LMFDB - Embedded newform 75.5.c.h.26.4

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			26.4
Root			$2.54951 + 1.58114i$ of defining polynomial
Character	$\chi$	$=$	75.26
Dual form			75.5.c.h.26.2

$q$-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	$-0.450110\pi$
$7$	15.2971			0.312185			0.156092	+	0.987742i	$0.450110\pi$
$8$			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	$-0.869086\pi$
$11$		−	96.7471i		−	0.799563i	0.916611	−	0.399781i	$-0.130914\pi$
$12$	45.8912	−	28.4605i	0.318689	−	0.197642i
$13$	244.753			1.44824			0.724121	−	0.689673i	$-0.242246\pi$
$13$	244.753			1.44824			0.724121	+	0.689673i	$0.242246\pi$
$14$			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	$-0.963301\pi$
$29$		−	193.494i		−	0.230076i	0.993361	−	0.115038i	$-0.0366990\pi$
$30$		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	$-0.655495\pi$
$37$	−1284.95			−0.938607			−0.469303	+	0.883037i	$0.655495\pi$
$38$		−	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	$-0.787660\pi$
$41$		−	2080.06i		−	1.23740i	0.785629	−	0.618698i	$-0.212340\pi$
$42$	229.456	+	369.986i	0.130077	+	0.209743i
$43$	−2585.20			−1.39816			−0.699081	−	0.715042i	$-0.746407\pi$
$43$	−2585.20			−1.39816			−0.699081	+	0.715042i	$0.746407\pi$
$44$		−	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	$0.192962\pi$
$59$			3966.63i			1.13951i	−0.821815	+	0.569754i	$0.807038\pi$
$60$		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	$-0.592973\pi$
$67$	−2585.20			−0.575897			−0.287949	+	0.957646i	$0.592973\pi$
$68$			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	$0.152369\pi$
$71$			4643.86i			0.921218i	−0.887603	+	0.460609i	$0.847631\pi$
$72$	5048.03	+	2504.52i	0.973771	+	0.483126i
$73$	4221.99			0.792266			0.396133	−	0.918193i	$-0.370352\pi$
$73$	4221.99			0.792266			0.396133	+	0.918193i	$0.370352\pi$
$74$		−	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	$-0.800595\pi$
$89$		−	9287.72i		−	1.17254i	0.810114	−	0.586272i	$-0.199405\pi$
$90$		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	$-0.542562\pi$
$97$	−2508.72			−0.266630			−0.133315	+	0.991074i	$0.542562\pi$
$98$		−	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	$0.0761976\pi$
$101$			4837.35i			0.474204i	−0.971485	+	0.237102i	$0.923802\pi$
$102$	−6730.71	+	4174.21i	−0.646934	+	0.401212i
$103$	−5491.64			−0.517640			−0.258820	−	0.965926i	$-0.583334\pi$
$103$	−5491.64			−0.517640			−0.258820	+	0.965926i	$0.583334\pi$
$104$			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	$-0.537673\pi$
$127$	−3808.97			−0.236156			−0.118078	+	0.993004i	$0.537673\pi$
$128$		−	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	$-0.924831\pi$
$131$		−	8030.01i		−	0.467922i	0.972246	−	0.233961i	$-0.0751688\pi$
$132$	−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	$-0.881081\pi$
$149$		−	16205.1i		−	0.729928i	0.931022	−	0.364964i	$-0.118919\pi$
$150$		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	$-0.297338\pi$
$157$	29309.2			1.18906			0.594530	+	0.804073i	$0.297338\pi$
$158$		−	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	$-0.425935\pi$
$163$	12252.9			0.461174			0.230587	+	0.973052i	$0.425935\pi$
$164$		−	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	$0.202186\pi$
$179$			38021.6i			1.18665i	−0.804961	+	0.593327i	$0.797814\pi$
$180$		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	$-0.724650\pi$
$191$		−	55532.8i		−	1.52224i	0.648611	−	0.761120i	$-0.275350\pi$
