LMFDB - Embedded newform 36.23.d.c.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,23,Mod(19,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 23, names="a")

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

chi := DirichletCharacter("36.19");

S:= CuspForms(chi, 23);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 23 $
Character orbit:	$[\chi]$	$=$	36.d (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:	$110.414676543$
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} - 5 x^{9} - 63342 x^{8} - 45742928 x^{7} + 34835133568 x^{6} + 12622768560288 x^{5} + \cdots + 11\!\cdots\!40 $ x^10 - 5x^9 - 63342x^8 - 45742928x^7 + 34835133568x^6 + 12622768560288x^5 + 13335465927292608x^4 - 404504858109047040x^3 - 95573988251584922880x^2 - 1820809561188275535801600*x + 1168838172864011361183920640
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{90}\cdot 3^{16} $
Twist minimal:	no (minimal twist has level 4)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.4
Root			$407.912 + 251.607i$ of defining polynomial
Character	$\chi$	$=$	36.19
Dual form			36.23.d.c.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1783.65 + 1006.43i) q^{2} +(2.16851e6 - 3.59023e6i) q^{4} -8.57934e7 q^{5} +2.80689e8i q^{7} +(-2.54549e8 + 8.58616e9i) q^{8} +O(q^{10})$	\(q+(-1783.65 + 1006.43i) q^{2} +(2.16851e6 - 3.59023e6i) q^{4} -8.57934e7 q^{5} +2.80689e8i q^{7} +(-2.54549e8 + 8.58616e9i) q^{8} +(1.53025e11 - 8.63449e10i) q^{10} -3.14573e11i q^{11} -8.66330e11 q^{13} +(-2.82493e11 - 5.00651e11i) q^{14} +(-8.18733e12 - 1.55709e13i) q^{16} +3.75137e12 q^{17} +1.33634e14i q^{19} +(-1.86044e14 + 3.08018e14i) q^{20} +(3.16595e14 + 5.61088e14i) q^{22} -6.25471e14i q^{23} +4.97633e15 q^{25} +(1.54523e15 - 8.71899e14i) q^{26} +(1.00774e15 + 6.08676e14i) q^{28} +8.54642e14 q^{29} +1.29693e16i q^{31} +(3.02743e16 + 1.95331e16i) q^{32} +(-6.69114e15 + 3.77549e15i) q^{34} -2.40813e16i q^{35} +7.84749e16 q^{37} +(-1.34493e17 - 2.38356e17i) q^{38} +(2.18386e16 - 7.36636e17i) q^{40} +1.08475e17 q^{41} -5.77743e17i q^{43} +(-1.12939e18 - 6.82154e17i) q^{44} +(6.29492e17 + 1.11562e18i) q^{46} +3.78620e18i q^{47} +3.83103e18 q^{49} +(-8.87602e18 + 5.00831e18i) q^{50} +(-1.87864e18 + 3.11033e18i) q^{52} +1.21175e19 q^{53} +2.69883e19i q^{55} +(-2.41004e18 - 7.14490e16i) q^{56} +(-1.52438e18 + 8.60136e17i) q^{58} +3.48973e19i q^{59} +3.03732e19 q^{61} +(-1.30527e19 - 2.31328e19i) q^{62} +(-7.36574e19 - 4.37119e18i) q^{64} +7.43254e19 q^{65} +9.42821e19i q^{67} +(8.13488e18 - 1.34683e19i) q^{68} +(2.42361e19 + 4.29525e19i) q^{70} -2.75278e20i q^{71} -4.18518e20 q^{73} +(-1.39972e20 + 7.89793e19i) q^{74} +(4.79777e20 + 2.89786e20i) q^{76} +8.82972e19 q^{77} +9.99374e20i q^{79} +(7.02419e20 + 1.33588e21i) q^{80} +(-1.93481e20 + 1.09172e20i) q^{82} +1.27883e20i q^{83} -3.21843e20 q^{85} +(5.81457e20 + 1.03049e21i) q^{86} +(2.70098e21 + 8.00741e19i) q^{88} -5.20354e21 q^{89} -2.43169e20i q^{91} +(-2.24559e21 - 1.35634e21i) q^{92} +(-3.81054e21 - 6.75326e21i) q^{94} -1.14649e22i q^{95} -2.44391e21 q^{97} +(-6.83322e21 + 3.85566e21i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 1540 q^{2} + 2264464 q^{4} + 17091100 q^{5} - 9804431680 q^{8}+O(q^{10}) $ 10 * q - 1540 * q^2 + 2264464 * q^4 + 17091100 * q^5 - 9804431680 * q^8	$ 10 q - 1540 q^{2} + 2264464 q^{4} + 17091100 q^{5} - 9804431680 q^{8} + 159414035240 q^{10} - 531230356540 q^{13} + 5894008940736 q^{14} - 27717620084480 q^{16} - 14058178115540 q^{17} - 233643631625120 q^{20} + 120589650366240 q^{22} + 77\!\cdots\!70 q^{25}+ \cdots + 23\!\cdots\!20 q^{98}+O(q^{100}) $ 10 * q - 1540 * q^2 + 2264464 * q^4 + 17091100 * q^5 - 9804431680 * q^8 + 159414035240 * q^10 - 531230356540 * q^13 + 5894008940736 * q^14 - 27717620084480 * q^16 - 14058178115540 * q^17 - 233643631625120 * q^20 + 120589650366240 * q^22 + 7710175817606670 * q^25 + 3953973318046744 * q^26 + 1177952265288960 * q^28 + 14464474185570172 * q^29 + 73831192092953600 * q^32 - 26625976920357496 * q^34 + 324587767823538020 * q^37 - 369140808808591200 * q^38 - 1158049295468479360 * q^40 + 1355457345814233100 * q^41 + 1919761520625210240 * q^44 + 6132624002565203904 * q^46 + 183553700661552298 * q^49 - 29084394113996178540 * q^50 - 38492433127521128800 * q^52 + 11424344766226018780 * q^53 + 102844865827678657536 * q^56 + 173059696836432320360 * q^58 + 58241718146183220740 * q^61 - 317897221476923285760 * q^62 - 412080172429987966976 * q^64 + 121531695066047433560 * q^65 + 667890522330713878240 * q^68 + 1014396282552321513600 * q^70 + 83030422224875883380 * q^73 - 801906083011176262184 * q^74 + 286747421140990627200 * q^76 + 704201825495570814720 * q^77 - 1509611955050789726720 * q^80 - 2389572513290905036600 * q^82 - 1796890366112110859960 * q^85 + 8221838255181360278496 * q^86 + 11178210842814940531200 * q^88 - 3420669206528505615668 * q^89 - 21476264197983864733440 * q^92 - 20874543047091388369536 * q^94 - 20429910746446196146540 * q^97 + 23110416876469762175420 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$1$

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 $

$2$	−1783.65	+	1006.43i	−0.870923	+	0.491420i
$2$	−1783.65	+	1006.43i	−0.870923	+	0.491420i
$3$		0			0
$3$		0			0
$4$	2.16851e6	−	3.59023e6i	0.517013	−	0.855978i
$5$	−8.57934e7			−1.75705			−0.878525	−	0.477697i	$-0.841472\pi$
$5$	−8.57934e7			−1.75705			−0.878525	+	0.477697i	$0.841472\pi$
$6$		0			0
$7$			2.80689e8i			0.141954i	0.997478	+	0.0709769i	$0.0226117\pi$
$7$			2.80689e8i			0.141954i	−0.997478	+	0.0709769i	$0.977388\pi$
$8$	−2.54549e8	+	8.58616e9i	−0.0296334	+	0.999561i
$9$		0			0
$10$	1.53025e11	−	8.63449e10i	1.53025	−	0.863449i
$11$		−	3.14573e11i		−	1.10256i	−0.834321	−	0.551280i	$-0.814140\pi$
$11$		−	3.14573e11i		−	1.10256i	0.834321	−	0.551280i	$-0.185860\pi$
$12$		0			0
$13$	−8.66330e11			−0.483400			−0.241700	−	0.970351i	$-0.577705\pi$
$13$	−8.66330e11			−0.483400			−0.241700	+	0.970351i	$0.577705\pi$
$14$	−2.82493e11	−	5.00651e11i	−0.0697589	−	0.123631i
$15$		0			0
$16$	−8.18733e12	−	1.55709e13i	−0.465396	−	0.885103i
$17$	3.75137e12			0.109459			0.0547296	−	0.998501i	$-0.482570\pi$
$17$	3.75137e12			0.109459			0.0547296	+	0.998501i	$0.482570\pi$
$18$		0			0
$19$			1.33634e14i			1.14717i	0.819147	+	0.573584i	$0.194447\pi$
$19$			1.33634e14i			1.14717i	−0.819147	+	0.573584i	$0.805553\pi$
$20$	−1.86044e14	+	3.08018e14i	−0.908417	+	1.50400i
$21$		0			0
$22$	3.16595e14	+	5.61088e14i	0.541820	+	0.960244i
$23$		−	6.25471e14i		−	0.656449i	−0.944600	−	0.328225i	$-0.893550\pi$
$23$		−	6.25471e14i		−	0.656449i	0.944600	−	0.328225i	$-0.106450\pi$
$24$		0			0
$25$	4.97633e15			2.08722
$26$	1.54523e15	−	8.71899e14i	0.421004	−	0.237552i
$27$		0			0
$28$	1.00774e15	+	6.08676e14i	0.121509	+	0.0733919i
$29$	8.54642e14			0.0700497			0.0350248	−	0.999386i	$-0.488849\pi$
$29$	8.54642e14			0.0700497			0.0350248	+	0.999386i	$0.488849\pi$
$30$		0			0
$31$			1.29693e16i			0.510433i	0.966884	+	0.255217i	$0.0821468\pi$
$31$			1.29693e16i			0.510433i	−0.966884	+	0.255217i	$0.917853\pi$
$32$	3.02743e16	+	1.95331e16i	0.840281	+	0.542151i
$33$		0			0
$34$	−6.69114e15	+	3.77549e15i	−0.0953305	+	0.0537904i
$35$		−	2.40813e16i		−	0.249420i
$36$		0			0
$37$	7.84749e16			0.441074			0.220537	−	0.975379i	$-0.429219\pi$
$37$	7.84749e16			0.441074			0.220537	+	0.975379i	$0.429219\pi$
$38$	−1.34493e17	−	2.38356e17i	−0.563742	−	0.999095i
$39$		0			0
$40$	2.18386e16	−	7.36636e17i	0.0520673	−	1.75628i
$41$	1.08475e17			0.197109			0.0985545	−	0.995132i	$-0.468578\pi$
