LMFDB - Embedded newform 119.5.h.a.101.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [119,5,Mod(33,119)] 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("119.33"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(119, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 119 = 7 \cdot 17 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	119.h (of order $6$, degree $2$, 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:	$12.3010256070$
Analytic rank:	$0$
Dimension:	$92$
Relative dimension:	$46$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.9
Character	$\chi$	$=$	119.101
Dual form			119.5.h.a.33.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.81094 - 4.86869i) q^{2} +(-1.92369 + 3.33193i) q^{3} +(-7.80276 + 13.5148i) q^{4} +(-11.7603 - 20.3694i) q^{5} +21.6295 q^{6} +(37.6635 + 31.3442i) q^{7} -2.21777 q^{8} +(33.0988 + 57.3289i) q^{9} +(-66.1150 + 114.514i) q^{10} +(-59.4120 - 34.3015i) q^{11} +(-30.0202 - 51.9964i) q^{12} +213.115i q^{13} +(46.7356 - 271.479i) q^{14} +90.4927 q^{15} +(131.078 + 227.034i) q^{16} +(218.564 - 189.078i) q^{17} +(186.078 - 322.296i) q^{18} +(286.304 - 165.298i) q^{19} +367.051 q^{20} +(-176.890 + 65.1954i) q^{21} +385.678i q^{22} +(177.873 - 102.695i) q^{23} +(4.26630 - 7.38945i) q^{24} +(35.8906 - 62.1644i) q^{25} +(1037.59 - 599.053i) q^{26} -566.325 q^{27} +(-717.489 + 264.442i) q^{28} +124.544i q^{29} +(-254.369 - 440.581i) q^{30} +(-24.4405 + 42.3322i) q^{31} +(719.163 - 1245.63i) q^{32} +(228.581 - 131.971i) q^{33} +(-1534.93 - 532.635i) q^{34} +(195.531 - 1135.80i) q^{35} -1033.05 q^{36} +(1608.18 - 928.485i) q^{37} +(-1609.57 - 929.284i) q^{38} +(-710.084 - 409.967i) q^{39} +(26.0817 + 45.1748i) q^{40} -599.653 q^{41} +(814.642 + 677.960i) q^{42} +2105.30 q^{43} +(927.155 - 535.293i) q^{44} +(778.505 - 1348.41i) q^{45} +(-999.980 - 577.339i) q^{46} +(188.821 - 109.016i) q^{47} -1008.61 q^{48} +(436.077 + 2361.07i) q^{49} -403.546 q^{50} +(209.545 + 1091.97i) q^{51} +(-2880.20 - 1662.88i) q^{52} +(-735.178 + 1273.37i) q^{53} +(1591.91 + 2757.26i) q^{54} +1613.59i q^{55} +(-83.5290 - 69.5144i) q^{56} +1271.93i q^{57} +(606.368 - 350.086i) q^{58} +(5225.08 + 3016.70i) q^{59} +(-706.092 + 1222.99i) q^{60} +(1942.09 + 3363.80i) q^{61} +274.803 q^{62} +(-550.312 + 3196.66i) q^{63} -3891.59 q^{64} +(4341.03 - 2506.30i) q^{65} +(-1285.05 - 741.925i) q^{66} +(-3643.41 + 6310.56i) q^{67} +(849.943 + 4429.18i) q^{68} +790.213i q^{69} +(-6079.49 + 2240.69i) q^{70} +307.620i q^{71} +(-73.4056 - 127.142i) q^{72} +(1368.52 - 2370.35i) q^{73} +(-9041.01 - 5219.83i) q^{74} +(138.085 + 239.170i) q^{75} +5159.11i q^{76} +(-1162.51 - 3154.14i) q^{77} +4609.57i q^{78} +(6176.74 - 3566.14i) q^{79} +(3083.04 - 5339.97i) q^{80} +(-1591.57 + 2756.68i) q^{81} +(1685.59 + 2919.52i) q^{82} +5312.92i q^{83} +(499.125 - 2899.33i) q^{84} +(-6421.80 - 2228.42i) q^{85} +(-5917.88 - 10250.1i) q^{86} +(-414.973 - 239.585i) q^{87} +(131.762 + 76.0730i) q^{88} +(10168.1 - 5870.54i) q^{89} -8753.32 q^{90} +(-6679.93 + 8026.65i) q^{91} +3205.22i q^{92} +(-94.0320 - 162.868i) q^{93} +(-1061.53 - 612.874i) q^{94} +(-6734.05 - 3887.90i) q^{95} +(2766.89 + 4792.40i) q^{96} +9939.90 q^{97} +(10269.5 - 8759.94i) q^{98} -4541.37i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 2 q^{2} - 354 q^{4} + 56 q^{8} - 1068 q^{9} + 464 q^{15} - 3146 q^{16} + 1104 q^{17} - 906 q^{18} - 6 q^{19} - 240 q^{21} - 3106 q^{25} + 468 q^{26} + 1858 q^{30} - 1680 q^{32} - 198 q^{33} - 5318 q^{35}+ \cdots + 107386 q^{98}+O(q^{100}) $ 92 * q - 2 * q^2 - 354 * q^4 + 56 * q^8 - 1068 * q^9 + 464 * q^15 - 3146 * q^16 + 1104 * q^17 - 906 * q^18 - 6 * q^19 - 240 * q^21 - 3106 * q^25 + 468 * q^26 + 1858 * q^30 - 1680 * q^32 - 198 * q^33 - 5318 * q^35 + 17304 * q^36 - 6 * q^38 + 1888 * q^42 + 3316 * q^43 - 7242 * q^47 - 1284 * q^49 + 2136 * q^50 - 11304 * q^51 - 5202 * q^52 + 28 * q^53 - 17826 * q^59 - 3182 * q^60 + 41768 * q^64 + 5988 * q^66 + 2924 * q^67 - 22788 * q^68 + 36898 * q^70 - 23660 * q^72 - 3162 * q^77 - 6194 * q^81 + 30426 * q^84 + 46552 * q^85 + 4118 * q^86 - 7026 * q^87 + 4944 * q^89 + 11034 * q^93 - 101214 * q^94 + 107386 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/119\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.81094	−	4.86869i	−0.702735	−	1.21717i	−0.967503	−	0.252860i	$-0.918629\pi$
$2$	−2.81094	−	4.86869i	−0.702735	−	1.21717i	0.264768	−	0.964312i	$-0.414705\pi$
$3$	−1.92369	+	3.33193i	−0.213743	+	0.370214i	−0.952883	−	0.303338i	$-0.901899\pi$
$3$	−1.92369	+	3.33193i	−0.213743	+	0.370214i	0.739140	+	0.673552i	$0.235232\pi$
$4$	−7.80276	+	13.5148i	−0.487672	+	0.844673i
$5$	−11.7603	−	20.3694i	−0.470412	−	0.814778i	0.529015	−	0.848612i	$-0.322561\pi$
$5$	−11.7603	−	20.3694i	−0.470412	−	0.814778i	−0.999427	+	0.0338347i	$0.989228\pi$
$6$	21.6295			0.600819
$7$	37.6635	+	31.3442i	0.768643	+	0.639678i
$7$	37.6635	+	31.3442i	0.768643	+	0.639678i
$8$	−2.21777			−0.0346527
$9$	33.0988	+	57.3289i	0.408628	+	0.707764i
$10$	−66.1150	+	114.514i	−0.661150	+	1.14514i
$11$	−59.4120	−	34.3015i	−0.491008	−	0.283484i	0.233984	−	0.972240i	$-0.424824\pi$
$11$	−59.4120	−	34.3015i	−0.491008	−	0.283484i	−0.724993	+	0.688757i	$0.758157\pi$
$12$	−30.0202	−	51.9964i	−0.208473	−	0.361086i
$13$			213.115i			1.26104i	0.776175	+	0.630518i	$0.217157\pi$
$13$			213.115i			1.26104i	−0.776175	+	0.630518i	$0.782843\pi$
$14$	46.7356	−	271.479i	0.238447	−	1.38509i
$15$	90.4927			0.402190
$16$	131.078	+	227.034i	0.512024	+	0.886851i
$17$	218.564	−	189.078i	0.756279	−	0.654250i
$17$	218.564	−	189.078i	0.756279	−	0.654250i
$18$	186.078	−	322.296i	0.574314	−	0.994740i
$19$	286.304	−	165.298i	0.793086	−	0.457889i	−0.0479616	−	0.998849i	$-0.515272\pi$
$19$	286.304	−	165.298i	0.793086	−	0.457889i	0.841048	+	0.540961i	$0.181939\pi$
$20$	367.051			0.917628
$21$	−176.890	+	65.1954i	−0.401110	+	0.147835i
$22$			385.678i			0.796856i
$23$	177.873	−	102.695i	0.336244	−	0.194130i	−0.322366	−	0.946615i	$-0.604478\pi$
$23$	177.873	−	102.695i	0.336244	−	0.194130i	0.658610	+	0.752485i	$0.271145\pi$
$24$	4.26630	−	7.38945i	0.00740678	−	0.0128289i
$25$	35.8906	−	62.1644i	0.0574250	−	0.0994631i
$26$	1037.59	−	599.053i	1.53490	−	0.886173i
$27$	−566.325			−0.776852
$28$	−717.489	+	264.442i	−0.915165	+	0.337298i
$29$			124.544i			0.148091i	0.997255	+	0.0740454i	$0.0235910\pi$
$29$			124.544i			0.148091i	−0.997255	+	0.0740454i	$0.976409\pi$
$30$	−254.369	−	440.581i	−0.282633	−	0.489534i
$31$	−24.4405	+	42.3322i	−0.0254324	+	0.0440502i	−0.878461	−	0.477813i	$-0.841430\pi$
$31$	−24.4405	+	42.3322i	−0.0254324	+	0.0440502i	0.853029	+	0.521863i	$0.174763\pi$
$32$	719.163	−	1245.63i	0.702308	−	1.21643i
$33$	228.581	−	131.971i	0.209900	−	0.121186i
$34$	−1534.93	−	532.635i	−1.32780	−	0.460757i
$35$	195.531	−	1135.80i	0.159617	−	0.927185i
$36$	−1033.05			−0.797105
$37$	1608.18	−	928.485i	1.17471	−	0.678221i	0.219928	−	0.975516i	$-0.429418\pi$
$37$	1608.18	−	928.485i	1.17471	−	0.678221i	0.954786	+	0.297295i	$0.0960843\pi$
$38$	−1609.57	−	929.284i	−1.11466	−	0.643549i
$39$	−710.084	−	409.967i	−0.466853	−	0.269538i
$40$	26.0817	+	45.1748i	0.0163010	+	0.0282342i
$41$	−599.653			−0.356724			−0.178362	−	0.983965i	$-0.557080\pi$
$41$	−599.653			−0.356724			−0.178362	+	0.983965i	$0.557080\pi$
$42$	814.642	+	677.960i	0.461815	+	0.384331i
$43$	2105.30			1.13862			0.569308	−	0.822124i	$-0.307211\pi$
$43$	2105.30			1.13862			0.569308	+	0.822124i	$0.307211\pi$
$44$	927.155	−	535.293i	0.478902	−	0.276494i
$45$	778.505	−	1348.41i	0.384447	−	0.665881i
$46$	−999.980	−	577.339i	−0.472580	−	0.272844i
$47$	188.821	−	109.016i	0.0854781	−	0.0493508i	−0.456652	−	0.889646i	$-0.650951\pi$
$47$	188.821	−	109.016i	0.0854781	−	0.0493508i	0.542130	+	0.840295i	$0.317618\pi$
$48$	−1008.61			−0.437767
$49$	436.077	+	2361.07i	0.181623	+	0.983368i
$50$	−403.546			−0.161418
$51$	209.545	+	1091.97i	0.0805631	+	0.419827i
$52$	−2880.20	−	1662.88i	−1.06516	−	0.614972i
$53$	−735.178	+	1273.37i	−0.261722	+	0.453316i	−0.966700	−	0.255913i	$-0.917624\pi$
$53$	−735.178	+	1273.37i	−0.261722	+	0.453316i	0.704977	+	0.709230i	$0.250957\pi$
$54$	1591.91	+	2757.26i	0.545921	+	0.945563i
$55$			1613.59i			0.533417i
$56$	−83.5290	−	69.5144i	−0.0266355	−	0.0221666i
$57$			1271.93i			0.391482i
$58$	606.368	−	350.086i	0.180252	−	0.104069i
$59$	5225.08	+	3016.70i	1.50103	+	0.866619i	0.999999	+	0.00118871i	$0.000378377\pi$
$59$	5225.08	+	3016.70i	1.50103	+	0.866619i	0.501029	+	0.865430i	$0.332955\pi$
$60$	−706.092	+	1222.99i	−0.196137	+	0.339719i
$61$	1942.09	+	3363.80i	0.521927	+	0.904003i	0.999675	+	0.0255065i	$0.00811985\pi$
$61$	1942.09	+	3363.80i	0.521927	+	0.904003i	−0.477748	+	0.878497i	$0.658547\pi$
$62$	274.803			0.0714889
$63$	−550.312	+	3196.66i	−0.138653	+	0.805408i