$192$	−32613.3	+	20225.9i	−0.884693	+	0.548663i
$193$	50725.0			1.36178			0.680891	−	0.732384i	$-0.261593\pi$
$193$	50725.0			1.36178			0.680891	+	0.732384i	$0.261593\pi$
$194$		−	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	$-0.776892\pi$
$223$	−76011.1			−1.52851			−0.764253	+	0.644916i	$0.776892\pi$
$224$			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	$-0.717385\pi$
$239$		−	88620.3i		−	1.55145i	0.631072	−	0.775725i	$-0.282615\pi$
$240$		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	$-0.959564\pi$
$251$		−	15963.3i		−	0.253381i	0.991942	−	0.126691i	$-0.0404355\pi$
$252$	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	$-0.991381\pi$
$269$		−	3918.26i		−	0.0541487i	0.999633	−	0.0270744i	$-0.00861909\pi$
$270$		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	$-0.478534\pi$
$277$	10340.8			0.134771			0.0673853	+	0.997727i	$0.478534\pi$
$278$			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	$-0.954901\pi$
$281$		−	22300.2i		−	0.282420i	0.989980	−	0.141210i	$-0.0450994\pi$
$282$	59123.1	−	36666.6i	0.743463	−	0.461076i
$283$	−117466.			−1.46669			−0.733347	−	0.679854i	$-0.762043\pi$
$283$	−117466.			−1.46669			−0.733347	+	0.679854i	$0.762043\pi$
$284$			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	$-0.482400\pi$
$307$	10417.3			0.110530			0.0552648	+	0.998472i	$0.482400\pi$
$308$		−	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	$0.176736\pi$
$311$			101971.i			1.05428i	−0.849777	+	0.527142i	$0.823264\pi$
$312$	80768.5	+	130235.i	0.829722	+	1.33789i
$313$	182586.			1.86371			0.931854	−	0.362832i	$-0.118190\pi$
$313$	182586.			1.86371			0.931854	+	0.362832i	$0.118190\pi$
$314$			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	$-0.436643\pi$
$337$	44912.2			0.395461			0.197731	+	0.980256i	$0.436643\pi$
$338$			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	$-0.759972\pi$
$359$		−	176467.i		−	1.36922i	0.728909	−	0.684611i	$-0.240028\pi$
$360$		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	$-0.729842\pi$
$367$	−178042.			−1.32188			−0.660939	+	0.750440i	$0.729842\pi$
$368$		−	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	$-0.590165\pi$
$373$	−77770.2			−0.558979			−0.279490	+	0.960149i	$0.590165\pi$
$374$			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	$0.106963\pi$
$389$			99794.6i			0.659490i	−0.944070	+	0.329745i	$0.893037\pi$
$390$		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	$-0.650501\pi$
$397$	−143548.			−0.910783			−0.455391	+	0.890291i	$0.650501\pi$
$398$		−	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	$-0.723181\pi$
$401$		−	245738.i		−	1.52821i	0.645092	−	0.764105i	$-0.276819\pi$
$402$	−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	$0.214755\pi$
$419$			219326.i			1.24928i	−0.780911	+	0.624642i	$0.785245\pi$
$420$		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	$0.136979\pi$
$431$			154989.i			0.834345i	−0.908827	+	0.417173i	$0.863021\pi$
$432$	8535.76	+	89992.1i	0.0457377	+	0.482211i
$433$	−153644.			−0.819481			−0.409740	−	0.912202i	$-0.634381\pi$
$433$	−153644.			−0.819481			−0.409740	+	0.912202i	$0.634381\pi$
$434$			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	$-0.937154\pi$
$449$		−	79090.7i		−	0.392313i	0.980573	−	0.196157i	$-0.0628461\pi$
$450$		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	$-0.117836\pi$
$457$	389402.			1.86451			0.932257	+	0.361797i	$0.117836\pi$
$458$		−	127433.i		−	0.607509i
