LMFDB - Embedded newform 119.5.h.a.101.10

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			101.10
Character	$\chi$	$=$	119.101
Dual form			119.5.h.a.33.10

$q$-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} +(-54.4643 + 283.821i) 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} +(840.900 + 727.455i) 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} +(-3410.81 - 2950.66i) 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	−0.739140	−	0.673552i	$-0.764768\pi$
$3$	1.92369	−	3.33193i	0.213743	−	0.370214i	0.952883	+	0.303338i	$0.0981011\pi$
$4$	−7.80276	+	13.5148i	−0.487672	+	0.844673i
$5$	11.7603	+	20.3694i	0.470412	+	0.814778i	0.999427	−	0.0338347i	$-0.0107720\pi$
$5$	11.7603	+	20.3694i	0.470412	+	0.814778i	−0.529015	+	0.848612i	$0.677439\pi$
$6$	−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	0.724993	−	0.688757i	$-0.241843\pi$
$11$	59.4120	+	34.3015i	0.491008	+	0.283484i	−0.233984	+	0.972240i	$0.575176\pi$
$12$	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
$17$	−54.4643	+	283.821i	−0.188458	+	0.982081i
$17$	−54.4643	+	283.821i	−0.188458	+	0.982081i
$18$	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	−0.658610	−	0.752485i	$-0.728855\pi$
$23$	−177.873	+	102.695i	−0.336244	+	0.194130i	0.322366	+	0.946615i	$0.395522\pi$
$24$	−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	$-0.976409\pi$
$29$		−	124.544i		−	0.148091i	0.997255	−	0.0740454i	$-0.0235910\pi$
$30$	−254.369	−	440.581i	−0.282633	−	0.489534i
$31$	24.4405	−	42.3322i	0.0254324	−	0.0440502i	−0.853029	−	0.521863i	$-0.825237\pi$
$31$	24.4405	−	42.3322i	0.0254324	−	0.0440502i	0.878461	+	0.477813i	$0.158570\pi$
$32$	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	−0.954786	−	0.297295i	$-0.903916\pi$
$37$	−1608.18	+	928.485i	−1.17471	+	0.678221i	−0.219928	+	0.975516i	$0.570582\pi$
$38$	−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	$-0.442920\pi$
$41$	599.653			0.356724			0.178362	+	0.983965i	$0.442920\pi$
$42$	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
$51$	840.900	+	727.455i	0.323299	+	0.279683i
$52$	−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	$-0.991880\pi$
$61$	−1942.09	−	3363.80i	−0.521927	−	0.904003i	0.477748	−	0.878497i	$-0.341453\pi$
$62$	−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	$0.865247\pi$
$68$	−3410.81	−	2950.66i	−0.737632	−	0.638119i
$69$			790.213i			0.165976i
$70$	−6079.49	+	2240.69i	−1.24071	+	0.457284i
$71$		−	307.620i		−	0.0610236i	−0.999534	−	0.0305118i	$-0.990286\pi$
$71$		−	307.620i		−	0.0610236i	0.999534	−	0.0305118i	$-0.00971371\pi$
$72$	−73.4056	−	127.142i	−0.0141600	−	0.0245259i
$73$	−1368.52	+	2370.35i	−0.256807	+	0.444803i	−0.965385	−	0.260830i	$-0.916004\pi$
$73$	−1368.52	+	2370.35i	−0.256807	+	0.444803i	0.708578	+	0.705633i	$0.249337\pi$
$74$	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	−0.905186	−	0.425016i	$-0.860268\pi$
$79$	−6176.74	+	3566.14i	−0.989704	+	0.571406i	−0.0845183	+	0.996422i	$0.526935\pi$
$80$	−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	$-0.677137\pi$
$97$	−9939.90			−1.05642			−0.528212	+	0.849112i	$0.677137\pi$
$98$	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	$0.571737\pi$
$102$	1178.03	−	6138.92i	0.113229	−	0.590053i
$103$	−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	$-0.288728\pi$
$107$	18390.0	−	10617.5i	1.60626	−	0.927373i	0.990198	−	0.139674i	$-0.0446055\pi$
$108$	−4418.90	+	7653.75i	−0.378849	+	0.656186i
$109$	12587.9	+	7267.61i	1.05950	+	0.611701i	0.925293	−	0.379253i	$-0.123819\pi$
