LMFDB - Embedded newform 75.9.c.f.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(26,75)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("75.26");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$30.5533957546$
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} + 1634x^{8} + 776307x^{6} + 148116566x^{4} + 10575941812x^{2} + 105274575720 $ x^10 + 1634x^8 + 776307x^6 + 148116566x^4 + 10575941812x^2 + 105274575720
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8}\cdot 3^{11}\cdot 5^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			26.1
Root			$3.43232i$ of defining polynomial
Character	$\chi$	$=$	75.26
Dual form			75.9.c.f.26.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-29.4751i q^{2} +(29.7353 + 75.3446i) q^{3} -612.784 q^{4} +(2220.79 - 876.451i) q^{6} +3164.62 q^{7} +10516.3i q^{8} +(-4792.63 + 4480.79i) q^{9} +O(q^{10})$	\(q-29.4751i q^{2} +(29.7353 + 75.3446i) q^{3} -612.784 q^{4} +(2220.79 - 876.451i) q^{6} +3164.62 q^{7} +10516.3i q^{8} +(-4792.63 + 4480.79i) q^{9} -20143.2i q^{11} +(-18221.3 - 46170.0i) q^{12} -31424.2 q^{13} -93277.7i q^{14} +153096. q^{16} +26183.5i q^{17} +(132072. + 141263. i) q^{18} -127845. q^{19} +(94100.9 + 238437. i) q^{21} -593723. q^{22} -378595. i q^{23} +(-792344. + 312704. i) q^{24} +926234. i q^{26} +(-480113. - 227861. i) q^{27} -1.93923e6 q^{28} +759951. i q^{29} -832390. q^{31} -1.82036e6i q^{32} +(1.51768e6 - 598962. i) q^{33} +771762. q^{34} +(2.93685e6 - 2.74575e6i) q^{36} -1.09633e6 q^{37} +3.76824e6i q^{38} +(-934408. - 2.36765e6i) q^{39} +22335.5i q^{41} +(7.02798e6 - 2.77364e6i) q^{42} -4.00943e6 q^{43} +1.23434e7i q^{44} -1.11591e7 q^{46} +3.13980e6i q^{47} +(4.55234e6 + 1.15349e7i) q^{48} +4.25004e6 q^{49} +(-1.97278e6 + 778572. i) q^{51} +1.92563e7 q^{52} -6.05943e6i q^{53} +(-6.71625e6 + 1.41514e7i) q^{54} +3.32800e7i q^{56} +(-3.80150e6 - 9.63242e6i) q^{57} +2.23997e7 q^{58} -1.74124e6i q^{59} +7.86006e6 q^{61} +2.45348e7i q^{62} +(-1.51669e7 + 1.41800e7i) q^{63} -1.44627e7 q^{64} +(-1.76545e7 - 4.47338e7i) q^{66} -9.88860e6 q^{67} -1.60448e7i q^{68} +(2.85251e7 - 1.12576e7i) q^{69} -5.43494e6i q^{71} +(-4.71211e7 - 5.04006e7i) q^{72} -5.05573e7 q^{73} +3.23144e7i q^{74} +7.83412e7 q^{76} -6.37455e7i q^{77} +(-6.97867e7 + 2.75418e7i) q^{78} -4.35502e7 q^{79} +(2.89185e6 - 4.29495e7i) q^{81} +658341. q^{82} -4.69277e7i q^{83} +(-5.76636e7 - 1.46111e8i) q^{84} +1.18178e8i q^{86} +(-5.72582e7 + 2.25973e7i) q^{87} +2.11831e8 q^{88} +1.88276e7i q^{89} -9.94458e7 q^{91} +2.31997e8i q^{92} +(-2.47513e7 - 6.27161e7i) q^{93} +9.25460e7 q^{94} +(1.37154e8 - 5.41288e7i) q^{96} -3.52136e7 q^{97} -1.25271e8i q^{98} +(9.02572e7 + 9.65387e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 25 q^{3} - 1554 q^{4} + 2257 q^{6} - 1960 q^{7} - 11207 q^{9}+O(q^{10}) $ 10 * q + 25 * q^3 - 1554 * q^4 + 2257 * q^6 - 1960 * q^7 - 11207 * q^9	$ 10 q + 25 q^{3} - 1554 q^{4} + 2257 q^{6} - 1960 q^{7} - 11207 q^{9} + 5915 q^{12} + 16920 q^{13} + 44634 q^{16} + 224875 q^{18} - 143934 q^{19} + 673428 q^{21} - 818990 q^{22} - 1016859 q^{24} + 260830 q^{27} - 3810100 q^{28} - 3014060 q^{31} + 4677515 q^{33} + 4977146 q^{34} + 4500527 q^{36} - 3016760 q^{37} - 7513282 q^{39} + 4001760 q^{42} - 11747340 q^{43} - 13938636 q^{46} + 14748755 q^{48} + 8953546 q^{49} + 6209287 q^{51} + 38918320 q^{52} - 8886272 q^{54} - 14759525 q^{57} + 48407900 q^{58} + 1520220 q^{61} - 74748240 q^{63} - 4536998 q^{64} + 10465295 q^{66} + 16269290 q^{67} + 11394978 q^{69} - 172231185 q^{72} + 52090170 q^{73} - 29529046 q^{76} - 198205810 q^{78} + 8549896 q^{79} + 22612945 q^{81} + 295714190 q^{82} - 136883292 q^{84} - 318901610 q^{87} + 310673250 q^{88} - 107224264 q^{91} - 79679130 q^{93} + 356118596 q^{94} + 525424001 q^{96} + 402167800 q^{97} - 382421335 q^{99}+O(q^{100}) $ 10 * q + 25 * q^3 - 1554 * q^4 + 2257 * q^6 - 1960 * q^7 - 11207 * q^9 + 5915 * q^12 + 16920 * q^13 + 44634 * q^16 + 224875 * q^18 - 143934 * q^19 + 673428 * q^21 - 818990 * q^22 - 1016859 * q^24 + 260830 * q^27 - 3810100 * q^28 - 3014060 * q^31 + 4677515 * q^33 + 4977146 * q^34 + 4500527 * q^36 - 3016760 * q^37 - 7513282 * q^39 + 4001760 * q^42 - 11747340 * q^43 - 13938636 * q^46 + 14748755 * q^48 + 8953546 * q^49 + 6209287 * q^51 + 38918320 * q^52 - 8886272 * q^54 - 14759525 * q^57 + 48407900 * q^58 + 1520220 * q^61 - 74748240 * q^63 - 4536998 * q^64 + 10465295 * q^66 + 16269290 * q^67 + 11394978 * q^69 - 172231185 * q^72 + 52090170 * q^73 - 29529046 * q^76 - 198205810 * q^78 + 8549896 * q^79 + 22612945 * q^81 + 295714190 * q^82 - 136883292 * q^84 - 318901610 * q^87 + 310673250 * q^88 - 107224264 * q^91 - 79679130 * q^93 + 356118596 * q^94 + 525424001 * q^96 + 402167800 * q^97 - 382421335 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$		−	29.4751i		−	1.84220i	−0.389330	−	0.921098i	$-0.627293\pi$
$2$		−	29.4751i		−	1.84220i	0.389330	−	0.921098i	$-0.372707\pi$
$3$	29.7353	+	75.3446i	0.367102	+	0.930181i
$3$	29.7353	+	75.3446i	0.367102	+	0.930181i
$4$	−612.784			−2.39369
$5$		0			0
$5$		0			0
$6$	2220.79	−	876.451i	1.71358	−	0.676274i
$7$	3164.62			1.31804			0.659022	−	0.752124i	$-0.270970\pi$
$7$	3164.62			1.31804			0.659022	+	0.752124i	$0.270970\pi$
$8$			10516.3i			2.56745i
$9$	−4792.63	+	4480.79i	−0.730472	+	0.682942i
$10$		0			0
$11$		−	20143.2i		−	1.37581i	−0.725803	−	0.687903i	$-0.758532\pi$
$11$		−	20143.2i		−	1.37581i	0.725803	−	0.687903i	$-0.241468\pi$
$12$	−18221.3	−	46170.0i	−0.878728	−	2.22656i
$13$	−31424.2			−1.10025			−0.550125	−	0.835083i	$-0.685420\pi$
$13$	−31424.2			−1.10025			−0.550125	+	0.835083i	$0.685420\pi$
$14$		−	93277.7i		−	2.42810i
$15$		0			0
$16$	153096.			2.33606
$17$			26183.5i			0.313496i	0.987639	+	0.156748i	$0.0501010\pi$
$17$			26183.5i			0.313496i	−0.987639	+	0.156748i	$0.949899\pi$
$18$	132072.	+	141263.i	1.25811	+	1.34567i
$19$	−127845.			−0.980999			−0.490499	−	0.871442i	$-0.663186\pi$
$19$	−127845.			−0.980999			−0.490499	+	0.871442i	$0.663186\pi$
$20$		0			0
$21$	94100.9	+	238437.i	0.483857	+	1.22602i
$22$	−593723.			−2.53450
$23$		−	378595.i		−	1.35289i	−0.736492	−	0.676446i	$-0.763519\pi$
$23$		−	378595.i		−	1.35289i	0.736492	−	0.676446i	$-0.236481\pi$
$24$	−792344.	+	312704.i	−2.38819	+	0.942515i
$25$		0			0
$26$			926234.i			2.02688i
$27$	−480113.	−	227861.i	−0.903418	−	0.428762i
$28$	−1.93923e6			−3.15499
$29$			759951.i			1.07447i	0.843433	+	0.537234i	$0.180531\pi$
$29$			759951.i			1.07447i	−0.843433	+	0.537234i	$0.819469\pi$
$30$		0			0
$31$	−832390.			−0.901322			−0.450661	−	0.892695i	$-0.648812\pi$
$31$	−832390.			−0.901322			−0.450661	+	0.892695i	$0.648812\pi$
$32$		−	1.82036e6i		−	1.73603i
$33$	1.51768e6	−	598962.i	1.27975	−	0.505061i
$34$	771762.			0.577521
$35$		0			0
$36$	2.93685e6	−	2.74575e6i	1.74852	−	1.63475i
$37$	−1.09633e6			−0.584969			−0.292484	−	0.956270i	$-0.594482\pi$
$37$	−1.09633e6			−0.584969			−0.292484	+	0.956270i	$0.594482\pi$
$38$			3.76824e6i			1.80719i
$39$	−934408.	−	2.36765e6i	−0.403904	−	1.02343i
$40$		0			0
$41$			22335.5i			0.00790423i	0.999992	+	0.00395212i	$0.00125800\pi$
$41$			22335.5i			0.00790423i	−0.999992	+	0.00395212i	$0.998742\pi$
$42$	7.02798e6	−	2.77364e6i	2.25857	−	0.891359i
$43$	−4.00943e6			−1.17276			−0.586379	−	0.810037i	$-0.699447\pi$
$43$	−4.00943e6			−1.17276			−0.586379	+	0.810037i	$0.699447\pi$
$44$			1.23434e7i			3.29325i
$45$		0			0
$46$	−1.11591e7			−2.49229
$47$			3.13980e6i			0.643443i	0.946834	+	0.321722i	$0.104262\pi$
