LMFDB - Embedded newform 45.18.b.c.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,18,Mod(19,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("45.19");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	45.b (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:	$82.4499393051$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} - 1682025200 x^{14} - 16813165927404 x^{13} + \cdots + 36\!\cdots\!64 $ x^16 - 2x^15 - 1682025200x^14 - 16813165927404x^13 + 796193499528494077x^12 + 16301244096602769412534x^11 + 22468988706757383219149998x^10 - 2031337430834232484626265965288x^9 - 18965778077394737678963728161357692x^8 + 25704126016361292501091646945485563832x^7 + 1644988399708750269938578582195442295700744x^6 + 14232521872815010732766246857708462237763067840x^5 + 67152285951153667387295269789516112222302378490976x^4 + 200750173873523679964327426765877619483061237847842560x^3 + 397851771611595237118165695936875382658256196788975559168x^2 + 518025736280135169275335244745754264186455072537349946738688*x + 369441263867398942845365267821438853432252606507544720063780864
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{73}\cdot 3^{42}\cdot 5^{34} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.2
Root			$-5646.66 + 2204.84i$ of defining polynomial
Character	$\chi$	$=$	45.19
Dual form			45.18.b.c.19.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-665.993i q^{2} -312475. q^{4} +(847574. - 211088. i) q^{5} +5.21087e6i q^{7} +1.20813e8i q^{8} +O(q^{10})$	\(q-665.993i q^{2} -312475. q^{4} +(847574. - 211088. i) q^{5} +5.21087e6i q^{7} +1.20813e8i q^{8} +(-1.40583e8 - 5.64478e8i) q^{10} -1.07723e9 q^{11} -4.68523e9i q^{13} +3.47040e9 q^{14} +3.95038e10 q^{16} -4.29653e10i q^{17} -4.87532e10 q^{19} +(-2.64845e11 + 6.59596e10i) q^{20} +7.17430e11i q^{22} -1.84229e11i q^{23} +(6.73823e11 - 3.57825e11i) q^{25} -3.12033e12 q^{26} -1.62826e12i q^{28} -3.65335e12 q^{29} +4.38186e12 q^{31} -1.04741e13i q^{32} -2.86146e13 q^{34} +(1.09995e12 + 4.41659e12i) q^{35} +1.84006e13i q^{37} +3.24693e13i q^{38} +(2.55021e13 + 1.02398e14i) q^{40} +8.83454e12 q^{41} +3.88064e13i q^{43} +3.36608e14 q^{44} -1.22695e14 q^{46} +9.35743e13i q^{47} +2.05477e14 q^{49} +(-2.38309e14 - 4.48761e14i) q^{50} +1.46402e15i q^{52} +7.26941e14i q^{53} +(-9.13035e14 + 2.27391e14i) q^{55} -6.29539e14 q^{56} +2.43310e15i q^{58} -1.18763e15 q^{59} -7.15539e14 q^{61} -2.91829e15i q^{62} -1.79782e15 q^{64} +(-9.88996e14 - 3.97108e15i) q^{65} -1.34197e15i q^{67} +1.34256e16i q^{68} +(2.94142e15 - 7.32560e14i) q^{70} +9.07627e15 q^{71} +3.50025e15i q^{73} +1.22547e16 q^{74} +1.52341e16 q^{76} -5.61332e15i q^{77} -8.33094e15 q^{79} +(3.34824e16 - 8.33878e15i) q^{80} -5.88374e15i q^{82} +1.85440e16i q^{83} +(-9.06946e15 - 3.64163e16i) q^{85} +2.58448e16 q^{86} -1.30144e17i q^{88} -4.34920e16 q^{89} +2.44141e16 q^{91} +5.75670e16i q^{92} +6.23198e16 q^{94} +(-4.13219e16 + 1.02912e16i) q^{95} -6.88619e16i q^{97} -1.36846e17i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 1473168 q^{4}+O(q^{10}) $ 16 * q - 1473168 * q^4	$ 16 q - 1473168 q^{4} - 670199320 q^{10} + 35028482624 q^{16} + 236279498336 q^{19} + 2507484007120 q^{25} - 12501422403232 q^{31} - 36533616605360 q^{34} - 44259047245280 q^{40} - 28675167752480 q^{46} - 430197530548688 q^{49} - 16\!\cdots\!00 q^{55}+ \cdots - 20\!\cdots\!80 q^{94}+O(q^{100}) $ 16 * q - 1473168 * q^4 - 670199320 * q^10 + 35028482624 * q^16 + 236279498336 * q^19 + 2507484007120 * q^25 - 12501422403232 * q^31 - 36533616605360 * q^34 - 44259047245280 * q^40 - 28675167752480 * q^46 - 430197530548688 * q^49 - 1615648303533600 * q^55 - 6459270800401888 * q^61 - 4539898356653312 * q^64 + 1120556748124800 * q^70 + 72078801859831872 * q^76 - 2212561840444576 * q^79 - 75398163530251360 * q^85 + 201977821610712000 * q^91 - 20802101586267680 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	665.993i		−	1.83956i	−0.392431	−	0.919781i	$-0.628366\pi$
$2$		−	665.993i		−	1.83956i	0.392431	−	0.919781i	$-0.371634\pi$
$3$		0			0
$3$		0			0
$4$	−312475.			−2.38399
$5$	847574.	−	211088.i	0.970359	−	0.241668i
$5$	847574.	−	211088.i	0.970359	−	0.241668i
$6$		0			0
$7$			5.21087e6i			0.341646i	0.985302	+	0.170823i	$0.0546427\pi$
$7$			5.21087e6i			0.341646i	−0.985302	+	0.170823i	$0.945357\pi$
$8$			1.20813e8i			2.54594i
$9$		0			0
$10$	−1.40583e8	−	5.64478e8i	−0.444563	−	1.78504i
$11$	−1.07723e9			−1.51521			−0.757604	−	0.652715i	$-0.773630\pi$
$11$	−1.07723e9			−1.51521			−0.757604	+	0.652715i	$0.773630\pi$
$12$		0			0
$13$		−	4.68523e9i		−	1.59299i	−0.604646	−	0.796494i	$-0.706686\pi$
$13$		−	4.68523e9i		−	1.59299i	0.604646	−	0.796494i	$-0.293314\pi$
$14$	3.47040e9			0.628480
$15$		0			0
$16$	3.95038e10			2.29942
$17$		−	4.29653e10i		−	1.49383i	−0.664918	−	0.746916i	$-0.731534\pi$
$17$		−	4.29653e10i		−	1.49383i	0.664918	−	0.746916i	$-0.268466\pi$
$18$		0			0
$19$	−4.87532e10			−0.658563			−0.329281	−	0.944232i	$-0.606806\pi$
$19$	−4.87532e10			−0.658563			−0.329281	+	0.944232i	$0.606806\pi$
$20$	−2.64845e11	+	6.59596e10i	−2.31333	+	0.576134i
$21$		0			0
$22$			7.17430e11i			2.78732i
$23$		−	1.84229e11i		−	0.490537i	−0.969455	−	0.245269i	$-0.921124\pi$
$23$		−	1.84229e11i		−	0.490537i	0.969455	−	0.245269i	$-0.0788762\pi$
$24$		0			0
$25$	6.73823e11	−	3.57825e11i	0.883193	−	0.469009i
$26$	−3.12033e12			−2.93040
$27$		0			0
$28$		−	1.62826e12i		−	0.814482i
$29$	−3.65335e12			−1.35615			−0.678075	−	0.734992i	$-0.737186\pi$
$29$	−3.65335e12			−1.35615			−0.678075	+	0.734992i	$0.737186\pi$
$30$		0			0
$31$	4.38186e12			0.922751			0.461375	−	0.887205i	$-0.347356\pi$
$31$	4.38186e12			0.922751			0.461375	+	0.887205i	$0.347356\pi$
$32$		−	1.04741e13i		−	1.68399i
$33$		0			0
$34$	−2.86146e13			−2.74800
$35$	1.09995e12	+	4.41659e12i	0.0825649	+	0.331519i
$36$		0			0
$37$			1.84006e13i			0.861226i	0.902537	+	0.430613i	$0.141703\pi$
$37$			1.84006e13i			0.861226i	−0.902537	+	0.430613i	$0.858297\pi$
$38$			3.24693e13i			1.21147i
$39$		0			0
$40$	2.55021e13	+	1.02398e14i	0.615271	+	2.47047i
$41$	8.83454e12			0.172791			0.0863955	−	0.996261i	$-0.472465\pi$
$41$	8.83454e12			0.172791			0.0863955	+	0.996261i	$0.472465\pi$
$42$		0			0
$43$			3.88064e13i			0.506315i	0.967425	+	0.253158i	$0.0814692\pi$
$43$			3.88064e13i			0.506315i	−0.967425	+	0.253158i	$0.918531\pi$
$44$	3.36608e14			3.61224
$45$		0			0
$46$	−1.22695e14			−0.902374
$47$			9.35743e13i			0.573224i	0.958047	+	0.286612i	$0.0925291\pi$
$47$			9.35743e13i			0.573224i	−0.958047	+	0.286612i	$0.907471\pi$
$48$		0			0