$109$	12587.9	+	7267.61i	1.05950	+	0.611701i	0.134204	+	0.990954i	$0.457152\pi$
$110$	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	$0.223165\pi$
$113$			16473.4i			1.29011i	−0.764138	+	0.645053i	$0.776835\pi$
$114$	−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
$119$	10947.5	−	8982.57i	0.773073	−	0.634317i
$120$	−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	$-0.865169\pi$
$131$	−13930.8	−	24128.9i	−0.811774	−	1.40603i	0.0998478	−	0.995003i	$-0.468164\pi$
$132$			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
$136$	120.789	−	629.451i	0.00653056	−	0.0340317i
$137$	−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	$-0.714166\pi$
$139$	−24081.6			−1.24639			−0.623196	+	0.782065i	$0.714166\pi$
$140$	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	−0.660432	−	0.750885i	$-0.729627\pi$
$163$	−9043.10	+	5221.04i	−0.340363	+	0.196509i	0.320070	+	0.947394i	$0.396294\pi$
$164$	−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	$-0.678185\pi$
$167$	−29618.4			−1.06201			−0.531005	+	0.847369i	$0.678185\pi$
$168$	392.301	−	144.589i	0.0138995	−	0.00512289i
$169$	−16857.0			−0.590211
$170$	28900.8	+	25001.8i	1.00003	+	0.865114i
$171$	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	$-0.972311\pi$
$173$	−17159.8	−	29721.6i	−0.573349	−	0.993069i	0.422870	−	0.906190i	$-0.361023\pi$
$174$			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	$-0.367079\pi$
$181$	26572.7			0.811107			0.405554	+	0.914071i	$0.367079\pi$
$182$	−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
$187$	−12971.3	+	14994.2i	−0.370939	+	0.428786i
$188$			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	0.984363	−	0.176152i	$-0.0563650\pi$
$193$	49317.4	+	28473.4i	1.32399	+	0.764407i	0.339629	+	0.940559i	$0.389698\pi$
$194$	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	$-0.834116\pi$
$197$		−	38643.7i		−	0.995740i	0.867252	−	0.497870i	$-0.165884\pi$
$198$	22110.5	−	12765.5i	0.563986	−	0.325617i
$199$	−11999.1	+	20783.0i	−0.303000	+	0.524811i	−0.976814	−	0.214090i	$-0.931321\pi$
$199$	−11999.1	+	20783.0i	−0.303000	+	0.524811i	0.673814	+	0.738901i	$0.264655\pi$
$200$	−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	$-0.845644\pi$
$211$		−	41506.0i		−	0.932280i	0.884711	−	0.466140i	$-0.154356\pi$
$212$	−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
$221$	−60486.6	−	11607.2i	−1.23844	−	0.237652i
$222$	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	−0.998252	−	0.0590951i	$-0.981178\pi$
$227$	−23082.3	+	39979.8i	−0.447948	+	0.775869i	0.550304	+	0.834964i	$0.314512\pi$
$228$	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	−0.0500620	−	0.998746i	$-0.515942\pi$
$233$	42880.0	−	24756.8i	0.789846	−	0.456018i	0.839908	+	0.542728i	$0.182609\pi$
$234$	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
$238$	−74506.0	−	28050.5i	−1.31534	−	0.495206i
$239$	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	−0.922731	−	0.385444i	$-0.874048\pi$
$241$	−7408.86	+	12832.5i	−0.127561	+	0.220942i	0.795170	+	0.606386i	$0.207381\pi$
$242$	−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
$255$	−4928.62	+	25683.8i	−0.0757957	+	0.394983i
$256$	−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	−0.562344	−	0.826903i	$-0.690100\pi$
$269$	31473.2	−	54513.2i	0.434947	−	0.753351i	0.997291	+	0.0735524i	$0.0234336\pi$
$270$	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	0.859714	−	0.510776i	$-0.170642\pi$
$277$	65006.8	+	37531.7i	0.847226	+	0.489146i	−0.0124879	+	0.999922i	$0.503975\pi$