$459$	201960.	−	19155.9i	0.958606	−	0.0909238i
$460$		0			0
$461$		−	236643.i		−	1.11351i	−0.830678	−	0.556753i	$-0.812047\pi$
$461$		−	236643.i		−	1.11351i	0.830678	−	0.556753i	$-0.187953\pi$
$462$	35795.1	−	22199.2i	0.167703	−	0.104005i
$463$	253793.			1.18391			0.591955	−	0.805971i	$-0.298356\pi$
$463$	253793.			1.18391			0.591955	+	0.805971i	$0.298356\pi$
$464$			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	$-0.811945\pi$
$479$		−	255606.i		−	1.11404i	0.830500	−	0.557019i	$-0.188055\pi$
$480$		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	$-0.110733\pi$
$487$	445925.			1.88020			0.940099	+	0.340902i	$0.110733\pi$
$488$		−	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	$0.157822\pi$
$491$			229387.i			0.951495i	−0.879582	+	0.475747i	$0.842178\pi$
$492$	−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	$0.0956946\pi$
$509$			153441.i			0.592251i	−0.955149	+	0.296125i	$0.904305\pi$
$510$		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	$0.147490\pi$
$521$			242642.i			0.893902i	−0.894558	+	0.446951i	$0.852510\pi$
$522$	22027.8	−	44398.4i	0.0808406	−	0.162939i
$523$	133865.			0.489398			0.244699	−	0.969599i	$-0.421311\pi$
$523$	133865.			0.489398			0.244699	+	0.969599i	$0.421311\pi$
$524$		−	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	$-0.576898\pi$
$547$	−143165.			−0.478479			−0.239239	+	0.970961i	$0.576898\pi$
$548$			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	$0.184996\pi$
$569$			355497.i			1.09802i	−0.835815	+	0.549012i	$0.815004\pi$
$570$		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	$-0.549516\pi$
$577$	−103163.			−0.309866			−0.154933	+	0.987925i	$0.549516\pi$
$578$			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	$-0.694885\pi$
$599$		−	587255.i		−	1.63671i	0.574710	−	0.818357i	$-0.305115\pi$
$600$		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	$-0.361166\pi$
$607$	311310.			0.844921			0.422461	+	0.906381i	$0.361166\pi$
$608$		−	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	$-0.596478\pi$
$613$	−224316.			−0.596952			−0.298476	+	0.954417i	$0.596478\pi$
$614$			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	$0.118055\pi$
$641$			297836.i			0.724871i	−0.932009	+	0.362436i	$0.881945\pi$
$642$	−70748.9	+	43876.6i	−0.171652	+	0.106454i
$643$	130805.			0.316376			0.158188	−	0.987409i	$-0.449435\pi$
$643$	130805.			0.316376			0.158188	+	0.987409i	$0.449435\pi$
$644$			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	$-0.955214\pi$
$659$		−	121805.i		−	0.280474i	0.990118	−	0.140237i	$-0.0447865\pi$
$660$		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	$-0.564316\pi$
$673$	−181790.			−0.401366			−0.200683	+	0.979656i	$0.564316\pi$
$674$			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	$-0.992244\pi$
$701$		−	23944.9i		−	0.0487278i	0.999703	−	0.0243639i	$-0.00775604\pi$
$702$	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	$0.353982\pi$
$719$			927031.i			1.79323i	−0.442810	+	0.896616i	$0.646018\pi$
$720$		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	$-0.615114\pi$
$727$	−373998.			−0.707620			−0.353810	+	0.935317i	$0.615114\pi$
$728$			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	$-0.595704\pi$
$733$	−318240.			−0.592307			−0.296153	+	0.955140i	$0.595704\pi$
$734$		−	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	$-0.781303\pi$
$757$	−886067.			−1.54623			−0.773116	+	0.634265i	$0.781303\pi$
