LMFDB - Embedded newform 75.5.c.h.26.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [75,5,Mod(26,75)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(75, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("75.26"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	75.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.75274723129$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-10}, \sqrt{26})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 8x^{2} + 81 $ x^4 - 8*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			26.3
Root			$-2.54951 + 1.58114i$ of defining polynomial
Character	$\chi$	$=$	75.26
Dual form			75.5.c.h.26.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.16228i q^{2} +(-7.64853 - 4.74342i) q^{3} +6.00000 q^{4} +(15.0000 - 24.1868i) q^{6} -15.2971 q^{7} +69.5701i q^{8} +(36.0000 + 72.5603i) q^{9} +96.7471i q^{11} +(-45.8912 - 28.4605i) q^{12} -244.753 q^{13} -48.3735i q^{14} -124.000 q^{16} +278.280i q^{17} +(-229.456 + 113.842i) q^{18} -308.000 q^{19} +(117.000 + 72.5603i) q^{21} -305.941 q^{22} +414.258i q^{23} +(330.000 - 532.109i) q^{24} -773.977i q^{26} +(68.8368 - 725.743i) q^{27} -91.7824 q^{28} +193.494i q^{29} +32.0000 q^{31} +720.999i q^{32} +(458.912 - 739.973i) q^{33} -880.000 q^{34} +(216.000 + 435.362i) q^{36} +1284.95 q^{37} -973.982i q^{38} +(1872.00 + 1160.97i) q^{39} +2080.06i q^{41} +(-229.456 + 369.986i) q^{42} +2585.20 q^{43} +580.483i q^{44} -1310.00 q^{46} -2444.44i q^{47} +(948.418 + 588.184i) q^{48} -2167.00 q^{49} +(1320.00 - 2128.44i) q^{51} -1468.52 q^{52} -1416.70i q^{53} +(2295.00 + 217.681i) q^{54} -1064.22i q^{56} +(2355.75 + 1460.97i) q^{57} -611.882 q^{58} -3966.63i q^{59} -928.000 q^{61} +101.193i q^{62} +(-550.694 - 1109.96i) q^{63} -4264.00 q^{64} +(2340.00 + 1451.21i) q^{66} +2585.20 q^{67} +1669.68i q^{68} +(1965.00 - 3168.47i) q^{69} -4643.86i q^{71} +(-5048.03 + 2504.52i) q^{72} -4221.99 q^{73} +4063.38i q^{74} -1848.00 q^{76} -1479.95i q^{77} +(-3671.29 + 5919.78i) q^{78} -8.00000 q^{79} +(-3969.00 + 5224.34i) q^{81} -6577.74 q^{82} +4436.68i q^{83} +(702.000 + 435.362i) q^{84} +8175.13i q^{86} +(917.824 - 1479.95i) q^{87} -6730.71 q^{88} +9287.72i q^{89} +3744.00 q^{91} +2485.55i q^{92} +(-244.753 - 151.789i) q^{93} +7730.00 q^{94} +(3420.00 - 5514.58i) q^{96} +2508.72 q^{97} -6852.66i q^{98} +(-7020.00 + 3482.90i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 24 q^{4} + 60 q^{6} + 144 q^{9} - 496 q^{16} - 1232 q^{19} + 468 q^{21} + 1320 q^{24} + 128 q^{31} - 3520 q^{34} + 864 q^{36} + 7488 q^{39} - 5240 q^{46} - 8668 q^{49} + 5280 q^{51} + 9180 q^{54}+ \cdots - 28080 q^{99}+O(q^{100}) $ 4 * q + 24 * q^4 + 60 * q^6 + 144 * q^9 - 496 * q^16 - 1232 * q^19 + 468 * q^21 + 1320 * q^24 + 128 * q^31 - 3520 * q^34 + 864 * q^36 + 7488 * q^39 - 5240 * q^46 - 8668 * q^49 + 5280 * q^51 + 9180 * q^54 - 3712 * q^61 - 17056 * q^64 + 9360 * q^66 + 7860 * q^69 - 7392 * q^76 - 32 * q^79 - 15876 * q^81 + 2808 * q^84 + 14976 * q^91 + 30920 * q^94 + 13680 * q^96 - 28080 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$1$

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 $

$2$			3.16228i			0.790569i	0.918559	+	0.395285i	$0.129354\pi$
$2$			3.16228i			0.790569i	−0.918559	+	0.395285i	$0.870646\pi$
$3$	−7.64853	−	4.74342i	−0.849837	−	0.527046i
$3$	−7.64853	−	4.74342i	−0.849837	−	0.527046i
$4$	6.00000			0.375000
$5$		0			0
$5$		0			0
$6$	15.0000	−	24.1868i	0.416667	−	0.671855i
$7$	−15.2971			−0.312185			−0.156092	−	0.987742i	$-0.549890\pi$
$7$	−15.2971			−0.312185			−0.156092	+	0.987742i	$0.549890\pi$
$8$			69.5701i			1.08703i
$9$	36.0000	+	72.5603i	0.444444	+	0.895806i
$10$		0			0
$11$			96.7471i			0.799563i	0.916611	+	0.399781i	$0.130914\pi$
$11$			96.7471i			0.799563i	−0.916611	+	0.399781i	$0.869086\pi$
$12$	−45.8912	−	28.4605i	−0.318689	−	0.197642i
$13$	−244.753			−1.44824			−0.724121	−	0.689673i	$-0.757754\pi$
$13$	−244.753			−1.44824			−0.724121	+	0.689673i	$0.757754\pi$
$14$		−	48.3735i		−	0.246804i
$15$		0			0
$16$	−124.000			−0.484375
$17$			278.280i			0.962908i	0.876471	+	0.481454i	$0.159891\pi$
$17$			278.280i			0.962908i	−0.876471	+	0.481454i	$0.840109\pi$
$18$	−229.456	+	113.842i	−0.708197	+	0.351364i
$19$	−308.000			−0.853186			−0.426593	−	0.904444i	$-0.640286\pi$
$19$	−308.000			−0.853186			−0.426593	+	0.904444i	$0.640286\pi$
$20$		0			0
$21$	117.000	+	72.5603i	0.265306	+	0.164536i
$22$	−305.941			−0.632110
$23$			414.258i			0.783097i	0.920157	+	0.391549i	$0.128060\pi$
$23$			414.258i			0.783097i	−0.920157	+	0.391549i	$0.871940\pi$
$24$	330.000	−	532.109i	0.572917	−	0.923800i
$25$		0			0
$26$		−	773.977i		−	1.14494i
$27$	68.8368	−	725.743i	0.0944263	−	0.995532i
$28$	−91.7824			−0.117069
$29$			193.494i			0.230076i	0.993361	+	0.115038i	$0.0366990\pi$
$29$			193.494i			0.230076i	−0.993361	+	0.115038i	$0.963301\pi$
$30$		0			0
$31$	32.0000			0.0332986			0.0166493	−	0.999861i	$-0.494700\pi$
$31$	32.0000			0.0332986			0.0166493	+	0.999861i	$0.494700\pi$
$32$			720.999i			0.704101i
$33$	458.912	−	739.973i	0.421407	−	0.679498i
$34$	−880.000			−0.761246
$35$		0			0
$36$	216.000	+	435.362i	0.166667	+	0.335927i
$37$	1284.95			0.938607			0.469303	−	0.883037i	$-0.344505\pi$
$37$	1284.95			0.938607			0.469303	+	0.883037i	$0.344505\pi$
$38$		−	973.982i		−	0.674502i
$39$	1872.00	+	1160.97i	1.23077	+	0.763291i
$40$		0			0
$41$			2080.06i			1.23740i	0.785629	+	0.618698i	$0.212340\pi$
$41$			2080.06i			1.23740i	−0.785629	+	0.618698i	$0.787660\pi$
$42$	−229.456	+	369.986i	−0.130077	+	0.209743i
$43$	2585.20			1.39816			0.699081	−	0.715042i	$-0.253593\pi$
$43$	2585.20			1.39816			0.699081	+	0.715042i	$0.253593\pi$
$44$			580.483i			0.299836i
$45$		0			0
$46$	−1310.00			−0.619093
$47$		−	2444.44i		−	1.10658i	−0.832988	−	0.553291i	$-0.813372\pi$
$47$		−	2444.44i		−	1.10658i	0.832988	−	0.553291i	$-0.186628\pi$
$48$	948.418	+	588.184i	0.411640	+	0.255288i
$49$	−2167.00			−0.902541
$50$		0			0
$51$	1320.00	−	2128.44i	0.507497	−	0.818315i
$52$	−1468.52			−0.543091
$53$		−	1416.70i		−	0.504343i	−0.967683	−	0.252172i	$-0.918855\pi$
$53$		−	1416.70i		−	0.504343i	0.967683	−	0.252172i	$-0.0811448\pi$
$54$	2295.00	+	217.681i	0.787037	+	0.0746505i
$55$		0			0
$56$		−	1064.22i		−	0.339355i
$57$	2355.75	+	1460.97i	0.725068	+	0.449668i
$58$	−611.882			−0.181891
$59$		−	3966.63i		−	1.13951i	−0.821815	−	0.569754i	$-0.807038\pi$
$59$		−	3966.63i		−	1.13951i	0.821815	−	0.569754i	$-0.192962\pi$
$60$		0			0
$61$	−928.000			−0.249395			−0.124698	−	0.992195i	$-0.539796\pi$
$61$	−928.000			−0.249395			−0.124698	+	0.992195i	$0.539796\pi$
$62$			101.193i			0.0263249i
$63$	−550.694	−	1109.96i	−0.138749	−	0.279657i
$64$	−4264.00			−1.04102
$65$		0			0
$66$	2340.00	+	1451.21i	0.537190	+	0.333151i
