LMFDB - Embedded newform 92.5.g.a.3.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [92,5,Mod(3,92)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(92, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 16])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("92.3"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	92.g (of order $22$, degree $10$, 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:	$9.51003660371$
Analytic rank:	$0$
Dimension:	$460$
Relative dimension:	$46$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			3.6
Character	$\chi$	$=$	92.3
Dual form			92.5.g.a.31.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.79675 + 1.25886i) q^{2} +(-8.69828 - 3.97237i) q^{3} +(12.8306 - 9.55912i) q^{4} +(17.8389 - 20.5871i) q^{5} +(38.0258 + 4.13220i) q^{6} +(-0.355839 - 0.553696i) q^{7} +(-36.6808 + 52.4454i) q^{8} +(6.83659 + 7.88985i) q^{9} +(-41.8134 + 100.621i) q^{10} +(177.855 + 25.5717i) q^{11} +(-149.576 + 32.1801i) q^{12} +(85.7828 + 55.1293i) q^{13} +(2.04805 + 1.65429i) q^{14} +(-236.947 + 108.210i) q^{15} +(73.2466 - 245.298i) q^{16} +(-456.893 - 134.156i) q^{17} +(-35.8890 - 21.3495i) q^{18} +(-173.008 - 589.211i) q^{19} +(32.0877 - 434.668i) q^{20} +(0.895700 + 6.22973i) q^{21} +(-707.461 + 126.805i) q^{22} +(-164.776 - 502.683i) q^{23} +(527.392 - 310.475i) q^{24} +(-16.6587 - 115.864i) q^{25} +(-395.095 - 101.324i) q^{26} +(190.092 + 647.395i) q^{27} +(-9.85846 - 3.70273i) q^{28} +(-144.384 - 42.3950i) q^{29} +(763.407 - 709.129i) q^{30} +(-449.764 + 205.400i) q^{31} +(30.6958 + 1023.54i) q^{32} +(-1445.45 - 928.935i) q^{33} +(1903.59 - 65.8069i) q^{34} +(-17.7468 - 2.55160i) q^{35} +(163.137 + 35.8794i) q^{36} +(-900.755 - 1039.53i) q^{37} +(1398.60 + 2019.29i) q^{38} +(-527.169 - 820.291i) q^{39} +(425.356 + 1690.72i) q^{40} +(-808.382 + 932.923i) q^{41} +(-11.2431 - 22.5251i) q^{42} +(-1101.78 - 503.166i) q^{43} +(2526.42 - 1372.04i) q^{44} +284.386 q^{45} +(1258.42 + 1701.13i) q^{46} +1008.92i q^{47} +(-1611.53 + 1842.70i) q^{48} +(997.231 - 2183.63i) q^{49} +(209.105 + 418.934i) q^{50} +(3441.27 + 2981.88i) q^{51} +(1627.63 - 112.668i) q^{52} +(-3691.19 + 2372.18i) q^{53} +(-1536.71 - 2218.70i) q^{54} +(3699.18 - 3205.35i) q^{55} +(42.0913 + 1.64793i) q^{56} +(-835.693 + 5812.37i) q^{57} +(601.559 - 20.7958i) q^{58} +(-725.160 + 1128.37i) q^{59} +(-2005.77 + 3653.40i) q^{60} +(-2143.38 - 4693.34i) q^{61} +(1449.07 - 1346.04i) q^{62} +(1.93585 - 6.59291i) q^{63} +(-1405.03 - 3847.48i) q^{64} +(2665.22 - 782.580i) q^{65} +(6657.41 + 1707.31i) q^{66} +(1583.80 - 227.717i) q^{67} +(-7144.61 + 2646.20i) q^{68} +(-563.576 + 5027.02i) q^{69} +(70.5921 - 12.6529i) q^{70} +(857.416 - 123.278i) q^{71} +(-664.558 + 69.1415i) q^{72} +(6655.10 - 1954.11i) q^{73} +(4728.55 + 2812.90i) q^{74} +(-315.352 + 1073.99i) q^{75} +(-7852.13 - 5906.11i) q^{76} +(-49.1288 - 107.577i) q^{77} +(3034.15 + 2450.81i) q^{78} +(332.381 - 517.194i) q^{79} +(-3743.34 - 5883.77i) q^{80} +(1038.56 - 7223.35i) q^{81} +(1894.81 - 4559.71i) q^{82} +(2573.69 - 2230.12i) q^{83} +(71.0430 + 71.3688i) q^{84} +(-10912.3 + 7012.94i) q^{85} +(4816.60 + 523.411i) q^{86} +(1087.48 + 942.310i) q^{87} +(-7864.98 + 8389.67i) q^{88} +(1203.01 - 2634.23i) q^{89} +(-1079.74 + 358.002i) q^{90} -67.1148i q^{91} +(-6919.37 - 4874.59i) q^{92} +4728.10 q^{93} +(-1270.09 - 3830.62i) q^{94} +(-15216.4 - 6949.11i) q^{95} +(3798.88 - 9024.97i) q^{96} +(11078.7 - 12785.5i) q^{97} +(-1037.36 + 9546.07i) q^{98} +(1014.16 + 1578.07i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 460 q - 3 q^{2} - 43 q^{4} - 18 q^{5} - 44 q^{6} + 144 q^{8} + 1116 q^{9} - 77 q^{10} - 156 q^{12} - 18 q^{13} + 253 q^{14} - 795 q^{16} - 18 q^{17} - 676 q^{18} + 113 q^{20} + 266 q^{21} - 818 q^{22} + 1006 q^{24}+ \cdots + 52545 q^{98}+O(q^{100}) $ 460 * q - 3 * q^2 - 43 * q^4 - 18 * q^5 - 44 * q^6 + 144 * q^8 + 1116 * q^9 - 77 * q^10 - 156 * q^12 - 18 * q^13 + 253 * q^14 - 795 * q^16 - 18 * q^17 - 676 * q^18 + 113 * q^20 + 266 * q^21 - 818 * q^22 + 1006 * q^24 - 4768 * q^25 + 1100 * q^26 + 499 * q^28 + 654 * q^29 - 1401 * q^30 - 2163 * q^32 - 342 * q^33 - 5959 * q^34 - 3317 * q^36 - 3666 * q^37 + 4444 * q^38 + 23023 * q^40 - 1266 * q^41 + 23419 * q^42 + 7066 * q^44 + 5464 * q^45 - 8019 * q^46 - 14166 * q^48 + 14620 * q^49 - 25358 * q^50 - 36264 * q^52 - 9138 * q^53 - 6990 * q^54 - 7592 * q^56 - 3862 * q^57 + 31769 * q^58 + 34819 * q^60 + 7534 * q^61 - 9320 * q^62 + 4562 * q^64 + 9106 * q^65 + 6490 * q^66 - 4842 * q^68 - 22 * q^69 - 4258 * q^70 - 27815 * q^72 - 18 * q^73 - 202 * q^74 + 73926 * q^76 - 56086 * q^77 - 328 * q^78 - 47488 * q^80 + 9788 * q^81 - 42110 * q^82 - 111651 * q^84 + 117026 * q^85 - 55391 * q^86 - 44639 * q^88 + 44574 * q^89 - 4626 * q^90 + 18106 * q^92 - 85004 * q^93 + 55547 * q^94 + 150069 * q^96 - 34146 * q^97 + 52545 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$-1$

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 $

$2$	−3.79675	+	1.25886i	−0.949187	+	0.314714i
$2$	−3.79675	+	1.25886i	−0.949187	+	0.314714i
$3$	−8.69828	−	3.97237i	−0.966475	−	0.441374i	−0.131291	−	0.991344i	$-0.541912\pi$
$3$	−8.69828	−	3.97237i	−0.966475	−	0.441374i	−0.835185	+	0.549969i	$0.814639\pi$
$4$	12.8306	−	9.55912i	0.801910	−	0.597445i
$5$	17.8389	−	20.5871i	0.713554	−	0.823486i	−0.276962	−	0.960881i	$-0.589328\pi$
$5$	17.8389	−	20.5871i	0.713554	−	0.823486i	0.990516	+	0.137395i	$0.0438731\pi$
$6$	38.0258	+	4.13220i	1.05627	+	0.114783i
$7$	−0.355839	−	0.553696i	−0.00726202	−	0.0112999i	0.837604	−	0.546279i	$-0.183956\pi$
$7$	−0.355839	−	0.553696i	−0.00726202	−	0.0112999i	−0.844866	+	0.534979i	$0.820320\pi$
$8$	−36.6808	+	52.4454i	−0.573138	+	0.819459i
$9$	6.83659	+	7.88985i	0.0844024	+	0.0974055i
$10$	−41.8134	+	100.621i	−0.418134	+	1.00621i
$11$	177.855	+	25.5717i	1.46987	+	0.211336i	0.830267	−	0.557366i	$-0.188188\pi$
$11$	177.855	+	25.5717i	1.46987	+	0.211336i	0.639608	+	0.768702i	$0.279097\pi$
$12$	−149.576	+	32.1801i	−1.03872	+	0.223473i
$13$	85.7828	+	55.1293i	0.507591	+	0.326209i	0.769246	−	0.638953i	$-0.220632\pi$
$13$	85.7828	+	55.1293i	0.507591	+	0.326209i	−0.261655	+	0.965161i	$0.584268\pi$
$14$	2.04805	+	1.65429i	0.0104493	+	0.00844028i
$15$	−236.947	+	108.210i	−1.05310	+	0.480934i
$16$	73.2466	−	245.298i	0.286120	−	0.958194i
$17$	−456.893	−	134.156i	−1.58095	−	0.464208i	−0.630783	−	0.775960i	$-0.717266\pi$
$17$	−456.893	−	134.156i	−1.58095	−	0.464208i	−0.950164	+	0.311752i	$0.899084\pi$
$18$	−35.8890	−	21.3495i	−0.110769	−	0.0658934i
$19$	−173.008	−	589.211i	−0.479247	−	1.63216i	−0.744239	−	0.667913i	$-0.767188\pi$
$19$	−173.008	−	589.211i	−0.479247	−	1.63216i	0.264993	−	0.964250i	$-0.414630\pi$
$20$	32.0877	−	434.668i	0.0802192	−	1.08667i
$21$	0.895700	+	6.22973i	0.00203107	+	0.0141264i
$22$	−707.461	+	126.805i	−1.46170	+	0.261993i
$23$	−164.776	−	502.683i	−0.311486	−	0.950251i
$23$	−164.776	−	502.683i	−0.311486	−	0.950251i
$24$	527.392	−	310.475i	0.915612	−	0.539018i
$25$	−16.6587	−	115.864i	−0.0266539	−	0.185382i
$26$	−395.095	−	101.324i	−0.584461	−	0.149887i
$27$	190.092	+	647.395i	0.260758	+	0.888059i
$28$	−9.85846	−	3.70273i	−0.0125746	−	0.00472287i
$29$	−144.384	−	42.3950i	−0.171681	−	0.0504102i	0.194762	−	0.980851i	$-0.437607\pi$
$29$	−144.384	−	42.3950i	−0.171681	−	0.0504102i	−0.366443	+	0.930440i	$0.619425\pi$
$30$	763.407	−	709.129i	0.848230	−	0.787921i
$31$	−449.764	+	205.400i	−0.468017	+	0.213736i	−0.635442	−	0.772149i	$-0.719182\pi$
$31$	−449.764	+	205.400i	−0.468017	+	0.213736i	0.167425	+	0.985885i	$0.446455\pi$
$32$	30.6958	+	1023.54i	0.0299764	+	0.999551i
$33$	−1445.45	−	928.935i	−1.32732	−	0.853016i
$34$	1903.59	−	65.8069i	1.64671	−	0.0569264i
$35$	−17.7468	−	2.55160i	−0.0144872	−	0.00208294i
$36$	163.137	+	35.8794i	0.125878	+	0.0276847i
$37$	−900.755	−	1039.53i	−0.657966	−	0.759333i	0.324478	−	0.945893i	$-0.394811\pi$
$37$	−900.755	−	1039.53i	−0.657966	−	0.759333i	−0.982443	+	0.186560i	$0.940266\pi$
$38$	1398.60	+	2019.29i	0.968559	+	1.39840i
$39$	−527.169	−	820.291i	−0.346594	−	0.539310i
$40$	425.356	+	1690.72i	0.265848	+	1.05670i
$41$	−808.382	+	932.923i	−0.480894	+	0.554981i	−0.943409	−	0.331630i	$-0.892401\pi$
$41$	−808.382	+	932.923i	−0.480894	+	0.554981i	0.462516	+	0.886611i	$0.346947\pi$
$42$	−11.2431	−	22.5251i	−0.00637363	−	0.0127694i
$43$	−1101.78	−	503.166i	−0.595879	−	0.272129i	0.0945602	−	0.995519i	$-0.469856\pi$
$43$	−1101.78	−	503.166i	−0.595879	−	0.272129i	−0.690439	+	0.723390i	$0.742583\pi$
$44$	2526.42	−	1372.04i	1.30497	−	0.708696i
$45$	284.386			0.140438
$46$	1258.42	+	1701.13i	0.594715	+	0.803936i
$47$			1008.92i			0.456732i	0.973575	+	0.228366i	$0.0733383\pi$
$47$			1008.92i			0.456732i	−0.973575	+	0.228366i	$0.926662\pi$
$48$	−1611.53	+	1842.70i	−0.699450	+	0.799785i
$49$	997.231	−	2183.63i	0.415340	−	0.909468i
$50$	209.105	+	418.934i	0.0836419	+	0.167574i
$51$	3441.27	+	2981.88i	1.32306	+	1.14643i
$52$	1627.63	−	112.668i	0.601934	−	0.0416673i
$53$	−3691.19	+	2372.18i	−1.31406	+	0.844494i	−0.994668	−	0.103129i	$-0.967114\pi$
$53$	−3691.19	+	2372.18i	−1.31406	+	0.844494i	−0.319390	+	0.947623i	$0.603478\pi$
$54$	−1536.71	−	2218.70i	−0.526992	−	0.760870i
$55$	3699.18	−	3205.35i	1.22287	−	1.05962i
$56$	42.0913	+	1.64793i	0.0134220	+	0.000525488i
$57$	−835.693	+	5812.37i	−0.257216	+	1.78897i
$58$	601.559	−	20.7958i	0.178822	−	0.00618187i
$59$	−725.160	+	1128.37i	−0.208319	+	0.324151i	−0.929653	−	0.368437i	$-0.879893\pi$
$59$	−725.160	+	1128.37i	−0.208319	+	0.324151i	0.721333	+	0.692588i	$0.243530\pi$
$60$	−2005.77	+	3653.40i	−0.557159	+	1.01483i
