LMFDB - Embedded newform 95.5.m.a.68.4

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			68.4
Character	$\chi$	$=$	95.68
Dual form			95.5.m.a.7.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.79516 - 6.69961i) q^{2} +(11.7300 - 3.14304i) q^{3} +(-27.8058 + 16.0537i) q^{4} +(-11.9846 - 21.9401i) 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} +(-125.476 + 119.678i) q^{10} -107.854 q^{11} +(-275.705 + 275.705i) q^{12} +(21.7057 - 81.0069i) q^{13} +(-326.646 - 188.589i) q^{14} +(-209.538 - 219.689i) q^{15} +(130.584 - 226.178i) q^{16} +(83.1155 + 310.191i) 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} +(193.615 + 722.580i) q^{22} +(13.3756 - 49.9183i) q^{23} +(1174.94 + 678.353i) q^{24} +(-337.737 + 525.889i) q^{25} -581.680 q^{26} +(-124.759 + 124.759i) q^{27} +(-451.900 + 1686.51i) q^{28} +(-46.5624 + 26.8828i) q^{29} +(-1095.68 + 1798.20i) q^{30} +1099.57 q^{31} +(-23.1076 - 6.19167i) q^{32} +(-1265.12 + 338.989i) q^{33} +(1928.96 - 1113.68i) q^{34} +(-1304.50 - 382.814i) q^{35} +(-1067.11 + 1848.29i) q^{36} +(1723.28 - 1723.28i) q^{37} +(-2217.69 + 1162.44i) q^{38} -1018.43i q^{39} +(786.464 - 2679.99i) q^{40} +(-413.838 + 716.789i) q^{41} +(-4424.30 - 1185.49i) q^{42} +(2116.82 - 567.199i) q^{43} +(2998.97 - 1731.46i) q^{44} +(-1419.10 - 864.681i) q^{45} -358.444 q^{46} +(-3267.50 - 875.523i) q^{47} +(820.861 - 3063.49i) q^{48} -556.206i q^{49} +(4129.54 + 1318.65i) q^{50} +(1949.89 + 3377.30i) q^{51} +(696.915 + 2600.92i) q^{52} +(1135.12 - 4236.32i) q^{53} +(1059.80 + 611.874i) q^{54} +(1292.59 + 2366.33i) q^{55} +6075.37 q^{56} +(-2035.25 - 3882.83i) q^{57} +(263.691 + 263.691i) q^{58} +(-2638.49 - 1523.33i) q^{59} +(9353.21 + 2744.77i) q^{60} +(-3378.69 - 5852.06i) q^{61} +(-1973.91 - 7366.72i) q^{62} +(935.556 - 3491.54i) q^{63} -4012.76i q^{64} +(-2037.44 + 494.613i) q^{65} +(4542.19 + 7867.31i) q^{66} +(4381.84 + 1174.11i) q^{67} +(-7290.82 - 7290.82i) q^{68} -627.580i q^{69} +(-222.930 + 9426.83i) q^{70} +(-1374.27 + 2380.31i) q^{71} +(7173.13 + 1922.04i) q^{72} +(171.844 - 46.0454i) 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} +(-6823.10 + 1828.24i) q^{78} +(610.073 + 352.226i) q^{79} +(-6527.37 - 154.363i) q^{80} +(-3763.38 + 6518.36i) q^{81} +(5545.12 + 1485.81i) q^{82} +(3582.82 + 3582.82i) q^{83} +21203.1i q^{84} +(5809.52 - 5541.10i) 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} +(-3245.53 + 11059.6i) q^{90} +(-2280.29 - 3949.57i) q^{91} +(429.455 + 1602.75i) q^{92} +(12898.0 - 3456.00i) q^{93} +23462.7i q^{94} +(-6779.40 + 5957.38i) q^{95} -290.513 q^{96} +(-2621.06 - 9781.95i) q^{97} +(-3726.37 + 998.477i) 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 $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.79516	−	6.69961i	−0.448789	−	1.67490i	−0.705733	−	0.708477i	$-0.749382\pi$
$2$	−1.79516	−	6.69961i	−0.448789	−	1.67490i	0.256944	−	0.966426i	$-0.417284\pi$
$3$	11.7300	−	3.14304i	1.30333	−	0.349227i	0.460622	−	0.887596i	$-0.347626\pi$
$3$	11.7300	−	3.14304i	1.30333	−	0.349227i	0.842709	+	0.538370i	$0.180960\pi$
$4$	−27.8058	+	16.0537i	−1.73787	+	1.00336i
$5$	−11.9846	−	21.9401i	−0.479386	−	0.877604i
$5$	−11.9846	−	21.9401i	−0.479386	−	0.877604i
$6$	−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
$10$	−125.476	+	119.678i	−1.25476	+	1.19678i
$11$	−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
$13$	21.7057	−	81.0069i	0.128436	−	0.479331i	−0.871503	−	0.490391i	$-0.836854\pi$
$13$	21.7057	−	81.0069i	0.128436	−	0.479331i	0.999939	+	0.0110602i	$0.00352063\pi$
$14$	−326.646	−	188.589i	−1.66656	−	0.962190i
$15$	−209.538	−	219.689i	−0.931281	−	0.976395i
$16$	130.584	−	226.178i	0.510094	−	0.883508i
$17$	83.1155	+	310.191i	0.287597	+	1.07333i	0.946921	+	0.321467i	$0.104176\pi$
$17$	83.1155	+	310.191i	0.287597	+	1.07333i	−0.659324	+	0.751859i	$0.729157\pi$
$18$	−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
$22$	193.615	+	722.580i	0.400030	+	1.49293i
$23$	13.3756	−	49.9183i	0.0252846	−	0.0943635i	−0.952131	−	0.305692i	$-0.901112\pi$
$23$	13.3756	−	49.9183i	0.0252846	−	0.0943635i	0.977415	+	0.211328i	$0.0677789\pi$
$24$	1174.94	+	678.353i	2.03983	+	1.17770i
$25$	−337.737	+	525.889i	−0.540379	+	0.841422i
$26$	−581.680			−0.860474
$27$	−124.759	+	124.759i	−0.171137	+	0.171137i
$28$	−451.900	+	1686.51i	−0.576403	+	2.15117i
$29$	−46.5624	+	26.8828i	−0.0553655	+	0.0319653i	−0.527427	−	0.849600i	$-0.676843\pi$
$29$	−46.5624	+	26.8828i	−0.0553655	+	0.0319653i	0.472062	+	0.881565i	$0.343510\pi$
$30$	−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	$0.306129\pi$
$32$	−23.1076	−	6.19167i	−0.0225661	−	0.00604656i
$33$	−1265.12	+	338.989i	−1.16173	+	0.311285i
$34$	1928.96	−	1113.68i	1.66865	−	0.963395i
$35$	−1304.50	−	382.814i	−1.06489	−	0.312501i
$36$	−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	$-0.0993646\pi$
$38$	−2217.69	+	1162.44i	−1.53580	+	0.805013i
$39$		−	1018.43i		−	0.669580i
$40$	786.464	−	2679.99i	0.491540	−	1.67500i
$41$	−413.838	+	716.789i	−0.246186	+	0.426406i	−0.962464	−	0.271408i	$-0.912511\pi$
$41$	−413.838	+	716.789i	−0.246186	+	0.426406i	0.716279	+	0.697815i	$0.245844\pi$
$42$	−4424.30	−	1185.49i	−2.50810	−	0.672044i
$43$	2116.82	−	567.199i	1.14484	−	0.306760i	0.363946	−	0.931420i	$-0.381429\pi$
$43$	2116.82	−	567.199i	1.14484	−	0.306760i	0.780897	+	0.624660i	$0.214762\pi$
$44$	2998.97	−	1731.46i	1.54905	−	0.894347i
$45$	−1419.10	−	864.681i	−0.700788	−	0.427003i
$46$	−358.444			−0.169397
$47$	−3267.50	−	875.523i	−1.47917	−	0.396344i	−0.573108	−	0.819480i	$-0.694262\pi$
$47$	−3267.50	−	875.523i	−1.47917	−	0.396344i	−0.906066	+	0.423136i	$0.860929\pi$
$48$	820.861	−	3063.49i	0.356276	−	1.32964i
$49$		−	556.206i		−	0.231656i
$50$	4129.54	+	1318.65i	1.65182	+	0.527461i
$51$	1949.89	+	3377.30i	0.749668	+	1.29846i
$52$	696.915	+	2600.92i	0.257735	+	0.961880i
$53$	1135.12	−	4236.32i	0.404101	−	1.50812i	−0.401608	−	0.915812i	$-0.631548\pi$
$53$	1135.12	−	4236.32i	0.404101	−	1.50812i	0.805708	−	0.592313i	$-0.201785\pi$
$54$	1059.80	+	611.874i	0.363442	+	0.209833i
$55$	1292.59	+	2366.33i	0.427303	+	0.782257i
$56$	6075.37			1.93730
$57$	−2035.25	−	3882.83i	−0.626423	−	1.19508i
$58$	263.691	+	263.691i	0.0783863	+	0.0783863i
$59$	−2638.49	−	1523.33i	−0.757969	−	0.437614i	0.0705969	−	0.997505i	$-0.477510\pi$
$59$	−2638.49	−	1523.33i	−0.757969	−	0.437614i	−0.828566	+	0.559891i	$0.810843\pi$
$60$	9353.21	+	2744.77i	2.59811	+	0.762435i
$61$	−3378.69	−	5852.06i	−0.908005	−	1.57271i	−0.816832	−	0.576876i	$-0.804272\pi$
$61$	−3378.69	−	5852.06i	−0.908005	−	1.57271i	−0.0911733	−	0.995835i	$-0.529062\pi$
$62$	−1973.91	−	7366.72i	−0.513503	−	1.91642i
$63$	935.556	−	3491.54i	0.235716	−	0.879704i
$64$		−	4012.76i		−	0.979677i
$65$	−2037.44	+	494.613i	−0.482233	+	0.117068i
$66$	4542.19	+	7867.31i	1.04274	+	1.80609i
$67$	4381.84	+	1174.11i	0.976128	+	0.261553i	0.711413	−	0.702774i	$-0.248055\pi$
$67$	4381.84	+	1174.11i	0.976128	+	0.261553i	0.264715	+	0.964327i	$0.414722\pi$
$68$	−7290.82	−	7290.82i	−1.57673	−	1.57673i
$69$		−	627.580i		−	0.131817i
$70$	−222.930	+	9426.83i	−0.0454960	+	1.92384i
$71$	−1374.27	+	2380.31i	−0.272619	+	0.472190i	−0.969532	−	0.244966i	$-0.921223\pi$
$71$	−1374.27	+	2380.31i	−0.272619	+	0.472190i	0.696913	+	0.717156i	$0.254557\pi$
$72$	7173.13	+	1922.04i	1.38371	+	0.370763i
$73$	171.844	−	46.0454i	0.0322469	−	0.00864054i	−0.242660	−	0.970112i	$-0.578020\pi$
$73$	171.844	−	46.0454i	0.0322469	−	0.00864054i	0.274906	+	0.961471i	$0.411353\pi$
