LMFDB - Embedded newform 75.9.d.d.74.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(74,75)]

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, 1]))

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

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

chi := DirichletCharacter("75.74");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.d (of order $2$, degree $1$, not 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:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 3278 x^{18} + 4245491 x^{16} + 2854629536 x^{14} + 1117319469691 x^{12} + 266849787342054 x^{10} + \cdots + 89\!\cdots\!00 $ x^20 + 3278x^18 + 4245491x^16 + 2854629536x^14 + 1117319469691x^12 + 266849787342054x^10 + 38935163332201981x^8 + 3308855301815965532x^6 + 143709036159536320436x^4 + 2262672788809149782000*x^2 + 8995759125454185640000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{22}\cdot 5^{26} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			74.2
Root			$-2.43232i$ of defining polynomial
Character	$\chi$	$=$	75.74
Dual form			75.9.d.d.74.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-29.4751 q^{2} +(-75.3446 + 29.7353i) q^{3} +612.784 q^{4} +(2220.79 - 876.451i) q^{6} -3164.62i q^{7} -10516.3 q^{8} +(4792.63 - 4480.79i) q^{9} +O(q^{10})$	\(q-29.4751 q^{2} +(-75.3446 + 29.7353i) q^{3} +612.784 q^{4} +(2220.79 - 876.451i) q^{6} -3164.62i q^{7} -10516.3 q^{8} +(4792.63 - 4480.79i) q^{9} -20143.2i q^{11} +(-46170.0 + 18221.3i) q^{12} -31424.2i q^{13} +93277.7i q^{14} +153096. q^{16} +26183.5 q^{17} +(-141263. + 132072. i) q^{18} +127845. q^{19} +(94100.9 + 238437. i) q^{21} +593723. i q^{22} +378595. q^{23} +(792344. - 312704. i) q^{24} +926234. i q^{26} +(-227861. + 480113. i) q^{27} -1.93923e6i q^{28} -759951. i q^{29} -832390. q^{31} -1.82036e6 q^{32} +(598962. + 1.51768e6i) q^{33} -771762. q^{34} +(2.93685e6 - 2.74575e6i) q^{36} +1.09633e6i q^{37} -3.76824e6 q^{38} +(934408. + 2.36765e6i) q^{39} +22335.5i q^{41} +(-2.77364e6 - 7.02798e6i) q^{42} -4.00943e6i q^{43} -1.23434e7i q^{44} -1.11591e7 q^{46} +3.13980e6 q^{47} +(-1.15349e7 + 4.55234e6i) q^{48} -4.25004e6 q^{49} +(-1.97278e6 + 778572. i) q^{51} -1.92563e7i q^{52} +6.05943e6 q^{53} +(6.71625e6 - 1.41514e7i) q^{54} +3.32800e7i q^{56} +(-9.63242e6 + 3.80150e6i) q^{57} +2.23997e7i q^{58} +1.74124e6i q^{59} +7.86006e6 q^{61} +2.45348e7 q^{62} +(-1.41800e7 - 1.51669e7i) q^{63} +1.44627e7 q^{64} +(-1.76545e7 - 4.47338e7i) q^{66} +9.88860e6i q^{67} +1.60448e7 q^{68} +(-2.85251e7 + 1.12576e7i) q^{69} -5.43494e6i q^{71} +(-5.04006e7 + 4.71211e7i) q^{72} -5.05573e7i q^{73} -3.23144e7i q^{74} +7.83412e7 q^{76} -6.37455e7 q^{77} +(-2.75418e7 - 6.97867e7i) q^{78} +4.35502e7 q^{79} +(2.89185e6 - 4.29495e7i) q^{81} -658341. i q^{82} +4.69277e7 q^{83} +(5.76636e7 + 1.46111e8i) q^{84} +1.18178e8i q^{86} +(2.25973e7 + 5.72582e7i) q^{87} +2.11831e8i q^{88} -1.88276e7i q^{89} -9.94458e7 q^{91} +2.31997e8 q^{92} +(6.27161e7 - 2.47513e7i) q^{93} -9.25460e7 q^{94} +(1.37154e8 - 5.41288e7i) q^{96} +3.52136e7i q^{97} +1.25271e8 q^{98} +(-9.02572e7 - 9.65387e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 3108 q^{4} + 4514 q^{6} + 22414 q^{9}+O(q^{10}) $ 20 * q + 3108 * q^4 + 4514 * q^6 + 22414 * q^9	$ 20 q + 3108 q^{4} + 4514 q^{6} + 22414 q^{9} + 89268 q^{16} + 287868 q^{19} + 1346856 q^{21} + 2033718 q^{24} - 6028120 q^{31} - 9954292 q^{34} + 9001054 q^{36} + 15026564 q^{39} - 27877272 q^{46} - 17907092 q^{49} + 12418574 q^{51} + 17772544 q^{54} + 3040440 q^{61} + 9073996 q^{64} + 20930590 q^{66} - 22789956 q^{69} - 59058092 q^{76} - 17099792 q^{79} + 45225890 q^{81} + 273766584 q^{84} - 214448528 q^{91} - 712237192 q^{94} + 1050848002 q^{96} + 764842670 q^{99}+O(q^{100}) $ 20 * q + 3108 * q^4 + 4514 * q^6 + 22414 * q^9 + 89268 * q^16 + 287868 * q^19 + 1346856 * q^21 + 2033718 * q^24 - 6028120 * q^31 - 9954292 * q^34 + 9001054 * q^36 + 15026564 * q^39 - 27877272 * q^46 - 17907092 * q^49 + 12418574 * q^51 + 17772544 * q^54 + 3040440 * q^61 + 9073996 * q^64 + 20930590 * q^66 - 22789956 * q^69 - 59058092 * q^76 - 17099792 * q^79 + 45225890 * q^81 + 273766584 * q^84 - 214448528 * q^91 - 712237192 * q^94 + 1050848002 * q^96 + 764842670 * 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 $

$2$	−29.4751			−1.84220			−0.921098	−	0.389330i	$-0.872707\pi$
$2$	−29.4751			−1.84220			−0.921098	+	0.389330i	$0.872707\pi$
$3$	−75.3446	+	29.7353i	−0.930181	+	0.367102i
$3$	−75.3446	+	29.7353i	−0.930181	+	0.367102i
$4$	612.784			2.39369
$5$		0			0
$5$		0			0
$6$	2220.79	−	876.451i	1.71358	−	0.676274i
$7$		−	3164.62i		−	1.31804i	−0.752124	−	0.659022i	$-0.770970\pi$
$7$		−	3164.62i		−	1.31804i	0.752124	−	0.659022i	$-0.229030\pi$
$8$	−10516.3			−2.56745
$9$	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	$-0.241468\pi$
$12$	−46170.0	+	18221.3i	−2.22656	+	0.878728i
$13$		−	31424.2i		−	1.10025i	−0.835083	−	0.550125i	$-0.814580\pi$
$13$		−	31424.2i		−	1.10025i	0.835083	−	0.550125i	$-0.185420\pi$
$14$			93277.7i			2.42810i
$15$		0			0
$16$	153096.			2.33606
$17$	26183.5			0.313496			0.156748	−	0.987639i	$-0.449899\pi$
$17$	26183.5			0.313496			0.156748	+	0.987639i	$0.449899\pi$
$18$	−141263.	+	132072.i	−1.34567	+	1.25811i
$19$	127845.			0.980999			0.490499	−	0.871442i	$-0.336814\pi$
$19$	127845.			0.980999			0.490499	+	0.871442i	$0.336814\pi$
$20$		0			0
$21$	94100.9	+	238437.i	0.483857	+	1.22602i
$22$			593723.i			2.53450i
$23$	378595.			1.35289			0.676446	−	0.736492i	$-0.263519\pi$
$23$	378595.			1.35289			0.676446	+	0.736492i	$0.263519\pi$
$24$	792344.	−	312704.i	2.38819	−	0.942515i
$25$		0			0
$26$			926234.i			2.02688i
$27$	−227861.	+	480113.i	−0.428762	+	0.903418i
$28$		−	1.93923e6i		−	3.15499i
$29$		−	759951.i		−	1.07447i	−0.843433	−	0.537234i	$-0.819469\pi$
$29$		−	759951.i		−	1.07447i	0.843433	−	0.537234i	$-0.180531\pi$
$30$		0			0
$31$	−832390.			−0.901322			−0.450661	−	0.892695i	$-0.648812\pi$
$31$	−832390.			−0.901322			−0.450661	+	0.892695i	$0.648812\pi$
$32$	−1.82036e6			−1.73603
$33$	598962.	+	1.51768e6i	0.505061	+	1.27975i
$34$	−771762.			−0.577521
$35$		0			0
$36$	2.93685e6	−	2.74575e6i	1.74852	−	1.63475i
$37$			1.09633e6i			0.584969i	0.956270	+	0.292484i	$0.0944820\pi$
$37$			1.09633e6i			0.584969i	−0.956270	+	0.292484i	$0.905518\pi$
$38$	−3.76824e6			−1.80719
$39$	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	$0.998742\pi$
$42$	−2.77364e6	−	7.02798e6i	−0.891359	−	2.25857i
$43$		−	4.00943e6i		−	1.17276i	−0.810037	−	0.586379i	$-0.800553\pi$
$43$		−	4.00943e6i		−	1.17276i	0.810037	−	0.586379i	$-0.199447\pi$
$44$		−	1.23434e7i		−	3.29325i
$45$		0			0
$46$	−1.11591e7			−2.49229
$47$	3.13980e6			0.643443			0.321722	−	0.946834i	$-0.395738\pi$
$47$	3.13980e6			0.643443			0.321722	+	0.946834i	$0.395738\pi$
$48$	−1.15349e7	+	4.55234e6i	−2.17295	+	0.857571i
