LMFDB - Embedded newform 96.6.o.a.11.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [96,6,Mod(11,96)] 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("96.11"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(96, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 5, 4])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 96 = 2^{5} \cdot 3 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	96.o (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$15.3968467020$
Analytic rank:	$0$
Dimension:	$312$
Relative dimension:	$78$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	96.11
Dual form			96.6.o.a.35.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.55856 - 1.04998i) q^{2} +(-2.52416 + 15.3827i) q^{3} +(29.7951 + 11.6727i) q^{4} +(18.4880 + 7.65797i) q^{5} +(30.1822 - 82.8555i) q^{6} +(-168.744 + 168.744i) q^{7} +(-153.362 - 96.1675i) q^{8} +(-230.257 - 77.6568i) q^{9} +(-94.7257 - 61.9791i) q^{10} +(370.212 + 153.347i) q^{11} +(-254.765 + 428.867i) q^{12} +(217.625 + 525.392i) q^{13} +(1115.15 - 760.794i) q^{14} +(-164.467 + 265.066i) q^{15} +(751.496 + 695.578i) q^{16} -1243.80 q^{17} +(1198.36 + 673.424i) q^{18} +(1864.33 - 772.230i) q^{19} +(461.462 + 443.974i) q^{20} +(-2169.80 - 3021.67i) q^{21} +(-1896.83 - 1241.10i) q^{22} +(-2096.69 + 2096.69i) q^{23} +(1866.43 - 2116.38i) q^{24} +(-1926.55 - 1926.55i) q^{25} +(-658.030 - 3148.92i) q^{26} +(1775.78 - 3345.97i) q^{27} +(-6997.43 + 3058.04i) q^{28} +(-471.407 - 1138.08i) q^{29} +(1192.51 - 1300.70i) q^{30} -4342.93i q^{31} +(-3446.90 - 4655.46i) q^{32} +(-3293.37 + 5307.80i) q^{33} +(6913.75 + 1305.96i) q^{34} +(-4411.96 + 1827.49i) q^{35} +(-5954.07 - 5001.52i) q^{36} +(-2241.70 + 5411.95i) q^{37} +(-11173.8 + 2334.99i) q^{38} +(-8631.29 + 2021.49i) q^{39} +(-2098.90 - 2952.38i) q^{40} +(-8063.32 - 8063.32i) q^{41} +(8888.30 + 19074.4i) q^{42} +(1557.93 - 3761.17i) q^{43} +(9240.54 + 8890.36i) q^{44} +(-3662.29 - 3199.02i) q^{45} +(13856.0 - 9453.10i) q^{46} -6200.25i q^{47} +(-12596.8 + 9804.32i) q^{48} -40141.8i q^{49} +(8686.00 + 12731.7i) q^{50} +(3139.55 - 19133.1i) q^{51} +(351.404 + 18194.4i) q^{52} +(8867.88 - 21409.0i) q^{53} +(-13384.0 + 16734.2i) q^{54} +(5670.14 + 5670.14i) q^{55} +(42106.5 - 9651.17i) q^{56} +(7173.16 + 30627.7i) q^{57} +(1425.39 + 6821.03i) q^{58} +(-19289.2 + 46568.2i) q^{59} +(-7994.34 + 5977.88i) q^{60} +(7630.87 - 3160.81i) q^{61} +(-4559.97 + 24140.4i) q^{62} +(51958.6 - 25750.4i) q^{63} +(14271.6 + 29496.8i) q^{64} +11380.0i q^{65} +(23879.4 - 26045.8i) q^{66} +(-15696.3 - 37894.2i) q^{67} +(-37059.3 - 14518.5i) q^{68} +(-26960.5 - 37545.2i) q^{69} +(26442.9 - 5525.78i) q^{70} +(23598.6 + 23598.6i) q^{71} +(27844.6 + 34052.8i) q^{72} +(-52850.5 + 52850.5i) q^{73} +(18143.1 - 27728.9i) q^{74} +(34498.5 - 24772.7i) q^{75} +(64561.9 - 1246.94i) q^{76} +(-88347.2 + 36594.6i) q^{77} +(50100.1 - 2173.93i) q^{78} +46031.8 q^{79} +(8566.92 + 18614.8i) q^{80} +(46987.8 + 35762.1i) q^{81} +(36354.1 + 53286.7i) q^{82} +(1184.00 + 2858.44i) q^{83} +(-29378.5 - 115359. i) q^{84} +(-22995.4 - 9525.01i) q^{85} +(-12609.0 + 19270.9i) q^{86} +(18696.6 - 4378.84i) q^{87} +(-42029.4 - 59119.9i) q^{88} +(-82758.3 + 82758.3i) q^{89} +(16998.2 + 21627.2i) q^{90} +(-125379. - 51933.9i) q^{91} +(-86945.1 + 37997.1i) q^{92} +(66806.2 + 10962.2i) q^{93} +(-6510.11 + 34464.5i) q^{94} +40381.4 q^{95} +(80314.3 - 41271.6i) q^{96} +55557.4 q^{97} +(-42147.9 + 223131. i) q^{98} +(-73335.6 - 64058.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 312 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9} + 192 q^{10} - 4 q^{12} - 8 q^{13} - 8 q^{15} - 6696 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} + 5576 q^{22} - 11024 q^{24} - 8 q^{25} + 7460 q^{27}+ \cdots + 339516 q^{99}+O(q^{100}) $ 312 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 4 * q^9 + 192 * q^10 - 4 * q^12 - 8 * q^13 - 8 * q^15 - 6696 * q^16 - 4 * q^18 - 8 * q^19 - 4 * q^21 + 5576 * q^22 - 11024 * q^24 - 8 * q^25 + 7460 * q^27 - 8 * q^28 + 32564 * q^30 - 8 * q^33 - 264 * q^34 + 3264 * q^36 - 8 * q^37 + 44900 * q^39 - 60136 * q^40 - 7264 * q^42 - 8 * q^43 - 4 * q^45 + 63320 * q^46 + 112368 * q^48 - 976 * q^51 - 55024 * q^52 - 115328 * q^54 - 110056 * q^55 - 4 * q^57 - 123568 * q^58 + 44648 * q^60 - 96168 * q^61 + 187432 * q^64 + 17564 * q^66 + 97848 * q^67 - 4 * q^69 - 143480 * q^70 + 179936 * q^72 - 8 * q^73 + 12496 * q^75 - 234928 * q^76 - 708428 * q^78 + 355344 * q^79 + 251552 * q^82 + 387560 * q^84 - 25008 * q^85 - 282188 * q^87 + 111632 * q^88 + 453536 * q^90 + 200104 * q^91 + 968 * q^93 - 671008 * q^94 - 911336 * q^96 - 16 * q^97 + 339516 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$-1$	$e\left(\frac{5}{8}\right)$	$-1$

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 $

$2$	−5.55856	−	1.04998i	−0.982623	−	0.185611i
$2$	−5.55856	−	1.04998i	−0.982623	−	0.185611i
$3$	−2.52416	+	15.3827i	−0.161925	+	0.986803i
$3$	−2.52416	+	15.3827i	−0.161925	+	0.986803i
$4$	29.7951	+	11.6727i	0.931097	+	0.364772i
$5$	18.4880	+	7.65797i	0.330723	+	0.136990i	0.541865	−	0.840465i	$-0.317718\pi$
$5$	18.4880	+	7.65797i	0.330723	+	0.136990i	−0.211142	+	0.977455i	$0.567718\pi$
$6$	30.1822	−	82.8555i	0.342273	−	0.939601i
$7$	−168.744	+	168.744i	−1.30161	+	1.30161i	−0.374311	+	0.927303i	$0.622121\pi$
$7$	−168.744	+	168.744i	−1.30161	+	1.30161i	−0.927303	+	0.374311i	$0.877879\pi$
$8$	−153.362	−	96.1675i	−0.847212	−	0.531255i
$9$	−230.257	−	77.6568i	−0.947561	−	0.319575i
$10$	−94.7257	−	61.9791i	−0.299549	−	0.195995i
$11$	370.212	+	153.347i	0.922505	+	0.382114i	0.792830	−	0.609442i	$-0.208607\pi$
$11$	370.212	+	153.347i	0.922505	+	0.382114i	0.129675	+	0.991557i	$0.458607\pi$
$12$	−254.765	+	428.867i	−0.510725	+	0.859744i
$13$	217.625	+	525.392i	0.357149	+	0.862235i	0.995698	+	0.0926536i	$0.0295349\pi$
$13$	217.625	+	525.392i	0.357149	+	0.862235i	−0.638549	+	0.769581i	$0.720465\pi$
$14$	1115.15	−	760.794i	1.52059	−	1.03740i
$15$	−164.467	+	265.066i	−0.188734	+	0.304176i
$16$	751.496	+	695.578i	0.733883	+	0.679276i
$17$	−1243.80			−1.04383			−0.521915	−	0.852998i	$-0.674782\pi$
$17$	−1243.80			−1.04383			−0.521915	+	0.852998i	$0.674782\pi$
$18$	1198.36	+	673.424i	0.871779	+	0.489900i
$19$	1864.33	−	772.230i	1.18478	−	0.490753i	0.298730	−	0.954338i	$-0.403437\pi$
$19$	1864.33	−	772.230i	1.18478	−	0.490753i	0.886053	+	0.463585i	$0.153437\pi$
$20$	461.462	+	443.974i	0.257965	+	0.248189i
$21$	−2169.80	−	3021.67i	−1.07367	−	1.49520i
$22$	−1896.83	−	1241.10i	−0.835550	−	0.546702i
$23$	−2096.69	+	2096.69i	−0.826446	+	0.826446i	−0.987023	−	0.160577i	$-0.948665\pi$
$23$	−2096.69	+	2096.69i	−0.826446	+	0.826446i	0.160577	+	0.987023i	$0.448665\pi$
$24$	1866.43	−	2116.38i	0.661429	−	0.750008i
$25$	−1926.55	−	1926.55i	−0.616495	−	0.616495i
$26$	−658.030	−	3148.92i	−0.190903	−	0.913543i
$27$	1775.78	−	3345.97i	0.468791	−	0.883309i
$28$	−6997.43	+	3058.04i	−1.68672	+	0.737137i
$29$	−471.407	−	1138.08i	−0.104088	−	0.251291i	0.863252	−	0.504773i	$-0.168424\pi$
$29$	−471.407	−	1138.08i	−0.104088	−	0.251291i	−0.967340	+	0.253483i	$0.918424\pi$
$30$	1192.51	−	1300.70i	0.241913	−	0.263859i
$31$		−	4342.93i		−	0.811669i	−0.913947	−	0.405834i	$-0.866981\pi$
$31$		−	4342.93i		−	0.811669i	0.913947	−	0.405834i	$-0.133019\pi$
$32$	−3446.90	−	4655.46i	−0.595050	−	0.803689i
$33$	−3293.37	+	5307.80i	−0.526448	+	0.848457i
$34$	6913.75	+	1305.96i	1.02569	+	0.193746i
$35$	−4411.96	+	1827.49i	−0.608781	+	0.252166i
$36$	−5954.07	−	5001.52i	−0.765699	−	0.643199i
$37$	−2241.70	+	5411.95i	−0.269199	+	0.649905i	−0.999446	−	0.0332789i	$-0.989405\pi$
$37$	−2241.70	+	5411.95i	−0.269199	+	0.649905i	0.730247	+	0.683183i	$0.239405\pi$
$38$	−11173.8	+	2334.99i	−1.25528	+	0.262316i
$39$	−8631.29	+	2021.49i	−0.908687	+	0.212819i
$40$	−2098.90	−	2952.38i	−0.207416	−	0.291758i
$41$	−8063.32	−	8063.32i	−0.749125	−	0.749125i	0.225190	−	0.974315i	$-0.427700\pi$
$41$	−8063.32	−	8063.32i	−0.749125	−	0.749125i	−0.974315	+	0.225190i	$0.927700\pi$
$42$	8888.30	+	19074.4i	0.777491	+	1.66850i
$43$	1557.93	−	3761.17i	0.128492	−	0.310207i	−0.846521	−	0.532356i	$-0.821307\pi$
$43$	1557.93	−	3761.17i	0.128492	−	0.310207i	0.975013	+	0.222148i	$0.0713069\pi$
$44$	9240.54	+	8890.36i	0.719557	+	0.692289i
$45$	−3662.29	−	3199.02i	−0.269601	−	0.235497i
$46$	13856.0	−	9453.10i	0.965483	−	0.658688i
$47$		−	6200.25i		−	0.409416i	−0.978823	−	0.204708i	$-0.934376\pi$
$47$		−	6200.25i		−	0.409416i	0.978823	−	0.204708i	$-0.0656245\pi$
$48$	−12596.8	+	9804.32i	−0.789145	+	0.614207i
$49$		−	40141.8i		−	2.38840i
$50$	8686.00	+	12731.7i	0.491354	+	0.720211i
$51$	3139.55	−	19133.1i	0.169022	−	1.03005i
$52$	351.404	+	18194.4i	0.0180218	+	0.933102i
$53$	8867.88	−	21409.0i	0.433641	−	1.04690i	−0.544463	−	0.838785i	$-0.683267\pi$
$53$	8867.88	−	21409.0i	0.433641	−	1.04690i	0.978104	−	0.208117i	$-0.0667334\pi$
$54$	−13384.0	+	16734.2i	−0.624597	+	0.780947i
$55$	5670.14	+	5670.14i	0.252748	+	0.252748i
$56$	42106.5	−	9651.17i	1.79423	−	0.411254i
$57$	7173.16	+	30627.7i	0.292431	+	1.24861i
$58$	1425.39	+	6821.03i	0.0556369	+	0.266244i
$59$	−19289.2	+	46568.2i	−0.721413	+	1.74165i	−0.0521273	+	0.998640i	$0.516600\pi$
$59$	−19289.2	+	46568.2i	−0.721413	+	1.74165i	−0.669286	+	0.743005i	$0.733400\pi$
$60$	−7994.34	+	5977.88i	−0.286685	+	0.214373i
$61$	7630.87	−	3160.81i	0.262573	−	0.108761i	−0.247514	−	0.968884i	$-0.579613\pi$
$61$	7630.87	−	3160.81i	0.262573	−	0.108761i	0.510086	+	0.860123i	$0.329613\pi$
$62$	−4559.97	+	24140.4i	−0.150655	+	0.797565i
$63$	51958.6	−	25750.4i	1.64932	−	0.817395i
$64$	14271.6	+	29496.8i	0.435536	+	0.900171i
$65$			11380.0i			0.334086i
$66$	23879.4	−	26045.8i	0.674783	−	0.735999i