$74$	−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
$78$	−6823.10	+	1828.24i	−1.12148	+	0.300500i
$79$	610.073	+	352.226i	0.0977525	+	0.0564374i	0.548079	−	0.836426i	$-0.315359\pi$
$79$	610.073	+	352.226i	0.0977525	+	0.0564374i	−0.450327	+	0.892864i	$0.648693\pi$
$80$	−6527.37	−	154.363i	−1.01990	−	0.0241191i
$81$	−3763.38	+	6518.36i	−0.573598	+	0.993501i
$82$	5545.12	+	1485.81i	0.824675	+	0.220971i
$83$	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
$85$	5809.52	−	5541.10i	0.804086	−	0.766934i
$86$	−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	$-0.374350\pi$
$89$	10901.5	−	6293.99i	1.37628	−	0.794596i	0.991710	+	0.128500i	$0.0410162\pi$
$90$	−3245.53	+	11059.6i	−0.400683	+	1.36539i
$91$	−2280.29	−	3949.57i	−0.275364	−	0.476944i
$92$	429.455	+	1602.75i	0.0507390	+	0.189360i
$93$	12898.0	−	3456.00i	1.49127	−	0.399584i
$94$			23462.7i			2.65535i
$95$	−6779.40	+	5957.38i	−0.751180	+	0.660098i
$96$	−290.513			−0.0315227
$97$	−2621.06	−	9781.95i	−0.278570	−	1.03964i	−0.953411	−	0.301674i	$-0.902455\pi$
$97$	−2621.06	−	9781.95i	−0.278570	−	1.03964i	0.674841	−	0.737963i	$-0.264212\pi$
$98$	−3726.37	+	998.477i	−0.388002	+	0.103965i
$99$	−6208.69	+	3584.59i	−0.633475	+	0.365737i
$100$	948.585	−	20044.7i	0.0948585	−	2.00447i
$101$	7684.74	+	13310.4i	0.753332	+	1.30481i	0.946199	+	0.323585i	$0.104888\pi$
$101$	7684.74	+	13310.4i	0.753332	+	1.30481i	−0.192867	+	0.981225i	$0.561778\pi$
$102$	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
$105$	−16504.9	−	390.316i	−1.49704	−	0.0354028i
$106$	−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	$0.170638\pi$
$108$	1466.18	−	5471.86i	0.125701	−	0.469124i
$109$	17466.9	+	10084.5i	1.47016	+	0.848796i	0.999439	−	0.0334873i	$-0.0106613\pi$
$109$	17466.9	+	10084.5i	1.47016	+	0.848796i	0.470719	+	0.882283i	$0.343995\pi$
$110$	13533.1	−	12907.8i	1.11844	−	1.06676i
$111$	14797.7	−	25630.4i	1.20102	−	2.08022i
$112$	−3675.84	−	13718.4i	−0.293036	−	1.09362i
$113$	−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
$117$	−1442.80	−	5384.62i	−0.105399	−	0.393354i
$118$	−5469.24	+	20411.5i	−0.392793	+	1.46592i
$119$	15123.7	+	8731.66i	1.06798	+	0.616599i
$120$	801.877	−	33908.2i	0.0556859	−	2.35473i
$121$	−3008.52			−0.205486
$122$	−33141.3	+	33141.3i	−2.22664	+	2.22664i
$123$	−2601.42	+	9708.63i	−0.171949	+	0.641723i
$124$	−30574.6	+	17652.2i	−1.98846	+	1.14804i
$125$	15585.7	+	1107.39i	0.997485	+	0.0708728i
$126$	−25071.5			−1.57921
$127$	−14856.1	−	3980.67i	−0.921078	−	0.246802i	−0.233032	−	0.972469i	$-0.574865\pi$
$127$	−14856.1	−	3980.67i	−0.921078	−	0.246802i	−0.688046	+	0.725667i	$0.741531\pi$
$128$	−27253.7	+	7302.60i	−1.66343	+	0.445715i
$129$	23047.5	−	13306.5i	1.38498	−	0.799619i
$130$	6971.23	+	12762.1i	0.412499	+	0.755156i
$131$	5158.23	−	8934.31i	0.300579	−	0.520617i	−0.675689	−	0.737187i	$-0.736154\pi$
$131$	5158.23	−	8934.31i	0.300579	−	0.520617i	0.976267	+	0.216570i	$0.0694869\pi$
$132$	29735.8	−	29735.8i	1.70660	−	1.70660i
$133$	−16586.6	−	10501.0i	−0.937678	−	0.593646i
$134$		−	31464.3i		−	1.75230i
$135$	4232.41	+	1242.03i	0.232231	+	0.0681498i
$136$	−17938.6	+	31070.5i	−0.969863	+	1.67985i
$137$	−2915.89	−	781.310i	−0.155357	−	0.0416277i	0.180302	−	0.983611i	$-0.442292\pi$
$137$	−2915.89	−	781.310i	−0.155357	−	0.0416277i	−0.335659	+	0.941984i	$0.608959\pi$
$138$	−4204.55	+	1126.60i	−0.220781	+	0.0591580i
$139$	−6826.19	+	3941.11i	−0.353304	+	0.203980i	−0.666140	−	0.745827i	$-0.732055\pi$
$139$	−6826.19	+	3941.11i	−0.353304	+	0.203980i	0.312835	+	0.949807i	$0.398721\pi$
$140$	42418.2	−	10297.5i	2.16419	−	0.525385i
$141$	−41079.5			−2.06627
$142$	18414.2	+	4934.07i	0.913221	+	0.244697i
$143$	−2341.05	+	8736.92i	−0.114482	+	0.427254i
$144$		−	17360.1i		−	0.837197i
$145$	1147.85	+	699.403i	0.0545943	+	0.0332653i
$146$	−616.974	−	1068.63i	−0.0289442	−	0.0501327i
$147$	−1748.18	−	6524.29i	−0.0809005	−	0.301925i
$148$	−20252.2	+	75582.4i	−0.924591	+	3.45062i
$149$	8190.14	+	4728.58i	0.368909	+	0.212990i	0.672982	−	0.739659i	$-0.265013\pi$
$149$	8190.14	+	4728.58i	0.368909	+	0.212990i	−0.304073	+	0.952649i	$0.598347\pi$
$150$	52584.0	+	2488.46i	2.33707	+	0.110598i
$151$	−4722.04			−0.207098			−0.103549	−	0.994624i	$-0.533020\pi$
$151$	−4722.04			−0.207098			−0.103549	+	0.994624i	$0.533020\pi$
$152$	21573.6	−	34076.0i	0.933759	−	1.47490i
$153$	15094.0	+	15094.0i	0.644794	+	0.644794i
$154$	35230.1	+	20340.1i	1.48550	+	0.857653i
$155$	−13178.0	−	24124.8i	−0.548512	−	1.00415i
$156$	16349.6	+	28318.3i	0.671828	+	1.16364i
$157$	2220.97	+	8288.76i	0.0901037	+	0.336272i	0.996232	−	0.0867320i	$-0.0276424\pi$
$157$	2220.97	+	8288.76i	0.0901037	+	0.336272i	−0.906128	+	0.423004i	$0.860976\pi$
$158$	1264.60	−	4719.56i	0.0506570	−	0.189054i
$159$		−	53259.7i		−	2.10671i
$160$	141.091	+	581.189i	0.00551136	+	0.0227027i
$161$	−1405.16	−	2433.81i	−0.0542094	−	0.0938935i
$162$	50426.3	+	13511.7i	1.92144	+	0.514849i
$163$	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
$165$	22599.5	+	23694.3i	0.830102	+	0.870314i
$166$	17571.8	−	30435.3i	0.637676	−	1.10449i
$167$	43901.1	+	11763.3i	1.57414	+	0.421789i	0.937105	−	0.349048i	$-0.113495\pi$
$167$	43901.1	+	11763.3i	1.57414	+	0.421789i	0.637032	+	0.770837i	$0.280162\pi$
$168$	71264.0	−	19095.1i	2.52494	−	0.676557i
$169$	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
$173$	13071.2	−	3502.43i	0.436741	−	0.117024i	−0.0337476	−	0.999430i	$-0.510744\pi$
$173$	13071.2	−	3502.43i	0.436741	−	0.117024i	0.470489	+	0.882406i	$0.344078\pi$
$174$	3921.89	+	2264.30i	0.129538	+	0.0747887i
$175$	7234.94	+	33208.6i	0.236243	+	1.08436i
$176$	−14084.0	+	24394.2i	−0.454674	+	0.787519i
$177$	−35737.3	−	9575.79i	−1.14071	−	0.305653i
$178$	−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	$0.817318\pi$
$180$	53340.5	+	1261.42i	1.64631	+	0.0389328i
$181$	12888.8	+	22324.1i	0.393419	+	0.681422i	0.992898	−	0.118969i	$-0.0379589\pi$
$181$	12888.8	+	22324.1i	0.393419	+	0.681422i	−0.599479	+	0.800390i	$0.704626\pi$
$182$	−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
$185$	−58461.9	−	17156.1i	−1.70816	−	0.501273i
$186$	−46307.8	−	80207.4i	−1.33853	−	2.31840i
$187$	−8964.34	−	33455.4i	−0.256351	−	0.956715i
$188$	104911.	−	28110.8i	2.96828	−	0.795348i
$189$			9594.60i			0.268598i
$190$	52082.2	+	34724.9i	1.44272	+	0.961909i
$191$	−18470.6			−0.506308			−0.253154	−	0.967426i	$-0.581468\pi$
$191$	−18470.6			−0.506308			−0.253154	+	0.967426i	$0.581468\pi$
$192$	−12612.3	−	47069.6i	−0.342129	−	1.27684i
$193$	−45183.5	+	12106.9i	−1.21301	+	0.325026i	−0.807944	−	0.589260i	$-0.799420\pi$
$193$	−45183.5	+	12106.9i	−1.21301	+	0.325026i	−0.405070	+	0.914286i	$0.632753\pi$
$194$	−60830.1	+	35120.3i	−1.61627	+	0.933156i
$195$	−22344.5	+	12205.5i	−0.587626	+	0.320987i
$196$	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	$-0.643773\pi$
$199$	4928.94	−	2845.72i	0.124465	−	0.0718599i	0.560940	+	0.827857i	$0.310440\pi$
$200$	−68224.8	+	14863.7i	−1.70562	+	0.371592i
$201$	55089.2			1.36356
$202$	75379.0	−	75379.0i	1.84734	−	1.84734i
$203$	−756.732	+	2824.16i	−0.0183633	+	0.0685326i
$204$	−108437.	−	62605.8i	−2.60564	−	1.50437i
$205$	20686.1	+	489.196i	0.492234	+	0.0116406i
$206$	53946.4	−	93438.0i	1.27124	−	2.20186i
$207$	−889.088	−	3318.12i	−0.0207493	−	0.0774376i
$208$	−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	−0.886855	−	0.462047i	$-0.847115\pi$