$67$	2585.20			0.575897			0.287949	−	0.957646i	$-0.407027\pi$
$67$	2585.20			0.575897			0.287949	+	0.957646i	$0.407027\pi$
$68$			1669.68i			0.361091i
$69$	1965.00	−	3168.47i	0.412728	−	0.665505i
$70$		0			0
$71$		−	4643.86i		−	0.921218i	−0.887603	−	0.460609i	$-0.847631\pi$
$71$		−	4643.86i		−	0.921218i	0.887603	−	0.460609i	$-0.152369\pi$
$72$	−5048.03	+	2504.52i	−0.973771	+	0.483126i
$73$	−4221.99			−0.792266			−0.396133	−	0.918193i	$-0.629648\pi$
$73$	−4221.99			−0.792266			−0.396133	+	0.918193i	$0.629648\pi$
$74$			4063.38i			0.742034i
$75$		0			0
$76$	−1848.00			−0.319945
$77$		−	1479.95i		−	0.249611i
$78$	−3671.29	+	5919.78i	−0.603434	+	0.973009i
$79$	−8.00000			−0.00128185			−0.000640923	−	1.00000i	$-0.500204\pi$
$79$	−8.00000			−0.00128185			−0.000640923		1.00000i	$0.500204\pi$
$80$		0			0
$81$	−3969.00	+	5224.34i	−0.604938	+	0.796272i
$82$	−6577.74			−0.978247
$83$			4436.68i			0.644023i	0.946736	+	0.322012i	$0.104359\pi$
$83$			4436.68i			0.644023i	−0.946736	+	0.322012i	$0.895641\pi$
$84$	702.000	+	435.362i	0.0994898	+	0.0617010i
$85$		0			0
$86$			8175.13i			1.10534i
$87$	917.824	−	1479.95i	0.121261	−	0.195527i
$88$	−6730.71			−0.869151
$89$			9287.72i			1.17254i	0.810114	+	0.586272i	$0.199405\pi$
$89$			9287.72i			1.17254i	−0.810114	+	0.586272i	$0.800595\pi$
$90$		0			0
$91$	3744.00			0.452119
$92$			2485.55i			0.293661i
$93$	−244.753	−	151.789i	−0.0282984	−	0.0175499i
$94$	7730.00			0.874830
$95$		0			0
$96$	3420.00	−	5514.58i	0.371094	−	0.598371i
$97$	2508.72			0.266630			0.133315	−	0.991074i	$-0.457438\pi$
$97$	2508.72			0.266630			0.133315	+	0.991074i	$0.457438\pi$
$98$		−	6852.66i		−	0.713521i
$99$	−7020.00	+	3482.90i	−0.716253	+	0.355361i
$100$		0			0
$101$		−	4837.35i		−	0.474204i	−0.971485	−	0.237102i	$-0.923802\pi$
$101$		−	4837.35i		−	0.474204i	0.971485	−	0.237102i	$-0.0761976\pi$
$102$	6730.71	+	4174.21i	0.646934	+	0.401212i
$103$	5491.64			0.517640			0.258820	−	0.965926i	$-0.416666\pi$
$103$	5491.64			0.517640			0.258820	+	0.965926i	$0.416666\pi$
$104$		−	17027.5i		−	1.57429i
$105$		0			0
$106$	4480.00			0.398718
$107$			2925.11i			0.255490i	0.991807	+	0.127745i	$0.0407739\pi$
$107$			2925.11i			0.255490i	−0.991807	+	0.127745i	$0.959226\pi$
$108$	413.021	−	4354.46i	0.0354099	−	0.373324i
$109$	6352.00			0.534635			0.267318	−	0.963608i	$-0.413863\pi$
$109$	6352.00			0.534635			0.267318	+	0.963608i	$0.413863\pi$
$110$		0			0
$111$	−9828.00	−	6095.07i	−0.797663	−	0.494689i
$112$	1896.84			0.151215
$113$			8867.03i			0.694418i	0.937788	+	0.347209i	$0.112871\pi$
$113$			8867.03i			0.694418i	−0.937788	+	0.347209i	$0.887129\pi$
$114$	−4620.00	+	7449.53i	−0.355494	+	0.573217i
$115$		0			0
$116$			1160.97i			0.0862786i
$117$	−8811.11	−	17759.4i	−0.643663	−	1.29734i
$118$	12543.6			0.900861
$119$		−	4256.87i		−	0.300605i
$120$		0			0
$121$	5281.00			0.360699
$122$		−	2934.59i		−	0.197164i
$123$	9866.60	−	15909.4i	0.652165	−	1.05158i
$124$	192.000			0.0124870
$125$		0			0
$126$	3510.00	−	1741.45i	0.221088	−	0.109691i
$127$	3808.97			0.236156			0.118078	−	0.993004i	$-0.462327\pi$
$127$	3808.97			0.236156			0.118078	+	0.993004i	$0.462327\pi$
$128$		−	1947.96i		−	0.118894i
$129$	−19773.0	−	12262.7i	−1.18821	−	0.736896i
$130$		0			0
$131$			8030.01i			0.467922i	0.972246	+	0.233961i	$0.0751688\pi$
$131$			8030.01i			0.467922i	−0.972246	+	0.233961i	$0.924831\pi$
$132$	2753.47	−	4439.84i	0.158027	−	0.254812i
$133$	4711.49			0.266352
$134$			8175.13i			0.455287i
$135$		0			0
$136$	−19360.0			−1.04671
$137$			21263.2i			1.13289i	0.824101	+	0.566443i	$0.191681\pi$
$137$			21263.2i			1.13289i	−0.824101	+	0.566443i	$0.808319\pi$
$138$	10019.6	+	6213.88i	0.526128	+	0.326290i
$139$	19372.0			1.00264			0.501320	−	0.865262i	$-0.332848\pi$
$139$	19372.0			1.00264			0.501320	+	0.865262i	$0.332848\pi$
$140$		0			0
$141$	−11595.0	+	18696.4i	−0.583220	+	0.940414i
$142$	14685.2			0.728287
$143$		−	23679.1i		−	1.15796i
$144$	−4464.00	−	8997.48i	−0.215278	−	0.433906i
$145$		0			0
$146$		−	13351.1i		−	0.626342i
$147$	16574.4	+	10279.0i	0.767012	+	0.475681i
$148$	7709.72			0.351978
$149$			16205.1i			0.729928i	0.931022	+	0.364964i	$0.118919\pi$
$149$			16205.1i			0.729928i	−0.931022	+	0.364964i	$0.881081\pi$
$150$		0			0
$151$	33272.0			1.45923			0.729617	−	0.683856i	$-0.239698\pi$
$151$	33272.0			1.45923			0.729617	+	0.683856i	$0.239698\pi$
$152$		−	21427.6i		−	0.927441i
$153$	−20192.1	+	10018.1i	−0.862579	+	0.427959i
$154$	4680.00			0.197335
$155$		0			0
$156$	11232.0	+	6965.79i	0.461538	+	0.286234i
$157$	−29309.2			−1.18906			−0.594530	−	0.804073i	$-0.702662\pi$
$157$	−29309.2			−1.18906			−0.594530	+	0.804073i	$0.702662\pi$
$158$		−	25.2982i		−	0.00101339i
$159$	−6720.00	+	10835.7i	−0.265812	+	0.428609i
$160$		0			0
$161$		−	6336.93i		−	0.244471i
$162$	−16520.8	−	12551.1i	−0.629509	−	0.478246i
$163$	−12252.9			−0.461174			−0.230587	−	0.973052i	$-0.574065\pi$
$163$	−12252.9			−0.461174			−0.230587	+	0.973052i	$0.574065\pi$
$164$			12480.4i			0.464023i
$165$		0			0
$166$	−14030.0			−0.509145
$167$		−	2520.34i		−	0.0903702i	−0.998979	−	0.0451851i	$-0.985612\pi$
$167$		−	2520.34i		−	0.0903702i	0.998979	−	0.0451851i	$-0.0143878\pi$
$168$	−5048.03	+	8139.70i	−0.178856	+	0.288396i
$169$	31343.0			1.09741
$170$		0			0
$171$	−11088.0	−	22348.6i	−0.379194	−	0.764289i
$172$	15511.2			0.524311
$173$			49318.9i			1.64786i	0.566690	+	0.823931i	$0.308224\pi$
$173$			49318.9i			1.64786i	−0.566690	+	0.823931i	$0.691776\pi$
$174$	4680.00	+	2902.41i	0.154578	+	0.0958651i
$175$		0			0
$176$		−	11996.6i		−	0.387288i
$177$	−18815.4	+	30338.9i	−0.600574	+	0.968396i
$178$	−29370.4			−0.926977
$179$		−	38021.6i		−	1.18665i	−0.804961	−	0.593327i	$-0.797814\pi$
$179$		−	38021.6i		−	1.18665i	0.804961	−	0.593327i	$-0.202186\pi$
$180$		0			0
$181$	20342.0			0.620921			0.310461	−	0.950586i	$-0.399517\pi$
$181$	20342.0			0.620921			0.310461	+	0.950586i	$0.399517\pi$
$182$			11839.6i			0.357432i
$183$	7097.84	+	4401.89i	0.211945	+	0.131443i
$184$	−28820.0			−0.851252
$185$		0			0
$186$	480.000	−	773.977i	0.0138744	−	0.0223719i
$187$	−26922.8			−0.769905
$188$		−	14666.6i		−	0.414968i
$189$	−1053.00	+	11101.7i	−0.0294785	+	0.310790i
$190$		0			0
$191$			55532.8i			1.52224i	0.648611	+	0.761120i	$0.275350\pi$
$191$			55532.8i			1.52224i	−0.648611	+	0.761120i	$0.724650\pi$
$192$	32613.3	+	20225.9i	0.884693	+	0.548663i
$193$	−50725.0			−1.36178			−0.680891	−	0.732384i	$-0.738407\pi$
$193$	−50725.0			−1.36178			−0.680891	+	0.732384i	$0.738407\pi$
$194$			7933.26i			0.210789i
$195$		0			0
$196$	−13002.0			−0.338453
$197$		−	28865.3i		−	0.743778i	−0.928277	−	0.371889i	$-0.878710\pi$
$197$		−	28865.3i		−	0.743778i	0.928277	−	0.371889i	$-0.121290\pi$
$198$	−11013.9	−	22199.2i	−0.280938	−	0.566248i