$49$	2.05477e14			0.883278
$50$	−2.38309e14	−	4.48761e14i	−0.862771	−	1.62469i
$51$		0			0
$52$			1.46402e15i			3.79767i
$53$			7.26941e14i			1.60382i	0.597448	+	0.801908i	$0.296182\pi$
$53$			7.26941e14i			1.60382i	−0.597448	+	0.801908i	$0.703818\pi$
$54$		0			0
$55$	−9.13035e14	+	2.27391e14i	−1.47030	+	0.366177i
$56$	−6.29539e14			−0.869810
$57$		0			0
$58$			2.43310e15i			2.49472i
$59$	−1.18763e15			−1.05302			−0.526511	−	0.850168i	$-0.676500\pi$
$59$	−1.18763e15			−1.05302			−0.526511	+	0.850168i	$0.676500\pi$
$60$		0			0
$61$	−7.15539e14			−0.477892			−0.238946	−	0.971033i	$-0.576802\pi$
$61$	−7.15539e14			−0.477892			−0.238946	+	0.971033i	$0.576802\pi$
$62$		−	2.91829e15i		−	1.69746i
$63$		0			0
$64$	−1.79782e15			−0.798391
$65$	−9.88996e14	−	3.97108e15i	−0.384974	−	1.54577i
$66$		0			0
$67$		−	1.34197e15i		−	0.403743i	−0.979412	−	0.201872i	$-0.935298\pi$
$67$		−	1.34197e15i		−	0.403743i	0.979412	−	0.201872i	$-0.0647024\pi$
$68$			1.34256e16i			3.56128i
$69$		0			0
$70$	2.94142e15	−	7.32560e14i	0.609851	−	0.151883i
$71$	9.07627e15			1.66806			0.834029	−	0.551720i	$-0.186028\pi$
$71$	9.07627e15			1.66806			0.834029	+	0.551720i	$0.186028\pi$
$72$		0			0
$73$			3.50025e15i			0.507990i	0.967206	+	0.253995i	$0.0817447\pi$
$73$			3.50025e15i			0.507990i	−0.967206	+	0.253995i	$0.918255\pi$
$74$	1.22547e16			1.58428
$75$		0			0
$76$	1.52341e16			1.57001
$77$		−	5.61332e15i		−	0.517665i
$78$		0			0
$79$	−8.33094e15			−0.617823			−0.308911	−	0.951091i	$-0.599965\pi$
$79$	−8.33094e15			−0.617823			−0.308911	+	0.951091i	$0.599965\pi$
$80$	3.34824e16	−	8.33878e15i	2.23127	−	0.555696i
$81$		0			0
$82$		−	5.88374e15i		−	0.317860i
$83$			1.85440e16i			0.903733i	0.892086	+	0.451866i	$0.149242\pi$
$83$			1.85440e16i			0.903733i	−0.892086	+	0.451866i	$0.850758\pi$
$84$		0			0
$85$	−9.06946e15	−	3.64163e16i	−0.361011	−	1.44955i
$86$	2.58448e16			0.931399
$87$		0			0
$88$		−	1.30144e17i		−	3.85763i
$89$	−4.34920e16			−1.17110			−0.585550	−	0.810636i	$-0.699121\pi$
$89$	−4.34920e16			−1.17110			−0.585550	+	0.810636i	$0.699121\pi$
$90$		0			0
$91$	2.44141e16			0.544238
$92$			5.75670e16i			1.16944i
$93$		0			0
$94$	6.23198e16			1.05448
$95$	−4.13219e16	+	1.02912e16i	−0.639042	+	0.159153i
$96$		0			0
$97$		−	6.88619e16i		−	0.892112i	−0.895005	−	0.446056i	$-0.852828\pi$
$97$		−	6.88619e16i		−	0.892112i	0.895005	−	0.446056i	$-0.147172\pi$
$98$		−	1.36846e17i		−	1.62485i
$99$		0			0
$100$	−2.10553e17	+	1.11811e17i	−2.10553	+	1.11811i
$101$	3.01559e16			0.277102			0.138551	−	0.990355i	$-0.455755\pi$
$101$	3.01559e16			0.277102			0.138551	+	0.990355i	$0.455755\pi$
$102$		0			0
$103$			1.96946e17i			1.53190i	0.642902	+	0.765949i	$0.277730\pi$
$103$			1.96946e17i			1.53190i	−0.642902	+	0.765949i	$0.722270\pi$
$104$	5.66036e17			4.05565
$105$		0			0
$106$	4.84138e17			2.95032
$107$			4.84166e16i			0.272416i	0.990680	+	0.136208i	$0.0434915\pi$
$107$			4.84166e16i			0.272416i	−0.990680	+	0.136208i	$0.956509\pi$
$108$		0			0
$109$	−3.77189e17			−1.81315			−0.906575	−	0.422045i	$-0.861312\pi$
$109$	−3.77189e17			−1.81315			−0.906575	+	0.422045i	$0.861312\pi$
$110$	1.51441e17	+	6.08075e17i	0.673605	+	2.70470i
$111$		0			0
$112$			2.05849e17i			0.785589i
$113$		−	2.14053e17i		−	0.757450i	−0.925509	−	0.378725i	$-0.876363\pi$
$113$		−	2.14053e17i		−	0.757450i	0.925509	−	0.378725i	$-0.123637\pi$
$114$		0			0
$115$	−3.88886e16	−	1.56148e17i	−0.118547	−	0.475997i
$116$	1.14158e18			3.23305
$117$		0			0
$118$			7.90950e17i			1.93710i
$119$	2.23886e17			0.510362
$120$		0			0
$121$	6.54986e17			1.29586
$122$			4.76544e17i			0.879112i
$123$		0			0
$124$	−1.36922e18			−2.19983
$125$	4.95582e17	−	4.45519e17i	0.743670	−	0.668546i
$126$		0			0
$127$			1.28045e18i			1.67892i	0.543423	+	0.839459i	$0.317128\pi$
$127$			1.28045e18i			1.67892i	−0.543423	+	0.839459i	$0.682872\pi$
$128$		−	1.75525e17i		−	0.215305i
$129$		0			0
$130$	−2.64471e18	+	6.58665e17i	−2.84354	+	0.708184i
$131$	−1.74108e18			−1.75393			−0.876965	−	0.480554i	$-0.840436\pi$
$131$	−1.74108e18			−1.75393			−0.876965	+	0.480554i	$0.840436\pi$
$132$		0			0
$133$		−	2.54046e17i		−	0.224995i
$134$	−8.93739e17			−0.742711
$135$		0			0
$136$	5.19076e18			3.80321
$137$		−	9.96460e17i		−	0.686018i	−0.939332	−	0.343009i	$-0.888554\pi$
$137$		−	9.96460e17i		−	0.686018i	0.939332	−	0.343009i	$-0.111446\pi$
$138$		0			0
$139$	1.45693e18			0.886773			0.443387	−	0.896330i	$-0.353777\pi$
$139$	1.45693e18			0.886773			0.443387	+	0.896330i	$0.353777\pi$
$140$	−3.43707e17	−	1.38007e18i	−0.196834	−	0.790340i
$141$		0			0
$142$		−	6.04473e18i		−	3.06850i
$143$			5.04709e18i			2.41371i
$144$		0			0
$145$	−3.09648e18	+	7.71178e17i	−1.31595	+	0.327738i
$146$	2.33114e18			0.934479
$147$		0			0
$148$		−	5.74972e18i		−	2.05316i
$149$	−6.09200e17			−0.205436			−0.102718	−	0.994711i	$-0.532754\pi$
$149$	−6.09200e17			−0.205436			−0.102718	+	0.994711i	$0.532754\pi$
$150$		0			0
$151$	4.77447e18			1.43754			0.718772	−	0.695245i	$-0.244704\pi$
$151$	4.77447e18			1.43754			0.718772	+	0.695245i	$0.244704\pi$
$152$		−	5.89001e18i		−	1.67666i
$153$		0			0
$154$	−3.73843e18			−0.952277
$155$	3.71395e18	−	9.24959e17i	0.895399	−	0.222999i
$156$		0			0
$157$			7.06387e18i			1.52720i	0.645691	+	0.763599i	$0.276570\pi$
$157$			7.06387e18i			1.52720i	−0.645691	+	0.763599i	$0.723430\pi$
$158$			5.54835e18i			1.13652i
$159$		0			0
$160$	−2.21095e18	−	8.87755e18i	−0.406967	−	1.63408i
$161$	9.59994e17			0.167590
$162$		0			0
$163$		−	3.59321e18i		−	0.564792i	−0.959298	−	0.282396i	$-0.908871\pi$
$163$		−	3.59321e18i		−	0.564792i	0.959298	−	0.282396i	$-0.0911291\pi$
$164$	−2.76057e18			−0.411932
$165$		0			0
$166$	1.23502e19			1.66247
$167$		−	4.03527e18i		−	0.516158i	−0.966124	−	0.258079i	$-0.916911\pi$
$167$		−	4.03527e18i		−	0.516158i	0.966124	−	0.258079i	$-0.0830895\pi$
$168$		0			0
$169$	−1.33010e19			−1.53761
$170$	−2.42530e19	+	6.04020e18i	−2.66655	+	0.664103i
$171$		0			0
$172$		−	1.21260e19i		−	1.20705i
$173$		−	1.30593e19i		−	1.23745i	−0.785608	−	0.618724i	$-0.787650\pi$
$173$		−	1.30593e19i		−	1.23745i	0.785608	−	0.618724i	$-0.212350\pi$
$174$		0			0
$175$	1.86458e18	+	3.51120e18i	0.160235	+	0.301740i
$176$	−4.25548e19			−3.48410
$177$		0			0
$178$			2.89653e19i			2.15431i
$179$	−5.15443e18			−0.365536			−0.182768	−	0.983156i	$-0.558506\pi$
$179$	−5.15443e18			−0.365536			−0.182768	+	0.983156i	$0.558506\pi$
$180$		0			0
$181$	−1.57587e19			−1.01684			−0.508419	−	0.861110i	$-0.669770\pi$
$181$	−1.57587e19			−1.01684			−0.508419	+	0.861110i	$0.669770\pi$
$182$		−	1.62596e19i		−	1.00116i