$211$	−1926.99	+	3337.65i	−0.0432828	+	0.0749680i	0.843572	+	0.537015i	$0.180448\pi$
$212$	36445.7	+	136017.i	0.810915	+	3.02637i
$213$	−8638.78	+	32240.4i	−0.190412	+	0.710626i
$214$	−33938.2	−	19594.2i	−0.741074	−	0.427859i
$215$	−37813.7	−	39645.5i	−0.818035	−	0.857663i
$216$	−19711.4			−0.422484
$217$	42281.5	−	42281.5i	0.897906	−	0.897906i
$218$	36206.7	−	135125.i	0.761861	−	2.84330i
$219$	1871.00	−	1080.22i	0.0390109	−	0.0225230i
$220$	−73929.9	−	45046.8i	−1.52748	−	0.930720i
$221$	26931.7			0.551417
$222$	−198278.	−	53128.5i	−4.02317	−	1.07801i
$223$	−41123.1	+	11018.9i	−0.826945	+	0.221579i	−0.647380	−	0.762167i	$-0.724135\pi$
$223$	−41123.1	+	11018.9i	−0.826945	+	0.221579i	−0.179564	+	0.983746i	$0.557469\pi$
$224$	−1126.63	+	650.463i	−0.0224537	+	0.0129636i
$225$	−1963.83	+	41498.0i	−0.0387917	+	0.819714i
$226$	−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	$0.489183\pi$
$228$	118926.	+	75292.0i	2.28773	+	1.44837i
$229$		−	63021.3i		−	1.20176i	−0.799340	−	0.600879i	$-0.794818\pi$
$229$		−	63021.3i		−	1.20176i	0.799340	−	0.600879i	$-0.205182\pi$
$230$	4295.83	+	7864.31i	0.0812066	+	0.148664i
$231$	−35612.3	+	61682.4i	−0.667385	+	1.15594i
$232$	−5802.04	−	1554.65i	−0.107797	−	0.0288840i
$233$	22169.8	−	5940.37i	0.408366	−	0.109421i	−0.0487875	−	0.998809i	$-0.515536\pi$
$233$	22169.8	−	5940.37i	0.408366	−	0.109421i	0.457153	+	0.889388i	$0.348869\pi$
$234$	−33484.8	+	19332.5i	−0.611528	+	0.353066i
$235$	19950.7	+	82182.0i	0.361262	+	1.48813i
$236$	97820.6			1.75633
$237$	8263.21	+	2214.12i	0.147113	+	0.0394189i
$238$	31349.4	−	116998.i	0.553446	−	2.06549i
$239$		−	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	0.999552	+	0.0299255i	$0.00952702\pi$
$241$	30532.7	+	52884.3i	0.525692	+	0.910526i	−0.473860	+	0.880600i	$0.657140\pi$
$242$	5400.77	+	20156.0i	0.0922200	+	0.344170i
$243$	−19958.0	+	74484.3i	−0.337991	+	1.26140i
$244$	187894.	+	108481.i	3.15598	+	1.82211i
$245$	−12203.2	+	6665.94i	−0.203302	+	0.111053i
$246$	69714.0			1.15199
$247$	−30249.9	−	1235.04i	−0.495827	−	0.0202436i
$248$	86864.4	+	86864.4i	1.41234	+	1.41234i
$249$	53287.4	+	30765.5i	0.859460	+	0.496210i
$250$	−20559.7	−	106406.i	−0.328955	−	1.70250i
$251$	−19301.6	−	33431.4i	−0.306370	−	0.530648i	0.671195	−	0.741280i	$-0.265781\pi$
$251$	−19301.6	−	33431.4i	−0.306370	−	0.530648i	−0.977565	+	0.210632i	$0.932448\pi$
$252$	30038.3	+	112104.i	0.473014	+	1.76531i
$253$	−1442.61	+	5383.88i	−0.0225376	+	0.0841113i
$254$			106676.i			1.65348i
$255$	50729.7	−	83256.5i	0.780157	−	1.28038i
$256$	65747.1	+	113877.i	1.00322	+	1.73763i
$257$	−36795.3	−	9859.26i	−0.557090	−	0.149272i	−0.0307211	−	0.999528i	$-0.509780\pi$
$257$	−36795.3	−	9859.26i	−0.557090	−	0.149272i	−0.526369	+	0.850256i	$0.676447\pi$
$258$	−130522.	−	130522.i	−1.96085	−	1.96085i
$259$		−	132529.i		−	1.97566i
$260$	48712.3	−	46461.5i	0.720596	−	0.687301i
$261$	−1786.93	+	3095.06i	−0.0262317	+	0.0454347i
$262$	−69116.3	−	18519.7i	−1.00688	−	0.269793i
$263$	−90090.8	+	24139.8i	−1.30247	+	0.348997i	−0.842385	−	0.538876i	$-0.818849\pi$
$263$	−90090.8	+	24139.8i	−1.30247	+	0.348997i	−0.460089	+	0.887873i	$0.652182\pi$
$264$	−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
$268$	−140690.	+	37697.7i	−1.95881	+	0.524862i
$269$	39017.8	+	22527.0i	0.539211	+	0.311313i	0.744759	−	0.667334i	$-0.232564\pi$
$269$	39017.8	+	22527.0i	0.539211	+	0.311313i	−0.205548	+	0.978647i	$0.565898\pi$
$270$	723.293	−	30585.1i	0.00992171	−	0.419549i
$271$	11003.8	−	19059.1i	0.149832	−	0.259516i	−0.781334	−	0.624114i	$-0.785460\pi$
$271$	11003.8	−	19059.1i	0.149832	−	0.259516i	0.931165	+	0.364598i	$0.118794\pi$
$272$	81012.0	+	21707.1i	1.09499	+	0.293403i
$273$	−39161.3	−	39161.3i	−0.525451	−	0.525451i
$274$			20937.9i			0.278890i
$275$	36426.2	−	56719.2i	0.481669	−	0.750006i
$276$	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
$280$	−72811.2	−	133294.i	−0.928714	−	1.70018i
$281$	−13239.7	−	22931.9i	−0.167674	−	0.290420i	0.769927	−	0.638131i	$-0.220292\pi$
$281$	−13239.7	−	22931.9i	−0.167674	−	0.290420i	−0.937602	+	0.347711i	$0.886959\pi$
$282$	73744.1	+	275217.i	0.927318	+	3.46080i
$283$	7099.71	−	1902.36i	0.0886478	−	0.0237531i	−0.214223	−	0.976785i	$-0.568722\pi$
$283$	7099.71	−	1902.36i	0.0886478	−	0.0237531i	0.302870	+	0.953032i	$0.402055\pi$
$284$		−	88248.7i		−	1.09414i
$285$	−60797.9	+	91187.9i	−0.748512	+	1.12266i
$286$	62736.5			0.766988
$287$	11649.2	+	43475.6i	0.141428	+	0.527815i
$288$	−1535.99	+	411.567i	−0.0185184	+	0.00496199i
$289$	−16979.2	+	9802.95i	−0.203293	+	0.117371i
$290$	2625.17	−	8945.66i	0.0312149	−	0.106369i
$291$	−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
$295$	−1800.72	+	76145.4i	−0.0206920	+	0.874983i
$296$	272272.			3.10756
$297$	13455.7	−	13455.7i	0.152544	−	0.152544i
$298$	16977.1	−	63359.4i	0.191175	−	0.713474i
$299$	−3753.40	−	2167.03i	−0.0419839	−	0.0242394i
$300$	−51874.4	−	238105.i	−0.576382	−	2.64562i
$301$	59586.8	−	103207.i	0.657684	−	1.13914i
$302$	8476.79	+	31635.8i	0.0929432	+	0.346869i
$303$	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
$307$	−36994.3	−	138064.i	−0.392516	−	1.46489i	−0.825970	−	0.563714i	$-0.809372\pi$
$307$	−36994.3	−	138064.i	−0.392516	−	1.46489i	0.433454	−	0.901176i	$-0.357295\pi$
$308$	48739.2	−	181897.i	0.513780	−	1.91745i
$309$	163595.	+	94451.8i	1.71338	+	0.989221i
$310$	−137970.	+	131595.i	−1.43569	+	1.36936i
$311$	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
$313$	−16933.0	+	63194.9i	−0.172841	+	0.645050i	0.824069	+	0.566490i	$0.191699\pi$
$313$	−16933.0	+	63194.9i	−0.172841	+	0.645050i	−0.996909	+	0.0785602i	$0.974968\pi$
$314$	51544.5	−	29759.2i	0.522785	−	0.301830i
$315$	−87817.2	+	21318.7i	−0.885031	+	0.214852i
$316$	−22618.1			−0.226508
$317$	−26867.8	−	7199.21i	−0.267371	−	0.0716417i	0.122643	−	0.992451i	$-0.460863\pi$
$317$	−26867.8	−	7199.21i	−0.267371	−	0.0716417i	−0.390014	+	0.920809i	$0.627530\pi$
$318$	−356819.	+	95609.5i	−3.52853	+	0.945468i
$319$	5021.94	−	2899.42i	0.0493503	−	0.0284924i
$320$	−88040.4	+	48091.5i	−0.859769	+	0.469643i
$321$	34306.4	−	59420.5i	0.332940	−	0.576669i
$322$	−13783.1	+	13783.1i	−0.132934	+	0.132934i
$323$	102679.	−	53820.8i	0.984182	−	0.515875i
$324$		−	241665.i		−	2.30209i
$325$	35269.8	+	38773.8i	0.333915	+	0.367089i
$326$	113692.	−	196921.i	1.06978	−	1.85292i
$327$	236583.	+	63392.2i	2.21252	+	0.592844i
$328$	−89317.5	+	23932.6i	−0.830212	+	0.222455i
$329$	−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	$0.396484\pi$
$332$	−157141.	−	42105.8i	−1.42565	−	0.382002i
$333$	41927.7	−	156476.i	0.378105	−	1.41111i
$334$		−	315237.i		−	2.82582i
$335$	−26754.7	−	110209.i	−0.238402	−	0.982039i
$336$	−86235.1	−	149364.i	−0.763845	−	1.32302i
$337$	−3396.08	−	12674.3i	−0.0299032	−	0.111600i	0.949361	−	0.314187i	$-0.101732\pi$
$337$	−3396.08	−	12674.3i	−0.0299032	−	0.111600i	−0.979264	+	0.202587i	$0.935065\pi$
$338$	38645.7	−	144228.i	0.338273	−	1.26245i
$339$	−93210.7	−	53815.2i	−0.811085	−	0.468280i
$340$	−72583.5	+	247339.i	−0.627885	+	2.13961i
$341$	−118593.			−1.01989
$342$	−89028.5	+	140623.i	−0.761161	+	1.20227i
$343$	70937.1	+	70937.1i	0.602956	+	0.602956i
$344$	212032.	+	122417.i	1.79178	+	1.03449i
$345$	−13769.2	+	7521.32i	−0.115683	+	0.0631911i
$346$	−46929.8	−	81284.8i	−0.392009	−	0.678980i
$347$	−22115.4	−	82535.8i	−0.183669	−	0.685462i	−0.994912	−	0.100752i	$-0.967875\pi$
$347$	−22115.4	−	82535.8i	−0.183669	−	0.685462i	0.811243	−	0.584710i	$-0.198792\pi$
