LMFDB - Embedded newform 95.5.m.a.83.35

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [95,5,Mod(7,95)] 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("95.7"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 4])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	95.m (of order $12$, degree $4$, 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:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			83.35
Character	$\chi$	$=$	95.83
Dual form			95.5.m.a.87.35

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(6.69961 + 1.79516i) q^{2} +(-3.14304 + 11.7300i) q^{3} +(27.8058 + 16.0537i) q^{4} +(24.9930 + 0.591047i) q^{5} +(-42.1143 + 72.9441i) q^{6} +(38.4526 - 38.4526i) q^{7} +(78.9982 + 78.9982i) q^{8} +(-57.5657 - 33.2356i) q^{9} +(166.383 + 48.8262i) q^{10} -107.854 q^{11} +(-275.705 + 275.705i) q^{12} +(-81.0069 + 21.7057i) q^{13} +(326.646 - 188.589i) q^{14} +(-85.4870 + 291.310i) q^{15} +(130.584 + 226.178i) q^{16} +(-310.191 - 83.1155i) q^{17} +(-326.005 - 326.005i) q^{18} +(79.1311 - 352.220i) q^{19} +(685.463 + 417.665i) q^{20} +(330.190 + 571.906i) q^{21} +(-722.580 - 193.615i) q^{22} +(-49.9183 + 13.3756i) q^{23} +(-1174.94 + 678.353i) q^{24} +(624.301 + 29.5441i) q^{25} -581.680 q^{26} +(-124.759 + 124.759i) q^{27} +(1686.51 - 451.900i) q^{28} +(46.5624 + 26.8828i) q^{29} +(-1095.68 + 1798.20i) q^{30} +1099.57 q^{31} +(6.19167 + 23.1076i) q^{32} +(338.989 - 1265.12i) q^{33} +(-1928.96 - 1113.68i) q^{34} +(983.774 - 938.319i) q^{35} +(-1067.11 - 1848.29i) q^{36} +(1723.28 - 1723.28i) q^{37} +(1162.44 - 2217.69i) q^{38} -1018.43i q^{39} +(1927.71 + 2021.09i) q^{40} +(-413.838 - 716.789i) q^{41} +(1185.49 + 4424.30i) q^{42} +(-567.199 + 2116.82i) q^{43} +(-2998.97 - 1731.46i) q^{44} +(-1419.10 - 864.681i) q^{45} -358.444 q^{46} +(875.523 + 3267.50i) q^{47} +(-3063.49 + 820.861i) q^{48} -556.206i q^{49} +(4129.54 + 1318.65i) q^{50} +(1949.89 - 3377.30i) q^{51} +(-2600.92 - 696.915i) q^{52} +(-4236.32 + 1135.12i) q^{53} +(-1059.80 + 611.874i) q^{54} +(-2695.60 - 63.7468i) q^{55} +6075.37 q^{56} +(3882.83 + 2035.25i) q^{57} +(263.691 + 263.691i) q^{58} +(2638.49 - 1523.33i) q^{59} +(-7053.64 + 6727.73i) q^{60} +(-3378.69 + 5852.06i) q^{61} +(7366.72 + 1973.91i) q^{62} +(-3491.54 + 935.556i) q^{63} -4012.76i q^{64} +(-2037.44 + 494.613i) q^{65} +(4542.19 - 7867.31i) q^{66} +(-1174.11 - 4381.84i) q^{67} +(-7290.82 - 7290.82i) q^{68} -627.580i q^{69} +(8275.34 - 4520.35i) q^{70} +(-1374.27 - 2380.31i) q^{71} +(-1922.04 - 7173.13i) q^{72} +(-46.0454 + 171.844i) q^{73} +(14638.9 - 8451.77i) q^{74} +(-2308.75 + 7230.18i) q^{75} +(7854.75 - 8523.44i) q^{76} +(-4147.27 + 4147.27i) q^{77} +(1828.24 - 6823.10i) q^{78} +(-610.073 + 352.226i) q^{79} +(3130.00 + 5730.05i) q^{80} +(-3763.38 - 6518.36i) q^{81} +(-1485.81 - 5545.12i) q^{82} +(3582.82 + 3582.82i) q^{83} +21203.1i q^{84} +(-7703.49 - 2260.65i) q^{85} +(-7600.03 + 13163.6i) q^{86} +(-461.682 + 461.682i) q^{87} +(-8520.27 - 8520.27i) q^{88} +(-10901.5 - 6293.99i) q^{89} +(-7955.16 - 8340.53i) q^{90} +(-2280.29 + 3949.57i) q^{91} +(-1602.75 - 429.455i) q^{92} +(-3456.00 + 12898.0i) q^{93} +23462.7i q^{94} +(2185.90 - 8756.28i) q^{95} -290.513 q^{96} +(9781.95 + 2621.06i) q^{97} +(998.477 - 3726.37i) q^{98} +(6208.69 + 3584.59i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q - 2 q^{2} - 2 q^{3} - 20 q^{5} - 40 q^{6} + 52 q^{7} + 108 q^{8} - 2 q^{10} - 304 q^{11} - 268 q^{12} + 198 q^{13} + 172 q^{15} + 4064 q^{16} + 238 q^{17} + 3792 q^{18} + 528 q^{20} - 796 q^{21} - 2774 q^{22}+ \cdots + 15572 q^{98}+O(q^{100}) $ 152 * q - 2 * q^2 - 2 * q^3 - 20 * q^5 - 40 * q^6 + 52 * q^7 + 108 * q^8 - 2 * q^10 - 304 * q^11 - 268 * q^12 + 198 * q^13 + 172 * q^15 + 4064 * q^16 + 238 * q^17 + 3792 * q^18 + 528 * q^20 - 796 * q^21 - 2774 * q^22 - 1622 * q^23 - 1648 * q^25 - 2608 * q^26 + 88 * q^27 + 56 * q^28 + 188 * q^30 - 1728 * q^31 - 1916 * q^32 + 1696 * q^33 + 6898 * q^35 - 19748 * q^36 - 1288 * q^37 + 5394 * q^38 + 2232 * q^40 + 5372 * q^41 + 2266 * q^42 - 372 * q^43 - 3000 * q^45 - 12664 * q^46 - 1712 * q^47 + 2028 * q^48 + 34564 * q^50 + 3636 * q^51 + 5342 * q^52 - 1952 * q^53 - 13500 * q^55 + 7152 * q^56 + 16344 * q^57 - 19932 * q^58 + 2238 * q^60 - 2668 * q^61 - 2044 * q^62 + 27314 * q^63 - 46784 * q^65 - 4132 * q^66 + 18598 * q^67 + 18884 * q^68 - 4570 * q^70 - 4420 * q^71 - 20560 * q^72 - 10382 * q^73 - 61252 * q^75 + 16524 * q^76 - 20356 * q^77 + 35972 * q^78 + 44590 * q^80 + 20256 * q^81 - 16708 * q^82 - 4148 * q^83 + 3838 * q^85 - 68200 * q^86 - 139812 * q^87 - 102744 * q^88 - 57328 * q^90 + 59052 * q^91 - 38588 * q^92 + 69836 * q^93 + 33510 * q^95 + 13440 * q^96 + 5928 * q^97 + 15572 * q^98

Character values

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

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	6.69961	+	1.79516i	1.67490	+	0.448789i	0.966426	−	0.256944i	$-0.0827157\pi$
$2$	6.69961	+	1.79516i	1.67490	+	0.448789i	0.708477	+	0.705733i	$0.249382\pi$
$3$	−3.14304	+	11.7300i	−0.349227	+	1.30333i	0.538370	+	0.842709i	$0.319040\pi$
$3$	−3.14304	+	11.7300i	−0.349227	+	1.30333i	−0.887596	+	0.460622i	$0.847626\pi$
$4$	27.8058	+	16.0537i	1.73787	+	1.00336i
$5$	24.9930	+	0.591047i	0.999720	+	0.0236419i
$5$	24.9930	+	0.591047i	0.999720	+	0.0236419i
$6$	−42.1143	+	72.9441i	−1.16984	+	2.02622i
$7$	38.4526	−	38.4526i	0.784747	−	0.784747i	−0.195881	−	0.980628i	$-0.562757\pi$
$7$	38.4526	−	38.4526i	0.784747	−	0.784747i	0.980628	+	0.195881i	$0.0627565\pi$
$8$	78.9982	+	78.9982i	1.23435	+	1.23435i
$9$	−57.5657	−	33.2356i	−0.710687	−	0.410316i
$10$	166.383	+	48.8262i	1.66383	+	0.488262i
$11$	−107.854			−0.891355			−0.445678	−	0.895194i	$-0.647037\pi$
$11$	−107.854			−0.891355			−0.445678	+	0.895194i	$0.647037\pi$
$12$	−275.705	+	275.705i	−1.91461	+	1.91461i
$13$	−81.0069	+	21.7057i	−0.479331	+	0.128436i	−0.490391	−	0.871503i	$-0.663146\pi$
$13$	−81.0069	+	21.7057i	−0.479331	+	0.128436i	0.0110602	+	0.999939i	$0.496479\pi$
$14$	326.646	−	188.589i	1.66656	−	0.962190i
$15$	−85.4870	+	291.310i	−0.379942	+	1.29471i
$16$	130.584	+	226.178i	0.510094	+	0.883508i
$17$	−310.191	−	83.1155i	−1.07333	−	0.287597i	−0.321467	−	0.946921i	$-0.604176\pi$
$17$	−310.191	−	83.1155i	−1.07333	−	0.287597i	−0.751859	+	0.659324i	$0.770843\pi$
$18$	−326.005	−	326.005i	−1.00619	−	1.00619i
$19$	79.1311	−	352.220i	0.219200	−	0.975680i
$19$	79.1311	−	352.220i	0.219200	−	0.975680i
$20$	685.463	+	417.665i	1.71366	+	1.04416i
$21$	330.190	+	571.906i	0.748731	+	1.29684i
$22$	−722.580	−	193.615i	−1.49293	−	0.400030i
$23$	−49.9183	+	13.3756i	−0.0943635	+	0.0252846i	−0.305692	−	0.952131i	$-0.598888\pi$
$23$	−49.9183	+	13.3756i	−0.0943635	+	0.0252846i	0.211328	+	0.977415i	$0.432221\pi$
$24$	−1174.94	+	678.353i	−2.03983	+	1.17770i
$25$	624.301	+	29.5441i	0.998882	+	0.0472706i
$26$	−581.680			−0.860474
$27$	−124.759	+	124.759i	−0.171137	+	0.171137i
$28$	1686.51	−	451.900i	2.15117	−	0.576403i
$29$	46.5624	+	26.8828i	0.0553655	+	0.0319653i	0.527427	−	0.849600i	$-0.323157\pi$
$29$	46.5624	+	26.8828i	0.0553655	+	0.0319653i	−0.472062	+	0.881565i	$0.656490\pi$
$30$	−1095.68	+	1798.20i	−1.21742	+	1.99800i
$31$	1099.57			1.14420			0.572099	−	0.820185i	$-0.306129\pi$
$31$	1099.57			1.14420			0.572099	+	0.820185i	$0.306129\pi$
$32$	6.19167	+	23.1076i	0.00604656	+	0.0225661i
$33$	338.989	−	1265.12i	0.311285	−	1.16173i
$34$	−1928.96	−	1113.68i	−1.66865	−	0.963395i
$35$	983.774	−	938.319i	0.803081	−	0.765975i
$36$	−1067.11	−	1848.29i	−0.823386	−	1.42615i
$37$	1723.28	−	1723.28i	1.25879	−	1.25879i	0.307118	−	0.951671i	$-0.400635\pi$
$37$	1723.28	−	1723.28i	1.25879	−	1.25879i	0.951671	−	0.307118i	$-0.0993646\pi$
$38$	1162.44	−	2217.69i	0.805013	−	1.53580i
$39$		−	1018.43i		−	0.669580i
$40$	1927.71	+	2021.09i	1.20482	+	1.26318i
$41$	−413.838	−	716.789i	−0.246186	−	0.426406i	0.716279	−	0.697815i	$-0.245844\pi$
$41$	−413.838	−	716.789i	−0.246186	−	0.426406i	−0.962464	+	0.271408i	$0.912511\pi$
$42$	1185.49	+	4424.30i	0.672044	+	2.50810i
$43$	−567.199	+	2116.82i	−0.306760	+	1.14484i	0.624660	+	0.780897i	$0.285238\pi$
$43$	−567.199	+	2116.82i	−0.306760	+	1.14484i	−0.931420	+	0.363946i	$0.881429\pi$
$44$	−2998.97	−	1731.46i	−1.54905	−	0.894347i
$45$	−1419.10	−	864.681i	−0.700788	−	0.427003i
$46$	−358.444			−0.169397
$47$	875.523	+	3267.50i	0.396344	+	1.47917i	0.819480	+	0.573108i	$0.194262\pi$
$47$	875.523	+	3267.50i	0.396344	+	1.47917i	−0.423136	+	0.906066i	$0.639071\pi$
$48$	−3063.49	+	820.861i	−1.32964	+	0.356276i
$49$		−	556.206i		−	0.231656i
$50$	4129.54	+	1318.65i	1.65182	+	0.527461i
$51$	1949.89	−	3377.30i	0.749668	−	1.29846i
$52$	−2600.92	−	696.915i	−0.961880	−	0.257735i
$53$	−4236.32	+	1135.12i	−1.50812	+	0.404101i	−0.915812	−	0.401608i	$-0.868452\pi$
$53$	−4236.32	+	1135.12i	−1.50812	+	0.404101i	−0.592313	+	0.805708i	$0.701785\pi$
$54$	−1059.80	+	611.874i	−0.363442	+	0.209833i
$55$	−2695.60	−	63.7468i	−0.891106	−	0.0210733i
$56$	6075.37			1.93730
$57$	3882.83	+	2035.25i	1.19508	+	0.626423i
$58$	263.691	+	263.691i	0.0783863	+	0.0783863i
$59$	2638.49	−	1523.33i	0.757969	−	0.437614i	−0.0705969	−	0.997505i	$-0.522490\pi$
$59$	2638.49	−	1523.33i	0.757969	−	0.437614i	0.828566	+	0.559891i	$0.189157\pi$
$60$	−7053.64	+	6727.73i	−1.95934	+	1.86881i
