LMFDB - Embedded newform 95.5.q.a.17.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	95.q (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.82014649297$
Analytic rank:	$0$
Dimension:	$456$
Relative dimension:	$38$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			17.20
Character	$\chi$	$=$	95.17
Dual form			95.5.q.a.28.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.470940 - 0.329756i) q^{2} +(-3.66462 + 0.320613i) q^{3} +(-5.35928 + 14.7245i) q^{4} +(24.1757 - 6.36689i) q^{5} +(-1.62009 + 1.35942i) q^{6} +(-0.0600223 + 0.224006i) q^{7} +(4.71236 + 17.5867i) q^{8} +(-66.4428 + 11.7157i) q^{9} +(9.28576 - 10.9705i) q^{10} +(11.3596 - 19.6754i) q^{11} +(14.9189 - 55.6779i) q^{12} +(-14.5970 + 166.845i) q^{13} +(0.0456004 + 0.125286i) q^{14} +(-86.5533 + 31.0833i) q^{15} +(-184.038 - 154.426i) q^{16} +(-353.403 + 247.455i) q^{17} +(-27.4273 + 27.4273i) q^{18} +(72.7400 + 353.596i) q^{19} +(-35.8148 + 390.096i) q^{20} +(0.148140 - 0.840142i) q^{21} +(-1.13839 - 13.0118i) q^{22} +(-737.093 + 343.712i) q^{23} +(-22.9075 - 62.9379i) q^{24} +(543.925 - 307.848i) q^{25} +(48.1437 + 83.3874i) q^{26} +(527.546 - 141.356i) q^{27} +(-2.97670 - 2.08431i) q^{28} +(142.868 - 25.1915i) q^{29} +(-30.5115 + 43.1798i) q^{30} +(580.013 + 1004.61i) q^{31} +(-427.799 - 37.4276i) q^{32} +(-35.3205 + 75.7450i) q^{33} +(-84.8317 + 233.073i) q^{34} +(-0.0248551 + 5.79766i) q^{35} +(183.578 - 1041.12i) q^{36} +(-1016.31 - 1016.31i) q^{37} +(150.856 + 142.536i) q^{38} -616.103i q^{39} +(225.897 + 395.168i) q^{40} +(-766.646 - 643.292i) q^{41} +(-0.207277 - 0.444506i) q^{42} +(716.732 - 1537.04i) q^{43} +(228.831 + 272.711i) q^{44} +(-1531.71 + 706.268i) q^{45} +(-233.785 + 404.928i) q^{46} +(-881.417 + 1258.79i) q^{47} +(723.939 + 506.908i) q^{48} +(2079.28 + 1200.47i) q^{49} +(154.642 - 324.340i) q^{50} +(1215.75 - 1020.13i) q^{51} +(-2378.48 - 1109.10i) q^{52} +(3889.98 - 1813.93i) q^{53} +(201.830 - 240.531i) q^{54} +(149.355 - 547.992i) q^{55} -4.22239 q^{56} +(-379.932 - 1272.47i) q^{57} +(58.9752 - 58.9752i) q^{58} +(-4242.27 - 748.027i) q^{59} +(6.17787 - 1441.04i) q^{60} +(5951.72 + 2166.25i) q^{61} +(604.427 + 281.849i) q^{62} +(1.36367 - 15.5868i) q^{63} +(3115.11 - 1798.51i) q^{64} +(709.391 + 4126.53i) q^{65} +(8.34352 + 47.3185i) q^{66} +(1082.90 - 1546.54i) q^{67} +(-1749.67 - 6529.86i) q^{68} +(2590.97 - 1495.89i) q^{69} +(1.90010 + 2.73854i) q^{70} +(374.200 - 136.198i) q^{71} +(-519.142 - 1113.30i) q^{72} +(5569.88 - 487.302i) q^{73} +(-813.757 - 143.487i) q^{74} +(-1894.58 + 1302.53i) q^{75} +(-5596.35 - 823.958i) q^{76} +(3.72559 + 3.72559i) q^{77} +(-203.164 - 290.148i) q^{78} +(-5820.48 + 6936.58i) q^{79} +(-5432.45 - 2561.60i) q^{80} +(3247.38 - 1181.95i) q^{81} +(-573.173 - 50.1461i) q^{82} +(-1255.12 - 336.308i) q^{83} +(11.5767 + 6.68383i) q^{84} +(-6968.22 + 8232.47i) q^{85} +(-169.309 - 960.198i) q^{86} +(-515.480 + 138.122i) q^{87} +(399.558 + 107.061i) q^{88} +(9187.05 + 10948.7i) q^{89} +(-488.446 + 837.698i) q^{90} +(-36.4982 - 13.2843i) q^{91} +(-1110.70 - 12695.4i) q^{92} +(-2447.62 - 3495.56i) q^{93} +883.469i q^{94} +(4009.84 + 8085.28i) q^{95} +1579.72 q^{96} +(-9414.90 + 6592.38i) q^{97} +(1375.08 - 120.304i) q^{98} +(-524.254 + 1440.38i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 456 q - 12 q^{2} - 12 q^{3} - 12 q^{5} + 84 q^{6} - 96 q^{7} - 6 q^{8} - 12 q^{10} - 12 q^{11} - 6 q^{12} - 12 q^{13} - 534 q^{15} + 4092 q^{16} - 1362 q^{17} - 3864 q^{18} - 2364 q^{20} - 4776 q^{21} + 2004 q^{22}+ \cdots + 123726 q^{98}+O(q^{100}) $ 456 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 + 84 * q^6 - 96 * q^7 - 6 * q^8 - 12 * q^10 - 12 * q^11 - 6 * q^12 - 12 * q^13 - 534 * q^15 + 4092 * q^16 - 1362 * q^17 - 3864 * q^18 - 2364 * q^20 - 4776 * q^21 + 2004 * q^22 + 1968 * q^23 + 3252 * q^25 + 7332 * q^26 - 6 * q^27 - 9648 * q^28 - 6 * q^30 - 12 * q^31 + 5922 * q^32 + 16494 * q^33 - 1794 * q^35 + 9048 * q^36 - 24 * q^37 - 15222 * q^38 - 9786 * q^40 - 5640 * q^41 + 7764 * q^42 - 19032 * q^43 - 6144 * q^45 - 12 * q^46 - 4332 * q^47 + 29328 * q^48 + 18426 * q^50 - 10944 * q^51 + 84 * q^52 + 1878 * q^53 + 27018 * q^55 - 48 * q^56 - 14202 * q^57 + 16536 * q^58 - 84108 * q^60 - 14688 * q^61 - 46536 * q^62 - 46098 * q^63 - 13236 * q^65 + 42408 * q^66 + 44748 * q^67 + 20154 * q^68 + 37620 * q^70 - 24 * q^71 + 82680 * q^72 - 10542 * q^73 + 90024 * q^75 - 21600 * q^76 + 20328 * q^77 + 63426 * q^78 - 32688 * q^80 + 41976 * q^81 - 184332 * q^82 - 43476 * q^83 - 51396 * q^85 + 11316 * q^86 - 59286 * q^87 - 1254 * q^88 - 9294 * q^90 - 33312 * q^91 + 163884 * q^92 - 106566 * q^93 - 11424 * q^95 - 200208 * q^96 + 12168 * q^97 + 123726 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	0.470940	−	0.329756i	0.117735	−	0.0824389i	−0.513226	−	0.858254i	$-0.671550\pi$
$2$	0.470940	−	0.329756i	0.117735	−	0.0824389i	0.630961	+	0.775815i	$0.282661\pi$
$3$	−3.66462	+	0.320613i	−0.407180	+	0.0356236i	−0.288906	−	0.957357i	$-0.593292\pi$
$3$	−3.66462	+	0.320613i	−0.407180	+	0.0356236i	−0.118274	+	0.992981i	$0.537736\pi$
$4$	−5.35928	+	14.7245i	−0.334955	+	0.920281i
$5$	24.1757	−	6.36689i	0.967027	−	0.254676i
$5$	24.1757	−	6.36689i	0.967027	−	0.254676i
$6$	−1.62009	+	1.35942i	−0.0450025	+	0.0377616i
$7$	−0.0600223	+	0.224006i	−0.00122494	+	0.00457156i	−0.966536	−	0.256533i	$-0.917420\pi$
$7$	−0.0600223	+	0.224006i	−0.00122494	+	0.00457156i	0.965311	+	0.261104i	$0.0840866\pi$
$8$	4.71236	+	17.5867i	0.0736306	+	0.274793i
$9$	−66.4428	+	11.7157i	−0.820281	+	0.144638i
$10$	9.28576	−	10.9705i	0.0928576	−	0.109705i
$11$	11.3596	−	19.6754i	0.0938811	−	0.162607i	−0.815260	−	0.579095i	$-0.803406\pi$
$11$	11.3596	−	19.6754i	0.0938811	−	0.162607i	0.909141	+	0.416488i	$0.136739\pi$
$12$	14.9189	−	55.6779i	0.103603	−	0.386652i
$13$	−14.5970	+	166.845i	−0.0863731	+	0.987249i	0.822110	+	0.569328i	$0.192797\pi$
$13$	−14.5970	+	166.845i	−0.0863731	+	0.987249i	−0.908484	+	0.417921i	$0.862759\pi$
$14$	0.0456004	+	0.125286i	0.000232655	+	0.000639215i
$15$	−86.5533	+	31.0833i	−0.384681	+	0.138148i
$16$	−184.038	−	154.426i	−0.718897	−	0.603226i
$17$	−353.403	+	247.455i	−1.22285	+	0.856247i	−0.993131	−	0.117011i	$-0.962669\pi$
$17$	−353.403	+	247.455i	−1.22285	+	0.856247i	−0.229716	+	0.973258i	$0.573780\pi$
$18$	−27.4273	+	27.4273i	−0.0846520	+	0.0846520i
$19$	72.7400	+	353.596i	0.201496	+	0.979489i
$19$	72.7400	+	353.596i	0.201496	+	0.979489i
$20$	−35.8148	+	390.096i	−0.0895370	+	0.975241i
$21$	0.148140	−	0.840142i	0.000335918	−	0.00190508i
$22$	−1.13839	−	13.0118i	−0.00235204	−	0.0268840i
$23$	−737.093	+	343.712i	−1.39337	+	0.649739i	−0.966992	−	0.254806i	$-0.917988\pi$
$23$	−737.093	+	343.712i	−1.39337	+	0.649739i	−0.426378	+	0.904545i	$0.640211\pi$
$24$	−22.9075	−	62.9379i	−0.0397700	−	0.109267i
$25$	543.925	−	307.848i	0.870281	−	0.492556i
$26$	48.1437	+	83.3874i	0.0712186	+	0.123354i
$27$	527.546	−	141.356i	0.723658	−	0.193903i
$28$	−2.97670	−	2.08431i	−0.00379681	−	0.00265856i
$29$	142.868	−	25.1915i	0.169879	−	0.0299542i	−0.0880617	−	0.996115i	$-0.528067\pi$
$29$	142.868	−	25.1915i	0.169879	−	0.0299542i	0.257940	+	0.966161i	$0.416956\pi$
$30$	−30.5115	+	43.1798i	−0.0339017	+	0.0479775i
$31$	580.013	+	1004.61i	0.603551	+	1.04538i	0.992279	+	0.124028i	$0.0395814\pi$
$31$	580.013	+	1004.61i	0.603551	+	1.04538i	−0.388728	+	0.921353i	$0.627085\pi$
$32$	−427.799	−	37.4276i	−0.417773	−	0.0365504i
$33$	−35.3205	+	75.7450i	−0.0324339	+	0.0695547i
$34$	−84.8317	+	233.073i	−0.0733838	+	0.201620i
$35$	−0.0248551	+	5.79766i	−2.02899e−5	+	0.00473278i
$36$	183.578	−	1041.12i	0.141650	−	0.803336i
$37$	−1016.31	−	1016.31i	−0.742376	−	0.742376i	0.230659	−	0.973035i	$-0.425912\pi$
$37$	−1016.31	−	1016.31i	−0.742376	−	0.742376i	−0.973035	+	0.230659i	$0.925912\pi$
$38$	150.856	+	142.536i	0.104471	+	0.0987091i
$39$		−	616.103i		−	0.405065i
$40$	225.897	+	395.168i	0.141186	+	0.246980i
$41$	−766.646	−	643.292i	−0.456065	−	0.382684i	0.385616	−	0.922660i	$-0.373989\pi$
$41$	−766.646	−	643.292i	−0.456065	−	0.382684i	−0.841681	+	0.539975i	$0.818434\pi$
$42$	−0.207277	−	0.444506i	−0.000117504	−	0.000251988i
$43$	716.732	−	1537.04i	0.387632	−	0.831280i	−0.611564	−	0.791195i	$-0.709459\pi$
$43$	716.732	−	1537.04i	0.387632	−	0.831280i	0.999196	−	0.0400849i	$-0.0127628\pi$
$44$	228.831	+	272.711i	0.118198	+	0.140863i
$45$	−1531.71	+	706.268i	−0.756398	+	0.348774i
$46$	−233.785	+	404.928i	−0.110485	+	0.191365i
$47$	−881.417	+	1258.79i	−0.399012	+	0.569848i	−0.967509	−	0.252837i	$-0.918636\pi$
$47$	−881.417	+	1258.79i	−0.399012	+	0.569848i	0.568497	+	0.822685i	$0.307525\pi$
$48$	723.939	+	506.908i	0.314210	+	0.220012i
$49$	2079.28	+	1200.47i	0.866006	+	0.499989i
$50$	154.642	−	324.340i	0.0618566	−	0.129736i
$51$	1215.75	−	1020.13i	0.467416	−	0.392209i
$52$	−2378.48	−	1109.10i	−0.879615	−	0.410171i
$53$	3889.98	−	1813.93i	1.38483	−	0.645756i	0.419731	−	0.907649i	$-0.362125\pi$
$53$	3889.98	−	1813.93i	1.38483	−	0.645756i	0.965097	+	0.261893i	$0.0843468\pi$
$54$	201.830	−	240.531i	0.0692146	−	0.0824868i
$55$	149.355	−	547.992i	0.0493735	−	0.181154i
$56$	−4.22239			−0.00134642
$57$	−379.932	−	1272.47i	−0.116938	−	0.391650i
$58$	58.9752	−	58.9752i	0.0175313	−	0.0175313i
$59$	−4242.27	−	748.027i	−1.21869	−	0.214888i	−0.472930	−	0.881100i	$-0.656804\pi$
$59$	−4242.27	−	748.027i	−1.21869	−	0.214888i	−0.745763	+	0.666211i	$0.767915\pi$
$60$	6.17787	−	1441.04i	0.00171607	−	0.400288i
$61$	5951.72	+	2166.25i	1.59949	+	0.582168i	0.979324	−	0.202300i	$-0.0648415\pi$
$61$	5951.72	+	2166.25i	1.59949	+	0.582168i	0.620170	+	0.784468i	$0.287064\pi$
$62$	604.427	+	281.849i	0.157239	+	0.0733218i
$63$	1.36367	−	15.5868i	0.000343580	−	0.00392714i
