LMFDB - Embedded newform 180.9.c.b.91.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [180,9,Mod(91,180)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(180, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("180.91"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	180.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$73.3281498110$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.3
Character	$\chi$	$=$	180.91
Dual form			180.9.c.b.91.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-15.8926 - 1.85034i) q^{2} +(249.152 + 58.8137i) q^{4} +279.508 q^{5} -4368.38i q^{7} +(-3850.87 - 1395.72i) q^{8} +(-4442.13 - 517.186i) q^{10} +12642.2i q^{11} -40361.3 q^{13} +(-8083.00 + 69425.2i) q^{14} +(58617.9 + 29307.1i) q^{16} +124816. q^{17} +203639. i q^{19} +(69640.2 + 16438.9i) q^{20} +(23392.4 - 200918. i) q^{22} -226436. i q^{23} +78125.0 q^{25} +(641447. + 74682.1i) q^{26} +(256921. - 1.08839e6i) q^{28} -25415.0 q^{29} +1.29831e6i q^{31} +(-877366. - 574231. i) q^{32} +(-1.98365e6 - 230952. i) q^{34} -1.22100e6i q^{35} +1.08541e6 q^{37} +(376802. - 3.23637e6i) q^{38} +(-1.07635e6 - 390116. i) q^{40} +4.60203e6 q^{41} +2.89375e6i q^{43} +(-743535. + 3.14984e6i) q^{44} +(-418985. + 3.59867e6i) q^{46} +3.71574e6i q^{47} -1.33180e7 q^{49} +(-1.24161e6 - 144558. i) q^{50} +(-1.00561e7 - 2.37379e6i) q^{52} -50193.3 q^{53} +3.53361e6i q^{55} +(-6.09705e6 + 1.68221e7i) q^{56} +(403912. + 47026.4i) q^{58} +9.55718e6i q^{59} -5.54455e6 q^{61} +(2.40232e6 - 2.06336e7i) q^{62} +(1.28811e7 + 1.07495e7i) q^{64} -1.12813e7 q^{65} -2.75178e7i q^{67} +(3.10982e7 + 7.34088e6i) q^{68} +(-2.25927e6 + 1.94049e7i) q^{70} -4.03081e7i q^{71} -4.73829e6 q^{73} +(-1.72500e7 - 2.00838e6i) q^{74} +(-1.19768e7 + 5.07373e7i) q^{76} +5.52261e7 q^{77} -5.91316e7i q^{79} +(1.63842e7 + 8.19159e6i) q^{80} +(-7.31385e7 - 8.51533e6i) q^{82} -2.39189e7i q^{83} +3.48871e7 q^{85} +(5.35442e6 - 4.59893e7i) q^{86} +(1.76450e7 - 4.86835e7i) q^{88} +2.09673e7 q^{89} +1.76313e8i q^{91} +(1.33176e7 - 5.64172e7i) q^{92} +(6.87538e6 - 5.90529e7i) q^{94} +5.69189e7i q^{95} +2.09675e7 q^{97} +(2.11658e8 + 2.46428e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 610 q^{4} - 8750 q^{10} - 51392 q^{13} + 11986 q^{16} - 758068 q^{22} + 2500000 q^{25} + 976324 q^{28} - 6117428 q^{34} + 5152064 q^{37} - 96250 q^{40} - 10391752 q^{46} - 11002976 q^{49} + 13976584 q^{52}+ \cdots + 80579520 q^{97}+O(q^{100}) $ 32 * q + 610 * q^4 - 8750 * q^10 - 51392 * q^13 + 11986 * q^16 - 758068 * q^22 + 2500000 * q^25 + 976324 * q^28 - 6117428 * q^34 + 5152064 * q^37 - 96250 * q^40 - 10391752 * q^46 - 11002976 * q^49 + 13976584 * q^52 - 36333948 * q^58 - 7802048 * q^61 + 116259994 * q^64 - 49897500 * q^70 - 94303680 * q^73 + 248840592 * q^76 - 428557904 * q^82 + 106960000 * q^85 + 510719924 * q^88 - 692727576 * q^94 + 80579520 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−15.8926	−	1.85034i	−0.993290	−	0.115646i
$2$	−15.8926	−	1.85034i	−0.993290	−	0.115646i
$3$		0			0
$3$		0			0
$4$	249.152	+	58.8137i	0.973252	+	0.229741i
$5$	279.508			0.447214
$5$	279.508			0.447214
$6$		0			0
$7$		−	4368.38i		−	1.81940i	−0.415264	−	0.909701i	$-0.636311\pi$
$7$		−	4368.38i		−	1.81940i	0.415264	−	0.909701i	$-0.363689\pi$
$8$	−3850.87	−	1395.72i	−0.940153	−	0.340752i
$9$		0			0
$10$	−4442.13	−	517.186i	−0.444213	−	0.0517186i
$11$			12642.2i			0.863481i	0.901998	+	0.431740i	$0.142100\pi$
$11$			12642.2i			0.863481i	−0.901998	+	0.431740i	$0.857900\pi$
$12$		0			0
$13$	−40361.3			−1.41316			−0.706580	−	0.707633i	$-0.749763\pi$
$13$	−40361.3			−1.41316			−0.706580	+	0.707633i	$0.749763\pi$
$14$	−8083.00	+	69425.2i	−0.210407	+	1.80719i
$15$		0			0
$16$	58617.9	+	29307.1i	0.894438	+	0.447191i
$17$	124816.			1.49443			0.747213	−	0.664585i	$-0.231392\pi$
$17$	124816.			1.49443			0.747213	+	0.664585i	$0.231392\pi$
$18$		0			0
$19$			203639.i			1.56260i	0.624157	+	0.781299i	$0.285443\pi$
$19$			203639.i			1.56260i	−0.624157	+	0.781299i	$0.714557\pi$
$20$	69640.2	+	16438.9i	0.435251	+	0.102743i
$21$		0			0
$22$	23392.4	−	200918.i	0.0998584	−	0.857687i
$23$		−	226436.i		−	0.809161i	−0.914502	−	0.404580i	$-0.867418\pi$
$23$		−	226436.i		−	0.809161i	0.914502	−	0.404580i	$-0.132582\pi$
$24$		0			0
$25$	78125.0			0.200000
$26$	641447.	+	74682.1i	1.40368	+	0.163427i
$27$		0			0
$28$	256921.	−	1.08839e6i	0.417991	−	1.77074i
$29$	−25415.0			−0.0359334			−0.0179667	−	0.999839i	$-0.505719\pi$
$29$	−25415.0			−0.0359334			−0.0179667	+	0.999839i	$0.505719\pi$
$30$		0			0
$31$			1.29831e6i			1.40583i	0.711274	+	0.702915i	$0.248118\pi$
$31$			1.29831e6i			1.40583i	−0.711274	+	0.702915i	$0.751882\pi$
$32$	−877366.	−	574231.i	−0.836721	−	0.547629i
$33$		0			0
$34$	−1.98365e6	−	230952.i	−1.48440	−	0.172825i
$35$		−	1.22100e6i		−	0.813661i
$36$		0			0
$37$	1.08541e6			0.579145			0.289572	−	0.957156i	$-0.406487\pi$
$37$	1.08541e6			0.579145			0.289572	+	0.957156i	$0.406487\pi$
$38$	376802.	−	3.23637e6i	0.180709	−	1.55211i
$39$		0			0
$40$	−1.07635e6	−	390116.i	−0.420449	−	0.152389i
$41$	4.60203e6			1.62860			0.814300	−	0.580445i	$-0.197121\pi$
$41$	4.60203e6			1.62860			0.814300	+	0.580445i	$0.197121\pi$
$42$		0			0
$43$			2.89375e6i			0.846422i	0.906031	+	0.423211i	$0.139097\pi$
$43$			2.89375e6i			0.846422i	−0.906031	+	0.423211i	$0.860903\pi$
$44$	−743535.	+	3.14984e6i	−0.198377	+	0.840384i
$45$		0			0
$46$	−418985.	+	3.59867e6i	−0.0935765	+	0.803732i
$47$			3.71574e6i			0.761471i	0.924684	+	0.380736i	$0.124329\pi$
$47$			3.71574e6i			0.761471i	−0.924684	+	0.380736i	$0.875671\pi$
$48$		0			0
$49$	−1.33180e7			−2.31022
$50$	−1.24161e6	−	144558.i	−0.198658	−	0.0231293i
$51$		0			0
$52$	−1.00561e7	−	2.37379e6i	−1.37536	−	0.324661i
$53$	−50193.3			−0.00636125			−0.00318062	−	0.999995i	$-0.501012\pi$
$53$	−50193.3			−0.00636125			−0.00318062	+	0.999995i	$0.501012\pi$
$54$		0			0
$55$			3.53361e6i			0.386160i
$56$	−6.09705e6	+	1.68221e7i	−0.619966	+	1.71052i
$57$		0			0
$58$	403912.	+	47026.4i	0.0356923	+	0.00415557i
$59$			9.55718e6i			0.788718i	0.918956	+	0.394359i	$0.129033\pi$
$59$			9.55718e6i			0.788718i	−0.918956	+	0.394359i	$0.870967\pi$
$60$		0			0
$61$	−5.54455e6			−0.400449			−0.200225	−	0.979750i	$-0.564167\pi$
$61$	−5.54455e6			−0.400449			−0.200225	+	0.979750i	$0.564167\pi$
$62$	2.40232e6	−	2.06336e7i	0.162579	−	1.39640i
$63$		0			0
$64$	1.28811e7	+	1.07495e7i	0.767776	+	0.640719i
$65$	−1.12813e7			−0.631984
$66$		0			0
$67$		−	2.75178e7i		−	1.36557i	−0.730618	−	0.682787i	$-0.760768\pi$
$67$		−	2.75178e7i		−	1.36557i	0.730618	−	0.682787i	$-0.239232\pi$
$68$	3.10982e7	+	7.34088e6i	1.45445	+	0.343330i
$69$		0			0
$70$	−2.25927e6	+	1.94049e7i	−0.0940970	+	0.808202i
$71$		−	4.03081e7i		−	1.58620i	−0.609089	−	0.793102i	$-0.708465\pi$
$71$		−	4.03081e7i		−	1.58620i	0.609089	−	0.793102i	$-0.291535\pi$
$72$		0			0
