LMFDB - Embedded newform 95.5.m.a.87.33

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			87.33
Character	$\chi$	$=$	95.87
Dual form			95.5.m.a.83.33

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(6.02596 - 1.61465i) q^{2} +(0.324275 + 1.21021i) q^{3} +(19.8487 - 11.4597i) q^{4} +(10.8778 + 22.5094i) q^{5} +(3.90814 + 6.76910i) q^{6} +(-1.87404 - 1.87404i) q^{7} +(30.5232 - 30.5232i) q^{8} +(68.7886 - 39.7151i) q^{9} +(101.894 + 118.077i) q^{10} +227.680 q^{11} +(20.3050 + 20.3050i) q^{12} +(-85.3054 - 22.8575i) q^{13} +(-14.3188 - 8.26696i) q^{14} +(-23.7137 + 20.4637i) q^{15} +(-48.7071 + 84.3632i) q^{16} +(-372.957 + 99.9336i) q^{17} +(350.391 - 350.391i) q^{18} +(93.0748 - 348.795i) q^{19} +(473.860 + 322.126i) q^{20} +(1.66028 - 2.87569i) q^{21} +(1371.99 - 367.624i) q^{22} +(-681.203 - 182.528i) q^{23} +(46.8375 + 27.0416i) q^{24} +(-388.346 + 489.706i) q^{25} -550.954 q^{26} +(142.131 + 142.131i) q^{27} +(-58.6730 - 15.7214i) q^{28} +(680.797 - 393.058i) q^{29} +(-109.856 + 161.603i) q^{30} +25.3853 q^{31} +(-336.046 + 1254.14i) q^{32} +(73.8309 + 275.541i) q^{33} +(-2086.07 + 1204.39i) q^{34} +(21.7980 - 62.5689i) q^{35} +(910.243 - 1576.59i) q^{36} +(-1475.85 - 1475.85i) q^{37} +(-2.31763 - 2252.11i) q^{38} -110.650i q^{39} +(1019.09 + 355.033i) q^{40} +(-1423.08 + 2464.84i) q^{41} +(5.36154 - 20.0095i) q^{42} +(-280.069 - 1045.23i) q^{43} +(4519.15 - 2609.13i) q^{44} +(1642.23 + 1116.38i) q^{45} -4399.62 q^{46} +(-469.599 + 1752.57i) q^{47} +(-117.892 - 31.5890i) q^{48} -2393.98i q^{49} +(-1549.45 + 3577.99i) q^{50} +(-241.881 - 418.951i) q^{51} +(-1955.14 + 523.878i) q^{52} +(4574.74 + 1225.80i) q^{53} +(1085.97 + 626.984i) q^{54} +(2476.66 + 5124.94i) q^{55} -114.403 q^{56} +(452.298 - 0.465456i) q^{57} +(3467.80 - 3467.80i) q^{58} +(-2630.51 - 1518.72i) q^{59} +(-236.180 + 677.929i) q^{60} +(-3200.16 - 5542.83i) q^{61} +(152.971 - 40.9884i) q^{62} +(-203.340 - 54.4848i) q^{63} +6541.38i q^{64} +(-413.428 - 2168.81i) q^{65} +(889.805 + 1541.19i) q^{66} +(-50.2571 + 187.562i) q^{67} +(-6257.51 + 6257.51i) q^{68} -883.589i q^{69} +(30.3271 - 412.234i) q^{70} +(-2948.16 + 5106.36i) q^{71} +(887.416 - 3311.88i) q^{72} +(-666.053 - 2485.74i) q^{73} +(-11276.4 - 6510.42i) q^{74} +(-718.579 - 311.181i) q^{75} +(-2149.66 - 7989.74i) q^{76} +(-426.681 - 426.681i) q^{77} +(-178.661 - 666.771i) q^{78} +(4814.50 + 2779.65i) q^{79} +(-2428.79 - 178.681i) q^{80} +(3091.01 - 5353.78i) q^{81} +(-4595.55 + 17150.8i) q^{82} +(4589.51 - 4589.51i) q^{83} -76.1048i q^{84} +(-6306.40 - 7307.98i) q^{85} +(-3375.37 - 5846.31i) q^{86} +(696.449 + 696.449i) q^{87} +(6949.52 - 6949.52i) q^{88} +(-381.402 + 220.203i) q^{89} +(11698.6 + 4075.61i) q^{90} +(117.030 + 202.701i) q^{91} +(-15612.7 + 4183.41i) q^{92} +(8.23182 + 30.7216i) q^{93} +11319.1i q^{94} +(8863.62 - 1699.07i) q^{95} -1626.75 q^{96} +(4007.15 - 1073.71i) q^{97} +(-3865.44 - 14426.0i) q^{98} +(15661.8 - 9042.33i) 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 $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	6.02596	−	1.61465i	1.50649	−	0.403663i	0.591222	−	0.806509i	$-0.298646\pi$
$2$	6.02596	−	1.61465i	1.50649	−	0.403663i	0.915268	+	0.402846i	$0.131979\pi$
$3$	0.324275	+	1.21021i	0.0360306	+	0.134468i	0.981598	−	0.190957i	$-0.0611592\pi$
$3$	0.324275	+	1.21021i	0.0360306	+	0.134468i	−0.945568	+	0.325425i	$0.894493\pi$
$4$	19.8487	−	11.4597i	1.24054	−	0.716228i
$5$	10.8778	+	22.5094i	0.435113	+	0.900376i
$5$	10.8778	+	22.5094i	0.435113	+	0.900376i
$6$	3.90814	+	6.76910i	0.108559	+	0.188030i
$7$	−1.87404	−	1.87404i	−0.0382457	−	0.0382457i	0.687725	−	0.725971i	$-0.258609\pi$
$7$	−1.87404	−	1.87404i	−0.0382457	−	0.0382457i	−0.725971	+	0.687725i	$0.758609\pi$
$8$	30.5232	−	30.5232i	0.476925	−	0.476925i
$9$	68.7886	−	39.7151i	0.849242	−	0.490310i
$10$	101.894	+	118.077i	1.01894	+	1.18077i
$11$	227.680			1.88165			0.940826	−	0.338890i	$-0.110052\pi$
$11$	227.680			1.88165			0.940826	+	0.338890i	$0.110052\pi$
$12$	20.3050	+	20.3050i	0.141007	+	0.141007i
$13$	−85.3054	−	22.8575i	−0.504766	−	0.135252i	−0.00255473	−	0.999997i	$-0.500813\pi$
$13$	−85.3054	−	22.8575i	−0.504766	−	0.135252i	−0.502211	+	0.864745i	$0.667480\pi$
$14$	−14.3188	−	8.26696i	−0.0730551	−	0.0421784i
$15$	−23.7137	+	20.4637i	−0.105394	+	0.0909498i
$16$	−48.7071	+	84.3632i	−0.190262	+	0.329544i
$17$	−372.957	+	99.9336i	−1.29051	+	0.345791i	−0.837854	−	0.545895i	$-0.816190\pi$
$17$	−372.957	+	99.9336i	−1.29051	+	0.345791i	−0.452655	+	0.891686i	$0.649523\pi$
$18$	350.391	−	350.391i	1.08145	−	1.08145i
$19$	93.0748	−	348.795i	0.257825	−	0.966192i
$19$	93.0748	−	348.795i	0.257825	−	0.966192i
$20$	473.860	+	322.126i	1.18465	+	0.805316i
$21$	1.66028	−	2.87569i	0.00376480	−	0.00652083i
$22$	1371.99	−	367.624i	2.83469	−	0.759553i
$23$	−681.203	−	182.528i	−1.28772	−	0.345043i	−0.450925	−	0.892562i	$-0.648906\pi$
$23$	−681.203	−	182.528i	−1.28772	−	0.345043i	−0.836794	+	0.547518i	$0.815573\pi$
$24$	46.8375	+	27.0416i	0.0813150	+	0.0469473i
$25$	−388.346	+	489.706i	−0.621354	+	0.783530i
$26$	−550.954			−0.815020
$27$	142.131	+	142.131i	0.194967	+	0.194967i
$28$	−58.6730	−	15.7214i	−0.0748381	−	0.0200528i
$29$	680.797	−	393.058i	0.809509	−	0.467370i	−0.0372766	−	0.999305i	$-0.511868\pi$
$29$	680.797	−	393.058i	0.809509	−	0.467370i	0.846785	+	0.531935i	$0.178535\pi$
$30$	−109.856	+	161.603i	−0.122063	+	0.179559i
$31$	25.3853			0.0264155			0.0132077	−	0.999913i	$-0.495796\pi$
$31$	25.3853			0.0264155			0.0132077	+	0.999913i	$0.495796\pi$
$32$	−336.046	+	1254.14i	−0.328170	+	1.22475i
$33$	73.8309	+	275.541i	0.0677970	+	0.253022i
$34$	−2086.07	+	1204.39i	−1.80456	+	1.04186i
$35$	21.7980	−	62.5689i	0.0177943	−	0.0510767i
$36$	910.243	−	1576.59i	0.702348	−	1.21650i
$37$	−1475.85	−	1475.85i	−1.07805	−	1.07805i	−0.996685	−	0.0813633i	$-0.974073\pi$
$37$	−1475.85	−	1475.85i	−1.07805	−	1.07805i	−0.0813633	−	0.996685i	$-0.525927\pi$
$38$	−2.31763	−	2252.11i	−0.00160501	−	1.55963i
$39$		−	110.650i		−	0.0727480i
$40$	1019.09	+	355.033i	0.636928	+	0.221896i
$41$	−1423.08	+	2464.84i	−0.846567	+	1.46630i	0.0376866	+	0.999290i	$0.488001\pi$
$41$	−1423.08	+	2464.84i	−0.846567	+	1.46630i	−0.884254	+	0.467007i	$0.845332\pi$
$42$	5.36154	−	20.0095i	0.00303942	−	0.0113433i
$43$	−280.069	−	1045.23i	−0.151471	−	0.565296i	−0.999382	−	0.0351576i	$-0.988807\pi$
$43$	−280.069	−	1045.23i	−0.151471	−	0.565296i	0.847911	−	0.530138i	$-0.177860\pi$
$44$	4519.15	−	2609.13i	2.33427	−	1.34769i
$45$	1642.23	+	1116.38i	0.810979	+	0.551297i
$46$	−4399.62			−2.07922
$47$	−469.599	+	1752.57i	−0.212584	+	0.793375i	0.774419	+	0.632673i	$0.218042\pi$
$47$	−469.599	+	1752.57i	−0.212584	+	0.793375i	−0.987003	+	0.160702i	$0.948624\pi$
$48$	−117.892	−	31.5890i	−0.0511683	−	0.0137105i
$49$		−	2393.98i		−	0.997075i
$50$	−1549.45	+	3577.99i	−0.619782	+	1.43120i
$51$	−241.881	−	418.951i	−0.0929956	−	0.161073i
$52$	−1955.14	+	523.878i	−0.723055	+	0.193742i
$53$	4574.74	+	1225.80i	1.62860	+	0.436382i	0.953512	−	0.301356i	$-0.0974391\pi$
$53$	4574.74	+	1225.80i	1.62860	+	0.436382i	0.675088	+	0.737738i	$0.264106\pi$
$54$	1085.97	+	626.984i	0.372417	+	0.215015i
$55$	2476.66	+	5124.94i	0.818731	+	1.69419i
$56$	−114.403			−0.0364806
$57$	452.298	−	0.465456i	0.139211	−	0.000143261i
$58$	3467.80	−	3467.80i	1.03086	−	1.03086i
$59$	−2630.51	−	1518.72i	−0.755676	−	0.436290i	0.0720651	−	0.997400i	$-0.477041\pi$
$59$	−2630.51	−	1518.72i	−0.755676	−	0.436290i	−0.827741	+	0.561110i	$0.810374\pi$
$60$	−236.180	+	677.929i	−0.0656055	+	0.188314i
$61$	−3200.16	−	5542.83i	−0.860026	−	1.48961i	−0.871903	−	0.489679i	$-0.837114\pi$
$61$	−3200.16	−	5542.83i	−0.860026	−	1.48961i	0.0118764	−	0.999929i	$-0.496220\pi$
$62$	152.971	−	40.9884i	0.0397947	−	0.0106630i
$63$	−203.340	−	54.4848i	−0.0512321	−	0.0137276i
$64$			6541.38i			1.59702i
$65$	−413.428	−	2168.81i	−0.0978527	−	0.513328i
$66$	889.805	+	1541.19i	0.204271	+	0.353808i
$67$	−50.2571	+	187.562i	−0.0111956	+	0.0417826i	−0.971298	−	0.237867i	$-0.923552\pi$
$67$	−50.2571	+	187.562i	−0.0111956	+	0.0417826i	0.960102	+	0.279650i	$0.0902184\pi$
$68$	−6257.51	+	6257.51i	−1.35327	+	1.35327i
$69$		−	883.589i		−	0.185589i
$70$	30.3271	−	412.234i	0.00618920	−	0.0841294i
$71$	−2948.16	+	5106.36i	−0.584836	+	1.01296i	0.410060	+	0.912058i	$0.365508\pi$
$71$	−2948.16	+	5106.36i	−0.584836	+	1.01296i	−0.994896	+	0.100907i	$0.967826\pi$
$72$	887.416	−	3311.88i	0.171184	−	0.638866i
$73$	−666.053	−	2485.74i	−0.124987	−	0.466456i	0.874853	−	0.484389i	$-0.160958\pi$
$73$	−666.053	−	2485.74i	−0.124987	−	0.466456i	−0.999839	+	0.0179330i	$0.994291\pi$
$74$	−11276.4	−	6510.42i	−2.05924	−	1.18890i
$75$	−718.579	−	311.181i	−0.127747	−	0.0553211i
$76$	−2149.66	−	7989.74i	−0.372171	−	1.38326i
$77$	−426.681	−	426.681i	−0.0719650	−	0.0719650i
$78$	−178.661	−	666.771i	−0.0293657	−	0.109594i
$79$	4814.50	+	2779.65i	0.771430	+	0.445385i	0.833385	−	0.552694i	$-0.186400\pi$
