737	−	0.000898829i
$834$	−906830.	−	159899.i	−1.30375	−	0.229886i
$835$	−1.12977e6	+	608723.i	−1.62038	+	0.873066i
$836$	−74385.2	+	6265.16i	−0.106432	+	0.00896437i
$837$	196896.	+	196896.i	0.281051	+	0.281051i
$838$	−179795.	−	256774.i	−0.256030	−	0.365648i
$839$	387814.	−	462179.i	0.550935	−	0.656578i	−0.416667	−	0.909059i	$-0.636802\pi$
$839$	387814.	−	462179.i	0.550935	−	0.656578i	0.967602	+	0.252481i	$0.0812465\pi$
$840$	−90417.0	−	618580.i	−0.128142	−	0.876673i
$841$	−417732.	+	152042.i	−0.590617	+	0.214967i
$842$	−1.01885e6	−	89137.7i	−1.43709	−	0.125729i
$843$	−50867.6	−	13629.9i	−0.0715790	−	0.0191795i
$844$	−26737.0	−	15436.6i	−0.0375343	−	0.0216704i
$845$	−149627.	+	1.27678e6i	−0.209554	+	1.78814i
$846$	−3397.49	−	19268.1i	−0.00474698	−	0.0269215i
$847$	−365411.	+	97911.6i	−0.509348	+	0.136479i
$848$	−1.34728e6	−	361003.i	−1.87356	−	0.502018i
$849$	400411.	+	477191.i	0.555508	+	0.662029i
$850$	164398.	−	691780.i	0.227541	−	0.957481i
$851$	293040.	+	106658.i	0.404639	+	0.147276i
$852$	−10924.2	−	124864.i	−0.0150490	−	0.172011i
$853$	175604.	+	250788.i	0.241343	+	0.344674i	0.921490	−	0.388402i	$-0.126973\pi$
$853$	175604.	+	250788.i	0.241343	+	0.344674i	−0.680147	+	0.733076i	$0.738084\pi$
$854$		−	1.19319e6i		−	1.63604i
$855$	−24485.6	−	9828.08i	−0.0334949	−	0.0134442i
$856$	−572889.			−0.781849
$857$	371576.	−	260180.i	0.505925	−	0.354252i	−0.292580	−	0.956241i	$-0.594514\pi$
$857$	371576.	−	260180.i	0.505925	−	0.354252i	0.798505	+	0.601989i	$0.205625\pi$
$858$	887770.	−	77669.8i	1.20594	−	0.105506i
$859$	−131653.	+	361714.i	−0.178420	+	0.490206i	−0.996374	−	0.0850778i	$-0.972886\pi$
$859$	−131653.	+	361714.i	−0.178420	+	0.490206i	0.817954	+	0.575284i	$0.195108\pi$
$860$	−99846.0	+	112127.i	−0.135000	+	0.151606i
$861$	−793397.	+	665739.i	−1.07025	+	0.898045i
$862$	108358.	−	404399.i	0.145831	−	0.544247i
$863$	−293967.	−	1.09710e6i	−0.394709	−	1.47307i	−0.822275	−	0.569090i	$-0.807295\pi$
$863$	−293967.	−	1.09710e6i	−0.394709	−	1.47307i	0.427566	−	0.903984i	$-0.359371\pi$
$864$	231072.	−	40744.1i	0.309542	−	0.0545805i
$865$	708774.	−	560076.i	0.947274	−	0.748540i
$866$	−666681.	+	1.15473e6i	−0.888960	+	1.53972i
$867$	−30952.6	+	115517.i	−0.0411773	+	0.153676i
$868$	3976.16	−	45447.7i	0.00527745	−	0.0603215i
$869$	151352.	+	415837.i	0.200424	+	0.550660i
$870$	−390496.	−	290898.i	−0.515915	−	0.384328i
$871$	−160491.	−	134668.i	−0.211551	−	0.177513i
$872$	−705409.	+	493933.i	−0.927701	+	0.649583i
$873$	15876.0	−	15876.0i	0.0208312	−	0.0208312i
$874$	433147.	+	936797.i	0.567038	+	1.22637i
$875$	−758342.	−	67042.0i	−0.990488	−	0.0875651i