$183$		0			0
$184$	2.22573e19			1.24888
$185$	3.88415e18	+	1.55959e19i	0.208131	+	0.835699i
$186$		0			0
$187$			4.62837e19i			2.26347i
$188$		−	2.92396e19i		−	1.36656i
$189$		0			0
$190$	6.85387e18	+	2.75201e19i	0.292773	+	1.17556i
$191$	2.48726e18			0.101610			0.0508052	−	0.998709i	$-0.483821\pi$
$191$	2.48726e18			0.101610			0.0508052	+	0.998709i	$0.483821\pi$
$192$		0			0
$193$			4.04064e19i			1.51082i	0.655252	+	0.755411i	$0.272563\pi$
$193$			4.04064e19i			1.51082i	−0.655252	+	0.755411i	$0.727437\pi$
$194$	−4.58616e19			−1.64110
$195$		0			0
$196$	−6.42064e19			−2.10573
$197$			1.97018e19i			0.618791i	0.950934	+	0.309395i	$0.100127\pi$
$197$			1.97018e19i			0.618791i	−0.950934	+	0.309395i	$0.899873\pi$
$198$		0			0
$199$	2.55557e19			0.736609			0.368304	−	0.929705i	$-0.379938\pi$
$199$	2.55557e19			0.736609			0.368304	+	0.929705i	$0.379938\pi$
$200$	4.32299e19	+	8.14064e19i	1.19407	+	2.24856i
$201$		0			0
$202$		−	2.00836e19i		−	0.509747i
$203$		−	1.90371e19i		−	0.463324i
$204$		0			0
$205$	7.48793e18	−	1.86487e18i	0.167669	−	0.0417580i
$206$	1.31164e20			2.81802
$207$		0			0
$208$		−	1.85084e20i		−	3.66295i
$209$	5.25186e19			0.997860
$210$		0			0
$211$	−1.01792e20			−1.78367			−0.891835	−	0.452361i	$-0.850582\pi$
$211$	−1.01792e20			−1.78367			−0.891835	+	0.452361i	$0.850582\pi$
$212$		−	2.27151e20i		−	3.82348i
$213$		0			0
$214$	3.22451e19			0.501126
$215$	8.19156e18	+	3.28913e19i	0.122360	+	0.491308i
$216$		0			0
$217$			2.28333e19i			0.315254i
$218$			2.51205e20i			3.33540i
$219$		0			0
$220$	2.85300e20	−	7.10540e19i	3.50517	−	0.872962i
$221$	−2.01302e20			−2.37966
$222$		0			0
$223$			1.58434e20i			1.73483i	0.497584	+	0.867416i	$0.334221\pi$
$223$			1.58434e20i			1.73483i	−0.497584	+	0.867416i	$0.665779\pi$
$224$	5.45790e19			0.575330
$225$		0			0
$226$	−1.42558e20			−1.39338
$227$		−	9.47405e19i		−	0.891900i	−0.895058	−	0.445950i	$-0.852866\pi$
$227$		−	9.47405e19i		−	0.891900i	0.895058	−	0.445950i	$-0.147134\pi$
$228$		0			0
$229$	−1.16266e18			−0.0101590			−0.00507951	−	0.999987i	$-0.501617\pi$
$229$	−1.16266e18			−0.0101590			−0.00507951	+	0.999987i	$0.501617\pi$
$230$	−1.03993e20	+	2.58995e19i	−0.875627	+	0.218075i
$231$		0			0
$232$		−	4.41371e20i		−	3.45268i
$233$			9.49887e19i			0.716385i	0.933648	+	0.358193i	$0.116607\pi$
$233$			9.49887e19i			0.716385i	−0.933648	+	0.358193i	$0.883393\pi$
$234$		0			0
$235$	1.97524e19	+	7.93111e19i	0.138530	+	0.556234i
$236$	3.71103e20			2.51040
$237$		0			0
$238$		−	1.49107e20i		−	0.938843i
$239$	−1.65177e19			−0.100361			−0.0501807	−	0.998740i	$-0.515980\pi$
$239$	−1.65177e19			−0.100361			−0.0501807	+	0.998740i	$0.515980\pi$
$240$		0			0
$241$	3.05366e19			0.172852			0.0864262	−	0.996258i	$-0.472455\pi$
$241$	3.05366e19			0.172852			0.0864262	+	0.996258i	$0.472455\pi$
$242$		−	4.36216e20i		−	2.38381i
$243$		0			0
$244$	2.23588e20			1.13929
$245$	1.74157e20	−	4.33738e19i	0.857097	−	0.213460i
$246$		0			0
$247$			2.28420e20i			1.04908i
$248$			5.29385e20i			2.34927i
$249$		0			0
$250$	−2.96713e20	−	3.30054e20i	−1.22983	−	1.36803i
$251$	2.14549e19			0.0859606			0.0429803	−	0.999076i	$-0.486315\pi$
$251$	2.14549e19			0.0859606			0.0429803	+	0.999076i	$0.486315\pi$
$252$		0			0
$253$			1.98458e20i			0.743266i
$254$	8.52768e20			3.08848
$255$		0			0
$256$	−3.52542e20			−1.19446
$257$		−	4.28916e20i		−	1.40586i	−0.711261	−	0.702928i	$-0.751876\pi$
$257$		−	4.28916e20i		−	1.40586i	0.711261	−	0.702928i	$-0.248124\pi$
$258$		0			0
$259$	−9.58831e19			−0.294235
$260$	3.09036e20	+	1.24086e21i	0.917774	+	3.68510i
$261$		0			0
$262$			1.15955e21i			3.22646i
$263$			1.93550e20i			0.521397i	0.965420	+	0.260698i	$0.0839528\pi$
$263$			1.93550e20i			0.521397i	−0.965420	+	0.260698i	$0.916047\pi$
$264$		0			0
$265$	1.53449e20	+	6.16136e20i	0.387591	+	1.55628i
$266$	−1.69193e20			−0.413893
$267$		0			0
$268$			4.19330e20i			0.962521i
$269$	−1.28516e20			−0.285800			−0.142900	−	0.989737i	$-0.545643\pi$
$269$	−1.28516e20			−0.285800			−0.142900	+	0.989737i	$0.545643\pi$
$270$		0			0
$271$	3.28898e20			0.686787			0.343393	−	0.939192i	$-0.388424\pi$
$271$	3.28898e20			0.686787			0.343393	+	0.939192i	$0.388424\pi$
$272$		−	1.69729e21i		−	3.43495i
$273$		0			0
$274$	−6.63636e20			−1.26197
$275$	−7.25865e20	+	3.85462e20i	−1.33822	+	0.710646i
$276$		0			0
$277$		−	2.74157e20i		−	0.475249i	−0.971357	−	0.237624i	$-0.923631\pi$
$277$		−	2.74157e20i		−	0.475249i	0.971357	−	0.237624i	$-0.0763687\pi$
$278$		−	9.70304e20i		−	1.63128i
$279$		0			0
$280$	−5.33581e20	+	1.32888e20i	−0.844028	+	0.210205i
$281$	3.08350e20			0.473195			0.236598	−	0.971608i	$-0.423968\pi$
$281$	3.08350e20			0.473195			0.236598	+	0.971608i	$0.423968\pi$
$282$		0			0
$283$		−	6.83969e20i		−	0.988215i	−0.869401	−	0.494108i	$-0.835495\pi$
$283$		−	6.83969e20i		−	0.988215i	0.869401	−	0.494108i	$-0.164505\pi$
$284$	−2.83610e21			−3.97664
$285$		0			0
$286$	3.36133e21			4.44017
$287$			4.60356e19i			0.0590334i
$288$		0			0
$289$	−1.01878e21			−1.23154
$290$	5.13599e20	+	2.06223e21i	0.602894	+	2.42078i
$291$		0			0
$292$		−	1.09374e21i		−	1.21104i
$293$		−	3.32513e20i		−	0.357630i	−0.983883	−	0.178815i	$-0.942774\pi$
$293$		−	3.32513e20i		−	0.357630i	0.983883	−	0.178815i	$-0.0572263\pi$
$294$		0			0
$295$	−1.00660e21	+	2.50694e20i	−1.02181	+	0.254481i
$296$	−2.22303e21			−2.19263
$297$		0			0
$298$			4.05723e20i			0.377913i
$299$	−8.63157e20			−0.781420
$300$		0			0
$301$	−2.02215e20			−0.172981
$302$		−	3.17977e21i		−	2.64445i
$303$		0			0
$304$	−1.92593e21			−1.51431
$305$	−6.06472e20	+	1.51042e20i	−0.463727	+	0.115491i
$306$		0			0
$307$		−	8.30641e20i		−	0.600810i	−0.953812	−	0.300405i	$-0.902878\pi$
$307$		−	8.30641e20i		−	0.600810i	0.953812	−	0.300405i	$-0.0971218\pi$
$308$			1.75402e21i			1.23411i
$309$		0			0
$310$	−6.16016e20	−	2.47347e21i	−0.410221	−	1.64714i
$311$	1.60254e21			1.03836			0.519178	−	0.854666i	$-0.326238\pi$
$311$	1.60254e21			1.03836			0.519178	+	0.854666i	$0.326238\pi$
$312$		0			0
$313$		−	2.11429e21i		−	1.29729i	−0.761091	−	0.648645i	$-0.775336\pi$
$313$		−	2.11429e21i		−	1.29729i	0.761091	−	0.648645i	$-0.224664\pi$
$314$	4.70448e21			2.80938
$315$		0			0
$316$	2.60321e21			1.47288
$317$		−	1.01751e21i		−	0.560445i	−0.959935	−	0.280223i	$-0.909592\pi$
$317$		−	1.01751e21i		−	0.560445i	0.959935	−	0.280223i	$-0.0904083\pi$
$318$		0			0
$319$	3.93551e21			2.05485
$320$	−1.52378e21	+	3.79498e20i	−0.774726	+	0.192945i
$321$		0			0
$322$		−	6.39349e20i		−	0.308293i
$323$			2.09469e21i			0.983783i
$324$		0			0