$73$	−4.73829e6			−0.166852			−0.0834258	−	0.996514i	$-0.526586\pi$
$73$	−4.73829e6			−0.166852			−0.0834258	+	0.996514i	$0.526586\pi$
$74$	−1.72500e7	−	2.00838e6i	−0.575259	−	0.0669760i
$75$		0			0
$76$	−1.19768e7	+	5.07373e7i	−0.358993	+	1.52080i
$77$	5.52261e7			1.57102
$78$		0			0
$79$		−	5.91316e7i		−	1.51814i	−0.651010	−	0.759069i	$-0.725655\pi$
$79$		−	5.91316e7i		−	1.51814i	0.651010	−	0.759069i	$-0.274345\pi$
$80$	1.63842e7	+	8.19159e6i	0.400005	+	0.199990i
$81$		0			0
$82$	−7.31385e7	−	8.51533e6i	−1.61767	−	0.188342i
$83$		−	2.39189e7i		−	0.503997i	−0.967728	−	0.251999i	$-0.918912\pi$
$83$		−	2.39189e7i		−	0.503997i	0.967728	−	0.251999i	$-0.0810878\pi$
$84$		0			0
$85$	3.48871e7			0.668327
$86$	5.35442e6	−	4.59893e7i	0.0978856	−	0.840743i
$87$		0			0
$88$	1.76450e7	−	4.86835e7i	0.294233	−	0.811804i
$89$	2.09673e7			0.334182			0.167091	−	0.985942i	$-0.446563\pi$
$89$	2.09673e7			0.334182			0.167091	+	0.985942i	$0.446563\pi$
$90$		0			0
$91$			1.76313e8i			2.57111i
$92$	1.33176e7	−	5.64172e7i	0.185897	−	0.787517i
$93$		0			0
$94$	6.87538e6	−	5.90529e7i	0.0880614	−	0.756362i
$95$			5.69189e7i			0.698815i
$96$		0			0
$97$	2.09675e7			0.236843			0.118421	−	0.992963i	$-0.462217\pi$
$97$	2.09675e7			0.236843			0.118421	+	0.992963i	$0.462217\pi$
$98$	2.11658e8	+	2.46428e7i	2.29472	+	0.267169i
$99$		0			0
$100$	1.94650e7	+	4.59482e6i	0.194650	+	0.0459482i
$101$	1.97668e8			1.89955			0.949774	−	0.312937i	$-0.101313\pi$
$101$	1.97668e8			1.89955			0.949774	+	0.312937i	$0.101313\pi$
$102$		0			0
$103$		−	1.16938e7i		−	0.103898i	−0.998650	−	0.0519489i	$-0.983457\pi$
$103$		−	1.16938e7i		−	0.103898i	0.998650	−	0.0519489i	$-0.0165433\pi$
$104$	1.55426e8	+	5.63331e7i	1.32859	+	0.481538i
$105$		0			0
$106$	797704.	+	92874.7i	0.00631856	+	0.000735655i
$107$			1.59457e8i			1.21649i	0.793750	+	0.608245i	$0.208126\pi$
$107$			1.59457e8i			1.21649i	−0.793750	+	0.608245i	$0.791874\pi$
$108$		0			0
$109$	9.43814e7			0.668622			0.334311	−	0.942463i	$-0.391496\pi$
$109$	9.43814e7			0.668622			0.334311	+	0.942463i	$0.391496\pi$
$110$	6.53838e6	−	5.61584e7i	0.0446580	−	0.383569i
$111$		0			0
$112$	1.28025e8	−	2.56066e8i	0.813621	−	1.62734i
$113$	−3.56175e7			−0.218449			−0.109224	−	0.994017i	$-0.534837\pi$
$113$	−3.56175e7			−0.218449			−0.109224	+	0.994017i	$0.534837\pi$
$114$		0			0
$115$		−	6.32909e7i		−	0.361868i
$116$	−6.33221e6	−	1.49475e6i	−0.0349722	−	0.00825537i
$117$		0			0
$118$	1.76841e7	−	1.51889e8i	0.0912124	−	0.783426i
$119$		−	5.45244e8i		−	2.71896i
$120$		0			0
$121$	5.45330e7			0.254401
$122$	8.81176e7	+	1.02593e7i	0.397762	+	0.0463105i
$123$		0			0
$124$	−7.63585e7	+	3.23478e8i	−0.322976	+	1.36823i
$125$	2.18366e7			0.0894427
$126$		0			0
$127$			4.09021e7i			0.157228i	0.996905	+	0.0786142i	$0.0250495\pi$
$127$			4.09021e7i			0.157228i	−0.996905	+	0.0786142i	$0.974950\pi$
$128$	−1.84825e8	−	1.94672e8i	−0.688527	−	0.725210i
$129$		0			0
$130$	1.79290e8	+	2.08743e7i	0.627744	+	0.0730867i
$131$			3.07316e8i			1.04352i	0.853093	+	0.521759i	$0.174724\pi$
$131$			3.07316e8i			1.04352i	−0.853093	+	0.521759i	$0.825276\pi$
$132$		0			0
$133$	8.89575e8			2.84299
$134$	−5.09174e7	+	4.37331e8i	−0.157924	+	1.35641i
$135$		0			0
$136$	−4.80649e8	−	1.74208e8i	−1.40499	−	0.509229i
$137$	4.97786e8			1.41306			0.706529	−	0.707684i	$-0.250260\pi$
$137$	4.97786e8			1.41306			0.706529	+	0.707684i	$0.250260\pi$
$138$		0			0
$139$		−	1.74953e8i		−	0.468663i	−0.972157	−	0.234332i	$-0.924710\pi$
$139$		−	1.74953e8i		−	0.468663i	0.972157	−	0.234332i	$-0.0752902\pi$
$140$	7.18115e7	−	3.04215e8i	0.186931	−	0.791897i
$141$		0			0
$142$	−7.45838e7	+	6.40603e8i	−0.183439	+	1.57556i
$143$		−	5.10256e8i		−	1.22024i
$144$		0			0
$145$	−7.10371e6			−0.0160699
$146$	7.53040e7	+	8.76746e6i	0.165732	+	0.0192958i
$147$		0			0
$148$	2.70433e8	+	6.38369e7i	0.563654	+	0.133053i
$149$	6.94152e8			1.40835			0.704174	−	0.710028i	$-0.251318\pi$
$149$	6.94152e8			1.40835			0.704174	+	0.710028i	$0.251318\pi$
$150$		0			0
$151$		−	6.69606e8i		−	1.28799i	−0.765031	−	0.643994i	$-0.777276\pi$
$151$		−	6.69606e8i		−	1.28799i	0.765031	−	0.643994i	$-0.222724\pi$
$152$	2.84224e8	−	7.84188e8i	0.532459	−	1.46908i
$153$		0			0
$154$	−8.77689e8	−	1.02187e8i	−1.56048	−	0.181683i
$155$			3.62889e8i			0.628706i
$156$		0			0
$157$	−1.47338e8			−0.242502			−0.121251	−	0.992622i	$-0.538691\pi$
$157$	−1.47338e8			−0.242502			−0.121251	+	0.992622i	$0.538691\pi$
$158$	−1.09414e8	+	9.39757e8i	−0.175567	+	1.50795i
$159$		0			0
$160$	−2.45231e8	−	1.60502e8i	−0.374193	−	0.244907i
$161$	−9.89161e8			−1.47219
$162$		0			0
$163$		−	2.50170e8i		−	0.354393i	−0.984175	−	0.177197i	$-0.943297\pi$
$163$		−	2.50170e8i		−	0.354393i	0.984175	−	0.177197i	$-0.0567028\pi$
$164$	1.14661e9	+	2.70662e8i	1.58504	+	0.374156i
$165$		0			0
$166$	−4.42581e7	+	3.80134e8i	−0.0582854	+	0.500616i
$167$			1.42570e9i			1.83301i	0.400028	+	0.916503i	$0.369000\pi$
$167$			1.42570e9i			1.83301i	−0.400028	+	0.916503i	$0.631000\pi$
$168$		0			0
$169$	8.13301e8			0.997021
$170$	−5.54448e8	−	6.45531e7i	−0.663843	−	0.0772896i
$171$		0			0
$172$	−1.70192e8	+	7.20984e8i	−0.194458	+	0.823782i
$173$	1.04922e9			1.17134			0.585668	−	0.810551i	$-0.300832\pi$
$173$	1.04922e9			1.17134			0.585668	+	0.810551i	$0.300832\pi$
$174$		0			0
$175$		−	3.41280e8i		−	0.363880i
$176$	−3.70507e8	+	7.41061e8i	−0.386141	+	0.772330i
$177$		0			0
$178$	−3.33226e8	−	3.87967e7i	−0.331939	−	0.0386469i
$179$		−	1.18529e9i		−	1.15455i	−0.816551	−	0.577273i	$-0.804117\pi$
$179$		−	1.18529e9i		−	1.15455i	0.816551	−	0.577273i	$-0.195883\pi$
$180$		0			0
$181$	−5.14430e8			−0.479305			−0.239652	−	0.970859i	$-0.577033\pi$
$181$	−5.14430e8			−0.479305			−0.239652	+	0.970859i	$0.577033\pi$
$182$	3.26240e8	−	2.80209e9i	0.297339	−	2.55386i
$183$		0			0
$184$	−3.16042e8	+	8.71976e8i	−0.275724	+	0.760735i
$185$	3.03381e8			0.259001
$186$		0			0
$187$			1.57795e9i			1.29041i
$188$	−2.18536e8	+	9.25785e8i	−0.174941	+	0.741103i
$189$		0			0
$190$	1.05319e8	−	9.04593e8i	0.0808154	−	0.694127i
$191$		−	1.69019e9i		−	1.27000i	−0.772513	−	0.634999i	$-0.781000\pi$
$191$		−	1.69019e9i		−	1.27000i	0.772513	−	0.634999i	$-0.219000\pi$
$192$		0			0
$193$	4.15397e8			0.299388			0.149694	−	0.988732i	$-0.452171\pi$
$193$	4.15397e8			0.299388			0.149694	+	0.988732i	$0.452171\pi$
$194$	−3.33229e8	−	3.87971e7i	−0.235254	−	0.0273900i
$195$		0			0
$196$	−3.31821e9	−	7.83279e8i	−2.24843	−	0.530753i
$197$	−2.42620e8			−0.161088			−0.0805439	−	0.996751i	$-0.525666\pi$
$197$	−2.42620e8			−0.161088			−0.0805439	+	0.996751i	$0.525666\pi$
$198$		0			0
$199$			2.32340e9i			1.48154i	0.671760	+	0.740769i	$0.265539\pi$
$199$			2.32340e9i			1.48154i	−0.671760	+	0.740769i	$0.734461\pi$
$200$	−3.00849e8	−	1.09041e8i	−0.188031	−	0.0681505i
$201$		0			0
$202$	−3.14146e9	−	3.65753e8i	−1.88680	−	0.219676i
$203$			1.11023e8i			0.0653773i
$204$		0			0
$205$	1.28631e9			0.728332