$67$	−15696.3	−	37894.2i	−0.427179	−	1.03130i	−0.980178	−	0.198120i	$-0.936517\pi$
$67$	−15696.3	−	37894.2i	−0.427179	−	1.03130i	0.552999	−	0.833182i	$-0.313483\pi$
$68$	−37059.3	−	14518.5i	−0.971907	−	0.380760i
$69$	−26960.5	−	37545.2i	−0.681718	−	0.949362i
$70$	26442.9	−	5525.78i	0.645008	−	0.134787i
$71$	23598.6	+	23598.6i	0.555572	+	0.555572i	0.928043	−	0.372472i	$-0.121490\pi$
$71$	23598.6	+	23598.6i	0.555572	+	0.555572i	−0.372472	+	0.928043i	$0.621490\pi$
$72$	27844.6	+	34052.8i	0.633009	+	0.774145i
$73$	−52850.5	+	52850.5i	−1.16076	+	1.16076i	−0.176450	+	0.984310i	$0.556461\pi$
$73$	−52850.5	+	52850.5i	−1.16076	+	1.16076i	−0.984310	+	0.176450i	$0.943539\pi$
$74$	18143.1	−	27728.9i	0.385151	−	0.588645i
$75$	34498.5	−	24772.7i	0.708185	−	0.508534i
$76$	64561.9	−	1246.94i	1.28216	−	0.0247635i
$77$	−88347.2	+	36594.6i	−1.69811	+	0.703381i
$78$	50100.1	−	2173.93i	0.932399	−	0.0404584i
$79$	46031.8			0.829831			0.414916	−	0.909860i	$-0.363811\pi$
$79$	46031.8			0.829831			0.414916	+	0.909860i	$0.363811\pi$
$80$	8566.92	+	18614.8i	0.149658	+	0.325186i
$81$	46987.8	+	35762.1i	0.795743	+	0.605634i
$82$	36354.1	+	53286.7i	0.597062	+	0.875153i
$83$	1184.00	+	2858.44i	0.0188650	+	0.0455442i	0.933031	−	0.359795i	$-0.117153\pi$
$83$	1184.00	+	2858.44i	0.0188650	+	0.0455442i	−0.914166	+	0.405339i	$0.867153\pi$
$84$	−29378.5	−	115359.i	−0.454287	−	1.78382i
$85$	−22995.4	−	9525.01i	−0.345218	−	0.142994i
$86$	−12609.0	+	19270.9i	−0.183837	+	0.280967i
$87$	18696.6	−	4378.84i	0.264829	−	0.0620242i
$88$	−42029.4	−	59119.9i	−0.578557	−	0.813817i
$89$	−82758.3	+	82758.3i	−1.10748	+	1.10748i	−0.114001	+	0.993481i	$0.536367\pi$
$89$	−82758.3	+	82758.3i	−1.10748	+	1.10748i	−0.993481	+	0.114001i	$0.963633\pi$
$90$	16998.2	+	21627.2i	0.221206	+	0.281446i
$91$	−125379.	−	51933.9i	−1.58717	−	0.657426i
$92$	−86945.1	+	37997.1i	−1.07097	+	0.468037i
$93$	66806.2	+	10962.2i	0.800957	+	0.131429i
$94$	−6510.11	+	34464.5i	−0.0759922	+	0.402302i
$95$	40381.4			0.459063
$96$	80314.3	−	41271.6i	0.889436	−	0.457060i
$97$	55557.4			0.599532			0.299766	−	0.954013i	$-0.403091\pi$
$97$	55557.4			0.599532			0.299766	+	0.954013i	$0.403091\pi$
$98$	−42147.9	+	223131.i	−0.443314	+	2.34690i
$99$	−73335.6	−	64058.7i	−0.752016	−	0.656886i
$100$	−34913.7	−	79889.7i	−0.349137	−	0.798897i
$101$	6031.72	+	2498.42i	0.0588353	+	0.0243704i	0.411907	−	0.911226i	$-0.364863\pi$
$101$	6031.72	+	2498.42i	0.0588353	+	0.0243704i	−0.353072	+	0.935596i	$0.614863\pi$
$102$	−37540.7	+	103056.i	−0.357274	+	0.980783i
$103$	26649.1	−	26649.1i	0.247509	−	0.247509i	−0.572439	−	0.819947i	$-0.694003\pi$
$103$	26649.1	−	26649.1i	0.247509	−	0.247509i	0.819947	+	0.572439i	$0.194003\pi$
$104$	17150.4	−	101504.i	0.155486	−	0.920233i
$105$	−16975.4	−	72480.9i	−0.150261	−	0.641579i
$106$	−71771.5	+	109692.i	−0.620422	+	0.948221i
$107$	−23917.3	−	9906.85i	−0.201954	−	0.0836520i	0.279414	−	0.960171i	$-0.409860\pi$
$107$	−23917.3	−	9906.85i	−0.201954	−	0.0836520i	−0.481368	+	0.876519i	$0.659860\pi$
$108$	91966.0	−	78965.4i	0.758696	−	0.651444i
$109$	63476.0	+	153245.i	0.511733	+	1.23543i	0.942874	+	0.333149i	$0.108111\pi$
$109$	63476.0	+	153245.i	0.511733	+	1.23543i	−0.431141	+	0.902284i	$0.641889\pi$
$110$	−25564.3	−	37471.3i	−0.201443	−	0.295269i
$111$	−77592.2	−	48144.1i	−0.597738	−	0.370882i
$112$	−244185.	+	9435.82i	−1.83939	+	0.0710779i
$113$	−74209.6			−0.546719			−0.273359	−	0.961912i	$-0.588135\pi$
$113$	−74209.6			−0.546719			−0.273359	+	0.961912i	$0.588135\pi$
$114$	−7714.08	−	177778.i	−0.0555933	−	1.28119i
$115$	−54819.9	+	22707.2i	−0.386539	+	0.160110i
$116$	−761.192	−	39411.7i	−0.00525229	−	0.271944i
$117$	−9309.35	−	137875.i	−0.0628717	−	0.931156i
$118$	156116.	−	238599.i	1.03215	−	1.57748i
$119$	209884.	−	209884.i	1.35866	−	1.35866i
$120$	50713.6	−	24834.6i	0.321493	−	0.157436i
$121$	−338.537	−	338.537i	−0.00210205	−	0.00210205i
$122$	−45735.4	+	9557.32i	−0.278197	+	0.0581348i
$123$	144389.	−	103683.i	0.860541	−	0.617937i
$124$	50693.7	−	129398.i	0.296074	−	0.755742i
$125$	−44795.7	−	108146.i	−0.256425	−	0.619065i
$126$	−315852.	+	88579.6i	−1.77238	+	0.497058i
$127$			234610.i			1.29074i	0.763871	+	0.645369i	$0.223296\pi$
$127$			234610.i			1.29074i	−0.763871	+	0.645369i	$0.776704\pi$
$128$	−48358.8	−	178945.i	−0.260886	−	0.965370i
$129$	53924.6	+	33459.0i	0.285307	+	0.177026i
$130$	11948.7	−	63256.4i	0.0620102	−	0.328281i
$131$	199418.	−	82601.8i	1.01528	−	0.420544i	0.187903	−	0.982188i	$-0.439831\pi$
$131$	199418.	−	82601.8i	1.01528	−	0.420544i	0.827379	+	0.561644i	$0.189831\pi$
$132$	−160083.	+	119704.i	−0.799667	+	0.597963i
$133$	−184285.	+	444903.i	−0.903359	+	2.18090i
$134$	47460.8	+	227118.i	0.228335	+	1.09267i
$135$	58453.9	−	48261.3i	0.276044	−	0.227911i
$136$	190752.	+	119613.i	0.884345	+	0.554540i
$137$	−89634.0	−	89634.0i	−0.408010	−	0.408010i	0.473034	−	0.881044i	$-0.343159\pi$
$137$	−89634.0	−	89634.0i	−0.408010	−	0.408010i	−0.881044	+	0.473034i	$0.843159\pi$
$138$	110440.	+	237005.i	0.493660	+	1.05940i
$139$	−73183.1	+	176680.i	−0.321273	+	0.775620i	0.677908	+	0.735147i	$0.262887\pi$
$139$	−73183.1	+	176680.i	−0.321273	+	0.775620i	−0.999181	+	0.0404738i	$0.987113\pi$
$140$	−152787.	+	2950.90i	−0.658817	+	0.0127243i
$141$	95376.9	+	15650.4i	0.404013	+	0.0662945i
$142$	−106396.	−	155952.i	−0.442797	−	0.649038i
$143$			227879.i			0.931888i
$144$	−119021.	−	218521.i	−0.478319	−	0.878186i
$145$		−	24650.7i		−	0.0973665i
$146$	349264.	−	238281.i	1.35604	−	0.925139i
$147$	617491.	+	101324.i	2.35688	+	0.386741i
$148$	−129964.	+	135083.i	−0.487717	+	0.506928i
$149$	−155603.	+	375659.i	−0.574186	+	1.38621i	0.323776	+	0.946134i	$0.395048\pi$
$149$	−155603.	+	375659.i	−0.574186	+	1.38621i	−0.897962	+	0.440073i	$0.854952\pi$
$150$	−217773.	+	101478.i	−0.790269	+	0.368250i
$151$	−160775.	−	160775.i	−0.573821	−	0.573821i	0.359373	−	0.933194i	$-0.382991\pi$
$151$	−160775.	−	160775.i	−0.573821	−	0.573821i	−0.933194	+	0.359373i	$0.882991\pi$
$152$	−360180.	−	60857.2i	−1.26448	−	0.213650i
$153$	286395.	+	96589.9i	0.989092	+	0.333582i
$154$	529507.	−	110651.i	1.79916	−	0.375970i
$155$	33258.0	−	80292.0i	0.111190	−	0.268437i
$156$	−280767.	−	40519.9i	−0.923706	−	0.133308i
$157$	−266686.	+	110465.i	−0.863477	+	0.357664i	−0.770066	−	0.637964i	$-0.779777\pi$
$157$	−266686.	+	110465.i	−0.863477	+	0.357664i	−0.0934106	+	0.995628i	$0.529777\pi$
$158$	−255870.	−	48332.2i	−0.815412	−	0.154026i
$159$	306944.	+	190452.i	0.962869	+	0.597437i
$160$	−28074.7	−	112466.i	−0.0866992	−	0.347314i
$161$		−	707606.i		−	2.15143i
$162$	−223635.	−	248122.i	−0.669503	−	0.742809i
$163$	−96367.8	−	232652.i	−0.284094	−	0.685865i	0.715829	−	0.698276i	$-0.246049\pi$
$163$	−96367.8	−	232652.i	−0.284094	−	0.685865i	−0.999923	+	0.0124115i	$0.996049\pi$
$164$	−146127.	−	334368.i	−0.424248	−	0.970767i
$165$	−101535.	+	72910.0i	−0.290338	+	0.208486i
$166$	−3580.06	−	17131.9i	−0.0100837	−	0.0482544i
$167$	243174.	+	243174.i	0.674722	+	0.674722i	0.958801	−	0.284079i	$-0.0916877\pi$
$167$	243174.	+	243174.i	0.674722	+	0.674722i	−0.284079	+	0.958801i	$0.591688\pi$
$168$	42178.2	+	672074.i	0.115296	+	1.83715i
$169$	33867.0	−	33867.0i	0.0912138	−	0.0912138i
$170$	117820.	+	77089.9i	0.312678	+	0.204586i
$171$	−489244.	+	33033.8i	−1.27949	+	0.0863909i
$172$	90321.6	−	93879.2i	0.232793	−	0.241963i
$173$	−47789.8	+	19795.2i	−0.121400	+	0.0502856i	−0.442557	−	0.896741i	$-0.645928\pi$
$173$	−47789.8	+	19795.2i	−0.121400	+	0.0502856i	0.321156	+	0.947026i	$0.395928\pi$
$174$	−108524.	+	4709.05i	−0.271739	+	0.0117912i
$175$	650186.			1.60488
$176$	171548.	+	372751.i	0.417450	+	0.907063i
$177$	−667658.	−	414266.i	−1.60185	−	0.993908i
$178$	546911.	−	373123.i	1.29380	−	0.882676i
$179$	209677.	+	506205.i	0.489123	+	1.18085i	0.955162	+	0.296084i	$0.0956808\pi$
$179$	209677.	+	506205.i	0.489123	+	1.18085i	−0.466039	+	0.884764i	$0.654319\pi$
$180$	−71777.3	−	138064.i	−0.165122	−	0.317614i
$181$	−392962.	−	162770.i	−0.891567	−	0.369299i	−0.110595	−	0.993866i	$-0.535276\pi$
$181$	−392962.	−	162770.i	−0.891567	−	0.369299i	−0.780972	+	0.624567i	$0.785276\pi$
$182$	642399.	+	420323.i	1.43756	+	0.940599i
$183$	29360.4	+	125362.i	0.0648089	+	0.276719i
$184$	523185.	−	119919.i	1.13923	−	0.261121i
$185$	−82889.1	+	82889.1i	−0.178061	+	0.178061i
$186$	−359836.	−	131079.i	−0.762644	−	0.277812i
$187$	−460471.	−	190733.i	−0.962938	−	0.398862i
$188$	72373.7	−	184737.i	0.149343	−	0.381206i
$189$	264960.	+	864263.i	0.539542	+	1.75991i
$190$	−224462.	−	42399.4i	−0.451086	−	0.0852072i
$191$	−576967.			−1.14437			−0.572187	−	0.820123i	$-0.693905\pi$
$191$	−576967.			−1.14437			−0.572187	+	0.820123i	$0.693905\pi$
$192$	−489766.	+	145082.i	−0.958816	+	0.284028i
$193$	11.0193			2.12942e−5			1.06471e−5	−	1.00000i	$-0.499997\pi$
$193$	11.0193			2.12942e−5			1.06471e−5		1.00000i	$0.499997\pi$
$194$	−308819.	−	58333.9i	−0.589114	−	0.111280i
$195$	−175056.	−	28724.9i	−0.329678	−	0.0540968i
$196$	468563.	−	1.19603e6i	0.871221	−	2.22383i
$197$	790380.	+	327386.i	1.45101	+	0.601028i	0.962439	−	0.271496i	$-0.0875185\pi$
$197$	790380.	+	327386.i	1.45101	+	0.601028i	0.488571	+	0.872524i	$0.337518\pi$
$198$	340380.	+	433075.i	0.617023	+	0.785054i
$199$	−536917.	+	536917.i	−0.961112	+	0.961112i	−0.999272	−	0.0381594i	$-0.987851\pi$
$199$	−536917.	+	536917.i	−0.961112	+	0.961112i	0.0381594	+	0.999272i	$0.487851\pi$
$200$	110188.	+	480730.i	0.194786	+	0.849819i
$201$	622537.	−	145801.i	1.08686	−	0.254549i
$202$	−30904.4	−	20220.8i	−0.0532895	−	0.0348674i
$203$	271590.	+	112496.i	0.462566	+	0.191601i
$204$	316878.	−	533426.i	0.533110	−	0.897426i
$205$	−87325.7	−	210823.i	−0.145130	−	0.350375i