$199$	−34328.0			−0.866847			−0.433423	−	0.901190i	$-0.642695\pi$
$199$	−34328.0			−0.866847			−0.433423	+	0.901190i	$0.642695\pi$
$200$		0			0
$201$	−19773.0	−	12262.7i	−0.489419	−	0.303525i
$202$	15297.1			0.374891
$203$		−	2959.89i		−	0.0718263i
$204$	7920.00	−	12770.6i	0.190311	−	0.306868i
$205$		0			0
$206$			17366.1i			0.409230i
$207$	−30058.7	+	14913.3i	−0.701503	+	0.348043i
$208$	30349.4			0.701492
$209$		−	29798.1i		−	0.682175i
$210$		0			0
$211$	−33268.0			−0.747243			−0.373621	−	0.927581i	$-0.621884\pi$
$211$	−33268.0			−0.747243			−0.373621	+	0.927581i	$0.621884\pi$
$212$		−	8500.20i		−	0.189129i
$213$	−22027.8	+	35518.7i	−0.485525	+	0.782885i
$214$	−9250.00			−0.201983
$215$		0			0
$216$	50490.0	+	4788.98i	1.08218	+	0.102644i
$217$	−489.506			−0.0103953
$218$			20086.8i			0.422666i
$219$	32292.0	+	20026.6i	0.673297	+	0.417561i
$220$		0			0
$221$		−	68110.0i		−	1.39452i
$222$	19274.3	−	31078.9i	0.391086	−	0.630608i
$223$	76011.1			1.52851			0.764253	−	0.644916i	$-0.223108\pi$
$223$	76011.1			1.52851			0.764253	+	0.644916i	$0.223108\pi$
$224$		−	11029.2i		−	0.219810i
$225$		0			0
$226$	−28040.0			−0.548986
$227$		−	16788.5i		−	0.325807i	−0.986642	−	0.162904i	$-0.947914\pi$
$227$		−	16788.5i		−	0.325807i	0.986642	−	0.162904i	$-0.0520860\pi$
$228$	14134.5	+	8765.83i	0.271901	+	0.168626i
$229$	−40298.0			−0.768445			−0.384222	−	0.923241i	$-0.625530\pi$
$229$	−40298.0			−0.768445			−0.384222	+	0.923241i	$0.625530\pi$
$230$		0			0
$231$	−7020.00	+	11319.4i	−0.131557	+	0.212129i
$232$	−13461.4			−0.250101
$233$		−	87253.6i		−	1.60721i	−0.595166	−	0.803603i	$-0.702914\pi$
$233$		−	87253.6i		−	1.60721i	0.595166	−	0.803603i	$-0.297086\pi$
$234$	56160.0	−	27863.2i	1.02564	−	0.508860i
$235$		0			0
$236$		−	23799.8i		−	0.427316i
$237$	61.1882	+	37.9473i	0.00108936	+	0.000675592i
$238$	13461.4			0.237649
$239$			88620.3i			1.55145i	0.631072	+	0.775725i	$0.282615\pi$
$239$			88620.3i			1.55145i	−0.631072	+	0.775725i	$0.717385\pi$
$240$		0			0
$241$	72152.0			1.24227			0.621133	−	0.783706i	$-0.286673\pi$
$241$	72152.0			1.24227			0.621133	+	0.783706i	$0.286673\pi$
$242$			16700.0i			0.285158i
$243$	55138.2	−	21131.9i	0.933771	−	0.357871i
$244$	−5568.00			−0.0935232
$245$		0			0
$246$	50310.0	+	31200.9i	0.831350	+	0.515582i
$247$	75383.9			1.23562
$248$			2226.24i			0.0361967i
$249$	21045.0	−	33934.0i	0.339430	−	0.547314i
$250$		0			0
$251$			15963.3i			0.253381i	0.991942	+	0.126691i	$0.0404355\pi$
$251$			15963.3i			0.253381i	−0.991942	+	0.126691i	$0.959564\pi$
$252$	−3304.16	−	6659.76i	−0.0520308	−	0.104871i
$253$	−40078.3			−0.626135
$254$			12045.0i			0.186698i
$255$		0			0
$256$	−62064.0			−0.947021
$257$			84938.8i			1.28600i	0.765868	+	0.642998i	$0.222310\pi$
$257$			84938.8i			1.28600i	−0.765868	+	0.642998i	$0.777690\pi$
$258$	38778.0	−	62527.7i	0.582568	−	0.939362i
$259$	−19656.0			−0.293019
$260$		0			0
$261$	−14040.0	+	6965.79i	−0.206104	+	0.102256i
$262$	−25393.1			−0.369925
$263$		−	2849.21i		−	0.0411920i	−0.999788	−	0.0205960i	$-0.993444\pi$
$263$		−	2849.21i		−	0.0411920i	0.999788	−	0.0205960i	$-0.00655638\pi$
$264$	51480.0	+	31926.5i	0.738636	+	0.458083i
$265$		0			0
$266$			14899.1i			0.210569i
$267$	44055.5	−	71037.4i	0.617985	−	0.996471i
$268$	15511.2			0.215961
$269$			3918.26i			0.0541487i	0.999633	+	0.0270744i	$0.00861909\pi$
$269$			3918.26i			0.0541487i	−0.999633	+	0.0270744i	$0.991381\pi$
$270$		0			0
$271$	−67048.0			−0.912951			−0.456475	−	0.889736i	$-0.650888\pi$
$271$	−67048.0			−0.912951			−0.456475	+	0.889736i	$0.650888\pi$
$272$		−	34506.8i		−	0.466409i
$273$	−28636.1	−	17759.4i	−0.384228	−	0.238288i
$274$	−67240.0			−0.895626
$275$		0			0
$276$	11790.0	−	19010.8i	0.154773	−	0.249564i
$277$	−10340.8			−0.134771			−0.0673853	−	0.997727i	$-0.521466\pi$
$277$	−10340.8			−0.134771			−0.0673853	+	0.997727i	$0.521466\pi$
$278$			61259.6i			0.792656i
$279$	1152.00	+	2321.93i	0.0147994	+	0.0298291i
$280$		0			0
$281$			22300.2i			0.282420i	0.989980	+	0.141210i	$0.0450994\pi$
$281$			22300.2i			0.282420i	−0.989980	+	0.141210i	$0.954901\pi$
$282$	−59123.1	−	36666.6i	−0.743463	−	0.461076i
$283$	117466.			1.46669			0.733347	−	0.679854i	$-0.237957\pi$
$283$	117466.			1.46669			0.733347	+	0.679854i	$0.237957\pi$
$284$		−	27863.2i		−	0.345457i
$285$		0			0
$286$	74880.0			0.915448
$287$		−	31818.8i		−	0.386296i
$288$	−52315.9	+	25956.0i	−0.630738	+	0.312934i
$289$	6081.00			0.0728080
$290$		0			0
$291$	−19188.0	−	11899.9i	−0.226592	−	0.140526i
$292$	−25331.9			−0.297100
$293$			57363.7i			0.668193i	0.942539	+	0.334097i	$0.108431\pi$
$293$			57363.7i			0.668193i	−0.942539	+	0.334097i	$0.891569\pi$
$294$	−32505.0	+	52412.7i	−0.376059	+	0.606376i
$295$		0			0
$296$			89394.3i			1.02030i
$297$	70213.5	+	6659.76i	0.795990	+	0.0754997i
$298$	−51245.1			−0.577059
$299$		−	101391.i		−	1.13411i
$300$		0			0
$301$	−39546.0			−0.436485
$302$			105215.i			1.15363i
$303$	−22945.6	+	36998.6i	−0.249927	+	0.402996i
$304$	38192.0			0.413262
$305$		0			0
$306$	−31680.0	−	63853.1i	−0.338331	−	0.681929i
$307$	−10417.3			−0.110530			−0.0552648	−	0.998472i	$-0.517600\pi$
$307$	−10417.3			−0.110530			−0.0552648	+	0.998472i	$0.517600\pi$
$308$		−	8879.68i		−	0.0936043i
$309$	−42003.0	−	26049.2i	−0.439910	−	0.272820i
$310$		0			0
$311$		−	101971.i		−	1.05428i	−0.849777	−	0.527142i	$-0.823264\pi$
$311$		−	101971.i		−	1.05428i	0.849777	−	0.527142i	$-0.176736\pi$
$312$	−80768.5	+	130235.i	−0.829722	+	1.33789i
$313$	−182586.			−1.86371			−0.931854	−	0.362832i	$-0.881810\pi$
$313$	−182586.			−1.86371			−0.931854	+	0.362832i	$0.881810\pi$
$314$		−	92683.7i		−	0.940035i
$315$		0			0
$316$	−48.0000			−0.000480692
$317$		−	33494.8i		−	0.333319i	−0.986015	−	0.166659i	$-0.946702\pi$
$317$		−	33494.8i		−	0.333319i	0.986015	−	0.166659i	$-0.0532980\pi$
$318$	−34265.4	−	21250.5i	−0.338845	−	0.210143i
$319$	−18720.0			−0.183960
$320$		0			0
$321$	13875.0	−	22372.8i	0.134655	−	0.217125i
$322$	20039.1			0.193271
$323$		−	85710.4i		−	0.821539i
$324$	−23814.0	+	31346.1i	−0.226852	+	0.298602i
$325$		0			0
$326$		−	38747.2i		−	0.364590i
$327$	−48583.5	−	30130.2i	−0.454352	−	0.281777i
$328$	−144710.			−1.34509
$329$			37392.8i			0.345458i
$330$		0			0
$331$	204092.			1.86282			0.931408	−	0.363977i	$-0.118581\pi$
$331$	204092.			1.86282			0.931408	+	0.363977i	$0.118581\pi$
$332$			26620.1i			0.241509i
$333$	46258.3	+	93236.6i	0.417159	+	0.840810i
$334$	7970.00			0.0714439
$335$		0			0
$336$	−14508.0	−	8997.48i	−0.128508	−	0.0796971i
$337$	−44912.2			−0.395461			−0.197731	−	0.980256i	$-0.563357\pi$
$337$	−44912.2			−0.395461			−0.197731	+	0.980256i	$0.563357\pi$
$338$			99115.3i			0.867575i
$339$	42060.0	−	67819.7i	0.365991	−	0.590142i
$340$		0			0
$341$			3095.91i			0.0266244i
$342$	70672.4	−	35063.3i	0.604224	−	0.299779i