$61$	−2143.38	−	4693.34i	−0.576022	−	1.26131i	−0.943529	−	0.331291i	$-0.892516\pi$
$61$	−2143.38	−	4693.34i	−0.576022	−	1.26131i	0.367507	−	0.930021i	$-0.380212\pi$
$62$	1449.07	−	1346.04i	0.376969	−	0.350167i
$63$	1.93585	−	6.59291i	0.000487743	−	0.00166110i
$64$	−1405.03	−	3847.48i	−0.343026	−	0.939326i
$65$	2665.22	−	782.580i	0.630822	−	0.185226i
$66$	6657.41	+	1707.31i	1.52833	+	0.391946i
$67$	1583.80	−	227.717i	0.352819	−	0.0507277i	0.0363732	−	0.999338i	$-0.488420\pi$
$67$	1583.80	−	227.717i	0.352819	−	0.0507277i	0.316446	+	0.948611i	$0.397510\pi$
$68$	−7144.61	+	2646.20i	−1.54512	+	0.572275i
$69$	−563.576	+	5027.02i	−0.118373	+	1.05588i
$70$	70.5921	−	12.6529i	0.0144066	−	0.00258222i
$71$	857.416	−	123.278i	0.170088	−	0.0244550i	−0.0567443	−	0.998389i	$-0.518072\pi$
$71$	857.416	−	123.278i	0.170088	−	0.0244550i	0.226833	+	0.973934i	$0.427163\pi$
$72$	−664.558	+	69.1415i	−0.128194	+	0.0133375i
$73$	6655.10	−	1954.11i	1.24885	−	0.366694i	0.410514	−	0.911854i	$-0.365349\pi$
$73$	6655.10	−	1954.11i	1.24885	−	0.366694i	0.838332	+	0.545160i	$0.183531\pi$
$74$	4728.55	+	2812.90i	0.863505	+	0.513677i
$75$	−315.352	+	1073.99i	−0.0560625	+	0.190931i
$76$	−7852.13	−	5906.11i	−1.35944	−	1.02253i
$77$	−49.1288	−	107.577i	−0.00828618	−	0.0181442i
$78$	3034.15	+	2450.81i	0.498711	+	0.402828i
$79$	332.381	−	517.194i	0.0532576	−	0.0828704i	−0.813604	−	0.581420i	$-0.802497\pi$
$79$	332.381	−	517.194i	0.0532576	−	0.0828704i	0.866861	+	0.498549i	$0.166134\pi$
$80$	−3743.34	−	5883.77i	−0.584897	−	0.919339i
$81$	1038.56	−	7223.35i	0.158293	−	1.10095i
$82$	1894.81	−	4559.71i	0.281798	−	0.678124i
$83$	2573.69	−	2230.12i	0.373594	−	0.323721i	−0.447745	−	0.894161i	$-0.647773\pi$
$83$	2573.69	−	2230.12i	0.373594	−	0.323721i	0.821339	+	0.570440i	$0.193227\pi$
$84$	71.0430	+	71.3688i	0.0100685	+	0.0101146i
$85$	−10912.3	+	7012.94i	−1.51036	+	0.970649i
$86$	4816.60	+	523.411i	0.651243	+	0.0707695i
$87$	1087.48	+	942.310i	0.143676	+	0.124496i
$88$	−7864.98	+	8389.67i	−1.01562	+	1.08338i
$89$	1203.01	−	2634.23i	0.151876	−	0.332563i	−0.818367	−	0.574697i	$-0.805120\pi$
$89$	1203.01	−	2634.23i	0.151876	−	0.332563i	0.970243	+	0.242134i	$0.0778474\pi$
$90$	−1079.74	+	358.002i	−0.133302	+	0.0441977i
$91$		−	67.1148i		−	0.00810467i
$92$	−6919.37	−	4874.59i	−0.817506	−	0.575920i
$93$	4728.10			0.546664
$94$	−1270.09	−	3830.62i	−0.143740	−	0.433524i
$95$	−15216.4	−	6949.11i	−1.68603	−	0.769985i
$96$	3798.88	−	9024.97i	0.412205	−	0.979272i
$97$	11078.7	−	12785.5i	1.17746	−	1.35886i	0.257772	−	0.966206i	$-0.417012\pi$
$97$	11078.7	−	12785.5i	1.17746	−	1.35886i	0.919686	−	0.392654i	$-0.128443\pi$
$98$	−1037.36	+	9546.07i	−0.108013	+	0.993968i
$99$	1014.16	+	1578.07i	0.103476	+	0.161011i
$100$	−1321.30	−	1327.35i	−0.132130	−	0.132735i
$101$	2597.39	+	2997.54i	0.254621	+	0.293848i	0.868641	−	0.495442i	$-0.164994\pi$
$101$	2597.39	+	2997.54i	0.254621	+	0.293848i	−0.614020	+	0.789290i	$0.710449\pi$
$102$	−16819.4	−	6989.36i	−1.61663	−	0.671796i
$103$	−14591.8	−	2097.98i	−1.37542	−	0.197755i	−0.585351	−	0.810780i	$-0.699043\pi$
$103$	−14591.8	−	2097.98i	−1.37542	−	0.197755i	−0.790064	+	0.613025i	$0.789953\pi$
$104$	−6037.86	+	2476.72i	−0.558234	+	0.228987i
$105$	144.231	+	92.6914i	0.0130821	+	0.00840738i
$106$	11028.3	−	13653.3i	0.981512	−	1.21513i
$107$	−13626.9	+	6223.21i	−1.19023	+	0.543559i	−0.909289	−	0.416166i	$-0.863374\pi$
$107$	−13626.9	+	6223.21i	−1.19023	+	0.543559i	−0.280940	+	0.959725i	$0.590646\pi$
$108$	8627.52	+	6489.33i	0.739670	+	0.556355i
$109$	11127.4	+	3267.29i	0.936569	+	0.275001i	0.714184	−	0.699958i	$-0.246798\pi$
$109$	11127.4	+	3267.29i	0.936569	+	0.275001i	0.222384	+	0.974959i	$0.428616\pi$
$110$	−10009.7	+	16826.6i	−0.827252	+	1.39063i
$111$	3705.63	+	12620.2i	0.300757	+	1.02429i
$112$	−161.884	+	46.7301i	−0.0129053	+	0.00372530i
$113$	1706.57	+	11869.4i	0.133649	+	0.929551i	0.940741	+	0.339125i	$0.110131\pi$
$113$	1706.57	+	11869.4i	0.133649	+	0.929551i	−0.807092	+	0.590426i	$0.798960\pi$
$114$	−4144.03	−	23120.1i	−0.318870	−	1.77902i
$115$	−13288.2	−	5575.02i	−1.00478	−	0.421552i
$116$	−2257.79	+	836.232i	−0.167790	+	0.0621457i
$117$	151.501	+	1053.71i	0.0110673	+	0.0769749i
$118$	1332.79	−	5197.01i	0.0957190	−	0.373241i
$119$	88.2988	+	300.718i	0.00623535	+	0.0212357i
$120$	3016.30	−	16396.0i	0.209465	−	1.13861i
$121$	16930.5	+	4971.24i	1.15638	+	0.339543i
$122$	14046.1	+	15121.2i	0.943705	+	1.01594i
$123$	10737.5	−	4903.63i	0.709726	−	0.324121i
$124$	−3807.28	+	6934.75i	−0.247612	+	0.451011i
$125$	11640.2	+	7480.72i	0.744975	+	0.478766i
$126$	0.949585	+	27.4686i	5.98126e−5	+	0.00173019i
$127$	17517.4	+	2518.62i	1.08608	+	0.156155i	0.662026	−	0.749481i	$-0.269697\pi$
$127$	17517.4	+	2518.62i	1.08608	+	0.156155i	0.424056	+	0.905636i	$0.360606\pi$
$128$	10178.0	+	12839.2i	0.621215	+	0.783640i
$129$	7584.83	+	8753.36i	0.455792	+	0.526012i
$130$	−9134.01	+	6326.39i	−0.540474	+	0.374342i
$131$	2204.82	+	3430.77i	0.128479	+	0.199917i	0.899533	−	0.436853i	$-0.143907\pi$
$131$	2204.82	+	3430.77i	0.128479	+	0.199917i	−0.771055	+	0.636769i	$0.780270\pi$
$132$	−27425.7	+	1898.48i	−1.57402	+	0.108958i
$133$	−264.681	+	305.458i	−0.0149630	+	0.0172683i
$134$	−5726.64	+	2858.37i	−0.318926	+	0.159187i
$135$	16719.0	+	7635.33i	0.917369	+	0.418948i
$136$	23795.1	−	19041.0i	1.28650	−	1.02947i
$137$	−20126.2			−1.07231			−0.536154	−	0.844120i	$-0.680123\pi$
$137$	−20126.2			−1.07231			−0.536154	+	0.844120i	$0.680123\pi$
$138$	−4188.55	−	19795.8i	−0.219941	−	1.03948i
$139$		−	17016.5i		−	0.880727i	−0.897820	−	0.440363i	$-0.854850\pi$
$139$		−	17016.5i		−	0.880727i	0.897820	−	0.440363i	$-0.145150\pi$
$140$	−252.092	+	136.905i	−0.0128619	+	0.00698495i
$141$	4007.81	−	8775.87i	0.201590	−	0.441420i
$142$	−3100.20	+	1547.42i	−0.153749	+	0.0767416i
$143$	13847.1	+	11998.6i	0.677155	+	0.586758i
$144$	2436.12	−	1099.10i	0.117483	−	0.0530042i
$145$	−3448.44	+	2216.18i	−0.164016	+	0.105407i
$146$	−22807.8	+	15797.1i	−1.06998	+	0.741091i
$147$	−17348.4	+	15032.5i	−0.802832	+	0.695658i
$148$	−21494.1	−	4727.29i	−0.981289	−	0.215819i
$149$	3522.54	−	24499.8i	0.158666	−	1.10355i	−0.742429	−	0.669924i	$-0.766327\pi$
$149$	3522.54	−	24499.8i	0.158666	−	1.10355i	0.901095	−	0.433621i	$-0.142764\pi$
$150$	−154.688	−	4474.65i	−0.00687502	−	0.198873i
$151$	9291.25	−	14457.5i	0.407493	−	0.634072i	−0.575481	−	0.817815i	$-0.695185\pi$
$151$	9291.25	−	14457.5i	0.407493	−	0.634072i	0.982974	+	0.183743i	$0.0588215\pi$
$152$	37247.5	+	12539.3i	1.61217	+	0.542732i
$153$	−2065.12	−	4521.99i	−0.0882192	−	0.193173i
$154$	321.953	+	346.596i	0.0135754	+	0.0146145i
$155$	−3794.67	+	12923.5i	−0.157947	+	0.537917i
$156$	−14605.1	−	5485.52i	−0.600145	−	0.225408i
$157$	−26022.6	+	7640.93i	−1.05573	+	0.309990i	−0.763129	−	0.646246i	$-0.776338\pi$
$157$	−26022.6	+	7640.93i	−1.05573	+	0.309990i	−0.292598	+	0.956235i	$0.594520\pi$
$158$	−610.891	+	2382.08i	−0.0244709	+	0.0954204i
$159$	41530.2	−	5971.14i	1.64274	−	0.236191i
$160$	21619.3	+	17626.8i	0.844505	+	0.688549i
$161$	−219.700	+	270.110i	−0.00847575	+	0.0104205i
$162$	5150.01	+	28732.6i	0.196236	+	1.09483i
$163$	1791.18	−	257.532i	0.0674160	−	0.00969296i	−0.108524	−	0.994094i	$-0.534613\pi$
$163$	1791.18	−	257.532i	0.0674160	−	0.00969296i	0.175940	+	0.984401i	$0.443703\pi$
$164$	−1454.08	+	19697.3i	−0.0540631	+	0.732352i
$165$	−44909.3	+	13186.6i	−1.64956	+	0.484355i
$166$	−6964.26	+	11707.1i	−0.252731	+	0.424847i
$167$	13579.4	−	46247.3i	0.486910	−	1.65826i	−0.239420	−	0.970916i	$-0.576957\pi$
$167$	13579.4	−	46247.3i	0.486910	−	1.65826i	0.726330	−	0.687347i	$-0.241225\pi$
$168$	−359.575	−	181.536i	−0.0127401	−	0.00643198i
$169$	−7545.21	−	16521.7i	−0.264179	−	0.578471i
$170$	32603.1	−	40363.4i	1.12814	−	1.39666i
$171$	3466.00	−	5393.20i	0.118532	−	0.184440i
$172$	−18946.3	+	4076.14i	−0.640423	+	0.137782i
$173$	2651.21	−	18439.5i	0.0885832	−	0.616110i	−0.896372	−	0.443302i	$-0.853807\pi$
$173$	2651.21	−	18439.5i	0.0885832	−	0.616110i	0.984956	−	0.172808i	$-0.0552839\pi$
$174$	−5315.13	−	2208.73i	−0.175556	−	0.0729530i
$175$	−58.2255	+	50.4527i	−0.00190124	+	0.00164744i
$176$	19299.9	−	41754.3i	0.623061	−	1.34796i
$177$	10790.0	−	6934.28i	0.344408	−	0.221337i
$178$	−1251.41	+	11515.9i	−0.0394967	+	0.363461i
$179$	18162.8	+	15738.2i	0.566863	+	0.491189i	0.890495	−	0.454994i	$-0.150359\pi$
$179$	18162.8	+	15738.2i	0.566863	+	0.491189i	−0.323632	+	0.946183i	$0.604904\pi$
$180$	3648.84	−	2718.48i	0.112618	−	0.0839038i
$181$	−10035.6	+	21974.9i	−0.306327	+	0.670763i	−0.998711	−	0.0507667i	$-0.983834\pi$
$181$	−10035.6	+	21974.9i	−0.306327	+	0.670763i	0.692383	+	0.721530i	$0.256561\pi$
$182$	84.4879	+	254.818i	0.00255065	+	0.00769284i
$183$			49338.3i			1.47327i
$184$	32407.5	+	9797.09i	0.957216	+	0.289375i
$185$	−37469.3			−1.09479
$186$	−17951.4	+	5952.00i	−0.518886	+	0.172043i
$187$	−77830.1	−	35543.8i	−2.22569	−	1.01644i
$188$	9644.39	+	12945.0i	0.272872	+	0.366258i
$189$	290.818	−	335.622i	0.00814137	−	0.00939564i
$190$	66520.9	+	7228.71i	1.84268	+	0.200241i
$191$	21883.8	+	34051.9i	0.599869	+	0.933414i	0.999857	+	0.0168939i	$0.00537775\pi$
$191$	21883.8	+	34051.9i	0.599869	+	0.933414i	−0.399988	+	0.916520i	$0.630986\pi$
$192$	−3062.24	+	39047.8i	−0.0830685	+	1.05924i
$193$	39371.0	+	45436.6i	1.05697	+	1.21981i	0.974775	+	0.223190i	$0.0716471\pi$
$193$	39371.0	+	45436.6i	1.05697	+	1.21981i	0.0821934	+	0.996616i	$0.473807\pi$
$194$	−25967.9	+	62489.8i	−0.689975	+	1.66037i
$195$	−26291.5	−	3780.15i	−0.691428	−	0.0994123i
$196$	−8078.56	−	37549.9i	−0.210291	−	0.977454i
$197$	24572.4	+	15791.7i	0.633162	+	0.406909i	0.817479	−	0.575958i	$-0.195371\pi$