$206$	−2.16375e7	+	1.85845e8i	−0.0120154	+	0.103201i
$207$		0			0
$208$	−2.36589e9	−	1.18287e9i	−1.26398	−	0.631953i
$209$	−2.57446e9			−1.34927
$210$		0			0
$211$			1.49574e8i			0.0754617i	0.999288	+	0.0377309i	$0.0120130\pi$
$211$			1.49574e8i			0.0754617i	−0.999288	+	0.0377309i	$0.987987\pi$
$212$	−1.25058e7	−	2.95205e6i	−0.00619109	−	0.00146144i
$213$		0			0
$214$	2.95050e8	−	2.53419e9i	0.140683	−	1.20833i
$215$			8.08827e8i			0.378531i
$216$		0			0
$217$	5.67153e9			2.55777
$218$	−1.49997e9	−	1.74638e8i	−0.664135	−	0.0773236i
$219$		0			0
$220$	−2.07824e8	+	8.80407e8i	−0.0887168	+	0.375831i
$221$	−5.03773e9			−2.11186
$222$		0			0
$223$		−	1.40993e9i		−	0.570134i	−0.958508	−	0.285067i	$-0.907984\pi$
$223$		−	1.40993e9i		−	0.570134i	0.958508	−	0.285067i	$-0.0920158\pi$
$224$	−2.50846e9	+	3.83267e9i	−0.996358	+	1.52233i
$225$		0			0
$226$	5.66056e8	+	6.59045e7i	0.216983	+	0.0252628i
$227$			3.59996e9i			1.35580i	0.735156	+	0.677898i	$0.237109\pi$
$227$			3.59996e9i			1.35580i	−0.735156	+	0.677898i	$0.762891\pi$
$228$		0			0
$229$	3.59311e7			0.0130656			0.00653280	−	0.999979i	$-0.497921\pi$
$229$	3.59311e7			0.0130656			0.00653280	+	0.999979i	$0.497921\pi$
$230$	−1.17110e8	+	1.00586e9i	−0.0418487	+	0.359440i
$231$		0			0
$232$	9.78698e7	+	3.54723e7i	0.0337829	+	0.0122444i
$233$	−1.95989e9			−0.664980			−0.332490	−	0.943107i	$-0.607889\pi$
$233$	−1.95989e9			−0.664980			−0.332490	+	0.943107i	$0.607889\pi$
$234$		0			0
$235$			1.03858e9i			0.340540i
$236$	−5.62093e8	+	2.38120e9i	−0.181201	+	0.767621i
$237$		0			0
$238$	−1.00889e9	+	8.66537e9i	−0.314438	+	2.70072i
$239$		−	1.44446e9i		−	0.442703i	−0.975194	−	0.221352i	$-0.928953\pi$
$239$		−	1.44446e9i		−	0.442703i	0.975194	−	0.221352i	$-0.0710468\pi$
$240$		0			0
$241$	6.55022e9			1.94172			0.970862	−	0.239639i	$-0.0770292\pi$
$241$	6.55022e9			1.94172			0.970862	+	0.239639i	$0.0770292\pi$
$242$	−8.66674e8	−	1.00905e8i	−0.252694	−	0.0294205i
$243$		0			0
$244$	−1.38144e9	−	3.26095e8i	−0.389738	−	0.0919995i
$245$	−3.72249e9			−1.03316
$246$		0			0
$247$		−	8.21914e9i		−	2.20820i
$248$	1.81208e9	−	4.99963e9i	0.479040	−	1.32169i
$249$		0			0
$250$	−3.47041e8	−	4.04052e7i	−0.0888426	−	0.0103437i
$251$			7.57863e9i			1.90939i	0.297579	+	0.954697i	$0.403821\pi$
$251$			7.57863e9i			1.90939i	−0.297579	+	0.954697i	$0.596179\pi$
$252$		0			0
$253$	2.86266e9			0.698695
$254$	7.56829e7	−	6.50043e8i	0.0181829	−	0.156174i
$255$		0			0
$256$	2.57715e9	+	3.43585e9i	0.600040	+	0.799970i
$257$	4.60039e9			1.05454			0.527269	−	0.849698i	$-0.323216\pi$
$257$	4.60039e9			1.05454			0.527269	+	0.849698i	$0.323216\pi$
$258$		0			0
$259$		−	4.74149e9i		−	1.05370i
$260$	−2.81077e9	−	6.63495e8i	−0.615080	−	0.145193i
$261$		0			0
$262$	5.68639e8	−	4.88406e9i	0.120679	−	1.03652i
$263$		−	4.62139e9i		−	0.965938i	−0.875637	−	0.482969i	$-0.839558\pi$
$263$		−	4.62139e9i		−	0.965938i	0.875637	−	0.482969i	$-0.160442\pi$
$264$		0			0
$265$	−1.40295e7			−0.00284484
$266$	−1.41377e10	−	1.64602e9i	−2.82392	−	0.328782i
$267$		0			0
$268$	1.61842e9	−	6.85614e9i	0.313728	−	1.32905i
$269$	3.50882e9			0.670120			0.335060	−	0.942197i	$-0.391243\pi$
$269$	3.50882e9			0.670120			0.335060	+	0.942197i	$0.391243\pi$
$270$		0			0
$271$			2.00636e9i			0.371990i	0.982551	+	0.185995i	$0.0595509\pi$
$271$			2.00636e9i			0.371990i	−0.982551	+	0.185995i	$0.940449\pi$
$272$	7.31645e9	+	3.65800e9i	1.33667	+	0.668294i
$273$		0			0
$274$	−7.91113e9	−	9.21074e8i	−1.40358	−	0.163415i
$275$			9.87674e8i			0.172696i
$276$		0			0
$277$	5.03028e9			0.854423			0.427211	−	0.904152i	$-0.359496\pi$
$277$	5.03028e9			0.854423			0.427211	+	0.904152i	$0.359496\pi$
$278$	−3.23722e8	+	2.78046e9i	−0.0541992	+	0.465519i
$279$		0			0
$280$	−1.70418e9	+	4.70191e9i	−0.277257	+	0.764966i
$281$	−5.15967e8			−0.0827555			−0.0413778	−	0.999144i	$-0.513175\pi$
$281$	−5.15967e8			−0.0827555			−0.0413778	+	0.999144i	$0.513175\pi$
$282$		0			0
$283$		−	1.20680e9i		−	0.188143i	−0.995565	−	0.0940715i	$-0.970012\pi$
$283$		−	1.20680e9i		−	0.188143i	0.995565	−	0.0940715i	$-0.0299882\pi$
$284$	2.37067e9	−	1.00429e10i	0.364416	−	1.54378i
$285$		0			0
$286$	−9.44148e8	+	8.10932e9i	−0.141116	+	1.21205i
$287$		−	2.01034e10i		−	2.96308i
$288$		0			0
$289$	8.60325e9			1.23331
$290$	1.12897e8	+	1.31443e7i	0.0159621	+	0.00185843i
$291$		0			0
$292$	−1.18056e9	−	2.78676e8i	−0.162389	−	0.0383326i
$293$	−6.72328e9			−0.912244			−0.456122	−	0.889917i	$-0.650762\pi$
$293$	−6.72328e9			−0.912244			−0.456122	+	0.889917i	$0.650762\pi$
$294$		0			0
$295$			2.67131e9i			0.352726i
$296$	−4.17977e9	−	1.51493e9i	−0.544485	−	0.197345i
$297$		0			0
$298$	−1.10319e10	−	1.28442e9i	−1.39890	−	0.162870i
$299$			9.13926e9i			1.14347i
$300$		0			0
$301$	1.26410e10			1.53998
$302$	−1.23900e9	+	1.06418e10i	−0.148951	+	1.27935i
$303$		0			0
$304$	−5.96809e9	+	1.19369e10i	−0.698781	+	1.39765i
$305$	−1.54975e9			−0.179086
$306$		0			0
$307$			4.05556e9i			0.456559i	0.973596	+	0.228280i	$0.0733100\pi$
$307$			4.05556e9i			0.456559i	−0.973596	+	0.228280i	$0.926690\pi$
$308$	1.37597e10	+	3.24805e9i	1.52900	+	0.360927i
$309$		0			0
$310$	6.71469e8	−	5.76727e9i	0.0727075	−	0.624488i
$311$		−	2.64705e8i		−	0.0282957i	−0.999900	−	0.0141479i	$-0.995496\pi$
$311$		−	2.64705e8i		−	0.0282957i	0.999900	−	0.0141479i	$-0.00450356\pi$
$312$		0			0
$313$	−2.46207e9			−0.256521			−0.128260	−	0.991741i	$-0.540939\pi$
$313$	−2.46207e9			−0.256521			−0.128260	+	0.991741i	$0.540939\pi$
$314$	2.34159e9	+	2.72626e8i	0.240875	+	0.0280445i
$315$		0			0
$316$	3.47774e9	−	1.47328e10i	0.348778	−	1.47753i
$317$	1.05210e10			1.04188			0.520942	−	0.853592i	$-0.325581\pi$
$317$	1.05210e10			1.04188			0.520942	+	0.853592i	$0.325581\pi$
$318$		0			0
$319$		−	3.21302e8i		−	0.0310278i
$320$	3.60039e9	+	3.00457e9i	0.343360	+	0.286538i
$321$		0			0
$322$	1.57204e10	+	1.83029e9i	1.46231	+	0.170253i
$323$			2.54174e10i			2.33519i
$324$		0			0
$325$	−3.15322e9			−0.282632
$326$	−4.62900e8	+	3.97587e9i	−0.0409843	+	0.352015i
$327$		0			0
$328$	−1.77218e10	−	6.42316e9i	−1.53113	−	0.554949i
$329$	1.62318e10			1.38542
$330$		0			0
$331$		−	1.35452e9i		−	0.112842i	−0.998407	−	0.0564212i	$-0.982031\pi$
$331$		−	1.35452e9i		−	0.112842i	0.998407	−	0.0564212i	$-0.0179690\pi$
$332$	1.40676e9	−	5.95944e9i	0.115789	−	0.490516i
$333$		0			0
$334$	2.63804e9	−	2.26582e10i	0.211980	−	1.82071i
$335$		−	7.69147e9i		−	0.610703i
$336$		0			0
$337$	4.60152e9			0.356765			0.178382	−	0.983961i	$-0.442914\pi$
$337$	4.60152e9			0.356765			0.178382	+	0.983961i	$0.442914\pi$
$338$	−1.29255e10	−	1.50488e9i	−0.990332	−	0.115302i
$339$		0			0
$340$	8.69221e9	+	2.05184e9i	0.650451	+	0.153542i
$341$	−1.64136e10			−1.21391
$342$		0			0
$343$			3.29952e10i			2.38382i
$344$	4.03887e9	−	1.11434e10i	0.288420	−	0.795766i
$345$		0			0
$346$	−1.66748e10	−	1.94141e9i	−1.16348	−	0.135461i