$47$			3.13980e6i			0.643443i	−0.946834	+	0.321722i	$0.895738\pi$
$48$	4.55234e6	+	1.15349e7i	0.857571	+	2.17295i
$49$	4.25004e6			0.737240
$50$		0			0
$51$	−1.97278e6	+	778572.i	−0.291608	+	0.115085i
$52$	1.92563e7			2.63365
$53$		−	6.05943e6i		−	0.767941i	−0.923345	−	0.383971i	$-0.874556\pi$
$53$		−	6.05943e6i		−	0.767941i	0.923345	−	0.383971i	$-0.125444\pi$
$54$	−6.71625e6	+	1.41514e7i	−0.789863	+	1.66427i
$55$		0			0
$56$			3.32800e7i			3.38401i
$57$	−3.80150e6	−	9.63242e6i	−0.360127	−	0.912506i
$58$	2.23997e7			1.97938
$59$		−	1.74124e6i		−	0.143698i	−0.997416	−	0.0718489i	$-0.977110\pi$
$59$		−	1.74124e6i		−	0.143698i	0.997416	−	0.0718489i	$-0.0228899\pi$
$60$		0			0
$61$	7.86006e6			0.567684			0.283842	−	0.958871i	$-0.408391\pi$
$61$	7.86006e6			0.567684			0.283842	+	0.958871i	$0.408391\pi$
$62$			2.45348e7i			1.66041i
$63$	−1.51669e7	+	1.41800e7i	−0.962794	+	0.900148i
$64$	−1.44627e7			−0.862046
$65$		0			0
$66$	−1.76545e7	−	4.47338e7i	−0.930422	−	2.35755i
$67$	−9.88860e6			−0.490722			−0.245361	−	0.969432i	$-0.578906\pi$
$67$	−9.88860e6			−0.490722			−0.245361	+	0.969432i	$0.578906\pi$
$68$		−	1.60448e7i		−	0.750411i
$69$	2.85251e7	−	1.12576e7i	1.25843	−	0.496649i
$70$		0			0
$71$		−	5.43494e6i		−	0.213876i	−0.994266	−	0.106938i	$-0.965895\pi$
$71$		−	5.43494e6i		−	0.213876i	0.994266	−	0.106938i	$-0.0341046\pi$
$72$	−4.71211e7	−	5.04006e7i	−1.75342	−	1.87545i
$73$	−5.05573e7			−1.78030			−0.890148	−	0.455672i	$-0.849399\pi$
$73$	−5.05573e7			−1.78030			−0.890148	+	0.455672i	$0.849399\pi$
$74$			3.23144e7i			1.07763i
$75$		0			0
$76$	7.83412e7			2.34821
$77$		−	6.37455e7i		−	1.81337i
$78$	−6.97867e7	+	2.75418e7i	−1.88536	+	0.744070i
$79$	−4.35502e7			−1.11810			−0.559051	−	0.829133i	$-0.688834\pi$
$79$	−4.35502e7			−1.11810			−0.559051	+	0.829133i	$0.688834\pi$
$80$		0			0
$81$	2.89185e6	−	4.29495e7i	0.0671793	−	0.997741i
$82$	658341.			0.0145611
$83$		−	4.69277e7i		−	0.988819i	−0.869229	−	0.494409i	$-0.835384\pi$
$83$		−	4.69277e7i		−	0.988819i	0.869229	−	0.494409i	$-0.164616\pi$
$84$	−5.76636e7	−	1.46111e8i	−1.15820	−	2.93471i
$85$		0			0
$86$			1.18178e8i			2.16045i
$87$	−5.72582e7	+	2.25973e7i	−0.999449	+	0.394439i
$88$	2.11831e8			3.53231
$89$			1.88276e7i			0.300078i	0.988680	+	0.150039i	$0.0479399\pi$
$89$			1.88276e7i			0.300078i	−0.988680	+	0.150039i	$0.952060\pi$
$90$		0			0
$91$	−9.94458e7			−1.45018
$92$			2.31997e8i			3.23840i
$93$	−2.47513e7	−	6.27161e7i	−0.330877	−	0.838392i
$94$	9.25460e7			1.18535
$95$		0			0
$96$	1.37154e8	−	5.41288e7i	1.61482	−	0.637299i
$97$	−3.52136e7			−0.397762			−0.198881	−	0.980024i	$-0.563731\pi$
$97$	−3.52136e7			−0.397762			−0.198881	+	0.980024i	$0.563731\pi$
$98$		−	1.25271e8i		−	1.35814i
$99$	9.02572e7	+	9.65387e7i	0.939596	+	1.00499i
$100$		0			0
$101$			4.96736e7i			0.477353i	0.971099	+	0.238677i	$0.0767136\pi$
$101$			4.96736e7i			0.477353i	−0.971099	+	0.238677i	$0.923286\pi$
$102$	2.29485e7	+	5.81481e7i	0.212009	+	0.537199i
$103$	−1.30485e8			−1.15934			−0.579670	−	0.814851i	$-0.696819\pi$
$103$	−1.30485e8			−1.15934			−0.579670	+	0.814851i	$0.696819\pi$
$104$		−	3.30466e8i		−	2.82483i
$105$		0			0
$106$	−1.78602e8			−1.41470
$107$			8.06696e7i			0.615425i	0.951479	+	0.307712i	$0.0995635\pi$
$107$			8.06696e7i			0.615425i	−0.951479	+	0.307712i	$0.900437\pi$
$108$	2.94206e8	+	1.39630e8i	2.16250	+	1.02632i
$109$	2.38708e8			1.69107			0.845533	−	0.533923i	$-0.179283\pi$
$109$	2.38708e8			1.69107			0.845533	+	0.533923i	$0.179283\pi$
$110$		0			0
$111$	−3.25995e7	−	8.26023e7i	−0.214743	−	0.544127i
$112$	4.84490e8			3.07902
$113$			9.23822e7i			0.566597i	0.959032	+	0.283299i	$0.0914288\pi$
$113$			9.23822e7i			0.566597i	−0.959032	+	0.283299i	$0.908571\pi$
$114$	−2.83917e8	+	1.12050e8i	−1.68102	+	0.663424i
$115$		0			0
$116$		−	4.65686e8i		−	2.57194i
$117$	1.50605e8	−	1.40805e8i	0.803702	−	0.751407i
$118$	−5.13232e7			−0.264720
$119$			8.28608e7i			0.413201i
$120$		0			0
$121$	−1.91388e8			−0.892841
$122$		−	2.31676e8i		−	1.04578i
$123$	−1.68286e6	+	664151.i	−0.00735236	+	0.00290166i
$124$	5.10075e8			2.15748
$125$		0			0
$126$	4.17958e8	+	4.47046e8i	1.65825	+	1.77366i
$127$	−1.90148e7			−0.0730931			−0.0365466	−	0.999332i	$-0.511636\pi$
$127$	−1.90148e7			−0.0730931			−0.0365466	+	0.999332i	$0.511636\pi$
$128$		−	3.97199e7i		−	0.147968i
$129$	−1.19221e8	−	3.02089e8i	−0.430522	−	1.09088i
$130$		0			0
$131$		−	4.89021e8i		−	1.66051i	−0.557380	−	0.830257i	$-0.688194\pi$
$131$		−	4.89021e8i		−	1.66051i	0.557380	−	0.830257i	$-0.311806\pi$
$132$	−9.30010e8	+	3.67035e8i	−3.06332	+	1.20896i
$133$	−4.04580e8			−1.29300
$134$			2.91468e8i			0.904007i
$135$		0			0
$136$	−2.75352e8			−0.804884
$137$		−	1.33995e8i		−	0.380370i	−0.981748	−	0.190185i	$-0.939091\pi$
$137$		−	1.33995e8i		−	0.380370i	0.981748	−	0.190185i	$-0.0609087\pi$
$138$	−3.31820e8	−	8.40780e8i	−0.914926	−	2.31828i
$139$	−5.44407e6			−0.0145836			−0.00729180	−	0.999973i	$-0.502321\pi$
$139$	−5.44407e6			−0.0145836			−0.00729180	+	0.999973i	$0.502321\pi$
$140$		0			0
$141$	−2.36567e8	+	9.33627e7i	−0.598519	+	0.236209i
$142$	−1.60196e8			−0.394001
$143$			6.32984e8i			1.51373i
$144$	−7.33731e8	+	6.85989e8i	−1.70642	+	1.59539i
$145$		0			0
$146$			1.49018e9i			3.27965i
$147$	1.26376e8	+	3.20218e8i	0.270642	+	0.685766i
$148$	6.71811e8			1.40023
$149$			1.55067e8i			0.314612i	0.987550	+	0.157306i	$0.0502809\pi$
$149$			1.55067e8i			0.314612i	−0.987550	+	0.157306i	$0.949719\pi$
$150$		0			0
$151$	9.60323e8			1.84718			0.923591	−	0.383379i	$-0.125240\pi$
$151$	9.60323e8			1.84718			0.923591	+	0.383379i	$0.125240\pi$
$152$		−	1.34445e9i		−	2.51866i
$153$	−1.17323e8	−	1.25488e8i	−0.214099	−	0.229000i
$154$	−1.87891e9			−3.34059
$155$		0			0
$156$	5.72590e8	+	1.45086e9i	0.966820	+	2.44977i
$157$	2.42826e8			0.399666			0.199833	−	0.979830i	$-0.435960\pi$
$157$	2.42826e8			0.399666			0.199833	+	0.979830i	$0.435960\pi$
$158$			1.28365e9i			2.05976i
$159$	4.56545e8	−	1.80179e8i	0.714324	−	0.281913i
$160$		0			0
$161$		−	1.19811e9i		−	1.78317i
$162$	−1.26594e9	−	8.52377e7i	−1.83803	−	0.123757i
$163$	9.42493e8			1.33514			0.667571	−	0.744546i	$-0.267334\pi$
$163$	9.42493e8			1.33514			0.667571	+	0.744546i	$0.267334\pi$
$164$		−	1.36868e7i		−	0.0189203i
$165$		0			0
$166$	−1.38320e9			−1.82160
$167$		−	1.18718e9i		−	1.52634i	−0.646197	−	0.763170i	$-0.723642\pi$
$167$		−	1.18718e9i		−	1.52634i	0.646197	−	0.763170i	$-0.276358\pi$
$168$	−2.50747e9	+	9.89590e8i	−3.14774	+	1.24228i
$169$	1.71751e8			0.210549
$170$		0			0
$171$	6.12712e8	−	5.72845e8i	0.716592	−	0.669966i
$172$	2.45691e9			2.80722
$173$		−	2.03038e8i		−	0.226669i	−0.993557	−	0.113335i	$-0.963847\pi$
$173$		−	2.03038e8i		−	0.226669i	0.993557	−	0.113335i	$-0.0361532\pi$
$174$	6.66060e8	+	1.68769e9i	0.726635	+	1.84118i
$175$		0			0
$176$		−	3.08383e9i		−	3.21396i
$177$	1.31193e8	−	5.17762e7i	0.133665	−	0.0527517i
$178$	5.54946e8			0.552803
$179$		−	1.00612e9i		−	0.980030i	−0.871714	−	0.490015i	$-0.836991\pi$
$179$		−	1.00612e9i		−	0.980030i	0.871714	−	0.490015i	$-0.163009\pi$
$180$		0			0
$181$	8.87701e8			0.827089			0.413545	−	0.910484i	$-0.364291\pi$
$181$	8.87701e8			0.827089			0.413545	+	0.910484i	$0.364291\pi$
$182$			2.93118e9i			2.67151i
$183$	2.33721e8	+	5.92213e8i	0.208398	+	0.528048i
$184$	3.98140e9			3.47348
$185$		0			0
$186$	−1.84857e9	+	7.29549e8i	−1.54448	+	0.609541i
$187$	5.27418e8			0.431309
$188$		−	1.92402e9i		−	1.54020i
$189$	−1.51938e9	−	7.21096e8i	−1.19074	−	0.565127i
$190$		0			0