$64$	−3891.59			−0.950096
$65$	4341.03	−	2506.30i	1.02746	−	0.593206i
$66$	−1285.05	−	741.925i	−0.295007	−	0.170323i
$67$	−3643.41	+	6310.56i	−0.811630	+	1.40578i	0.100093	+	0.994978i	$0.468086\pi$
$67$	−3643.41	+	6310.56i	−0.811630	+	1.40578i	−0.911723	+	0.410806i	$0.865247\pi$
$68$	849.943	+	4429.18i	0.183811	+	0.957868i
$69$			790.213i			0.165976i
$70$	−6079.49	+	2240.69i	−1.24071	+	0.457284i
$71$			307.620i			0.0610236i	0.999534	+	0.0305118i	$0.00971371\pi$
$71$			307.620i			0.0610236i	−0.999534	+	0.0305118i	$0.990286\pi$
$72$	−73.4056	−	127.142i	−0.0141600	−	0.0245259i
$73$	1368.52	−	2370.35i	0.256807	−	0.444803i	−0.708578	−	0.705633i	$-0.750663\pi$
$73$	1368.52	−	2370.35i	0.256807	−	0.444803i	0.965385	+	0.260830i	$0.0839962\pi$
$74$	−9041.01	−	5219.83i	−1.65102	−	0.953220i
$75$	138.085	+	239.170i	0.0245484	+	0.0425191i
$76$			5159.11i			0.893198i
$77$	−1162.51	−	3154.14i	−0.196071	−	0.531985i
$78$			4609.57i			0.757654i
$79$	6176.74	−	3566.14i	0.989704	−	0.571406i	0.0845183	−	0.996422i	$-0.473065\pi$
$79$	6176.74	−	3566.14i	0.989704	−	0.571406i	0.905186	+	0.425016i	$0.139732\pi$
$80$	3083.04	−	5339.97i	0.481724	−	0.834371i
$81$	−1591.57	+	2756.68i	−0.242581	+	0.420162i
$82$	1685.59	+	2919.52i	0.250682	+	0.434194i
$83$			5312.92i			0.771217i	0.922662	+	0.385609i	$0.126009\pi$
$83$			5312.92i			0.771217i	−0.922662	+	0.385609i	$0.873991\pi$
$84$	499.125	−	2899.33i	0.0707377	−	0.410902i
$85$	−6421.80	−	2228.42i	−0.888831	−	0.308432i
$86$	−5917.88	−	10250.1i	−0.800146	−	1.38589i
$87$	−414.973	−	239.585i	−0.0548253	−	0.0316534i
$88$	131.762	+	76.0730i	0.0170148	+	0.00982347i
$89$	10168.1	−	5870.54i	1.28369	−	0.741136i	0.306166	−	0.951978i	$-0.400954\pi$
$89$	10168.1	−	5870.54i	1.28369	−	0.741136i	0.977520	+	0.210842i	$0.0676205\pi$
$90$	−8753.32			−1.08066
$91$	−6679.93	+	8026.65i	−0.806657	+	0.969286i
$92$			3205.22i			0.378688i
$93$	−94.0320	−	162.868i	−0.0108720	−	0.0188309i
$94$	−1061.53	−	612.874i	−0.120137	−	0.0693610i
$95$	−6734.05	−	3887.90i	−0.746155	−	0.430793i
$96$	2766.89	+	4792.40i	0.300227	+	0.520008i
$97$	9939.90			1.05642			0.528212	−	0.849112i	$-0.322863\pi$
$97$	9939.90			1.05642			0.528212	+	0.849112i	$0.322863\pi$
$98$	10269.5	−	8759.94i	1.06930	−	0.912113i
$99$		−	4541.37i		−	0.463357i
$100$	560.092	+	970.108i	0.0560092	+	0.0970108i
$101$	5191.55	+	2997.34i	0.508925	+	0.293828i	0.732392	−	0.680883i	$-0.238404\pi$
$101$	5191.55	+	2997.34i	0.508925	+	0.293828i	−0.223466	+	0.974712i	$0.571737\pi$
$102$	4727.44	−	4089.67i	0.454387	−	0.393086i
$103$	−4227.16	+	2440.55i	−0.398450	+	0.230045i	−0.685815	−	0.727776i	$-0.740554\pi$
$103$	−4227.16	+	2440.55i	−0.398450	+	0.230045i	0.287365	+	0.957821i	$0.407221\pi$
$104$		−	472.640i		−	0.0436983i
$105$	3408.27	+	2836.42i	0.309140	+	0.257272i
$106$	8266.16			0.735686
$107$	−18390.0	+	10617.5i	−1.60626	+	0.927373i	−0.616060	+	0.787699i	$0.711272\pi$
$107$	−18390.0	+	10617.5i	−1.60626	+	0.927373i	−0.990198	+	0.139674i	$0.955394\pi$
$108$	4418.90	−	7653.75i	0.378849	−	0.656186i
$109$	−12587.9	−	7267.61i	−1.05950	−	0.611701i	−0.134204	−	0.990954i	$-0.542848\pi$
$109$	−12587.9	−	7267.61i	−1.05950	−	0.611701i	−0.925293	+	0.379253i	$0.876181\pi$
$110$	7856.05	−	4535.69i	0.649260	−	0.374851i
$111$			7144.47i			0.579861i
$112$	−2179.35	+	12659.4i	−0.173736	+	1.00920i
$113$		−	16473.4i		−	1.29011i	−0.764138	−	0.645053i	$-0.776835\pi$
$113$		−	16473.4i		−	1.29011i	0.764138	−	0.645053i	$-0.223165\pi$
$114$	6192.62	−	3575.31i	0.476502	−	0.275108i
$115$	−4183.68	−	2415.45i	−0.316346	−	0.182643i
$116$	−1683.19	−	971.789i	−0.125088	−	0.0722197i
$117$	−12217.6	+	7053.86i	−0.892515	+	0.515294i
$118$		−	33919.1i		−	2.43601i
$119$	14158.4	−	270.605i	0.999817	−	0.0191092i
$120$	−200.692			−0.0139369
$121$	−4967.31	−	8603.63i	−0.339274	−	0.587639i
$122$	10918.2	−	18910.9i	0.733552	−	1.27055i
$123$	1153.55	−	1998.00i	0.0762473	−	0.132064i
$124$	−381.407	−	660.616i	−0.0248053	−	0.0429641i
$125$	−16388.7			−1.04888
$126$	17110.5	−	6306.32i	1.07776	−	0.397224i
$127$	−12852.7			−0.796866			−0.398433	−	0.917197i	$-0.630446\pi$
$127$	−12852.7			−0.796866			−0.398433	+	0.917197i	$0.630446\pi$
$128$	−567.577	−	983.072i	−0.0346421	−	0.0600019i
$129$	−4049.95	+	7014.72i	−0.243372	+	0.421532i
$130$	−24404.8	−	14090.1i	−1.44407	−	0.833733i
$131$	13930.8	+	24128.9i	0.811774	+	1.40603i	0.911622	+	0.411031i	$0.134831\pi$
$131$	13930.8	+	24128.9i	0.811774	+	1.40603i	−0.0998478	+	0.995003i	$0.531836\pi$
$132$			4118.95i			0.236395i
$133$	15964.3	+	2748.30i	0.902502	+	0.155368i
$134$	40965.6			2.28144
$135$	6660.16	+	11535.7i	0.365441	+	0.632962i
$136$	−484.726	+	419.332i	−0.0262071	+	0.0226715i
$137$	−6498.03	+	11254.9i	−0.346211	+	0.599655i	−0.985573	−	0.169251i	$-0.945865\pi$
$137$	−6498.03	+	11254.9i	−0.346211	+	0.599655i	0.639362	+	0.768906i	$0.279198\pi$
$138$	3847.30	−	2221.24i	0.202022	−	0.116637i
$139$	24081.6			1.24639			0.623196	−	0.782065i	$-0.285834\pi$
$139$	24081.6			1.24639			0.623196	+	0.782065i	$0.285834\pi$
$140$	13824.4	+	11504.9i	0.705328	+	0.586987i
$141$			838.851i			0.0421936i
$142$	1497.71	−	864.700i	0.0742762	−	0.0428834i
$143$	7310.17	−	12661.6i	0.357483	−	0.619179i
$144$	−8677.07	+	15029.1i	−0.418454	+	0.724784i
$145$	2536.90	−	1464.68i	0.120661	−	0.0696637i
$146$	−15387.4			−0.721869
$147$	−8705.78	−	3088.98i	−0.402878	−	0.142949i
$148$			28979.0i			1.32300i
$149$	5688.95	+	9853.56i	0.256248	+	0.443834i	0.965234	−	0.261389i	$-0.0841804\pi$
$149$	5688.95	+	9853.56i	0.256248	+	0.443834i	−0.708986	+	0.705223i	$0.750847\pi$
$150$	776.296	−	1344.58i	0.0345021	−	0.0597593i
$151$	2210.95	−	3829.48i	0.0969674	−	0.167952i	−0.813461	−	0.581620i	$-0.802419\pi$
$151$	2210.95	−	3829.48i	0.0969674	−	0.167952i	0.910428	+	0.413668i	$0.135752\pi$
$152$	−634.957	+	366.593i	−0.0274826	+	0.0158671i
$153$	18073.9	+	6271.79i	0.772091	+	0.267922i
$154$	−12088.8	+	14526.0i	−0.509732	+	0.612497i
$155$	1149.71			0.0478548
$156$	11081.2	−	6397.75i	0.455343	−	0.262892i
$157$	−15155.9	−	8750.26i	−0.614868	−	0.354994i	0.160000	−	0.987117i	$-0.448851\pi$
$157$	−15155.9	−	8750.26i	−0.614868	−	0.354994i	−0.774868	+	0.632123i	$0.782184\pi$
$158$	−34724.9	−	20048.4i	−1.39100	−	0.803094i
$159$	−2828.51	−	4899.12i	−0.111883	−	0.193787i
$160$	−33830.3			−1.32150
$161$	9918.21	+	1707.44i	0.382632	+	0.0658710i
$162$	17895.2			0.681880
$163$	9043.10	−	5221.04i	0.340363	−	0.196509i	−0.320070	−	0.947394i	$-0.603706\pi$
$163$	9043.10	−	5221.04i	0.340363	−	0.196509i	0.660432	+	0.750885i	$0.270373\pi$
$164$	4678.94	−	8104.17i	0.173964	−	0.301315i
$165$	−5376.35	−	3104.04i	−0.197479	−	0.114014i
$166$	25866.9	−	14934.3i	0.938704	−	0.541961i
$167$	29618.4			1.06201			0.531005	−	0.847369i	$-0.321815\pi$
$167$	29618.4			1.06201			0.531005	+	0.847369i	$0.321815\pi$
$168$	392.301	−	144.589i	0.0138995	−	0.00512289i
$169$	−16857.0			−0.590211
$170$	7201.81	+	37529.7i	0.249197	+	1.29861i
$171$	18952.7	+	10942.3i	0.648154	+	0.374212i
$172$	−16427.2	+	28452.7i	−0.555272	+	0.961759i
$173$	17159.8	+	29721.6i	0.573349	+	0.993069i	0.996219	+	0.0868789i	$0.0276893\pi$
$173$	17159.8	+	29721.6i	0.573349	+	0.993069i	−0.422870	+	0.906190i	$0.638977\pi$
$174$			2693.83i			0.0889758i
$175$	3300.26	−	1216.36i	0.107764	−	0.0397180i
$176$		−	17984.7i		−	0.580602i
$177$	−20102.9	+	11606.4i	−0.641669	+	0.370468i
$178$	−57163.7	−	33003.5i	−1.80418	−	1.04164i
$179$	23678.7	−	41012.7i	0.739011	−	1.28001i	−0.213929	−	0.976849i	$-0.568626\pi$
$179$	23678.7	−	41012.7i	0.739011	−	1.28001i	0.952941	−	0.303156i	$-0.0980404\pi$
$180$	12149.0	+	21042.6i	0.374968	+	0.649464i
$181$	−26572.7			−0.811107			−0.405554	−	0.914071i	$-0.632921\pi$
$181$	−26572.7			−0.811107			−0.405554	+	0.914071i	$0.632921\pi$
$182$	57856.2	+	9960.06i	1.74665	+	0.300690i
$183$	−14943.9			−0.446233
$184$	−394.482	+	227.754i	−0.0116517	+	0.00672714i
$185$	−37825.4	−	21838.5i	−1.10520	−	0.638087i
$186$	−528.636	+	915.625i	−0.0152803	+	0.0264662i
$187$	−19471.0	+	3736.42i	−0.556808	+	0.106849i
$188$			3402.50i			0.0962680i
$189$	−21329.8	−	17751.0i	−0.597122	−	0.496936i
$190$			43714.6i			1.21093i
$191$	−14610.6	−	25306.2i	−0.400498	−	0.693683i	0.593288	−	0.804990i	$-0.297829\pi$
$191$	−14610.6	−	25306.2i	−0.400498	−	0.693683i	−0.993786	+	0.111308i	$0.964496\pi$
$192$	7486.22	−	12966.5i	0.203077	−	0.351739i
$193$	−49317.4	−	28473.4i	−1.32399	−	0.764407i	−0.339629	−	0.940559i	$-0.610302\pi$
$193$	−49317.4	−	28473.4i	−1.32399	−	0.764407i	−0.984363	+	0.176152i	$0.943635\pi$
$194$	−27940.4	−	48394.3i	−0.742386	−	1.28585i
$195$			19285.3i			0.507175i
$196$	−35311.9	−	12529.4i	−0.919197	−	0.326149i
$197$			38643.7i			0.995740i	0.867252	+	0.497870i	$0.165884\pi$
$197$			38643.7i			0.995740i	−0.867252	+	0.497870i	$0.834116\pi$
$198$	−22110.5	+	12765.5i	−0.563986	+	0.325617i