$343$	69877.0			0.593944
$344$			179853.i			1.51985i
$345$		0			0
$346$	−155960.			−1.30275
$347$		−	135260.i		−	1.12334i	−0.827362	−	0.561669i	$-0.810159\pi$
$347$		−	135260.i		−	1.12334i	0.827362	−	0.561669i	$-0.189841\pi$
$348$	5506.94	−	8879.68i	0.0454728	−	0.0733227i
$349$	228682.			1.87751			0.938753	−	0.344592i	$-0.111983\pi$
$349$	228682.			1.87751			0.938753	+	0.344592i	$0.111983\pi$
$350$		0			0
$351$	−16848.0	+	177628.i	−0.136752	+	1.44177i
$352$	−69754.6			−0.562973
$353$			106923.i			0.858067i	0.903288	+	0.429034i	$0.141146\pi$
$353$			106923.i			0.858067i	−0.903288	+	0.429034i	$0.858854\pi$
$354$	−95940.0	−	59499.5i	−0.765585	−	0.474795i
$355$		0			0
$356$			55726.3i			0.439704i
$357$	−20192.1	+	32558.8i	−0.158433	+	0.255465i
$358$	120235.			0.938133
$359$			176467.i			1.36922i	0.728909	+	0.684611i	$0.240028\pi$
$359$			176467.i			1.36922i	−0.728909	+	0.684611i	$0.759972\pi$
$360$		0			0
$361$	−35457.0			−0.272074
$362$			64327.1i			0.490881i
$363$	−40391.9	−	25050.0i	−0.306536	−	0.190105i
$364$	22464.0			0.169545
$365$		0			0
$366$	−13920.0	+	22445.3i	−0.103915	+	0.167557i
$367$	178042.			1.32188			0.660939	−	0.750440i	$-0.270158\pi$
$367$	178042.			1.32188			0.660939	+	0.750440i	$0.270158\pi$
$368$		−	51368.0i		−	0.379313i
$369$	−150930.	+	74882.2i	−1.10847	+	0.549954i
$370$		0			0
$371$			21671.3i			0.157448i
$372$	−1468.52	−	910.736i	−0.0106119	−	0.00658122i
$373$	77770.2			0.558979			0.279490	−	0.960149i	$-0.409835\pi$
$373$	77770.2			0.558979			0.279490	+	0.960149i	$0.409835\pi$
$374$		−	85137.4i		−	0.608664i
$375$		0			0
$376$	170060.			1.20289
$377$		−	47358.3i		−	0.333206i
$378$	−35106.7	−	3329.88i	−0.245701	−	0.0233048i
$379$	12292.0			0.0855745			0.0427872	−	0.999084i	$-0.486376\pi$
$379$	12292.0			0.0855745			0.0427872	+	0.999084i	$0.486376\pi$
$380$		0			0
$381$	−29133.0	−	18067.5i	−0.200694	−	0.124465i
$382$	−175610.			−1.20344
$383$		−	246111.i		−	1.67777i	−0.544308	−	0.838886i	$-0.683208\pi$
$383$		−	246111.i		−	1.67777i	0.544308	−	0.838886i	$-0.316792\pi$
$384$	−9240.00	+	14899.1i	−0.0626628	+	0.101041i
$385$		0			0
$386$		−	160407.i		−	1.07658i
$387$	93067.3	+	187583.i	0.621406	+	1.25248i
$388$	15052.3			0.0999861
$389$		−	99794.6i		−	0.659490i	−0.944070	−	0.329745i	$-0.893037\pi$
$389$		−	99794.6i		−	0.659490i	0.944070	−	0.329745i	$-0.106963\pi$
$390$		0			0
$391$	−115280.			−0.754051
$392$		−	150758.i		−	0.981091i
$393$	38089.7	−	61417.8i	0.246617	−	0.397657i
$394$	91280.0			0.588008
$395$		0			0
$396$	−42120.0	+	20897.4i	−0.268595	+	0.133260i
$397$	143548.			0.910783			0.455391	−	0.890291i	$-0.349499\pi$
$397$	143548.			0.910783			0.455391	+	0.890291i	$0.349499\pi$
$398$		−	108555.i		−	0.685303i
$399$	−36036.0	−	22348.6i	−0.226355	−	0.140380i
$400$		0			0
$401$			245738.i			1.52821i	0.645092	+	0.764105i	$0.276819\pi$
$401$			245738.i			1.52821i	−0.645092	+	0.764105i	$0.723181\pi$
$402$	38778.0	−	62527.7i	0.239957	−	0.386919i
$403$	−7832.09			−0.0482245
$404$		−	29024.1i		−	0.177826i
$405$		0			0
$406$	9360.00			0.0567837
$407$			124315.i			0.750475i
$408$	148076.	+	91832.5i	0.889535	+	0.551666i
$409$	−34808.0			−0.208081			−0.104041	−	0.994573i	$-0.533177\pi$
$409$	−34808.0			−0.208081			−0.104041	+	0.994573i	$0.533177\pi$
$410$		0			0
$411$	100860.	−	162632.i	0.597084	−	0.962769i
$412$	32949.9			0.194115
$413$			60677.8i			0.355737i
$414$	−47160.0	−	95054.0i	−0.275152	−	0.554587i
$415$		0			0
$416$		−	176467.i		−	1.01971i
$417$	−148167.	−	91889.5i	−0.852080	−	0.528437i
$418$	94229.9			0.539307
$419$		−	219326.i		−	1.24928i	−0.780911	−	0.624642i	$-0.785245\pi$
$419$		−	219326.i		−	1.24928i	0.780911	−	0.624642i	$-0.214755\pi$
$420$		0			0
$421$	168992.			0.953459			0.476729	−	0.879050i	$-0.341822\pi$
$421$	168992.			0.953459			0.476729	+	0.879050i	$0.341822\pi$
$422$		−	105203.i		−	0.590747i
$423$	177369.	−	87999.9i	0.991284	−	0.491814i
$424$	98560.0			0.548238
$425$		0			0
$426$	−112320.	−	69657.9i	−0.618925	−	0.383841i
$427$	14195.7			0.0778574
$428$			17550.6i			0.0958088i
$429$	−112320.	+	181111.i	−0.610299	+	0.984077i
$430$		0			0
$431$		−	154989.i		−	0.834345i	−0.908827	−	0.417173i	$-0.863021\pi$
$431$		−	154989.i		−	0.834345i	0.908827	−	0.417173i	$-0.136979\pi$
$432$	−8535.76	+	89992.1i	−0.0457377	+	0.482211i
$433$	153644.			0.819481			0.409740	−	0.912202i	$-0.365619\pi$
$433$	153644.			0.819481			0.409740	+	0.912202i	$0.365619\pi$
$434$		−	1547.95i		−	0.00821823i
$435$		0			0
$436$	38112.0			0.200488
$437$		−	127592.i		−	0.668127i
$438$	−63329.8	+	102116.i	−0.330111	+	0.532288i
$439$	−65168.0			−0.338147			−0.169073	−	0.985603i	$-0.554078\pi$
$439$	−65168.0			−0.338147			−0.169073	+	0.985603i	$0.554078\pi$
$440$		0			0
$441$	−78012.0	−	157238.i	−0.401129	−	0.808502i
$442$	215383.			1.10247
$443$			116514.i			0.593706i	0.954923	+	0.296853i	$0.0959371\pi$
$443$			116514.i			0.593706i	−0.954923	+	0.296853i	$0.904063\pi$
$444$	−58968.0	−	36570.4i	−0.299123	−	0.185508i
$445$		0			0
$446$			240368.i			1.20839i
$447$	76867.7	−	123945.i	0.384706	−	0.620320i
$448$	65226.7			0.324989
$449$			79090.7i			0.392313i	0.980573	+	0.196157i	$0.0628461\pi$
$449$			79090.7i			0.392313i	−0.980573	+	0.196157i	$0.937154\pi$
$450$		0			0
$451$	−201240.			−0.989376
$452$			53202.2i			0.260407i
$453$	−254482.	−	157823.i	−1.24011	−	0.769084i
$454$	53090.0			0.257573
$455$		0			0
$456$	−101640.	+	163890.i	−0.488804	+	0.788173i
$457$	−389402.			−1.86451			−0.932257	−	0.361797i	$-0.882164\pi$
$457$	−389402.			−1.86451			−0.932257	+	0.361797i	$0.882164\pi$
$458$		−	127433.i		−	0.607509i
$459$	201960.	+	19155.9i	0.958606	+	0.0909238i
$460$		0			0
$461$			236643.i			1.11351i	0.830678	+	0.556753i	$0.187953\pi$
$461$			236643.i			1.11351i	−0.830678	+	0.556753i	$0.812047\pi$
$462$	−35795.1	−	22199.2i	−0.167703	−	0.104005i
$463$	−253793.			−1.18391			−0.591955	−	0.805971i	$-0.701644\pi$
$463$	−253793.			−1.18391			−0.591955	+	0.805971i	$0.701644\pi$
$464$		−	23993.3i		−	0.111443i
$465$		0			0
$466$	275920.			1.27061
$467$			365853.i			1.67754i	0.544485	+	0.838771i	$0.316725\pi$
$467$			365853.i			1.67754i	−0.544485	+	0.838771i	$0.683275\pi$
$468$	−52866.6	−	106556.i	−0.241374	−	0.486504i
$469$	−39546.0			−0.179786
$470$		0			0
$471$	224172.	+	139026.i	1.01051	+	0.626690i
$472$	275959.			1.23868
$473$			250111.i			1.11792i
$474$	−120.000	+	193.494i	−0.000534102	+	0.000861214i
$475$		0			0
$476$		−	25541.2i		−	0.112727i
$477$	102796.	−	51001.2i	0.451794	−	0.224153i
$478$	−280242.			−1.22653
$479$			255606.i			1.11404i	0.830500	+	0.557019i	$0.188055\pi$
$479$			255606.i			1.11404i	−0.830500	+	0.557019i	$0.811945\pi$
$480$		0			0
$481$	−314496.			−1.35933
$482$			228165.i			0.982097i
$483$	−30058.7	+	48468.2i	−0.128848	+	0.207760i
$484$	31686.0			0.135262