$191$			2.16005e9i			1.62305i	0.584320	+	0.811523i	$0.301361\pi$
$191$			2.16005e9i			1.62305i	−0.584320	+	0.811523i	$0.698639\pi$
$192$	−4.30053e8	−	1.08969e9i	−0.316459	−	0.801859i
$193$	1.50434e9			1.08422			0.542108	−	0.840309i	$-0.317626\pi$
$193$	1.50434e9			1.08422			0.542108	+	0.840309i	$0.317626\pi$
$194$			1.03793e9i			0.732755i
$195$		0			0
$196$	−2.60436e9			−1.76472
$197$		−	3.65705e8i		−	0.242809i	−0.992603	−	0.121405i	$-0.961260\pi$
$197$		−	3.65705e8i		−	0.242809i	0.992603	−	0.121405i	$-0.0387399\pi$
$198$	2.84549e9	−	2.66034e9i	1.85139	−	1.73092i
$199$	−1.84128e9			−1.17411			−0.587053	−	0.809549i	$-0.699712\pi$
$199$	−1.84128e9			−1.17411			−0.587053	+	0.809549i	$0.699712\pi$
$200$		0			0
$201$	−2.94040e8	−	7.45053e8i	−0.180145	−	0.456460i
$202$	1.46414e9			0.879379
$203$			2.40496e9i			1.41620i
$204$	1.20889e9	−	4.77097e8i	0.698018	−	0.275477i
$205$		0			0
$206$			3.84606e9i			2.13573i
$207$	1.69640e9	+	1.81446e9i	0.923947	+	0.988250i
$208$	−4.81092e9			−2.57024
$209$			2.57520e9i			1.34966i
$210$		0			0
$211$	−8.21239e8			−0.414323			−0.207162	−	0.978307i	$-0.566423\pi$
$211$	−8.21239e8			−0.414323			−0.207162	+	0.978307i	$0.566423\pi$
$212$			3.71312e9i			1.83821i
$213$	4.09494e8	−	1.61609e8i	0.198943	−	0.0785142i
$214$	2.37775e9			1.13373
$215$		0			0
$216$	2.39625e9	−	5.04900e9i	1.10082	−	2.31948i
$217$	−2.63420e9			−1.18798
$218$		−	7.03595e9i		−	3.11528i
$219$	−1.50333e9	−	3.80922e9i	−0.653550	−	1.65600i
$220$		0			0
$221$		−	8.22795e8i		−	0.344923i
$222$	−2.43471e9	+	9.60876e8i	−1.00239	+	0.395599i
$223$	−3.76056e8			−0.152066			−0.0760332	−	0.997105i	$-0.524225\pi$
$223$	−3.76056e8			−0.152066			−0.0760332	+	0.997105i	$0.524225\pi$
$224$		−	5.76074e9i		−	2.28816i
$225$		0			0
$226$	2.72298e9			1.04378
$227$		−	4.58046e9i		−	1.72507i	−0.506000	−	0.862533i	$-0.668876\pi$
$227$		−	4.58046e9i		−	1.72507i	0.506000	−	0.862533i	$-0.331124\pi$
$228$	2.32950e9	+	5.90259e9i	0.862031	+	2.18426i
$229$	1.66628e9			0.605906			0.302953	−	0.953005i	$-0.402027\pi$
$229$	1.66628e9			0.605906			0.302953	+	0.953005i	$0.402027\pi$
$230$		0			0
$231$	4.80289e9	−	1.89549e9i	1.68676	−	0.665693i
$232$	−7.99184e9			−2.75864
$233$			4.25125e9i			1.44243i	0.692714	+	0.721213i	$0.256415\pi$
$233$			4.25125e9i			1.44243i	−0.692714	+	0.721213i	$0.743585\pi$
$234$	−4.15025e9	−	4.43909e9i	−1.38424	−	1.48058i
$235$		0			0
$236$			1.06700e9i			0.343968i
$237$	−1.29498e9	−	3.28127e9i	−0.410458	−	1.04004i
$238$	2.44233e9			0.761198
$239$		−	1.85631e9i		−	0.568930i	−0.958686	−	0.284465i	$-0.908184\pi$
$239$		−	1.85631e9i		−	0.568930i	0.958686	−	0.284465i	$-0.0918159\pi$
$240$		0			0
$241$	5.00083e9			1.48243			0.741215	−	0.671268i	$-0.234250\pi$
$241$	5.00083e9			1.48243			0.741215	+	0.671268i	$0.234250\pi$
$242$			5.64120e9i			1.64479i
$243$	3.32200e9	−	1.05923e9i	0.952741	−	0.303784i
$244$	−4.81652e9			−1.35886
$245$		0			0
$246$	1.95760e7	+	4.96025e7i	0.00534543	+	0.0135445i
$247$	4.01742e9			1.07934
$248$		−	8.75363e9i		−	2.31410i
$249$	3.53575e9	−	1.39541e9i	0.919780	−	0.362997i
$250$		0			0
$251$			1.91602e8i			0.0482732i	0.999709	+	0.0241366i	$0.00768367\pi$
$251$			1.91602e8i			0.0482732i	−0.999709	+	0.0241366i	$0.992316\pi$
$252$	9.29401e9	−	8.68928e9i	2.30463	−	2.15467i
$253$	−7.62609e9			−1.86132
$254$			5.60464e8i			0.134652i
$255$		0			0
$256$	−4.87321e9			−1.13463
$257$			2.54083e9i			0.582429i	0.956658	+	0.291215i	$0.0940594\pi$
$257$			2.54083e9i			0.582429i	−0.956658	+	0.291215i	$0.905941\pi$
$258$	−8.90411e9	+	3.51407e9i	−2.00961	+	0.793106i
$259$	−3.46946e9			−0.771015
$260$		0			0
$261$	−3.40518e9	−	3.64216e9i	−0.733800	−	0.784869i
$262$	−1.44140e10			−3.05899
$263$			1.61586e9i			0.337740i	0.985638	+	0.168870i	$0.0540117\pi$
$263$			1.61586e9i			0.337740i	−0.985638	+	0.168870i	$0.945988\pi$
$264$	6.29885e9	+	1.59603e10i	1.29672	+	3.28569i
$265$		0			0
$266$			1.19251e10i			2.38196i
$267$	−1.41856e9	+	5.59843e8i	−0.279127	+	0.110159i
$268$	6.05958e9			1.17464
$269$			7.37100e9i			1.40772i	0.710337	+	0.703861i	$0.248542\pi$
$269$			7.37100e9i			1.40772i	−0.710337	+	0.703861i	$0.751458\pi$
$270$		0			0
$271$	−3.90024e9			−0.723126			−0.361563	−	0.932348i	$-0.617757\pi$
$271$	−3.90024e9			−0.723126			−0.361563	+	0.932348i	$0.617757\pi$
$272$			4.00858e9i			0.732343i
$273$	−2.95705e9	−	7.49271e9i	−0.532363	−	1.34893i
$274$	−3.94952e9			−0.700716
$275$		0			0
$276$	−1.74797e10	+	6.89848e9i	−3.01230	+	1.18882i
$277$	8.18524e9			1.39031			0.695157	−	0.718858i	$-0.255335\pi$
$277$	8.18524e9			1.39031			0.695157	+	0.718858i	$0.255335\pi$
$278$			1.60465e8i			0.0268659i
$279$	3.98933e9	−	3.72976e9i	0.658391	−	0.615551i
$280$		0			0
$281$		−	7.15119e9i		−	1.14697i	−0.819215	−	0.573486i	$-0.805591\pi$
$281$		−	7.15119e9i		−	1.14697i	0.819215	−	0.573486i	$-0.194409\pi$
$282$	2.75188e9	+	6.97285e9i	0.435144	+	1.10259i
$283$	7.42098e9			1.15695			0.578476	−	0.815699i	$-0.303648\pi$
$283$	7.42098e9			1.15695			0.578476	+	0.815699i	$0.303648\pi$
$284$			3.33045e9i			0.511952i
$285$		0			0
$286$	1.86573e10			2.78859
$287$			7.06834e7i			0.0104181i
$288$	8.15662e9	+	8.72429e9i	1.18561	+	1.26812i
$289$	6.29018e9			0.901720
$290$		0			0
$291$	−1.04708e9	−	2.65315e9i	−0.146019	−	0.369990i
$292$	3.09807e10			4.26147
$293$			1.73588e8i			0.0235531i	0.999931	+	0.0117766i	$0.00374868\pi$
$293$			1.73588e8i			0.0235531i	−0.999931	+	0.0117766i	$0.996251\pi$
$294$	9.43846e9	−	3.72495e9i	1.26332	−	0.498576i
$295$		0			0
$296$		−	1.15293e10i		−	1.50188i
$297$	−4.58985e9	+	9.67100e9i	−0.589893	+	1.24293i
$298$	4.57063e9			0.579577
$299$			1.18970e10i			1.48852i
$300$		0			0
$301$	−1.26883e10			−1.54575
$302$		−	2.83057e10i		−	3.40287i
$303$	−3.74264e9	+	1.47706e9i	−0.444025	+	0.175237i
$304$	−1.95725e10			−2.29167
$305$		0			0
$306$	−3.69877e9	+	3.45810e9i	−0.421863	+	0.394413i
$307$	−1.38868e10			−1.56332			−0.781661	−	0.623703i	$-0.785627\pi$
$307$	−1.38868e10			−1.56332			−0.781661	+	0.623703i	$0.785627\pi$
$308$			3.90623e10i			4.34065i
$309$	−3.88000e9	−	9.83133e9i	−0.425596	−	1.07840i
$310$		0			0
$311$			9.61567e9i			1.02787i	0.857829	+	0.513935i	$0.171813\pi$
$311$			9.61567e9i			1.02787i	−0.857829	+	0.513935i	$0.828187\pi$
$312$	2.48988e10	−	9.82648e9i	2.62761	−	1.03700i
$313$	−1.68395e10			−1.75450			−0.877248	−	0.480037i	$-0.840623\pi$
$313$	−1.68395e10			−1.75450			−0.877248	+	0.480037i	$0.840623\pi$
$314$		−	7.15734e9i		−	0.736263i
$315$		0			0
$316$	2.66869e10			2.67639
$317$		−	1.96153e10i		−	1.94248i	−0.238094	−	0.971242i	$-0.576523\pi$
$317$		−	1.96153e10i		−	1.94248i	0.238094	−	0.971242i	$-0.423477\pi$
$318$	−5.31079e9	−	1.34567e10i	−0.519339	−	1.31593i
$319$	1.53078e10			1.47826
$320$		0			0
$321$	−6.07802e9	+	2.39873e9i	−0.572456	+	0.225924i
$322$	−3.53144e10			−3.28495
$323$		−	3.34742e9i		−	0.307539i
$324$	−1.77208e9	+	2.63188e10i	−0.160806	+	2.38828i
$325$		0			0
$326$		−	2.77801e10i		−	2.45960i
$327$	7.09804e9	+	1.79853e10i	0.620794	+	1.57300i
$328$	−2.34886e8			−0.0202937
$329$			9.93628e9i			0.848087i
$330$		0			0
$331$	−1.12041e10			−0.933396			−0.466698	−	0.884417i	$-0.654557\pi$
$331$	−1.12041e10			−0.933396			−0.466698	+	0.884417i	$0.654557\pi$
$332$			2.87565e10i			2.36692i
$333$	5.25428e9	−	4.91240e9i	0.427304	−	0.399500i
$334$	−3.49924e10			−2.81182
$335$		0			0
$336$	1.44065e10	+	3.65038e10i	1.13032	+	2.86405i
$337$	8.17992e8			0.0634205			0.0317102	−	0.999497i	$-0.489905\pi$
$337$	8.17992e8			0.0634205			0.0317102	+	0.999497i	$0.489905\pi$