$347$		−	1.95596e10i		−	1.34910i	−0.738231	−	0.674548i	$-0.764339\pi$
$347$		−	1.95596e10i		−	1.34910i	0.738231	−	0.674548i	$-0.235661\pi$
$348$		0			0
$349$	−1.63778e10			−1.10396			−0.551979	−	0.833858i	$-0.686127\pi$
$349$	−1.63778e10			−1.10396			−0.551979	+	0.833858i	$0.686127\pi$
$350$	−6.31485e8	+	5.42384e9i	−0.0420814	+	0.361439i
$351$		0			0
$352$	7.25956e9	−	1.10919e10i	0.472868	−	0.722493i
$353$	1.06945e10			0.688749			0.344374	−	0.938832i	$-0.388091\pi$
$353$	1.06945e10			0.688749			0.344374	+	0.938832i	$0.388091\pi$
$354$		0			0
$355$		−	1.12665e10i		−	0.709372i
$356$	5.22406e9	+	1.23316e9i	0.325243	+	0.0767752i
$357$		0			0
$358$	−2.19318e9	+	1.88373e10i	−0.133519	+	1.14680i
$359$			1.20508e10i			0.725502i	0.931886	+	0.362751i	$0.118162\pi$
$359$			1.20508e10i			0.725502i	−0.931886	+	0.362751i	$0.881838\pi$
$360$		0			0
$361$	−2.44854e10			−1.44171
$362$	8.17565e9	+	9.51870e8i	0.476089	+	0.0554298i
$363$		0			0
$364$	−1.03696e10	+	4.39289e10i	−0.590688	+	2.50233i
$365$	−1.32439e9			−0.0746183
$366$		0			0
$367$			1.44305e9i			0.0795456i	0.999209	+	0.0397728i	$0.0126634\pi$
$367$			1.44305e9i			0.0795456i	−0.999209	+	0.0397728i	$0.987337\pi$
$368$	6.63620e9	−	1.32732e10i	0.361850	−	0.723745i
$369$		0			0
$370$	−4.82153e9	−	5.61359e8i	−0.257264	−	0.0299526i
$371$			2.19264e8i			0.0115737i
$372$		0			0
$373$	−3.11346e10			−1.60845			−0.804225	−	0.594325i	$-0.797419\pi$
$373$	−3.11346e10			−1.60845			−0.804225	+	0.594325i	$0.797419\pi$
$374$	2.91975e9	−	2.50778e10i	0.149231	−	1.28175i
$375$		0			0
$376$	5.18614e9	−	1.43088e10i	0.259473	−	0.715900i
$377$	1.02578e9			0.0507796
$378$		0			0
$379$			3.66642e9i			0.177699i	0.996045	+	0.0888496i	$0.0283190\pi$
$379$			3.66642e9i			0.177699i	−0.996045	+	0.0888496i	$0.971681\pi$
$380$	−3.34761e9	+	1.41815e10i	−0.160546	+	0.680123i
$381$		0			0
$382$	−3.12744e9	+	2.68617e10i	−0.146871	+	1.26148i
$383$		−	1.86782e10i		−	0.868039i	−0.900904	−	0.434019i	$-0.857095\pi$
$383$		−	1.86782e10i		−	0.868039i	0.900904	−	0.434019i	$-0.142905\pi$
$384$		0			0
$385$	1.54362e10			0.702581
$386$	−6.60176e9	−	7.68627e8i	−0.297379	−	0.0346231i
$387$		0			0
$388$	5.22411e9	+	1.23318e9i	0.230508	+	0.0544125i
$389$	2.09415e10			0.914553			0.457276	−	0.889325i	$-0.348825\pi$
$389$	2.09415e10			0.914553			0.457276	+	0.889325i	$0.348825\pi$
$390$		0			0
$391$		−	2.82629e10i		−	1.20923i
$392$	5.12858e10	+	1.85882e10i	2.17196	+	0.787214i
$393$		0			0
$394$	3.85588e9	+	4.48931e8i	0.160007	+	0.0186292i
$395$		−	1.65278e10i		−	0.678932i
$396$		0			0
$397$	3.24559e10			1.30657			0.653284	−	0.757113i	$-0.273391\pi$
$397$	3.24559e10			1.30657			0.653284	+	0.757113i	$0.273391\pi$
$398$	4.29909e9	−	3.69251e10i	0.171334	−	1.47160i
$399$		0			0
$400$	4.57952e9	+	2.28962e9i	0.178888	+	0.0894383i
$401$	−3.03188e9			−0.117256			−0.0586279	−	0.998280i	$-0.518673\pi$
$401$	−3.03188e9			−0.117256			−0.0586279	+	0.998280i	$0.518673\pi$
$402$		0			0
$403$		−	5.24015e10i		−	1.98666i
$404$	4.92494e10	+	1.16256e10i	1.84874	+	0.436404i
$405$		0			0
$406$	2.05430e8	−	1.76444e9i	0.00756064	−	0.0649386i
$407$			1.37220e10i			0.500080i
$408$		0			0
$409$	−4.74551e10			−1.69586			−0.847929	−	0.530110i	$-0.822150\pi$
$409$	−4.74551e10			−1.69586			−0.847929	+	0.530110i	$0.822150\pi$
$410$	−2.04428e10	−	2.38011e9i	−0.723445	−	0.0842289i
$411$		0			0
$412$	6.87754e8	−	2.91354e9i	0.0238696	−	0.101119i
$413$	4.17494e10			1.43500
$414$		0			0
$415$		−	6.68553e9i		−	0.225394i
$416$	3.54116e10	+	2.31767e10i	1.18242	+	0.773888i
$417$		0			0
$418$	4.09149e10	+	4.76362e9i	1.34022	+	0.156039i
$419$		−	1.14560e9i		−	0.0371685i	−0.999827	−	0.0185843i	$-0.994084\pi$
$419$		−	1.14560e9i		−	0.0371685i	0.999827	−	0.0185843i	$-0.00591590\pi$
$420$		0			0
$421$	−2.44199e10			−0.777348			−0.388674	−	0.921375i	$-0.627067\pi$
$421$	−2.44199e10			−0.777348			−0.388674	+	0.921375i	$0.627067\pi$
$422$	2.76763e8	−	2.37713e9i	0.00872687	−	0.0749554i
$423$		0			0
$424$	1.93288e8	+	7.00559e7i	0.00598054	+	0.00216761i
$425$	9.75124e9			0.298885
$426$		0			0
$427$			2.42207e10i			0.728578i
$428$	−9.37824e9	+	3.97291e10i	−0.279477	+	1.18395i
$429$		0			0
$430$	1.49661e9	−	1.28544e10i	0.0437758	−	0.375992i
$431$			8.40599e9i			0.243601i	0.992555	+	0.121801i	$0.0388669\pi$
$431$			8.40599e9i			0.243601i	−0.992555	+	0.121801i	$0.961133\pi$
$432$		0			0
$433$	6.24569e9			0.177676			0.0888381	−	0.996046i	$-0.471685\pi$
$433$	6.24569e9			0.177676			0.0888381	+	0.996046i	$0.471685\pi$
$434$	−9.01356e10	−	1.04943e10i	−2.54061	−	0.295797i
$435$		0			0
$436$	2.35154e10	+	5.55091e9i	0.650737	+	0.153610i
$437$	4.61114e10			1.26439
$438$		0			0
$439$			2.74130e10i			0.738071i	0.929415	+	0.369036i	$0.120312\pi$
$439$			2.74130e10i			0.738071i	−0.929415	+	0.369036i	$0.879688\pi$
$440$	4.93194e9	−	1.36075e10i	0.131585	−	0.363050i
$441$		0			0
$442$	8.00628e10	+	9.32152e9i	2.09769	+	0.244229i
$443$		−	2.85603e10i		−	0.741564i	−0.928720	−	0.370782i	$-0.879090\pi$
$443$		−	2.85603e10i		−	0.741564i	0.928720	−	0.370782i	$-0.120910\pi$
$444$		0			0
$445$	5.86054e9			0.149451
$446$	−2.60884e9	+	2.24074e10i	−0.0659339	+	0.566308i
$447$		0			0
$448$	4.69578e10	−	5.62698e10i	1.16573	−	1.39689i
$449$	−2.90101e10			−0.713780			−0.356890	−	0.934146i	$-0.616163\pi$
$449$	−2.90101e10			−0.713780			−0.356890	+	0.934146i	$0.616163\pi$
$450$		0			0
$451$			5.81799e10i			1.40626i
$452$	−8.87419e9	−	2.09480e9i	−0.212606	−	0.0501866i
$453$		0			0
$454$	6.66116e9	−	5.72129e10i	0.156793	−	1.34670i
$455$			4.92811e10i			1.14983i
$456$		0			0
$457$	2.85196e10			0.653851			0.326926	−	0.945050i	$-0.393987\pi$
$457$	2.85196e10			0.653851			0.326926	+	0.945050i	$0.393987\pi$
$458$	−5.71041e8	−	6.64849e7i	−0.0129779	−	0.00151099i
$459$		0			0
$460$	3.72237e9	−	1.57691e10i	0.0831358	−	0.352188i
$461$	−2.22816e10			−0.493336			−0.246668	−	0.969100i	$-0.579336\pi$
$461$	−2.22816e10			−0.493336			−0.246668	+	0.969100i	$0.579336\pi$
$462$		0			0
$463$			3.04341e10i			0.662272i	0.943583	+	0.331136i	$0.107432\pi$
$463$			3.04341e10i			0.662272i	−0.943583	+	0.331136i	$0.892568\pi$
$464$	−1.48977e9	−	7.44841e8i	−0.0321402	−	0.0160691i
$465$		0			0
$466$	3.11479e10	+	3.62647e9i	0.660519	+	0.0769025i
$467$		−	1.21705e10i		−	0.255883i	−0.991782	−	0.127942i	$-0.959163\pi$
$467$		−	1.21705e10i		−	0.255883i	0.991782	−	0.127942i	$-0.0408370\pi$
$468$		0			0
$469$	−1.20208e11			−2.48453
$470$	1.92173e9	−	1.65058e10i	0.0393822	−	0.338255i
$471$		0			0
$472$	1.33392e10	−	3.68034e10i	0.268758	−	0.741516i
$473$	−3.65834e10			−0.730869
$474$		0			0
$475$			1.59093e10i			0.312520i
$476$	3.20678e10	−	1.35849e11i	0.624656	−	2.64623i
$477$		0			0
$478$	−2.67274e9	+	2.29562e10i	−0.0511970	+	0.439733i
$479$		−	1.66815e10i		−	0.316879i	−0.987369	−	0.158440i	$-0.949354\pi$
$479$		−	1.66815e10i		−	0.316879i	0.987369	−	0.158440i	$-0.0506463\pi$
$480$		0			0
$481$	−4.38085e10			−0.818424