$61$	−3378.69	+	5852.06i	−0.908005	+	1.57271i	−0.0911733	+	0.995835i	$0.529062\pi$
$61$	−3378.69	+	5852.06i	−0.908005	+	1.57271i	−0.816832	+	0.576876i	$0.804272\pi$
$62$	7366.72	+	1973.91i	1.91642	+	0.513503i
$63$	−3491.54	+	935.556i	−0.879704	+	0.235716i
$64$		−	4012.76i		−	0.979677i
$65$	−2037.44	+	494.613i	−0.482233	+	0.117068i
$66$	4542.19	−	7867.31i	1.04274	−	1.80609i
$67$	−1174.11	−	4381.84i	−0.261553	−	0.976128i	−0.964327	−	0.264715i	$-0.914722\pi$
$67$	−1174.11	−	4381.84i	−0.261553	−	0.976128i	0.702774	−	0.711413i	$-0.251945\pi$
$68$	−7290.82	−	7290.82i	−1.57673	−	1.57673i
$69$		−	627.580i		−	0.131817i
$70$	8275.34	−	4520.35i	1.68884	−	0.922520i
$71$	−1374.27	−	2380.31i	−0.272619	−	0.472190i	0.696913	−	0.717156i	$-0.254557\pi$
$71$	−1374.27	−	2380.31i	−0.272619	−	0.472190i	−0.969532	+	0.244966i	$0.921223\pi$
$72$	−1922.04	−	7173.13i	−0.370763	−	1.38371i
$73$	−46.0454	+	171.844i	−0.00864054	+	0.0322469i	−0.970112	−	0.242660i	$-0.921980\pi$
$73$	−46.0454	+	171.844i	−0.00864054	+	0.0322469i	0.961471	+	0.274906i	$0.0886469\pi$
$74$	14638.9	−	8451.77i	2.67328	−	1.54342i
$75$	−2308.75	+	7230.18i	−0.410445	+	1.28537i
$76$	7854.75	−	8523.44i	1.35989	−	1.47567i
$77$	−4147.27	+	4147.27i	−0.699488	+	0.699488i
$78$	1828.24	−	6823.10i	0.300500	−	1.12148i
$79$	−610.073	+	352.226i	−0.0977525	+	0.0564374i	−0.548079	−	0.836426i	$-0.684641\pi$
$79$	−610.073	+	352.226i	−0.0977525	+	0.0564374i	0.450327	+	0.892864i	$0.351307\pi$
$80$	3130.00	+	5730.05i	0.489063	+	0.895321i
$81$	−3763.38	−	6518.36i	−0.573598	−	0.993501i
$82$	−1485.81	−	5545.12i	−0.220971	−	0.824675i
$83$	3582.82	+	3582.82i	0.520079	+	0.520079i	0.917595	−	0.397516i	$-0.130128\pi$
$83$	3582.82	+	3582.82i	0.520079	+	0.520079i	−0.397516	+	0.917595i	$0.630128\pi$
$84$			21203.1i			3.00498i
$85$	−7703.49	−	2260.65i	−1.06623	−	0.312892i
$86$	−7600.03	+	13163.6i	−1.02759	+	1.77983i
$87$	−461.682	+	461.682i	−0.0609965	+	0.0609965i
$88$	−8520.27	−	8520.27i	−1.10024	−	1.10024i
$89$	−10901.5	−	6293.99i	−1.37628	−	0.794596i	−0.384571	−	0.923096i	$-0.625650\pi$
$89$	−10901.5	−	6293.99i	−1.37628	−	0.794596i	−0.991710	+	0.128500i	$0.958984\pi$
$90$	−7955.16	−	8340.53i	−0.982118	−	1.02969i
$91$	−2280.29	+	3949.57i	−0.275364	+	0.476944i
$92$	−1602.75	−	429.455i	−0.189360	−	0.0507390i
$93$	−3456.00	+	12898.0i	−0.399584	+	1.49127i
$94$			23462.7i			2.65535i
$95$	2185.90	−	8756.28i	0.242205	−	0.970225i
$96$	−290.513			−0.0315227
$97$	9781.95	+	2621.06i	1.03964	+	0.278570i	0.737963	−	0.674841i	$-0.235788\pi$
$97$	9781.95	+	2621.06i	1.03964	+	0.278570i	0.301674	+	0.953411i	$0.402455\pi$
$98$	998.477	−	3726.37i	0.103965	−	0.388002i
$99$	6208.69	+	3584.59i	0.633475	+	0.365737i
$100$	16884.9	+	10843.9i	1.68849	+	1.08439i
$101$	7684.74	−	13310.4i	0.753332	−	1.30481i	−0.192867	−	0.981225i	$-0.561778\pi$
$101$	7684.74	−	13310.4i	0.753332	−	1.30481i	0.946199	−	0.323585i	$-0.104888\pi$
$102$	19126.3	−	19126.3i	1.83836	−	1.83836i
$103$	10999.5	+	10999.5i	1.03681	+	1.03681i	0.999296	+	0.0375090i	$0.0119423\pi$
$103$	10999.5	+	10999.5i	1.03681	+	1.03681i	0.0375090	+	0.999296i	$0.488058\pi$
$104$	−8114.11	−	4684.69i	−0.750195	−	0.433126i
$105$	7914.43	+	14488.8i	0.717862	+	1.31418i
$106$	−30419.4			−2.70732
$107$	3995.19	−	3995.19i	0.348955	−	0.348955i	−0.510765	−	0.859720i	$-0.670638\pi$
$107$	3995.19	−	3995.19i	0.348955	−	0.348955i	0.859720	+	0.510765i	$0.170638\pi$
$108$	−5471.86	+	1466.18i	−0.469124	+	0.125701i
$109$	−17466.9	+	10084.5i	−1.47016	+	0.848796i	−0.999439	−	0.0334873i	$-0.989339\pi$
$109$	−17466.9	+	10084.5i	−1.47016	+	0.848796i	−0.470719	+	0.882283i	$0.656005\pi$
$110$	−17945.0	−	5266.09i	−1.48306	−	0.435214i
$111$	14797.7	+	25630.4i	1.20102	+	2.08022i
$112$	13718.4	+	3675.84i	1.09362	+	0.293036i
$113$	−6267.10	−	6267.10i	−0.490806	−	0.490806i	0.417754	−	0.908560i	$-0.362817\pi$
$113$	−6267.10	−	6267.10i	−0.490806	−	0.490806i	−0.908560	+	0.417754i	$0.862817\pi$
$114$	22359.9	+	20605.7i	1.72052	+	1.58554i
$115$	−1255.51	+	304.791i	−0.0949349	+	0.0230466i
$116$	863.138	+	1495.00i	0.0641452	+	0.111103i
$117$	5384.62	+	1442.80i	0.393354	+	0.105399i
$118$	20411.5	−	5469.24i	1.46592	−	0.392793i
$119$	−15123.7	+	8731.66i	−1.06798	+	0.616599i
$120$	−29766.3	+	16259.6i	−2.06710	+	1.12914i
$121$	−3008.52			−0.205486
$122$	−33141.3	+	33141.3i	−2.22664	+	2.22664i
$123$	9708.63	−	2601.42i	0.641723	−	0.171949i
$124$	30574.6	+	17652.2i	1.98846	+	1.14804i
$125$	15585.7	+	1107.39i	0.997485	+	0.0708728i
$126$	−25071.5			−1.57921
$127$	3980.67	+	14856.1i	0.246802	+	0.921078i	0.972469	+	0.233032i	$0.0748647\pi$
$127$	3980.67	+	14856.1i	0.246802	+	0.921078i	−0.725667	+	0.688046i	$0.758469\pi$
$128$	7302.60	−	27253.7i	0.445715	−	1.66343i
$129$	−23047.5	−	13306.5i	−1.38498	−	0.799619i
$130$	−14537.9	−	343.801i	−0.860233	−	0.0203432i
$131$	5158.23	+	8934.31i	0.300579	+	0.520617i	0.976267	−	0.216570i	$-0.0694869\pi$
$131$	5158.23	+	8934.31i	0.300579	+	0.520617i	−0.675689	+	0.737187i	$0.736154\pi$
$132$	29735.8	−	29735.8i	1.70660	−	1.70660i
$133$	−10501.0	−	16586.6i	−0.593646	−	0.937678i
$134$		−	31464.3i		−	1.75230i
$135$	−3191.83	+	3044.36i	−0.175135	+	0.167043i
$136$	−17938.6	−	31070.5i	−0.969863	−	1.67985i
$137$	781.310	+	2915.89i	0.0416277	+	0.155357i	0.983611	−	0.180302i	$-0.0577076\pi$
$137$	781.310	+	2915.89i	0.0416277	+	0.155357i	−0.941984	+	0.335659i	$0.891041\pi$
$138$	1126.60	−	4204.55i	0.0591580	−	0.220781i
$139$	6826.19	+	3941.11i	0.353304	+	0.203980i	0.666140	−	0.745827i	$-0.267945\pi$
$139$	6826.19	+	3941.11i	0.353304	+	0.203980i	−0.312835	+	0.949807i	$0.601279\pi$
$140$	42418.2	−	10297.5i	2.16419	−	0.525385i
$141$	−41079.5			−2.06627
$142$	−4934.07	−	18414.2i	−0.244697	−	0.913221i
$143$	8736.92	−	2341.05i	0.427254	−	0.114482i
$144$		−	17360.1i		−	0.837197i
$145$	1147.85	+	699.403i	0.0545943	+	0.0332653i
$146$	−616.974	+	1068.63i	−0.0289442	+	0.0501327i
$147$	6524.29	+	1748.18i	0.301925	+	0.0809005i
$148$	75582.4	−	20252.2i	3.45062	−	0.924591i
$149$	−8190.14	+	4728.58i	−0.368909	+	0.212990i	−0.672982	−	0.739659i	$-0.734987\pi$
$149$	−8190.14	+	4728.58i	−0.368909	+	0.212990i	0.304073	+	0.952649i	$0.401653\pi$
$150$	−28447.1	+	44294.9i	−1.26431	+	1.96866i
$151$	−4722.04			−0.207098			−0.103549	−	0.994624i	$-0.533020\pi$
$151$	−4722.04			−0.207098			−0.103549	+	0.994624i	$0.533020\pi$
$152$	34076.0	−	21573.6i	1.47490	−	0.933759i
$153$	15094.0	+	15094.0i	0.644794	+	0.644794i
$154$	−35230.1	+	20340.1i	−1.48550	+	0.857653i
$155$	27481.7	+	649.900i	1.14388	+	0.0270510i
$156$	16349.6	−	28318.3i	0.671828	−	1.16364i
$157$	−8288.76	−	2220.97i	−0.336272	−	0.0901037i	0.0867320	−	0.996232i	$-0.472358\pi$
$157$	−8288.76	−	2220.97i	−0.336272	−	0.0901037i	−0.423004	+	0.906128i	$0.639024\pi$
$158$	−4719.56	+	1264.60i	−0.189054	+	0.0506570i
$159$		−	53259.7i		−	2.10671i
$160$	141.091	+	581.189i	0.00551136	+	0.0227027i
$161$	−1405.16	+	2433.81i	−0.0542094	+	0.0938935i
$162$	−13511.7	−	50426.3i	−0.514849	−	1.92144i
$163$	23181.4	+	23181.4i	0.872499	+	0.872499i	0.992744	−	0.120245i	$-0.0383680\pi$
$163$	23181.4	+	23181.4i	0.872499	+	0.872499i	−0.120245	+	0.992744i	$0.538368\pi$
$164$		−	26574.6i		−	0.988049i
$165$	9220.11	−	31418.9i	0.338663	−	1.15405i
$166$	17571.8	+	30435.3i	0.637676	+	1.10449i
$167$	−11763.3	−	43901.1i	−0.421789	−	1.57414i	−0.770837	−	0.637032i	$-0.780162\pi$
$167$	−11763.3	−	43901.1i	−0.421789	−	1.57414i	0.349048	−	0.937105i	$-0.386505\pi$
$168$	−19095.1	+	71264.0i	−0.676557	+	2.52494i
$169$	−18643.6	+	10763.9i	−0.652763	+	0.376873i
$170$	−47552.2	−	28974.4i	−1.64541	−	1.00258i
$171$	−16261.5	+	17645.8i	−0.556119	+	0.603462i
$172$	−49754.2	+	49754.2i	−1.68179	+	1.68179i
$173$	−3502.43	+	13071.2i	−0.117024	+	0.436741i	−0.999430	−	0.0337476i	$-0.989256\pi$
$173$	−3502.43	+	13071.2i	−0.117024	+	0.436741i	0.882406	+	0.470489i	$0.155922\pi$
$174$	−3921.89	+	2264.30i	−0.129538	+	0.0747887i
$175$	25142.1	−	22870.0i	0.820965	−	0.746774i
$176$	−14084.0	−	24394.2i	−0.454674	−	0.787519i
$177$	9575.79	+	35737.3i	0.305653	+	1.14071i
$178$	−61737.2	−	61737.2i	−1.94853	−	1.94853i
$179$			34791.5i			1.08584i	0.839784	+	0.542921i	$0.182682\pi$
$179$			34791.5i			1.08584i	−0.839784	+	0.542921i	$0.817318\pi$
$180$	−25577.8	−	46824.9i	−0.789439	−	1.44521i
$181$	12888.8	−	22324.1i	0.393419	−	0.681422i	−0.599479	−	0.800390i	$-0.704626\pi$
$181$	12888.8	−	22324.1i	0.393419	−	0.681422i	0.992898	+	0.118969i	$0.0379589\pi$
$182$	−22367.1	+	22367.1i	−0.675254	+	0.675254i
$183$	−58025.2	−	58025.2i	−1.73266	−	1.73266i
$184$	−5000.10	−	2886.81i	−0.147687	−	0.0852672i
$185$	44088.6	−	42051.5i	1.28820	−	1.22868i
$186$	−46307.8	+	80207.4i	−1.33853	+	2.31840i
$187$	33455.4	+	8964.34i	0.956715	+	0.256351i
$188$	−28110.8	+	104911.i	−0.795348	+	2.96828i
$189$			9594.60i			0.268598i
$190$	30363.6	−	54739.7i	0.841097	−	1.51633i
$191$	−18470.6			−0.506308			−0.253154	−	0.967426i	$-0.581468\pi$
$191$	−18470.6			−0.506308			−0.253154	+	0.967426i	$0.581468\pi$
$192$	47069.6	+	12612.3i	1.27684	+	0.342129i
$193$	12106.9	−	45183.5i	0.325026	−	1.21301i	−0.589260	−	0.807944i	$-0.700580\pi$
$193$	12106.9	−	45183.5i	0.325026	−	1.21301i	0.914286	−	0.405070i	$-0.132753\pi$
$194$	60830.1	+	35120.3i	1.61627	+	0.933156i
$195$	601.941	−	25453.7i	0.0158301	−	0.669393i
$196$	8929.18	−	15465.8i	0.232434	−	0.402587i