$338$		−	5.06239e9i		−	0.387872i
$339$	−6.96050e9	+	2.74701e9i	−0.527038	+	0.207999i
$340$		0			0
$341$			1.67670e10i			1.24004i
$342$	−1.68847e10	−	1.80598e10i	−1.23421	−	1.32010i
$343$	−4.79365e9			−0.346330
$344$		−	4.21642e10i		−	3.01099i
$345$		0			0
$346$	−5.98458e9			−0.417570
$347$			1.44473e10i			0.996479i	0.867039	+	0.498239i	$0.166020\pi$
$347$			1.44473e10i			0.996479i	−0.867039	+	0.498239i	$0.833980\pi$
$348$	3.50869e10	−	1.38473e10i	2.39237	−	0.944165i
$349$	−1.45400e9			−0.0980080			−0.0490040	−	0.998799i	$-0.515605\pi$
$349$	−1.45400e9			−0.0980080			−0.0490040	+	0.998799i	$0.515605\pi$
$350$		0			0
$351$	1.50872e10	+	7.16037e9i	0.993985	+	0.471745i
$352$	−3.66677e10			−2.38844
$353$		−	1.22501e10i		−	0.788934i	−0.918910	−	0.394467i	$-0.870929\pi$
$353$		−	1.22501e10i		−	0.788934i	0.918910	−	0.394467i	$-0.129071\pi$
$354$	−1.52611e9	−	3.86693e9i	−0.0971791	−	0.246237i
$355$		0			0
$356$		−	1.15372e10i		−	0.718294i
$357$	−6.24312e9	+	2.46389e9i	−0.384352	+	0.151687i
$358$	−2.96557e10			−1.80541
$359$		−	1.08842e10i		−	0.655271i	−0.944804	−	0.327635i	$-0.893748\pi$
$359$		−	1.08842e10i		−	0.655271i	0.944804	−	0.327635i	$-0.106252\pi$
$360$		0			0
$361$	−6.39283e8			−0.0376413
$362$		−	2.61651e10i		−	1.52366i
$363$	−5.69099e9	−	1.44201e10i	−0.327764	−	0.830504i
$364$	6.09388e10			3.47127
$365$		0			0
$366$	1.74556e10	−	6.88896e9i	0.972769	−	0.383910i
$367$	−2.34324e10			−1.29167			−0.645836	−	0.763476i	$-0.723491\pi$
$367$	−2.34324e10			−1.29167			−0.645836	+	0.763476i	$0.723491\pi$
$368$		−	5.79612e10i		−	3.16043i
$369$	−1.00080e8	−	1.07046e8i	−0.00539814	−	0.00577382i
$370$		0			0
$371$		−	1.91758e10i		−	1.01218i
$372$	1.51672e10	+	3.84314e10i	0.792017	+	2.00685i
$373$	−1.29023e10			−0.666548			−0.333274	−	0.942830i	$-0.608153\pi$
$373$	−1.29023e10			−0.666548			−0.333274	+	0.942830i	$0.608153\pi$
$374$		−	1.55457e10i		−	0.794556i
$375$		0			0
$376$	−3.30190e10			−1.65201
$377$		−	2.38809e10i		−	1.18218i
$378$	−2.12544e10	+	4.47839e10i	−1.04107	+	2.19358i
$379$	−5.12576e9			−0.248429			−0.124214	−	0.992255i	$-0.539641\pi$
$379$	−5.12576e9			−0.248429			−0.124214	+	0.992255i	$0.539641\pi$
$380$		0			0
$381$	−5.65410e8	−	1.43266e9i	−0.0268326	−	0.0679898i
$382$	6.36679e10			2.98997
$383$			3.66239e10i			1.70204i	0.525136	+	0.851018i	$0.324014\pi$
$383$			3.66239e10i			1.70204i	−0.525136	+	0.851018i	$0.675986\pi$
$384$	2.99268e9	−	1.18108e9i	0.137637	−	0.0543194i
$385$		0			0
$386$		−	4.43406e10i		−	1.99734i
$387$	1.92157e10	−	1.79654e10i	0.856667	−	0.800926i
$388$	2.15783e10			0.952118
$389$			3.16164e10i			1.38075i	0.723453	+	0.690373i	$0.242554\pi$
$389$			3.16164e10i			1.38075i	−0.723453	+	0.690373i	$0.757446\pi$
$390$		0			0
$391$	9.91292e9			0.424126
$392$			4.46946e10i			1.89282i
$393$	3.68451e10	−	1.45412e10i	1.54458	−	0.609578i
$394$	−1.07792e10			−0.447303
$395$		0			0
$396$	−5.53082e10	−	5.91574e10i	−2.24910	−	2.40563i
$397$	−5.05225e8			−0.0203387			−0.0101693	−	0.999948i	$-0.503237\pi$
$397$	−5.05225e8			−0.0203387			−0.0101693	+	0.999948i	$0.503237\pi$
$398$			5.42719e10i			2.16293i
$399$	−1.20303e10	−	3.04830e10i	−0.474663	−	1.20272i
$400$		0			0
$401$			3.67187e10i			1.42007i	0.704167	+	0.710035i	$0.251321\pi$
$401$			3.67187e10i			1.42007i	−0.704167	+	0.710035i	$0.748679\pi$
$402$	−2.19605e10	+	8.66688e9i	−0.840889	+	0.331863i
$403$	2.61572e10			0.991679
$404$		−	3.04392e10i		−	1.14264i
$405$		0			0
$406$	7.08865e10			2.60891
$407$			2.20835e10i			0.804804i
$408$	−8.18768e9	−	2.07463e10i	−0.295474	−	0.748687i
$409$	7.11197e9			0.254154			0.127077	−	0.991893i	$-0.459441\pi$
$409$	7.11197e9			0.254154			0.127077	+	0.991893i	$0.459441\pi$
$410$		0			0
$411$	1.00958e10	−	3.98437e9i	0.353813	−	0.139635i
$412$	7.99590e10			2.77510
$413$		−	5.51036e9i		−	0.189400i
$414$	5.34816e10	−	5.00017e10i	1.82055	−	1.70209i
$415$		0			0
$416$			5.72033e10i			1.91006i
$417$	−1.61881e8	−	4.10182e8i	−0.00535367	−	0.0135654i
$418$	7.59044e10			2.48635
$419$			2.61481e10i			0.848369i	0.905576	+	0.424184i	$0.139439\pi$
$419$			2.61481e10i			0.848369i	−0.905576	+	0.424184i	$0.860561\pi$
$420$		0			0
$421$	5.80276e9			0.184717			0.0923584	−	0.995726i	$-0.470559\pi$
$421$	5.80276e9			0.184717			0.0923584	+	0.995726i	$0.470559\pi$
$422$			2.42061e10i			0.763265i
$423$	−1.40688e10	−	1.50479e10i	−0.439435	−	0.470017i
$424$	6.37225e10			1.97165
$425$		0			0
$426$	−4.76346e9	−	1.20699e10i	−0.144639	−	0.366492i
$427$	2.48741e10			0.748232
$428$		−	4.94331e10i		−	1.47314i
$429$	−4.76919e10	+	1.88219e10i	−1.40804	+	0.555693i
$430$		0			0
$431$			4.45744e10i			1.29175i	0.763445	+	0.645873i	$0.223506\pi$
$431$			4.45744e10i			1.29175i	−0.763445	+	0.645873i	$0.776494\pi$
$432$	−7.35033e10	−	3.48846e10i	−2.11043	−	1.00161i
$433$	3.20554e10			0.911905			0.455952	−	0.890004i	$-0.349299\pi$
$433$	3.20554e10			0.911905			0.455952	+	0.890004i	$0.349299\pi$
$434$			7.76434e10i			2.18850i
$435$		0			0
$436$	−1.46276e11			−4.04789
$437$			4.84013e10i			1.32718i
$438$	−1.12277e11	+	4.43110e10i	−3.05067	+	1.20397i
$439$	−2.57341e10			−0.692867			−0.346434	−	0.938074i	$-0.612607\pi$
$439$	−2.57341e10			−0.692867			−0.346434	+	0.938074i	$0.612607\pi$
$440$		0			0
$441$	−2.03689e10	+	1.90435e10i	−0.538533	+	0.503492i
$442$	−2.42520e10			−0.635417
$443$		−	7.09037e10i		−	1.84100i	−0.390743	−	0.920500i	$-0.627782\pi$
$443$		−	7.09037e10i		−	1.84100i	0.390743	−	0.920500i	$-0.372218\pi$
$444$	1.99765e10	+	5.06174e10i	0.514028	+	1.30247i
$445$		0			0
$446$			1.10843e10i			0.280136i
$447$	−1.16835e10	+	4.61097e9i	−0.292646	+	0.115495i
$448$	−4.57691e10			−1.13621
$449$		−	6.41882e10i		−	1.57932i	−0.613545	−	0.789660i	$-0.710257\pi$
$449$		−	6.41882e10i		−	1.57932i	0.613545	−	0.789660i	$-0.289743\pi$
$450$		0			0
$451$	4.49907e8			0.0108747
$452$		−	5.66103e10i		−	1.35626i
$453$	2.85555e10	+	7.23552e10i	0.678104	+	1.71821i
$454$	−1.35010e11			−3.17791
$455$		0			0
$456$	1.01297e11	−	3.99776e10i	2.34281	−	0.924607i
$457$	−1.93552e10			−0.443745			−0.221873	−	0.975076i	$-0.571217\pi$
$457$	−1.93552e10			−0.443745			−0.221873	+	0.975076i	$0.571217\pi$
$458$		−	4.91138e10i		−	1.11620i
$459$	5.96620e9	−	1.25710e10i	0.134415	−	0.283218i
$460$		0			0
$461$			5.65186e10i			1.25138i	0.780073	+	0.625688i	$0.215182\pi$
$461$			5.65186e10i			1.25138i	−0.780073	+	0.625688i	$0.784818\pi$
$462$	−5.58699e10	−	1.41566e11i	−1.22634	−	3.10735i
$463$	−2.73707e9			−0.0595610			−0.0297805	−	0.999556i	$-0.509481\pi$
$463$	−2.73707e9			−0.0595610			−0.0297805	+	0.999556i	$0.509481\pi$
$464$			1.16345e11i			2.51002i
$465$		0			0
$466$	1.25306e11			2.65723
$467$			1.99286e10i			0.418995i	0.977809	+	0.209498i	$0.0671829\pi$
$467$			1.99286e10i			0.418995i	−0.977809	+	0.209498i	$0.932817\pi$
$468$	−9.22881e10	+	8.62832e10i	−1.92381	+	1.79863i
$469$	−3.12937e10			−0.646793
$470$		0			0
$471$	7.22050e9	+	1.82957e10i	0.146718	+	0.371762i
$472$	1.83113e10			0.368937
$473$			8.07625e10i			1.61349i
$474$	−9.67160e10	+	3.81696e10i	−1.91595	+	0.756144i
$475$		0			0
$476$		−	5.07758e10i		−	0.989075i
$477$	2.71510e10	+	2.90406e10i	0.524460	+	0.560960i
$478$	−5.47150e10			−1.04808
$479$		−	3.16925e10i		−	0.602024i	−0.953620	−	0.301012i	$-0.902676\pi$
$479$		−	3.16925e10i		−	0.602024i	0.953620	−	0.301012i	$-0.0973245\pi$
$480$		0			0
$481$	3.44512e10			0.643612
$482$		−	1.47400e11i		−	2.73093i
$483$	9.02711e10	−	3.56261e10i	1.65867	−	0.654605i
$484$	1.17280e11			2.13718
$485$		0			0
$486$	−3.12209e10	−	9.79165e10i	−0.559630	−	1.75514i