$79$	4814.50	+	2779.65i	0.771430	+	0.445385i	−0.0619544	+	0.998079i	$0.519733\pi$
$80$	−2428.79	−	178.681i	−0.379499	−	0.0279188i
$81$	3091.01	−	5353.78i	0.471118	−	0.816000i
$82$	−4595.55	+	17150.8i	−0.683455	+	2.55069i
$83$	4589.51	−	4589.51i	0.666208	−	0.666208i	−0.290628	−	0.956836i	$-0.593864\pi$
$83$	4589.51	−	4589.51i	0.666208	−	0.666208i	0.956836	+	0.290628i	$0.0938641\pi$
$84$		−	76.1048i		−	0.0107858i
$85$	−6306.40	−	7307.98i	−0.872859	−	1.01149i
$86$	−3375.37	−	5846.31i	−0.456378	−	0.790470i
$87$	696.449	+	696.449i	0.0920133	+	0.0920133i
$88$	6949.52	−	6949.52i	0.897407	−	0.897407i
$89$	−381.402	+	220.203i	−0.0481508	+	0.0277999i	−0.523882	−	0.851791i	$-0.675517\pi$
$89$	−381.402	+	220.203i	−0.0481508	+	0.0277999i	0.475731	+	0.879591i	$0.342183\pi$
$90$	11698.6	+	4075.61i	1.44427	+	0.503161i
$91$	117.030	+	202.701i	0.0141323	+	0.0244779i
$92$	−15612.7	+	4183.41i	−1.84460	+	0.494260i
$93$	8.23182	+	30.7216i	0.000951765	+	0.00355204i
$94$			11319.1i			1.28102i
$95$	8863.62	−	1699.07i	0.982119	−	0.188263i
$96$	−1626.75			−0.176514
$97$	4007.15	−	1073.71i	0.425885	−	0.114116i	−0.0395088	−	0.999219i	$-0.512579\pi$
$97$	4007.15	−	1073.71i	0.425885	−	0.114116i	0.465394	+	0.885104i	$0.345913\pi$
$98$	−3865.44	−	14426.0i	−0.402482	−	1.50208i
$99$	15661.8	−	9042.33i	1.59798	−	0.922593i
$100$	−2096.30	+	14170.3i	−0.209630	+	1.41703i
$101$	4399.09	+	7619.44i	0.431241	+	0.746931i	0.996980	−	0.0776530i	$-0.0247426\pi$
$101$	4399.09	+	7619.44i	0.431241	+	0.746931i	−0.565740	+	0.824584i	$0.691409\pi$
$102$	−2134.03	−	2134.03i	−0.205116	−	0.205116i
$103$	−3945.45	+	3945.45i	−0.371897	+	0.371897i	−0.868168	−	0.496271i	$-0.834702\pi$
$103$	−3945.45	+	3945.45i	−0.371897	+	0.371897i	0.496271	+	0.868168i	$0.334702\pi$
$104$	−3301.48	+	1906.11i	−0.305240	+	0.176231i
$105$	82.7902	+	6.09068i	0.00750931	+	0.000552442i
$106$	29546.4			2.62962
$107$	5533.31	+	5533.31i	0.483300	+	0.483300i	0.906184	−	0.422884i	$-0.138982\pi$
$107$	5533.31	+	5533.31i	0.483300	+	0.483300i	−0.422884	+	0.906184i	$0.638982\pi$
$108$	4449.89	+	1192.34i	0.381506	+	0.102224i
$109$	13525.2	+	7808.80i	1.13839	+	0.657251i	0.946032	−	0.324074i	$-0.105053\pi$
$109$	13525.2	+	7808.80i	1.13839	+	0.657251i	0.192360	+	0.981324i	$0.438386\pi$
$110$	23199.2	+	26883.7i	1.91729	+	2.22180i
$111$	1307.51	−	2264.67i	0.106120	−	0.183806i
$112$	249.379	−	66.8209i	0.0198803	−	0.00532692i
$113$	−708.981	+	708.981i	−0.0555236	+	0.0555236i	−0.734323	−	0.678800i	$-0.762500\pi$
$113$	−708.981	+	708.981i	−0.0555236	+	0.0555236i	0.678800	+	0.734323i	$0.262500\pi$
$114$	2724.78	−	733.108i	0.209663	−	0.0564103i
$115$	−3301.41	−	17319.0i	−0.249634	−	1.30956i
$116$	9008.62	−	15603.4i	0.669487	−	1.15959i
$117$	−6775.83	+	1815.58i	−0.494983	+	0.132630i
$118$	−18303.6	−	4904.42i	−1.31453	−	0.352228i
$119$	886.215	+	511.656i	0.0625814	+	0.0361314i
$120$	−99.2013	+	1348.44i	−0.00688898	+	0.0936414i
$121$	37197.1			2.54061
$122$	−28233.8	−	28233.8i	−1.89692	−	1.89692i
$123$	−3444.45	−	922.938i	−0.227672	−	0.0610046i
$124$	503.865	−	290.907i	0.0327696	−	0.0189195i
$125$	−15247.4	−	3414.50i	−0.975831	−	0.218528i
$126$	−1313.29			−0.0827219
$127$	1370.61	−	5115.19i	0.0849781	−	0.317143i	−0.910332	−	0.413879i	$-0.864174\pi$
$127$	1370.61	−	5115.19i	0.0849781	−	0.317143i	0.995310	+	0.0967363i	$0.0308403\pi$
$128$	5185.31	+	19351.8i	0.316486	+	1.18114i
$129$	1174.13	−	677.886i	0.0705566	−	0.0407359i
$130$	−5993.17	−	12401.6i	−0.354626	−	0.733825i
$131$	−6119.33	+	10599.0i	−0.356584	+	0.617621i	−0.987388	−	0.158321i	$-0.949392\pi$
$131$	−6119.33	+	10599.0i	−0.356584	+	0.617621i	0.630804	+	0.775942i	$0.282725\pi$
$132$	4623.05	+	4623.05i	0.265327	+	0.265327i
$133$	−828.081	+	479.230i	−0.0468133	+	0.0270920i
$134$			1211.39i			0.0674644i
$135$	−1653.21	+	4745.36i	−0.0907110	+	0.260376i
$136$	−8333.56	+	14434.1i	−0.450560	+	0.780393i
$137$	7068.94	−	26381.7i	0.376629	−	1.40560i	−0.474322	−	0.880351i	$-0.657307\pi$
$137$	7068.94	−	26381.7i	0.376629	−	1.40560i	0.850951	−	0.525246i	$-0.176027\pi$
$138$	−1426.69	−	5324.48i	−0.0749154	−	0.279588i
$139$	7655.84	−	4420.10i	0.396244	−	0.228772i	−0.288618	−	0.957444i	$-0.593196\pi$
$139$	7655.84	−	4420.10i	0.396244	−	0.228772i	0.684862	+	0.728673i	$0.259862\pi$
$140$	−284.355	−	1491.71i	−0.0145079	−	0.0761076i
$141$	−2273.25			−0.114343
$142$	−9520.49	+	35531.0i	−0.472153	+	1.76210i
$143$	−19422.3	−	5204.19i	−0.949793	−	0.254496i
$144$			7737.64i			0.373150i
$145$	16253.1	+	11048.7i	0.773036	+	0.525503i
$146$	−8027.22	−	13903.6i	−0.376582	−	0.652259i
$147$	2897.22	−	776.307i	0.134075	−	0.0359252i
$148$	−46206.4	−	12381.0i	−2.10949	−	0.565237i
$149$	−2699.45	−	1558.53i	−0.121591	−	0.0702007i	0.437971	−	0.898989i	$-0.355697\pi$
$149$	−2699.45	−	1558.53i	−0.121591	−	0.0702007i	−0.559562	+	0.828788i	$0.689031\pi$
$150$	−4832.58	−	714.912i	−0.214781	−	0.0317739i
$151$	−1990.86			−0.0873144			−0.0436572	−	0.999047i	$-0.513901\pi$
$151$	−1990.86			−0.0873144			−0.0436572	+	0.999047i	$0.513901\pi$
$152$	−7805.41	−	13487.3i	−0.337838	−	0.583764i
$153$	−21686.3	+	21686.3i	−0.926410	+	0.926410i
$154$	−3260.10	−	1882.22i	−0.137464	−	0.0793650i
$155$	276.136	+	571.407i	0.0114937	+	0.0237839i
$156$	−1268.01	−	2196.25i	−0.0521042	−	0.0902471i
$157$	−7717.34	+	2067.86i	−0.313089	+	0.0838921i	−0.411942	−	0.911210i	$-0.635149\pi$
$157$	−7717.34	+	2067.86i	−0.313089	+	0.0838921i	0.0988527	+	0.995102i	$0.468483\pi$
$158$	33500.1	+	8976.33i	1.34194	+	0.359571i
$159$			5933.89i			0.234717i
$160$	−31885.4	+	6078.13i	−1.24553	+	0.237427i
$161$	934.537	+	1618.66i	0.0360533	+	0.0624461i
$162$	9981.79	−	37252.6i	0.380346	−	1.41947i
$163$	−11624.3	+	11624.3i	−0.437514	+	0.437514i	−0.891175	−	0.453660i	$-0.850118\pi$
$163$	−11624.3	+	11624.3i	−0.437514	+	0.437514i	0.453660	+	0.891175i	$0.350118\pi$
$164$			65232.0i			2.42534i
$165$	−5399.14	+	4659.17i	−0.198315	+	0.171136i
$166$	20245.8	−	35066.7i	0.734713	−	1.27256i
$167$	−7283.25	+	27181.5i	−0.261151	+	0.974630i	0.703413	+	0.710782i	$0.251659\pi$
$167$	−7283.25	+	27181.5i	−0.261151	+	0.974630i	−0.964564	+	0.263849i	$0.915008\pi$
$168$	−37.0981	−	138.452i	−0.00131442	−	0.00490548i
$169$	−17980.0	−	10380.8i	−0.629530	−	0.363459i
$170$	−49802.0	−	33855.0i	−1.72325	−	1.17145i
$171$	−7449.96	−	27689.6i	−0.254778	−	0.946945i
$172$	−17537.0	−	17537.0i	−0.592787	−	0.592787i
$173$	1597.59	+	5962.29i	0.0533793	+	0.199214i	0.987466	−	0.157832i	$-0.0504505\pi$
$173$	1597.59	+	5962.29i	0.0533793	+	0.199214i	−0.934087	+	0.357046i	$0.883784\pi$
$174$	5321.30	+	3072.25i	0.175760	+	0.101475i
$175$	1645.50	−	189.953i	0.0537307	−	0.00620253i
$176$	−11089.6	+	19207.8i	−0.358007	+	0.620087i
$177$	984.969	−	3675.96i	0.0314395	−	0.117334i
$178$	−1942.77	+	1942.77i	−0.0613169	+	0.0613169i
$179$		−	8456.68i		−	0.263933i	−0.991254	−	0.131967i	$-0.957871\pi$
$179$		−	8456.68i		−	0.263933i	0.991254	−	0.131967i	$-0.0421291\pi$
$180$	45389.5	+	3339.20i	1.40091	+	0.103062i
$181$	12145.6	+	21036.8i	0.370734	+	0.642130i	0.989679	−	0.143305i	$-0.0457729\pi$
$181$	12145.6	+	21036.8i	0.370734	+	0.642130i	−0.618945	+	0.785434i	$0.712440\pi$
$182$	1032.51	+	1032.51i	0.0311710	+	0.0311710i
$183$	5670.27	−	5670.27i	0.169317	−	0.169317i
$184$	−26363.9	+	15221.2i	−0.778705	+	0.449586i
$185$	17166.4	−	49274.4i	0.501576	−	1.43972i
$186$	99.2092	+	171.835i	0.00286765	+	0.00496692i
$187$	−84914.8	+	22752.9i	−2.42829	+	0.650658i
$188$	10762.9	+	40167.6i	0.304518	+	1.13648i
$189$		−	532.717i		−	0.0149133i
$190$	50668.4	−	24550.2i	1.40356	−	0.680061i
$191$	23327.4			0.639440			0.319720	−	0.947512i	$-0.396411\pi$
$191$	23327.4			0.639440			0.319720	+	0.947512i	$0.396411\pi$
$192$	−7916.46	+	2121.21i	−0.214748	+	0.0575414i
$193$	861.579	+	3215.46i	0.0231303	+	0.0863233i	0.976526	−	0.215399i	$-0.0691052\pi$
$193$	861.579	+	3215.46i	0.0231303	+	0.0863233i	−0.953396	+	0.301722i	$0.902438\pi$
$194$	22413.3	−	12940.3i	0.595528	−	0.343828i
$195$	2490.66	−	1203.63i	0.0655005	−	0.0316536i
$196$	−27434.1	−	47517.3i	−0.714133	−	1.23691i
$197$	36555.4	+	36555.4i	0.941932	+	0.941932i	0.998404	−	0.0564720i	$-0.0179852\pi$
$197$	36555.4	+	36555.4i	0.941932	+	0.941932i	−0.0564720	+	0.998404i	$0.517985\pi$
$198$	79777.1	−	79777.1i	2.03492	−	2.03492i
$199$	−13035.0	+	7525.76i	−0.329158	+	0.190040i	−0.655467	−	0.755224i	$-0.727528\pi$
$199$	−13035.0	+	7525.76i	−0.329158	+	0.190040i	0.326309	+	0.945263i	$0.394195\pi$
$200$	3093.84	+	26801.0i	0.0773459	+	0.670024i
$201$	−243.287			−0.00602181
$202$	38811.5	+	38811.5i	0.951168	+	0.951168i
$203$	−2012.44	−	539.233i	−0.0488351	−	0.0130853i
$204$	−9602.07	−	5543.76i	−0.230730	−	0.133212i
$205$	−70962.2	−	5220.52i	−1.68857	−	0.124224i
$206$	−17404.6	+	30145.7i	−0.410138	+	0.710380i
$207$	−54108.1	+	14498.2i	−1.26276	+	0.338356i
$208$	6083.31	−	6083.31i	0.140609	−	0.140609i
$209$	21191.3	−	79413.6i	0.485137	−	1.81804i
$210$	508.725	−	96.9751i	0.0115357	−	0.00219898i
$211$	−40778.5	+	70630.4i	−0.915938	+	1.58645i	−0.110416	+	0.993886i	$0.535218\pi$