$41$	1.08475e17			0.197109			0.0985545	+	0.995132i	$0.468578\pi$
$42$		0			0
$43$		−	5.77743e17i		−	0.621701i	−0.950459	−	0.310851i	$-0.899386\pi$
$43$		−	5.77743e17i		−	0.621701i	0.950459	−	0.310851i	$-0.100614\pi$
$44$	−1.12939e18	−	6.82154e17i	−0.943766	−	0.570037i
$45$		0			0
$46$	6.29492e17	+	1.11562e18i	0.322592	+	0.571716i
$47$			3.78620e18i			1.53154i	0.643116	+	0.765769i	$0.277641\pi$
$47$			3.78620e18i			1.53154i	−0.643116	+	0.765769i	$0.722359\pi$
$48$		0			0
$49$	3.83103e18			0.979849
$50$	−8.87602e18	+	5.00831e18i	−1.81781	+	1.02570i
$51$		0			0
$52$	−1.87864e18	+	3.11033e18i	−0.249924	+	0.413780i
$53$	1.21175e19			1.30731			0.653653	−	0.756795i	$-0.273236\pi$
$53$	1.21175e19			1.30731			0.653653	+	0.756795i	$0.273236\pi$
$54$		0			0
$55$			2.69883e19i			1.93725i
$56$	−2.41004e18	−	7.14490e16i	−0.141891	−	0.00420657i
$57$		0			0
$58$	−1.52438e18	+	8.60136e17i	−0.0610078	+	0.0344238i
$59$			3.48973e19i			1.15723i	0.815600	+	0.578615i	$0.196407\pi$
$59$			3.48973e19i			1.15723i	−0.815600	+	0.578615i	$0.803593\pi$
$60$		0			0
$61$	3.03732e19			0.698010			0.349005	−	0.937121i	$-0.386520\pi$
$61$	3.03732e19			0.698010			0.349005	+	0.937121i	$0.386520\pi$
$62$	−1.30527e19	−	2.31328e19i	−0.250837	−	0.444548i
$63$		0			0
$64$	−7.36574e19	−	4.37119e18i	−0.998244	−	0.0592407i
$65$	7.43254e19			0.849357
$66$		0			0
$67$			9.42821e19i			0.771980i	0.922503	+	0.385990i	$0.126140\pi$
$67$			9.42821e19i			0.771980i	−0.922503	+	0.385990i	$0.873860\pi$
$68$	8.13488e18	−	1.34683e19i	0.0565918	−	0.0936946i
$69$		0			0
$70$	2.42361e19	+	4.29525e19i	0.122570	+	0.217225i
$71$		−	2.75278e20i		−	1.19105i	−0.803337	−	0.595525i	$-0.796944\pi$
$71$		−	2.75278e20i		−	1.19105i	0.803337	−	0.595525i	$-0.203056\pi$
$72$		0			0
$73$	−4.18518e20			−1.33402			−0.667011	−	0.745048i	$-0.732427\pi$
$73$	−4.18518e20			−1.33402			−0.667011	+	0.745048i	$0.732427\pi$
$74$	−1.39972e20	+	7.89793e19i	−0.384141	+	0.216753i
$75$		0			0
$76$	4.79777e20	+	2.89786e20i	0.981951	+	0.593101i
$77$	8.82972e19			0.156512
$78$		0			0
$79$			9.99374e20i			1.33607i	0.744129	+	0.668036i	$0.232865\pi$
$79$			9.99374e20i			1.33607i	−0.744129	+	0.668036i	$0.767135\pi$
$80$	7.02419e20	+	1.33588e21i	0.817724	+	1.55517i
$81$		0			0
$82$	−1.93481e20	+	1.09172e20i	−0.171667	+	0.0968633i
$83$			1.27883e20i			0.0993010i	0.998767	+	0.0496505i	$0.0158108\pi$
$83$			1.27883e20i			0.0993010i	−0.998767	+	0.0496505i	$0.984189\pi$
$84$		0			0
$85$	−3.21843e20			−0.192325
$86$	5.81457e20	+	1.03049e21i	0.305517	+	0.541454i
$87$		0			0
$88$	2.70098e21	+	8.00741e19i	1.10208	+	0.0326725i
$89$	−5.20354e21			−1.87503			−0.937517	−	0.347939i	$-0.886882\pi$
$89$	−5.20354e21			−1.87503			−0.937517	+	0.347939i	$0.886882\pi$
$90$		0			0
$91$		−	2.43169e20i		−	0.0686204i
$92$	−2.24559e21	−	1.35634e21i	−0.561906	−	0.339393i
$93$		0			0
$94$	−3.81054e21	−	6.75326e21i	−0.752628	−	1.33385i
$95$		−	1.14649e22i		−	2.01563i
$96$		0			0
$97$	−2.44391e21			−0.341661			−0.170831	−	0.985300i	$-0.554645\pi$
$97$	−2.44391e21			−0.341661			−0.170831	+	0.985300i	$0.554645\pi$
$98$	−6.83322e21	+	3.85566e21i	−0.853373	+	0.481518i
$99$		0			0
$100$	1.07912e22	−	1.78662e22i	1.07912	−	1.78662i
$101$	1.82886e22			1.63925			0.819625	−	0.572900i	$-0.194182\pi$
$101$	1.82886e22			1.63925			0.819625	+	0.572900i	$0.194182\pi$
$102$		0			0
$103$		−	1.47608e22i		−	1.06635i	−0.846005	−	0.533175i	$-0.820999\pi$
$103$		−	1.47608e22i		−	1.06635i	0.846005	−	0.533175i	$-0.179001\pi$
$104$	2.20523e20	−	7.43845e21i	0.0143248	−	0.483188i
$105$		0			0
$106$	−2.16133e22	+	1.21954e22i	−1.13856	+	0.642436i
$107$		−	1.08643e22i		−	0.516154i	−0.966124	−	0.258077i	$-0.916911\pi$
$107$		−	1.08643e22i		−	0.516154i	0.966124	−	0.258077i	$-0.0830888\pi$
$108$		0			0
$109$	−3.84349e21			−0.148948			−0.0744740	−	0.997223i	$-0.523728\pi$
$109$	−3.84349e21			−0.148948			−0.0744740	+	0.997223i	$0.523728\pi$
$110$	−2.71618e22	−	4.81377e22i	−0.952004	−	1.68720i
$111$		0			0
$112$	4.37058e21	−	2.29809e21i	0.125644	−	0.0660647i
$113$	2.39468e22			0.624288			0.312144	−	0.950035i	$-0.398953\pi$
$113$	2.39468e22			0.624288			0.312144	+	0.950035i	$0.398953\pi$
$114$		0			0
$115$			5.36613e22i			1.15341i
$116$	1.85330e21	−	3.06836e21i	0.0362166	−	0.0599610i
$117$		0			0
$118$	−3.51217e22	−	6.22446e22i	−0.568687	−	1.00786i
$119$			1.05297e21i			0.0155381i
$120$		0			0
$121$	−1.75534e22			−0.215637
$122$	−5.41751e22	+	3.05684e22i	−0.607913	+	0.343016i
$123$		0			0
$124$	4.65629e22	+	2.81241e22i	0.436920	+	0.263901i
$125$	−2.22389e23			−1.91030
$126$		0			0
$127$		−	2.31209e23i		−	1.66787i	−0.551859	−	0.833937i	$-0.686081\pi$
$127$		−	2.31209e23i		−	1.66787i	0.551859	−	0.833937i	$-0.313919\pi$
$128$	1.35778e23	−	6.63342e22i	0.898505	−	0.438963i
$129$		0			0
$130$	−1.32571e23	+	7.48032e22i	−0.739725	+	0.417391i
$131$		−	2.78891e23i		−	1.43038i	−0.698931	−	0.715189i	$-0.746341\pi$
$131$		−	2.78891e23i		−	1.43038i	0.698931	−	0.715189i	$-0.253659\pi$
$132$		0			0
$133$	−3.75096e22			−0.162845
$134$	−9.48881e22	−	1.68166e23i	−0.379367	−	0.672335i
$135$		0			0
$136$	−9.54907e20	+	3.22099e22i	−0.00324364	+	0.109411i
$137$	−3.76004e23			−1.17833			−0.589164	−	0.808014i	$-0.700543\pi$
$137$	−3.76004e23			−1.17833			−0.589164	+	0.808014i	$0.700543\pi$
$138$		0			0
$139$		−	1.58212e23i		−	0.422742i	−0.977406	−	0.211371i	$-0.932207\pi$
$139$		−	1.58212e23i		−	0.422742i	0.977406	−	0.211371i	$-0.0677929\pi$
$140$	−8.64573e22	−	5.22204e22i	−0.213498	−	0.128953i
$141$		0			0
$142$	2.77048e23	+	4.91000e23i	0.585306	+	1.03731i
$143$			2.72524e23i			0.532977i
$144$		0			0
$145$	−7.33226e22			−0.123081
$146$	7.46490e23	−	4.21209e23i	1.16183	−	0.655565i
$147$		0			0
$148$	1.70173e23	−	2.81743e23i	0.228041	−	0.377550i
$149$	−2.83081e23			−0.352259			−0.176129	−	0.984367i	$-0.556358\pi$
$149$	−2.83081e23			−0.352259			−0.176129	+	0.984367i	$0.556358\pi$
$150$		0			0
$151$		−	4.36848e22i		−	0.0469444i	−0.999724	−	0.0234722i	$-0.992528\pi$
$151$		−	4.36848e22i		−	0.0469444i	0.999724	−	0.0234722i	$-0.00747213\pi$
$152$	−1.14740e24	−	3.40163e22i	−1.14666	−	0.0339944i
$153$		0			0
$154$	−1.57491e23	+	8.88648e22i	−0.136310	+	0.0769134i
$155$		−	1.11268e24i		−	0.896857i
$156$		0			0
$157$	4.00138e22			0.0280100			0.0140050	−	0.999902i	$-0.495542\pi$
$157$	4.00138e22			0.0280100			0.0140050	+	0.999902i	$0.495542\pi$
$158$	−1.00580e24	−	1.78253e24i	−0.656573	−	1.16362i
$159$		0			0
$160$	−2.59734e24	−	1.67581e24i	−1.47642	−	0.952586i
$161$	1.75563e23			0.0931854
$162$		0			0
$163$		−	1.75209e24i		−	0.811883i	−0.913899	−	0.405941i	$-0.866944\pi$
$163$		−	1.75209e24i		−	0.811883i	0.913899	−	0.405941i	$-0.133056\pi$
$164$	2.35228e23	−	3.89449e23i	0.101908	−	0.168721i
$165$		0			0
$166$	−1.28705e23	−	2.28098e23i	−0.0487985	−	0.0864835i
$167$		−	6.61040e23i		−	0.234610i	−0.993096	−	0.117305i	$-0.962574\pi$
$167$		−	6.61040e23i		−	0.234610i	0.993096	−	0.117305i	$-0.0374255\pi$
$168$		0			0
$169$	−2.46131e24			−0.766325
$170$	5.74056e23	−	3.23912e23i	0.167500	−	0.0945125i
$171$		0			0
$172$	−2.07423e24	−	1.25284e24i	−0.532163	−	0.321427i
$173$	4.58679e24			1.10408			0.552041	−	0.833817i	$-0.313849\pi$
$173$	4.58679e24			1.10408			0.552041	+	0.833817i	$0.313849\pi$
$174$		0			0
$175$			1.39680e24i			0.296289i
$176$	−4.89818e24	+	2.57551e24i	−0.975878	+	0.513127i
$177$		0			0
$178$	9.28130e24	−	5.23699e24i	1.63301	−	0.921430i
$179$		−	5.77013e24i		−	0.954557i	−0.878752	−	0.477279i	$-0.841623\pi$