$482$	−1.04100e11	−	1.21201e10i	−1.92870	−	0.224553i
$483$		0			0
$484$	1.35870e10	+	3.20729e9i	0.247596	+	0.0584462i
$485$	5.86060e9			0.105919
$486$		0			0
$487$		−	1.00085e11i		−	1.77931i	−0.456630	−	0.889657i	$-0.650944\pi$
$487$		−	1.00085e11i		−	1.77931i	0.456630	−	0.889657i	$-0.349056\pi$
$488$	2.13513e10	+	7.73866e9i	0.376483	+	0.136454i
$489$		0			0
$490$	5.91602e10	+	6.88787e9i	1.02623	+	0.119482i
$491$		−	1.22682e10i		−	0.211084i	−0.994415	−	0.105542i	$-0.966342\pi$
$491$		−	1.22682e10i		−	0.211084i	0.994415	−	0.105542i	$-0.0336578\pi$
$492$		0			0
$493$	−3.17220e9			−0.0536998
$494$	−1.52082e10	+	1.30624e11i	−0.255370	+	2.19339i
$495$		0			0
$496$	−3.80498e10	+	7.61044e10i	−0.628675	+	1.25743i
$497$	−1.76081e11			−2.88594
$498$		0			0
$499$			5.81617e10i			0.938070i	0.883180	+	0.469035i	$0.155398\pi$
$499$			5.81617e10i			0.938070i	−0.883180	+	0.469035i	$0.844602\pi$
$500$	5.44064e9	+	1.28429e9i	0.0870503	+	0.0205486i
$501$		0			0
$502$	1.40230e10	−	1.20444e11i	0.220814	−	1.89658i
$503$			5.45264e10i			0.851795i	0.904771	+	0.425897i	$0.140042\pi$
$503$			5.45264e10i			0.851795i	−0.904771	+	0.425897i	$0.859958\pi$
$504$		0			0
$505$	5.52498e10			0.849503
$506$	−4.54952e10	−	5.29690e9i	−0.694007	−	0.0808015i
$507$		0			0
$508$	−2.40560e9	+	1.01909e10i	−0.0361218	+	0.153023i
$509$	−1.54749e10			−0.230545			−0.115273	−	0.993334i	$-0.536774\pi$
$509$	−1.54749e10			−0.230545			−0.115273	+	0.993334i	$0.536774\pi$
$510$		0			0
$511$			2.06987e10i			0.303570i
$512$	−3.46003e10	−	5.93733e10i	−0.503500	−	0.863995i
$513$		0			0
$514$	−7.31124e10	−	8.51229e9i	−1.04746	−	0.121953i
$515$		−	3.26851e9i		−	0.0464645i
$516$		0			0
$517$	−4.69752e10			−0.657516
$518$	−8.77337e9	+	7.53548e10i	−0.121856	+	1.04663i
$519$		0			0
$520$	4.34428e10	+	1.57456e10i	0.594162	+	0.215350i
$521$	1.23711e11			1.67903			0.839516	−	0.543335i	$-0.182839\pi$
$521$	1.23711e11			1.67903			0.839516	+	0.543335i	$0.182839\pi$
$522$		0			0
$523$		−	3.37623e10i		−	0.451258i	−0.974213	−	0.225629i	$-0.927556\pi$
$523$		−	3.37623e10i		−	0.451258i	0.974213	−	0.225629i	$-0.0724438\pi$
$524$	−1.80744e10	+	7.65685e10i	−0.239739	+	1.01561i
$525$		0			0
$526$	−8.55115e9	+	7.34461e10i	−0.111707	+	0.959457i
$527$			1.62050e11i			2.10091i
$528$		0			0
$529$	2.70375e10			0.345259
$530$	2.22965e8	+	2.59593e7i	0.00282575	+	0.000328995i
$531$		0			0
$532$	2.21640e11	+	5.23192e10i	2.76695	+	0.653152i
$533$	−1.85744e11			−2.30147
$534$		0			0
$535$			4.45696e10i			0.544030i
$536$	−3.84072e10	+	1.05968e11i	−0.465322	+	1.28385i
$537$		0			0
$538$	−5.57645e10	−	6.49252e9i	−0.665624	−	0.0774969i
$539$		−	1.68369e11i		−	1.99483i
$540$		0			0
$541$	−1.16336e11			−1.35808			−0.679042	−	0.734099i	$-0.737605\pi$
$541$	−1.16336e11			−1.35808			−0.679042	+	0.734099i	$0.737605\pi$
$542$	3.71245e9	−	3.18864e10i	0.0430193	−	0.369494i
$543$		0			0
$544$	−1.09509e11	−	7.16732e10i	−1.25042	−	0.818391i
$545$	2.63804e10			0.299017
$546$		0			0
$547$		−	4.21968e10i		−	0.471335i	−0.971834	−	0.235668i	$-0.924272\pi$
$547$		−	4.21968e10i		−	0.471335i	0.971834	−	0.235668i	$-0.0757277\pi$
$548$	1.24025e11	+	2.92766e10i	1.37526	+	0.324637i
$549$		0			0
$550$	1.82753e9	−	1.56968e10i	0.0199717	−	0.171537i
$551$		−	5.17550e9i		−	0.0561495i
$552$		0			0
$553$	−2.58309e11			−2.76210
$554$	−7.99444e10	−	9.30773e9i	−0.848690	−	0.0988108i
$555$		0			0
$556$	1.02896e10	−	4.35899e10i	0.107671	−	0.456128i
$557$	8.59325e10			0.892764			0.446382	−	0.894842i	$-0.352712\pi$
$557$	8.59325e10			0.892764			0.446382	+	0.894842i	$0.352712\pi$
$558$		0			0
$559$		−	1.16795e11i		−	1.19613i
$560$	3.57840e10	−	7.15725e10i	0.363862	−	0.727770i
$561$		0			0
$562$	8.20009e9	+	9.54716e8i	0.0822002	+	0.00957037i
$563$		−	4.69376e10i		−	0.467183i	−0.972335	−	0.233592i	$-0.924952\pi$
$563$		−	4.69376e10i		−	0.467183i	0.972335	−	0.233592i	$-0.0750479\pi$
$564$		0			0
$565$	−9.95539e9			−0.0976933
$566$	−2.23298e9	+	1.91792e10i	−0.0217580	+	0.186881i
$567$		0			0
$568$	−5.62589e10	+	1.55221e11i	−0.540503	+	1.49127i
$569$	3.18471e10			0.303823			0.151912	−	0.988394i	$-0.451457\pi$
$569$	3.18471e10			0.303823			0.151912	+	0.988394i	$0.451457\pi$
$570$		0			0
$571$			4.11114e10i			0.386739i	0.981126	+	0.193369i	$0.0619416\pi$
$571$			4.11114e10i			0.386739i	−0.981126	+	0.193369i	$0.938058\pi$
$572$	3.00100e10	−	1.27132e11i	0.280338	−	1.18760i
$573$		0			0
$574$	−3.71982e10	+	3.19497e11i	−0.342669	+	2.94320i
$575$		−	1.76903e10i		−	0.161832i
$576$		0			0
$577$	6.42574e10			0.579722			0.289861	−	0.957069i	$-0.406391\pi$
$577$	6.42574e10			0.579722			0.289861	+	0.957069i	$0.406391\pi$
$578$	−1.36728e11	−	1.59189e10i	−1.22503	−	0.142627i
$579$		0			0
$580$	−1.76991e9	−	4.17795e8i	−0.0156401	−	0.00369191i
$581$	−1.04487e11			−0.916973
$582$		0			0
$583$		−	6.34555e8i		−	0.00549281i
$584$	1.82465e10	+	6.61334e9i	0.156866	+	0.0568551i
$585$		0			0
$586$	1.06851e11	+	1.24404e10i	0.906123	+	0.105498i
$587$			1.67243e11i			1.40862i	0.709891	+	0.704312i	$0.248744\pi$
$587$			1.67243e11i			1.40862i	−0.709891	+	0.704312i	$0.751256\pi$
$588$		0			0
$589$	−2.64388e11			−2.19675
$590$	4.94284e9	−	4.24543e10i	0.0407914	−	0.350359i
$591$		0			0
$592$	6.36245e10	+	3.18103e10i	0.518009	+	0.258988i
$593$	−1.87457e11			−1.51595			−0.757973	−	0.652286i	$-0.773810\pi$
$593$	−1.87457e11			−1.51595			−0.757973	+	0.652286i	$0.773810\pi$
$594$		0			0
$595$		−	1.52400e11i		−	1.21596i
$596$	1.72950e11	+	4.08256e10i	1.37068	+	0.323555i
$597$		0			0
$598$	1.69108e10	−	1.45247e11i	0.132239	−	1.13580i
$599$			3.78563e10i			0.294057i	0.989132	+	0.147028i	$0.0469709\pi$
$599$			3.78563e10i			0.294057i	−0.989132	+	0.147028i	$0.953029\pi$
$600$		0			0
$601$	7.11140e10			0.545076			0.272538	−	0.962145i	$-0.412137\pi$
$601$	7.11140e10			0.545076			0.272538	+	0.962145i	$0.412137\pi$
$602$	−2.00899e11	−	2.33902e10i	−1.52965	−	0.178093i
$603$		0			0
$604$	3.93820e10	−	1.66834e11i	0.295903	−	1.25354i
$605$	1.52424e10			0.113771
$606$		0			0
$607$			1.42793e11i			1.05184i	0.850533	+	0.525922i	$0.176280\pi$
$607$			1.42793e11i			1.05184i	−0.850533	+	0.525922i	$0.823720\pi$
$608$	1.16936e11	−	1.78666e11i	0.855725	−	1.30746i
$609$		0			0
$610$	2.46296e10	+	2.86757e9i	0.177885	+	0.0207107i
$611$		−	1.49972e11i		−	1.07608i
$612$		0			0
$613$	1.82775e11			1.29442			0.647209	−	0.762313i	$-0.275936\pi$
$613$	1.82775e11			1.29442			0.647209	+	0.762313i	$0.275936\pi$
$614$	7.50417e9	−	6.44535e10i	0.0527994	−	0.453496i
$615$		0			0
$616$	−2.12668e11	−	7.70803e10i	−1.47700	−	0.535328i
$617$	−1.21589e11			−0.838984			−0.419492	−	0.907759i	$-0.637792\pi$
$617$	−1.21589e11			−0.838984			−0.419492	+	0.907759i	$0.637792\pi$
$618$		0			0
$619$			2.11081e11i			1.43776i	0.695133	+	0.718881i	$0.255345\pi$
$619$			2.11081e11i			1.43776i	−0.695133	+	0.718881i	$0.744655\pi$
$620$	−2.13429e10	+	9.04148e10i	−0.144439	+	0.611889i