$206$	−176112.	+	120150.i	−0.289148	+	0.197267i
$207$	645601.	−	319956.i	1.04722	−	0.518996i
$208$	−201907.	+	546206.i	−0.323589	+	0.875382i
$209$	808616.			1.28049
$210$	18255.5	+	420713.i	0.0285657	+	0.658321i
$211$	418799.	−	173472.i	0.647589	−	0.268240i	−0.0346165	−	0.999401i	$-0.511021\pi$
$211$	418799.	−	173472.i	0.647589	−	0.268240i	0.682205	+	0.731161i	$0.261021\pi$
$212$	514120.	−	534370.i	0.785642	−	0.816587i
$213$	−422577.	+	303444.i	−0.638201	+	0.458279i
$214$	122544.	+	80180.3i	0.182918	+	0.119683i
$215$	57605.8	−	57605.8i	0.0849905	−	0.0849905i
$216$	−594110.	+	342371.i	−0.866428	+	0.499302i
$217$	732842.	+	732842.i	1.05648	+	1.05648i
$218$	−191932.	−	918468.i	−0.273531	−	1.30895i
$219$	−679583.	−	946389.i	−0.957485	−	1.33340i
$220$	102757.	+	235128.i	0.143137	+	0.327528i
$221$	−270682.	−	653485.i	−0.372803	−	0.900026i
$222$	380751.	+	349082.i	0.518511	+	0.475384i
$223$			381783.i			0.514109i	0.966397	+	0.257054i	$0.0827519\pi$
$223$			381783.i			0.514109i	−0.966397	+	0.257054i	$0.917248\pi$
$224$	1.36722e6	+	203938.i	1.82062	+	0.271568i
$225$	293992.	+	593211.i	0.387150	+	0.781184i
$226$	412498.	+	77918.3i	0.537219	+	0.101477i
$227$	−378191.	+	156652.i	−0.487132	+	0.201777i	−0.612711	−	0.790307i	$-0.709921\pi$
$227$	−378191.	+	156652.i	−0.487132	+	0.201777i	0.125579	+	0.992084i	$0.459921\pi$
$228$	−143783.	+	996286.i	−0.183177	+	1.26925i
$229$	347552.	−	839064.i	0.437956	−	1.05732i	−0.538698	−	0.842499i	$-0.681083\pi$
$229$	347552.	−	839064.i	0.437956	−	1.05732i	0.976654	−	0.214820i	$-0.0689166\pi$
$230$	328562.	−	68659.4i	0.409541	−	0.0855816i
$231$	−339923.	−	1.45139e6i	−0.419132	−	1.78960i
$232$	−37150.2	+	219871.i	−0.0453149	+	0.268194i
$233$	−863124.	−	863124.i	−1.04156	−	1.04156i	−0.999098	−	0.0424600i	$-0.986480\pi$
$233$	−863124.	−	863124.i	−1.04156	−	1.04156i	−0.0424600	−	0.999098i	$-0.513520\pi$
$234$	−93019.3	+	776163.i	−0.111054	+	0.926645i
$235$	47481.3	−	114630.i	0.0560858	−	0.135403i
$236$	−1.11830e6	+	1.16235e6i	−1.30701	+	1.35849i
$237$	−116191.	+	708094.i	−0.134370	+	0.818880i
$238$	−1.38703e6	+	946279.i	−1.58724	+	1.08287i
$239$		−	696357.i		−	0.788565i	−0.918989	−	0.394282i	$-0.870993\pi$
$239$		−	696357.i		−	0.788565i	0.918989	−	0.394282i	$-0.129007\pi$
$240$	−307970.	+	84796.2i	−0.345128	+	0.0950273i
$241$		−	667571.i		−	0.740380i	−0.928956	−	0.370190i	$-0.879293\pi$
$241$		−	667571.i		−	0.740380i	0.928956	−	0.370190i	$-0.120707\pi$
$242$	1526.32	+	2237.23i	0.00167536	+	0.00245569i
$243$	−668724.	+	632532.i	−0.726492	+	0.687175i
$244$	264258.	−	5103.84i	0.284154	−	0.00548810i
$245$	307405.	−	742141.i	0.327187	−	0.789898i
$246$	−911459.	+	424722.i	−0.960283	+	0.447473i
$247$	811448.	+	811448.i	0.846288	+	0.846288i
$248$	−417649.	+	666040.i	−0.431203	+	0.687655i
$249$	−46959.2	+	10998.1i	−0.0479979	+	0.0112413i
$250$	135448.	+	648172.i	0.137064	+	0.655904i
$251$	−610977.	+	1.47503e6i	−0.612126	+	1.47780i	0.248535	+	0.968623i	$0.420051\pi$
$251$	−610977.	+	1.47503e6i	−0.612126	+	1.47780i	−0.860661	+	0.509179i	$0.829949\pi$
$252$	1.84869e6	−	160738.i	1.83384	−	0.159448i
$253$	−1.09774e6	+	454699.i	−1.07820	+	0.446604i
$254$	246335.	−	1.30410e6i	0.239575	−	1.26831i
$255$	204565.	−	329690.i	0.197006	−	0.317508i
$256$	80917.6	+	1.04545e6i	0.0771690	+	0.997018i
$257$		−	1.70812e6i		−	1.61319i	−0.591103	−	0.806596i	$-0.701307\pi$
$257$		−	1.70812e6i		−	1.61319i	0.591103	−	0.806596i	$-0.298693\pi$
$258$	−264612.	−	242603.i	−0.247492	−	0.226907i
$259$	−534959.	−	1.29151e6i	−0.495531	−	1.19632i
$260$	−132835.	+	339068.i	−0.121865	+	0.311067i
$261$	20165.4	+	298658.i	0.0183234	+	0.271377i
$262$	−1.19521e6	+	249762.i	−1.07570	+	0.224788i
$263$	61706.3	+	61706.3i	0.0550098	+	0.0550098i	0.734077	−	0.679067i	$-0.237615\pi$
$263$	61706.3	+	61706.3i	0.0550098	+	0.0550098i	−0.679067	+	0.734077i	$0.737615\pi$
$264$	1.01551e6	−	497299.i	0.896760	−	0.439145i
$265$	327898.	−	327898.i	0.286830	−	0.286830i
$266$	1.49149e6	−	2.27952e6i	1.29246	−	1.97533i
$267$	−1.06415e6	−	1.48194e6i	−0.913538	−	1.27219i
$268$	−25345.2	−	1.31228e6i	−0.0215555	−	1.11606i
$269$	−403100.	+	166970.i	−0.339651	+	0.140688i	−0.545988	−	0.837793i	$-0.683846\pi$
$269$	−403100.	+	166970.i	−0.339651	+	0.140688i	0.206337	+	0.978481i	$0.433846\pi$
$270$	−375592.	+	206888.i	−0.313550	+	0.172713i
$271$	−2.13103e6			−1.76265			−0.881325	−	0.472511i	$-0.843348\pi$
$271$	−2.13103e6			−1.76265			−0.881325	+	0.472511i	$0.843348\pi$
$272$	−934714.	−	865163.i	−0.766049	−	0.709048i
$273$	1.11536e6	−	1.79759e6i	0.905752	−	1.45977i
$274$	404122.	+	592349.i	0.325189	+	0.476652i
$275$	−417801.	−	1.00866e6i	−0.333149	−	0.804292i
$276$	−365036.	−	1.43336e6i	−0.288445	−	1.13262i
$277$	−959369.	−	397384.i	−0.751253	−	0.311179i	−0.0260003	−	0.999662i	$-0.508277\pi$
$277$	−959369.	−	397384.i	−0.751253	−	0.311179i	−0.725253	+	0.688483i	$0.758277\pi$
$278$	592301.	−	905243.i	0.459654	−	0.702511i
$279$	−337258.	+	999992.i	−0.259389	+	0.769105i
$280$	852371.	+	144019.i	0.649731	+	0.109781i
$281$	−1.12869e6	+	1.12869e6i	−0.852725	+	0.852725i	−0.990468	−	0.137743i	$-0.956015\pi$
$281$	−1.12869e6	+	1.12869e6i	−0.852725	+	0.852725i	0.137743	+	0.990468i	$0.456015\pi$
$282$	−513725.	−	187137.i	−0.384687	−	0.140132i
$283$	−179653.	−	74414.7i	−0.133342	−	0.0552322i	0.315014	−	0.949087i	$-0.397991\pi$
$283$	−179653.	−	74414.7i	−0.133342	−	0.0552322i	−0.448357	+	0.893855i	$0.647991\pi$
$284$	427663.	+	978581.i	0.314634	+	0.719948i
$285$	−101929.	+	621176.i	−0.0743335	+	0.453004i
$286$	239267.	−	1.26668e6i	0.172969	−	0.915695i
$287$	2.72127e6			1.95014
$288$	432144.	+	1.33963e6i	0.307006	+	0.951707i
$289$	127191.			0.0895802
$290$	−25882.7	+	137022.i	−0.0180723	+	0.0956746i
$291$	−140235.	+	854625.i	−0.0970790	+	0.591620i
$292$	−2.19160e6	+	957779.i	−1.50419	+	0.657367i
$293$	1.56641e6	+	648828.i	1.06595	+	0.441531i	0.845559	−	0.533881i	$-0.179267\pi$
$293$	1.56641e6	+	648828.i	1.06595	+	0.441531i	0.220390	+	0.975412i	$0.429267\pi$
$294$	−3.32597e6	−	1.21157e6i	−2.24414	−	0.817484i
$295$	−713236.	+	713236.i	−0.477175	+	0.477175i
$296$	864245.	−	614407.i	0.573334	−	0.407593i
$297$	1.17051e6	−	966408.i	0.769987	−	0.635725i
$298$	1.25936e6	−	1.92474e6i	0.821504	−	1.25554i
$299$	−1.55788e6	−	645294.i	−1.00776	−	0.417426i
$300$	1.31705e6	−	335414.i	0.844888	−	0.215168i
$301$	371783.	+	897564.i	0.236523	+	0.571017i
$302$	724868.	+	1.06249e6i	0.457342	+	0.670358i
$303$	−53657.5	+	86478.0i	−0.0335756	+	0.0541127i
$304$	1.93818e6	+	716459.i	1.20285	+	0.444639i
$305$	165285.			0.101738
$306$	−1.49053e6	−	837608.i	−0.909988	−	0.511372i
$307$	−699138.	+	289592.i	−0.423367	+	0.175364i	−0.584186	−	0.811620i	$-0.698586\pi$
$307$	−699138.	+	289592.i	−0.423367	+	0.175364i	0.160820	+	0.986984i	$0.448586\pi$
$308$	−3.05947e6	+	59090.2i	−1.83768	+	0.0354927i
$309$	342670.	+	477203.i	0.204164	+	0.284320i
$310$	−269171.	+	411387.i	−0.159083	+	0.243135i
$311$	−1.89796e6	+	1.89796e6i	−1.11272	+	1.11272i	−0.119942	+	0.992781i	$0.538271\pi$
$311$	−1.89796e6	+	1.89796e6i	−1.11272	+	1.11272i	−0.992781	+	0.119942i	$0.961729\pi$
$312$	1.51811e6	+	520030.i	0.882912	+	0.302442i
$313$	−1.01009e6	−	1.01009e6i	−0.582770	−	0.582770i	0.352893	−	0.935664i	$-0.385198\pi$
$313$	−1.01009e6	−	1.01009e6i	−0.582770	−	0.582770i	−0.935664	+	0.352893i	$0.885198\pi$
$314$	1.59837e6	−	334012.i	0.914859	−	0.191178i
$315$	1.15780e6	−	78174.9i	0.657443	−	0.0443906i
$316$	1.37152e6	+	537315.i	0.772653	+	0.302699i
$317$	327431.	+	790489.i	0.183009	+	0.441822i	0.988584	−	0.150671i	$-0.0481435\pi$
$317$	327431.	+	790489.i	0.183009	+	0.441822i	−0.805575	+	0.592494i	$0.798143\pi$
$318$	−1.50620e6	−	1.38092e6i	−0.835246	−	0.765775i
$319$		−	493618.i		−	0.271590i
$320$	37967.9	+	654628.i	0.0207273	+	0.357371i
$321$	212765.	−	342907.i	0.115249	−	0.185743i
$322$	−742969.	+	3.93327e6i	−0.399329	+	2.11404i
$323$	−2.31886e6	+	960503.i	−1.23671	+	0.512262i
$324$	982567.	+	1.61401e6i	0.519996	+	0.854169i
$325$	592930.	−	1.43146e6i	0.311383	−	0.751745i
$326$	291386.	+	1.39439e6i	0.151854	+	0.726678i
$327$	−2.51755e6	+	589622.i	−1.30199	+	0.304933i
$328$	461176.	+	2.01203e6i	0.236691	+	1.03264i
$329$	1.04625e6	+	1.04625e6i	0.532902	+	0.532902i
$330$	640940.	−	298665.i	0.323991	−	0.150973i
$331$	−63229.3	+	152649.i	−0.0317211	+	0.0765816i	−0.938946	−	0.344064i	$-0.888196\pi$
$331$	−63229.3	+	152649.i	−0.0317211	+	0.0765816i	0.907225	+	0.420645i	$0.138196\pi$
$332$	1911.84	+	98987.9i	0.000951932	+	0.0492875i
$333$	936444.	−	1.07206e6i	0.462776	−	0.529795i
$334$	−1.09637e6	−	1.60702e6i	−0.537762	−	0.788234i
$335$		−	820788.i		−	0.399594i
$336$	471211.	−	3.78005e6i	0.227702	−	1.82662i
$337$			989412.i			0.474573i	0.971440	+	0.237286i	$0.0762579\pi$
$337$			989412.i			0.474573i	−0.971440	+	0.237286i	$0.923742\pi$
$338$	−223811.	+	152692.i	−0.106559	+	0.0726985i
$339$	187317.	−	1.14155e6i	0.0885273	−	0.539504i
$340$	−573968.	−	552217.i	−0.269271	−	0.259067i
$341$	665975.	−	1.60781e6i	0.310150	−	0.748769i
$342$	2.75418e6	+	330074.i	1.27329	+	0.152597i
$343$	3.93761e6	+	3.93761e6i	1.80716	+	1.80716i
$344$	−600629.	+	426998.i	−0.273659	+	0.194549i
$345$	−210924.	−	900597.i	−0.0954067	−	0.407364i
$346$	286426.	−	59854.5i	0.128624	−	0.0268786i
$347$	56693.8	−	136871.i	0.0252762	−	0.0610222i	−0.910737	−	0.412986i	$-0.864486\pi$
$347$	56693.8	−	136871.i	0.0252762	−	0.0610222i	0.936014	+	0.351964i	$0.114486\pi$
$348$	608181.	+	87772.0i	0.269206	+	0.0388515i
$349$	688922.	−	285361.i	0.302766	−	0.125410i	−0.226128	−	0.974097i	$-0.572607\pi$
$349$	688922.	−	285361.i	0.302766	−	0.125410i	0.528894	+	0.848688i	$0.322607\pi$
$350$	−3.61409e6	−	682679.i	−1.57699	−	0.297883i
$351$	2.14440e6	+	204816.i	0.929048	+	0.0887351i