$199$	11999.1	−	20783.0i	0.303000	−	0.524811i	−0.673814	−	0.738901i	$-0.735345\pi$
$199$	11999.1	−	20783.0i	0.303000	−	0.524811i	0.976814	+	0.214090i	$0.0686786\pi$
$200$	−79.5972	+	137.866i	−0.00198993	+	0.00344666i
$201$	−14017.6	−	24279.1i	−0.346961	−	0.600954i
$202$		−	33701.4i		−	0.825933i
$203$	−3903.75	+	4690.77i	−0.0947305	+	0.113829i
$204$	−16392.7	−	5688.42i	−0.393905	−	0.136688i
$205$	7052.10	+	12214.6i	0.167807	+	0.290651i
$206$	23764.6	+	13720.5i	0.560009	+	0.323322i
$207$	11774.8	+	6798.17i	0.274797	+	0.158654i
$208$	−48384.3	+	27934.7i	−1.11835	+	0.645680i
$209$	−22679.9			−0.519216
$210$	4229.23	−	24566.8i	0.0959009	−	0.557071i
$211$			41506.0i			0.932280i	0.884711	+	0.466140i	$0.154356\pi$
$211$			41506.0i			0.932280i	−0.884711	+	0.466140i	$0.845644\pi$
$212$	−11472.8	−	19871.5i	−0.255269	−	0.442140i
$213$	−1024.97	−	591.765i	−0.0225918	−	0.0130434i
$214$	103387.	+	59690.3i	2.25755	+	1.30339i
$215$	−24759.0	−	42883.8i	−0.535619	−	0.927719i
$216$	1255.98			0.0269200
$217$	−2247.39	+	828.310i	−0.0477264	+	0.0175903i
$218$			81715.3i			1.71945i
$219$	5265.23	+	9119.65i	0.109782	+	0.190147i
$220$	−21807.2	−	12590.4i	−0.450563	−	0.260133i
$221$	40295.4	+	46579.4i	0.825032	+	0.953694i
$222$	34784.2	−	20082.7i	0.705791	−	0.407489i
$223$		−	23688.2i		−	0.476345i	−0.971223	−	0.238173i	$-0.923452\pi$
$223$		−	23688.2i		−	0.476345i	0.971223	−	0.238173i	$-0.0765484\pi$
$224$	66129.4	−	24373.0i	1.31795	−	0.485751i
$225$	4751.75			0.0938618
$226$	−80203.6	+	46305.6i	−1.57028	+	0.906602i
$227$	23082.3	−	39979.8i	0.447948	−	0.775869i	−0.550304	−	0.834964i	$-0.685488\pi$
$227$	23082.3	−	39979.8i	0.447948	−	0.775869i	0.998252	+	0.0590951i	$0.0188215\pi$
$228$	−17189.8	−	9924.53i	−0.330675	−	0.190915i
$229$	42286.9	−	24414.3i	0.806371	−	0.465558i	−0.0393233	−	0.999227i	$-0.512520\pi$
$229$	42286.9	−	24414.3i	0.806371	−	0.465558i	0.845694	+	0.533668i	$0.179187\pi$
$230$			27158.7i			0.513397i
$231$	12745.7	+	2194.20i	0.238858	+	0.0411198i
$232$		−	276.211i		−	0.00513174i
$233$	−42880.0	+	24756.8i	−0.789846	+	0.456018i	−0.839908	−	0.542728i	$-0.817391\pi$
$233$	−42880.0	+	24756.8i	−0.789846	+	0.456018i	0.0500620	+	0.998746i	$0.484058\pi$
$234$	68686.1	+	39655.9i	1.25440	+	0.724230i
$235$	−4441.19	−	2564.12i	−0.0804198	−	0.0464304i
$236$	−81540.0	+	47077.2i	−1.46402	+	0.845252i
$237$			27440.6i			0.488537i
$238$	−41115.9	−	68172.3i	−0.725866	−	1.20352i
$239$	99252.3			1.73758			0.868790	−	0.495180i	$-0.164898\pi$
$239$	99252.3			1.73758			0.868790	+	0.495180i	$0.164898\pi$
$240$	11861.6	+	20544.9i	0.205931	+	0.356682i
$241$	7408.86	−	12832.5i	0.127561	−	0.220942i	−0.795170	−	0.606386i	$-0.792619\pi$
$241$	7408.86	−	12832.5i	0.127561	−	0.220942i	0.922731	+	0.385444i	$0.125952\pi$
$242$	−27925.6	+	48368.6i	−0.476839	+	0.825909i
$243$	−29059.6	−	50332.6i	−0.492126	−	0.852387i
$244$	−60614.6			−1.01812
$245$	42965.2	−	36649.5i	0.715789	−	0.610571i
$246$	−12970.2			−0.214327
$247$	35227.4	+	61015.7i	0.577414	+	1.00011i
$248$	54.2035	−	93.8832i	0.000881300	−	0.00152646i
$249$	−17702.3	−	10220.4i	−0.285516	−	0.164843i
$250$	46067.7	+	79791.6i	0.737083	+	1.27666i
$251$			20241.1i			0.321282i	0.987013	+	0.160641i	$0.0513561\pi$
$251$			20241.1i			0.321282i	−0.987013	+	0.160641i	$0.948644\pi$
$252$	−38908.2	−	32380.1i	−0.612689	−	0.509891i
$253$	−14090.4			−0.220131
$254$	36128.0	+	62575.6i	0.559986	+	0.969924i
$255$	19778.5	−	17110.2i	0.304167	−	0.263132i
$256$	−34323.6	+	59450.2i	−0.523736	+	0.907138i
$257$	−8318.87	+	4802.90i	−0.125950	+	0.0727173i	−0.561651	−	0.827374i	$-0.689834\pi$
$257$	−8318.87	+	4802.90i	−0.125950	+	0.0727173i	0.435701	+	0.900091i	$0.356500\pi$
$258$	45536.6			0.684103
$259$	89672.5	+	15437.3i	1.33678	+	0.230129i
$260$			78224.1i			1.15716i
$261$	−7139.98	+	4122.27i	−0.104813	+	0.0605140i
$262$	78317.5	−	135650.i	1.14092	−	1.97614i
$263$	19831.4	−	34348.9i	0.286709	−	0.496594i	−0.686313	−	0.727306i	$-0.740772\pi$
$263$	19831.4	−	34348.9i	0.286709	−	0.496594i	0.973022	+	0.230712i	$0.0741055\pi$
$264$	−506.939	+	292.682i	−0.00727358	+	0.00419940i
$265$	34583.7			0.492469
$266$	−31494.2	−	85450.8i	−0.445110	−	1.20768i
$267$			45172.4i			0.633652i
$268$	−56857.2	−	98479.6i	−0.791618	−	1.37112i
$269$	−31473.2	+	54513.2i	−0.434947	+	0.753351i	−0.997291	−	0.0735524i	$-0.976566\pi$
$269$	−31473.2	+	54513.2i	−0.434947	+	0.753351i	0.562344	+	0.826903i	$0.309900\pi$
$270$	37442.6	−	64852.4i	0.513616	−	0.889608i
$271$	−22114.0	+	12767.5i	−0.301113	+	0.173848i	−0.642943	−	0.765914i	$-0.722287\pi$
$271$	−22114.0	+	12767.5i	−0.301113	+	0.173848i	0.341830	+	0.939762i	$0.388953\pi$
$272$	71576.2	+	24837.5i	0.967455	+	0.335715i
$273$	−13894.1	−	37697.8i	−0.186426	−	0.505814i
$274$	73062.2			0.973177
$275$	−4264.67	+	2462.21i	−0.0563924	+	0.0325581i
$276$	−10679.5	−	6165.84i	−0.140196	−	0.0809420i
$277$	−65006.8	−	37531.7i	−0.847226	−	0.489146i	0.0124879	−	0.999922i	$-0.496025\pi$
$277$	−65006.8	−	37531.7i	−0.847226	−	0.489146i	−0.859714	+	0.510776i	$0.829358\pi$
$278$	−67691.8	−	117246.i	−0.875883	−	1.51707i
$279$	−3235.81			−0.0415695
$280$	−433.642	+	2518.95i	−0.00553115	+	0.0321294i
$281$	−75294.3			−0.953563			−0.476782	−	0.879022i	$-0.658197\pi$
$281$	−75294.3			−0.953563			−0.476782	+	0.879022i	$0.658197\pi$
$282$	4084.10	−	2357.96i	0.0513569	−	0.0296509i
$283$	−77744.7	+	134658.i	−0.970728	+	1.68135i	−0.277362	+	0.960765i	$0.589460\pi$
$283$	−77744.7	+	134658.i	−0.970728	+	1.68135i	−0.693366	+	0.720585i	$0.743873\pi$
$284$	−4157.41	−	2400.28i	−0.0515450	−	0.0297595i
$285$	25908.4	−	14958.2i	0.318971	−	0.184158i
$286$	−82193.8			−1.00486
$287$	−22585.0	−	18795.7i	−0.274193	−	0.228189i
$288$	95213.8			1.14793
$289$	12019.9	−	82651.6i	0.143914	−	0.989590i
$290$	−14262.1	−	8234.24i	−0.169585	−	0.0979102i
$291$	−19121.3	+	33119.0i	−0.225804	+	0.391103i
$292$	21356.5	+	36990.6i	0.250475	+	0.433836i
$293$		−	114123.i		−	1.32934i	−0.747136	−	0.664672i	$-0.768571\pi$
$293$		−	114123.i		−	1.32934i	0.747136	−	0.664672i	$-0.231429\pi$
$294$	9432.12	+	51068.7i	0.109123	+	0.590827i
$295$		−	141909.i		−	1.63067i
$296$	−3566.58	+	2059.17i	−0.0407070	+	0.0235022i
$297$	33646.5	+	19425.8i	0.381441	+	0.220225i
$298$	31982.6	−	55395.5i	0.360148	−	0.623795i
$299$	21885.8	+	37907.4i	0.244805	+	0.424015i
$300$	−4309.77			−0.0478863
$301$	79293.0	+	65989.1i	0.875189	+	0.728349i
$302$	−24859.4			−0.272569
$303$	−19973.9	+	11531.9i	−0.217559	+	0.125608i
$304$	75056.4	+	43333.8i	0.812158	+	0.468900i
$305$	45679.1	−	79118.5i	0.491041	−	0.850508i
$306$	−20269.2	−	105626.i	−0.216468	−	1.12805i
$307$		−	31444.4i		−	0.333632i	−0.985988	−	0.166816i	$-0.946651\pi$
$307$		−	31444.4i		−	0.333632i	0.985988	−	0.166816i	$-0.0533485\pi$
$308$	51698.3	+	8899.97i	0.544972	+	0.0938182i
$309$		−	18779.4i		−	0.196682i
$310$	−3231.77	−	5597.59i	−0.0336292	−	0.0582475i
$311$	1257.20	−	2177.54i	0.0129982	−	0.0225136i	−0.859453	−	0.511215i	$-0.829196\pi$
$311$	1257.20	−	2177.54i	0.0129982	−	0.0225136i	0.872451	+	0.488701i	$0.162529\pi$
$312$	1574.80	+	909.213i	0.0161777	+	0.00934021i
$313$	11111.6	+	19245.9i	0.113420	+	0.196449i	0.917147	−	0.398549i	$-0.130486\pi$
$313$	11111.6	+	19245.9i	0.113420	+	0.196449i	−0.803727	+	0.594998i	$0.797153\pi$
$314$			98385.7i			0.997867i
$315$	71586.1	−	26384.2i	0.721452	−	0.265902i
$316$			111303.i			1.11464i
$317$	−126007.	+	72750.1i	−1.25394	+	0.723960i	−0.971889	−	0.235440i	$-0.924347\pi$
$317$	−126007.	+	72750.1i	−1.25394	+	0.723960i	−0.282047	+	0.959400i	$0.591014\pi$
$318$	−15901.5	+	27542.3i	−0.157248	+	0.272361i
$319$	4272.06	−	7399.43i	0.0419813	−	0.0727138i
$320$	45766.3	+	79269.6i	0.446937	+	0.774117i
$321$		−	81699.1i		−	0.792879i
$322$	−19566.5	−	53088.2i	−0.188713	−	0.512019i
$323$	31321.7	−	90262.1i	0.300221	−	0.865168i
$324$	−24837.3	−	43019.5i	−0.236600	−	0.409803i
$325$	13248.2	+	7648.83i	0.125426	+	0.0724150i
$326$	−50839.2	−	29352.0i	−0.478369	−	0.276187i
$327$	48430.3	−	27961.3i	0.452921	−	0.261494i
$328$	1329.89			0.0123614
$329$	10528.7	+	1812.54i	0.0972707	+	0.0167454i
$330$			34901.1i			0.320487i
$331$	−23178.2	−	40145.8i	−0.211555	−	0.366424i	0.740646	−	0.671895i	$-0.234519\pi$
$331$	−23178.2	−	40145.8i	−0.211555	−	0.366424i	−0.952201	+	0.305471i	$0.901186\pi$
$332$	−71802.8	−	41455.4i	−0.651426	−	0.376101i
$333$	106458.	+	61463.6i	0.960041	+	0.554280i
$334$	−83255.5	−	144203.i	−0.746311	−	1.29265i
$335$	171390.			1.52720
$336$	−37987.9	−	31614.3i	−0.336486	−	0.280030i
$337$		−	96455.4i		−	0.849311i	−0.905355	−	0.424656i	$-0.860395\pi$
$337$		−	96455.4i		−	0.849311i	0.905355	−	0.424656i	$-0.139605\pi$
$338$	47384.0	+	82071.5i	0.414761	+	0.718388i
$339$	54888.0	+	31689.6i	0.477615	+	0.275751i
$340$	80224.3	−	69401.3i	0.693982	−	0.600358i