$211$	−40778.5	+	70630.4i	−0.915938	+	1.58645i	−0.805522	+	0.592565i	$0.798115\pi$
$212$	104850.	−	28094.4i	2.33290	−	0.625098i
$213$	−7135.78	−	1912.03i	−0.157283	−	0.0421439i
$214$	42277.9	+	24409.1i	0.923178	+	0.532997i
$215$	20481.0	−	17674.0i	0.443072	−	0.382348i
$216$	8676.59			0.185969
$217$	−47.5730	−	47.5730i	−0.00101028	−	0.00101028i
$218$	94111.0	+	25217.0i	1.98028	+	0.530615i
$219$	2792.29	−	1612.13i	0.0582201	−	0.0336134i
$220$	107888.	+	73341.7i	2.22910	+	1.51532i
$221$	34099.5			0.698173
$222$	4222.34	−	15758.0i	0.0856736	−	0.319738i
$223$	9591.24	+	35795.0i	0.192870	+	0.719801i	0.992808	+	0.119718i	$0.0381992\pi$
$223$	9591.24	+	35795.0i	0.192870	+	0.719801i	−0.799938	+	0.600083i	$0.795134\pi$
$224$	2980.07	−	1720.55i	0.0593924	−	0.0342902i
$225$	−7265.05	+	49109.4i	−0.143507	+	0.970063i
$226$	−3127.54	+	5417.05i	−0.0612330	+	0.106059i
$227$	28688.2	+	28688.2i	0.556740	+	0.556740i	0.928378	−	0.371638i	$-0.121204\pi$
$227$	28688.2	+	28688.2i	0.556740	+	0.556740i	−0.371638	+	0.928378i	$0.621204\pi$
$228$	8972.19	−	5192.41i	0.172595	−	0.0998849i
$229$		−	395.573i		−	0.00754321i	−0.999993	−	0.00377160i	$-0.998799\pi$
$229$		−	395.573i		−	0.00754321i	0.999993	−	0.00377160i	$-0.00120054\pi$
$230$	−47858.3	−	99032.9i	−0.904694	−	1.87208i
$231$	378.012	−	654.736i	0.00708405	−	0.0122699i
$232$	8782.70	−	32777.5i	0.163174	−	0.608975i
$233$	−6870.44	−	25640.8i	−0.126553	−	0.472302i	0.873337	−	0.487116i	$-0.161951\pi$
$233$	−6870.44	−	25640.8i	−0.126553	−	0.472302i	−0.999890	+	0.0148137i	$0.995284\pi$
$234$	−37899.3	+	21881.2i	−0.692150	+	0.399613i
$235$	−44557.4	+	8493.71i	−0.806834	+	0.153802i
$236$	−69616.2			−1.24993
$237$	−1802.74	+	6727.93i	−0.0320950	+	0.119780i
$238$	6166.44	+	1652.29i	0.108863	+	0.0291698i
$239$			1569.09i			0.0274696i	0.999906	+	0.0137348i	$0.00437206\pi$
$239$			1569.09i			0.0274696i	−0.999906	+	0.0137348i	$0.995628\pi$
$240$	−571.356	−	2997.29i	−0.00991937	−	0.0520364i
$241$	10772.8	+	18659.0i	0.185478	+	0.321258i	0.943738	−	0.330695i	$-0.107283\pi$
$241$	10772.8	+	18659.0i	0.185478	+	0.321258i	−0.758259	+	0.651953i	$0.773950\pi$
$242$	224148.	−	60060.4i	3.82741	−	1.02555i
$243$	23208.1	+	6218.58i	0.393030	+	0.105312i
$244$	−127038.	−	73345.4i	−2.13380	−	1.23195i
$245$	53887.0	−	26041.2i	0.897742	−	0.433840i
$246$	−22246.4			−0.367611
$247$	−15912.4	+	27626.6i	−0.260820	+	0.452829i
$248$	774.840	−	774.840i	0.0125982	−	0.0125982i
$249$	7042.54	+	4066.01i	0.113588	+	0.0655798i
$250$	−97393.2	+	4043.49i	−1.55829	+	0.0646959i
$251$	−5212.77	−	9028.78i	−0.0827411	−	0.143312i	0.821685	−	0.569941i	$-0.193034\pi$
$251$	−5212.77	−	9028.78i	−0.0827411	−	0.143312i	−0.904426	+	0.426630i	$0.859701\pi$
$252$	−4660.41	+	1248.75i	−0.0733877	+	0.0196642i
$253$	−155096.	−	41557.9i	−2.42304	−	0.649251i
$254$		−	33037.0i		−	0.512075i
$255$	6799.19	−	10001.9i	0.104563	−	0.153816i
$256$	10161.9	+	17600.9i	0.155058	+	0.268569i
$257$	1305.78	−	4873.25i	0.0197699	−	0.0737823i	−0.955336	−	0.295521i	$-0.904507\pi$
$257$	1305.78	−	4873.25i	0.0197699	−	0.0737823i	0.975106	+	0.221739i	$0.0711733\pi$
$258$	5980.73	−	5980.73i	0.0898493	−	0.0898493i
$259$			5531.59i			0.0824613i
$260$	−33059.8	−	38310.4i	−0.489051	−	0.566722i
$261$	31220.7	−	54075.8i	0.458312	−	0.793820i
$262$	−19761.2	+	73749.7i	−0.287879	+	1.07438i
$263$	1164.31	+	4345.28i	0.0168329	+	0.0628212i	0.973831	−	0.227272i	$-0.0729805\pi$
$263$	1164.31	+	4345.28i	0.0168329	+	0.0628212i	−0.956999	+	0.290093i	$0.906314\pi$
$264$	10663.9	+	6156.83i	0.153007	+	0.0883384i
$265$	22171.2	+	116309.i	0.315716	+	1.65623i
$266$	−4216.19	+	4224.88i	−0.0595878	+	0.0597106i
$267$	−390.171	−	390.171i	−0.00547309	−	0.00547309i
$268$	1151.86	+	4298.80i	0.0160372	+	0.0598518i
$269$	−62608.7	−	36147.2i	−0.865227	−	0.499539i	0.000531858	−	1.00000i	$-0.499831\pi$
$269$	−62608.7	−	36147.2i	−0.865227	−	0.499539i	−0.865759	+	0.500461i	$0.833164\pi$
$270$	−2300.07	+	31264.7i	−0.0315510	+	0.428871i
$271$	−59542.8	+	103131.i	−0.810757	+	1.40427i	0.101578	+	0.994828i	$0.467611\pi$
$271$	−59542.8	+	103131.i	−0.810757	+	1.40427i	−0.912335	+	0.409444i	$0.865723\pi$
$272$	9734.95	−	36331.3i	0.131582	−	0.491070i
$273$	−207.362	+	207.362i	−0.00278229	+	0.00278229i
$274$		−	170389.i		−	2.26955i
$275$	−88418.6	+	111496.i	−1.16917	+	1.47433i
$276$	−10125.6	−	17538.1i	−0.132924	−	0.230231i
$277$	−14410.0	−	14410.0i	−0.187804	−	0.187804i	0.606942	−	0.794746i	$-0.292396\pi$
$277$	−14410.0	−	14410.0i	−0.187804	−	0.187804i	−0.794746	+	0.606942i	$0.792396\pi$
$278$	38996.8	−	38996.8i	0.504591	−	0.504591i
$279$	1746.22	−	1008.18i	0.0224331	−	0.0129518i
$280$	−1244.46	−	2575.15i	−0.0158732	−	0.0328463i
$281$	−20661.5	−	35786.8i	−0.261667	−	0.453221i	0.705018	−	0.709190i	$-0.250939\pi$
$281$	−20661.5	−	35786.8i	−0.261667	−	0.453221i	−0.966685	+	0.255968i	$0.917606\pi$
$282$	−13698.5	+	3670.51i	−0.172257	+	0.0461560i
$283$	−8862.08	−	33073.7i	−0.110653	−	0.412962i	0.888272	−	0.459318i	$-0.151906\pi$
$283$	−8862.08	−	33073.7i	−0.110653	−	0.412962i	−0.998925	+	0.0463553i	$0.985239\pi$
$284$			135139.i			1.67550i
$285$	4930.49	+	10175.9i	0.0607016	+	0.125280i
$286$	−125441.			−1.53358
$287$	7286.12	−	1952.31i	0.0884570	−	0.0237020i
$288$	26692.2	+	99616.8i	0.321810	+	1.20101i
$289$	56779.0	−	32781.4i	0.679817	−	0.392493i
$290$	115780.	+	40336.0i	1.37670	+	0.479620i
$291$	2598.84	+	4501.33i	0.0306898	+	0.0531563i
$292$	−41706.1	−	41706.1i	−0.489140	−	0.489140i
$293$	25118.0	−	25118.0i	0.292584	−	0.292584i	−0.545517	−	0.838100i	$-0.683666\pi$
$293$	25118.0	−	25118.0i	0.292584	−	0.292584i	0.838100	+	0.545517i	$0.183666\pi$
$294$	16205.1	−	9355.99i	0.187480	−	0.108242i
$295$	5571.39	−	75731.6i	0.0640206	−	0.870228i
$296$	−90095.2			−1.02830
$297$	32360.4	+	32360.4i	0.366860	+	0.366860i
$298$	−18783.2	−	5032.95i	−0.211513	−	0.0566749i
$299$	53938.2	+	31141.2i	0.603329	+	0.348332i
$300$	−17828.9	+	2058.12i	−0.198099	+	0.0228680i
$301$	−1433.94	+	2483.66i	−0.0158270	+	0.0274132i
$302$	−11996.8	+	3214.54i	−0.131538	+	0.0352456i
$303$	−7794.62	+	7794.62i	−0.0849004	+	0.0849004i
$304$	24892.1	+	24840.9i	0.269348	+	0.268794i
$305$	89955.2	−	132328.i	0.967000	−	1.42249i
$306$	−95665.1	+	165697.i	−1.02167	+	1.76958i
$307$	132231.	−	35431.1i	1.40299	−	0.375931i	0.523575	−	0.851979i	$-0.324598\pi$
$307$	132231.	−	35431.1i	1.40299	−	0.375931i	0.879419	+	0.476048i	$0.157931\pi$
$308$	−13358.7	−	3579.44i	−0.140819	−	0.0377324i
$309$	−6054.24	−	3495.42i	−0.0634078	−	0.0366085i
$310$	2586.61	+	2997.42i	0.0269158	+	0.0311906i
$311$	−2976.90			−0.0307782			−0.0153891	−	0.999882i	$-0.504899\pi$
$311$	−2976.90			−0.0307782			−0.0153891	+	0.999882i	$0.504899\pi$
$312$	−3377.38	−	3377.38i	−0.0346953	−	0.0346953i
$313$	94324.3	+	25274.1i	0.962797	+	0.257981i	0.705784	−	0.708427i	$-0.250595\pi$
$313$	94324.3	+	25274.1i	0.962797	+	0.257981i	0.257013	+	0.966408i	$0.417262\pi$
$314$	−43165.5	+	24921.6i	−0.437802	+	0.252765i
$315$	−985.476	−	5169.74i	−0.00993173	−	0.0521012i
$316$	127415.			1.27599
$317$	36548.4	−	136401.i	0.363706	−	1.35737i	−0.505461	−	0.862850i	$-0.668677\pi$
$317$	36548.4	−	136401.i	0.363706	−	1.35737i	0.869167	−	0.494519i	$-0.164656\pi$
$318$	9581.17	+	35757.4i	0.0947467	+	0.353600i
$319$	155004.	−	89491.4i	1.52321	−	0.879428i
$320$	−147243.	+	71156.0i	−1.43792	+	0.694882i
$321$	−4902.16	+	8490.78i	−0.0475748	+	0.0824020i
$322$	8245.06	+	8245.06i	0.0795210	+	0.0795210i
$323$	143.442	+	139387.i	0.00137490	+	1.33603i
$324$		−	141687.i		−	1.34971i
$325$	44321.5	−	32898.0i	0.419612	−	0.311460i
$326$	−51278.5	+	88816.9i	−0.482503	+	0.835720i
$327$	−5064.40	+	18900.6i	−0.0473622	+	0.176758i
$328$	31798.0	+	118672.i	0.295565	+	1.10306i
$329$	4164.42	−	2404.33i	0.0384736	−	0.0222127i
$330$	−25012.1	+	36793.7i	−0.229679	+	0.337867i
$331$	121273.			1.10690			0.553452	−	0.832881i	$-0.313310\pi$
$331$	121273.			1.10690			0.553452	+	0.832881i	$0.313310\pi$
$332$	38501.6	−	143690.i	0.349303	−	1.30362i
$333$	−160135.	−	42908.0i	−1.44410	−	0.386946i
$334$			175554.i			1.57369i
$335$	−4768.60	+	909.009i	−0.0424914	+	0.00809988i
$336$	161.735	+	280.133i	0.00143260	+	0.00248133i
$337$	−97033.0	+	25999.9i	−0.854397	+	0.228935i	−0.659329	−	0.751855i	$-0.729159\pi$
$337$	−97033.0	+	25999.9i	−0.854397	+	0.228935i	−0.195068	+	0.980790i	$0.562493\pi$
$338$	−125108.	−	33522.6i	−1.09510	−	0.293430i
$339$	−1087.92	−	628.112i	−0.00946670	−	0.00546560i
$340$	−208921.	−	72784.8i	−1.80727	−	0.629626i
$341$	5779.72			0.0497047
$342$	−89602.2	−	154827.i	−0.766067	−	1.32372i
$343$	−8985.96	+	8985.96i	−0.0763794	+	0.0763794i
$344$	−40452.4	−	23355.2i	−0.341844	−	0.197364i
$345$	19889.1	−	9611.52i	0.167100	−	0.0807521i
$346$	19254.0	+	33349.0i	0.160831	+	0.278567i
$347$	122506.	−	32825.5i	1.01742	−	0.272616i	0.288693	−	0.957422i	$-0.406779\pi$
$347$	122506.	−	32825.5i	1.01742	−	0.272616i	0.728726	+	0.684805i	$0.240113\pi$
$348$	21804.7	+	5842.54i	0.180049	+	0.0482440i
$349$		−	91660.1i		−	0.752540i	−0.926510	−	0.376270i	$-0.877207\pi$