$876$	−22055.1	+	125081.i	−0.0287409	+	0.162998i
$877$	18157.9	+	207545.i	0.0236084	+	0.269845i	0.998820	+	0.0485697i	$0.0154663\pi$
$877$	18157.9	+	207545.i	0.0236084	+	0.269845i	−0.975211	+	0.221275i	$0.928978\pi$
$878$	−1.19488e6	+	557183.i	−1.55002	+	0.722784i
$879$	310514.	+	853129.i	0.401886	+	1.10417i
$880$	237698.	+	551505.i	0.306944	+	0.712171i
$881$	359686.	+	622995.i	0.463417	+	0.802662i	0.999129	−	0.0417389i	$-0.0132898\pi$
$881$	359686.	+	622995.i	0.463417	+	0.802662i	−0.535711	+	0.844401i	$0.679956\pi$
$882$	328.487	−	88.0178i	0.000422261	−	0.000113144i
$883$	−709617.	−	496879.i	−0.910128	−	0.637279i	0.0218623	−	0.999761i	$-0.493040\pi$
$883$	−709617.	−	496879.i	−0.910128	−	0.637279i	−0.931991	+	0.362482i	$0.881929\pi$
$884$	183729.	−	32396.4i	0.235112	−	0.0414565i
$885$	10148.6	−	345180.i	0.0129574	−	0.440717i
$886$	−274105.	−	474764.i	−0.349180	−	0.604798i
$887$	777719.	+	68041.6i	0.988498	+	0.0864824i	0.569921	−	0.821699i	$-0.306974\pi$
$887$	777719.	+	68041.6i	0.988498	+	0.0864824i	0.418576	+	0.908182i	$0.362529\pi$
$888$	−101742.	+	218187.i	−0.129025	+	0.276696i
$889$	−74426.7	+	204486.i	−0.0941727	+	0.258737i
$890$	−252593.	+	1.22144e6i	−0.318890	+	1.54202i
$891$	90945.0	−	515775.i	0.114557	−	0.649687i
$892$	100039.	+	100039.i	0.125730	+	0.125730i
$893$	190438.	+	528543.i	0.238808	+	0.662792i
$894$		−	544835.i		−	0.681694i
$895$	12705.0	−	25278.7i	0.0158610	−	0.0315579i
$896$	714491.	+	599529.i	0.889981	+	0.746783i
$897$	−702106.	−	1.50567e6i	−0.872605	−	1.87131i
$898$	−338137.	+	725137.i	−0.419315	+	0.899223i
$899$	123719.	+	147443.i	0.153080	+	0.182434i
$900$	267.681	−	4548.34i	0.000330470	−	0.00561524i
$901$	−636905.	+	1.10315e6i	−0.784558	+	1.35889i
$902$	492077.	−	702758.i	0.604811	−	0.863760i
$903$	849357.	+	594726.i	1.04163	+	0.729360i
$904$	−989928.	−	571535.i	−1.21134	−	0.699369i
$905$	86883.8	−	20564.0i	0.106082	−	0.0251079i
$906$	508931.	−	427044.i	0.620015	−	0.520255i
$907$	642684.	+	299689.i	0.781237	+	0.364297i	0.771969	−	0.635660i	$-0.219272\pi$
$907$	642684.	+	299689.i	0.781237	+	0.364297i	0.00926829	+	0.999957i	$0.497050\pi$
$908$	−229832.	+	107172.i	−0.278765	+	0.129990i
$909$	9584.41	−	11422.3i	0.0115995	−	0.0138237i
$910$	−465550.	−	1.40638e6i	−0.562190	−	1.69832i
$911$	263695.			0.317735			0.158868	−	0.987300i	$-0.449216\pi$
$911$	263695.			0.317735			0.158868	+	0.987300i	$0.449216\pi$
$912$	−869321.	+	313222.i	−1.04518	+	0.376585i
$913$	230387.	−	230387.i	0.276386	−	0.276386i
$914$	991409.	+	174812.i	1.18675	+	0.209257i
$915$	254754.	−	1.23189e6i	0.304284	−	1.47139i