$485$		0			0
$486$	66825.0	+	174362.i	0.282922	+	0.738211i
$487$	−445925.			−1.88020			−0.940099	−	0.340902i	$-0.889267\pi$
$487$	−445925.			−1.88020			−0.940099	+	0.340902i	$0.889267\pi$
$488$		−	64561.1i		−	0.271101i
$489$	93717.0	+	58120.8i	0.391923	+	0.243060i
$490$		0			0
$491$		−	229387.i		−	0.951495i	−0.879582	−	0.475747i	$-0.842178\pi$
$491$		−	229387.i		−	0.951495i	0.879582	−	0.475747i	$-0.157822\pi$
$492$	59199.6	−	95456.5i	0.244562	−	0.394344i
$493$	−53845.6			−0.221542
$494$			238385.i			0.976843i
$495$		0			0
$496$	−3968.00			−0.0161290
$497$			71037.4i			0.287590i
$498$	107309.	+	66550.1i	0.432690	+	0.268343i
$499$	−157748.			−0.633524			−0.316762	−	0.948505i	$-0.602596\pi$
$499$	−157748.			−0.633524			−0.316762	+	0.948505i	$0.602596\pi$
$500$		0			0
$501$	−11955.0	+	19276.9i	−0.0476293	+	0.0767999i
$502$	−50480.3			−0.200315
$503$			499630.i			1.97475i	0.158390	+	0.987377i	$0.449370\pi$
$503$			499630.i			1.97475i	−0.158390	+	0.987377i	$0.550630\pi$
$504$	77220.0	−	38311.8i	0.303997	−	0.150825i
$505$		0			0
$506$		−	126739.i		−	0.495003i
$507$	−239728.	−	148673.i	−0.932615	−	0.578384i
$508$	22853.8			0.0885587
$509$		−	153441.i		−	0.592251i	−0.955149	−	0.296125i	$-0.904305\pi$
$509$		−	153441.i		−	0.592251i	0.955149	−	0.296125i	$-0.0956946\pi$
$510$		0			0
$511$	64584.0			0.247334
$512$		−	227431.i		−	0.867580i
$513$	−21201.7	+	223529.i	−0.0805631	+	0.849373i
$514$	−268600.			−1.01667
$515$		0			0
$516$	−118638.	−	73576.2i	−0.445579	−	0.276336i
$517$	236493.			0.884782
$518$		−	62157.7i		−	0.231652i
$519$	233940.	−	377217.i	0.868500	−	1.40041i
$520$		0			0
$521$		−	242642.i		−	0.893902i	−0.894558	−	0.446951i	$-0.852510\pi$
$521$		−	242642.i		−	0.893902i	0.894558	−	0.446951i	$-0.147490\pi$
$522$	−22027.8	−	44398.4i	−0.0808406	−	0.162939i
$523$	−133865.			−0.489398			−0.244699	−	0.969599i	$-0.578689\pi$
$523$	−133865.			−0.489398			−0.244699	+	0.969599i	$0.578689\pi$
$524$			48180.1i			0.175471i
$525$		0			0
$526$	9010.00			0.0325652
$527$			8904.97i			0.0320635i
$528$	−56905.1	+	91756.6i	−0.204119	+	0.329132i
$529$	108231.			0.386759
$530$		0			0
$531$	287820.	−	142799.i	1.02078	−	0.506448i
$532$	28269.0			0.0998819
$533$		−	509101.i		−	1.79205i
$534$	224640.	+	139316.i	0.787779	+	0.488560i
$535$		0			0
$536$			179853.i			0.626019i
$537$	−180352.	+	290809.i	−0.625422	+	1.00846i
$538$	−12390.6			−0.0428083
$539$		−	209651.i		−	0.721638i
$540$		0			0
$541$	−195478.			−0.667888			−0.333944	−	0.942593i	$-0.608380\pi$
$541$	−195478.			−0.667888			−0.333944	+	0.942593i	$0.608380\pi$
$542$		−	212024.i		−	0.721751i
$543$	−155586.	−	96490.6i	−0.527682	−	0.327254i
$544$	−200640.			−0.677984
$545$		0			0
$546$	56160.0	−	90555.3i	0.188383	−	0.303759i
$547$	143165.			0.478479			0.239239	−	0.970961i	$-0.423102\pi$
$547$	143165.			0.478479			0.239239	+	0.970961i	$0.423102\pi$
$548$			127579.i			0.424833i
$549$	−33408.0	−	67336.0i	−0.110842	−	0.223410i
$550$		0			0
$551$		−	59596.2i		−	0.196298i
$552$	220431.	+	136705.i	0.723425	+	0.448649i
$553$	122.376			0.000400173
$554$		−	32700.5i		−	0.106545i
$555$		0			0
$556$	116232.			0.375990
$557$			401799.i			1.29509i	0.762029	+	0.647543i	$0.224203\pi$
$557$			401799.i			1.29509i	−0.762029	+	0.647543i	$0.775797\pi$
$558$	−7342.59	+	3642.94i	−0.0235820	+	0.0117000i
$559$	−632736.			−2.02488
$560$		0			0
$561$	205920.	+	127706.i	0.654294	+	0.405776i
$562$	−70519.4			−0.223273
$563$		−	126178.i		−	0.398077i	−0.979992	−	0.199038i	$-0.936218\pi$
$563$		−	126178.i		−	0.398077i	0.979992	−	0.199038i	$-0.0637819\pi$
$564$	−69570.0	+	112178.i	−0.218708	+	0.352655i
$565$		0			0
$566$			371460.i			1.15952i
$567$	60714.0	−	79917.1i	0.188853	−	0.248584i
$568$	323074.			1.00139
$569$		−	355497.i		−	1.09802i	−0.835815	−	0.549012i	$-0.815004\pi$
$569$		−	355497.i		−	1.09802i	0.835815	−	0.549012i	$-0.184996\pi$
$570$		0			0
$571$	−454108.			−1.39279			−0.696397	−	0.717657i	$-0.745215\pi$
$571$	−454108.			−1.39279			−0.696397	+	0.717657i	$0.745215\pi$
$572$		−	142075.i		−	0.434235i
$573$	263415.	−	424744.i	0.802291	−	1.29366i
$574$	100620.			0.305394
$575$		0			0
$576$	−153504.	−	309397.i	−0.462674	−	0.932548i
$577$	103163.			0.309866			0.154933	−	0.987925i	$-0.450484\pi$
$577$	103163.			0.309866			0.154933	+	0.987925i	$0.450484\pi$
$578$			19229.8i			0.0575598i
$579$	387972.	+	240610.i	1.15729	+	0.717723i
$580$		0			0
$581$		−	67868.1i		−	0.201054i
$582$	37630.8	−	60677.8i	0.111096	−	0.179136i
$583$	137062.			0.403254
$584$		−	293724.i		−	0.861220i
$585$		0			0
$586$	−181400.			−0.528253
$587$		−	474661.i		−	1.37755i	−0.724975	−	0.688775i	$-0.758149\pi$
$587$		−	474661.i		−	1.37755i	0.724975	−	0.688775i	$-0.241851\pi$
$588$	99446.2	+	61673.9i	0.287630	+	0.178380i
$589$	−9856.00			−0.0284099
$590$		0			0
$591$	−136920.	+	220777.i	−0.392005	+	0.632090i
$592$	−159334.			−0.454638
$593$			173103.i			0.492261i	0.969237	+	0.246130i	$0.0791592\pi$
$593$			173103.i			0.492261i	−0.969237	+	0.246130i	$0.920841\pi$
$594$	−21060.0	+	222035.i	−0.0596878	+	0.629285i
$595$		0			0
$596$			97230.8i			0.273723i
$597$	262559.	+	162832.i	0.736678	+	0.456868i
$598$	320626.			0.896596
$599$			587255.i			1.63671i	0.574710	+	0.818357i	$0.305115\pi$
$599$			587255.i			1.63671i	−0.574710	+	0.818357i	$0.694885\pi$
$600$		0			0
$601$	475352.			1.31603			0.658016	−	0.753004i	$-0.271396\pi$
$601$	475352.			1.31603			0.658016	+	0.753004i	$0.271396\pi$
$602$		−	125055.i		−	0.345072i
$603$	93067.3	+	187583.i	0.255954	+	0.515892i
$604$	199632.			0.547213
$605$		0			0
$606$	−117000.	−	72560.3i	−0.318596	−	0.197585i
$607$	−311310.			−0.844921			−0.422461	−	0.906381i	$-0.638834\pi$
$607$	−311310.			−0.844921			−0.422461	+	0.906381i	$0.638834\pi$
$608$		−	222068.i		−	0.600729i
$609$	−14040.0	+	22638.8i	−0.0378558	+	0.0610407i
$610$		0			0
$611$			598284.i			1.60260i
$612$	−121153.	+	60108.6i	−0.323467	+	0.160485i
$613$	224316.			0.596952			0.298476	−	0.954417i	$-0.403522\pi$
$613$	224316.			0.596952			0.298476	+	0.954417i	$0.403522\pi$
$614$		−	32942.4i		−	0.0873813i
$615$		0			0
$616$	102960.			0.271336
$617$		−	200463.i		−	0.526580i	−0.964717	−	0.263290i	$-0.915192\pi$
$617$		−	200463.i		−	0.526580i	0.964717	−	0.263290i	$-0.0848076\pi$
$618$	82374.7	−	132825.i	0.215683	−	0.347779i
$619$	−22508.0			−0.0587429			−0.0293715	−	0.999569i	$-0.509351\pi$
$619$	−22508.0			−0.0587429			−0.0293715	+	0.999569i	$0.509351\pi$
$620$		0			0
$621$	300645.	+	28516.2i	0.779598	+	0.0739450i
$622$	322462.			0.833485
$623$		−	142075.i		−	0.366050i
$624$	−232128.	−	143960.i	−0.596154	−	0.369719i
$625$		0			0
$626$		−	577387.i		−	1.47339i
$627$	−141345.	+	227912.i	−0.359538	+	0.579738i
$628$	−175855.			−0.445898
$629$			357577.i			0.903792i
$630$		0			0
$631$	−157408.			−0.395338			−0.197669	−	0.980269i	$-0.563337\pi$