$349$		−	91660.1i		−	0.752540i	0.926510	−	0.376270i	$-0.122793\pi$
$350$	9609.03	−	3801.56i	0.0784411	−	0.0310332i
$351$	−8875.78	−	15373.3i	−0.0720431	−	0.124782i
$352$	−76511.0	+	285543.i	−0.617502	+	2.30455i
$353$	79400.6	−	79400.6i	0.637198	−	0.637198i	−0.312665	−	0.949863i	$-0.601222\pi$
$353$	79400.6	−	79400.6i	0.637198	−	0.637198i	0.949863	+	0.312665i	$0.101222\pi$
$354$		−	23741.6i		−	0.189453i
$355$	−147011.	−	10815.2i	−1.16652	−	0.0858180i
$356$	−5046.89	+	8741.48i	−0.0398221	+	0.0689739i
$357$	−331.835	+	1238.42i	−0.00260367	+	0.00971702i
$358$	−13654.6	−	50959.6i	−0.106540	−	0.397613i
$359$	−139913.	−	80778.9i	−1.08560	−	0.626772i	−0.153198	−	0.988195i	$-0.548957\pi$
$359$	−139913.	−	80778.9i	−1.08560	−	0.626772i	−0.932402	+	0.361424i	$0.882291\pi$
$360$	84201.6	−	16050.8i	0.649704	−	0.123849i
$361$	−112995.	−	64928.1i	−0.867053	−	0.498217i
$362$	107156.	+	107156.i	0.817711	+	0.817711i
$363$	12062.1	+	45016.4i	0.0915398	+	0.341631i
$364$	4645.77	+	2682.24i	0.0350635	+	0.0202439i
$365$	48707.4	−	42031.9i	0.365603	−	0.315496i
$366$	25013.3	−	43324.3i	0.186728	−	0.323422i
$367$	−28985.9	+	108177.i	−0.215206	+	0.803161i	0.770887	+	0.636972i	$0.219813\pi$
$367$	−28985.9	+	108177.i	−0.215206	+	0.803161i	−0.986094	+	0.166190i	$0.946854\pi$
$368$	48578.1	−	48578.1i	0.358711	−	0.358711i
$369$			226071.i			1.66032i
$370$	23883.3	−	324644.i	0.174458	−	2.37139i
$371$	−6276.04	−	10870.4i	−0.0455971	−	0.0789766i
$372$	515.449	+	515.449i	0.00372478	+	0.00372478i
$373$	−127084.	+	127084.i	−0.913423	+	0.913423i	−0.996540	−	0.0831168i	$-0.973513\pi$
$373$	−127084.	+	127084.i	−0.913423	+	0.913423i	0.0831168	+	0.996540i	$0.473513\pi$
$374$	−474956.	+	274216.i	−3.39555	+	1.96042i
$375$	−812.066	−	19559.8i	−0.00577469	−	0.139092i
$376$	39160.3	+	67827.6i	0.276994	+	0.479767i
$377$	−67059.9	+	17968.7i	−0.471825	+	0.126425i
$378$	−860.153	−	3210.13i	−0.00601994	−	0.0224667i
$379$		−	34874.4i		−	0.242789i	−0.992604	−	0.121394i	$-0.961263\pi$
$379$		−	34874.4i		−	0.242789i	0.992604	−	0.121394i	$-0.0387366\pi$
$380$	156461.	−	135298.i	1.08352	−	0.936970i
$381$	6634.92			0.0457073
$382$	140570.	−	37665.6i	0.963310	−	0.258118i
$383$	49378.3	+	184282.i	0.336619	+	1.25628i	0.902103	+	0.431520i	$0.142023\pi$
$383$	49378.3	+	184282.i	0.336619	+	1.25628i	−0.565485	+	0.824759i	$0.691311\pi$
$384$	−21738.3	+	12550.6i	−0.147423	+	0.0851145i
$385$	4962.97	−	14245.7i	0.0334827	−	0.0961085i
$386$	10383.7	+	17985.1i	0.0696910	+	0.120708i
$387$	−60777.1	−	60777.1i	−0.405805	−	0.405805i
$388$	67232.4	−	67232.4i	0.446597	−	0.446597i
$389$	115638.	−	66763.7i	0.764191	−	0.441206i	−0.0666074	−	0.997779i	$-0.521218\pi$
$389$	115638.	−	66763.7i	0.764191	−	0.441206i	0.830798	+	0.556573i	$0.187884\pi$
$390$	13065.2	−	11274.6i	0.0858985	−	0.0741259i
$391$	272300.			1.78113
$392$	−73071.8	−	73071.8i	−0.475530	−	0.475530i
$393$	−14811.4	−	3968.69i	−0.0958981	−	0.0256958i
$394$	279306.	+	161257.i	1.79923	+	1.03879i
$395$	−10197.1	+	138608.i	−0.0653553	+	0.888370i
$396$	207244.	−	358957.i	1.32157	−	2.28903i
$397$	209892.	−	56240.3i	1.33172	−	0.356834i	0.478366	−	0.878161i	$-0.341229\pi$
$397$	209892.	−	56240.3i	1.33172	−	0.356834i	0.853357	+	0.521326i	$0.174563\pi$
$398$	−66396.9	+	66396.9i	−0.419162	+	0.419162i
$399$	−848.495	−	846.751i	−0.00532971	−	0.00531875i
$400$	−22398.0	−	56614.3i	−0.139987	−	0.353840i
$401$	32201.6	−	55774.8i	0.200257	−	0.346856i	−0.748354	−	0.663300i	$-0.769156\pi$
$401$	32201.6	−	55774.8i	0.200257	−	0.346856i	0.948611	+	0.316444i	$0.102489\pi$
$402$	−1466.04	+	392.824i	−0.00907179	+	0.00243078i
$403$	−2165.50	−	580.244i	−0.0133336	−	0.00357273i
$404$	174632.	+	100824.i	1.06995	+	0.617734i
$405$	154134.	+	11339.3i	0.939697	+	0.0691313i
$406$	−12997.6			−0.0788516
$407$	−336021.	−	336021.i	−2.02851	−	2.02851i
$408$	−20170.7	−	5404.73i	−0.121172	−	0.0324679i
$409$	33079.0	−	19098.1i	0.197745	−	0.114168i	−0.397858	−	0.917447i	$-0.630246\pi$
$409$	33079.0	−	19098.1i	0.197745	−	0.114168i	0.595603	+	0.803279i	$0.296913\pi$
$410$	−436045.	+	83120.5i	−2.59396	+	0.494471i
$411$	34219.7			0.202578
$412$	−33098.6	+	123526.i	−0.194991	+	0.727717i
$413$	2083.52	+	7775.82i	0.0122151	+	0.0455875i
$414$	−302644.	+	174732.i	−1.76576	+	1.01946i
$415$	153231.	+	53383.3i	0.889714	+	0.309962i
$416$	57333.1	−	99303.9i	0.331298	−	0.573825i
$417$	7831.85	+	7831.85i	0.0450394	+	0.0450394i
$418$	−527.677	−	512760.i	−0.00302006	−	2.93469i
$419$			132362.i			0.753936i	0.926226	+	0.376968i	$0.123033\pi$
$419$			132362.i			0.753936i	−0.926226	+	0.376968i	$0.876967\pi$
$420$	1713.07	−	827.854i	0.00971130	−	0.00469305i
$421$	123326.	−	213606.i	0.695807	−	1.20517i	−0.274101	−	0.961701i	$-0.588380\pi$
$421$	123326.	−	213606.i	0.695807	−	1.20517i	0.969908	−	0.243472i	$-0.0782864\pi$
$422$	−131686.	+	491459.i	−0.739460	+	2.75970i
$423$	37300.3	+	139207.i	0.208464	+	0.778000i
$424$	177051.	−	102220.i	0.984842	−	0.568599i
$425$	95898.4	−	221448.i	0.530925	−	1.22601i
$426$	−46087.2			−0.253958
$427$	−4390.27	+	16384.7i	−0.0240788	+	0.0898633i
$428$	173239.	+	46419.2i	0.945709	+	0.253402i
$429$		−	25192.7i		−	0.136886i
$430$	94880.3	−	139573.i	0.513144	−	0.754855i
$431$	98737.3	+	171018.i	0.531529	+	0.920635i	0.999323	+	0.0367971i	$0.0117155\pi$
$431$	98737.3	+	171018.i	0.531529	+	0.920635i	−0.467794	+	0.883837i	$0.654951\pi$
$432$	−18913.4	+	5067.83i	−0.101345	+	0.0271553i
$433$	199571.	+	53474.9i	1.06444	+	0.285216i	0.748208	−	0.663465i	$-0.230915\pi$
$433$	199571.	+	53474.9i	1.06444	+	0.285216i	0.316234	+	0.948681i	$0.397581\pi$
$434$	−363.487	−	209.859i	−0.00192979	−	0.00111416i
$435$	−8100.80	+	23252.5i	−0.0428104	+	0.122883i
$436$	357944.			1.88297
$437$	−127068.	+	220612.i	−0.665384	+	1.15522i
$438$	14223.2	−	14223.2i	0.0741395	−	0.0741395i
$439$	−266020.	−	153587.i	−1.38034	−	0.796939i	−0.388140	−	0.921600i	$-0.626882\pi$
$439$	−266020.	−	153587.i	−1.38034	−	0.796939i	−0.992199	+	0.124661i	$0.960216\pi$
$440$	232025.	+	80833.9i	1.19848	+	0.417531i
$441$	−95077.0	−	164678.i	−0.488876	−	0.846758i
$442$	205482.	−	55058.8i	1.05179	−	0.281827i
$443$	104563.	+	28017.6i	0.532808	+	0.142765i	0.515185	−	0.857079i	$-0.327723\pi$
$443$	104563.	+	28017.6i	0.532808	+	0.142765i	0.0176232	+	0.999845i	$0.494390\pi$
$444$		−	59934.3i		−	0.304025i
$445$	−9105.46	−	6189.81i	−0.0459814	−	0.0312577i
$446$	115593.	+	200213.i	0.581114	+	1.00652i
$447$	1010.78	−	3772.29i	0.00505875	−	0.0188795i
$448$	12258.8	−	12258.8i	0.0610790	−	0.0610790i
$449$		−	68207.3i		−	0.338328i	−0.985588	−	0.169164i	$-0.945893\pi$
$449$		−	68207.3i		−	0.338328i	0.985588	−	0.169164i	$-0.0541068\pi$
$450$	35515.7	+	307662.i	0.175386	+	1.51932i
$451$	−324006.	+	561196.i	−1.59294	+	2.75906i
$452$	−5947.68	+	22197.0i	−0.0291119	+	0.108647i
$453$	−645.585	−	2409.36i	−0.00314599	−	0.0117410i
$454$	219196.	+	126553.i	1.06346	+	0.613988i
$455$	−3289.66	+	4839.21i	−0.0158901	+	0.0233750i
$456$	13791.4	−	13819.8i	0.0663251	−	0.0664617i
$457$	−188915.	−	188915.i	−0.904554	−	0.904554i	0.0912716	−	0.995826i	$-0.470907\pi$
$457$	−188915.	−	188915.i	−0.904554	−	0.904554i	−0.995826	+	0.0912716i	$0.970907\pi$
$458$	−638.713	−	2383.71i	−0.00304491	−	0.0113638i
$459$	−67212.4	−	38805.1i	−0.319025	−	0.184189i
$460$	−263998.	−	305926.i	−1.24763	−	1.44578i
$461$	119434.	−	206866.i	0.561987	−	0.973390i	−0.435336	−	0.900268i	$-0.643370\pi$
$461$	119434.	−	206866.i	0.561987	−	0.973390i	0.997323	−	0.0731222i	$-0.0232963\pi$
$462$	1220.71	−	4555.77i	0.00571913	−	0.0213441i
$463$	−150954.	+	150954.i	−0.704177	+	0.704177i	−0.965304	−	0.261127i	$-0.915906\pi$
$463$	−150954.	+	150954.i	−0.704177	+	0.704177i	0.261127	+	0.965304i	$0.415906\pi$
$464$			76578.9i			0.355691i
$465$	−601.980	+	519.477i	−0.00278404	+	0.00240248i
$466$	−82802.0	−	143417.i	−0.381302	−	0.660434i
$467$	−180998.	−	180998.i	−0.829925	−	0.829925i	0.157581	−	0.987506i	$-0.449631\pi$
$467$	−180998.	−	180998.i	−0.829925	−	0.829925i	−0.987506	+	0.157581i	$0.949631\pi$
$468$	−113685.	+	113685.i	−0.519055	+	0.519055i
$469$	445.682	−	257.315i	0.00202619	−	0.00116982i
$470$	−254787.	+	123127.i	−1.15340	+	0.557390i
$471$	−5005.08	−	8669.06i	−0.0225616	−	0.0390778i
$472$	−126648.	+	33935.2i	−0.568478	+	0.152323i
$473$	−63766.1	−	237978.i	−0.285015	−	1.06369i
$474$			43453.0i			0.193403i
$475$	134662.	+	181033.i	0.596840	+	0.802360i
$476$	23453.6			0.103513
$477$	363372.	−	97365.3i	1.59704	−	0.427925i
$478$	2533.53	+	9455.27i	0.0110884	+	0.0413826i
$479$	38764.8	−	22380.9i	0.168953	−	0.0975453i	−0.413139	−	0.910668i	$-0.635568\pi$
$479$	38764.8	−	22380.9i	0.168953	−	0.0975453i	0.582092	+	0.813123i	$0.302234\pi$
$480$	−17695.5	−	36617.1i	−0.0768033	−	0.158929i
$481$	92163.5	+	159632.i	0.398354	+	0.689969i
$482$	95044.0	+	95044.0i	0.409101	+	0.409101i
$483$	−1655.88	+	1655.88i	−0.00709798	+	0.00709798i
$484$	738315.	−	426266.i	3.15174	−	1.81966i
$485$	67757.7	+	78519.0i	0.288055	+	0.333804i
$486$	149892.			0.634607