$197$	24572.4	+	15791.7i	0.633162	+	0.406909i	−0.184317	+	0.982867i	$0.559007\pi$
$198$	−5837.09	−	4714.85i	−0.148890	−	0.120264i
$199$	−19347.8	+	8835.83i	−0.488568	+	0.223121i	−0.644439	−	0.764656i	$-0.722909\pi$
$199$	−19347.8	+	8835.83i	−0.488568	+	0.223121i	0.155871	+	0.987777i	$0.450182\pi$
$200$	6687.57	+	3376.31i	0.167189	+	0.0844077i
$201$	−14681.0	−	4310.72i	−0.363381	−	0.106698i
$202$	−13635.1	−	8111.17i	−0.334161	−	0.198784i
$203$	27.9035	+	95.0307i	0.000677122	+	0.00230607i
$204$	72657.5	+	5363.66i	1.74590	+	0.128885i
$205$	4785.60	+	33284.6i	0.113875	+	0.792018i
$206$	58042.3	−	10403.5i	1.36776	−	0.245156i
$207$	2839.59	−	4736.69i	0.0662696	−	0.110544i
$208$	19806.4	−	17004.3i	0.457803	−	0.393036i
$209$	−15703.2	−	109218.i	−0.359497	−	2.50036i
$210$	−664.292	−	170.360i	−0.0150633	−	0.00386304i
$211$	−5692.82	−	19388.0i	−0.127868	−	0.435479i	0.870526	−	0.492122i	$-0.163779\pi$
$211$	−5692.82	−	19388.0i	−0.127868	−	0.435479i	−0.998395	+	0.0566429i	$0.981960\pi$
$212$	−24684.1	+	65720.9i	−0.549218	+	1.46229i
$213$	−7947.75	−	2333.67i	−0.175180	−	0.0514375i
$214$	43903.9	−	40782.3i	0.958684	−	0.890521i
$215$	−30013.3	+	13706.6i	−0.649286	+	0.296519i
$216$	−40925.6	−	13777.5i	−0.877178	−	0.295300i
$217$	273.773	+	175.943i	0.00581395	+	0.00373640i
$218$	−46360.9	+	1602.69i	−0.975525	+	0.0337238i
$219$	−65650.4	−	9439.10i	−1.36883	−	0.196808i
$220$	16822.1	−	76487.3i	0.347565	−	1.58032i
$221$	−31797.7	−	36696.5i	−0.651045	−	0.751346i
$222$	−29956.4	−	43250.9i	−0.607832	−	0.877586i
$223$	−33972.6	−	52862.3i	−0.683154	−	1.06301i	−0.993659	−	0.112437i	$-0.964134\pi$
$223$	−33972.6	−	52862.3i	−0.683154	−	1.06301i	0.310505	−	0.950572i	$-0.399502\pi$
$224$	555.807	−	381.212i	0.0110772	−	0.00759749i
$225$	800.259	−	923.548i	0.0158076	−	0.0182429i
$226$	−21421.3	−	42916.9i	−0.419401	−	0.840256i
$227$	444.623	+	203.053i	0.00862860	+	0.00394055i	0.419725	−	0.907651i	$-0.362127\pi$
$227$	444.623	+	203.053i	0.00862860	+	0.00394055i	−0.411096	+	0.911592i	$0.634854\pi$
$228$	44838.7	+	82564.5i	0.862549	+	1.58827i
$229$	3769.85			0.0718875			0.0359437	−	0.999354i	$-0.488556\pi$
$229$	3769.85			0.0718875			0.0359437	+	0.999354i	$0.488556\pi$
$230$	57470.1	+	4438.99i	1.08639	+	0.0839129i
$231$			1130.89i			0.0211932i
$232$	7519.55	−	6017.19i	0.139706	−	0.111794i
$233$	−8601.84	+	18835.4i	−0.158445	+	0.346947i	−0.972160	−	0.234317i	$-0.924715\pi$
$233$	−8601.84	+	18835.4i	−0.158445	+	0.346947i	0.813715	+	0.581264i	$0.197442\pi$
$234$	−1901.68	−	3809.95i	−0.0347301	−	0.0695805i
$235$	20770.8	+	17998.0i	0.376112	+	0.325903i
$236$	1482.02	+	21409.5i	0.0266091	+	0.384400i
$237$	−4945.63	+	3178.36i	−0.0880490	+	0.0565857i
$238$	−713.809	−	1030.59i	−0.0126017	−	0.0181942i
$239$	55599.9	−	48177.6i	0.973371	−	0.843430i	−0.0143126	−	0.999898i	$-0.504556\pi$
$239$	55599.9	−	48177.6i	0.973371	−	0.843430i	0.987683	+	0.156467i	$0.0500105\pi$
$240$	9188.12	+	66048.6i	0.159516	+	1.14668i
$241$	−2366.92	+	16462.3i	−0.0407521	+	0.283437i	0.959248	+	0.282567i	$0.0911860\pi$
$241$	−2366.92	+	16462.3i	−0.0407521	+	0.283437i	−1.00000		0.000869972i	$0.999723\pi$
$242$	−70538.9	+	2438.52i	−1.20448	+	0.0416386i
$243$	−8179.98	+	12728.3i	−0.138529	+	0.215555i
$244$	−72364.9	−	39729.4i	−1.21548	−	0.667318i
$245$	−27165.3	−	59483.7i	−0.452566	−	0.990981i
$246$	−34594.4	+	32134.7i	−0.571657	+	0.531012i
$247$	17641.7	−	60082.0i	0.289165	−	0.984805i
$248$	5725.42	−	31122.3i	0.0930902	−	0.506021i
$249$	−31245.5	+	9174.51i	−0.503952	+	0.147974i
$250$	−53612.1	−	13749.0i	−0.857794	−	0.219984i
$251$	2475.57	−	355.933i	0.0392941	−	0.00564964i	−0.122640	−	0.992451i	$-0.539136\pi$
$251$	2475.57	−	355.933i	0.0392941	−	0.00564964i	0.161934	+	0.986802i	$0.448227\pi$
$252$	−38.1843	−	103.096i	−0.000601290	−	0.00162345i
$253$	−16451.8	−	93618.2i	−0.257022	−	1.46258i
$254$	−69679.7	+	12489.3i	−1.08004	+	0.193585i
$255$	122777.	−	17652.6i	1.88814	−	0.271474i
$256$	−54805.9	−	35934.4i	−0.836271	−	0.548316i
$257$	−88637.7	+	26026.4i	−1.34200	+	0.394046i	−0.872382	−	0.488824i	$-0.837426\pi$
$257$	−88637.7	+	26026.4i	−1.34200	+	0.394046i	−0.469616	+	0.882871i	$0.655608\pi$
$258$	−39816.9	−	23686.1i	−0.598175	−	0.355839i
$259$	−255.058	+	868.649i	−0.00380224	+	0.0129493i
$260$	26715.5	−	35518.1i	0.395200	−	0.525416i
$261$	−652.605	−	1429.01i	−0.00958008	−	0.0209775i
$262$	−12690.0	−	10250.2i	−0.184867	−	0.149324i
$263$	−27892.0	+	43400.9i	−0.403245	+	0.627461i	−0.982187	−	0.187908i	$-0.939829\pi$
$263$	−27892.0	+	43400.9i	−0.403245	+	0.627461i	0.578942	+	0.815369i	$0.303466\pi$
$264$	101739.	−	41733.1i	1.45975	−	0.598788i
$265$	−17010.1	+	118308.i	−0.242223	+	1.68470i
$266$	620.399	−	1492.94i	0.00876814	−	0.0210999i
$267$	−20928.3	+	18134.4i	−0.293569	+	0.254379i
$268$	18144.3	−	18061.5i	0.252622	−	0.251469i
$269$	44338.2	−	28494.4i	0.612736	−	0.393781i	−0.197146	−	0.980374i	$-0.563167\pi$
$269$	44338.2	−	28494.4i	0.612736	−	0.393781i	0.809882	+	0.586593i	$0.199531\pi$
$270$	−73089.7	−	7942.54i	−1.00260	−	0.108951i
$271$	85111.8	+	73749.8i	1.15891	+	1.00421i	0.999857	+	0.0169358i	$0.00539109\pi$
$271$	85111.8	+	73749.8i	1.15891	+	1.00421i	0.159058	+	0.987269i	$0.449154\pi$
$272$	−66374.0	+	102248.i	−0.897141	+	1.38203i
$273$	−266.605	+	583.783i	−0.00357719	+	0.00783296i
$274$	76413.9	−	25335.9i	1.01782	−	0.337470i
$275$		−	21032.9i		−	0.278121i
$276$	40822.9	+	69886.8i	0.535903	+	0.917439i
$277$	102576.			1.33686			0.668430	−	0.743775i	$-0.266967\pi$
$277$	102576.			1.33686			0.668430	+	0.743775i	$0.266967\pi$
$278$	21421.4	+	64607.4i	0.277177	+	0.835974i
$279$	−4695.43	−	2144.33i	−0.0603208	−	0.0275476i
$280$	784.786	−	837.142i	0.0100100	−	0.0106778i
$281$	74786.3	−	86308.0i	0.947129	−	1.09305i	−0.0484222	−	0.998827i	$-0.515419\pi$
$281$	74786.3	−	86308.0i	0.947129	−	1.09305i	0.995552	−	0.0942185i	$-0.0300352\pi$
$282$	−4169.06	+	38365.0i	−0.0524252	+	0.482433i
$283$	19132.2	+	29770.3i	0.238887	+	0.371715i	0.939909	−	0.341424i	$-0.110909\pi$
$283$	19132.2	+	29770.3i	0.238887	+	0.371715i	−0.701023	+	0.713139i	$0.747273\pi$
$284$	9822.70	−	9777.86i	0.121785	−	0.121229i
$285$	104752.	+	120891.i	1.28966	+	1.48834i
$286$	−67678.6	−	28124.1i	−0.827407	−	0.343833i
$287$	804.210	+	115.628i	0.00976350	+	0.00140378i
$288$	−7865.72	+	7239.71i	−0.0948317	+	0.0872843i
$289$	120491.	+	77435.1i	1.44265	+	0.927134i
$290$	10303.0	−	12755.3i	0.122509	−	0.151669i
$291$	−147154.	+	67203.2i	−1.73775	+	0.793604i
$292$	66709.1	−	88689.3i	0.782383	−	1.04017i
$293$	36201.8	+	10629.8i	0.421691	+	0.123820i	0.485692	−	0.874130i	$-0.338568\pi$
$293$	36201.8	+	10629.8i	0.421691	+	0.123820i	−0.0640006	+	0.997950i	$0.520386\pi$
$294$	46943.7	−	78913.6i	0.543104	−	0.912971i
$295$	10293.9	+	35057.8i	0.118287	+	0.402848i
$296$	87558.8	−	9109.73i	0.999347	−	0.103973i
$297$	17253.9	+	120003.i	0.195602	+	1.36044i
$298$	17467.5	+	97453.9i	0.196698	+	1.09740i
$299$	13577.6	−	52205.5i	0.151873	−	0.583948i
$300$	6220.25	+	16794.4i	0.0691139	+	0.186604i
$301$	113.455	+	789.098i	0.00125225	+	0.00870960i
$302$	−17076.6	+	66587.7i	−0.187236	+	0.730096i
$303$	−10685.4	−	36391.2i	−0.116388	−	0.396380i
$304$	−157204.	−	719.253i	−1.70105	−	0.00778278i
$305$	−134858.	−	39597.9i	−1.44970	−	0.425669i
$306$	13533.3	+	14569.2i	0.144531	+	0.155594i
$307$	122195.	−	55804.6i	1.29651	−	0.592098i	0.356838	−	0.934166i	$-0.383855\pi$
$307$	122195.	−	55804.6i	1.29651	−	0.592098i	0.939675	+	0.342069i	$0.111128\pi$
$308$	−1658.69	−	910.645i	−0.0174849	−	0.00959948i
$309$	118589.	+	76212.8i	1.24202	+	0.798198i
$310$	−1861.38	−	53844.1i	−0.0193692	−	0.560292i
$311$	78420.3	+	11275.1i	0.810789	+	0.116574i	0.535226	−	0.844709i	$-0.320227\pi$
$311$	78420.3	+	11275.1i	0.810789	+	0.116574i	0.275563	+	0.961283i	$0.411136\pi$
$312$	62357.4	+	2441.38i	0.640589	+	0.0250799i
$313$	−47157.4	−	54422.6i	−0.481350	−	0.555508i	0.462183	−	0.886784i	$-0.347066\pi$
$313$	−47157.4	−	54422.6i	−0.481350	−	0.555508i	−0.943534	+	0.331276i	$0.892521\pi$
$314$	89182.5	−	61769.4i	0.904524	−	0.626490i
$315$	−101.196	−	157.464i	−0.00101986	−	0.00158694i
$316$	−679.291	−	9813.16i	−0.00680271	−	0.0982731i
$317$	17661.6	−	20382.6i	0.175757	−	0.202834i	−0.661036	−	0.750355i	$-0.729883\pi$
$317$	17661.6	−	20382.6i	0.175757	−	0.202834i	0.836792	+	0.547521i	$0.184428\pi$
$318$	−150163.	+	74951.4i	−1.48494	+	0.741183i
$319$	−24595.3	−	11232.3i	−0.241697	−	0.110379i
$320$	−104273.	−	39709.0i	−1.01829	−	0.387783i
$321$	143252.			1.39024
$322$	494.115	−	1302.11i	0.00476559	−	0.0125584i
$323$			292417.i			2.80283i
$324$	−55723.5	−	102607.i	−0.530822	−	0.977437i
$325$	4958.45	−	10857.5i	0.0469439	−	0.102793i
$326$	−6476.44	+	3232.62i	−0.0609399	+	0.0304172i
$327$	−83810.1	−	72621.9i	−0.783792	−	0.679160i
$328$	−19275.4	−	76616.3i	−0.179166	−	0.712153i
$329$	558.636	−	359.013i	0.00516104	−	0.00331680i
$330$	153909.	−	106600.i	1.41331	−	0.978883i
$331$	−124552.	+	107925.i	−1.13683	+	0.985067i	−0.999985	−	0.00552556i	$-0.998241\pi$
$331$	−124552.	+	107925.i	−1.13683	+	0.985067i	−0.136843	+	0.990593i	$0.543696\pi$
$332$	11704.0	−	53215.9i	0.106183	−	0.482797i
$333$	2043.61	−	14213.6i	0.0184294	−	0.128179i
$334$	6661.05	+	192684.i	0.0597104	+	1.72724i
$335$	23565.2	−	36668.2i	0.209982	−	0.326738i
$336$	1593.74	+	236.593i	0.0141169	+	0.00209568i
$337$	−23408.9	−	51258.3i	−0.206120	−	0.451340i	0.778134	−	0.628098i	$-0.216166\pi$
$337$	−23408.9	−	51258.3i	−0.206120	−	0.451340i	−0.984254	+	0.176758i	$0.943439\pi$
$338$	49445.7	+	53230.4i	0.432808	+	0.465936i
$339$	32305.6	−	110023.i	0.281111	−	0.957377i
$340$	−72974.0	+	194292.i	−0.631263	+	1.68073i
