LMFDB - Embedded newform 75.18.b.g.49.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [75,18,Mod(49,75)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("75.49"); S:= CuspForms(chi, 18); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(75, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 18, names="a")

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	75.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,0,-524352] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$137.416565508$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} + 2 x^{8} - 1889754 x^{7} + 1938226081 x^{6} - 95481875708 x^{5} + \cdots + 14\!\cdots\!52 $ x^10 - 2x^9 + 2x^8 - 1889754x^7 + 1938226081x^6 - 95481875708x^5 + 1972672389512x^4 + 323008934556288x^3 + 416576363441361984x^2 - 11017896653965453056*x + 145704434205795697152
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{6}\cdot 5^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.2
Root			$119.753 - 119.753i$ of defining polynomial
Character	$\chi$	$=$	75.49
Dual form			75.18.b.g.49.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-519.013i q^{2} +6561.00i q^{3} -138303. q^{4} +3.40525e6 q^{6} -2.20319e7i q^{7} +3.75290e6i q^{8} -4.30467e7 q^{9} -1.24093e9 q^{11} -9.07405e8i q^{12} -4.30552e9i q^{13} -1.14348e10 q^{14} -1.61798e10 q^{16} -2.30313e10i q^{17} +2.23418e10i q^{18} +4.02946e9 q^{19} +1.44551e11 q^{21} +6.44058e11i q^{22} -5.76743e11i q^{23} -2.46228e10 q^{24} -2.23462e12 q^{26} -2.82430e11i q^{27} +3.04707e12i q^{28} +4.15476e12 q^{29} -3.90835e12 q^{31} +8.88944e12i q^{32} -8.14173e12i q^{33} -1.19535e13 q^{34} +5.95348e12 q^{36} -2.59508e13i q^{37} -2.09134e12i q^{38} +2.82485e13 q^{39} +2.13728e13 q^{41} -7.50239e13i q^{42} -7.22020e13i q^{43} +1.71624e14 q^{44} -2.99337e14 q^{46} -1.29859e14i q^{47} -1.06156e14i q^{48} -2.52773e14 q^{49} +1.51108e14 q^{51} +5.95466e14i q^{52} -2.09491e14i q^{53} -1.46585e14 q^{54} +8.26834e13 q^{56} +2.64373e13i q^{57} -2.15638e15i q^{58} -9.51957e14 q^{59} +1.05903e14 q^{61} +2.02848e15i q^{62} +9.48400e14i q^{63} +2.49302e15 q^{64} -4.22567e15 q^{66} +3.73528e15i q^{67} +3.18529e15i q^{68} +3.78401e15 q^{69} +9.20903e15 q^{71} -1.61550e14i q^{72} +1.67249e15i q^{73} -1.34688e16 q^{74} -5.57286e14 q^{76} +2.73400e16i q^{77} -1.46614e16i q^{78} -8.95327e15 q^{79} +1.85302e15 q^{81} -1.10928e16i q^{82} -1.10780e16i q^{83} -1.99918e16 q^{84} -3.74738e16 q^{86} +2.72594e16i q^{87} -4.65708e15i q^{88} -3.12179e16 q^{89} -9.48586e16 q^{91} +7.97652e16i q^{92} -2.56427e16i q^{93} -6.73986e16 q^{94} -5.83236e16 q^{96} +1.37306e17i q^{97} +1.31192e17i q^{98} +5.34179e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 524352 q^{4} + 2676888 q^{6} - 430467210 q^{9} - 1738071156 q^{11} - 15639914856 q^{14} - 66104662272 q^{16} + 64503397086 q^{19} - 28467772218 q^{21} + 455863318848 q^{24} - 1998349267080 q^{26}+ \cdots + 74\!\cdots\!76 q^{99}+O(q^{100}) $ 10 * q - 524352 * q^4 + 2676888 * q^6 - 430467210 * q^9 - 1738071156 * q^11 - 15639914856 * q^14 - 66104662272 * q^16 + 64503397086 * q^19 - 28467772218 * q^21 + 455863318848 * q^24 - 1998349267080 * q^26 + 5038974971532 * q^29 - 3489865725722 * q^31 - 1491591755504 * q^34 + 22571634249792 * q^36 + 44606871044622 * q^39 - 133243570719792 * q^41 + 464958581702400 * q^44 - 505909078820112 * q^46 + 452446566258524 * q^49 + 228379365399060 * q^51 - 115231250884248 * q^54 + 2926573946176320 * q^56 + 2701499222853564 * q^59 + 5840018660275806 * q^61 + 11386481551585280 * q^64 + 1505903745960720 * q^66 + 2909437774402284 * q^69 + 7244811708974160 * q^71 - 21913820768686896 * q^74 + 26044164027809216 * q^76 - 4680370945616080 * q^79 + 18530201888518410 * q^81 - 22778461047507264 * q^84 - 76129165470984216 * q^86 - 11696951721213504 * q^89 - 233416679038137442 * q^91 - 75086521605753488 * q^94 - 121856486730352128 * q^96 + 74818264130479476 * 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 $

$2$	− 519.013i	− 1.43359i	−0.697286	−	0.716793i	$-0.745609\pi$
$2$	− 519.013i	− 1.43359i	0.697286	−	0.716793i	$-0.254391\pi$
$3$	6561.00i	0.577350i
$3$	6561.00i	0.577350i
$4$	−138303.	−1.05517
$5$	0	0
$5$	0	0
$6$	3.40525e6	0.827681
$7$	− 2.20319e7i	− 1.44450i	−0.691631	−	0.722251i	$-0.743108\pi$
$7$	− 2.20319e7i	− 1.44450i	0.691631	−	0.722251i	$-0.256892\pi$
$8$	3.75290e6i	0.0790864i
$9$	−4.30467e7	−0.333333
$10$	0	0
$11$	−1.24093e9	−1.74546	−0.872728	−	0.488207i	$-0.837651\pi$
$11$	−1.24093e9	−1.74546	−0.872728	+	0.488207i	$0.837651\pi$
$12$	− 9.07405e8i	− 0.609201i
$13$	− 4.30552e9i	− 1.46389i	−0.681366	−	0.731943i	$-0.738614\pi$
$13$	− 4.30552e9i	− 1.46389i	0.681366	−	0.731943i	$-0.261386\pi$
$14$	−1.14348e10	−2.07082
$15$	0	0
$16$	−1.61798e10	−0.941790
$17$	− 2.30313e10i	− 0.800759i	−0.916349	−	0.400380i	$-0.868878\pi$
$17$	− 2.30313e10i	− 0.800759i	0.916349	−	0.400380i	$-0.131122\pi$
$18$	2.23418e10i	0.477862i
$19$	4.02946e9	0.0544304	0.0272152	−	0.999630i	$-0.491336\pi$
$19$	4.02946e9	0.0544304	0.0272152	+	0.999630i	$0.491336\pi$
$20$	0	0
$21$	1.44551e11	0.833983
$22$	6.44058e11i	2.50226i
$23$	− 5.76743e11i	− 1.53566i	−0.640653	−	0.767831i	$-0.721336\pi$
$23$	− 5.76743e11i	− 1.53566i	0.640653	−	0.767831i	$-0.278664\pi$
$24$	−2.46228e10	−0.0456606
$25$	0	0
$26$	−2.23462e12	−2.09860
$27$	− 2.82430e11i	− 0.192450i
$28$	3.04707e12i	1.52419i
$29$	4.15476e12	1.54228	0.771140	−	0.636666i	$-0.219687\pi$
$29$	4.15476e12	1.54228	0.771140	+	0.636666i	$0.219687\pi$
$30$	0	0
$31$	−3.90835e12	−0.823036	−0.411518	−	0.911402i	$-0.635001\pi$
$31$	−3.90835e12	−0.823036	−0.411518	+	0.911402i	$0.635001\pi$
$32$	8.88944e12i	1.42922i
$33$	− 8.14173e12i	− 1.00774i
$34$	−1.19535e13	−1.14796
$35$	0	0
$36$	5.95348e12	0.351722
$37$	− 2.59508e13i	− 1.21461i	−0.794470	−	0.607304i	$-0.792251\pi$
$37$	− 2.59508e13i	− 1.21461i	0.794470	−	0.607304i	$-0.207749\pi$
$38$	− 2.09134e12i	− 0.0780306i
$39$	2.82485e13	0.845175
$40$	0	0
$41$	2.13728e13	0.418022	0.209011	−	0.977913i	$-0.432975\pi$
$41$	2.13728e13	0.418022	0.209011	+	0.977913i	$0.432975\pi$
$42$	− 7.50239e13i	− 1.19559i