$631$	−157408.			−0.395338			−0.197669	+	0.980269i	$0.563337\pi$
$632$		−	556.561i		−	0.00139341i
$633$	254451.	+	157804.i	0.635034	+	0.393832i
$634$	105920.			0.263511
$635$		0			0
$636$	−40320.0	+	65014.0i	−0.0996796	+	0.160729i
$637$	530380.			1.30710
$638$		−	59197.8i		−	0.145434i
$639$	336960.	−	167179.i	0.825233	−	0.409430i
$640$		0			0
$641$		−	297836.i		−	0.724871i	−0.932009	−	0.362436i	$-0.881945\pi$
$641$		−	297836.i		−	0.724871i	0.932009	−	0.362436i	$-0.118055\pi$
$642$	70748.9	+	43876.6i	0.171652	+	0.106454i
$643$	−130805.			−0.316376			−0.158188	−	0.987409i	$-0.550565\pi$
$643$	−130805.			−0.316376			−0.158188	+	0.987409i	$0.550565\pi$
$644$		−	38021.6i		−	0.0916767i
$645$		0			0
$646$	271040.			0.649484
$647$		−	117520.i		−	0.280739i	−0.990099	−	0.140369i	$-0.955171\pi$
$647$		−	117520.i		−	0.280739i	0.990099	−	0.140369i	$-0.0448290\pi$
$648$	−363458.	−	276124.i	−0.865574	−	0.657588i
$649$	383760.			0.911109
$650$		0			0
$651$	3744.00	+	2321.93i	0.00883433	+	0.00547882i
$652$	−73517.7			−0.172940
$653$		−	640829.i		−	1.50285i	−0.659818	−	0.751426i	$-0.729367\pi$
$653$		−	640829.i		−	1.50285i	0.659818	−	0.751426i	$-0.270633\pi$
$654$	95280.0	−	153634.i	0.222765	−	0.359197i
$655$		0			0
$656$		−	257928.i		−	0.599364i
$657$	−151992.	−	306349.i	−0.352118	−	0.709717i
$658$	−118246.			−0.273109
$659$			121805.i			0.280474i	0.990118	+	0.140237i	$0.0447865\pi$
$659$			121805.i			0.280474i	−0.990118	+	0.140237i	$0.955214\pi$
$660$		0			0
$661$	5072.00			0.0116085			0.00580425	−	0.999983i	$-0.498152\pi$
$661$	5072.00			0.0116085			0.00580425	+	0.999983i	$0.498152\pi$
$662$			645396.i			1.47269i
$663$	−323074.	+	520941.i	−0.734979	+	1.18512i
$664$	−308660.			−0.700074
$665$		0			0
$666$	−294840.	+	146282.i	−0.664719	+	0.329793i
$667$	−80156.6			−0.180172
$668$		−	15122.0i		−	0.0338888i
$669$	−581373.	−	360552.i	−1.29898	−	0.805593i
$670$		0			0
$671$		−	89781.3i		−	0.199407i
$672$	−52315.9	+	84356.9i	−0.115850	+	0.186802i
$673$	181790.			0.401366			0.200683	−	0.979656i	$-0.435684\pi$
$673$	181790.			0.401366			0.200683	+	0.979656i	$0.435684\pi$
$674$		−	142025.i		−	0.312640i
$675$		0			0
$676$	188058.			0.411527
$677$		−	304666.i		−	0.664733i	−0.943150	−	0.332367i	$-0.892153\pi$
$677$		−	304666.i		−	0.664733i	0.943150	−	0.332367i	$-0.107847\pi$
$678$	214465.	+	133005.i	0.466548	+	0.289341i
$679$	−38376.0			−0.0832377
$680$		0			0
$681$	−79635.0	+	128408.i	−0.171716	+	0.276883i
$682$	−9790.12			−0.0210484
$683$			627816.i			1.34583i	0.739718	+	0.672917i	$0.234959\pi$
$683$			627816.i			1.34583i	−0.739718	+	0.672917i	$0.765041\pi$
$684$	−66528.0	−	134091.i	−0.142198	−	0.286608i
$685$		0			0
$686$			220970.i			0.469554i
$687$	308220.	+	191150.i	0.653052	+	0.405006i
$688$	−320565.			−0.677235
$689$			346742.i			0.730411i
$690$		0			0
$691$	−17308.0			−0.0362486			−0.0181243	−	0.999836i	$-0.505769\pi$
$691$	−17308.0			−0.0362486			−0.0181243	+	0.999836i	$0.505769\pi$
$692$			295913.i			0.617949i
$693$	107385.	−	53278.1i	0.223603	−	0.110938i
$694$	427730.			0.888077
$695$		0			0
$696$	102960.	+	63853.1i	0.212545	+	0.131815i
$697$	−578841.			−1.19150
$698$			723156.i			1.48430i
$699$	−413880.	+	667361.i	−0.847072	+	1.36586i
$700$		0			0
$701$			23944.9i			0.0487278i	0.999703	+	0.0243639i	$0.00775604\pi$
$701$			23944.9i			0.0487278i	−0.999703	+	0.0243639i	$0.992244\pi$
$702$	−561708.	−	53278.1i	−1.13982	−	0.108112i
$703$	−395765.			−0.800806
$704$		−	412530.i		−	0.832357i
$705$		0			0
$706$	−338120.			−0.678362
$707$			73997.3i			0.148039i
$708$	−112892.	+	182033.i	−0.225215	+	0.363149i
$709$	381322.			0.758577			0.379288	−	0.925279i	$-0.376169\pi$
$709$	381322.			0.758577			0.379288	+	0.925279i	$0.376169\pi$
$710$		0			0
$711$	−288.000	−	580.483i	−0.000569709	−	0.00114829i
$712$	−646148.			−1.27459
$713$			13256.3i			0.0260761i
$714$	−102960.	−	63853.1i	−0.201963	−	0.125252i
$715$		0			0
$716$		−	228130.i		−	0.444996i
$717$	420363.	−	677815.i	0.817686	−	1.31848i
$718$	−558037.			−1.08247
$719$		−	927031.i		−	1.79323i	−0.442810	−	0.896616i	$-0.646018\pi$
$719$		−	927031.i		−	1.79323i	0.442810	−	0.896616i	$-0.353982\pi$
$720$		0			0
$721$	−84006.0			−0.161599
$722$		−	112125.i		−	0.215094i
$723$	−551857.	−	342247.i	−1.05572	−	0.654731i
$724$	122052.			0.232845
$725$		0			0
$726$	79215.0	−	127730.i	0.150291	−	0.242338i
$727$	373998.			0.707620			0.353810	−	0.935317i	$-0.384886\pi$
$727$	373998.			0.707620			0.353810	+	0.935317i	$0.384886\pi$
$728$			260470.i			0.491469i
$729$	−521964.	−	99915.6i	−0.982167	−	0.188009i
$730$		0			0
$731$			719411.i			1.34630i
$732$	42587.0	+	26411.3i	0.0794795	+	0.0492911i
$733$	318240.			0.592307			0.296153	−	0.955140i	$-0.404296\pi$
$733$	318240.			0.592307			0.296153	+	0.955140i	$0.404296\pi$
$734$			563020.i			1.04504i
$735$		0			0
$736$	−298680.			−0.551379
$737$			250111.i			0.460466i
$738$	−236798.	−	477283.i	−0.434777	−	0.876320i
$739$	−409268.			−0.749409			−0.374705	−	0.927144i	$-0.622256\pi$
$739$	−409268.			−0.749409			−0.374705	+	0.927144i	$0.622256\pi$
$740$		0			0
$741$	−576576.	−	357577.i	−1.05007	−	0.651229i
$742$	−68530.8			−0.124474
$743$			11400.0i			0.0206504i	0.999947	+	0.0103252i	$0.00328667\pi$
$743$			11400.0i			0.0206504i	−0.999947	+	0.0103252i	$0.996713\pi$
$744$	10560.0	−	17027.5i	0.0190773	−	0.0307613i
$745$		0			0
$746$			245931.i			0.441912i
$747$	−321927.	+	159720.i	−0.576920	+	0.286233i
$748$	−161537.			−0.288715
$749$		−	44745.5i		−	0.0797602i
$750$		0			0
$751$	347432.			0.616013			0.308007	−	0.951384i	$-0.400338\pi$
$751$	347432.			0.616013			0.308007	+	0.951384i	$0.400338\pi$
$752$			303111.i			0.536001i
$753$	75720.4	−	122096.i	0.133544	−	0.215333i
$754$	149760.			0.263423
$755$		0			0
$756$	−6318.00	+	66610.4i	−0.0110544	+	0.116546i
$757$	886067.			1.54623			0.773116	−	0.634265i	$-0.218697\pi$
$757$	886067.			1.54623			0.773116	+	0.634265i	$0.218697\pi$
$758$			38870.7i			0.0676525i
$759$	306540.	+	190108.i	0.532113	+	0.330002i
$760$		0			0
$761$		−	261604.i		−	0.451726i	−0.974159	−	0.225863i	$-0.927480\pi$
$761$		−	261604.i		−	0.451726i	0.974159	−	0.225863i	$-0.0725202\pi$
$762$	57134.5	−	92126.6i	0.0983985	−	0.158663i
$763$	−97166.9			−0.166905
$764$			333197.i			0.570840i
$765$		0			0
$766$	778270.			1.32639
$767$			970845.i			1.65029i
$768$	474698.	+	294395.i	0.804814	+	0.499124i
$769$	832882.			1.40842			0.704208	−	0.709994i	$-0.251302\pi$
$769$	832882.			1.40842			0.704208	+	0.709994i	$0.251302\pi$
$770$		0			0
$771$	402900.	−	649657.i	0.677780	−	1.09289i
$772$	−304350.			−0.510669
$773$		−	38529.2i		−	0.0644809i	−0.999480	−	0.0322404i	$-0.989736\pi$
$773$		−	38529.2i		−	0.0644809i	0.999480	−	0.0322404i	$-0.0102642\pi$
$774$	−593190.	+	294305.i	−0.990175	+	0.491264i