$64$	3115.11	−	1798.51i	0.760525	−	0.439089i
$65$	709.391	+	4126.53i	0.167903	+	0.976693i
$66$	8.34352	+	47.3185i	0.00191541	+	0.0108628i
$67$	1082.90	−	1546.54i	0.241235	−	0.344519i	−0.680218	−	0.733010i	$-0.738115\pi$
$67$	1082.90	−	1546.54i	0.241235	−	0.344519i	0.921452	+	0.388491i	$0.127004\pi$
$68$	−1749.67	−	6529.86i	−0.378389	−	1.41217i
$69$	2590.97	−	1495.89i	0.544206	−	0.314198i
$70$	1.90010	+	2.73854i	0.000387776	+	0.000558886i
$71$	374.200	−	136.198i	0.0742312	−	0.0270180i	−0.304638	−	0.952468i	$-0.598535\pi$
$71$	374.200	−	136.198i	0.0742312	−	0.0270180i	0.378869	+	0.925450i	$0.376313\pi$
$72$	−519.142	−	1113.30i	−0.100143	−	0.214758i
$73$	5569.88	−	487.302i	1.04520	−	0.0914434i	0.448401	−	0.893832i	$-0.351994\pi$
$73$	5569.88	−	487.302i	1.04520	−	0.0914434i	0.596801	+	0.802389i	$0.296438\pi$
$74$	−813.757	−	143.487i	−0.148604	−	0.0262029i
$75$	−1894.58	+	1302.53i	−0.336814	+	0.231562i
$76$	−5596.35	−	823.958i	−0.968897	−	0.142652i
$77$	3.72559	+	3.72559i	0.000628367	+	0.000628367i
$78$	−203.164	−	290.148i	−0.0333931	−	0.0476903i
$79$	−5820.48	+	6936.58i	−0.932620	+	1.11145i	0.0609392	+	0.998141i	$0.480590\pi$
$79$	−5820.48	+	6936.58i	−0.932620	+	1.11145i	−0.993559	+	0.113312i	$0.963854\pi$
$80$	−5432.45	−	2561.60i	−0.848820	−	0.400250i
$81$	3247.38	−	1181.95i	0.494952	−	0.180148i
$82$	−573.173	−	50.1461i	−0.0852429	−	0.00745779i
$83$	−1255.12	−	336.308i	−0.182192	−	0.0488181i	0.166570	−	0.986030i	$-0.446731\pi$
$83$	−1255.12	−	336.308i	−0.182192	−	0.0488181i	−0.348761	+	0.937212i	$0.613398\pi$
$84$	11.5767	+	6.68383i	0.00164069	+	0.000947255i
$85$	−6968.22	+	8232.47i	−0.964460	+	1.13944i
$86$	−169.309	−	960.198i	−0.0228919	−	0.129827i
$87$	−515.480	+	138.122i	−0.0681041	+	0.0182484i
$88$	399.558	+	107.061i	0.0515958	+	0.0138250i
$89$	9187.05	+	10948.7i	1.15983	+	1.38224i	0.910340	+	0.413861i	$0.135820\pi$
$89$	9187.05	+	10948.7i	1.15983	+	1.38224i	0.249494	+	0.968376i	$0.419736\pi$
$90$	−488.446	+	837.698i	−0.0603019	+	0.103420i
$91$	−36.4982	−	13.2843i	−0.00440746	−	0.00160418i
$92$	−1110.70	−	12695.4i	−0.131226	−	1.49992i
$93$	−2447.62	−	3495.56i	−0.282994	−	0.404158i
$94$			883.469i			0.0999851i
$95$	4009.84	+	8085.28i	0.444304	+	0.895876i
$96$	1579.72			0.171411
$97$	−9414.90	+	6592.38i	−1.00063	+	0.700647i	−0.954476	−	0.298288i	$-0.903584\pi$
$97$	−9414.90	+	6592.38i	−1.00063	+	0.700647i	−0.0461510	+	0.998934i	$0.514696\pi$
$98$	1375.08	−	120.304i	0.143178	−	0.0125264i
$99$	−524.254	+	1440.38i	−0.0534899	+	0.146962i
$100$	1617.85	+	9658.87i	0.161785	+	0.965887i
$101$	9566.06	−	8026.88i	0.937757	−	0.786872i	−0.0394363	−	0.999222i	$-0.512556\pi$
$101$	9566.06	−	8026.88i	0.937757	−	0.786872i	0.977194	+	0.212350i	$0.0681118\pi$
$102$	236.150	−	881.322i	0.0226980	−	0.0847099i
$103$	−907.507	−	3386.86i	−0.0855412	−	0.319244i	0.909875	−	0.414883i	$-0.136177\pi$
$103$	−907.507	−	3386.86i	−0.0855412	−	0.319244i	−0.995416	+	0.0956385i	$0.969511\pi$
$104$	−3003.05	+	529.518i	−0.277649	+	0.0489569i
$105$	−1.76772	−	21.2542i	−0.000160337	−	0.00192782i
$106$	1233.79	−	2136.99i	0.109807	−	0.190192i
$107$	−1336.01	+	4986.07i	−0.116693	+	0.435503i	−0.999408	−	0.0344055i	$-0.989046\pi$
$107$	−1336.01	+	4986.07i	−0.116693	+	0.435503i	0.882715	+	0.469908i	$0.155713\pi$
$108$	−745.877	+	8525.42i	−0.0639470	+	0.730917i
$109$	−1403.90	−	3857.19i	−0.118164	−	0.324652i	0.866484	−	0.499204i	$-0.166374\pi$
$109$	−1403.90	−	3857.19i	−0.118164	−	0.324652i	−0.984648	+	0.174552i	$0.944152\pi$
$110$	−110.366	−	307.322i	−0.00912118	−	0.0253985i
$111$	4050.24	+	3398.56i	0.328727	+	0.275834i
$112$	45.6387	−	31.9566i	0.00363829	−	0.00254756i
$113$	−9366.16	+	9366.16i	−0.733508	+	0.733508i	−0.971313	−	0.237805i	$-0.923572\pi$
$113$	−9366.16	+	9366.16i	−0.733508	+	0.733508i	0.237805	+	0.971313i	$0.423572\pi$
$114$	−598.530	−	473.973i	−0.0460549	−	0.0364707i
$115$	−15631.3	+	13002.5i	−1.18195	+	0.983172i
$116$	−394.737	+	2238.67i	−0.0293354	+	0.166369i
$117$	−984.830	−	11256.7i	−0.0719432	−	0.822314i
$118$	−2244.52	+	1046.64i	−0.161198	+	0.0751678i
$119$	−34.2195	−	94.0173i	−0.00241646	−	0.00663917i
$120$	−954.523	−	1375.72i	−0.0662863	−	0.0955358i
$121$	7062.42	+	12232.5i	0.482373	+	0.835494i
$122$	3517.23	−	942.439i	0.236310	−	0.0633190i
$123$	3015.71	+	2111.62i	0.199333	+	0.139575i
$124$	−17900.8	+	3156.40i	−1.16421	+	0.205281i
$125$	11189.7	−	10905.5i	0.716142	−	0.697954i
$126$	−4.49763	−	7.79012i	−0.000283297	−	0.000490685i
$127$	−23624.1	−	2066.84i	−1.46469	−	0.128144i	−0.673263	−	0.739403i	$-0.735108\pi$
$127$	−23624.1	−	2066.84i	−1.46469	−	0.128144i	−0.791431	+	0.611259i	$0.790664\pi$
$128$	3777.74	−	8101.40i	0.230575	−	0.494470i
$129$	−2133.76	+	5862.45i	−0.128223	+	0.352289i
$130$	1694.83	+	1709.42i	0.100286	+	0.101149i
$131$	1023.86	−	5806.58i	0.0596619	−	0.338359i	−0.940336	−	0.340246i	$-0.889490\pi$
$131$	1023.86	−	5806.58i	0.0596619	−	0.338359i	0.999998	+	0.00188701i	$0.000600655\pi$
$132$	−926.015	−	926.015i	−0.0531459	−	0.0531459i
$133$	−83.5737	−	4.92942i	−0.00472461	−	0.000278671i
$134$		−	1085.42i		−	0.0604490i
$135$	11853.8	−	6776.20i	0.650414	−	0.371808i
$136$	−6017.29	−	5049.11i	−0.325329	−	0.272984i
$137$	−2724.45	−	5842.59i	−0.145157	−	0.311289i	0.820265	−	0.571984i	$-0.193826\pi$
$137$	−2724.45	−	5842.59i	−0.145157	−	0.311289i	−0.965421	+	0.260695i	$0.916048\pi$
$138$	726.909	−	1558.86i	0.0381700	−	0.0818558i
$139$	−4491.83	−	5353.16i	−0.232485	−	0.277064i	0.637172	−	0.770722i	$-0.280104\pi$
$139$	−4491.83	−	5353.16i	−0.232485	−	0.277064i	−0.869656	+	0.493657i	$0.835660\pi$
$140$	−85.2343	−	31.4372i	−0.00434869	−	0.00160394i
$141$	2826.47	−	4895.60i	0.142170	−	0.246245i
$142$	131.314	−	187.535i	0.00651228	−	0.00930050i
$143$	3116.93	+	2182.50i	0.152425	+	0.106729i
$144$	14037.2	+	8104.37i	0.676947	+	0.390836i
$145$	3293.54	−	1518.65i	0.156649	−	0.0722305i
$146$	2462.39	−	2066.19i	0.115518	−	0.0969314i
$147$	−8004.66	−	3732.63i	−0.370432	−	0.172735i
$148$	20411.4	−	9517.98i	0.931856	−	0.434532i
$149$	17893.7	−	21324.9i	0.805986	−	0.960536i	−0.193804	−	0.981040i	$-0.562083\pi$
$149$	17893.7	−	21324.9i	0.805986	−	0.960536i	0.999790	+	0.0205038i	$0.00652701\pi$
$150$	−462.715	+	1238.16i	−0.0205651	+	0.0550295i
$151$	25211.7			1.10573			0.552863	−	0.833272i	$-0.313535\pi$
$151$	25211.7			1.10573			0.552863	+	0.833272i	$0.313535\pi$
$152$	−5875.82	+	2945.53i	−0.254321	+	0.127490i
$153$	20582.0	−	20582.0i	0.879233	−	0.879233i
$154$	2.98306	+	0.525995i	0.000125783	+	2.21789e-5i
$155$	20418.4	+	20594.3i	0.849883	+	0.857202i
$156$	9071.81	+	3301.87i	0.372773	+	0.135678i
$157$	−6126.66	−	2856.91i	−0.248556	−	0.115904i	0.294348	−	0.955698i	$-0.404898\pi$
$157$	−6126.66	−	2856.91i	−0.248556	−	0.115904i	−0.542904	+	0.839795i	$0.682675\pi$
$158$	−453.721	+	5186.05i	−0.0181750	+	0.207741i
$159$	−13673.7	+	7894.53i	−0.540870	+	0.312271i
$160$	−10580.6	+	1818.91i	−0.413306	+	0.0710514i
$161$	−32.7516	−	185.744i	−0.00126352	−	0.00716576i
$162$	1139.57	−	1627.47i	0.0434220	−	0.0620130i
$163$	277.370	+	1035.16i	0.0104396	+	0.0389611i	0.970949	−	0.239286i	$-0.0769133\pi$
$163$	277.370	+	1035.16i	0.0104396	+	0.0389611i	−0.960510	+	0.278247i	$0.910247\pi$
$164$	13580.8	−	7840.89i	0.504938	−	0.291526i
$165$	−371.636	+	2056.07i	−0.0136505	+	0.0755213i
$166$	−701.985	+	255.502i	−0.0254748	+	0.00927208i
$167$	−19769.0	−	42394.8i	−0.708847	−	1.52013i	−0.848080	−	0.529868i	$-0.822242\pi$
$167$	−19769.0	−	42394.8i	−0.708847	−	1.52013i	0.139233	−	0.990260i	$-0.455536\pi$
$168$	15.4734	−	1.35375i	0.000548237	−	4.79645e-5i
$169$	502.910	+	88.6767i	0.0176083	+	0.00310482i
$170$	−566.911	+	6174.81i	−0.0196163	+	0.213661i
$171$	−8975.65	−	22641.7i	−0.306954	−	0.774313i
$172$	18790.9	+	18790.9i	0.635171	+	0.635171i
$173$	−9288.41	−	13265.2i	−0.310348	−	0.443223i	0.633431	−	0.773799i	$-0.281646\pi$
$173$	−9288.41	−	13265.2i	−0.310348	−	0.443223i	−0.943779	+	0.330576i	$0.892757\pi$
$174$	−197.213	+	235.030i	−0.00651385	+	0.00776291i
$175$	36.3122	+	140.320i	0.00118570	+	0.00458189i
$176$	−5129.00	+	1866.80i	−0.165580	+	0.0602661i
$177$	15786.1	+	1381.11i	0.503883	+	0.0440840i
$178$	7936.94	+	2126.70i	0.250503	+	0.0671221i
$179$	20796.0	+	12006.6i	0.649044	+	0.374726i	0.788090	−	0.615560i	$-0.211070\pi$
$179$	20796.0	+	12006.6i	0.649044	+	0.374726i	−0.139046	+	0.990286i	$0.544404\pi$
$180$	−2190.60	−	26338.7i	−0.0676110	−	0.812922i
$181$	9706.07	+	55045.9i	0.296269	+	1.68023i	0.661999	+	0.749504i	$0.269708\pi$
$181$	9706.07	+	55045.9i	0.296269	+	1.68023i	−0.365730	+	0.930721i	$0.619181\pi$
$182$	−21.5690	+	5.77940i	−0.000651159	+	0.000174478i
$183$	−22505.3	−	6030.28i	−0.672021	−	0.180067i
$184$	−9518.22	−	11343.4i	−0.281138	−	0.335048i
$185$	−31040.8	−	18099.3i	−0.906962	−	0.528832i
$186$	−2305.36	−	839.083i	−0.0666366	−	0.0242537i
$187$	854.270	+	9764.35i	0.0244294	+	0.279229i
$188$	−13811.3	−	19724.6i	−0.390769	−	0.558076i
$189$			126.658i			0.00354576i
$190$	4554.56	+	2485.41i	0.126165	+	0.0688480i
$191$	−12710.3			−0.348408			−0.174204	−	0.984710i	$-0.555735\pi$
$191$	−12710.3			−0.348408			−0.174204	+	0.984710i	$0.555735\pi$
$192$	−10839.1	+	7589.60i	−0.294029	+	0.205881i
$193$	1259.74	−	110.213i	0.0338195	−	0.00295882i	−0.0702334	−	0.997531i	$-0.522374\pi$
$193$	1259.74	−	110.213i	0.0338195	−	0.00295882i	0.104053	+	0.994572i	$0.466819\pi$
$194$	−2259.98	+	6209.23i	−0.0600482	+	0.164981i
$195$	−3922.66	−	14894.7i	−0.103160	−	0.391708i
$196$	−28819.8	+	24182.7i	−0.750203	+	0.629495i
$197$	−4311.19	+	16089.6i	−0.111087	+	0.414584i	−0.998964	−	0.0454969i	$-0.985513\pi$
$197$	−4311.19	+	16089.6i	−0.111087	+	0.414584i	0.887877	+	0.460081i	$0.152180\pi$
$198$	228.080	+	851.206i	0.00581777	+	0.0217122i