$487$	−284067.	−	284067.i	−1.19774	−	1.19774i	−0.974841	−	0.222902i	$-0.928447\pi$
$487$	−284067.	−	284067.i	−1.19774	−	1.19774i	−0.222902	−	0.974841i	$-0.571553\pi$
$488$	−266864.	−	71506.0i	−1.12060	−	0.300264i
$489$	−17837.4	−	10298.4i	−0.0745956	−	0.0430678i
$490$	282673.	−	243932.i	1.17731	−	1.01596i
$491$	100256.	−	173648.i	0.415859	−	0.720289i	−0.579659	−	0.814859i	$-0.696814\pi$
$491$	100256.	−	173648.i	0.415859	−	0.720289i	0.995518	+	0.0945702i	$0.0301477\pi$
$492$	−78944.5	+	21153.1i	−0.326131	+	0.0873864i
$493$	−214628.	+	214628.i	−0.883066	+	0.883066i
$494$	−51279.9	+	192170.i	−0.210133	+	0.787466i
$495$	373903.	+	254176.i	1.52598	+	1.03735i
$496$	−1236.44	+	2141.58i	−0.00502587	+	0.00870506i
$497$	15094.5	−	4044.55i	0.0611089	−	0.0163741i
$498$	49003.3	+	13130.4i	0.197591	+	0.0529443i
$499$	197387.	+	113962.i	0.792717	+	0.457676i	0.840918	−	0.541162i	$-0.182015\pi$
$499$	197387.	+	113962.i	0.792717	+	0.457676i	−0.0482010	+	0.998838i	$0.515349\pi$
$500$	−341769.	+	106956.i	−1.36708	+	0.427824i
$501$	−35257.1			−0.140466
$502$	−45990.3	−	45990.3i	−0.182498	−	0.182498i
$503$	−299406.	−	80225.7i	−1.18338	−	0.317086i	−0.387115	−	0.922031i	$-0.626528\pi$
$503$	−299406.	−	80225.7i	−1.18338	−	0.317086i	−0.796267	+	0.604945i	$0.793195\pi$
$504$	−7869.64	+	4543.54i	−0.0309809	+	0.0178868i
$505$	−123657.	+	181904.i	−0.484880	+	0.713278i
$506$	−1.00171e6			−3.91236
$507$	6732.45	−	25125.8i	0.0261913	−	0.0977473i
$508$	−31413.5	−	117237.i	−0.121727	−	0.454293i
$509$	−186533.	+	107695.i	−0.719978	+	0.415680i	−0.814745	−	0.579820i	$-0.803123\pi$
$509$	−186533.	+	107695.i	−0.719978	+	0.415680i	0.0947664	+	0.995500i	$0.469790\pi$
$510$	24822.1	−	71249.3i	0.0954330	−	0.273930i
$511$	−3410.17	+	5906.59i	−0.0130597	+	0.0226201i
$512$	−137010.	−	137010.i	−0.522652	−	0.522652i
$513$	62803.4	−	36345.8i	0.238643	−	0.138108i
$514$		−	31474.4i		−	0.119133i
$515$	−131728.	−	45891.9i	−0.496664	−	0.173030i
$516$	15536.7	−	26910.3i	0.0583524	−	0.101069i
$517$	−106918.	+	399024.i	−0.400010	+	1.49286i
$518$	8931.58	+	33333.1i	0.0332866	+	0.124227i
$519$	−6697.57	+	3866.84i	−0.0248647	+	0.0143556i
$520$	−78818.3	−	53580.0i	−0.291488	−	0.198151i
$521$	164775.			0.607037			0.303519	−	0.952826i	$-0.401839\pi$
$521$	164775.			0.607037			0.303519	+	0.952826i	$0.401839\pi$
$522$	100821.	−	376269.i	0.370007	−	1.38089i
$523$	−453126.	−	121415.i	−1.65659	−	0.443882i	−0.695143	−	0.718871i	$-0.744659\pi$
$523$	−453126.	−	121415.i	−1.65659	−	0.443882i	−0.961447	+	0.274989i	$0.911326\pi$
$524$			280502.i			1.02158i
$525$	763.479	+	1929.81i	0.00276999	+	0.00700158i
$526$	14032.2	+	24304.5i	0.0507172	+	0.0878447i
$527$	−9467.62	+	2536.84i	−0.0340894	+	0.00913423i
$528$	−26841.6	−	7192.19i	−0.0962810	−	0.0257984i
$529$	188372.	+	108757.i	0.673140	+	0.388638i
$530$	321401.	+	665072.i	1.14418	+	2.36765i
$531$	−241265.			−0.855669
$532$	−10944.5	+	19001.6i	−0.0386700	+	0.0671378i
$533$	177736.	−	177736.i	0.625637	−	0.625637i
$534$	−2981.15	−	1721.17i	−0.0104544	−	0.00603588i
$535$	−64361.1	+	184742.i	−0.224862	+	0.645442i
$536$	4190.99	+	7259.01i	0.0145877	+	0.0252667i
$537$	10234.4	−	2742.29i	0.0354905	−	0.00950966i
$538$	−435643.	−	116730.i	−1.50510	−	0.403291i
$539$		−	545060.i		−	1.87615i
$540$	21566.1	+	113134.i	0.0739579	+	0.387978i
$541$	−199915.	−	346263.i	−0.683048	−	1.18307i	−0.974046	−	0.226350i	$-0.927321\pi$
$541$	−199915.	−	346263.i	−0.683048	−	1.18307i	0.290998	−	0.956724i	$-0.406013\pi$
$542$	−192282.	+	717605.i	−0.654545	+	2.44279i
$543$	−21520.5	+	21520.5i	−0.0729881	+	0.0729881i
$544$		−	501324.i		−	1.69403i
$545$	−28646.3	+	389387.i	−0.0964441	+	1.31096i
$546$	−914.736	+	1584.37i	−0.00306839	+	0.00531461i
$547$	88695.2	−	331015.i	0.296432	−	1.10630i	−0.643641	−	0.765328i	$-0.722577\pi$
$547$	88695.2	−	331015.i	0.296432	−	1.10630i	0.940073	−	0.340973i	$-0.110756\pi$
$548$	−162015.	−	604649.i	−0.539504	−	2.01346i
$549$	−440269.	−	254189.i	−1.46074	−	0.843359i
$550$	−352780.	+	814637.i	−1.16621	+	2.69302i
$551$	−73731.8	−	274042.i	−0.242858	−	0.902640i
$552$	−26970.0	−	26970.0i	−0.0885121	−	0.0885121i
$553$	−3813.38	−	14231.7i	−0.0124698	−	0.0465379i
$554$	−110101.	−	63567.0i	−0.358734	−	0.207115i
$555$	65199.1	+	4796.55i	0.211668	+	0.0155719i
$556$	101306.	−	175466.i	0.327706	−	0.567603i
$557$	−99297.1	+	370582.i	−0.320056	+	1.19447i	0.599133	+	0.800649i	$0.295512\pi$
$557$	−99297.1	+	370582.i	−0.320056	+	1.19447i	−0.919189	+	0.393816i	$0.871155\pi$
$558$	8894.78	−	8894.78i	0.0285672	−	0.0285672i
$559$			95565.6i			0.305828i
$560$	4216.79	+	4886.50i	0.0134464	+	0.0155820i
$561$	−55071.5	−	95386.7i	−0.174985	−	0.303083i
$562$	−182289.	−	182289.i	−0.577148	−	0.577148i
$563$	353136.	−	353136.i	1.11410	−	1.11410i	0.121514	−	0.992590i	$-0.461225\pi$
$563$	353136.	−	353136.i	1.11410	−	1.11410i	0.992590	−	0.121514i	$-0.0387748\pi$
$564$	−45121.1	+	26050.7i	−0.141848	+	0.0818957i
$565$	−23670.9	−	8246.57i	−0.0741512	−	0.0258331i
$566$	−106805.	−	184992.i	−0.333395	−	0.577457i
$567$	−15825.8	+	4240.52i	−0.0492267	+	0.0131903i
$568$	65875.2	+	245850.i	0.204186	+	0.762031i
$569$			217664.i			0.672297i	0.941809	+	0.336149i	$0.109124\pi$
$569$			217664.i			0.672297i	−0.941809	+	0.336149i	$0.890876\pi$
$570$	46141.5	+	53358.5i	0.142017	+	0.164230i
$571$	−217816.			−0.668064			−0.334032	−	0.942562i	$-0.608409\pi$
$571$	−217816.			−0.668064			−0.334032	+	0.942562i	$0.608409\pi$
$572$	−445146.	+	119277.i	−1.36054	+	0.364555i
$573$	7564.50	+	28231.1i	0.0230394	+	0.0859842i
$574$	40753.5	−	23529.1i	0.123692	−	0.0714136i
$575$	353928.	−	262706.i	1.07048	−	0.794573i
$576$	259792.	+	449973.i	0.783034	+	1.35625i
$577$	93758.0	+	93758.0i	0.281616	+	0.281616i	0.833753	−	0.552137i	$-0.186188\pi$
$577$	93758.0	+	93758.0i	0.281616	+	0.281616i	−0.552137	+	0.833753i	$0.686188\pi$
$578$	289218.	−	289218.i	0.865703	−	0.865703i
$579$	−3611.99	+	2085.39i	−0.0107743	+	0.00622056i
$580$	449217.	+	33047.8i	1.33537	+	0.0982397i
$581$	−17201.8			−0.0509592
$582$	22928.6	+	22928.6i	0.0676911	+	0.0676911i
$583$	1.04158e6	+	279089.i	3.06446	+	0.821119i
$584$	−96203.0	−	55542.8i	−0.282074	−	0.162855i
$585$	−114574.	−	132770.i	−0.334791	−	0.387962i
$586$	110803.	−	191917.i	0.322669	−	0.558879i
$587$	302535.	−	81064.1i	0.878010	−	0.235262i	0.208462	−	0.978030i	$-0.433154\pi$
$587$	302535.	−	81064.1i	0.878010	−	0.235262i	0.669549	+	0.742768i	$0.266488\pi$
$588$	48609.8	−	48609.8i	0.140595	−	0.140595i
$589$	2362.73	−	8854.26i	0.00681057	−	0.0255224i
$590$	−88707.1	−	465351.i	−0.254832	−	1.33683i
$591$	−32385.8	+	56093.8i	−0.0927213	+	0.160598i
$592$	196392.	−	52623.0i	0.560376	−	0.150152i
$593$	−252660.	−	67700.1i	−0.718501	−	0.192522i	−0.118998	−	0.992894i	$-0.537968\pi$
$593$	−252660.	−	67700.1i	−0.718501	−	0.192522i	−0.599503	+	0.800373i	$0.704635\pi$
$594$	247253.	+	142752.i	0.700759	+	0.404583i
$595$	−1877.00	+	25513.9i	−0.00530187	+	0.0720680i
$596$	−71440.7			−0.201119
$597$	−13334.7	−	13334.7i	−0.0374140	−	0.0374140i
$598$	375312.	+	100564.i	1.04952	+	0.281217i
$599$	−350588.	+	202412.i	−0.977110	+	0.564135i	−0.901396	−	0.432995i	$-0.857457\pi$
$599$	−350588.	+	202412.i	−0.977110	+	0.564135i	−0.0757139	+	0.997130i	$0.524124\pi$
$600$	−31431.6	+	12435.1i	−0.0873100	+	0.0345419i
$601$	−112456.			−0.311339			−0.155670	−	0.987809i	$-0.549754\pi$
$601$	−112456.			−0.311339			−0.155670	+	0.987809i	$0.549754\pi$
$602$	−4630.64	+	17281.8i	−0.0127776	+	0.0476865i
$603$	3991.94	+	14898.1i	0.0109786	+	0.0409729i
$604$	−39515.9	+	22814.5i	−0.108317	+	0.0625371i
$605$	404624.	+	837285.i	1.10545	+	2.28751i
$606$	−34384.5	+	59555.7i	−0.0936305	+	0.162173i
$607$	351929.	+	351929.i	0.955164	+	0.955164i	0.999037	−	0.0438728i	$-0.0139696\pi$
$607$	351929.	+	351929.i	0.955164	+	0.955164i	−0.0438728	+	0.999037i	$0.513970\pi$
$608$	406161.	+	233940.i	1.09873	+	0.632846i
$609$		−	2610.34i		−	0.00703822i
$610$	328403.	−	942647.i	0.882568	−	2.53332i
$611$	80118.6	−	138769.i	0.214610	−	0.371716i
$612$	−181928.	+	678963.i	−0.485731	+	1.81277i
$613$	132492.	+	494466.i	0.352588	+	1.31588i	0.883493	+	0.468445i	$0.155186\pi$
$613$	132492.	+	494466.i	0.352588	+	1.31588i	−0.530904	+	0.847432i	$0.678148\pi$
$614$	739609.	−	427013.i	1.96185	−	1.13267i
$615$	−16693.3	−	87572.1i	−0.0441360	−	0.231534i
$616$	−26047.3			−0.0686439
$617$	140329.	−	523716.i	0.368619	−	1.37571i	−0.493829	−	0.869559i	$-0.664403\pi$
$617$	140329.	−	523716.i	0.368619	−	1.37571i	0.862448	−	0.506146i	$-0.168930\pi$
$618$	−42126.5	−	11287.8i	−0.110301	−	0.0295550i
$619$			109763.i			0.286467i	0.989689	+	0.143234i	$0.0457500\pi$
$619$			109763.i			0.286467i	−0.989689	+	0.143234i	$0.954250\pi$
$620$	12029.1	+	8177.27i	0.0312931	+	0.0212728i
$621$	−70877.2	−	122763.i	−0.183791	−	0.318335i
$622$	−17938.7	+	4806.66i	−0.0463671	+	0.0124240i
$623$	1127.43	+	302.094i	0.00290478	+	0.000778334i
$624$	9334.76	+	5389.43i	0.0239736	+	0.0138412i
$625$	−88999.5	−	380351.i	−0.227839	−	0.973699i
$626$	609203.			1.55458