$278$	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	$-0.410540\pi$
$283$	77744.7	−	134658.i	0.970728	−	1.68135i	0.693366	−	0.720585i	$-0.256127\pi$
$284$	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
$289$	−77588.3	−	30916.3i	−0.928967	−	0.370162i
$290$	−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
$306$	81339.9	+	70366.4i	0.868682	+	0.751489i
$307$		−	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	−0.872451	−	0.488701i	$-0.837471\pi$
$311$	−1257.20	+	2177.54i	−0.0129982	+	0.0225136i	0.859453	+	0.511215i	$0.170804\pi$
$312$	−1574.80	−	909.213i	−0.0161777	−	0.00934021i
$313$	−11111.6	−	19245.9i	−0.113420	−	0.196449i	0.803727	−	0.594998i	$-0.202847\pi$
$313$	−11111.6	−	19245.9i	−0.113420	−	0.196449i	−0.917147	+	0.398549i	$0.869514\pi$
$314$			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	0.282047	−	0.959400i	$-0.408986\pi$
$317$	126007.	−	72750.1i	1.25394	−	0.723960i	0.971889	+	0.235440i	$0.0756531\pi$
$318$	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	$0.139605\pi$
$337$			96455.4i			0.849311i	−0.905355	+	0.424656i	$0.860395\pi$
$338$	47384.0	+	82071.5i	0.414761	+	0.718388i
$339$	54888.0	+	31689.6i	0.477615	+	0.275751i
$340$	19991.2	−	104177.i	0.172934	−	0.901185i
$341$	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	0.999612	−	0.0278566i	$-0.00886817\pi$
$347$	177639.	+	102560.i	1.47529	+	0.851761i	0.475681	+	0.879618i	$0.342202\pi$
$348$	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
$357$	−8869.70	−	53755.9i	−0.0695941	−	0.421784i
$358$	−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	−0.555345	−	0.831620i	$-0.687414\pi$
$367$	59604.1	−	103237.i	0.442531	−	0.766487i	0.997877	+	0.0651331i	$0.0207472\pi$
$368$	−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	$-0.362751\pi$
$374$	109464.	+	21005.7i	0.782577	+	0.150174i
$375$	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	$0.152611\pi$
$379$			132518.i			0.922565i	−0.887253	+	0.461283i	$0.847389\pi$
$380$	−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	0.709703	−	0.704501i	$-0.248829\pi$
$397$	−40232.0	−	69683.9i	−0.255265	−	0.442132i	−0.964967	+	0.262370i	$0.915496\pi$
$398$	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	−0.418937	−	0.908015i	$-0.637597\pi$
$401$	25400.0	−	14664.7i	0.157959	−	0.0911978i	0.576896	+	0.816818i	$0.304264\pi$
$402$	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
$408$	−1864.92	−	1613.33i	−0.0112032	−	0.00969176i
$409$	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	$-0.654894\pi$
$419$	−164197.			−0.935273			−0.467637	+	0.883921i	$0.654894\pi$
$420$	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
$425$	15688.8	+	13572.3i	0.0868586	+	0.0751406i
$426$			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	0.771536	−	0.636186i	$-0.219489\pi$
$431$	112636.	+	65030.7i	0.606351	+	0.350077i	−0.165185	+	0.986263i	$0.552822\pi$
$432$	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	$-0.839237\pi$
$439$	−165085.	−	285936.i	−0.856603	−	1.48368i	0.0185470	−	0.999828i	$-0.494096\pi$
$440$		−	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	$0.0960667\pi$
$449$			119848.i			0.594484i	−0.954802	+	0.297242i	$0.903933\pi$
$450$	−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
$459$	−30844.5	+	160735.i	−0.146404	+	0.762932i
$460$	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
$476$	35976.8	+	218041.i	0.158784	+	0.962333i
$477$	−97334.2			−0.427788
$478$	−278992.	−	483229.i	−1.22106	−	2.11493i