$199$	5003.79	−	882.303i	0.126355	−	0.0222798i	−0.110113	−	0.993919i	$-0.535121\pi$
$199$	5003.79	−	882.303i	0.126355	−	0.0222798i	0.236468	+	0.971639i	$0.424010\pi$
$200$	7977.21	+	8115.19i	0.199430	+	0.202880i
$201$	−3472.58	+	6014.69i	−0.0859529	+	0.148875i
$202$	1858.13	−	6934.64i	0.0455380	−	0.169950i
$203$	−2.93221	+	33.5154i	−7.11547e−5	+	0.000813302i
$204$	8505.43	+	23368.5i	0.204379	+	0.561526i
$205$	−22629.9	−	10670.9i	−0.538487	−	0.253917i
$206$	−1544.22	−	1295.75i	−0.0363893	−	0.0305343i
$207$	44947.7	−	31472.7i	1.04898	−	0.734503i
$208$	28451.6	−	28451.6i	0.657628	−	0.657628i
$209$	7783.45	+	2585.52i	0.178188	+	0.0591910i
$210$	−7.84117	−	9.42652i	−0.000177804	−	0.000213753i
$211$	2602.19	−	14757.8i	0.0584486	−	0.331479i	−0.941537	−	0.336911i	$-0.890618\pi$
$211$	2602.19	−	14757.8i	0.0584486	−	0.331479i	0.999985	+	0.00543205i	$0.00172908\pi$
$212$	5861.68	+	66999.3i	0.130422	+	1.49073i
$213$	−1327.63	+	619.085i	−0.0292630	+	0.0136456i
$214$	1015.00	+	2788.70i	0.0221636	+	0.0608939i
$215$	7541.32	−	41722.2i	0.163144	−	0.902590i
$216$	4971.97	+	8611.71i	0.106567	+	0.184579i
$217$	−259.853	+	69.6274i	−0.00551834	+	0.00147863i
$218$	−1933.08	−	1353.56i	−0.0406760	−	0.0284816i
$219$	−20255.3	+	3571.55i	−0.422328	+	0.0744678i
$220$	7268.47	+	5136.02i	0.150175	+	0.106116i
$221$	−36128.0	−	62575.6i	−0.739707	−	1.28121i
$222$	3028.11	+	264.925i	0.0614421	+	0.00537549i
$223$	−37014.3	+	79377.5i	−0.744321	+	1.59620i	0.0572915	+	0.998357i	$0.481754\pi$
$223$	−37014.3	+	79377.5i	−0.744321	+	1.59620i	−0.801612	+	0.597844i	$0.796024\pi$
$224$	34.0615	−	93.5832i	0.000678841	−	0.00186510i
$225$	−32533.3	+	26826.7i	−0.642633	+	0.529910i
$226$	−1322.35	+	7499.45i	−0.0258899	+	0.146829i
$227$	64888.6	+	64888.6i	1.25926	+	1.25926i	0.951445	+	0.307818i	$0.0995988\pi$
$227$	64888.6	+	64888.6i	1.25926	+	1.25926i	0.307818	+	0.951445i	$0.400401\pi$
$228$	20772.7	+	1225.23i	0.399597	+	0.0235694i
$229$		−	26734.8i		−	0.509807i	−0.966966	−	0.254904i	$-0.917956\pi$
$229$		−	26734.8i		−	0.509807i	0.966966	−	0.254904i	$-0.0820438\pi$
$230$	−3073.78	+	11277.9i	−0.0581055	+	0.213193i
$231$	−14.8473	−	12.4584i	−0.000278243	−	0.000233474i
$232$	1116.28	+	2393.87i	0.0207395	+	0.0444759i
$233$	−13245.8	+	28405.8i	−0.243988	+	0.523233i	−0.989721	−	0.143011i	$-0.954322\pi$
$233$	−13245.8	+	28405.8i	−0.243988	+	0.523233i	0.745733	+	0.666244i	$0.232099\pi$
$234$	−4175.74	−	4976.46i	−0.0762609	−	0.0908842i
$235$	−13294.2	+	36044.1i	−0.240729	+	0.652677i
$236$	33749.8	−	58456.4i	0.605965	−	1.04956i
$237$	19105.9	−	27286.1i	0.340150	−	0.485785i
$238$	−47.1180	−	32.9924i	−0.000831828	−	0.000582452i
$239$	3457.57	+	1996.23i	0.0605307	+	0.0349474i	0.529960	−	0.848023i	$-0.322207\pi$
$239$	3457.57	+	1996.23i	0.0605307	+	0.0349474i	−0.469429	+	0.882970i	$0.655540\pi$
$240$	20729.1	+	7645.58i	0.359881	+	0.132736i
$241$	−45068.1	+	37816.6i	−0.775953	+	0.651102i	−0.942226	−	0.334978i	$-0.891271\pi$
$241$	−45068.1	+	37816.6i	−0.775953	+	0.651102i	0.166273	+	0.986080i	$0.446827\pi$
$242$	7359.70	+	3431.88i	0.125669	+	0.0586006i
$243$	−51615.3	+	24068.6i	−0.874110	+	0.407604i
$244$	−63793.8	+	76026.5i	−1.07152	+	1.27698i
$245$	57911.3	+	15783.7i	0.964786	+	0.262952i
$246$	2116.54			0.0349749
$247$	−60057.5	+	6974.85i	−0.984403	+	0.114325i
$248$	−14934.6	+	14934.6i	−0.242824	+	0.242824i
$249$	4707.36	+	830.034i	0.0759239	+	0.0133874i
$250$	1673.52	−	8825.73i	0.0267764	−	0.141212i
$251$	−107182.	−	39010.9i	−1.70127	−	0.619211i	−0.705300	−	0.708909i	$-0.749188\pi$
$251$	−107182.	−	39010.9i	−1.70127	−	0.619211i	−0.995969	+	0.0896979i	$0.971410\pi$
$252$	222.199	+	103.613i	0.00349898	+	0.00163160i
$253$	−1610.41	+	18407.1i	−0.0251591	+	0.287570i
$254$	−11807.1	+	6816.81i	−0.183010	+	0.105661i
$255$	22896.5	−	32403.0i	0.352118	−	0.498316i
$256$	9101.46	+	51617.0i	0.138877	+	0.787612i
$257$	−13477.0	+	19247.2i	−0.204046	+	0.291408i	−0.908113	−	0.418726i	$-0.862477\pi$
$257$	−13477.0	+	19247.2i	−0.204046	+	0.291408i	0.704067	+	0.710134i	$0.251366\pi$
$258$	928.304	+	3464.48i	0.0139460	+	0.0520473i
$259$	288.662	−	166.659i	0.00430318	−	0.00248444i
$260$	−64562.8	−	11669.8i	−0.955071	−	0.172630i
$261$	−9197.41	+	3347.58i	−0.135016	+	0.0491417i
$262$	−1432.58	−	3072.17i	−0.0208697	−	0.0447552i
$263$	−53477.9	+	4678.71i	−0.773149	+	0.0676418i	−0.466900	−	0.884310i	$-0.654629\pi$
$263$	−53477.9	+	4678.71i	−0.773149	+	0.0676418i	−0.306248	+	0.951952i	$0.599074\pi$
$264$	−1498.55	−	264.235i	−0.0215013	−	0.00379125i
$265$	82493.8	−	68620.0i	1.17471	−	0.977145i
$266$	−40.9837	+	25.2374i	−0.000579225	+	0.000356682i
$267$	−37177.3	−	37177.3i	−0.521502	−	0.521502i
$268$	16968.5	+	24233.5i	0.236251	+	0.337402i
$269$	58772.5	−	70042.4i	0.812213	−	0.967957i	−0.187685	−	0.982229i	$-0.560099\pi$
$269$	58772.5	−	70042.4i	0.812213	−	0.967957i	0.999898	+	0.0142717i	$0.00454298\pi$
$270$	3347.93	−	7100.03i	0.0459250	−	0.0973942i
$271$	3786.68	−	1378.24i	0.0515609	−	0.0187666i	−0.316111	−	0.948722i	$-0.602377\pi$
$271$	3786.68	−	1378.24i	0.0515609	−	0.0187666i	0.367672	+	0.929956i	$0.380155\pi$
$272$	103253.	+	9033.46i	1.39561	+	0.122100i
$273$	138.011	+	36.9799i	0.00185178	+	0.000496182i
$274$	−3209.68	−	1853.11i	−0.0427524	−	0.0246831i
$275$	121.747	−	14199.0i	0.00160988	−	0.187755i
$276$	8140.59	+	46167.6i	0.106866	+	0.606065i
$277$	114080.	−	30567.8i	1.48680	−	0.398386i	0.578143	−	0.815936i	$-0.303778\pi$
$277$	114080.	−	30567.8i	1.48680	−	0.398386i	0.908654	+	0.417550i	$0.137111\pi$
$278$	−3880.62	−	1039.81i	−0.0502124	−	0.0134544i
$279$	−50307.3	−	59953.9i	−0.646283	−	0.770210i
$280$	−102.079	+	26.8835i	−0.00130203	+	0.000342902i
$281$	4124.24	+	1501.10i	0.0522314	+	0.0190107i	0.368004	−	0.929824i	$-0.380041\pi$
$281$	4124.24	+	1501.10i	0.0522314	+	0.0190107i	−0.315772	+	0.948835i	$0.602264\pi$
$282$	−283.251	−	3237.58i	−0.00356183	−	0.0407119i
$283$	36980.0	+	52812.9i	0.461736	+	0.659428i	0.980734	−	0.195348i	$-0.0625836\pi$
$283$	36980.0	+	52812.9i	0.461736	+	0.659428i	−0.518998	+	0.854776i	$0.673695\pi$
$284$			6239.82i			0.0773634i
$285$	−17286.8	−	28343.9i	−0.212826	−	0.348955i
$286$	2187.58			0.0267443
$287$	190.117	−	133.122i	0.00230812	−	0.00161616i
$288$	28862.7	−	2525.16i	0.347978	−	0.0304441i
$289$	35093.5	−	96418.7i	0.420176	−	1.15442i
$290$	1050.28	−	1801.25i	0.0124884	−	0.0214180i
$291$	32388.4	−	27177.1i	0.382476	−	0.320935i
$292$	−22675.3	+	84625.3i	−0.265942	+	0.992509i
$293$	−1660.70	−	6197.83i	−0.0193445	−	0.0721946i	0.955579	−	0.294736i	$-0.0952316\pi$
$293$	−1660.70	−	6197.83i	−0.0193445	−	0.0721946i	−0.974923	+	0.222541i	$0.928565\pi$
$294$	−5000.57	+	881.735i	−0.0578529	+	0.0102010i
$295$	−107322.	+	8926.04i	−1.23324	+	0.102569i
$296$	13084.4	−	22662.9i	0.149338	−	0.258661i
$297$	3211.49	−	11985.5i	0.0364078	−	0.135876i
$298$	1394.86	−	15943.3i	0.0157071	−	0.179533i
$299$	−46587.3	−	127997.i	−0.521104	−	1.43172i
$300$	−9025.57	−	34877.4i	−0.100284	−	0.387526i
$301$	301.286	+	252.809i	0.00332541	+	0.00279035i
$302$	11873.2	−	8313.69i	0.130183	−	0.0911548i
$303$	−32482.5	+	32482.5i	−0.353805	+	0.353805i
$304$	41217.5	−	76307.9i	0.445999	−	0.825700i
$305$	157679.	+	14476.5i	1.69502	+	0.155620i
$306$	2905.85	−	16479.9i	0.0310334	−	0.175999i
$307$	10655.8	+	121796.i	0.113060	+	1.29228i	0.814756	+	0.579803i	$0.196871\pi$
$307$	10655.8	+	121796.i	0.113060	+	1.29228i	−0.701697	+	0.712476i	$0.747574\pi$
$308$	−74.8239	+	34.8910i	−0.000788749	+	0.000367800i
$309$	4411.54	+	12120.6i	0.0462033	+	0.126943i
$310$	16406.9	+	2965.56i	0.170728	+	0.0308592i
$311$	66598.2	+	115351.i	0.688560	+	1.19262i	0.972304	+	0.233720i	$0.0750900\pi$
$311$	66598.2	+	115351.i	0.688560	+	1.19262i	−0.283744	+	0.958900i	$0.591577\pi$
$312$	10835.3	−	2903.30i	0.111309	−	0.0298251i
$313$	59818.3	+	41885.2i	0.610584	+	0.427536i	0.837545	−	0.546368i	$-0.183990\pi$
$313$	59818.3	+	41885.2i	0.610584	+	0.427536i	−0.226961	+	0.973904i	$0.572879\pi$
$314$	−3827.37	+	674.869i	−0.0388187	+	0.00684479i
$315$	−66.2719	−	385.504i	−0.000667895	−	0.00388515i
$316$	−70944.1	−	122879.i	−0.710464	−	1.23056i
$317$	40689.4	+	3559.86i	0.404914	+	0.0354253i	0.287794	−	0.957692i	$-0.407078\pi$
$317$	40689.4	+	3559.86i	0.404914	+	0.0354253i	0.117120	+	0.993118i	$0.462634\pi$
$318$	−3836.24	+	8226.84i	−0.0379360	+	0.0813540i
$319$	1127.27	−	3097.16i	0.0110776	−	0.0304356i
$320$	63858.9	−	63313.7i	0.623623	−	0.618298i
$321$	3297.38	−	18700.4i	0.0320007	−	0.181485i
$322$	−76.6741	−	76.6741i	−0.000739498	−	0.000739498i
$323$	−113206.	−	106962.i	−1.08508	−	1.02524i
$324$			54150.4i			0.515836i
$325$	43423.1	+	95244.9i	0.411107	+	0.901727i
$326$	471.974	+	396.033i	0.00444102	+	0.00372646i
$327$	6381.43	+	13685.0i	0.0596792	+	0.127982i
$328$	7700.71	−	16514.2i	0.0715786	−	0.153501i
$329$	−229.073	−	272.999i	−0.00211632	−	0.00252214i
$330$	502.982	+	1090.83i	0.00461875	+	0.0100168i
$331$	1705.05	−	2953.23i	0.0155626	−	0.0269552i	−0.858139	−	0.513417i	$-0.828379\pi$
$331$	1705.05	−	2953.23i	0.0155626	−	0.0269552i	0.873702	+	0.486462i	$0.161713\pi$
$332$	11678.5	−	16678.6i	0.105952	−	0.151316i
$333$	79433.4	+	55619.9i	0.716332	+	0.501581i
$334$	−23290.0	−	13446.5i	−0.208774	−	0.120536i
$335$	16333.2	−	44283.4i	0.145540	−	0.394595i
$336$	−157.003	+	131.741i	−0.00139069	+	0.00116692i
$337$	−185921.	−	86696.3i	−1.63707	−	0.763380i	−0.637102	−	0.770780i	$-0.719867\pi$
$337$	−185921.	−	86696.3i	−1.63707	−	0.763380i	−0.999973	+	0.00739959i	$0.997645\pi$
$338$	266.082	−	124.076i	0.00232907	−	0.00108606i
$339$	31320.5	−	37326.3i	0.272540	−	0.324800i
$340$	−83874.3	−	146724.i	−0.725556	−	1.26924i
$341$	26354.9			0.226648
$342$	−11693.2	−	7703.10i	−0.0999728	−	0.0658587i
$343$	−787.442	+	787.442i	−0.00669315	+	0.00669315i