$916$	101684.	+	37010.0i	0.121189	+	0.0441091i
$917$	124212.	+	57921.2i	0.147716	+	0.0688809i
$918$	73528.8	−	840438.i	0.0872514	−	0.997288i
$919$	−1.01193e6	+	584236.i	−1.19817	+	0.691763i	−0.960147	−	0.279497i	$-0.909832\pi$
$919$	−1.01193e6	+	584236.i	−1.19817	+	0.691763i	−0.238022	+	0.971260i	$0.576499\pi$
$920$	702378.	−	662257.i	0.829842	−	0.782440i
$921$	−99195.3	−	562564.i	−0.116942	−	0.663213i
$922$	−238683.	+	340874.i	−0.280775	+	0.400989i
$923$	416389.	+	1.55398e6i	0.488760	+	1.82408i
$924$	−77097.7	+	44512.4i	−0.0903020	+	0.0521359i
$925$	229858.	+	181975.i	0.268644	+	0.212681i
$926$	−601306.	+	218857.i	−0.701251	+	0.255235i
$927$	−13508.8	−	28969.8i	−0.0157202	−	0.0337121i
$928$	161569.	−	14135.5i	0.187613	−	0.0164140i
$929$	−314405.	−	55438.1i	−0.364299	−	0.0642357i	−0.0114973	−	0.999934i	$-0.503660\pi$
$929$	−314405.	−	55438.1i	−0.364299	−	0.0642357i	−0.352802	+	0.935698i	$0.614771\pi$
$930$	102410.	−	341696.i	0.118407	−	0.395070i
$931$	−8863.39	+	4098.17i	−0.0102259	+	0.00472814i
$932$	20608.1	+	20608.1i	0.0237249	+	0.0237249i
$933$	307589.	+	439282.i	0.353352	+	0.504638i
$934$	−657702.	+	783818.i	−0.753937	+	0.898507i
$935$	542684.	−	79323.3i	0.620760	−	0.0907356i
$936$	−45126.5	+	16424.7i	−0.0515086	+	0.0187476i
$937$	−1.03560e6	−	90602.8i	−1.17954	−	0.103196i	−0.519527	−	0.854454i	$-0.673892\pi$
$937$	−1.03560e6	−	90602.8i	−1.17954	−	0.103196i	−0.660008	+	0.751258i	$0.729447\pi$
$938$	149931.	+	40174.0i	0.170407	+	0.0456604i
$939$	382909.	+	221072.i	0.434274	+	0.250728i
$940$	−76118.9	+	60149.5i	−0.0861464	+	0.0680732i
$941$	−210583.	−	1.19428e6i	−0.237818	−	1.34873i	−0.836597	−	0.547819i	$-0.815458\pi$
$941$	−210583.	−	1.19428e6i	−0.237818	−	1.34873i	0.598779	−	0.800914i	$-0.295653\pi$
$942$	−1.23239e6	+	330219.i	−1.38883	+	0.372135i
$943$	−1.54484e6	−	413938.i	−1.73724	−	0.465492i
$944$	291084.	+	346901.i	0.326644	+	0.389279i
$945$	−901762.	+	52247.1i	−1.00978	+	0.0585057i
$946$	−807080.	−	293753.i	−0.901850	−	0.328246i
$947$	−35652.2	−	407507.i	−0.0397545	−	0.454396i	−0.989818	−	0.142339i	$-0.954538\pi$
$947$	−35652.2	−	407507.i	−0.0397545	−	0.454396i	0.950063	−	0.312057i	$-0.101018\pi$
$948$	−67440.8	−	96315.4i	−0.0750423	−	0.107171i
$949$		−	1.63023e6i		−	1.81016i
$950$	108936.	+	964147.i	0.120704	+	1.06831i
$951$	349924.			0.386912
$952$	613279.	−	429423.i	0.676682	−	0.473818i
$953$	599864.	−	52481.3i	0.660492	−	0.0577855i	0.248018	−	0.968755i	$-0.420221\pi$
$953$	599864.	−	52481.3i	0.660492	−	0.0577855i	0.412473	+	0.910970i	$0.364665\pi$
$954$	−20704.2	+	56884.4i	−0.0227490	+	0.0625024i
$955$	23686.6	+	408820.i	0.0259714	+	0.448255i