$621$		0			0
$622$	−4.89795e8	+	4.20687e9i	−0.00327230	+	0.0281059i
$623$		−	9.15933e10i		−	0.608011i
$624$		0			0
$625$	6.10352e9			0.0400000
$626$	3.91288e10	+	4.55567e9i	0.254800	+	0.0296657i
$627$		0			0
$628$	−3.67096e10	−	8.66549e9i	−0.236016	−	0.0557127i
$629$	1.35476e11			0.865488
$630$		0			0
$631$		−	1.00370e11i		−	0.633123i	−0.948572	−	0.316561i	$-0.897472\pi$
$631$		−	1.00370e11i		−	0.633123i	0.948572	−	0.316561i	$-0.102528\pi$
$632$	−8.25312e10	+	2.27708e11i	−0.517309	+	1.42728i
$633$		0			0
$634$	−1.67206e11	−	1.94674e10i	−1.03489	−	0.120490i
$635$			1.14325e10i			0.0703147i
$636$		0			0
$637$	5.37530e11			3.26471
$638$	−5.94519e8	+	5.10634e9i	−0.00358825	+	0.0308196i
$639$		0			0
$640$	−5.16602e10	−	5.44125e10i	−0.307919	−	0.324324i
$641$	2.75025e11			1.62907			0.814534	−	0.580116i	$-0.196993\pi$
$641$	2.75025e11			1.62907			0.814534	+	0.580116i	$0.196993\pi$
$642$		0			0
$643$			2.19775e11i			1.28569i	0.765998	+	0.642844i	$0.222245\pi$
$643$			2.19775e11i			1.28569i	−0.765998	+	0.642844i	$0.777755\pi$
$644$	−2.46452e11	−	5.81762e10i	−1.43281	−	0.338222i
$645$		0			0
$646$	4.70309e10	−	4.03950e11i	0.270056	−	2.31952i
$647$			1.48831e11i			0.849330i	0.905351	+	0.424665i	$0.139608\pi$
$647$			1.48831e11i			0.849330i	−0.905351	+	0.424665i	$0.860392\pi$
$648$		0			0
$649$	−1.20824e11			−0.681043
$650$	5.01131e10	+	5.83454e9i	0.280736	+	0.0326854i
$651$		0			0
$652$	1.47134e10	−	6.23305e10i	0.0814186	−	0.344914i
$653$	1.78058e11			0.979287			0.489643	−	0.871923i	$-0.337127\pi$
$653$	1.78058e11			0.979287			0.489643	+	0.871923i	$0.337127\pi$
$654$		0			0
$655$			8.58974e10i			0.466675i
$656$	2.69762e11	+	1.34872e11i	1.45668	+	0.728296i
$657$		0			0
$658$	−2.57966e11	−	3.00343e10i	−1.37613	−	0.160219i
$659$			1.79592e11i			0.952236i	0.879381	+	0.476118i	$0.157957\pi$
$659$			1.79592e11i			0.952236i	−0.879381	+	0.476118i	$0.842043\pi$
$660$		0			0
$661$	2.69158e11			1.40994			0.704971	−	0.709236i	$-0.250960\pi$
$661$	2.69158e11			1.40994			0.704971	+	0.709236i	$0.250960\pi$
$662$	−2.50632e9	+	2.15268e10i	−0.0130498	+	0.112085i
$663$		0			0
$664$	−3.33841e10	+	9.21084e10i	−0.171738	+	0.473835i
$665$	2.48644e11			1.27143
$666$		0			0
$667$			5.75488e9i			0.0290759i
$668$	−8.38509e10	+	3.55218e11i	−0.421116	+	1.78398i
$669$		0			0
$670$	−1.42318e10	+	1.22238e11i	−0.0706256	+	0.606605i
$671$		−	7.00955e10i		−	0.345780i
$672$		0			0
$673$	−3.00192e11			−1.46332			−0.731659	−	0.681671i	$-0.761253\pi$
$673$	−3.00192e11			−1.46332			−0.731659	+	0.681671i	$0.761253\pi$
$674$	−7.31303e10	−	8.51438e9i	−0.354371	−	0.0412585i
$675$		0			0
$676$	2.02636e11	+	4.78332e10i	0.970353	+	0.229057i
$677$	−2.84577e11			−1.35471			−0.677354	−	0.735657i	$-0.736873\pi$
$677$	−2.84577e11			−1.35471			−0.677354	+	0.735657i	$0.736873\pi$
$678$		0			0
$679$		−	9.15942e10i		−	0.430912i
$680$	−1.34346e11	−	4.86927e10i	−0.628330	−	0.227734i
$681$		0			0
$682$	2.60855e11	+	3.03707e10i	1.20576	+	0.140384i
$683$			1.74603e11i			0.802361i	0.915999	+	0.401180i	$0.131400\pi$
$683$			1.74603e11i			0.802361i	−0.915999	+	0.401180i	$0.868600\pi$
$684$		0			0
$685$	1.39135e11			0.631939
$686$	6.10523e10	−	5.24381e11i	0.275680	−	2.36783i
$687$		0			0
$688$	−8.48075e10	+	1.69625e11i	−0.378513	+	0.757072i
$689$	2.02586e9			0.00898946
$690$		0			0
$691$		−	3.71403e11i		−	1.62905i	−0.580131	−	0.814523i	$-0.696999\pi$
$691$		−	3.71403e11i		−	1.62905i	0.580131	−	0.814523i	$-0.303001\pi$
$692$	2.61415e11	+	6.17083e10i	1.14000	+	0.269104i
$693$		0			0
$694$	−3.61920e10	+	3.10854e11i	−0.156018	+	1.34004i
$695$		−	4.89007e10i		−	0.209593i
$696$		0			0
$697$	5.74407e11			2.43382
$698$	2.60286e11	+	3.03045e10i	1.09655	+	0.127669i
$699$		0			0
$700$	2.00719e10	−	8.50308e10i	0.0835982	−	0.354147i
$701$	−1.55083e9			−0.00642231			−0.00321115	−	0.999995i	$-0.501022\pi$
$701$	−1.55083e9			−0.00642231			−0.00321115	+	0.999995i	$0.501022\pi$
$702$		0			0
$703$			2.21032e11i			0.904971i
$704$	−1.35897e11	+	1.62846e11i	−0.553249	+	0.662960i
$705$		0			0
$706$	−1.69964e11	−	1.97884e10i	−0.684127	−	0.0796513i
$707$		−	8.63488e11i		−	3.45604i
$708$		0			0
$709$	1.19935e10			0.0474636			0.0237318	−	0.999718i	$-0.492445\pi$
$709$	1.19935e10			0.0474636			0.0237318	+	0.999718i	$0.492445\pi$
$710$	−2.08468e10	+	1.79054e11i	−0.0820363	+	0.704613i
$711$		0			0
$712$	−8.07423e10	−	2.92645e10i	−0.314182	−	0.113873i
$713$	2.93985e11			1.13754
$714$		0			0
$715$		−	1.42621e11i		−	0.545706i
$716$	6.97110e10	−	2.95317e11i	0.265246	−	1.12366i
$717$		0			0
$718$	2.22981e10	−	1.91519e11i	0.0839016	−	0.720634i
$719$		−	1.87951e11i		−	0.703283i	−0.936135	−	0.351642i	$-0.885624\pi$
$719$		−	1.87951e11i		−	0.703283i	0.936135	−	0.351642i	$-0.114376\pi$
$720$		0			0
$721$	−5.10829e10			−0.189032
$722$	3.89139e11	+	4.53064e10i	1.43204	+	0.166729i
$723$		0			0
$724$	−1.28171e11	−	3.02555e10i	−0.466484	−	0.110116i
$725$	−1.98555e9			−0.00718668
$726$		0			0
$727$		−	4.79347e11i		−	1.71598i	−0.513666	−	0.857990i	$-0.671713\pi$
$727$		−	4.79347e11i		−	1.71598i	0.513666	−	0.857990i	$-0.328287\pi$
$728$	2.46085e11	−	6.78960e11i	0.876111	−	2.41723i
$729$		0			0
$730$	2.10481e10	+	2.45058e9i	0.0741177	+	0.00862934i
$731$			3.61186e11i			1.26491i
$732$		0			0
$733$	1.15290e11			0.399369			0.199685	−	0.979860i	$-0.436008\pi$
$733$	1.15290e11			0.399369			0.199685	+	0.979860i	$0.436008\pi$
$734$	2.67013e9	−	2.29338e10i	0.00919916	−	0.0790119i
$735$		0			0
$736$	−1.30027e11	+	1.98667e11i	−0.443120	+	0.677042i
$737$	3.47887e11			1.17915
$738$		0			0
$739$		−	2.61705e11i		−	0.877474i	−0.898615	−	0.438737i	$-0.855426\pi$
$739$		−	2.61705e11i		−	0.877474i	0.898615	−	0.438737i	$-0.144574\pi$
$740$	7.55882e10	+	1.78430e10i	0.252074	+	0.0595032i
$741$		0			0
$742$	4.05712e8	−	3.48468e9i	0.00133845	−	0.0114960i
$743$			2.22326e11i			0.729518i	0.931102	+	0.364759i	$0.118849\pi$
$743$			2.22326e11i			0.729518i	−0.931102	+	0.364759i	$0.881151\pi$
$744$		0			0
$745$	1.94021e11			0.629832
$746$	4.94811e11	+	5.76096e10i	1.59766	+	0.186011i
$747$		0			0
$748$	−9.28050e10	+	3.93150e11i	−0.296459	+	1.25589i
$749$	6.96569e11			2.21328
$750$		0			0
$751$			2.58047e11i			0.811220i	0.914046	+	0.405610i	$0.132941\pi$
$751$			2.58047e11i			0.811220i	−0.914046	+	0.405610i	$0.867059\pi$
$752$	−1.08898e11	+	2.17809e11i	−0.340523	+	0.681089i
$753$		0			0
$754$	−1.63024e10	−	1.89805e9i	−0.0504389	−	0.00587248i
$755$		−	1.87161e11i		−	0.576005i
$756$		0			0
$757$	1.26938e11			0.386552			0.193276	−	0.981144i	$-0.438089\pi$
$757$	1.26938e11			0.386552			0.193276	+	0.981144i	$0.438089\pi$
$758$	6.78413e9	−	5.82691e10i	0.0205503	−	0.176507i
$759$		0			0
$760$	7.94430e10	−	2.19187e11i	0.238123	−	0.656993i
$761$	−4.95235e11			−1.47663			−0.738316	−	0.674454i	$-0.764379\pi$
$761$	−4.95235e11			−1.47663			−0.738316	+	0.674454i	$0.764379\pi$
$762$		0			0
$763$		−	4.12294e11i		−	1.21649i