$341$	−85245.2	+	25030.2i	−0.733096	+	0.215256i
$342$	−6370.26	+	24839.8i	−0.0544634	+	0.212372i
$343$	−3128.13	+	449.757i	−0.0265887	+	0.00382287i
$344$	66803.0	−	39326.7i	0.564519	−	0.332331i
$345$	93438.5	+	101279.i	0.785033	+	0.850904i
$346$	13146.8	+	73347.8i	0.109816	+	0.612681i
$347$	−57565.6	+	8276.68i	−0.478084	+	0.0687381i	−0.377144	−	0.926154i	$-0.623094\pi$
$347$	−57565.6	+	8276.68i	−0.478084	+	0.0687381i	−0.100940	+	0.994893i	$0.532185\pi$
$348$	22960.7	+	1694.98i	0.189595	+	0.0139961i
$349$	−77011.2	+	22612.5i	−0.632270	+	0.185651i	−0.582136	−	0.813091i	$-0.697783\pi$
$349$	−77011.2	+	22612.5i	−0.632270	+	0.185651i	−0.0501340	+	0.998742i	$0.515965\pi$
$350$	157.555	−	264.854i	0.00128616	−	0.00216207i
$351$	−19383.8	+	66015.0i	−0.157334	+	0.535832i
$352$	−20714.2	+	182826.i	−0.167180	+	1.47555i
$353$	−77597.0	−	169914.i	−0.622724	−	1.36358i	−0.913521	−	0.406791i	$-0.866648\pi$
$353$	−77597.0	−	169914.i	−0.622724	−	1.36358i	0.290797	−	0.956785i	$-0.406079\pi$
$354$	−32237.4	+	39910.7i	−0.257249	+	0.318481i
$355$	12757.4	−	19850.9i	0.101229	−	0.157515i
$356$	−9745.58	−	45298.3i	−0.0768967	−	0.357423i
$357$	426.516	−	2966.49i	0.00334656	−	0.0232759i
$358$	−88771.8	−	36889.5i	−0.692642	−	0.287830i
$359$	127508.	−	110487.i	0.989350	−	0.857277i	−0.000412702	−	1.00000i	$-0.500131\pi$
$359$	127508.	−	110487.i	0.989350	−	0.857277i	0.989763	+	0.142723i	$0.0455859\pi$
$360$	−10431.5	+	14914.8i	−0.0804902	+	0.115083i
$361$	−207605.	+	133420.i	−1.59303	+	1.02378i
$362$	10439.4	−	96066.4i	0.0796631	−	0.733085i
$363$	−127519.	−	110495.i	−0.967743	−	0.838554i
$364$	−641.558	−	861.120i	−0.00484209	−	0.00649922i
$365$	78489.8	−	171869.i	0.589152	−	1.29006i
$366$	−62109.8	−	187325.i	−0.463658	−	1.39841i
$367$			59959.7i			0.445172i	0.974913	+	0.222586i	$0.0714497\pi$
$367$			59959.7i			0.445172i	−0.974913	+	0.222586i	$0.928550\pi$
$368$	−135376.	+	3599.33i	−0.999647	+	0.0265783i
$369$	−12887.2			−0.0946468
$370$	142261.	−	47168.5i	1.03916	−	0.344547i
$371$	2626.94	+	1199.68i	0.0190854	+	0.00871603i
$372$	60664.2	−	45196.5i	0.438376	−	0.326602i
$373$	141638.	−	163459.i	1.01803	−	1.17487i	0.0335426	−	0.999437i	$-0.489321\pi$
$373$	141638.	−	163459.i	1.01803	−	1.17487i	0.984491	−	0.175436i	$-0.0561335\pi$
$374$	340246.	+	36973.9i	2.43248	+	0.264334i
$375$	−71533.8	−	111309.i	−0.508684	−	0.791528i
$376$	−52913.2	−	37008.0i	−0.374273	−	0.261770i
$377$	−10048.5	−	11596.5i	−0.0706996	−	0.0815917i
$378$	−681.662	+	1640.37i	−0.00477074	+	0.0114804i
$379$	−114214.	−	16421.5i	−0.795135	−	0.114323i	−0.267237	−	0.963631i	$-0.586111\pi$
$379$	−114214.	−	16421.5i	−0.795135	−	0.114323i	−0.527898	+	0.849308i	$0.677020\pi$
$380$	−261663.	+	56294.7i	−1.81207	+	0.389852i
$381$	−142366.	−	91493.3i	−0.980748	−	0.630289i
$382$	−125954.	−	101738.i	−0.863146	−	0.697197i
$383$	224622.	−	102581.i	1.53128	−	0.699311i	0.541338	−	0.840805i	$-0.317918\pi$
$383$	224622.	−	102581.i	1.53128	−	0.699311i	0.989939	+	0.141494i	$0.0451905\pi$
$384$	−37529.0	−	152109.i	−0.254510	−	1.03156i
$385$	−3091.10	−	907.630i	−0.0208541	−	0.00612332i
$386$	−206680.	−	122949.i	−1.38715	−	0.825181i
$387$	−3562.52	−	12132.8i	−0.0237868	−	0.0810103i
$388$	19927.9	−	269948.i	0.132372	−	1.79315i
$389$	36443.4	+	253469.i	0.240835	+	1.67504i	0.647963	+	0.761672i	$0.275621\pi$
$389$	36443.4	+	253469.i	0.240835	+	1.67504i	−0.407128	+	0.913371i	$0.633470\pi$
$390$	104581.	−	18745.0i	0.687580	−	0.123241i
$391$	7847.10	+	251778.i	0.0513281	+	1.64689i
$392$	77942.1	+	132398.i	0.507224	+	0.861605i
$393$	−5549.86	−	38600.1i	−0.0359333	−	0.249922i
$394$	−113175.	−	29024.0i	−0.729049	−	0.186967i
$395$	−4718.26	−	16068.9i	−0.0302404	−	0.102989i
$396$	28097.3	+	10553.0i	0.179173	+	0.0672955i
$397$	297598.	+	87382.6i	1.88820	+	0.554427i	0.994361	+	0.106045i	$0.0338186\pi$
$397$	297598.	+	87382.6i	1.88820	+	0.554427i	0.893842	+	0.448382i	$0.148000\pi$
$398$	62335.5	−	57903.5i	0.393522	−	0.365543i
$399$	3515.66	−	1605.55i	0.0220832	−	0.0100850i
$400$	−29641.3	−	4400.29i	−0.185258	−	0.0275018i
$401$	115785.	+	74410.4i	0.720050	+	0.462748i	0.848654	−	0.528948i	$-0.177413\pi$
$401$	115785.	+	74410.4i	0.720050	+	0.462748i	−0.128604	+	0.991696i	$0.541050\pi$
$402$	61166.4	−	2114.51i	0.378496	−	0.0130845i
$403$	−49905.6	−	7175.34i	−0.307284	−	0.0441807i
$404$	61979.8	+	13631.4i	0.379741	+	0.0835178i
$405$	−130181.	−	150237.i	−0.793668	−	0.915942i
$406$	−225.573	−	325.681i	−0.00136847	−	0.00197579i
$407$	−133621.	−	207919.i	−0.806653	−	1.25518i
$408$	−282614.	+	71100.9i	−1.69775	+	0.427125i
$409$	151066.	−	174339.i	0.903065	−	1.04219i	−0.0958393	−	0.995397i	$-0.530553\pi$
$409$	151066.	−	174339.i	0.903065	−	1.04219i	0.998904	−	0.0467960i	$-0.0149011\pi$
$410$	−60070.2	−	120349.i	−0.357348	−	0.715935i
$411$	175063.	+	79948.5i	1.03636	+	0.473289i
$412$	−207276.	+	112566.i	−1.22111	+	0.663153i
$413$	882.815			0.00517571
$414$	−4818.37	+	21558.7i	−0.0281125	+	0.125783i
$415$		−	92767.7i		−	0.538642i
$416$	−53793.8	+	89494.4i	−0.310846	+	0.517141i
$417$	−67595.9	+	148014.i	−0.388730	+	0.851201i
$418$	197111.	+	394906.i	1.12813	+	2.26017i
$419$	−112324.	−	97329.4i	−0.639801	−	0.554391i	0.273400	−	0.961901i	$-0.411852\pi$
$419$	−112324.	−	97329.4i	−0.639801	−	0.554391i	−0.913201	+	0.407510i	$0.866397\pi$
$420$	2736.61	−	189.435i	0.0155136	−	0.00107389i
$421$	−255279.	+	164058.i	−1.44029	+	0.925621i	−0.440685	+	0.897662i	$0.645264\pi$
$421$	−255279.	+	164058.i	−1.44029	+	0.925621i	−0.999609	+	0.0279586i	$0.991099\pi$
$422$	46020.8	+	66444.7i	0.258422	+	0.373109i
$423$	−7960.23	+	6897.58i	−0.0444882	+	0.0385493i
$424$	10985.8	−	280599.i	0.0611085	−	1.56083i
$425$	−7932.57	+	55172.3i	−0.0439174	+	0.305452i
$426$	33113.3	−	1144.72i	0.182467	−	0.00630785i
$427$	−1835.99	+	2856.85i	−0.0100696	+	0.0156687i
$428$	−115353.	+	210109.i	−0.629710	+	1.14698i
$429$	−72783.3	−	159373.i	−0.395474	−	0.865966i
$430$	96698.1	−	89822.9i	0.522975	−	0.485792i
$431$	−37157.8	+	126548.i	−0.200030	+	0.681240i	0.796983	+	0.604002i	$0.206428\pi$
$431$	−37157.8	+	126548.i	−0.200030	+	0.681240i	−0.997013	+	0.0772377i	$0.975390\pi$
$432$	172728.	+	790.279i	0.925541	+	0.00423460i
$433$	−153157.	+	44970.9i	−0.816884	+	0.239859i	−0.663374	−	0.748288i	$-0.730876\pi$
$433$	−153157.	+	44970.9i	−0.816884	+	0.239859i	−0.153510	+	0.988147i	$0.549058\pi$
$434$	−1260.93	−	323.371i	−0.00669442	−	0.00171681i
$435$	38798.9	−	5578.45i	0.205041	−	0.0294805i
$436$	174003.	−	64446.7i	0.915342	−	0.339022i
$437$	−267679.	+	184056.i	−1.40169	+	0.963800i
$438$	261140.	−	46806.5i	1.36121	−	0.243982i
$439$	364434.	−	52397.6i	1.89099	−	0.271883i	0.903384	−	0.428832i	$-0.141075\pi$
$439$	364434.	−	52397.6i	1.89099	−	0.271883i	0.987607	+	0.156949i	$0.0501658\pi$
$440$	32417.1	+	311580.i	0.167444	+	1.60940i
$441$	24046.2	−	7060.60i	0.123643	−	0.0363048i
$442$	166923.	+	99298.5i	0.854422	+	0.508274i
$443$	−63730.0	+	217044.i	−0.324740	+	1.10596i	0.621746	+	0.783219i	$0.286424\pi$
$443$	−63730.0	+	217044.i	−0.324740	+	1.10596i	−0.946486	+	0.322745i	$0.895394\pi$
$444$	168184.	+	126502.i	0.853135	+	0.641699i
$445$	−32770.9	−	71758.2i	−0.165489	−	0.362369i
$446$	195531.	+	157938.i	0.982984	+	0.793995i
$447$	−127962.	+	199113.i	−0.640423	+	0.996518i
$448$	−1630.37	+	2147.05i	−0.00812325	+	0.0106976i
$449$	29923.8	−	208125.i	0.148431	−	1.03236i	−0.770359	−	0.637611i	$-0.779923\pi$
$449$	29923.8	−	208125.i	0.148431	−	1.03236i	0.918789	−	0.394748i	$-0.129168\pi$
$450$	−1875.77	+	4513.89i	−0.00926304	+	0.0222908i
$451$	−167631.	+	145253.i	−0.824141	+	0.714122i
$452$	135358.	+	135978.i	0.662530	+	0.665568i
$453$	−138248.	+	88846.8i	−0.673695	+	0.432958i
$454$	−1943.74	−	211.222i	−0.00943030	−	0.00102477i
$455$	−1381.70	−	1197.25i	−0.00667408	−	0.00578312i
$456$	−274178.	−	257031.i	−1.31857	−	1.23611i
$457$	−36058.6	+	78957.3i	−0.172654	+	0.378059i	−0.976101	−	0.217317i	$-0.930270\pi$
$457$	−36058.6	+	78957.3i	−0.172654	+	0.378059i	0.803447	+	0.595376i	$0.202997\pi$
$458$	−14313.2	+	4745.70i	−0.0682346	+	0.0226240i
$459$		−	321293.i		−	1.52502i
$460$	−223788.	+	55492.9i	−1.05760	+	0.262254i
$461$	48117.5			0.226413			0.113206	−	0.993571i	$-0.463888\pi$
$461$	48117.5			0.226413			0.113206	+	0.993571i	$0.463888\pi$
$462$	−1423.63	−	4293.71i	−0.00666981	−	0.0201163i
$463$	284142.	+	129763.i	1.32548	+	0.605326i	0.947283	−	0.320399i	$-0.103817\pi$
$463$	284142.	+	129763.i	1.32548	+	0.605326i	0.378197	+	0.925725i	$0.376544\pi$
$464$	−20975.0	+	32311.8i	−0.0974241	+	0.150081i
$465$	84343.9	−	97338.1i	0.390075	−	0.450170i
$466$	8947.94	−	82341.7i	0.0412051	−	0.379182i
$467$	−218213.	−	339545.i	−1.00057	−	1.55691i	−0.819209	−	0.573495i	$-0.805587\pi$
$467$	−218213.	−	339545.i	−1.00057	−	1.55691i	−0.181357	−	0.983417i	$-0.558049\pi$
$468$	12016.4	+	12071.5i	0.0548633	+	0.0551149i
$469$	−689.666	−	795.916i	−0.00313540	−	0.00361844i
$470$	−101518.	−	42186.4i	−0.459567	−	0.190975i
$471$	256705.	+	36908.6i	1.15716	+	0.166374i
$472$	−32578.4	−	79420.9i	−0.146233	−	0.356493i
$473$	−183090.	−	117665.i	−0.818357	−	0.525926i
$474$	14776.2	−	18293.3i	0.0657667	−	0.0814206i
$475$	−65386.1	+	29860.8i	−0.289800	+	0.132347i
$476$	4007.52	+	3014.32i	0.0176873	+	0.0133038i
$477$	−43951.3	−	12905.3i	−0.193168	−	0.0567192i
$478$	−150450.	+	252910.i	−0.658471	+	1.10691i
$479$	−51309.5	−	174744.i	−0.223628	−	0.761608i	−0.992504	−	0.122210i	$-0.961002\pi$
$479$	−51309.5	−	174744.i	−0.223628	−	0.761608i	0.768876	−	0.639398i	$-0.220816\pi$
$480$	−118031.	−	239203.i	−0.512286	−	1.03821i
$481$	−19961.0	−	138831.i	−0.0862762	−	0.600064i
$482$	−11737.1	−	65482.8i	−0.0505203	−	0.281860i