$956$	53096.7	−	44553.4i	0.0580967	−	0.0487489i
$957$	97209.7	−	362791.i	0.106142	−	0.396126i
$958$	−303455.	−	1.13251e6i	−0.330646	−	1.23399i
$959$	671918.	−	118477.i	0.730599	−	0.128824i
$960$	448427.	+	567482.i	0.486574	+	0.615757i
$961$	391261.	−	677684.i	0.423662	−	0.733805i
$962$	−147654.	+	551051.i	−0.159549	+	0.595445i
$963$	−2513.13	+	28725.2i	−0.00270996	+	0.0309750i
$964$	−13457.0	−	36972.8i	−0.0144809	−	0.0397858i
$965$	31071.7	+	212575.i	0.0333665	+	0.228274i
$966$	942886.	+	791175.i	1.01043	+	0.847849i
$967$	−1.18161e6	+	827375.i	−1.26364	+	0.884808i	−0.996878	−	0.0789550i	$-0.974842\pi$
$967$	−1.18161e6	+	827375.i	−1.26364	+	0.884808i	−0.266759	+	0.963763i	$0.585953\pi$
$968$	318888.	−	318888.i	0.340320	−	0.340320i
$969$	70824.8	+	840891.i	0.0754289	+	0.895555i
$970$	−790914.	−	237046.i	−0.840593	−	0.251935i
$971$	−153887.	+	872738.i	−0.163216	+	0.925647i	0.787668	+	0.616100i	$0.211288\pi$
$971$	−153887.	+	872738.i	−0.163216	+	0.925647i	−0.950884	+	0.309547i	$0.899823\pi$
$972$	−925.897	−	10583.1i	−0.000980009	−	0.0112016i
$973$	−1.07008e6	+	498985.i	−1.13029	+	0.527063i
$974$	−230975.	−	634599.i	−0.243471	−	0.668931i
$975$	−180377.	−	1.55139e6i	−0.189745	−	1.63196i
$976$	824806.	+	1.42861e6i	0.865869	+	1.49973i
$977$	13817.7	−	3702.44i	0.0144759	−	0.00387882i	−0.251574	−	0.967838i	$-0.580948\pi$
$977$	13817.7	−	3702.44i	0.0144759	−	0.00387882i	0.266050	+	0.963959i	$0.414281\pi$
$978$	641881.	+	449450.i	0.671084	+	0.469898i
$979$	−947449.	+	167061.i	−0.988531	+	0.174305i
$980$	−1156.82	−	1226.90i	−0.00120452	−	0.00127749i
$981$	21671.8	+	37536.7i	0.0225194	+	0.0390048i
$982$	−348175.	−	30461.4i	−0.361056	−	0.0315883i
$983$	−58303.0	+	125031.i	−0.0603370	+	0.129393i	−0.934164	−	0.356844i	$-0.883853\pi$
$983$	−58303.0	+	125031.i	−0.0603370	+	0.129393i	0.873827	+	0.486237i	$0.161631\pi$
$984$	422283.	−	1.16021e6i	0.436127	−	1.19825i
$985$	1.77332e6	+	366722.i	1.82774	+	0.377976i
$986$	101263.	−	574291.i	0.104159	−	0.590716i
$987$	473761.	+	473761.i	0.486323	+	0.486323i
$988$	−220885.	+	126576.i	−0.226283	+	0.129669i
$989$			1.60114e6i			1.63695i
$990$	24743.5	−	8190.78i	0.0252459	−	0.00835708i
$991$	−953502.	−	800083.i	−0.970899	−	0.814681i	0.0117923	−	0.999930i	$-0.496246\pi$
$991$	−953502.	−	800083.i	−0.970899	−	0.814681i	−0.982692	+	0.185249i	$0.940691\pi$
$992$	50211.9	+	107680.i	0.0510251	+	0.109424i
$993$	−329428.	+	706461.i	−0.334089	+	0.716457i
$994$	−766163.	−	913077.i	−0.775440	−	0.924134i
$995$	119296.	+	504029.i	0.120498	+	0.509108i
$996$	−43285.0	+	74971.8i	−0.0436334	+	0.0755752i