$49$	−4.25004e6			−0.737240
$50$		0			0
$51$	−1.97278e6	+	778572.i	−0.291608	+	0.115085i
$52$		−	1.92563e7i		−	2.63365i
$53$	6.05943e6			0.767941			0.383971	−	0.923345i	$-0.374556\pi$
$53$	6.05943e6			0.767941			0.383971	+	0.923345i	$0.374556\pi$
$54$	6.71625e6	−	1.41514e7i	0.789863	−	1.66427i
$55$		0			0
$56$			3.32800e7i			3.38401i
$57$	−9.63242e6	+	3.80150e6i	−0.912506	+	0.360127i
$58$			2.23997e7i			1.97938i
$59$			1.74124e6i			0.143698i	0.997416	+	0.0718489i	$0.0228899\pi$
$59$			1.74124e6i			0.143698i	−0.997416	+	0.0718489i	$0.977110\pi$
$60$		0			0
$61$	7.86006e6			0.567684			0.283842	−	0.958871i	$-0.408391\pi$
$61$	7.86006e6			0.567684			0.283842	+	0.958871i	$0.408391\pi$
$62$	2.45348e7			1.66041
$63$	−1.41800e7	−	1.51669e7i	−0.900148	−	0.962794i
$64$	1.44627e7			0.862046
$65$		0			0
$66$	−1.76545e7	−	4.47338e7i	−0.930422	−	2.35755i
$67$			9.88860e6i			0.490722i	0.969432	+	0.245361i	$0.0789065\pi$
$67$			9.88860e6i			0.490722i	−0.969432	+	0.245361i	$0.921094\pi$
$68$	1.60448e7			0.750411
$69$	−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	$-0.0341046\pi$
$72$	−5.04006e7	+	4.71211e7i	−1.87545	+	1.75342i
$73$		−	5.05573e7i		−	1.78030i	−0.455672	−	0.890148i	$-0.650601\pi$
$73$		−	5.05573e7i		−	1.78030i	0.455672	−	0.890148i	$-0.349399\pi$
$74$		−	3.23144e7i		−	1.07763i
$75$		0			0
$76$	7.83412e7			2.34821
$77$	−6.37455e7			−1.81337
$78$	−2.75418e7	−	6.97867e7i	−0.744070	−	1.88536i
$79$	4.35502e7			1.11810			0.559051	−	0.829133i	$-0.311166\pi$
$79$	4.35502e7			1.11810			0.559051	+	0.829133i	$0.311166\pi$
$80$		0			0
$81$	2.89185e6	−	4.29495e7i	0.0671793	−	0.997741i
$82$		−	658341.i		−	0.0145611i
$83$	4.69277e7			0.988819			0.494409	−	0.869229i	$-0.335384\pi$
$83$	4.69277e7			0.988819			0.494409	+	0.869229i	$0.335384\pi$
$84$	5.76636e7	+	1.46111e8i	1.15820	+	2.93471i
$85$		0			0
$86$			1.18178e8i			2.16045i
$87$	2.25973e7	+	5.72582e7i	0.394439	+	0.999449i
$88$			2.11831e8i			3.53231i
$89$		−	1.88276e7i		−	0.300078i	−0.988680	−	0.150039i	$-0.952060\pi$
$89$		−	1.88276e7i		−	0.300078i	0.988680	−	0.150039i	$-0.0479399\pi$
$90$		0			0
$91$	−9.94458e7			−1.45018
$92$	2.31997e8			3.23840
$93$	6.27161e7	−	2.47513e7i	0.838392	−	0.330877i
$94$	−9.25460e7			−1.18535
$95$		0			0
$96$	1.37154e8	−	5.41288e7i	1.61482	−	0.637299i
$97$			3.52136e7i			0.397762i	0.980024	+	0.198881i	$0.0637307\pi$
$97$			3.52136e7i			0.397762i	−0.980024	+	0.198881i	$0.936269\pi$
$98$	1.25271e8			1.35814
$99$	−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	$0.923286\pi$
$102$	5.81481e7	−	2.29485e7i	0.537199	−	0.212009i
$103$		−	1.30485e8i		−	1.15934i	−0.814851	−	0.579670i	$-0.803181\pi$
$103$		−	1.30485e8i		−	1.15934i	0.814851	−	0.579670i	$-0.196819\pi$
$104$			3.30466e8i			2.82483i
$105$		0			0
$106$	−1.78602e8			−1.41470
$107$	8.06696e7			0.615425			0.307712	−	0.951479i	$-0.400437\pi$
$107$	8.06696e7			0.615425			0.307712	+	0.951479i	$0.400437\pi$
$108$	−1.39630e8	+	2.94206e8i	−1.02632	+	2.16250i
$109$	−2.38708e8			−1.69107			−0.845533	−	0.533923i	$-0.820717\pi$
$109$	−2.38708e8			−1.69107			−0.845533	+	0.533923i	$0.820717\pi$
$110$		0			0
$111$	−3.25995e7	−	8.26023e7i	−0.214743	−	0.544127i
$112$		−	4.84490e8i		−	3.07902i
$113$	−9.23822e7			−0.566597			−0.283299	−	0.959032i	$-0.591429\pi$
$113$	−9.23822e7			−0.566597			−0.283299	+	0.959032i	$0.591429\pi$
$114$	2.83917e8	−	1.12050e8i	1.68102	−	0.663424i
$115$		0			0
$116$		−	4.65686e8i		−	2.57194i
$117$	−1.40805e8	−	1.50605e8i	−0.751407	−	0.803702i
$118$		−	5.13232e7i		−	0.264720i
$119$		−	8.28608e7i		−	0.413201i
$120$		0			0
$121$	−1.91388e8			−0.892841
$122$	−2.31676e8			−1.04578
$123$	−664151.	−	1.68286e6i	−0.00290166	−	0.00735236i
$124$	−5.10075e8			−2.15748
$125$		0			0
$126$	4.17958e8	+	4.47046e8i	1.65825	+	1.77366i
$127$			1.90148e7i			0.0730931i	0.999332	+	0.0365466i	$0.0116357\pi$
$127$			1.90148e7i			0.0730931i	−0.999332	+	0.0365466i	$0.988364\pi$
$128$	3.97199e7			0.147968
$129$	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	$-0.311806\pi$
$132$	3.67035e8	+	9.30010e8i	1.20896	+	3.06332i
$133$		−	4.04580e8i		−	1.29300i
$134$		−	2.91468e8i		−	0.904007i
$135$		0			0
$136$	−2.75352e8			−0.804884
$137$	−1.33995e8			−0.380370			−0.190185	−	0.981748i	$-0.560909\pi$
$137$	−1.33995e8			−0.380370			−0.190185	+	0.981748i	$0.560909\pi$
$138$	8.40780e8	−	3.31820e8i	2.31828	−	0.914926i
$139$	5.44407e6			0.0145836			0.00729180	−	0.999973i	$-0.497679\pi$
$139$	5.44407e6			0.0145836			0.00729180	+	0.999973i	$0.497679\pi$
$140$		0			0
$141$	−2.36567e8	+	9.33627e7i	−0.598519	+	0.236209i
$142$			1.60196e8i			0.394001i
$143$	−6.32984e8			−1.51373
$144$	7.33731e8	−	6.85989e8i	1.70642	−	1.59539i
$145$		0			0
$146$			1.49018e9i			3.27965i
$147$	3.20218e8	−	1.26376e8i	0.685766	−	0.270642i
$148$			6.71811e8i			1.40023i
$149$		−	1.55067e8i		−	0.314612i	−0.987550	−	0.157306i	$-0.949719\pi$
$149$		−	1.55067e8i		−	0.314612i	0.987550	−	0.157306i	$-0.0502809\pi$
$150$		0			0
$151$	9.60323e8			1.84718			0.923591	−	0.383379i	$-0.125240\pi$
$151$	9.60323e8			1.84718			0.923591	+	0.383379i	$0.125240\pi$
$152$	−1.34445e9			−2.51866
$153$	1.25488e8	−	1.17323e8i	0.229000	−	0.214099i
$154$	1.87891e9			3.34059
$155$		0			0
$156$	5.72590e8	+	1.45086e9i	0.966820	+	2.44977i
$157$		−	2.42826e8i		−	0.399666i	−0.979830	−	0.199833i	$-0.935960\pi$
$157$		−	2.42826e8i		−	0.399666i	0.979830	−	0.199833i	$-0.0640400\pi$
$158$	−1.28365e9			−2.05976
$159$	−4.56545e8	+	1.80179e8i	−0.714324	+	0.281913i
$160$		0			0
$161$		−	1.19811e9i		−	1.78317i
$162$	−8.52377e7	+	1.26594e9i	−0.123757	+	1.83803i
$163$			9.42493e8i			1.33514i	0.744546	+	0.667571i	$0.232666\pi$
$163$			9.42493e8i			1.33514i	−0.744546	+	0.667571i	$0.767334\pi$
$164$			1.36868e7i			0.0189203i
$165$		0			0
$166$	−1.38320e9			−1.82160
$167$	−1.18718e9			−1.52634			−0.763170	−	0.646197i	$-0.776358\pi$
$167$	−1.18718e9			−1.52634			−0.763170	+	0.646197i	$0.776358\pi$
$168$	−9.89590e8	−	2.50747e9i	−1.24228	−	3.14774i
$169$	−1.71751e8			−0.210549
$170$		0			0
$171$	6.12712e8	−	5.72845e8i	0.716592	−	0.669966i
$172$		−	2.45691e9i		−	2.80722i
$173$	2.03038e8			0.226669			0.113335	−	0.993557i	$-0.463847\pi$
$173$	2.03038e8			0.226669			0.113335	+	0.993557i	$0.463847\pi$
$174$	−6.66060e8	−	1.68769e9i	−0.726635	−	1.84118i
$175$		0			0
$176$		−	3.08383e9i		−	3.21396i
$177$	−5.17762e7	−	1.31193e8i	−0.0527517	−	0.133665i
$178$			5.54946e8i			0.552803i
$179$			1.00612e9i			0.980030i	0.871714	+	0.490015i	$0.163009\pi$
$179$			1.00612e9i			0.980030i	−0.871714	+	0.490015i	$0.836991\pi$
$180$		0			0
$181$	8.87701e8			0.827089			0.413545	−	0.910484i	$-0.364291\pi$
$181$	8.87701e8			0.827089			0.413545	+	0.910484i	$0.364291\pi$
$182$	2.93118e9			2.67151
$183$	−5.92213e8	+	2.33721e8i	−0.528048	+	0.208398i
$184$	−3.98140e9			−3.47348
$185$		0			0
$186$	−1.84857e9	+	7.29549e8i	−1.54448	+	0.609541i