$348$	5425.75	−	20249.2i	0.0448024	−	0.167205i
$349$			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
$352$	2492.25	+	667.796i	0.0201144	+	0.00538963i
$353$	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
$355$	68694.4	+	1624.52i	0.545086	+	0.0128905i
$356$	−202084.	+	350020.i	−1.59453	+	2.76180i
$357$	204844.	+	54887.9i	1.60727	+	0.430665i
$358$	233089.	−	62456.1i	1.81868	−	0.487314i
$359$	−75617.3	−	43657.6i	−0.586721	−	0.338744i	0.177079	−	0.984197i	$-0.443335\pi$
$359$	−75617.3	−	43657.6i	−0.586721	−	0.338744i	−0.763800	+	0.645453i	$0.776669\pi$
$360$	−43797.8	−	180414.i	−0.337946	−	1.39208i
$361$	−117798.	+	55743.2i	−0.903903	+	0.427737i
$362$	126425.	−	126425.i	0.964753	−	0.964753i
$363$	−35289.9	+	9455.91i	−0.267817	+	0.0717612i
$364$	126811.	+	73214.1i	0.957089	+	0.552576i
$365$	−3069.73	−	3218.44i	−0.0230417	−	0.0241579i
$366$	−284582.	+	492911.i	−2.12444	+	3.67965i
$367$	81920.5	+	21950.5i	0.608220	+	0.162972i	0.549767	−	0.835318i	$-0.314717\pi$
$367$	81920.5	+	21950.5i	0.608220	+	0.162972i	0.0584528	+	0.998290i	$0.481383\pi$
$368$	−9543.78	−	9543.78i	−0.0704733	−	0.0704733i
$369$			55016.6i			0.404055i
$370$	−9990.79	+	422470.i	−0.0729787	+	3.08598i
$371$	−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
$375$	186301.	−	35996.9i	1.32480	−	0.255978i
$376$	−188962.	−	327291.i	−1.33659	−	2.31504i
$377$	1167.02	+	4355.39i	0.00821101	+	0.0306439i
$378$	64280.1	−	17223.8i	0.449876	−	0.120544i
$379$		−	185328.i		−	1.29022i	−0.764092	−	0.645108i	$-0.776812\pi$
$379$		−	185328.i		−	1.29022i	0.764092	−	0.645108i	$-0.223188\pi$
$380$	92868.8	−	274485.i	0.643136	−	1.90086i
$381$	−186773.			−1.28666
$382$	33157.7	+	123746.i	0.227226	+	0.848017i
$383$	40600.1	−	10878.8i	0.276776	−	0.0741620i	−0.117761	−	0.993042i	$-0.537572\pi$
$383$	40600.1	−	10878.8i	0.276776	−	0.0741620i	0.394537	+	0.918880i	$0.370905\pi$
$384$	−296733.	+	171319.i	−2.01235	+	1.16183i
$385$	140695.	+	41288.0i	0.949199	+	0.278549i
$386$	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	$-0.536748\pi$
$389$	104030.	−	60061.5i	0.687476	−	0.396914i	0.802666	+	0.596429i	$0.203414\pi$
$390$	121884.	+	127789.i	0.801343	+	0.840162i
$391$	16595.9			0.108555
$392$	43939.3	−	43939.3i	0.285944	−	0.285944i
$393$	32425.0	−	121012.i	0.209940	−	0.783507i
$394$	364208.	+	210275.i	2.34615	+	1.35455i
$395$	416.364	−	17606.4i	0.00266857	−	0.112843i
$396$	115092.	−	199345.i	0.733929	−	1.27120i
$397$	−14742.3	−	55018.8i	−0.0935369	−	0.349084i	0.903257	−	0.429101i	$-0.141169\pi$
$397$	−14742.3	−	55018.8i	−0.0935369	−	0.349084i	−0.996794	+	0.0800163i	$0.974503\pi$
$398$	−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	0.259791	+	0.965665i	$0.416346\pi$
$401$	−113589.	+	196742.i	−0.706395	+	1.22351i	−0.966186	+	0.257847i	$0.916987\pi$
$402$	−98893.6	−	369076.i	−0.611951	−	2.28383i
$403$	23867.1	−	89073.1i	0.146957	−	0.548449i
$404$	−427362.	−	246737.i	−2.61838	−	1.51172i
$405$	188116.	+	4448.67i	1.14688	+	0.0271219i
$406$	20279.2			0.123027
$407$	−185863.	+	185863.i	−1.12203	+	1.12203i
$408$	−112763.	+	420838.i	−0.677404	+	2.52810i
$409$	69014.5	−	39845.5i	0.412566	−	0.238195i	−0.279326	−	0.960196i	$-0.590111\pi$
$409$	69014.5	−	39845.5i	0.412566	−	0.238195i	0.691892	+	0.722001i	$0.256778\pi$
$410$	−33857.4	−	139467.i	−0.201412	−	0.829669i
$411$	−36659.0			−0.217019
$412$	−482432.	−	129267.i	−2.84211	−	0.761542i
$413$	−160033.	+	42880.7i	−0.938230	+	0.251398i
$414$	−20634.1	+	11913.1i	−0.120388	+	0.0695063i
$415$	35668.7	−	121546.i	0.207105	−	0.705742i
$416$	−1003.14	+	1737.48i	−0.00579660	+	0.0100400i
$417$	−67684.1	+	67684.1i	−0.389237	+	0.389237i
$418$	239187.	−	125374.i	1.36894	−	0.717552i
$419$		−	30996.3i		−	0.176555i	−0.996096	−	0.0882777i	$-0.971864\pi$
$419$		−	30996.3i		−	0.176555i	0.996096	−	0.0882777i	$-0.0281363\pi$
$420$	465199.	−	254112.i	2.63718	−	1.44054i
$421$	41008.6	−	71029.0i	0.231372	−	0.400748i	−0.726840	−	0.686807i	$-0.759012\pi$
$421$	41008.6	−	71029.0i	0.231372	−	0.400748i	0.958212	+	0.286059i	$0.0923452\pi$
$422$	25820.2	+	6918.51i	0.144989	+	0.0388497i
$423$	−217194.	+	58197.0i	−1.21386	+	0.325252i
$424$	424334.	−	244989.i	2.36035	−	1.36275i
$425$	−191197.	−	61053.5i	−1.05853	−	0.338012i
$426$	231506.			1.27568
$427$	−354946.	−	95107.6i	−1.94673	−	0.521626i
$428$	−46952.0	+	175227.i	−0.256311	+	0.956564i
$429$			109842.i			0.596834i
$430$	−197728.	+	324507.i	−1.06938	+	1.75504i
$431$	−29969.1	−	51907.9i	−0.161331	−	0.279434i	0.774015	−	0.633167i	$-0.218245\pi$
$431$	−29969.1	−	51907.9i	−0.161331	−	0.279434i	−0.935346	+	0.353733i	$0.884912\pi$
$432$	11926.2	+	44509.2i	0.0639049	+	0.238496i
$433$	−65465.1	+	244319.i	−0.349168	+	1.30311i	0.538499	+	0.842626i	$0.318992\pi$
$433$	−65465.1	+	244319.i	−0.349168	+	1.30311i	−0.887667	+	0.460486i	$0.847675\pi$
$434$	−359172.	−	207368.i	−1.90688	−	1.10094i
$435$	15662.5	+	4596.26i	0.0827716	+	0.0242899i
$436$	−647578.			−3.40658
$437$	−18640.7	−	761.061i	−0.0976109	−	0.00398526i
$438$	−10595.8	−	10595.8i	−0.0552315	−	0.0552315i
$439$	−180185.	−	104030.i	−0.934950	−	0.539794i	−0.0465766	−	0.998915i	$-0.514831\pi$
$439$	−180185.	−	104030.i	−0.934950	−	0.539794i	−0.888374	+	0.459121i	$0.848164\pi$
$440$	−84823.2	+	289048.i	−0.438136	+	1.49302i
$441$	−18485.8	−	32018.4i	−0.0950521	−	0.164635i
$442$	−48346.7	−	180432.i	−0.247470	−	0.923570i
$443$	57162.4	−	213333.i	0.291275	−	1.08705i	−0.652856	−	0.757482i	$-0.726429\pi$
$443$	57162.4	−	213333.i	0.291275	−	1.08705i	0.944131	−	0.329571i	$-0.106904\pi$
$444$			950234.i			4.82019i
$445$	−268742.	−	163749.i	−1.35711	−	0.826911i
$446$	147645.	+	255729.i	0.742248	+	1.28561i
$447$	110932.	+	29724.2i	0.555192	+	0.148763i
$448$	−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	$-0.154313\pi$
$450$	281546.	−	61338.5i	1.39035	−	0.302906i
$451$	44634.1	−	77308.5i	0.219439	−	0.380079i
$452$	274872.	+	73651.8i	1.34541	+	0.360501i
$453$	−55389.4	+	14841.5i	−0.269917	+	0.0723240i
$454$	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	$0.00162663\pi$
$458$	−422219.	+	113133.i	−2.01283	+	0.539335i
$459$	−49068.5	−	28329.7i	−0.232904	−	0.134467i
$460$	30017.6	−	28630.6i	0.141860	−	0.135305i
$461$	56105.4	−	97177.4i	0.263999	−	0.457260i	−0.703302	−	0.710892i	$-0.748292\pi$
$461$	56105.4	−	97177.4i	0.263999	−	0.457260i	0.967301	+	0.253631i	$0.0816250\pi$
$462$	477178.	+	127859.i	2.23561	+	0.599030i
$463$	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
$465$	−230403.	−	241564.i	−1.06557	−	1.11719i
$466$	−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
$470$	514773.	−	281192.i	2.33035	−	1.27294i
$471$	52103.8	+	90246.4i	0.234870	+	0.406807i
$472$	−88095.4	−	328777.i	−0.395430	−	1.47576i
$473$	−228307.	+	61174.6i	−1.02046	+	0.273432i
$474$		−	59335.0i		−	0.264091i
$475$	211954.	+	77343.6i	0.939409	+	0.342797i
$476$	−560702.			−2.47468
$477$	−75452.6	−	281593.i	−0.331618	−	1.23761i
$478$	−384682.	+	103075.i	−1.68363	+	0.451126i
$479$	73282.9	−	42309.9i	0.319398	−	0.184404i	−0.331726	−	0.943376i	$-0.607631\pi$
$479$	73282.9	−	42309.9i	0.319398	−	0.184404i	0.651124	+	0.758971i	$0.274298\pi$
$480$	3481.69	+	6373.88i	0.0151115	+	0.0276644i
$481$	−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
$485$	−183204.	+	174740.i	−0.778848	+	0.742862i
$486$	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	$0.286096\pi$
$488$	195392.	−	729212.i	0.820477	−	3.06206i
$489$	344778.	+	199058.i	1.44186	+	0.832455i
$490$	66565.9	+	69790.5i	0.277242	+	0.290673i