$341$	2904.12	−	1676.70i	0.0249750	−	0.0144193i
$342$		−	123033.i		−	1.05189i
$343$	−57581.7	+	102595.i	−0.489436	+	0.872039i
$344$	−4669.08			−0.0394561
$345$	16096.2	−	9293.15i	0.135234	−	0.0780773i
$346$	96470.0	−	167091.i	0.805824	−	1.39573i
$347$	−177639.	−	102560.i	−1.47529	−	0.851761i	−0.475681	−	0.879618i	$-0.657798\pi$
$347$	−177639.	−	102560.i	−1.47529	−	0.851761i	−0.999612	+	0.0278566i	$0.991132\pi$
$348$	6475.86	−	3738.84i	0.0534736	−	0.0308730i
$349$			71255.7i			0.585018i	0.956263	+	0.292509i	$0.0944901\pi$
$349$			71255.7i			0.585018i	−0.956263	+	0.292509i	$0.905510\pi$
$350$	−15198.9	−	12648.8i	−0.124073	−	0.103256i
$351$		−	120692.i		−	0.979638i
$352$	−85453.9	+	49336.8i	−0.689678	+	0.398186i
$353$	−201502.	−	116337.i	−1.61707	−	0.933617i	−0.987672	−	0.156535i	$-0.949968\pi$
$353$	−201502.	−	116337.i	−1.61707	−	0.933617i	−0.629399	−	0.777082i	$-0.716699\pi$
$354$	113016.	+	65249.7i	0.901847	+	0.520682i
$355$	6266.04	−	3617.70i	0.0497206	−	0.0287062i
$356$			183226.i			1.44573i
$357$	−26334.8	+	47695.4i	−0.206630	+	0.374231i
$358$	−266237.			−2.07732
$359$	65440.0	+	113345.i	0.507755	+	0.879458i	0.999960	+	0.00897805i	$0.00285784\pi$
$359$	65440.0	+	113345.i	0.507755	+	0.879458i	−0.492205	+	0.870480i	$0.663809\pi$
$360$	−1726.55	+	2990.46i	−0.0133221	+	0.0230746i
$361$	−10513.8	+	18210.4i	−0.0806759	+	0.139735i
$362$	74694.2	+	129374.i	0.569993	+	0.987258i
$363$	38222.2			0.290070
$364$	−56356.5	−	152908.i	−0.425345	−	1.15406i
$365$	−64377.0			−0.483220
$366$	42006.4	+	72757.2i	0.313584	+	0.543143i
$367$	−59604.1	+	103237.i	−0.442531	+	0.766487i	−0.997877	−	0.0651331i	$-0.979253\pi$
$367$	−59604.1	+	103237.i	−0.442531	+	0.766487i	0.555345	+	0.831620i	$0.312586\pi$
$368$	46630.5	+	26922.1i	0.344330	+	0.198799i
$369$	−19847.8	−	34377.4i	−0.145767	−	0.252476i
$370$			245547.i			1.79362i
$371$	−67602.1	+	24915.8i	−0.491148	+	0.181020i
$372$	2934.83			0.0212079
$373$	−80387.1	−	139235.i	−0.577788	−	1.00076i	−0.995733	−	0.0922859i	$-0.970583\pi$
$373$	−80387.1	−	139235.i	−0.577788	−	1.00076i	0.417944	−	0.908473i	$-0.362751\pi$
$374$	72923.3	+	84295.6i	0.521343	+	0.602645i
$375$	31526.8	−	54606.0i	0.224191	−	0.388309i
$376$	−418.762	+	241.772i	−0.00296204	+	0.00171014i
$377$	−26542.3			−0.186748
$378$	−26467.6	+	153745.i	−0.185238	+	1.07601i
$379$		−	132518.i		−	0.922565i	−0.887253	−	0.461283i	$-0.847389\pi$
$379$		−	132518.i		−	0.922565i	0.887253	−	0.461283i	$-0.152611\pi$
$380$	105088.	−	60672.7i	0.727758	−	0.420171i
$381$	24724.5	−	42824.1i	0.170325	−	0.295011i
$382$	−82138.8	+	142269.i	−0.562887	+	0.974950i
$383$	−147636.	+	85237.7i	−1.00646	+	0.581077i	−0.910152	−	0.414275i	$-0.864035\pi$
$383$	−147636.	+	85237.7i	−1.00646	+	0.581077i	−0.0963037	+	0.995352i	$0.530702\pi$
$384$	4367.37			0.0296181
$385$	−50576.6	+	60773.3i	−0.341215	+	0.410007i
$386$			320148.i			2.14870i
$387$	69683.1	+	120695.i	0.465270	+	0.805872i
$388$	−77558.6	+	134335.i	−0.515189	+	0.892333i
$389$	−123748.	+	214338.i	−0.817785	+	1.41644i	0.0895262	+	0.995984i	$0.471465\pi$
$389$	−123748.	+	214338.i	−0.817785	+	1.41644i	−0.907311	+	0.420460i	$0.861869\pi$
$390$	93894.4	−	54209.9i	0.617320	−	0.356410i
$391$	19459.3	−	56077.4i	0.127284	−	0.366804i
$392$	−967.118	−	5236.31i	−0.00629372	−	0.0340763i
$393$	−107195.			−0.694045
$394$	188144.	−	108625.i	1.21199	−	0.699741i
$395$	−145281.	−	83877.9i	−0.931138	−	0.537592i
$396$	61375.5	+	35435.2i	0.391385	+	0.225967i
$397$	40232.0	+	69683.9i	0.255265	+	0.442132i	0.964967	−	0.262370i	$-0.0845040\pi$
$397$	40232.0	+	69683.9i	0.255265	+	0.442132i	−0.709703	+	0.704501i	$0.751171\pi$
$398$	−134915.			−0.851713
$399$	−39867.6	+	47905.2i	−0.250423	+	0.300910i
$400$	18817.9			0.117612
$401$	−25400.0	+	14664.7i	−0.157959	+	0.0911978i	−0.576896	−	0.816818i	$-0.695736\pi$
$401$	−25400.0	+	14664.7i	−0.157959	+	0.0911978i	0.418937	+	0.908015i	$0.362403\pi$
$402$	−78805.0	+	136494.i	−0.487643	+	0.844622i
$403$	−9021.63	−	5208.64i	−0.0555489	−	0.0320711i
$404$	−81016.8	+	46775.0i	−0.496378	+	0.286584i
$405$	74869.5			0.456452
$406$	33811.1	+	5820.66i	0.205120	+	0.0353118i
$407$	−127394.			−0.769059
$408$	−464.722	−	2421.74i	−0.00279173	−	0.0145481i
$409$	76041.8	+	43902.8i	0.454575	+	0.262449i	0.709761	−	0.704443i	$-0.248803\pi$
$409$	76041.8	+	43902.8i	0.454575	+	0.262449i	−0.255185	+	0.966892i	$0.582136\pi$
$410$	39646.0	−	68668.9i	0.235848	−	0.408501i
$411$	−25000.4	−	43301.9i	−0.148000	−	0.256344i
$412$		−	76172.0i		−	0.448747i
$413$	102239.	+	277396.i	0.599397	+	1.62630i
$414$		−	76437.0i		−	0.445967i
$415$	108221.	−	62481.5i	0.628371	−	0.362790i
$416$	265462.	+	153264.i	1.53396	+	0.885635i
$417$	−46325.4	+	80238.0i	−0.266408	+	0.461432i
$418$	63751.8	+	110421.i	0.364871	+	0.631976i
$419$	164197.			0.935273			0.467637	−	0.883921i	$-0.345106\pi$
$419$	164197.			0.935273			0.467637	+	0.883921i	$0.345106\pi$
$420$	−64927.5	+	23930.0i	−0.368070	+	0.135658i
$421$	−81.6864			−0.000460877			−0.000230439	−	1.00000i	$-0.500073\pi$
$421$	−81.6864			−0.000460877			−0.000230439		1.00000i	$0.500073\pi$
$422$	202080.	−	116671.i	1.13475	−	0.655145i
$423$	12499.5	+	7216.60i	0.0698574	+	0.0403322i
$424$	1630.46	−	2824.03i	0.00906938	−	0.0157086i
$425$	−3909.52	−	20373.1i	−0.0216444	−	0.112792i
$426$			6653.66i			0.0366641i
$427$	−32289.8	+	187566.i	−0.177096	+	1.02872i
$428$		−	331383.i		−	1.80902i
$429$	28125.0	+	48714.0i	0.152819	+	0.264691i
$430$	−139192.	+	241088.i	−0.752796	+	1.30388i
$431$	−112636.	−	65030.7i	−0.606351	−	0.350077i	0.165185	−	0.986263i	$-0.447178\pi$
$431$	−112636.	−	65030.7i	−0.606351	−	0.350077i	−0.771536	+	0.636186i	$0.780511\pi$
$432$	−74232.8	−	128575.i	−0.397767	−	0.688952i
$433$		−	265420.i		−	1.41566i	−0.706384	−	0.707829i	$-0.749675\pi$
$433$		−	265420.i		−	1.41566i	0.706384	−	0.707829i	$-0.250325\pi$
$434$	10350.0	+	8613.50i	0.0549494	+	0.0457299i
$435$			11270.3i			0.0595606i
$436$	196440.	−	113415.i	1.03337	−	0.596619i
$437$	33950.5	−	58804.0i	0.177780	−	0.307924i
$438$	29600.5	−	51269.5i	0.154295	−	0.267246i
$439$	165085.	+	285936.i	0.856603	+	1.48368i	0.875150	+	0.483852i	$0.160763\pi$
$439$	165085.	+	285936.i	0.856603	+	1.48368i	−0.0185470	+	0.999828i	$0.505904\pi$
$440$		−	3578.56i		−	0.0184843i
$441$	−120924.	+	103148.i	−0.621776	+	0.530378i
$442$	113513.	−	327118.i	0.581031	−	1.67440i
$443$	−2168.12	−	3755.29i	−0.0110478	−	0.0191353i	0.860449	−	0.509537i	$-0.170183\pi$
$443$	−2168.12	−	3755.29i	−0.0110478	−	0.0191353i	−0.871496	+	0.490402i	$0.836850\pi$
$444$	−96555.8	−	55746.5i	−0.489793	−	0.282782i
$445$	−239159.	−	138079.i	−1.20772	−	0.697279i
$446$	−115330.	+	66586.0i	−0.579794	+	0.334744i
$447$	−43775.1			−0.219085
$448$	−146571.	−	121979.i	−0.730284	−	0.607756i
$449$		−	119848.i		−	0.594484i	−0.954802	−	0.297242i	$-0.903933\pi$
$449$		−	119848.i		−	0.594484i	0.954802	−	0.297242i	$-0.0960667\pi$
$450$	−13356.9	−	23134.8i	−0.0659600	−	0.114246i
$451$	35626.6	+	20569.0i	0.175154	+	0.101125i
$452$	222634.	+	128538.i	1.08972	+	0.629148i
$453$	8506.37	+	14733.5i	0.0414522	+	0.0717974i
$454$	−259532.			−1.25916
$455$	242056.	+	41670.5i	1.16921	+	0.201283i
$456$		−	2820.84i		−	0.0135659i
$457$	−48284.3	−	83630.8i	−0.231192	−	0.400437i	0.726967	−	0.686672i	$-0.240929\pi$
$457$	−48284.3	−	83630.8i	−0.231192	−	0.400437i	−0.958159	+	0.286236i	$0.907596\pi$
$458$	−237732.	−	137254.i	−1.13333	−	0.654328i
$459$	−123779.	+	107080.i	−0.587517	+	0.508255i
$460$	65288.5	−	37694.3i	0.308547	−	0.178139i
$461$		−	228992.i		−	1.07750i	−0.842465	−	0.538751i	$-0.818896\pi$
$461$		−	228992.i		−	1.07750i	0.842465	−	0.538751i	$-0.181104\pi$
$462$	−25144.5	−	68222.5i	−0.117804	−	0.319627i
$463$	257753.			1.20238			0.601189	−	0.799107i	$-0.294694\pi$
$463$	257753.			1.20238			0.601189	+	0.799107i	$0.294694\pi$
$464$	−28275.8	+	16325.0i	−0.131334	+	0.0758260i
$465$	−2211.69	+	3830.76i	−0.0102286	+	0.0177165i
$466$	241066.	+	139180.i	1.11011	+	0.640919i
$467$	343367.	−	198243.i	1.57444	−	0.909000i	0.578820	−	0.815455i	$-0.303513\pi$
$467$	343367.	−	198243.i	1.57444	−	0.909000i	0.995615	−	0.0935452i	$-0.0298200\pi$
$468$		−	220158.i		−	1.00518i
$469$	−335023.	+	123478.i	−1.52310	+	0.561363i
$470$			28830.3i			0.130513i
$471$	58310.4	−	33665.6i	0.262848	−	0.151755i
$472$	−11588.0	−	6690.35i	−0.0520146	−	0.0300307i
$473$	−125080.	−	72215.1i	−0.559071	−	0.322780i
$474$	133600.	−	77133.9i	0.594633	−	0.343312i
$475$		−	23730.6i		−	0.105177i
$476$	−106817.	+	193459.i	−0.471442	+	0.853838i
$477$	−97334.2			−0.427788
$478$	−278992.	−	483229.i	−1.22106	−	2.11493i
$479$	−21977.6	+	38066.3i	−0.0957876	+	0.165909i	−0.909937	−	0.414746i	$-0.863870\pi$
$479$	−21977.6	+	38066.3i	−0.0957876	+	0.165909i	0.814149	+	0.580655i	$0.197204\pi$
$480$	65079.0	−	112720.i	0.282461	−	0.489236i