$43$	− 7.22020e13i	− 0.942035i	−0.882124	−	0.471018i	$-0.843887\pi$
$43$	− 7.22020e13i	− 0.942035i	0.882124	−	0.471018i	$-0.156113\pi$
$44$	1.71624e14	1.84175
$45$	0	0
$46$	−2.99337e14	−2.20150
$47$	− 1.29859e14i	− 0.795500i	−0.917494	−	0.397750i	$-0.869791\pi$
$47$	− 1.29859e14i	− 0.795500i	0.917494	−	0.397750i	$-0.130209\pi$
$48$	− 1.06156e14i	− 0.543743i
$49$	−2.52773e14	−1.08658
$50$	0	0
$51$	1.51108e14	0.462319
$52$	5.95466e14i	1.54464i
$53$	− 2.09491e14i	− 0.462189i	−0.972931	−	0.231095i	$-0.925769\pi$
$53$	− 2.09491e14i	− 0.462189i	0.972931	−	0.231095i	$-0.0742307\pi$
$54$	−1.46585e14	−0.275894
$55$	0	0
$56$	8.26834e13	0.114240
$57$	2.64373e13i	0.0314254i
$58$	− 2.15638e15i	− 2.21099i
$59$	−9.51957e14	−0.844064	−0.422032	−	0.906581i	$-0.638683\pi$
$59$	−9.51957e14	−0.844064	−0.422032	+	0.906581i	$0.638683\pi$
$60$	0	0
$61$	1.05903e14	0.0707299	0.0353649	−	0.999374i	$-0.488741\pi$
$61$	1.05903e14	0.0707299	0.0353649	+	0.999374i	$0.488741\pi$
$62$	2.02848e15i	1.17989i
$63$	9.48400e14i	0.481501i
$64$	2.49302e15	1.10712
$65$	0	0
$66$	−4.22567e15	−1.44468
$67$	3.73528e15i	1.12379i	0.827207	+	0.561897i	$0.189928\pi$
$67$	3.73528e15i	1.12379i	−0.827207	+	0.561897i	$0.810072\pi$
$68$	3.18529e15i	0.844935i
$69$	3.78401e15	0.886615
$70$	0	0
$71$	9.20903e15	1.69246	0.846229	−	0.532820i	$-0.178868\pi$
$71$	9.20903e15	1.69246	0.846229	+	0.532820i	$0.178868\pi$
$72$	− 1.61550e14i	− 0.0263621i
$73$	1.67249e15i	0.242728i	0.992608	+	0.121364i	$0.0387268\pi$
$73$	1.67249e15i	0.242728i	−0.992608	+	0.121364i	$0.961273\pi$
$74$	−1.34688e16	−1.74124
$75$	0	0
$76$	−5.57286e14	−0.0574331
$77$	2.73400e16i	2.52131i
$78$	− 1.46614e16i	− 1.21163i
$79$	−8.95327e15	−0.663975	−0.331987	−	0.943284i	$-0.607719\pi$
$79$	−8.95327e15	−0.663975	−0.331987	+	0.943284i	$0.607719\pi$
$80$	0	0
$81$	1.85302e15	0.111111
$82$	− 1.10928e16i	− 0.599271i
$83$	− 1.10780e16i	− 0.539882i	−0.962877	−	0.269941i	$-0.912996\pi$
$83$	− 1.10780e16i	− 0.539882i	0.962877	−	0.269941i	$-0.0870043\pi$
$84$	−1.99918e16	−0.879992
$85$	0	0
$86$	−3.74738e16	−1.35049
$87$	2.72594e16i	0.890435i
$88$	− 4.65708e15i	− 0.138042i
$89$	−3.12179e16	−0.840599	−0.420300	−	0.907385i	$-0.638075\pi$
$89$	−3.12179e16	−0.840599	−0.420300	+	0.907385i	$0.638075\pi$
$90$	0	0
$91$	−9.48586e16	−2.11458
$92$	7.97652e16i	1.62038i
$93$	− 2.56427e16i	− 0.475180i
$94$	−6.73986e16	−1.14042
$95$	0	0
$96$	−5.83236e16	−0.825162
$97$	1.37306e17i	1.77881i	0.457118	+	0.889406i	$0.348882\pi$
$97$	1.37306e17i	1.77881i	−0.457118	+	0.889406i	$0.651118\pi$
$98$	1.31192e17i	1.55771i
$99$	5.34179e16	0.581819
$100$	0	0
$101$	−8.46639e16	−0.777976	−0.388988	−	0.921243i	$-0.627175\pi$
$101$	−8.46639e16	−0.777976	−0.388988	+	0.921243i	$0.627175\pi$
$102$	− 7.84271e16i	− 0.662773i
$103$	− 2.31605e17i	− 1.80149i	−0.434351	−	0.900743i	$-0.643022\pi$
$103$	− 2.31605e17i	− 1.80149i	0.434351	−	0.900743i	$-0.356978\pi$
$104$	1.61582e16	0.115773
$105$	0	0
$106$	−1.08728e17	−0.662588
$107$	− 1.94868e17i	− 1.09642i	−0.836340	−	0.548211i	$-0.815309\pi$
$107$	− 1.94868e17i	− 1.09642i	0.836340	−	0.548211i	$-0.184691\pi$
$108$	3.90608e16i	0.203067i
$109$	1.35039e17	0.649135	0.324568	−	0.945863i	$-0.394781\pi$
$109$	1.35039e17	0.649135	0.324568	+	0.945863i	$0.394781\pi$
$110$	0	0
$111$	1.70263e17	0.701254
$112$	3.56472e17i	1.36042i
$113$	2.22867e16i	0.0788639i	0.999222	+	0.0394320i	$0.0125548\pi$
$113$	2.22867e16i	0.0788639i	−0.999222	+	0.0394320i	$0.987445\pi$
$114$	1.37213e16	0.0450510
$115$	0	0
$116$	−5.74615e17	−1.62736
$117$	1.85338e17i	0.487962i
$118$	4.94079e17i	1.21004i
$119$	−5.07422e17	−1.15670
$120$	0	0
$121$	1.03446e18	2.04662
$122$	− 5.49648e16i	− 0.101397i
$123$	1.40227e17i	0.241345i
$124$	5.40535e17	0.868440
$125$	0	0
$126$	4.92232e17	0.690272
$127$	5.43551e17i	0.712703i	0.934352	+	0.356351i	$0.115979\pi$
$127$	5.43551e17i	0.712703i	−0.934352	+	0.356351i	$0.884021\pi$
$128$	− 1.28752e17i	− 0.157932i
$129$	4.73717e17	0.543884
$130$	0	0
$131$	−2.36018e17	−0.237760	−0.118880	−	0.992909i	$-0.537930\pi$
$131$	−2.36018e17	−0.237760	−0.118880	+	0.992909i	$0.537930\pi$
$132$	1.12602e18i	1.06333i
$133$	− 8.87766e16i	− 0.0786248i
$134$	1.93866e18	1.61106
$135$	0	0
$136$	8.64340e16	0.0633292
$137$	− 9.97906e17i	− 0.687013i	−0.939150	−	0.343506i	$-0.888385\pi$
$137$	− 9.97906e17i	− 0.687013i	0.939150	−	0.343506i	$-0.111615\pi$
$138$	− 1.96395e18i	− 1.27104i
$139$	4.46737e17	0.271910	0.135955	−	0.990715i	$-0.456590\pi$
$139$	4.46737e17	0.271910	0.135955	+	0.990715i	$0.456590\pi$
$140$	0	0
$141$	8.52005e17	0.459282
$142$	− 4.77961e18i	− 2.42628i
$143$	5.34284e18i	2.55515i
$144$	6.96488e17	0.313930
$145$	0	0
$146$	8.68045e17	0.347971
$147$	− 1.65844e18i	− 0.627340i
$148$	3.58907e18i	1.28161i
$149$	5.02835e18	1.69567	0.847836	−	0.530258i	$-0.177905\pi$
$149$	5.02835e18	1.69567	0.847836	+	0.530258i	$0.177905\pi$
$150$	0	0
$151$	4.15635e18	1.25144	0.625718	−	0.780050i	$-0.284806\pi$
$151$	4.15635e18	1.25144	0.625718	+	0.780050i	$0.284806\pi$
$152$	1.51222e16i	0.00430470i
$153$	9.91421e17i	0.266920i
$154$	1.41898e19	3.61452
$155$	0	0
$156$	−3.90685e18	−0.891800
$157$	7.18880e18i	1.55421i	0.629372	+	0.777104i	$0.283312\pi$
$157$	7.18880e18i	1.55421i	−0.629372	+	0.777104i	$0.716688\pi$
$158$	4.64687e18i	0.951865i
$159$	1.37447e18	0.266845
$160$	0	0
$161$	−1.27067e19	−2.21827
$162$	− 9.61742e17i	− 0.159287i
$163$	− 5.83085e18i	− 0.916511i	−0.888821	−	0.458255i	$-0.848475\pi$
$163$	− 5.83085e18i	− 0.916511i	0.888821	−	0.458255i	$-0.151525\pi$
$164$	−2.95593e18	−0.441083
$165$	0	0
$166$	−5.74965e18	−0.773968
$167$	− 9.43164e18i	− 1.20642i	−0.797584	−	0.603208i	$-0.793889\pi$
$167$	− 9.43164e18i	− 1.20642i	0.797584	−	0.603208i	$-0.206111\pi$
$168$	5.42486e17i	0.0659567i
$169$	−9.88708e18	−1.14296
$170$	0	0
$171$	−1.73455e17	−0.0181435
$172$	9.98573e18i	0.994004i
$173$	6.90079e18i	0.653893i	0.945043	+	0.326947i	$0.106020\pi$
$173$	6.90079e18i	0.653893i	−0.945043	+	0.326947i	$0.893980\pi$
$174$	1.41480e19	1.27651
$175$	0	0
$176$	2.00780e19	1.64385
$177$	− 6.24579e18i	− 0.487321i
$178$	1.62025e19i	1.20507i
$179$	−4.06827e18	−0.288509	−0.144254	−	0.989541i	$-0.546078\pi$