$491$	−153673.	+	266169.i	−0.637432	+	1.10406i	0.348563	+	0.937285i	$0.386670\pi$
$491$	−153673.	+	266169.i	−0.637432	+	1.10406i	−0.985994	+	0.166778i	$0.946664\pi$
$492$	−83524.9	−	311719.i	−0.345053	−	1.28776i
$493$	−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
$497$	38684.8	+	144374.i	0.156613	+	0.584487i
$498$	110458.	−	412234.i	0.445387	−	1.66221i
$499$	−139092.	−	80304.9i	−0.558601	−	0.322508i	0.193983	−	0.981005i	$-0.437859\pi$
$499$	−139092.	−	80304.9i	−0.558601	−	0.322508i	−0.752584	+	0.658497i	$0.771193\pi$
$500$	−451151.	+	219417.i	−1.80461	+	0.877667i
$501$	551931.			2.19892
$502$	−189328.	+	189328.i	−0.751289	+	0.751289i
$503$	46228.0	−	172525.i	0.182713	−	0.681894i	−0.812396	−	0.583107i	$-0.801837\pi$
$503$	46228.0	−	172525.i	0.182713	−	0.681894i	0.995109	−	0.0987873i	$-0.0314963\pi$
$504$	349733.	−	201918.i	1.37681	−	0.794904i
$505$	199932.	−	328124.i	0.783970	−	1.28664i
$506$	38659.6			0.150993
$507$	252520.	+	67662.5i	0.982381	+	0.263228i
$508$	476990.	−	127809.i	1.84834	−	0.495261i
$509$	−400576.	+	231273.i	−1.54614	+	0.892666i	−0.547711	+	0.836668i	$0.684501\pi$
$509$	−400576.	+	231273.i	−1.54614	+	0.892666i	−0.998431	+	0.0559980i	$0.982166\pi$
$510$	−648854.	−	190411.i	−2.49463	−	0.732068i
$511$	4837.28	−	8378.42i	0.0185251	−	0.0320863i
$512$	325691.	−	325691.i	1.24241	−	1.24241i
$513$	53814.9	+	34070.3i	0.204488	+	0.129462i
$514$			264213.i			1.00006i
$515$	109505.	−	373154.i	0.412875	−	1.40693i
$516$	−427236.	+	739995.i	−1.60461	+	2.77926i
$517$	352412.	+	94428.6i	1.31847	+	0.353283i
$518$	−887896.	+	237911.i	−3.30904	+	0.886656i
$519$	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	$0.472452\pi$
$522$	23943.5	+	6415.64i	0.0878712	+	0.0235450i
$523$	−39587.7	+	147743.i	−0.144729	+	0.540137i	0.855038	+	0.518565i	$0.173534\pi$
$523$	−39587.7	+	147743.i	−0.144729	+	0.540137i	−0.999767	+	0.0215717i	$0.993133\pi$
$524$			331235.i			1.20635i
$525$	189242.	+	366797.i	0.686591	+	1.33078i
$526$	323454.	+	560239.i	1.16907	+	2.02489i
$527$	91391.7	+	341078.i	0.329068	+	1.22810i
$528$	−88533.1	+	330410.i	−0.317569	+	1.18518i
$529$	240036.	+	138585.i	0.857760	+	0.495228i
$530$	364566.	+	667406.i	1.29785	+	2.37595i
$531$	−202515.			−0.718239
$532$	629784.	+	25712.8i	2.22520	+	0.0908504i
$533$	49082.2	+	49082.2i	0.172771	+	0.172771i
$534$	−918219.	−	530134.i	−3.22006	−	1.85910i
$535$	−135536.	−	39773.9i	−0.473529	−	0.138960i
$536$	253405.	+	438910.i	0.882034	+	1.52773i
$537$	109351.	+	408103.i	0.379205	+	1.41521i
$538$	80878.8	−	301844.i	0.279428	−	1.04284i
$539$			59989.1i			0.206488i
$540$	−137625.	+	33410.1i	−0.471965	+	0.114575i
$541$	−25095.2	−	43466.1i	−0.0857424	−	0.148510i	0.819965	−	0.572414i	$-0.193993\pi$
$541$	−25095.2	−	43466.1i	−0.0857424	−	0.148510i	−0.905707	+	0.423904i	$0.860660\pi$
$542$	−147442.	−	39507.0i	−0.501907	−	0.134486i
$543$	221351.	+	221351.i	0.750726	+	0.750726i
$544$		−	7682.41i		−	0.0259597i
$545$	11920.9	−	504086.i	0.0401343	−	1.69712i
$546$	−192065.	+	332667.i	−0.644263	+	1.11590i
$547$	42218.5	+	11312.4i	0.141100	+	0.0378077i	0.328678	−	0.944442i	$-0.393397\pi$
$547$	42218.5	+	11312.4i	0.141100	+	0.0378077i	−0.187578	+	0.982250i	$0.560064\pi$
$548$	93621.7	−	25085.9i	0.311757	−	0.0835349i
$549$	−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
$553$	37002.9	−	9914.90i	0.121000	−	0.0324219i
$554$	473860.	+	273583.i	1.54394	+	0.891395i
$555$	−739679.	−	17492.3i	−2.40136	−	0.0567886i
$556$	126539.	−	219172.i	0.409330	−	0.708981i
$557$	85262.2	+	22845.9i	0.274819	+	0.0736374i	0.393596	−	0.919283i	$-0.371231\pi$
$557$	85262.2	+	22845.9i	0.274819	+	0.0736374i	−0.118777	+	0.992921i	$0.537898\pi$
$558$	−358466.	−	358466.i	−1.15128	−	1.15128i
$559$		−	183788.i		−	0.588158i
$560$	−256930.	+	245059.i	−0.819293	+	0.781438i
$561$	−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
$565$	−62391.9	+	212610.i	−0.195448	+	0.666018i
$566$	−25490.2	−	44150.3i	−0.0795683	−	0.137816i
$567$	105936.	+	395359.i	0.329518	+	1.22978i
$568$	−296605.	+	79475.1i	−0.919353	+	0.246340i
$569$		−	287624.i		−	0.888384i	−0.895932	−	0.444192i	$-0.853491\pi$
$569$		−	287624.i		−	0.888384i	0.895932	−	0.444192i	$-0.146509\pi$
$570$	720065.	+	243626.i	2.21627	+	0.749850i
$571$	344049.			1.05523			0.527616	−	0.849483i	$-0.323086\pi$
$571$	344049.			1.05523			0.527616	+	0.849483i	$0.323086\pi$
$572$	−75165.1	−	280520.i	−0.229733	−	0.857377i
$573$	−216660.	+	58053.9i	−0.659887	+	0.176816i
$574$	270357.	−	156091.i	0.820568	−	0.473755i
$575$	21734.0	+	23893.3i	0.0657362	+	0.0722670i
$576$	−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
$580$	−43144.8	−	1020.31i	−0.128255	−	0.00303303i
$581$	275538.			0.816261
$582$	−603151.	+	603151.i	−1.78066	+	1.78066i
$583$	−122427.	+	456904.i	−0.360197	+	1.34427i
$584$	17212.9	+	9937.85i	0.0504693	+	0.0291385i
$585$	−100848.	+	96188.0i	−0.294682	+	0.281067i
$586$	345721.	−	598805.i	1.00677	−	1.74378i
$587$	−141634.	−	528585.i	−0.411047	−	1.53405i	−0.792624	−	0.609711i	$-0.791285\pi$
$587$	−141634.	−	528585.i	−0.411047	−	1.53405i	0.381577	−	0.924337i	$-0.375381\pi$
$588$	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
$592$	−164736.	−	614802.i	−0.470050	−	1.75425i
$593$	158934.	−	593150.i	0.451968	−	1.68677i	−0.244885	−	0.969552i	$-0.578750\pi$
$593$	158934.	−	593150.i	0.451968	−	1.68677i	0.696853	−	0.717214i	$-0.254583\pi$
$594$	−114303.	−	65993.0i	−0.323956	−	0.187036i
$595$	10321.6	−	436461.i	0.0291551	−	1.23285i
$596$	−303645.			−0.854818
$597$	48872.1	−	48872.1i	0.137124	−	0.137124i
$598$	−7780.30	+	29036.5i	−0.0217567	+	0.0811973i
$599$	−260375.	+	150328.i	−0.725681	+	0.418972i	−0.816840	−	0.576864i	$-0.804276\pi$
$599$	−260375.	+	150328.i	−0.725681	+	0.418972i	0.0911592	+	0.995836i	$0.470943\pi$
$600$	−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	$0.376102\pi$
$602$	−798417.	−	213935.i	−2.20311	−	0.590322i
$603$	291266.	−	78044.4i	0.801041	−	0.214638i
$604$	131300.	−	75806.2i	0.359908	−	0.207793i
$605$	36056.1	+	66007.3i	0.0985072	+	0.180336i
$606$	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	$0.996056\pi$
$608$	−352.302	+	8628.94i	−0.000953034	+	0.0233426i
$609$			35505.8i			0.0957336i
$610$	1.12431e6	+	329937.i	3.02152	+	0.886688i
$611$	−141847.	+	245686.i	−0.379959	+	0.658109i
$612$	−662015.	−	177387.i	−1.76752	−	0.473607i
$613$	50561.7	−	13548.0i	0.134555	−	0.0360540i	−0.190913	−	0.981607i	$-0.561145\pi$
$613$	50561.7	−	13548.0i	0.134555	−	0.0360540i	0.325468	+	0.945553i	$0.394478\pi$
$614$	−858568.	+	495695.i	−2.27739	+	1.31485i
$615$	244186.	−	59279.1i	0.645609	−	0.156730i
$616$	−655253.			−1.72682
$617$	−250831.	−	67210.0i	−0.658887	−	0.176548i	−0.0861434	−	0.996283i	$-0.527454\pi$
$617$	−250831.	−	67210.0i	−0.658887	−	0.176548i	−0.572744	+	0.819734i	$0.694121\pi$
$618$	339111.	−	1.26558e6i	0.887903	−	3.31370i
$619$			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
$622$	−125734.	−	469246.i	−0.324992	−	1.21289i
$623$	177171.	−	661212.i	0.456475	−	1.70359i
$624$	−230347.	−	132991.i	−0.591579	−	0.341549i
$625$	−162493.	−	355224.i	−0.415982	−	0.909373i
$626$	453779.			1.15797
$627$	219510.	+	418778.i	0.558365	+	1.06524i
$628$	−194821.	−	194821.i	−0.493989	−	0.493989i
$629$	677779.	+	391316.i	1.71312	+	0.989068i
$630$	300473.	+	550071.i	0.757049	+	1.38592i
$631$	281837.	+	488156.i	0.707847	+	1.22603i	0.965654	+	0.259831i	$0.0836668\pi$
$631$	281837.	+	488156.i	0.707847	+	1.22603i	−0.257807	+	0.966196i	$0.583000\pi$