$481$	197874.	+	342728.i	0.855261	+	1.48136i
$482$	−83303.4			−0.358566
$483$	−24768.6	+	29762.2i	−0.106171	+	0.127576i
$484$	155035.			0.661818
$485$	−116896.	−	202470.i	−0.496955	−	0.860751i
$486$	−163369.	+	282964.i	−0.691668	+	1.19800i
$487$	243124.	+	140368.i	1.02511	+	0.591848i	0.915580	−	0.402135i	$-0.131732\pi$
$487$	243124.	+	140368.i	1.02511	+	0.591848i	0.109531	+	0.993983i	$0.465065\pi$
$488$	−4307.11	−	7460.13i	−0.0180862	−	0.0313261i
$489$			40174.6i			0.168010i
$490$	−299208.	−	106165.i	−1.24618	−	0.442169i
$491$	120722.			0.500753			0.250376	−	0.968149i	$-0.419446\pi$
$491$	120722.			0.500753			0.250376	+	0.968149i	$0.419446\pi$
$492$	18001.7	+	31179.8i	0.0743674	+	0.128808i
$493$	23548.6	+	27221.0i	0.0968883	+	0.111998i
$494$	198044.	−	343023.i	0.811538	−	1.40562i
$495$	−92505.1	+	53407.8i	−0.377533	+	0.217969i
$496$	−12814.5			−0.0520880
$497$	−9642.11	+	11586.0i	−0.0390355	+	0.0469053i
$498$			114916.i			0.463362i
$499$	327901.	−	189314.i	1.31687	−	0.760293i	0.333643	−	0.942699i	$-0.391722\pi$
$499$	327901.	−	189314.i	1.31687	−	0.760293i	0.983223	+	0.182406i	$0.0583886\pi$
$500$	127877.	−	221490.i	0.511509	−	0.885959i
$501$	−56976.6	+	98686.4i	−0.226997	+	0.393171i
$502$	98547.5	−	56896.4i	0.391055	−	0.225776i
$503$	−364292.			−1.43984			−0.719918	−	0.694059i	$-0.755821\pi$
$503$	−364292.			−1.43984			−0.719918	+	0.694059i	$0.755821\pi$
$504$	1220.47	−	7089.47i	0.00480469	−	0.0279095i
$505$		−	140999.i		−	0.552881i
$506$	39607.2	+	68601.7i	0.154694	+	0.267938i
$507$	32427.6	−	56166.3i	0.126154	−	0.218504i
$508$	100286.	−	173701.i	0.388610	−	0.673092i
$509$	−159882.	+	92307.9i	−0.617112	+	0.356290i	−0.775744	−	0.631048i	$-0.782625\pi$
$509$	−159882.	+	92307.9i	−0.617112	+	0.356290i	0.158632	+	0.987338i	$0.449292\pi$
$510$	−138900.	−	48199.6i	−0.534027	−	0.185312i
$511$	125840.	−	46380.4i	0.481923	−	0.177620i
$512$	367764.			1.40291
$513$	−162141.	+	93612.3i	−0.616111	+	0.355712i
$514$	46767.7	+	27001.3i	0.177019	+	0.102202i
$515$	99425.3	+	57403.2i	0.374871	+	0.216432i
$516$	−63201.5	−	109468.i	−0.237371	−	0.411139i
$517$	−14957.7			−0.0559606
$518$	−176904.	−	479981.i	−0.659294	−	1.78881i
$519$	−132040.			−0.490198
$520$	−9627.42	+	5558.39i	−0.0356044	+	0.0205562i
$521$	172490.	−	298761.i	0.635460	−	1.10065i	−0.350958	−	0.936391i	$-0.614144\pi$
$521$	172490.	−	298761.i	0.635460	−	1.10065i	0.986418	−	0.164257i	$-0.0525227\pi$
$522$	40140.1	+	23174.9i	0.147312	+	0.0850505i
$523$	13258.7	−	7654.91i	0.0484727	−	0.0279857i	−0.475568	−	0.879679i	$-0.657757\pi$
$523$	13258.7	−	7654.91i	0.0484727	−	0.0279857i	0.524041	+	0.851693i	$0.324424\pi$
$524$	−434796.			−1.58352
$525$	−2295.85	+	13336.1i	−0.00832960	+	0.0483851i
$526$	−222979.			−0.805921
$527$	2662.27	+	13873.5i	0.00958586	+	0.0499533i
$528$	59923.8	+	34597.0i	0.214947	+	0.124100i
$529$	−118828.	+	205816.i	−0.424627	+	0.735475i
$530$	−97212.6	−	168377.i	−0.346075	−	0.599420i
$531$			399397.i			1.41650i
$532$	−161709.	+	194310.i	−0.571360	+	0.686550i
$533$		−	127795.i		−	0.449841i
$534$	219930.	−	126977.i	0.771263	−	0.445289i
$535$	432545.	+	249730.i	1.51121	+	0.872495i
$536$	8080.24	−	13995.4i	0.0281251	−	0.0487142i
$537$	91100.8	+	157791.i	0.315917	+	0.547185i
$538$	353877.			1.22261
$539$	55080.1	−	155234.i	0.189591	−	0.534329i
$540$	−207870.			−0.712861
$541$	395550.	−	228371.i	1.35147	−	0.780273i	0.363017	−	0.931783i	$-0.381747\pi$
$541$	395550.	−	228371.i	1.35147	−	0.780273i	0.988456	+	0.151510i	$0.0484134\pi$
$542$	124322.	+	71777.6i	0.423205	+	0.244338i
$543$	51117.6	−	88538.3i	0.173369	−	0.300284i
$544$	−78337.4	−	408228.i	−0.264710	−	1.37945i
$545$			341877.i			1.15101i
$546$	−144483.	+	173612.i	−0.484655	+	0.582366i
$547$		−	340305.i		−	1.13735i	−0.822562	−	0.568675i	$-0.807456\pi$
$547$		−	340305.i		−	1.13735i	0.822562	−	0.568675i	$-0.192544\pi$
$548$	−101405.	−	175639.i	−0.337675	−	0.584870i
$549$	−128562.	+	222676.i	−0.426547	+	0.738802i
$550$	23975.5	+	13842.2i	0.0792577	+	0.0457595i
$551$	20586.9	+	35657.6i	0.0678091	+	0.117449i
$552$		−	1752.51i		−	0.00575152i
$553$	344416.	+	59291.9i	1.12624	+	0.193885i
$554$			421997.i			1.37496i
$555$	145529.	−	84021.1i	0.472458	−	0.272774i
$556$	−187902.	+	325457.i	−0.607831	+	1.05279i
$557$	256041.	−	443476.i	0.825275	−	1.42942i	−0.0764339	−	0.997075i	$-0.524353\pi$
$557$	256041.	−	443476.i	0.825275	−	1.42942i	0.901709	−	0.432344i	$-0.142313\pi$
$558$	9095.67	+	15754.2i	0.0292123	+	0.0505972i
$559$			448672.i			1.43584i
$560$	283495.	−	104487.i	0.904003	−	0.333184i
$561$	25006.8	−	72063.8i	0.0794569	−	0.228977i
$562$	211648.	+	366585.i	0.670102	+	1.16065i
$563$	159233.	+	91933.0i	0.502360	+	0.290038i	0.729688	−	0.683781i	$-0.239665\pi$
$563$	159233.	+	91933.0i	0.502360	+	0.290038i	−0.227327	+	0.973818i	$0.572999\pi$
$564$	−11336.9	−	6545.35i	−0.0356398	−	0.0205766i
$565$	−335553.	+	193732.i	−1.05115	+	0.606881i
$566$	874142.			2.72866
$567$	−146350.	+	53939.7i	−0.455226	+	0.167781i
$568$		−	682.230i		−	0.00211463i
$569$	−26117.2	−	45236.2i	−0.0806680	−	0.139721i	0.822869	−	0.568231i	$-0.192372\pi$
$569$	−26117.2	−	45236.2i	−0.0806680	−	0.139721i	−0.903537	+	0.428510i	$0.859039\pi$
$570$	−145654.	−	84093.4i	−0.448304	−	0.258829i
$571$	−221162.	−	127688.i	−0.678327	−	0.391632i	0.120897	−	0.992665i	$-0.461423\pi$
$571$	−221162.	−	127688.i	−0.678327	−	0.391632i	−0.799224	+	0.601033i	$0.794756\pi$
$572$	114079.	+	197591.i	0.348669	+	0.603913i
$573$	112425.			0.342415
$574$	−28025.1	+	162793.i	−0.0850598	+	0.494096i
$575$		−	14743.2i		−	0.0445918i
$576$	−128807.	−	223101.i	−0.388235	−	0.672444i
$577$	195194.	+	112695.i	0.586292	+	0.338496i	0.763630	−	0.645654i	$-0.223415\pi$
$577$	195194.	+	112695.i	0.586292	+	0.338496i	−0.177338	+	0.984150i	$0.556749\pi$
$578$	−436192.	+	173807.i	−1.30564	+	0.520251i
$579$	189743.	−	109548.i	0.565989	−	0.326774i
$580$			45714.1i			0.135892i
$581$	−166529.	+	200103.i	−0.493331	+	0.592790i
$582$	214995.			0.634720
$583$	87356.8	−	50435.5i	0.257016	−	0.148388i
$584$	−3035.07	+	5256.90i	−0.00889905	+	0.0154136i
$585$	287366.	+	165911.i	0.839700	+	0.484801i
$586$	−555628.	+	320792.i	−1.61804	+	0.934176i
$587$			375023.i			1.08838i	0.838961	+	0.544192i	$0.183164\pi$
$587$			375023.i			1.08838i	−0.838961	+	0.544192i	$0.816836\pi$
$588$	109676.	−	93554.0i	0.317217	−	0.270588i
$589$			16159.9i			0.0465808i
$590$	−690912.	+	398898.i	−1.98481	+	1.14593i
$591$	−128758.	−	74338.5i	−0.368637	−	0.212833i
$592$	421595.	+	243408.i	1.20296	+	0.694531i
$593$	243124.	−	140368.i	0.691382	−	0.399170i	−0.112748	−	0.993624i	$-0.535965\pi$
$593$	243124.	−	140368.i	0.691382	−	0.399170i	0.804130	+	0.594454i	$0.202632\pi$
$594$		−	218419.i		−	0.619039i
$595$	−172019.	−	285217.i	−0.485896	−	0.805640i
$596$	−177558.			−0.499859
$597$	46165.0	+	79960.2i	0.129528	+	0.224350i
$598$	123040.	−	213111.i	0.344067	−	0.595941i
$599$	67152.5	−	116311.i	0.187158	−	0.324167i	−0.757144	−	0.653248i	$-0.773406\pi$
$599$	67152.5	−	116311.i	0.187158	−	0.324167i	0.944302	+	0.329081i	$0.106739\pi$
$600$	−306.241	−	530.425i	−0.000850669	−	0.00147340i
$601$	−70939.3			−0.196398			−0.0981992	−	0.995167i	$-0.531308\pi$
$601$	−70939.3			−0.196398			−0.0981992	+	0.995167i	$0.531308\pi$
$602$	98392.6	−	571545.i	0.271500	−	1.57709i
$603$	−482370.			−1.32662
$604$	34503.0	+	59761.0i	0.0945766	+	0.163811i
$605$	−116834.	+	202363.i	−0.319197	+	0.552865i
$606$	112291.	+	64831.0i	0.305772	+	0.176538i
$607$	−61573.1	−	106648.i	−0.167114	−	0.289451i	0.770290	−	0.637694i	$-0.220112\pi$
$607$	−61573.1	−	106648.i	−0.167114	−	0.289451i	−0.937404	+	0.348243i	$0.886778\pi$
$608$		−	475504.i		−	1.28631i
$609$	−8119.72	−	22030.6i	−0.0218931	−	0.0594007i
$610$	−513605.			−1.38029
$611$	23232.9	+	40240.6i	0.0622331	+	0.107791i
$612$	−225788.	+	195327.i	−0.602834	+	0.521506i
$613$	−337587.	+	584717.i	−0.898389	+	1.55606i	−0.0688352	+	0.997628i	$0.521928\pi$
$613$	−337587.	+	584717.i	−0.898389	+	1.55606i	−0.829554	+	0.558427i	$0.811405\pi$
$614$	−153093.	+	88388.4i	−0.406087	+	0.234455i
$615$	−54264.2			−0.143471
$616$	2578.18	+	6995.16i	0.00679440	+	0.0184347i
$617$			130047.i			0.341609i	0.985305	+	0.170805i	$0.0546367\pi$
$617$			130047.i			0.341609i	−0.985305	+	0.170805i	$0.945363\pi$
$618$	−91431.2	+	52787.9i	−0.239396	+	0.138216i
$619$	−228880.	+	396432.i	−0.597347	+	1.03463i	0.395864	+	0.918309i	$0.370445\pi$
$619$	−228880.	+	396432.i	−0.597347	+	1.03463i	−0.993211	+	0.116326i	$0.962888\pi$
$620$	−8970.92	+	15538.1i	−0.0233375	+	0.0404217i
$621$	−100734.	+	58158.8i	−0.261212	+	0.150811i
$622$	−14135.7			−0.0365372
$623$	566973.	+	97605.6i	1.46078	+	0.251477i
$624$		−	214951.i		−	0.552039i
$625$	170305.	+	294976.i	0.435980	+	0.755139i
$626$	62468.3	−	108198.i	0.159408	−	0.276103i
$627$	43629.1	−	75567.7i	0.110979	−	0.192221i