$487$	−4.71599e10			−0.838411			−0.419205	−	0.907891i	$-0.637691\pi$
$487$	−4.71599e10			−0.838411			−0.419205	+	0.907891i	$0.637691\pi$
$488$			8.26585e10i			1.45750i
$489$	2.80253e10	+	7.10118e10i	0.490134	+	1.24192i
$490$		0			0
$491$		−	6.61089e10i		−	1.13745i	−0.822526	−	0.568727i	$-0.807436\pi$
$491$		−	6.61089e10i		−	1.13745i	0.822526	−	0.568727i	$-0.192564\pi$
$492$	1.03123e9	−	4.06981e8i	0.0175993	−	0.00694567i
$493$	−1.98981e10			−0.336841
$494$		−	1.18414e11i		−	1.98836i
$495$		0			0
$496$	−1.27435e11			−2.10554
$497$		−	1.71995e10i		−	0.281898i
$498$	−4.11298e10	−	1.04217e11i	−0.668713	−	1.69442i
$499$	7.91261e10			1.27620			0.638098	−	0.769955i	$-0.279721\pi$
$499$	7.91261e10			1.27620			0.638098	+	0.769955i	$0.279721\pi$
$500$		0			0
$501$	8.94478e10	−	3.53012e10i	1.41977	−	0.560323i
$502$	5.64751e9			0.0889287
$503$		−	6.52715e10i		−	1.01965i	−0.860278	−	0.509826i	$-0.829710\pi$
$503$		−	6.52715e10i		−	1.01965i	0.860278	−	0.509826i	$-0.170290\pi$
$504$	−1.49121e11	−	1.59499e11i	−2.31108	−	2.47192i
$505$		0			0
$506$			2.24780e11i			3.42891i
$507$	5.10707e9	+	1.29405e10i	0.0772929	+	0.195848i
$508$	1.16520e10			0.174962
$509$			4.80429e10i			0.715745i	0.933771	+	0.357872i	$0.116498\pi$
$509$			4.80429e10i			0.715745i	−0.933771	+	0.357872i	$0.883502\pi$
$510$		0			0
$511$	−1.59995e11			−2.34651
$512$			1.33470e11i			1.94225i
$513$	6.13800e10	+	2.91309e10i	0.886252	+	0.420615i
$514$	7.48914e10			1.07295
$515$		0			0
$516$	7.30569e10	+	1.85115e11i	1.03053	+	2.61122i
$517$	6.32455e10			0.885253
$518$			1.02263e11i			1.42036i
$519$	1.52978e10	−	6.03739e9i	0.210844	−	0.0832108i
$520$		0			0
$521$		−	6.97814e10i		−	0.947085i	−0.880771	−	0.473542i	$-0.842975\pi$
$521$		−	6.97814e10i		−	0.947085i	0.880771	−	0.473542i	$-0.157025\pi$
$522$	−1.07353e11	+	1.00368e11i	−1.44588	+	1.35180i
$523$	−1.13309e11			−1.51445			−0.757227	−	0.653152i	$-0.773446\pi$
$523$	−1.13309e11			−1.51445			−0.757227	+	0.653152i	$0.773446\pi$
$524$			2.99665e11i			3.97475i
$525$		0			0
$526$	4.76278e10			0.622183
$527$		−	2.17948e10i		−	0.282560i
$528$	2.32350e11	−	9.16986e10i	2.98956	−	1.17985i
$529$	−6.50228e10			−0.830315
$530$		0			0
$531$	7.80211e9	+	8.34511e9i	0.0981373	+	0.104967i
$532$	2.47921e11			3.09504
$533$		−	7.01875e8i		−	0.00869663i
$534$	1.65015e10	+	4.18122e10i	0.202935	+	0.514207i
$535$		0			0
$536$		−	1.03991e11i		−	1.25990i
$537$	7.58061e10	−	2.99174e10i	0.911605	−	0.359771i
$538$	2.17261e11			2.59330
$539$		−	8.56093e10i		−	1.01430i
$540$		0			0
$541$	−3.53511e10			−0.412680			−0.206340	−	0.978480i	$-0.566155\pi$
$541$	−3.53511e10			−0.412680			−0.206340	+	0.978480i	$0.566155\pi$
$542$			1.14960e11i			1.33214i
$543$	2.63960e10	+	6.68835e10i	0.303626	+	0.769342i
$544$	4.76632e10			0.544237
$545$		0			0
$546$	−2.20849e11	+	8.71594e10i	−2.48499	+	0.980717i
$547$	3.44410e10			0.384703			0.192352	−	0.981326i	$-0.438389\pi$
$547$	3.44410e10			0.384703			0.192352	+	0.981326i	$0.438389\pi$
$548$			8.21100e10i			0.910487i
$549$	−3.76703e10	+	3.52192e10i	−0.414677	+	0.387695i
$550$		0			0
$551$		−	9.71557e10i		−	1.05405i
$552$	1.18388e11	+	2.99977e11i	1.27512	+	3.23096i
$553$	−1.37820e11			−1.47371
$554$		−	2.41261e11i		−	2.56123i
$555$		0			0
$556$	3.33604e9			0.0349086
$557$			1.45667e9i			0.0151335i	0.999971	+	0.00756676i	$0.00240860\pi$
$557$			1.45667e9i			0.0151335i	−0.999971	+	0.00756676i	$0.997591\pi$
$558$	−1.09935e11	−	1.17586e11i	−1.13397	−	1.21288i
$559$	1.25993e11			1.29033
$560$		0			0
$561$	1.56829e10	+	3.97381e10i	0.158334	+	0.401195i
$562$	−2.10782e11			−2.11295
$563$		−	1.15715e11i		−	1.15175i	−0.817539	−	0.575873i	$-0.804662\pi$
$563$		−	1.15715e11i		−	1.15175i	0.817539	−	0.575873i	$-0.195338\pi$
$564$	1.44964e11	−	5.72112e10i	1.43267	−	0.565412i
$565$		0			0
$566$		−	2.18734e11i		−	2.13133i
$567$	9.15161e9	−	1.35919e11i	0.0885453	−	1.31507i
$568$	5.71553e10			0.549115
$569$			3.28384e10i			0.313280i	0.987656	+	0.156640i	$0.0500663\pi$
$569$			3.28384e10i			0.313280i	−0.987656	+	0.156640i	$0.949934\pi$
$570$		0			0
$571$	1.02275e11			0.962111			0.481055	−	0.876690i	$-0.340254\pi$
$571$	1.02275e11			0.962111			0.481055	+	0.876690i	$0.340254\pi$
$572$		−	3.87882e11i		−	3.62340i
$573$	−1.62748e11	+	6.42298e10i	−1.50973	+	0.595824i
$574$	2.08340e9			0.0191922
$575$		0			0
$576$	6.93145e10	−	6.48044e10i	0.629701	−	0.588728i
$577$	−1.74070e10			−0.157043			−0.0785217	−	0.996912i	$-0.525020\pi$
$577$	−1.74070e10			−0.157043			−0.0785217	+	0.996912i	$0.525020\pi$
$578$		−	1.85404e11i		−	1.66115i
$579$	4.47319e10	+	1.13344e11i	0.398018	+	1.00852i
$580$		0			0
$581$		−	1.48508e11i		−	1.30331i
$582$	−7.82021e10	+	3.08630e10i	−0.681595	+	0.268996i
$583$	−1.22056e11			−1.05654
$584$		−	5.31674e11i		−	4.57082i
$585$		0			0
$586$	5.11652e9			0.0433895
$587$			5.82932e10i			0.490982i	0.969399	+	0.245491i	$0.0789492\pi$
$587$			5.82932e10i			0.490982i	−0.969399	+	0.245491i	$0.921051\pi$
$588$	−7.74413e10	−	1.96224e11i	−0.647833	−	1.64151i
$589$	1.06417e11			0.884196
$590$		0			0
$591$	2.75539e10	−	1.08743e10i	0.225857	−	0.0891359i
$592$	−1.67843e11			−1.36652
$593$			9.05975e10i			0.732652i	0.930487	+	0.366326i	$0.119384\pi$
$593$			9.05975e10i			0.732652i	−0.930487	+	0.366326i	$0.880616\pi$
$594$	2.85054e11	+	1.35287e11i	2.28972	+	1.08670i
$595$		0			0
$596$		−	9.50228e10i		−	0.753083i
$597$	−5.47509e10	−	1.38730e11i	−0.431016	−	1.09213i
$598$	3.50667e11			2.74214
$599$		−	2.21600e11i		−	1.72133i	−0.509175	−	0.860663i	$-0.670049\pi$
$599$		−	2.21600e11i		−	1.72133i	0.509175	−	0.860663i	$-0.329951\pi$
$600$		0			0
$601$	−9.42710e10			−0.722571			−0.361285	−	0.932455i	$-0.617662\pi$
$601$	−9.42710e10			−0.722571			−0.361285	+	0.932455i	$0.617662\pi$
$602$			3.73990e11i			2.84757i
$603$	4.73924e10	−	4.43087e10i	0.358459	−	0.335135i
$604$	−5.88471e11			−4.42158
$605$		0			0
$606$	4.35365e10	+	1.10315e11i	0.322822	+	0.817981i
$607$	−2.52304e11			−1.85853			−0.929265	−	0.369415i	$-0.879558\pi$
$607$	−2.52304e11			−1.85853			−0.929265	+	0.369415i	$0.879558\pi$
$608$			2.32723e11i			1.70304i
$609$	−1.81201e11	+	7.15120e10i	−1.31732	+	0.519888i
$610$		0			0
$611$		−	9.86657e10i		−	0.707948i
$612$	7.18934e10	+	7.68968e10i	0.512487	+	0.548154i
$613$	1.39397e11			0.987213			0.493607	−	0.869685i	$-0.335678\pi$
$613$	1.39397e11			0.987213			0.493607	+	0.869685i	$0.335678\pi$
$614$			4.09315e11i			2.87995i
$615$		0			0
$616$	6.70365e11			4.65574
$617$		−	4.85857e10i		−	0.335249i	−0.985851	−	0.167625i	$-0.946390\pi$
$617$		−	4.85857e10i		−	0.335249i	0.985851	−	0.167625i	$-0.0536096\pi$
$618$	−2.89780e11	+	1.14364e11i	−1.98662	+	0.784032i
$619$	1.67889e11			1.14356			0.571781	−	0.820406i	$-0.306253\pi$
$619$	1.67889e11			1.14356			0.571781	+	0.820406i	$0.306253\pi$
$620$		0			0
$621$	−8.62671e10	+	1.81768e11i	−0.580068	+	1.22223i
$622$	2.83423e11			1.89354
$623$			5.95822e10i			0.395516i
$624$	−1.43054e11	−	3.62477e11i	−0.943542	−	2.39079i
$625$		0			0
$626$			4.96347e11i			3.23213i
$627$	−1.94027e11	+	7.65742e10i	−1.25543	+	0.495464i
$628$	−1.48800e11			−0.956676
$629$		−	2.87056e10i		−	0.183385i
$630$		0			0
$631$	−7.74846e10			−0.488763			−0.244381	−	0.969679i	$-0.578585\pi$
$631$	−7.74846e10			−0.488763			−0.244381	+	0.969679i	$0.578585\pi$
$632$		−	4.57985e11i		−	2.87067i
$633$	−2.44197e10	−	6.18759e10i	−0.152099	−	0.385396i
$634$	−5.78163e11			−3.57844
$635$		0			0
$636$	−2.79764e11	+	1.10411e11i	−1.70987	+	0.674811i
$637$	−1.33554e11			−0.811148
$638$		−	4.51200e11i		−	2.72324i