$483$	2983.99	−	1476.76i	0.0127909	−	0.00633018i
$484$	264749.	−	98056.8i	1.13017	−	0.418588i
$485$	−65585.6	−	456158.i	−0.278821	−	1.93924i
$486$	15034.2	−	58623.6i	0.0636514	−	0.248199i
$487$	−48603.6	−	165529.i	−0.204932	−	0.697936i	−0.996249	−	0.0865294i	$-0.972422\pi$
$487$	−48603.6	−	165529.i	−0.204932	−	0.697936i	0.791317	−	0.611406i	$-0.209396\pi$
$488$	324765.	+	59745.4i	1.36373	+	0.250879i
$489$	−16603.2	−	4875.13i	−0.0694341	−	0.0203877i
$490$	178021.	+	191647.i	0.741445	+	0.798197i
$491$	−143385.	+	65481.5i	−0.594757	+	0.271616i	−0.689967	−	0.723841i	$-0.742375\pi$
$491$	−143385.	+	65481.5i	−0.594757	+	0.271616i	0.0952103	+	0.995457i	$0.469648\pi$
$492$	90893.2	−	165557.i	0.375492	−	0.683938i
$493$	60280.6	+	38740.0i	0.248018	+	0.159392i
$494$	8653.68	+	250324.i	0.0354607	+	1.02577i
$495$	50579.5	+	7272.24i	0.206426	+	0.0296796i
$496$	17440.5	+	125371.i	0.0708919	+	0.509605i
$497$	−373.361	−	430.881i	−0.00151153	−	0.00174439i
$498$	107082.	−	74166.9i	0.431775	−	0.299055i
$499$	100623.	+	156573.i	0.404108	+	0.628804i	0.982348	−	0.187062i	$-0.0598967\pi$
$499$	100623.	+	156573.i	0.404108	+	0.628804i	−0.578240	+	0.815867i	$0.696260\pi$
$500$	220860.	−	15288.5i	0.883439	−	0.0611538i
$501$	−301829.	+	348329.i	−1.20250	+	1.38776i
$502$	−8951.04	+	4467.77i	−0.0355194	+	0.0177290i
$503$	127409.	+	58185.8i	0.503575	+	0.229975i	0.650971	−	0.759102i	$-0.274362\pi$
$503$	127409.	+	58185.8i	0.503575	+	0.229975i	−0.147396	+	0.989078i	$0.547089\pi$
$504$	274.759	+	343.360i	0.00108166	+	0.00135173i
$505$	108045.			0.423665
$506$	180315.	+	334734.i	0.704256	+	1.30737i
$507$			173683.i			0.675680i
$508$	248834.	−	135136.i	0.964234	−	0.523651i
$509$	−37786.7	+	82741.4i	−0.145849	+	0.319365i	−0.968431	−	0.249282i	$-0.919806\pi$
$509$	−37786.7	+	82741.4i	−0.145849	+	0.319365i	0.822582	+	0.568647i	$0.192533\pi$
$510$	−443930.	+	221581.i	−1.70676	+	0.851905i
$511$	−3450.13	−	2989.55i	−0.0132128	−	0.0114489i
$512$	253320.	+	67441.2i	0.966340	+	0.257268i
$513$	348565.	−	224009.i	1.32449	−	0.851198i
$514$	303771.	−	210398.i	1.14979	−	0.796369i
$515$	−303492.	+	262977.i	−1.14428	+	0.991526i
$516$	180992.	+	39806.3i	0.679767	+	0.149504i
$517$	−25799.8	+	179441.i	−0.0965239	+	0.671339i
$518$	−125.113	−	3619.12i	−0.000466274	−	0.0134879i
$519$	−96309.6	+	149861.i	−0.357549	+	0.556356i
$520$	−56719.9	+	168484.i	−0.209763	+	0.623092i
$521$	58378.8	+	127832.i	0.215070	+	0.470938i	0.986162	−	0.165787i	$-0.0530163\pi$
$521$	58378.8	+	127832.i	0.215070	+	0.470938i	−0.771092	+	0.636724i	$0.780289\pi$
$522$	4276.69	+	4604.03i	0.0156952	+	0.0168965i
$523$	80149.2	−	272963.i	0.293019	−	0.997931i	−0.673039	−	0.739607i	$-0.735012\pi$
$523$	80149.2	−	272963.i	0.293019	−	0.997931i	0.966058	−	0.258324i	$-0.0831702\pi$
$524$	61084.2	+	22942.5i	0.222467	+	0.0835562i
$525$	706.879	−	207.558i	0.00256464	−	0.000753046i
$526$	51263.5	−	199894.i	0.185284	−	0.722484i
$527$	233050.	−	33507.5i	0.839127	−	0.120648i
$528$	−333740.	+	286524.i	−1.19713	+	1.02776i
$529$	−225539.	+	165660.i	−0.805954	+	0.591979i
$530$	−84349.7	−	470599.i	−0.300284	−	1.67533i
$531$	−13860.3	+	1992.81i	−0.0491568	+	0.00706768i
$532$	−476.096	+	6449.32i	−0.00168217	+	0.0227872i
$533$	−120777.	+	35463.2i	−0.425137	+	0.124831i
$534$	56630.6	−	95197.5i	0.198595	−	0.333844i
$535$	−114971.	+	391555.i	−0.401680	+	1.36800i
$536$	−46152.6	+	91416.1i	−0.160645	+	0.318195i
$537$	−95467.5	−	209045.i	−0.331060	−	0.724921i
$538$	−132470.	+	164001.i	−0.457672	+	0.566608i
$539$	233202.	−	362869.i	0.802701	−	1.24903i
$540$	287502.	−	61853.7i	0.985946	−	0.212118i
$541$	−64244.9	+	446833.i	−0.219505	+	1.52669i	0.520367	+	0.853943i	$0.325795\pi$
$541$	−64244.9	+	446833.i	−0.219505	+	1.52669i	−0.739872	+	0.672748i	$0.765114\pi$
$542$	−415988.	−	172866.i	−1.41606	−	0.588451i
$543$	174585.	−	151278.i	0.592116	−	0.513071i
$544$	123289.	−	471767.i	0.416608	−	1.59415i
$545$	265764.	−	170796.i	0.894752	−	0.575023i
$546$	277.332	−	2552.09i	0.000930281	−	0.00856074i
$547$	228332.	+	197851.i	0.763118	+	0.661245i	0.946830	−	0.321735i	$-0.104266\pi$
$547$	228332.	+	197851.i	0.763118	+	0.661245i	−0.183712	+	0.982980i	$0.558811\pi$
$548$	−258230.	+	192388.i	−0.859895	+	0.640645i
$549$	22376.4	−	48997.4i	0.0742412	−	0.162565i
$550$	26477.4	+	79856.7i	0.0875287	+	0.263989i
$551$			92407.3i			0.304371i
$552$	−242972.	−	213952.i	−0.797403	−	0.702165i
$553$	−404.643			−0.00132319
$554$	−389455.	+	129128.i	−1.26893	+	0.420728i
$555$	325919.	+	148842.i	1.05809	+	0.483214i
$556$	−162663.	−	218332.i	−0.526186	−	0.706264i
$557$	93718.9	−	108157.i	0.302076	−	0.348615i	−0.584336	−	0.811512i	$-0.698645\pi$
$557$	93718.9	−	108157.i	0.302076	−	0.348615i	0.886412	+	0.462898i	$0.153190\pi$
$558$	20526.8	+	2230.61i	0.0659253	+	0.00716399i
$559$	−66774.6	−	103903.i	−0.213692	−	0.332511i
$560$	−1925.79	+	4166.35i	−0.00614092	+	0.0132855i
$561$	535795.	+	618340.i	1.70244	+	1.96472i
$562$	−175295.	+	421835.i	−0.555006	+	1.33558i
$563$	−326224.	−	46903.9i	−1.02920	−	0.147976i	−0.393029	−	0.919526i	$-0.628573\pi$
$563$	−326224.	−	46903.9i	−1.02920	−	0.147976i	−0.636169	+	0.771550i	$0.719482\pi$
$564$	−32467.2	−	150910.i	−0.102067	−	0.474418i
$565$	274801.	+	176604.i	0.860838	+	0.553227i
$566$	−110117.	−	88945.6i	−0.343732	−	0.277646i
$567$	−4369.10	+	1995.30i	−0.0135902	+	0.00620644i
$568$	−24985.4	+	49489.4i	−0.0774443	+	0.153397i
$569$	86306.3	+	25341.8i	0.266574	+	0.0782732i	0.412288	−	0.911054i	$-0.364730\pi$
$569$	86306.3	+	25341.8i	0.266574	+	0.0782732i	−0.145714	+	0.989327i	$0.546548\pi$
$570$	−549902.	−	327123.i	−1.69253	−	1.00684i
$571$	−86354.4	−	294096.i	−0.264857	−	0.902022i	−0.979315	−	0.202343i	$-0.935145\pi$
$571$	−86354.4	−	294096.i	−0.264857	−	0.902022i	0.714457	−	0.699679i	$-0.246674\pi$
$572$	292363.	+	21582.5i	0.893573	+	0.0659646i
$573$	−55084.8	−	383123.i	−0.167773	−	1.16689i
$574$	−3198.94	+	573.375i	−0.00970918	+	0.00174026i
$575$	−55497.8	+	27465.6i	−0.167857	+	0.0830717i
$576$	20750.4	−	37389.2i	0.0625434	−	0.112694i
$577$	−56272.4	−	391383.i	−0.169022	−	1.17557i	−0.880911	−	0.473282i	$-0.843069\pi$
$577$	−56272.4	−	391383.i	−0.169022	−	1.17557i	0.711889	−	0.702292i	$-0.247840\pi$
$578$	−554955.	−	142320.i	−1.66112	−	0.426001i
$579$	−161969.	−	551616.i	−0.483142	−	1.64543i
$580$	−23060.7	+	61398.8i	−0.0685514	+	0.182517i
$581$	−2150.63	−	631.481i	−0.00637108	−	0.00187072i
$582$	474109.	−	440400.i	1.39969	−	1.30017i
$583$	−717157.	+	327514.i	−2.10997	+	0.963592i
$584$	−141630.	+	420708.i	−0.415270	+	1.23354i
$585$	24395.5	+	15678.0i	0.0712849	+	0.0458120i
$586$	−150830.	+	5214.18i	−0.439231	+	0.0151842i
$587$	643866.	+	92573.9i	1.86861	+	0.268666i	0.981297	−	0.192499i	$-0.0616592\pi$
$587$	643866.	+	92573.9i	1.86861	+	0.268666i	0.887315	+	0.461165i	$0.152568\pi$
$588$	−78892.5	+	358710.i	−0.228182	+	1.03750i
$589$	198837.	+	229470.i	0.573148	+	0.661448i
$590$	−83216.1	−	120147.i	−0.239058	−	0.345151i
$591$	−151007.	−	234971.i	−0.432337	−	0.672729i
$592$	−320971.	+	144811.i	−0.915845	+	0.413199i
$593$	77382.1	−	89303.7i	0.220055	−	0.253957i	−0.634978	−	0.772530i	$-0.718991\pi$
$593$	77382.1	−	89303.7i	0.220055	−	0.253957i	0.855033	+	0.518573i	$0.173536\pi$
$594$	−216576.	−	433902.i	−0.613814	−	1.22976i
$595$	7766.08	+	3546.65i	0.0219365	+	0.0100181i
$596$	−189000.	−	348019.i	−0.532072	−	0.979738i
$597$	203392.			0.570669
$598$	14168.6	+	215303.i	0.0396208	+	0.602072i
$599$			304909.i			0.849799i	0.905241	+	0.424899i	$0.139691\pi$
$599$			304909.i			0.849799i	−0.905241	+	0.424899i	$0.860309\pi$
$600$	−44758.4	−	55933.6i	−0.124329	−	0.155371i
$601$	−207042.	+	453358.i	−0.573204	+	1.25514i	0.371870	+	0.928285i	$0.378717\pi$
$601$	−207042.	+	453358.i	−0.573204	+	1.25514i	−0.945074	+	0.326856i	$0.894011\pi$
$602$	−1424.12	−	2853.18i	−0.00392965	−	0.00787293i
$603$	12624.5	+	10939.2i	0.0347199	+	0.0300850i
$604$	−18988.7	−	274314.i	−0.0520500	−	0.751923i
$605$	404365.	−	259869.i	1.10475	−	0.709977i
$606$	86381.2	+	124717.i	0.235220	+	0.339610i
$607$	159623.	−	138314.i	0.433230	−	0.375396i	−0.410770	−	0.911739i	$-0.634740\pi$
$607$	159623.	−	138314.i	0.433230	−	0.375396i	0.844000	+	0.536343i	$0.180195\pi$
$608$	597770.	−	195167.i	1.61706	−	0.527957i
$609$	134.784	−	937.446i	0.000363417	−	0.00252762i
$610$	561869.	−	19423.7i	1.51000	−	0.0522003i
$611$	−55621.1	+	86548.1i	−0.148990	+	0.231833i
$612$	−69722.9	−	38278.9i	−0.186154	−	0.102201i
$613$	−212289.	−	464849.i	−0.564947	−	1.23706i	−0.949445	−	0.313935i	$-0.898353\pi$
$613$	−212289.	−	464849.i	−0.564947	−	1.23706i	0.384498	−	0.923126i	$-0.374375\pi$
$614$	−393694.	+	365702.i	−1.04429	+	0.970042i
$615$	90592.2	−	308529.i	0.239519	−	0.815728i
$616$	7444.00	+	1369.44i	0.0196176	+	0.00360895i
$617$	−450233.	+	132200.i	−1.18268	+	0.347266i	−0.813207	−	0.581975i	$-0.802280\pi$
$617$	−450233.	+	132200.i	−1.18268	+	0.347266i	−0.369473	+	0.929241i	$0.620462\pi$
$618$	−546195.	−	140074.i	−1.43011	−	0.366758i
$619$	−352797.	+	50724.6i	−0.920755	+	0.132385i	−0.586362	−	0.810049i	$-0.699440\pi$
$619$	−352797.	+	50724.6i	−0.920755	+	0.132385i	−0.334393	+	0.942434i	$0.608531\pi$
$620$	74849.1	+	202089.i	0.194717	+	0.525726i
$621$	294112.	−	202231.i	0.762657	−	0.524403i
$622$	−311936.	+	55911.1i	−0.806277	+	0.144516i
$623$	−1886.64	+	271.258i	−0.00486086	+	0.000698886i
$624$	−239829.	+	69229.8i	−0.615931	+	0.177797i
$625$	431851.	−	126803.i	1.10554	−	0.324615i
$626$	247555.	+	147264.i	0.631718	+	0.375793i
$627$	−297264.	+	1.01239e6i	−0.756149	+	2.57521i
$628$	−260844.	+	346791.i	−0.661397	+	0.879323i
$629$	272090.	+	595795.i	0.687720	+	1.50590i