$352$	−562181.	−	2.25208e6i	−0.241835	−	0.968784i
$353$		−	378061.i		−	0.161482i	−0.996735	−	0.0807411i	$-0.974271\pi$
$353$		−	378061.i		−	0.161482i	0.996735	−	0.0807411i	$-0.0257287\pi$
$354$	3.27625e6	+	3.00375e6i	1.38953	+	1.27396i
$355$	255573.	+	617007.i	0.107633	+	0.259848i
$356$	−3.43180e6	+	1.49978e6i	−1.43515	+	0.627195i
$357$	2.69881e6	+	3.75837e6i	1.12073	+	1.56073i
$358$	−633999.	−	3.03393e6i	−0.261445	−	1.25112i
$359$	1.03916e6	+	1.03916e6i	0.425544	+	0.425544i	0.887107	−	0.461563i	$-0.152711\pi$
$359$	1.03916e6	+	1.03916e6i	0.425544	+	0.425544i	−0.461563	+	0.887107i	$0.652711\pi$
$360$	254014.	+	842801.i	0.103300	+	0.342743i
$361$	1.12852e6	−	1.12852e6i	0.455764	−	0.455764i
$362$	2.01340e6	+	1.31737e6i	0.807528	+	0.528366i
$363$	6062.15	−	4353.11i	0.00241468	−	0.00173394i
$364$	−3.12949e6	−	3.01089e6i	−1.23800	−	1.19108i
$365$	−1.38183e6	+	572371.i	−0.542902	+	0.224877i
$366$	−31574.4	−	727660.i	−0.0123206	−	0.283939i
$367$	5.12336e6			1.98559			0.992795	−	0.119829i	$-0.0382346\pi$
$367$	5.12336e6			1.98559			0.992795	+	0.119829i	$0.0382346\pi$
$368$	−3.03407e6	+	117243.i	−1.16790	+	0.0451302i
$369$	1.23047e6	+	2.48281e6i	0.470439	+	0.949243i
$370$	547775.	−	373712.i	0.208017	−	0.141916i
$371$	2.11623e6	+	5.10902e6i	0.798229	+	1.92710i
$372$	1.86254e6	+	1.10643e6i	0.697827	+	0.414540i
$373$	1.25392e6	+	519391.i	0.466657	+	0.193296i	0.603607	−	0.797282i	$-0.293730\pi$
$373$	1.25392e6	+	519391.i	0.466657	+	0.193296i	−0.136949	+	0.990578i	$0.543730\pi$
$374$	2.35929e6	+	1.54369e6i	0.872172	+	0.570663i
$375$	1.77666e6	−	416102.i	0.652417	−	0.152799i
$376$	−596263.	+	950881.i	−0.217504	+	0.346862i
$377$	495347.	−	495347.i	0.179497	−	0.179497i
$378$	−565338.	−	5.08225e6i	−0.203507	−	1.82948i
$379$	−1.89851e6	−	786389.i	−0.678914	−	0.281215i	0.0164588	−	0.999865i	$-0.494761\pi$
$379$	−1.89851e6	−	786389.i	−0.678914	−	0.281215i	−0.695373	+	0.718649i	$0.744761\pi$
$380$	1.20317e6	+	471359.i	0.427432	+	0.167453i
$381$	−3.60895e6	−	592193.i	−1.27370	−	0.209002i
$382$	3.20711e6	+	605802.i	1.12449	+	0.212409i
$383$	2.20522e6			0.768166			0.384083	−	0.923299i	$-0.374518\pi$
$383$	2.20522e6			0.768166			0.384083	+	0.923299i	$0.374518\pi$
$384$	2.87472e6	−	292207.i	0.994874	−	0.101126i
$385$	−1.91360e6			−0.657960
$386$	−61.2515	−	11.5700i	−2.09242e−5	−	3.95244e-6i
$387$	−650805.	+	745053.i	−0.220889	+	0.252877i
$388$	1.65534e6	+	648505.i	0.558223	+	0.218692i
$389$	−29537.5	−	12234.8i	−0.00989690	−	0.00409943i	0.377729	−	0.925916i	$-0.376705\pi$
$389$	−29537.5	−	12234.8i	−0.00989690	−	0.00409943i	−0.387626	+	0.921817i	$0.626705\pi$
$390$	942896.	+	343473.i	0.313908	+	0.114349i
$391$	2.60787e6	−	2.60787e6i	0.862669	−	0.862669i
$392$	−3.86034e6	+	6.15622e6i	−1.26885	+	2.02348i
$393$	767279.	+	3.27610e6i	0.250595	+	1.06998i
$394$	−4.04962e6	−	2.64967e6i	−1.31424	−	0.859908i
$395$	851033.	+	352510.i	0.274444	+	0.113678i
$396$	−1.43730e6	−	2.76466e6i	−0.460586	−	0.885939i
$397$	189961.	+	458606.i	0.0604906	+	0.146037i	0.951235	−	0.308468i	$-0.0998162\pi$
$397$	189961.	+	458606.i	0.0604906	+	0.146037i	−0.890744	+	0.454505i	$0.849816\pi$
$398$	3.54823e6	−	2.42073e6i	1.12280	−	0.766018i
$399$	−6.37866e6	−	3.95781e6i	−2.00584	−	1.24458i
$400$	−107729.	−	2.78786e6i	−0.0336653	−	0.871206i
$401$	−1.90486e6			−0.591564			−0.295782	−	0.955255i	$-0.595580\pi$
$401$	−1.90486e6			−0.591564			−0.295782	+	0.955255i	$0.595580\pi$
$402$	−3.61349e6	+	156796.i	−1.11522	+	0.0483915i
$403$	2.28174e6	−	945129.i	0.699849	−	0.289887i
$404$	150552.	+	144847.i	0.0458917	+	0.0441526i
$405$	594844.	+	1.02100e6i	0.180205	+	0.309306i
$406$	−1.39153e6	−	910479.i	−0.418965	−	0.274129i
$407$	−1.65981e6	+	1.65981e6i	−0.496676	+	0.496676i
$408$	−2.32147e6	+	2.63236e6i	−0.690419	+	0.782881i
$409$	1.85007e6	+	1.85007e6i	0.546864	+	0.546864i	0.925532	−	0.378668i	$-0.123618\pi$
$409$	1.85007e6	+	1.85007e6i	0.546864	+	0.546864i	−0.378668	+	0.925532i	$0.623618\pi$
$410$	264046.	+	1.26356e6i	0.0775747	+	0.371225i
$411$	1.60507e6	−	1.15257e6i	0.468693	−	0.336559i
$412$	1.10508e6	−	482947.i	0.320739	−	0.140170i
$413$	−4.60316e6	−	1.11130e7i	−1.32795	−	3.20595i
$414$	−3.92455e6	+	1.10063e6i	−1.12535	+	0.315602i
$415$			61913.7i			0.0176468i
$416$	1.69582e6	−	2.82412e6i	0.480447	−	0.800109i
$417$	−2.53309e6	−	1.57172e6i	−0.713363	−	0.442625i
$418$	−4.49474e6	−	849027.i	−1.25824	−	0.237674i
$419$	1.64567e6	−	681658.i	0.457939	−	0.189684i	−0.141775	−	0.989899i	$-0.545281\pi$
$419$	1.64567e6	−	681658.i	0.457939	−	0.189684i	0.599714	+	0.800214i	$0.295281\pi$
$420$	340264.	−	2.35772e6i	0.0941224	−	0.652183i
$421$	1.85058e6	−	4.46769e6i	0.508864	−	1.22851i	−0.435674	−	0.900105i	$-0.643490\pi$
$421$	1.85058e6	−	4.46769e6i	0.508864	−	1.22851i	0.944538	−	0.328402i	$-0.106510\pi$
$422$	−2.51006e6	+	524527.i	−0.686124	+	0.143379i
$423$	−481492.	+	1.42765e6i	−0.130839	+	0.387946i
$424$	−3.41884e6	+	2.43051e6i	−0.923558	+	0.656573i
$425$	2.39625e6	+	2.39625e6i	0.643516	+	0.643516i
$426$	2.66753e6	−	1.24302e6i	0.712172	−	0.331859i
$427$	−754294.	+	1.82103e6i	−0.200203	+	0.483333i
$428$	−596978.	−	574355.i	−0.157525	−	0.151555i
$429$	−3.50540e6	−	575201.i	−0.919590	−	0.150896i
$430$	−380690.	+	259720.i	−0.0992888	+	0.0677384i
$431$			1.95392e6i			0.506656i	0.967380	+	0.253328i	$0.0815252\pi$
$431$			1.95392e6i			0.506656i	−0.967380	+	0.253328i	$0.918475\pi$
$432$	3.66188e6	−	1.27929e6i	0.944048	−	0.329807i
$433$			3.02038e6i			0.774180i	0.922042	+	0.387090i	$0.126520\pi$
$433$			3.02038e6i			0.774180i	−0.922042	+	0.387090i	$0.873480\pi$
$434$	−3.30408e6	−	4.84301e6i	−0.842027	−	1.23422i
$435$	379196.	+	62222.2i	0.0960816	+	0.0157660i
$436$	102496.	+	5.30688e6i	0.0258221	+	1.33697i
$437$	−2.28979e6	+	5.52805e6i	−0.573578	+	1.38474i
$438$	2.78382e6	+	5.97410e6i	0.693354	+	1.48795i
$439$	113807.	+	113807.i	0.0281844	+	0.0281844i	0.721059	−	0.692874i	$-0.243656\pi$
$439$	113807.	+	113807.i	0.0281844	+	0.0281844i	−0.692874	+	0.721059i	$0.743656\pi$
$440$	−324300.	−	1.41487e6i	−0.0798573	−	0.348404i
$441$	−3.11729e6	+	9.24295e6i	−0.763274	+	2.26315i
$442$	818460.	+	3.91664e6i	0.199270	+	0.953583i
$443$	2.04246e6	−	4.93093e6i	0.494475	−	1.19377i	−0.457946	−	0.888980i	$-0.651415\pi$
$443$	2.04246e6	−	4.93093e6i	0.494475	−	1.19377i	0.952420	−	0.304787i	$-0.0985854\pi$
$444$	−1.74990e6	−	2.34017e6i	−0.421265	−	0.563365i
$445$	−2.16379e6	+	896272.i	−0.517983	+	0.214556i
$446$	400863.	−	2.12216e6i	0.0954243	−	0.505175i
$447$	−5.38590e6	−	3.34182e6i	−1.27494	−	0.791069i
$448$	−7.38565e6	−	2.56915e6i	−1.73858	−	0.604776i
$449$		−	5.35385e6i		−	1.25329i	−0.779307	−	0.626643i	$-0.784428\pi$
$449$		−	5.35385e6i		−	1.25329i	0.779307	−	0.626643i	$-0.215572\pi$
$450$	−1.01131e6	−	3.60608e6i	−0.235426	−	0.839469i
$451$	−1.74865e6	−	4.22162e6i	−0.404820	−	0.977323i
$452$	−2.21108e6	−	866226.i	−0.509048	−	0.199428i
$453$	2.87898e6	−	2.06734e6i	0.659164	−	0.473333i
$454$	2.26668e6	−	473667.i	0.516119	−	0.107853i
$455$	−1.92030e6	−	1.92030e6i	−0.434852	−	0.434852i
$456$	1.84530e6	−	5.38694e6i	0.415581	−	1.21319i
$457$	796376.	−	796376.i	0.178372	−	0.178372i	−0.612274	−	0.790646i	$-0.709745\pi$
$457$	796376.	−	796376.i	0.178372	−	0.178372i	0.790646	+	0.612274i	$0.209745\pi$
$458$	−2.81288e6	+	4.29906e6i	−0.626596	+	0.957657i
$459$	−2.20872e6	+	4.16173e6i	−0.489338	+	0.922024i
$460$	−1.89842e6	+	36665.8i	−0.418309	+	0.00807917i
$461$	598697.	−	247988.i	0.131206	−	0.0543474i	−0.316114	−	0.948721i	$-0.602378\pi$
$461$	598697.	−	247988.i	0.131206	−	0.0543474i	0.447321	+	0.894374i	$0.352378\pi$
$462$	365557.	+	8.42456e6i	0.0796801	+	1.83629i
$463$	−3.81533e6			−0.827142			−0.413571	−	0.910472i	$-0.635719\pi$
$463$	−3.81533e6			−0.827142			−0.413571	+	0.910472i	$0.635719\pi$
$464$	437361.	−	1.18316e6i	0.0943072	−	0.255122i
$465$	1.15116e6	+	714269.i	0.246890	+	0.153190i
$466$	3.89147e6	+	5.70398e6i	0.830134	+	1.21678i
$467$	2.72402e6	+	6.57636e6i	0.577987	+	1.39538i	0.894617	+	0.446834i	$0.147449\pi$
$467$	2.72402e6	+	6.57636e6i	0.577987	+	1.39538i	−0.316630	+	0.948549i	$0.602551\pi$
$468$	1.33201e6	−	4.21668e6i	0.281120	−	0.889930i
$469$	9.04306e6	+	3.74576e6i	1.89838	+	0.786335i
$470$	−384286.	+	587323.i	−0.0802436	+	0.122640i
$471$	−1.02610e6	−	4.38119e6i	−0.213126	−	0.909996i
$472$	7.43657e6	−	5.28679e6i	1.53645	−	1.09229i
$473$	1.15353e6	−	1.15353e6i	0.237069	−	0.237069i
$474$	1.38934e6	−	3.81398e6i	0.284028	−	0.779710i
$475$	−5.07946e6	−	2.10398e6i	−1.03296	−	0.427866i
$476$	8.70343e6	−	3.80360e6i	1.76065	−	0.769446i
$477$	−3.70445e6	+	4.24092e6i	−0.745465	+	0.853422i
$478$	−731158.	+	3.87074e6i	−0.146366	+	0.774862i
$479$	5.08710e6			1.01305			0.506525	−	0.862225i	$-0.330930\pi$
$479$	5.08710e6			1.01305			0.506525	+	0.862225i	$0.330930\pi$
$480$	1.80090e6	−	147983.i	0.356769	−	0.0293163i
$481$	−3.33125e6			−0.656515
$482$	−700933.	+	3.71073e6i	−0.137423	+	0.727515i
$483$	1.08849e7	+	1.78611e6i	2.12304	+	0.348369i
$484$	−6135.11	−	14038.4i	−0.00119044	−	0.00272398i
$485$	1.02714e6	+	425457.i	0.198279	+	0.0821298i
$486$	4.38128e6	−	2.81382e6i	0.841416	−	0.540389i
$487$	−2.54195e6	+	2.54195e6i	−0.485674	+	0.485674i	−0.906938	−	0.421264i	$-0.861587\pi$
$487$	−2.54195e6	+	2.54195e6i	−0.485674	+	0.485674i	0.421264	+	0.906938i	$0.361587\pi$
$488$	−1.47425e6	−	249094.i	−0.280235	−	0.0473493i
$489$	3.82208e6	−	895149.i	0.722815	−	0.169287i
$490$	−2.48796e6	+	3.80246e6i	−0.468115	+	0.715443i
$491$	−2.57999e6	−	1.06867e6i	−0.482963	−	0.200050i	0.127899	−	0.991787i	$-0.459177\pi$
$491$	−2.57999e6	−	1.06867e6i	−0.482963	−	0.200050i	−0.610861	+	0.791738i	$0.709177\pi$
$492$	5.51234e6	−	1.40383e6i	1.02665	−	0.261458i
$493$	586337.	+	1.41554e6i	0.108650	+	0.262305i