$627$	102979.	−	105.975i	0.261947	−	0.000269568i
$628$	−129482.	+	129482.i	−0.328315	+	0.328315i
$629$	697915.	+	402941.i	1.76401	+	1.01845i
$630$	−14285.8	−	29561.4i	−0.0359934	−	0.0744808i
$631$	210950.	+	365376.i	0.529811	+	0.917659i	0.999395	+	0.0347714i	$0.0110703\pi$
$631$	210950.	+	365376.i	0.529811	+	0.917659i	−0.469585	+	0.882887i	$0.655596\pi$
$632$	231798.	−	62110.0i	0.580330	−	0.155499i
$633$	−98701.1	−	26446.9i	−0.246329	−	0.0660035i
$634$		−	880958.i		−	2.19168i
$635$	130049.	−	24790.5i	0.322523	−	0.0614805i
$636$	68000.4	+	117780.i	0.168111	+	0.291177i
$637$	−54720.3	+	204219.i	−0.134856	+	0.503289i
$638$	789549.	−	789549.i	1.93971	−	1.93971i
$639$			468345.i			1.14700i
$640$	−379193.	+	327224.i	−0.925765	+	0.798887i
$641$	−102724.	+	177924.i	−0.250010	+	0.433030i	−0.963528	−	0.267607i	$-0.913767\pi$
$641$	−102724.	+	177924.i	−0.250010	+	0.433030i	0.713518	+	0.700637i	$0.247101\pi$
$642$	−15830.5	+	59080.4i	−0.0384084	+	0.143342i
$643$	−138853.	−	518207.i	−0.335841	−	1.25338i	−0.902954	−	0.429736i	$-0.858606\pi$
$643$	−138853.	−	518207.i	−0.335841	−	1.25338i	0.567113	−	0.823640i	$-0.308060\pi$
$644$	37098.7	+	21418.9i	0.0894513	+	0.0516447i
$645$	28030.8	+	19055.1i	0.0673777	+	0.0458028i
$646$	225926.	+	839709.i	0.541378	+	2.01217i
$647$	136323.	+	136323.i	0.325658	+	0.325658i	0.850933	−	0.525275i	$-0.176037\pi$
$647$	136323.	+	136323.i	0.325658	+	0.325658i	−0.525275	+	0.850933i	$0.676037\pi$
$648$	−69067.1	−	257762.i	−0.164483	−	0.613859i
$649$	−598914.	−	345783.i	−1.42192	−	0.820945i
$650$	213961.	−	269806.i	0.506416	−	0.638593i
$651$	42.1466	−	73.0001i	9.94491e−5	−	0.000172251i
$652$	−97517.0	+	363938.i	−0.229396	+	0.856116i
$653$	37504.1	−	37504.1i	0.0879533	−	0.0879533i	−0.661761	−	0.749715i	$-0.730191\pi$
$653$	37504.1	−	37504.1i	0.0879533	−	0.0879533i	0.749715	+	0.661761i	$0.230191\pi$
$654$			122071.i			0.285403i
$655$	−305142.	−	22448.6i	−0.711245	−	0.0523246i
$656$	−138628.	−	240111.i	−0.322139	−	0.557962i
$657$	−144539.	−	144539.i	−0.334852	−	0.334852i
$658$	21212.5	−	21212.5i	0.0489936	−	0.0489936i
$659$	−666590.	+	384856.i	−1.53493	+	0.886190i	−0.535803	+	0.844343i	$0.679991\pi$
$659$	−666590.	+	384856.i	−1.53493	+	0.886190i	−0.999124	+	0.0418472i	$0.986676\pi$
$660$	−53773.4	+	154351.i	−0.123447	+	0.354341i
$661$	264693.	+	458462.i	0.605814	+	1.04930i	0.991922	+	0.126847i	$0.0404858\pi$
$661$	264693.	+	458462.i	0.605814	+	1.04930i	−0.386108	+	0.922454i	$0.626181\pi$
$662$	730789.	−	195814.i	1.66754	−	0.446816i
$663$	11057.6	+	41267.6i	0.0251556	+	0.0938819i
$664$		−	280173.i		−	0.635463i
$665$	−19794.9	−	13426.6i	−0.0447620	−	0.0303615i
$666$	−1.03425e6			−2.33172
$667$	−535505.	+	143488.i	−1.20368	+	0.322526i
$668$	166927.	+	622980.i	0.374088	+	1.39612i
$669$	−40209.3	+	23214.9i	−0.0898410	+	0.0518697i
$670$	−27267.7	+	13177.3i	−0.0607433	+	0.0293546i
$671$	−728611.	−	1.26199e6i	−1.61827	−	2.80293i
$672$	3048.59	+	3048.59i	0.00675088	+	0.00675088i
$673$	−12595.4	+	12595.4i	−0.0278088	+	0.0278088i	−0.720874	−	0.693066i	$-0.756260\pi$
$673$	−12595.4	+	12595.4i	−0.0278088	+	0.0278088i	0.693066	+	0.720874i	$0.256260\pi$
$674$	−542736.	+	313349.i	−1.19473	+	0.689776i
$675$	−124798.	+	14406.4i	−0.273906	+	0.0316190i
$676$	−475840.			−1.04128
$677$	128844.	+	128844.i	0.281118	+	0.281118i	0.833555	−	0.552437i	$-0.186302\pi$
$677$	128844.	+	128844.i	0.281118	+	0.281118i	−0.552437	+	0.833555i	$0.686302\pi$
$678$	−7569.96	−	2028.36i	−0.0164677	−	0.00441252i
$679$	−9521.74	−	5497.38i	−0.0206527	−	0.0119238i
$680$	−415555.	−	30571.4i	−0.898691	−	0.0661146i
$681$	−25416.0	+	44021.7i	−0.0548040	+	0.0949233i
$682$	34828.4	−	9332.23i	0.0748797	−	0.0200640i
$683$	−181159.	+	181159.i	−0.388345	+	0.388345i	−0.874097	−	0.485752i	$-0.838546\pi$
$683$	−181159.	+	181159.i	−0.388345	+	0.388345i	0.485752	+	0.874097i	$0.338546\pi$
$684$	−465185.	−	464229.i	−0.994292	−	0.992247i
$685$	670730.	−	127857.i	1.42944	−	0.272486i
$686$	−39639.9	+	68658.3i	−0.0842333	+	0.145896i
$687$	478.728	−	128.275i	0.00101432	−	0.000271786i
$688$	101820.	+	27282.7i	0.215109	+	0.0576383i
$689$	−362231.	−	209134.i	−0.763040	−	0.440541i
$690$	104331.	−	90032.6i	0.219138	−	0.189104i
$691$	689230.			1.44347			0.721736	−	0.692168i	$-0.243344\pi$
$691$	689230.			1.44347			0.721736	+	0.692168i	$0.243344\pi$
$692$	100036.	+	100036.i	0.208902	+	0.208902i
$693$	−46296.4	−	12405.1i	−0.0964009	−	0.0258305i
$694$	685217.	−	395610.i	1.42269	−	0.821388i
$695$	182773.	+	124247.i	0.378391	+	0.257227i
$696$	42515.7			0.0877669
$697$	284427.	−	1.06149e6i	0.585470	−	2.18500i
$698$	−147999.	−	552340.i	−0.303772	−	1.13369i
$699$	28802.9	−	16629.4i	0.0589498	−	0.0340347i
$700$	30484.3	−	22627.2i	0.0622129	−	0.0461780i
$701$	90311.2	−	156424.i	0.183783	−	0.318322i	−0.759383	−	0.650644i	$-0.774499\pi$
$701$	90311.2	−	156424.i	0.183783	−	0.318322i	0.943166	+	0.332323i	$0.107832\pi$
$702$	−78307.6	−	78307.6i	−0.158902	−	0.158902i
$703$	−652133.	+	377404.i	−1.31955	+	0.763653i
$704$			1.48934e6i			3.00503i
$705$	−24728.0	−	51169.6i	−0.0497521	−	0.102952i
$706$	350261.	−	606669.i	0.702719	−	1.21715i
$707$	6035.07	−	22523.2i	0.0120738	−	0.0450600i
$708$	−22574.8	−	84250.4i	−0.0450358	−	0.168076i
$709$	−103895.	+	59983.6i	−0.206681	+	0.119327i	−0.599768	−	0.800174i	$-0.704740\pi$
$709$	−103895.	+	59983.6i	−0.206681	+	0.119327i	0.393087	+	0.919501i	$0.371407\pi$
$710$	−903343.	+	172199.i	−1.79199	+	0.341596i
$711$	441577.			0.873508
$712$	−4920.33	+	18362.9i	−0.00970586	+	0.0362228i
$713$	−17292.5	−	4633.52i	−0.0340157	−	0.00911449i
$714$			7998.50i			0.0156896i
$715$	−94129.1	−	493795.i	−0.184125	−	0.965905i
$716$	−96910.6	−	167854.i	−0.189036	−	0.327421i
$717$	−1898.93	+	508.817i	−0.00369378	+	0.000989745i
$718$	−973541.	−	260860.i	−1.88845	−	0.506009i
$719$	21566.7	+	12451.5i	0.0417182	+	0.0240860i	0.520714	−	0.853731i	$-0.325666\pi$
$719$	21566.7	+	12451.5i	0.0417182	+	0.0240860i	−0.478996	+	0.877817i	$0.658999\pi$
$720$	−174170.	+	84168.6i	−0.335975	+	0.162362i
$721$	14787.9			0.0284469
$722$	−785741.	−	208806.i	−1.50732	−	0.400561i
$723$	−19088.0	+	19088.0i	−0.0365160	+	0.0365160i
$724$	482149.	+	278369.i	0.919823	+	0.531060i
$725$	−71901.7	+	486033.i	−0.136793	+	0.924676i
$726$	145372.	+	251791.i	0.275808	+	0.477713i
$727$	−416205.	+	111522.i	−0.787478	+	0.211004i	−0.630079	−	0.776531i	$-0.716978\pi$
$727$	−416205.	+	111522.i	−0.787478	+	0.211004i	−0.157399	+	0.987535i	$0.550311\pi$
$728$	9759.21	+	2614.97i	0.0184142	+	0.00493406i
$729$		−	470640.i		−	0.885592i
$730$	225642.	−	331928.i	0.423423	−	0.622872i
$731$	208908.	+	361838.i	0.390948	+	0.677142i
$732$	47568.2	−	177527.i	0.0887757	−	0.331316i
$733$	50544.6	−	50544.6i	0.0940734	−	0.0940734i	−0.658504	−	0.752577i	$-0.728810\pi$
$733$	50544.6	−	50544.6i	0.0940734	−	0.0940734i	0.752577	+	0.658504i	$0.228810\pi$
$734$			698673.i			1.29683i
$735$	48989.6	+	56770.1i	0.0906837	+	0.105086i
$736$	457832.	−	792988.i	0.845182	−	1.46390i
$737$	−11442.5	+	42704.1i	−0.0210663	+	0.0786203i
$738$	365026.	+	1.36229e6i	0.670210	+	2.50126i
$739$	250765.	+	144779.i	0.459175	+	0.265105i	0.711697	−	0.702486i	$-0.247927\pi$
$739$	250765.	+	144779.i	0.459175	+	0.265105i	−0.252522	+	0.967591i	$0.581260\pi$
$740$	−223936.	−	1.17476e6i	−0.408942	−	2.14528i
$741$	−38594.1	−	10298.7i	−0.0702885	−	0.0187562i
$742$	−55371.1	−	55371.1i	−0.100572	−	0.100572i
$743$	158734.	+	592404.i	0.287536	+	1.07310i	0.946966	+	0.321334i	$0.104131\pi$
$743$	158734.	+	592404.i	0.287536	+	1.07310i	−0.659430	+	0.751766i	$0.729202\pi$
$744$	1188.98	+	686.459i	0.00214798	+	0.00124013i
$745$	5717.40	−	77716.3i	0.0103012	−	0.140023i
$746$	−560605.	+	970997.i	−1.00735	+	1.74478i
$747$	133433.	−	497979.i	0.239123	−	0.892421i
$748$	−1.42471e6	+	1.42471e6i	−2.54638	+	2.54638i
$749$		−	20739.2i		−	0.0369683i
$750$	−36475.7	−	116555.i	−0.0648456	−	0.207209i
$751$	−3019.57	−	5230.04i	−0.00535383	−	0.00927311i	0.863336	−	0.504629i	$-0.168371\pi$
$751$	−3019.57	−	5230.04i	−0.00535383	−	0.00927311i	−0.868690	+	0.495356i	$0.835038\pi$
$752$	−124979.	−	124979.i	−0.221005	−	0.221005i
$753$	9236.36	−	9236.36i	0.0162896	−	0.0162896i
$754$	−375088.	+	216557.i	−0.659766	+	0.380916i
$755$	−21656.2	−	44813.0i	−0.0379916	−	0.0786158i
$756$	−6104.76	−	10573.8i	−0.0106813	−	0.0185006i
$757$	−433868.	+	116254.i	−0.757121	+	0.202870i	−0.616675	−	0.787218i	$-0.711521\pi$
$757$	−433868.	+	116254.i	−0.757121	+	0.202870i	−0.140447	+	0.990088i	$0.544854\pi$
$758$	−56310.0	−	210152.i	−0.0980048	−	0.365759i
$759$		−	201176.i		−	0.349214i
$760$	218685.	−	322407.i	0.378610	−	0.558184i
$761$	185456.			0.320237			0.160119	−	0.987098i	$-0.448812\pi$
$761$	185456.			0.320237			0.160119	+	0.987098i	$0.448812\pi$
$762$	39981.8	−	10713.1i	0.0688577	−	0.0184504i
$763$	−10712.8	−	39980.8i	−0.0184016	−	0.0686755i
$764$	463019.	−	267324.i	0.793253	−	0.457985i
$765$	−724046.	−	252246.i	−1.23721	−	0.431024i
$766$	595103.	+	1.03075e6i	1.01423	+	1.75669i
$767$	189682.	+	189682.i	0.322430	+	0.322430i