$197$	−42874.3	+	42874.3i	−1.10475	+	1.10475i	−0.110923	+	0.993829i	$0.535381\pi$
$197$	−42874.3	+	42874.3i	−1.10475	+	1.10475i	−0.993829	+	0.110923i	$0.964619\pi$
$198$	35160.9	+	35160.9i	0.896870	+	0.896870i
$199$	−4928.94	−	2845.72i	−0.124465	−	0.0718599i	0.436475	−	0.899716i	$-0.356227\pi$
$199$	−4928.94	−	2845.72i	−0.124465	−	0.0718599i	−0.560940	+	0.827857i	$0.689560\pi$
$200$	46984.7	+	51652.6i	1.17462	+	1.29132i
$201$	55089.2			1.36356
$202$	75379.0	−	75379.0i	1.84734	−	1.84734i
$203$	2824.16	−	756.732i	0.0685326	−	0.0183633i
$204$	108437.	−	62605.8i	2.60564	−	1.50437i
$205$	−9919.41	−	18159.3i	−0.236036	−	0.432108i
$206$	53946.4	+	93438.0i	1.27124	+	2.20186i
$207$	3318.12	+	889.088i	0.0774376	+	0.0207493i
$208$	−15487.6	−	15487.6i	−0.357978	−	0.357978i
$209$	−8534.60	+	37988.4i	−0.195385	+	0.869677i
$210$	27013.9	+	111277.i	0.612560	+	2.52329i
$211$	−1926.99	−	3337.65i	−0.0432828	−	0.0749680i	0.843572	−	0.537015i	$-0.180448\pi$
$211$	−1926.99	−	3337.65i	−0.0432828	−	0.0749680i	−0.886855	+	0.462047i	$0.847115\pi$
$212$	−136017.	−	36445.7i	−3.02637	−	0.810915i
$213$	32240.4	−	8638.78i	0.710626	−	0.190412i
$214$	33938.2	−	19594.2i	0.741074	−	0.427859i
$215$	−15427.1	+	52570.3i	−0.333740	+	1.13727i
$216$	−19711.4			−0.422484
$217$	42281.5	−	42281.5i	0.897906	−	0.897906i
$218$	−135125.	+	36206.7i	−2.84330	+	0.761861i
$219$	−1871.00	−	1080.22i	−0.0390109	−	0.0225230i
$220$	−73929.9	−	45046.8i	−1.52748	−	0.930720i
$221$	26931.7			0.551417
$222$	53128.5	+	198278.i	1.07801	+	4.02317i
$223$	11018.9	−	41123.1i	0.221579	−	0.826945i	−0.762167	−	0.647380i	$-0.775865\pi$
$223$	11018.9	−	41123.1i	0.221579	−	0.826945i	0.983746	−	0.179564i	$-0.0574688\pi$
$224$	1126.63	+	650.463i	0.0224537	+	0.0129636i
$225$	−34956.4	−	22449.7i	−0.690497	−	0.443451i
$226$	−30736.7	−	53237.6i	−0.601784	−	1.04232i
$227$	−49748.5	+	49748.5i	−0.965448	+	0.965448i	−0.999423	−	0.0339751i	$-0.989183\pi$
$227$	−49748.5	+	49748.5i	−0.965448	+	0.965448i	0.0339751	+	0.999423i	$0.489183\pi$
$228$	75292.0	+	118926.i	1.44837	+	2.28773i
$229$		−	63021.3i		−	1.20176i	−0.799340	−	0.600879i	$-0.794818\pi$
$229$		−	63021.3i		−	1.20176i	0.799340	−	0.600879i	$-0.205182\pi$
$230$	−8958.60	−	211.858i	−0.169350	−	0.00400487i
$231$	−35612.3	−	61682.4i	−0.667385	−	1.15594i
$232$	1554.65	+	5802.04i	0.0288840	+	0.107797i
$233$	−5940.37	+	22169.8i	−0.109421	+	0.408366i	−0.998809	−	0.0487875i	$-0.984464\pi$
$233$	−5940.37	+	22169.8i	−0.109421	+	0.408366i	0.889388	+	0.457153i	$0.151131\pi$
$234$	33484.8	+	19332.5i	0.611528	+	0.353066i
$235$	19950.7	+	82182.0i	0.361262	+	1.48813i
$236$	97820.6			1.75633
$237$	−2214.12	−	8263.21i	−0.0394189	−	0.147113i
$238$	−116998.	+	31349.4i	−2.06549	+	0.553446i
$239$		−	57418.5i		−	1.00521i	−0.864517	−	0.502604i	$-0.832375\pi$
$239$		−	57418.5i		−	1.00521i	0.864517	−	0.502604i	$-0.167625\pi$
$240$	−77051.1	+	18705.1i	−1.33769	+	0.324742i
$241$	30532.7	−	52884.3i	0.525692	−	0.910526i	−0.473860	−	0.880600i	$-0.657140\pi$
$241$	30532.7	−	52884.3i	0.525692	−	0.910526i	0.999552	−	0.0299255i	$-0.00952702\pi$
$242$	−20156.0	−	5400.77i	−0.344170	−	0.0922200i
$243$	74484.3	−	19958.0i	1.26140	−	0.337991i
$244$	−187894.	+	108481.i	−3.15598	+	1.82211i
$245$	328.744	−	13901.3i	0.00547679	−	0.231591i
$246$	69714.0			1.15199
$247$	1235.04	+	30249.9i	0.0202436	+	0.495827i
$248$	86864.4	+	86864.4i	1.41234	+	1.41234i
$249$	−53287.4	+	30765.5i	−0.859460	+	0.496210i
$250$	102430.	+	35397.9i	1.63888	+	0.566366i
$251$	−19301.6	+	33431.4i	−0.306370	+	0.530648i	−0.977565	−	0.210632i	$-0.932448\pi$
$251$	−19301.6	+	33431.4i	−0.306370	+	0.530648i	0.671195	+	0.741280i	$0.265781\pi$
$252$	−112104.	−	30038.3i	−1.76531	−	0.473014i
$253$	5383.88	−	1442.61i	0.0841113	−	0.0225376i
$254$			106676.i			1.65348i
$255$	50729.7	−	83256.5i	0.780157	−	1.28038i
$256$	65747.1	−	113877.i	1.00322	−	1.73763i
$257$	9859.26	+	36795.3i	0.149272	+	0.557090i	0.999528	+	0.0307211i	$0.00978036\pi$
$257$	9859.26	+	36795.3i	0.149272	+	0.557090i	−0.850256	+	0.526369i	$0.823553\pi$
$258$	−130522.	−	130522.i	−1.96085	−	1.96085i
$259$		−	132529.i		−	1.97566i
$260$	−64593.0	−	18955.3i	−0.955518	−	0.280404i
$261$	−1786.93	−	3095.06i	−0.0262317	−	0.0454347i
$262$	18519.7	+	69116.3i	0.269793	+	1.00688i
$263$	24139.8	−	90090.8i	0.348997	−	1.30247i	−0.538876	−	0.842385i	$-0.681151\pi$
$263$	24139.8	−	90090.8i	0.348997	−	1.30247i	0.887873	−	0.460089i	$-0.152182\pi$
$264$	126722.	−	73163.0i	1.81821	−	1.04975i
$265$	−106549.	+	25866.2i	−1.51726	+	0.368333i
$266$	−40577.1	−	129975.i	−0.573480	−	1.83694i
$267$	108092.	−	108092.i	1.51625	−	1.51625i
$268$	37697.7	−	140690.i	0.524862	−	1.95881i
$269$	−39017.8	+	22527.0i	−0.539211	+	0.311313i	−0.744759	−	0.667334i	$-0.767436\pi$
$269$	−39017.8	+	22527.0i	−0.539211	+	0.311313i	0.205548	+	0.978647i	$0.434102\pi$
$270$	−26849.2	+	14666.2i	−0.368301	+	0.201182i
$271$	11003.8	+	19059.1i	0.149832	+	0.259516i	0.931165	−	0.364598i	$-0.118794\pi$
$271$	11003.8	+	19059.1i	0.149832	+	0.259516i	−0.781334	+	0.624114i	$0.785460\pi$
$272$	−21707.1	−	81012.0i	−0.293403	−	1.09499i
$273$	−39161.3	−	39161.3i	−0.525451	−	0.525451i
$274$			20937.9i			0.278890i
$275$	−67333.4	−	3186.45i	−0.890359	−	0.0421348i
$276$	10075.0	−	17450.4i	0.132259	−	0.229080i
$277$	−55782.6	+	55782.6i	−0.727008	+	0.727008i	−0.970023	−	0.243015i	$-0.921864\pi$
$277$	−55782.6	+	55782.6i	−0.727008	+	0.727008i	0.243015	+	0.970023i	$0.421864\pi$
$278$	38658.0	+	38658.0i	0.500207	+	0.500207i
$279$	−63297.7	−	36545.0i	−0.813167	−	0.469482i
$280$	151842.	+	3590.83i	1.93676	+	0.0458014i
$281$	−13239.7	+	22931.9i	−0.167674	+	0.290420i	−0.937602	−	0.347711i	$-0.886959\pi$
$281$	−13239.7	+	22931.9i	−0.167674	+	0.290420i	0.769927	+	0.638131i	$0.220292\pi$
$282$	−275217.	−	73744.1i	−3.46080	−	0.927318i
$283$	−1902.36	+	7099.71i	−0.0237531	+	0.0886478i	−0.976785	−	0.214223i	$-0.931278\pi$
$283$	−1902.36	+	7099.71i	−0.0237531	+	0.0886478i	0.953032	+	0.302870i	$0.0979449\pi$
$284$		−	88248.7i		−	1.09414i
$285$	95840.6	+	53161.9i	1.17994	+	0.654502i
$286$	62736.5			0.766988
$287$	−43475.6	−	11649.2i	−0.527815	−	0.141428i
$288$	411.567	−	1535.99i	0.00496199	−	0.0185184i
$289$	16979.2	+	9802.95i	0.203293	+	0.117371i
$290$	6434.59	+	6746.30i	0.0765111	+	0.0802175i
$291$	−61490.1	+	106504.i	−0.726138	+	1.25771i
$292$	−4039.07	+	4039.07i	−0.0473713	+	0.0473713i
$293$	70491.1	+	70491.1i	0.821105	+	0.821105i	0.986267	−	0.165161i	$-0.0528145\pi$
$293$	70491.1	+	70491.1i	0.821105	+	0.821105i	−0.165161	+	0.986267i	$0.552814\pi$
$294$	40572.0	+	23424.2i	0.469387	+	0.271001i
$295$	66844.2	−	36513.2i	0.768103	−	0.419572i
$296$	272272.			3.10756
$297$	13455.7	−	13455.7i	0.152544	−	0.152544i
$298$	−63359.4	+	16977.1i	−0.713474	+	0.191175i
$299$	3753.40	−	2167.03i	0.0419839	−	0.0242394i
$300$	−180268.	+	163977.i	−2.00298	+	1.82197i
$301$	59586.8	+	103207.i	0.657684	+	1.13914i
$302$	−31635.8	−	8476.79i	−0.346869	−	0.0929432i
$303$	131977.	+	131977.i	1.43752	+	1.43752i
$304$	89997.8	−	28096.6i	0.973833	−	0.304023i
$305$	−87902.4	+	144264.i	−0.944933	+	1.55080i
$306$	74027.8	+	128220.i	0.790591	+	1.36934i
$307$	138064.	+	36994.3i	1.46489	+	0.392516i	0.901176	−	0.433454i	$-0.142705\pi$
$307$	138064.	+	36994.3i	1.46489	+	0.392516i	0.563714	+	0.825970i	$0.309372\pi$
$308$	−181897.	+	48739.2i	−1.91745	+	0.513780i
$309$	−163595.	+	94451.8i	−1.71338	+	0.989221i
$310$	182950.	+	53688.0i	1.90375	+	0.558668i
$311$	70040.8			0.724153			0.362076	−	0.932148i	$-0.382068\pi$
$311$	70040.8			0.724153			0.362076	+	0.932148i	$0.382068\pi$
$312$	80454.2	−	80454.2i	0.826494	−	0.826494i
$313$	63194.9	−	16933.0i	0.645050	−	0.172841i	0.0785602	−	0.996909i	$-0.474968\pi$
$313$	63194.9	−	16933.0i	0.645050	−	0.172841i	0.566490	+	0.824069i	$0.308301\pi$
$314$	−51544.5	−	29759.2i	−0.522785	−	0.301830i
$315$	−87817.2	+	21318.7i	−0.885031	+	0.214852i
$316$	−22618.1			−0.226508
$317$	7199.21	+	26867.8i	0.0716417	+	0.267371i	0.992451	−	0.122643i	$-0.0391370\pi$
$317$	7199.21	+	26867.8i	0.0716417	+	0.267371i	−0.920809	+	0.390014i	$0.872470\pi$
$318$	95609.5	−	356819.i	0.945468	−	3.52853i
$319$	−5021.94	−	2899.42i	−0.0493503	−	0.0284924i
$320$	2371.73	−	100291.i	0.0231614	−	0.979404i
$321$	34306.4	+	59420.5i	0.332940	+	0.576669i
$322$	−13783.1	+	13783.1i	−0.132934	+	0.132934i
$323$	−53820.8	+	102679.i	−0.515875	+	0.984182i
$324$		−	241665.i		−	2.30209i
$325$	−51214.0	+	11157.6i	−0.484866	+	0.105635i
$326$	113692.	+	196921.i	1.06978	+	1.85292i
$327$	−63392.2	−	236583.i	−0.592844	−	2.21252i
$328$	23932.6	−	89317.5i	0.222455	−	0.830212i
$329$	159310.	+	91977.6i	1.47181	+	0.849748i
$330$	118173.	−	193943.i	1.08515	−	1.78093i
$331$	70010.2			0.639007			0.319503	−	0.947585i	$-0.396484\pi$
$331$	70010.2			0.639007			0.319503	+	0.947585i	$0.396484\pi$
$332$	42105.8	+	157141.i	0.382002	+	1.42565i
$333$	−156476.	+	41927.7i	−1.41111	+	0.378105i
$334$		−	315237.i		−	2.82582i
$335$	−26754.7	−	110209.i	−0.238402	−	0.982039i
$336$	−86235.1	+	149364.i	−0.763845	+	1.32302i
$337$	12674.3	+	3396.08i	0.111600	+	0.0299032i	0.314187	−	0.949361i	$-0.398268\pi$
$337$	12674.3	+	3396.08i	0.111600	+	0.0299032i	−0.202587	+	0.979264i	$0.564935\pi$
$338$	−144228.	+	38645.7i	−1.26245	+	0.338273i
$339$	93210.7	−	53815.2i	0.811085	−	0.468280i
$340$	−177910.	−	186529.i	−1.53902	−	1.61357i