$494$	−3.65848e6	−	5.36248e6i	−0.674502	−	0.988663i
$495$	−865266.	−	1.74592e6i	−0.158722	−	0.320266i
$496$	3.02085e6	−	3.26370e6i	0.551347	−	0.595670i
$497$	−7.96422e6			−1.44628
$498$	272573.	−	11827.4i	0.0492503	−	0.00213706i
$499$	−838843.	+	347460.i	−0.150810	+	0.0624674i	−0.456812	−	0.889563i	$-0.651009\pi$
$499$	−838843.	+	347460.i	−0.150810	+	0.0624674i	0.306002	+	0.952031i	$0.401009\pi$
$500$	−72332.6	−	3.74512e6i	−0.0129393	−	0.669947i
$501$	−4.35448e6	+	3.12687e6i	−0.775072	+	0.556564i
$502$	4.94489e6	−	7.55752e6i	0.875785	−	1.33851i
$503$	−5.77046e6	+	5.77046e6i	−1.01693	+	1.01693i	−0.0170747	+	0.999854i	$0.505435\pi$
$503$	−5.77046e6	+	5.77046e6i	−1.01693	+	1.01693i	−0.999854	+	0.0170747i	$0.994565\pi$
$504$	−1.04448e7	−	1.04760e6i	−1.83157	−	0.183705i
$505$	92381.4	+	92381.4i	0.0161197	+	0.0161197i
$506$	6.57928e6	−	1.37487e6i	1.14236	−	0.238718i
$507$	435482.	+	606453.i	0.0752403	+	0.104780i
$508$	−2.73854e6	+	6.99024e6i	−0.470825	+	1.20180i
$509$	1.52095e6	+	3.67189e6i	0.260207	+	0.628196i	0.998951	−	0.0457904i	$-0.0145806\pi$
$509$	1.52095e6	+	3.67189e6i	0.260207	+	0.628196i	−0.738744	+	0.673986i	$0.764581\pi$
$510$	−1.48325e6	+	1.61781e6i	−0.252516	+	0.275424i
$511$		−	1.78364e7i		−	3.02172i
$512$	647911.	−	5.89615e6i	0.109230	−	0.994017i
$513$	726779.	−	7.60930e6i	0.121929	−	1.27659i
$514$	−1.79349e6	+	9.49470e6i	−0.299427	+	1.58516i
$515$	696767.	−	288610.i	0.115763	−	0.0479505i
$516$	1.21613e6	+	1.62636e6i	0.201075	+	0.268901i
$517$	950789.	−	2.29541e6i	0.156444	−	0.377688i
$518$	1.61755e6	+	7.74060e6i	0.264871	+	1.26751i
$519$	−183875.	−	785103.i	−0.0299643	−	0.127941i
$520$	1.09439e6	−	1.74526e6i	0.177485	−	0.283042i
$521$	−6.00952e6	−	6.00952e6i	−0.969942	−	0.969942i	0.0296192	−	0.999561i	$-0.490571\pi$
$521$	−6.00952e6	−	6.00952e6i	−0.969942	−	0.969942i	−0.999561	+	0.0296192i	$0.990571\pi$
$522$	201493.	−	1.68128e6i	0.0323656	−	0.270062i
$523$	2.59345e6	−	6.26115e6i	0.414595	−	1.00092i	−0.569293	−	0.822135i	$-0.692783\pi$
$523$	2.59345e6	−	6.26115e6i	0.414595	−	1.00092i	0.983888	−	0.178786i	$-0.0572171\pi$
$524$	6.90587e6	−	133379.i	1.09873	−	0.0212207i
$525$	−1.64117e6	+	1.00016e7i	−0.259869	+	1.58370i
$526$	−278208.	−	407788.i	−0.0438435	−	0.0642643i
$527$			5.40176e6i			0.847244i
$528$	−6.16695e6	+	1.69800e6i	−0.962688	+	0.265065i
$529$		−	2.35588e6i		−	0.366027i
$530$	−2.16693e6	+	1.47836e6i	−0.335084	+	0.228607i
$531$	8.05782e6	−	9.22474e6i	1.24017	−	1.41977i
$532$	−1.06840e7	+	1.11048e7i	−1.63665	+	1.70111i
$533$	2.48163e6	−	5.99119e6i	0.378372	−	0.913471i
$534$	4.35916e6	+	9.35481e6i	0.661530	+	1.41965i
$535$	−366315.	−	366315.i	−0.0553312	−	0.0553312i
$536$	−1.23698e6	+	7.32099e6i	−0.185973	+	1.10067i
$537$	−8.31608e6	+	1.94767e6i	−1.24447	+	0.291460i
$538$	2.41597e6	−	504865.i	0.359862	−	0.0752003i
$539$	6.15563e6	−	1.48610e7i	0.912642	−	2.20331i
$540$	2.30498e6	−	755636.i	0.340159	−	0.111514i
$541$	3.09896e6	−	1.28363e6i	0.455221	−	0.188559i	−0.143278	−	0.989683i	$-0.545764\pi$
$541$	3.09896e6	−	1.28363e6i	0.455221	−	0.188559i	0.598499	+	0.801124i	$0.295764\pi$
$542$	1.18454e7	+	2.23753e6i	1.73202	+	0.327167i
$543$	3.49575e6	−	5.63397e6i	0.508792	−	0.820002i
$544$	4.28726e6	+	5.79048e6i	0.621130	+	0.838914i
$545$			3.31928e6i			0.478688i
$546$	−8.08723e6	+	8.82090e6i	−1.16096	+	1.26628i
$547$	4.07870e6	+	9.84685e6i	0.582845	+	1.40711i	0.890223	+	0.455525i	$0.150549\pi$
$547$	4.07870e6	+	9.84685e6i	0.582845	+	1.40711i	−0.307378	+	0.951588i	$0.599451\pi$
$548$	−1.62438e6	−	3.71692e6i	−0.231067	−	0.528728i
$549$	−2.00252e6	+	135210.i	−0.283561	+	0.0191460i
$550$	1.26330e6	+	6.04538e6i	0.178074	+	0.852152i
$551$	−1.75771e6	−	1.75771e6i	−0.246643	−	0.246643i
$552$	524076.	+	8.35072e6i	0.0732060	+	1.16648i
$553$	−7.76757e6	+	7.76757e6i	−1.08012	+	1.08012i
$554$	4.91546e6	+	3.21619e6i	0.680440	+	0.445213i
$555$	−1.06584e6	−	1.48429e6i	−0.146878	−	0.204543i
$556$	−4.24282e6	+	4.40994e6i	−0.582060	+	0.604987i
$557$	−1.06173e7	+	4.39784e6i	−1.45003	+	0.600623i	−0.962207	−	0.272319i	$-0.912209\pi$
$557$	−1.06173e7	+	4.39784e6i	−1.45003	+	0.600623i	−0.487825	+	0.872942i	$0.662209\pi$
$558$	2.92464e6	−	5.20440e6i	0.397637	−	0.707595i
$559$	2.31513e6			0.313362
$560$	−4.58674e6	−	1.69551e6i	−0.618064	−	0.228470i
$561$	4.09630e6	−	6.60187e6i	0.549522	−	0.885645i
$562$	7.45899e6	−	5.08879e6i	0.996183	−	0.679632i
$563$	4.17325e6	+	1.00751e7i	0.554885	+	1.33961i	0.913771	+	0.406229i	$0.133157\pi$
$563$	4.17325e6	+	1.00751e7i	0.554885	+	1.33961i	−0.358886	+	0.933381i	$0.616843\pi$
$564$	2.65908e6	+	1.57961e6i	0.351993	+	0.209099i
$565$	−1.37198e6	−	568295.i	−0.180812	−	0.0748949i
$566$	920478.	+	602270.i	0.120774	+	0.0790223i
$567$	−1.39635e7	+	1.89427e6i	−1.82405	+	0.247448i
$568$	−1.34970e6	−	5.88854e6i	−0.175537	−	0.765837i
$569$	−941652.	+	941652.i	−0.121930	+	0.121930i	−0.765439	−	0.643509i	$-0.777478\pi$
$569$	−941652.	+	941652.i	−0.121930	+	0.121930i	0.643509	+	0.765439i	$0.277478\pi$
$570$	1.21880e6	−	3.34582e6i	0.157125	−	0.431336i
$571$	3.80749e6	+	1.57711e6i	0.488706	+	0.202429i	0.613409	−	0.789765i	$-0.289798\pi$
$571$	3.80749e6	+	1.57711e6i	0.488706	+	0.202429i	−0.124703	+	0.992194i	$0.539798\pi$
$572$	−2.65996e6	+	6.78967e6i	−0.339926	+	0.867678i
$573$	1.45636e6	−	8.87534e6i	0.185302	−	1.12927i
$574$	−1.51263e7	−	2.85726e6i	−1.91626	−	0.361968i
$575$	8.07875e6			1.01900
$576$	−995519.	−	7.90015e6i	−0.125024	−	0.992154i
$577$	−7.00890e6			−0.876417			−0.438208	−	0.898873i	$-0.644387\pi$
$577$	−7.00890e6			−0.876417			−0.438208	+	0.898873i	$0.644387\pi$
$578$	−706999.	−	133547.i	−0.0880236	−	0.0166271i
$579$	−27.8145	+	169.507i	−3.44805e−6	+	2.10132e-5i
$580$	287740.	−	734471.i	0.0355166	−	0.0906577i
$581$	−682136.	−	282550.i	−0.0838360	−	0.0347260i
$582$	1.67684e6	−	4.60324e6i	0.205203	−	0.563321i
$583$	6.56599e6	−	6.56599e6i	0.800072	−	0.800072i
$584$	1.31878e7	−	3.02275e6i	1.60007	−	0.366750i
$585$	883735.	−	2.62033e6i	0.106766	−	0.316567i
$586$	−8.02573e6	−	5.25124e6i	−0.965473	−	0.631710i
$587$	7.92115e6	+	3.28105e6i	0.948840	+	0.393022i	0.802795	−	0.596256i	$-0.203346\pi$
$587$	7.92115e6	+	3.28105e6i	0.948840	+	0.393022i	0.146045	+	0.989278i	$0.453346\pi$
$588$	1.72155e7	+	1.02268e7i	2.05341	+	1.21982i
$589$	−3.35374e6	−	8.09665e6i	−0.398329	−	0.961651i
$590$	4.71344e6	−	3.21568e6i	0.557453	−	0.380315i
$591$	−7.03114e6	+	1.13318e7i	−0.828051	+	1.33454i
$592$	−5.44907e6	+	2.50778e6i	−0.639025	+	0.294093i
$593$	1.06003e7			1.23789			0.618944	−	0.785435i	$-0.287561\pi$
$593$	1.06003e7			1.23789			0.618944	+	0.785435i	$0.287561\pi$
$594$	−7.52105e6	+	4.14283e6i	−0.874605	+	0.481760i
$595$	5.48761e6	−	2.27304e6i	0.635464	−	0.263218i
$596$	−9.02116e6	+	9.37649e6i	−1.04027	+	1.08125i
$597$	−6.90399e6	−	9.61451e6i	−0.792801	−	1.10406i
$598$	7.98200e6	+	5.22263e6i	0.912765	+	0.597223i
$599$	−7.75639e6	+	7.75639e6i	−0.883268	+	0.883268i	−0.993865	−	0.110598i	$-0.964724\pi$
$599$	−7.75639e6	+	7.75639e6i	−0.883268	+	0.883268i	0.110598	+	0.993865i	$0.464724\pi$
$600$	−7.67307e6	+	481549.i	−0.870144	+	0.0546087i
$601$	4.91544e6	+	4.91544e6i	0.555107	+	0.555107i	0.927910	−	0.372804i	$-0.121604\pi$
$601$	4.91544e6	+	4.91544e6i	0.555107	+	0.555107i	−0.372804	+	0.927910i	$0.621604\pi$
$602$	−1.12416e6	−	5.37952e6i	−0.126426	−	0.604996i
$603$	671442.	+	9.94434e6i	0.0751995	+	1.11374i
$604$	−2.91363e6	−	6.66699e6i	−0.324969	−	0.743597i
$605$	−3666.36	−	8851.37i	−0.000407236	−	0.000983155i
$606$	389058.	−	424354.i	0.0430361	−	0.0469403i
$607$			1.50924e7i			1.66260i	0.555827	+	0.831298i	$0.312402\pi$
$607$			1.50924e7i			1.66260i	−0.555827	+	0.831298i	$0.687598\pi$
$608$	−1.00212e7	−	6.01752e6i	−1.09942	−	0.660174i
$609$	−2.41604e6	+	3.89384e6i	−0.263973	+	0.425437i
$610$	−918744.	−	173545.i	−0.0999701	−	0.0188837i
$611$	3.25757e6	−	1.34933e6i	0.353013	−	0.146223i
$612$	7.40570e6	+	6.22091e6i	0.799259	+	0.671390i
$613$	5.36641e6	−	1.29556e7i	0.576809	−	1.39254i	−0.318852	−	0.947804i	$-0.603297\pi$
$613$	5.36641e6	−	1.29556e7i	0.576809	−	1.39254i	0.895661	−	0.444736i	$-0.146703\pi$
$614$	4.19026e6	−	875638.i	0.448560	−	0.0937354i
$615$	3.46346e6	−	811159.i	0.369251	−	0.0864805i
$616$	1.70683e7	+	2.88392e6i	1.81233	+	0.306218i
$617$	5.19729e6	+	5.19729e6i	0.549622	+	0.549622i	0.926332	−	0.376709i	$-0.122944\pi$
$617$	5.19729e6	+	5.19729e6i	0.549622	+	0.549622i	−0.376709	+	0.926332i	$0.622944\pi$
$618$	−1.40370e6	−	3.01236e6i	−0.147844	−	0.317275i
$619$	−4.98631e6	+	1.20380e7i	−0.523061	+	1.26278i	0.412932	+	0.910762i	$0.364505\pi$
$619$	−4.98631e6	+	1.20380e7i	−0.523061	+	1.26278i	−0.935993	+	0.352019i	$0.885495\pi$
$620$	1.92815e6	−	2.00410e6i	0.201447	−	0.209382i
$621$	3.29220e6	+	1.07387e7i	0.342576	+	1.11744i
$622$	1.25428e7	−	8.55712e6i	1.29992	−	0.886853i
$623$		−	2.79299e7i		−	2.88303i
$624$	−7.89249e6	−	4.48460e6i	−0.811433	−	0.461065i
$625$			6.17177e6i			0.631990i
$626$	4.55405e6	+	6.67519e6i	0.464475	+	0.680812i
$627$	−2.04107e6	+	1.24387e7i	−0.207343	+	1.26359i
$628$	−9.23535e6	+	178370.i	−0.934446	+	0.0180478i
$629$	2.78824e6	−	6.73141e6i	0.280998	−	0.678390i
$630$	−6.51780e6	−	781125.i	−0.654259	−	0.0784096i
$631$	1.10644e6	+	1.10644e6i	0.110625	+	0.110625i	0.760253	−	0.649628i	$-0.225075\pi$
$631$	1.10644e6	+	1.10644e6i	0.110625	+	0.110625i	−0.649628	+	0.760253i	$0.725075\pi$
$632$	−7.05951e6	−	4.42676e6i	−0.703043	−	0.440852i
$633$	1.61136e6	+	6.88015e6i	0.159840	+	0.682478i
$634$	−990051.	−	4.73777e6i	−0.0978216	−	0.468114i
$635$	−1.79664e6	+	4.33747e6i	−0.176818	+	0.426876i
$636$	6.92236e6	+	9.25740e6i	0.678596	+	0.907499i
$637$	2.10902e7	−	8.73586e6i	2.05936	−	0.853015i
$638$	−518287.	+	2.74380e6i	−0.0504102	+	0.266871i