$632$	20369.5	+	76019.9i	0.0509971	+	0.190324i
$633$	−12113.2	+	45207.2i	−0.0302310	+	0.112824i
$634$			192928.i			0.479972i
$635$	90708.4	+	373651.i	0.224957	+	0.926656i
$636$	855016.	+	1.48093e6i	2.11378	+	3.66117i
$637$	−45056.6	−	12072.9i	−0.111040	−	0.0297531i
$638$	−28440.2	−	28440.2i	−0.0698700	−	0.0698700i
$639$			182699.i			0.447439i
$640$	486845.	+	510429.i	1.18859	+	1.24617i
$641$	−297563.	+	515394.i	−0.724207	+	1.25436i	0.235092	+	0.971973i	$0.424461\pi$
$641$	−297563.	+	515394.i	−0.724207	+	1.25436i	−0.959300	+	0.282391i	$0.908873\pi$
$642$	−459680.	−	123171.i	−1.11528	−	0.298839i
$643$	−138111.	+	37006.7i	−0.334046	+	0.0895073i	−0.421943	−	0.906622i	$-0.638652\pi$
$643$	−138111.	+	37006.7i	−0.334046	+	0.0895073i	0.0878974	+	0.996130i	$0.471985\pi$
$644$	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	$0.152274\pi$
$648$	−812238.	+	217639.i	−1.93434	+	0.518306i
$649$	284572.	+	164298.i	0.675620	+	0.390069i
$650$	196455.	−	305899.i	0.464982	−	0.724022i
$651$	363069.	−	628853.i	0.856696	−	1.48384i
$652$	−1.01673e6	−	272431.i	−2.39171	−	0.640858i
$653$	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
$655$	−257839.	−	6097.51i	−0.600989	−	0.0142125i
$656$	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	$-0.517523\pi$
$659$	339686.	−	196118.i	0.782180	−	0.451592i	0.837202	+	0.546893i	$0.184190\pi$
$660$	−1.00878e6	−	296034.i	−2.31584	−	0.679600i
$661$	64613.0	+	111913.i	0.147883	+	0.256140i	0.930445	−	0.366432i	$-0.119421\pi$
$661$	64613.0	+	111913.i	0.147883	+	0.256140i	−0.782562	+	0.622573i	$0.786088\pi$
$662$	−125679.	−	469042.i	−0.286779	−	1.07027i
$663$	315909.	−	84647.5i	0.718678	−	0.192569i
$664$			566073.i			1.28392i
$665$	−31608.7	+	489762.i	−0.0714765	+	1.10750i
$666$	−1.12360e6			−2.53316
$667$	719.146	+	2683.89i	0.00161646	+	0.00603271i
$668$	−1.40955e6	+	377688.i	−3.15884	+	0.846409i
$669$	−447741.	+	258503.i	−1.00040	+	0.577582i
$670$	−690331.	+	377089.i	−1.53783	+	0.840029i
$671$	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
$675$	−23473.6	−	107745.i	−0.0515196	−	0.236477i
$676$	−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	$0.349492\pi$
$678$	−193213.	+	721082.i	−0.420318	+	1.56865i
$679$	−476928.	−	275355.i	−1.03446	−	0.597245i
$680$	896678.	+	21205.1i	1.93918	+	0.0458588i
$681$	−427188.	+	739911.i	−0.921138	+	1.59546i
$682$	212894.	+	794530.i	0.457714	+	1.70821i
$683$	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
$687$	−198079.	−	739239.i	−0.419685	−	1.56629i
$688$	148134.	−	552844.i	0.312952	−	1.16795i
$689$	−318533.	−	183905.i	−0.670989	−	0.387396i
$690$	75107.8	+	78746.2i	0.157756	+	0.165398i
$691$	−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
$693$	−100903.	+	376577.i	−0.210107	+	0.784128i
$694$	−513257.	+	296329.i	−1.06565	+	0.615255i
$695$	168278.	+	102535.i	0.348383	+	0.212276i
$696$	−72944.2			−0.150582
$697$	−256738.	−	68792.8i	−0.528476	−	0.141605i
$698$	878981.	−	235522.i	1.80413	−	0.483416i
$699$	241380.	−	139361.i	0.494023	−	0.285224i
$700$	−734296.	−	807247.i	−1.49856	−	1.64744i
$701$	−135461.	+	234625.i	−0.275663	+	0.477462i	−0.970302	−	0.241896i	$-0.922231\pi$
$701$	−135461.	+	234625.i	−0.275663	+	0.477462i	0.694639	+	0.719358i	$0.255564\pi$
$702$	72569.7	−	72569.7i	0.147259	−	0.147259i
$703$	−743341.	−	470610.i	−1.50410	−	0.952250i
$704$			432792.i			0.873240i
$705$	492323.	+	901288.i	0.990539	+	1.81337i
$706$	761857.	−	1.31958e6i	1.52850	−	2.64743i
$707$	807317.	+	216320.i	1.61512	+	0.432771i
$708$	1.14743e6	−	307454.i	2.28908	−	0.613357i
$709$	−98316.5	+	56763.1i	−0.195584	+	0.112921i	−0.594594	−	0.804026i	$-0.702687\pi$
$709$	−98316.5	+	56763.1i	−0.195584	+	0.112921i	0.399010	+	0.916947i	$0.369354\pi$
$710$	−112434.	−	463142.i	−0.223038	−	0.918751i
$711$	46825.7			0.0926286
$712$	1.35841e6	+	363986.i	2.67961	+	0.718000i
$713$	14707.4	−	54888.8i	0.0289306	−	0.107970i
$714$		−	1.47091e6i		−	2.88529i
$715$	219746.	−	53346.0i	0.429841	−	0.104349i
$716$	−558532.	−	967406.i	−1.08949	−	1.88705i
$717$	−180468.	−	673517.i	−0.351045	−	1.31012i
$718$	−156745.	+	584979.i	−0.304049	+	1.13473i
$719$	499830.	+	288577.i	0.966862	+	0.558218i	0.898278	−	0.439428i	$-0.144819\pi$
$719$	499830.	+	288577.i	0.966862	+	0.558218i	0.0685836	+	0.997645i	$0.478152\pi$
$720$	−380883.	+	208055.i	−0.734728	+	0.401340i
$721$	845916.			1.62726
$722$	584923.	+	689131.i	1.12208	+	1.32199i
$723$	524366.	+	524366.i	1.00313	+	1.00313i
$724$	−716768.	−	413826.i	−1.36742	−	0.789479i
$725$	1588.46	−	33566.0i	0.00302204	−	0.0638591i
$726$	126702.	+	219454.i	0.240386	+	0.416361i
$727$	172172.	+	642556.i	0.325758	+	1.21574i	0.913548	+	0.406731i	$0.133331\pi$
$727$	172172.	+	642556.i	0.325758	+	1.21574i	−0.587790	+	0.809013i	$0.700002\pi$
$728$	131870.	−	492147.i	0.248820	−	0.928608i
$729$			326762.i			0.614860i
$730$	−16051.6	+	26343.6i	−0.0301213	+	0.0494344i
$731$	351880.	+	609475.i	0.658507	+	1.14057i
$732$	2.54496e6	+	681920.i	4.74962	+	1.27266i
$733$	−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
$735$	−122192.	+	116546.i	−0.226188	+	0.215737i
$736$	−618.155	+	1070.68i	−0.00114115	+	0.00197653i
$737$	−472599.	−	126632.i	−0.870077	−	0.233136i
$738$	368590.	−	98763.4i	0.676754	−	0.181336i
$739$	−230112.	−	132855.i	−0.421357	−	0.243270i	0.274301	−	0.961644i	$-0.411554\pi$
$739$	−230112.	−	132855.i	−0.421357	−	0.243270i	−0.695658	+	0.718374i	$0.744887\pi$
$740$	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
$743$	101109.	−	27091.9i	0.183151	−	0.0490753i	−0.166078	−	0.986113i	$-0.553110\pi$
$743$	101109.	−	27091.9i	0.183151	−	0.0490753i	0.349229	+	0.937037i	$0.386444\pi$
$744$	1.29194e6	+	745899.i	2.33397	+	1.34752i
$745$	5589.63	−	236363.i	0.0100710	−	0.425860i
$746$	347038.	−	601087.i	0.623590	−	1.08009i
$747$	325325.	+	87170.5i	0.583010	+	0.156217i
$748$	786344.	+	786344.i	1.40543	+	1.40543i
$749$		−	307251.i		−	0.547683i
$750$	−575604.	−	1.18352e6i	−1.02330	−	2.10404i
$751$	−488835.	−	846687.i	−0.866727	−	1.50121i	−0.865322	−	0.501216i	$-0.832886\pi$
$751$	−488835.	−	846687.i	−0.866727	−	1.50121i	−0.00140432	−	0.999999i	$-0.500447\pi$
$752$	−624706.	+	624706.i	−1.10469	+	1.10469i
$753$	−331484.	−	331484.i	−0.584618	−	0.584618i
$754$	27084.4	−	15637.2i	0.0476406	−	0.0275053i
$755$	56591.9	+	103602.i	0.0992797	+	0.181750i
$756$	−154029.	−	266786.i	−0.269500	−	0.466787i
$757$	169820.	+	633775.i	0.296344	+	1.10597i	0.940144	+	0.340777i	$0.110690\pi$
$757$	169820.	+	633775.i	0.296344	+	1.10597i	−0.643800	+	0.765194i	$0.722643\pi$
$758$	−1.24163e6	+	332692.i	−2.16099	+	0.579035i
$759$			67687.0i			0.117496i
$760$	−1.00618e6	−	64937.8i	−1.74201	−	0.112427i
$761$	−146475.			−0.252927			−0.126463	−	0.991971i	$-0.540363\pi$
$761$	−146475.			−0.252927			−0.126463	+	0.991971i	$0.540363\pi$
$762$	335286.	+	1.25131e6i	0.577439	+	2.15503i
$763$	1.05943e6	−	283873.i	1.81979	−	0.487612i
$764$	513591.	−	296522.i	0.879895	−	0.508008i
$765$	150268.	−	512060.i	0.256769	−	0.874979i
$766$	−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	$-0.573752\pi$
$769$	294756.	−	170177.i	0.498437	−	0.287773i	0.728068	+	0.685505i	$0.240419\pi$
$770$	24043.9	−	1.01672e6i	0.0405531	−	1.71483i
$771$	−462596.			−0.778203
$772$	1.06201e6	−	1.06201e6i	1.78194	−	1.78194i
$773$	−298073.	+	1.11242e6i	−0.498843	+	1.86171i	0.00849974	+	0.999964i	$0.497294\pi$
$773$	−298073.	+	1.11242e6i	−0.498843	+	1.86171i	−0.507343	+	0.861744i	$0.669372\pi$
$774$	−875001.	−	505182.i	−1.46059	−	0.843269i