$187$		−	5.27418e8i		−	0.431309i
$188$	1.92402e9			1.54020
$189$	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	$0.698639\pi$
$192$	−1.08969e9	+	4.30053e8i	−0.801859	+	0.316459i
$193$			1.50434e9i			1.08422i	0.840309	+	0.542108i	$0.182374\pi$
$193$			1.50434e9i			1.08422i	−0.840309	+	0.542108i	$0.817626\pi$
$194$		−	1.03793e9i		−	0.732755i
$195$		0			0
$196$	−2.60436e9			−1.76472
$197$	−3.65705e8			−0.242809			−0.121405	−	0.992603i	$-0.538740\pi$
$197$	−3.65705e8			−0.242809			−0.121405	+	0.992603i	$0.538740\pi$
$198$	2.66034e9	+	2.84549e9i	1.73092	+	1.85139i
$199$	1.84128e9			1.17411			0.587053	−	0.809549i	$-0.300288\pi$
$199$	1.84128e9			1.17411			0.587053	+	0.809549i	$0.300288\pi$
$200$		0			0
$201$	−2.94040e8	−	7.45053e8i	−0.180145	−	0.456460i
$202$		−	1.46414e9i		−	0.879379i
$203$	−2.40496e9			−1.41620
$204$	−1.20889e9	+	4.77097e8i	−0.698018	+	0.275477i
$205$		0			0
$206$			3.84606e9i			2.13573i
$207$	1.81446e9	−	1.69640e9i	0.988250	−	0.923947i
$208$		−	4.81092e9i		−	2.57024i
$209$		−	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	$0.566423\pi$
$212$	3.71312e9			1.83821
$213$	1.61609e8	+	4.09494e8i	0.0785142	+	0.198943i
$214$	−2.37775e9			−1.13373
$215$		0			0
$216$	2.39625e9	−	5.04900e9i	1.10082	−	2.31948i
$217$			2.63420e9i			1.18798i
$218$	7.03595e9			3.11528
$219$	1.50333e9	+	3.80922e9i	0.653550	+	1.65600i
$220$		0			0
$221$		−	8.22795e8i		−	0.344923i
$222$	9.60876e8	+	2.43471e9i	0.395599	+	1.00239i
$223$		−	3.76056e8i		−	0.152066i	−0.997105	−	0.0760332i	$-0.975775\pi$
$223$		−	3.76056e8i		−	0.152066i	0.997105	−	0.0760332i	$-0.0242255\pi$
$224$			5.76074e9i			2.28816i
$225$		0			0
$226$	2.72298e9			1.04378
$227$	−4.58046e9			−1.72507			−0.862533	−	0.506000i	$-0.831124\pi$
$227$	−4.58046e9			−1.72507			−0.862533	+	0.506000i	$0.831124\pi$
$228$	−5.90259e9	+	2.32950e9i	−2.18426	+	0.862031i
$229$	−1.66628e9			−0.605906			−0.302953	−	0.953005i	$-0.597973\pi$
$229$	−1.66628e9			−0.605906			−0.302953	+	0.953005i	$0.597973\pi$
$230$		0			0
$231$	4.80289e9	−	1.89549e9i	1.68676	−	0.665693i
$232$			7.99184e9i			2.75864i
$233$	−4.25125e9			−1.44243			−0.721213	−	0.692714i	$-0.756415\pi$
$233$	−4.25125e9			−1.44243			−0.721213	+	0.692714i	$0.756415\pi$
$234$	4.15025e9	+	4.43909e9i	1.38424	+	1.48058i
$235$		0			0
$236$			1.06700e9i			0.343968i
$237$	−3.28127e9	+	1.29498e9i	−1.04004	+	0.410458i
$238$			2.44233e9i			0.761198i
$239$			1.85631e9i			0.568930i	0.958686	+	0.284465i	$0.0918159\pi$
$239$			1.85631e9i			0.568930i	−0.958686	+	0.284465i	$0.908184\pi$
$240$		0			0
$241$	5.00083e9			1.48243			0.741215	−	0.671268i	$-0.234250\pi$
$241$	5.00083e9			1.48243			0.741215	+	0.671268i	$0.234250\pi$
$242$	5.64120e9			1.64479
$243$	1.05923e9	+	3.32200e9i	0.303784	+	0.952741i
$244$	4.81652e9			1.35886
$245$		0			0
$246$	1.95760e7	+	4.96025e7i	0.00534543	+	0.0135445i
$247$		−	4.01742e9i		−	1.07934i
$248$	8.75363e9			2.31410
$249$	−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	$0.992316\pi$
$252$	−8.68928e9	−	9.29401e9i	−2.15467	−	2.30463i
$253$		−	7.62609e9i		−	1.86132i
$254$		−	5.60464e8i		−	0.134652i
$255$		0			0
$256$	−4.87321e9			−1.13463
$257$	2.54083e9			0.582429			0.291215	−	0.956658i	$-0.405941\pi$
$257$	2.54083e9			0.582429			0.291215	+	0.956658i	$0.405941\pi$
$258$	−3.51407e9	−	8.90411e9i	−0.793106	−	2.00961i
$259$	3.46946e9			0.771015
$260$		0			0
$261$	−3.40518e9	−	3.64216e9i	−0.733800	−	0.784869i
$262$			1.44140e10i			3.05899i
$263$	−1.61586e9			−0.337740			−0.168870	−	0.985638i	$-0.554012\pi$
$263$	−1.61586e9			−0.337740			−0.168870	+	0.985638i	$0.554012\pi$
$264$	−6.29885e9	−	1.59603e10i	−1.29672	−	3.28569i
$265$		0			0
$266$			1.19251e10i			2.38196i
$267$	5.59843e8	+	1.41856e9i	0.110159	+	0.279127i
$268$			6.05958e9i			1.17464i
$269$		−	7.37100e9i		−	1.40772i	−0.710337	−	0.703861i	$-0.751458\pi$
$269$		−	7.37100e9i		−	1.40772i	0.710337	−	0.703861i	$-0.248542\pi$
$270$		0			0
$271$	−3.90024e9			−0.723126			−0.361563	−	0.932348i	$-0.617757\pi$
$271$	−3.90024e9			−0.723126			−0.361563	+	0.932348i	$0.617757\pi$
$272$	4.00858e9			0.732343
$273$	7.49271e9	−	2.95705e9i	1.34893	−	0.532363i
$274$	3.94952e9			0.700716
$275$		0			0
$276$	−1.74797e10	+	6.89848e9i	−3.01230	+	1.18882i
$277$		−	8.18524e9i		−	1.39031i	−0.718858	−	0.695157i	$-0.755335\pi$
$277$		−	8.18524e9i		−	1.39031i	0.718858	−	0.695157i	$-0.244665\pi$
$278$	−1.60465e8			−0.0268659
$279$	−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	$-0.194409\pi$
$282$	6.97285e9	−	2.75188e9i	1.10259	−	0.435144i
$283$			7.42098e9i			1.15695i	0.815699	+	0.578476i	$0.196352\pi$
$283$			7.42098e9i			1.15695i	−0.815699	+	0.578476i	$0.803648\pi$
$284$		−	3.33045e9i		−	0.511952i
$285$		0			0
$286$	1.86573e10			2.78859
$287$	7.06834e7			0.0104181
$288$	−8.72429e9	+	8.15662e9i	−1.26812	+	1.18561i
$289$	−6.29018e9			−0.901720
$290$		0			0
$291$	−1.04708e9	−	2.65315e9i	−0.146019	−	0.369990i
$292$		−	3.09807e10i		−	4.26147i
$293$	−1.73588e8			−0.0235531			−0.0117766	−	0.999931i	$-0.503749\pi$
$293$	−1.73588e8			−0.0235531			−0.0117766	+	0.999931i	$0.503749\pi$
$294$	−9.43846e9	+	3.72495e9i	−1.26332	+	0.498576i
$295$		0			0
$296$		−	1.15293e10i		−	1.50188i
$297$	9.67100e9	+	4.58985e9i	1.24293	+	0.589893i
$298$			4.57063e9i			0.579577i
$299$		−	1.18970e10i		−	1.48852i
$300$		0			0
$301$	−1.26883e10			−1.54575
$302$	−2.83057e10			−3.40287
$303$	−1.47706e9	−	3.74264e9i	−0.175237	−	0.444025i
$304$	1.95725e10			2.29167
$305$		0			0
$306$	−3.69877e9	+	3.45810e9i	−0.421863	+	0.394413i
$307$			1.38868e10i			1.56332i	0.623703	+	0.781661i	$0.285627\pi$
$307$			1.38868e10i			1.56332i	−0.623703	+	0.781661i	$0.714373\pi$
$308$	−3.90623e10			−4.34065
$309$	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	$0.828187\pi$
$312$	−9.82648e9	−	2.48988e10i	−1.03700	−	2.62761i
$313$		−	1.68395e10i		−	1.75450i	−0.480037	−	0.877248i	$-0.659377\pi$
$313$		−	1.68395e10i		−	1.75450i	0.480037	−	0.877248i	$-0.340623\pi$
$314$			7.15734e9i			0.736263i
$315$		0			0
$316$	2.66869e10			2.67639
$317$	−1.96153e10			−1.94248			−0.971242	−	0.238094i	$-0.923477\pi$
$317$	−1.96153e10			−1.94248			−0.971242	+	0.238094i	$0.923477\pi$
$318$	1.34567e10	−	5.31079e9i	1.31593	−	0.519339i
$319$	−1.53078e10			−1.47826
$320$		0			0
$321$	−6.07802e9	+	2.39873e9i	−0.572456	+	0.225924i
$322$			3.53144e10i			3.28495i
$323$	3.34742e9			0.307539
$324$	1.77208e9	−	2.63188e10i	0.160806	−	2.38828i
$325$		0			0
$326$		−	2.77801e10i		−	2.45960i
$327$	1.79853e10	−	7.09804e9i	1.57300	−	0.620794i
$328$		−	2.34886e8i		−	0.0202937i
$329$		−	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	$0.654557\pi$
$332$	2.87565e10			2.36692
$333$	4.91240e9	+	5.25428e9i	0.399500	+	0.427304i
$334$	3.49924e10			2.81182
$335$		0			0
$336$	1.44065e10	+	3.65038e10i	1.13032	+	2.86405i
$337$		−	8.17992e8i		−	0.0634205i	−0.999497	−	0.0317102i	$-0.989905\pi$