$639$	−3.60115e6	−	7.26634e6i	−0.348891	−	0.703985i
$640$	476296.	−	3.67865e6i	0.0459650	−	0.355008i
$641$			6.70198e6i			0.644256i	0.946696	+	0.322128i	$0.104398\pi$
$641$			6.70198e6i			0.644256i	−0.946696	+	0.322128i	$0.895602\pi$
$642$	−1.54271e6	+	1.68267e6i	−0.147723	+	0.161124i
$643$	−5.84445e6	−	1.41097e7i	−0.557463	−	1.34583i	−0.911768	−	0.410705i	$-0.865283\pi$
$643$	−5.84445e6	−	1.41097e7i	−0.557463	−	1.34583i	0.354305	−	0.935130i	$-0.384717\pi$
$644$	8.25967e6	−	2.10832e7i	0.784780	−	2.00319i
$645$	740729.	+	1.03154e6i	0.0701068	+	0.0976309i
$646$	1.38980e7	−	2.90427e6i	1.31030	−	0.273814i
$647$	−5.28905e6	−	5.28905e6i	−0.496727	−	0.496727i	0.413691	−	0.910417i	$-0.364239\pi$
$647$	−5.28905e6	−	5.28905e6i	−0.496727	−	0.496727i	−0.910417	+	0.413691i	$0.864239\pi$
$648$	−3.76698e6	−	1.00032e7i	−0.352417	−	0.935843i
$649$	−1.42822e7	+	1.42822e7i	−1.33101	+	1.33101i
$650$	−4.79883e6	+	7.33428e6i	−0.445504	+	0.680886i
$651$	−1.31229e7	+	9.42331e6i	−1.21361	+	0.871467i
$652$	−155607.	−	8.05677e6i	−0.0143354	−	0.742236i
$653$	−1.88498e6	+	780786.i	−0.172991	+	0.0716554i	−0.467498	−	0.883994i	$-0.654845\pi$
$653$	−1.88498e6	+	780786.i	−0.172991	+	0.0716554i	0.294507	+	0.955649i	$0.404845\pi$
$654$	1.46130e7	−	634085.i	1.33597	−	0.0579699i
$655$	4.31940e6			0.393387
$656$	−450885.	−	1.16682e7i	−0.0409078	−	1.05863i
$657$	1.62734e7	−	8.06501e6i	1.47084	−	0.728940i
$658$	−4.71712e6	−	6.91420e6i	−0.424729	−	0.622554i
$659$	−5.83455e6	−	1.40858e7i	−0.523352	−	1.26348i	−0.935809	−	0.352506i	$-0.885329\pi$
$659$	−5.83455e6	−	1.40858e7i	−0.523352	−	1.26348i	0.412458	−	0.910977i	$-0.364671\pi$
$660$	−3.87629e6	+	987178.i	−0.346383	+	0.0882136i
$661$	−1.71212e7	−	7.09182e6i	−1.52416	−	0.631327i	−0.545738	−	0.837956i	$-0.683751\pi$
$661$	−1.71212e7	−	7.09182e6i	−1.52416	−	0.631327i	−0.978419	+	0.206629i	$0.933751\pi$
$662$	511742.	−	782120.i	0.0453843	−	0.0693630i
$663$	1.07356e7	−	2.51434e6i	0.948515	−	0.222147i
$664$	93307.8	−	552237.i	0.00821292	−	0.0486077i
$665$	−6.81410e6	+	6.81410e6i	−0.597523	+	0.597523i
$666$	−6.33091e6	+	4.97585e6i	−0.553070	+	0.434692i
$667$	3.37459e6	+	1.39780e6i	0.293701	+	0.121655i
$668$	4.40689e6	+	1.00839e7i	0.382112	+	0.874352i
$669$	−5.87287e6	−	963680.i	−0.507324	−	0.0832468i
$670$	−861808.	+	4.56240e6i	−0.0741691	+	0.392651i
$671$	3.30974e6			0.283784
$672$	−6.58821e6	+	2.05168e7i	−0.562787	+	1.75262i
$673$	−1.62878e7			−1.38619			−0.693096	−	0.720845i	$-0.743754\pi$
$673$	−1.62878e7			−1.38619			−0.693096	+	0.720845i	$0.743754\pi$
$674$	1.03886e6	−	5.49970e6i	0.0880860	−	0.466326i
$675$	−9.86730e6	+	3.02505e6i	−0.833564	+	0.255548i
$676$	1.40439e6	−	613752.i	0.118201	−	0.0516567i
$677$	5.83406e6	+	2.41655e6i	0.489214	+	0.202639i	0.613634	−	0.789591i	$-0.289707\pi$
$677$	5.83406e6	+	2.41655e6i	0.489214	+	0.202639i	−0.124420	+	0.992230i	$0.539707\pi$
$678$	−2.23981e6	+	6.14868e6i	−0.187127	+	0.513697i
$679$	−9.37496e6	+	9.37496e6i	−0.780360	+	0.780360i
$680$	2.61062e6	+	3.67218e6i	0.216507	+	0.304545i
$681$	−1.45512e6	−	6.21303e6i	−0.120235	−	0.513376i
$682$	−5.39002e6	+	8.23782e6i	−0.443741	+	0.678190i
$683$	−5.35342e6	−	2.21746e6i	−0.439116	−	0.181888i	0.152162	−	0.988356i	$-0.451376\pi$
$683$	−5.35342e6	−	2.21746e6i	−0.439116	−	0.181888i	−0.591278	+	0.806468i	$0.701376\pi$
$684$	−1.49627e7	−	4.72656e6i	−1.22284	−	0.386282i
$685$	−970736.	−	2.34356e6i	−0.0790450	−	0.190832i
$686$	−1.77530e7	−	2.60218e7i	−1.44033	−	2.11119i
$687$	1.20298e7	+	7.46422e6i	0.972450	+	0.603382i
$688$	3.78697e6	−	1.74284e6i	0.305014	−	0.140374i
$689$	1.31780e7			1.05755
$690$	226830.	+	5.22748e6i	0.0181375	+	0.417994i
$691$	−9.67785e6	+	4.00870e6i	−0.771052	+	0.319380i	−0.733299	−	0.679907i	$-0.762020\pi$
$691$	−9.67785e6	+	4.00870e6i	−0.771052	+	0.319380i	−0.0377538	+	0.999287i	$0.512020\pi$
$692$	−1.65496e6	+	31963.7i	−0.131378	+	0.00253742i
$693$	2.31844e7	−	1.56541e6i	1.83385	−	0.123821i
$694$	−458847.	+	701278.i	−0.0361634	+	0.0552703i
$695$	−2.70601e6	+	2.70601e6i	−0.212504	+	0.212504i
$696$	−3.28845e6	−	1.12646e6i	−0.257317	−	0.0881440i
$697$	1.00292e7	+	1.00292e7i	0.781959	+	0.781959i
$698$	−4.12903e6	+	862843.i	−0.320782	+	0.0670337i
$699$	1.54559e7	−	1.10986e7i	1.19647	−	0.859159i
$700$	1.93723e7	+	7.58942e6i	1.49430	+	0.585414i
$701$	−3.30858e6	−	7.98763e6i	−0.254300	−	0.613936i	0.744242	−	0.667910i	$-0.232811\pi$
$701$	−3.30858e6	−	7.98763e6i	−0.254300	−	0.613936i	−0.998542	+	0.0539746i	$0.982811\pi$
$702$	−1.17047e7	−	3.39005e6i	−0.896434	−	0.259635i
$703$			1.18208e7i			0.902106i
$704$	760289.	+	1.31086e7i	0.0578158	+	0.996837i
$705$	1.64347e6	+	1.01974e6i	0.124535	+	0.0772708i
$706$	−396954.	+	2.10147e6i	−0.0299729	+	0.158676i
$707$	−1.43941e6	+	596222.i	−0.108302	+	0.0448600i
$708$	−1.50573e7	−	2.01365e7i	−1.12893	−	1.50973i
$709$	1.05030e6	−	2.53566e6i	0.0784691	−	0.189441i	−0.879777	−	0.475387i	$-0.842308\pi$
$709$	1.05030e6	−	2.53566e6i	0.0784691	−	0.189441i	0.958246	+	0.285946i	$0.0923079\pi$
$710$	−772773.	−	3.69801e6i	−0.0575315	−	0.275310i
$711$	−1.05991e7	−	3.57468e6i	−0.786316	−	0.265194i
$712$	2.06506e7	−	4.73330e6i	1.52663	−	0.349916i
$713$	9.10578e6	+	9.10578e6i	0.670801	+	0.670801i
$714$	−1.10553e7	−	2.37248e7i	−0.811568	−	1.74163i
$715$	−1.74509e6	+	4.21301e6i	−0.127659	+	0.308197i
$716$	338571.	+	1.75299e7i	0.0246812	+	1.27790i
$717$	1.07119e7	+	1.75771e6i	0.778158	+	0.127688i
$718$	−4.68512e6	−	6.86729e6i	−0.339164	−	0.497135i
$719$			1.12076e7i			0.808521i	0.914644	+	0.404260i	$0.132471\pi$
$719$			1.12076e7i			0.808521i	−0.914644	+	0.404260i	$0.867529\pi$
$720$	−527033.	−	4.95146e6i	−0.0378884	−	0.355961i
$721$			8.99375e6i			0.644321i
$722$	−7.45784e6	+	5.08801e6i	−0.532439	+	0.363250i
$723$	1.02691e7	+	1.68505e6i	0.730609	+	0.119886i
$724$	−9.80837e6	−	9.43667e6i	−0.695425	−	0.669071i
$725$	−1.28437e6	+	3.10075e6i	−0.0907498	+	0.219089i
$726$	−38267.5	+	17831.9i	−0.00269456	+	0.00125561i
$727$	−5.28359e6	−	5.28359e6i	−0.370760	−	0.370760i	0.496994	−	0.867754i	$-0.334437\pi$
$727$	−5.28359e6	−	5.28359e6i	−0.370760	−	0.370760i	−0.867754	+	0.496994i	$0.834437\pi$
$728$	1.42341e7	+	2.00221e7i	0.995406	+	1.40017i
$729$	−8.04212e6	−	1.18834e7i	−0.560469	−	0.828175i
$730$	8.28194e6	−	1.73067e6i	0.575208	−	0.120201i
$731$	−1.93776e6	+	4.67816e6i	−0.134124	+	0.323803i
$732$	−588517.	+	4.07789e6i	−0.0405958	+	0.281292i
$733$	9.64955e6	−	3.99698e6i	0.663357	−	0.274771i	−0.0254935	−	0.999675i	$-0.508116\pi$
$733$	9.64955e6	−	3.99698e6i	0.663357	−	0.274771i	0.688850	+	0.724904i	$0.258116\pi$
$734$	−2.84785e7	−	5.37940e6i	−1.95109	−	0.368548i
$735$	1.06402e7	+	6.60201e6i	0.726494	+	0.450773i
$736$	1.69881e7	+	2.53400e6i	1.15598	+	0.172429i
$737$		−	1.64359e7i		−	1.11461i
$738$	−4.23273e6	−	1.50928e7i	−0.286075	−	1.02007i
$739$	4.38276e6	+	1.05809e7i	0.295214	+	0.712709i	0.999995	+	0.00328377i	$0.00104526\pi$
$739$	4.38276e6	+	1.05809e7i	0.295214	+	0.712709i	−0.704781	+	0.709425i	$0.748955\pi$
$740$	−3.43723e6	+	1.50215e6i	−0.230743	+	0.100840i
$741$	−1.45305e7	+	1.04341e7i	−0.972155	+	0.698085i
$742$	−6.39882e6	−	3.06208e7i	−0.426668	−	2.04177i
$743$	1.14722e7	+	1.14722e7i	0.762386	+	0.762386i	0.976753	−	0.214367i	$-0.0687690\pi$
$743$	1.14722e7	+	1.14722e7i	0.762386	+	0.762386i	−0.214367	+	0.976753i	$0.568769\pi$
$744$	−9.19130e6	−	8.10577e6i	−0.608758	−	0.536861i
$745$	−5.75357e6	+	5.75357e6i	−0.379793	+	0.379793i
$746$	−6.42464e6	−	4.20365e6i	−0.422671	−	0.276554i
$747$	−50648.2	−	750121.i	−0.00332095	−	0.0491847i
$748$	−1.14934e7	−	1.10579e7i	−0.751095	−	0.722632i
$749$	5.70760e6	−	2.36417e6i	0.371749	−	0.153983i
$750$	−1.03125e7	+	447480.i	−0.669442	+	0.0290483i
$751$	−5.19828e6			−0.336326			−0.168163	−	0.985759i	$-0.553783\pi$
$751$	−5.19828e6			−0.336326			−0.168163	+	0.985759i	$0.553783\pi$
$752$	4.31276e6	−	4.65947e6i	0.278106	−	0.300463i
$753$	−2.11478e7	−	1.31217e7i	−1.35918	−	0.843340i
$754$	−3.27352e6	+	2.23331e6i	−0.209694	+	0.143061i
$755$	−1.74119e6	−	4.20362e6i	−0.111168	−	0.268383i
$756$	−2.19378e6	+	2.88436e7i	−0.139601	+	1.83546i
$757$	1.49143e6	+	617771.i	0.0945939	+	0.0391821i	0.429479	−	0.903077i	$-0.358697\pi$
$757$	1.49143e6	+	617771.i	0.0945939	+	0.0391821i	−0.334885	+	0.942259i	$0.608697\pi$
$758$	9.72729e6	+	6.36457e6i	0.614920	+	0.402343i
$759$	−4.22365e6	−	1.80340e7i	−0.266124	−	1.13629i
$760$	−6.19296e6	−	3.88337e6i	−0.388923	−	0.243879i
$761$	4.59587e6	−	4.59587e6i	0.287678	−	0.287678i	−0.548484	−	0.836161i	$-0.684795\pi$
$761$	4.59587e6	−	4.59587e6i	0.287678	−	0.287678i	0.836161	+	0.548484i	$0.184795\pi$
$762$	1.94388e7	+	7.08105e6i	1.21278	+	0.441784i
$763$	−3.65702e7	−	1.51479e7i	−2.27414	−	0.941978i
$764$	−1.71908e7	−	6.73476e6i	−1.06552	−	0.417435i
$765$	4.55518e6	+	3.97895e6i	0.281418	+	0.245819i
$766$	−1.22578e7	−	2.31543e6i	−0.754818	−	0.142580i
$767$	−2.86644e7			−1.75936
$768$	−1.62861e7	−	1.39414e6i	−0.996356	−	0.0852911i
$769$	−2.25660e6			−0.137607			−0.0688033	−	0.997630i	$-0.521918\pi$
$769$	−2.25660e6			−0.137607			−0.0688033	+	0.997630i	$0.521918\pi$
$770$	1.06369e7	+	2.00923e6i	0.646527	+	0.122125i
$771$	2.62756e7	+	4.31157e6i	1.59190	+	0.261216i
$772$	328.322	+	128.625i	1.98270e−5	+	7.76752e-6i
$773$	2.32853e7	+	9.64507e6i	1.40163	+	0.580573i	0.950173	−	0.311722i	$-0.100906\pi$
$773$	2.32853e7	+	9.64507e6i	1.40163	+	0.580573i	0.451453	+	0.892295i	$0.350906\pi$
$774$	4.39982e6	−	3.45809e6i	0.263987	−	0.207484i
$775$	−8.36687e6	+	8.36687e6i	−0.500390	+	0.500390i
$776$	−8.52038e6	−	5.34281e6i	−0.507931	−	0.318505i
$777$	2.12172e7	−	4.96918e6i	1.26077	−	0.295279i
$778$	151339.	+	99021.5i	0.00896402	+	0.00586517i
$779$	−2.12594e7	−	8.80594e6i	−1.25519	−	0.519915i