$997$	664867.	−	949528.i	0.668874	−	0.955251i	−0.331059	−	0.943610i	$-0.607406\pi$
$997$	664867.	−	949528.i	0.668874	−	0.955251i	0.999932	−	0.0116405i	$-0.00370536\pi$
$998$	451160.	+	315906.i	0.452970	+	0.317173i
$999$	301243.	+	173923.i	0.301846	+	0.174271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.5.q.a.17.10	✓	456
5.3	odd	4	inner	95.5.q.a.93.29	yes	456
19.9	even	9	inner	95.5.q.a.47.29	yes	456
95.28	odd	36	inner	95.5.q.a.28.10	yes	456

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.5.q.a.17.10	✓	456	1.1	even	1	trivial
95.5.q.a.28.10	yes	456	95.28	odd	36	inner
95.5.q.a.47.29	yes	456	19.9	even	9	inner
95.5.q.a.93.29	yes	456	5.3	odd	4	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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	95.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.52270 + 2.46662i) q^{2} +(8.80247 - 0.770116i) q^{3} +(0.852857 - 2.34320i) q^{4} +(-1.44605 - 24.9581i) q^{5} +(-29.1088 + 24.4252i) q^{6} +(-12.6105 + 47.0630i) q^{7} +(-15.0330 - 56.1041i) q^{8} +(-2.87906 + 0.507657i) q^{9} +(66.6562 + 84.3531i) q^{10} +(-41.4630 + 71.8159i) q^{11} +(5.70270 - 21.2828i) q^{12} +(-24.6485 + 281.734i) q^{13} +(-71.6635 - 196.894i) q^{14} +(-31.9495 - 218.580i) q^{15} +(221.907 + 186.202i) q^{16} +(216.706 - 151.739i) q^{17} +(8.88987 - 8.88987i) q^{18} +(-208.018 + 295.042i) q^{19} +(-59.7153 - 17.8973i) q^{20} +(-74.7595 + 423.982i) q^{21} +(-31.0811 - 355.259i) q^{22} +(-602.524 + 280.962i) q^{23} +(-175.535 - 482.277i) q^{24} +(-620.818 + 72.1813i) q^{25} +(-608.101 - 1053.26i) q^{26} +(-716.288 + 191.929i) q^{27} +(99.5233 + 69.6869i) q^{28} +(-504.794 + 89.0088i) q^{29} +(651.701 + 691.182i) q^{30} +(-187.749 - 325.191i) q^{31} +(-315.207 - 27.5770i) q^{32} +(-309.670 + 664.089i) q^{33} +(-389.107 + 1069.06i) q^{34} +(1192.84 + 246.679i) q^{35} +(-1.26589 + 7.17919i) q^{36} +(-331.686 - 331.686i) q^{37} +(5.02829 - 1552.44i) q^{38} +2498.94i q^{39} +(-1378.52 + 456.326i) q^{40} +(1842.87 + 1546.35i) q^{41} +(-782.447 - 1677.96i) q^{42} +(1017.84 - 2182.76i) q^{43} +(132.917 + 158.405i) q^{44} +(16.8334 + 71.1220i) q^{45} +(1429.48 - 2475.94i) q^{46} +(892.625 - 1274.80i) q^{47} +(2096.73 + 1468.15i) q^{48} +(23.4258 + 13.5249i) q^{49} +(2008.91 - 1785.59i) q^{50} +(1790.69 - 1502.57i) q^{51} +(639.139 + 298.035i) q^{52} +(-4363.88 + 2034.91i) q^{53} +(2049.85 - 2442.91i) q^{54} +(1852.35 + 930.989i) q^{55} +2830.00 q^{56} +(-1603.85 + 2757.29i) q^{57} +(1558.69 - 1558.69i) q^{58} +(1539.52 + 271.459i) q^{59} +(-539.425 - 111.553i) q^{60} +(5351.19 + 1947.67i) q^{61} +(1463.50 + 682.443i) q^{62} +(12.4146 - 141.899i) q^{63} +(-2835.52 + 1637.09i) q^{64} +(7067.21 + 207.781i) q^{65} +(-547.181 - 3103.22i) q^{66} +(-424.907 + 606.830i) q^{67} +(-170.737 - 637.200i) q^{68} +(-5087.33 + 2937.17i) q^{69} +(-4810.48 + 2073.31i) q^{70} +(5345.56 - 1945.62i) q^{71} +(71.7627 + 153.896i) q^{72} +(-5742.46 + 502.400i) q^{73} +(1986.57 + 350.286i) q^{74} +(-5409.14 + 1113.48i) q^{75} +(513.934 + 739.056i) q^{76} +(-2857.01 - 2857.01i) q^{77} +(-6163.93 - 8803.00i) q^{78} +(3430.16 - 4087.90i) q^{79} +(4326.38 - 5807.65i) q^{80} +(-5934.77 + 2160.08i) q^{81} +(-10306.1 - 901.669i) q^{82} +(-3795.13 - 1016.90i) q^{83} +(929.717 + 536.773i) q^{84} +(-4100.50 - 5189.17i) q^{85} +(1798.50 + 10199.8i) q^{86} +(-4374.89 + 1172.25i) q^{87} +(4652.48 + 1246.63i) q^{88} +(7457.30 + 8887.26i) q^{89} +(-234.730 - 209.019i) q^{90} +(-12948.4 - 4712.84i) q^{91} +(144.484 + 1651.46i) q^{92} +(-1903.09 - 2717.89i) q^{93} +6692.50i q^{94} +(7664.50 + 4765.09i) q^{95} -2795.84 q^{96} +(-6291.03 + 4405.03i) q^{97} +(-115.883 + 10.1384i) q^{98} +(82.9166 - 227.812i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 456 q - 12 q^{2} - 12 q^{3} - 12 q^{5} + 84 q^{6} - 96 q^{7} - 6 q^{8} - 12 q^{10} - 12 q^{11} - 6 q^{12} - 12 q^{13} - 534 q^{15} + 4092 q^{16} - 1362 q^{17} - 3864 q^{18} - 2364 q^{20} - 4776 q^{21} + 2004 q^{22}+ \cdots + 123726 q^{98}+O(q^{100}) \) 456 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 + 84 * q^6 - 96 * q^7 - 6 * q^8 - 12 * q^10 - 12 * q^11 - 6 * q^12 - 12 * q^13 - 534 * q^15 + 4092 * q^16 - 1362 * q^17 - 3864 * q^18 - 2364 * q^20 - 4776 * q^21 + 2004 * q^22 + 1968 * q^23 + 3252 * q^25 + 7332 * q^26 - 6 * q^27 - 9648 * q^28 - 6 * q^30 - 12 * q^31 + 5922 * q^32 + 16494 * q^33 - 1794 * q^35 + 9048 * q^36 - 24 * q^37 - 15222 * q^38 - 9786 * q^40 - 5640 * q^41 + 7764 * q^42 - 19032 * q^43 - 6144 * q^45 - 12 * q^46 - 4332 * q^47 + 29328 * q^48 + 18426 * q^50 - 10944 * q^51 + 84 * q^52 + 1878 * q^53 + 27018 * q^55 - 48 * q^56 - 14202 * q^57 + 16536 * q^58 - 84108 * q^60 - 14688 * q^61 - 46536 * q^62 - 46098 * q^63 - 13236 * q^65 + 42408 * q^66 + 44748 * q^67 + 20154 * q^68 + 37620 * q^70 - 24 * q^71 + 82680 * q^72 - 10542 * q^73 + 90024 * q^75 - 21600 * q^76 + 20328 * q^77 + 63426 * q^78 - 32688 * q^80 + 41976 * q^81 - 184332 * q^82 - 43476 * q^83 - 51396 * q^85 + 11316 * q^86 - 59286 * q^87 - 1254 * q^88 - 9294 * q^90 - 33312 * q^91 + 163884 * q^92 - 106566 * q^93 - 11424 * q^95 - 200208 * q^96 + 12168 * q^97 + 123726 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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