$628$	236515.	−	136552.i	0.599708	−	0.346242i
$629$	175936.	−	507006.i	0.444685	−	1.28148i
$630$	−329680.	−	274366.i	−0.830638	−	0.691273i
$631$	518932.			1.30332			0.651661	−	0.758510i	$-0.274072\pi$
$631$	518932.			1.30332			0.651661	+	0.758510i	$0.274072\pi$
$632$	−13698.6	+	7908.89i	−0.0342959	+	0.0198007i
$633$	−138295.	−	79844.7i	−0.345143	−	0.199269i
$634$	708395.	+	408992.i	1.76237	+	1.01750i
$635$	151151.	+	261801.i	0.374856	+	0.649269i
$636$	88280.6			0.218249
$637$	−503179.	+	92934.5i	−1.24006	+	0.229033i
$638$	−48034.0			−0.118007
$639$	−17635.5	+	10181.9i	−0.0431903	+	0.0249359i
$640$	−13349.7	+	23122.4i	−0.0325922	+	0.0564513i
$641$	−93315.4	−	53875.7i	−0.227111	−	0.131122i	0.382128	−	0.924109i	$-0.375191\pi$
$641$	−93315.4	−	53875.7i	−0.227111	−	0.131122i	−0.609238	+	0.792987i	$0.708525\pi$
$642$	−397767.	+	229651.i	−0.965071	+	0.557184i
$643$	21723.0			0.0525410			0.0262705	−	0.999655i	$-0.491637\pi$
$643$	21723.0			0.0525410			0.0262705	+	0.999655i	$0.491637\pi$
$644$	−100465.	+	120720.i	−0.242239	+	0.291076i
$645$	190514.			0.457940
$646$	−527502.	+	101226.i	−1.26403	+	0.242563i
$647$	−177443.	−	102447.i	−0.423887	−	0.244731i	0.272852	−	0.962056i	$-0.412033\pi$
$647$	−177443.	−	102447.i	−0.423887	−	0.244731i	−0.696739	+	0.717325i	$0.745366\pi$
$648$	3529.74	−	6113.69i	0.00840607	−	0.0145597i
$649$	−206955.	−	358457.i	−0.491345	−	0.851035i
$650$		−	86001.6i		−	0.203554i
$651$	1563.41	−	9081.54i	0.00368901	−	0.0214288i
$652$			162954.i			0.383327i
$653$	−387468.	+	223705.i	−0.908676	+	0.524625i	−0.880005	−	0.474964i	$-0.842461\pi$
$653$	−387468.	+	223705.i	−0.908676	+	0.524625i	−0.0286714	+	0.999589i	$0.509128\pi$
$654$	−272269.	−	157195.i	−0.636566	−	0.367522i
$655$	327662.	−	567527.i	0.763736	−	1.32283i
$656$	−78601.4	−	136142.i	−0.182651	−	0.316361i
$657$	181186.			0.419754
$658$	−20770.8	−	56355.8i	−0.0479735	−	0.130163i
$659$	−296066.			−0.681739			−0.340869	−	0.940111i	$-0.610721\pi$
$659$	−296066.			−0.681739			−0.340869	+	0.940111i	$0.610721\pi$
$660$	83900.7	−	48440.1i	0.192610	−	0.111203i
$661$	57960.7	+	33463.6i	0.132657	+	0.0765896i	0.564860	−	0.825187i	$-0.308930\pi$
$661$	57960.7	+	33463.6i	0.132657	+	0.0765896i	−0.432203	+	0.901776i	$0.642264\pi$
$662$	−130305.	+	225695.i	−0.297334	+	0.514998i
$663$	−232715.	+	44657.1i	−0.529416	+	0.101593i
$664$		−	11782.8i		−	0.0267247i
$665$	−131764.	−	357506.i	−0.297958	−	0.808425i
$666$		−	691081.i		−	1.55805i
$667$	12790.1	+	22153.1i	0.0287489	+	0.0497946i
$668$	−231105.	+	400286.i	−0.517913	+	0.897051i
$669$	78927.3	+	45568.7i	0.176350	+	0.101816i
$670$	−481767.	−	834445.i	−1.07322	−	1.85887i
$671$		−	266467.i		−	0.591831i
$672$	−46003.3	+	267225.i	−0.101871	+	0.591749i
$673$			179564.i			0.396452i	0.980156	+	0.198226i	$0.0635179\pi$
$673$			179564.i			0.396452i	−0.980156	+	0.198226i	$0.936482\pi$
$674$	−469611.	+	271130.i	−1.03376	+	0.596840i
$675$	−20325.8	+	35205.3i	−0.0446108	+	0.0772681i
$676$	131531.	−	227819.i	0.287829	−	0.498535i
$677$	−418195.	−	724334.i	−0.912433	−	1.58038i	−0.810617	−	0.585577i	$-0.800868\pi$
$677$	−418195.	−	724334.i	−0.912433	−	1.58038i	−0.101816	−	0.994803i	$-0.532465\pi$
$678$		−	356310.i		−	0.775120i
$679$	374371.	+	311559.i	0.812013	+	0.675772i
$680$	14242.1	+	4942.12i	0.0308004	+	0.0106880i
$681$	88806.5	+	153817.i	0.191492	+	0.331674i
$682$	−16326.6	−	9426.18i	−0.0351017	−	0.0202659i
$683$	−535158.	−	308973.i	−1.14720	−	0.662338i	−0.198999	−	0.980000i	$-0.563769\pi$
$683$	−535158.	−	308973.i	−1.14720	−	0.662338i	−0.948204	+	0.317662i	$0.897102\pi$
$684$	−295766.	+	170761.i	−0.632173	+	0.364985i
$685$	305675.			0.651447
$686$	661359.	−	8039.50i	1.40537	−	0.0170836i
$687$			187862.i			0.398040i
$688$	275959.	+	477975.i	0.582999	+	1.00978i
$689$	−271373.	−	156677.i	−0.571648	−	0.330041i
$690$	−90490.9	−	52244.9i	−0.190067	−	0.109735i
$691$	131157.	+	227171.i	0.274686	+	0.475770i	0.970056	−	0.242882i	$-0.0780928\pi$
$691$	131157.	+	227171.i	0.274686	+	0.475770i	−0.695370	+	0.718652i	$0.744759\pi$
$692$	−535573.			−1.11843
$693$	142346.	−	171044.i	0.296400	−	0.356156i
$694$			1.15316e6i			2.39425i
$695$	−283206.	−	490528.i	−0.586318	−	1.01553i
$696$	920.314	+	531.344i	0.00189984	+	0.00109688i
$697$	−131063.	+	113381.i	−0.269783	+	0.233387i
$698$	346922.	−	200296.i	0.712067	−	0.411112i
$699$		−	190497.i		−	0.389883i
$700$	−9312.28	+	54093.3i	−0.0190046	+	0.110394i
$701$	284366.			0.578685			0.289342	−	0.957226i	$-0.406563\pi$
$701$	284366.			0.578685			0.289342	+	0.957226i	$0.406563\pi$
$702$	−587614.	+	339259.i	−1.19239	+	0.688426i
$703$	306953.	−	531658.i	0.621100	−	1.07578i
$704$	231207.	+	133488.i	0.466505	+	0.269337i
$705$	17086.9	−	9865.14i	0.0343784	−	0.0198484i
$706$			1.30807e6i			2.62434i
$707$	101582.	+	275615.i	0.203226	+	0.551397i
$708$		−	362247.i		−	0.722668i
$709$	526378.	−	303904.i	1.04714	−	0.604567i	0.125293	−	0.992120i	$-0.460013\pi$
$709$	526378.	−	303904.i	1.04714	−	0.604567i	0.921848	+	0.387553i	$0.126679\pi$
$710$	−35226.9	−	20338.3i	−0.0698808	−	0.0403457i
$711$	408886.	+	236070.i	0.808841	+	0.466985i
$712$	−22550.5	+	13019.5i	−0.0444832	+	0.0256824i
$713$			10039.7i			0.0197488i
$714$	306239.	−	5853.04i	0.600710	−	0.0114812i
$715$	−343879.			−0.672658
$716$	369518.	+	640023.i	0.720791	+	1.24845i
$717$	−190931.	+	330702.i	−0.371396	+	0.643277i
$718$	367896.	−	637214.i	0.713634	−	1.23605i
$719$	143297.	+	248197.i	0.277191	+	0.480108i	0.970685	−	0.240353i	$-0.0772633\pi$
$719$	143297.	+	248197.i	0.277191	+	0.480108i	−0.693495	+	0.720462i	$0.743930\pi$
$720$	408180.			0.787384
$721$	−235707.	−	40577.4i	−0.453421	−	0.0780573i
$722$	118214.			0.226775
$723$	28504.7	+	49371.6i	0.0545305	+	0.0944497i
$724$	207340.	−	359124.i	0.395555	−	0.685121i
$725$	7742.23	+	4469.98i	0.0147296	+	0.00850412i
$726$	−107440.	−	186092.i	−0.203842	−	0.353065i
$727$			258561.i			0.489209i	0.969623	+	0.244605i	$0.0786582\pi$
$727$			258561.i			0.489209i	−0.969623	+	0.244605i	$0.921342\pi$
$728$	14814.6	−	17801.3i	0.0279528	−	0.0335883i
$729$	−34228.4			−0.0644068
$730$	180960.	+	313432.i	0.339576	+	0.588162i
$731$	460144.	−	398067.i	0.861111	−	0.744940i
$732$	116604.	−	201963.i	0.217616	−	0.376921i
$733$	764357.	−	441302.i	1.42262	−	0.821349i	0.426096	−	0.904678i	$-0.359889\pi$
$733$	764357.	−	441302.i	1.42262	−	0.821349i	0.996522	+	0.0833289i	$0.0265552\pi$
$734$	670174.			1.24393
$735$	39461.7	+	213659.i	0.0730468	+	0.395501i
$736$		−	295418.i		−	0.545357i
$737$	432924.	−	249949.i	0.797034	−	0.460168i
$738$	−111582.	+	193266.i	−0.204871	+	0.354848i
$739$	88032.2	−	152476.i	0.161195	−	0.279199i	−0.774102	−	0.633061i	$-0.781798\pi$
$739$	88032.2	−	152476.i	0.161195	−	0.279199i	0.935298	+	0.353862i	$0.115132\pi$
$740$	590285.	−	340801.i	1.07795	−	0.622355i
$741$	−271067.			−0.493673
$742$	311333.	+	259097.i	0.565479	+	0.470602i
$743$			138911.i			0.251628i	0.992054	+	0.125814i	$0.0401543\pi$
$743$			138911.i			0.251628i	−0.992054	+	0.125814i	$0.959846\pi$
$744$	208.541	+	361.204i	0.000376744	+	0.000652540i
$745$	133808.	−	231762.i	0.241084	−	0.417570i
$746$	−451926.	+	782760.i	−0.812064	+	1.40654i
$747$	−304583.	+	175851.i	−0.545840	+	0.315141i
$748$	101431.	−	292301.i	0.181287	−	0.522429i
$749$	−1.02543e6	−	176530.i	−1.82786	−	0.314670i
$750$	−354480.			−0.630186
$751$	−780773.	+	450780.i	−1.38435	+	0.799253i	−0.992671	−	0.120850i	$-0.961438\pi$
$751$	−780773.	+	450780.i	−1.38435	+	0.799253i	−0.391676	+	0.920103i	$0.628105\pi$
$752$	49500.6	+	28579.2i	0.0875336	+	0.0505376i
$753$	−67441.8	−	38937.5i	−0.118943	−	0.0686718i
$754$	74608.7	+	129226.i	0.131234	+	0.227304i
$755$	−104006.			−0.182458
$756$	406332.	−	149760.i	0.710948	−	0.262031i
$757$	−772341.			−1.34777			−0.673887	−	0.738834i	$-0.735377\pi$
$757$	−772341.			−1.34777			−0.673887	+	0.738834i	$0.735377\pi$
$758$	−645190.	+	372501.i	−1.12292	+	0.648319i
$759$	27105.5	−	46948.2i	0.0470516	−	0.0814958i
$760$	14934.6	+	8622.48i	0.0258563	+	0.0149281i
$761$	238062.	−	137445.i	0.411074	−	0.237334i	−0.280177	−	0.959948i	$-0.590393\pi$
$761$	238062.	−	137445.i	0.411074	−	0.237334i	0.691251	+	0.722615i	$0.257060\pi$
$762$	−277996.			−0.478773
$763$	−246305.	−	668281.i	−0.423082	−	1.14792i
$764$	456011.			0.781247
$765$	−84801.4	−	441913.i	−0.144904	−	0.755116i
$766$	829991.	+	479196.i	1.41454	+	0.816687i
$767$	−642904.	+	1.11354e6i	−1.09284	+	1.89285i
$768$	−132056.	−	228727.i	−0.223890	−	0.387789i
$769$		−	1.08512e6i		−	1.83495i	−0.397795	−	0.917474i	$-0.630224\pi$
$769$		−	1.08512e6i		−	1.83495i	0.397795	−	0.917474i	$-0.369776\pi$
$770$	438054.	+	75412.0i	0.738833	+	0.127192i
$771$		−	36957.2i		−	0.0621713i
$772$	769623.	−	444342.i	1.29135	−	0.745560i
$773$	125457.	+	72432.7i	0.209960	+	0.121220i	0.601293	−	0.799029i	$-0.294653\pi$