$764$	9.94065e10	−	4.21116e11i	0.291770	−	1.23603i
$765$		0			0
$766$	−3.45610e10	+	2.96845e11i	−0.100385	+	0.862214i
$767$		−	3.85740e11i		−	1.11459i
$768$		0			0
$769$	6.39754e11			1.82940			0.914698	−	0.404137i	$-0.132428\pi$
$769$	6.39754e11			1.82940			0.914698	+	0.404137i	$0.132428\pi$
$770$	−2.45321e11	−	2.85622e10i	−0.697867	−	0.0812509i
$771$		0			0
$772$	1.03497e11	+	2.44310e10i	0.291380	+	0.0687817i
$773$	−2.25549e11			−0.631717			−0.315859	−	0.948806i	$-0.602293\pi$
$773$	−2.25549e11			−0.631717			−0.315859	+	0.948806i	$0.602293\pi$
$774$		0			0
$775$			1.01431e11i			0.281166i
$776$	−8.07431e10	−	2.92648e10i	−0.222668	−	0.0807047i
$777$		0			0
$778$	−3.32815e11	−	3.87489e10i	−0.908417	−	0.105765i
$779$			9.37155e11i			2.54485i
$780$		0			0
$781$	5.09584e11			1.36966
$782$	−5.22959e10	+	4.49172e11i	−0.139843	+	1.20112i
$783$		0			0
$784$	−7.80672e11	−	3.90312e11i	−2.06635	−	1.03311i
$785$	−4.11822e10			−0.108450
$786$		0			0
$787$			1.74074e11i			0.453770i	0.973922	+	0.226885i	$0.0728542\pi$
$787$			1.74074e11i			0.453770i	−0.973922	+	0.226885i	$0.927146\pi$
$788$	−6.04495e10	−	1.42694e10i	−0.156779	−	0.0370084i
$789$		0			0
$790$	−3.05820e10	+	2.62670e11i	−0.0785160	+	0.674376i
$791$			1.55591e11i			0.397446i
$792$		0			0
$793$	2.23785e11			0.565899
$794$	−5.15810e11	−	6.00545e10i	−1.29780	−	0.151100i
$795$		0			0
$796$	−1.36648e11	+	5.78882e11i	−0.340370	+	1.44191i
$797$	−6.58151e9			−0.0163114			−0.00815572	−	0.999967i	$-0.502596\pi$
$797$	−6.58151e9			−0.0163114			−0.00815572	+	0.999967i	$0.502596\pi$
$798$		0			0
$799$			4.63783e11i			1.13796i
$800$	−6.85442e10	−	4.48618e10i	−0.167344	−	0.109526i
$801$		0			0
$802$	4.81846e10	+	5.61001e9i	0.116469	+	0.0135602i
$803$		−	5.99026e10i		−	0.144073i
$804$		0			0
$805$	−2.76479e11			−0.658383
$806$	−9.69608e10	+	8.32799e11i	−0.229750	+	1.97333i
$807$		0			0
$808$	−7.61192e11	−	2.75889e11i	−1.78587	−	0.647275i
$809$	3.64249e11			0.850362			0.425181	−	0.905108i	$-0.360210\pi$
$809$	3.64249e11			0.850362			0.425181	+	0.905108i	$0.360210\pi$
$810$		0			0
$811$			4.01599e11i			0.928344i	0.885745	+	0.464172i	$0.153648\pi$
$811$			4.01599e11i			0.928344i	−0.885745	+	0.464172i	$0.846352\pi$
$812$	−6.52964e9	+	2.76615e10i	−0.0150198	+	0.0636286i
$813$		0			0
$814$	2.53904e10	−	2.18079e11i	0.0578325	−	0.496725i
$815$		−	6.99247e10i		−	0.158489i
$816$		0			0
$817$	−5.89281e11			−1.32262
$818$	7.54187e11	+	8.78081e10i	1.68448	+	0.196120i
$819$		0			0
$820$	3.20487e11	+	7.56524e10i	0.708850	+	0.167328i
$821$	2.94708e10			0.0648663			0.0324332	−	0.999474i	$-0.489674\pi$
$821$	2.94708e10			0.0648663			0.0324332	+	0.999474i	$0.489674\pi$
$822$		0			0
$823$		−	4.79437e11i		−	1.04504i	−0.852628	−	0.522519i	$-0.824992\pi$
$823$		−	4.79437e11i		−	1.04504i	0.852628	−	0.522519i	$-0.175008\pi$
$824$	−1.63213e10	+	4.50312e10i	−0.0354034	+	0.0976798i
$825$		0			0
$826$	−6.63509e11	−	7.72507e10i	−1.42537	−	0.165952i
$827$			2.36828e11i			0.506304i	0.967427	+	0.253152i	$0.0814673\pi$
$827$			2.36828e11i			0.506304i	−0.967427	+	0.253152i	$0.918533\pi$
$828$		0			0
$829$	−6.87687e11			−1.45604			−0.728019	−	0.685557i	$-0.759559\pi$
$829$	−6.87687e11			−1.45604			−0.728019	+	0.685557i	$0.759559\pi$
$830$	−1.23705e10	+	1.06251e11i	−0.0260660	+	0.223882i
$831$		0			0
$832$	−5.19899e11	−	4.33863e11i	−1.08499	−	0.905438i
$833$	−1.66229e12			−3.45246
$834$		0			0
$835$			3.98497e11i			0.819745i
$836$	−6.41432e11	−	1.51413e11i	−1.31318	−	0.309983i
$837$		0			0
$838$	−2.11974e9	+	1.82066e10i	−0.00429841	+	0.0369192i
$839$		−	4.88865e11i		−	0.986600i	−0.869859	−	0.493300i	$-0.835790\pi$
$839$		−	4.88865e11i		−	0.986600i	0.869859	−	0.493300i	$-0.164210\pi$
$840$		0			0
$841$	−4.99600e11			−0.998709
$842$	3.88097e11	+	4.51852e10i	0.772133	+	0.0898975i
$843$		0			0
$844$	−8.79700e9	+	3.72668e10i	−0.0173366	+	0.0734432i
$845$	2.27325e11			0.445882
$846$		0			0
$847$		−	2.38221e11i		−	0.462857i
$848$	−2.94223e9	−	1.47102e9i	−0.00568974	−	0.00284469i
$849$		0			0
$850$	−1.54973e11	−	1.80431e10i	−0.296880	−	0.0345650i
$851$		−	2.45776e11i		−	0.468621i
$852$		0			0
$853$	5.55737e11			1.04972			0.524860	−	0.851189i	$-0.324118\pi$
$853$	5.55737e11			1.04972			0.524860	+	0.851189i	$0.324118\pi$
$854$	4.48166e10	−	3.84932e11i	0.0842574	−	0.723689i
$855$		0			0
$856$	2.22557e11	−	6.14047e11i	0.414522	−	1.14369i
$857$	−4.82150e11			−0.893837			−0.446919	−	0.894575i	$-0.647479\pi$
$857$	−4.82150e11			−0.893837			−0.446919	+	0.894575i	$0.647479\pi$
$858$		0			0
$859$			2.04322e11i			0.375269i	0.982239	+	0.187635i	$0.0600821\pi$
$859$			2.04322e11i			0.375269i	−0.982239	+	0.187635i	$0.939918\pi$
$860$	−4.75701e10	+	2.01521e11i	−0.0869641	+	0.368406i
$861$		0			0
$862$	1.55540e10	−	1.33593e11i	0.0281716	−	0.241967i
$863$		−	2.90900e11i		−	0.524445i	−0.965007	−	0.262223i	$-0.915545\pi$
$863$		−	2.90900e11i		−	0.524445i	0.965007	−	0.262223i	$-0.0844555\pi$
$864$		0			0
$865$	2.93265e11			0.523837
$866$	−9.92606e10	−	1.15567e10i	−0.176484	−	0.0205476i
$867$		0			0
$868$	1.41308e12	+	3.33563e11i	2.48935	+	0.587624i
$869$	7.47555e11			1.31088
$870$		0			0
$871$			1.11065e12i			1.92977i
$872$	−3.63450e11	−	1.31730e11i	−0.628607	−	0.227834i
$873$		0			0
$874$	−7.32832e11	−	8.53218e10i	−1.25591	−	0.146223i
$875$		−	9.53907e10i		−	0.162732i
$876$		0			0
$877$	−6.58753e10			−0.111359			−0.0556794	−	0.998449i	$-0.517732\pi$
$877$	−6.58753e10			−0.111359			−0.0556794	+	0.998449i	$0.517732\pi$
$878$	5.07234e10	−	4.35665e11i	0.0853552	−	0.733119i
$879$		0			0
$880$	−1.03560e11	+	2.07133e11i	−0.172688	+	0.345397i
$881$	−6.86010e11			−1.13875			−0.569373	−	0.822080i	$-0.692814\pi$
$881$	−6.86010e11			−1.13875			−0.569373	+	0.822080i	$0.692814\pi$
$882$		0			0
$883$			5.29575e11i			0.871133i	0.900157	+	0.435567i	$0.143452\pi$
$883$			5.29575e11i			0.871133i	−0.900157	+	0.435567i	$0.856548\pi$
$884$	−1.25516e12	−	2.96287e11i	−2.05537	−	0.485181i
$885$		0			0
$886$	−5.28464e10	+	4.53899e11i	−0.0857591	+	0.736588i
$887$			4.13533e11i			0.668061i	0.942562	+	0.334031i	$0.108409\pi$
$887$			4.13533e11i			0.668061i	−0.942562	+	0.334031i	$0.891591\pi$
$888$		0			0
$889$	1.78676e11			0.286062
$890$	−9.31395e10	−	1.08440e10i	−0.148448	−	0.0172834i
$891$		0			0
$892$	8.29229e10	−	3.51286e11i	0.130983	−	0.554884i
$893$	−7.56671e11			−1.18987
$894$		0			0
$895$		−	3.31298e11i		−	0.516329i
$896$	−8.50403e11	+	8.07387e11i	−1.31945	+	1.25271i
$897$		0			0
$898$	4.61048e11	+	5.36787e10i	0.708991	+	0.0825460i
$899$		−	3.29966e10i		−	0.0505162i
$900$		0			0
$901$	−6.26492e9			−0.00950641
$902$	1.07653e11	−	9.24633e11i	0.162629	−	1.39683i
$903$		0			0
$904$	1.37158e11	+	4.97121e10i	0.205375	+	0.0744369i
$905$	−1.43787e11			−0.214352
$906$		0			0
$907$			3.08875e11i			0.456408i	0.973613	+	0.228204i	$0.0732853\pi$
$907$			3.08875e11i			0.456408i	−0.973613	+	0.228204i	$0.926715\pi$