$337$		−	8.17992e8i		−	0.0634205i	0.999497	−	0.0317102i	$-0.0100954\pi$
$338$	5.06239e9			0.387872
$339$	6.96050e9	−	2.74701e9i	0.527038	−	0.207999i
$340$		0			0
$341$			1.67670e10i			1.24004i
$342$	−1.80598e10	+	1.68847e10i	−1.32010	+	1.23421i
$343$		−	4.79365e9i		−	0.346330i
$344$			4.21642e10i			3.01099i
$345$		0			0
$346$	−5.98458e9			−0.417570
$347$	1.44473e10			0.996479			0.498239	−	0.867039i	$-0.333980\pi$
$347$	1.44473e10			0.996479			0.498239	+	0.867039i	$0.333980\pi$
$348$	1.38473e10	+	3.50869e10i	0.944165	+	2.39237i
$349$	1.45400e9			0.0980080			0.0490040	−	0.998799i	$-0.484395\pi$
$349$	1.45400e9			0.0980080			0.0490040	+	0.998799i	$0.484395\pi$
$350$		0			0
$351$	1.50872e10	+	7.16037e9i	0.993985	+	0.471745i
$352$			3.66677e10i			2.38844i
$353$	1.22501e10			0.788934			0.394467	−	0.918910i	$-0.370929\pi$
$353$	1.22501e10			0.788934			0.394467	+	0.918910i	$0.370929\pi$
$354$	1.52611e9	+	3.86693e9i	0.0971791	+	0.246237i
$355$		0			0
$356$		−	1.15372e10i		−	0.718294i
$357$	2.46389e9	+	6.24312e9i	0.151687	+	0.384352i
$358$		−	2.96557e10i		−	1.80541i
$359$			1.08842e10i			0.655271i	0.944804	+	0.327635i	$0.106252\pi$
$359$			1.08842e10i			0.655271i	−0.944804	+	0.327635i	$0.893748\pi$
$360$		0			0
$361$	−6.39283e8			−0.0376413
$362$	−2.61651e10			−1.52366
$363$	1.44201e10	−	5.69099e9i	0.830504	−	0.327764i
$364$	−6.09388e10			−3.47127
$365$		0			0
$366$	1.74556e10	−	6.88896e9i	0.972769	−	0.383910i
$367$			2.34324e10i			1.29167i	0.763476	+	0.645836i	$0.223491\pi$
$367$			2.34324e10i			1.29167i	−0.763476	+	0.645836i	$0.776509\pi$
$368$	5.79612e10			3.16043
$369$	1.00080e8	+	1.07046e8i	0.00539814	+	0.00577382i
$370$		0			0
$371$		−	1.91758e10i		−	1.01218i
$372$	3.84314e10	−	1.51672e10i	2.00685	−	0.792017i
$373$		−	1.29023e10i		−	0.666548i	−0.942830	−	0.333274i	$-0.891847\pi$
$373$		−	1.29023e10i		−	0.666548i	0.942830	−	0.333274i	$-0.108153\pi$
$374$			1.55457e10i			0.794556i
$375$		0			0
$376$	−3.30190e10			−1.65201
$377$	−2.38809e10			−1.18218
$378$	−4.47839e10	−	2.12544e10i	−2.19358	−	1.04107i
$379$	5.12576e9			0.248429			0.124214	−	0.992255i	$-0.460359\pi$
$379$	5.12576e9			0.248429			0.124214	+	0.992255i	$0.460359\pi$
$380$		0			0
$381$	−5.65410e8	−	1.43266e9i	−0.0268326	−	0.0679898i
$382$		−	6.36679e10i		−	2.98997i
$383$	−3.66239e10			−1.70204			−0.851018	−	0.525136i	$-0.824014\pi$
$383$	−3.66239e10			−1.70204			−0.851018	+	0.525136i	$0.824014\pi$
$384$	−2.99268e9	+	1.18108e9i	−0.137637	+	0.0543194i
$385$		0			0
$386$		−	4.43406e10i		−	1.99734i
$387$	−1.79654e10	−	1.92157e10i	−0.800926	−	0.856667i
$388$			2.15783e10i			0.952118i
$389$		−	3.16164e10i		−	1.38075i	−0.723453	−	0.690373i	$-0.757446\pi$
$389$		−	3.16164e10i		−	1.38075i	0.723453	−	0.690373i	$-0.242554\pi$
$390$		0			0
$391$	9.91292e9			0.424126
$392$	4.46946e10			1.89282
$393$	1.45412e10	+	3.68451e10i	0.609578	+	1.54458i
$394$	1.07792e10			0.447303
$395$		0			0
$396$	−5.53082e10	−	5.91574e10i	−2.24910	−	2.40563i
$397$			5.05225e8i			0.0203387i	0.999948	+	0.0101693i	$0.00323706\pi$
$397$			5.05225e8i			0.0203387i	−0.999948	+	0.0101693i	$0.996763\pi$
$398$	−5.42719e10			−2.16293
$399$	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	$0.748679\pi$
$402$	8.66688e9	+	2.19605e10i	0.331863	+	0.840889i
$403$			2.61572e10i			0.991679i
$404$			3.04392e10i			1.14264i
$405$		0			0
$406$	7.08865e10			2.60891
$407$	2.20835e10			0.804804
$408$	2.07463e10	−	8.18768e9i	0.748687	−	0.295474i
$409$	−7.11197e9			−0.254154			−0.127077	−	0.991893i	$-0.540559\pi$
$409$	−7.11197e9			−0.254154			−0.127077	+	0.991893i	$0.540559\pi$
$410$		0			0
$411$	1.00958e10	−	3.98437e9i	0.353813	−	0.139635i
$412$		−	7.99590e10i		−	2.77510i
$413$	5.51036e9			0.189400
$414$	−5.34816e10	+	5.00017e10i	−1.82055	+	1.70209i
$415$		0			0
$416$			5.72033e10i			1.91006i
$417$	−4.10182e8	+	1.61881e8i	−0.0135654	+	0.00535367i
$418$			7.59044e10i			2.48635i
$419$		−	2.61481e10i		−	0.848369i	−0.905576	−	0.424184i	$-0.860561\pi$
$419$		−	2.61481e10i		−	0.848369i	0.905576	−	0.424184i	$-0.139439\pi$
$420$		0			0
$421$	5.80276e9			0.184717			0.0923584	−	0.995726i	$-0.470559\pi$
$421$	5.80276e9			0.184717			0.0923584	+	0.995726i	$0.470559\pi$
$422$	2.42061e10			0.763265
$423$	1.50479e10	−	1.40688e10i	0.470017	−	0.439435i
$424$	−6.37225e10			−1.97165
$425$		0			0
$426$	−4.76346e9	−	1.20699e10i	−0.144639	−	0.366492i
$427$		−	2.48741e10i		−	0.748232i
$428$	4.94331e10			1.47314
$429$	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	$0.776494\pi$
$432$	−3.48846e10	+	7.35033e10i	−1.00161	+	2.11043i
$433$			3.20554e10i			0.911905i	0.890004	+	0.455952i	$0.150701\pi$
$433$			3.20554e10i			0.911905i	−0.890004	+	0.455952i	$0.849299\pi$
$434$		−	7.76434e10i		−	2.18850i
$435$		0			0
$436$	−1.46276e11			−4.04789
$437$	4.84013e10			1.32718
$438$	−4.43110e10	−	1.12277e11i	−1.20397	−	3.05067i
$439$	2.57341e10			0.692867			0.346434	−	0.938074i	$-0.387393\pi$
$439$	2.57341e10			0.692867			0.346434	+	0.938074i	$0.387393\pi$
$440$		0			0
$441$	−2.03689e10	+	1.90435e10i	−0.538533	+	0.503492i
$442$			2.42520e10i			0.635417i
$443$	7.09037e10			1.84100			0.920500	−	0.390743i	$-0.127782\pi$
$443$	7.09037e10			1.84100			0.920500	+	0.390743i	$0.127782\pi$
$444$	−1.99765e10	−	5.06174e10i	−0.514028	−	1.30247i
$445$		0			0
$446$			1.10843e10i			0.280136i
$447$	4.61097e9	+	1.16835e10i	0.115495	+	0.292646i
$448$		−	4.57691e10i		−	1.13621i
$449$			6.41882e10i			1.57932i	0.613545	+	0.789660i	$0.289743\pi$
$449$			6.41882e10i			1.57932i	−0.613545	+	0.789660i	$0.710257\pi$
$450$		0			0
$451$	4.49907e8			0.0108747
$452$	−5.66103e10			−1.35626
$453$	−7.23552e10	+	2.85555e10i	−1.71821	+	0.678104i
$454$	1.35010e11			3.17791
$455$		0			0
$456$	1.01297e11	−	3.99776e10i	2.34281	−	0.924607i
$457$			1.93552e10i			0.443745i	0.975076	+	0.221873i	$0.0712169\pi$
$457$			1.93552e10i			0.443745i	−0.975076	+	0.221873i	$0.928783\pi$
$458$	4.91138e10			1.11620
$459$	−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	$0.784818\pi$
$462$	−1.41566e11	+	5.58699e10i	−3.10735	+	1.22634i
$463$		−	2.73707e9i		−	0.0595610i	−0.999556	−	0.0297805i	$-0.990519\pi$
$463$		−	2.73707e9i		−	0.0595610i	0.999556	−	0.0297805i	$-0.00948083\pi$
$464$		−	1.16345e11i		−	2.51002i
$465$		0			0
$466$	1.25306e11			2.65723
$467$	1.99286e10			0.418995			0.209498	−	0.977809i	$-0.432817\pi$
$467$	1.99286e10			0.418995			0.209498	+	0.977809i	$0.432817\pi$
$468$	−8.62832e10	−	9.22881e10i	−1.79863	−	1.92381i
$469$	3.12937e10			0.646793
$470$		0			0
$471$	7.22050e9	+	1.82957e10i	0.146718	+	0.371762i
$472$		−	1.83113e10i		−	0.368937i
$473$	−8.07625e10			−1.61349
$474$	9.67160e10	−	3.81696e10i	1.91595	−	0.756144i
$475$		0			0
$476$		−	5.07758e10i		−	0.989075i
$477$	2.90406e10	−	2.71510e10i	0.560960	−	0.524460i
$478$		−	5.47150e10i		−	1.04808i