$773$	125457.	+	72432.7i	0.209960	+	0.121220i	−0.391333	+	0.920249i	$0.627986\pi$
$774$	391750.	−	678530.i	0.653923	−	1.13263i
$775$	1754.37	+	3038.66i	0.00292091	+	0.00505917i
$776$	−22044.4			−0.0366079
$777$	−223938.	+	269086.i	−0.370925	+	0.445706i
$778$	1.39139e6			2.29874
$779$	−171683.	+	99121.3i	−0.282913	+	0.163340i
$780$	−260637.	−	150479.i	−0.428397	−	0.247335i
$781$	10551.8	−	18276.3i	0.0172992	−	0.0299631i
$782$	−327722.	+	62888.7i	−0.535911	+	0.102839i
$783$		−	70532.6i		−	0.115045i
$784$	−478882.	+	408488.i	−0.779106	+	0.664580i
$785$			411623.i			0.667974i
$786$	301317.	+	521897.i	0.487729	+	0.844772i
$787$	76403.0	−	132334.i	0.123356	−	0.213659i	−0.797733	−	0.603011i	$-0.793968\pi$
$787$	76403.0	−	132334.i	0.123356	−	0.213659i	0.921089	+	0.389352i	$0.127301\pi$
$788$	−522261.	−	301527.i	−0.841075	−	0.485595i
$789$	76298.7	+	132153.i	0.122564	+	0.212287i
$790$			943102.i			1.51114i
$791$	516345.	−	620444.i	0.825253	−	0.991630i
$792$			10071.7i			0.0160566i
$793$	−716876.	+	413888.i	−1.13998	+	0.658168i
$794$	226180.	−	391755.i	0.358767	−	0.621403i
$795$	−66528.2	+	115230.i	−0.105262	+	0.182319i
$796$	187252.	+	324330.i	0.295529	+	0.511871i
$797$			561869.i			0.884542i	0.896881	+	0.442271i	$0.145827\pi$
$797$			561869.i			0.884542i	−0.896881	+	0.442271i	$0.854173\pi$
$798$	345301.	+	59444.3i	0.542240	+	0.0933478i
$799$	20657.1	−	59529.0i	0.0323575	−	0.0932470i
$800$	−51622.4	−	89412.7i	−0.0806601	−	0.139707i
$801$	673103.	+	388616.i	1.04910	+	0.605698i
$802$	142796.	+	82443.1i	0.222007	+	0.128176i
$803$	−162614.	+	93885.0i	−0.252189	+	0.145601i
$804$	437502.			0.676812
$805$	−81861.6	−	222109.i	−0.126325	−	0.342747i
$806$			58564.7i			0.0901500i
$807$	−121089.	−	209733.i	−0.185934	−	0.322047i
$808$	−11513.7	−	6647.42i	−0.0176356	−	0.0101819i
$809$	−874791.	−	505061.i	−1.33662	−	0.771697i	−0.350314	−	0.936632i	$-0.613925\pi$
$809$	−874791.	−	505061.i	−1.33662	−	0.771697i	−0.986304	+	0.164935i	$0.947258\pi$
$810$	−210453.	−	364516.i	−0.320764	−	0.555580i
$811$	−3692.39			−0.00561391			−0.00280696	−	0.999996i	$-0.500893\pi$
$811$	−3692.39			−0.00561391			−0.00280696	+	0.999996i	$0.500893\pi$
$812$	−32934.7	−	89359.2i	−0.0499508	−	0.135527i
$813$		−	98243.2i		−	0.148635i
$814$	358097.	+	620241.i	0.540445	+	0.936078i
$815$	−212699.	−	122802.i	−0.320221	−	0.184880i
$816$	−220447.	+	190707.i	−0.331073	+	0.286409i
$817$	602757.	−	348002.i	0.903022	−	0.521360i
$818$		−	493632.i		−	0.737729i
$819$	−681257.	−	117280.i	−1.01565	−	0.174846i
$820$	−220103.			−0.327340
$821$	244284.	−	141038.i	0.362418	−	0.209242i	−0.307723	−	0.951476i	$-0.599567\pi$
$821$	244284.	−	141038.i	0.362418	−	0.209242i	0.670141	+	0.742234i	$0.266234\pi$
$822$	−140549.	+	243438.i	−0.208010	+	0.360284i
$823$	707949.	+	408735.i	1.04521	+	0.603451i	0.921304	−	0.388843i	$-0.127125\pi$
$823$	707949.	+	408735.i	1.04521	+	0.603451i	0.123904	+	0.992294i	$0.460459\pi$
$824$	9374.86	−	5412.58i	0.0138074	−	0.00797168i
$825$		−	18946.1i		−	0.0278363i
$826$	1.06317e6	−	1.27751e6i	1.55827	−	1.87242i
$827$			1.10873e6i			1.62111i	0.585661	+	0.810556i	$0.300835\pi$
$827$			1.10873e6i			1.62111i	−0.585661	+	0.810556i	$0.699165\pi$
$828$	−183751.	+	106089.i	−0.268022	+	0.154742i
$829$	−454470.	−	262389.i	−0.661297	−	0.381800i	0.131474	−	0.991320i	$-0.458029\pi$
$829$	−454470.	−	262389.i	−0.661297	−	0.381800i	−0.792771	+	0.609520i	$0.791362\pi$
$830$	−608406.	−	351263.i	−0.883156	−	0.509890i
$831$	250106.	−	144399.i	0.362178	−	0.209103i
$832$		−	829357.i		−	1.19810i
$833$	541737.	+	433593.i	0.780726	+	0.624874i
$834$	520872.			0.748857
$835$	−348321.	−	603310.i	−0.499582	−	0.865302i
$836$	176966.	−	306513.i	0.253207	−	0.438568i
$837$	13841.3	−	23973.8i	0.0197572	−	0.0342205i
$838$	−461549.	−	799426.i	−0.657249	−	1.13839i
$839$	−633873.			−0.900489			−0.450244	−	0.892905i	$-0.648663\pi$
$839$	−633873.			−0.900489			−0.450244	+	0.892905i	$0.648663\pi$
$840$	−7558.76	−	6290.54i	−0.0107125	−	0.00891516i
$841$	691770.			0.978069
$842$	229.615	+	397.706i	0.000323875	+	0.000560967i
$843$	144843.	−	250875.i	0.203818	−	0.353023i
$844$	−560944.	−	323861.i	−0.787472	−	0.454647i
$845$	198243.	+	343368.i	0.277642	+	0.480890i
$846$		−	81141.7i		−	0.113371i
$847$	82588.1	−	479739.i	0.115120	−	0.668711i
$848$	−385463.			−0.536032
$849$	−299113.	−	518079.i	−0.414973	−	0.718755i
$850$	−88200.7	+	76301.7i	−0.122077	+	0.105608i
$851$	190702.	−	330305.i	0.263327	−	0.456096i
$852$	15995.1	−	9234.79i	0.0220348	−	0.0127218i
$853$	−827459.			−1.13723			−0.568615	−	0.822604i	$-0.692521\pi$
$853$	−827459.			−1.13723			−0.568615	+	0.822604i	$0.692521\pi$
$854$	1.00396e6	−	370026.i	1.37658	−	0.507361i
$855$		−	514740.i		−	0.704135i
$856$	40784.9	−	23547.2i	0.0556611	−	0.0321360i
$857$	45236.5	−	78351.8i	0.0615924	−	0.106681i	−0.833585	−	0.552391i	$-0.813715\pi$
$857$	45236.5	−	78351.8i	0.0615924	−	0.106681i	0.895177	+	0.445710i	$0.147049\pi$
$858$	158115.	−	273864.i	0.214783	−	0.372015i
$859$	434207.	−	250690.i	0.588452	−	0.339743i	−0.176033	−	0.984384i	$-0.556327\pi$
$859$	434207.	−	250690.i	0.588452	−	0.339743i	0.764485	+	0.644642i	$0.222993\pi$
$860$	772753.			1.04483
$861$	106072.	−	39094.6i	0.143086	−	0.0527364i
$862$			731189.i			0.984045i
$863$	123581.	+	214049.i	0.165932	+	0.287403i	0.936986	−	0.349367i	$-0.113603\pi$
$863$	123581.	+	214049.i	0.165932	+	0.287403i	−0.771054	+	0.636770i	$0.780270\pi$
$864$	−407280.	+	705430.i	−0.545589	+	0.944988i
$865$	403608.	−	699069.i	0.539420	−	0.934303i
$866$	−1.29225e6	+	746080.i	−1.72310	+	0.994832i
$867$	252267.	+	199045.i	0.335600	+	0.264797i
$868$	6341.40	−	36836.0i	0.00841677	−	0.0488915i
$869$	−489297.			−0.647938
$870$	54871.8	−	31680.3i	0.0724955	−	0.0418553i
$871$	−1.34488e6	−	776464.i	−1.77274	−	1.02349i
$872$	27917.0	+	16117.9i	0.0367144	+	0.0211971i
$873$	328999.	+	569843.i	0.431684	+	0.747699i
$874$	−381731.			−0.499730
$875$	−617256.	−	513692.i	−0.806212	−	0.670945i
$876$	−164333.			−0.214150
$877$	1.10091e6	−	635611.i	1.43137	−	0.826404i	0.434147	−	0.900842i	$-0.357050\pi$
$877$	1.10091e6	−	635611.i	1.43137	−	0.826404i	0.997226	+	0.0744383i	$0.0237164\pi$
$878$	928090.	−	1.60750e6i	1.20393	−	2.08527i
$879$	380249.	+	219537.i	0.492142	+	0.284138i
$880$	−366339.	+	211506.i	−0.473061	+	0.273122i
$881$	−1.10109e6			−1.41864			−0.709321	−	0.704886i	$-0.750998\pi$
$881$	−1.10109e6			−1.41864			−0.709321	+	0.704886i	$0.750998\pi$
$882$	842106.	+	298796.i	1.08250	+	0.384094i
$883$	1.16077e6			1.48876			0.744380	−	0.667756i	$-0.232745\pi$
$883$	1.16077e6			1.48876			0.744380	+	0.667756i	$0.232745\pi$
$884$	−943925.	+	181136.i	−1.20790	+	0.231792i
$885$	472831.	+	272989.i	0.603698	+	0.348545i
$886$	−12188.9	+	21111.8i	−0.0155273	+	0.0268941i
$887$	344772.	+	597162.i	0.438212	+	0.759006i	0.997552	−	0.0699329i	$-0.0222785\pi$
$887$	344772.	+	597162.i	0.438212	+	0.759006i	−0.559339	+	0.828939i	$0.688945\pi$
$888$		−	15844.8i		−	0.0200937i
$889$	−484076.	−	402857.i	−0.612505	−	0.509738i
$890$			1.55252e6i			1.96001i
$891$	189117.	−	109187.i	0.238218	−	0.137535i
$892$	320140.	+	184833.i	0.402356	+	0.232300i
$893$	36040.2	−	62423.4i	0.0451943	−	0.0782789i
$894$	123049.	+	213127.i	0.153959	+	0.266664i
$895$	−1.11387e6			−1.39056
$896$	9436.72	−	54816.2i	0.0117545	−	0.0682799i
$897$	−168406.			−0.209302
$898$	−583505.	+	336887.i	−0.723589	+	0.417764i
$899$	−5272.24	−	3043.93i	−0.00652343	−	0.00376630i
$900$	−37076.8	+	64218.9i	−0.0457738	+	0.0792825i
$901$	80081.9	+	417319.i	0.0986472	+	0.514065i
$902$		−	231273.i		−	0.284258i
$903$	−372406.	+	137256.i	−0.456711	+	0.168328i
$904$			36534.1i			0.0447056i
$905$	312503.	+	541271.i	0.381555	+	0.660872i
$906$	47821.8	−	82829.8i	0.0582599	−	0.100909i
$907$	−1.04966e6	−	606020.i	−1.27595	−	0.736669i	−0.299847	−	0.953987i	$-0.596936\pi$
$907$	−1.04966e6	−	606020.i	−1.27595	−	0.736669i	−0.976101	+	0.217318i	$0.930269\pi$
$908$	360212.	+	623905.i	0.436904	+	0.756740i
$909$			396834.i			0.480265i
$910$	−477525.	−	1.29563e6i	−0.576651	−	1.56458i
$911$			938475.i			1.13080i	0.824817	+	0.565400i	$0.191278\pi$
$911$			938475.i			1.13080i	−0.824817	+	0.565400i	$0.808722\pi$
$912$	−288771.	+	166722.i	−0.347187	+	0.200448i
$913$	182241.	−	315651.i	0.218628	−	0.378674i
$914$	−271448.	+	470162.i	−0.324934	+	0.562802i
$915$	175745.	+	304399.i	0.209913	+	0.363581i
$916$			761997.i			0.908159i
$917$	−231619.	+	1.34543e6i	−0.275445	+	1.60001i
$918$	869272.	+	301645.i	1.03150	+	0.357940i
$919$	−638231.	−	1.10545e6i	−0.755696	−	1.30890i	−0.945028	−	0.326991i	$-0.893965\pi$
$919$	−638231.	−	1.10545e6i	−0.755696	−	1.30890i	0.189331	−	0.981913i	$-0.439368\pi$
$920$	9278.44	+	5356.91i	0.0109622	+	0.00632906i
$921$	104771.	+	60489.4i	0.123515	+	0.0713115i
$922$	−1.11489e6	+	643682.i	−1.31151	+	0.757198i