$179$	−4.06827e18	−0.288509	−0.144254	+	0.989541i	$0.546078\pi$
$180$	0	0
$181$	−2.33689e19	−1.50789	−0.753945	−	0.656937i	$-0.771852\pi$
$181$	−2.33689e19	−1.50789	−0.753945	+	0.656937i	$0.771852\pi$
$182$	4.92329e19i	3.03144i
$183$	6.94827e17i	0.0408359i
$184$	2.16446e18	0.121450
$185$	0	0
$186$	−1.33089e19	−0.681211
$187$	2.85802e19i	1.39769i
$188$	1.79599e19i	0.839386i
$189$	−6.22245e18	−0.277994
$190$	0	0
$191$	−5.52013e18	−0.225510	−0.112755	−	0.993623i	$-0.535967\pi$
$191$	−5.52013e18	−0.225510	−0.112755	+	0.993623i	$0.535967\pi$
$192$	1.63567e19i	0.639197i
$193$	4.10756e19i	1.53584i	0.640545	+	0.767921i	$0.278709\pi$
$193$	4.10756e19i	1.53584i	−0.640545	+	0.767921i	$0.721291\pi$
$194$	7.12637e19	2.55008
$195$	0	0
$196$	3.49592e19	1.14653
$197$	1.39245e19i	0.437338i	0.975799	+	0.218669i	$0.0701714\pi$
$197$	1.39245e19i	0.437338i	−0.975799	+	0.218669i	$0.929829\pi$
$198$	− 2.77246e19i	− 0.834087i
$199$	4.25157e19	1.22546	0.612729	−	0.790293i	$-0.290072\pi$
$199$	4.25157e19	1.22546	0.612729	+	0.790293i	$0.290072\pi$
$200$	0	0
$201$	−2.45072e19	−0.648823
$202$	4.39417e19i	1.11530i
$203$	− 9.15371e19i	− 2.22782i
$204$	−2.08987e19	−0.487823
$205$	0	0
$206$	−1.20206e20	−2.58259
$207$	2.48269e19i	0.511887i
$208$	6.96625e19i	1.37867i
$209$	−5.00027e18	−0.0950058
$210$	0	0
$211$	5.93453e19	1.03989	0.519943	−	0.854201i	$-0.325953\pi$
$211$	5.93453e19	1.03989	0.519943	+	0.854201i	$0.325953\pi$
$212$	2.89732e19i	0.487687i
$213$	6.04204e19i	0.977141i
$214$	−1.01139e20	−1.57181
$215$	0	0
$216$	1.05993e18	0.0152202
$217$	8.61082e19i	1.18888i
$218$	− 7.00872e19i	− 0.930591i
$219$	−1.09732e19	−0.140139
$220$	0	0
$221$	−9.91616e19	−1.17222
$222$	− 8.83689e19i	− 1.00531i
$223$	− 1.03851e20i	− 1.13715i	−0.822631	−	0.568576i	$-0.807495\pi$
$223$	− 1.03851e20i	− 1.13715i	0.822631	−	0.568576i	$-0.192505\pi$
$224$	1.95851e20	2.06451
$225$	0	0
$226$	1.15671e19	0.113058
$227$	2.21819e19i	0.208824i	0.994534	+	0.104412i	$0.0332960\pi$
$227$	2.21819e19i	0.208824i	−0.994534	+	0.104412i	$0.966704\pi$
$228$	− 3.65635e18i	− 0.0331590i
$229$	6.34370e19	0.554295	0.277147	−	0.960827i	$-0.410611\pi$
$229$	6.34370e19	0.554295	0.277147	+	0.960827i	$0.410611\pi$
$230$	0	0
$231$	−1.79378e20	−1.45568
$232$	1.55924e19i	0.121973i
$233$	− 4.78003e19i	− 0.360500i	−0.983621	−	0.180250i	$-0.942309\pi$
$233$	− 4.78003e19i	− 0.360500i	0.983621	−	0.180250i	$-0.0576907\pi$
$234$	9.61931e19	0.699535
$235$	0	0
$236$	1.31658e20	0.890628
$237$	− 5.87424e19i	− 0.383346i
$238$	2.63359e20i	1.65823i
$239$	−1.70167e20	−1.03394	−0.516968	−	0.856005i	$-0.672939\pi$
$239$	−1.70167e20	−1.03394	−0.516968	+	0.856005i	$0.672939\pi$
$240$	0	0
$241$	2.67750e20	1.51560	0.757800	−	0.652487i	$-0.226274\pi$
$241$	2.67750e20	1.51560	0.757800	+	0.652487i	$0.226274\pi$
$242$	− 5.36896e20i	− 2.93400i
$243$	1.21577e19i	0.0641500i
$244$	−1.46466e19	−0.0746318
$245$	0	0
$246$	7.27798e19	0.345989
$247$	− 1.73489e19i	− 0.0796798i
$248$	− 1.46676e19i	− 0.0650909i
$249$	7.26830e19	0.311701
$250$	0	0
$251$	2.81621e20	1.12834	0.564168	−	0.825660i	$-0.309197\pi$
$251$	2.81621e20	1.12834	0.564168	+	0.825660i	$0.309197\pi$
$252$	− 1.31166e20i	− 0.508063i
$253$	7.15697e20i	2.68043i
$254$	2.82110e20	1.02172
$255$	0	0
$256$	2.59941e20	0.880713
$257$	− 2.62465e20i	− 0.860279i	−0.902762	−	0.430140i	$-0.858464\pi$
$257$	− 2.62465e20i	− 0.860279i	0.902762	−	0.430140i	$-0.141536\pi$
$258$	− 2.45865e20i	− 0.779704i
$259$	−5.71745e20	−1.75450
$260$	0	0
$261$	−1.78849e20	−0.514093
$262$	1.22496e20i	0.340849i
$263$	2.06589e20i	0.556524i	0.960505	+	0.278262i	$0.0897583\pi$
$263$	2.06589e20i	0.556524i	−0.960505	+	0.278262i	$0.910242\pi$
$264$	3.05551e19	0.0796985
$265$	0	0
$266$	−4.60762e19	−0.112715
$267$	− 2.04821e20i	− 0.485320i
$268$	− 5.16599e20i	− 1.18579i
$269$	6.17347e19	0.137289	0.0686443	−	0.997641i	$-0.478133\pi$
$269$	6.17347e19	0.137289	0.0686443	+	0.997641i	$0.478133\pi$
$270$	0	0
$271$	5.96491e20	1.24556	0.622780	−	0.782397i	$-0.286003\pi$
$271$	5.96491e20	1.24556	0.622780	+	0.782397i	$0.286003\pi$
$272$	3.72642e20i	0.754147i
$273$	− 6.22368e20i	− 1.22086i
$274$	−5.17926e20	−0.984891
$275$	0	0
$276$	−5.23339e20	−0.935527
$277$	− 2.11230e20i	− 0.366165i	−0.983098	−	0.183082i	$-0.941392\pi$
$277$	− 2.11230e20i	− 0.366165i	0.983098	−	0.183082i	$-0.0586075\pi$
$278$	− 2.31862e20i	− 0.389807i
$279$	1.68242e20	0.274345
$280$	0	0
$281$	−8.38666e20	−1.28702	−0.643510	−	0.765437i	$-0.722523\pi$
$281$	−8.38666e20	−1.28702	−0.643510	+	0.765437i	$0.722523\pi$
$282$	− 4.42202e20i	− 0.658421i
$283$	1.12406e20i	0.162407i	0.996698	+	0.0812036i	$0.0258764\pi$
$283$	1.12406e20i	0.162407i	−0.996698	+	0.0812036i	$0.974124\pi$
$284$	−1.27363e21	−1.78583
$285$	0	0
$286$	2.77301e21	3.66302
$287$	− 4.70884e20i	− 0.603834i
$288$	− 3.82661e20i	− 0.476407i
$289$	2.96801e20	0.358784
$290$	0	0
$291$	−9.00865e20	−1.02700
$292$	− 2.31310e20i	− 0.256118i
$293$	4.51054e20i	0.485125i	0.970136	+	0.242563i	$0.0779880\pi$
$293$	4.51054e20i	0.485125i	−0.970136	+	0.242563i	$0.922012\pi$
$294$	−8.60754e20	−0.899345
$295$	0	0
$296$	9.73907e19	0.0960590
$297$	3.50475e20i	0.335913i
$298$	− 2.60978e21i	− 2.43089i
$299$	−2.48318e21	−2.24803
$300$	0	0
$301$	−1.59074e21	−1.36077
$302$	− 2.15720e21i	− 1.79404i
$303$	− 5.55480e20i	− 0.449165i
$304$	−6.51960e19	−0.0512620
$305$	0	0
$306$	5.14560e20	0.382652
$307$	1.85145e21i	1.33917i	0.742736	+	0.669584i	$0.233528\pi$
$307$	1.85145e21i	1.33917i	−0.742736	+	0.669584i	$0.766472\pi$
$308$	− 3.78120e21i	− 2.66041i
$309$	1.51956e21	1.04009
$310$	0	0
$311$	−2.47754e21	−1.60530	−0.802651	−	0.596449i	$-0.796578\pi$
$311$	−2.47754e21	−1.60530	−0.802651	+	0.596449i	$0.796578\pi$
$312$	1.06014e20i	0.0668418i
$313$	3.14503e21i	1.92973i	0.262740	+	0.964867i	$0.415374\pi$
$313$	3.14503e21i	1.92973i	−0.262740	+	0.964867i	$0.584626\pi$
$314$	3.73108e21	2.22809
$315$	0	0
$316$	1.23826e21	0.700604
$317$	− 1.00160e21i	− 0.551682i	−0.961203	−	0.275841i	$-0.911044\pi$
$317$	− 1.00160e21i	− 0.551682i	0.961203	−	0.275841i	$-0.0889564\pi$
$318$	− 7.13368e20i	− 0.382545i
$319$	−5.15576e21	−2.69198
$320$	0	0
$321$	1.27853e21	0.633020