$639$	2.43528e10	+	2.60477e10i	0.146065	+	0.156230i
$640$		0			0
$641$			2.34664e11i			1.39000i	0.719012	+	0.694998i	$0.244595\pi$
$641$			2.34664e11i			1.39000i	−0.719012	+	0.694998i	$0.755405\pi$
$642$	7.07030e10	+	1.79151e11i	0.416196	+	1.05458i
$643$	−3.28468e11			−1.92154			−0.960768	−	0.277353i	$-0.910543\pi$
$643$	−3.28468e11			−1.92154			−0.960768	+	0.277353i	$0.910543\pi$
$644$			7.34182e11i			4.26835i
$645$		0			0
$646$	−9.86657e10			−0.566547
$647$			1.20987e11i			0.690435i	0.938523	+	0.345217i	$0.112195\pi$
$647$			1.20987e11i			0.690435i	−0.938523	+	0.345217i	$0.887805\pi$
$648$	4.51668e11	+	3.04115e10i	2.56165	+	0.172479i
$649$	−3.50740e10			−0.197700
$650$		0			0
$651$	−7.83286e10	−	1.98473e11i	−0.436110	−	1.10504i
$652$	−5.77545e11			−3.19592
$653$		−	6.71025e9i		−	0.0369051i	−0.999830	−	0.0184525i	$-0.994126\pi$
$653$		−	6.71025e9i		−	0.0369051i	0.999830	−	0.0184525i	$-0.00587396\pi$
$654$	5.30121e11	−	2.09216e11i	2.89777	−	1.14362i
$655$		0			0
$656$			3.41947e9i			0.0184647i
$657$	2.42302e11	−	2.26536e11i	1.30046	−	1.21584i
$658$	2.92873e11			1.56234
$659$		−	2.82641e11i		−	1.49863i	−0.662214	−	0.749315i	$-0.730383\pi$
$659$		−	2.82641e11i		−	1.49863i	0.662214	−	0.749315i	$-0.269617\pi$
$660$		0			0
$661$	−3.05260e10			−0.159906			−0.0799530	−	0.996799i	$-0.525477\pi$
$661$	−3.05260e10			−0.159906			−0.0799530	+	0.996799i	$0.525477\pi$
$662$			3.30243e11i			1.71950i
$663$	6.19932e10	−	2.44660e10i	0.320841	−	0.126622i
$664$	4.93504e11			2.53874
$665$		0			0
$666$	−1.44794e11	−	1.54871e11i	−0.735958	−	0.787177i
$667$	2.87713e11			1.45364
$668$			7.27486e11i			3.65358i
$669$	−1.11821e10	−	2.83338e10i	−0.0558239	−	0.141449i
$670$		0			0
$671$		−	1.58326e11i		−	0.781022i
$672$	4.34041e11	−	1.71297e11i	2.12840	−	0.839988i
$673$	−1.35686e11			−0.661417			−0.330708	−	0.943733i	$-0.607288\pi$
$673$	−1.35686e11			−0.661417			−0.330708	+	0.943733i	$0.607288\pi$
$674$		−	2.41104e10i		−	0.116833i
$675$		0			0
$676$	−1.05246e11			−0.503988
$677$		−	3.54740e11i		−	1.68871i	−0.535783	−	0.844356i	$-0.679984\pi$
$677$		−	3.54740e11i		−	1.68871i	0.535783	−	0.844356i	$-0.320016\pi$
$678$	8.09685e10	+	2.05162e11i	0.383175	+	0.970907i
$679$	−1.11438e11			−0.524268
$680$		0			0
$681$	3.45113e11	−	1.36201e11i	1.60462	−	0.633276i
$682$	4.94209e11			2.28440
$683$		−	3.26911e11i		−	1.50227i	−0.660151	−	0.751133i	$-0.729508\pi$
$683$		−	3.26911e11i		−	1.50227i	0.660151	−	0.751133i	$-0.270492\pi$
$684$	−3.75460e11	+	3.51030e11i	−1.71530	+	1.60369i
$685$		0			0
$686$			1.41293e11i			0.638007i
$687$	4.95472e10	+	1.25545e11i	0.222429	+	0.563603i
$688$	−6.13826e11			−2.73963
$689$			1.90413e11i			0.844927i
$690$		0			0
$691$	2.99967e11			1.31571			0.657856	−	0.753143i	$-0.271463\pi$
$691$	2.99967e11			1.31571			0.657856	+	0.753143i	$0.271463\pi$
$692$			1.24418e11i			0.542576i
$693$	2.85630e11	+	3.05509e11i	1.23843	+	1.32462i
$694$	4.25836e11			1.83571
$695$		0			0
$696$	−2.37640e11	−	6.02143e11i	−1.01270	−	2.56603i
$697$	−5.84820e8			−0.00247794
$698$			4.28567e10i			0.180550i
$699$	−3.20309e11	+	1.26412e11i	−1.34172	+	0.529517i
$700$		0			0
$701$		−	1.72997e11i		−	0.716416i	−0.933642	−	0.358208i	$-0.883388\pi$
$701$		−	1.72997e11i		−	0.716416i	0.933642	−	0.358208i	$-0.116612\pi$
$702$	2.11053e11	−	4.44697e11i	0.869047	−	1.83112i
$703$	1.40160e11			0.573854
$704$			2.91325e11i			1.18601i
$705$		0			0
$706$	−3.61073e11			−1.45337
$707$			1.57198e11i			0.629173i
$708$	−8.03930e10	+	3.17276e10i	−0.319952	+	0.126271i
$709$	2.67236e11			1.05757			0.528786	−	0.848755i	$-0.322648\pi$
$709$	2.67236e11			1.05757			0.528786	+	0.848755i	$0.322648\pi$
$710$		0			0
$711$	2.08720e11	−	1.95139e11i	0.816743	−	0.763600i
$712$	−1.97996e11			−0.770435
$713$			3.15138e11i			1.21939i
$714$	7.26235e10	+	1.84017e11i	0.279437	+	0.708051i
$715$		0			0
$716$			6.16537e11i			2.34589i
$717$	1.39863e11	−	5.51979e10i	0.529208	−	0.208855i
$718$	−3.20815e11			−1.20714
$719$		−	3.27548e11i		−	1.22563i	−0.790227	−	0.612815i	$-0.790037\pi$
$719$		−	3.27548e11i		−	1.22563i	0.790227	−	0.612815i	$-0.209963\pi$
$720$		0			0
$721$	−4.12935e11			−1.52806
$722$			1.88430e10i			0.0693427i
$723$	1.48701e11	+	3.76786e11i	0.544203	+	1.37893i
$724$	−5.43969e11			−1.97979
$725$		0			0
$726$	−4.25034e11	+	1.67743e11i	−1.52995	+	0.603805i
$727$	8.40255e10			0.300797			0.150398	−	0.988625i	$-0.451944\pi$
$727$	8.40255e10			0.300797			0.150398	+	0.988625i	$0.451944\pi$
$728$		−	1.04580e12i		−	3.72325i
$729$	1.78588e11	+	2.18799e11i	0.632327	+	0.774702i
$730$		0			0
$731$		−	1.04981e11i		−	0.367654i
$732$	−1.43220e11	−	3.62899e11i	−0.498839	−	1.26398i
$733$	−4.23327e10			−0.146643			−0.0733213	−	0.997308i	$-0.523360\pi$
$733$	−4.23327e10			−0.146643			−0.0733213	+	0.997308i	$0.523360\pi$
$734$			6.90673e11i			2.37951i
$735$		0			0
$736$	−6.89177e11			−2.34866
$737$			1.99188e11i			0.675138i
$738$	−3.15518e9	+	2.94989e9i	−0.0106365	+	0.00994443i
$739$	2.88845e11			0.968473			0.484236	−	0.874937i	$-0.339097\pi$
$739$	2.88845e11			0.968473			0.484236	+	0.874937i	$0.339097\pi$
$740$		0			0
$741$	1.19459e11	+	3.02691e11i	0.396229	+	1.00398i
$742$	−5.65210e11			−1.86464
$743$		−	3.03005e11i		−	0.994247i	−0.867680	−	0.497123i	$-0.834390\pi$
$743$		−	3.03005e11i		−	0.994247i	0.867680	−	0.497123i	$-0.165610\pi$
$744$	6.59539e11	−	2.60292e11i	2.15253	−	0.849510i
$745$		0			0
$746$			3.80297e11i			1.22791i
$747$	2.10273e11	+	2.24907e11i	0.675306	+	0.722305i
$748$	−3.23194e11			−1.03242
$749$			2.55289e11i			0.811157i
$750$		0			0
$751$	4.66239e11			1.46571			0.732856	−	0.680383i	$-0.238187\pi$
$751$	4.66239e11			1.46571			0.732856	+	0.680383i	$0.238187\pi$
$752$			4.80690e11i			1.50312i
$753$	−1.44362e10	+	5.69735e9i	−0.0449028	+	0.0177212i
$754$	−7.03892e11			−2.17781
$755$		0			0
$756$	9.31051e11	+	4.41876e11i	2.85027	+	1.35274i
$757$	−1.41830e11			−0.431901			−0.215951	−	0.976404i	$-0.569285\pi$
$757$	−1.41830e11			−0.431901			−0.215951	+	0.976404i	$0.569285\pi$
$758$			1.51083e11i			0.457655i
$759$	−2.26764e11	−	5.74585e11i	−0.683293	−	1.73136i
$760$		0			0
$761$			2.61107e11i			0.778538i	0.921124	+	0.389269i	$0.127272\pi$
$761$			2.61107e11i			0.778538i	−0.921124	+	0.389269i	$0.872728\pi$
$762$	−4.22279e10	+	1.66655e10i	−0.125251	+	0.0494310i
$763$	7.55420e11			2.22890
$764$		−	1.32365e12i		−	3.88507i
$765$		0			0
$766$	1.07949e12			3.13549
$767$			5.47170e10i			0.158103i
$768$	−1.44906e11	−	3.67170e11i	−0.416526	−	1.05541i
$769$	−6.57270e11			−1.87948			−0.939742	−	0.341884i	$-0.888935\pi$
$769$	−6.57270e11			−1.87948			−0.939742	+	0.341884i	$0.888935\pi$
$770$		0			0
$771$	−1.91438e11	+	7.55523e10i	−0.541764	+	0.213811i
$772$	−9.21835e11			−2.59528
$773$		−	2.64170e10i		−	0.0739887i	−0.999315	−	0.0369943i	$-0.988222\pi$
$773$		−	2.64170e10i		−	0.0739887i	0.999315	−	0.0369943i	$-0.0117784\pi$
$774$	−5.29532e11	−	5.66385e11i	−1.47546	−	1.57815i
$775$		0			0
$776$		−	3.70315e11i		−	1.02123i
$777$	−1.03165e11	−	2.61405e11i	−0.283041	−	0.717183i
$778$	9.31898e11			2.54361
$779$		−	2.85547e9i		−	0.00775404i
$780$		0			0
$781$	−1.09477e11			−0.294251
$782$		−	2.92185e11i		−	0.781323i
$783$	1.73163e11	−	3.64862e11i	0.460691	−	0.970693i
$784$	6.50663e11			1.72223
$785$		0			0
$786$	−4.28603e11	−	1.08602e12i	−1.12296	−	2.84542i
$787$	1.72594e11			0.449911			0.224956	−	0.974369i	$-0.427776\pi$
$787$	1.72594e11			0.449911			0.224956	+	0.974369i	$0.427776\pi$
$788$			2.24098e11i			0.581210i
$789$	−1.21747e11	+	4.80482e10i	−0.314159	+	0.123985i