$341$	−118593.			−1.01989
$342$	−140623.	+	89028.5i	−1.20227	+	0.761161i
$343$	70937.1	+	70937.1i	0.602956	+	0.602956i
$344$	−212032.	+	122417.i	−1.79178	+	1.03449i
$345$	370.929	−	15685.1i	0.00311640	−	0.131780i
$346$	−46929.8	+	81284.8i	−0.392009	+	0.678980i
$347$	82535.8	+	22115.4i	0.685462	+	0.183669i	0.584710	−	0.811243i	$-0.301208\pi$
$347$	82535.8	+	22115.4i	0.685462	+	0.183669i	0.100752	+	0.994912i	$0.467875\pi$
$348$	−20249.2	+	5425.75i	−0.167205	+	0.0448024i
$349$			131199.i			1.07716i	0.842576	+	0.538578i	$0.181038\pi$
$349$			131199.i			1.07716i	−0.842576	+	0.538578i	$0.818962\pi$
$350$	209497.	−	108086.i	1.71018	−	0.882335i
$351$	7398.34	−	12814.3i	0.0600510	−	0.104011i
$352$	−667.796	−	2492.25i	−0.00538963	−	0.0201144i
$353$	155340.	+	155340.i	1.24662	+	1.24662i	0.957204	+	0.289413i	$0.0934602\pi$
$353$	155340.	+	155340.i	1.24662	+	1.24662i	0.289413	+	0.957204i	$0.406540\pi$
$354$			256616.i			2.04776i
$355$	−32940.3	−	60303.4i	−0.261379	−	0.478503i
$356$	−202084.	−	350020.i	−1.59453	−	2.76180i
$357$	−54887.9	−	204844.i	−0.430665	−	1.60727i
$358$	−62456.1	+	233089.i	−0.487314	+	1.81868i
$359$	75617.3	−	43657.6i	0.586721	−	0.338744i	−0.177079	−	0.984197i	$-0.556665\pi$
$359$	75617.3	−	43657.6i	0.586721	−	0.338744i	0.763800	+	0.645453i	$0.223331\pi$
$360$	−43797.8	−	180414.i	−0.337946	−	1.39208i
$361$	−117798.	−	55743.2i	−0.903903	−	0.427737i
$362$	126425.	−	126425.i	0.964753	−	0.964753i
$363$	9455.91	−	35289.9i	0.0717612	−	0.267817i
$364$	−126811.	+	73214.1i	−0.957089	+	0.552576i
$365$	−1252.38	+	4267.68i	−0.00940051	+	0.0320336i
$366$	−284582.	−	492911.i	−2.12444	−	3.67965i
$367$	−21950.5	−	81920.5i	−0.162972	−	0.608220i	−0.998290	−	0.0584528i	$-0.981383\pi$
$367$	−21950.5	−	81920.5i	−0.162972	−	0.608220i	0.835318	−	0.549767i	$-0.185283\pi$
$368$	−9543.78	−	9543.78i	−0.0704733	−	0.0704733i
$369$			55016.6i			0.404055i
$370$	370865.	−	202583.i	2.70902	−	1.47979i
$371$	−119249.	+	206546.i	−0.866379	+	1.50061i
$372$	−303158.	+	303158.i	−2.19070	+	2.19070i
$373$	70759.6	+	70759.6i	0.508590	+	0.508590i	0.914093	−	0.405503i	$-0.132904\pi$
$373$	70759.6	+	70759.6i	0.508590	+	0.508590i	−0.405503	+	0.914093i	$0.632904\pi$
$374$	208046.	+	120115.i	1.48736	+	0.858727i
$375$	−61976.1	+	179339.i	−0.440719	+	1.27530i
$376$	−188962.	+	327291.i	−1.33659	+	2.31504i
$377$	−4355.39	−	1167.02i	−0.0306439	−	0.00821101i
$378$	−17223.8	+	64280.1i	−0.120544	+	0.449876i
$379$		−	185328.i		−	1.29022i	−0.764092	−	0.645108i	$-0.776812\pi$
$379$		−	185328.i		−	1.29022i	0.764092	−	0.645108i	$-0.223188\pi$
$380$	201352.	−	208384.i	1.39440	−	1.44310i
$381$	−186773.			−1.28666
$382$	−123746.	−	33157.7i	−0.848017	−	0.227226i
$383$	−10878.8	+	40600.1i	−0.0741620	+	0.276776i	−0.993042	−	0.117761i	$-0.962428\pi$
$383$	−10878.8	+	40600.1i	−0.0741620	+	0.276776i	0.918880	+	0.394537i	$0.129095\pi$
$384$	296733.	+	171319.i	2.01235	+	1.16183i
$385$	−106104.	+	101201.i	−0.715830	+	0.682756i
$386$	162223.	−	280979.i	1.08877	−	1.88581i
$387$	103005.	−	103005.i	0.687757	−	0.687757i
$388$	229917.	+	229917.i	1.52724	+	1.52724i
$389$	−104030.	−	60061.5i	−0.687476	−	0.396914i	0.115190	−	0.993343i	$-0.463252\pi$
$389$	−104030.	−	60061.5i	−0.687476	−	0.396914i	−0.802666	+	0.596429i	$0.796586\pi$
$390$	49726.1	−	169449.i	0.326930	−	1.11406i
$391$	16595.9			0.108555
$392$	43939.3	−	43939.3i	0.285944	−	0.285944i
$393$	−121012.	+	32425.0i	−0.783507	+	0.209940i
$394$	−364208.	+	210275.i	−2.34615	+	1.35455i
$395$	−15455.7	+	8442.60i	−0.0990594	+	0.0541106i
$396$	115092.	+	199345.i	0.733929	+	1.27120i
$397$	55018.8	+	14742.3i	0.349084	+	0.0935369i	0.429101	−	0.903257i	$-0.358831\pi$
$397$	55018.8	+	14742.3i	0.349084	+	0.0935369i	−0.0800163	+	0.996794i	$0.525497\pi$
$398$	−27913.5	−	27913.5i	−0.176217	−	0.176217i
$399$	227565.	−	71044.2i	1.42942	−	0.446255i
$400$	74841.5	+	145061.i	0.467759	+	0.906633i
$401$	−113589.	−	196742.i	−0.706395	−	1.22351i	−0.966186	−	0.257847i	$-0.916987\pi$
$401$	−113589.	−	196742.i	−0.706395	−	1.22351i	0.259791	−	0.965665i	$-0.416346\pi$
$402$	369076.	+	98893.6i	2.28383	+	0.611951i
$403$	−89073.1	+	23867.1i	−0.548449	+	0.146957i
$404$	427362.	−	246737.i	2.61838	−	1.51172i
$405$	−90205.4	−	165138.i	−0.549949	−	1.00678i
$406$	20279.2			0.123027
$407$	−185863.	+	185863.i	−1.12203	+	1.12203i
$408$	420838.	−	112763.i	2.52810	−	0.677404i
$409$	−69014.5	−	39845.5i	−0.412566	−	0.238195i	0.279326	−	0.960196i	$-0.409889\pi$
$409$	−69014.5	−	39845.5i	−0.412566	−	0.238195i	−0.691892	+	0.722001i	$0.743222\pi$
$410$	−33857.4	−	139467.i	−0.201412	−	0.829669i
$411$	−36659.0			−0.217019
$412$	129267.	+	482432.i	0.761542	+	2.84211i
$413$	42880.7	−	160033.i	0.251398	−	0.938230i
$414$	20634.1	+	11913.1i	0.120388	+	0.0695063i
$415$	87427.9	+	91663.2i	0.507638	+	0.532229i
$416$	−1003.14	−	1737.48i	−0.00579660	−	0.0100400i
$417$	−67684.1	+	67684.1i	−0.389237	+	0.389237i
$418$	−125374.	+	239187.i	−0.717552	+	1.36894i
$419$		−	30996.3i		−	0.176555i	−0.996096	−	0.0882777i	$-0.971864\pi$
$419$		−	30996.3i		−	0.176555i	0.996096	−	0.0882777i	$-0.0281363\pi$
$420$	−12532.0	+	529930.i	−0.0710433	+	3.00414i
$421$	41008.6	+	71029.0i	0.231372	+	0.400748i	0.958212	−	0.286059i	$-0.0923452\pi$
$421$	41008.6	+	71029.0i	0.231372	+	0.400748i	−0.726840	+	0.686807i	$0.759012\pi$
$422$	−6918.51	−	25820.2i	−0.0388497	−	0.144989i
$423$	58197.0	−	217194.i	0.325252	−	1.21386i
$424$	−424334.	−	244989.i	−2.36035	−	1.36275i
$425$	−191197.	−	61053.5i	−1.05853	−	0.338012i
$426$	231506.			1.27568
$427$	95107.6	+	354946.i	0.521626	+	1.94673i
$428$	175227.	−	46952.0i	0.956564	−	0.256311i
$429$			109842.i			0.596834i
$430$	−197728.	+	324507.i	−1.06938	+	1.75504i
$431$	−29969.1	+	51907.9i	−0.161331	+	0.279434i	−0.935346	−	0.353733i	$-0.884912\pi$
$431$	−29969.1	+	51907.9i	−0.161331	+	0.279434i	0.774015	+	0.633167i	$0.218245\pi$
$432$	−44509.2	−	11926.2i	−0.238496	−	0.0639049i
$433$	244319.	−	65465.1i	1.30311	−	0.349168i	0.460486	−	0.887667i	$-0.347675\pi$
$433$	244319.	−	65465.1i	1.30311	−	0.349168i	0.842626	+	0.538499i	$0.181008\pi$
$434$	359172.	−	207368.i	1.90688	−	1.10094i
$435$	−11811.7	+	11266.0i	−0.0624215	+	0.0595374i
$436$	−647578.			−3.40658
$437$	761.061	+	18640.7i	0.00398526	+	0.0976109i
$438$	−10595.8	−	10595.8i	−0.0552315	−	0.0552315i
$439$	180185.	−	104030.i	0.934950	−	0.539794i	0.0465766	−	0.998915i	$-0.485169\pi$
$439$	180185.	−	104030.i	0.934950	−	0.539794i	0.888374	+	0.459121i	$0.151836\pi$
$440$	−207911.	−	217983.i	−1.07392	−	1.12595i
$441$	−18485.8	+	32018.4i	−0.0950521	+	0.164635i
$442$	180432.	+	48346.7i	0.923570	+	0.247470i
$443$	−213333.	+	57162.4i	−1.08705	+	0.291275i	−0.757482	−	0.652856i	$-0.773571\pi$
$443$	−213333.	+	57162.4i	−1.08705	+	0.291275i	−0.329571	+	0.944131i	$0.606904\pi$
$444$			950234.i			4.82019i
$445$	−268742.	−	163749.i	−1.35711	−	0.826911i
$446$	147645.	−	255729.i	0.742248	−	1.28561i
$447$	−29724.2	−	110932.i	−0.148763	−	0.555192i
$448$	−154301.	−	154301.i	−0.768799	−	0.768799i
$449$		−	187901.i		−	0.932043i	−0.884774	−	0.466021i	$-0.845687\pi$
$449$		−	187901.i		−	0.932043i	0.884774	−	0.466021i	$-0.154313\pi$
$450$	−193894.	−	213157.i	−0.957500	−	1.05263i
$451$	44634.1	+	77308.5i	0.219439	+	0.380079i
$452$	−73651.8	−	274872.i	−0.360501	−	1.34541i
$453$	14841.5	−	55389.4i	0.0723240	−	0.269917i
$454$	−422603.	+	243990.i	−2.05031	+	1.18375i
$455$	−59325.6	+	97363.9i	−0.286562	+	0.470300i
$456$	145955.	+	467517.i	0.701925	+	2.24837i
$457$	207779.	−	207779.i	0.994877	−	0.994877i	−0.00511018	−	0.999987i	$-0.501627\pi$
$457$	207779.	−	207779.i	0.994877	−	0.994877i	0.999987	+	0.00511018i	$0.00162663\pi$
$458$	113133.	−	422219.i	0.539335	−	2.01283i
$459$	49068.5	−	28329.7i	0.232904	−	0.134467i
$460$	−39803.6	−	11680.7i	−0.188108	−	0.0552016i
$461$	56105.4	+	97177.4i	0.263999	+	0.457260i	0.967301	−	0.253631i	$-0.0816250\pi$
$461$	56105.4	+	97177.4i	0.263999	+	0.457260i	−0.703302	+	0.710892i	$0.748292\pi$
$462$	−127859.	−	477178.i	−0.599030	−	2.23561i
$463$	154960.	+	154960.i	0.722867	+	0.722867i	0.969188	−	0.246321i	$-0.0792219\pi$
$463$	154960.	+	154960.i	0.722867	+	0.722867i	−0.246321	+	0.969188i	$0.579222\pi$
$464$			14041.9i			0.0652212i
$465$	−93999.2	+	320317.i	−0.434729	+	1.48140i
$466$	−79596.4	+	137865.i	−0.366540	+	0.634866i
$467$	−90373.5	+	90373.5i	−0.414388	+	0.414388i	−0.883264	−	0.468876i	$-0.844659\pi$
$467$	−90373.5	+	90373.5i	−0.414388	+	0.414388i	0.468876	+	0.883264i	$0.344659\pi$
$468$	126562.	+	126562.i	0.577843	+	0.577843i
$469$	−213641.	−	123346.i	−0.971266	−	0.560761i
$470$	−13867.5	+	586403.i	−0.0627775	+	2.65461i
$471$	52103.8	−	90246.4i	0.234870	−	0.406807i
$472$	328777.	+	88095.4i	1.47576	+	0.395430i
$473$	61174.6	−	228307.i	0.273432	−	1.02046i
$474$		−	59335.0i		−	0.264091i
$475$	59807.7	−	217554.i	0.265075	−	0.964228i
$476$	−560702.			−2.47468
$477$	281593.	+	75452.6i	1.23761	+	0.331618i
$478$	103075.	−	384682.i	0.451126	−	1.68363i
$479$	−73282.9	−	42309.9i	−0.319398	−	0.184404i	0.331726	−	0.943376i	$-0.392369\pi$
$479$	−73282.9	−	42309.9i	−0.319398	−	0.184404i	−0.651124	+	0.758971i	$0.725702\pi$
$480$	−7260.79	−	171.707i	−0.0315138	−	0.000745255i
$481$	−102193.	+	177003.i	−0.441702	+	0.765051i
$482$	299493.	−	299493.i	1.28912	−	1.28912i
$483$	−24132.1	−	24132.1i	−0.103443	−	0.103443i