$179$		−	5.77013e24i		−	0.954557i	0.878752	−	0.477279i	$-0.158377\pi$
$180$		0			0
$181$	2.20708e24			0.323112			0.161556	−	0.986864i	$-0.448349\pi$
$181$	2.20708e24			0.323112			0.161556	+	0.986864i	$0.448349\pi$
$182$	2.44733e23	+	4.33729e23i	0.0337215	+	0.0597631i
$183$		0			0
$184$	5.37040e24	+	1.59213e23i	0.656161	+	0.0194528i
$185$	−6.73263e24			−0.774989
$186$		0			0
$187$		−	1.18008e24i		−	0.120685i
$188$	1.35933e25	+	8.21041e24i	1.31096	+	0.791824i
$189$		0			0
$190$	1.15386e25	+	2.04494e25i	0.990522	+	1.75546i
$191$			8.70625e24i			0.705446i	0.935728	+	0.352723i	$0.114744\pi$
$191$			8.70625e24i			0.705446i	−0.935728	+	0.352723i	$0.885256\pi$
$192$		0			0
$193$	−1.26103e25			−0.911162			−0.455581	−	0.890194i	$-0.650568\pi$
$193$	−1.26103e25			−0.911162			−0.455581	+	0.890194i	$0.650568\pi$
$194$	4.35908e24	−	2.45962e24i	0.297561	−	0.167899i
$195$		0			0
$196$	8.30763e24	−	1.37543e25i	0.506594	−	0.838729i
$197$	−1.67517e25			−0.965897			−0.482949	−	0.875649i	$-0.660434\pi$
$197$	−1.67517e25			−0.965897			−0.482949	+	0.875649i	$0.660434\pi$
$198$		0			0
$199$			1.44695e25i			0.746570i	0.927717	+	0.373285i	$0.121769\pi$
$199$			1.44695e25i			0.746570i	−0.927717	+	0.373285i	$0.878231\pi$
$200$	−1.26672e24	+	4.27275e25i	−0.0618514	+	2.08631i
$201$		0			0
$202$	−3.26205e25	+	1.84062e25i	−1.42766	+	0.805561i
$203$			2.39888e23i			0.00994381i
$204$		0			0
$205$	−9.30642e24			−0.346330
$206$	1.48557e25	+	2.63280e25i	0.524026	+	0.928708i
$207$		0			0
$208$	7.09293e24	+	1.34895e25i	0.224972	+	0.427859i
$209$	4.20376e25			1.26482
$210$		0			0
$211$			7.78670e23i			0.0210983i	0.999944	+	0.0105491i	$0.00335795\pi$
$211$			7.78670e23i			0.0210983i	−0.999944	+	0.0105491i	$0.996642\pi$
$212$	2.62768e25	−	4.35045e25i	0.675893	−	1.11902i
$213$		0			0
$214$	1.09341e25	+	1.93781e25i	0.253648	+	0.449530i
$215$			4.95666e25i			1.09236i
$216$		0			0
$217$	−3.64035e24			−0.0724579
$218$	6.85545e24	−	3.86820e24i	0.129722	−	0.0731961i
$219$		0			0
$220$	9.68942e25	+	5.85243e25i	1.65824	+	1.00158i
$221$	−3.24993e24			−0.0529126
$222$		0			0
$223$			4.07489e25i			0.600845i	0.953806	+	0.300422i	$0.0971276\pi$
$223$			4.07489e25i			0.600845i	−0.953806	+	0.300422i	$0.902872\pi$
$224$	−5.48271e24	+	8.49767e24i	−0.0769604	+	0.119281i
$225$		0			0
$226$	−4.27127e25	+	2.41007e25i	−0.543706	+	0.306787i
$227$			1.44325e26i			1.75008i	0.484055	+	0.875038i	$0.339164\pi$
$227$			1.44325e26i			1.75008i	−0.484055	+	0.875038i	$0.660836\pi$
$228$		0			0
$229$	2.44064e25			0.268729			0.134364	−	0.990932i	$-0.457101\pi$
$229$	2.44064e25			0.268729			0.134364	+	0.990932i	$0.457101\pi$
$230$	−5.40063e25	−	9.57130e25i	−0.566811	−	1.00453i
$231$		0			0
$232$	−2.17548e23	+	7.33809e24i	−0.00207581	+	0.0700189i
$233$	5.11004e25			0.465060			0.232530	−	0.972589i	$-0.425300\pi$
$233$	5.11004e25			0.465060			0.232530	+	0.972589i	$0.425300\pi$
$234$		0			0
$235$		−	3.24831e26i		−	2.69099i
$236$	1.25289e26	+	7.56751e25i	0.990564	+	0.598303i
$237$		0			0
$238$	−1.05974e24	−	1.87813e24i	−0.00763576	−	0.0135325i
$239$		−	2.84734e26i		−	1.95912i	−0.201141	−	0.979562i	$-0.564465\pi$
$239$		−	2.84734e26i		−	1.95912i	0.201141	−	0.979562i	$-0.435535\pi$
$240$		0			0
$241$	−1.87072e26			−1.17441			−0.587206	−	0.809438i	$-0.699772\pi$
$241$	−1.87072e26			−1.17441			−0.587206	+	0.809438i	$0.699772\pi$
$242$	3.13092e25	−	1.76663e25i	0.187803	−	0.105968i
$243$		0			0
$244$	6.58644e25	−	1.09047e26i	0.360880	−	0.597481i
$245$	−3.28678e26			−1.72164
$246$		0			0
$247$		−	1.15771e26i		−	0.554541i
$248$	−1.11357e26	−	3.30133e24i	−0.510209	−	0.0151259i
$249$		0			0
$250$	3.96663e26	−	2.23818e26i	1.66373	−	0.938761i
$251$		−	1.85043e26i		−	0.742782i	−0.928477	−	0.371391i	$-0.878881\pi$
$251$		−	1.85043e26i		−	0.742782i	0.928477	−	0.371391i	$-0.121119\pi$
$252$		0			0
$253$	−1.96756e26			−0.723774
$254$	2.32695e26	+	4.12396e26i	0.819627	+	1.45259i
$255$		0			0
$256$	−1.75420e26	+	2.54968e26i	−0.566813	+	0.823846i
$257$	−5.48207e26			−1.69699			−0.848497	−	0.529201i	$-0.822492\pi$
$257$	−5.48207e26			−1.69699			−0.848497	+	0.529201i	$0.822492\pi$
$258$		0			0
$259$			2.20270e25i			0.0626121i
$260$	1.61175e26	−	2.66845e26i	0.439129	−	0.727031i
$261$		0			0
$262$	2.80684e26	+	4.97444e26i	0.702916	+	1.24575i
$263$			8.51401e24i			0.0204466i	0.999948	+	0.0102233i	$0.00325423\pi$
$263$			8.51401e24i			0.0204466i	−0.999948	+	0.0102233i	$0.996746\pi$
$264$		0			0
$265$	−1.03960e27			−2.29700
$266$	6.69039e25	−	3.77507e25i	0.141825	−	0.0800252i
$267$		0			0
$268$	3.38494e26	+	2.04451e26i	0.660798	+	0.399124i
$269$	−7.78681e24			−0.0145910			−0.00729549	−	0.999973i	$-0.502322\pi$
$269$	−7.78681e24			−0.0145910			−0.00729549	+	0.999973i	$0.502322\pi$
$270$		0			0
$271$		−	2.88467e26i		−	0.498234i	−0.968473	−	0.249117i	$-0.919860\pi$
$271$		−	2.88467e26i		−	0.498234i	0.968473	−	0.249117i	$-0.0801404\pi$
$272$	−3.07137e25	−	5.84122e25i	−0.0509419	−	0.0968826i
$273$		0			0
$274$	6.70659e26	−	3.78421e26i	1.02623	−	0.579054i
$275$		−	1.56542e27i		−	2.30129i
$276$		0			0
$277$	−3.96390e26			−0.538078			−0.269039	−	0.963129i	$-0.586706\pi$
$277$	−3.96390e26			−0.538078			−0.269039	+	0.963129i	$0.586706\pi$
$278$	1.59229e26	+	2.82194e26i	0.207744	+	0.368176i
$279$		0			0
$280$	2.06766e26	+	6.12985e24i	0.249310	+	0.00739114i
$281$	1.00095e27			1.16049			0.580247	−	0.814440i	$-0.302956\pi$
$281$	1.00095e27			1.16049			0.580247	+	0.814440i	$0.302956\pi$
$282$		0			0
$283$			9.65777e26i			1.03568i	0.855477	+	0.517840i	$0.173264\pi$
$283$			9.65777e26i			1.03568i	−0.855477	+	0.517840i	$0.826736\pi$
$284$	−9.88313e26	−	5.96943e26i	−1.01951	−	0.615788i
$285$		0			0
$286$	−2.74276e26	−	4.86088e26i	−0.261916	−	0.464182i
$287$			3.04477e25i			0.0279804i
$288$		0			0
$289$	−1.16049e27			−0.988019
$290$	1.30782e26	−	7.37940e25i	0.107194	−	0.0604843i
$291$		0			0
$292$	−9.07561e26	+	1.50258e27i	−0.689706	+	1.14189i
$293$	−1.47998e27			−1.08321			−0.541605	−	0.840633i	$-0.682183\pi$
$293$	−1.47998e27			−1.08321			−0.541605	+	0.840633i	$0.682183\pi$
$294$		0			0
$295$		−	2.99396e27i		−	2.03331i
$296$	−1.99757e25	+	6.73798e26i	−0.0130705	+	0.440880i
$297$		0			0
$298$	5.04918e26	−	2.84901e26i	0.306790	−	0.173107i
$299$			5.41865e26i			0.317327i
$300$		0			0
$301$	1.62166e26			0.0882528
$302$	4.39656e25	+	7.79184e25i	0.0230694	+	0.0408850i
$303$		0			0
$304$	2.08080e27	−	1.09411e27i	1.01536	−	0.533887i
$305$	−2.60582e27			−1.22644
$306$		0			0
$307$		−	6.27649e24i		−	0.00274913i	−0.999999	−	0.00137456i	$-0.999562\pi$
$307$		−	6.27649e24i		−	0.00274913i	0.999999	−	0.00137456i	$-0.000437537\pi$
$308$	1.91473e26	−	3.17007e26i	0.0809189	−	0.133971i
$309$		0			0
$310$	1.11984e27	+	1.98464e27i	0.440733	+	0.781093i
$311$			1.91039e27i			0.725703i	0.931847	+	0.362851i	$0.118197\pi$
$311$			1.91039e27i			0.725703i	−0.931847	+	0.362851i	$0.881803\pi$
$312$		0			0
$313$	−3.82065e26			−0.135254			−0.0676268	−	0.997711i	$-0.521543\pi$
$313$	−3.82065e26			−0.135254			−0.0676268	+	0.997711i	$0.521543\pi$
$314$	−7.13706e25	+	4.02710e25i	−0.0243946	+	0.0137647i
$315$		0			0
$316$	3.58798e27	+	2.16715e27i	1.14365	+	0.690767i
$317$	3.27599e26			0.100854			0.0504268	−	0.998728i	$-0.483942\pi$
$317$	3.27599e26			0.100854			0.0504268	+	0.998728i	$0.483942\pi$
$318$		0			0
$319$		−	2.68847e26i		−	0.0772339i
$320$	6.31932e27	+	3.75019e26i	1.75396	+	0.104089i
$321$		0			0
$322$	−3.13143e26	+	1.76691e26i	−0.0811573	+	0.0457932i
$323$			5.01311e26i			0.125568i
$324$		0			0
$325$	−4.31114e27			−1.00896
$326$	1.76336e27	+	3.12512e27i	0.398976	+	0.707087i