$479$	21977.6	−	38066.3i	0.0957876	−	0.165909i	−0.814149	−	0.580655i	$-0.802796\pi$
$479$	21977.6	−	38066.3i	0.0957876	−	0.165909i	0.909937	+	0.414746i	$0.136130\pi$
$480$	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	−0.109531	−	0.993983i	$-0.534935\pi$
$487$	−243124.	−	140368.i	−1.02511	−	0.591848i	−0.915580	+	0.402135i	$0.868268\pi$
$488$	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
$493$	35348.4	+	6783.22i	0.145437	+	0.0279088i
$494$	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	−0.983223	−	0.182406i	$-0.941611\pi$
$499$	−327901.	+	189314.i	−1.31687	+	0.760293i	−0.333643	+	0.942699i	$0.608278\pi$
$500$	−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	$-0.244179\pi$
$503$	364292.			1.43984			0.719918	+	0.694059i	$0.244179\pi$
$504$	−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	$0.385856\pi$
$521$	−172490.	+	298761.i	−0.635460	+	1.10065i	−0.986418	+	0.164257i	$0.947477\pi$
$522$	−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
$527$	10683.7	+	9242.34i	0.0384679	+	0.0332783i
$528$	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	−0.988456	−	0.151510i	$-0.951587\pi$
$541$	−395550.	+	228371.i	−1.35147	+	0.780273i	−0.363017	+	0.931783i	$0.618253\pi$
$542$	124322.	+	71777.6i	0.423205	+	0.244338i
$543$	51117.6	−	88538.3i	0.173369	−	0.300284i
$544$	314367.	+	271956.i	1.06228	+	0.918969i
$545$			341877.i			1.15101i
$546$	−144483.	+	173612.i	−0.484655	+	0.582366i
$547$			340305.i			1.13735i	0.822562	+	0.568675i	$0.192544\pi$
$547$			340305.i			1.13735i	−0.822562	+	0.568675i	$0.807456\pi$
$548$	−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	0.799224	−	0.601033i	$-0.205244\pi$
$571$	221162.	+	127688.i	0.678327	+	0.391632i	−0.120897	+	0.992665i	$0.538577\pi$
$572$	−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	$0.556749\pi$
$578$	67574.3	+	464657.i	0.202267	+	1.39084i
$579$	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
$595$	311716.	+	117356.i	0.880490	+	0.331492i
$596$	−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	$-0.468692\pi$
$601$	70939.3			0.196398			0.0981992	+	0.995167i	$0.468692\pi$
$602$	−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	0.937404	−	0.348243i	$-0.113222\pi$
$607$	61573.1	+	106648.i	0.167114	+	0.289451i	−0.770290	+	0.637694i	$0.779888\pi$
$608$		−	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
$612$	56264.2	−	293201.i	0.150221	−	0.782822i
$613$	−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	$-0.945363\pi$
$617$		−	130047.i		−	0.341609i	0.985305	−	0.170805i	$-0.0546367\pi$
$618$	91431.2	−	52787.9i	0.239396	−	0.138216i
$619$	228880.	−	396432.i	0.597347	−	1.03463i	−0.395864	−	0.918309i	$-0.629555\pi$
$619$	228880.	−	396432.i	0.597347	−	1.03463i	0.993211	−	0.116326i	$-0.0371117\pi$
$620$	−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	0.609238	−	0.792987i	$-0.291475\pi$
$641$	93315.4	+	53875.7i	0.227111	+	0.131122i	−0.382128	+	0.924109i	$0.624809\pi$
$642$	−397767.	+	229651.i	−0.965071	+	0.557184i
$643$	−21723.0			−0.0525410			−0.0262705	−	0.999655i	$-0.508363\pi$
$643$	−21723.0			−0.0525410			−0.0262705	+	0.999655i	$0.508363\pi$
$644$	−100465.	+	120720.i	−0.242239	+	0.291076i
$645$	190514.			0.457940
$646$	351415.	−	406217.i	0.842083	−	0.973404i
$647$	−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	0.0286714	−	0.999589i	$-0.490872\pi$
$653$	387468.	−	223705.i	0.908676	−	0.524625i	0.880005	+	0.474964i	$0.157539\pi$
$654$	−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