$484$	−83654.5	−	48298.0i	−0.357107	−	0.206176i
$485$	242931.	+	71289.9i	1.03276	+	0.303071i
$486$	534844.			2.26441
$487$	−37953.2	+	37953.2i	−0.160026	+	0.160026i	−0.782578	−	0.622552i	$-0.786096\pi$
$487$	−37953.2	+	37953.2i	−0.160026	+	0.160026i	0.622552	+	0.782578i	$0.286096\pi$
$488$	−729212.	+	195392.i	−3.06206	+	0.820477i
$489$	−344778.	+	199058.i	−1.44186	+	0.832455i
$490$	27157.4	−	92543.0i	0.113109	−	0.385435i
$491$	−153673.	−	266169.i	−0.637432	−	1.10406i	−0.985994	−	0.166778i	$-0.946664\pi$
$491$	−153673.	−	266169.i	−0.637432	−	1.10406i	0.348563	−	0.937285i	$-0.386670\pi$
$492$	311719.	+	83524.9i	1.28776	+	0.345053i
$493$	−12208.9	−	12208.9i	−0.0502322	−	0.0502322i
$494$	−46029.0	+	204880.i	−0.188616	+	0.839547i
$495$	153055.	+	93259.2i	0.624651	+	0.380611i
$496$	143587.	+	248699.i	0.583648	+	1.01091i
$497$	−144374.	−	38684.8i	−0.584487	−	0.156613i
$498$	−412234.	+	110458.i	−1.66221	+	0.445387i
$499$	139092.	−	80304.9i	0.558601	−	0.322508i	−0.193983	−	0.981005i	$-0.562141\pi$
$499$	139092.	−	80304.9i	0.558601	−	0.322508i	0.752584	+	0.658497i	$0.228807\pi$
$500$	415596.	+	281000.i	1.66238	+	1.12400i
$501$	551931.			2.19892
$502$	−189328.	+	189328.i	−0.751289	+	0.751289i
$503$	−172525.	+	46228.0i	−0.681894	+	0.182713i	−0.583107	−	0.812396i	$-0.698163\pi$
$503$	−172525.	+	46228.0i	−0.681894	+	0.182713i	−0.0987873	+	0.995109i	$0.531496\pi$
$504$	−349733.	−	201918.i	−1.37681	−	0.794904i
$505$	199932.	−	328124.i	0.783970	−	1.28664i
$506$	38659.6			0.150993
$507$	−67662.5	−	252520.i	−0.263228	−	0.982381i
$508$	−127809.	+	476990.i	−0.495261	+	1.84834i
$509$	400576.	+	231273.i	1.54614	+	0.892666i	0.998431	+	0.0559980i	$0.0178340\pi$
$509$	400576.	+	231273.i	1.54614	+	0.892666i	0.547711	+	0.836668i	$0.315499\pi$
$510$	489328.	−	466719.i	1.88131	−	1.79438i
$511$	4837.28	+	8378.42i	0.0185251	+	0.0320863i
$512$	325691.	−	325691.i	1.24241	−	1.24241i
$513$	34070.3	+	53814.9i	0.129462	+	0.204488i
$514$			264213.i			1.00006i
$515$	268409.	+	281411.i	1.01200	+	1.06103i
$516$	−427236.	−	739995.i	−1.60461	−	2.77926i
$517$	−94428.6	−	352412.i	−0.353283	−	1.31847i
$518$	237911.	−	887896.i	0.886656	−	3.30904i
$519$	−142317.	−	82166.7i	−0.528350	−	0.305043i
$520$	−200027.	−	121880.i	−0.739746	−	0.450741i
$521$	46925.0			0.172874			0.0864368	−	0.996257i	$-0.472452\pi$
$521$	46925.0			0.172874			0.0864368	+	0.996257i	$0.472452\pi$
$522$	−6415.64	−	23943.5i	−0.0235450	−	0.0878712i
$523$	147743.	−	39587.7i	0.540137	−	0.144729i	0.0215717	−	0.999767i	$-0.493133\pi$
$523$	147743.	−	39587.7i	0.540137	−	0.144729i	0.518565	+	0.855038i	$0.326466\pi$
$524$			331235.i			1.20635i
$525$	189242.	+	366797.i	0.686591	+	1.33078i
$526$	323454.	−	560239.i	1.16907	−	2.02489i
$527$	−341078.	−	91391.7i	−1.22810	−	0.329068i
$528$	330410.	−	88533.1i	1.18518	−	0.317569i
$529$	−240036.	+	138585.i	−0.857760	+	0.495228i
$530$	−760273.	−	17979.3i	−2.70656	−	0.0640061i
$531$	−202515.			−0.718239
$532$	−25712.8	−	629784.i	−0.0908504	−	2.22520i
$533$	49082.2	+	49082.2i	0.172771	+	0.172771i
$534$	918219.	−	530134.i	3.22006	−	1.85910i
$535$	102213.	−	97490.4i	0.357108	−	0.340608i
$536$	253405.	−	438910.i	0.882034	−	1.52773i
$537$	−408103.	−	109351.i	−1.41521	−	0.379205i
$538$	−301844.	+	80878.8i	−1.04284	+	0.279428i
$539$			59989.1i			0.206488i
$540$	−137625.	+	33410.1i	−0.471965	+	0.114575i
$541$	−25095.2	+	43466.1i	−0.0857424	+	0.148510i	−0.905707	−	0.423904i	$-0.860660\pi$
$541$	−25095.2	+	43466.1i	−0.0857424	+	0.148510i	0.819965	+	0.572414i	$0.193993\pi$
$542$	39507.0	+	147442.i	0.134486	+	0.501907i
$543$	221351.	+	221351.i	0.750726	+	0.750726i
$544$		−	7682.41i		−	0.0259597i
$545$	−442512.	+	241719.i	−1.48981	+	0.813801i
$546$	−192065.	−	332667.i	−0.644263	−	1.11590i
$547$	−11312.4	−	42218.5i	−0.0378077	−	0.141100i	0.944442	−	0.328678i	$-0.106603\pi$
$547$	−11312.4	−	42218.5i	−0.0378077	−	0.141100i	−0.982250	+	0.187578i	$0.939936\pi$
$548$	−25085.9	+	93621.7i	−0.0835349	+	0.311757i
$549$	388993.	−	224585.i	1.29062	−	0.745137i
$550$	−445387.	−	142222.i	−1.47236	−	0.470155i
$551$	13153.2	−	14273.0i	0.0433240	−	0.0470123i
$552$	49577.7	−	49577.7i	0.162708	−	0.162708i
$553$	−9914.90	+	37002.9i	−0.0324219	+	0.121000i
$554$	−473860.	+	273583.i	−1.54394	+	0.891395i
$555$	354691.	+	649327.i	1.15150	+	2.10803i
$556$	126539.	+	219172.i	0.409330	+	0.708981i
$557$	−22845.9	−	85262.2i	−0.0736374	−	0.274819i	0.919283	−	0.393596i	$-0.128769\pi$
$557$	−22845.9	−	85262.2i	−0.0736374	−	0.274819i	−0.992921	+	0.118777i	$0.962102\pi$
$558$	−358466.	−	358466.i	−1.15128	−	1.15128i
$559$		−	183788.i		−	0.588158i
$560$	340692.	+	99978.6i	1.08639	+	0.318809i
$561$	−210303.	+	364256.i	−0.668221	+	1.15739i
$562$	−129867.	+	129867.i	−0.411176	+	0.411176i
$563$	−230537.	−	230537.i	−0.727318	−	0.727318i	0.242766	−	0.970085i	$-0.421945\pi$
$563$	−230537.	−	230537.i	−0.727318	−	0.727318i	−0.970085	+	0.242766i	$0.921945\pi$
$564$	−1.14225e6	−	659478.i	−3.59089	−	2.07320i
$565$	−152930.	−	160338.i	−0.479065	−	0.502272i
$566$	−25490.2	+	44150.3i	−0.0795683	+	0.137816i
$567$	−395359.	−	105936.i	−1.22978	−	0.329518i
$568$	79475.1	−	296605.i	0.246340	−	0.919353i
$569$		−	287624.i		−	0.888384i	−0.895932	−	0.444192i	$-0.853491\pi$
$569$		−	287624.i		−	0.888384i	0.895932	−	0.444192i	$-0.146509\pi$
$570$	546661.	+	528213.i	1.68255	+	1.62577i
$571$	344049.			1.05523			0.527616	−	0.849483i	$-0.323086\pi$
$571$	344049.			1.05523			0.527616	+	0.849483i	$0.323086\pi$
$572$	280520.	+	75165.1i	0.857377	+	0.229733i
$573$	58053.9	−	216660.i	0.176816	−	0.659887i
$574$	−270357.	−	156091.i	−0.820568	−	0.473755i
$575$	−31559.2	+	6875.59i	−0.0954532	+	0.0207957i
$576$	−133366.	+	230997.i	−0.401977	+	0.696244i
$577$	316537.	−	316537.i	0.950765	−	0.950765i	−0.0480787	−	0.998844i	$-0.515310\pi$
$577$	316537.	−	316537.i	0.950765	−	0.950765i	0.998844	+	0.0480787i	$0.0153098\pi$
$578$	96156.3	+	96156.3i	0.287821	+	0.287821i
$579$	491950.	+	284027.i	1.46745	+	0.847233i
$580$	20688.8	+	37874.7i	0.0615006	+	0.112588i
$581$	275538.			0.816261
$582$	−603151.	+	603151.i	−1.78066	+	1.78066i
$583$	456904.	−	122427.i	1.34427	−	0.360197i
$584$	−17212.9	+	9937.85i	−0.0504693	+	0.0291385i
$585$	133725.	+	39242.6i	0.390752	+	0.114669i
$586$	345721.	+	598805.i	1.00677	+	1.74378i
$587$	528585.	+	141634.i	1.53405	+	0.411047i	0.924337	−	0.381577i	$-0.124619\pi$
$587$	528585.	+	141634.i	1.53405	+	0.411047i	0.609711	+	0.792624i	$0.291285\pi$
$588$	153349.	+	153349.i	0.443532	+	0.443532i
$589$	87010.4	−	387292.i	0.250808	−	1.11637i
$590$	513377.	−	124629.i	1.47480	−	0.358026i
$591$	−368159.	−	637671.i	−1.05405	−	1.82567i
$592$	614802.	+	164736.i	1.75425	+	0.470050i
$593$	−593150.	+	158934.i	−1.68677	+	0.451968i	−0.969552	−	0.244885i	$-0.921250\pi$
$593$	−593150.	+	158934.i	−1.68677	+	0.451968i	−0.717214	+	0.696853i	$0.754583\pi$
$594$	114303.	−	65993.0i	0.323956	−	0.187036i
$595$	−383147.	+	209292.i	−1.08226	+	0.591178i
$596$	−303645.			−0.854818
$597$	48872.1	−	48872.1i	0.137124	−	0.137124i
$598$	29036.5	−	7780.30i	0.0811973	−	0.0217567i
$599$	260375.	+	150328.i	0.725681	+	0.418972i	0.816840	−	0.576864i	$-0.195724\pi$
$599$	260375.	+	150328.i	0.725681	+	0.418972i	−0.0911592	+	0.995836i	$0.529057\pi$
$600$	−753559.	+	388784.i	−2.09322	+	1.07996i
$601$	274138.			0.758963			0.379481	−	0.925199i	$-0.376102\pi$
$601$	274138.			0.758963			0.379481	+	0.925199i	$0.376102\pi$
$602$	213935.	+	798417.i	0.590322	+	2.20311i
$603$	−78044.4	+	291266.i	−0.214638	+	0.801041i
$604$	−131300.	−	75806.2i	−0.359908	−	0.207793i
$605$	−75192.1	−	1778.18i	−0.205429	−	0.00485808i
$606$	647275.	+	1.12111e6i	1.76256	+	3.05284i
$607$	−372986.	+	372986.i	−1.01231	+	1.01231i	−0.0123903	+	0.999923i	$0.503944\pi$
$607$	−372986.	+	372986.i	−1.01231	+	1.01231i	−0.999923	+	0.0123903i	$0.996056\pi$
$608$	8628.94	−	352.302i	0.0233426	−	0.000953034i
$609$			35505.8i			0.0957336i
$610$	−847888.	+	808712.i	−2.27866	+	2.17337i
$611$	−141847.	−	245686.i	−0.379959	−	0.658109i
$612$	177387.	+	662015.i	0.473607	+	1.76752i
$613$	−13548.0	+	50561.7i	−0.0360540	+	0.134555i	−0.981607	−	0.190913i	$-0.938855\pi$
$613$	−13548.0	+	50561.7i	−0.0360540	+	0.134555i	0.945553	+	0.325468i	$0.105522\pi$
$614$	858568.	+	495695.i	2.27739	+	1.31485i
$615$	244186.	−	59279.1i	0.645609	−	0.156730i
$616$	−655253.			−1.72682
$617$	67210.0	+	250831.i	0.176548	+	0.658887i	0.996283	+	0.0861434i	$0.0274543\pi$
$617$	67210.0	+	250831.i	0.176548	+	0.658887i	−0.819734	+	0.572744i	$0.805879\pi$
$618$	−1.26558e6	+	339111.i	−3.31370	+	0.887903i
$619$			444900.i			1.16113i	0.814213	+	0.580566i	$0.197169\pi$
$619$			444900.i			1.16113i	−0.814213	+	0.580566i	$0.802831\pi$
$620$	753718.	+	459254.i	1.96076	+	1.19473i
$621$	4559.02	−	7896.46i	0.0118219	−	0.0204762i
$622$	469246.	+	125734.i	1.21289	+	0.324992i
$623$	−661212.	+	177171.i	−1.70359	+	0.456475i
$624$	230347.	−	132991.i	0.591579	−	0.341549i
$625$	388879.	+	36888.8i	0.995531	+	0.0944354i
$626$	453779.			1.15797
$627$	−418778.	−	219510.i	−1.06524	−	0.558365i
$628$	−194821.	−	194821.i	−0.493989	−	0.493989i
$629$	−677779.	+	391316.i	−1.71312	+	0.989068i
$630$	−626612.	−	14818.4i	−1.57876	−	0.0373354i
$631$	281837.	−	488156.i	0.707847	−	1.22603i	−0.257807	−	0.966196i	$-0.583000\pi$
$631$	281837.	−	488156.i	0.707847	−	1.22603i	0.965654	−	0.259831i	$-0.0836668\pi$