$344$	30409.0	+	5361.92i	0.256971	+	0.0453110i
$345$	53114.1	−	52660.7i	0.446243	−	0.442434i
$346$	−8748.56	−	3184.22i	−0.0730776	−	0.0265981i
$347$	−35058.8	−	16348.2i	−0.291164	−	0.135772i	0.271548	−	0.962425i	$-0.412464\pi$
$347$	−35058.8	−	16348.2i	−0.291164	−	0.135772i	−0.562712	+	0.826653i	$0.690242\pi$
$348$	728.817	−	8330.42i	0.00601811	−	0.0687873i
$349$	−100072.	+	57776.7i	−0.821605	+	0.474354i	−0.850969	−	0.525215i	$-0.823985\pi$
$349$	−100072.	+	57776.7i	−0.821605	+	0.474354i	0.0293649	+	0.999569i	$0.490652\pi$
$350$	63.3723	+	54.1083i	0.000517325	+	0.000441701i
$351$	15883.9	+	90081.9i	0.128926	+	0.731178i
$352$	−5596.04	+	7991.97i	−0.0451643	+	0.0645013i
$353$	7533.17	+	28114.2i	0.0604544	+	0.225619i	0.989543	−	0.144238i	$-0.0460732\pi$
$353$	7533.17	+	28114.2i	0.0604544	+	0.225619i	−0.929089	+	0.369857i	$0.879407\pi$
$354$	7889.75	−	4555.15i	0.0629588	−	0.0363493i
$355$	8179.37	−	5675.16i	0.0649028	−	0.0450320i
$356$	−210450.	+	76597.5i	−1.66054	+	0.604386i
$357$	155.545	+	333.566i	0.00122045	+	0.00261725i
$358$	13752.9	−	1203.22i	0.107307	−	0.00938816i
$359$	19543.1	+	3445.98i	0.151637	+	0.0267377i	0.248951	−	0.968516i	$-0.419914\pi$
$359$	19543.1	+	3445.98i	0.151637	+	0.0267377i	−0.0973144	+	0.995254i	$0.531025\pi$
$360$	−19638.9	−	23609.5i	−0.151535	−	0.182172i
$361$	−119739.	+	51441.1i	−0.918799	+	0.394726i
$362$	22722.7	+	22722.7i	0.173397	+	0.173397i
$363$	−29803.0	−	42563.0i	−0.226176	−	0.323013i
$364$	391.208	−	466.223i	0.00295260	−	0.00351877i
$365$	131553.	−	47243.7i	0.987450	−	0.354616i
$366$	−12587.2	+	4581.35i	−0.0939649	+	0.0342004i
$367$	196976.	+	17233.2i	1.46245	+	0.127948i	0.790417	−	0.612570i	$-0.209864\pi$
$367$	196976.	+	17233.2i	1.46245	+	0.127948i	0.672037	+	0.740518i	$0.265420\pi$
$368$	188731.	+	50570.3i	1.39363	+	0.373422i
$369$	58474.7	+	33760.4i	0.429452	+	0.247944i
$370$	−20586.7	+	1712.20i	−0.150377	+	0.0125069i
$371$	172.846	+	980.256i	0.00125577	+	0.00712183i
$372$	64587.8	−	17306.2i	0.466729	−	0.125060i
$373$	−48602.6	−	13023.0i	−0.349335	−	0.0936040i	0.0798849	−	0.996804i	$-0.474545\pi$
$373$	−48602.6	−	13023.0i	−0.349335	−	0.0936040i	−0.429220	+	0.903200i	$0.641211\pi$
$374$	3622.16	+	4316.72i	0.0258955	+	0.0308611i
$375$	−37509.6	+	43552.2i	−0.266735	+	0.309705i
$376$	−26291.6	−	9569.38i	−0.185970	−	0.0676874i
$377$	2117.62	+	24204.5i	0.0148993	+	0.170300i
$378$	41.7662	+	59.6484i	0.000292309	+	0.000417460i
$379$			167769.i			1.16798i	0.811762	+	0.583989i	$0.198509\pi$
$379$			167769.i			1.16798i	−0.811762	+	0.583989i	$0.801491\pi$
$380$	−140542.	+	15711.6i	−0.973279	+	0.108806i
$381$	87235.8			0.600959
$382$	−5985.77	+	4191.28i	−0.0410198	+	0.0287224i
$383$	−143937.	+	12592.9i	−0.981240	+	0.0858474i	−0.566473	−	0.824080i	$-0.691692\pi$
$383$	−143937.	+	12592.9i	−0.981240	+	0.0858474i	−0.414767	+	0.909928i	$0.636137\pi$
$384$	−11246.6	+	30899.7i	−0.0762708	+	0.209552i
$385$	113.789	+	66.3482i	0.000767678	+	0.000447618i
$386$	556.920	−	467.311i	0.00373782	−	0.00313640i
$387$	−29614.3	+	110522.i	−0.197733	+	0.737949i
$388$	−46612.4	−	173960.i	−0.309627	−	1.15554i
$389$	−82620.3	+	14568.2i	−0.545993	+	0.0962734i	−0.439840	−	0.898076i	$-0.644965\pi$
$389$	−82620.3	+	14568.2i	−0.545993	+	0.0962734i	−0.106154	+	0.994350i	$0.533854\pi$
$390$	−6758.95	−	5720.99i	−0.0444376	−	0.0376134i
$391$	175437.	−	303866.i	1.14754	−	1.98760i
$392$	−11314.1	+	42224.8i	−0.0736289	+	0.274787i
$393$	−1890.38	+	21607.2i	−0.0122395	+	0.139898i
$394$	3275.32	+	8998.87i	0.0210990	+	0.0579689i
$395$	−96549.6	+	204755.i	−0.618808	+	1.31232i
$396$	−18399.2	−	15438.7i	−0.117330	−	0.0984514i
$397$	81373.5	−	56978.3i	0.516300	−	0.361517i	−0.286200	−	0.958170i	$-0.592392\pi$
$397$	81373.5	−	56978.3i	0.516300	−	0.361517i	0.802499	+	0.596653i	$0.203503\pi$
$398$	2065.54	−	2065.54i	0.0130397	−	0.0130397i
$399$	307.846	−	8.73034i	0.00193369	−	5.48385e-5i
$400$	−147642.	−	27340.6i	−0.922765	−	0.170879i
$401$	−36098.9	+	204727.i	−0.224494	+	1.27317i	0.639156	+	0.769077i	$0.279284\pi$
$401$	−36098.9	+	204727.i	−0.224494	+	1.27317i	−0.863650	+	0.504092i	$0.831827\pi$
$402$	348.000	+	3977.66i	0.00215341	+	0.0246136i
$403$	−176081.	+	82107.8i	−1.08418	+	0.505562i
$404$	66924.5	+	183874.i	0.410037	+	1.12657i
$405$	70982.2	−	49250.1i	0.432752	−	0.300260i
$406$	9.67098	+	16.7506i	5.86703e−5	+	0.000101620i
$407$	−31541.3	+	8451.47i	−0.190410	+	0.0510203i
$408$	23669.9	+	16573.8i	0.142192	+	0.0995641i
$409$	142660.	−	25154.7i	0.852814	−	0.150374i	0.269880	−	0.962894i	$-0.413016\pi$
$409$	142660.	−	25154.7i	0.852814	−	0.150374i	0.582934	+	0.812520i	$0.301905\pi$
$410$	−14176.1	+	2437.01i	−0.0843314	+	0.0144974i
$411$	11857.3	+	20537.4i	0.0701941	+	0.121580i
$412$	54733.4	+	4788.55i	0.322447	+	0.0282104i
$413$	422.194	−	905.397i	0.00247521	−	0.00530810i
$414$	10789.4	−	29643.5i	0.0629498	−	0.172953i
$415$	−32484.6	−	139.265i	−0.188617	−	0.000808620i
$416$	12489.2	−	70829.8i	0.0721686	−	0.409289i
$417$	18177.2	+	18177.2i	0.104533	+	0.104533i
$418$	4518.13	−	1349.01i	0.0258586	−	0.00772081i
$419$			89955.8i			0.512391i	0.966625	+	0.256195i	$0.0824690\pi$
$419$			89955.8i			0.512391i	−0.966625	+	0.256195i	$0.917531\pi$
$420$	322.431	+	87.8782i	0.00182784	+	0.000498176i
$421$	71944.2	+	60368.4i	0.405912	+	0.340601i	0.822773	−	0.568369i	$-0.192426\pi$
$421$	71944.2	+	60368.4i	0.405912	+	0.340601i	−0.416862	+	0.908970i	$0.636870\pi$
$422$	−3640.98	−	7808.10i	−0.0204453	−	0.0438451i
$423$	43816.2	−	93964.2i	0.244880	−	0.525148i
$424$	50232.1	+	59864.2i	0.279415	+	0.332994i
$425$	−116046.	+	243391.i	−0.642470	+	1.34750i
$426$	−421.088	+	729.346i	−0.00232035	+	0.00401897i
$427$	−842.489	+	1203.20i	−0.00462071	+	0.00659905i
$428$	−66257.3	−	46393.8i	−0.361698	−	0.253264i
$429$	−12122.1	−	6998.70i	−0.0658663	−	0.0380279i
$430$	−10206.6	−	22135.4i	−0.0552008	−	0.119716i
$431$	−196984.	+	165290.i	−1.06042	+	0.889797i	−0.994150	−	0.108005i	$-0.965554\pi$
$431$	−196984.	+	165290.i	−1.06042	+	0.889797i	−0.0662682	+	0.997802i	$0.521109\pi$
$432$	−118917.	−	55452.1i	−0.637203	−	0.297133i
$433$	57670.4	−	26892.2i	0.307594	−	0.143433i	−0.262692	−	0.964880i	$-0.584610\pi$
$433$	57670.4	−	26892.2i	0.307594	−	0.143433i	0.570286	+	0.821447i	$0.306833\pi$
$434$	−99.4151	+	118.478i	−0.000527804	+	0.000629012i
$435$	−11582.7	+	6621.21i	−0.0612111	+	0.0349912i
$436$	64319.1			0.338350
$437$	−175151.	−	235631.i	−0.917171	−	1.23387i
$438$	−8361.27	+	8361.27i	−0.0435837	+	0.0435837i
$439$	−114622.	−	20211.0i	−0.594757	−	0.104872i	−0.131836	−	0.991272i	$-0.542087\pi$
$439$	−114622.	−	20211.0i	−0.594757	−	0.104872i	−0.462920	+	0.886400i	$0.653198\pi$
$440$	10341.2	+	44.3338i	0.0534154	+	0.000228997i
$441$	−152218.	−	55402.6i	−0.782686	−	0.284874i
$442$	−37648.8	−	17555.9i	−0.192711	−	0.0898626i
$443$	15123.1	−	172857.i	0.0770606	−	0.880806i	−0.855029	−	0.518580i	$-0.826461\pi$
$443$	15123.1	−	172857.i	0.0770606	−	0.880806i	0.932090	−	0.362227i	$-0.117983\pi$
$444$	−71748.4	+	41423.9i	−0.363954	+	0.210129i
$445$	291812.	+	206199.i	1.47361	+	1.04128i
$446$	8743.65	+	49587.7i	0.0439565	+	0.249290i
$447$	−58736.5	+	83884.5i	−0.293963	+	0.419823i
$448$	215.901	+	805.755i	0.00107572	+	0.00401464i
$449$	177983.	−	102759.i	0.882849	−	0.509713i	0.0112520	−	0.999937i	$-0.496418\pi$
$449$	177983.	−	102759.i	0.882849	−	0.509713i	0.871597	+	0.490224i	$0.163085\pi$
$450$	−6474.96	+	23361.8i	−0.0319751	+	0.115367i
$451$	−21365.9	+	7776.53i	−0.105043	+	0.0382325i
$452$	−87716.1	−	188108.i	−0.429341	−	0.920725i
$453$	−92391.1	+	8083.18i	−0.450229	+	0.0393900i
$454$	51956.0	+	9161.24i	0.252072	+	0.0444470i
$455$	−966.947	−	88.7756i	−0.00467068	−	0.000428816i
$456$	20588.3	−	12678.1i	0.0990126	−	0.0609712i
$457$	65539.3	+	65539.3i	0.313812	+	0.313812i	0.846384	−	0.532572i	$-0.178775\pi$
$457$	65539.3	+	65539.3i	0.313812	+	0.313812i	−0.532572	+	0.846384i	$0.678775\pi$
$458$	−8815.95	−	12590.5i	−0.0420280	−	0.0600221i
$459$	−151457.	+	180500.i	−0.718893	+	0.856744i
$460$	−107682.	−	299847.i	−0.508894	−	1.41705i
$461$	271770.	−	98916.2i	1.27879	−	0.465442i	0.388759	−	0.921339i	$-0.372904\pi$
$461$	271770.	−	98916.2i	1.27879	−	0.465442i	0.890033	+	0.455897i	$0.150681\pi$
$462$	−11.1004	−	0.971162i	−5.20063e−5	−	4.54996e-6i
$463$	143083.	+	38339.0i	0.667462	+	0.178846i	0.576611	−	0.817019i	$-0.304375\pi$
$463$	143083.	+	38339.0i	0.667462	+	0.178846i	0.0908506	+	0.995865i	$0.471041\pi$
$464$	−30183.3	−	17426.3i	−0.140194	−	0.0809413i
$465$	−81428.6	−	68923.7i	−0.376592	−	0.318759i
$466$	3128.98	+	17745.3i	0.0144089	+	0.0817169i
$467$	−30984.3	+	8302.22i	−0.142072	+	0.0380680i	−0.329154	−	0.944276i	$-0.606764\pi$
$467$	−30984.3	+	8302.22i	−0.142072	+	0.0380680i	0.187082	+	0.982344i	$0.440097\pi$
$468$	171027.	+	45826.4i	0.780858	+	0.209230i
$469$	281.437	+	335.404i	0.00127949	+	0.00152483i
$470$	5624.95	+	21358.4i	0.0254638	+	0.0966883i
$471$	23367.8	+	8505.20i	0.105336	+	0.0383392i
$472$	−6835.73	−	78132.7i	−0.0306832	−	0.350711i
$473$	−22100.1	−	31562.2i	−0.0987805	−	0.141073i
$474$		−	19150.4i		−	0.0852355i
$475$	148419.	+	169937.i	0.657811	+	0.753183i
$476$	1567.75			0.00691930
$477$	−237210.	+	166096.i	−1.04255	+	0.730000i
$478$	2286.58	−	200.050i	0.0100076	−	0.000875552i
$479$	30033.7	−	82516.9i	0.130899	−	0.359643i	−0.856877	−	0.515521i	$-0.827598\pi$
$479$	30033.7	−	82516.9i	0.130899	−	0.359643i	0.987776	+	0.155878i	$0.0498206\pi$
$480$	38190.8	−	10057.9i	0.165759	−	0.0436541i
$481$	184402.	−	154731.i	0.797031	−	0.668788i
$482$	−8754.12	+	32670.8i	−0.0376807	+	0.140626i
$483$	179.574	+	670.180i	0.000769749	+	0.00287274i
$484$	−217966.	+	38433.3i	−0.930462	+	0.164066i
$485$	−185638.	+	219319.i	−0.789195	+	0.932379i
$486$	−16370.9	+	28355.3i	−0.0693108	+	0.120050i