$663$	−155032.	+	179209.i	−0.352690	+	0.407691i
$664$		−	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	$-0.936482\pi$
$673$		−	179564.i		−	0.396452i	0.980156	−	0.198226i	$-0.0635179\pi$
$674$	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	$0.199132\pi$
$677$	418195.	+	724334.i	0.912433	+	1.58038i	0.101816	+	0.994803i	$0.467535\pi$
$678$		−	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	0.948204	−	0.317662i	$-0.102898\pi$
$683$	535158.	+	308973.i	1.14720	+	0.662338i	0.198999	+	0.980000i	$0.436231\pi$
$684$	−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	0.695370	−	0.718652i	$-0.255241\pi$
$691$	−131157.	−	227171.i	−0.274686	−	0.475770i	−0.970056	+	0.242882i	$0.921907\pi$
$692$	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
$697$	−32659.7	+	170194.i	−0.0672273	+	0.350332i
$698$	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	−0.921848	−	0.387553i	$-0.873321\pi$
$709$	−526378.	+	303904.i	−1.04714	+	0.604567i	−0.125293	+	0.992120i	$0.539987\pi$
$710$	−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
$714$	−236789.	+	194288.i	−0.464477	+	0.381110i
$715$	−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	0.693495	−	0.720462i	$-0.256070\pi$
$719$	−143297.	−	248197.i	−0.277191	−	0.480108i	−0.970685	+	0.240353i	$0.922737\pi$
$720$	−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
$731$	−114664.	+	597530.i	−0.214581	+	1.11821i
$732$	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	$-0.959846\pi$
$743$		−	138911.i		−	0.251628i	0.992054	−	0.125814i	$-0.0401543\pi$
$744$	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	0.391676	−	0.920103i	$-0.371895\pi$
$751$	780773.	−	450780.i	1.38435	−	0.799253i	0.992671	+	0.120850i	$0.0385619\pi$
$752$	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
$765$	−340307.	−	294396.i	−0.581498	−	0.503048i
$766$	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
$782$	−218324.	+	252372.i	−0.357017	+	0.412693i
$783$		−	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	−0.921089	−	0.389352i	$-0.872699\pi$
$787$	−76403.0	+	132334.i	−0.123356	+	0.213659i	0.797733	+	0.603011i	$0.206032\pi$
$788$	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	0.986304	−	0.164935i	$-0.0527416\pi$
$809$	874791.	+	505061.i	1.33662	+	0.771697i	0.350314	+	0.936632i	$0.386075\pi$
$810$	210453.	+	364516.i	0.320764	+	0.555580i
$811$	3692.39			0.00561391			0.00280696	−	0.999996i	$-0.499107\pi$
$811$	3692.39			0.00561391			0.00280696	+	0.999996i	$0.499107\pi$
$812$	−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
$816$	−54933.4	+	286266.i	−0.0825005	+	0.429922i
$817$	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	−0.670141	−	0.742234i	$-0.733766\pi$
$821$	−244284.	+	141038.i	−0.362418	+	0.209242i	0.307723	+	0.951476i	$0.400433\pi$
$822$	140549.	−	243438.i	0.208010	−	0.360284i
$823$	−707949.	−	408735.i	−1.04521	−	0.603451i	−0.123904	−	0.992294i	$-0.539541\pi$
$823$	−707949.	−	408735.i	−1.04521	−	0.603451i	−0.921304	+	0.388843i	$0.872875\pi$
$824$	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	$-0.699165\pi$
$827$		−	1.10873e6i		−	1.62111i	0.585661	−	0.810556i	$-0.300835\pi$
$828$	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
$833$	−693872.	−	4825.89i	−0.999976	−	0.00695485i
$834$	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	$-0.351337\pi$
$839$	633873.			0.900489			0.450244	+	0.892905i	$0.351337\pi$
$840$	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
$850$	21978.8	−	114535.i	0.0304205	−	0.158526i