$325$	−1.67649e21	−	3.15702e21i	−0.747126	−	1.40692i
$326$	−2.39305e21			−1.03897
$327$		0			0
$328$			1.06733e21i			0.439916i
$329$	−4.87603e20			−0.195840
$330$		0			0
$331$	2.68968e21			1.02604			0.513018	−	0.858378i	$-0.328527\pi$
$331$	2.68968e21			1.02604			0.513018	+	0.858378i	$0.328527\pi$
$332$		−	5.79453e21i		−	2.15449i
$333$		0			0
$334$	−2.68746e21			−0.949505
$335$	−2.83273e20	−	1.13741e21i	−0.0975718	−	0.391776i
$336$		0			0
$337$		−	2.89853e21i		−	0.949125i	−0.880222	−	0.474563i	$-0.842606\pi$
$337$		−	2.89853e21i		−	0.949125i	0.880222	−	0.474563i	$-0.157394\pi$
$338$			8.85836e21i			2.82853i
$339$		0			0
$340$	2.83398e21	+	1.13792e22i	0.860647	+	3.45572i
$341$	−4.72029e21			−1.39816
$342$		0			0
$343$			2.28292e21i			0.643415i
$344$	−4.68831e21			−1.28905
$345$		0			0
$346$	−8.69738e21			−2.27636
$347$		−	4.41980e21i		−	1.12876i	−0.825514	−	0.564381i	$-0.809115\pi$
$347$		−	4.41980e21i		−	1.12876i	0.825514	−	0.564381i	$-0.190885\pi$
$348$		0			0
$349$	−4.07398e21			−0.990839			−0.495420	−	0.868654i	$-0.664986\pi$
$349$	−4.07398e21			−0.990839			−0.495420	+	0.868654i	$0.664986\pi$
$350$	2.33844e21	−	1.24180e21i	0.555069	−	0.294763i
$351$		0			0
$352$			1.12830e22i			2.55160i
$353$		−	4.21940e21i		−	0.931462i	−0.884926	−	0.465731i	$-0.845791\pi$
$353$		−	4.21940e21i		−	0.931462i	0.884926	−	0.465731i	$-0.154209\pi$
$354$		0			0
$355$	7.69281e21	−	1.91589e21i	1.61862	−	0.403116i
$356$	1.35901e22			2.79189
$357$		0			0
$358$			3.43281e21i			0.672426i
$359$	−6.40666e21			−1.22554			−0.612772	−	0.790260i	$-0.709945\pi$
$359$	−6.40666e21			−1.22554			−0.612772	+	0.790260i	$0.709945\pi$
$360$		0			0
$361$	−3.10352e21			−0.566295
$362$			1.04952e22i			1.87054i
$363$		0			0
$364$	−7.62879e21			−1.29746
$365$	7.38862e20	+	2.96672e21i	0.122765	+	0.492933i
$366$		0			0
$367$			1.99645e21i			0.316663i	0.987386	+	0.158331i	$0.0506114\pi$
$367$			1.99645e21i			0.316663i	−0.987386	+	0.158331i	$0.949389\pi$
$368$		−	7.27776e21i		−	1.12795i
$369$		0			0
$370$	1.03867e22	−	2.58681e21i	1.53732	−	0.382869i
$371$	−3.78799e21			−0.547938
$372$		0			0
$373$		−	1.02378e22i		−	1.41475i	−0.706836	−	0.707377i	$-0.749878\pi$
$373$		−	1.02378e22i		−	1.41475i	0.706836	−	0.707377i	$-0.250122\pi$
$374$	3.08246e22			4.16379
$375$		0			0
$376$	−1.13050e22			−1.45939
$377$			1.71168e22i			2.16033i
$378$		0			0
$379$	7.84977e21			0.947161			0.473580	−	0.880751i	$-0.342961\pi$
$379$	7.84977e21			0.947161			0.473580	+	0.880751i	$0.342961\pi$
$380$	1.29120e22	−	3.21574e21i	1.52347	−	0.379420i
$381$		0			0
$382$		−	1.65650e21i		−	0.186919i
$383$		−	9.29062e21i		−	1.02531i	−0.858595	−	0.512655i	$-0.828662\pi$
$383$		−	9.29062e21i		−	1.02531i	0.858595	−	0.512655i	$-0.171338\pi$
$384$		0			0
$385$	−1.18491e21	−	4.75770e21i	−0.125103	−	0.502321i
$386$	2.69104e22			2.77925
$387$		0			0
$388$			2.15176e22i			2.12679i
$389$	−9.29019e21			−0.898366			−0.449183	−	0.893440i	$-0.648285\pi$
$389$	−9.29019e21			−0.898366			−0.449183	+	0.893440i	$0.648285\pi$
$390$		0			0
$391$	−7.91547e21			−0.732781
$392$			2.48243e22i			2.24877i
$393$		0			0
$394$	1.31213e22			1.13830
$395$	−7.06109e21	+	1.75856e21i	−0.599510	+	0.149308i
$396$		0			0
$397$			3.43305e21i			0.279229i	0.990206	+	0.139614i	$0.0445863\pi$
$397$			3.43305e21i			0.279229i	−0.990206	+	0.139614i	$0.955414\pi$
$398$		−	1.70199e22i		−	1.35504i
$399$		0			0
$400$	2.66186e22	−	1.41355e22i	2.03084	−	1.07845i
$401$	−6.75438e21			−0.504497			−0.252248	−	0.967663i	$-0.581170\pi$
$401$	−6.75438e21			−0.504497			−0.252248	+	0.967663i	$0.581170\pi$
$402$		0			0
$403$		−	2.05300e22i		−	1.46993i
$404$	−9.42294e21			−0.660610
$405$		0			0
$406$	−1.26786e22			−0.852313
$407$		−	1.98218e22i		−	1.30494i
$408$		0			0
$409$	8.58242e21			0.541953			0.270976	−	0.962586i	$-0.412653\pi$
$409$	8.58242e21			0.541953			0.270976	+	0.962586i	$0.412653\pi$
$410$	−1.24199e21	−	4.98691e21i	−0.0768165	−	0.308438i
$411$		0			0
$412$		−	6.15405e22i		−	3.65203i
$413$		−	6.18856e21i		−	0.359761i
$414$		0			0
$415$	3.91442e21	+	1.57174e22i	0.218403	+	0.876945i
$416$	−4.90734e22			−2.68258
$417$		0			0
$418$		−	3.49770e22i		−	1.83563i
$419$	2.30477e21			0.118525			0.0592623	−	0.998242i	$-0.481125\pi$
$419$	2.30477e21			0.118525			0.0592623	+	0.998242i	$0.481125\pi$
$420$		0			0
$421$	−2.97665e20			−0.0147004			−0.00735022	−	0.999973i	$-0.502340\pi$
$421$	−2.97665e20			−0.0147004			−0.00735022	+	0.999973i	$0.502340\pi$
$422$			6.77930e22i			3.28117i
$423$		0			0
$424$	−8.78238e22			−4.08322
$425$	−1.53741e22	−	2.89510e22i	−0.700621	−	1.31934i
$426$		0			0
$427$		−	3.72858e21i		−	0.163270i
$428$		−	1.51290e22i		−	0.649437i
$429$		0			0
$430$	2.19053e22	−	5.45552e21i	0.903791	−	0.225089i
$431$	−3.18798e22			−1.28961			−0.644806	−	0.764346i	$-0.723062\pi$
$431$	−3.18798e22			−1.28961			−0.644806	+	0.764346i	$0.723062\pi$
$432$		0			0
$433$			3.73383e22i			1.45214i	0.687622	+	0.726069i	$0.258655\pi$
$433$			3.73383e22i			1.45214i	−0.687622	+	0.726069i	$0.741345\pi$
$434$	1.52068e22			0.579930
$435$		0			0
$436$	1.17862e23			4.32253
$437$			8.98176e21i			0.323050i
$438$		0			0
$439$	−2.59880e22			−0.899133			−0.449566	−	0.893247i	$-0.648421\pi$
$439$	−2.59880e22			−0.899133			−0.449566	+	0.893247i	$0.648421\pi$
$440$	−2.74718e22	−	1.10306e23i	−0.932264	−	3.74328i
$441$		0			0
$442$			1.34066e23i			4.37753i
$443$			4.88410e22i			1.56442i	0.623015	+	0.782210i	$0.285907\pi$
$443$			4.88410e22i			1.56442i	−0.623015	+	0.782210i	$0.714093\pi$
$444$		0			0
$445$	−3.68627e22	+	9.18064e21i	−1.13639	+	0.283017i
$446$	1.05516e23			3.19133
$447$		0			0
$448$		−	9.36818e21i		−	0.272767i
$449$	−2.32315e21			−0.0663719			−0.0331859	−	0.999449i	$-0.510565\pi$
$449$	−2.32315e21			−0.0663719			−0.0331859	+	0.999449i	$0.510565\pi$
$450$		0			0
$451$	−9.51687e21			−0.261814
$452$			6.68860e22i			1.80575i
$453$		0			0
$454$	−6.30965e22			−1.64071
$455$	2.06928e22	−	5.15353e21i	0.528107	−	0.131525i
$456$		0			0
$457$			5.43285e21i			0.133579i	0.997767	+	0.0667897i	$0.0212757\pi$
$457$			5.43285e21i			0.133579i	−0.997767	+	0.0667897i	$0.978724\pi$
$458$			7.74324e20i			0.0186882i
$459$		0			0
$460$	1.21517e22	+	4.87922e22i	0.282615	+	1.13477i
$461$	−4.90580e22			−1.12009			−0.560044	−	0.828463i	$-0.689216\pi$
$461$	−4.90580e22			−1.12009			−0.560044	+	0.828463i	$0.689216\pi$
$462$		0			0
$463$			5.71450e22i			1.25759i	0.777570	+	0.628796i	$0.216452\pi$
$463$			5.71450e22i			1.25759i	−0.777570	+	0.628796i	$0.783548\pi$
$464$	−1.44321e23			−3.11836
$465$		0			0
$466$	6.32618e22			1.31784
$467$			2.45387e22i			0.501948i	0.967994	+	0.250974i	$0.0807509\pi$