$487$	99965.3	−	373076.i	0.421494	−	1.57304i	−0.349968	−	0.936762i	$-0.613807\pi$
$487$	99965.3	−	373076.i	0.421494	−	1.57304i	0.771462	−	0.636276i	$-0.219526\pi$
$488$	−10050.6	+	114879.i	−0.0422041	+	0.482395i
$489$	−1348.34	−	3704.53i	−0.00563874	−	0.0154923i
$490$	32477.5	−	11663.4i	0.135266	−	0.0485773i
$491$	239163.	+	200681.i	0.992043	+	0.832423i	0.985862	−	0.167558i	$-0.0535881\pi$
$491$	239163.	+	200681.i	0.992043	+	0.832423i	0.00618102	+	0.999981i	$0.498033\pi$
$492$	−47254.6	+	33088.0i	−0.195215	+	0.136691i
$493$	−44256.2	+	44256.2i	−0.182087	+	0.182087i
$494$	−25983.5	+	23089.0i	−0.106474	+	0.0946132i
$495$	−3503.47	+	38159.9i	−0.0142984	+	0.155739i
$496$	48393.9	−	274455.i	0.196710	−	1.11560i
$497$	8.04878	+	91.9980i	3.25850e−5	+	0.000372448i
$498$	2490.59	−	1161.38i	0.0100425	−	0.00468291i
$499$	−122398.	−	336286.i	−0.491557	−	1.35054i	−0.899255	−	0.437424i	$-0.855891\pi$
$499$	−122398.	−	336286.i	−0.491557	−	1.35054i	0.407699	−	0.913117i	$-0.366331\pi$
$500$	100610.	+	223209.i	0.402439	+	0.892835i
$501$	86038.3	+	149023.i	0.342781	+	0.593714i
$502$	−63340.2	+	16971.9i	−0.251346	+	0.0673479i
$503$	48495.9	+	33957.2i	0.191676	+	0.134213i	0.665475	−	0.746420i	$-0.268229\pi$
$503$	48495.9	+	33957.2i	0.191676	+	0.134213i	−0.473799	+	0.880633i	$0.657118\pi$
$504$	280.547	−	49.4680i	0.00110445	−	0.000194744i
$505$	180160.	−	254961.i	0.706439	−	0.999750i
$506$	5311.42	+	9199.66i	0.0207448	+	0.0359311i
$507$	−1871.41	−	163.727i	−0.00728035	−	0.000636948i
$508$	157041.	−	336775.i	0.608535	−	1.30501i
$509$	52805.6	−	145082.i	0.203819	−	0.559988i	−0.795100	−	0.606479i	$-0.792582\pi$
$509$	52805.6	−	145082.i	0.203819	−	0.559988i	0.998919	+	0.0464905i	$0.0148037\pi$
$510$	97.7891	−	22810.1i	0.000375967	−	0.0876974i
$511$	−225.159	+	1276.94i	−0.000862277	+	0.00489021i
$512$	122439.	+	122439.i	0.467069	+	0.467069i
$513$	88356.4	+	176256.i	0.335740	+	0.669744i
$514$			13508.4i			0.0511302i
$515$	−43503.4	−	76101.6i	−0.164024	−	0.286932i
$516$	−74886.1	−	62836.9i	−0.281256	−	0.236002i
$517$	14754.8	+	31641.7i	0.0552015	+	0.118380i
$518$	80.9856	−	173.674i	0.000301820	−	0.000647255i
$519$	38291.5	+	45634.0i	0.142157	+	0.169416i
$520$	−69229.3	+	31921.5i	−0.256025	+	0.118053i
$521$	235449.	−	407810.i	0.867405	−	1.50239i	0.00276596	−	0.999996i	$-0.499120\pi$
$521$	235449.	−	407810.i	0.867405	−	1.50239i	0.864639	−	0.502393i	$-0.167547\pi$
$522$	−3227.54	+	4609.41i	−0.0118449	+	0.0169163i
$523$	391987.	+	274472.i	1.43307	+	1.00345i	0.994498	+	0.104754i	$0.0334055\pi$
$523$	391987.	+	274472.i	1.43307	+	1.00345i	0.438575	+	0.898695i	$0.355483\pi$
$524$	80011.9	+	46194.9i	0.291402	+	0.168241i
$525$	−178.059	−	502.579i	−0.000646018	−	0.00182342i
$526$	−23642.1	+	19838.0i	−0.0854503	+	0.0717013i
$527$	−453574.	−	211505.i	−1.63315	−	0.761553i
$528$	18197.3	−	8485.54i	0.0652738	−	0.0304377i
$529$	245289.	−	292325.i	0.876531	−	1.04461i
$530$	16221.8	−	59518.7i	0.0577493	−	0.211886i
$531$	290632.			1.03075
$532$	520.478	−	1204.16i	0.00183899	−	0.00425463i
$533$	118521.	−	118521.i	0.417196	−	0.417196i
$534$	−29767.7	−	5248.85i	−0.104391	−	0.0184070i
$535$	−553.241	+	129048.i	−0.00193289	+	0.450861i
$536$	32301.7	+	11756.9i	0.112434	+	0.0409225i
$537$	−80059.0	−	37332.1i	−0.277627	−	0.129460i
$538$	4581.46	−	52366.3i	0.0158285	−	0.180920i
$539$	47239.7	−	27273.8i	0.162603	−	0.0938790i
$540$	36248.3	+	210857.i	0.124308	+	0.723102i
$541$	−1955.57	−	11090.6i	−0.00668157	−	0.0378931i	0.981285	−	0.192563i	$-0.0616798\pi$
$541$	−1955.57	−	11090.6i	−0.00668157	−	0.0378931i	−0.987966	+	0.154670i	$0.950569\pi$
$542$	1328.82	−	1897.75i	0.00452342	−	0.00646011i
$543$	−53217.5	−	198610.i	−0.180491	−	0.673600i
$544$	160447.	−	92634.2i	0.542168	−	0.313021i
$545$	−58498.6	−	84311.6i	−0.196948	−	0.283854i
$546$	77.1892	−	28.0946i	0.000258924	−	9.42405e-5i
$547$	−178454.	−	382697.i	−0.596421	−	1.27903i	−0.940406	−	0.340054i	$-0.889555\pi$
$547$	−178454.	−	382697.i	−0.596421	−	1.27903i	0.343985	−	0.938975i	$-0.388223\pi$
$548$	100630.	−	8804.01i	0.335095	−	0.0293170i
$549$	−420828.	−	74203.3i	−1.39624	−	0.246194i
$550$	−4624.86	−	6727.02i	−0.0152888	−	0.0222381i
$551$	19299.8	+	48685.1i	0.0635696	+	0.160359i
$552$	38517.5	+	38517.5i	0.126409	+	0.126409i
$553$	−1204.48	−	1720.17i	−0.00393866	−	0.00562500i
$554$	43645.1	−	52014.2i	0.142205	−	0.169474i
$555$	119555.	+	56374.9i	0.388136	+	0.183020i
$556$	102896.	−	37450.9i	0.332849	−	0.121147i
$557$	−298659.	−	26129.3i	−0.962643	−	0.0842204i	−0.405014	−	0.914310i	$-0.632733\pi$
$557$	−298659.	−	26129.3i	−0.962643	−	0.0842204i	−0.557629	+	0.830090i	$0.688289\pi$
$558$	−43461.9	−	11645.6i	−0.139585	−	0.0374018i
$559$	245985.	+	142019.i	0.787199	+	0.454489i
$560$	899.883	−	1063.15i	0.00286952	−	0.00339014i
$561$	−6261.15	−	35508.7i	−0.0198943	−	0.112826i
$562$	2437.27	−	653.064i	0.00771668	−	0.00206768i
$563$	−352381.	−	94420.1i	−1.11172	−	0.297884i	−0.344191	−	0.938900i	$-0.611847\pi$
$563$	−352381.	−	94420.1i	−1.11172	−	0.297884i	−0.767528	+	0.641015i	$0.778513\pi$
$564$	56937.3	+	67855.2i	0.178994	+	0.213317i
$565$	−166800.	+	286067.i	−0.522515	+	0.896128i
$566$	34830.7	+	12677.3i	0.108725	+	0.0395727i
$567$	69.8489	+	798.377i	0.000217267	+	0.00248337i
$568$	4158.63	+	5939.15i	0.0128900	+	0.0184089i
$569$			132959.i			0.410670i	0.978692	+	0.205335i	$0.0658284\pi$
$569$			132959.i			0.410670i	−0.978692	+	0.205335i	$0.934172\pi$
$570$	−17487.6	−	7647.84i	−0.0538245	−	0.0235391i
$571$	−133146.			−0.408371			−0.204185	−	0.978932i	$-0.565455\pi$
$571$	−133146.			−0.408371			−0.204185	+	0.978932i	$0.565455\pi$
$572$	−48840.7	+	34198.6i	−0.149276	+	0.104524i
$573$	46578.3	−	4075.07i	0.141865	−	0.0124116i
$574$	45.6362	−	125.384i	0.000138512	−	0.000380557i
$575$	−295112.	+	413866.i	−0.892590	+	1.25177i
$576$	−185906.	+	155994.i	−0.560336	+	0.470177i
$577$	−1728.59	+	6451.20i	−0.00519208	+	0.0193771i	−0.968473	−	0.249117i	$-0.919859\pi$
$577$	−1728.59	+	6451.20i	−0.00519208	+	0.0193771i	0.963281	+	0.268495i	$0.0865261\pi$
$578$	−15267.7	−	56979.7i	−0.0457001	−	0.170555i
$579$	−4581.14	+	807.779i	−0.0136652	+	0.00240955i
$580$	4710.31	+	56634.5i	0.0140021	+	0.168355i
$581$	150.670	−	260.968i	0.000446349	−	0.000773100i
$582$	6291.19	−	23479.0i	0.0185732	−	0.0693162i
$583$	8498.88	−	97142.6i	0.0250049	−	0.285807i
$584$	34817.3	+	95659.8i	0.102087	+	0.280481i
$585$	−95478.9	−	265867.i	−0.278994	−	0.776878i
$586$	−2825.86	−	2371.18i	−0.00822917	−	0.00690509i
$587$	459457.	−	321715.i	1.33343	−	0.933675i	0.333467	−	0.942762i	$-0.391781\pi$
$587$	459457.	−	321715.i	1.33343	−	0.933675i	0.999959	+	0.00908669i	$0.00289242\pi$
$588$	97860.3	−	97860.3i	0.283043	−	0.283043i
$589$	−313036.	+	278165.i	−0.902327	+	0.801812i
$590$	−47598.9	+	39593.8i	−0.136739	+	0.113742i
$591$	10640.4	−	60344.4i	0.0304636	−	0.172768i
$592$	30094.8	+	343985.i	0.0858712	+	0.981512i
$593$	−242266.	+	112970.i	−0.688942	+	0.321259i	−0.735373	−	0.677662i	$-0.762993\pi$
$593$	−242266.	+	112970.i	−0.688942	+	0.321259i	0.0464309	+	0.998922i	$0.485215\pi$
$594$	−2439.85	−	6703.43i	−0.00691497	−	0.0189987i
$595$	−1425.88	−	2055.06i	−0.00402762	−	0.00580484i
$596$	218101.	+	377761.i	0.613994	+	1.06347i
$597$	−18054.1	+	4837.58i	−0.0506556	+	0.0135731i
$598$	−64147.7	−	44916.7i	−0.179382	−	0.125605i
$599$	−501569.	+	88440.2i	−1.39790	+	0.246488i	−0.821282	−	0.570523i	$-0.806740\pi$
$599$	−501569.	+	88440.2i	−1.39790	+	0.246488i	−0.576622	+	0.817011i	$0.695629\pi$
$600$	−31835.3	−	27181.5i	−0.0884313	−	0.0755042i
$601$	−42281.2	−	73233.2i	−0.117057	−	0.202749i	0.801543	−	0.597937i	$-0.204013\pi$
$601$	−42281.2	−	73233.2i	−0.117057	−	0.202749i	−0.918600	+	0.395188i	$0.870679\pi$
$602$	225.253	+	19.7071i	0.000621551	+	5.43787e-5i
$603$	−53832.2	+	115444.i	−0.148050	+	0.317494i
$604$	−135116.	+	371229.i	−0.370368	+	1.01758i
$605$	248621.	+	250762.i	0.679247	+	0.685096i
$606$	−4586.01	+	26008.6i	−0.0124879	+	0.0708225i
$607$	8773.53	+	8773.53i	0.0238121	+	0.0238121i	0.718913	−	0.695101i	$-0.244640\pi$
$607$	8773.53	+	8773.53i	0.0238121	+	0.0238121i	−0.695101	+	0.718913i	$0.744640\pi$
$608$	−17883.9	−	153990.i	−0.0483787	−	0.416569i
$609$		−	123.761i		−	0.000333695i
$610$	79031.0	−	45177.9i	0.212392	−	0.121413i
$611$	−197157.	−	165435.i	−0.528118	−	0.443143i
$612$	192755.	+	413363.i	0.514638	+	1.10364i
$613$	−13947.3	+	29910.0i	−0.0371166	+	0.0795968i	−0.923992	−	0.382412i	$-0.875093\pi$
$613$	−13947.3	+	29910.0i	−0.0371166	+	0.0795968i	0.886875	+	0.462009i	$0.152871\pi$
$614$	45181.2	+	53844.8i	0.119845	+	0.142826i
$615$	86351.3	+	31849.2i	0.228307	+	0.0842070i
$616$	−47.9647	+	83.0773i	−0.000126404	+	0.000218938i
$617$	344999.	−	492709.i	0.906248	−	1.29426i	−0.0491064	−	0.998794i	$-0.515637\pi$
$617$	344999.	−	492709.i	0.906248	−	1.29426i	0.955354	−	0.295463i	$-0.0954738\pi$
$618$	6074.40	+	4253.34i	0.0159047	+	0.0111366i
$619$	540219.	+	311896.i	1.40990	+	0.814007i	0.995378	−	0.0960316i	$-0.0306150\pi$
$619$	540219.	+	311896.i	1.40990	+	0.814007i	0.414523	+	0.910039i	$0.363948\pi$
$620$	−412668.	+	190281.i	−1.07354	+	0.495007i
$621$	−340265.	+	285516.i	−0.882336	+	0.740368i
$622$	69401.5	+	32362.5i	0.179386	+	0.0836490i
$623$	−3004.00	+	1400.79i	−0.00773971	+	0.00360908i
$624$	−95142.4	+	113386.i	−0.244346	+	0.291200i
$625$	201085.	−	334892.i	0.514777	−	0.857324i
$626$	41982.7			0.107133
$627$	−29352.3	−	6979.48i	−0.0746633	−	0.0177537i
$628$	74901.0	−	74901.0i	0.189919	−	0.189919i
$629$	610659.	+	107676.i	1.54347	+	0.272155i
$630$	−158.332	−	159.695i	−0.000398922	−	0.000402357i
$631$	−265457.	−	96618.4i	−0.666708	−	0.242662i	−0.0135780	−	0.999908i	$-0.504322\pi$
$631$	−265457.	−	96618.4i	−0.666708	−	0.242662i	−0.653130	+	0.757246i	$0.726544\pi$