$327$		0			0
$328$	−2.76121e25	+	9.31382e26i	−0.00584100	+	0.197022i
$329$	−1.06275e27			−0.217407
$330$		0			0
$331$		−	1.01525e28i		−	1.94296i	−0.237113	−	0.971482i	$-0.576201\pi$
$331$		−	1.01525e28i		−	1.94296i	0.237113	−	0.971482i	$-0.423799\pi$
$332$	4.59129e26	+	2.77315e26i	0.0849995	+	0.0513399i
$333$		0			0
$334$	6.65290e26	+	1.17906e27i	0.115292	+	0.204327i
$335$		−	8.08878e27i		−	1.35641i
$336$		0			0
$337$	−4.94241e27			−0.776265			−0.388132	−	0.921604i	$-0.626880\pi$
$337$	−4.94241e27			−0.776265			−0.388132	+	0.921604i	$0.626880\pi$
$338$	4.39012e27	−	2.47713e27i	0.667409	−	0.376587i
$339$		0			0
$340$	−6.97920e26	+	1.15549e27i	−0.0994345	+	0.164626i
$341$	4.07980e27			0.562783
$342$		0			0
$343$			2.17277e27i			0.281047i
$344$	4.96060e27	+	1.47064e26i	0.621428	+	0.0184231i
$345$		0			0
$346$	−8.18122e27	+	4.61627e27i	−0.961571	+	0.542568i
$347$			1.36988e28i			1.55977i	0.625926	+	0.779883i	$0.284721\pi$
$347$			1.36988e28i			1.55977i	−0.625926	+	0.779883i	$0.715279\pi$
$348$		0			0
$349$	1.40195e28			1.49849			0.749244	−	0.662295i	$-0.230417\pi$
$349$	1.40195e28			1.49849			0.749244	+	0.662295i	$0.230417\pi$
$350$	−1.40578e27	−	2.49140e27i	−0.145602	−	0.258045i
$351$		0			0
$352$	6.14457e27	−	9.52348e27i	0.597754	−	0.926460i
$353$	−8.46104e27			−0.797814			−0.398907	−	0.916991i	$-0.630610\pi$
$353$	−8.46104e27			−0.797814			−0.398907	+	0.916991i	$0.630610\pi$
$354$		0			0
$355$			2.36171e28i			2.09273i
$356$	−1.12839e28	+	1.86819e28i	−0.969416	+	1.60499i
$357$		0			0
$358$	5.80722e27	+	1.02919e28i	0.469089	+	0.831346i
$359$			1.04685e28i			0.820057i	0.912073	+	0.410028i	$0.134481\pi$
$359$			1.04685e28i			0.820057i	−0.912073	+	0.410028i	$0.865519\pi$
$360$		0			0
$361$	−4.28805e27			−0.315995
$362$	−3.93666e27	+	2.22127e27i	−0.281406	+	0.158784i
$363$		0			0
$364$	−8.73034e26	−	5.27315e26i	−0.0587376	−	0.0354776i
$365$	3.59061e28			2.34394
$366$		0			0
$367$			2.54112e28i			1.56206i	0.624492	+	0.781031i	$0.285306\pi$
$367$			2.54112e28i			1.56206i	−0.624492	+	0.781031i	$0.714694\pi$
$368$	−9.73914e27	+	5.12094e27i	−0.581025	+	0.305509i
$369$		0			0
$370$	1.20086e28	−	6.77591e27i	0.674955	−	0.380845i
$371$			3.40124e27i			0.185577i
$372$		0			0
$373$	2.29802e28			1.18183			0.590917	−	0.806733i	$-0.298766\pi$
$373$	2.29802e28			1.18183			0.590917	+	0.806733i	$0.298766\pi$
$374$	1.18767e27	+	2.10485e27i	0.0593071	+	0.105108i
$375$		0			0
$376$	−3.25090e28	−	9.63773e26i	−1.53086	−	0.0453846i
$377$	−7.40402e26			−0.0338620
$378$		0			0
$379$		−	2.30104e28i		−	0.992872i	−0.868073	−	0.496436i	$-0.834642\pi$
$379$		−	2.30104e28i		−	0.992872i	0.868073	−	0.496436i	$-0.165358\pi$
$380$	−4.11617e28	−	2.48618e28i	−1.72534	−	1.04211i
$381$		0			0
$382$	−8.76222e27	−	1.55289e28i	−0.346671	−	0.614389i
$383$			2.48176e27i			0.0954053i	0.998862	+	0.0477027i	$0.0151900\pi$
$383$			2.48176e27i			0.0954053i	−0.998862	+	0.0477027i	$0.984810\pi$
$384$		0			0
$385$	−7.57532e27			−0.275000
$386$	2.24924e28	−	1.26914e28i	0.793552	−	0.447763i
$387$		0			0
$388$	−5.29963e27	+	8.77419e27i	−0.176643	+	0.292454i
$389$	−8.25579e27			−0.267493			−0.133747	−	0.991016i	$-0.542701\pi$
$389$	−8.25579e27			−0.267493			−0.133747	+	0.991016i	$0.542701\pi$
$390$		0			0
$391$		−	2.34638e27i		−	0.0718544i
$392$	−9.75184e26	+	3.28939e28i	−0.0290362	+	0.979419i
$393$		0			0
$394$	2.98792e28	−	1.68594e28i	0.841222	−	0.474661i
$395$		−	8.57397e28i		−	2.34755i
$396$		0			0
$397$	−1.00296e28			−0.259771			−0.129885	−	0.991529i	$-0.541461\pi$
$397$	−1.00296e28			−0.259771			−0.129885	+	0.991529i	$0.541461\pi$
$398$	−1.45625e28	−	2.58086e28i	−0.366879	−	0.650204i
$399$		0			0
$400$	−4.07428e28	−	7.74858e28i	−0.971385	−	1.84741i
$401$	−3.46650e28			−0.804088			−0.402044	−	0.915620i	$-0.631700\pi$
$401$	−3.46650e28			−0.804088			−0.402044	+	0.915620i	$0.631700\pi$
$402$		0			0
$403$		−	1.12357e28i		−	0.246743i
$404$	3.96590e28	−	6.56603e28i	0.847513	−	1.40316i
$405$		0			0
$406$	−2.41431e26	−	4.27877e26i	−0.00488659	−	0.00866029i
$407$		−	2.46861e28i		−	0.486310i
$408$		0			0
$409$	4.91690e28			0.917773			0.458887	−	0.888495i	$-0.348248\pi$
$409$	4.91690e28			0.917773			0.458887	+	0.888495i	$0.348248\pi$
$410$	1.65994e28	−	9.36625e27i	0.301627	−	0.170194i
$411$		0			0
$412$	−5.29946e28	−	3.20089e28i	−0.912772	−	0.551316i
$413$	−9.79530e27			−0.164273
$414$		0			0
$415$		−	1.09715e28i		−	0.174477i
$416$	−2.62276e28	−	1.69221e28i	−0.406192	−	0.262076i
$417$		0			0
$418$	−7.49804e28	+	4.23079e28i	−1.10156	+	0.621558i
$419$			6.76307e28i			0.967810i	0.875121	+	0.483905i	$0.160782\pi$
$419$			6.76307e28i			0.967810i	−0.875121	+	0.483905i	$0.839218\pi$
$420$		0			0
$421$	9.52059e28			1.29289			0.646444	−	0.762961i	$-0.276255\pi$
$421$	9.52059e28			1.29289			0.646444	+	0.762961i	$0.276255\pi$
$422$	−7.83676e26	−	1.38887e27i	−0.0103681	−	0.0183749i
$423$		0			0
$424$	−3.08448e27	+	1.04042e29i	−0.0387398	+	1.30673i
$425$	1.86681e28			0.228466
$426$		0			0
$427$			8.52541e27i			0.0990852i
$428$	−3.90052e28	−	2.35593e28i	−0.441816	−	0.266858i
$429$		0			0
$430$	−4.98852e28	−	8.84094e28i	−0.536808	−	0.951361i
$431$			8.12075e28i			0.851817i	0.904766	+	0.425909i	$0.140045\pi$
$431$			8.12075e28i			0.851817i	−0.904766	+	0.425909i	$0.859955\pi$
$432$		0			0
$433$	−1.24571e29			−1.24180			−0.620900	−	0.783890i	$-0.713233\pi$
$433$	−1.24571e29			−1.24180			−0.620900	+	0.783890i	$0.713233\pi$
$434$	6.49311e27	−	3.66375e27i	0.0631053	−	0.0356073i
$435$		0			0
$436$	−8.33465e27	+	1.37990e28i	−0.0770080	+	0.127496i
$437$	8.35842e28			0.753058
$438$		0			0
$439$			4.66769e28i			0.399937i	0.979802	+	0.199969i	$0.0640840\pi$
$439$			4.66769e28i			0.399937i	−0.979802	+	0.199969i	$0.935916\pi$
$440$	−2.31726e29	−	6.86983e27i	−1.93640	−	0.0574072i
$441$		0			0
$442$	5.79673e27	−	3.27082e27i	0.0460827	−	0.0260023i
$443$			3.78978e28i			0.293882i	0.989145	+	0.146941i	$0.0469427\pi$
$443$			3.78978e28i			0.293882i	−0.989145	+	0.146941i	$0.953057\pi$
$444$		0			0
$445$	4.46430e29			3.29453
$446$	−4.10108e28	−	7.26817e28i	−0.295267	−	0.523289i
$447$		0			0
$448$	1.22694e27	−	2.06748e28i	0.00840944	−	0.141704i
$449$	3.23098e28			0.216085			0.108042	−	0.994146i	$-0.465542\pi$
$449$	3.23098e28			0.216085			0.108042	+	0.994146i	$0.465542\pi$
$450$		0			0
$451$		−	3.41232e28i		−	0.217324i
$452$	5.19288e28	−	8.59746e28i	0.322765	−	0.534376i
$453$		0			0
$454$	−1.45253e29	−	2.57425e29i	−0.860022	−	1.52418i
$455$			2.08623e28i			0.120569i
$456$		0			0
$457$	−1.33674e29			−0.736153			−0.368077	−	0.929796i	$-0.619984\pi$
$457$	−1.33674e29			−0.736153			−0.368077	+	0.929796i	$0.619984\pi$
$458$	−4.35325e28	+	2.45633e28i	−0.234042	+	0.132059i
$459$		0			0
$460$	1.92657e29	+	1.16365e29i	0.987296	+	0.596329i
$461$	1.95249e29			0.976966			0.488483	−	0.872574i	$-0.337551\pi$
$461$	1.95249e29			0.976966			0.488483	+	0.872574i	$0.337551\pi$
$462$		0			0
$463$			1.90763e29i			0.910129i	0.890458	+	0.455064i	$0.150384\pi$
$463$			1.90763e29i			0.910129i	−0.890458	+	0.455064i	$0.849616\pi$
$464$	−6.99723e27	−	1.33075e28i	−0.0326008	−	0.0620011i
$465$		0			0
$466$	−9.11452e28	+	5.14289e28i	−0.405031	+	0.228540i
$467$			1.72854e29i			0.750229i	0.926978	+	0.375114i	$0.122397\pi$
$467$			1.72854e29i			0.750229i	−0.926978	+	0.375114i	$0.877603\pi$
$468$		0			0
$469$	−2.64639e28			−0.109586
$470$	3.26920e29	+	5.79385e29i	1.32240	+	2.34364i
$471$		0			0
$472$	−2.99634e29	−	8.88306e27i	−1.15672	−	0.0342926i
$473$	−1.81742e29			−0.685463
$474$		0			0