$467$			2.45387e22i			0.501948i	−0.967994	+	0.250974i	$0.919249\pi$
$468$		0			0
$469$	6.99280e21			0.137937
$470$	5.28206e22	−	1.31550e22i	1.02323	−	0.254834i
$471$		0			0
$472$		−	1.43480e23i		−	2.68093i
$473$		−	4.18035e22i		−	0.767173i
$474$		0			0
$475$	−3.28510e22	+	1.74451e22i	−0.581638	+	0.308872i
$476$	−6.99588e22			−1.21670
$477$		0			0
$478$			1.10007e22i			0.184621i
$479$	−4.87996e22			−0.804572			−0.402286	−	0.915514i	$-0.631784\pi$
$479$	−4.87996e22			−0.804572			−0.402286	+	0.915514i	$0.631784\pi$
$480$		0			0
$481$	8.62111e22			1.37192
$482$		−	2.03371e22i		−	0.317973i
$483$		0			0
$484$	−2.04666e23			−3.08931
$485$	−1.45359e22	−	5.83656e22i	−0.215595	−	0.865669i
$486$		0			0
$487$			6.75469e22i			0.967407i	0.875232	+	0.483703i	$0.160709\pi$
$487$			6.75469e22i			0.967407i	−0.875232	+	0.483703i	$0.839291\pi$
$488$		−	8.64463e22i		−	1.21668i
$489$		0			0
$490$	−2.88867e22	−	1.15987e23i	−0.392673	−	1.57668i
$491$	−9.44565e22			−1.26194			−0.630971	−	0.775807i	$-0.717343\pi$
$491$	−9.44565e22			−1.26194			−0.630971	+	0.775807i	$0.717343\pi$
$492$		0			0
$493$			1.56967e23i			2.02586i
$494$	1.52126e23			1.92985
$495$		0			0
$496$	1.73100e23			2.12179
$497$			4.72952e22i			0.569886i
$498$		0			0
$499$	−6.29077e21			−0.0732570			−0.0366285	−	0.999329i	$-0.511662\pi$
$499$	−6.29077e21			−0.0732570			−0.0366285	+	0.999329i	$0.511662\pi$
$500$	−1.54857e23	+	1.39213e23i	−1.77290	+	1.59381i
$501$		0			0
$502$		−	1.42888e22i		−	0.158130i
$503$		−	1.45150e23i		−	1.57939i	−0.613500	−	0.789695i	$-0.710239\pi$
$503$		−	1.45150e23i		−	1.57939i	0.613500	−	0.789695i	$-0.289761\pi$
$504$		0			0
$505$	2.55593e22	−	6.36554e21i	0.268889	−	0.0669667i
$506$	1.32172e23			1.36728
$507$		0			0
$508$		−	4.00107e23i		−	4.00253i
$509$	−3.74667e22			−0.368590			−0.184295	−	0.982871i	$-0.559000\pi$
$509$	−3.74667e22			−0.368590			−0.184295	+	0.982871i	$0.559000\pi$
$510$		0			0
$511$	−1.82393e22			−0.173553
$512$			2.11784e23i			1.98197i
$513$		0			0
$514$	−2.85655e23			−2.58616
$515$	4.15729e22	+	1.66926e23i	0.370210	+	1.48649i
$516$		0			0
$517$		−	1.00801e23i		−	0.868554i
$518$			6.38574e22i			0.541263i
$519$		0			0
$520$	4.79757e23	−	1.19483e23i	3.93544	−	0.980120i
$521$	1.42079e23			1.14659			0.573295	−	0.819349i	$-0.305665\pi$
$521$	1.42079e23			1.14659			0.573295	+	0.819349i	$0.305665\pi$
$522$		0			0
$523$		−	1.00844e23i		−	0.787748i	−0.919164	−	0.393874i	$-0.871135\pi$
$523$		−	1.00844e23i		−	0.787748i	0.919164	−	0.393874i	$-0.128865\pi$
$524$	5.44043e23			4.18135
$525$		0			0
$526$	1.28903e23			0.959142
$527$		−	1.88268e23i		−	1.37844i
$528$		0			0
$529$	1.07110e23			0.759373
$530$	4.10343e23	−	1.02196e23i	2.86287	−	0.712997i
$531$		0			0
$532$			7.93830e22i			0.536387i
$533$		−	4.13919e22i		−	0.275254i
$534$		0			0
$535$	1.02202e22	+	4.10366e22i	0.0658341	+	0.264341i
$536$	1.62127e23			1.02791
$537$		0			0
$538$			8.55905e22i			0.525746i
$539$	−2.21347e23			−1.33835
$540$		0			0
$541$	−2.41487e23			−1.41487			−0.707437	−	0.706776i	$-0.750149\pi$
$541$	−2.41487e23			−1.41487			−0.707437	+	0.706776i	$0.750149\pi$
$542$		−	2.19043e23i		−	1.26339i
$543$		0			0
$544$	−4.50022e23			−2.51561
$545$	−3.19695e23	+	7.96201e22i	−1.75941	+	0.438180i
$546$		0			0
$547$			8.33868e22i			0.444841i	0.974951	+	0.222421i	$0.0713958\pi$
$547$			8.33868e22i			0.444841i	−0.974951	+	0.222421i	$0.928604\pi$
$548$			3.11368e23i			1.63546i
$549$		0			0
$550$	2.56715e23	+	4.83421e23i	1.30728	+	2.46174i
$551$	1.78112e23			0.893110
$552$		0			0
$553$		−	4.34114e22i		−	0.211077i
$554$	−1.82586e23			−0.874250
$555$		0			0
$556$	−4.55253e23			−2.11406
$557$			2.03945e23i			0.932706i	0.884599	+	0.466353i	$0.154432\pi$
$557$			2.03945e23i			0.932706i	−0.884599	+	0.466353i	$0.845568\pi$
$558$		0			0
$559$	1.81817e23			0.806554
$560$	4.34523e22	+	1.74472e23i	0.189852	+	0.762304i
$561$		0			0
$562$		−	2.05359e23i		−	0.870472i
$563$			3.44953e23i			1.44025i	0.693843	+	0.720127i	$0.255916\pi$
$563$			3.44953e23i			1.44025i	−0.693843	+	0.720127i	$0.744084\pi$
$564$		0			0
$565$	−4.51840e22	−	1.81425e23i	−0.183051	−	0.734998i
$566$	−4.55518e23			−1.81788
$567$		0			0
$568$			1.09653e24i			4.24678i
$569$	4.85663e22			0.185302			0.0926511	−	0.995699i	$-0.470466\pi$
$569$	4.85663e22			0.185302			0.0926511	+	0.995699i	$0.470466\pi$
$570$		0			0
$571$	−3.27105e23			−1.21138			−0.605689	−	0.795701i	$-0.707102\pi$
$571$	−3.27105e23			−1.21138			−0.605689	+	0.795701i	$0.707102\pi$
$572$		−	1.57709e24i		−	5.75426i
$573$		0			0
$574$	3.06594e22			0.108596
$575$	−6.59219e22	−	1.24138e23i	−0.230066	−	0.433239i
$576$		0			0
$577$			2.63713e23i			0.893588i	0.894637	+	0.446794i	$0.147434\pi$
$577$			2.63713e23i			0.893588i	−0.894637	+	0.446794i	$0.852566\pi$
$578$			6.78498e23i			2.26549i
$579$		0			0
$580$	9.67571e23	−	2.40973e23i	3.13722	−	0.781324i
$581$	−9.66304e22			−0.308757
$582$		0			0
$583$		−	7.83086e23i		−	2.43011i
$584$	−4.22875e23			−1.29331
$585$		0			0
$586$	−2.21451e23			−0.657883
$587$		−	4.44331e23i		−	1.30102i	−0.759500	−	0.650508i	$-0.774556\pi$
$587$		−	4.44331e23i		−	1.30102i	0.759500	−	0.650508i	$-0.225444\pi$
$588$		0			0
$589$	−2.13630e23			−0.607689
$590$	1.66960e23	+	6.70389e23i	0.468135	+	1.87968i
$591$		0			0
$592$			7.26894e23i			1.98032i
$593$		−	1.92533e23i		−	0.517058i	−0.966003	−	0.258529i	$-0.916762\pi$
$593$		−	1.92533e23i		−	0.517058i	0.966003	−	0.258529i	$-0.0832378\pi$
$594$		0			0
$595$	1.89760e23	−	4.72597e22i	0.495235	−	0.123338i
$596$	1.90360e23			0.489758
$597$		0			0
$598$			5.74856e23i			1.43747i
$599$	2.59948e23			0.640853			0.320426	−	0.947273i	$-0.396174\pi$
$599$	2.59948e23			0.640853			0.320426	+	0.947273i	$0.396174\pi$
$600$		0			0
$601$	7.44017e23			1.78299			0.891497	−	0.453026i	$-0.149656\pi$
$601$	7.44017e23			1.78299			0.891497	+	0.453026i	$0.149656\pi$
$602$			1.34674e23i			0.318209i
$603$		0			0
$604$	−1.49190e24			−3.42709
$605$	5.55149e23	−	1.38260e23i	1.25744	−	0.313166i
$606$		0			0
$607$		−	5.55606e23i		−	1.22367i	−0.790987	−	0.611833i	$-0.790432\pi$
$607$		−	5.55606e23i		−	1.22367i	0.790987	−	0.611833i	$-0.209568\pi$
$608$			5.10644e23i			1.10902i
$609$		0			0
$610$	1.00593e23	+	4.03906e23i	0.212453	+	0.853054i
$611$	4.38417e23			0.913140
$612$		0			0
$613$			1.52685e23i			0.309301i	0.987969	+	0.154651i	$0.0494252\pi$
$613$			1.52685e23i			0.309301i	−0.987969	+	0.154651i	$0.950575\pi$
$614$	−5.53201e23			−1.10523
$615$		0			0
$616$	6.78161e23			1.31794
$617$		−	9.08539e22i		−	0.174148i	−0.996202	−	0.0870742i	$-0.972248\pi$