$632$	−149420.	−	69675.7i	−0.374089	−	0.174441i
$633$	−4804.52	+	54915.9i	−0.0119906	+	0.137054i
$634$	20336.1	−	11741.1i	0.0505929	−	0.0292098i
$635$	−584286.	+	100445.i	−1.44903	+	0.249103i
$636$	−42961.7	−	243648.i	−0.106210	−	0.602349i
$637$	−230644.	+	329394.i	−0.568413	+	0.811778i
$638$	−490.427	−	1830.30i	−0.00120485	−	0.00449656i
$639$	−23267.2	+	13433.3i	−0.0569827	+	0.0328990i
$640$	39748.7	−	219909.i	0.0970428	−	0.536887i
$641$	320822.	−	116770.i	0.780816	−	0.284194i	0.0793030	−	0.996851i	$-0.474731\pi$
$641$	320822.	−	116770.i	0.780816	−	0.284194i	0.701513	+	0.712657i	$0.252508\pi$
$642$	−4613.69	−	9894.09i	−0.0111938	−	0.0240052i
$643$	−380441.	+	33284.3i	−0.920165	+	0.0805040i	−0.537387	−	0.843336i	$-0.680588\pi$
$643$	−380441.	+	33284.3i	−0.920165	+	0.0805040i	−0.382779	+	0.923840i	$0.625033\pi$
$644$	2910.51	+	513.201i	0.00701774	+	0.00123742i
$645$	−14259.4	+	155314.i	−0.0342753	+	0.373328i
$646$	−88584.3	−	13042.4i	−0.212271	−	0.0312530i
$647$	140502.	+	140502.i	0.335641	+	0.335641i	0.854724	−	0.519083i	$-0.173726\pi$
$647$	140502.	+	140502.i	0.335641	+	0.335641i	−0.519083	+	0.854724i	$0.673726\pi$
$648$	36089.5	+	51541.1i	0.0859469	+	0.122745i
$649$	−62908.3	+	74971.2i	−0.149355	+	0.177994i
$650$	51857.2	+	30535.6i	0.122739	+	0.0722736i
$651$	929.939	−	338.470i	0.00219428	−	0.000798653i
$652$	−16728.7	−	1463.57i	−0.0393520	−	0.00344285i
$653$	−90875.4	−	24350.0i	−0.213118	−	0.0571048i	0.150680	−	0.988583i	$-0.451854\pi$
$653$	−90875.4	−	24350.0i	−0.213118	−	0.0571048i	−0.363798	+	0.931478i	$0.618520\pi$
$654$	7517.99	+	4340.51i	0.0175770	+	0.0101481i
$655$	−12217.5	−	146897.i	−0.0284773	−	0.342397i
$656$	41750.7	+	236780.i	0.0970188	+	0.550221i
$657$	−364369.	+	97632.5i	−0.844134	+	0.226185i
$658$	−197.902	−	53.0278i	−0.000457088	−	0.000122476i
$659$	−205974.	−	245470.i	−0.474287	−	0.565233i	0.474862	−	0.880060i	$-0.342498\pi$
$659$	−205974.	−	245470.i	−0.474287	−	0.565233i	−0.949149	+	0.314827i	$0.898054\pi$
$660$	−28282.9	−	16491.2i	−0.0649285	−	0.0378586i
$661$	−336145.	−	122347.i	−0.769349	−	0.280020i	−0.0726249	−	0.997359i	$-0.523138\pi$
$661$	−336145.	−	122347.i	−0.769349	−	0.280020i	−0.696724	+	0.717339i	$0.745360\pi$
$662$	−170.869	−	1953.05i	−0.000389895	−	0.00445652i
$663$	152458.	+	217733.i	0.346835	+	0.495332i
$664$		−	23658.3i		−	0.0536595i
$665$	−2051.83	+	412.933i	−0.00463980	+	0.000933761i
$666$	55749.3			0.125687
$667$	−96648.3	+	67673.9i	−0.217241	+	0.152114i
$668$	730190.	−	63883.4i	1.63638	−	0.143164i
$669$	110194.	−	302756.i	0.246210	−	0.676457i
$670$	−6910.77	−	26240.8i	−0.0153949	−	0.0584558i
$671$	110231.	−	92494.9i	0.244827	−	0.205434i
$672$	−94.8185	+	353.867i	−0.000209969	+	0.000783614i
$673$	−27983.9	−	104437.i	−0.0617844	−	0.230582i	0.928128	−	0.372260i	$-0.121417\pi$
$673$	−27983.9	−	104437.i	−0.0617844	−	0.230582i	−0.989913	+	0.141678i	$0.954750\pi$
$674$	−116146.	+	20479.7i	−0.255673	+	0.0450821i
$675$	243430.	−	239291.i	0.534277	−	0.525193i
$676$	−4000.95	+	6929.86i	−0.00875528	+	0.0151646i
$677$	−45125.0	+	168409.i	−0.0984555	+	0.367441i	−0.997521	−	0.0703738i	$-0.977581\pi$
$677$	−45125.0	+	168409.i	−0.0984555	+	0.367441i	0.899065	+	0.437815i	$0.144247\pi$
$678$	2441.51	−	27906.6i	0.00531128	−	0.0607082i
$679$	−911.631	−	2504.69i	−0.00197733	−	0.00543268i
$680$	−177619.	−	83754.1i	−0.384125	−	0.181129i
$681$	−258596.	−	216988.i	−0.557606	−	0.467887i
$682$	12411.6	−	8690.67i	0.0266844	−	0.0186846i
$683$	−201866.	+	201866.i	−0.432734	+	0.432734i	−0.889557	−	0.456823i	$-0.848987\pi$
$683$	−201866.	+	201866.i	−0.432734	+	0.432734i	0.456823	+	0.889557i	$0.348987\pi$
$684$	381490.	−	10818.8i	0.815401	−	0.0231243i
$685$	−103064.	−	123902.i	−0.219648	−	0.264057i
$686$	−111.174	+	630.501i	−0.000236242	+	0.00133979i
$687$	8571.52	+	97972.9i	0.0181612	+	0.207583i
$688$	−369264.	+	172191.i	−0.780117	+	0.363775i
$689$	245863.	+	675502.i	0.517910	+	1.42294i
$690$	7648.41	−	42314.7i	0.0160647	−	0.0888777i
$691$	−64046.6	−	110932.i	−0.134134	−	0.232328i	0.791132	−	0.611645i	$-0.209492\pi$
$691$	−64046.6	−	110932.i	−0.134134	−	0.232328i	−0.925266	+	0.379318i	$0.876159\pi$
$692$	245103.	−	65675.1i	0.511842	−	0.137148i
$693$	−291.186	−	203.891i	−0.000606324	−	0.000424552i
$694$	−21901.5	+	3861.83i	−0.0454731	+	0.00801814i
$695$	−142676.	−	100817.i	−0.295380	−	0.208720i
$696$	−4858.25	−	8414.74i	−0.0100291	−	0.0173709i
$697$	430121.	+	37630.7i	0.885370	+	0.0774598i
$698$	−28075.8	+	60208.8i	−0.0576264	+	0.123580i
$699$	39433.7	−	108343.i	0.0807074	−	0.221742i
$700$	−2260.75	−	217.338i	−0.00461378	−	0.000443547i
$701$	−135936.	+	770933.i	−0.276630	+	1.56885i	0.457106	+	0.889412i	$0.348886\pi$
$701$	−135936.	+	770933.i	−0.276630	+	1.56885i	−0.733736	+	0.679435i	$0.762225\pi$
$702$	37185.3	+	37185.3i	0.0754567	+	0.0754567i
$703$	285437.	−	433290.i	0.577564	−	0.876735i
$704$		−	81721.6i		−	0.164889i
$705$	37162.1	−	136350.i	0.0747692	−	0.274332i
$706$	12818.5	+	10756.0i	0.0257174	+	0.0215794i
$707$	1223.89	+	2624.65i	0.00244853	+	0.00525089i
$708$	−104938.	+	225041.i	−0.209348	+	0.448947i
$709$	−340989.	−	406375.i	−0.678340	−	0.808415i	0.311553	−	0.950229i	$-0.399151\pi$
$709$	−340989.	−	406375.i	−0.678340	−	0.808415i	−0.989893	+	0.141814i	$0.954706\pi$
$710$	1980.58	−	5369.85i	0.00392894	−	0.0106524i
$711$	305462.	−	529077.i	0.604253	−	1.04660i
$712$	−149259.	+	213164.i	−0.294430	+	0.420489i
$713$	−772820.	−	541134.i	−1.52019	−	1.06445i
$714$	183.247	+	105.798i	0.000359453	+	0.000207530i
$715$	89249.6	+	32918.2i	0.174580	+	0.0643908i
$716$	−288243.	+	241864.i	−0.562253	+	0.471787i
$717$	−13310.7	−	6206.89i	−0.0258918	−	0.0120736i
$718$	10340.0	−	4821.60i	0.0200572	−	0.00935282i
$719$	288729.	−	344094.i	0.558512	−	0.665609i	−0.410719	−	0.911762i	$-0.634722\pi$
$719$	288729.	−	344094.i	0.558512	−	0.665609i	0.969231	+	0.246153i	$0.0791666\pi$
$720$	390958.	+	106555.i	0.754162	+	0.205546i
$721$	813.149			0.00156423
$722$	−39426.8	+	63710.2i	−0.0756340	+	0.122218i
$723$	153033.	−	153033.i	0.292758	−	0.292758i
$724$	−862540.	−	152089.i	−1.64552	−	0.290149i
$725$	69954.4	−	57683.9i	0.133088	−	0.109743i
$726$	−28070.8	−	10216.9i	−0.0532576	−	0.0193842i
$727$	182055.	+	84893.9i	0.344457	+	0.160623i	0.587146	−	0.809481i	$-0.300252\pi$
$727$	182055.	+	84893.9i	0.344457	+	0.160623i	−0.242689	+	0.970104i	$0.578029\pi$
$728$	61.6344	−	704.484i	0.000116295	−	0.00132926i
$729$	−60983.2	+	35208.7i	−0.114751	+	0.0662513i
$730$	46374.7	−	65629.3i	0.0870232	−	0.123155i
$731$	127053.	+	720552.i	0.237766	+	1.34844i
$732$	209405.	−	299061.i	0.390809	−	0.558133i
$733$	135488.	+	505648.i	0.252170	+	0.941110i	0.969643	+	0.244524i	$0.0786317\pi$
$733$	135488.	+	505648.i	0.252170	+	0.941110i	−0.717474	+	0.696586i	$0.754702\pi$
$734$	98446.8	−	56838.3i	0.182730	−	0.105499i
$735$	−217283.	−	39274.1i	−0.402209	−	0.0726995i
$736$	328192.	−	119452.i	0.605860	−	0.220515i
$737$	−18127.6	−	38874.7i	−0.0333737	−	0.0715702i
$738$	38670.7	−	3383.25i	0.0710018	−	0.00621185i
$739$	−191404.	−	33749.7i	−0.350480	−	0.0617990i	−0.00436296	−	0.999990i	$-0.501389\pi$
$739$	−191404.	−	33749.7i	−0.350480	−	0.0617990i	−0.346117	+	0.938191i	$0.612500\pi$
$740$	432859.	−	360061.i	0.790465	−	0.657525i
$741$	217852.	−	44815.3i	0.396757	−	0.0816188i
$742$	404.645	+	404.645i	0.000734964	+	0.000734964i
$743$	374329.	+	534598.i	0.678072	+	0.968388i	0.999768	+	0.0215446i	$0.00685840\pi$
$743$	374329.	+	534598.i	0.678072	+	0.968388i	−0.321695	+	0.946843i	$0.604253\pi$
$744$	49941.5	−	59517.9i	0.0902226	−	0.107523i
$745$	296819.	−	629470.i	0.534784	−	1.13413i
$746$	−27183.3	+	9893.92i	−0.0488455	+	0.0177783i
$747$	87333.6	+	7640.70i	0.156509	+	0.0136928i
$748$	−148353.	−	39751.2i	−0.265152	−	0.0710472i
$749$	−1036.72	−	598.551i	−0.00184798	−	0.00106693i
$750$	−3303.19	+	32879.5i	−0.00587234	+	0.0584524i
$751$	46174.5	+	261868.i	0.0818695	+	0.464305i	0.997988	+	0.0633981i	$0.0201938\pi$
$751$	46174.5	+	261868.i	0.0818695	+	0.464305i	−0.916119	+	0.400907i	$0.868695\pi$
$752$	356604.	−	95551.9i	0.630596	−	0.168968i
$753$	405287.	+	108596.i	0.714781	+	0.191525i
$754$	8978.85	+	10700.6i	0.0157935	+	0.0188219i
$755$	609509.	−	160520.i	1.06927	−	0.281602i
$756$	−1864.98	−	678.796i	−0.00326310	−	0.00118767i
$757$	25114.5	+	287060.i	0.0438261	+	0.500934i	0.986107	+	0.166111i	$0.0531210\pi$
$757$	25114.5	+	287060.i	0.0438261	+	0.500934i	−0.942281	+	0.334823i	$0.891323\pi$
$758$	55322.9	+	79009.3i	0.0962868	+	0.137512i
$759$		−	67971.2i		−	0.117989i
$760$	−123298.	+	108621.i	−0.213466	+	0.188055i
$761$	−738901.			−1.27590			−0.637950	−	0.770077i	$-0.720218\pi$
$761$	−738901.			−1.27590			−0.637950	+	0.770077i	$0.720218\pi$
$762$	41082.8	−	28766.5i	0.0707539	−	0.0495424i
$763$	948.300	−	82.9655i	0.00162891	−	0.000142511i
$764$	68117.9	−	187152.i	0.116701	−	0.320633i
$765$	366539.	−	628626.i	0.626322	−	1.07416i
$766$	−63633.2	+	53394.6i	−0.108449	+	0.0909996i
$767$	186729.	−	696883.i	0.317411	−	1.18459i
$768$	−49902.5	−	186239.i	−0.0846057	−	0.315753i
$769$	512502.	−	90367.8i	0.866647	−	0.152813i	0.277389	−	0.960758i	$-0.410531\pi$
$769$	512502.	−	90367.8i	0.866647	−	0.152813i	0.589259	+	0.807944i	$0.299420\pi$
$770$	75.4665	−	6.27658i	0.000127284	−	1.05862e-5i
$771$	43217.3	−	74854.5i	0.0727024	−	0.125924i
$772$	−5128.48	+	19139.7i	−0.00860506	+	0.0321145i
$773$	45216.5	−	516827.i	0.0756726	−	0.864941i	−0.859590	−	0.510985i	$-0.829281\pi$
$773$	45216.5	−	516827.i	0.0756726	−	0.864941i	0.935262	−	0.353956i	$-0.115164\pi$
$774$	22498.7	+	61814.7i	0.0375557	+	0.103183i
$775$	624751.	+	367878.i	1.04017	+	0.612492i
$776$	−160305.	−	134512.i	−0.266209	−	0.223376i
$777$	−1004.40	+	703.290i	−0.00166366	+	0.00116491i