$475$			6.65006e29i			2.39440i
$476$	3.78040e27	+	2.28337e27i	0.0133003	+	0.00803342i
$477$		0			0
$478$	2.86564e29	+	5.07865e29i	0.962753	+	1.70625i
$479$			3.61418e28i			0.118664i	0.998238	+	0.0593320i	$0.0188971\pi$
$479$			3.61418e28i			0.118664i	−0.998238	+	0.0593320i	$0.981103\pi$
$480$		0			0
$481$	−6.79851e28			−0.213215
$482$	3.33670e29	−	1.88274e29i	1.02282	−	0.577129i
$483$		0			0
$484$	−3.80648e28	+	6.30209e28i	−0.111487	+	0.184580i
$485$	2.09671e29			0.600316
$486$		0			0
$487$		−	4.99770e29i		−	1.36758i	−0.729680	−	0.683788i	$-0.760331\pi$
$487$		−	4.99770e29i		−	1.36758i	0.729680	−	0.683788i	$-0.239669\pi$
$488$	−7.73144e27	+	2.60789e29i	−0.0206844	+	0.697704i
$489$		0			0
$490$	5.86246e29	−	3.30790e29i	1.49942	−	0.846050i
$491$		−	2.47728e29i		−	0.619552i	−0.950810	−	0.309776i	$-0.899746\pi$
$491$		−	2.47728e29i		−	0.619552i	0.950810	−	0.309776i	$-0.100254\pi$
$492$		0			0
$493$	3.20608e27			0.00766758
$494$	1.16515e29	+	2.06495e29i	0.272513	+	0.482962i
$495$		0			0
$496$	2.01944e29	−	1.06184e29i	0.451786	−	0.237554i
$497$	7.72676e28			0.169074
$498$		0			0
$499$		−	3.25496e29i		−	0.681459i	−0.940161	−	0.340729i	$-0.889326\pi$
$499$		−	3.25496e29i		−	0.681459i	0.940161	−	0.340729i	$-0.110674\pi$
$500$	−4.82251e29	+	7.98426e29i	−0.987651	+	1.63518i
$501$		0			0
$502$	1.86232e29	+	3.30052e29i	0.365018	+	0.646906i
$503$		−	8.60359e29i		−	1.64980i	−0.565277	−	0.824901i	$-0.691231\pi$
$503$		−	8.60359e29i		−	1.64980i	0.565277	−	0.824901i	$-0.308769\pi$
$504$		0			0
$505$	−1.56904e30			−2.88024
$506$	3.50944e29	−	1.98021e29i	0.630351	−	0.355677i
$507$		0			0
$508$	−8.30093e29	−	5.01378e29i	−1.42766	−	0.862312i
$509$	−5.03542e29			−0.847500			−0.423750	−	0.905779i	$-0.639287\pi$
$509$	−5.03542e29			−0.847500			−0.423750	+	0.905779i	$0.639287\pi$
$510$		0			0
$511$		−	1.17473e29i		−	0.189369i
$512$	5.62811e28	−	6.31322e29i	0.0887960	−	0.996050i
$513$		0			0
$514$	9.77809e29	−	5.51731e29i	1.47795	−	0.833937i
$515$			1.26638e30i			1.87363i
$516$		0			0
$517$	1.19104e30			1.68861
$518$	−2.21686e28	−	3.92885e28i	−0.0307689	−	0.0545303i
$519$		0			0
$520$	−1.89194e28	+	6.38170e29i	−0.0251693	+	0.848984i
$521$	−2.77421e29			−0.361348			−0.180674	−	0.983543i	$-0.557828\pi$
$521$	−2.77421e29			−0.361348			−0.180674	+	0.983543i	$0.557828\pi$
$522$		0			0
$523$		−	1.12615e30i		−	1.40630i	−0.711041	−	0.703151i	$-0.751776\pi$
$523$		−	1.12615e30i		−	1.40630i	0.711041	−	0.703151i	$-0.248224\pi$
$524$	−1.00128e30	−	6.04778e29i	−1.22437	−	0.739523i
$525$		0			0
$526$	−8.56874e27	−	1.51860e28i	−0.0100479	−	0.0178074i
$527$			4.86528e28i			0.0558716i
$528$		0			0
$529$	5.16632e29			0.569074
$530$	1.85428e30	−	1.04628e30i	2.00051	−	1.12879i
$531$		0			0
$532$	−8.13398e28	+	1.34668e29i	−0.0841929	+	0.139392i
$533$	−9.39750e28			−0.0952824
$534$		0			0
$535$			9.32083e29i			0.906907i
$536$	−8.09521e29	−	2.39994e28i	−0.771641	−	0.0228764i
$537$		0			0
$538$	1.38889e28	−	7.83687e27i	0.0127076	−	0.00717030i
$539$		−	1.20514e30i		−	1.08034i
$540$		0			0
$541$	−1.55221e30			−1.33592			−0.667961	−	0.744196i	$-0.732833\pi$
$541$	−1.55221e30			−1.33592			−0.667961	+	0.744196i	$0.732833\pi$
$542$	2.90321e29	+	5.14523e29i	0.244842	+	0.433923i
$543$		0			0
$544$	1.13570e29	+	7.32758e28i	0.0919765	+	0.0593434i
$545$	3.29747e29			0.261709
$546$		0			0
$547$		−	1.63115e30i		−	1.24346i	−0.783231	−	0.621730i	$-0.786430\pi$
$547$		−	1.63115e30i		−	1.24346i	0.783231	−	0.621730i	$-0.213570\pi$
$548$	−8.15367e29	+	1.34994e30i	−0.609210	+	1.00862i
$549$		0			0
$550$	1.57548e30	+	2.79216e30i	1.13090	+	2.00424i
$551$			1.14209e29i			0.0803588i
$552$		0			0
$553$	−2.80513e29			−0.189661
$554$	7.07020e29	−	3.98938e29i	0.468624	−	0.264422i
$555$		0			0
$556$	−5.68016e29	−	3.43083e29i	−0.361858	−	0.218563i
$557$	−8.52258e29			−0.532309			−0.266155	−	0.963930i	$-0.585753\pi$
$557$	−8.52258e29			−0.532309			−0.266155	+	0.963930i	$0.585753\pi$
$558$		0			0
$559$			5.00516e29i			0.300530i
$560$	−3.74967e29	+	1.97161e29i	−0.220762	+	0.116079i
$561$		0			0
$562$	−1.78535e30	+	1.00739e30i	−1.01070	+	0.570290i
$563$			1.42628e30i			0.791795i	0.918295	+	0.395898i	$0.129566\pi$
$563$			1.42628e30i			0.791795i	−0.918295	+	0.395898i	$0.870434\pi$
$564$		0			0
$565$	−2.05448e30			−1.09690
$566$	−9.71985e29	−	1.72261e30i	−0.508954	−	0.901998i
$567$		0			0
$568$	2.36358e30	+	7.00717e28i	1.19053	+	0.0352948i
$569$	−3.71992e30			−1.83780			−0.918900	−	0.394491i	$-0.870921\pi$
$569$	−3.71992e30			−1.83780			−0.918900	+	0.394491i	$0.870921\pi$
$570$		0			0
$571$		−	2.41058e29i		−	0.114584i	−0.998357	−	0.0572920i	$-0.981753\pi$
$571$		−	2.41058e29i		−	0.114584i	0.998357	−	0.0572920i	$-0.0182466\pi$
$572$	9.78425e29	+	5.90971e29i	0.456217	+	0.275556i
$573$		0			0
$574$	−3.06434e28	−	5.43080e28i	−0.0137501	−	0.0243687i
$575$		−	3.11255e30i		−	1.37016i
$576$		0			0
$577$	−3.06040e30			−1.29671			−0.648356	−	0.761337i	$-0.724543\pi$
$577$	−3.06040e30			−1.29671			−0.648356	+	0.761337i	$0.724543\pi$
$578$	2.06991e30	−	1.16795e30i	0.860488	−	0.485532i
$579$		0			0
$580$	−1.59001e29	+	2.63245e29i	−0.0636343	+	0.105354i
$581$	−3.58953e28			−0.0140962
$582$		0			0
$583$		−	3.81183e30i		−	1.44138i
$584$	1.06533e29	−	3.59347e30i	0.0395316	−	1.33344i
$585$		0			0
$586$	2.63977e30	−	1.48950e30i	0.943392	−	0.532311i
$587$		−	5.23600e30i		−	1.83646i	−0.396053	−	0.918228i	$-0.629620\pi$
$587$		−	5.23600e30i		−	1.83646i	0.396053	−	0.918228i	$-0.370380\pi$
$588$		0			0
$589$	−1.73314e30			−0.585553
$590$	3.01321e30	+	5.34018e30i	0.999210	+	1.77086i
$591$		0			0
$592$	−6.42500e29	−	1.22192e30i	−0.205274	−	0.390396i
$593$	−5.59907e29			−0.175596			−0.0877980	−	0.996138i	$-0.527983\pi$
$593$	−5.59907e29			−0.175596			−0.0877980	+	0.996138i	$0.527983\pi$
$594$		0			0
$595$		−	9.03378e28i		−	0.0273013i
$596$	−6.13864e29	+	1.01633e30i	−0.182122	+	0.301526i
$597$		0			0
$598$	−5.45348e29	−	9.66497e29i	−0.155941	−	0.276368i
$599$			4.68629e30i			1.31563i	0.753179	+	0.657816i	$0.228519\pi$
$599$			4.68629e30i			1.31563i	−0.753179	+	0.657816i	$0.771481\pi$
$600$		0			0
$601$	5.27119e30			1.42656			0.713279	−	0.700880i	$-0.247209\pi$
$601$	5.27119e30			1.42656			0.713279	+	0.700880i	$0.247209\pi$
$602$	−2.89248e29	+	1.63209e29i	−0.0768614	+	0.0433692i
$603$		0			0
$604$	−1.56839e29	−	9.47309e28i	−0.0401834	−	0.0242709i
$605$	1.50597e30			0.378885
$606$		0			0
$607$			6.32056e30i			1.53349i	0.641954	+	0.766743i	$0.278124\pi$
$607$			6.32056e30i			1.53349i	−0.641954	+	0.766743i	$0.721876\pi$
$608$	−2.61028e30	+	4.04568e30i	−0.621939	+	0.963944i
$609$		0			0
$610$	4.64786e30	−	2.62257e30i	1.06813	−	0.602696i
$611$		−	3.28010e30i		−	0.740345i
$612$		0			0
$613$	−1.22641e30			−0.267036			−0.133518	−	0.991046i	$-0.542627\pi$
$613$	−1.22641e30			−0.267036			−0.133518	+	0.991046i	$0.542627\pi$
$614$	6.31684e27	+	1.11951e28i	0.00135098	+	0.00239428i
$615$		0			0
$616$	−2.24759e28	+	7.58134e29i	−0.00463799	+	0.156444i
$617$	5.14844e30			1.04361			0.521806	−	0.853064i	$-0.325259\pi$
$617$	5.14844e30			1.04361			0.521806	+	0.853064i	$0.325259\pi$
$618$		0			0
$619$			5.64491e29i			0.110423i	0.998475	+	0.0552115i	$0.0175833\pi$
$619$			5.64491e29i			0.110423i	−0.998475	+	0.0552115i	$0.982417\pi$
$620$	−3.99479e30	−	2.41286e30i	−0.767689	−	0.463686i
$621$		0			0
$622$	−1.92268e30	−	3.40747e30i	−0.356625	−	0.632031i
$623$		−	1.46058e30i		−	0.266168i
$624$		0			0
$625$	7.21499e30			1.26927
$626$	6.81469e29	−	3.84521e29i	0.117795	−	0.0664664i
$627$		0			0