$775$	−371366.	+	578254.i	−0.618300	+	0.962753i
$776$	565697.	−	979816.i	0.939421	−	1.62712i
$777$	−416545.	−	1.55457e6i	−0.689954	−	2.57494i
$778$	−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
$782$	−29792.3	−	111186.i	−0.0487181	−	0.181818i
$783$	2455.20	−	9162.93i	0.00400464	−	0.0149455i
$784$	−125802.	−	72631.6i	−0.204670	−	0.118166i
$785$	155239.	−	148066.i	0.251919	−	0.240279i
$786$	−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	$0.339850\pi$
$788$	503865.	−	1.88045e6i	0.811450	−	3.02837i
$789$	−980891.	+	566318.i	−1.57568	+	0.909717i
$790$	−118703.	+	28816.7i	−0.190199	+	0.0461732i
$791$	−481973.			−0.770317
$792$	−773651.	−	207299.i	−1.23337	−	0.330481i
$793$	−547394.	+	146674.i	−0.870470	+	0.233242i
$794$	−342140.	+	197535.i	−0.542704	+	0.313331i
$795$	−1.16852e6	+	638298.i	−1.84886	+	1.00993i
$796$	−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	$0.0347400\pi$
$798$	−67453.5	+	1.65214e6i	−0.105925	+	2.59442i
$799$		−	1.08632e6i		−	1.70162i
$800$	11060.4	−	10060.9i	0.0172819	−	0.0157201i
$801$	418369.	−	724636.i	0.652070	−	1.12942i
$802$	1.52201e6	+	407820.i	2.36629	+	0.634045i
$803$	−18534.0	+	4966.18i	−0.0287435	+	0.00770179i
$804$	−1.53180e6	+	884385.i	−2.36968	+	1.36814i
$805$	−36557.7	+	59997.8i	−0.0564141	+	0.0925856i
$806$	−639601.			−0.984552
$807$	528481.	+	141606.i	0.811489	+	0.217438i
$808$	−444414.	+	1.65858e6i	−0.680715	+	2.54046i
$809$		−	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	−0.996576	−	0.0826769i	$-0.973653\pi$
$811$	−374828.	−	649221.i	−0.569889	−	0.987076i	0.426688	−	0.904399i	$-0.359680\pi$
$812$	−24296.7	−	90676.5i	−0.0368498	−	0.137525i
$813$	69170.6	−	258148.i	0.104650	−	0.390560i
$814$	1.57886e6	+	911557.i	2.38284	+	1.37574i
$815$	230782.	−	786424.i	0.347445	−	1.18397i
$816$	1.01850e6			1.52960
$817$	−367285.	−	700703.i	−0.550249	−	1.04976i
$818$	−390841.	−	390841.i	−0.584109	−	0.584109i
$819$	−262532.	−	151573.i	−0.391395	−	0.225972i
$820$	−583049.	+	318487.i	−0.867116	+	0.473657i
$821$	−364575.	−	631463.i	−0.540880	−	0.936831i	−0.998854	−	0.0478657i	$-0.984758\pi$
$821$	−364575.	−	631463.i	−0.540880	−	0.936831i	0.457974	−	0.888966i	$-0.348575\pi$
$822$	65808.7	+	245601.i	0.0973956	+	0.363485i
$823$	220092.	−	821395.i	0.324941	−	1.21270i	−0.589430	−	0.807819i	$-0.700648\pi$
$823$	220092.	−	821395.i	0.324941	−	1.21270i	0.914371	−	0.404877i	$-0.132686\pi$
$824$			1.73788e6i			2.55955i
$825$	249008.	−	779804.i	0.365852	−	1.14572i
$826$	574569.	+	995182.i	0.842135	+	1.45862i
$827$	82048.7	+	21984.9i	0.119967	+	0.0321450i	0.318303	−	0.947989i	$-0.396887\pi$
$827$	82048.7	+	21984.9i	0.119967	+	0.0321450i	−0.198336	+	0.980134i	$0.563554\pi$
$828$	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	$-0.0528534\pi$
$830$	−878345.	−	20771.5i	−1.27500	−	0.0301517i
$831$	−479002.	+	829656.i	−0.693642	+	1.20142i
$832$	−325061.	−	87099.9i	−0.469590	−	0.125826i
$833$	172530.	−	46229.4i	0.248643	−	0.0666236i
$834$	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
$838$	−207663.	+	55643.1i	−0.295713	+	0.0792362i
$839$	−272858.	−	157534.i	−0.387625	−	0.223796i	0.293505	−	0.955957i	$-0.405178\pi$
$839$	−272858.	−	157534.i	−0.387625	−	0.223796i	−0.681131	+	0.732162i	$0.738511\pi$
$840$	−1.27302e6	−	1.33469e6i	−1.80417	−	1.89157i
$841$	−352195.	+	610020.i	−0.497956	+	0.862486i
$842$	−549484.	−	147234.i	−0.775052	−	0.207674i
$843$	−227377.	−	227377.i	−0.319958	−	0.319958i
$844$		−	123742.i		−	0.173712i
$845$	12723.9	−	538043.i	0.0178200	−	0.753535i
$846$	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
$850$	−65805.6	+	1.39055e6i	−0.0910804	+	1.92464i
$851$	−62973.4	−	109073.i	−0.0869557	−	0.150612i
$852$	−277369.	−	1.03516e6i	−0.382102	−	1.42602i
$853$	−161722.	+	43333.3i	−0.222265	+	0.0595558i	−0.368233	−	0.929734i	$-0.620037\pi$
$853$	−161722.	+	43333.3i	−0.222265	+	0.0595558i	0.145968	+	0.989289i	$0.453370\pi$
$854$			2.54874e6i			3.49469i
$855$	−192264.	+	568258.i	−0.263006	+	0.777344i
$856$	631225.			0.861463
$857$	61502.7	+	229531.i	0.0837400	+	0.312522i	0.995073	−	0.0991489i	$-0.0316120\pi$
$857$	61502.7	+	229531.i	0.0837400	+	0.312522i	−0.911333	+	0.411671i	$0.864945\pi$
$858$	735898.	−	197183.i	0.999639	−	0.267852i
$859$	149542.	−	86338.3i	0.202664	−	0.117008i	−0.395233	−	0.918581i	$-0.629336\pi$
$859$	149542.	−	86338.3i	0.202664	−	0.117008i	0.597898	+	0.801572i	$0.296003\pi$
$860$	1.68790e6	+	495326.i	2.28218	+	0.669721i
$861$	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
$865$	−233498.	−	244809.i	−0.312069	−	0.327186i
$866$	1.75436e6			2.33929
$867$	−168355.	+	168355.i	−0.223969	+	0.223969i
$868$	−496898.	+	1.85445e6i	−0.659519	+	2.46136i
$869$	−65798.8	−	37989.0i	−0.0871322	−	0.0503058i
$870$	2676.62	−	113183.i	0.00353629	−	0.149536i
$871$	190222.	−	329474.i	0.250741	−	0.434295i
$872$	583196.	+	2.17652e6i	0.766976	+	2.86239i
$873$	−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
$877$	11770.2	+	43927.0i	0.0153033	+	0.0571127i	0.973155	−	0.230150i	$-0.0739215\pi$
$877$	11770.2	+	43927.0i	0.0153033	+	0.0571127i	−0.957852	+	0.287262i	$0.907255\pi$
$878$	−373499.	+	1.39392e6i	−0.484507	+	1.80821i
$879$	1.04841e6	+	605303.i	1.35692	+	0.783420i
$880$	704003.	+	16648.6i	0.909095	+	0.0214987i
$881$	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
$883$	−135719.	+	506511.i	−0.174069	+	0.649633i	0.822640	+	0.568563i	$0.192500\pi$
$883$	−135719.	+	506511.i	−0.174069	+	0.649633i	−0.996708	+	0.0810699i	$0.974166\pi$
$884$	−748860.	+	432354.i	−0.958288	+	0.553268i
$885$	218205.	+	898844.i	0.278599	+	1.14762i
$886$	−1.53187e6			−1.95143
$887$	−225689.	−	60473.3i	−0.286856	−	0.0768628i	0.112522	−	0.993649i	$-0.464107\pi$
$887$	−225689.	−	60473.3i	−0.286856	−	0.0768628i	−0.399378	+	0.916786i	$0.630774\pi$
$888$	3.19375e6	−	855763.i	4.05019	−	1.08524i
$889$	−724322.	+	418188.i	−0.916491	+	0.529136i
$890$	−614623.	+	2.09442e6i	−0.775941	+	2.64414i
$891$	405895.	−	703031.i	0.511279	−	0.885562i
$892$	966569.	−	966569.i	1.21480	−	1.21480i
$893$	−49816.7	+	1.22016e6i	−0.0624701	+	1.53008i
$894$		−	796564.i		−	0.996656i
$895$	763329.	−	416963.i	0.952940	−	0.520537i
$896$	−767170.	+	1.32878e6i	−0.955599	+	1.65515i
$897$	−50838.3	−	13622.1i	−0.0631839	−	0.0169301i
$898$	−1.25886e6	+	337311.i	−1.56108	+	0.418291i
$899$	−51198.8	+	29559.7i	−0.0633491	+	0.0365746i
$900$	−611591.	−	1.18541e6i	−0.755051	−	1.46347i
$901$	1.40842e6			1.73493
$902$	−598063.	−	160250.i	−0.735078	−	0.196964i
$903$	374567.	−	1.39790e6i	0.459361	−	1.71436i
$904$		−	990179.i		−	1.21165i
$905$	335324.	−	550327.i	0.409419	−	0.671930i
$906$	198865.	+	344445.i	0.242272	+	0.419627i
$907$	−94209.0	−	351593.i	−0.114519	−	0.427391i	0.884731	−	0.466101i	$-0.154342\pi$
$907$	−94209.0	−	351593.i	−0.114519	−	0.427391i	−0.999250	+	0.0387103i	$0.987675\pi$
$908$	584652.	−	2.18195e6i	0.709129	−	2.64651i
$909$	884755.	+	510814.i	1.07077	+	0.618208i
$910$	758799.	+	222675.i	0.916314	+	0.268899i
$911$	−524864.			−0.632426			−0.316213	−	0.948688i	$-0.602411\pi$
$911$	−524864.			−0.632426			−0.316213	+	0.948688i	$0.602411\pi$
$912$	−1.14398e6	−	46706.5i	−1.37540	−	0.0561549i
$913$	−386422.	−	386422.i	−0.463575	−	0.463575i
$914$	−1.76504e6	−	1.01904e6i	−2.11281	−	1.21983i
$915$	−577667.	+	1.96849e6i	−0.689979	+	2.35121i
$916$	1.01173e6	+	1.75236e6i	1.20579	+	2.08849i
$917$	−145200.	−	541895.i	−0.172675	−	0.644431i
$918$	−101712.	+	379596.i	−0.120695	+	0.450439i