$632$	−76019.9	−	20369.5i	−0.190324	−	0.0509971i
$633$	45207.2	−	12113.2i	0.112824	−	0.0302310i
$634$			192928.i			0.479972i
$635$	90708.4	+	373651.i	0.224957	+	0.926656i
$636$	855016.	−	1.48093e6i	2.11378	−	3.66117i
$637$	12072.9	+	45056.6i	0.0297531	+	0.111040i
$638$	−28440.2	−	28440.2i	−0.0698700	−	0.0698700i
$639$			182699.i			0.447439i
$640$	198622.	−	676835.i	0.484917	−	1.65243i
$641$	−297563.	−	515394.i	−0.724207	−	1.25436i	−0.959300	−	0.282391i	$-0.908873\pi$
$641$	−297563.	−	515394.i	−0.724207	−	1.25436i	0.235092	−	0.971973i	$-0.424461\pi$
$642$	123171.	+	459680.i	0.298839	+	1.11528i
$643$	37006.7	−	138111.i	0.0895073	−	0.334046i	−0.906622	−	0.421943i	$-0.861348\pi$
$643$	37006.7	−	138111.i	0.0895073	−	0.334046i	0.996130	+	0.0878974i	$0.0280148\pi$
$644$	−78143.5	+	45116.1i	−0.188417	+	0.108783i
$645$	−568161.	−	346191.i	−1.36569	−	0.832139i
$646$	−544903.	+	591291.i	−1.30573	+	1.41689i
$647$	178912.	−	178912.i	0.427397	−	0.427397i	−0.460344	−	0.887741i	$-0.652274\pi$
$647$	178912.	−	178912.i	0.427397	−	0.427397i	0.887741	+	0.460344i	$0.152274\pi$
$648$	217639.	−	812238.i	0.518306	−	1.93434i
$649$	−284572.	+	164298.i	−0.675620	+	0.390069i
$650$	−363144.	−	17185.2i	−0.859512	−	0.0406751i
$651$	363069.	+	628853.i	0.856696	+	1.48384i
$652$	272431.	+	1.01673e6i	0.640858	+	2.39171i
$653$	486072.	+	486072.i	1.13992	+	1.13992i	0.988464	+	0.151455i	$0.0483957\pi$
$653$	486072.	+	486072.i	1.13992	+	1.13992i	0.151455	+	0.988464i	$0.451604\pi$
$654$		−	1.69881e6i		−	3.97183i
$655$	123639.	+	226344.i	0.288186	+	0.527578i
$656$	108081.	−	187202.i	0.251156	−	0.435014i
$657$	8361.97	−	8361.97i	0.0193721	−	0.0193721i
$658$	902201.	+	902201.i	2.08378	+	2.08378i
$659$	−339686.	−	196118.i	−0.782180	−	0.451592i	0.0550221	−	0.998485i	$-0.482477\pi$
$659$	−339686.	−	196118.i	−0.782180	−	0.451592i	−0.837202	+	0.546893i	$0.815810\pi$
$660$	760763.	−	725613.i	1.74647	−	1.66578i
$661$	64613.0	−	111913.i	0.147883	−	0.256140i	−0.782562	−	0.622573i	$-0.786088\pi$
$661$	64613.0	−	111913.i	0.147883	−	0.256140i	0.930445	+	0.366432i	$0.119421\pi$
$662$	469042.	+	125679.i	1.07027	+	0.286779i
$663$	−84647.5	+	315909.i	−0.192569	+	0.718678i
$664$			566073.i			1.28392i
$665$	−252648.	−	420755.i	−0.571311	−	0.951451i
$666$	−1.12360e6			−2.53316
$667$	−2683.89	−	719.146i	−0.00603271	−	0.00161646i
$668$	377688.	−	1.40955e6i	0.846409	−	3.15884i
$669$	447741.	+	258503.i	1.00040	+	0.577582i
$670$	18596.9	−	786389.i	0.0414277	−	1.75181i
$671$	364405.	−	631168.i	0.809355	−	1.40184i
$672$	−11171.0	+	11171.0i	−0.0247373	+	0.0247373i
$673$	−238773.	−	238773.i	−0.527174	−	0.527174i	0.392554	−	0.919729i	$-0.371591\pi$
$673$	−238773.	−	238773.i	−0.527174	−	0.527174i	−0.919729	+	0.392554i	$0.871591\pi$
$674$	78816.7	+	45504.9i	0.173500	+	0.100170i
$675$	−81572.9	+	74201.1i	−0.179035	+	0.162856i
$676$	−691200.			−1.51255
$677$	−199313.	+	199313.i	−0.434869	+	0.434869i	−0.890281	−	0.455412i	$-0.849492\pi$
$677$	−199313.	+	199313.i	−0.434869	+	0.434869i	0.455412	+	0.890281i	$0.349492\pi$
$678$	721082.	−	193213.i	1.56865	−	0.420318i
$679$	476928.	−	275355.i	1.03446	−	0.597245i
$680$	−429975.	−	787149.i	−0.929877	−	1.70231i
$681$	−427188.	−	739911.i	−0.921138	−	1.59546i
$682$	−794530.	−	212894.i	−1.70821	−	0.457714i
$683$	354081.	+	354081.i	0.759034	+	0.759034i	0.976147	−	0.217113i	$-0.0696639\pi$
$683$	354081.	+	354081.i	0.759034	+	0.759034i	−0.217113	+	0.976147i	$0.569664\pi$
$684$	−735445.	+	229601.i	−1.57195	+	0.490751i
$685$	17803.9	+	73338.7i	0.0379431	+	0.156297i
$686$	347908.	+	602595.i	0.739293	+	1.28049i
$687$	739239.	+	198079.i	1.56629	+	0.419685i
$688$	−552844.	+	148134.i	−1.16795	+	0.312952i
$689$	318533.	−	183905.i	0.670989	−	0.387396i
$690$	30642.3	−	104418.i	0.0643611	−	0.219320i
$691$	−554507.			−1.16132			−0.580658	−	0.814147i	$-0.697205\pi$
$691$	−554507.			−1.16132			−0.580658	+	0.814147i	$0.697205\pi$
$692$	−307230.	+	307230.i	−0.641580	+	0.641580i
$693$	376577.	−	100903.i	0.784128	−	0.210107i
$694$	513257.	+	296329.i	1.06565	+	0.615255i
$695$	168278.	+	102535.i	0.348383	+	0.212276i
$696$	−72944.2			−0.150582
$697$	68792.8	+	256738.i	0.141605	+	0.528476i
$698$	−235522.	+	878981.i	−0.483416	+	1.80413i
$699$	−241380.	−	139361.i	−0.494023	−	0.285224i
$700$	1.06624e6	−	232295.i	2.17601	−	0.474072i
$701$	−135461.	−	234625.i	−0.275663	−	0.477462i	0.694639	−	0.719358i	$-0.255564\pi$
$701$	−135461.	−	234625.i	−0.275663	−	0.477462i	−0.970302	+	0.241896i	$0.922231\pi$
$702$	72569.7	−	72569.7i	0.147259	−	0.147259i
$703$	−470610.	−	743341.i	−0.952250	−	1.50410i
$704$			432792.i			0.873240i
$705$	−1.02670e6	−	24279.9i	−2.06569	−	0.0488505i
$706$	761857.	+	1.31958e6i	1.52850	+	2.64743i
$707$	−216320.	−	807317.i	−0.432771	−	1.61512i
$708$	−307454.	+	1.14743e6i	−0.613357	+	2.28908i
$709$	98316.5	+	56763.1i	0.195584	+	0.112921i	0.594594	−	0.804026i	$-0.297313\pi$
$709$	98316.5	+	56763.1i	0.195584	+	0.112921i	−0.399010	+	0.916947i	$0.630646\pi$
$710$	−112434.	−	463142.i	−0.223038	−	0.918751i
$711$	46825.7			0.0926286
$712$	−363986.	−	1.35841e6i	−0.718000	−	2.67961i
$713$	−54888.8	+	14707.4i	−0.107970	+	0.0289306i
$714$		−	1.47091e6i		−	2.88529i
$715$	219746.	−	53346.0i	0.429841	−	0.104349i
$716$	−558532.	+	967406.i	−1.08949	+	1.88705i
$717$	673517.	+	180468.i	1.31012	+	0.351045i
$718$	584979.	−	156745.i	1.13473	−	0.304049i
$719$	−499830.	+	288577.i	−0.966862	+	0.558218i	−0.898278	−	0.439428i	$-0.855181\pi$
$719$	−499830.	+	288577.i	−0.966862	+	0.558218i	−0.0685836	+	0.997645i	$0.521848\pi$
$720$	10260.6	−	433882.i	0.0197929	−	0.836963i
$721$	845916.			1.62726
$722$	−689131.	−	584923.i	−1.32199	−	1.12208i
$723$	524366.	+	524366.i	1.00313	+	1.00313i
$724$	716768.	−	413826.i	1.36742	−	0.789479i
$725$	28274.7	+	18158.6i	0.0537926	+	0.0345467i
$726$	126702.	−	219454.i	0.240386	−	0.416361i
$727$	−642556.	−	172172.i	−1.21574	−	0.325758i	−0.406731	−	0.913548i	$-0.633331\pi$
$727$	−642556.	−	172172.i	−1.21574	−	0.325758i	−0.809013	+	0.587790i	$0.799998\pi$
$728$	−492147.	+	131870.i	−0.928608	+	0.248820i
$729$			326762.i			0.614860i
$730$	−16051.6	+	26343.6i	−0.0301213	+	0.0494344i
$731$	351880.	−	609475.i	0.658507	−	1.14057i
$732$	−681920.	−	2.54496e6i	−1.27266	−	4.74962i
$733$	−327076.	−	327076.i	−0.608753	−	0.608753i	0.333867	−	0.942620i	$-0.391646\pi$
$733$	−327076.	−	327076.i	−0.608753	−	0.608753i	−0.942620	+	0.333867i	$0.891646\pi$
$734$		−	588240.i		−	1.09185i
$735$	162028.	+	47548.4i	0.299928	+	0.0880159i
$736$	−618.155	−	1070.68i	−0.00114115	−	0.00197653i
$737$	126632.	+	472599.i	0.233136	+	0.870077i
$738$	−98763.4	+	368590.i	−0.181336	+	0.676754i
$739$	230112.	−	132855.i	0.421357	−	0.243270i	−0.274301	−	0.961644i	$-0.588446\pi$
$739$	230112.	−	132855.i	0.421357	−	0.243270i	0.695658	+	0.718374i	$0.255113\pi$
$740$	1.90100e6	−	461492.i	3.47152	−	0.842754i
$741$	−358712.	−	80589.6i	−0.653296	−	0.146772i
$742$	−1.16971e6	+	1.16971e6i	−2.12456	+	2.12456i
$743$	−27091.9	+	101109.i	−0.0490753	+	0.183151i	−0.986113	−	0.166078i	$-0.946890\pi$
$743$	−27091.9	+	101109.i	−0.0490753	+	0.183151i	0.937037	+	0.349229i	$0.113556\pi$
$744$	−1.29194e6	+	745899.i	−2.33397	+	1.34752i
$745$	−207491.	+	113341.i	−0.373841	+	0.204208i
$746$	347038.	+	601087.i	0.623590	+	1.08009i
$747$	−87170.5	−	325325.i	−0.156217	−	0.583010i
$748$	786344.	+	786344.i	1.40543	+	1.40543i
$749$		−	307251.i		−	0.547683i
$750$	−737159.	+	1.09025e6i	−1.31050	+	1.93822i
$751$	−488835.	+	846687.i	−0.866727	+	1.50121i	−0.00140432	+	0.999999i	$0.500447\pi$
$751$	−488835.	+	846687.i	−0.866727	+	1.50121i	−0.865322	+	0.501216i	$0.832886\pi$
$752$	−624706.	+	624706.i	−1.10469	+	1.10469i
$753$	−331484.	−	331484.i	−0.584618	−	0.584618i
$754$	−27084.4	−	15637.2i	−0.0476406	−	0.0275053i
$755$	−118018.	−	2790.95i	−0.207040	−	0.00489618i
$756$	−154029.	+	266786.i	−0.269500	+	0.466787i
$757$	−633775.	−	169820.i	−1.10597	−	0.296344i	−0.340777	−	0.940144i	$-0.610690\pi$
$757$	−633775.	−	169820.i	−1.10597	−	0.296344i	−0.765194	+	0.643800i	$0.777357\pi$
$758$	332692.	−	1.24163e6i	0.579035	−	2.16099i
$759$			67687.0i			0.117496i
$760$	864413.	−	519048.i	1.49656	−	0.898629i
$761$	−146475.			−0.252927			−0.126463	−	0.991971i	$-0.540363\pi$
$761$	−146475.			−0.252927			−0.126463	+	0.991971i	$0.540363\pi$
$762$	−1.25131e6	−	335286.i	−2.15503	−	0.577439i
$763$	−283873.	+	1.05943e6i	−0.487612	+	1.81979i
$764$	−513591.	−	296522.i	−0.879895	−	0.508008i
$765$	368323.	+	386165.i	0.629370	+	0.659858i
$766$	−145767.	+	252476.i	−0.248429	+	0.430291i
$767$	−180671.	+	180671.i	−0.307113	+	0.307113i
$768$	1.12913e6	+	1.12913e6i	1.91436	+	1.91436i
$769$	−294756.	−	170177.i	−0.498437	−	0.287773i	0.229631	−	0.973278i	$-0.426248\pi$
$769$	−294756.	−	170177.i	−0.498437	−	0.287773i	−0.728068	+	0.685505i	$0.759581\pi$
$770$	−892528.	+	487538.i	−1.50536	+	0.822293i
$771$	−462596.			−0.778203
$772$	1.06201e6	−	1.06201e6i	1.78194	−	1.78194i
$773$	1.11242e6	−	298073.i	1.86171	−	0.498843i	0.861744	−	0.507343i	$-0.169372\pi$
$773$	1.11242e6	−	298073.i	1.86171	−	0.498843i	0.999964	+	0.00849974i	$0.00270558\pi$
$774$	875001.	−	505182.i	1.46059	−	0.843269i
$775$	686465.	+	32485.9i	1.14292	+	0.0540869i
$776$	565697.	+	979816.i	0.939421	+	1.62712i
$777$	1.55457e6	+	416545.i	2.57494	+	0.689954i