$851$	190702.	−	330305.i	0.263327	−	0.456096i
$852$	15995.1	−	9234.79i	0.0220348	−	0.0127218i
$853$	827459.			1.13723			0.568615	−	0.822604i	$-0.307479\pi$
$853$	827459.			1.13723			0.568615	+	0.822604i	$0.307479\pi$
$854$	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	−0.895177	−	0.445710i	$-0.852951\pi$
$857$	−45236.5	+	78351.8i	−0.0615924	+	0.106681i	0.833585	+	0.552391i	$0.186285\pi$
$858$	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	−0.997226	−	0.0744383i	$-0.976284\pi$
$877$	−1.10091e6	+	635611.i	−1.43137	+	0.826404i	−0.434147	+	0.900842i	$0.642950\pi$
$878$	−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	$-0.249002\pi$
$881$	1.10109e6			1.41864			0.709321	+	0.704886i	$0.249002\pi$
$882$	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	$0.232745\pi$
$884$	628830.	−	726895.i	0.804691	−	0.930180i
$885$	472831.	+	272989.i	0.603698	+	0.348545i
$886$	−12188.9	+	21111.8i	−0.0155273	+	0.0268941i
$887$	−344772.	−	597162.i	−0.438212	−	0.759006i	0.559339	−	0.828939i	$-0.311055\pi$
$887$	−344772.	−	597162.i	−0.438212	−	0.759006i	−0.997552	+	0.0699329i	$0.977721\pi$
$888$		−	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
$901$	−321368.	−	278012.i	−0.395870	−	0.342464i
$902$		−	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	0.976101	−	0.217318i	$-0.0697309\pi$
$907$	1.04966e6	+	606020.i	1.27595	+	0.736669i	0.299847	+	0.953987i	$0.403064\pi$
$908$	−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	$-0.808722\pi$
$911$		−	938475.i		−	1.13080i	0.824817	−	0.565400i	$-0.191278\pi$
$912$	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	0.793783	−	0.608200i	$-0.208108\pi$
$929$	−112045.	−	194067.i	−0.129825	−	0.224864i	−0.923609	+	0.383336i	$0.874775\pi$
$930$	−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
$935$	−457970.	−	87882.8i	−0.523859	−	0.100527i
$936$	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	$0.375205\pi$
$941$	−539499.	+	934440.i	−0.609273	+	1.05529i	−0.991361	+	0.131165i	$0.958128\pi$
$942$	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	−0.953732	−	0.300659i	$-0.902793\pi$
$947$	−1.04946e6	+	605908.i	−1.17022	+	0.675627i	−0.216488	+	0.976285i	$0.569460\pi$
$948$	−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
$952$	−24279.0	+	19921.3i	−0.0267890	+	0.0219808i
$953$	−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
$969$	361000.	+	69274.6i	0.384468	+	0.0737779i
$970$	−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	$0.385036\pi$
$983$	−612114.	+	1.06021e6i	−0.633469	+	1.09720i	−0.986837	+	0.161716i	$0.948297\pi$
$984$	−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	0.994635	−	0.103444i	$-0.0329861\pi$
$991$	1.37724e6	+	795149.i	1.40237	+	0.809658i	0.407733	+	0.913101i	$0.366319\pi$
$992$	−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	−0.660546	−	0.750785i	$-0.729675\pi$
$997$	318009.	−	550808.i	0.319926	−	0.554128i	0.980472	+	0.196657i	$0.0630086\pi$
$998$	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.101.10	yes	92
7.5	odd	6	inner	119.5.h.a.33.9	✓	92
17.16	even	2	inner	119.5.h.a.101.9	yes	92
119.33	odd	6	inner	119.5.h.a.33.10	yes	92

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
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} +(-54.4643 + 283.821i) 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} +(840.900 + 727.455i) 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} +(-3410.81 - 2950.66i) 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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