$790$		0			0
$791$			2.92355e11i			0.746800i
$792$	−1.01523e12	+	9.49169e11i	−2.58025	+	2.41236i
$793$	−2.46996e11			−0.624594
$794$			1.48916e10i			0.0374679i
$795$		0			0
$796$	1.12831e12			2.81044
$797$		−	7.06159e9i		−	0.0175013i	−0.999962	−	0.00875063i	$-0.997215\pi$
$797$		−	7.06159e9i		−	0.0175013i	0.999962	−	0.00875063i	$-0.00278545\pi$
$798$	−8.98490e11	+	3.54595e11i	−2.21565	+	0.874422i
$799$	−8.22108e10			−0.201717
$800$		0			0
$801$	−8.43623e10	−	9.02336e10i	−0.204936	−	0.219199i
$802$	1.08229e12			2.61605
$803$			1.01838e12i			2.44934i
$804$	1.80183e11	+	4.56557e11i	0.431211	+	1.09262i
$805$		0			0
$806$		−	7.70987e11i		−	1.82687i
$807$	−5.55365e11	+	2.19179e11i	−1.30944	+	0.516778i
$808$	−5.22381e11			−1.22558
$809$			5.66925e11i			1.32352i	0.749714	+	0.661762i	$0.230191\pi$
$809$			5.66925e11i			1.32352i	−0.749714	+	0.661762i	$0.769809\pi$
$810$		0			0
$811$	−5.11294e11			−1.18192			−0.590959	−	0.806702i	$-0.701250\pi$
$811$	−5.11294e11			−1.18192			−0.590959	+	0.806702i	$0.701250\pi$
$812$		−	1.47372e12i		−	3.38993i
$813$	−1.15975e11	−	2.93862e11i	−0.265461	−	0.672638i
$814$	6.50914e11			1.48261
$815$		0			0
$816$	−3.02025e11	+	1.19196e11i	−0.681212	+	0.268845i
$817$	5.12584e11			1.15047
$818$		−	2.09626e11i		−	0.468201i
$819$	4.76607e11	−	4.45595e11i	1.05931	−	0.990387i
$820$		0			0
$821$			4.92725e10i			0.108451i	0.998529	+	0.0542253i	$0.0172689\pi$
$821$			4.92725e10i			0.108451i	−0.998529	+	0.0542253i	$0.982731\pi$
$822$	−1.17440e11	−	2.97575e11i	−0.257234	−	0.651792i
$823$	2.61102e11			0.569130			0.284565	−	0.958657i	$-0.408151\pi$
$823$	2.61102e11			0.569130			0.284565	+	0.958657i	$0.408151\pi$
$824$		−	1.37221e12i		−	2.97655i
$825$		0			0
$826$	−1.62419e11			−0.348912
$827$			5.67337e11i			1.21288i	0.795128	+	0.606442i	$0.207404\pi$
$827$			5.67337e11i			1.21288i	−0.795128	+	0.606442i	$0.792596\pi$
$828$	−1.03953e12	−	1.11187e12i	−2.21164	−	2.36556i
$829$	−6.10109e11			−1.29178			−0.645891	−	0.763430i	$-0.723514\pi$
$829$	−6.10109e11			−1.29178			−0.645891	+	0.763430i	$0.723514\pi$
$830$		0			0
$831$	2.43390e11	+	6.16714e11i	0.510387	+	1.29324i
$832$	4.54480e11			0.948466
$833$			1.11281e11i			0.231121i
$834$	−1.20902e10	+	4.77147e9i	−0.0249901	+	0.00986251i
$835$		0			0
$836$		−	1.57804e12i		−	3.23067i
$837$	3.99641e11	+	1.89670e11i	0.814270	+	0.386452i
$838$	7.70720e11			1.56286
$839$		−	1.77752e10i		−	0.0358729i	−0.999839	−	0.0179365i	$-0.994290\pi$
$839$		−	1.77752e10i		−	0.0358729i	0.999839	−	0.0179365i	$-0.00570966\pi$
$840$		0			0
$841$	−7.72785e10			−0.154481
$842$		−	1.71037e11i		−	0.340285i
$843$	5.38804e11	−	2.12642e11i	1.06689	−	0.421056i
$844$	5.03242e11			0.991761
$845$		0			0
$846$	−4.43539e11	+	4.14679e11i	−0.865865	+	0.809525i
$847$	−6.05672e11			−1.17680
$848$		−	9.27672e11i		−	1.79395i
$849$	2.20665e11	+	5.59131e11i	0.424720	+	1.07617i
$850$		0			0
$851$			4.15063e11i			0.791399i
$852$	−2.50931e11	+	9.90317e10i	−0.476208	+	0.187939i
$853$	−4.79452e11			−0.905626			−0.452813	−	0.891606i	$-0.649579\pi$
$853$	−4.79452e11			−0.905626			−0.452813	+	0.891606i	$0.649579\pi$
$854$		−	7.33168e11i		−	1.37839i
$855$		0			0
$856$	−8.48344e11			−1.58007
$857$			9.38022e10i			0.173896i	0.996213	+	0.0869480i	$0.0277114\pi$
$857$			9.38022e10i			0.173896i	−0.996213	+	0.0869480i	$0.972289\pi$
$858$	5.54779e11	+	1.40573e12i	1.02370	+	2.59389i
$859$	4.46094e11			0.819320			0.409660	−	0.912238i	$-0.365647\pi$
$859$	4.46094e11			0.819320			0.409660	+	0.912238i	$0.365647\pi$
$860$		0			0
$861$	−5.32561e9	+	2.10179e9i	−0.00969074	+	0.00382451i
$862$	1.31384e12			2.37965
$863$		−	8.85309e11i		−	1.59607i	−0.602612	−	0.798035i	$-0.705873\pi$
$863$		−	8.85309e11i		−	1.59607i	0.602612	−	0.798035i	$-0.294127\pi$
$864$	−4.14789e11	+	8.73977e11i	−0.744341	+	1.56836i
$865$		0			0
$866$		−	9.44837e11i		−	1.67991i
$867$	1.87040e11	+	4.73932e11i	0.331023	+	0.838763i
$868$	1.61420e12			2.84366
$869$			8.77239e11i			1.53829i
$870$		0			0
$871$	3.10742e11			0.539917
$872$			2.51031e12i			4.34172i
$873$	1.68766e11	−	1.57784e11i	0.290554	−	0.271648i
$874$	1.42664e12			2.44494
$875$		0			0
$876$	9.21219e11	+	2.33423e12i	1.56440	+	3.96394i
$877$	1.47075e11			0.248622			0.124311	−	0.992243i	$-0.460328\pi$
$877$	1.47075e11			0.248622			0.124311	+	0.992243i	$0.460328\pi$
$878$			7.58515e11i			1.27640i
$879$	−1.30789e10	+	5.16168e9i	−0.0219087	+	0.00864640i
$880$		0			0
$881$			1.00879e11i			0.167455i	0.996489	+	0.0837275i	$0.0266825\pi$
$881$			1.00879e11i			0.167455i	−0.996489	+	0.0837275i	$0.973317\pi$
$882$	5.61310e11	+	6.00375e11i	0.927532	+	0.992084i
$883$	−1.17637e11			−0.193509			−0.0967543	−	0.995308i	$-0.530846\pi$
$883$	−1.17637e11			−0.193509			−0.0967543	+	0.995308i	$0.530846\pi$
$884$			5.04196e11i			0.825639i
$885$		0			0
$886$	−2.08990e12			−3.39148
$887$		−	1.03512e12i		−	1.67223i	−0.548552	−	0.836117i	$-0.684821\pi$
$887$		−	1.03512e12i		−	1.67223i	0.548552	−	0.836117i	$-0.315179\pi$
$888$	8.68668e11	−	3.42826e11i	1.39702	−	0.551342i
$889$	−6.01747e10			−0.0963400
$890$		0			0
$891$	−8.65139e11	−	5.82510e10i	−1.37270	−	0.0924257i
$892$	2.30441e11			0.364000
$893$		−	4.01407e11i		−	0.631217i
$894$	1.35909e11	+	3.44373e11i	0.212764	+	0.539111i
$895$		0			0
$896$		−	1.25699e11i		−	0.195029i
$897$	−8.96378e11	+	3.53762e11i	−1.38459	+	0.546438i
$898$	−1.89196e12			−2.90942
$899$		−	6.32575e11i		−	0.968441i
$900$		0			0
$901$	1.58657e11			0.240746
$902$		−	1.32611e10i		−	0.0200333i
$903$	−3.77291e11	−	9.55997e11i	−0.567447	−	1.43782i
$904$	−9.71516e11			−1.45471
$905$		0			0
$906$	2.13268e12	−	8.41677e11i	3.16529	−	1.24920i
$907$	−5.01146e11			−0.740516			−0.370258	−	0.928929i	$-0.620731\pi$
$907$	−5.01146e11			−0.740516			−0.370258	+	0.928929i	$0.620731\pi$
$908$			2.80684e12i			4.12927i
$909$	−2.22577e11	−	2.38067e11i	−0.326005	−	0.348693i
$910$		0			0
$911$			4.27267e11i			0.620334i	0.950682	+	0.310167i	$0.100385\pi$
$911$			4.27267e11i			0.620334i	−0.950682	+	0.310167i	$0.899615\pi$
$912$	−5.81993e11	−	1.47468e12i	−0.841276	−	2.13167i
$913$	−9.45272e11			−1.36042
$914$			5.70498e11i			0.817466i
$915$		0			0
$916$	−1.02107e12			−1.45035
$917$		−	1.54757e12i		−	2.18863i
$918$	−3.70533e11	−	1.75855e11i	−0.521742	−	0.247619i
$919$	−1.00999e11			−0.141598			−0.0707990	−	0.997491i	$-0.522555\pi$
$919$	−1.00999e11			−0.141598			−0.0707990	+	0.997491i	$0.522555\pi$
$920$		0			0
$921$	−4.12928e11	−	1.04630e12i	−0.573899	−	1.45417i
$922$	1.66589e12			2.30528
$923$			1.70789e11i			0.235317i
$924$	−2.94313e12	+	1.16153e12i	−4.03759	+	1.59346i
$925$		0			0
$926$			8.06756e10i			0.109723i
$927$	6.25365e11	−	5.84674e11i	0.846866	−	0.791763i
$928$	1.38338e12			1.86530
$929$			7.10245e11i			0.953554i	0.879024	+	0.476777i	$0.158195\pi$
$929$			7.10245e11i			0.953554i	−0.879024	+	0.476777i	$0.841805\pi$
$930$		0			0
$931$	−5.43345e11			−0.723231
$932$		−	2.60510e12i		−	3.45272i
$933$	−7.24489e11	+	2.85925e11i	−0.956105	+	0.377333i
$934$	5.87398e11			0.771872
$935$		0			0
$936$	1.48075e12	+	1.58380e12i	1.92920	+	2.06346i
$937$	−9.65584e11			−1.25266			−0.626328	−	0.779560i	$-0.715443\pi$
$937$	−9.65584e11			−1.25266			−0.626328	+	0.779560i	$0.715443\pi$
$938$			9.22386e11i			1.19152i
$939$	−5.00728e11	−	1.26877e12i	−0.644079	−	1.63200i
$940$		0			0
$941$			2.54695e11i			0.324835i	0.986722	+	0.162417i	$0.0519291\pi$
$941$			2.54695e11i			0.324835i	−0.986722	+	0.162417i	$0.948071\pi$
$942$	5.39267e11	−	2.12825e11i	0.684858	−	0.270284i
$943$	8.45609e9			0.0106936