$768$	−18005.6	+	18005.6i	−0.0305270	+	0.0305270i
$769$	−167854.	+	96910.7i	−0.283844	+	0.163877i	−0.635162	−	0.772379i	$-0.719067\pi$
$769$	−167854.	+	96910.7i	−0.283844	+	0.163877i	0.351318	+	0.936256i	$0.385733\pi$
$770$	6904.86	−	93857.4i	0.0116459	−	0.158302i
$771$	6321.09			0.0106337
$772$	53949.2	+	53949.2i	0.0905213	+	0.0905213i
$773$	−866837.	−	232268.i	−1.45070	−	0.388714i	−0.554434	−	0.832228i	$-0.687065\pi$
$773$	−866837.	−	232268.i	−1.45070	−	0.388714i	−0.896268	+	0.443513i	$0.853732\pi$
$774$	−464374.	−	268106.i	−0.775150	−	0.447533i
$775$	−9858.28	+	12431.3i	−0.0164134	+	0.0206973i
$776$	89538.0	−	155084.i	0.148691	−	0.257540i
$777$	−6694.39	+	1793.76i	−0.0110884	+	0.00297113i
$778$	589031.	−	589031.i	0.973148	−	0.973148i
$779$	727273.	+	725778.i	1.19846	+	1.19599i
$780$	35643.2	−	52432.5i	0.0585851	−	0.0861810i
$781$	−671236.	+	1.16261e6i	−1.10046	+	1.90605i
$782$	1.64087e6	−	439670.i	2.68325	−	0.718974i
$783$	152628.	+	40896.6i	0.248949	+	0.0667057i
$784$	201964.	+	116604.i	0.328580	+	0.189706i
$785$	−130494.	−	151219.i	−0.211764	−	0.245396i
$786$	−95660.8			−0.154842
$787$	546629.	+	546629.i	0.882558	+	0.882558i	0.993794	−	0.111236i	$-0.0354810\pi$
$787$	546629.	+	546629.i	0.882558	+	0.882558i	−0.111236	+	0.993794i	$0.535481\pi$
$788$	1.14449e6	+	306665.i	1.84315	+	0.493870i
$789$	−4881.15	+	2818.13i	−0.00784094	+	0.00452697i
$790$	162356.	+	851711.i	0.260145	+	1.36470i
$791$	2657.31			0.00424708
$792$	202047.	−	754049.i	0.322108	−	1.20212i
$793$	146295.	+	545981.i	0.232640	+	0.868223i
$794$	1.17399e6	−	677803.i	1.86219	−	1.07513i
$795$	−133568.	+	64547.8i	−0.211334	+	0.102129i
$796$	−172485.	+	298753.i	−0.272223	+	0.471505i
$797$	−38973.5	−	38973.5i	−0.0613555	−	0.0613555i	0.675763	−	0.737119i	$-0.263814\pi$
$797$	−38973.5	−	38973.5i	−0.0613555	−	0.0613555i	−0.737119	+	0.675763i	$0.763814\pi$
$798$	−6480.21	−	3732.46i	−0.0101761	−	0.00586124i
$799$		−	700561.i		−	1.09737i
$800$	−483659.	−	651605.i	−0.755717	−	1.01813i
$801$	−17490.8	+	30294.9i	−0.0272611	+	0.0472176i
$802$	103989.	−	388091.i	0.161673	−	0.603371i
$803$	−151647.	−	565954.i	−0.235181	−	0.877708i
$804$	−4828.93	+	2787.99i	−0.00747032	+	0.00431299i
$805$	−26269.5	+	38643.4i	−0.0405377	+	0.0596326i
$806$	−13986.1			−0.0215292
$807$	23443.3	−	87491.4i	0.0359974	−	0.134344i
$808$	366844.	+	98295.6i	0.561900	+	0.150561i
$809$		−	578058.i		−	0.883232i	−0.897204	−	0.441616i	$-0.854405\pi$
$809$		−	578058.i		−	0.883232i	0.897204	−	0.441616i	$-0.145595\pi$
$810$	947113.	−	180542.i	1.44355	−	0.275175i
$811$	−260850.	−	451806.i	−0.396597	−	0.686927i	0.596706	−	0.802460i	$-0.296476\pi$
$811$	−260850.	−	451806.i	−0.396597	−	0.686927i	−0.993304	+	0.115533i	$0.963142\pi$
$812$	−46123.8	+	12358.8i	−0.0699541	+	0.0187441i
$813$	−144119.	−	38616.5i	−0.218042	−	0.0584241i
$814$	−2.56740e6	−	1.48229e6i	−3.87477	−	2.23710i
$815$	−388104.	−	135209.i	−0.584296	−	0.203559i
$816$	47125.4			0.0707742
$817$	−390639.	+	402.004i	−0.585237	+	0.000602263i
$818$	168496.	−	168496.i	0.251815	−	0.251815i
$819$	16100.6	+	9295.69i	0.0240035	+	0.0138584i
$820$	−1.46833e6	+	709581.i	−2.18372	+	1.05530i
$821$	405241.	+	701897.i	0.601211	+	1.04133i	0.992638	+	0.121119i	$0.0386481\pi$
$821$	405241.	+	701897.i	0.601211	+	1.04133i	−0.391427	+	0.920209i	$0.628019\pi$
$822$	206206.	−	55252.8i	0.305182	−	0.0817732i
$823$	−412986.	−	110659.i	−0.609728	−	0.163376i	−0.0592741	−	0.998242i	$-0.518879\pi$
$823$	−412986.	−	110659.i	−0.609728	−	0.163376i	−0.550454	+	0.834866i	$0.685545\pi$
$824$			240856.i			0.354734i
$825$	−163606.	−	70849.7i	−0.240376	−	0.104095i
$826$	25110.5	+	43492.6i	0.0368040	+	0.0637464i
$827$	−58526.2	+	218423.i	−0.0855735	+	0.319365i	−0.995422	−	0.0955755i	$-0.969531\pi$
$827$	−58526.2	+	218423.i	−0.0855735	+	0.319365i	0.909849	+	0.414940i	$0.136198\pi$
$828$	−907832.	+	907832.i	−1.32417	+	1.32417i
$829$			249096.i			0.362458i	0.983441	+	0.181229i	$0.0580075\pi$
$829$			249096.i			0.362458i	−0.983441	+	0.181229i	$0.941993\pi$
$830$	1.00956e6	+	74270.9i	1.46547	+	0.107811i
$831$	12766.3	−	22111.9i	0.0184869	−	0.0320203i
$832$	149520.	−	558015.i	0.215999	−	0.806119i
$833$	239239.	+	892850.i	0.344779	+	1.28673i
$834$	59840.1	+	34548.7i	0.0860321	+	0.0496707i
$835$	−691064.	+	131733.i	−0.991164	+	0.188940i
$836$	−489434.	−	1.81910e6i	−0.700296	−	2.60282i
$837$	3608.03	+	3608.03i	0.00515015	+	0.00515015i
$838$	213718.	+	797606.i	0.304336	+	1.13580i
$839$	−470779.	−	271804.i	−0.668795	−	0.386129i	0.126825	−	0.991925i	$-0.459521\pi$
$839$	−470779.	−	271804.i	−0.668795	−	0.386129i	−0.795620	+	0.605796i	$0.792855\pi$
$840$	2712.93	−	2341.11i	0.00384485	−	0.00331791i
$841$	−44651.1	+	77337.9i	−0.0631306	+	0.109345i
$842$	398255.	−	1.48631e6i	0.561743	−	2.09645i
$843$	36609.6	−	36609.6i	0.0515157	−	0.0515157i
$844$			1.86923e6i			2.62408i
$845$	38081.5	−	517639.i	0.0533336	−	0.724960i
$846$	449541.	+	778627.i	0.628099	+	1.08790i
$847$	−69708.8	−	69708.8i	−0.0971675	−	0.0971675i
$848$	−326234.	+	326234.i	−0.453668	+	0.453668i
$849$	37152.5	−	21450.0i	0.0515433	−	0.0297585i
$850$	220318.	−	1.48928e6i	0.304939	−	2.06129i
$851$	735969.	+	1.27474e6i	1.01625	+	1.76020i
$852$	−163547.	+	43822.4i	−0.225301	+	0.0603693i
$853$	75210.4	+	280689.i	0.103367	+	0.385769i	0.998155	−	0.0607217i	$-0.0193402\pi$
$853$	75210.4	+	280689.i	0.103367	+	0.385769i	−0.894788	+	0.446491i	$0.852674\pi$
$854$			105822.i			0.145098i
$855$	542237.	−	468897.i	0.741749	−	0.641423i
$856$	337789.			0.460996
$857$	−273606.	+	73312.5i	−0.372532	+	0.0998197i	−0.440227	−	0.897886i	$-0.645102\pi$
$857$	−273606.	+	73312.5i	−0.372532	+	0.0998197i	0.0676952	+	0.997706i	$0.478435\pi$
$858$	−40677.4	−	151810.i	−0.0552559	−	0.206218i
$859$	580198.	−	334978.i	0.786303	−	0.453973i	−0.0523561	−	0.998628i	$-0.516673\pi$
$859$	580198.	−	334978.i	0.786303	−	0.453973i	0.838660	+	0.544656i	$0.183340\pi$
$860$	203983.	−	585512.i	0.275802	−	0.791660i
$861$	4725.41	+	8184.65i	0.00637431	+	0.0110406i
$862$	871122.	+	871122.i	1.17237	+	1.17237i
$863$	808434.	−	808434.i	1.08548	−	1.08548i	0.0894960	−	0.995987i	$-0.471474\pi$
$863$	808434.	−	808434.i	1.08548	−	1.08548i	0.995987	−	0.0894960i	$-0.0285256\pi$
$864$	−226015.	+	130490.i	−0.302768	+	0.174803i
$865$	−116829.	+	100817.i	−0.156142	+	0.134742i
$866$	1.28895e6			1.71870
$867$	58084.4	+	58084.4i	0.0772719	+	0.0772719i
$868$	−1489.43	−	399.092i	−0.00197688	−	0.000529704i
$869$	1.09616e6	+	632870.i	1.45156	+	0.838060i
$870$	−11270.5	+	153199.i	−0.0148903	+	0.202403i
$871$	8574.41	−	14851.3i	0.0113023	−	0.0195762i
$872$	651183.	−	174484.i	0.856387	−	0.229468i
$873$	233004.	−	233004.i	0.305728	−	0.305728i
$874$	−409494.	+	1.53457e6i	−0.536074	+	2.00892i
$875$	22175.2	+	34973.0i	0.0289635	+	0.0456790i
$876$	36948.9	−	63997.4i	0.0481497	−	0.0833977i
$877$	−567266.	+	151998.i	−0.737543	+	0.197624i	−0.607986	−	0.793948i	$-0.708022\pi$
$877$	−567266.	+	151998.i	−0.737543	+	0.197624i	−0.129557	+	0.991572i	$0.541356\pi$
$878$	−1.85102e6	−	495979.i	−2.40116	−	0.643390i
$879$	38543.2	+	22253.0i	0.0498851	+	0.0288012i
$880$	−552987.	−	40682.0i	−0.714085	−	0.0525335i
$881$	266262.			0.343050			0.171525	−	0.985180i	$-0.445131\pi$
$881$	266262.			0.343050			0.171525	+	0.985180i	$0.445131\pi$
$882$	−838829.	−	838829.i	−1.07829	−	1.07829i
$883$	−1.40620e6	−	376791.i	−1.80355	−	0.483259i	−0.809023	−	0.587777i	$-0.800003\pi$
$883$	−1.40620e6	−	376791.i	−1.80355	−	0.483259i	−0.994523	+	0.104519i	$0.966670\pi$
$884$	676830.	−	390768.i	0.866115	−	0.500052i
$885$	93457.9	−	17815.3i	0.119324	−	0.0227461i
$886$	675331.			0.860299
$887$	158763.	−	592512.i	0.201791	−	0.753095i	−0.788612	−	0.614891i	$-0.789200\pi$
$887$	158763.	−	592512.i	0.201791	−	0.753095i	0.990404	−	0.138205i	$-0.0441332\pi$
$888$	−29215.6	−	109034.i	−0.0370501	−	0.138273i
$889$	−12154.6	+	7017.49i	−0.0153794	+	0.00887929i
$890$	−64863.5	−	22597.4i	−0.0818880	−	0.0285285i
$891$	703760.	−	1.21895e6i	0.886480	−	1.53543i
$892$	600572.	+	600572.i	0.754806	+	0.754806i
$893$	567579.	+	326913.i	0.711743	+	0.409949i
$894$		−	24363.8i		−	0.0304838i
$895$	190355.	−	91990.2i	0.237639	−	0.114841i
$896$	26548.6	−	45983.5i	0.0330694	−	0.0572778i
$897$	−20196.7	+	75374.9i	−0.0251012	+	0.0936790i
$898$	−110131.	−	411015.i	−0.136571	−	0.509688i
$899$	17282.2	−	9977.89i	0.0213836	−	0.0123458i
$900$	418575.	+	1.05801e6i	0.516760	+	1.30619i
$901$	−1.82868e6			−2.25262
$902$	−1.04631e6	+	3.90490e6i	−1.28602	+	4.79951i
$903$	−3470.75	−	929.985i	−0.00425645	−	0.00114051i
$904$			43280.8i			0.0529612i
$905$	−341408.	+	502225.i	−0.416847	+	0.613199i
$906$	−7780.54	−	13476.3i	−0.00947880	−	0.0164178i
$907$	970082.	−	259933.i	1.17922	−	0.315970i	0.384601	−	0.923083i	$-0.374339\pi$
$907$	970082.	−	259933.i	1.17922	−	0.315970i	0.794616	+	0.607112i	$0.207672\pi$
$908$	898182.	+	240667.i	1.08941	+	0.291907i
$909$	605214.	+	349421.i	0.732456	+	0.422883i
$910$	−12009.7	+	34472.6i	−0.0145027	+	0.0416285i