$780$	−4.88050e6	−	2.89923e6i	−0.287229	−	0.170626i
$781$	5.11771e6	+	1.23552e7i	0.300226	+	0.724810i
$782$	−1.72342e7	+	1.17578e7i	−1.00780	+	0.687558i
$783$	−4.64508e6	−	443661.i	−0.270763	−	0.0258611i
$784$	2.79218e7	−	3.01664e7i	1.62238	−	1.75281i
$785$	−5.77641e6			−0.334568
$786$	−825138.	−	1.90160e7i	−0.0476398	−	1.09790i
$787$	2.75357e7	−	1.14057e7i	1.58474	−	0.656423i	0.595588	−	0.803290i	$-0.296919\pi$
$787$	2.75357e7	−	1.14057e7i	1.58474	−	0.656423i	0.989156	+	0.146867i	$0.0469189\pi$
$788$	1.97280e7	+	1.89804e7i	1.13179	+	1.08890i
$789$	−1.10497e6	+	793455.i	−0.0631913	+	0.0453764i
$790$	−4.36039e6	−	2.85301e6i	−0.248575	−	0.162643i
$791$	1.25224e7	−	1.25224e7i	0.711617	−	0.711617i
$792$	5.08651e6	+	1.68767e7i	0.288142	+	0.956034i
$793$	3.32133e6	+	3.32133e6i	0.187555	+	0.187555i
$794$	−574384.	−	2.74864e6i	−0.0323334	−	0.154727i
$795$	4.21631e6	+	5.87164e6i	0.236600	+	0.329489i
$796$	−2.22647e7	+	9.73022e6i	−1.24548	+	0.544302i
$797$	−1.27743e6	−	3.08399e6i	−0.0712347	−	0.171976i	0.884252	−	0.467010i	$-0.154669\pi$
$797$	−1.27743e6	−	3.08399e6i	−0.0712347	−	0.171976i	−0.955487	+	0.295034i	$0.904669\pi$
$798$	3.13005e7	+	2.86971e7i	1.73998	+	1.59526i
$799$			7.71190e6i			0.427360i
$800$	−2.32837e6	+	1.56096e7i	−0.128625	+	0.862316i
$801$	2.54824e7	−	1.26290e7i	1.40333	−	0.695482i
$802$	1.05883e7	+	2.00006e6i	0.581285	+	0.109801i
$803$	−2.76704e7	+	1.14614e7i	−1.51435	+	0.627264i
$804$	2.02504e7	+	2.92252e6i	1.10483	+	0.159447i
$805$	5.41882e6	−	1.30822e7i	0.294724	−	0.711527i
$806$	−1.36756e7	+	2.85778e6i	−0.741494	+	0.154950i
$807$	−1.55096e6	−	6.62225e6i	−0.0838335	−	0.357949i
$808$	−684768.	−	963217.i	−0.0368990	−	0.0519034i
$809$	1.02672e7	+	1.02672e7i	0.551543	+	0.551543i	0.926886	−	0.375343i	$-0.122475\pi$
$809$	1.02672e7	+	1.02672e7i	0.551543	+	0.551543i	−0.375343	+	0.926886i	$0.622475\pi$
$810$	−2.23445e6	−	6.29986e6i	−0.119663	−	0.337379i
$811$	−713606.	+	1.72280e6i	−0.0380984	+	0.0919776i	−0.941783	−	0.336220i	$-0.890851\pi$
$811$	−713606.	+	1.72280e6i	−0.0380984	+	0.0919776i	0.903685	+	0.428198i	$0.140851\pi$
$812$	6.77892e6	+	6.52202e6i	0.360803	+	0.347130i
$813$	5.37904e6	−	3.27810e7i	0.285416	−	1.73939i
$814$	1.09689e7	−	7.48339e6i	0.580233	−	0.395856i
$815$		−	5.03925e6i		−	0.265749i
$816$	1.56679e7	−	1.21947e7i	0.823733	−	0.641127i
$817$		−	8.21514e6i		−	0.430586i
$818$	−8.34118e6	−	1.22262e7i	−0.435857	−	0.638865i
$819$	2.48365e7	+	2.16947e7i	1.29384	+	1.13017i
$820$	−141007.	−	7.30082e6i	−0.00732329	−	0.379173i
$821$	−3.87720e6	+	9.36038e6i	−0.200752	+	0.484658i	−0.991908	−	0.126956i	$-0.959479\pi$
$821$	−3.87720e6	+	9.36038e6i	−0.200752	+	0.484658i	0.791156	+	0.611614i	$0.209479\pi$
$822$	−1.01320e7	+	4.72132e6i	−0.523018	+	0.243716i
$823$	1.87095e7	+	1.87095e7i	0.962859	+	0.962859i	0.999335	−	0.0364752i	$-0.0116130\pi$
$823$	1.87095e7	+	1.87095e7i	0.962859	+	0.962859i	−0.0364752	+	0.999335i	$0.511613\pi$
$824$	−6.64974e6	+	1.52418e6i	−0.341182	+	0.0782020i
$825$	1.65706e7	−	3.88091e6i	0.847623	−	0.198517i
$826$	1.39186e7	+	6.66056e7i	0.709813	+	3.39673i
$827$	4.64811e6	−	1.12215e7i	0.236326	−	0.570542i	−0.760571	−	0.649255i	$-0.775081\pi$
$827$	4.64811e6	−	1.12215e7i	0.236326	−	0.570542i	0.996897	+	0.0787124i	$0.0250809\pi$
$828$	2.29705e7	−	1.99722e6i	1.16438	−	0.101240i
$829$	−3.25191e7	+	1.34699e7i	−1.64343	+	0.680732i	−0.996638	−	0.0819309i	$-0.973891\pi$
$829$	−3.25191e7	+	1.34699e7i	−1.64343	+	0.680732i	−0.646796	+	0.762663i	$0.723891\pi$
$830$	65007.9	−	344151.i	0.00327545	−	0.0173402i
$831$	8.53444e6	−	1.37547e7i	0.428719	−	0.690951i
$832$	−1.23915e7	+	1.39174e7i	−0.620608	+	0.697030i
$833$			4.99286e7i			2.49308i
$834$	1.24301e7	+	1.13962e7i	0.618811	+	0.567341i
$835$	2.63357e6	+	6.35800e6i	0.130716	+	0.315576i
$836$	2.40928e7	+	9.43873e6i	1.19226	+	0.467087i
$837$	−1.45313e7	−	7.71209e6i	−0.716954	−	0.380503i
$838$	−9.86327e6	+	2.06112e6i	−0.485189	+	0.101390i
$839$	7.78914e6	+	7.78914e6i	0.382019	+	0.382019i	0.871829	−	0.489810i	$-0.162934\pi$
$839$	7.78914e6	+	7.78914e6i	0.382019	+	0.382019i	−0.489810	+	0.871829i	$0.662934\pi$
$840$	−4.36693e6	+	1.27483e7i	−0.213539	+	0.623380i
$841$	1.34306e7	−	1.34306e7i	0.654794	−	0.654794i
$842$	−1.49775e7	+	2.28908e7i	−0.728046	+	1.11271i
$843$	−1.45134e7	−	2.02113e7i	−0.703395	−	0.979549i
$844$	1.45030e7	−	280110.i	0.700815	−	0.0135354i
$845$	885485.	−	366780.i	0.0426618	−	0.0176711i
$846$	4.17540e6	−	7.43014e6i	0.200573	−	0.356920i
$847$	114252.			0.00547212
$848$	2.15558e7	−	9.92045e6i	1.02938	−	0.473742i
$849$	1.59817e6	−	2.57572e6i	0.0760948	−	0.122639i
$850$	−1.08037e7	−	1.58357e7i	−0.512890	−	0.751778i
$851$	−6.64703e6	−	1.60473e7i	−0.314632	−	0.759590i
$852$	−1.61327e7	+	4.10854e6i	−0.761394	+	0.193905i
$853$	3.08620e7	+	1.27834e7i	1.45228	+	0.601555i	0.962741	−	0.270425i	$-0.0871643\pi$
$853$	3.08620e7	+	1.27834e7i	1.45228	+	0.601555i	0.489541	+	0.871980i	$0.337164\pi$
$854$	6.10482e6	−	9.33030e6i	0.286436	−	0.437775i
$855$	−9.29810e6	−	3.13589e6i	−0.434990	−	0.146705i
$856$	2.71528e6	+	3.81939e6i	0.126657	+	0.178160i
$857$	−1.96691e6	+	1.96691e6i	−0.0914814	+	0.0914814i	−0.751367	−	0.659885i	$-0.770605\pi$
$857$	−1.96691e6	+	1.96691e6i	−0.0914814	+	0.0914814i	0.659885	+	0.751367i	$0.270605\pi$
$858$	1.88810e7	+	6.87787e6i	0.875602	+	0.318960i
$859$	−4.56584e6	−	1.89123e6i	−0.211124	−	0.0874504i	0.274615	−	0.961554i	$-0.411450\pi$
$859$	−4.56584e6	−	1.89123e6i	−0.211124	−	0.0874504i	−0.485739	+	0.874104i	$0.661450\pi$
$860$	2.38879e6	−	1.04396e6i	0.110136	−	0.0481322i
$861$	−6.86890e6	+	4.18606e7i	−0.315776	+	1.92441i
$862$	2.05157e6	−	1.08610e7i	0.0940410	−	0.497852i
$863$	−3.84318e7			−1.75656			−0.878282	−	0.478143i	$-0.841310\pi$
$863$	−3.84318e7			−1.75656			−0.878282	+	0.478143i	$0.841310\pi$
$864$	−2.16980e7	+	3.26613e6i	−0.988860	+	0.148850i
$865$	−1.03513e6			−0.0470384
$866$	3.17133e6	−	1.67890e7i	0.143697	−	0.760728i
$867$	−321050.	+	1.95655e6i	−0.0145052	+	0.0883980i
$868$	1.32809e7	+	3.03894e7i	0.598311	+	1.36906i
$869$	1.70415e7	+	7.05882e6i	0.765524	+	0.317090i
$870$	−2.04245e6	−	744012.i	−0.0914856	−	0.0333259i
$871$	1.64934e7	−	1.64934e7i	0.736657	−	0.736657i
$872$	5.00236e6	−	2.96062e7i	0.222784	−	1.31853i
$873$	−1.27925e7	−	4.31441e6i	−0.568093	−	0.191596i
$874$	1.85323e7	−	2.83237e7i	0.820634	−	1.25422i
$875$	2.58080e7	+	1.06900e7i	1.13955	+	0.472018i
$876$	−9.20134e6	−	3.61303e7i	−0.405126	−	1.59079i
$877$	−2.76064e6	−	6.66478e6i	−0.121202	−	0.292608i	0.851621	−	0.524159i	$-0.175620\pi$
$877$	−2.76064e6	−	6.66478e6i	−0.121202	−	0.292608i	−0.972823	+	0.231550i	$0.925620\pi$
$878$	−513109.	−	752098.i	−0.0224633	−	0.0329260i
$879$	−1.39346e7	+	2.24579e7i	−0.608307	+	0.980387i
$880$	317063.	+	8.20512e6i	0.0138019	+	0.357173i
$881$	−780159.			−0.0338644			−0.0169322	−	0.999857i	$-0.505390\pi$
$881$	−780159.			−0.0338644			−0.0169322	+	0.999857i	$0.505390\pi$
$882$	2.70325e7	−	4.81044e7i	1.17008	−	2.08216i
$883$	−4.03465e7	+	1.67121e7i	−1.74142	+	0.721321i	−0.742763	+	0.669555i	$0.766485\pi$
$883$	−4.03465e7	+	1.67121e7i	−1.74142	+	0.721321i	−0.998659	+	0.0517659i	$0.983515\pi$
$884$	−437078.	−	2.26303e7i	−0.0188117	−	0.974000i
$885$	−9.17120e6	−	1.27718e7i	−0.393612	−	0.548145i
$886$	−1.65305e7	+	2.52643e7i	−0.707459	+	1.08124i
$887$	−7.36115e6	+	7.36115e6i	−0.314150	+	0.314150i	−0.846515	−	0.532365i	$-0.821303\pi$
$887$	−7.36115e6	+	7.36115e6i	−0.314150	+	0.314150i	0.532365	+	0.846515i	$0.321303\pi$
$888$	7.26978e6	+	1.48453e7i	0.309377	+	0.631767i
$889$	−3.95890e7	−	3.95890e7i	−1.68004	−	1.68004i
$890$	1.29686e7	−	2.71005e6i	0.548806	−	0.114684i
$891$	1.19115e7	+	2.04450e7i	0.502656	+	0.862766i
$892$	−4.45644e6	+	1.13753e7i	−0.187532	+	0.478685i
$893$	−4.78802e6	−	1.15593e7i	−0.200922	−	0.485069i
$894$	2.64290e7	+	2.42308e7i	1.10595	+	1.01397i
$895$			1.09644e7i			0.457538i
$896$	3.83560e7	+	2.20355e7i	1.59611	+	0.916966i
$897$	1.38587e7	−	2.23356e7i	0.575098	−	0.926865i
$898$	−5.62141e6	+	2.97597e7i	−0.232624	+	1.23151i
$899$	−4.94259e6	+	2.04729e6i	−0.203965	+	0.0844849i
$900$	1.83515e6	+	2.11065e7i	0.0755206	+	0.868579i
$901$	−1.10299e7	+	2.66285e7i	−0.452647	+	1.09279i
$902$	5.28739e6	+	2.53022e7i	0.216384	+	1.03548i
$903$	−1.47454e7	+	3.45345e6i	−0.601780	+	0.140940i
$904$	1.13809e7	+	7.13655e6i	0.463187	+	0.290447i
$905$	−6.01857e6	−	6.01857e6i	−0.244271	−	0.244271i
$906$	−1.81736e7	+	8.46857e6i	−0.735566	+	0.342760i
$907$	−4.69550e6	+	1.13359e7i	−0.189524	+	0.457550i	−0.989868	−	0.141990i	$-0.954650\pi$
$907$	−4.69550e6	+	1.13359e7i	−0.189524	+	0.457550i	0.800345	+	0.599540i	$0.204650\pi$
$908$	−1.30968e7	+	252950.i	−0.527170	+	0.0101817i
$909$	−1.19483e6	−	1.04368e6i	−0.0479618	−	0.0418947i
$910$	8.65784e6	+	1.26904e7i	0.346582	+	0.508009i
$911$		−	1.20997e7i		−	0.483037i	−0.970396	−	0.241518i	$-0.922355\pi$
$911$		−	1.20997e7i		−	0.483037i	0.970396	−	0.241518i	$-0.0776454\pi$
$912$	−1.59134e7	+	2.80061e7i	−0.633542	+	1.11498i
$913$			1.23979e6i			0.0492234i
$914$	−5.26288e6	+	3.59053e6i	−0.208381	+	0.142165i
$915$	−417204.	+	2.54253e6i	−0.0164739	+	0.100395i
$916$	2.01495e7	−	2.09431e7i	0.793460	−	0.824713i
$917$	−1.97120e7	+	4.75891e7i	−0.774120	+	1.86889i
$918$	1.66470e7	−	2.08141e7i	0.651973	−	0.815175i
$919$	2.26697e7	+	2.26697e7i	0.885435	+	0.885435i	0.994081	−	0.108646i	$-0.0346515\pi$
$919$	2.26697e7	+	2.26697e7i	0.885435	+	0.885435i	−0.108646	+	0.994081i	$0.534651\pi$
$920$	1.05910e7	+	1.78948e6i	0.412540	+	0.0697041i
$921$	−2.68999e6	−	1.14856e7i	−0.104496	−	0.446175i
$922$	−3.58827e6	+	749840.i	−0.139014	+	0.0290497i
$923$	−7.26288e6	+	1.75342e7i	−0.280611	+	0.677455i
$924$	6.81362e6	−	4.72122e7i	0.262541	−	1.81918i
$925$	1.47451e7	−	6.10764e6i	0.566623	−	0.234703i