$775$		0			0
$776$			174532.i			0.289835i
$777$	150339.	+	93236.6i	0.249018	+	0.154435i
$778$	315578.			0.521372
$779$		−	640659.i		−	1.05573i
$780$		0			0
$781$	449280.			0.736572
$782$		−	364547.i		−	0.596129i
$783$	140427.	+	13319.5i	0.229048	+	0.0217253i
$784$	268708.			0.437168
$785$		0			0
$786$	194220.	+	120450.i	0.314376	+	0.194967i
$787$	627164.			1.01259			0.506293	−	0.862362i	$-0.331016\pi$
$787$	627164.			1.01259			0.506293	+	0.862362i	$0.331016\pi$
$788$		−	173192.i		−	0.278917i
$789$	−13515.0	+	21792.3i	−0.0217101	+	0.0350065i
$790$		0			0
$791$		−	135639.i		−	0.216787i
$792$	−242305.	−	488382.i	−0.386289	−	0.778591i
$793$	227131.			0.361185
$794$			453937.i			0.720037i
$795$		0			0
$796$	−205968.			−0.325068
$797$		−	1.09025e6i		−	1.71637i	−0.513343	−	0.858184i	$-0.671593\pi$
$797$		−	1.09025e6i		−	1.71637i	0.513343	−	0.858184i	$-0.328407\pi$
$798$	70672.4	−	113956.i	0.110980	−	0.178950i
$799$	680240.			1.06554
$800$		0			0
$801$	−673920.	+	334358.i	−1.05037	+	0.521131i
$802$	−777091.			−1.20816
$803$		−	408465.i		−	0.633467i
$804$	−118638.	−	73576.2i	−0.183532	−	0.113822i
$805$		0			0
$806$		−	24767.3i		−	0.0381248i
$807$	18585.9	−	29968.9i	0.0285389	−	0.0460176i
$808$	336535.			0.515475
$809$			101004.i			0.154327i	0.997018	+	0.0771634i	$0.0245863\pi$
$809$			101004.i			0.154327i	−0.997018	+	0.0771634i	$0.975414\pi$
$810$		0			0
$811$	−400948.			−0.609602			−0.304801	−	0.952416i	$-0.598590\pi$
$811$	−400948.			−0.609602			−0.304801	+	0.952416i	$0.598590\pi$
$812$		−	17759.4i		−	0.0269349i
$813$	512819.	+	318037.i	0.775859	+	0.481167i
$814$	−393120.			−0.593303
$815$		0			0
$816$	−163680.	+	263926.i	−0.245819	+	0.396371i
$817$	−796242.			−1.19289
$818$		−	110073.i		−	0.164502i
$819$	134784.	+	271666.i	0.200942	+	0.405011i
$820$		0			0
$821$		−	777895.i		−	1.15408i	−0.816717	−	0.577038i	$-0.804208\pi$
$821$		−	777895.i		−	1.15408i	0.816717	−	0.577038i	$-0.195792\pi$
$822$	514287.	+	318947.i	0.761136	+	0.472036i
$823$	−218457.			−0.322528			−0.161264	−	0.986911i	$-0.551557\pi$
$823$	−218457.			−0.322528			−0.161264	+	0.986911i	$0.551557\pi$
$824$			382054.i			0.562692i
$825$		0			0
$826$	−191880.			−0.281235
$827$		−	460867.i		−	0.673852i	−0.941531	−	0.336926i	$-0.890613\pi$
$827$		−	460867.i		−	0.673852i	0.941531	−	0.336926i	$-0.109387\pi$
$828$	−180352.	+	89479.8i	−0.263064	+	0.130516i
$829$	60352.0			0.0878178			0.0439089	−	0.999036i	$-0.486019\pi$
$829$	60352.0			0.0878178			0.0439089	+	0.999036i	$0.486019\pi$
$830$		0			0
$831$	79092.0	+	49050.8i	0.114533	+	0.0710303i
$832$	1.04363e6			1.50764
$833$		−	603034.i		−	0.869064i
$834$	290580.	−	468546.i	0.417767	−	0.673628i
$835$		0			0
$836$		−	178789.i		−	0.255816i
$837$	2202.78	−	23223.8i	0.00314427	−	0.0331499i
$838$	693569.			0.987646
$839$			162148.i			0.230350i	0.993345	+	0.115175i	$0.0367429\pi$
$839$			162148.i			0.230350i	−0.993345	+	0.115175i	$0.963257\pi$
$840$		0			0
$841$	669841.			0.947065
$842$			534400.i			0.753775i
$843$	105779.	−	170564.i	0.148849	−	0.240011i
$844$	−199608.			−0.280216
$845$		0			0
$846$	278280.	+	560891.i	0.388813	+	0.783679i
$847$	−80783.8			−0.112605
$848$			175671.i			0.244291i
$849$	−898443.	−	557191.i	−1.24645	−	0.773016i
$850$		0			0
$851$			532303.i			0.735020i
$852$	−132167.	+	213112.i	−0.182072	+	0.293582i
$853$	1.27675e6			1.75472			0.877362	−	0.479828i	$-0.159301\pi$
$853$	1.27675e6			1.75472			0.877362	+	0.479828i	$0.159301\pi$
$854$			44890.7i			0.0615517i
$855$		0			0
$856$	−203500.			−0.277726
$857$			311105.i			0.423589i	0.977314	+	0.211795i	$0.0679308\pi$
$857$			311105.i			0.423589i	−0.977314	+	0.211795i	$0.932069\pi$
$858$	−572722.	−	355187.i	−0.777981	−	0.482484i
$859$	−1.14631e6			−1.55351			−0.776757	−	0.629801i	$-0.783137\pi$
$859$	−1.14631e6			−1.55351			−0.776757	+	0.629801i	$0.783137\pi$
$860$		0			0
$861$	−150930.	+	243367.i	−0.203596	+	0.328289i
$862$	490118.			0.659608
$863$		−	640839.i		−	0.860453i	−0.902721	−	0.430227i	$-0.858434\pi$
$863$		−	640839.i		−	0.860453i	0.902721	−	0.430227i	$-0.141566\pi$
$864$	523260.	+	49631.3i	0.700955	+	0.0664856i
$865$		0			0
$866$			485864.i			0.647857i
$867$	−46510.7	−	28844.7i	−0.0618749	−	0.0383732i
$868$	−2937.04			−0.00389825
$869$		−	773.977i		−	0.00102492i
$870$		0			0
$871$	−632736.			−0.834039
$872$			441909.i			0.581166i
$873$	90313.8	+	182033.i	0.118502	+	0.238848i
$874$	403480.			0.528201
$875$		0			0
$876$	193752.	+	120160.i	0.252486	+	0.156585i
$877$	447959.			0.582424			0.291212	−	0.956659i	$-0.405942\pi$
$877$	447959.			0.582424			0.291212	+	0.956659i	$0.405942\pi$
$878$		−	206079.i		−	0.267329i
$879$	272100.	−	438748.i	0.352169	−	0.567855i
$880$		0			0
$881$		−	72995.7i		−	0.0940471i	−0.998894	−	0.0470235i	$-0.985026\pi$
$881$		−	72995.7i		−	0.0940471i	0.998894	−	0.0470235i	$-0.0149736\pi$
$882$	497231.	−	246696.i	0.639177	−	0.317120i
$883$	−797910.			−1.02337			−0.511685	−	0.859173i	$-0.670978\pi$
$883$	−797910.			−1.02337			−0.511685	+	0.859173i	$0.670978\pi$
$884$		−	408660.i		−	0.522947i
$885$		0			0
$886$	−368450.			−0.469365
$887$		−	1.04890e6i		−	1.33317i	−0.745428	−	0.666586i	$-0.767755\pi$
$887$		−	1.04890e6i		−	1.33317i	0.745428	−	0.666586i	$-0.232245\pi$
$888$	424034.	−	683735.i	0.537744	−	0.867085i
$889$	−58266.0			−0.0737245
$890$		0			0
$891$	−505440.	−	383989.i	−0.636670	−	0.483686i
$892$	456067.			0.573190
$893$			752888.i			0.944120i
$894$	391950.	+	243077.i	0.490406	+	0.304137i
$895$		0			0
$896$			29798.1i			0.0371170i
$897$	−480940.	+	775492.i	−0.597731	+	0.963812i
$898$	−250107.			−0.310151
$899$			6191.81i			0.00766123i
$900$		0			0
$901$	394240.			0.485636
$902$		−	636377.i		−	0.782170i
$903$	302469.	+	187583.i	0.370941	+	0.230048i
$904$	−616880.			−0.754856
$905$		0			0
$906$	499080.	−	804742.i	0.608014	−	0.980394i
$907$	−1.06515e6			−1.29478			−0.647390	−	0.762159i	$-0.724139\pi$
$907$	−1.06515e6			−1.29478			−0.647390	+	0.762159i	$0.724139\pi$
$908$		−	100731.i		−	0.122178i
$909$	351000.	−	174145.i	0.424795	−	0.210757i
$910$		0			0
$911$		−	1.25520e6i		−	1.51243i	−0.654324	−	0.756215i	$-0.727047\pi$
$911$		−	1.25520e6i		−	1.51243i	0.654324	−	0.756215i	$-0.272953\pi$
$912$	−292113.	−	181161.i	−0.351205	−	0.217808i
$913$	−429235.			−0.514937
$914$		−	1.23140e6i		−	1.47403i
$915$		0			0
$916$	−241788.			−0.288167
$917$		−	122836.i		−	0.146078i
$918$	−60576.4	+	638654.i	−0.0718816	+	0.757844i
$919$	−552368.			−0.654030			−0.327015	−	0.945019i	$-0.606043\pi$
$919$	−552368.			−0.654030			−0.327015	+	0.945019i	$0.606043\pi$
$920$		0			0
$921$	79677.0	+	49413.6i	0.0939320	+	0.0582542i
$922$	−748332.			−0.880304
$923$			1.13660e6i			1.33415i
$924$	−42120.0	+	67916.5i	−0.0493338	+	0.0795483i
$925$		0			0
$926$		−	802566.i		−	0.935963i