$944$		−	2.66576e11i		−	0.335686i
$945$		0			0
$946$	2.38049e12			2.97236
$947$			1.42329e12i			1.76967i	0.465905	+	0.884835i	$0.345729\pi$
$947$			1.42329e12i			1.76967i	−0.465905	+	0.884835i	$0.654271\pi$
$948$	7.93541e11	+	2.01071e12i	0.982508	+	2.48953i
$949$	1.58872e12			1.95877
$950$		0			0
$951$	1.47791e12	−	5.83266e11i	1.80686	−	0.713090i
$952$	−8.71387e11			−1.06087
$953$			9.36372e11i			1.13521i	0.823300	+	0.567606i	$0.192130\pi$
$953$			9.36372e11i			1.13521i	−0.823300	+	0.567606i	$0.807870\pi$
$954$	8.55975e11	−	8.00279e11i	1.03340	−	0.966158i
$955$		0			0
$956$			1.13752e12i			1.36184i
$957$	4.55182e11	+	1.15336e12i	0.542672	+	1.37505i
$958$	−9.34140e11			−1.10905
$959$		−	4.24043e11i		−	0.501344i
$960$		0			0
$961$	−1.60019e11			−0.187619
$962$		−	1.01545e12i		−	1.18566i
$963$	−3.61463e11	−	3.86620e11i	−0.420300	−	0.449551i
$964$	−3.06443e12			−3.54848
$965$		0			0
$966$	−1.05008e12	−	2.66075e12i	−1.20591	−	3.05560i
$967$	−1.17155e11			−0.133984			−0.0669921	−	0.997754i	$-0.521340\pi$
$967$	−1.17155e11			−0.133984			−0.0669921	+	0.997754i	$0.521340\pi$
$968$		−	2.01269e12i		−	2.29232i
$969$	2.52210e11	−	9.95364e10i	0.286067	−	0.112898i
$970$		0			0
$971$		−	3.28921e11i		−	0.370011i	−0.982737	−	0.185006i	$-0.940770\pi$
$971$		−	3.28921e11i		−	0.370011i	0.982737	−	0.185006i	$-0.0592303\pi$
$972$	−2.03567e12	+	6.49079e11i	−2.28057	+	0.727164i
$973$	−1.72284e10			−0.0192218
$974$			1.39004e12i			1.54452i
$975$		0			0
$976$	1.20334e12			1.32614
$977$		−	1.00676e12i		−	1.10496i	−0.833525	−	0.552482i	$-0.813681\pi$
$977$		−	1.00676e12i		−	1.10496i	0.833525	−	0.552482i	$-0.186319\pi$
$978$	2.09308e12	−	8.26049e11i	2.28787	−	0.902922i
$979$	3.79247e11			0.412849
$980$		0			0
$981$	−1.14404e12	+	1.06960e12i	−1.23528	+	1.15490i
$982$	−1.94857e12			−2.09542
$983$		−	1.03088e12i		−	1.10406i	−0.833823	−	0.552032i	$-0.813852\pi$
$983$		−	1.03088e12i		−	1.10406i	0.833823	−	0.552032i	$-0.186148\pi$
$984$	−6.98439e9	−	1.76974e10i	−0.00744986	−	0.0188768i
$985$		0			0
$986$			5.86501e11i			0.620527i
$987$	−7.48645e11	+	2.95458e11i	−0.788874	+	0.311334i
$988$	−2.46181e12			−2.58361
$989$			1.51795e12i			1.58661i
$990$		0			0
$991$	−1.00159e11			−0.103847			−0.0519236	−	0.998651i	$-0.516535\pi$
$991$	−1.00159e11			−0.103847			−0.0519236	+	0.998651i	$0.516535\pi$
$992$			1.51525e12i			1.56472i
$993$	−3.33158e11	−	8.44171e11i	−0.342652	−	0.868227i
$994$	−5.06959e11			−0.519311
$995$		0			0
$996$	−2.16665e12	+	8.55083e11i	−2.20167	+	0.868903i
$997$	−1.30987e12			−1.32570			−0.662852	−	0.748750i	$-0.730654\pi$
$997$	−1.30987e12			−1.32570			−0.662852	+	0.748750i	$0.730654\pi$
$998$		−	2.33225e12i		−	2.35100i
$999$	5.26361e11	+	2.49810e11i	0.528471	+	0.250812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.c.f.26.1	yes	10
3.2	odd	2	inner	75.9.c.f.26.10	yes	10
5.2	odd	4		75.9.d.d.74.19		20
5.3	odd	4		75.9.d.d.74.2		20
5.4	even	2		75.9.c.e.26.10	yes	10
15.2	even	4		75.9.d.d.74.1		20
15.8	even	4		75.9.d.d.74.20		20
15.14	odd	2		75.9.c.e.26.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.9.c.e.26.1	✓	10	15.14	odd	2
75.9.c.e.26.10	yes	10	5.4	even	2
75.9.c.f.26.1	yes	10	1.1	even	1	trivial
75.9.c.f.26.10	yes	10	3.2	odd	2	inner
75.9.d.d.74.1		20	15.2	even	4
75.9.d.d.74.2		20	5.3	odd	4
75.9.d.d.74.19		20	5.2	odd	4
75.9.d.d.74.20		20	15.8	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-29.4751i q^{2} +(29.7353 + 75.3446i) q^{3} -612.784 q^{4} +(2220.79 - 876.451i) q^{6} +3164.62 q^{7} +10516.3i q^{8} +(-4792.63 + 4480.79i) q^{9} +O(q^{10})\)	\(q-29.4751i q^{2} +(29.7353 + 75.3446i) q^{3} -612.784 q^{4} +(2220.79 - 876.451i) q^{6} +3164.62 q^{7} +10516.3i q^{8} +(-4792.63 + 4480.79i) q^{9} -20143.2i q^{11} +(-18221.3 - 46170.0i) q^{12} -31424.2 q^{13} -93277.7i q^{14} +153096. q^{16} +26183.5i q^{17} +(132072. + 141263. i) q^{18} -127845. q^{19} +(94100.9 + 238437. i) q^{21} -593723. q^{22} -378595. i q^{23} +(-792344. + 312704. i) q^{24} +926234. i q^{26} +(-480113. - 227861. i) q^{27} -1.93923e6 q^{28} +759951. i q^{29} -832390. q^{31} -1.82036e6i q^{32} +(1.51768e6 - 598962. i) q^{33} +771762. q^{34} +(2.93685e6 - 2.74575e6i) q^{36} -1.09633e6 q^{37} +3.76824e6i q^{38} +(-934408. - 2.36765e6i) q^{39} +22335.5i q^{41} +(7.02798e6 - 2.77364e6i) q^{42} -4.00943e6 q^{43} +1.23434e7i q^{44} -1.11591e7 q^{46} +3.13980e6i q^{47} +(4.55234e6 + 1.15349e7i) q^{48} +4.25004e6 q^{49} +(-1.97278e6 + 778572. i) q^{51} +1.92563e7 q^{52} -6.05943e6i q^{53} +(-6.71625e6 + 1.41514e7i) q^{54} +3.32800e7i q^{56} +(-3.80150e6 - 9.63242e6i) q^{57} +2.23997e7 q^{58} -1.74124e6i q^{59} +7.86006e6 q^{61} +2.45348e7i q^{62} +(-1.51669e7 + 1.41800e7i) q^{63} -1.44627e7 q^{64} +(-1.76545e7 - 4.47338e7i) q^{66} -9.88860e6 q^{67} -1.60448e7i q^{68} +(2.85251e7 - 1.12576e7i) q^{69} -5.43494e6i q^{71} +(-4.71211e7 - 5.04006e7i) q^{72} -5.05573e7 q^{73} +3.23144e7i q^{74} +7.83412e7 q^{76} -6.37455e7i q^{77} +(-6.97867e7 + 2.75418e7i) q^{78} -4.35502e7 q^{79} +(2.89185e6 - 4.29495e7i) q^{81} +658341. q^{82} -4.69277e7i q^{83} +(-5.76636e7 - 1.46111e8i) q^{84} +1.18178e8i q^{86} +(-5.72582e7 + 2.25973e7i) q^{87} +2.11831e8 q^{88} +1.88276e7i q^{89} -9.94458e7 q^{91} +2.31997e8i q^{92} +(-2.47513e7 - 6.27161e7i) q^{93} +9.25460e7 q^{94} +(1.37154e8 - 5.41288e7i) q^{96} -3.52136e7 q^{97} -1.25271e8i q^{98} +(9.02572e7 + 9.65387e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 25 q^{3} - 1554 q^{4} + 2257 q^{6} - 1960 q^{7} - 11207 q^{9}+O(q^{10}) \) 10 * q + 25 * q^3 - 1554 * q^4 + 2257 * q^6 - 1960 * q^7 - 11207 * q^9	\( 10 q + 25 q^{3} - 1554 q^{4} + 2257 q^{6} - 1960 q^{7} - 11207 q^{9} + 5915 q^{12} + 16920 q^{13} + 44634 q^{16} + 224875 q^{18} - 143934 q^{19} + 673428 q^{21} - 818990 q^{22} - 1016859 q^{24} + 260830 q^{27} - 3810100 q^{28} - 3014060 q^{31} + 4677515 q^{33} + 4977146 q^{34} + 4500527 q^{36} - 3016760 q^{37} - 7513282 q^{39} + 4001760 q^{42} - 11747340 q^{43} - 13938636 q^{46} + 14748755 q^{48} + 8953546 q^{49} + 6209287 q^{51} + 38918320 q^{52} - 8886272 q^{54} - 14759525 q^{57} + 48407900 q^{58} + 1520220 q^{61} - 74748240 q^{63} - 4536998 q^{64} + 10465295 q^{66} + 16269290 q^{67} + 11394978 q^{69} - 172231185 q^{72} + 52090170 q^{73} - 29529046 q^{76} - 198205810 q^{78} + 8549896 q^{79} + 22612945 q^{81} + 295714190 q^{82} - 136883292 q^{84} - 318901610 q^{87} + 310673250 q^{88} - 107224264 q^{91} - 79679130 q^{93} + 356118596 q^{94} + 525424001 q^{96} + 402167800 q^{97} - 382421335 q^{99}+O(q^{100}) \) 10 * q + 25 * q^3 - 1554 * q^4 + 2257 * q^6 - 1960 * q^7 - 11207 * q^9 + 5915 * q^12 + 16920 * q^13 + 44634 * q^16 + 224875 * q^18 - 143934 * q^19 + 673428 * q^21 - 818990 * q^22 - 1016859 * q^24 + 260830 * q^27 - 3810100 * q^28 - 3014060 * q^31 + 4677515 * q^33 + 4977146 * q^34 + 4500527 * q^36 - 3016760 * q^37 - 7513282 * q^39 + 4001760 * q^42 - 11747340 * q^43 - 13938636 * q^46 + 14748755 * q^48 + 8953546 * q^49 + 6209287 * q^51 + 38918320 * q^52 - 8886272 * q^54 - 14759525 * q^57 + 48407900 * q^58 + 1520220 * q^61 - 74748240 * q^63 - 4536998 * q^64 + 10465295 * q^66 + 16269290 * q^67 + 11394978 * q^69 - 172231185 * q^72 + 52090170 * q^73 - 29529046 * q^76 - 198205810 * q^78 + 8549896 * q^79 + 22612945 * q^81 + 295714190 * q^82 - 136883292 * q^84 - 318901610 * q^87 + 310673250 * q^88 - 107224264 * q^91 - 79679130 * q^93 + 356118596 * q^94 + 525424001 * q^96 + 402167800 * q^97 - 382421335 * q^99

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