$778$	−34105.2	+	34105.2i	−0.0563458	+	0.0563458i
$779$	171699.	−	317876.i	0.282940	−	0.523820i
$780$	240340.	+	22065.6i	0.395036	+	0.0362683i
$781$	1571.02	−	8909.69i	0.00257561	−	0.0146070i
$782$	−17581.2	−	200954.i	−0.0287498	−	0.328612i
$783$	71808.5	−	33484.9i	0.117126	−	0.0546166i
$784$	−197282.	−	542027.i	−0.320963	−	0.881838i
$785$	−166306.	−	30059.9i	−0.269878	−	0.0487807i
$786$	6234.83	+	10799.0i	0.0100921	+	0.0174800i
$787$	−860962.	+	230694.i	−1.39006	+	0.372466i	−0.874766	−	0.484545i	$-0.838985\pi$
$787$	−860962.	+	230694.i	−1.39006	+	0.372466i	−0.515297	+	0.857011i	$0.672319\pi$
$788$	−213806.	−	149709.i	−0.344324	−	0.241098i
$789$	194476.	−	34291.4i	0.312401	−	0.0550847i
$790$	22050.0	+	128265.i	0.0353309	+	0.205520i
$791$	−1535.90	−	2660.26i	−0.00245477	−	0.00425178i
$792$	−27802.0	−	2432.36i	−0.0443227	−	0.00387773i
$793$	−448305.	+	961393.i	−0.712898	+	1.52881i
$794$	19533.1	−	53666.7i	0.0309835	−	0.0851264i
$795$	−280308.	+	277915.i	−0.443508	+	0.439721i
$796$	−13825.2	+	78406.8i	−0.0218196	+	0.123745i
$797$	250236.	+	250236.i	0.393942	+	0.393942i	0.876090	−	0.482148i	$-0.160143\pi$
$797$	250236.	+	250236.i	0.393942	+	0.393942i	−0.482148	+	0.876090i	$0.660143\pi$
$798$	142.098	−	105.625i	0.000223143	−	0.000165868i
$799$		−	662973.i		−	1.03849i
$800$	−244213.	+	111339.i	−0.381583	+	0.173967i
$801$	−738684.	−	619830.i	−1.15131	−	0.966067i
$802$	50509.4	+	108318.i	0.0785278	+	0.168403i
$803$	53683.9	−	115125.i	0.0832555	−	0.178542i
$804$	−69952.7	−	83366.4i	−0.108216	−	0.128967i
$805$	−1974.40	−	4281.95i	−0.00304680	−	0.00660770i
$806$	−55848.0	+	96731.5i	−0.0859681	+	0.148901i
$807$	−192922.	+	275522.i	−0.296235	+	0.423067i
$808$	186245.	+	130410.i	0.285274	+	0.199751i
$809$	−782873.	−	451992.i	−1.19617	−	0.690611i	−0.236473	−	0.971638i	$-0.575992\pi$
$809$	−782873.	−	451992.i	−1.19617	−	0.690611i	−0.959700	+	0.281027i	$0.909325\pi$
$810$	17187.8	−	46600.6i	0.0261970	−	0.0710267i
$811$	792172.	−	664711.i	1.20442	−	1.01063i	0.204927	−	0.978777i	$-0.434304\pi$
$811$	792172.	−	664711.i	1.20442	−	1.01063i	0.999493	−	0.0318506i	$-0.0101401\pi$
$812$	−477.782	−	222.794i	−0.000724633	−	0.000337902i
$813$	−13434.9	+	6264.79i	−0.0203260	+	0.00947818i
$814$	−12067.1	+	14381.1i	−0.0182119	+	0.0217041i
$815$	13296.3	+	23259.7i	0.0200178	+	0.0350177i
$816$	−381279.			−0.572615
$817$	595624.	+	141629.i	0.892336	+	0.212182i
$818$	58889.2	−	58889.2i	0.0880094	−	0.0880094i
$819$	2580.67	+	455.043i	0.00384738	+	0.000678397i
$820$	278403.	−	276026.i	0.414044	−	0.410509i
$821$	583409.	+	212344.i	0.865540	+	0.315031i	0.736360	−	0.676590i	$-0.236543\pi$
$821$	583409.	+	212344.i	0.865540	+	0.315031i	0.129180	+	0.991621i	$0.458765\pi$
$822$	12356.4	+	5761.87i	0.0182872	+	0.00852747i
$823$	−50601.3	+	578376.i	−0.0747071	+	0.853906i	0.862710	+	0.505699i	$0.168765\pi$
$823$	−50601.3	+	578376.i	−0.0747071	+	0.853906i	−0.937417	+	0.348208i	$0.886790\pi$
$824$	55287.4	−	31920.2i	0.0814276	−	0.0470122i
$825$	4106.22	+	52073.0i	0.00603302	+	0.0765076i
$826$	−99.7320	−	565.608i	−0.000146175	−	0.000829002i
$827$	255480.	−	364863.i	0.373547	−	0.533481i	−0.587732	−	0.809055i	$-0.699979\pi$
$827$	255480.	−	364863.i	0.373547	−	0.533481i	0.961280	+	0.275574i	$0.0888681\pi$
$828$	222533.	+	830503.i	0.324588	+	1.21138i
$829$	−656235.	+	378878.i	−0.954884	+	0.551302i	−0.894595	−	0.446879i	$-0.852536\pi$
$829$	−656235.	+	378878.i	−0.954884	+	0.551302i	−0.0602891	+	0.998181i	$0.519202\pi$
$830$	−15344.2	+	10646.4i	−0.0222735	+	0.0154542i
$831$	−408261.	+	148595.i	−0.591202	+	0.215180i
$832$	254601.	+	545994.i	0.367801	+	0.788753i
$833$	−1.03189e6	+	90278.4i	−1.48711	+	0.130105i
$834$	14554.4	+	2566.33i	0.0209248	+	0.00368961i
$835$	−747853.	−	899056.i	−1.07261	−	1.28948i
$836$	−79784.1	+	100751.i	−0.114157	+	0.144157i
$837$	447991.	+	447991.i	0.639467	+	0.639467i
$838$	29663.4	+	42363.8i	0.0422409	+	0.0603263i
$839$	343513.	−	409383.i	0.488000	−	0.581575i	−0.464708	−	0.885464i	$-0.653841\pi$
$839$	343513.	−	409383.i	0.488000	−	0.581575i	0.952708	+	0.303889i	$0.0982851\pi$
$840$	365.462	−	131.246i	0.000517945	−	0.000186006i
$841$	−644850.	+	234706.i	−0.911731	+	0.331843i
$842$	53788.2	+	4705.86i	0.0758688	+	0.00663766i
$843$	−15595.1	−	4178.68i	−0.0219448	−	0.00588009i
$844$	203355.	+	117407.i	0.285476	+	0.164819i
$845$	12722.8	−	1058.16i	0.0178184	−	0.00148196i
$846$	−10350.4	−	58700.1i	−0.0144616	−	0.0820159i
$847$	−3164.05	+	847.805i	−0.00441039	+	0.00118176i
$848$	−996021.	−	266883.i	−1.38509	−	0.371133i
$849$	−152450.	−	181683.i	−0.211501	−	0.252057i
$850$	25608.9	+	152890.i	0.0354449	+	0.211612i
$851$	1.09844e6	+	399798.i	1.51675	+	0.552053i
$852$	−2000.57	−	22866.6i	−0.00275596	−	0.0315008i
$853$	−31496.5	−	44981.6i	−0.0432876	−	0.0618211i	0.796925	−	0.604078i	$-0.206459\pi$
$853$	−31496.5	−	44981.6i	−0.0432876	−	0.0618211i	−0.840212	+	0.542257i	$0.817570\pi$
$854$			844.449i			0.00115786i
$855$	−361149.	−	490231.i	−0.494032	−	0.670607i
$856$	−93984.5			−0.128265
$857$	196388.	−	137512.i	0.267395	−	0.187232i	−0.432188	−	0.901784i	$-0.642258\pi$
$857$	196388.	−	137512.i	0.267395	−	0.187232i	0.699583	+	0.714552i	$0.253369\pi$
$858$	−8016.64	+	701.365i	−0.0108898	+	0.000952730i
$859$	−390890.	+	1.07396e6i	−0.529746	+	1.45547i	0.329624	+	0.944112i	$0.393078\pi$
$859$	−390890.	+	1.07396e6i	−0.529746	+	1.45547i	−0.859370	+	0.511354i	$0.829144\pi$
$860$	573922.	+	334643.i	0.775990	+	0.452465i
$861$	−654.027	+	548.794i	−0.000882245	+	0.000740292i
$862$	−38262.7	+	142798.i	−0.0514945	+	0.192180i
$863$	3885.20	+	14499.8i	0.00521665	+	0.0194688i	0.968485	−	0.249071i	$-0.0801254\pi$
$863$	3885.20	+	14499.8i	0.00521665	+	0.0194688i	−0.963268	+	0.268540i	$0.913459\pi$
$864$	−230975.	+	40727.0i	−0.309412	+	0.0545576i
$865$	−309012.	−	261557.i	−0.412993	−	0.349570i
$866$	18291.5	−	31681.7i	0.0243900	−	0.0422448i
$867$	−97691.4	+	364589.i	−0.129963	+	0.485027i
$868$	367.396	−	4199.35i	0.000487635	−	0.00557369i
$869$	70361.8	+	193317.i	0.0931746	+	0.255995i
$870$	−3271.36	+	6937.64i	−0.00432205	+	0.00916586i
$871$	242226.	+	203252.i	0.319289	+	0.267916i
$872$	61219.8	−	42866.5i	0.0805116	−	0.0563749i
$873$	548318.	−	548318.i	0.719456	−	0.719456i
$874$	−160186.	−	53211.0i	−0.209702	−	0.0696593i
$875$	1771.28	+	3161.14i	0.00231350	+	0.00412884i
$876$	55964.3	−	317389.i	0.0729295	−	0.413604i
$877$	57002.1	+	651537.i	0.0741125	+	0.847110i	0.938724	+	0.344669i	$0.112009\pi$
$877$	57002.1	+	651537.i	0.0741125	+	0.847110i	−0.864612	+	0.502441i	$0.832436\pi$
$878$	−60644.8	+	28279.1i	−0.0786691	+	0.0366840i
$879$	8072.95	+	22180.3i	0.0104485	+	0.0287071i
$880$	−112111.	+	77786.9i	−0.144772	+	0.100448i
$881$	−552288.	−	956591.i	−0.711564	−	1.23247i	−0.964270	−	0.264922i	$-0.914654\pi$
$881$	−552288.	−	956591.i	−0.711564	−	1.23247i	0.252706	−	0.967543i	$-0.418680\pi$
$882$	−89954.6	+	24103.3i	−0.115634	+	0.0309841i
$883$	1.18619e6	+	830578.i	1.52136	+	1.06527i	0.973497	+	0.228702i	$0.0734480\pi$
$883$	1.18619e6	+	830578.i	1.52136	+	1.06527i	0.547865	+	0.836567i	$0.315441\pi$
$884$	1.11501e6	−	196607.i	1.42684	−	0.251591i
$885$	390434.	−	67119.4i	0.498495	−	0.0856962i
$886$	−49878.6	−	86392.3i	−0.0635400	−	0.110055i
$887$	1.00640e6	+	88048.6i	1.27916	+	0.111912i	0.706399	−	0.707814i	$-0.250318\pi$
$887$	1.00640e6	+	88048.6i	1.27916	+	0.111912i	0.572757	+	0.819725i	$0.305874\pi$
$888$	−40683.4	+	87245.8i	−0.0515930	+	0.110642i
$889$	1880.95	−	5167.88i	0.00237999	−	0.00653896i
$890$	205421.	+	880.662i	0.259338	+	0.00111181i
$891$	13633.6	−	77320.1i	0.0171734	−	0.0973951i
$892$	−970423.	−	970423.i	−1.21964	−	1.21964i
$893$	−509218.	−	220101.i	−0.638559	−	0.276006i
$894$			58873.3i			0.0736619i
$895$	579202.	+	157861.i	0.723076	+	0.197074i
$896$	1588.01	+	1332.50i	0.00197806	+	0.00165979i
$897$	211762.	+	454125.i	0.263186	+	0.564405i
$898$	49934.1	−	107084.i	0.0619220	−	0.132792i
$899$	108173.	+	128915.i	0.133844	+	0.159509i
$900$	−220655.	−	622808.i	−0.272413	−	0.768898i
$901$	−925864.	+	1.60364e6i	−1.14051	+	1.97541i
$902$	−7497.67	+	10707.8i	−0.00921539	+	0.0131609i
$903$	−1185.15	−	829.852i	−0.00145344	−	0.00101771i
$904$	−208857.	−	120584.i	−0.255571	−	0.147554i
$905$	585122.	+	1.26897e6i	0.714413	+	1.54937i
$906$	−40845.2	+	34273.2i	−0.0497605	+	0.0417540i
$907$	1.00010e6	+	466355.i	1.21571	+	0.566894i	0.921325	−	0.388794i	$-0.127108\pi$
$907$	1.00010e6	+	466355.i	1.21571	+	0.566894i	0.294383	+	0.955688i	$0.404886\pi$
$908$	−1.30321e6	+	607695.i	−1.58067	+	0.737079i
$909$	−541556.	+	645401.i	−0.655413	+	0.781091i
$910$	−484.648	+	277.048i	−0.000585253	+	0.000334559i
$911$	−958290.			−1.15468			−0.577338	−	0.816505i	$-0.695909\pi$
$911$	−958290.			−1.15468			−0.577338	+	0.816505i	$0.695909\pi$
$912$	−126581.	+	292854.i	−0.152187	+	0.352096i
$913$	−20874.7	+	20874.7i	−0.0250425	+	0.0250425i
$914$	52477.0	+	9253.12i	0.0628170	+	0.0110763i
$915$	−582475.	−	2497.13i	−0.695721	−	0.00298262i
$916$	393656.	+	143279.i	0.469166	+	0.170762i
$917$	1239.26	+	577.875i	0.00147375	+	0.000687219i
$918$	−11806.4	+	134948.i	−0.0140099	+	0.160133i
$919$	146781.	−	84743.8i	0.173795	−	0.100341i	−0.410579	−	0.911825i	$-0.634673\pi$
$919$	146781.	−	84743.8i	0.173795	−	0.100341i	0.584374	+	0.811484i	$0.301340\pi$
$920$	−302331.	−	213632.i	−0.357197	−	0.252401i
$921$	−78098.7	−	442920.i	−0.0920714	−	0.522163i
$922$	95369.2	−	136201.i	0.112188	−	0.160221i
$923$	17261.7	+	64421.4i	0.0202619	+	0.0756183i
$924$	263.015	−	151.852i	0.000308060	−	0.000177859i
$925$	−865667.	−	239929.i	−1.01174	−	0.280413i
$926$	80026.0	−	29127.1i	0.0933274	−	0.0339684i
$927$	99976.6	+	214400.i	0.116343	+	0.249497i
$928$	−62061.7	+	5429.69i	−0.0720655	+	0.00630492i