$479$			3.16925e10i			0.602024i	0.953620	+	0.301012i	$0.0973245\pi$
$479$			3.16925e10i			0.602024i	−0.953620	+	0.301012i	$0.902676\pi$
$480$		0			0
$481$	3.44512e10			0.643612
$482$	−1.47400e11			−2.73093
$483$	3.56261e10	+	9.02711e10i	0.654605	+	1.65867i
$484$	−1.17280e11			−2.13718
$485$		0			0
$486$	−3.12209e10	−	9.79165e10i	−0.559630	−	1.75514i
$487$			4.71599e10i			0.838411i	0.907891	+	0.419205i	$0.137691\pi$
$487$			4.71599e10i			0.838411i	−0.907891	+	0.419205i	$0.862309\pi$
$488$	−8.26585e10			−1.45750
$489$	−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	$-0.192564\pi$
$492$	−4.06981e8	−	1.03123e9i	−0.00694567	−	0.0175993i
$493$		−	1.98981e10i		−	0.336841i
$494$			1.18414e11i			1.98836i
$495$		0			0
$496$	−1.27435e11			−2.10554
$497$	−1.71995e10			−0.281898
$498$	1.04217e11	−	4.11298e10i	1.69442	−	0.668713i
$499$	−7.91261e10			−1.27620			−0.638098	−	0.769955i	$-0.720279\pi$
$499$	−7.91261e10			−1.27620			−0.638098	+	0.769955i	$0.720279\pi$
$500$		0			0
$501$	8.94478e10	−	3.53012e10i	1.41977	−	0.560323i
$502$		−	5.64751e9i		−	0.0889287i
$503$	6.52715e10			1.01965			0.509826	−	0.860278i	$-0.329710\pi$
$503$	6.52715e10			1.01965			0.509826	+	0.860278i	$0.329710\pi$
$504$	1.49121e11	+	1.59499e11i	2.31108	+	2.47192i
$505$		0			0
$506$			2.24780e11i			3.42891i
$507$	1.29405e10	−	5.10707e9i	0.195848	−	0.0772929i
$508$			1.16520e10i			0.174962i
$509$		−	4.80429e10i		−	0.715745i	−0.933771	−	0.357872i	$-0.883502\pi$
$509$		−	4.80429e10i		−	0.715745i	0.933771	−	0.357872i	$-0.116498\pi$
$510$		0			0
$511$	−1.59995e11			−2.34651
$512$	1.33470e11			1.94225
$513$	−2.91309e10	+	6.13800e10i	−0.420615	+	0.886252i
$514$	−7.48914e10			−1.07295
$515$		0			0
$516$	7.30569e10	+	1.85115e11i	1.03053	+	2.61122i
$517$		−	6.32455e10i		−	0.885253i
$518$	−1.02263e11			−1.42036
$519$	−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	$-0.157025\pi$
$522$	1.00368e11	+	1.07353e11i	1.35180	+	1.44588i
$523$		−	1.13309e11i		−	1.51445i	−0.653152	−	0.757227i	$-0.726554\pi$
$523$		−	1.13309e11i		−	1.51445i	0.653152	−	0.757227i	$-0.273446\pi$
$524$		−	2.99665e11i		−	3.97475i
$525$		0			0
$526$	4.76278e10			0.622183
$527$	−2.17948e10			−0.282560
$528$	9.16986e10	+	2.32350e11i	1.17985	+	2.98956i
$529$	6.50228e10			0.830315
$530$		0			0
$531$	7.80211e9	+	8.34511e9i	0.0981373	+	0.104967i
$532$		−	2.47921e11i		−	3.09504i
$533$	7.01875e8			0.00869663
$534$	−1.65015e10	−	4.18122e10i	−0.202935	−	0.514207i
$535$		0			0
$536$		−	1.03991e11i		−	1.25990i
$537$	−2.99174e10	−	7.58061e10i	−0.359771	−	0.911605i
$538$			2.17261e11i			2.59330i
$539$			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	$0.566155\pi$
$542$	1.14960e11			1.33214
$543$	−6.68835e10	+	2.63960e10i	−0.769342	+	0.303626i
$544$	−4.76632e10			−0.544237
$545$		0			0
$546$	−2.20849e11	+	8.71594e10i	−2.48499	+	0.980717i
$547$		−	3.44410e10i		−	0.384703i	−0.981326	−	0.192352i	$-0.938389\pi$
$547$		−	3.44410e10i		−	0.384703i	0.981326	−	0.192352i	$-0.0616114\pi$
$548$	−8.21100e10			−0.910487
$549$	3.76703e10	−	3.52192e10i	0.414677	−	0.387695i
$550$		0			0
$551$		−	9.71557e10i		−	1.05405i
$552$	2.99977e11	−	1.18388e11i	3.23096	−	1.27512i
$553$		−	1.37820e11i		−	1.47371i
$554$			2.41261e11i			2.56123i
$555$		0			0
$556$	3.33604e9			0.0349086
$557$	1.45667e9			0.0151335			0.00756676	−	0.999971i	$-0.497591\pi$
$557$	1.45667e9			0.0151335			0.00756676	+	0.999971i	$0.497591\pi$
$558$	1.17586e11	−	1.09935e11i	1.21288	−	1.13397i
$559$	−1.25993e11			−1.29033
$560$		0			0
$561$	1.56829e10	+	3.97381e10i	0.158334	+	0.401195i
$562$			2.10782e11i			2.11295i
$563$	1.15715e11			1.15175			0.575873	−	0.817539i	$-0.304662\pi$
$563$	1.15715e11			1.15175			0.575873	+	0.817539i	$0.304662\pi$
$564$	−1.44964e11	+	5.72112e10i	−1.43267	+	0.565412i
$565$		0			0
$566$		−	2.18734e11i		−	2.13133i
$567$	−1.35919e11	−	9.15161e9i	−1.31507	−	0.0885453i
$568$			5.71553e10i			0.549115i
$569$		−	3.28384e10i		−	0.313280i	−0.987656	−	0.156640i	$-0.949934\pi$
$569$		−	3.28384e10i		−	0.313280i	0.987656	−	0.156640i	$-0.0500663\pi$
$570$		0			0
$571$	1.02275e11			0.962111			0.481055	−	0.876690i	$-0.340254\pi$
$571$	1.02275e11			0.962111			0.481055	+	0.876690i	$0.340254\pi$
$572$	−3.87882e11			−3.62340
$573$	−6.42298e10	−	1.62748e11i	−0.595824	−	1.50973i
$574$	−2.08340e9			−0.0191922
$575$		0			0
$576$	6.93145e10	−	6.48044e10i	0.629701	−	0.588728i
$577$			1.74070e10i			0.157043i	0.996912	+	0.0785217i	$0.0250200\pi$
$577$			1.74070e10i			0.157043i	−0.996912	+	0.0785217i	$0.974980\pi$
$578$	1.85404e11			1.66115
$579$	−4.47319e10	−	1.13344e11i	−0.398018	−	1.00852i
$580$		0			0
$581$		−	1.48508e11i		−	1.30331i
$582$	3.08630e10	+	7.82021e10i	0.268996	+	0.681595i
$583$		−	1.22056e11i		−	1.05654i
$584$			5.31674e11i			4.57082i
$585$		0			0
$586$	5.11652e9			0.0433895
$587$	5.82932e10			0.490982			0.245491	−	0.969399i	$-0.421051\pi$
$587$	5.82932e10			0.490982			0.245491	+	0.969399i	$0.421051\pi$
$588$	1.96224e11	−	7.74413e10i	1.64151	−	0.647833i
$589$	−1.06417e11			−0.884196
$590$		0			0
$591$	2.75539e10	−	1.08743e10i	0.225857	−	0.0891359i
$592$			1.67843e11i			1.36652i
$593$	−9.05975e10			−0.732652			−0.366326	−	0.930487i	$-0.619384\pi$
$593$	−9.05975e10			−0.732652			−0.366326	+	0.930487i	$0.619384\pi$
$594$	−2.85054e11	−	1.35287e11i	−2.28972	−	1.08670i
$595$		0			0
$596$		−	9.50228e10i		−	0.753083i
$597$	−1.38730e11	+	5.47509e10i	−1.09213	+	0.431016i
$598$			3.50667e11i			2.74214i
$599$			2.21600e11i			1.72133i	0.509175	+	0.860663i	$0.329951\pi$
$599$			2.21600e11i			1.72133i	−0.509175	+	0.860663i	$0.670049\pi$
$600$		0			0
$601$	−9.42710e10			−0.722571			−0.361285	−	0.932455i	$-0.617662\pi$
$601$	−9.42710e10			−0.722571			−0.361285	+	0.932455i	$0.617662\pi$
$602$	3.73990e11			2.84757
$603$	4.43087e10	+	4.73924e10i	0.335135	+	0.358459i
$604$	5.88471e11			4.42158
$605$		0			0
$606$	4.35365e10	+	1.10315e11i	0.322822	+	0.817981i
$607$			2.52304e11i			1.85853i	0.369415	+	0.929265i	$0.379558\pi$
$607$			2.52304e11i			1.85853i	−0.369415	+	0.929265i	$0.620442\pi$
$608$	−2.32723e11			−1.70304
$609$	1.81201e11	−	7.15120e10i	1.31732	−	0.519888i
$610$		0			0
$611$		−	9.86657e10i		−	0.707948i
$612$	7.68968e10	−	7.18934e10i	0.548154	−	0.512487i
$613$			1.39397e11i			0.987213i	0.869685	+	0.493607i	$0.164322\pi$
$613$			1.39397e11i			0.987213i	−0.869685	+	0.493607i	$0.835678\pi$
$614$		−	4.09315e11i		−	2.87995i
$615$		0			0
$616$	6.70365e11			4.65574
$617$	−4.85857e10			−0.335249			−0.167625	−	0.985851i	$-0.553610\pi$
$617$	−4.85857e10			−0.335249			−0.167625	+	0.985851i	$0.553610\pi$
$618$	−1.14364e11	−	2.89780e11i	−0.784032	−	1.98662i
$619$	−1.67889e11			−1.14356			−0.571781	−	0.820406i	$-0.693747\pi$
$619$	−1.67889e11			−1.14356			−0.571781	+	0.820406i	$0.693747\pi$
$620$		0			0
$621$	−8.62671e10	+	1.81768e11i	−0.580068	+	1.22223i
$622$		−	2.83423e11i		−	1.89354i
$623$	−5.95822e10			−0.395516