$758$			38870.7i			0.0676525i
$759$	306540.	−	190108.i	0.532113	−	0.330002i
$760$		0			0
$761$			261604.i			0.451726i	0.974159	+	0.225863i	$0.0725202\pi$
$761$			261604.i			0.451726i	−0.974159	+	0.225863i	$0.927480\pi$
$762$	−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	$-0.668984\pi$
$787$	−627164.			−1.01259			−0.506293	+	0.862362i	$0.668984\pi$
$788$		−	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	$-0.975414\pi$
$809$		−	101004.i		−	0.154327i	0.997018	−	0.0771634i	$-0.0245863\pi$
$810$		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	$0.195792\pi$
$821$			777895.i			1.15408i	−0.816717	+	0.577038i	$0.804208\pi$
$822$	−514287.	+	318947.i	−0.761136	+	0.472036i
$823$	218457.			0.322528			0.161264	−	0.986911i	$-0.448443\pi$
$823$	218457.			0.322528			0.161264	+	0.986911i	$0.448443\pi$
$824$		−	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	$-0.963257\pi$
$839$		−	162148.i		−	0.230350i	0.993345	−	0.115175i	$-0.0367429\pi$
$840$		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	$-0.840699\pi$
$853$	−1.27675e6			−1.75472			−0.877362	+	0.479828i	$0.840699\pi$
$854$		−	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	$-0.594058\pi$
$877$	−447959.			−0.582424			−0.291212	+	0.956659i	$0.594058\pi$
$878$		−	206079.i		−	0.267329i
$879$	272100.	+	438748.i	0.352169	+	0.567855i
$880$		0			0
$881$			72995.7i			0.0940471i	0.998894	+	0.0470235i	$0.0149736\pi$
$881$			72995.7i			0.0940471i	−0.998894	+	0.0470235i	$0.985026\pi$
$882$	−497231.	−	246696.i	−0.639177	−	0.317120i
$883$	797910.			1.02337			0.511685	−	0.859173i	$-0.329022\pi$
$883$	797910.			1.02337			0.511685	+	0.859173i	$0.329022\pi$
$884$			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	$-0.275861\pi$
$907$	1.06515e6			1.29478			0.647390	+	0.762159i	$0.275861\pi$
$908$		−	100731.i		−	0.122178i
$909$	351000.	+	174145.i	0.424795	+	0.210757i
$910$		0			0
$911$			1.25520e6i			1.51243i	0.654324	+	0.756215i	$0.272953\pi$
$911$			1.25520e6i			1.51243i	−0.654324	+	0.756215i	$0.727047\pi$
$912$	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	$-0.857271\pi$
$929$		−	748290.i		−	0.867039i	0.901144	−	0.433520i	$-0.142729\pi$
$930$		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	$-0.468570\pi$
$937$	173102.			0.197161			0.0985807	+	0.995129i	$0.468570\pi$
$938$		−	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	$-0.550630\pi$
$941$		−	1.74861e6i		−	1.97475i	0.158388	−	0.987377i	$-0.449370\pi$
$942$	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	$-0.357040\pi$
$967$	811983.			0.868349			0.434174	+	0.900829i	$0.357040\pi$
$968$			367400.i			0.392092i
$969$	−406560.	−	655558.i	−0.432989	−	0.698174i
$970$		0			0
$971$		−	333487.i		−	0.353705i	−0.984237	−	0.176852i	$-0.943409\pi$
$971$		−	333487.i		−	0.353705i	0.984237	−	0.176852i	$-0.0565915\pi$
$972$	−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	$-0.520549\pi$
$997$	−128251.			−0.129024			−0.0645118	+	0.997917i	$0.520549\pi$
$998$		−	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.26.4		4
3.2	odd	2	inner	75.5.c.h.26.2		4
5.2	odd	4		15.5.d.c.14.1	✓	4
5.3	odd	4		15.5.d.c.14.4	yes	4
5.4	even	2	inner	75.5.c.h.26.1		4
15.2	even	4		15.5.d.c.14.3	yes	4
15.8	even	4		15.5.d.c.14.2	yes	4
15.14	odd	2	inner	75.5.c.h.26.3		4
20.3	even	4		240.5.c.c.209.1		4
20.7	even	4		240.5.c.c.209.4		4
60.23	odd	4		240.5.c.c.209.3		4
60.47	odd	4		240.5.c.c.209.2		4

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