$630$	582.439	+	470.459i	0.00146747	+	0.00118533i
$631$	51997.8	−	80910.1i	0.130595	−	0.203210i	−0.769798	−	0.638288i	$-0.779643\pi$
$631$	51997.8	−	80910.1i	0.130595	−	0.203210i	0.900393	+	0.435078i	$0.143279\pi$
$632$	14932.5	+	36402.9i	0.0373850	+	0.0911386i
$633$	−27498.4	+	191256.i	−0.0686279	+	0.477317i
$634$	−41397.9	+	99621.0i	−0.102991	+	0.247841i
$635$	364342.	−	315704.i	0.903569	−	0.782947i
$636$	475777.	−	473605.i	1.17622	−	1.17085i
$637$	205927.	−	132341.i	0.507499	−	0.326150i
$638$	107522.	+	11684.2i	0.264153	+	0.0287051i
$639$	6834.45	+	5922.08i	0.0167379	+	0.0145035i
$640$	445885.	+	19500.5i	1.08859	+	0.0476088i
$641$	231833.	−	507644.i	0.564234	−	1.23550i	−0.385577	−	0.922676i	$-0.625997\pi$
$641$	231833.	−	507644.i	0.564234	−	1.23550i	0.949811	−	0.312825i	$-0.101275\pi$
$642$	−543890.	+	180333.i	−1.31960	+	0.437528i
$643$		−	221615.i		−	0.536014i	−0.963417	−	0.268007i	$-0.913635\pi$
$643$		−	221615.i		−	0.536014i	0.963417	−	0.268007i	$-0.0863651\pi$
$644$	−236.861	+	5565.80i	−0.000571112	+	0.0134201i
$645$	315511.			0.758395
$646$	−368111.	−	1.11023e6i	−0.882091	−	2.66041i
$647$	−397384.	−	181479.i	−0.949297	−	0.433529i	−0.120272	−	0.992741i	$-0.538377\pi$
$647$	−397384.	−	181479.i	−0.949297	−	0.433529i	−0.829025	+	0.559211i	$0.811104\pi$
$648$	340736.	+	319426.i	0.811462	+	0.760713i
$649$	−157828.	+	182143.i	−0.374708	+	0.432437i
$650$	−5157.96	+	47465.2i	−0.0122082	+	0.112344i
$651$	−1682.44	−	2617.93i	−0.00396989	−	0.00617727i
$652$	20520.0	−	20426.3i	0.0482706	−	0.0480502i
$653$	−335172.	−	386809.i	−0.786034	−	0.907132i	0.211495	−	0.977379i	$-0.432167\pi$
$653$	−335172.	−	386809.i	−0.786034	−	0.907132i	−0.997530	+	0.0702469i	$0.977621\pi$
$654$	409626.	+	170222.i	0.957706	+	0.397979i
$655$	109961.	+	15810.0i	0.256305	+	0.0368511i
$656$	169633.	+	266628.i	0.394186	+	0.619580i
$657$	60915.9	+	39148.3i	0.141124	+	0.0906946i
$658$	−1669.05	+	2066.32i	−0.00385494	+	0.00477251i
$659$	−507451.	+	231745.i	−1.16848	+	0.533629i	−0.902644	−	0.430388i	$-0.858377\pi$
$659$	−507451.	+	231745.i	−1.16848	+	0.533629i	−0.265841	+	0.964017i	$0.585650\pi$
$660$	−450160.	+	598484.i	−1.03342	+	1.37393i
$661$	−271083.	−	79597.0i	−0.620438	−	0.182177i	−0.0436182	−	0.999048i	$-0.513888\pi$
$661$	−271083.	−	79597.0i	−0.620438	−	0.182177i	−0.576820	+	0.816871i	$0.695707\pi$
$662$	337030.	−	566557.i	0.769047	−	1.29279i
$663$	130813.	+	445508.i	0.297594	+	1.01351i
$664$	22554.1	+	216781.i	0.0511552	+	0.491682i
$665$	1566.90	+	10898.1i	0.00354323	+	0.0246437i
$666$	10133.9	+	56538.2i	0.0228468	+	0.127466i
$667$	2479.78	+	79565.0i	0.00557393	+	0.178842i
$668$	−267852.	−	723186.i	−0.600262	−	1.62068i
$669$	85514.0	+	594763.i	0.191067	+	1.32890i
$670$	−43311.2	+	168885.i	−0.0964829	+	0.376220i
$671$	−261194.	−	889543.i	−0.580119	−	1.97570i
$672$	−6348.88	+	1108.01i	−0.0140591	+	0.00245361i
$673$	160498.	+	47126.5i	0.354356	+	0.104048i	0.454066	−	0.890968i	$-0.349973\pi$
$673$	160498.	+	47126.5i	0.354356	+	0.104048i	−0.0997096	+	0.995017i	$0.531791\pi$
$674$	153404.	+	165146.i	0.337690	+	0.363537i
$675$	71842.9	−	32809.6i	0.157680	−	0.0720100i
$676$	−254742.	−	139857.i	−0.557452	−	0.306049i
$677$	−24037.0	−	15447.6i	−0.0524449	−	0.0337043i	0.514156	−	0.857697i	$-0.328105\pi$
$677$	−24037.0	−	15447.6i	−0.0524449	−	0.0337043i	−0.566601	+	0.823993i	$0.691742\pi$
$678$	15846.7	+	458397.i	0.0344731	+	0.997199i
$679$	−11021.5	−	1584.66i	−0.0239057	−	0.00343713i
$680$	32477.7	−	829542.i	0.0702372	−	1.79399i
$681$	−3060.86	−	3532.42i	−0.00660007	−	0.00761689i
$682$	292145.	−	202345.i	0.628101	−	0.435034i
$683$	472679.	+	735503.i	1.01327	+	1.57668i	0.800283	+	0.599623i	$0.204683\pi$
$683$	472679.	+	735503.i	1.01327	+	1.57668i	0.212987	+	0.977055i	$0.431681\pi$
$684$	−7083.52	−	102330.i	−0.0151404	−	0.218721i
$685$	−359028.	+	414340.i	−0.765150	+	0.883030i
$686$	11310.5	−	5645.48i	0.0240345	−	0.0119964i
$687$	−32791.2	−	14975.2i	−0.0694774	−	0.0317293i
$688$	−204127.	+	233409.i	−0.431245	+	0.493106i
$689$	−447417.			−0.942485
$690$	−482258.	−	266904.i	−1.01293	−	0.560605i
$691$		−	457193.i		−	0.957510i	−0.877948	−	0.478755i	$-0.841088\pi$
$691$		−	457193.i		−	0.957510i	0.877948	−	0.478755i	$-0.158912\pi$
$692$	−142249.	−	261933.i	−0.297056	−	0.546988i
$693$	512.893	−	1123.08i	0.00106797	−	0.00233853i
$694$	208143.	−	103891.i	0.432158	−	0.215705i
$695$	−350322.	−	303555.i	−0.725266	−	0.628446i
$696$	−89309.6	+	22468.8i	−0.184366	+	0.0463832i
$697$	494502.	−	317797.i	1.01789	−	0.654160i
$698$	263926.	−	182800.i	0.541715	−	0.375202i
$699$	149642.	−	129666.i	0.306267	−	0.265382i
$700$	−264.783	+	1203.92i	−0.000540373	+	0.00245698i
$701$	42333.5	−	294436.i	0.0861486	−	0.599177i	−0.900320	−	0.435228i	$-0.856668\pi$
$701$	42333.5	−	294436.i	0.0861486	−	0.599177i	0.986469	−	0.163949i	$-0.0524231\pi$
$702$	−9508.22	−	275044.i	−0.0192941	−	0.558120i
$703$	−456663.	+	710581.i	−0.924028	+	1.43782i
$704$	−151506.	−	720222.i	−0.305692	−	1.45319i
$705$	−109175.	−	239061.i	−0.219658	−	0.480984i
$706$	508513.	+	547436.i	1.02022	+	1.09831i
$707$	735.477	−	2504.81i	0.00147140	−	0.00501112i
$708$	72155.5	−	192113.i	0.143947	−	0.383257i
$709$	−194765.	+	57188.3i	−0.387453	+	0.113766i	−0.469657	−	0.882849i	$-0.655622\pi$
$709$	−194765.	+	57188.3i	−0.387453	+	0.113766i	0.0822038	+	0.996616i	$0.473804\pi$
$710$	−23447.1	+	91428.5i	−0.0465129	+	0.181370i
$711$	6352.94	−	913.414i	0.0125671	−	0.00180688i
$712$	94025.6	+	159718.i	0.185475	+	0.315061i
$713$	177361.	+	192244.i	0.348883	+	0.378158i
$714$	2115.01	+	11799.9i	0.00414873	+	0.0231463i
$715$	494034.	−	71031.4i	0.966374	−	0.138944i
$716$	383483.	+	28309.1i	0.748031	+	0.0552205i
$717$	−675003.	+	198199.i	−1.31301	+	0.385534i
$718$	−345030.	+	580005.i	−0.669281	+	1.12508i
$719$	119124.	−	405698.i	0.230430	−	0.784774i	−0.760376	−	0.649484i	$-0.774985\pi$
$719$	119124.	−	405698.i	0.230430	−	0.784774i	0.990806	−	0.135290i	$-0.0431967\pi$
$720$	20830.3	−	69759.3i	0.0401820	−	0.134567i
$721$	4030.68	+	8825.96i	0.00775368	+	0.0169782i
$722$	620267.	−	767905.i	1.18988	−	1.47310i
$723$	85982.6	−	133791.i	0.164488	−	0.255948i
$724$	81298.1	+	377881.i	0.155097	+	0.720905i
$725$	−2506.79	+	17435.1i	−0.00476916	+	0.0331703i
$726$	623254.	+	258996.i	1.18247	+	0.491382i
$727$	497362.	−	430966.i	0.941030	−	0.815407i	−0.0419501	−	0.999120i	$-0.513357\pi$
$727$	497362.	−	430966.i	0.941030	−	0.815407i	0.982980	+	0.183713i	$0.0588116\pi$
$728$	3519.86	+	2461.83i	0.00664144	+	0.00464509i
$729$	−375559.	+	241357.i	−0.706680	+	0.454155i
$730$	−81647.8	+	751349.i	−0.153214	+	1.40992i
$731$	435894.	+	377704.i	0.815729	+	0.706833i
$732$	471630.	+	633038.i	0.880196	+	1.18143i
$733$	65223.7	−	142820.i	0.121394	−	0.265816i	−0.839173	−	0.543865i	$-0.816960\pi$
$733$	65223.7	−	142820.i	0.121394	−	0.265816i	0.960567	+	0.278049i	$0.0896877\pi$
$734$	−75480.7	−	227652.i	−0.140102	−	0.422551i
$735$			625316.i			1.15751i
$736$	509458.	−	184085.i	0.940487	−	0.339831i
$737$	287510.			0.529321
$738$	48929.4	−	16223.1i	0.0898375	−	0.0297867i
$739$	60193.6	+	27489.5i	0.110220	+	0.0503359i	0.469762	−	0.882793i	$-0.344340\pi$
$739$	60193.6	+	27489.5i	0.110220	+	0.0503359i	−0.359542	+	0.933129i	$0.617067\pi$
$740$	−480752.	+	358174.i	−0.877926	+	0.654079i
$741$	−392120.	+	452531.i	−0.714139	+	0.824160i
$742$	−11484.0	−	1247.95i	−0.0208587	−	0.00226668i
$743$	−189331.	−	294604.i	−0.342960	−	0.533656i	0.626336	−	0.779553i	$-0.284554\pi$
$743$	−189331.	−	294604.i	−0.342960	−	0.533656i	−0.969296	+	0.245897i	$0.920917\pi$
$744$	−173431.	+	247967.i	−0.313314	+	0.447969i
$745$	−441543.	−	509568.i	−0.795537	−	0.918099i
$746$	−331992.	+	798914.i	−0.596554	+	1.43556i
$747$	35190.6	+	5059.64i	0.0630645	+	0.00906731i
$748$	−1.33837e6	+	287940.i	−2.39207	+	0.514634i
$749$	8294.76	+	5330.72i	0.0147856	+	0.00950216i
$750$	411717.	+	332560.i	0.731942	+	0.591218i
$751$	−547678.	+	250116.i	−0.971059	+	0.443468i	−0.836818	−	0.547481i	$-0.815587\pi$
$751$	−547678.	+	250116.i	−0.971059	+	0.443468i	−0.134241	+	0.990949i	$0.542860\pi$
$752$	247486.	+	73900.0i	0.437638	+	0.130680i
$753$	−22947.1	−	6737.87i	−0.0404704	−	0.0118832i
$754$	52749.9	+	31379.6i	0.0927852	+	0.0551956i
$755$	−131893.	−	449185.i	−0.231381	−	0.788010i
$756$	523.110	−	7086.18i	0.000915270	−	0.0123985i
$757$	−46726.2	−	324988.i	−0.0815396	−	0.567121i	−0.989105	−	0.147210i	$-0.952971\pi$
$757$	−46726.2	−	324988.i	−0.0815396	−	0.567121i	0.907566	−	0.419910i	$-0.137939\pi$
$758$	454314.	−	81430.8i	0.790711	−	0.141726i
$759$	−228784.	+	879669.i	−0.397139	+	1.52699i
$760$	922600.	−	543132.i	1.59730	−	0.940326i
$761$	51178.6	+	355955.i	0.0883729	+	0.614647i	0.985090	+	0.172042i	$0.0550365\pi$
$761$	51178.6	+	355955.i	0.0883729	+	0.614647i	−0.896717	+	0.442605i	$0.854054\pi$
$762$	655706.	+	168158.i	1.12927	+	0.289606i
$763$	−2150.47	−	7323.82i	−0.00369389	−	0.0125802i
$764$	606287.	+	227715.i	1.03870	+	0.390126i
$765$	−129934.	−	38152.2i	−0.222025	−	0.0651923i
$766$	−723696.	+	672241.i	−1.23338	+	1.14569i
$767$	−124413.	+	56817.3i	−0.211482	+	0.0965806i
$768$	333972.	+	530277.i	0.566223	+	0.899043i
$769$	−613186.	−	394070.i	−1.03691	−	0.666379i	−0.0926861	−	0.995695i	$-0.529545\pi$
$769$	−613186.	−	394070.i	−1.03691	−	0.666379i	−0.944220	+	0.329317i	$0.893182\pi$
$770$	12878.7	−	445.215i	0.0217216	−	0.000750911i
$771$	874381.	+	125717.i	1.47093	+	0.211488i
$772$	939486.	+	206625.i	1.57636	+	0.346695i
$773$	101139.	+	116721.i	0.169262	+	0.195339i	0.834043	−	0.551700i	$-0.186021\pi$
$773$	101139.	+	116721.i	0.169262	+	0.195339i	−0.664781	+	0.747038i	$0.731475\pi$
$774$	28799.5	+	41580.6i	0.0480731	+	0.0694078i