$624$	1.43054e11	+	3.62477e11i	0.943542	+	2.39079i
$625$		0			0
$626$			4.96347e11i			3.23213i
$627$	7.65742e10	+	1.94027e11i	0.495464	+	1.25543i
$628$		−	1.48800e11i		−	0.956676i
$629$			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	$0.578585\pi$
$632$	−4.57985e11			−2.87067
$633$	6.18759e10	−	2.44197e10i	0.385396	−	0.152099i
$634$	5.78163e11			3.57844
$635$		0			0
$636$	−2.79764e11	+	1.10411e11i	−1.70987	+	0.674811i
$637$			1.33554e11i			0.811148i
$638$	4.51200e11			2.72324
$639$	−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	$0.755405\pi$
$642$	1.79151e11	−	7.07030e10i	1.05458	−	0.416196i
$643$		−	3.28468e11i		−	1.92154i	−0.277353	−	0.960768i	$-0.589457\pi$
$643$		−	3.28468e11i		−	1.92154i	0.277353	−	0.960768i	$-0.410543\pi$
$644$		−	7.34182e11i		−	4.26835i
$645$		0			0
$646$	−9.86657e10			−0.566547
$647$	1.20987e11			0.690435			0.345217	−	0.938523i	$-0.387805\pi$
$647$	1.20987e11			0.690435			0.345217	+	0.938523i	$0.387805\pi$
$648$	−3.04115e10	+	4.51668e11i	−0.172479	+	2.56165i
$649$	3.50740e10			0.197700
$650$		0			0
$651$	−7.83286e10	−	1.98473e11i	−0.436110	−	1.10504i
$652$			5.77545e11i			3.19592i
$653$	6.71025e9			0.0369051			0.0184525	−	0.999830i	$-0.494126\pi$
$653$	6.71025e9			0.0369051			0.0184525	+	0.999830i	$0.494126\pi$
$654$	−5.30121e11	+	2.09216e11i	−2.89777	+	1.14362i
$655$		0			0
$656$			3.41947e9i			0.0184647i
$657$	−2.26536e11	−	2.42302e11i	−1.21584	−	1.30046i
$658$			2.92873e11i			1.56234i
$659$			2.82641e11i			1.49863i	0.662214	+	0.749315i	$0.269617\pi$
$659$			2.82641e11i			1.49863i	−0.662214	+	0.749315i	$0.730383\pi$
$660$		0			0
$661$	−3.05260e10			−0.159906			−0.0799530	−	0.996799i	$-0.525477\pi$
$661$	−3.05260e10			−0.159906			−0.0799530	+	0.996799i	$0.525477\pi$
$662$	3.30243e11			1.71950
$663$	2.44660e10	+	6.19932e10i	0.126622	+	0.320841i
$664$	−4.93504e11			−2.53874
$665$		0			0
$666$	−1.44794e11	−	1.54871e11i	−0.735958	−	0.787177i
$667$		−	2.87713e11i		−	1.45364i
$668$	−7.27486e11			−3.65358
$669$	1.11821e10	+	2.83338e10i	0.0558239	+	0.141449i
$670$		0			0
$671$		−	1.58326e11i		−	0.781022i
$672$	−1.71297e11	−	4.34041e11i	−0.839988	−	2.12840i
$673$		−	1.35686e11i		−	0.661417i	−0.943733	−	0.330708i	$-0.892712\pi$
$673$		−	1.35686e11i		−	0.661417i	0.943733	−	0.330708i	$-0.107288\pi$
$674$			2.41104e10i			0.116833i
$675$		0			0
$676$	−1.05246e11			−0.503988
$677$	−3.54740e11			−1.68871			−0.844356	−	0.535783i	$-0.820016\pi$
$677$	−3.54740e11			−1.68871			−0.844356	+	0.535783i	$0.820016\pi$
$678$	−2.05162e11	+	8.09685e10i	−0.970907	+	0.383175i
$679$	1.11438e11			0.524268
$680$		0			0
$681$	3.45113e11	−	1.36201e11i	1.60462	−	0.633276i
$682$		−	4.94209e11i		−	2.28440i
$683$	3.26911e11			1.50227			0.751133	−	0.660151i	$-0.229508\pi$
$683$	3.26911e11			1.50227			0.751133	+	0.660151i	$0.229508\pi$
$684$	3.75460e11	−	3.51030e11i	1.71530	−	1.60369i
$685$		0			0
$686$			1.41293e11i			0.638007i
$687$	1.25545e11	−	4.95472e10i	0.563603	−	0.222429i
$688$		−	6.13826e11i		−	2.73963i
$689$		−	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	$0.271463\pi$
$692$	1.24418e11			0.542576
$693$	−3.05509e11	+	2.85630e11i	−1.32462	+	1.23843i
$694$	−4.25836e11			−1.83571
$695$		0			0
$696$	−2.37640e11	−	6.02143e11i	−1.01270	−	2.56603i
$697$			5.84820e8i			0.00247794i
$698$	−4.28567e10			−0.180550
$699$	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	$-0.116612\pi$
$702$	−4.44697e11	−	2.11053e11i	−1.83112	−	0.869047i
$703$			1.40160e11i			0.573854i
$704$		−	2.91325e11i		−	1.18601i
$705$		0			0
$706$	−3.61073e11			−1.45337
$707$	1.57198e11			0.629173
$708$	−3.17276e10	−	8.03930e10i	−0.126271	−	0.319952i
$709$	−2.67236e11			−1.05757			−0.528786	−	0.848755i	$-0.677352\pi$
$709$	−2.67236e11			−1.05757			−0.528786	+	0.848755i	$0.677352\pi$
$710$		0			0
$711$	2.08720e11	−	1.95139e11i	0.816743	−	0.763600i
$712$			1.97996e11i			0.770435i
$713$	−3.15138e11			−1.21939
$714$	−7.26235e10	−	1.84017e11i	−0.279437	−	0.708051i
$715$		0			0
$716$			6.16537e11i			2.34589i
$717$	−5.51979e10	−	1.39863e11i	−0.208855	−	0.529208i
$718$		−	3.20815e11i		−	1.20714i
$719$			3.27548e11i			1.22563i	0.790227	+	0.612815i	$0.209963\pi$
$719$			3.27548e11i			1.22563i	−0.790227	+	0.612815i	$0.790037\pi$
$720$		0			0
$721$	−4.12935e11			−1.52806
$722$	1.88430e10			0.0693427
$723$	−3.76786e11	+	1.48701e11i	−1.37893	+	0.544203i
$724$	5.43969e11			1.97979
$725$		0			0
$726$	−4.25034e11	+	1.67743e11i	−1.52995	+	0.603805i
$727$		−	8.40255e10i		−	0.300797i	−0.988625	−	0.150398i	$-0.951944\pi$
$727$		−	8.40255e10i		−	0.300797i	0.988625	−	0.150398i	$-0.0480556\pi$
$728$	1.04580e12			3.72325
$729$	−1.78588e11	−	2.18799e11i	−0.632327	−	0.774702i
$730$		0			0
$731$		−	1.04981e11i		−	0.367654i
$732$	−3.62899e11	+	1.43220e11i	−1.26398	+	0.498839i
$733$		−	4.23327e10i		−	0.146643i	−0.997308	−	0.0733213i	$-0.976640\pi$
$733$		−	4.23327e10i		−	0.146643i	0.997308	−	0.0733213i	$-0.0233598\pi$
$734$		−	6.90673e11i		−	2.37951i
$735$		0			0
$736$	−6.89177e11			−2.34866
$737$	1.99188e11			0.675138
$738$	−2.94989e9	−	3.15518e9i	−0.00994443	−	0.0106365i
$739$	−2.88845e11			−0.968473			−0.484236	−	0.874937i	$-0.660903\pi$
$739$	−2.88845e11			−0.968473			−0.484236	+	0.874937i	$0.660903\pi$
$740$		0			0
$741$	1.19459e11	+	3.02691e11i	0.396229	+	1.00398i
$742$			5.65210e11i			1.86464i
$743$	3.03005e11			0.994247			0.497123	−	0.867680i	$-0.334390\pi$
$743$	3.03005e11			0.994247			0.497123	+	0.867680i	$0.334390\pi$
$744$	−6.59539e11	+	2.60292e11i	−2.15253	+	0.849510i
$745$		0			0
$746$			3.80297e11i			1.22791i
$747$	2.24907e11	−	2.10273e11i	0.722305	−	0.675306i
$748$		−	3.23194e11i		−	1.03242i
$749$		−	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	$0.238187\pi$
$752$	4.80690e11			1.50312
$753$	−5.69735e9	−	1.44362e10i	−0.0177212	−	0.0449028i
$754$	7.03892e11			2.17781
$755$		0			0
$756$	9.31051e11	+	4.41876e11i	2.85027	+	1.35274i
$757$			1.41830e11i			0.431901i	0.976404	+	0.215951i	$0.0692850\pi$
$757$			1.41830e11i			0.431901i	−0.976404	+	0.215951i	$0.930715\pi$
$758$	−1.51083e11			−0.457655
$759$	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	$0.872728\pi$
$762$	1.66655e10	+	4.22279e10i	0.0494310	+	0.125251i
$763$			7.55420e11i			2.22890i
$764$			1.32365e12i			3.88507i
$765$		0			0
$766$	1.07949e12			3.13549
$767$	5.47170e10			0.158103
$768$	3.67170e11	−	1.44906e11i	1.05541	−	0.416526i
$769$	6.57270e11			1.87948			0.939742	−	0.341884i	$-0.111065\pi$
$769$	6.57270e11			1.87948			0.939742	+	0.341884i	$0.111065\pi$
$770$		0			0
$771$	−1.91438e11	+	7.55523e10i	−0.541764	+	0.213811i
$772$			9.21835e11i			2.59528i
$773$	2.64170e10			0.0739887			0.0369943	−	0.999315i	$-0.488222\pi$
$773$	2.64170e10			0.0739887			0.0369943	+	0.999315i	$0.488222\pi$
$774$	5.29532e11	+	5.66385e11i	1.47546	+	1.57815i
$775$		0			0
$776$		−	3.70315e11i		−	1.02123i