$322$	6.59496e21i	3.18007i
$323$	− 9.28036e19i	− 0.0435856i
$324$	−2.56278e20	−0.117241
$325$	0	0
$326$	−3.02629e21	−1.31390
$327$	8.85993e20i	0.374778i
$328$	8.02101e19i	0.0330599i
$329$	−2.86104e21	−1.14910
$330$	0	0
$331$	5.03132e20	0.191930	0.0959652	−	0.995385i	$-0.469406\pi$
$331$	5.03132e20	0.191930	0.0959652	+	0.995385i	$0.469406\pi$
$332$	1.53212e21i	0.569666i
$333$	1.11710e21i	0.404869i
$334$	−4.89515e21	−1.72950
$335$	0	0
$336$	−2.33881e21	−0.785437
$337$	8.97899e20i	0.294018i	0.989135	+	0.147009i	$0.0469646\pi$
$337$	8.97899e20i	0.294018i	−0.989135	+	0.147009i	$0.953035\pi$
$338$	5.13153e21i	1.63853i
$339$	−1.46223e20	−0.0455321
$340$	0	0
$341$	4.84998e21	1.43657
$342$	9.00255e19i	0.0260102i
$343$	4.43772e20i	0.125072i
$344$	2.70967e20	0.0745022
$345$	0	0
$346$	3.58160e21	0.937412
$347$	− 5.59661e21i	− 1.42930i	−0.699480	−	0.714652i	$-0.746585\pi$
$347$	− 5.59661e21i	− 1.42930i	0.699480	−	0.714652i	$-0.253415\pi$
$348$	− 3.77005e21i	− 0.939558i
$349$	3.71034e21	0.902397	0.451198	−	0.892424i	$-0.350997\pi$
$349$	3.71034e21	0.902397	0.451198	+	0.892424i	$0.350997\pi$
$350$	0	0
$351$	−1.21601e21	−0.281725
$352$	− 1.10312e22i	− 2.49464i
$353$	− 5.79513e21i	− 1.27932i	−0.768660	−	0.639658i	$-0.779076\pi$
$353$	− 5.79513e21i	− 1.27932i	0.768660	−	0.639658i	$-0.220924\pi$
$354$	−3.24165e21	−0.698616
$355$	0	0
$356$	4.31753e21	0.886972
$357$	− 3.32920e21i	− 0.667820i
$358$	2.11149e21i	0.413602i
$359$	5.80575e21	1.11059	0.555297	−	0.831652i	$-0.312604\pi$
$359$	5.80575e21	1.11059	0.555297	+	0.831652i	$0.312604\pi$
$360$	0	0
$361$	−5.46415e21	−0.997037
$362$	1.21288e22i	2.16169i
$363$	6.78707e21i	1.18161i
$364$	1.31192e22	2.23124
$365$	0	0
$366$	3.60624e20	0.0585418
$367$	− 9.07311e20i	− 0.143911i	−0.997408	−	0.0719556i	$-0.977076\pi$
$367$	− 9.07311e20i	− 0.143911i	0.997408	−	0.0719556i	$-0.0229240\pi$
$368$	9.33160e21i	1.44627i
$369$	−9.20031e20	−0.139341
$370$	0	0
$371$	−4.61547e21	−0.667633
$372$	3.54645e21i	0.501394i
$373$	6.74690e21i	0.932350i	0.884693	+	0.466175i	$0.154368\pi$
$373$	6.74690e21i	0.932350i	−0.884693	+	0.466175i	$0.845632\pi$
$374$	1.48335e22	2.00371
$375$	0	0
$376$	4.87348e20	0.0629133
$377$	− 1.78884e22i	− 2.25772i
$378$	3.22953e21i	0.398529i
$379$	6.46161e21	0.779664	0.389832	−	0.920886i	$-0.372533\pi$
$379$	6.46161e21	0.779664	0.389832	+	0.920886i	$0.372533\pi$
$380$	0	0
$381$	−3.56624e21	−0.411479
$382$	2.86502e21i	0.323288i
$383$	1.10387e22i	1.21823i	0.793083	+	0.609114i	$0.208475\pi$
$383$	1.10387e22i	1.21823i	−0.793083	+	0.609114i	$0.791525\pi$
$384$	8.44744e20	0.0911822
$385$	0	0
$386$	2.13188e22	2.20176
$387$	3.10806e21i	0.314012i
$388$	− 1.89898e22i	− 1.87694i
$389$	6.04364e21	0.584423	0.292211	−	0.956354i	$-0.405609\pi$
$389$	6.04364e21	0.584423	0.292211	+	0.956354i	$0.405609\pi$
$390$	0	0
$391$	−1.32831e22	−1.22970
$392$	− 9.48630e20i	− 0.0859341i
$393$	− 1.54851e21i	− 0.137271i
$394$	7.22700e21	0.626961
$395$	0	0
$396$	−7.38785e21	−0.613916
$397$	− 1.57055e22i	− 1.27741i	−0.769450	−	0.638707i	$-0.779470\pi$
$397$	− 1.57055e22i	− 1.27741i	0.769450	−	0.638707i	$-0.220530\pi$
$398$	− 2.20662e22i	− 1.75680i
$399$	5.82463e20	0.0453940
$400$	0	0
$401$	1.21091e22	0.904450	0.452225	−	0.891904i	$-0.350630\pi$
$401$	1.21091e22	0.904450	0.452225	+	0.891904i	$0.350630\pi$
$402$	1.27195e22i	0.930143i
$403$	1.68275e22i	1.20483i
$404$	1.17093e22	0.820895
$405$	0	0
$406$	−4.75090e22	−3.19378
$407$	3.22031e22i	2.12004i
$408$	5.67093e20i	0.0365631i
$409$	2.17164e21	0.137133	0.0685663	−	0.997647i	$-0.478158\pi$
$409$	2.17164e21	0.137133	0.0685663	+	0.997647i	$0.478158\pi$
$410$	0	0
$411$	6.54726e21	0.396647
$412$	3.20316e22i	1.90087i
$413$	2.09734e22i	1.21925i
$414$	1.28855e22	0.733834
$415$	0	0
$416$	3.82737e22	2.09222
$417$	2.93104e21i	0.156988i
$418$	2.59521e21i	0.136199i
$419$	−6.08872e21	−0.313117	−0.156559	−	0.987669i	$-0.550040\pi$
$419$	−6.08872e21	−0.313117	−0.156559	+	0.987669i	$0.550040\pi$
$420$	0	0
$421$	5.35697e21	0.264558	0.132279	−	0.991213i	$-0.457770\pi$
$421$	5.35697e21	0.264558	0.132279	+	0.991213i	$0.457770\pi$
$422$	− 3.08010e22i	− 1.49076i
$423$	5.59001e21i	0.265167i
$424$	7.86197e20	0.0365529
$425$	0	0
$426$	3.13590e22	1.40081
$427$	− 2.33323e21i	− 0.102169i
$428$	2.69508e22i	1.15691i
$429$	−3.50544e22	−1.47521
$430$	0	0
$431$	−3.25292e22	−1.31588	−0.657940	−	0.753070i	$-0.728572\pi$
$431$	−3.25292e22	−1.31588	−0.657940	+	0.753070i	$0.728572\pi$
$432$	4.56966e21i	0.181248i
$433$	− 2.71219e22i	− 1.05481i	−0.849614	−	0.527404i	$-0.823165\pi$
$433$	− 2.71219e22i	− 1.05481i	0.849614	−	0.527404i	$-0.176835\pi$
$434$	4.46913e22	1.70436
$435$	0	0
$436$	−1.86763e22	−0.684946
$437$	− 2.32396e21i	− 0.0835867i
$438$	5.69524e21i	0.200901i
$439$	−3.99818e22	−1.38329	−0.691645	−	0.722237i	$-0.743114\pi$
$439$	−3.99818e22	−1.38329	−0.691645	+	0.722237i	$0.743114\pi$
$440$	0	0
$441$	1.08810e22	0.362195
$442$	5.14662e22i	1.68048i
$443$	3.52585e22i	1.12936i	0.825310	+	0.564680i	$0.191000\pi$
$443$	3.52585e22i	1.12936i	−0.825310	+	0.564680i	$0.809000\pi$
$444$	−2.35479e22	−0.739940
$445$	0	0
$446$	−5.38999e22	−1.63020
$447$	3.29910e22i	0.978997i
$448$	− 5.49259e22i	− 1.59924i
$449$	−3.79861e22	−1.08525	−0.542626	−	0.839974i	$-0.682570\pi$
$449$	−3.79861e22	−1.08525	−0.542626	+	0.839974i	$0.682570\pi$
$450$	0	0
$451$	−2.65222e22	−0.729640
$452$	− 3.08231e21i	− 0.0832146i
$453$	2.72698e22i	0.722517i
$454$	1.15127e22	0.299367
$455$	0	0
$456$	−9.92165e19	−0.00248532
$457$	− 5.01797e22i	− 1.23379i	−0.787046	−	0.616894i	$-0.788391\pi$
$457$	− 5.01797e22i	− 1.23379i	0.787046	−	0.616894i	$-0.211609\pi$
$458$	− 3.29246e22i	− 0.794629i
$459$	−6.50471e21	−0.154106
$460$	0	0
$461$	1.92582e22	0.439700	0.219850	−	0.975534i	$-0.429443\pi$
$461$	1.92582e22	0.439700	0.219850	+	0.975534i	$0.429443\pi$
$462$	9.30993e22i	2.08684i
$463$	− 8.53566e22i	− 1.87845i	−0.343308	−	0.939223i	$-0.611548\pi$
$463$	− 8.53566e22i	− 1.87845i	0.343308	−	0.939223i	$-0.388452\pi$
$464$	−6.72233e22	−1.45250
$465$	0	0
$466$	−2.48090e22	−0.516807
$467$	1.82191e22i	0.372678i	0.982486	+	0.186339i	$0.0596622\pi$
$467$	1.82191e22i	0.372678i	−0.982486	+	0.186339i	$0.940338\pi$