$775$	31290.9	+	48689.7i	0.0520973	+	0.0810650i
$776$	264165.	+	1.05001e6i	0.438683	+	1.74369i
$777$	5669.16	−	6542.56i	0.00939024	−	0.0108369i
$778$	−457447.	−	916481.i	−0.755757	−	1.51413i
$779$	689545.	+	314905.i	1.13629	+	0.518925i
$780$	−373470.	+	202822.i	−0.613856	+	0.333370i
$781$	155648.			0.255177
$782$	−346746.	−	946059.i	−0.567019	−	1.54705i
$783$		−	101532.i		−	0.165608i
$784$	−462596.	−	404562.i	−0.752610	−	0.658193i
$785$	−306909.	+	672037.i	−0.498047	+	1.09057i
$786$	69663.4	+	139568.i	0.112761	+	0.225913i
$787$	395138.	+	342389.i	0.637968	+	0.552802i	0.912655	−	0.408731i	$-0.134029\pi$
$787$	395138.	+	342389.i	0.637968	+	0.552802i	−0.274687	+	0.961534i	$0.588574\pi$
$788$	466233.	−	32273.8i	0.750845	−	0.0519753i
$789$	415017.	−	266715.i	0.666671	−	0.428444i
$790$	38142.5	+	55070.0i	0.0611160	+	0.0882391i
$791$	5964.80	−	5168.53i	0.00953329	−	0.00826064i
$792$	−119963.	−	4696.71i	−0.191248	−	0.00748761i
$793$	74875.6	−	520771.i	0.119068	−	0.828134i
$794$	−1.23991e6	+	42863.4i	−1.96674	+	0.0679900i
$795$	617922.	−	961506.i	0.977687	−	1.52131i
$796$	−163780.	+	298316.i	−0.258485	+	0.470816i
$797$	9408.54	+	20601.8i	0.0148117	+	0.0324331i	0.916893	−	0.399132i	$-0.130689\pi$
$797$	9408.54	+	20601.8i	0.0148117	+	0.0324331i	−0.902082	+	0.431566i	$0.857961\pi$
$798$	−11326.9	+	10521.6i	−0.0177871	+	0.0165225i
$799$	135353.	−	460969.i	0.212018	−	0.722069i
$800$	118080.	−	20607.4i	0.184500	−	0.0321990i
$801$	29008.2	−	8517.56i	0.0452121	−	0.0132755i
$802$	−533278.	−	136761.i	−0.829096	−	0.212624i
$803$	1.23361e6	−	177367.i	1.91314	−	0.275068i
$804$	−229571.	+	85028.0i	−0.355145	+	0.131538i
$805$	1641.60	+	9341.44i	0.00253323	+	0.0144153i
$806$	198512.	−	35581.0i	0.305574	−	0.0547707i
$807$	−498856.	+	71724.7i	−0.765999	+	0.110134i
$808$	−252481.	+	26268.5i	−0.386729	+	0.0402358i
$809$	251488.	−	73843.6i	0.384256	−	0.112828i	−0.0838988	−	0.996474i	$-0.526737\pi$
$809$	251488.	−	73843.6i	0.384256	−	0.112828i	0.468154	+	0.883647i	$0.344919\pi$
$810$	683393.	+	406533.i	1.04160	+	0.619621i
$811$	35223.3	−	119959.i	0.0535535	−	0.182387i	−0.928373	−	0.371650i	$-0.878792\pi$
$811$	35223.3	−	119959.i	0.0535535	−	0.182387i	0.981926	+	0.189264i	$0.0606102\pi$
$812$	1266.43	+	952.564i	0.00192074	+	0.00144471i
$813$	−447365.	−	979592.i	−0.676832	−	1.48205i
$814$	769066.	+	621204.i	1.16069	+	0.937531i
$815$	26650.7	−	41469.3i	0.0401230	−	0.0624326i
$816$	983508.	−	625723.i	1.47706	−	0.939727i
$817$	−105854.	+	736233.i	−0.158586	+	1.10299i
$818$	−354090.	+	852091.i	−0.529185	+	1.27344i
$819$	529.525	−	458.836i	0.000789440	−	0.000684053i
$820$	379573.	+	381314.i	0.564505	+	0.567093i
$821$	130648.	−	83962.2i	0.193828	−	0.124565i	−0.440128	−	0.897935i	$-0.645067\pi$
$821$	130648.	−	83962.2i	0.193828	−	0.124565i	0.633955	+	0.773370i	$0.281430\pi$
$822$	−765313.	−	83165.3i	−1.13265	−	0.123083i
$823$	−130946.	−	113466.i	−0.193328	−	0.167519i	0.552818	−	0.833302i	$-0.313552\pi$
$823$	−130946.	−	113466.i	−0.193328	−	0.167519i	−0.746146	+	0.665783i	$0.768098\pi$
$824$	645268.	−	688316.i	0.950354	−	1.01376i
$825$	−83550.6	+	182950.i	−0.122756	+	0.268797i
$826$	−3351.83	+	1111.34i	−0.00491271	+	0.00162887i
$827$			1.00903e6i			1.47534i	0.675162	+	0.737669i	$0.264074\pi$
$827$			1.00903e6i			1.47534i	−0.675162	+	0.737669i	$0.735926\pi$
$828$	−8845.13	−	87918.4i	−0.0129016	−	0.128239i
$829$	488397.			0.710663			0.355331	−	0.934740i	$-0.384368\pi$
$829$	488397.			0.710663			0.355331	+	0.934740i	$0.384368\pi$
$830$	116781.	+	352215.i	0.169518	+	0.511272i
$831$	−892233.	−	407469.i	−1.29204	−	0.590056i
$832$	91581.0	−	407506.i	0.132300	−	0.588691i
$833$	−748576.	+	863903.i	−1.07881	+	1.24502i
$834$	70315.7	−	647067.i	0.101093	−	0.930287i
$835$	−709858.	−	1.10456e6i	−1.01812	−	1.58422i
$836$	−1.24551e6	−	1.25122e6i	−1.78211	−	1.79028i
$837$	−218472.	−	252130.i	−0.311849	−	0.359893i
$838$	548990.	+	228135.i	0.781765	+	0.324866i
$839$	−254160.	−	36542.7i	−0.361064	−	0.0519131i	−0.0406041	−	0.999175i	$-0.512928\pi$
$839$	−254160.	−	36542.7i	−0.361064	−	0.0519131i	−0.320460	+	0.947262i	$0.603837\pi$
$840$	−10151.7	+	4164.23i	−0.0143874	+	0.00590169i
$841$	−575953.	−	370143.i	−0.814320	−	0.523332i
$842$	762705.	−	944246.i	1.07580	−	1.33187i
$843$	−993359.	+	453652.i	−1.39782	+	0.638363i
$844$	−258374.	−	194340.i	−0.362713	−	0.272821i
$845$	−474733.	−	139394.i	−0.664869	−	0.195223i
$846$	21539.9	−	36209.2i	0.0300956	−	0.0505915i
$847$	−3271.97	−	11143.3i	−0.00456082	−	0.0155327i
$848$	311524.	+	1.07919e6i	0.433211	+	1.50075i
$849$	−48158.6	−	334951.i	−0.0668126	−	0.464692i
$850$	−39336.0	−	219461.i	−0.0544443	−	0.303752i
$851$	−374129.	+	624083.i	−0.516610	+	0.861754i
$852$	−124282.	+	46031.2i	−0.171210	+	0.0634122i
$853$	5712.60	+	39732.0i	0.00785119	+	0.0546062i	0.993370	−	0.114958i	$-0.0366732\pi$
$853$	5712.60	+	39732.0i	0.00785119	+	0.0546062i	−0.985519	+	0.169564i	$0.945764\pi$
$854$	3374.41	−	13158.0i	0.00462682	−	0.0180416i
$855$	−49201.1	−	167564.i	−0.0673043	−	0.229217i
$856$	173469.	−	942942.i	0.236741	−	1.28688i
$857$	249693.	+	73316.6i	0.339974	+	0.0998253i	0.447263	−	0.894403i	$-0.352399\pi$
$857$	249693.	+	73316.6i	0.339974	+	0.0998253i	−0.107289	+	0.994228i	$0.534217\pi$
$858$	476968.	+	513476.i	0.647910	+	0.697502i
$859$	221555.	−	101181.i	0.300259	−	0.137124i	−0.259589	−	0.965719i	$-0.583587\pi$
$859$	221555.	−	101181.i	0.300259	−	0.137124i	0.559848	+	0.828596i	$0.310860\pi$
$860$	−254064.	+	462764.i	−0.343515	+	0.625694i
$861$	−6535.93	−	4200.38i	−0.00881659	−	0.00566608i
$862$	−18226.8	−	527246.i	−0.0245299	−	0.709576i
$863$	−266808.	−	38361.2i	−0.358243	−	0.0515075i	−0.0391562	−	0.999233i	$-0.512467\pi$
$863$	−266808.	−	38361.2i	−0.358243	−	0.0515075i	−0.319087	+	0.947726i	$0.603376\pi$
$864$	−656800.	+	214439.i	−0.879843	+	0.287261i
$865$	−332323.	−	383521.i	−0.444149	−	0.512575i
$866$	524885.	−	363545.i	0.699888	−	0.484755i
$867$	−740467.	−	1.15219e6i	−0.985071	−	1.53280i
$868$	5194.52	−	359.578i	0.00689456	−	0.000477258i
$869$	72341.0	−	83486.0i	0.0957955	−	0.110554i
$870$	−140287.	+	70022.2i	−0.185345	+	0.0925119i
$871$	148417.	+	67779.8i	0.195636	+	0.0893437i
$872$	−579516.	+	463732.i	−0.762135	+	0.609866i
$873$	176616.			0.231741
$874$	784608.	−	1.03578e6i	1.02714	−	1.35596i
$875$		−	9107.08i		−	0.0118950i
$876$	−932561.	+	506451.i	−1.21526	+	0.659977i
$877$	213656.	−	467842.i	0.277790	−	0.608275i	−0.718386	−	0.695645i	$-0.755119\pi$
$877$	213656.	−	467842.i	0.277790	−	0.608275i	0.996176	+	0.0873694i	$0.0278460\pi$
$878$	−1.31770e6	+	657710.i	−1.70934	+	0.853190i
$879$	−272668.	−	236268.i	−0.352903	−	0.305792i
$880$	−515314.	−	1.14218e6i	−0.665436	−	1.47492i
$881$	−1.13904e6	+	732017.i	−1.46753	+	0.943126i	−0.469341	+	0.883017i	$0.655508\pi$
$881$	−1.13904e6	+	732017.i	−1.46753	+	0.943126i	−0.998192	+	0.0601086i	$0.980855\pi$
$882$	−82409.0	+	57078.0i	−0.105935	+	0.0733722i
$883$	−526676.	+	456368.i	−0.675495	+	0.585320i	−0.923574	−	0.383420i	$-0.874746\pi$
$883$	−526676.	+	456368.i	−0.675495	+	0.585320i	0.248079	+	0.968740i	$0.420201\pi$
$884$	−758768.	−	166879.i	−0.970967	−	0.213548i
$885$	49723.4	−	345834.i	0.0634855	−	0.441551i
$886$	−31261.2	−	904289.i	−0.0398233	−	1.15197i
$887$	−637556.	+	992057.i	−0.810347	+	1.26092i	0.151804	+	0.988411i	$0.451492\pi$
$887$	−637556.	+	992057.i	−0.810347	+	1.26092i	−0.962152	+	0.272514i	$0.912145\pi$
$888$	−797798.	−	268577.i	−1.01174	−	0.340599i
$889$	−4838.82	−	10595.5i	−0.00612261	−	0.0134066i
$890$	214756.	+	231194.i	0.271122	+	0.291875i
$891$	369426.	−	1.25815e6i	0.465342	−	1.58481i
$892$	−941204.	−	353506.i	−1.18292	−	0.444290i
$893$	594467.	−	174551.i	0.745461	−	0.218887i
$894$	235185.	−	917069.i	0.294263	−	1.14743i
$895$	648009.	−	93169.6i	0.808974	−	0.116313i
$896$	3487.28	−	10204.2i	0.00434380	−	0.0127105i
$897$	−325481.	+	400163.i	−0.404521	+	0.497338i
$898$	148386.	+	827866.i	0.184009	+	1.02661i
$899$	73646.7	−	10588.8i	0.0911242	−	0.0131017i
$900$	1439.47	−	19499.4i	0.00177712	−	0.0240733i
$901$	2.00472e6	−	588640.i	2.46948	−	0.725103i
$902$	453600.	−	762513.i	0.557519	−	0.937204i
$903$	2147.73	−	7314.48i	0.00263392	−	0.00897032i
$904$	−685095.	−	345879.i	−0.838328	−	0.423241i
$905$	273376.	+	598611.i	0.333783	+	0.730882i
$906$	413049.	−	511364.i	0.503205	−	0.622979i
$907$	372068.	−	578949.i	0.452280	−	0.703762i	−0.537985	−	0.842954i	$-0.680814\pi$
$907$	372068.	−	578949.i	0.452280	−	0.703762i	0.990265	+	0.139193i	$0.0444507\pi$
$908$	7645.77	−	1644.93i	0.00927362	−	0.00199515i
$909$	−5892.89	+	40986.0i	−0.00713182	+	0.0496029i
$910$	6753.14	+	2806.29i	0.00815498	+	0.00338884i
$911$	102820.	−	89093.7i	0.123891	−	0.107352i	−0.590712	−	0.806883i	$-0.701153\pi$
$911$	102820.	−	89093.7i	0.123891	−	0.107352i	0.714603	+	0.699531i	$0.246608\pi$
$912$	1.36455e6	+	630730.i	1.64059	+	0.758322i
$913$	514771.	−	330823.i	0.617551	−	0.396876i
$914$	37509.4	−	345173.i	0.0449002	−	0.413185i
$915$	1.01573e6	+	880139.i	1.21322	+	1.05126i
$916$	48369.3	−	36036.4i	0.0576473	−	0.0429488i
$917$	1115.04	−	2441.60i	0.00132603	−	0.00290360i
$918$	404461.	+	1.21987e6i	0.479945	+	1.44753i
$919$		−	226168.i		−	0.267794i	−0.990995	−	0.133897i	$-0.957251\pi$
$919$		−	226168.i		−	0.267794i	0.990995	−	0.133897i	$-0.0427491\pi$
$920$	779807.	−	492409.i	0.921322	−	0.581768i
$921$	−1.28456e6			−1.51438
$922$	−182690.	+	60573.0i	−0.214908	+	0.0712553i
$923$	80347.8	+	36693.6i	0.0943128	+	0.0430712i
$924$	10810.3	+	14510.0i	0.0126618	+	0.0169951i
$925$	−105438.	+	121682.i	−0.123229	+	0.142214i
$926$	−1.24217e6	−	134984.i	−1.44863	−	0.157420i
$927$	−83205.3	−	129470.i	−0.0968259	−	0.150664i