$777$	−2.61405e11	+	1.03165e11i	−0.717183	+	0.283041i
$778$			9.31898e11i			2.54361i
$779$			2.85547e9i			0.00775404i
$780$		0			0
$781$	−1.09477e11			−0.294251
$782$	−2.92185e11			−0.781323
$783$	3.64862e11	+	1.73163e11i	0.970693	+	0.460691i
$784$	−6.50663e11			−1.72223
$785$		0			0
$786$	−4.28603e11	−	1.08602e12i	−1.12296	−	2.84542i
$787$		−	1.72594e11i		−	0.449911i	−0.974369	−	0.224956i	$-0.927776\pi$
$787$		−	1.72594e11i		−	0.449911i	0.974369	−	0.224956i	$-0.0722237\pi$
$788$	−2.24098e11			−0.581210
$789$	1.21747e11	−	4.80482e10i	0.314159	−	0.123985i
$790$		0			0
$791$			2.92355e11i			0.746800i
$792$	9.49169e11	+	1.01523e12i	2.41236	+	2.58025i
$793$		−	2.46996e11i		−	0.624594i
$794$		−	1.48916e10i		−	0.0374679i
$795$		0			0
$796$	1.12831e12			2.81044
$797$	−7.06159e9			−0.0175013			−0.00875063	−	0.999962i	$-0.502785\pi$
$797$	−7.06159e9			−0.0175013			−0.00875063	+	0.999962i	$0.502785\pi$
$798$	−3.54595e11	−	8.98490e11i	−0.874422	−	2.21565i
$799$	8.22108e10			0.201717
$800$		0			0
$801$	−8.43623e10	−	9.02336e10i	−0.204936	−	0.219199i
$802$		−	1.08229e12i		−	2.61605i
$803$	−1.01838e12			−2.44934
$804$	−1.80183e11	−	4.56557e11i	−0.431211	−	1.09262i
$805$		0			0
$806$		−	7.70987e11i		−	1.82687i
$807$	2.19179e11	+	5.55365e11i	0.516778	+	1.30944i
$808$		−	5.22381e11i		−	1.22558i
$809$		−	5.66925e11i		−	1.32352i	−0.749714	−	0.661762i	$-0.769809\pi$
$809$		−	5.66925e11i		−	1.32352i	0.749714	−	0.661762i	$-0.230191\pi$
$810$		0			0
$811$	−5.11294e11			−1.18192			−0.590959	−	0.806702i	$-0.701250\pi$
$811$	−5.11294e11			−1.18192			−0.590959	+	0.806702i	$0.701250\pi$
$812$	−1.47372e12			−3.38993
$813$	2.93862e11	−	1.15975e11i	0.672638	−	0.265461i
$814$	−6.50914e11			−1.48261
$815$		0			0
$816$	−3.02025e11	+	1.19196e11i	−0.681212	+	0.268845i
$817$		−	5.12584e11i		−	1.15047i
$818$	2.09626e11			0.468201
$819$	−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	$0.982731\pi$
$822$	−2.97575e11	+	1.17440e11i	−0.651792	+	0.257234i
$823$			2.61102e11i			0.569130i	0.958657	+	0.284565i	$0.0918492\pi$
$823$			2.61102e11i			0.569130i	−0.958657	+	0.284565i	$0.908151\pi$
$824$			1.37221e12i			2.97655i
$825$		0			0
$826$	−1.62419e11			−0.348912
$827$	5.67337e11			1.21288			0.606442	−	0.795128i	$-0.292596\pi$
$827$	5.67337e11			1.21288			0.606442	+	0.795128i	$0.292596\pi$
$828$	1.11187e12	−	1.03953e12i	2.36556	−	2.21164i
$829$	6.10109e11			1.29178			0.645891	−	0.763430i	$-0.276486\pi$
$829$	6.10109e11			1.29178			0.645891	+	0.763430i	$0.276486\pi$
$830$		0			0
$831$	2.43390e11	+	6.16714e11i	0.510387	+	1.29324i
$832$		−	4.54480e11i		−	0.948466i
$833$	−1.11281e11			−0.231121
$834$	1.20902e10	−	4.77147e9i	0.0249901	−	0.00986251i
$835$		0			0
$836$		−	1.57804e12i		−	3.23067i
$837$	1.89670e11	−	3.99641e11i	0.386452	−	0.814270i
$838$			7.70720e11i			1.56286i
$839$			1.77752e10i			0.0358729i	0.999839	+	0.0179365i	$0.00570966\pi$
$839$			1.77752e10i			0.0358729i	−0.999839	+	0.0179365i	$0.994290\pi$
$840$		0			0
$841$	−7.72785e10			−0.154481
$842$	−1.71037e11			−0.340285
$843$	2.12642e11	+	5.38804e11i	0.421056	+	1.06689i
$844$	−5.03242e11			−0.991761
$845$		0			0
$846$	−4.43539e11	+	4.14679e11i	−0.865865	+	0.809525i
$847$			6.05672e11i			1.17680i
$848$	9.27672e11			1.79395
$849$	−2.20665e11	−	5.59131e11i	−0.424720	−	1.07617i
$850$		0			0
$851$			4.15063e11i			0.791399i
$852$	9.90317e10	+	2.50931e11i	0.187939	+	0.476208i
$853$		−	4.79452e11i		−	0.905626i	−0.891606	−	0.452813i	$-0.850421\pi$
$853$		−	4.79452e11i		−	0.905626i	0.891606	−	0.452813i	$-0.149579\pi$
$854$			7.33168e11i			1.37839i
$855$		0			0
$856$	−8.48344e11			−1.58007
$857$	9.38022e10			0.173896			0.0869480	−	0.996213i	$-0.472289\pi$
$857$	9.38022e10			0.173896			0.0869480	+	0.996213i	$0.472289\pi$
$858$	−1.40573e12	+	5.54779e11i	−2.59389	+	1.02370i
$859$	−4.46094e11			−0.819320			−0.409660	−	0.912238i	$-0.634353\pi$
$859$	−4.46094e11			−0.819320			−0.409660	+	0.912238i	$0.634353\pi$
$860$		0			0
$861$	−5.32561e9	+	2.10179e9i	−0.00969074	+	0.00382451i
$862$		−	1.31384e12i		−	2.37965i
$863$	8.85309e11			1.59607			0.798035	−	0.602612i	$-0.205873\pi$
$863$	8.85309e11			1.59607			0.798035	+	0.602612i	$0.205873\pi$
$864$	4.14789e11	−	8.73977e11i	0.744341	−	1.56836i
$865$		0			0
$866$		−	9.44837e11i		−	1.67991i
$867$	4.73932e11	−	1.87040e11i	0.838763	−	0.331023i
$868$			1.61420e12i			2.84366i
$869$		−	8.77239e11i		−	1.53829i
$870$		0			0
$871$	3.10742e11			0.539917
$872$	2.51031e12			4.34172
$873$	1.57784e11	+	1.68766e11i	0.271648	+	0.290554i
$874$	−1.42664e12			−2.44494
$875$		0			0
$876$	9.21219e11	+	2.33423e12i	1.56440	+	3.96394i
$877$		−	1.47075e11i		−	0.248622i	−0.992243	−	0.124311i	$-0.960328\pi$
$877$		−	1.47075e11i		−	0.248622i	0.992243	−	0.124311i	$-0.0396721\pi$
$878$	−7.58515e11			−1.27640
$879$	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	$0.973317\pi$
$882$	6.00375e11	−	5.61310e11i	0.992084	−	0.927532i
$883$		−	1.17637e11i		−	0.193509i	−0.995308	−	0.0967543i	$-0.969154\pi$
$883$		−	1.17637e11i		−	0.193509i	0.995308	−	0.0967543i	$-0.0308461\pi$
$884$		−	5.04196e11i		−	0.825639i
$885$		0			0
$886$	−2.08990e12			−3.39148
$887$	−1.03512e12			−1.67223			−0.836117	−	0.548552i	$-0.815179\pi$
$887$	−1.03512e12			−1.67223			−0.836117	+	0.548552i	$0.815179\pi$
$888$	3.42826e11	+	8.68668e11i	0.551342	+	1.39702i
$889$	6.01747e10			0.0963400
$890$		0			0
$891$	−8.65139e11	−	5.82510e10i	−1.37270	−	0.0924257i
$892$		−	2.30441e11i		−	0.364000i
$893$	4.01407e11			0.631217
$894$	−1.35909e11	−	3.44373e11i	−0.212764	−	0.539111i
$895$		0			0
$896$		−	1.25699e11i		−	0.195029i
$897$	3.53762e11	+	8.96378e11i	0.546438	+	1.38459i
$898$		−	1.89196e12i		−	2.90942i
$899$			6.32575e11i			0.968441i
$900$		0			0
$901$	1.58657e11			0.240746
$902$	−1.32611e10			−0.0200333
$903$	9.55997e11	−	3.77291e11i	1.43782	−	0.567447i
$904$	9.71516e11			1.45471
$905$		0			0
$906$	2.13268e12	−	8.41677e11i	3.16529	−	1.24920i
$907$			5.01146e11i			0.740516i	0.928929	+	0.370258i	$0.120731\pi$
$907$			5.01146e11i			0.740516i	−0.928929	+	0.370258i	$0.879269\pi$
$908$	−2.80684e12			−4.12927
$909$	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	$0.899615\pi$
$912$	−1.47468e12	+	5.81993e11i	−2.13167	+	0.841276i
$913$		−	9.45272e11i		−	1.36042i
$914$		−	5.70498e11i		−	0.817466i
$915$		0			0
$916$	−1.02107e12			−1.45035
$917$	−1.54757e12			−2.18863
$918$	1.75855e11	−	3.70533e11i	0.247619	−	0.521742i
$919$	1.00999e11			0.141598			0.0707990	−	0.997491i	$-0.477445\pi$
$919$	1.00999e11			0.141598			0.0707990	+	0.997491i	$0.477445\pi$
$920$		0			0
$921$	−4.12928e11	−	1.04630e12i	−0.573899	−	1.45417i
$922$		−	1.66589e12i		−	2.30528i
$923$	−1.70789e11			−0.235317
$924$	2.94313e12	−	1.16153e12i	4.03759	−	1.59346i
$925$		0			0
$926$			8.06756e10i			0.109723i
$927$	−5.84674e11	−	6.25365e11i	−0.791763	−	0.846866i
$928$			1.38338e12i			1.86530i