$778$	−589138.	−	589138.i	−0.973325	−	0.973325i
$779$	−285215.	+	89042.1i	−0.470000	+	0.146731i
$780$	425363.	−	698097.i	0.699151	−	1.14743i
$781$	148221.	+	256726.i	0.243000	+	0.420889i
$782$	111186.	+	29792.3i	0.181818	+	0.0487181i
$783$	−9162.93	+	2455.20i	−0.0149455	+	0.00400464i
$784$	125802.	−	72631.6i	0.204670	−	0.118166i
$785$	−205848.	−	60407.7i	−0.334047	−	0.0980286i
$786$	−868940.			−1.40652
$787$	−243978.	+	243978.i	−0.393913	+	0.393913i	−0.876080	−	0.482166i	$-0.839850\pi$
$787$	−243978.	+	243978.i	−0.393913	+	0.393913i	0.482166	+	0.876080i	$0.339850\pi$
$788$	−1.88045e6	+	503865.i	−3.02837	+	0.811450i
$789$	980891.	+	566318.i	1.57568	+	0.909717i
$790$	−118703.	+	28816.7i	−0.190199	+	0.0461732i
$791$	−481973.			−0.770317
$792$	207299.	+	773651.i	0.330481	+	1.23337i
$793$	146674.	−	547394.i	0.233242	−	0.870470i
$794$	342140.	+	197535.i	0.542704	+	0.313331i
$795$	31479.0	−	1.33112e6i	0.0498066	−	2.10612i
$796$	−91368.9	−	158256.i	−0.144202	−	0.249766i
$797$	562241.	−	562241.i	0.885128	−	0.885128i	−0.108922	−	0.994050i	$-0.534740\pi$
$797$	562241.	−	562241.i	0.885128	−	0.885128i	0.994050	+	0.108922i	$0.0347400\pi$
$798$	1.65214e6	−	67453.5i	2.59442	−	0.105925i
$799$		−	1.08632e6i		−	1.70162i
$800$	3182.78	+	14609.1i	0.00497309	+	0.0228267i
$801$	418369.	+	724636.i	0.652070	+	1.12942i
$802$	−407820.	−	1.52201e6i	−0.634045	−	2.36629i
$803$	4966.18	−	18534.0i	0.00770179	−	0.0287435i
$804$	1.53180e6	+	884385.i	2.36968	+	1.36814i
$805$	−36557.7	+	59997.8i	−0.0564141	+	0.0925856i
$806$	−639601.			−0.984552
$807$	−141606.	−	528481.i	−0.217438	−	0.811489i
$808$	1.65858e6	−	444414.i	2.54046	−	0.680715i
$809$		−	730221.i		−	1.11572i	−0.829933	−	0.557862i	$-0.811622\pi$
$809$		−	730221.i		−	1.11572i	0.829933	−	0.557862i	$-0.188378\pi$
$810$	−307894.	−	1.26829e6i	−0.469279	−	1.93308i
$811$	−374828.	+	649221.i	−0.569889	+	0.987076i	0.426688	+	0.904399i	$0.359680\pi$
$811$	−374828.	+	649221.i	−0.569889	+	0.987076i	−0.996576	+	0.0826769i	$0.973653\pi$
$812$	90676.5	+	24296.7i	0.137525	+	0.0368498i
$813$	−258148.	+	69170.6i	−0.390560	+	0.104650i
$814$	−1.57886e6	+	911557.i	−2.38284	+	1.37574i
$815$	565672.	+	593075.i	0.851628	+	0.892883i
$816$	1.01850e6			1.52960
$817$	700703.	+	367285.i	1.04976	+	0.550249i
$818$	−390841.	−	390841.i	−0.584109	−	0.584109i
$819$	262532.	−	151573.i	0.391395	−	0.225972i
$820$	15706.8	−	664179.i	0.0233593	−	0.987773i
$821$	−364575.	+	631463.i	−0.540880	+	0.936831i	0.457974	+	0.888966i	$0.348575\pi$
$821$	−364575.	+	631463.i	−0.540880	+	0.936831i	−0.998854	+	0.0478657i	$0.984758\pi$
$822$	−245601.	−	65808.7i	−0.363485	−	0.0973956i
$823$	−821395.	+	220092.i	−1.21270	+	0.324941i	−0.807819	−	0.589430i	$-0.799352\pi$
$823$	−821395.	+	220092.i	−1.21270	+	0.324941i	−0.404877	+	0.914371i	$0.632686\pi$
$824$			1.73788e6i			2.55955i
$825$	249008.	−	779804.i	0.365852	−	1.14572i
$826$	574569.	−	995182.i	0.842135	−	1.45862i
$827$	−21984.9	−	82048.7i	−0.0321450	−	0.119967i	0.947989	−	0.318303i	$-0.103113\pi$
$827$	−21984.9	−	82048.7i	−0.0321450	−	0.119967i	−0.980134	+	0.198336i	$0.936446\pi$
$828$	77990.0	+	77990.0i	0.113757	+	0.113757i
$829$		−	227177.i		−	0.330564i	−0.986246	−	0.165282i	$-0.947147\pi$
$829$		−	227177.i		−	0.330564i	0.986246	−	0.165282i	$-0.0528534\pi$
$830$	421184.	+	771055.i	0.611386	+	1.11926i
$831$	−479002.	−	829656.i	−0.693642	−	1.20142i
$832$	87099.9	+	325061.i	0.125826	+	0.469590i
$833$	−46229.4	+	172530.i	−0.0666236	+	0.248643i
$834$	−574961.	+	331954.i	−0.826620	+	0.477250i
$835$	−268052.	−	1.10417e6i	−0.384455	−	1.58367i
$836$	−847166.	+	919287.i	−1.21215	+	1.31534i
$837$	−137181.	+	137181.i	−0.195814	+	0.195814i
$838$	55643.1	−	207663.i	0.0792362	−	0.295713i
$839$	272858.	−	157534.i	0.387625	−	0.223796i	−0.293505	−	0.955957i	$-0.594822\pi$
$839$	272858.	−	157534.i	0.387625	−	0.223796i	0.681131	+	0.732162i	$0.261489\pi$
$840$	−519365.	+	1.76982e6i	−0.736062	+	2.50824i
$841$	−352195.	−	610020.i	−0.497956	−	0.862486i
$842$	147234.	+	549484.i	0.207674	+	0.775052i
$843$	−227377.	−	227377.i	−0.319958	−	0.319958i
$844$		−	123742.i		−	0.173712i
$845$	−472321.	+	258002.i	−0.661491	+	0.361335i
$846$	779795.	−	1.35064e6i	1.08953	−	1.88712i
$847$	−115686.	+	115686.i	−0.161255	+	0.161255i
$848$	−809934.	−	809934.i	−1.12631	−	1.12631i
$849$	−77300.3	−	44629.3i	−0.107242	−	0.0619163i
$850$	−1.17135e6	−	752264.i	−1.62124	−	1.04120i
$851$	−62973.4	+	109073.i	−0.0869557	+	0.150612i
$852$	1.03516e6	+	277369.i	1.42602	+	0.382102i
$853$	43333.3	−	161722.i	0.0595558	−	0.222265i	−0.929734	−	0.368233i	$-0.879963\pi$
$853$	43333.3	−	161722.i	0.0595558	−	0.222265i	0.989289	+	0.145968i	$0.0466296\pi$
$854$			2.54874e6i			3.49469i
$855$	−416853.	+	431412.i	−0.570231	+	0.590146i
$856$	631225.			0.861463
$857$	−229531.	−	61502.7i	−0.312522	−	0.0837400i	0.0991489	−	0.995073i	$-0.468388\pi$
$857$	−229531.	−	61502.7i	−0.312522	−	0.0837400i	−0.411671	+	0.911333i	$0.635055\pi$
$858$	−197183.	+	735898.i	−0.267852	+	0.999639i
$859$	−149542.	−	86338.3i	−0.202664	−	0.117008i	0.395233	−	0.918581i	$-0.370664\pi$
$859$	−149542.	−	86338.3i	−0.202664	−	0.117008i	−0.597898	+	0.801572i	$0.703997\pi$
$860$	−1.27291e6	+	1.21410e6i	−1.72108	+	1.64156i
$861$	273291.	−	473354.i	0.368654	−	0.638527i
$862$	−293964.	+	293964.i	−0.395621	+	0.395621i
$863$	642420.	+	642420.i	0.862576	+	0.862576i	0.991637	−	0.129060i	$-0.0411961\pi$
$863$	642420.	+	642420.i	0.862576	+	0.862576i	−0.129060	+	0.991637i	$0.541196\pi$
$864$	−3655.34	−	2110.41i	−0.00489667	−	0.00282709i
$865$	−95261.9	+	324619.i	−0.127317	+	0.433852i
$866$	1.75436e6			2.33929
$867$	−168355.	+	168355.i	−0.223969	+	0.223969i
$868$	1.85445e6	−	496898.i	2.46136	−	0.659519i
$869$	65798.8	−	37989.0i	0.0871322	−	0.0503058i
$870$	−99358.1	+	54273.7i	−0.131270	+	0.0717053i
$871$	190222.	+	329474.i	0.250741	+	0.434295i
$872$	−2.17652e6	−	583196.i	−2.86239	−	0.766976i
$873$	−475992.	−	475992.i	−0.624555	−	0.624555i
$874$	−28364.1	+	126251.i	−0.0371318	+	0.165277i
$875$	641893.	−	556729.i	0.838391	−	0.727157i
$876$	−34683.2	−	60073.1i	−0.0451972	−	0.0782838i
$877$	−43927.0	−	11770.2i	−0.0571127	−	0.0153033i	0.230150	−	0.973155i	$-0.426078\pi$
$877$	−43927.0	−	11770.2i	−0.0571127	−	0.0153033i	−0.287262	+	0.957852i	$0.592745\pi$
$878$	1.39392e6	−	373499.i	1.80821	−	0.484507i
$879$	−1.04841e6	+	605303.i	−1.35692	+	0.783420i
$880$	−337583.	−	618009.i	−0.435929	−	0.798048i
$881$	986811.			1.27140			0.635700	−	0.771937i	$-0.280712\pi$
$881$	986811.			1.27140			0.635700	+	0.771937i	$0.280712\pi$
$882$	−181326.	+	181326.i	−0.233090	+	0.233090i
$883$	506511.	−	135719.i	0.649633	−	0.174069i	0.0810699	−	0.996708i	$-0.474166\pi$
$883$	506511.	−	135719.i	0.649633	−	0.174069i	0.568563	+	0.822640i	$0.307500\pi$
$884$	748860.	+	432354.i	0.958288	+	0.553268i
$885$	218205.	+	898844.i	0.278599	+	1.14762i
$886$	−1.53187e6			−1.95143
$887$	60473.3	+	225689.i	0.0768628	+	0.286856i	0.993649	−	0.112522i	$-0.0358929\pi$
$887$	60473.3	+	225689.i	0.0768628	+	0.286856i	−0.916786	+	0.399378i	$0.869226\pi$
$888$	−855763.	+	3.19375e6i	−1.08524	+	4.05019i
$889$	724322.	+	418188.i	0.916491	+	0.529136i
$890$	−1.50651e6	−	1.57949e6i	−1.90192	−	1.99405i
$891$	405895.	+	703031.i	0.511279	+	0.885562i
$892$	966569.	−	966569.i	1.21480	−	1.21480i
$893$	1.22016e6	−	49816.7i	1.53008	−	0.0624701i
$894$		−	796564.i		−	0.996656i
$895$	−20563.4	+	869544.i	−0.0256714	+	1.08554i
$896$	−767170.	−	1.32878e6i	−0.955599	−	1.65515i
$897$	13622.1	+	50838.3i	0.0169301	+	0.0631839i
$898$	337311.	−	1.25886e6i	0.418291	−	1.56108i
$899$	51198.8	+	29559.7i	0.0633491	+	0.0365746i
$900$	−611591.	−	1.18541e6i	−0.755051	−	1.46347i
$901$	1.40842e6			1.73493
$902$	160250.	+	598063.i	0.196964	+	0.735078i
$903$	−1.39790e6	+	374567.i	−1.71436	+	0.459361i
$904$		−	990179.i		−	1.21165i
$905$	335324.	−	550327.i	0.409419	−	0.671930i
$906$	198865.	−	344445.i	0.242272	−	0.419627i
$907$	351593.	+	94209.0i	0.427391	+	0.114519i	0.466101	−	0.884731i	$-0.345658\pi$
$907$	351593.	+	94209.0i	0.427391	+	0.114519i	−0.0387103	+	0.999250i	$0.512325\pi$
$908$	−2.18195e6	+	584652.i	−2.64651	+	0.709129i
$909$	−884755.	+	510814.i	−1.07077	+	0.618208i
$910$	−572242.	+	545802.i	−0.691030	+	0.659101i
$911$	−524864.			−0.632426			−0.316213	−	0.948688i	$-0.602411\pi$
$911$	−524864.			−0.632426			−0.316213	+	0.948688i	$0.602411\pi$
$912$	46706.5	+	1.14398e6i	0.0561549	+	1.37540i
$913$	−386422.	−	386422.i	−0.463575	−	0.463575i
$914$	1.76504e6	−	1.01904e6i	2.11281	−	1.21983i
$915$	−1.41593e6	−	1.48452e6i	−1.69122	−	1.77314i
$916$	1.01173e6	−	1.75236e6i	1.20579	−	2.08849i
$917$	541895.	+	145200.i	0.644431	+	0.172675i
$918$	379596.	−	101712.i	0.450439	−	0.120695i
$919$		−	1.35687e6i		−	1.60660i	−0.595577	−	0.803298i	$-0.703077\pi$
$919$		−	1.35687e6i		−	1.60660i	0.595577	−	0.803298i	$-0.296923\pi$
$920$	−123261.	−	75105.3i	−0.145630	−	0.0887350i
$921$	−867884.	+	1.50322e6i	−1.02316	+	1.77216i
$922$	201436.	+	751769.i	0.236960	+	0.884347i
$923$	162992.	+	162992.i	0.191321	+	0.191321i
$924$		−	2.28684e6i		−	2.67850i
$925$	1.12676e6	−	1.02493e6i	1.31689	−	1.19788i
$926$	759996.	+	1.31635e6i	0.886317	+	1.53515i
$927$	−267618.	−	998765.i	−0.311427	−	1.16226i
$928$	−332.899	+	1242.40i	−0.000386560	+	0.00144266i
$929$	−1.05806e6	+	610870.i	−1.22597	+	0.707811i	−0.966183	−	0.257856i	$-0.916984\pi$