$927$	197699.	+	398475.i	0.230062	+	0.463705i
$928$	−139509.			−0.161997
$929$			748290.i			0.867039i	0.901144	+	0.433520i	$0.142729\pi$
$929$			748290.i			0.867039i	−0.901144	+	0.433520i	$0.857271\pi$
$930$		0			0
$931$	667436.			0.770035
$932$		−	523521.i		−	0.602702i
$933$	−483693.	+	779932.i	−0.555657	+	0.895969i
$934$	−1.15693e6			−1.32621
$935$		0			0
$936$	1.23552e6	−	612990.i	1.41026	−	0.699683i
$937$	−173102.			−0.197161			−0.0985807	−	0.995129i	$-0.531430\pi$
$937$	−173102.			−0.197161			−0.0985807	+	0.995129i	$0.531430\pi$
$938$		−	125055.i		−	0.142134i
$939$	1.39651e6	+	866080.i	1.58385	+	0.982261i
$940$		0			0
$941$			1.74861e6i			1.97475i	0.158388	+	0.987377i	$0.449370\pi$
$941$			1.74861e6i			1.97475i	−0.158388	+	0.987377i	$0.550630\pi$
$942$	−439637.	+	708894.i	−0.495442	+	0.798876i
$943$	−861683.			−0.969001
$944$			491862.i			0.551950i
$945$		0			0
$946$	−790920.			−0.883792
$947$			983427.i			1.09658i	0.836287	+	0.548292i	$0.184722\pi$
$947$			983427.i			1.09658i	−0.836287	+	0.548292i	$0.815278\pi$
$948$	367.129	+	227.684i	0.000408510	+	0.000253347i
$949$	1.03334e6			1.14739
$950$		0			0
$951$	−158880.	+	256186.i	−0.175674	+	0.283266i
$952$	296151.			0.326768
$953$		−	894507.i		−	0.984913i	−0.870337	−	0.492457i	$-0.836099\pi$
$953$		−	894507.i		−	0.984913i	0.870337	−	0.492457i	$-0.163901\pi$
$954$	161280.	+	325070.i	0.177208	+	0.357175i
$955$		0			0
$956$			531722.i			0.581793i
$957$	143180.	+	88796.8i	0.156336	+	0.0969557i
$958$	−808297.			−0.880724
$959$		−	325264.i		−	0.353670i
$960$		0			0
$961$	−922497.			−0.998891
$962$		−	994524.i		−	1.07464i
$963$	−212247.	+	105304.i	−0.228870	+	0.113551i
$964$	432912.			0.465849
$965$		0			0
$966$	−153270.	−	95054.0i	−0.164249	−	0.101863i
$967$	−811983.			−0.868349			−0.434174	−	0.900829i	$-0.642960\pi$
$967$	−811983.			−0.868349			−0.434174	+	0.900829i	$0.642960\pi$
$968$			367400.i			0.392092i
$969$	−406560.	+	655558.i	−0.432989	+	0.698174i
$970$		0			0
$971$			333487.i			0.353705i	0.984237	+	0.176852i	$0.0565915\pi$
$971$			333487.i			0.353705i	−0.984237	+	0.176852i	$0.943409\pi$
$972$	330829.	−	126792.i	0.350164	−	0.134202i
$973$	−296335.			−0.313009
$974$		−	1.41014e6i		−	1.48643i
$975$		0			0
$976$	115072.			0.120801
$977$			1.32479e6i			1.38790i	0.720023	+	0.693951i	$0.244131\pi$
$977$			1.32479e6i			1.38790i	−0.720023	+	0.693951i	$0.755869\pi$
$978$	−183794.	+	296359.i	−0.192156	+	0.309842i
$979$	−898560.			−0.937522
$980$		0			0
$981$	228672.	+	460903.i	0.237616	+	0.478930i
$982$	725387.			0.752223
$983$			815276.i			0.843719i	0.906661	+	0.421859i	$0.138622\pi$
$983$			815276.i			0.843719i	−0.906661	+	0.421859i	$0.861378\pi$
$984$	1.10682e6	+	686421.i	1.14311	+	0.708925i
$985$		0			0
$986$		−	170275.i		−	0.175145i
$987$	177369.	−	286000.i	0.182073	−	0.293583i
$988$	452303.			0.463357
$989$			1.07094e6i			1.09490i
$990$		0			0
$991$	1.57635e6			1.60511			0.802557	−	0.596575i	$-0.203472\pi$
$991$	1.57635e6			1.60511			0.802557	+	0.596575i	$0.203472\pi$
$992$			23072.0i			0.0234456i
$993$	−1.56100e6	−	968093.i	−1.58309	−	0.981790i
$994$	−224640.			−0.227360
$995$		0			0
$996$	126270.	−	203604.i	0.127286	−	0.205243i
$997$	128251.			0.129024			0.0645118	−	0.997917i	$-0.479451\pi$
$997$	128251.			0.129024			0.0645118	+	0.997917i	$0.479451\pi$
$998$		−	498843.i		−	0.500844i
$999$	88452.0	−	932545.i	0.0886292	−	0.934413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.5.c.h.26.3		4
3.2	odd	2	inner	75.5.c.h.26.1		4
5.2	odd	4		15.5.d.c.14.2	yes	4
5.3	odd	4		15.5.d.c.14.3	yes	4
5.4	even	2	inner	75.5.c.h.26.2		4
15.2	even	4		15.5.d.c.14.4	yes	4
15.8	even	4		15.5.d.c.14.1	✓	4
15.14	odd	2	inner	75.5.c.h.26.4		4
20.3	even	4		240.5.c.c.209.2		4
20.7	even	4		240.5.c.c.209.3		4
60.23	odd	4		240.5.c.c.209.4		4
60.47	odd	4		240.5.c.c.209.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.5.d.c.14.1	✓	4	15.8	even	4
15.5.d.c.14.2	yes	4	5.2	odd	4
15.5.d.c.14.3	yes	4	5.3	odd	4
15.5.d.c.14.4	yes	4	15.2	even	4
75.5.c.h.26.1		4	3.2	odd	2	inner
75.5.c.h.26.2		4	5.4	even	2	inner
75.5.c.h.26.3		4	1.1	even	1	trivial
75.5.c.h.26.4		4	15.14	odd	2	inner
240.5.c.c.209.1		4	60.47	odd	4
240.5.c.c.209.2		4	20.3	even	4
240.5.c.c.209.3		4	20.7	even	4
240.5.c.c.209.4		4	60.23	odd	4

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	75.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.16228i q^{2} +(-7.64853 - 4.74342i) q^{3} +6.00000 q^{4} +(15.0000 - 24.1868i) q^{6} -15.2971 q^{7} +69.5701i q^{8} +(36.0000 + 72.5603i) q^{9} +96.7471i q^{11} +(-45.8912 - 28.4605i) q^{12} -244.753 q^{13} -48.3735i q^{14} -124.000 q^{16} +278.280i q^{17} +(-229.456 + 113.842i) q^{18} -308.000 q^{19} +(117.000 + 72.5603i) q^{21} -305.941 q^{22} +414.258i q^{23} +(330.000 - 532.109i) q^{24} -773.977i q^{26} +(68.8368 - 725.743i) q^{27} -91.7824 q^{28} +193.494i q^{29} +32.0000 q^{31} +720.999i q^{32} +(458.912 - 739.973i) q^{33} -880.000 q^{34} +(216.000 + 435.362i) q^{36} +1284.95 q^{37} -973.982i q^{38} +(1872.00 + 1160.97i) q^{39} +2080.06i q^{41} +(-229.456 + 369.986i) q^{42} +2585.20 q^{43} +580.483i q^{44} -1310.00 q^{46} -2444.44i q^{47} +(948.418 + 588.184i) q^{48} -2167.00 q^{49} +(1320.00 - 2128.44i) q^{51} -1468.52 q^{52} -1416.70i q^{53} +(2295.00 + 217.681i) q^{54} -1064.22i q^{56} +(2355.75 + 1460.97i) q^{57} -611.882 q^{58} -3966.63i q^{59} -928.000 q^{61} +101.193i q^{62} +(-550.694 - 1109.96i) q^{63} -4264.00 q^{64} +(2340.00 + 1451.21i) q^{66} +2585.20 q^{67} +1669.68i q^{68} +(1965.00 - 3168.47i) q^{69} -4643.86i q^{71} +(-5048.03 + 2504.52i) q^{72} -4221.99 q^{73} +4063.38i q^{74} -1848.00 q^{76} -1479.95i q^{77} +(-3671.29 + 5919.78i) q^{78} -8.00000 q^{79} +(-3969.00 + 5224.34i) q^{81} -6577.74 q^{82} +4436.68i q^{83} +(702.000 + 435.362i) q^{84} +8175.13i q^{86} +(917.824 - 1479.95i) q^{87} -6730.71 q^{88} +9287.72i q^{89} +3744.00 q^{91} +2485.55i q^{92} +(-244.753 - 151.789i) q^{93} +7730.00 q^{94} +(3420.00 - 5514.58i) q^{96} +2508.72 q^{97} -6852.66i q^{98} +(-7020.00 + 3482.90i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 24 q^{4} + 60 q^{6} + 144 q^{9} - 496 q^{16} - 1232 q^{19} + 468 q^{21} + 1320 q^{24} + 128 q^{31} - 3520 q^{34} + 864 q^{36} + 7488 q^{39} - 5240 q^{46} - 8668 q^{49} + 5280 q^{51} + 9180 q^{54}+ \cdots - 28080 q^{99}+O(q^{100}) \) 4 * q + 24 * q^4 + 60 * q^6 + 144 * q^9 - 496 * q^16 - 1232 * q^19 + 468 * q^21 + 1320 * q^24 + 128 * q^31 - 3520 * q^34 + 864 * q^36 + 7488 * q^39 - 5240 * q^46 - 8668 * q^49 + 5280 * q^51 + 9180 * q^54 - 3712 * q^61 - 17056 * q^64 + 9360 * q^66 + 7860 * q^69 - 7392 * q^76 - 32 * q^79 - 15876 * q^81 + 2808 * q^84 + 14976 * q^91 + 30920 * q^94 + 13680 * q^96 - 28080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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