$468$	− 2.56328e22i	− 0.514881i
$469$	8.22951e22	1.62332
$470$	0	0
$471$	−4.71657e22	−0.897322
$472$	− 3.57260e21i	− 0.0667540i
$473$	8.95974e22i	1.64428i
$474$	−3.04881e22	−0.549559
$475$	0	0
$476$	7.01779e22	1.22051
$477$	9.01789e21i	0.154063i
$478$	8.83191e22i	1.48224i
$479$	2.42725e22	0.400187	0.200093	−	0.979777i	$-0.435875\pi$
$479$	2.42725e22	0.400187	0.200093	+	0.979777i	$0.435875\pi$
$480$	0	0
$481$	−1.11732e23	−1.77805
$482$	− 1.38966e23i	− 2.17274i
$483$	− 8.33688e22i	− 1.28072i
$484$	−1.43068e23	−2.15952
$485$	0	0
$486$	6.30999e21	0.0919645
$487$	− 2.64995e21i	− 0.0379527i	−0.999820	−	0.0189763i	$-0.993959\pi$
$487$	− 2.64995e21i	− 0.0379527i	0.999820	−	0.0189763i	$-0.00604071\pi$
$488$	3.97441e20i	0.00559377i
$489$	3.82562e22	0.529148
$490$	0	0
$491$	2.03318e22	0.271633	0.135816	−	0.990734i	$-0.456634\pi$
$491$	2.03318e22	0.271633	0.135816	+	0.990734i	$0.456634\pi$
$492$	− 1.93938e22i	− 0.254660i
$493$	− 9.56894e22i	− 1.23499i
$494$	−9.00432e21	−0.114228
$495$	0	0
$496$	6.32364e22	0.775127
$497$	− 2.02892e23i	− 2.44476i
$498$	− 3.77235e22i	− 0.446850i
$499$	5.53613e22	0.644691	0.322346	−	0.946622i	$-0.395529\pi$
$499$	5.53613e22	0.644691	0.322346	+	0.946622i	$0.395529\pi$
$500$	0	0
$501$	6.18810e22	0.696525
$502$	− 1.46165e23i	− 1.61757i
$503$	− 1.43348e23i	− 1.55978i	−0.625914	−	0.779892i	$-0.715274\pi$
$503$	− 1.43348e23i	− 1.55978i	0.625914	−	0.779892i	$-0.284726\pi$
$504$	−3.55925e21	−0.0380801
$505$	0	0
$506$	3.71456e23	3.84263
$507$	− 6.48691e22i	− 0.659888i
$508$	− 7.51746e22i	− 0.752020i
$509$	4.30562e22	0.423580	0.211790	−	0.977315i	$-0.432071\pi$
$509$	4.30562e22	0.423580	0.211790	+	0.977315i	$0.432071\pi$
$510$	0	0
$511$	3.68481e22	0.350620
$512$	− 1.51789e23i	− 1.42051i
$513$	− 1.13804e21i	− 0.0104751i
$514$	−1.36223e23	−1.23328
$515$	0	0
$516$	−6.55164e22	−0.573889
$517$	1.61146e23i	1.38851i
$518$	2.96743e23i	2.51523i
$519$	−4.52761e22	−0.377526
$520$	0	0
$521$	7.39392e22	0.596697	0.298349	−	0.954457i	$-0.403564\pi$
$521$	7.39392e22	0.596697	0.298349	+	0.954457i	$0.403564\pi$
$522$	9.28249e22i	0.736996i
$523$	− 2.07455e22i	− 0.162054i	−0.996712	−	0.0810271i	$-0.974180\pi$
$523$	− 2.07455e22i	− 0.162054i	0.996712	−	0.0810271i	$-0.0258200\pi$
$524$	3.26419e22	0.250876
$525$	0	0
$526$	1.07223e23	0.797824
$527$	9.00142e22i	0.659054i
$528$	1.31732e23i	0.949079i
$529$	−1.91582e23	−1.35826
$530$	0	0
$531$	4.09786e22	0.281355
$532$	1.22781e22i	0.0829623i
$533$	− 9.20212e22i	− 0.611937i
$534$	−1.06305e23	−0.695748
$535$	0	0
$536$	−1.40181e22	−0.0888769
$537$	− 2.66919e22i	− 0.166571i
$538$	− 3.20411e22i	− 0.196815i
$539$	3.13673e23	1.89659
$540$	0	0
$541$	4.66724e22	0.273454	0.136727	−	0.990609i	$-0.456342\pi$
$541$	4.66724e22	0.273454	0.136727	+	0.990609i	$0.456342\pi$
$542$	− 3.09587e23i	− 1.78562i
$543$	− 1.53323e23i	− 0.870581i
$544$	2.04735e23	1.14446
$545$	0	0
$546$	−3.23017e23	−1.75020
$547$	− 3.83315e22i	− 0.204486i	−0.994759	−	0.102243i	$-0.967398\pi$
$547$	− 3.83315e22i	− 0.204486i	0.994759	−	0.102243i	$-0.0326019\pi$
$548$	1.38013e23i	0.724913i
$549$	−4.55876e21	−0.0235766
$550$	0	0
$551$	1.67414e22	0.0839468
$552$	1.42010e22i	0.0701192i
$553$	1.97257e23i	0.959113i
$554$	−1.09631e23	−0.524929
$555$	0	0
$556$	−6.17849e22	−0.286911
$557$	1.00532e23i	0.459765i	0.973218	+	0.229883i	$0.0738342\pi$
$557$	1.00532e23i	0.459765i	−0.973218	+	0.229883i	$0.926166\pi$
$558$	− 8.73196e22i	− 0.393297i
$559$	−3.10867e23	−1.37903
$560$	0	0
$561$	−1.87514e23	−0.806957
$562$	4.35279e23i	1.84505i
$563$	− 3.08418e23i	− 1.28771i	−0.765148	−	0.643854i	$-0.777334\pi$
$563$	− 3.08418e23i	− 1.28771i	0.765148	−	0.643854i	$-0.222666\pi$
$564$	−1.17835e23	−0.484620
$565$	0	0
$566$	5.83403e22	0.232825
$567$	− 4.08255e22i	− 0.160500i
$568$	3.45605e22i	0.133850i
$569$	4.27688e23	1.63182	0.815911	−	0.578177i	$-0.196236\pi$
$569$	4.27688e23	1.63182	0.815911	+	0.578177i	$0.196236\pi$
$570$	0	0
$571$	1.60059e23	0.592751	0.296375	−	0.955072i	$-0.404222\pi$
$571$	1.60059e23	0.592751	0.296375	+	0.955072i	$0.404222\pi$
$572$	− 7.38930e23i	− 2.69611i
$573$	− 3.62176e22i	− 0.130198i
$574$	−2.44395e23	−0.865648
$575$	0	0
$576$	−1.07316e23	−0.369041
$577$	1.59919e23i	0.541882i	0.962596	+	0.270941i	$0.0873349\pi$
$577$	1.59919e23i	0.541882i	−0.962596	+	0.270941i	$0.912665\pi$
$578$	− 1.54044e23i	− 0.514348i
$579$	−2.69497e23	−0.886719
$580$	0	0
$581$	−2.44070e23	−0.779861
$582$	4.67561e23i	1.47229i
$583$	2.59963e23i	0.806731i
$584$	−6.27668e21	−0.0191965
$585$	0	0
$586$	2.34103e23	0.695468
$587$	− 4.74371e23i	− 1.38897i	−0.719506	−	0.694487i	$-0.755631\pi$
$587$	− 4.74371e23i	− 1.38897i	0.719506	−	0.694487i	$-0.244369\pi$
$588$	2.29367e23i	0.661948i
$589$	−1.57485e22	−0.0447981
$590$	0	0
$591$	−9.13587e22	−0.252497
$592$	4.19879e23i	1.14391i
$593$	− 6.92515e23i	− 1.85979i	−0.367822	−	0.929896i	$-0.619896\pi$
$593$	− 6.92515e23i	− 1.85979i	0.367822	−	0.929896i	$-0.380104\pi$
$594$	1.81901e23	0.481560
$595$	0	0
$596$	−6.95435e23	−1.78922
$597$	2.78946e23i	0.707519i
$598$	1.28880e24i	3.22275i
$599$	2.61860e23	0.645568	0.322784	−	0.946473i	$-0.395381\pi$
$599$	2.61860e23	0.645568	0.322784	+	0.946473i	$0.395381\pi$
$600$	0	0
$601$	−4.49867e23	−1.07808	−0.539041	−	0.842280i	$-0.681213\pi$
$601$	−4.49867e23	−1.07808	−0.539041	+	0.842280i	$0.681213\pi$
$602$	8.25617e23i	1.95078i
$603$	− 1.60791e23i	− 0.374598i
$604$	−5.74835e23	−1.32047
$605$	0	0
$606$	−2.88301e23	−0.643916
$607$	3.57662e23i	0.787714i	0.919172	+	0.393857i	$0.128860\pi$
$607$	3.57662e23i	0.787714i	−0.919172	+	0.393857i	$0.871140\pi$
$608$	3.58197e22i	0.0777931i
$609$	6.00575e23	1.28624
$610$	0	0
$611$	−5.59111e23	−1.16452
$612$	− 1.37116e23i	− 0.281645i
$613$	− 5.56592e23i	− 1.12752i	−0.825940	−	0.563758i	$-0.809355\pi$
$613$	− 5.56592e23i	− 1.12752i	0.825940	−	0.563758i	$-0.190645\pi$
$614$	9.60926e23	1.91981
$615$	0	0
$616$	−1.02604e23	−0.199402
$617$	3.14659e23i	0.603138i	0.953444	+	0.301569i	$0.0975103\pi$
$617$	3.14659e23i	0.603138i	−0.953444	+	0.301569i	$0.902490\pi$
$618$	− 7.88671e23i	− 1.49106i
$619$	6.41328e23	1.19594	0.597971	−	0.801518i	$-0.295974\pi$