$929$	−696996.	−	122899.i	−0.807605	−	0.142403i	−0.245423	−	0.969416i	$-0.578927\pi$
$929$	−696996.	−	122899.i	−0.807605	−	0.142403i	−0.562182	+	0.827014i	$0.690038\pi$
$930$	−61076.0	−	5607.40i	−0.0706162	−	0.00648329i
$931$	−273235.	+	822547.i	−0.315237	+	0.948989i
$932$	−347273.	−	347273.i	−0.399797	−	0.399797i
$933$	−281040.	−	401367.i	−0.322853	−	0.461082i
$934$	−11854.0	+	14127.1i	−0.0135885	+	0.0161942i
$935$	82821.1	+	230621.i	0.0947366	+	0.263800i
$936$	193327.	−	70365.3i	0.220669	−	0.0803169i
$937$	667211.	+	58373.4i	0.759948	+	0.0664869i	0.460541	−	0.887638i	$-0.347655\pi$
$937$	667211.	+	58373.4i	0.759948	+	0.0664869i	0.299407	+	0.954125i	$0.403211\pi$
$938$	243.141	+	65.1495i	0.000276346	+	7.40467e-5i
$939$	−232640.	−	134315.i	−0.263848	−	0.152333i
$940$	−459483.	−	388921.i	−0.520013	−	0.440155i
$941$	−235834.	−	1.33748e6i	−0.266334	−	1.51046i	−0.765209	−	0.643781i	$-0.777365\pi$
$941$	−235834.	−	1.33748e6i	−0.266334	−	1.51046i	0.498875	−	0.866674i	$-0.333747\pi$
$942$	13809.5	−	3700.24i	0.0155624	−	0.00416992i
$943$	786196.	+	210661.i	0.884112	+	0.236897i
$944$	665223.	+	792782.i	0.746489	+	0.889631i
$945$	806.419	+	3062.05i	0.000903019	+	0.00342885i
$946$	−20815.6	−	7576.26i	−0.0232598	−	0.00846589i
$947$	−93139.0	−	1.06458e6i	−0.103856	−	1.18708i	−0.851999	−	0.523543i	$-0.824610\pi$
$947$	−93139.0	−	1.06458e6i	−0.103856	−	1.18708i	0.748143	−	0.663537i	$-0.230946\pi$
$948$	299379.	+	427558.i	0.333124	+	0.475750i
$949$			936420.i			1.03977i
$950$	125934.	+	31088.1i	0.139539	+	0.0344467i
$951$	−150252.			−0.166135
$952$	1492.20	−	1044.85i	0.00164647	−	0.00115287i
$953$	−885036.	+	77430.6i	−0.974485	+	0.0852564i	−0.563262	−	0.826278i	$-0.690454\pi$
$953$	−885036.	+	77430.6i	−0.974485	+	0.0852564i	−0.411223	+	0.911535i	$0.634898\pi$
$954$	−56940.4	+	156443.i	−0.0625639	+	0.171893i
$955$	−307279.	+	80924.9i	−0.336920	+	0.0887311i
$956$	−47923.6	+	40212.7i	−0.0524365	+	0.0439994i
$957$	−3138.04	+	11711.3i	−0.00342637	+	0.0127874i
$958$	−13066.3	−	48764.3i	−0.0142372	−	0.0531338i
$959$	1472.30	−	259.607i	0.00160089	−	0.000282279i
$960$	−213720.	+	252495.i	−0.231901	+	0.273974i
$961$	−211069.	+	365582.i	−0.228548	+	0.395856i
$962$	35818.6	−	133677.i	0.0387042	−	0.144446i
$963$	30353.4	−	346941.i	0.0327306	−	0.374113i
$964$	−315298.	−	866275.i	−0.339287	−	0.932184i
$965$	29753.4	−	10685.1i	0.0319508	−	0.0114743i
$966$	305.564	+	256.399i	0.000327452	+	0.000274765i
$967$	−1.34438e6	+	941345.i	−1.43770	+	1.00669i	−0.443836	+	0.896108i	$0.646383\pi$
$967$	−1.34438e6	+	941345.i	−1.43770	+	1.00669i	−0.993867	+	0.110582i	$0.964728\pi$
$968$	−181849.	+	181849.i	−0.194070	+	0.194070i
$969$	449149.	+	355679.i	0.478347	+	0.378801i
$970$	−15102.9	+	164501.i	−0.0160515	+	0.174834i
$971$	−28516.5	+	161725.i	−0.0302453	+	0.171530i	−0.996189	−	0.0872235i	$-0.972201\pi$
$971$	−28516.5	+	161725.i	−0.0302453	+	0.171530i	0.965943	+	0.258753i	$0.0833117\pi$
$972$	−77777.4	−	888999.i	−0.0823229	−	0.940955i
$973$	1468.75	−	684.890i	0.00155140	−	0.000723428i
$974$	−75946.2	−	208660.i	−0.0800549	−	0.219949i
$975$	−189666.	−	335114.i	−0.199517	−	0.352520i
$976$	−760815.	−	1.31777e6i	−0.798692	−	1.38338i
$977$	1.39399e6	−	373517.i	1.46039	−	0.391311i	0.560766	−	0.827974i	$-0.310507\pi$
$977$	1.39399e6	−	373517.i	1.46039	−	0.391311i	0.899625	+	0.436663i	$0.143840\pi$
$978$	−1856.58	−	1299.99i	−0.00194104	−	0.00135913i
$979$	319782.	−	56386.2i	0.333648	−	0.0588311i
$980$	−542769.	+	768125.i	−0.565149	+	0.799797i
$981$	138469.	+	239835.i	0.143884	+	0.249215i
$982$	178807.	+	15643.6i	0.185422	+	0.0162223i
$983$	518446.	−	1.11181e6i	0.536533	−	1.15060i	−0.432037	−	0.901856i	$-0.642205\pi$
$983$	518446.	−	1.11181e6i	0.536533	−	1.15060i	0.968570	−	0.248742i	$-0.0800173\pi$
$984$	−22925.5	+	62987.3i	−0.0236771	+	0.0650523i
$985$	−1785.26	+	416425.i	−0.00184004	+	0.429205i
$986$	−6248.27	+	35435.7i	−0.00642697	+	0.0364491i
$987$	926.993	+	926.993i	0.000951573	+	0.000951573i
$988$	219163.	−	921696.i	0.224520	−	0.944221i
$989$			1.37929e6i			1.41014i
$990$	10933.5	+	19126.3i	0.0111555	+	0.0195147i
$991$	854836.	+	717293.i	0.870434	+	0.730380i	0.964189	−	0.265215i	$-0.0854429\pi$
$991$	854836.	+	717293.i	0.870434	+	0.730380i	−0.0937558	+	0.995595i	$0.529887\pi$
$992$	−210529.	−	451480.i	−0.213938	−	0.458792i
$993$	−5301.52	+	11369.1i	−0.00537652	+	0.0115300i
$994$	34.1273	+	40.6714i	3.45406e−5	+	4.11639e-5i
$995$	115352.	−	53188.8i	0.116515	−	0.0537248i
$996$	−37449.8	+	64865.0i	−0.0377513	+	0.0653871i
$997$	−967343.	+	1.38151e6i	−0.973173	+	1.38984i	−0.0528825	+	0.998601i	$0.516841\pi$
$997$	−967343.	+	1.38151e6i	−0.973173	+	1.38984i	−0.920291	+	0.391235i	$0.872048\pi$
$998$	−168534.	−	118009.i	−0.169211	−	0.118482i
$999$	−679813.	−	392490.i	−0.681175	−	0.393277i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.5.q.a.17.20	✓	456
5.3	odd	4	inner	95.5.q.a.93.19	yes	456
19.9	even	9	inner	95.5.q.a.47.19	yes	456
95.28	odd	36	inner	95.5.q.a.28.20	yes	456

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.5.q.a.17.20	✓	456	1.1	even	1	trivial
95.5.q.a.28.20	yes	456	95.28	odd	36	inner
95.5.q.a.47.19	yes	456	19.9	even	9	inner
95.5.q.a.93.19	yes	456	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	95.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.470940 - 0.329756i) q^{2} +(-3.66462 + 0.320613i) q^{3} +(-5.35928 + 14.7245i) q^{4} +(24.1757 - 6.36689i) q^{5} +(-1.62009 + 1.35942i) q^{6} +(-0.0600223 + 0.224006i) q^{7} +(4.71236 + 17.5867i) q^{8} +(-66.4428 + 11.7157i) q^{9} +(9.28576 - 10.9705i) q^{10} +(11.3596 - 19.6754i) q^{11} +(14.9189 - 55.6779i) q^{12} +(-14.5970 + 166.845i) q^{13} +(0.0456004 + 0.125286i) q^{14} +(-86.5533 + 31.0833i) q^{15} +(-184.038 - 154.426i) q^{16} +(-353.403 + 247.455i) q^{17} +(-27.4273 + 27.4273i) q^{18} +(72.7400 + 353.596i) q^{19} +(-35.8148 + 390.096i) q^{20} +(0.148140 - 0.840142i) q^{21} +(-1.13839 - 13.0118i) q^{22} +(-737.093 + 343.712i) q^{23} +(-22.9075 - 62.9379i) q^{24} +(543.925 - 307.848i) q^{25} +(48.1437 + 83.3874i) q^{26} +(527.546 - 141.356i) q^{27} +(-2.97670 - 2.08431i) q^{28} +(142.868 - 25.1915i) q^{29} +(-30.5115 + 43.1798i) q^{30} +(580.013 + 1004.61i) q^{31} +(-427.799 - 37.4276i) q^{32} +(-35.3205 + 75.7450i) q^{33} +(-84.8317 + 233.073i) q^{34} +(-0.0248551 + 5.79766i) q^{35} +(183.578 - 1041.12i) q^{36} +(-1016.31 - 1016.31i) q^{37} +(150.856 + 142.536i) q^{38} -616.103i q^{39} +(225.897 + 395.168i) q^{40} +(-766.646 - 643.292i) q^{41} +(-0.207277 - 0.444506i) q^{42} +(716.732 - 1537.04i) q^{43} +(228.831 + 272.711i) q^{44} +(-1531.71 + 706.268i) q^{45} +(-233.785 + 404.928i) q^{46} +(-881.417 + 1258.79i) q^{47} +(723.939 + 506.908i) q^{48} +(2079.28 + 1200.47i) q^{49} +(154.642 - 324.340i) q^{50} +(1215.75 - 1020.13i) q^{51} +(-2378.48 - 1109.10i) q^{52} +(3889.98 - 1813.93i) q^{53} +(201.830 - 240.531i) q^{54} +(149.355 - 547.992i) q^{55} -4.22239 q^{56} +(-379.932 - 1272.47i) q^{57} +(58.9752 - 58.9752i) q^{58} +(-4242.27 - 748.027i) q^{59} +(6.17787 - 1441.04i) q^{60} +(5951.72 + 2166.25i) q^{61} +(604.427 + 281.849i) q^{62} +(1.36367 - 15.5868i) q^{63} +(3115.11 - 1798.51i) q^{64} +(709.391 + 4126.53i) q^{65} +(8.34352 + 47.3185i) q^{66} +(1082.90 - 1546.54i) q^{67} +(-1749.67 - 6529.86i) q^{68} +(2590.97 - 1495.89i) q^{69} +(1.90010 + 2.73854i) q^{70} +(374.200 - 136.198i) q^{71} +(-519.142 - 1113.30i) q^{72} +(5569.88 - 487.302i) q^{73} +(-813.757 - 143.487i) q^{74} +(-1894.58 + 1302.53i) q^{75} +(-5596.35 - 823.958i) q^{76} +(3.72559 + 3.72559i) q^{77} +(-203.164 - 290.148i) q^{78} +(-5820.48 + 6936.58i) q^{79} +(-5432.45 - 2561.60i) q^{80} +(3247.38 - 1181.95i) q^{81} +(-573.173 - 50.1461i) q^{82} +(-1255.12 - 336.308i) q^{83} +(11.5767 + 6.68383i) q^{84} +(-6968.22 + 8232.47i) q^{85} +(-169.309 - 960.198i) q^{86} +(-515.480 + 138.122i) q^{87} +(399.558 + 107.061i) q^{88} +(9187.05 + 10948.7i) q^{89} +(-488.446 + 837.698i) q^{90} +(-36.4982 - 13.2843i) q^{91} +(-1110.70 - 12695.4i) q^{92} +(-2447.62 - 3495.56i) q^{93} +883.469i q^{94} +(4009.84 + 8085.28i) q^{95} +1579.72 q^{96} +(-9414.90 + 6592.38i) q^{97} +(1375.08 - 120.304i) q^{98} +(-524.254 + 1440.38i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 456 q - 12 q^{2} - 12 q^{3} - 12 q^{5} + 84 q^{6} - 96 q^{7} - 6 q^{8} - 12 q^{10} - 12 q^{11} - 6 q^{12} - 12 q^{13} - 534 q^{15} + 4092 q^{16} - 1362 q^{17} - 3864 q^{18} - 2364 q^{20} - 4776 q^{21} + 2004 q^{22}+ \cdots + 123726 q^{98}+O(q^{100}) \) 456 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 + 84 * q^6 - 96 * q^7 - 6 * q^8 - 12 * q^10 - 12 * q^11 - 6 * q^12 - 12 * q^13 - 534 * q^15 + 4092 * q^16 - 1362 * q^17 - 3864 * q^18 - 2364 * q^20 - 4776 * q^21 + 2004 * q^22 + 1968 * q^23 + 3252 * q^25 + 7332 * q^26 - 6 * q^27 - 9648 * q^28 - 6 * q^30 - 12 * q^31 + 5922 * q^32 + 16494 * q^33 - 1794 * q^35 + 9048 * q^36 - 24 * q^37 - 15222 * q^38 - 9786 * q^40 - 5640 * q^41 + 7764 * q^42 - 19032 * q^43 - 6144 * q^45 - 12 * q^46 - 4332 * q^47 + 29328 * q^48 + 18426 * q^50 - 10944 * q^51 + 84 * q^52 + 1878 * q^53 + 27018 * q^55 - 48 * q^56 - 14202 * q^57 + 16536 * q^58 - 84108 * q^60 - 14688 * q^61 - 46536 * q^62 - 46098 * q^63 - 13236 * q^65 + 42408 * q^66 + 44748 * q^67 + 20154 * q^68 + 37620 * q^70 - 24 * q^71 + 82680 * q^72 - 10542 * q^73 + 90024 * q^75 - 21600 * q^76 + 20328 * q^77 + 63426 * q^78 - 32688 * q^80 + 41976 * q^81 - 184332 * q^82 - 43476 * q^83 - 51396 * q^85 + 11316 * q^86 - 59286 * q^87 - 1254 * q^88 - 9294 * q^90 - 33312 * q^91 + 163884 * q^92 - 106566 * q^93 - 11424 * q^95 - 200208 * q^96 + 12168 * q^97 + 123726 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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