$628$	8.67703e28	−	1.43659e29i	0.0144815	−	0.0239760i
$629$	2.94389e29			0.0482796
$630$		0			0
$631$		−	3.98760e30i		−	0.631522i	−0.948839	−	0.315761i	$-0.897740\pi$
$631$		−	3.98760e30i		−	0.631522i	0.948839	−	0.315761i	$-0.102260\pi$
$632$	−8.58079e30	−	2.54389e29i	−1.33549	−	0.0395923i
$633$		0			0
$634$	−5.84323e29	+	3.29705e29i	−0.0878357	+	0.0495615i
$635$			1.98362e31i			2.93054i
$636$		0			0
$637$	−3.31894e30			−0.473659
$638$	2.70575e29	+	4.79529e29i	0.0379543	+	0.0672648i
$639$		0			0
$640$	−1.16489e31	+	5.69104e30i	−1.57872	+	0.771280i
$641$	1.15604e31			1.54005			0.770025	−	0.638014i	$-0.220244\pi$
$641$	1.15604e31			1.54005			0.770025	+	0.638014i	$0.220244\pi$
$642$		0			0
$643$		−	6.53408e29i		−	0.0841131i	−0.999115	−	0.0420566i	$-0.986609\pi$
$643$		−	6.53408e29i		−	0.0841131i	0.999115	−	0.0420566i	$-0.0133910\pi$
$644$	3.80709e29	−	6.30311e29i	0.0481780	−	0.0797647i
$645$		0			0
$646$	−5.04533e29	−	8.94163e29i	−0.0617067	−	0.109360i
$647$		−	3.52258e30i		−	0.423558i	−0.977318	−	0.211779i	$-0.932074\pi$
$647$		−	3.52258e30i		−	0.423558i	0.977318	−	0.211779i	$-0.0679258\pi$
$648$		0			0
$649$	1.09778e31			1.27592
$650$	7.68957e30	−	4.33885e30i	0.878729	−	0.495825i
$651$		0			0
$652$	−6.29042e30	−	3.79943e30i	−0.694954	−	0.419754i
$653$	8.05431e29			0.0874950			0.0437475	−	0.999043i	$-0.486070\pi$
$653$	8.05431e29			0.0874950			0.0437475	+	0.999043i	$0.486070\pi$
$654$		0			0
$655$			2.39270e31i			2.51324i
$656$	−8.88119e29	−	1.68905e30i	−0.0917337	−	0.174462i
$657$		0			0
$658$	1.89557e30	−	1.06958e30i	0.189345	−	0.106838i
$659$			1.21812e31i			1.19660i	0.801272	+	0.598300i	$0.204157\pi$
$659$			1.21812e31i			1.19660i	−0.801272	+	0.598300i	$0.795843\pi$
$660$		0			0
$661$	−1.00500e31			−0.954878			−0.477439	−	0.878665i	$-0.658435\pi$
$661$	−1.00500e31			−0.954878			−0.477439	+	0.878665i	$0.658435\pi$
$662$	1.02178e31	+	1.81085e31i	0.954811	+	1.69217i
$663$		0			0
$664$	−1.09802e30	−	3.25524e28i	−0.0992574	−	0.00294262i
$665$	3.21807e30			0.286126
$666$		0			0
$667$		−	5.34554e29i		−	0.0459840i
$668$	−2.37329e30	−	1.43347e30i	−0.200821	−	0.121296i
$669$		0			0
$670$	8.14078e30	+	1.44275e31i	0.666566	+	1.18133i
$671$		−	9.55458e30i		−	0.769598i
$672$		0			0
$673$	1.49663e31			1.16667			0.583337	−	0.812230i	$-0.301747\pi$
$673$	1.49663e31			1.16667			0.583337	+	0.812230i	$0.301747\pi$
$674$	8.81553e30	−	4.97418e30i	0.676066	−	0.381472i
$675$		0			0
$676$	−5.33737e30	+	8.83667e30i	−0.396199	+	0.655957i
$677$	−1.33892e31			−0.977868			−0.488934	−	0.872321i	$-0.662614\pi$
$677$	−1.33892e31			−0.977868			−0.488934	+	0.872321i	$0.662614\pi$
$678$		0			0
$679$		−	6.85978e29i		−	0.0485001i
$680$	8.19247e28	−	2.76340e30i	0.00569924	−	0.192241i
$681$		0			0
$682$	−7.27694e30	+	4.10603e30i	−0.490141	+	0.276563i
$683$		−	4.01559e30i		−	0.266147i	−0.991106	−	0.133074i	$-0.957515\pi$
$683$		−	4.01559e30i		−	0.266147i	0.991106	−	0.133074i	$-0.0424847\pi$
$684$		0			0
$685$	3.22587e31			2.07038
$686$	−2.18674e30	−	3.87547e30i	−0.138112	−	0.244770i
$687$		0			0
$688$	−8.99597e30	+	4.73017e30i	−0.550269	+	0.289337i
$689$	−1.04977e31			−0.631951
$690$		0			0
$691$		−	1.43806e31i		−	0.838530i	−0.907864	−	0.419265i	$-0.862288\pi$
$691$		−	1.43806e31i		−	0.838530i	0.907864	−	0.419265i	$-0.137712\pi$
$692$	9.94649e30	−	1.64676e31i	0.570825	−	0.945070i
$693$		0			0
$694$	−1.37869e31	−	2.44339e31i	−0.766500	−	1.35843i
$695$			1.35735e31i			0.742779i
$696$		0			0
$697$	4.06929e29			0.0215754
$698$	−2.50059e31	+	1.41096e31i	−1.30507	+	0.736387i
$699$		0			0
$700$	5.01483e30	+	3.02897e30i	0.253617	+	0.153185i
$701$	4.96499e30			0.247184			0.123592	−	0.992333i	$-0.460559\pi$
$701$	4.96499e30			0.247184			0.123592	+	0.992333i	$0.460559\pi$
$702$		0			0
$703$			1.04869e31i			0.505986i
$704$	−1.37506e30	+	2.31706e31i	−0.0653164	+	1.10062i
$705$		0			0
$706$	1.50915e31	−	8.51543e30i	0.694835	−	0.392062i
$707$			5.13341e30i			0.232698i
$708$		0			0
$709$	−2.61604e31			−1.14957			−0.574786	−	0.818304i	$-0.694915\pi$
$709$	−2.61604e31			−1.14957			−0.574786	+	0.818304i	$0.694915\pi$
$710$	−2.37689e31	−	4.21246e31i	−1.02841	−	1.82261i
$711$		0			0
$712$	1.32455e30	−	4.46785e31i	0.0555636	−	1.87421i
$713$	8.11195e30			0.335074
$714$		0			0
$715$		−	2.33808e31i		−	0.936467i
$716$	−2.07161e31	−	1.25126e31i	−0.817080	−	0.493518i
$717$		0			0
$718$	−1.05358e31	−	1.86721e31i	−0.402992	−	0.714206i
$719$		−	2.86784e31i		−	1.08028i	−0.841575	−	0.540141i	$-0.818371\pi$
$719$		−	2.86784e31i		−	1.08028i	0.841575	−	0.540141i	$-0.181629\pi$
$720$		0			0
$721$	4.14319e30			0.151372
$722$	7.64838e30	−	4.31561e30i	0.275207	−	0.155286i
$723$		0			0
$724$	4.78607e30	−	7.92393e30i	0.167053	−	0.276577i
$725$	4.25298e30			0.146209
$726$		0			0
$727$		−	1.94554e30i		−	0.0648875i	−0.999474	−	0.0324438i	$-0.989671\pi$
$727$		−	1.94554e30i		−	0.0648875i	0.999474	−	0.0324438i	$-0.0103290\pi$
$728$	2.08789e30	+	6.18984e28i	0.0685903	+	0.00203345i
$729$		0			0
$730$	−6.40439e31	+	3.61369e31i	−2.04139	+	1.15186i
$731$		−	2.16733e30i		−	0.0680509i
$732$		0			0
$733$	−9.29673e30			−0.283261			−0.141630	−	0.989920i	$-0.545234\pi$
$733$	−9.29673e30			−0.283261			−0.141630	+	0.989920i	$0.545234\pi$
$734$	−2.55745e31	−	4.53247e31i	−0.767629	−	1.36044i
$735$		0			0
$736$	1.22174e31	−	1.89357e31i	0.355895	−	0.551602i
$737$	2.96586e31			0.851154
$738$		0			0
$739$			4.98883e31i			1.38966i	0.719172	+	0.694832i	$0.244521\pi$
$739$			4.98883e31i			1.38966i	−0.719172	+	0.694832i	$0.755479\pi$
$740$	−1.45998e31	+	2.41717e31i	−0.400679	+	0.663373i
$741$		0			0
$742$	−3.42310e30	−	6.06662e30i	−0.0911962	−	0.161623i
$743$		−	4.92849e31i		−	1.29371i	−0.762613	−	0.646856i	$-0.776084\pi$
$743$		−	4.92849e31i		−	1.29371i	0.762613	−	0.646856i	$-0.223916\pi$
$744$		0			0
$745$	2.42865e31			0.618936
$746$	−4.09886e31	+	2.31279e31i	−1.02929	+	0.580777i
$747$		0			0
$748$	−4.23676e30	−	2.55902e30i	−0.103304	−	0.0623958i
$749$	3.04948e30			0.0732700
$750$		0			0
$751$		−	3.56833e31i		−	0.832579i	−0.909232	−	0.416289i	$-0.863330\pi$
$751$		−	3.56833e31i		−	0.832579i	0.909232	−	0.416289i	$-0.136670\pi$
$752$	5.89546e31	−	3.09989e31i	1.35557	−	0.712771i
$753$		0			0
$754$	1.32062e30	−	7.45161e29i	0.0294912	−	0.0166405i
$755$			3.74787e30i			0.0824837i
$756$		0			0
$757$	3.74576e31			0.800729			0.400365	−	0.916356i	$-0.368883\pi$
$757$	3.74576e31			0.800729			0.400365	+	0.916356i	$0.368883\pi$
$758$	2.31583e31	+	4.10425e31i	0.487917	+	0.864715i
$759$		0			0
$760$	9.84396e31	+	2.91838e30i	2.01475	+	0.0597299i
$761$	5.65983e30			0.114175			0.0570876	−	0.998369i	$-0.481819\pi$
$761$	5.65983e30			0.114175			0.0570876	+	0.998369i	$0.481819\pi$
$762$		0			0
$763$		−	1.07883e30i		−	0.0211437i
$764$	3.12574e31	+	1.88796e31i	0.603846	+	0.364725i
$765$		0			0
$766$	−2.49771e30	−	4.42658e30i	−0.0468841	−	0.0830907i
$767$		−	3.02326e31i		−	0.559405i
$768$		0			0
$769$	−9.56001e31			−1.71897			−0.859486	−	0.511160i	$-0.829216\pi$
$769$	−9.56001e31			−1.71897			−0.859486	+	0.511160i	$0.829216\pi$
$770$	1.35117e31	−	7.62401e30i	0.239504	−	0.135141i
$771$		0			0
$772$	−2.73456e31	+	4.52740e31i	−0.471082	+	0.779935i
$773$	−7.72862e31			−1.31258			−0.656292	−	0.754507i	$-0.727876\pi$
$773$	−7.72862e31			−1.31258			−0.656292	+	0.754507i	$0.727876\pi$
$774$		0			0
$775$			6.45396e31i			1.06539i
$776$	6.22093e29	−	2.09838e31i	0.0101246	−	0.341511i
$777$		0			0
$778$	1.47254e31	−	8.30886e30i	0.232966	−	0.131452i
$779$			1.44959e31i			0.226117i
$780$		0			0
$781$	−8.65952e31			−1.31320