$619$	6.41328e23	1.19594	0.597971	+	0.801518i	$0.295974\pi$
$620$	0	0
$621$	−1.62889e23	−0.295538
$622$	1.28587e24i	2.30134i
$623$	6.87789e23i	1.21425i
$624$	−4.57056e23	−0.795977
$625$	0	0
$626$	1.63231e24	2.76644
$627$	− 3.28068e22i	− 0.0548516i
$628$	− 9.94231e23i	− 1.63995i
$629$	−5.97680e23	−0.972608
$630$	0	0
$631$	7.21873e23	1.14344	0.571718	−	0.820451i	$-0.306277\pi$
$631$	7.21873e23	1.14344	0.571718	+	0.820451i	$0.306277\pi$
$632$	− 3.36007e22i	− 0.0525114i
$633$	3.89364e23i	0.600378i
$634$	−5.19842e23	−0.790884
$635$	0	0
$636$	−1.90093e23	−0.281566
$637$	1.08832e24i	1.59064i
$638$	2.67591e24i	3.85918i
$639$	−3.96418e23	−0.564153
$640$	0	0
$641$	4.63255e23	0.641987	0.320994	−	0.947081i	$-0.395983\pi$
$641$	4.63255e23	0.641987	0.320994	+	0.947081i	$0.395983\pi$
$642$	− 6.63573e23i	− 0.907488i
$643$	− 3.79864e23i	− 0.512666i	−0.966589	−	0.256333i	$-0.917486\pi$
$643$	− 3.79864e23i	− 0.512666i	0.966589	−	0.256333i	$-0.0825144\pi$
$644$	1.75738e24	2.34064
$645$	0	0
$646$	−4.81663e22	−0.0624837
$647$	− 1.41652e24i	− 1.81358i	−0.421586	−	0.906788i	$-0.638526\pi$
$647$	− 1.41652e24i	− 1.81358i	0.421586	−	0.906788i	$-0.361474\pi$
$648$	6.95420e21i	0.00878738i
$649$	1.18131e24	1.47328
$650$	0	0
$651$	−5.64956e23	−0.686398
$652$	8.06424e23i	0.967072i
$653$	− 7.42575e23i	− 0.878979i	−0.898248	−	0.439489i	$-0.855159\pi$
$653$	− 7.42575e23i	− 0.878979i	0.898248	−	0.439489i	$-0.144841\pi$
$654$	4.59842e23	0.537277
$655$	0	0
$656$	−3.45809e23	−0.393689
$657$	− 7.19952e22i	− 0.0809092i
$658$	1.48492e24i	1.64734i
$659$	−2.78539e23	−0.305043	−0.152521	−	0.988300i	$-0.548739\pi$
$659$	−2.78539e23	−0.305043	−0.152521	+	0.988300i	$0.548739\pi$
$660$	0	0
$661$	−2.46559e23	−0.263153	−0.131576	−	0.991306i	$-0.542004\pi$
$661$	−2.46559e23	−0.263153	−0.131576	+	0.991306i	$0.542004\pi$
$662$	− 2.61132e23i	− 0.275149i
$663$	− 6.50599e23i	− 0.676781i
$664$	4.15748e22	0.0426974
$665$	0	0
$666$	5.79788e23	0.580415
$667$	− 2.39623e24i	− 2.36842i
$668$	1.30442e24i	1.27297i
$669$	6.81365e23	0.656535
$670$	0	0
$671$	−1.31417e23	−0.123456
$672$	1.28498e24i	1.19195i
$673$	− 7.23723e23i	− 0.662894i	−0.943474	−	0.331447i	$-0.892463\pi$
$673$	− 7.23723e23i	− 0.662894i	0.943474	−	0.331447i	$-0.107537\pi$
$674$	4.66021e23	0.421499
$675$	0	0
$676$	1.36741e24	1.20601
$677$	− 1.76274e24i	− 1.53527i	−0.640888	−	0.767635i	$-0.721434\pi$
$677$	− 1.76274e24i	− 1.53527i	0.640888	−	0.767635i	$-0.278566\pi$
$678$	7.58916e22i	0.0652742i
$679$	3.02511e24	2.56950
$680$	0	0
$681$	−1.45536e23	−0.120564
$682$	− 2.51720e24i	− 2.05945i
$683$	− 5.00365e23i	− 0.404307i	−0.979354	−	0.202153i	$-0.935206\pi$
$683$	− 5.00365e23i	− 0.404307i	0.979354	−	0.202153i	$-0.0647940\pi$
$684$	2.39893e22	0.0191444
$685$	0	0
$686$	2.30324e23	0.179301
$687$	4.16210e23i	0.320022i
$688$	1.16821e24i	0.887199i
$689$	−9.01966e23	−0.676592
$690$	0	0
$691$	4.91535e23	0.359742	0.179871	−	0.983690i	$-0.442432\pi$
$691$	4.91535e23	0.359742	0.179871	+	0.983690i	$0.442432\pi$
$692$	− 9.54399e23i	− 0.689967i
$693$	− 1.17690e24i	− 0.840438i
$694$	−2.90471e24	−2.04903
$695$	0	0
$696$	−1.02302e23	−0.0704213
$697$	− 4.92244e23i	− 0.334735i
$698$	− 1.92572e24i	− 1.29366i
$699$	3.13618e23	0.208135
$700$	0	0
$701$	3.92859e22	0.0254468	0.0127234	−	0.999919i	$-0.495950\pi$
$701$	3.92859e22	0.0254468	0.0127234	+	0.999919i	$0.495950\pi$
$702$	6.31123e23i	0.403877i
$703$	− 1.04568e23i	− 0.0661116i
$704$	−3.09366e24	−1.93243
$705$	0	0
$706$	−3.00775e24	−1.83401
$707$	1.86530e24i	1.12379i
$708$	8.63811e23i	0.514205i
$709$	−1.90230e24	−1.11889	−0.559444	−	0.828868i	$-0.688985\pi$
$709$	−1.90230e24	−1.11889	−0.559444	+	0.828868i	$0.688985\pi$
$710$	0	0
$711$	3.85409e23	0.221325
$712$	− 1.17158e23i	− 0.0664800i
$713$	2.25411e24i	1.26390i
$714$	−1.72790e24	−0.957377
$715$	0	0
$716$	5.62654e23	0.304425
$717$	− 1.11647e24i	− 0.596943i
$718$	− 3.01326e24i	− 1.59213i
$719$	2.08973e24	1.09117	0.545587	−	0.838054i	$-0.316307\pi$
$719$	2.08973e24	1.09117	0.545587	+	0.838054i	$0.316307\pi$
$720$	0	0
$721$	−5.10269e24	−2.60225
$722$	2.83597e24i	1.42934i
$723$	1.75671e24i	0.875032i
$724$	3.23198e24	1.59108
$725$	0	0
$726$	3.52258e24	1.69395
$727$	− 1.27329e24i	− 0.605183i	−0.953120	−	0.302591i	$-0.902148\pi$
$727$	− 1.27329e24i	− 0.605183i	0.953120	−	0.302591i	$-0.0978517\pi$
$728$	− 3.55995e23i	− 0.167235i
$729$	−7.97664e22	−0.0370370
$730$	0	0
$731$	−1.66290e24	−0.754343
$732$	− 9.60965e22i	− 0.0430887i
$733$	1.04073e24i	0.461268i	0.973041	+	0.230634i	$0.0740800\pi$
$733$	1.04073e24i	0.461268i	−0.973041	+	0.230634i	$0.925920\pi$
$734$	−4.70907e23	−0.206309
$735$	0	0
$736$	5.12692e24	2.19480
$737$	− 4.63521e24i	− 1.96153i
$738$	4.77508e23i	0.199757i
$739$	2.00360e24	0.828580	0.414290	−	0.910145i	$-0.364030\pi$
$739$	2.00360e24	0.828580	0.414290	+	0.910145i	$0.364030\pi$
$740$	0	0
$741$	1.13826e23	0.0460032
$742$	2.39549e24i	0.957109i
$743$	− 1.24044e24i	− 0.489972i	−0.969527	−	0.244986i	$-0.921217\pi$
$743$	− 1.24044e24i	− 0.489972i	0.969527	−	0.244986i	$-0.0787834\pi$
$744$	9.62343e22	0.0375803
$745$	0	0
$746$	3.50173e24	1.33660
$747$	4.76873e23i	0.179961i
$748$	− 3.95272e24i	− 1.47480i
$749$	−4.29330e24	−1.58378
$750$	0	0
$751$	−1.56591e24	−0.564711	−0.282355	−	0.959310i	$-0.591116\pi$
$751$	−1.56591e24	−0.564711	−0.282355	+	0.959310i	$0.591116\pi$
$752$	2.10110e24i	0.749194i
$753$	1.84772e24i	0.651445i
$754$	−9.28432e24	−3.23663
$755$	0	0
$756$	8.60583e23	0.293331
$757$	2.06287e24i	0.695275i	0.937629	+	0.347637i	$0.113016\pi$
$757$	2.06287e24i	0.695275i	−0.937629	+	0.347637i	$0.886984\pi$
$758$	− 3.35366e24i	− 1.11771i
$759$	−4.69568e24	−1.54755
$760$	0	0
$761$	−6.26262e23	−0.201830	−0.100915	−	0.994895i	$-0.532177\pi$
$761$	−6.26262e23	−0.201830	−0.100915	+	0.994895i	$0.532177\pi$
$762$	1.85092e24i	0.589890i
$763$	− 2.97517e24i	− 0.937677i
$764$	7.63449e23	0.237950
$765$	0	0
$766$	5.72923e24	1.74643
$767$	4.09867e24i	1.23561i
$768$	1.70547e24i	0.508480i
$769$	−3.97601e24	−1.17240	−0.586198	−	0.810168i	$-0.699376\pi$
$769$	−3.97601e24	−1.17240	−0.586198	+	0.810168i	$0.699376\pi$
$770$	0	0
$771$	1.72203e24	0.496682
$772$	− 5.68087e24i	− 1.62057i