$617$		−	9.08539e22i		−	0.174148i	0.996202	−	0.0870742i	$-0.0277517\pi$
$618$		0			0
$619$	−1.31370e23			−0.244977			−0.122489	−	0.992470i	$-0.539087\pi$
$619$	−1.31370e23			−0.244977			−0.122489	+	0.992470i	$0.539087\pi$
$620$	−1.16052e24	+	2.89026e23i	−2.13462	+	0.531628i
$621$		0			0
$622$		−	1.06728e24i		−	1.91012i
$623$		−	2.26631e23i		−	0.400102i
$624$		0			0
$625$	3.25999e23	−	4.82222e23i	0.560061	−	0.828451i
$626$	−1.40810e24			−2.38645
$627$		0			0
$628$		−	2.20728e24i		−	3.64083i
$629$	7.90587e23			1.28653
$630$		0			0
$631$	8.97044e21			0.0142090			0.00710451	−	0.999975i	$-0.497739\pi$
$631$	8.97044e21			0.0142090			0.00710451	+	0.999975i	$0.497739\pi$
$632$		−	1.00648e24i		−	1.57294i
$633$		0			0
$634$	−6.77652e23			−1.03097
$635$	2.70287e23	+	1.08527e24i	0.405740	+	1.62915i
$636$		0			0
$637$		−	9.62709e23i		−	1.40705i
$638$		−	2.62102e24i		−	3.78003i
$639$		0			0
$640$	−3.70512e22	−	1.48770e23i	−0.0520323	−	0.208923i
$641$	−9.15570e23			−1.26882			−0.634408	−	0.772999i	$-0.718756\pi$
$641$	−9.15570e23			−1.26882			−0.634408	+	0.772999i	$0.718756\pi$
$642$		0			0
$643$		−	3.21374e23i		−	0.433727i	−0.976202	−	0.216864i	$-0.930417\pi$
$643$		−	3.21374e23i		−	0.433727i	0.976202	−	0.216864i	$-0.0695827\pi$
$644$	−2.99974e23			−0.399534
$645$		0			0
$646$	1.39505e24			1.80973
$647$			7.88455e23i			1.00946i	0.863276	+	0.504732i	$0.168409\pi$
$647$			7.88455e23i			1.00946i	−0.863276	+	0.504732i	$0.831591\pi$
$648$		0			0
$649$	1.27935e24			1.59555
$650$	−2.10255e24	+	1.11653e24i	−2.58811	+	1.37438i
$651$		0			0
$652$			1.12279e24i			1.34646i
$653$			5.48292e23i			0.649008i	0.945884	+	0.324504i	$0.105197\pi$
$653$			5.48292e23i			0.649008i	−0.945884	+	0.324504i	$0.894803\pi$
$654$		0			0
$655$	−1.47569e24	+	3.67521e23i	−1.70194	+	0.423868i
$656$	3.48998e23			0.397320
$657$		0			0
$658$			3.24740e23i			0.360260i
$659$	−8.98274e23			−0.983745			−0.491873	−	0.870667i	$-0.663687\pi$
$659$	−8.98274e23			−0.983745			−0.491873	+	0.870667i	$0.663687\pi$
$660$		0			0
$661$	−1.61443e23			−0.172308			−0.0861542	−	0.996282i	$-0.527458\pi$
$661$	−1.61443e23			−0.172308			−0.0861542	+	0.996282i	$0.527458\pi$
$662$		−	1.79131e24i		−	1.88746i
$663$		0			0
$664$	−2.24035e24			−2.30085
$665$	−5.36261e22	−	2.15323e23i	−0.0543741	−	0.218326i
$666$		0			0
$667$			6.73054e23i			0.665243i
$668$			1.26092e24i			1.23052i
$669$		0			0
$670$	−7.57510e23	+	1.88658e23i	−0.720697	+	0.179489i
$671$	7.70803e23			0.724106
$672$		0			0
$673$			1.67153e24i			1.53104i	0.643414	+	0.765519i	$0.277518\pi$
$673$			1.67153e24i			1.53104i	−0.643414	+	0.765519i	$0.722482\pi$
$674$	−1.93040e24			−1.74598
$675$		0			0
$676$	4.15622e24			3.66565
$677$		−	8.41862e22i		−	0.0733225i	−0.999328	−	0.0366612i	$-0.988328\pi$
$677$		−	8.41862e22i		−	0.0733225i	0.999328	−	0.0366612i	$-0.0116723\pi$
$678$		0			0
$679$	3.58830e23			0.304787
$680$	4.39955e24	−	1.09571e24i	3.69048	−	0.919112i
$681$		0			0
$682$			3.14368e24i			2.57200i
$683$		−	6.67252e23i		−	0.539156i	−0.962979	−	0.269578i	$-0.913116\pi$
$683$		−	6.67252e23i		−	0.539156i	0.962979	−	0.269578i	$-0.0868841\pi$
$684$		0			0
$685$	−2.10341e23	−	8.44574e23i	−0.165788	−	0.665683i
$686$	1.52041e24			1.18360
$687$		0			0
$688$			1.53300e24i			1.16423i
$689$	3.40589e24			2.55486
$690$		0			0
$691$	1.17485e24			0.859841			0.429921	−	0.902867i	$-0.358542\pi$
$691$	1.17485e24			0.859841			0.429921	+	0.902867i	$0.358542\pi$
$692$			4.08069e24i			2.95007i
$693$		0			0
$694$	−2.94356e24			−2.07643
$695$	1.23485e24	−	3.07540e23i	0.860488	−	0.214304i
$696$		0			0
$697$		−	3.79579e23i		−	0.258121i
$698$			2.71324e24i			1.82271i
$699$		0			0
$700$	−5.82634e23	−	1.09716e24i	−0.381999	−	0.719345i
$701$	7.55238e23			0.489194			0.244597	−	0.969625i	$-0.421344\pi$
$701$	7.55238e23			0.489194			0.244597	+	0.969625i	$0.421344\pi$
$702$		0			0
$703$		−	8.97088e23i		−	0.567172i
$704$	1.93667e24			1.20973
$705$		0			0
$706$	−2.81009e24			−1.71348
$707$			1.57138e23i			0.0946709i
$708$		0			0
$709$	−2.42561e24			−1.42668			−0.713342	−	0.700816i	$-0.752819\pi$
$709$	−2.42561e24			−1.42668			−0.713342	+	0.700816i	$0.752819\pi$
$710$	−1.27597e24	−	5.12335e24i	−0.741557	−	2.97755i
$711$		0			0
$712$		−	5.25439e24i		−	2.98155i
$713$		−	8.07268e23i		−	0.452644i
$714$		0			0
$715$	1.06538e24	+	4.27778e24i	0.583315	+	2.34216i
$716$	1.61063e24			0.871434
$717$		0			0
$718$			4.26679e24i			2.25446i
$719$	−9.01398e23			−0.470675			−0.235337	−	0.971914i	$-0.575620\pi$
$719$	−9.01398e23			−0.470675			−0.235337	+	0.971914i	$0.575620\pi$
$720$		0			0
$721$	−1.02626e24			−0.523367
$722$			2.06692e24i			1.04174i
$723$		0			0
$724$	4.92419e24			2.42414
$725$	−2.46171e24	+	1.30726e24i	−1.19774	+	0.636047i
$726$		0			0
$727$			1.20440e24i			0.572437i	0.958164	+	0.286219i	$0.0923984\pi$
$727$			1.20440e24i			0.572437i	−0.958164	+	0.286219i	$0.907602\pi$
$728$			2.94954e24i			1.38560i
$729$		0			0
$730$	1.97582e24	−	4.92077e23i	0.906781	−	0.225834i
$731$	1.66733e24			0.756350
$732$		0			0
$733$			1.04619e24i			0.463689i	0.972753	+	0.231844i	$0.0744760\pi$
$733$			1.04619e24i			0.463689i	−0.972753	+	0.231844i	$0.925524\pi$
$734$	1.32962e24			0.582521
$735$		0			0
$736$	−1.92963e24			−0.826062
$737$			1.44561e24i			0.611755i
$738$		0			0
$739$	−1.54703e24			−0.639767			−0.319884	−	0.947457i	$-0.603644\pi$
$739$	−1.54703e24			−0.639767			−0.319884	+	0.947457i	$0.603644\pi$
$740$	−1.21370e24	−	4.87331e24i	−0.496182	−	1.99230i
$741$		0			0
$742$			2.52278e24i			1.00797i
$743$		−	3.06018e24i		−	1.20877i	−0.796693	−	0.604384i	$-0.793419\pi$
$743$		−	3.06018e24i		−	1.20877i	0.796693	−	0.604384i	$-0.206581\pi$
$744$		0			0
$745$	−5.16342e23	+	1.28595e23i	−0.199347	+	0.0496473i
$746$	−6.81829e24			−2.60253
$747$		0			0
$748$		−	1.44625e25i		−	5.39609i
$749$	−2.52292e23			−0.0930698
$750$		0			0
$751$	6.94719e23			0.250536			0.125268	−	0.992123i	$-0.460021\pi$
$751$	6.94719e23			0.250536			0.125268	+	0.992123i	$0.460021\pi$
$752$			3.69654e24i			1.31809i
$753$		0			0
$754$	1.13997e25			3.97407
$755$	4.04672e24	−	1.00783e24i	1.39493	−	0.347408i
$756$		0			0
$757$			2.23696e24i			0.753952i	0.926223	+	0.376976i	$0.123036\pi$
$757$			2.23696e24i			0.753952i	−0.926223	+	0.376976i	$0.876964\pi$
$758$		−	5.22789e24i		−	1.74236i
$759$		0			0
$760$	−1.24331e24	−	4.99221e24i	−0.405195	−	1.62696i
$761$	−8.04622e23			−0.259312			−0.129656	−	0.991559i	$-0.541387\pi$
$761$	−8.04622e23			−0.259312			−0.129656	+	0.991559i	$0.541387\pi$
$762$		0			0
$763$		−	1.96548e24i		−	0.619456i
$764$	−7.77207e23			−0.242238