$929$	−1.05806e6	+	610870.i	−1.22597	+	0.707811i	−0.259782	+	0.965667i	$0.583651\pi$
$930$	−1.20478e6	+	1.97726e6i	−1.39297	+	2.28611i
$931$	−195907.	−	44013.2i	−0.226022	−	0.0507789i
$932$	−521084.	+	521084.i	−0.599896	+	0.599896i
$933$	−220141.	+	821577.i	−0.252893	+	0.943811i
$934$	−767703.	+	443233.i	−0.880034	+	0.508088i
$935$	830852.	+	243820.i	0.950387	+	0.278898i
$936$	311396.	+	539354.i	0.355436	+	0.615634i
$937$	339450.	+	1.26685e6i	0.386631	+	1.44293i	0.835580	+	0.549369i	$0.185132\pi$
$937$	339450.	+	1.26685e6i	0.386631	+	1.44293i	−0.448949	+	0.893558i	$0.648201\pi$
$938$	−1.20989e6	−	1.20989e6i	−1.37511	−	1.37511i
$939$			794496.i			0.901074i
$940$	−764580.	+	2.60542e6i	−0.865302	+	2.94865i
$941$	−343799.	+	595478.i	−0.388263	+	0.672491i	−0.992216	−	0.124529i	$-0.960258\pi$
$941$	−343799.	+	595478.i	−0.388263	+	0.672491i	0.603953	+	0.797020i	$0.293591\pi$
$942$	511082.	−	511082.i	0.575955	−	0.575955i
$943$	30245.6	+	30245.6i	0.0340125	+	0.0340125i
$944$	689089.	+	397846.i	0.773270	+	0.446448i
$945$	−5670.86	+	239798.i	−0.00635017	+	0.268523i
$946$	819693.	−	1.41975e6i	0.915944	−	1.58646i
$947$	−184317.	−	49387.7i	−0.205526	−	0.0550705i	0.154587	−	0.987979i	$-0.450595\pi$
$947$	−184317.	−	49387.7i	−0.205526	−	0.0550705i	−0.360113	+	0.932909i	$0.617262\pi$
$948$	71089.7	−	265310.i	0.0791024	−	0.295214i
$949$		−	14920.0i		−	0.0165667i
$950$	791231.	−	1.35016e6i	0.876711	−	1.49603i
$951$	−337786.			−0.373492
$952$	−1.88453e6	−	504958.i	−2.07936	−	0.557162i
$953$	177691.	−	663151.i	0.195650	−	0.730174i	−0.796448	−	0.604707i	$-0.793290\pi$
$953$	177691.	−	663151.i	0.195650	−	0.730174i	0.992098	−	0.125467i	$-0.0400430\pi$
$954$	1.75112e6	+	1.01101e6i	1.92406	+	1.11085i
$955$	−461637.	−	10917.0i	−0.506167	−	0.0119701i
$956$	921779.	−	1.59657e6i	1.00858	−	1.74692i
$957$	49794.3	−	49794.3i	0.0543695	−	0.0543695i
$958$	−415014.	−	415014.i	−0.452202	−	0.452202i
$959$	142167.	+	82080.2i	0.154583	+	0.0892485i
$960$	1.16896e6	+	343039.i	1.26840	+	0.372221i
$961$	285542.			0.309188
$962$	−1.00240e6	+	1.00240e6i	−1.08316	+	1.08316i
$963$	−362768.	+	97203.4i	−0.391180	+	0.104816i
$964$	1.69798e6	−	980328.i	1.82716	−	1.05491i
$965$	329293.	−	1.12212e6i	0.353613	−	1.20499i
$966$	−118355.	−	204997.i	−0.126833	−	0.219681i
$967$	−873614.	−	234084.i	−0.934257	−	0.250333i	−0.240588	−	0.970627i	$-0.577340\pi$
$967$	−873614.	−	234084.i	−0.934257	−	0.250333i	−0.693669	+	0.720294i	$0.744007\pi$
$968$	−237668.	−	237668.i	−0.253641	−	0.253641i
$969$	−1.03526e6	−	954040.i	−1.10256	−	1.01606i
$970$	1.49957e6	+	913714.i	1.59376	+	0.971107i
$971$	−82584.5	−	143041.i	−0.0875911	−	0.151712i	0.818901	−	0.573934i	$-0.194584\pi$
$971$	−82584.5	−	143041.i	−0.0875911	−	0.151712i	−0.906492	+	0.422222i	$0.861250\pi$
$972$	2.39150e6	+	640800.i	2.53127	+	0.678251i
$973$	414031.	−	110939.i	0.437328	−	0.117182i
$974$	−322404.	+	186140.i	−0.339846	+	0.196210i
$975$	30088.6	−	635808.i	0.0316514	−	0.668832i
$976$	−1.76481e6			−1.85267
$977$	−447655.	+	447655.i	−0.468980	+	0.468980i	−0.901584	−	0.432604i	$-0.857595\pi$
$977$	−447655.	+	447655.i	−0.468980	+	0.468980i	0.432604	+	0.901584i	$0.357595\pi$
$978$	−2.66722e6	+	714679.i	−2.78857	+	0.747194i
$979$	1.17577e6	+	678832.i	1.22675	+	0.708267i
$980$	232308.	−	381259.i	0.241887	−	0.396979i
$981$	1.34066e6			1.39310
$982$	−551733.	−	2.05909e6i	−0.572145	−	2.13527i
$983$	58244.6	−	217372.i	0.0602766	−	0.224955i	−0.929216	−	0.369536i	$-0.879517\pi$
$983$	58244.6	−	217372.i	0.0602766	−	0.224955i	0.989493	+	0.144581i	$0.0461833\pi$
$984$	972472.	+	561457.i	1.00435	+	0.579864i
$985$	−1.09690e6	+	1.04622e6i	−1.13056	+	1.07832i
$986$	−59877.9	−	103712.i	−0.0615904	−	0.106678i
$987$	−1.57961e6	+	1.57961e6i	−1.62150	+	1.62150i
$988$	−451282.	+	860951.i	−0.462311	+	0.881992i
$989$		−	113254.i		−	0.115788i
$990$	857995.	+	899559.i	0.875416	+	0.917823i
$991$	754784.	+	1.30732e6i	0.768556	+	1.33118i	0.938346	+	0.345697i	$0.112358\pi$
$991$	754784.	+	1.30732e6i	0.768556	+	1.33118i	−0.169790	+	0.985480i	$0.554309\pi$
$992$	6808.20	+	25408.6i	0.00691845	+	0.0258200i
$993$	−220045.	+	821218.i	−0.223158	+	0.832837i
$994$	−897802.	−	518346.i	−0.908673	−	0.524623i
$995$	−121507.	−	74036.4i	−0.122731	−	0.0747824i
$996$	−1.97560e6			−1.99150
$997$	254397.	+	949421.i	0.255930	+	0.955143i	0.967571	+	0.252600i	$0.0812857\pi$
$997$	254397.	+	949421.i	0.255930	+	0.955143i	−0.711641	+	0.702543i	$0.752048\pi$
$998$	1.07602e6	−	288320.i	1.08034	−	0.289476i
$999$			429989.i			0.430850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.5.m.a.83.35	yes	152
5.2	odd	4	inner	95.5.m.a.7.4	✓	152
19.11	even	3	inner	95.5.m.a.68.4	yes	152
95.87	odd	12	inner	95.5.m.a.87.35	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.5.m.a.7.4	✓	152	5.2	odd	4	inner
95.5.m.a.68.4	yes	152	19.11	even	3	inner
95.5.m.a.83.35	yes	152	1.1	even	1	trivial
95.5.m.a.87.35	yes	152	95.87	odd	12	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.m (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(6.69961 + 1.79516i) q^{2} +(-3.14304 + 11.7300i) q^{3} +(27.8058 + 16.0537i) q^{4} +(24.9930 + 0.591047i) q^{5} +(-42.1143 + 72.9441i) q^{6} +(38.4526 - 38.4526i) q^{7} +(78.9982 + 78.9982i) q^{8} +(-57.5657 - 33.2356i) q^{9} +(166.383 + 48.8262i) q^{10} -107.854 q^{11} +(-275.705 + 275.705i) q^{12} +(-81.0069 + 21.7057i) q^{13} +(326.646 - 188.589i) q^{14} +(-85.4870 + 291.310i) q^{15} +(130.584 + 226.178i) q^{16} +(-310.191 - 83.1155i) q^{17} +(-326.005 - 326.005i) q^{18} +(79.1311 - 352.220i) q^{19} +(685.463 + 417.665i) q^{20} +(330.190 + 571.906i) q^{21} +(-722.580 - 193.615i) q^{22} +(-49.9183 + 13.3756i) q^{23} +(-1174.94 + 678.353i) q^{24} +(624.301 + 29.5441i) q^{25} -581.680 q^{26} +(-124.759 + 124.759i) q^{27} +(1686.51 - 451.900i) q^{28} +(46.5624 + 26.8828i) q^{29} +(-1095.68 + 1798.20i) q^{30} +1099.57 q^{31} +(6.19167 + 23.1076i) q^{32} +(338.989 - 1265.12i) q^{33} +(-1928.96 - 1113.68i) q^{34} +(983.774 - 938.319i) q^{35} +(-1067.11 - 1848.29i) q^{36} +(1723.28 - 1723.28i) q^{37} +(1162.44 - 2217.69i) q^{38} -1018.43i q^{39} +(1927.71 + 2021.09i) q^{40} +(-413.838 - 716.789i) q^{41} +(1185.49 + 4424.30i) q^{42} +(-567.199 + 2116.82i) q^{43} +(-2998.97 - 1731.46i) q^{44} +(-1419.10 - 864.681i) q^{45} -358.444 q^{46} +(875.523 + 3267.50i) q^{47} +(-3063.49 + 820.861i) q^{48} -556.206i q^{49} +(4129.54 + 1318.65i) q^{50} +(1949.89 - 3377.30i) q^{51} +(-2600.92 - 696.915i) q^{52} +(-4236.32 + 1135.12i) q^{53} +(-1059.80 + 611.874i) q^{54} +(-2695.60 - 63.7468i) q^{55} +6075.37 q^{56} +(3882.83 + 2035.25i) q^{57} +(263.691 + 263.691i) q^{58} +(2638.49 - 1523.33i) q^{59} +(-7053.64 + 6727.73i) q^{60} +(-3378.69 + 5852.06i) q^{61} +(7366.72 + 1973.91i) q^{62} +(-3491.54 + 935.556i) q^{63} -4012.76i q^{64} +(-2037.44 + 494.613i) q^{65} +(4542.19 - 7867.31i) q^{66} +(-1174.11 - 4381.84i) q^{67} +(-7290.82 - 7290.82i) q^{68} -627.580i q^{69} +(8275.34 - 4520.35i) q^{70} +(-1374.27 - 2380.31i) q^{71} +(-1922.04 - 7173.13i) q^{72} +(-46.0454 + 171.844i) q^{73} +(14638.9 - 8451.77i) q^{74} +(-2308.75 + 7230.18i) q^{75} +(7854.75 - 8523.44i) q^{76} +(-4147.27 + 4147.27i) q^{77} +(1828.24 - 6823.10i) q^{78} +(-610.073 + 352.226i) q^{79} +(3130.00 + 5730.05i) q^{80} +(-3763.38 - 6518.36i) q^{81} +(-1485.81 - 5545.12i) q^{82} +(3582.82 + 3582.82i) q^{83} +21203.1i q^{84} +(-7703.49 - 2260.65i) q^{85} +(-7600.03 + 13163.6i) q^{86} +(-461.682 + 461.682i) q^{87} +(-8520.27 - 8520.27i) q^{88} +(-10901.5 - 6293.99i) q^{89} +(-7955.16 - 8340.53i) q^{90} +(-2280.29 + 3949.57i) q^{91} +(-1602.75 - 429.455i) q^{92} +(-3456.00 + 12898.0i) q^{93} +23462.7i q^{94} +(2185.90 - 8756.28i) q^{95} -290.513 q^{96} +(9781.95 + 2621.06i) q^{97} +(998.477 - 3726.37i) q^{98} +(6208.69 + 3584.59i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 2 q^{2} - 2 q^{3} - 20 q^{5} - 40 q^{6} + 52 q^{7} + 108 q^{8} - 2 q^{10} - 304 q^{11} - 268 q^{12} + 198 q^{13} + 172 q^{15} + 4064 q^{16} + 238 q^{17} + 3792 q^{18} + 528 q^{20} - 796 q^{21} - 2774 q^{22}+ \cdots + 15572 q^{98}+O(q^{100}) \) 152 * q - 2 * q^2 - 2 * q^3 - 20 * q^5 - 40 * q^6 + 52 * q^7 + 108 * q^8 - 2 * q^10 - 304 * q^11 - 268 * q^12 + 198 * q^13 + 172 * q^15 + 4064 * q^16 + 238 * q^17 + 3792 * q^18 + 528 * q^20 - 796 * q^21 - 2774 * q^22 - 1622 * q^23 - 1648 * q^25 - 2608 * q^26 + 88 * q^27 + 56 * q^28 + 188 * q^30 - 1728 * q^31 - 1916 * q^32 + 1696 * q^33 + 6898 * q^35 - 19748 * q^36 - 1288 * q^37 + 5394 * q^38 + 2232 * q^40 + 5372 * q^41 + 2266 * q^42 - 372 * q^43 - 3000 * q^45 - 12664 * q^46 - 1712 * q^47 + 2028 * q^48 + 34564 * q^50 + 3636 * q^51 + 5342 * q^52 - 1952 * q^53 - 13500 * q^55 + 7152 * q^56 + 16344 * q^57 - 19932 * q^58 + 2238 * q^60 - 2668 * q^61 - 2044 * q^62 + 27314 * q^63 - 46784 * q^65 - 4132 * q^66 + 18598 * q^67 + 18884 * q^68 - 4570 * q^70 - 4420 * q^71 - 20560 * q^72 - 10382 * q^73 - 61252 * q^75 + 16524 * q^76 - 20356 * q^77 + 35972 * q^78 + 44590 * q^80 + 20256 * q^81 - 16708 * q^82 - 4148 * q^83 + 3838 * q^85 - 68200 * q^86 - 139812 * q^87 - 102744 * q^88 - 57328 * q^90 + 59052 * q^91 - 38588 * q^92 + 69836 * q^93 + 33510 * q^95 + 13440 * q^96 + 5928 * q^97 + 15572 * q^98

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