$919$		−	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
$922$	−751769.	−	201436.i	−0.884347	−	0.236960i
$923$	162992.	+	162992.i	0.191321	+	0.191321i
$924$		−	2.28684e6i		−	2.67850i
$925$	324239.	+	1.48827e6i	0.378950	+	1.73940i
$926$	759996.	−	1.31635e6i	0.886317	−	1.53515i
$927$	998765.	+	267618.i	1.16226	+	0.311427i
$928$	1242.40	−	332.899i	0.00144266	−	0.000386560i
$929$	1.05806e6	+	610870.i	1.22597	+	0.707811i	0.966183	−	0.257856i	$-0.0830160\pi$
$929$	1.05806e6	+	610870.i	1.22597	+	0.707811i	0.259782	+	0.965667i	$0.416349\pi$
$930$	−1.20478e6	+	1.97726e6i	−1.39297	+	2.28611i
$931$	−195907.	+	44013.2i	−0.226022	+	0.0507789i
$932$	−521084.	+	521084.i	−0.599896	+	0.599896i
$933$	821577.	−	220141.i	0.943811	−	0.252893i
$934$	767703.	+	443233.i	0.880034	+	0.508088i
$935$	−626580.	+	597629.i	−0.716726	+	0.683610i
$936$	311396.	−	539354.i	0.355436	−	0.615634i
$937$	−1.26685e6	−	339450.i	−1.44293	−	0.386631i	−0.549369	−	0.835580i	$-0.685132\pi$
$937$	−1.26685e6	−	339450.i	−1.44293	−	0.386631i	−0.893558	+	0.448949i	$0.851799\pi$
$938$	−1.20989e6	−	1.20989e6i	−1.37511	−	1.37511i
$939$			794496.i			0.901074i
$940$	−1.87407e6	−	1.96486e6i	−2.12095	−	2.22370i
$941$	−343799.	−	595478.i	−0.388263	−	0.672491i	0.603953	−	0.797020i	$-0.293591\pi$
$941$	−343799.	−	595478.i	−0.388263	−	0.672491i	−0.992216	+	0.124529i	$0.960258\pi$
$942$	511082.	−	511082.i	0.575955	−	0.575955i
$943$	30245.6	+	30245.6i	0.0340125	+	0.0340125i
$944$	−689089.	+	397846.i	−0.773270	+	0.446448i
$945$	210506.	−	114988.i	0.235723	−	0.128762i
$946$	819693.	+	1.41975e6i	0.915944	+	1.58646i
$947$	49387.7	+	184317.i	0.0550705	+	0.205526i	0.987979	−	0.154587i	$-0.0494048\pi$
$947$	49387.7	+	184317.i	0.0550705	+	0.205526i	−0.932909	+	0.360113i	$0.882738\pi$
$948$	−265310.	+	71089.7i	−0.295214	+	0.0791024i
$949$		−	14920.0i		−	0.0165667i
$950$	137681.	−	1.55886e6i	0.152556	−	1.72726i
$951$	−337786.			−0.373492
$952$	504958.	+	1.88453e6i	0.557162	+	2.07936i
$953$	−663151.	+	177691.i	−0.730174	+	0.195650i	−0.604707	−	0.796448i	$-0.706710\pi$
$953$	−663151.	+	177691.i	−0.730174	+	0.195650i	−0.125467	+	0.992098i	$0.540043\pi$
$954$	−1.75112e6	+	1.01101e6i	−1.92406	+	1.11085i
$955$	221364.	+	405248.i	0.242717	+	0.444338i
$956$	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
$960$	−881558.	+	840826.i	−0.956552	+	0.912355i
$961$	285542.			0.309188
$962$	−1.00240e6	+	1.00240e6i	−1.08316	+	1.08316i
$963$	97203.4	−	362768.i	0.104816	−	0.391180i
$964$	−1.69798e6	−	980328.i	−1.82716	−	1.05491i
$965$	807135.	+	846235.i	0.866746	+	0.908733i
$966$	−118355.	+	204997.i	−0.126833	+	0.219681i
$967$	234084.	+	873614.i	0.250333	+	0.934257i	0.970627	+	0.240588i	$0.0773403\pi$
$967$	234084.	+	873614.i	0.250333	+	0.934257i	−0.720294	+	0.693669i	$0.755993\pi$
$968$	−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	−0.906492	−	0.422222i	$-0.861250\pi$
$971$	−82584.5	+	143041.i	−0.0875911	+	0.151712i	0.818901	+	0.573934i	$0.194584\pi$
$972$	−640800.	−	2.39150e6i	−0.678251	−	2.53127i
$973$	−110939.	+	414031.i	−0.117182	+	0.437328i
$974$	322404.	+	186140.i	0.339846	+	0.196210i
$975$	535582.	+	343962.i	0.563400	+	0.361827i
$976$	−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	$0.357595\pi$
$978$	714679.	−	2.66722e6i	0.747194	−	2.78857i
$979$	−1.17577e6	+	678832.i	−1.22675	+	0.708267i
$980$	232308.	−	381259.i	0.241887	−	0.396979i
$981$	1.34066e6			1.39310
$982$	2.05909e6	+	551733.i	2.13527	+	0.572145i
$983$	−217372.	+	58244.6i	−0.224955	+	0.0602766i	−0.369536	−	0.929216i	$-0.620483\pi$
$983$	−217372.	+	58244.6i	−0.224955	+	0.0602766i	0.144581	+	0.989493i	$0.453817\pi$
$984$	−972472.	+	561457.i	−1.00435	+	0.579864i
$985$	1.45450e6	+	426834.i	1.49914	+	0.439933i
$986$	−59877.9	+	103712.i	−0.0615904	+	0.106678i
$987$	−1.57961e6	+	1.57961e6i	−1.62150	+	1.62150i
$988$	860951.	−	451282.i	0.881992	−	0.462311i
$989$		−	113254.i		−	0.115788i
$990$	350043.	−	1.19283e6i	0.357150	−	1.21704i
$991$	754784.	−	1.30732e6i	0.768556	−	1.33118i	−0.169790	−	0.985480i	$-0.554309\pi$
$991$	754784.	−	1.30732e6i	0.768556	−	1.33118i	0.938346	−	0.345697i	$-0.112358\pi$
$992$	−25408.6	−	6808.20i	−0.0258200	−	0.00691845i
$993$	821218.	−	220045.i	0.832837	−	0.223158i
$994$	897802.	−	518346.i	0.908673	−	0.524623i
$995$	−121507.	−	74036.4i	−0.122731	−	0.0747824i
$996$	−1.97560e6			−1.99150
$997$	−949421.	−	254397.i	−0.955143	−	0.255930i	−0.252600	−	0.967571i	$-0.581286\pi$
$997$	−949421.	−	254397.i	−0.955143	−	0.255930i	−0.702543	+	0.711641i	$0.747952\pi$
$998$	−288320.	+	1.07602e6i	−0.289476	+	1.08034i
$999$			429989.i			0.430850i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.5.m.a.7.4	✓	152	95.7	odd	12	inner
95.5.m.a.68.4	yes	152	1.1	even	1	trivial
95.5.m.a.83.35	yes	152	19.7	even	3	inner
95.5.m.a.87.35	yes	152	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	95.m (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.79516 - 6.69961i) q^{2} +(11.7300 - 3.14304i) q^{3} +(-27.8058 + 16.0537i) q^{4} +(-11.9846 - 21.9401i) 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} +(-125.476 + 119.678i) q^{10} -107.854 q^{11} +(-275.705 + 275.705i) q^{12} +(21.7057 - 81.0069i) q^{13} +(-326.646 - 188.589i) q^{14} +(-209.538 - 219.689i) q^{15} +(130.584 - 226.178i) q^{16} +(83.1155 + 310.191i) 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} +(193.615 + 722.580i) q^{22} +(13.3756 - 49.9183i) q^{23} +(1174.94 + 678.353i) q^{24} +(-337.737 + 525.889i) q^{25} -581.680 q^{26} +(-124.759 + 124.759i) q^{27} +(-451.900 + 1686.51i) q^{28} +(-46.5624 + 26.8828i) q^{29} +(-1095.68 + 1798.20i) q^{30} +1099.57 q^{31} +(-23.1076 - 6.19167i) q^{32} +(-1265.12 + 338.989i) q^{33} +(1928.96 - 1113.68i) q^{34} +(-1304.50 - 382.814i) q^{35} +(-1067.11 + 1848.29i) q^{36} +(1723.28 - 1723.28i) q^{37} +(-2217.69 + 1162.44i) q^{38} -1018.43i q^{39} +(786.464 - 2679.99i) q^{40} +(-413.838 + 716.789i) q^{41} +(-4424.30 - 1185.49i) q^{42} +(2116.82 - 567.199i) q^{43} +(2998.97 - 1731.46i) q^{44} +(-1419.10 - 864.681i) q^{45} -358.444 q^{46} +(-3267.50 - 875.523i) q^{47} +(820.861 - 3063.49i) q^{48} -556.206i q^{49} +(4129.54 + 1318.65i) q^{50} +(1949.89 + 3377.30i) q^{51} +(696.915 + 2600.92i) q^{52} +(1135.12 - 4236.32i) q^{53} +(1059.80 + 611.874i) q^{54} +(1292.59 + 2366.33i) q^{55} +6075.37 q^{56} +(-2035.25 - 3882.83i) q^{57} +(263.691 + 263.691i) q^{58} +(-2638.49 - 1523.33i) q^{59} +(9353.21 + 2744.77i) q^{60} +(-3378.69 - 5852.06i) q^{61} +(-1973.91 - 7366.72i) q^{62} +(935.556 - 3491.54i) q^{63} -4012.76i q^{64} +(-2037.44 + 494.613i) q^{65} +(4542.19 + 7867.31i) q^{66} +(4381.84 + 1174.11i) q^{67} +(-7290.82 - 7290.82i) q^{68} -627.580i q^{69} +(-222.930 + 9426.83i) q^{70} +(-1374.27 + 2380.31i) q^{71} +(7173.13 + 1922.04i) q^{72} +(171.844 - 46.0454i) 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} +(-6823.10 + 1828.24i) q^{78} +(610.073 + 352.226i) q^{79} +(-6527.37 - 154.363i) q^{80} +(-3763.38 + 6518.36i) q^{81} +(5545.12 + 1485.81i) q^{82} +(3582.82 + 3582.82i) q^{83} +21203.1i q^{84} +(5809.52 - 5541.10i) 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} +(-3245.53 + 11059.6i) q^{90} +(-2280.29 - 3949.57i) q^{91} +(429.455 + 1602.75i) q^{92} +(12898.0 - 3456.00i) q^{93} +23462.7i q^{94} +(-6779.40 + 5957.38i) q^{95} -290.513 q^{96} +(-2621.06 - 9781.95i) q^{97} +(-3726.37 + 998.477i) 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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