$765$		0			0
$766$	−6.18749e24			−1.88612
$767$			5.56430e24i			1.67745i
$768$		0			0
$769$	−3.81239e23			−0.112415			−0.0562075	−	0.998419i	$-0.517901\pi$
$769$	−3.81239e23			−0.112415			−0.0562075	+	0.998419i	$0.517901\pi$
$770$	−3.16860e24	+	7.89139e23i	−0.924051	+	0.230135i
$771$		0			0
$772$		−	1.26260e25i		−	3.60178i
$773$		−	1.76590e24i		−	0.498242i	−0.968472	−	0.249121i	$-0.919858\pi$
$773$		−	1.76590e24i		−	0.498242i	0.968472	−	0.249121i	$-0.0801417\pi$
$774$		0			0
$775$	2.95260e24	−	1.56794e24i	0.814967	−	0.432778i
$776$	8.31940e24			2.27126
$777$		0			0
$778$			6.18720e24i			1.65260i
$779$	−4.30712e23			−0.113794
$780$		0			0
$781$	−9.77726e24			−2.52746
$782$			5.27164e24i			1.34800i
$783$		0			0
$784$	8.11714e24			2.03103
$785$	1.49110e24	+	5.98715e24i	0.369075	+	1.48193i
$786$		0			0
$787$			4.24393e24i			1.02798i	0.857797	+	0.513988i	$0.171832\pi$
$787$			4.24393e24i			1.02798i	−0.857797	+	0.513988i	$0.828168\pi$
$788$		−	6.15632e24i		−	1.47519i
$789$		0			0
$790$	1.17119e24	+	4.70263e24i	0.274661	+	1.10284i
$791$	1.11540e24			0.258780
$792$		0			0
$793$			3.35247e24i			0.761276i
$794$	2.28638e24			0.513659
$795$		0			0
$796$	−7.98551e24			−1.75607
$797$			1.31510e24i			0.286129i	0.989713	+	0.143065i	$0.0456957\pi$
$797$			1.31510e24i			0.286129i	−0.989713	+	0.143065i	$0.954304\pi$
$798$		0			0
$799$	4.02045e24			0.856301
$800$	−3.74789e24	−	7.05767e24i	−0.789809	−	1.48729i
$801$		0			0
$802$			4.49837e24i			0.928054i
$803$		−	3.77059e24i		−	0.769710i
$804$		0			0
$805$	8.13666e23	−	2.02643e23i	0.162623	−	0.0405011i
$806$	−1.36729e25			−2.70403
$807$		0			0
$808$			3.64321e24i			0.705486i
$809$	3.05085e24			0.584599			0.292300	−	0.956327i	$-0.405580\pi$
$809$	3.05085e24			0.584599			0.292300	+	0.956327i	$0.405580\pi$
$810$		0			0
$811$	6.27263e24			1.17699			0.588494	−	0.808501i	$-0.299721\pi$
$811$	6.27263e24			1.17699			0.588494	+	0.808501i	$0.299721\pi$
$812$			5.94861e24i			1.10456i
$813$		0			0
$814$	−1.32011e25			−2.40051
$815$	−7.58484e23	−	3.04551e24i	−0.136492	−	0.548051i
$816$		0			0
$817$		−	1.89193e24i		−	0.333441i
$818$		−	5.71583e24i		−	0.996956i
$819$		0			0
$820$	−2.33979e24	+	5.82723e23i	−0.399722	+	0.0995508i
$821$	2.38961e24			0.404027			0.202014	−	0.979383i	$-0.435251\pi$
$821$	2.38961e24			0.404027			0.202014	+	0.979383i	$0.435251\pi$
$822$		0			0
$823$			8.35852e24i			1.38430i	0.721753	+	0.692151i	$0.243337\pi$
$823$			8.35852e24i			1.38430i	−0.721753	+	0.692151i	$0.756663\pi$
$824$	−2.37935e25			−3.90012
$825$		0			0
$826$	−4.12154e24			−0.661803
$827$			1.54877e24i			0.246145i	0.992398	+	0.123072i	$0.0392747\pi$
$827$			1.54877e24i			0.246145i	−0.992398	+	0.123072i	$0.960725\pi$
$828$		0			0
$829$	2.83792e24			0.441862			0.220931	−	0.975289i	$-0.429090\pi$
$829$	2.83792e24			0.441862			0.220931	+	0.975289i	$0.429090\pi$
$830$	1.04677e25	−	2.60698e24i	1.61320	−	0.401766i
$831$		0			0
$832$			8.42318e24i			1.27183i
$833$		−	8.82840e24i		−	1.31947i
$834$		0			0
$835$	−8.51798e23	−	3.42019e24i	−0.124739	−	0.500859i
$836$	−1.64107e25			−2.37889
$837$		0			0
$838$		−	1.53496e24i		−	0.218034i
$839$	−7.94888e24			−1.11771			−0.558855	−	0.829265i	$-0.688759\pi$
$839$	−7.94888e24			−1.11771			−0.558855	+	0.829265i	$0.688759\pi$
$840$		0			0
$841$	6.08980e24			0.839145
$842$			1.98243e23i			0.0270424i
$843$		0			0
$844$	3.18075e25			4.25225
$845$	−1.12736e25	+	2.80768e24i	−1.49203	+	0.371591i
$846$		0			0
$847$			3.41304e24i			0.442724i
$848$			2.87169e25i			3.68785i
$849$		0			0
$850$	−1.92812e25	+	1.02390e25i	−2.42701	+	1.28884i
$851$	3.38993e24			0.422464
$852$		0			0
$853$		−	6.30848e23i		−	0.0770651i	−0.999257	−	0.0385326i	$-0.987732\pi$
$853$		−	6.30848e23i		−	0.0770651i	0.999257	−	0.0385326i	$-0.0122683\pi$
$854$	−2.48321e24			−0.300345
$855$		0			0
$856$	−5.84934e24			−0.693554
$857$		−	1.07597e25i		−	1.26317i	−0.775305	−	0.631587i	$-0.782404\pi$
$857$		−	1.07597e25i		−	1.26317i	0.775305	−	0.631587i	$-0.217596\pi$
$858$		0			0
$859$	−4.06020e24			−0.467310			−0.233655	−	0.972320i	$-0.575069\pi$
$859$	−4.06020e24			−0.467310			−0.233655	+	0.972320i	$0.575069\pi$
$860$	−2.55965e24	−	1.02777e25i	−0.291705	−	1.17127i
$861$		0			0
$862$			2.12317e25i			2.37232i
$863$			8.77622e24i			0.970992i	0.874239	+	0.485496i	$0.161361\pi$
$863$			8.77622e24i			0.970992i	−0.874239	+	0.485496i	$0.838639\pi$
$864$		0			0
$865$	−2.75666e24	−	1.10687e25i	−0.299051	−	1.20077i
$866$	2.48671e25			2.67130
$867$		0			0
$868$		−	7.13482e24i		−	0.751563i
$869$	8.97437e24			0.936130
$870$		0			0
$871$	−6.28742e24			−0.643158
$872$		−	4.55692e25i		−	4.61617i
$873$		0			0
$874$	5.98179e24			0.594270
$875$	2.32154e24	+	2.58241e24i	0.228406	+	0.254072i
$876$		0			0
$877$		−	1.19341e25i		−	1.15158i	−0.817598	−	0.575789i	$-0.804695\pi$
$877$		−	1.19341e25i		−	1.15158i	0.817598	−	0.575789i	$-0.195305\pi$
$878$			1.73078e25i			1.65401i
$879$		0			0
$880$	−3.60684e25	+	8.98282e24i	−3.38083	+	0.841996i
$881$	8.45862e22			0.00785244			0.00392622	−	0.999992i	$-0.498750\pi$
$881$	8.45862e22			0.00785244			0.00392622	+	0.999992i	$0.498750\pi$
$882$		0			0
$883$		−	1.78893e25i		−	1.62903i	−0.580145	−	0.814513i	$-0.697004\pi$
$883$		−	1.78893e25i		−	1.62903i	0.580145	−	0.814513i	$-0.302996\pi$
$884$	6.29019e25			5.67308
$885$		0			0
$886$	3.25278e25			2.87785
$887$			1.34367e25i			1.17745i	0.808334	+	0.588725i	$0.200370\pi$
$887$			1.34367e25i			1.17745i	−0.808334	+	0.588725i	$0.799630\pi$
$888$		0			0
$889$	−6.67223e24			−0.573596
$890$	6.11424e24	+	2.45503e25i	0.520628	+	2.09046i
$891$		0			0
$892$		−	4.95066e25i		−	4.13582i
$893$		−	4.56204e24i		−	0.377504i
$894$		0			0
$895$	−4.36876e24	+	1.08804e24i	−0.354701	+	0.0883382i
$896$	9.14637e23			0.0735581
$897$		0			0
$898$			1.54720e24i			0.122095i
$899$	−1.60085e25			−1.25139
$900$		0			0
$901$	3.12333e25			2.39583
$902$			6.33817e24i			0.481624i
$903$		0			0
$904$	2.58603e25			1.92842
$905$	−1.33566e25	+	3.32647e24i	−0.986699	+	0.245737i
$906$		0			0
$907$		−	2.36264e25i		−	1.71292i	−0.516217	−	0.856458i	$-0.672660\pi$
$907$		−	2.36264e25i		−	1.71292i	0.516217	−	0.856458i	$-0.327340\pi$
$908$			2.96040e25i			2.12628i
$909$		0			0
$910$	−3.43221e24	−	1.37812e25i	−0.241948	−	0.971485i
$911$	−1.06631e25			−0.744693			−0.372346	−	0.928094i	$-0.621447\pi$
$911$	−1.06631e25			−0.744693			−0.372346	+	0.928094i	$0.621447\pi$
$912$		0			0
$913$		−	1.99762e25i		−	1.36934i
$914$	3.61824e24			0.245728
$915$		0			0
$916$	3.63302e23			0.0242190
$917$		−	9.07253e24i		−	0.599224i
$918$		0			0