$773$	− 3.83057e24i	− 1.08078i	−0.841414	−	0.540391i	$-0.818276\pi$
$773$	− 3.83057e24i	− 1.08078i	0.841414	−	0.540391i	$-0.181724\pi$
$774$	1.61312e24	0.450163
$775$	0	0
$776$	−5.15296e23	−0.140680
$777$	− 3.75122e24i	− 1.01296i
$778$	− 3.13673e24i	− 0.837820i
$779$	8.61211e22	0.0227531
$780$	0	0
$781$	−1.14277e25	−2.95411
$782$	6.89412e24i	1.76287i
$783$	− 1.17343e24i	− 0.296812i
$784$	4.08982e24	1.02333
$785$	0	0
$786$	−8.03698e23	−0.196789
$787$	− 1.52457e24i	− 0.369285i	−0.982806	−	0.184642i	$-0.940887\pi$
$787$	− 1.52457e24i	− 0.369285i	0.982806	−	0.184642i	$-0.0591127\pi$
$788$	− 1.92580e24i	− 0.461464i
$789$	−1.35543e24	−0.321309
$790$	0	0
$791$	4.91017e23	0.113919
$792$	2.00472e23i	0.0460139i
$793$	− 4.55965e23i	− 0.103540i
$794$	−8.15135e24	−1.83128
$795$	0	0
$796$	−5.88005e24	−1.29306
$797$	− 6.82524e23i	− 0.148499i	−0.997240	−	0.0742493i	$-0.976344\pi$
$797$	− 6.82524e23i	− 0.148499i	0.997240	−	0.0742493i	$-0.0236561\pi$
$798$	− 3.02306e23i	− 0.0650762i
$799$	−2.99082e24	−0.637004
$800$	0	0
$801$	1.34383e24	0.280200
$802$	− 6.28478e24i	− 1.29661i
$803$	− 2.07544e24i	− 0.423670i
$804$	3.38941e24	0.684617
$805$	0	0
$806$	8.73368e24	1.72723
$807$	4.05041e23i	0.0792637i
$808$	− 3.17735e23i	− 0.0615274i
$809$	−6.25563e24	−1.19869	−0.599347	−	0.800489i	$-0.704573\pi$
$809$	−6.25563e24	−1.19869	−0.599347	+	0.800489i	$0.704573\pi$
$810$	0	0
$811$	−9.73185e24	−1.82607	−0.913036	−	0.407878i	$-0.866269\pi$
$811$	−9.73185e24	−1.82607	−0.913036	+	0.407878i	$0.866269\pi$
$812$	1.26598e25i	2.35073i
$813$	3.91357e24i	0.719124i
$814$	1.67138e25	3.03926
$815$	0	0
$816$	−2.44490e24	−0.435407
$817$	− 2.90935e23i	− 0.0512753i
$818$	− 1.12711e24i	− 0.196591i
$819$	4.08335e24	0.704862
$820$	0	0
$821$	−2.76559e24	−0.467597	−0.233798	−	0.972285i	$-0.575116\pi$
$821$	−2.76559e24	−0.467597	−0.233798	+	0.972285i	$0.575116\pi$
$822$	− 3.39811e24i	− 0.568627i
$823$	1.12749e25i	1.86729i	0.358194	+	0.933647i	$0.383393\pi$
$823$	1.12749e25i	1.86729i	−0.358194	+	0.933647i	$0.616607\pi$
$824$	8.69189e23	0.142473
$825$	0	0
$826$	1.08855e25	1.74790
$827$	1.58882e24i	0.252509i	0.991998	+	0.126254i	$0.0402956\pi$
$827$	1.58882e24i	0.252509i	−0.991998	+	0.126254i	$0.959704\pi$
$828$	− 3.43363e24i	− 0.540127i
$829$	9.40607e24	1.46452	0.732259	−	0.681027i	$-0.238466\pi$
$829$	9.40607e24	1.46452	0.732259	+	0.681027i	$0.238466\pi$
$830$	0	0
$831$	1.38588e24	0.211405
$832$	− 1.07337e25i	− 1.62070i
$833$	5.82168e24i	0.870093i
$834$	1.52125e24	0.225055
$835$	0	0
$836$	6.91552e23	0.100247
$837$	1.10383e24i	0.158393i
$838$	3.16013e24i	0.448880i
$839$	4.29122e24	0.603398	0.301699	−	0.953403i	$-0.402446\pi$
$839$	4.29122e24	0.603398	0.301699	+	0.953403i	$0.402446\pi$
$840$	0	0
$841$	1.00049e25	1.37863
$842$	− 2.78034e24i	− 0.379267i
$843$	− 5.50249e24i	− 0.743062i
$844$	−8.20762e24	−1.09725
$845$	0	0
$846$	2.90129e24	0.380139
$847$	− 2.27910e25i	− 2.95634i
$848$	3.38952e24i	0.435285i
$849$	−7.37496e23	−0.0937658
$850$	0	0
$851$	−1.49669e25	−1.86523
$852$	− 8.35632e24i	− 1.03105i
$853$	8.63727e24i	1.05514i	0.849512	+	0.527569i	$0.176896\pi$
$853$	8.63727e24i	1.05514i	−0.849512	+	0.527569i	$0.823104\pi$
$854$	−1.21098e24	−0.146469
$855$	0	0
$856$	7.31319e23	0.0867121
$857$	− 8.88080e24i	− 1.04259i	−0.853376	−	0.521297i	$-0.825449\pi$
$857$	− 8.88080e24i	− 1.04259i	0.853376	−	0.521297i	$-0.174551\pi$
$858$	1.81937e25i	2.11485i
$859$	4.68431e24	0.539142	0.269571	−	0.962980i	$-0.413118\pi$
$859$	4.68431e24	0.539142	0.269571	+	0.962980i	$0.413118\pi$
$860$	0	0
$861$	3.08947e24	0.348624
$862$	1.68831e25i	1.88643i
$863$	2.16363e24i	0.239382i	0.992811	+	0.119691i	$0.0381903\pi$
$863$	2.16363e24i	0.239382i	−0.992811	+	0.119691i	$0.961810\pi$
$864$	2.51064e24	0.275054
$865$	0	0
$866$	−1.40767e25	−1.51216
$867$	1.94731e24i	0.207144i
$868$	− 1.19090e25i	− 1.25446i
$869$	1.11104e25	1.15894
$870$	0	0
$871$	1.60823e25	1.64511
$872$	5.06789e23i	0.0513378i
$873$	− 5.91058e24i	− 0.592937i
$874$	−1.20617e24	−0.119829
$875$	0	0
$876$	1.51763e24	0.147870
$877$	2.01335e25i	1.94277i	0.237505	+	0.971386i	$0.423670\pi$
$877$	2.01335e25i	1.94277i	−0.237505	+	0.971386i	$0.576330\pi$
$878$	2.07511e25i	1.98307i
$879$	−2.95936e24	−0.280087
$880$	0	0
$881$	3.50326e24	0.325220	0.162610	−	0.986690i	$-0.448009\pi$
$881$	3.50326e24	0.325220	0.162610	+	0.986690i	$0.448009\pi$
$882$	− 5.64740e24i	− 0.519237i
$883$	− 7.92967e24i	− 0.722086i	−0.932549	−	0.361043i	$-0.882421\pi$
$883$	− 7.92967e24i	− 0.722086i	0.932549	−	0.361043i	$-0.117579\pi$
$884$	1.37143e25	1.23689
$885$	0	0
$886$	1.82996e25	1.61903
$887$	1.38155e25i	1.21064i	0.795981	+	0.605322i	$0.206956\pi$
$887$	1.38155e25i	1.21064i	−0.795981	+	0.605322i	$0.793044\pi$
$888$	6.38980e23i	0.0554597i
$889$	1.19754e25	1.02950
$890$	0	0
$891$	−2.29947e24	−0.193940
$892$	1.43629e25i	1.19988i
$893$	− 5.23262e23i	− 0.0432994i
$894$	1.71228e25	1.40348
$895$	0	0
$896$	−2.83666e24	−0.228133
$897$	− 1.62921e25i	− 1.29790i
$898$	1.97153e25i	1.55580i
$899$	−1.62382e25	−1.26935
$900$	0	0
$901$	−4.82484e24	−0.370102
$902$	1.37654e25i	1.04600i
$903$	− 1.04369e25i	− 0.785642i
$904$	−8.36396e22	−0.00623707
$905$	0	0
$906$	1.41534e25	1.03579
$907$	1.74791e25i	1.26723i	0.773647	+	0.633617i	$0.218431\pi$
$907$	1.74791e25i	1.26723i	−0.773647	+	0.633617i	$0.781569\pi$
$908$	− 3.06783e24i	− 0.220344i
$909$	3.64450e24	0.259325
$910$	0	0
$911$	−1.65006e25	−1.15237	−0.576186	−	0.817319i	$-0.695460\pi$
$911$	−1.65006e25	−1.15237	−0.576186	+	0.817319i	$0.695460\pi$
$912$	− 4.27751e23i	− 0.0295961i
$913$	1.37471e25i	0.942341i
$914$	−2.60439e25	−1.76874
$915$	0	0
$916$	−8.77351e24	−0.584874
$917$	5.19991e24i	0.343445i
$918$	3.37603e24i	0.220924i
$919$	3.23292e23	0.0209611	0.0104805	−	0.999945i	$-0.496664\pi$
$919$	3.23292e23	0.0209611	0.0104805	+	0.999945i	$0.496664\pi$
$920$	0	0
$921$	−1.21473e25	−0.773169
$922$	− 9.99524e24i	− 0.630348i
$923$	− 3.96496e25i	− 2.47756i
$924$	2.48084e25	1.53599
$925$	0	0
$926$	−4.43012e25	−2.69291
$927$	9.96983e24i	0.600496i
$928$	3.69335e25i	2.20426i
$929$	1.75534e25	1.03807	0.519037	−	0.854752i	$-0.326291\pi$