$928$	38961.0	−	149084.i	0.0452412	−	0.173115i
$929$	−559613.	−	645828.i	−0.648420	−	0.748316i	0.332420	−	0.943131i	$-0.392135\pi$
$929$	−559613.	−	645828.i	−0.648420	−	0.748316i	−0.980840	+	0.194815i	$0.937589\pi$
$930$	−197698.	+	475745.i	−0.228579	+	0.550057i
$931$	−1.45915e6	−	209794.i	−1.68345	−	0.242044i
$932$	69683.4	+	323895.i	0.0802227	+	0.372883i
$933$	−637332.	−	409589.i	−0.732154	−	0.470527i
$934$	1.25594e6	+	1.01447e6i	1.43971	+	1.16291i
$935$	−2.12015e6	+	968238.i	−2.42517	+	1.10754i
$936$	−60819.4	−	30705.4i	−0.0694209	−	0.0350480i
$937$	463505.	+	136097.i	0.527928	+	0.155014i	0.534826	−	0.844963i	$-0.320377\pi$
$937$	463505.	+	136097.i	0.527928	+	0.155014i	−0.00689735	+	0.999976i	$0.502196\pi$
$938$	3620.43	+	2153.70i	0.00411485	+	0.00244782i
$939$	194002.	+	660709.i	0.220026	+	0.749341i
$940$	438546.	+	32373.9i	0.496317	+	0.0366387i
$941$	215624.	+	1.49970e6i	0.243511	+	1.69366i	0.634228	+	0.773146i	$0.281318\pi$
$941$	215624.	+	1.49970e6i	0.243511	+	1.69366i	−0.390717	+	0.920511i	$0.627773\pi$
$942$	−1.02111e6	+	183022.i	−1.15072	+	0.206253i
$943$	602166.	+	252637.i	0.677163	+	0.284101i
$944$	223671.	+	260529.i	0.250996	+	0.292357i
$945$	−1721.63	−	11974.2i	−0.00192787	−	0.0134086i
$946$	843270.	+	216260.i	0.942290	+	0.241654i
$947$	45349.1	+	154445.i	0.0505672	+	0.172216i	0.980905	−	0.194488i	$-0.0623044\pi$
$947$	45349.1	+	154445.i	0.0505672	+	0.172216i	−0.930338	+	0.366704i	$0.880486\pi$
$948$	−33072.8	+	88056.0i	−0.0368006	+	0.0979811i
$949$	678622.	+	199261.i	0.753521	+	0.221254i
$950$	210664.	−	195686.i	0.233423	−	0.216826i
$951$	−234593.	+	107135.i	−0.259390	+	0.118460i
$952$	−19010.1	−	6399.73i	−0.0209755	−	0.00706135i
$953$	1.23321e6	+	792534.i	1.35784	+	0.872634i	0.998172	−	0.0604450i	$-0.0192520\pi$
$953$	1.23321e6	+	792534.i	1.35784	+	0.872634i	0.359673	+	0.933079i	$0.382888\pi$
$954$	183118.	−	6330.36i	0.201203	−	0.00695555i
$955$	1.09141e6	+	156922.i	1.19669	+	0.172058i
$956$	252843.	−	1.14963e6i	0.276653	−	1.25789i
$957$	169318.	+	195403.i	0.184875	+	0.213357i
$958$	414787.	+	598868.i	0.451954	+	0.652529i
$959$	7161.67	+	11143.8i	0.00778712	+	0.0121170i
$960$	749255.	+	759610.i	0.812994	+	0.824230i
$961$	−444679.	+	513187.i	−0.481504	+	0.555685i
$962$	250556.	+	501980.i	0.270741	+	0.542421i
$963$	−142262.	−	64968.9i	−0.153404	−	0.0700572i
$964$	126996.	+	233846.i	0.136659	+	0.251638i
$965$	1.63774e6			1.75870
$966$	−9470.41	+	9363.30i	−0.0101488	+	0.0100340i
$967$			728547.i			0.779120i	0.921001	+	0.389560i	$0.127373\pi$
$967$			728547.i			0.779120i	−0.921001	+	0.389560i	$0.872627\pi$
$968$	−881744.	+	705577.i	−0.941004	+	0.752998i
$969$	1.16159e6	−	2.54352e6i	1.23710	−	2.70887i
$970$	823249.	+	1.64935e6i	0.874959	+	1.75295i
$971$	−465105.	−	403016.i	−0.493302	−	0.427449i	0.372352	−	0.928092i	$-0.378551\pi$
$971$	−465105.	−	403016.i	−0.493302	−	0.427449i	−0.865654	+	0.500643i	$0.833097\pi$
$972$	16717.5	+	241505.i	0.0176946	+	0.255619i
$973$	−9421.99	+	6055.14i	−0.00995215	+	0.00639586i
$974$	392912.	+	567285.i	0.414169	+	0.597976i
$975$	−86260.0	+	74744.7i	−0.0907403	+	0.0786269i
$976$	−1.30826e6	+	181994.i	−1.37339	+	0.191055i
$977$	1247.60	−	8677.27i	0.00130703	−	0.00909063i	−0.989157	−	0.146859i	$-0.953084\pi$
$977$	1247.60	−	8677.27i	0.00130703	−	0.00909063i	0.990465	+	0.137768i	$0.0439928\pi$
$978$	69175.1	−	2391.37i	0.0723222	−	0.00250017i
$979$	281323.	−	437747.i	0.293522	−	0.456728i
$980$	−917157.	−	503533.i	−0.954974	−	0.524295i
$981$	50294.9	+	110130.i	0.0522620	+	0.114438i
$982$	461963.	−	429117.i	0.479053	−	0.444993i
$983$	145411.	−	495225.i	0.150484	−	0.512502i	−0.849400	−	0.527750i	$-0.823036\pi$
$983$	145411.	−	495225.i	0.150484	−	0.512502i	0.999884	+	0.0152485i	$0.00485393\pi$
$984$	−136686.	+	742999.i	−0.141167	+	0.767358i
$985$	763450.	−	224169.i	0.786879	−	0.231049i
$986$	−277638.	−	71201.3i	−0.285578	−	0.0732375i
$987$	−6285.30	+	903.690i	−0.00645196	+	0.000927652i
$988$	−347978.	−	939524.i	−0.356483	−	0.962485i
$989$	−71386.2	+	636756.i	−0.0729830	+	0.650999i
$990$	−201192.	+	36061.5i	−0.205277	+	0.0367937i
$991$	688569.	−	99001.3i	0.701133	−	0.100808i	0.217476	−	0.976066i	$-0.430218\pi$
$991$	688569.	−	99001.3i	0.701133	−	0.100808i	0.483656	+	0.875258i	$0.339308\pi$
$992$	−224041.	−	454047.i	−0.227669	−	0.461399i
$993$	1.51211e6	−	443994.i	1.53350	−	0.450276i
$994$	1959.97	+	1165.94i	0.00198371	+	0.00118006i
$995$	−163238.	+	555936.i	−0.164882	+	0.561538i
$996$	−313197.	+	416394.i	−0.315718	+	0.419745i
$997$	243651.	+	533522.i	0.245120	+	0.536737i	0.991702	−	0.128555i	$-0.0410340\pi$
$997$	243651.	+	533522.i	0.245120	+	0.536737i	−0.746583	+	0.665293i	$0.768307\pi$
$998$	−579144.	−	467797.i	−0.581467	−	0.469674i
$999$	501758.	−	780750.i	0.502763	−	0.782314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.5.g.a.3.6	✓	460
4.3	odd	2	inner	92.5.g.a.3.45	yes	460
23.8	even	11	inner	92.5.g.a.31.45	yes	460
92.31	odd	22	inner	92.5.g.a.31.6	yes	460

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.5.g.a.3.6	✓	460	1.1	even	1	trivial
92.5.g.a.3.45	yes	460	4.3	odd	2	inner
92.5.g.a.31.6	yes	460	92.31	odd	22	inner
92.5.g.a.31.45	yes	460	23.8	even	11	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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	92.g (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.79675 + 1.25886i) q^{2} +(-8.69828 - 3.97237i) q^{3} +(12.8306 - 9.55912i) q^{4} +(17.8389 - 20.5871i) q^{5} +(38.0258 + 4.13220i) q^{6} +(-0.355839 - 0.553696i) q^{7} +(-36.6808 + 52.4454i) q^{8} +(6.83659 + 7.88985i) q^{9} +(-41.8134 + 100.621i) q^{10} +(177.855 + 25.5717i) q^{11} +(-149.576 + 32.1801i) q^{12} +(85.7828 + 55.1293i) q^{13} +(2.04805 + 1.65429i) q^{14} +(-236.947 + 108.210i) q^{15} +(73.2466 - 245.298i) q^{16} +(-456.893 - 134.156i) q^{17} +(-35.8890 - 21.3495i) q^{18} +(-173.008 - 589.211i) q^{19} +(32.0877 - 434.668i) q^{20} +(0.895700 + 6.22973i) q^{21} +(-707.461 + 126.805i) q^{22} +(-164.776 - 502.683i) q^{23} +(527.392 - 310.475i) q^{24} +(-16.6587 - 115.864i) q^{25} +(-395.095 - 101.324i) q^{26} +(190.092 + 647.395i) q^{27} +(-9.85846 - 3.70273i) q^{28} +(-144.384 - 42.3950i) q^{29} +(763.407 - 709.129i) q^{30} +(-449.764 + 205.400i) q^{31} +(30.6958 + 1023.54i) q^{32} +(-1445.45 - 928.935i) q^{33} +(1903.59 - 65.8069i) q^{34} +(-17.7468 - 2.55160i) q^{35} +(163.137 + 35.8794i) q^{36} +(-900.755 - 1039.53i) q^{37} +(1398.60 + 2019.29i) q^{38} +(-527.169 - 820.291i) q^{39} +(425.356 + 1690.72i) q^{40} +(-808.382 + 932.923i) q^{41} +(-11.2431 - 22.5251i) q^{42} +(-1101.78 - 503.166i) q^{43} +(2526.42 - 1372.04i) q^{44} +284.386 q^{45} +(1258.42 + 1701.13i) q^{46} +1008.92i q^{47} +(-1611.53 + 1842.70i) q^{48} +(997.231 - 2183.63i) q^{49} +(209.105 + 418.934i) q^{50} +(3441.27 + 2981.88i) q^{51} +(1627.63 - 112.668i) q^{52} +(-3691.19 + 2372.18i) q^{53} +(-1536.71 - 2218.70i) q^{54} +(3699.18 - 3205.35i) q^{55} +(42.0913 + 1.64793i) q^{56} +(-835.693 + 5812.37i) q^{57} +(601.559 - 20.7958i) q^{58} +(-725.160 + 1128.37i) q^{59} +(-2005.77 + 3653.40i) q^{60} +(-2143.38 - 4693.34i) q^{61} +(1449.07 - 1346.04i) q^{62} +(1.93585 - 6.59291i) q^{63} +(-1405.03 - 3847.48i) q^{64} +(2665.22 - 782.580i) q^{65} +(6657.41 + 1707.31i) q^{66} +(1583.80 - 227.717i) q^{67} +(-7144.61 + 2646.20i) q^{68} +(-563.576 + 5027.02i) q^{69} +(70.5921 - 12.6529i) q^{70} +(857.416 - 123.278i) q^{71} +(-664.558 + 69.1415i) q^{72} +(6655.10 - 1954.11i) q^{73} +(4728.55 + 2812.90i) q^{74} +(-315.352 + 1073.99i) q^{75} +(-7852.13 - 5906.11i) q^{76} +(-49.1288 - 107.577i) q^{77} +(3034.15 + 2450.81i) q^{78} +(332.381 - 517.194i) q^{79} +(-3743.34 - 5883.77i) q^{80} +(1038.56 - 7223.35i) q^{81} +(1894.81 - 4559.71i) q^{82} +(2573.69 - 2230.12i) q^{83} +(71.0430 + 71.3688i) q^{84} +(-10912.3 + 7012.94i) q^{85} +(4816.60 + 523.411i) q^{86} +(1087.48 + 942.310i) q^{87} +(-7864.98 + 8389.67i) q^{88} +(1203.01 - 2634.23i) q^{89} +(-1079.74 + 358.002i) q^{90} -67.1148i q^{91} +(-6919.37 - 4874.59i) q^{92} +4728.10 q^{93} +(-1270.09 - 3830.62i) q^{94} +(-15216.4 - 6949.11i) q^{95} +(3798.88 - 9024.97i) q^{96} +(11078.7 - 12785.5i) q^{97} +(-1037.36 + 9546.07i) q^{98} +(1014.16 + 1578.07i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 460 q - 3 q^{2} - 43 q^{4} - 18 q^{5} - 44 q^{6} + 144 q^{8} + 1116 q^{9} - 77 q^{10} - 156 q^{12} - 18 q^{13} + 253 q^{14} - 795 q^{16} - 18 q^{17} - 676 q^{18} + 113 q^{20} + 266 q^{21} - 818 q^{22} + 1006 q^{24}+ \cdots + 52545 q^{98}+O(q^{100}) \) 460 * q - 3 * q^2 - 43 * q^4 - 18 * q^5 - 44 * q^6 + 144 * q^8 + 1116 * q^9 - 77 * q^10 - 156 * q^12 - 18 * q^13 + 253 * q^14 - 795 * q^16 - 18 * q^17 - 676 * q^18 + 113 * q^20 + 266 * q^21 - 818 * q^22 + 1006 * q^24 - 4768 * q^25 + 1100 * q^26 + 499 * q^28 + 654 * q^29 - 1401 * q^30 - 2163 * q^32 - 342 * q^33 - 5959 * q^34 - 3317 * q^36 - 3666 * q^37 + 4444 * q^38 + 23023 * q^40 - 1266 * q^41 + 23419 * q^42 + 7066 * q^44 + 5464 * q^45 - 8019 * q^46 - 14166 * q^48 + 14620 * q^49 - 25358 * q^50 - 36264 * q^52 - 9138 * q^53 - 6990 * q^54 - 7592 * q^56 - 3862 * q^57 + 31769 * q^58 + 34819 * q^60 + 7534 * q^61 - 9320 * q^62 + 4562 * q^64 + 9106 * q^65 + 6490 * q^66 - 4842 * q^68 - 22 * q^69 - 4258 * q^70 - 27815 * q^72 - 18 * q^73 - 202 * q^74 + 73926 * q^76 - 56086 * q^77 - 328 * q^78 - 47488 * q^80 + 9788 * q^81 - 42110 * q^82 - 111651 * q^84 + 117026 * q^85 - 55391 * q^86 - 44639 * q^88 + 44574 * q^89 - 4626 * q^90 + 18106 * q^92 - 85004 * q^93 + 55547 * q^94 + 150069 * q^96 - 34146 * q^97 + 52545 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more