$923$	−65558.4			−0.0769529
$924$	−129105.	+	155134.i	−0.151217	+	0.181703i
$925$		−	133296.i		−	0.155788i
$926$	−724527.	−	1.25492e6i	−0.844953	−	1.46350i
$927$	−279828.	−	161559.i	−0.325635	−	0.188006i
$928$	155136.	+	89567.7i	0.180142	+	0.104005i
$929$	112045.	+	194067.i	0.129825	+	0.224864i	0.923609	−	0.383336i	$-0.125225\pi$
$929$	112045.	+	194067.i	0.129825	+	0.224864i	−0.793783	+	0.608200i	$0.791892\pi$
$930$	24867.7			0.0287521
$931$	515130.	+	603901.i	0.594316	+	0.696733i
$932$		−	772684.i		−	0.889549i
$933$	4836.93	+	8377.81i	0.00555657	+	0.00962425i
$934$	−1.93037e6	−	1.11450e6i	−2.21282	−	1.27757i
$935$	305094.	+	352673.i	0.348988	+	0.403412i
$936$	27095.9	−	15643.8i	0.0309280	−	0.0178563i
$937$		−	1.52959e6i		−	1.74219i	−0.491113	−	0.871096i	$-0.663410\pi$
$937$		−	1.52959e6i		−	1.74219i	0.491113	−	0.871096i	$-0.336590\pi$
$938$	1.54291e6	+	1.28403e6i	1.75361	+	1.45939i
$939$	−85501.4			−0.0969711
$940$	69307.0	−	40014.4i	0.0784370	−	0.0452856i
$941$	539499.	−	934440.i	0.609273	−	1.05529i	−0.382088	−	0.924126i	$-0.624795\pi$
$941$	539499.	−	934440.i	0.609273	−	1.05529i	0.991361	−	0.131165i	$-0.0418718\pi$
$942$	−327814.	−	189264.i	−0.369425	−	0.213287i
$943$	−106662.	+	61581.4i	−0.119946	+	0.0692510i
$944$			1.58169e6i			1.77492i
$945$	−110734.	+	643233.i	−0.123999	+	0.720286i
$946$			811969.i			0.907314i
$947$	1.04946e6	−	605908.i	1.17022	−	0.675627i	0.216488	−	0.976285i	$-0.430540\pi$
$947$	1.04946e6	−	605908.i	1.17022	−	0.675627i	0.953732	+	0.300659i	$0.0972065\pi$
$948$	−370854.	−	214112.i	−0.412654	−	0.238246i
$949$	505158.	+	291653.i	0.560912	+	0.323843i
$950$	−115537.	+	66705.2i	−0.128019	+	0.0739116i
$951$		−	559794.i		−	0.618967i
$952$	−31400.1	+	600.139i	−0.0346463	+	0.000662183i
$953$	−698200.			−0.768766			−0.384383	−	0.923174i	$-0.625586\pi$
$953$	−698200.			−0.768766			−0.384383	+	0.923174i	$0.625586\pi$
$954$	273600.	+	473890.i	0.300621	+	0.520692i
$955$	−343649.	+	595218.i	−0.376798	+	0.652633i
$956$	−774442.	+	1.34137e6i	−0.847370	+	1.46769i
$957$	16436.2	+	28468.4i	0.0179465	+	0.0310842i
$958$	247111.			0.269253
$959$	−597515.	+	220224.i	−0.649698	+	0.239456i
$960$	−352161.			−0.382119
$961$	460566.	+	797723.i	0.498706	+	0.863785i
$962$	1.11242e6	−	1.92678e6i	1.20204	−	2.08200i
$963$	−1.21738e6	−	702854.i	−1.31272	−	0.757901i
$964$	115619.	+	200258.i	0.124416	+	0.215494i
$965$			1.33942e6i			1.43835i
$966$	214526.	+	36931.1i	0.229893	+	0.0395766i
$967$	972644.			1.04016			0.520081	−	0.854117i	$-0.325902\pi$
$967$	972644.			1.04016			0.520081	+	0.854117i	$0.325902\pi$
$968$	11016.4	+	19080.9i	0.0117567	+	0.0203633i
$969$	240494.	+	277998.i	0.256127	+	0.296070i
$970$	−657176.	+	1.13826e6i	−0.698455	+	1.20976i
$971$	−221978.	+	128159.i	−0.235436	+	0.135929i	−0.613077	−	0.790023i	$-0.710068\pi$
$971$	−221978.	+	128159.i	−0.235436	+	0.135929i	0.377642	+	0.925952i	$0.376735\pi$
$972$	906978.			0.959985
$973$	906995.	+	754818.i	0.958031	+	0.797291i
$974$		−	1.57826e6i		−	1.66365i
$975$	−50970.7	+	29428.0i	−0.0536181	+	0.0309564i
$976$	−509131.	+	881840.i	−0.534478	+	0.925743i
$977$	−569223.	+	985923.i	−0.596339	+	1.03289i	0.397017	+	0.917811i	$0.370045\pi$
$977$	−569223.	+	985923.i	−0.596339	+	1.03289i	−0.993356	+	0.115079i	$0.963288\pi$
$978$	195598.	−	112928.i	0.204497	−	0.118066i
$979$	−805475.			−0.840401
$980$	160062.	+	866632.i	0.166662	+	0.902366i
$981$		−	962198.i		−	0.999831i
$982$	−339342.	−	587758.i	−0.351896	−	0.609503i
$983$	612114.	−	1.06021e6i	0.633469	−	1.09720i	−0.353368	−	0.935484i	$-0.614964\pi$
$983$	612114.	−	1.06021e6i	0.633469	−	1.09720i	0.986837	−	0.161716i	$-0.0517030\pi$
$984$	−2558.30	+	4431.11i	−0.00264217	+	0.00457638i
$985$	787150.	−	454461.i	0.811307	−	0.468408i
$986$	66336.7	−	191167.i	0.0682339	−	0.196635i
$987$	−26293.2	+	31594.1i	−0.0269903	+	0.0324318i
$988$	−1.09948e6			−1.12635
$989$	374476.	−	216204.i	0.382853	−	0.221040i
$990$	520052.	+	300252.i	0.530611	+	0.306349i
$991$	−1.37724e6	−	795149.i	−1.40237	−	0.809658i	−0.407733	−	0.913101i	$-0.633681\pi$
$991$	−1.37724e6	−	795149.i	−1.40237	−	0.809658i	−0.994635	+	0.103444i	$0.967014\pi$
$992$	35153.4	+	60887.5i	0.0357227	+	0.0618736i
$993$	178351.			0.180874
$994$	83512.2	+	14376.8i	0.0845234	+	0.0145509i
$995$	−564452.			−0.570139
$996$	276253.	−	159495.i	0.278476	−	0.160778i
$997$	−318009.	+	550808.i	−0.319926	+	0.554128i	−0.980472	−	0.196657i	$-0.936991\pi$
$997$	−318009.	+	550808.i	−0.319926	+	0.554128i	0.660546	+	0.750785i	$0.270325\pi$
$998$	−1.84342e6	−	1.06430e6i	−1.85082	−	1.06857i
$999$	−910755.	+	525825.i	−0.912579	+	0.526878i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	119.5.h.a.101.9	yes	92
7.5	odd	6	inner	119.5.h.a.33.10	yes	92
17.16	even	2	inner	119.5.h.a.101.10	yes	92
119.33	odd	6	inner	119.5.h.a.33.9	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.5.h.a.33.9	✓	92	119.33	odd	6	inner
119.5.h.a.33.10	yes	92	7.5	odd	6	inner
119.5.h.a.101.9	yes	92	1.1	even	1	trivial
119.5.h.a.101.10	yes	92	17.16	even	2	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:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	119.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.81094 - 4.86869i) q^{2} +(-1.92369 + 3.33193i) q^{3} +(-7.80276 + 13.5148i) q^{4} +(-11.7603 - 20.3694i) q^{5} +21.6295 q^{6} +(37.6635 + 31.3442i) q^{7} -2.21777 q^{8} +(33.0988 + 57.3289i) q^{9} +(-66.1150 + 114.514i) q^{10} +(-59.4120 - 34.3015i) q^{11} +(-30.0202 - 51.9964i) q^{12} +213.115i q^{13} +(46.7356 - 271.479i) q^{14} +90.4927 q^{15} +(131.078 + 227.034i) q^{16} +(218.564 - 189.078i) q^{17} +(186.078 - 322.296i) q^{18} +(286.304 - 165.298i) q^{19} +367.051 q^{20} +(-176.890 + 65.1954i) q^{21} +385.678i q^{22} +(177.873 - 102.695i) q^{23} +(4.26630 - 7.38945i) q^{24} +(35.8906 - 62.1644i) q^{25} +(1037.59 - 599.053i) q^{26} -566.325 q^{27} +(-717.489 + 264.442i) q^{28} +124.544i q^{29} +(-254.369 - 440.581i) q^{30} +(-24.4405 + 42.3322i) q^{31} +(719.163 - 1245.63i) q^{32} +(228.581 - 131.971i) q^{33} +(-1534.93 - 532.635i) q^{34} +(195.531 - 1135.80i) q^{35} -1033.05 q^{36} +(1608.18 - 928.485i) q^{37} +(-1609.57 - 929.284i) q^{38} +(-710.084 - 409.967i) q^{39} +(26.0817 + 45.1748i) q^{40} -599.653 q^{41} +(814.642 + 677.960i) q^{42} +2105.30 q^{43} +(927.155 - 535.293i) q^{44} +(778.505 - 1348.41i) q^{45} +(-999.980 - 577.339i) q^{46} +(188.821 - 109.016i) q^{47} -1008.61 q^{48} +(436.077 + 2361.07i) q^{49} -403.546 q^{50} +(209.545 + 1091.97i) q^{51} +(-2880.20 - 1662.88i) q^{52} +(-735.178 + 1273.37i) q^{53} +(1591.91 + 2757.26i) q^{54} +1613.59i q^{55} +(-83.5290 - 69.5144i) q^{56} +1271.93i q^{57} +(606.368 - 350.086i) q^{58} +(5225.08 + 3016.70i) q^{59} +(-706.092 + 1222.99i) q^{60} +(1942.09 + 3363.80i) q^{61} +274.803 q^{62} +(-550.312 + 3196.66i) q^{63} -3891.59 q^{64} +(4341.03 - 2506.30i) q^{65} +(-1285.05 - 741.925i) q^{66} +(-3643.41 + 6310.56i) q^{67} +(849.943 + 4429.18i) q^{68} +790.213i q^{69} +(-6079.49 + 2240.69i) q^{70} +307.620i q^{71} +(-73.4056 - 127.142i) q^{72} +(1368.52 - 2370.35i) q^{73} +(-9041.01 - 5219.83i) q^{74} +(138.085 + 239.170i) q^{75} +5159.11i q^{76} +(-1162.51 - 3154.14i) q^{77} +4609.57i q^{78} +(6176.74 - 3566.14i) q^{79} +(3083.04 - 5339.97i) q^{80} +(-1591.57 + 2756.68i) q^{81} +(1685.59 + 2919.52i) q^{82} +5312.92i q^{83} +(499.125 - 2899.33i) q^{84} +(-6421.80 - 2228.42i) q^{85} +(-5917.88 - 10250.1i) q^{86} +(-414.973 - 239.585i) q^{87} +(131.762 + 76.0730i) q^{88} +(10168.1 - 5870.54i) q^{89} -8753.32 q^{90} +(-6679.93 + 8026.65i) q^{91} +3205.22i q^{92} +(-94.0320 - 162.868i) q^{93} +(-1061.53 - 612.874i) q^{94} +(-6734.05 - 3887.90i) q^{95} +(2766.89 + 4792.40i) q^{96} +9939.90 q^{97} +(10269.5 - 8759.94i) q^{98} -4541.37i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 2 q^{2} - 354 q^{4} + 56 q^{8} - 1068 q^{9} + 464 q^{15} - 3146 q^{16} + 1104 q^{17} - 906 q^{18} - 6 q^{19} - 240 q^{21} - 3106 q^{25} + 468 q^{26} + 1858 q^{30} - 1680 q^{32} - 198 q^{33} - 5318 q^{35}+ \cdots + 107386 q^{98}+O(q^{100}) \) 92 * q - 2 * q^2 - 354 * q^4 + 56 * q^8 - 1068 * q^9 + 464 * q^15 - 3146 * q^16 + 1104 * q^17 - 906 * q^18 - 6 * q^19 - 240 * q^21 - 3106 * q^25 + 468 * q^26 + 1858 * q^30 - 1680 * q^32 - 198 * q^33 - 5318 * q^35 + 17304 * q^36 - 6 * q^38 + 1888 * q^42 + 3316 * q^43 - 7242 * q^47 - 1284 * q^49 + 2136 * q^50 - 11304 * q^51 - 5202 * q^52 + 28 * q^53 - 17826 * q^59 - 3182 * q^60 + 41768 * q^64 + 5988 * q^66 + 2924 * q^67 - 22788 * q^68 + 36898 * q^70 - 23660 * q^72 - 3162 * q^77 - 6194 * q^81 + 30426 * q^84 + 46552 * q^85 + 4118 * q^86 - 7026 * q^87 + 4944 * q^89 + 11034 * q^93 - 101214 * q^94 + 107386 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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