$929$	1.75534e25	1.03807	0.519037	+	0.854752i	$0.326291\pi$
$930$	0	0
$931$	−1.01854e24	−0.0591432
$932$	6.61092e24i	0.380388i
$933$	− 1.62551e25i	− 0.926822i
$934$	9.45596e24	0.534265
$935$	0	0
$936$	−6.95556e23	−0.0385911
$937$	− 1.85877e25i	− 1.02197i	−0.859589	−	0.510985i	$-0.829281\pi$
$937$	− 1.85877e25i	− 1.02197i	0.859589	−	0.510985i	$-0.170719\pi$
$938$	− 4.27123e25i	− 2.32717i
$939$	−2.06345e25	−1.11413
$940$	0	0
$941$	−2.84870e25	−1.51055	−0.755275	−	0.655408i	$-0.772497\pi$
$941$	−2.84870e25	−1.51055	−0.755275	+	0.655408i	$0.772497\pi$
$942$	2.44796e25i	1.28639i
$943$	− 1.23266e25i	− 0.641941i
$944$	1.54025e25	0.794931
$945$	0	0
$946$	4.65023e25	2.35722
$947$	− 2.13986e25i	− 1.07500i	−0.843263	−	0.537502i	$-0.819368\pi$
$947$	− 2.13986e25i	− 1.07500i	0.843263	−	0.537502i	$-0.180632\pi$
$948$	8.12424e24i	0.404494i
$949$	7.20094e24	0.355325
$950$	0	0
$951$	6.57147e24	0.318514
$952$	− 1.90430e24i	− 0.0914791i
$953$	3.15181e25i	1.50062i	0.661087	+	0.750309i	$0.270095\pi$
$953$	3.15181e25i	1.50062i	−0.661087	+	0.750309i	$0.729905\pi$
$954$	4.68040e24	0.220863
$955$	0	0
$956$	2.35346e25	1.09098
$957$	− 3.38269e25i	− 1.55422i
$958$	− 1.25977e25i	− 0.573702i
$959$	−2.19857e25	−0.992391
$960$	0	0
$961$	−7.27494e24	−0.322612
$962$	5.79902e25i	2.54898i
$963$	8.38842e24i	0.365474i
$964$	−3.70306e25	−1.59921
$965$	0	0
$966$	−4.32695e25	−1.83602
$967$	4.19923e25i	1.76622i	0.469166	+	0.883110i	$0.344555\pi$
$967$	4.19923e25i	1.76622i	−0.469166	+	0.883110i	$0.655445\pi$
$968$	3.88221e24i	0.161860i
$969$	6.08884e23	0.0251642
$970$	0	0
$971$	−2.82344e24	−0.114661	−0.0573305	−	0.998355i	$-0.518259\pi$
$971$	−2.82344e24	−0.114661	−0.0573305	+	0.998355i	$0.518259\pi$
$972$	− 1.68144e24i	− 0.0676890i
$973$	− 9.84244e24i	− 0.392775i
$974$	−1.37536e24	−0.0544084
$975$	0	0
$976$	−1.71348e24	−0.0666127
$977$	2.48432e25i	0.957422i	0.877972	+	0.478711i	$0.158896\pi$
$977$	2.48432e25i	0.957422i	−0.877972	+	0.478711i	$0.841104\pi$
$978$	− 1.98555e25i	− 0.758578i
$979$	3.87392e25	1.46723
$980$	0	0
$981$	−5.81300e24	−0.216378
$982$	− 1.05525e25i	− 0.389409i
$983$	− 1.61789e24i	− 0.0591893i	−0.999562	−	0.0295946i	$-0.990578\pi$
$983$	− 1.61789e24i	− 0.0591893i	0.999562	−	0.0295946i	$-0.00942164\pi$
$984$	−5.26258e23	−0.0190871
$985$	0	0
$986$	−4.96641e25	−1.77047
$987$	− 1.87713e25i	− 0.663434i
$988$	2.39941e24i	0.0840755i
$989$	−4.16420e25	−1.44665
$990$	0	0
$991$	4.75277e25	1.62301	0.811503	−	0.584348i	$-0.198650\pi$
$991$	4.75277e25	1.62301	0.811503	+	0.584348i	$0.198650\pi$
$992$	− 3.47430e25i	− 1.17630i
$993$	3.30105e24i	0.110811i
$994$	−1.05304e26	−3.50477
$995$	0	0
$996$	−1.00523e25	−0.328897
$997$	4.19509e25i	1.36092i	0.732785	+	0.680460i	$0.238220\pi$
$997$	4.19509e25i	1.36092i	−0.732785	+	0.680460i	$0.761780\pi$
$998$	− 2.87333e25i	− 0.924220i
$999$	−7.32927e24	−0.233751

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.18.b.g.49.2		10
5.2	odd	4		75.18.a.h.1.5	yes	5
5.3	odd	4		75.18.a.g.1.1	✓	5
5.4	even	2	inner	75.18.b.g.49.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.18.a.g.1.1	✓	5	5.3	odd	4
75.18.a.h.1.5	yes	5	5.2	odd	4
75.18.b.g.49.2		10	1.1	even	1	trivial
75.18.b.g.49.9		10	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	75.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-519.013i q^{2} +6561.00i q^{3} -138303. q^{4} +3.40525e6 q^{6} -2.20319e7i q^{7} +3.75290e6i q^{8} -4.30467e7 q^{9} -1.24093e9 q^{11} -9.07405e8i q^{12} -4.30552e9i q^{13} -1.14348e10 q^{14} -1.61798e10 q^{16} -2.30313e10i q^{17} +2.23418e10i q^{18} +4.02946e9 q^{19} +1.44551e11 q^{21} +6.44058e11i q^{22} -5.76743e11i q^{23} -2.46228e10 q^{24} -2.23462e12 q^{26} -2.82430e11i q^{27} +3.04707e12i q^{28} +4.15476e12 q^{29} -3.90835e12 q^{31} +8.88944e12i q^{32} -8.14173e12i q^{33} -1.19535e13 q^{34} +5.95348e12 q^{36} -2.59508e13i q^{37} -2.09134e12i q^{38} +2.82485e13 q^{39} +2.13728e13 q^{41} -7.50239e13i q^{42} -7.22020e13i q^{43} +1.71624e14 q^{44} -2.99337e14 q^{46} -1.29859e14i q^{47} -1.06156e14i q^{48} -2.52773e14 q^{49} +1.51108e14 q^{51} +5.95466e14i q^{52} -2.09491e14i q^{53} -1.46585e14 q^{54} +8.26834e13 q^{56} +2.64373e13i q^{57} -2.15638e15i q^{58} -9.51957e14 q^{59} +1.05903e14 q^{61} +2.02848e15i q^{62} +9.48400e14i q^{63} +2.49302e15 q^{64} -4.22567e15 q^{66} +3.73528e15i q^{67} +3.18529e15i q^{68} +3.78401e15 q^{69} +9.20903e15 q^{71} -1.61550e14i q^{72} +1.67249e15i q^{73} -1.34688e16 q^{74} -5.57286e14 q^{76} +2.73400e16i q^{77} -1.46614e16i q^{78} -8.95327e15 q^{79} +1.85302e15 q^{81} -1.10928e16i q^{82} -1.10780e16i q^{83} -1.99918e16 q^{84} -3.74738e16 q^{86} +2.72594e16i q^{87} -4.65708e15i q^{88} -3.12179e16 q^{89} -9.48586e16 q^{91} +7.97652e16i q^{92} -2.56427e16i q^{93} -6.73986e16 q^{94} -5.83236e16 q^{96} +1.37306e17i q^{97} +1.31192e17i q^{98} +5.34179e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 524352 q^{4} + 2676888 q^{6} - 430467210 q^{9} - 1738071156 q^{11} - 15639914856 q^{14} - 66104662272 q^{16} + 64503397086 q^{19} - 28467772218 q^{21} + 455863318848 q^{24} - 1998349267080 q^{26}+ \cdots + 74\!\cdots\!76 q^{99}+O(q^{100}) \) 10 * q - 524352 * q^4 + 2676888 * q^6 - 430467210 * q^9 - 1738071156 * q^11 - 15639914856 * q^14 - 66104662272 * q^16 + 64503397086 * q^19 - 28467772218 * q^21 + 455863318848 * q^24 - 1998349267080 * q^26 + 5038974971532 * q^29 - 3489865725722 * q^31 - 1491591755504 * q^34 + 22571634249792 * q^36 + 44606871044622 * q^39 - 133243570719792 * q^41 + 464958581702400 * q^44 - 505909078820112 * q^46 + 452446566258524 * q^49 + 228379365399060 * q^51 - 115231250884248 * q^54 + 2926573946176320 * q^56 + 2701499222853564 * q^59 + 5840018660275806 * q^61 + 11386481551585280 * q^64 + 1505903745960720 * q^66 + 2909437774402284 * q^69 + 7244811708974160 * q^71 - 21913820768686896 * q^74 + 26044164027809216 * q^76 - 4680370945616080 * q^79 + 18530201888518410 * q^81 - 22778461047507264 * q^84 - 76129165470984216 * q^86 - 11696951721213504 * q^89 - 233416679038137442 * q^91 - 75086521605753488 * q^94 - 121856486730352128 * q^96 + 74818264130479476 * q^99

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