$926$	2.12078e7	+	4.00601e6i	0.812769	+	0.153527i
$927$	−8.20565e6	+	4.06667e6i	−0.313627	+	0.155432i
$928$	−3.67338e6	+	6.11744e6i	−0.140022	+	0.233185i
$929$		−	3.83298e7i		−	1.45712i	−0.684979	−	0.728562i	$-0.740189\pi$
$929$		−	3.83298e7i		−	1.45712i	0.684979	−	0.728562i	$-0.259811\pi$
$930$	−5.64883e6	−	5.17900e6i	−0.214166	−	0.196353i
$931$	−3.09988e7	−	7.48376e7i	−1.17211	−	2.82973i
$932$	−1.56419e7	−	3.57919e7i	−0.589861	−	1.34972i
$933$	−2.44051e7	−	3.39866e7i	−0.917861	−	1.27822i
$934$	−8.23659e6	−	3.94152e7i	−0.308944	−	1.47842i
$935$	−7.05254e6	−	7.05254e6i	−0.263826	−	0.263826i
$936$	−1.18314e7	+	2.20401e7i	−0.441416	+	0.822287i
$937$	1.35550e7	−	1.35550e7i	0.504373	−	0.504373i	−0.408421	−	0.912794i	$-0.633920\pi$
$937$	1.35550e7	−	1.35550e7i	0.504373	−	0.504373i	0.912794	+	0.408421i	$0.133920\pi$
$938$	−4.63334e7	−	3.03160e7i	−1.71944	−	1.12503i
$939$	1.80875e7	−	1.29883e7i	0.669445	−	0.480715i
$940$	2.75275e6	−	2.86118e6i	0.101613	−	0.105615i
$941$	−6.91126e6	+	2.86274e6i	−0.254439	+	0.105392i	−0.506257	−	0.862383i	$-0.668971\pi$
$941$	−6.91126e6	+	2.86274e6i	−0.254439	+	0.105392i	0.251819	+	0.967774i	$0.418971\pi$
$942$	1.10347e6	+	2.54305e7i	0.0405167	+	0.933742i
$943$	3.38126e7			1.23822
$944$	−4.68876e7	+	2.15787e7i	−1.71249	+	0.788126i
$945$	−1.71993e6	+	1.80075e7i	−0.0626515	+	0.655955i
$946$	−7.62312e6	+	5.20077e6i	−0.276952	+	0.188947i
$947$	−9.75213e6	−	2.35437e7i	−0.353366	−	0.853100i	−0.996200	−	0.0870951i	$-0.972242\pi$
$947$	−9.75213e6	−	2.35437e7i	−0.353366	−	0.853100i	0.642834	−	0.766005i	$-0.277758\pi$
$948$	−1.17273e7	+	1.97415e7i	−0.423816	+	0.713442i
$949$	−3.92689e7	−	1.62657e7i	−1.41541	−	0.586283i
$950$	2.60253e7	+	1.70284e7i	0.935594	+	0.612160i
$951$	−1.29864e7	+	3.04147e6i	−0.465625	+	0.109052i
$952$	−5.23722e7	+	1.20042e7i	−1.87287	+	0.429279i
$953$	1.25256e7	−	1.25256e7i	0.446752	−	0.446752i	−0.447521	−	0.894273i	$-0.647693\pi$
$953$	1.25256e7	−	1.25256e7i	0.446752	−	0.446752i	0.894273	+	0.447521i	$0.147693\pi$
$954$	2.50442e7	−	1.96838e7i	0.890916	−	0.700226i
$955$	−1.06670e7	−	4.41840e6i	−0.378470	−	0.156768i
$956$	8.12837e6	−	2.07480e7i	0.287646	−	0.734230i
$957$	7.59320e6	+	1.24597e6i	0.268006	+	0.0439772i
$958$	−2.82769e7	−	5.34133e6i	−0.995447	−	0.188034i
$959$	3.02503e7			1.06214
$960$	−1.01658e7	−	1.06833e6i	−0.356011	−	0.0374135i
$961$	9.76809e6			0.341194
$962$	1.85169e7	+	3.49773e6i	0.645106	+	0.121856i
$963$	4.73779e6	+	4.13846e6i	0.164630	+	0.143805i
$964$	7.79235e6	−	1.98903e7i	0.270070	−	0.689366i
$965$	203.725	+	84.3855i	7.04248e−6	+	2.91709e-6i
$966$	−5.86291e7	−	2.13571e7i	−2.02148	−	0.736375i
$967$	2.74100e7	−	2.74100e7i	0.942633	−	0.942633i	−0.0558085	−	0.998441i	$-0.517774\pi$
$967$	2.74100e7	−	2.74100e7i	0.942633	−	0.942633i	0.998441	+	0.0558085i	$0.0177736\pi$
$968$	19362.4	+	84474.9i	0.000664157	+	0.00289761i
$969$	−8.92201e6	−	3.80949e7i	−0.305248	−	1.30334i
$970$	−5.26271e6	−	3.44340e6i	−0.179589	−	0.117505i
$971$	4.28562e7	+	1.77516e7i	1.45870	+	0.604213i	0.964250	−	0.264993i	$-0.0853696\pi$
$971$	4.28562e7	+	1.77516e7i	1.45870	+	0.604213i	0.494450	+	0.869206i	$0.335370\pi$
$972$	−2.73080e7	+	1.10406e7i	−0.927097	+	0.374822i
$973$	−1.74644e7	−	4.21627e7i	−0.591386	−	1.42773i
$974$	1.67986e7	−	1.14606e7i	0.567381	−	0.387088i
$975$	2.05231e7	+	1.27341e7i	0.691403	+	0.429000i
$976$	7.93316e6	+	2.93253e6i	0.266576	+	0.0985412i
$977$	−5.33300e7			−1.78745			−0.893727	−	0.448611i	$-0.851919\pi$
$977$	−5.33300e7			−1.78745			−0.893727	+	0.448611i	$0.851919\pi$
$978$	−2.21851e7	+	962652.i	−0.741677	+	0.0321827i
$979$	−4.33288e7	+	1.79474e7i	−1.44484	+	0.598473i
$980$	1.78219e7	−	1.85239e7i	0.592775	−	0.616123i
$981$	−2.71532e6	−	4.02151e7i	−0.0900842	−	1.33419i
$982$	1.32189e7	+	8.64916e6i	0.437439	+	0.286217i
$983$	3.86757e7	−	3.86757e7i	1.27660	−	1.27660i	0.334042	−	0.942558i	$-0.391587\pi$
$983$	3.86757e7	−	3.86757e7i	1.27660	−	1.27660i	0.942558	−	0.334042i	$-0.108413\pi$
$984$	−3.21147e7	+	2.01546e6i	−1.05734	+	0.0663569i
$985$	1.21054e7	+	1.21054e7i	0.397547	+	0.397547i
$986$	−1.77290e6	−	8.48402e6i	−0.0580755	−	0.277913i
$987$	−1.87351e7	+	1.34533e7i	−0.612159	+	0.439579i
$988$	1.47054e7	+	3.36490e7i	0.479275	+	1.09668i
$989$	4.61952e6	+	1.11525e7i	0.150178	+	0.362561i
$990$	2.97646e6	+	1.06133e7i	0.0965189	+	0.344161i
$991$		−	1.90287e7i		−	0.615495i	−0.951468	−	0.307747i	$-0.900425\pi$
$991$		−	1.90287e7i		−	0.615495i	0.951468	−	0.307747i	$-0.0995752\pi$
$992$	−2.02184e7	+	1.49696e7i	−0.652329	+	0.482983i
$993$	−2.18856e6	−	1.35795e6i	−0.0704345	−	0.0437030i
$994$	4.42696e7	+	8.36224e6i	1.42115	+	0.268446i
$995$	−1.40382e7	+	5.81481e6i	−0.449524	+	0.186199i
$996$	−1.52753e6	−	220451.i	−0.0487912	−	0.00704149i
$997$	−1.04269e7	+	2.51728e7i	−0.332214	+	0.802035i	0.666202	+	0.745771i	$0.267919\pi$
$997$	−1.04269e7	+	2.51728e7i	−0.332214	+	0.802035i	−0.998416	+	0.0562636i	$0.982081\pi$
$998$	5.02758e6	−	1.05061e6i	0.159784	−	0.0333900i
$999$	1.41275e7	+	1.71111e7i	0.447868	+	0.542456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.6.o.a.11.5	✓	312
3.2	odd	2	inner	96.6.o.a.11.74	yes	312
32.3	odd	8	inner	96.6.o.a.35.74	yes	312
96.35	even	8	inner	96.6.o.a.35.5	yes	312

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.6.o.a.11.5	✓	312	1.1	even	1	trivial
96.6.o.a.11.74	yes	312	3.2	odd	2	inner
96.6.o.a.35.5	yes	312	96.35	even	8	inner
96.6.o.a.35.74	yes	312	32.3	odd	8	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:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	96.o (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.55856 - 1.04998i) q^{2} +(-2.52416 + 15.3827i) q^{3} +(29.7951 + 11.6727i) q^{4} +(18.4880 + 7.65797i) q^{5} +(30.1822 - 82.8555i) q^{6} +(-168.744 + 168.744i) q^{7} +(-153.362 - 96.1675i) q^{8} +(-230.257 - 77.6568i) q^{9} +(-94.7257 - 61.9791i) q^{10} +(370.212 + 153.347i) q^{11} +(-254.765 + 428.867i) q^{12} +(217.625 + 525.392i) q^{13} +(1115.15 - 760.794i) q^{14} +(-164.467 + 265.066i) q^{15} +(751.496 + 695.578i) q^{16} -1243.80 q^{17} +(1198.36 + 673.424i) q^{18} +(1864.33 - 772.230i) q^{19} +(461.462 + 443.974i) q^{20} +(-2169.80 - 3021.67i) q^{21} +(-1896.83 - 1241.10i) q^{22} +(-2096.69 + 2096.69i) q^{23} +(1866.43 - 2116.38i) q^{24} +(-1926.55 - 1926.55i) q^{25} +(-658.030 - 3148.92i) q^{26} +(1775.78 - 3345.97i) q^{27} +(-6997.43 + 3058.04i) q^{28} +(-471.407 - 1138.08i) q^{29} +(1192.51 - 1300.70i) q^{30} -4342.93i q^{31} +(-3446.90 - 4655.46i) q^{32} +(-3293.37 + 5307.80i) q^{33} +(6913.75 + 1305.96i) q^{34} +(-4411.96 + 1827.49i) q^{35} +(-5954.07 - 5001.52i) q^{36} +(-2241.70 + 5411.95i) q^{37} +(-11173.8 + 2334.99i) q^{38} +(-8631.29 + 2021.49i) q^{39} +(-2098.90 - 2952.38i) q^{40} +(-8063.32 - 8063.32i) q^{41} +(8888.30 + 19074.4i) q^{42} +(1557.93 - 3761.17i) q^{43} +(9240.54 + 8890.36i) q^{44} +(-3662.29 - 3199.02i) q^{45} +(13856.0 - 9453.10i) q^{46} -6200.25i q^{47} +(-12596.8 + 9804.32i) q^{48} -40141.8i q^{49} +(8686.00 + 12731.7i) q^{50} +(3139.55 - 19133.1i) q^{51} +(351.404 + 18194.4i) q^{52} +(8867.88 - 21409.0i) q^{53} +(-13384.0 + 16734.2i) q^{54} +(5670.14 + 5670.14i) q^{55} +(42106.5 - 9651.17i) q^{56} +(7173.16 + 30627.7i) q^{57} +(1425.39 + 6821.03i) q^{58} +(-19289.2 + 46568.2i) q^{59} +(-7994.34 + 5977.88i) q^{60} +(7630.87 - 3160.81i) q^{61} +(-4559.97 + 24140.4i) q^{62} +(51958.6 - 25750.4i) q^{63} +(14271.6 + 29496.8i) q^{64} +11380.0i q^{65} +(23879.4 - 26045.8i) q^{66} +(-15696.3 - 37894.2i) q^{67} +(-37059.3 - 14518.5i) q^{68} +(-26960.5 - 37545.2i) q^{69} +(26442.9 - 5525.78i) q^{70} +(23598.6 + 23598.6i) q^{71} +(27844.6 + 34052.8i) q^{72} +(-52850.5 + 52850.5i) q^{73} +(18143.1 - 27728.9i) q^{74} +(34498.5 - 24772.7i) q^{75} +(64561.9 - 1246.94i) q^{76} +(-88347.2 + 36594.6i) q^{77} +(50100.1 - 2173.93i) q^{78} +46031.8 q^{79} +(8566.92 + 18614.8i) q^{80} +(46987.8 + 35762.1i) q^{81} +(36354.1 + 53286.7i) q^{82} +(1184.00 + 2858.44i) q^{83} +(-29378.5 - 115359. i) q^{84} +(-22995.4 - 9525.01i) q^{85} +(-12609.0 + 19270.9i) q^{86} +(18696.6 - 4378.84i) q^{87} +(-42029.4 - 59119.9i) q^{88} +(-82758.3 + 82758.3i) q^{89} +(16998.2 + 21627.2i) q^{90} +(-125379. - 51933.9i) q^{91} +(-86945.1 + 37997.1i) q^{92} +(66806.2 + 10962.2i) q^{93} +(-6510.11 + 34464.5i) q^{94} +40381.4 q^{95} +(80314.3 - 41271.6i) q^{96} +55557.4 q^{97} +(-42147.9 + 223131. i) q^{98} +(-73335.6 - 64058.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 312 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9} + 192 q^{10} - 4 q^{12} - 8 q^{13} - 8 q^{15} - 6696 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} + 5576 q^{22} - 11024 q^{24} - 8 q^{25} + 7460 q^{27}+ \cdots + 339516 q^{99}+O(q^{100}) \) 312 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 4 * q^9 + 192 * q^10 - 4 * q^12 - 8 * q^13 - 8 * q^15 - 6696 * q^16 - 4 * q^18 - 8 * q^19 - 4 * q^21 + 5576 * q^22 - 11024 * q^24 - 8 * q^25 + 7460 * q^27 - 8 * q^28 + 32564 * q^30 - 8 * q^33 - 264 * q^34 + 3264 * q^36 - 8 * q^37 + 44900 * q^39 - 60136 * q^40 - 7264 * q^42 - 8 * q^43 - 4 * q^45 + 63320 * q^46 + 112368 * q^48 - 976 * q^51 - 55024 * q^52 - 115328 * q^54 - 110056 * q^55 - 4 * q^57 - 123568 * q^58 + 44648 * q^60 - 96168 * q^61 + 187432 * q^64 + 17564 * q^66 + 97848 * q^67 - 4 * q^69 - 143480 * q^70 + 179936 * q^72 - 8 * q^73 + 12496 * q^75 - 234928 * q^76 - 708428 * q^78 + 355344 * q^79 + 251552 * q^82 + 387560 * q^84 - 25008 * q^85 - 282188 * q^87 + 111632 * q^88 + 453536 * q^90 + 200104 * q^91 + 968 * q^93 - 671008 * q^94 - 911336 * q^96 - 16 * q^97 + 339516 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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