$782$	2.36146e30	+	4.18511e30i	0.0353107	+	0.0625796i
$783$		0			0
$784$	−3.13660e31	−	5.96526e31i	−0.456018	−	0.867267i
$785$	−3.43292e30			−0.0492150
$786$		0			0
$787$		−	9.08921e31i		−	1.26708i	−0.773710	−	0.633540i	$-0.781601\pi$
$787$		−	9.08921e31i		−	1.26708i	0.773710	−	0.633540i	$-0.218399\pi$
$788$	−3.63262e31	+	6.01425e31i	−0.499381	+	0.826787i
$789$		0			0
$790$	8.62909e31	+	1.52930e32i	1.15363	+	2.04453i
$791$			6.72160e30i			0.0886200i
$792$		0			0
$793$	−2.63132e31			−0.337418
$794$	1.78894e31	−	1.00941e31i	0.226240	−	0.127656i
$795$		0			0
$796$	5.19489e31	+	3.13773e31i	0.639047	+	0.385986i
$797$	−8.44018e31			−1.02402			−0.512012	−	0.858978i	$-0.671100\pi$
$797$	−8.44018e31			−1.02402			−0.512012	+	0.858978i	$0.671100\pi$
$798$		0			0
$799$			1.42035e31i			0.167641i
$800$	1.50655e32	+	9.72028e31i	1.75385	+	1.13159i
$801$		0			0
$802$	6.18303e31	−	3.48879e31i	0.700299	−	0.395145i
$803$			1.31655e32i			1.47084i
$804$		0			0
$805$	−1.50621e31			−0.163731
$806$	1.13080e31	+	2.00406e31i	0.121255	+	0.214895i
$807$		0			0
$808$	−4.65534e30	+	1.57029e32i	−0.0485765	+	1.63853i
$809$	−8.31537e31			−0.855949			−0.427975	−	0.903791i	$-0.640773\pi$
$809$	−8.31537e31			−0.855949			−0.427975	+	0.903791i	$0.640773\pi$
$810$		0			0
$811$		−	1.42183e32i		−	1.42435i	−0.702000	−	0.712177i	$-0.747709\pi$
$811$		−	1.42183e32i		−	1.42435i	0.702000	−	0.712177i	$-0.252291\pi$
$812$	8.61255e29	+	5.20200e29i	0.00851168	+	0.00514108i
$813$		0			0
$814$	2.48448e31	+	4.40313e31i	0.238983	+	0.423539i
$815$			1.50318e32i			1.42652i
$816$		0			0
$817$	7.72061e31			0.713196
$818$	−8.77003e31	+	4.94851e31i	−0.799309	+	0.451012i
$819$		0			0
$820$	−2.01811e31	+	3.34122e31i	−0.179057	+	0.296451i
$821$	1.47220e32			1.28882			0.644408	−	0.764682i	$-0.277104\pi$
$821$	1.47220e32			1.28882			0.644408	+	0.764682i	$0.277104\pi$
$822$		0			0
$823$			7.24701e31i			0.617676i	0.951115	+	0.308838i	$0.0999400\pi$
$823$			7.24701e31i			0.617676i	−0.951115	+	0.308838i	$0.900060\pi$
$824$	1.26738e32	+	3.75733e30i	1.06588	+	0.0315995i
$825$		0			0
$826$	1.74714e31	−	9.85826e30i	0.143069	−	0.0807272i
$827$		−	2.03312e31i		−	0.164287i	−0.996621	−	0.0821435i	$-0.973823\pi$
$827$		−	2.03312e31i		−	0.164287i	0.996621	−	0.0821435i	$-0.0261766\pi$
$828$		0			0
$829$	1.34305e32			1.05680			0.528400	−	0.848995i	$-0.322792\pi$
$829$	1.34305e32			1.05680			0.528400	+	0.848995i	$0.322792\pi$
$830$	1.10420e31	+	1.95693e31i	0.0857414	+	0.151956i
$831$		0			0
$832$	6.38116e31	+	3.78689e30i	0.482551	+	0.0286369i
$833$	1.43716e31			0.107253
$834$		0			0
$835$			5.67129e31i			0.412222i
$836$	9.11589e31	−	1.50925e32i	0.653928	−	1.08266i
$837$		0			0
$838$	−6.80655e31	−	1.20630e32i	−0.475601	−	0.842887i
$839$		−	2.32877e32i		−	1.60600i	−0.595979	−	0.803000i	$-0.703236\pi$
$839$		−	2.32877e32i		−	1.60600i	0.595979	−	0.803000i	$-0.296764\pi$
$840$		0			0
$841$	−1.48122e32			−0.995093
$842$	−1.69814e32	+	9.58179e31i	−1.12601	+	0.635351i
$843$		0			0
$844$	2.79561e30	+	1.68855e30i	0.0180596	+	0.0109081i
$845$	2.11164e32			1.34647
$846$		0			0
$847$		−	4.92706e30i		−	0.0306105i
$848$	−9.92096e31	−	1.88680e32i	−0.608414	−	1.15710i
$849$		0			0
$850$	−3.32973e31	+	1.87881e31i	−0.198976	+	0.112273i
$851$		−	4.90838e31i		−	0.289543i
$852$		0			0
$853$	−8.66959e31			−0.498379			−0.249189	−	0.968455i	$-0.580164\pi$
$853$	−8.66959e31			−0.498379			−0.249189	+	0.968455i	$0.580164\pi$
$854$	−8.58021e30	−	1.52063e31i	−0.0486924	−	0.0862955i
$855$		0			0
$856$	9.32824e31	+	2.76548e30i	0.515927	+	0.0152954i
$857$	−2.83995e32			−1.55068			−0.775338	−	0.631547i	$-0.782420\pi$
$857$	−2.83995e32			−1.55068			−0.775338	+	0.631547i	$0.782420\pi$
$858$		0			0
$859$		−	2.85305e32i		−	1.51839i	−0.650862	−	0.759196i	$-0.725592\pi$
$859$		−	2.85305e32i		−	1.51839i	0.650862	−	0.759196i	$-0.274408\pi$
$860$	1.77955e32	+	1.07485e32i	0.935036	+	0.564764i
$861$		0			0
$862$	−8.17296e31	−	1.44846e32i	−0.418600	−	0.741867i
$863$			2.61684e32i			1.32330i	0.749813	+	0.661650i	$0.230144\pi$
$863$			2.61684e32i			1.32330i	−0.749813	+	0.661650i	$0.769856\pi$
$864$		0			0
$865$	−3.93516e32			−1.93993
$866$	2.22192e32	−	1.25372e32i	1.08151	−	0.610245i
$867$		0			0
$868$	−7.89413e30	+	1.30697e31i	−0.0374617	+	0.0620224i
$869$	3.14376e32			1.47310
$870$		0			0
$871$		−	8.16794e31i		−	0.373175i
$872$	9.78356e29	−	3.30009e31i	0.00441383	−	0.148883i
$873$		0			0
$874$	−1.49085e32	+	8.41215e31i	−0.655855	+	0.370068i
$875$		−	6.24220e31i		−	0.271175i
$876$		0			0
$877$	1.57667e32			0.667950			0.333975	−	0.942582i	$-0.391610\pi$
$877$	1.57667e32			0.667950			0.333975	+	0.942582i	$0.391610\pi$
$878$	−4.69769e31	−	8.32552e31i	−0.196537	−	0.348314i
$879$		0			0
$880$	4.20232e32	−	2.20962e32i	1.71467	−	0.901589i
$881$	−1.25411e32			−0.505360			−0.252680	−	0.967550i	$-0.581312\pi$
$881$	−1.25411e32			−0.505360			−0.252680	+	0.967550i	$0.581312\pi$
$882$		0			0
$883$			1.75586e31i			0.0690115i	0.999404	+	0.0345057i	$0.0109857\pi$
$883$			1.75586e31i			0.0690115i	−0.999404	+	0.0345057i	$0.989014\pi$
$884$	−7.04750e30	+	1.16680e31i	−0.0273565	+	0.0452920i
$885$		0			0
$886$	−3.81414e31	−	6.75963e31i	−0.144419	−	0.255948i
$887$		−	5.04667e32i		−	1.88732i	−0.330920	−	0.943659i	$-0.607359\pi$
$887$		−	5.04667e32i		−	1.88732i	0.330920	−	0.943659i	$-0.392641\pi$
$888$		0			0
$889$	6.48978e31			0.236761
$890$	−7.96275e32	+	4.49300e32i	−2.86928	+	1.61900i
$891$		0			0
$892$	1.46298e32	+	8.83643e31i	0.514310	+	0.310644i
$893$	−5.05965e32			−1.75693
$894$		0			0
$895$			4.95039e32i			1.67720i
$896$	1.86193e31	+	3.81115e31i	0.0623124	+	0.127546i
$897$		0			0
$898$	−5.76294e31	+	3.25175e31i	−0.188193	+	0.106188i
$899$			1.10841e31i			0.0357557i
$900$		0			0
$901$	4.54571e31			0.143097
$902$	3.43426e31	+	6.08639e31i	0.106798	+	0.189273i
$903$		0			0
$904$	−6.09563e30	+	2.05611e32i	−0.0184997	+	0.624013i
$905$	−1.89353e32			−0.567725
$906$		0			0
$907$			2.36351e32i			0.691635i	0.938302	+	0.345818i	$0.112398\pi$
$907$			2.36351e32i			0.691635i	−0.938302	+	0.345818i	$0.887602\pi$
$908$	5.18160e32	+	3.12970e32i	1.49803	+	0.904811i
$909$		0			0
$910$	−2.09964e31	−	3.72111e31i	−0.0592503	−	0.105007i
$911$		−	2.67714e32i		−	0.746395i	−0.927752	−	0.373198i	$-0.878261\pi$
$911$		−	2.67714e32i		−	0.746395i	0.927752	−	0.373198i	$-0.121739\pi$
$912$		0			0
$913$	4.02285e31			0.109485
$914$	2.38427e32	−	1.34533e32i	0.641132	−	0.361760i
$915$		0			0
$916$	5.29255e31	−	8.76247e31i	0.138936	−	0.230026i
$917$	7.82817e31			0.203047
$918$		0			0
$919$		−	4.48284e32i		−	1.13523i	−0.823296	−	0.567613i	$-0.807867\pi$
$919$		−	4.48284e32i		−	1.13523i	0.823296	−	0.567613i	$-0.192133\pi$
$920$	−4.60745e32	−	1.36594e31i	−1.15291	−	0.0341795i
$921$		0			0
$922$	−3.48256e32	+	1.96504e32i	−0.850861	+	0.480100i
$923$			2.38482e32i			0.575754i
$924$		0			0
$925$	3.90516e32			0.920620
$926$	−1.91989e32	−	3.40254e32i	−0.447256	−	0.792652i
$927$		0			0
$928$	2.58737e31	+	1.66938e31i	0.0588614	+	0.0379775i
$929$	4.41033e32			0.991513			0.495756	−	0.868462i	$-0.334891\pi$
$929$	4.41033e32			0.991513			0.495756	+	0.868462i	$0.334891\pi$
$930$		0			0
$931$			5.11956e32i			1.12405i
$932$	1.10812e32	−	1.83462e32i	0.240442	−	0.398081i
$933$		0			0
$934$	−1.73965e32	−	3.08311e32i	−0.368678	−	0.653391i
$935$			1.01243e32i			0.212050i
$936$		0			0
$937$	−1.84224e32			−0.376887			−0.188443	−	0.982084i	$-0.560344\pi$
$937$	−1.84224e32			−0.376887			−0.188443	+	0.982084i	$0.560344\pi$
$938$	4.72024e31	−	2.66341e31i	0.0954405	−	0.0538525i
$939$		0			0