$919$	−2.28019e25			−1.47839			−0.739196	−	0.673490i	$-0.764794\pi$
$919$	−2.28019e25			−1.47839			−0.739196	+	0.673490i	$0.764794\pi$
$920$	1.88647e25	−	4.69824e24i	1.21186	−	0.301814i
$921$		0			0
$922$			3.26723e25i			2.06047i
$923$		−	4.25244e25i		−	2.65720i
$924$		0			0
$925$	6.58420e24	+	1.23988e25i	0.403923	+	0.760630i
$926$	3.80582e25			2.31342
$927$		0			0
$928$			3.82654e25i			2.28375i
$929$	−1.09016e25			−0.644696			−0.322348	−	0.946621i	$-0.604472\pi$
$929$	−1.09016e25			−0.644696			−0.322348	+	0.946621i	$0.604472\pi$
$930$		0			0
$931$	−1.00177e25			−0.581694
$932$		−	2.96816e25i		−	1.70786i
$933$		0			0
$934$	1.63426e25			0.923365
$935$	9.76993e24	+	3.92288e25i	0.547007	+	2.19638i
$936$		0			0
$937$			1.90296e25i			1.04627i	0.852251	+	0.523133i	$0.175237\pi$
$937$			1.90296e25i			1.04627i	−0.852251	+	0.523133i	$0.824763\pi$
$938$		−	4.65716e24i		−	0.253744i
$939$		0			0
$940$	−6.17213e24	−	2.47827e25i	−0.330254	−	1.32606i
$941$	−3.43765e25			−1.82285			−0.911424	−	0.411469i	$-0.865016\pi$
$941$	−3.43765e25			−1.82285			−0.911424	+	0.411469i	$0.865016\pi$
$942$		0			0
$943$		−	1.62758e24i		−	0.0847605i
$944$	−4.69157e25			−2.42134
$945$		0			0
$946$	−2.78409e25			−1.41126
$947$		−	2.00900e24i		−	0.100927i	−0.998726	−	0.0504633i	$-0.983930\pi$
$947$		−	2.00900e24i		−	0.100927i	0.998726	−	0.0504633i	$-0.0160698\pi$
$948$		0			0
$949$	1.63995e25			0.809222
$950$	1.16183e25	+	2.18785e25i	0.568189	+	1.06996i
$951$		0			0
$952$			2.70483e25i			1.29935i
$953$		−	3.18804e25i		−	1.51787i	−0.651168	−	0.758933i	$-0.725721\pi$
$953$		−	3.18804e25i		−	1.51787i	0.651168	−	0.758933i	$-0.274279\pi$
$954$		0			0
$955$	2.10814e24	−	5.25032e23i	0.0985986	−	0.0245560i
$956$	5.16135e24			0.239261
$957$		0			0
$958$			3.25002e25i			1.48006i
$959$	5.19242e24			0.234375
$960$		0			0
$961$	−3.34940e24			−0.148531
$962$		−	5.74160e25i		−	2.52374i
$963$		0			0
$964$	−9.54190e24			−0.412079
$965$	8.52931e24	+	3.42474e25i	0.365117	+	1.46604i
$966$		0			0
$967$		−	4.13906e25i		−	1.74091i	−0.492246	−	0.870456i	$-0.663824\pi$
$967$		−	4.13906e25i		−	1.74091i	0.492246	−	0.870456i	$-0.336176\pi$
$968$			7.91307e25i			3.29917i
$969$		0			0
$970$	−3.88711e25	+	9.68083e24i	−1.59245	+	0.396600i
$971$	−1.62997e25			−0.661938			−0.330969	−	0.943642i	$-0.607376\pi$
$971$	−1.62997e25			−0.661938			−0.330969	+	0.943642i	$0.607376\pi$
$972$		0			0
$973$			7.59186e24i			0.302963i
$974$	4.49857e25			1.77961
$975$		0			0
$976$	−2.82665e25			−1.09888
$977$			3.63045e25i			1.39913i	0.714571	+	0.699563i	$0.246622\pi$
$977$			3.63045e25i			1.39913i	−0.714571	+	0.699563i	$0.753378\pi$
$978$		0			0
$979$	4.68510e25			1.77446
$980$	−5.44197e25	+	1.35532e25i	−2.04331	+	0.508886i
$981$		0			0
$982$			6.29073e25i			2.32142i
$983$		−	4.10653e25i		−	1.50235i	−0.660105	−	0.751174i	$-0.729488\pi$
$983$		−	4.10653e25i		−	1.50235i	0.660105	−	0.751174i	$-0.270512\pi$
$984$		0			0
$985$	4.15882e24	+	1.66988e25i	0.149542	+	0.600449i
$986$	1.04539e26			3.72670
$987$		0			0
$988$		−	7.13754e25i		−	2.50100i
$989$	7.14927e24			0.248367
$990$		0			0
$991$	−1.91509e25			−0.653979			−0.326990	−	0.945028i	$-0.606034\pi$
$991$	−1.91509e25			−0.653979			−0.326990	+	0.945028i	$0.606034\pi$
$992$		−	4.58959e25i		−	1.55391i
$993$		0			0
$994$	3.14983e25			1.04834
$995$	2.16604e25	−	5.39451e24i	0.714775	−	0.178015i
$996$		0			0
$997$			2.38172e25i			0.772649i	0.922363	+	0.386324i	$0.126255\pi$
$997$			2.38172e25i			0.772649i	−0.922363	+	0.386324i	$0.873745\pi$
$998$			4.18961e24i			0.134761i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.18.b.c.19.2	yes	16
3.2	odd	2	inner	45.18.b.c.19.15	yes	16
5.4	even	2	inner	45.18.b.c.19.16	yes	16
15.14	odd	2	inner	45.18.b.c.19.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.18.b.c.19.1	✓	16	15.14	odd	2	inner
45.18.b.c.19.2	yes	16	1.1	even	1	trivial
45.18.b.c.19.15	yes	16	3.2	odd	2	inner
45.18.b.c.19.16	yes	16	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	45.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-665.993i q^{2} -312475. q^{4} +(847574. - 211088. i) q^{5} +5.21087e6i q^{7} +1.20813e8i q^{8} +O(q^{10})\)	\(q-665.993i q^{2} -312475. q^{4} +(847574. - 211088. i) q^{5} +5.21087e6i q^{7} +1.20813e8i q^{8} +(-1.40583e8 - 5.64478e8i) q^{10} -1.07723e9 q^{11} -4.68523e9i q^{13} +3.47040e9 q^{14} +3.95038e10 q^{16} -4.29653e10i q^{17} -4.87532e10 q^{19} +(-2.64845e11 + 6.59596e10i) q^{20} +7.17430e11i q^{22} -1.84229e11i q^{23} +(6.73823e11 - 3.57825e11i) q^{25} -3.12033e12 q^{26} -1.62826e12i q^{28} -3.65335e12 q^{29} +4.38186e12 q^{31} -1.04741e13i q^{32} -2.86146e13 q^{34} +(1.09995e12 + 4.41659e12i) q^{35} +1.84006e13i q^{37} +3.24693e13i q^{38} +(2.55021e13 + 1.02398e14i) q^{40} +8.83454e12 q^{41} +3.88064e13i q^{43} +3.36608e14 q^{44} -1.22695e14 q^{46} +9.35743e13i q^{47} +2.05477e14 q^{49} +(-2.38309e14 - 4.48761e14i) q^{50} +1.46402e15i q^{52} +7.26941e14i q^{53} +(-9.13035e14 + 2.27391e14i) q^{55} -6.29539e14 q^{56} +2.43310e15i q^{58} -1.18763e15 q^{59} -7.15539e14 q^{61} -2.91829e15i q^{62} -1.79782e15 q^{64} +(-9.88996e14 - 3.97108e15i) q^{65} -1.34197e15i q^{67} +1.34256e16i q^{68} +(2.94142e15 - 7.32560e14i) q^{70} +9.07627e15 q^{71} +3.50025e15i q^{73} +1.22547e16 q^{74} +1.52341e16 q^{76} -5.61332e15i q^{77} -8.33094e15 q^{79} +(3.34824e16 - 8.33878e15i) q^{80} -5.88374e15i q^{82} +1.85440e16i q^{83} +(-9.06946e15 - 3.64163e16i) q^{85} +2.58448e16 q^{86} -1.30144e17i q^{88} -4.34920e16 q^{89} +2.44141e16 q^{91} +5.75670e16i q^{92} +6.23198e16 q^{94} +(-4.13219e16 + 1.02912e16i) q^{95} -6.88619e16i q^{97} -1.36846e17i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 1473168 q^{4}+O(q^{10}) \) 16 * q - 1473168 * q^4	\( 16 q - 1473168 q^{4} - 670199320 q^{10} + 35028482624 q^{16} + 236279498336 q^{19} + 2507484007120 q^{25} - 12501422403232 q^{31} - 36533616605360 q^{34} - 44259047245280 q^{40} - 28675167752480 q^{46} - 430197530548688 q^{49} - 16\!\cdots\!00 q^{55}+ \cdots - 20\!\cdots\!80 q^{94}+O(q^{100}) \) 16 * q - 1473168 * q^4 - 670199320 * q^10 + 35028482624 * q^16 + 236279498336 * q^19 + 2507484007120 * q^25 - 12501422403232 * q^31 - 36533616605360 * q^34 - 44259047245280 * q^40 - 28675167752480 * q^46 - 430197530548688 * q^49 - 1615648303533600 * q^55 - 6459270800401888 * q^61 - 4539898356653312 * q^64 + 1120556748124800 * q^70 + 72078801859831872 * q^76 - 2212561840444576 * q^79 - 75398163530251360 * q^85 + 201977821610712000 * q^91 - 20802101586267680 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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