$929$		−	7.10245e11i		−	0.953554i	−0.879024	−	0.476777i	$-0.841805\pi$
$929$		−	7.10245e11i		−	0.953554i	0.879024	−	0.476777i	$-0.158195\pi$
$930$		0			0
$931$	−5.43345e11			−0.723231
$932$	−2.60510e12			−3.45272
$933$	−2.85925e11	−	7.24489e11i	−0.377333	−	0.956105i
$934$	−5.87398e11			−0.771872
$935$		0			0
$936$	1.48075e12	+	1.58380e12i	1.92920	+	2.06346i
$937$			9.65584e11i			1.25266i	0.779560	+	0.626328i	$0.215443\pi$
$937$			9.65584e11i			1.25266i	−0.779560	+	0.626328i	$0.784557\pi$
$938$	−9.22386e11			−1.19152
$939$	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	$0.948071\pi$
$942$	−2.12825e11	−	5.39267e11i	−0.270284	−	0.684858i
$943$			8.45609e9i			0.0106936i
$944$			2.66576e11i			0.335686i
$945$		0			0
$946$	2.38049e12			2.97236
$947$	1.42329e12			1.76967			0.884835	−	0.465905i	$-0.154271\pi$
$947$	1.42329e12			1.76967			0.884835	+	0.465905i	$0.154271\pi$
$948$	−2.01071e12	+	7.93541e11i	−2.48953	+	0.982508i
$949$	−1.58872e12			−1.95877
$950$		0			0
$951$	1.47791e12	−	5.83266e11i	1.80686	−	0.713090i
$952$			8.71387e11i			1.06087i
$953$	−9.36372e11			−1.13521			−0.567606	−	0.823300i	$-0.692130\pi$
$953$	−9.36372e11			−1.13521			−0.567606	+	0.823300i	$0.692130\pi$
$954$	−8.55975e11	+	8.00279e11i	−1.03340	+	0.966158i
$955$		0			0
$956$			1.13752e12i			1.36184i
$957$	1.15336e12	−	4.55182e11i	1.37505	−	0.542672i
$958$		−	9.34140e11i		−	1.10905i
$959$			4.24043e11i			0.501344i
$960$		0			0
$961$	−1.60019e11			−0.187619
$962$	−1.01545e12			−1.18566
$963$	3.86620e11	−	3.61463e11i	0.449551	−	0.420300i
$964$	3.06443e12			3.54848
$965$		0			0
$966$	−1.05008e12	−	2.66075e12i	−1.20591	−	3.05560i
$967$			1.17155e11i			0.133984i	0.997754	+	0.0669921i	$0.0213402\pi$
$967$			1.17155e11i			0.133984i	−0.997754	+	0.0669921i	$0.978660\pi$
$968$	2.01269e12			2.29232
$969$	−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	$-0.0592303\pi$
$972$	6.49079e11	+	2.03567e12i	0.727164	+	2.28057i
$973$		−	1.72284e10i		−	0.0192218i
$974$		−	1.39004e12i		−	1.54452i
$975$		0			0
$976$	1.20334e12			1.32614
$977$	−1.00676e12			−1.10496			−0.552482	−	0.833525i	$-0.686319\pi$
$977$	−1.00676e12			−1.10496			−0.552482	+	0.833525i	$0.686319\pi$
$978$	8.26049e11	+	2.09308e12i	0.902922	+	2.28787i
$979$	−3.79247e11			−0.412849
$980$		0			0
$981$	−1.14404e12	+	1.06960e12i	−1.23528	+	1.15490i
$982$			1.94857e12i			2.09542i
$983$	1.03088e12			1.10406			0.552032	−	0.833823i	$-0.313852\pi$
$983$	1.03088e12			1.10406			0.552032	+	0.833823i	$0.313852\pi$
$984$	6.98439e9	+	1.76974e10i	0.00744986	+	0.0188768i
$985$		0			0
$986$			5.86501e11i			0.620527i
$987$	2.95458e11	+	7.48645e11i	0.311334	+	0.788874i
$988$		−	2.46181e12i		−	2.58361i
$989$		−	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	$0.516535\pi$
$992$	1.51525e12			1.56472
$993$	8.44171e11	−	3.33158e11i	0.868227	−	0.342652i
$994$	5.06959e11			0.519311
$995$		0			0
$996$	−2.16665e12	+	8.55083e11i	−2.20167	+	0.868903i
$997$			1.30987e12i			1.32570i	0.748750	+	0.662852i	$0.230654\pi$
$997$			1.30987e12i			1.32570i	−0.748750	+	0.662852i	$0.769346\pi$
$998$	2.33225e12			2.35100
$999$	−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.d.d.74.2		20
3.2	odd	2	inner	75.9.d.d.74.20		20
5.2	odd	4		75.9.c.f.26.1	yes	10
5.3	odd	4		75.9.c.e.26.10	yes	10
5.4	even	2	inner	75.9.d.d.74.19		20
15.2	even	4		75.9.c.f.26.10	yes	10
15.8	even	4		75.9.c.e.26.1	✓	10
15.14	odd	2	inner	75.9.d.d.74.1		20

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

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-29.4751 q^{2} +(-75.3446 + 29.7353i) q^{3} +612.784 q^{4} +(2220.79 - 876.451i) q^{6} -3164.62i q^{7} -10516.3 q^{8} +(4792.63 - 4480.79i) q^{9} +O(q^{10})\)	\(q-29.4751 q^{2} +(-75.3446 + 29.7353i) q^{3} +612.784 q^{4} +(2220.79 - 876.451i) q^{6} -3164.62i q^{7} -10516.3 q^{8} +(4792.63 - 4480.79i) q^{9} -20143.2i q^{11} +(-46170.0 + 18221.3i) q^{12} -31424.2i q^{13} +93277.7i q^{14} +153096. q^{16} +26183.5 q^{17} +(-141263. + 132072. i) q^{18} +127845. q^{19} +(94100.9 + 238437. i) q^{21} +593723. i q^{22} +378595. q^{23} +(792344. - 312704. i) q^{24} +926234. i q^{26} +(-227861. + 480113. i) q^{27} -1.93923e6i q^{28} -759951. i q^{29} -832390. q^{31} -1.82036e6 q^{32} +(598962. + 1.51768e6i) q^{33} -771762. q^{34} +(2.93685e6 - 2.74575e6i) q^{36} +1.09633e6i q^{37} -3.76824e6 q^{38} +(934408. + 2.36765e6i) q^{39} +22335.5i q^{41} +(-2.77364e6 - 7.02798e6i) q^{42} -4.00943e6i q^{43} -1.23434e7i q^{44} -1.11591e7 q^{46} +3.13980e6 q^{47} +(-1.15349e7 + 4.55234e6i) q^{48} -4.25004e6 q^{49} +(-1.97278e6 + 778572. i) q^{51} -1.92563e7i q^{52} +6.05943e6 q^{53} +(6.71625e6 - 1.41514e7i) q^{54} +3.32800e7i q^{56} +(-9.63242e6 + 3.80150e6i) q^{57} +2.23997e7i q^{58} +1.74124e6i q^{59} +7.86006e6 q^{61} +2.45348e7 q^{62} +(-1.41800e7 - 1.51669e7i) q^{63} +1.44627e7 q^{64} +(-1.76545e7 - 4.47338e7i) q^{66} +9.88860e6i q^{67} +1.60448e7 q^{68} +(-2.85251e7 + 1.12576e7i) q^{69} -5.43494e6i q^{71} +(-5.04006e7 + 4.71211e7i) q^{72} -5.05573e7i q^{73} -3.23144e7i q^{74} +7.83412e7 q^{76} -6.37455e7 q^{77} +(-2.75418e7 - 6.97867e7i) q^{78} +4.35502e7 q^{79} +(2.89185e6 - 4.29495e7i) q^{81} -658341. i q^{82} +4.69277e7 q^{83} +(5.76636e7 + 1.46111e8i) q^{84} +1.18178e8i q^{86} +(2.25973e7 + 5.72582e7i) q^{87} +2.11831e8i q^{88} -1.88276e7i q^{89} -9.94458e7 q^{91} +2.31997e8 q^{92} +(6.27161e7 - 2.47513e7i) q^{93} -9.25460e7 q^{94} +(1.37154e8 - 5.41288e7i) q^{96} +3.52136e7i q^{97} +1.25271e8 q^{98} +(-9.02572e7 - 9.65387e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 3108 q^{4} + 4514 q^{6} + 22414 q^{9}+O(q^{10}) \) 20 * q + 3108 * q^4 + 4514 * q^6 + 22414 * q^9	\( 20 q + 3108 q^{4} + 4514 q^{6} + 22414 q^{9} + 89268 q^{16} + 287868 q^{19} + 1346856 q^{21} + 2033718 q^{24} - 6028120 q^{31} - 9954292 q^{34} + 9001054 q^{36} + 15026564 q^{39} - 27877272 q^{46} - 17907092 q^{49} + 12418574 q^{51} + 17772544 q^{54} + 3040440 q^{61} + 9073996 q^{64} + 20930590 q^{66} - 22789956 q^{69} - 59058092 q^{76} - 17099792 q^{79} + 45225890 q^{81} + 273766584 q^{84} - 214448528 q^{91} - 712237192 q^{94} + 1050848002 q^{96} + 764842670 q^{99}+O(q^{100}) \) 20 * q + 3108 * q^4 + 4514 * q^6 + 22414 * q^9 + 89268 * q^16 + 287868 * q^19 + 1346856 * q^21 + 2033718 * q^24 - 6028120 * q^31 - 9954292 * q^34 + 9001054 * q^36 + 15026564 * q^39 - 27877272 * q^46 - 17907092 * q^49 + 12418574 * q^51 + 17772544 * q^54 + 3040440 * q^61 + 9073996 * q^64 + 20930590 * q^66 - 22789956 * q^69 - 59058092 * q^76 - 17099792 * q^79 + 45225890 * q^81 + 273766584 * q^84 - 214448528 * q^91 - 712237192 * q^94 + 1050848002 * q^96 + 764842670 * q^99

Introduction

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Modular forms

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Database

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