$940$	−1.16622e33	−	7.04400e32i	−2.30342	−	1.39127i
$941$	−4.95672e31			−0.0967628			−0.0483814	−	0.998829i	$-0.515406\pi$
$941$	−4.95672e31			−0.0967628			−0.0483814	+	0.998829i	$0.515406\pi$
$942$		0			0
$943$		−	6.78478e31i		−	0.129392i
$944$	5.43382e32	−	2.85716e32i	1.02427	−	0.538571i
$945$		0			0
$946$	3.24165e32	−	1.82911e32i	0.596985	−	0.336850i
$947$			9.42481e31i			0.171563i	0.996314	+	0.0857814i	$0.0273387\pi$
$947$			9.42481e31i			0.171563i	−0.996314	+	0.0857814i	$0.972661\pi$
$948$		0			0
$949$	3.62575e32			0.644866
$950$	−6.69281e32	−	1.18614e33i	−1.17665	−	2.08533i
$951$		0			0
$952$	−9.04096e30	−	2.68032e29i	−0.0155313	−	0.000460447i
$953$	2.65478e32			0.450823			0.225412	−	0.974264i	$-0.427627\pi$
$953$	2.65478e32			0.450823			0.225412	+	0.974264i	$0.427627\pi$
$954$		0			0
$955$		−	7.46939e32i		−	1.23950i
$956$	−1.02226e33	−	6.17447e32i	−1.67697	−	1.01289i
$957$		0			0
$958$	−3.63741e31	−	6.44643e31i	−0.0583139	−	0.103347i
$959$		−	1.05540e32i		−	0.167268i
$960$		0			0
$961$	4.77387e32			0.739458
$962$	1.21262e32	−	6.84222e31i	0.185694	−	0.104778i
$963$		0			0
$964$	−4.05666e32	+	6.71630e32i	−0.607186	+	1.00527i
$965$	1.08188e33			1.60096
$966$		0			0
$967$			3.97701e31i			0.0575261i	0.999586	+	0.0287631i	$0.00915683\pi$
$967$			3.97701e31i			0.0575261i	−0.999586	+	0.0287631i	$0.990843\pi$
$968$	4.46820e30	−	1.50717e32i	0.00639005	−	0.215542i
$969$		0			0
$970$	−3.73980e32	+	2.11019e32i	−0.522829	+	0.295007i
$971$			6.20494e32i			0.857682i	0.903380	+	0.428841i	$0.141078\pi$
$971$			6.20494e32i			0.857682i	−0.903380	+	0.428841i	$0.858922\pi$
$972$		0			0
$973$	4.44083e31			0.0600099
$974$	5.02983e32	+	8.91415e32i	0.672055	+	1.19105i
$975$		0			0
$976$	−2.48675e32	−	4.72937e32i	−0.324851	−	0.617811i
$977$	2.10265e32			0.271598			0.135799	−	0.990736i	$-0.456640\pi$
$977$	2.10265e32			0.271598			0.135799	+	0.990736i	$0.456640\pi$
$978$		0			0
$979$			1.63689e33i			2.06734i
$980$	−7.12740e32	+	1.18003e33i	−0.890111	+	1.47369i
$981$		0			0
$982$	2.49320e32	+	4.41859e32i	0.304460	+	0.539582i
$983$			1.57482e33i			1.90171i	0.309644	+	0.950853i	$0.399790\pi$
$983$			1.57482e33i			1.90171i	−0.309644	+	0.950853i	$0.600210\pi$
$984$		0			0
$985$	1.43719e33			1.69713
$986$	−5.71852e30	+	3.22669e30i	−0.00667787	+	0.00376800i
$987$		0			0
$988$	−4.15645e32	−	2.51051e32i	−0.474675	−	0.286705i
$989$	−3.61362e32			−0.408115
$990$		0			0
$991$		−	8.27884e32i		−	0.914448i	−0.889351	−	0.457224i	$-0.848844\pi$
$991$		−	8.27884e32i		−	0.914448i	0.889351	−	0.457224i	$-0.151156\pi$
$992$	−2.53331e32	+	3.92638e32i	−0.276732	+	0.428908i
$993$		0			0
$994$	−1.37818e32	+	7.77643e31i	−0.147250	+	0.0830864i
$995$		−	1.24139e33i		−	1.31176i
$996$		0			0
$997$	9.51422e32			0.983392			0.491696	−	0.870767i	$-0.336377\pi$
$997$	9.51422e32			0.983392			0.491696	+	0.870767i	$0.336377\pi$
$998$	3.27588e32	+	5.80571e32i	0.334883	+	0.593498i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.23.d.c.19.4		10
3.2	odd	2		4.23.b.a.3.7	✓	10
4.3	odd	2	inner	36.23.d.c.19.3		10
12.11	even	2		4.23.b.a.3.8	yes	10
24.5	odd	2		64.23.c.e.63.9		10
24.11	even	2		64.23.c.e.63.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.23.b.a.3.7	✓	10	3.2	odd	2
4.23.b.a.3.8	yes	10	12.11	even	2
36.23.d.c.19.3		10	4.3	odd	2	inner
36.23.d.c.19.4		10	1.1	even	1	trivial
64.23.c.e.63.2		10	24.11	even	2
64.23.c.e.63.9		10	24.5	odd	2

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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 23 \)
Character orbit:	\([\chi]\)	\(=\)	36.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1783.65 + 1006.43i) q^{2} +(2.16851e6 - 3.59023e6i) q^{4} -8.57934e7 q^{5} +2.80689e8i q^{7} +(-2.54549e8 + 8.58616e9i) q^{8} +O(q^{10})\)	\(q+(-1783.65 + 1006.43i) q^{2} +(2.16851e6 - 3.59023e6i) q^{4} -8.57934e7 q^{5} +2.80689e8i q^{7} +(-2.54549e8 + 8.58616e9i) q^{8} +(1.53025e11 - 8.63449e10i) q^{10} -3.14573e11i q^{11} -8.66330e11 q^{13} +(-2.82493e11 - 5.00651e11i) q^{14} +(-8.18733e12 - 1.55709e13i) q^{16} +3.75137e12 q^{17} +1.33634e14i q^{19} +(-1.86044e14 + 3.08018e14i) q^{20} +(3.16595e14 + 5.61088e14i) q^{22} -6.25471e14i q^{23} +4.97633e15 q^{25} +(1.54523e15 - 8.71899e14i) q^{26} +(1.00774e15 + 6.08676e14i) q^{28} +8.54642e14 q^{29} +1.29693e16i q^{31} +(3.02743e16 + 1.95331e16i) q^{32} +(-6.69114e15 + 3.77549e15i) q^{34} -2.40813e16i q^{35} +7.84749e16 q^{37} +(-1.34493e17 - 2.38356e17i) q^{38} +(2.18386e16 - 7.36636e17i) q^{40} +1.08475e17 q^{41} -5.77743e17i q^{43} +(-1.12939e18 - 6.82154e17i) q^{44} +(6.29492e17 + 1.11562e18i) q^{46} +3.78620e18i q^{47} +3.83103e18 q^{49} +(-8.87602e18 + 5.00831e18i) q^{50} +(-1.87864e18 + 3.11033e18i) q^{52} +1.21175e19 q^{53} +2.69883e19i q^{55} +(-2.41004e18 - 7.14490e16i) q^{56} +(-1.52438e18 + 8.60136e17i) q^{58} +3.48973e19i q^{59} +3.03732e19 q^{61} +(-1.30527e19 - 2.31328e19i) q^{62} +(-7.36574e19 - 4.37119e18i) q^{64} +7.43254e19 q^{65} +9.42821e19i q^{67} +(8.13488e18 - 1.34683e19i) q^{68} +(2.42361e19 + 4.29525e19i) q^{70} -2.75278e20i q^{71} -4.18518e20 q^{73} +(-1.39972e20 + 7.89793e19i) q^{74} +(4.79777e20 + 2.89786e20i) q^{76} +8.82972e19 q^{77} +9.99374e20i q^{79} +(7.02419e20 + 1.33588e21i) q^{80} +(-1.93481e20 + 1.09172e20i) q^{82} +1.27883e20i q^{83} -3.21843e20 q^{85} +(5.81457e20 + 1.03049e21i) q^{86} +(2.70098e21 + 8.00741e19i) q^{88} -5.20354e21 q^{89} -2.43169e20i q^{91} +(-2.24559e21 - 1.35634e21i) q^{92} +(-3.81054e21 - 6.75326e21i) q^{94} -1.14649e22i q^{95} -2.44391e21 q^{97} +(-6.83322e21 + 3.85566e21i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 1540 q^{2} + 2264464 q^{4} + 17091100 q^{5} - 9804431680 q^{8}+O(q^{10}) \) 10 * q - 1540 * q^2 + 2264464 * q^4 + 17091100 * q^5 - 9804431680 * q^8	\( 10 q - 1540 q^{2} + 2264464 q^{4} + 17091100 q^{5} - 9804431680 q^{8} + 159414035240 q^{10} - 531230356540 q^{13} + 5894008940736 q^{14} - 27717620084480 q^{16} - 14058178115540 q^{17} - 233643631625120 q^{20} + 120589650366240 q^{22} + 77\!\cdots\!70 q^{25}+ \cdots + 23\!\cdots\!20 q^{98}+O(q^{100}) \) 10 * q - 1540 * q^2 + 2264464 * q^4 + 17091100 * q^5 - 9804431680 * q^8 + 159414035240 * q^10 - 531230356540 * q^13 + 5894008940736 * q^14 - 27717620084480 * q^16 - 14058178115540 * q^17 - 233643631625120 * q^20 + 120589650366240 * q^22 + 7710175817606670 * q^25 + 3953973318046744 * q^26 + 1177952265288960 * q^28 + 14464474185570172 * q^29 + 73831192092953600 * q^32 - 26625976920357496 * q^34 + 324587767823538020 * q^37 - 369140808808591200 * q^38 - 1158049295468479360 * q^40 + 1355457345814233100 * q^41 + 1919761520625210240 * q^44 + 6132624002565203904 * q^46 + 183553700661552298 * q^49 - 29084394113996178540 * q^50 - 38492433127521128800 * q^52 + 11424344766226018780 * q^53 + 102844865827678657536 * q^56 + 173059696836432320360 * q^58 + 58241718146183220740 * q^61 - 317897221476923285760 * q^62 - 412080172429987966976 * q^64 + 121531695066047433560 * q^65 + 667890522330713878240 * q^68 + 1014396282552321513600 * q^70 + 83030422224875883380 * q^73 - 801906083011176262184 * q^74 + 286747421140990627200 * q^76 + 704201825495570814720 * q^77 - 1509611955050789726720 * q^80 - 2389572513290905036600 * q^82 - 1796890366112110859960 * q^85 + 8221838255181360278496 * q^86 + 11178210842814940531200 * q^88 - 3420669206528505615668 * q^89 - 21476264197983864733440 * q^92 - 20874543047091388369536 * q^94 - 20429910746446196146540 * q^97 + 23110416876469762175420 * q^98

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