$911$	575.497			0.000693436			0.000346718	−	1.00000i	$-0.499890\pi$
$911$	575.497			0.000693436			0.000346718		1.00000i	$0.499890\pi$
$912$	−21990.9	+	38180.0i	−0.0264395	+	0.0459035i
$913$	1.04494e6	−	1.04494e6i	1.25357	−	1.25357i
$914$	−1.44343e6	−	833364.i	−1.72784	−	0.997567i
$915$	189315.	+	65954.2i	0.226121	+	0.0787772i
$916$	−4533.13	−	7851.62i	−0.00540266	−	0.00935768i
$917$	31330.8	−	8395.05i	0.0372591	−	0.00998354i
$918$	−467676.	−	125313.i	−0.554958	−	0.148700i
$919$			32778.9i			0.0388118i	0.999812	+	0.0194059i	$0.00617747\pi$
$919$			32778.9i			0.0388118i	−0.999812	+	0.0194059i	$0.993823\pi$
$920$	−629401.	−	427861.i	−0.743621	−	0.505507i
$921$	85758.3	+	148538.i	0.101101	+	0.175113i
$922$	385689.	−	1.43941e6i	0.453707	−	1.69326i
$923$	368212.	−	368212.i	0.432210	−	0.432210i
$924$		−	17327.5i		−	0.0202952i
$925$	1.29587e6	−	149592.i	1.51453	−	0.174834i
$926$	−665904.	+	1.15338e6i	−0.776586	+	1.34509i
$927$	−114708.	+	428096.i	−0.133486	+	0.498175i
$928$	264172.	+	985902.i	0.306754	+	1.14482i
$929$	−795967.	−	459552.i	−0.922281	−	0.532479i	−0.0379193	−	0.999281i	$-0.512073\pi$
$929$	−795967.	−	459552.i	−0.922281	−	0.532479i	−0.884362	+	0.466801i	$0.845406\pi$
$930$	−2788.73	+	4102.33i	−0.00322434	+	0.00474313i
$931$	−835007.	−	222819.i	−0.963365	−	0.257071i
$932$	−430204.	−	430204.i	−0.495271	−	0.495271i
$933$	−965.335	−	3602.68i	−0.00110896	−	0.00413869i
$934$	−1.38293e6	−	798436.i	−1.58528	−	0.915264i
$935$	−1.43584e6	−	1.66388e6i	−1.64242	−	1.90326i
$936$	−151403.	+	262237.i	−0.172815	+	0.299325i
$937$	−403015.	+	1.50407e6i	−0.459031	+	1.71313i	0.216929	+	0.976187i	$0.430396\pi$
$937$	−403015.	+	1.50407e6i	−0.459031	+	1.71313i	−0.675960	+	0.736939i	$0.736271\pi$
$938$	2270.19	−	2270.19i	0.00258022	−	0.00258022i
$939$			122348.i			0.138761i
$940$	−787072.	+	679202.i	−0.890756	+	0.768675i
$941$	−603298.	−	1.04494e6i	−0.681322	−	1.18009i	−0.974577	−	0.224051i	$-0.928072\pi$
$941$	−603298.	−	1.04494e6i	−0.681322	−	1.18009i	0.293255	−	0.956034i	$-0.405261\pi$
$942$	−44158.0	−	44158.0i	−0.0497631	−	0.0497631i
$943$	1.41931e6	−	1.41931e6i	1.59608	−	1.59608i
$944$	256249.	−	147945.i	0.287553	−	0.166019i
$945$	11991.2	−	5794.80i	0.0134276	−	0.00648896i
$946$	−768504.	−	1.33109e6i	−0.858744	−	1.48739i
$947$	108517.	−	29077.1i	0.121004	−	0.0324229i	−0.197809	−	0.980241i	$-0.563383\pi$
$947$	108517.	−	29077.1i	0.121004	−	0.0324229i	0.318813	+	0.947818i	$0.396716\pi$
$948$	41317.6	+	154199.i	0.0459747	+	0.171580i
$949$			227272.i			0.252356i
$950$	1.10377e6	+	873463.i	1.22302	+	0.967826i
$951$	176925.			0.195627
$952$	42667.5	−	11432.7i	0.0470786	−	0.0126147i
$953$	−8459.82	−	31572.5i	−0.00931484	−	0.0347635i	0.961112	−	0.276159i	$-0.0890616\pi$
$953$	−8459.82	−	31572.5i	−0.00931484	−	0.0347635i	−0.970427	+	0.241395i	$0.922395\pi$
$954$	2.03246e6	−	1.17344e6i	2.23318	−	1.28933i
$955$	253751.	+	525086.i	0.278228	+	0.575736i
$956$	17981.2	+	31144.4i	0.0196745	+	0.0340772i
$957$	158567.	+	158567.i	0.173137	+	0.173137i
$958$	197458.	−	197458.i	0.215151	−	0.215151i
$959$	−62687.7	+	36192.7i	−0.0681624	+	0.0393536i
$960$	−133861.	−	155121.i	−0.145248	−	0.168317i
$961$	−922877.			−0.999302
$962$	813124.	+	813124.i	0.878631	+	0.878631i
$963$	600384.	+	160872.i	0.647406	+	0.173472i
$964$	427651.	+	246904.i	0.460188	+	0.265690i
$965$	−63005.9	+	54370.8i	−0.0676592	+	0.0583863i
$966$	−7304.60	+	12651.9i	−0.00782784	+	0.0135582i
$967$	663103.	−	177678.i	0.709134	−	0.190012i	0.113816	−	0.993502i	$-0.463693\pi$
$967$	663103.	−	177678.i	0.709134	−	0.190012i	0.595318	+	0.803490i	$0.297026\pi$
$968$	1.13538e6	−	1.13538e6i	1.21168	−	1.21168i
$969$	−168641.	+	45373.3i	−0.179604	+	0.0483229i
$970$	535086.	+	363747.i	0.568696	+	0.386595i
$971$	50465.3	−	87408.5i	0.0535248	−	0.0927076i	−0.838022	−	0.545637i	$-0.816288\pi$
$971$	50465.3	−	87408.5i	0.0535248	−	0.0927076i	0.891546	+	0.452929i	$0.149621\pi$
$972$	531913.	−	142526.i	0.562999	−	0.150855i
$973$	−22630.8	−	6063.89i	−0.0239042	−	0.00640510i
$974$	−2.17045e6	−	1.25311e6i	−2.28787	−	1.32090i
$975$	54185.8	+	42970.4i	0.0570002	+	0.0452022i
$976$	623482.			0.654522
$977$	−65504.3	−	65504.3i	−0.0686247	−	0.0686247i	0.671961	−	0.740586i	$-0.265452\pi$
$977$	−65504.3	−	65504.3i	−0.0686247	−	0.0686247i	−0.740586	+	0.671961i	$0.765452\pi$
$978$	−124116.	−	33256.7i	−0.129762	−	0.0347697i
$979$	−86837.6	+	50135.7i	−0.0906030	+	0.0523097i
$980$	771163.	−	1.13441e6i	0.802960	−	1.18119i
$981$	1.24051e6			1.28903
$982$	323756.	−	1.20827e6i	0.335734	−	1.25297i
$983$	160866.	+	600362.i	0.166479	+	0.621307i	0.997847	+	0.0655850i	$0.0208913\pi$
$983$	160866.	+	600362.i	0.166479	+	0.621307i	−0.831368	+	0.555722i	$0.812442\pi$
$984$	−133307.	+	76964.7i	−0.137677	+	0.0794880i
$985$	−425198.	+	1.22048e6i	−0.438246	+	1.25794i
$986$	−946792.	+	1.63989e6i	−0.973869	+	1.68679i
$987$	4260.16	+	4260.16i	0.00437313	+	0.00437313i
$988$	751.961	+	730703.i	0.000770338	+	0.748561i
$989$			763136.i			0.780206i
$990$	2.66353e6	+	927934.i	2.71761	+	0.946774i
$991$	253126.	−	438427.i	0.257745	−	0.446427i	−0.707893	−	0.706320i	$-0.750354\pi$
$991$	253126.	−	438427.i	0.257745	−	0.446427i	0.965637	+	0.259893i	$0.0836873\pi$
$992$	−8530.63	+	31836.8i	−0.00866878	+	0.0323523i
$993$	39326.0	+	146767.i	0.0398824	+	0.148843i
$994$	84428.1	−	48744.6i	0.0854504	−	0.0493348i
$995$	−311193.	−	211546.i	−0.314328	−	0.213677i
$996$	186380.			0.187880
$997$	−251771.	+	939623.i	−0.253289	+	0.945286i	0.715746	+	0.698361i	$0.246087\pi$
$997$	−251771.	+	939623.i	−0.253289	+	0.945286i	−0.969035	+	0.246925i	$0.920580\pi$
$998$	1.37346e6	+	368017.i	1.37897	+	0.369493i
$999$		−	419527.i		−	0.420368i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.5.m.a.87.33	yes	152
5.3	odd	4	inner	95.5.m.a.68.6	yes	152
19.7	even	3	inner	95.5.m.a.7.6	✓	152
95.83	odd	12	inner	95.5.m.a.83.33	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.5.m.a.7.6	✓	152	19.7	even	3	inner
95.5.m.a.68.6	yes	152	5.3	odd	4	inner
95.5.m.a.83.33	yes	152	95.83	odd	12	inner
95.5.m.a.87.33	yes	152	1.1	even	1	trivial

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+(6.02596 - 1.61465i) q^{2} +(0.324275 + 1.21021i) q^{3} +(19.8487 - 11.4597i) q^{4} +(10.8778 + 22.5094i) q^{5} +(3.90814 + 6.76910i) q^{6} +(-1.87404 - 1.87404i) q^{7} +(30.5232 - 30.5232i) q^{8} +(68.7886 - 39.7151i) q^{9} +(101.894 + 118.077i) q^{10} +227.680 q^{11} +(20.3050 + 20.3050i) q^{12} +(-85.3054 - 22.8575i) q^{13} +(-14.3188 - 8.26696i) q^{14} +(-23.7137 + 20.4637i) q^{15} +(-48.7071 + 84.3632i) q^{16} +(-372.957 + 99.9336i) q^{17} +(350.391 - 350.391i) q^{18} +(93.0748 - 348.795i) q^{19} +(473.860 + 322.126i) q^{20} +(1.66028 - 2.87569i) q^{21} +(1371.99 - 367.624i) q^{22} +(-681.203 - 182.528i) q^{23} +(46.8375 + 27.0416i) q^{24} +(-388.346 + 489.706i) q^{25} -550.954 q^{26} +(142.131 + 142.131i) q^{27} +(-58.6730 - 15.7214i) q^{28} +(680.797 - 393.058i) q^{29} +(-109.856 + 161.603i) q^{30} +25.3853 q^{31} +(-336.046 + 1254.14i) q^{32} +(73.8309 + 275.541i) q^{33} +(-2086.07 + 1204.39i) q^{34} +(21.7980 - 62.5689i) q^{35} +(910.243 - 1576.59i) q^{36} +(-1475.85 - 1475.85i) q^{37} +(-2.31763 - 2252.11i) q^{38} -110.650i q^{39} +(1019.09 + 355.033i) q^{40} +(-1423.08 + 2464.84i) q^{41} +(5.36154 - 20.0095i) q^{42} +(-280.069 - 1045.23i) q^{43} +(4519.15 - 2609.13i) q^{44} +(1642.23 + 1116.38i) q^{45} -4399.62 q^{46} +(-469.599 + 1752.57i) q^{47} +(-117.892 - 31.5890i) q^{48} -2393.98i q^{49} +(-1549.45 + 3577.99i) q^{50} +(-241.881 - 418.951i) q^{51} +(-1955.14 + 523.878i) q^{52} +(4574.74 + 1225.80i) q^{53} +(1085.97 + 626.984i) q^{54} +(2476.66 + 5124.94i) q^{55} -114.403 q^{56} +(452.298 - 0.465456i) q^{57} +(3467.80 - 3467.80i) q^{58} +(-2630.51 - 1518.72i) q^{59} +(-236.180 + 677.929i) q^{60} +(-3200.16 - 5542.83i) q^{61} +(152.971 - 40.9884i) q^{62} +(-203.340 - 54.4848i) q^{63} +6541.38i q^{64} +(-413.428 - 2168.81i) q^{65} +(889.805 + 1541.19i) q^{66} +(-50.2571 + 187.562i) q^{67} +(-6257.51 + 6257.51i) q^{68} -883.589i q^{69} +(30.3271 - 412.234i) q^{70} +(-2948.16 + 5106.36i) q^{71} +(887.416 - 3311.88i) q^{72} +(-666.053 - 2485.74i) q^{73} +(-11276.4 - 6510.42i) q^{74} +(-718.579 - 311.181i) q^{75} +(-2149.66 - 7989.74i) q^{76} +(-426.681 - 426.681i) q^{77} +(-178.661 - 666.771i) q^{78} +(4814.50 + 2779.65i) q^{79} +(-2428.79 - 178.681i) q^{80} +(3091.01 - 5353.78i) q^{81} +(-4595.55 + 17150.8i) q^{82} +(4589.51 - 4589.51i) q^{83} -76.1048i q^{84} +(-6306.40 - 7307.98i) q^{85} +(-3375.37 - 5846.31i) q^{86} +(696.449 + 696.449i) q^{87} +(6949.52 - 6949.52i) q^{88} +(-381.402 + 220.203i) q^{89} +(11698.6 + 4075.61i) q^{90} +(117.030 + 202.701i) q^{91} +(-15612.7 + 4183.41i) q^{92} +(8.23182 + 30.7216i) q^{93} +11319.1i q^{94} +(8863.62 - 1699.07i) q^{95} -1626.75 q^{96} +(4007.15 - 1073.71i) q^{97} +(-3865.44 - 14426.0i) q^{98} +(15661.8 - 9042.33i) 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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