$908$	−2.11727e11	+	8.96939e11i	−0.311482	+	1.31953i
$909$		0			0
$910$	9.11869e10	−	7.83207e11i	0.132974	−	1.14212i
$911$		−	3.37516e11i		−	0.490027i	−0.969520	−	0.245014i	$-0.921208\pi$
$911$		−	3.37516e11i		−	0.490027i	0.969520	−	0.245014i	$-0.0787925\pi$
$912$		0			0
$913$	3.02388e11			0.435192
$914$	−4.53252e11	−	5.27710e10i	−0.649464	−	0.0756155i
$915$		0			0
$916$	8.95233e9	+	2.11324e9i	0.0127161	+	0.00300170i
$917$	1.34247e12			1.89858
$918$		0			0
$919$		−	3.72489e11i		−	0.522217i	−0.965309	−	0.261109i	$-0.915912\pi$
$919$		−	3.72489e11i		−	0.522217i	0.965309	−	0.261109i	$-0.0840880\pi$
$920$	−8.83365e10	+	2.43725e11i	−0.123307	+	0.340211i
$921$		0			0
$922$	3.54113e11	+	4.12286e10i	0.490026	+	0.0570525i
$923$			1.62689e12i			2.24156i
$924$		0			0
$925$	8.47977e10			0.115829
$926$	5.63135e10	−	4.83678e11i	0.0765894	−	0.657829i
$927$		0			0
$928$	2.22983e10	+	1.45941e10i	0.0300662	+	0.0196782i
$929$	1.27825e12			1.71614			0.858071	−	0.513531i	$-0.171663\pi$
$929$	1.27825e12			1.71614			0.858071	+	0.513531i	$0.171663\pi$
$930$		0			0
$931$		−	2.71206e12i		−	3.60995i
$932$	−4.88312e11	−	1.15268e11i	−0.647193	−	0.152773i
$933$		0			0
$934$	−2.25196e10	+	1.93422e11i	−0.0295920	+	0.254166i
$935$			4.41051e11i			0.577088i
$936$		0			0
$937$	5.59229e11			0.725490			0.362745	−	0.931888i	$-0.381840\pi$
$937$	5.59229e11			0.725490			0.362745	+	0.931888i	$0.381840\pi$
$938$	1.91043e12	+	2.22427e11i	2.46786	+	0.287326i
$939$		0			0
$940$	−6.10827e10	+	2.58765e11i	−0.0782360	+	0.331432i
$941$	−1.42863e12			−1.82205			−0.911026	−	0.412348i	$-0.864709\pi$
$941$	−1.42863e12			−1.82205			−0.911026	+	0.412348i	$0.864709\pi$
$942$		0			0
$943$		−	1.04207e12i		−	1.31780i
$944$	−2.80094e11	+	5.60222e11i	−0.352708	+	0.705460i
$945$		0			0
$946$	5.81407e11	+	6.76918e10i	0.725965	+	0.0845224i
$947$			5.72859e11i			0.712275i	0.934434	+	0.356137i	$0.115906\pi$
$947$			5.72859e11i			0.712275i	−0.934434	+	0.356137i	$0.884094\pi$
$948$		0			0
$949$	1.91243e11			0.235788
$950$	2.94377e10	−	2.52841e11i	0.0361418	−	0.310423i
$951$		0			0
$952$	−7.61009e11	+	2.09966e12i	−0.926492	+	2.55624i
$953$	−3.48415e11			−0.422401			−0.211200	−	0.977443i	$-0.567737\pi$
$953$	−3.48415e11			−0.422401			−0.211200	+	0.977443i	$0.567737\pi$
$954$		0			0
$955$		−	4.72424e11i		−	0.567961i
$956$	8.49537e10	−	3.59890e11i	0.101707	−	0.430862i
$957$		0			0
$958$	−3.08665e10	+	2.65114e11i	−0.0366459	+	0.314753i
$959$		−	2.17452e12i		−	2.57092i
$960$		0			0
$961$	−8.32725e11			−0.976356
$962$	6.96234e11	+	8.10608e10i	0.812933	+	0.0946478i
$963$		0			0
$964$	1.63200e12	+	3.85242e11i	1.88979	+	0.446093i
$965$	1.16107e11			0.133890
$966$		0			0
$967$		−	1.40801e11i		−	0.161028i	−0.996753	−	0.0805138i	$-0.974344\pi$
$967$		−	1.40801e11i		−	0.161028i	0.996753	−	0.0805138i	$-0.0256561\pi$
$968$	−2.09999e11	−	7.61129e10i	−0.239176	−	0.0866876i
$969$		0			0
$970$	−9.31404e10	−	1.08441e10i	−0.105209	−	0.0122492i
$971$			1.01522e12i			1.14204i	0.820936	+	0.571021i	$0.193452\pi$
$971$			1.01522e12i			1.14204i	−0.820936	+	0.571021i	$0.806548\pi$
$972$		0			0
$973$	−7.64260e11			−0.852687
$974$	−1.85191e11	+	1.59061e12i	−0.205771	+	1.76738i
$975$		0			0
$976$	−3.25010e11	−	1.62495e11i	−0.358177	−	0.179077i
$977$	−2.79503e11			−0.306766			−0.153383	−	0.988167i	$-0.549017\pi$
$977$	−2.79503e11			−0.306766			−0.153383	+	0.988167i	$0.549017\pi$
$978$		0			0
$979$			2.65073e11i			0.288560i
$980$	−9.27467e11	−	2.18933e11i	−1.00553	−	0.237360i
$981$		0			0
$982$	−2.27004e10	+	1.94974e11i	−0.0244111	+	0.209668i
$983$		−	1.01738e12i		−	1.08961i	−0.838563	−	0.544805i	$-0.816604\pi$
$983$		−	1.01738e12i		−	1.08961i	0.838563	−	0.544805i	$-0.183396\pi$
$984$		0			0
$985$	−6.78145e10			−0.0720406
$986$	5.04146e10	+	5.86965e9i	0.0533395	+	0.00621018i
$987$		0			0
$988$	4.83398e11	−	2.04782e12i	0.507314	−	2.14914i
$989$	6.55250e11			0.684892
$990$		0			0
$991$			1.27819e12i			1.32526i	0.748947	+	0.662630i	$0.230560\pi$
$991$			1.27819e12i			1.32526i	−0.748947	+	0.662630i	$0.769440\pi$
$992$	7.45532e11	−	1.13909e12i	0.769873	−	1.17629i
$993$		0			0
$994$	2.79840e12	+	3.25811e11i	2.86658	+	0.333749i
$995$			6.49411e11i			0.662564i
$996$		0			0
$997$	−6.24643e11			−0.632195			−0.316098	−	0.948727i	$-0.602373\pi$
$997$	−6.24643e11			−0.632195			−0.316098	+	0.948727i	$0.602373\pi$
$998$	1.07619e11	−	9.24344e11i	0.108484	−	0.931776i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.9.c.b.91.3	✓	32
3.2	odd	2	inner	180.9.c.b.91.30	yes	32
4.3	odd	2	inner	180.9.c.b.91.4	yes	32
12.11	even	2	inner	180.9.c.b.91.29	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.9.c.b.91.3	✓	32	1.1	even	1	trivial
180.9.c.b.91.4	yes	32	4.3	odd	2	inner
180.9.c.b.91.29	yes	32	12.11	even	2	inner
180.9.c.b.91.30	yes	32	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	180.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-15.8926 - 1.85034i) q^{2} +(249.152 + 58.8137i) q^{4} +279.508 q^{5} -4368.38i q^{7} +(-3850.87 - 1395.72i) q^{8} +(-4442.13 - 517.186i) q^{10} +12642.2i q^{11} -40361.3 q^{13} +(-8083.00 + 69425.2i) q^{14} +(58617.9 + 29307.1i) q^{16} +124816. q^{17} +203639. i q^{19} +(69640.2 + 16438.9i) q^{20} +(23392.4 - 200918. i) q^{22} -226436. i q^{23} +78125.0 q^{25} +(641447. + 74682.1i) q^{26} +(256921. - 1.08839e6i) q^{28} -25415.0 q^{29} +1.29831e6i q^{31} +(-877366. - 574231. i) q^{32} +(-1.98365e6 - 230952. i) q^{34} -1.22100e6i q^{35} +1.08541e6 q^{37} +(376802. - 3.23637e6i) q^{38} +(-1.07635e6 - 390116. i) q^{40} +4.60203e6 q^{41} +2.89375e6i q^{43} +(-743535. + 3.14984e6i) q^{44} +(-418985. + 3.59867e6i) q^{46} +3.71574e6i q^{47} -1.33180e7 q^{49} +(-1.24161e6 - 144558. i) q^{50} +(-1.00561e7 - 2.37379e6i) q^{52} -50193.3 q^{53} +3.53361e6i q^{55} +(-6.09705e6 + 1.68221e7i) q^{56} +(403912. + 47026.4i) q^{58} +9.55718e6i q^{59} -5.54455e6 q^{61} +(2.40232e6 - 2.06336e7i) q^{62} +(1.28811e7 + 1.07495e7i) q^{64} -1.12813e7 q^{65} -2.75178e7i q^{67} +(3.10982e7 + 7.34088e6i) q^{68} +(-2.25927e6 + 1.94049e7i) q^{70} -4.03081e7i q^{71} -4.73829e6 q^{73} +(-1.72500e7 - 2.00838e6i) q^{74} +(-1.19768e7 + 5.07373e7i) q^{76} +5.52261e7 q^{77} -5.91316e7i q^{79} +(1.63842e7 + 8.19159e6i) q^{80} +(-7.31385e7 - 8.51533e6i) q^{82} -2.39189e7i q^{83} +3.48871e7 q^{85} +(5.35442e6 - 4.59893e7i) q^{86} +(1.76450e7 - 4.86835e7i) q^{88} +2.09673e7 q^{89} +1.76313e8i q^{91} +(1.33176e7 - 5.64172e7i) q^{92} +(6.87538e6 - 5.90529e7i) q^{94} +5.69189e7i q^{95} +2.09675e7 q^{97} +(2.11658e8 + 2.46428e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 610 q^{4} - 8750 q^{10} - 51392 q^{13} + 11986 q^{16} - 758068 q^{22} + 2500000 q^{25} + 976324 q^{28} - 6117428 q^{34} + 5152064 q^{37} - 96250 q^{40} - 10391752 q^{46} - 11002976 q^{49} + 13976584 q^{52}+ \cdots + 80579520 q^{97}+O(q^{100}) \) 32 * q + 610 * q^4 - 8750 * q^10 - 51392 * q^13 + 11986 * q^16 - 758068 * q^22 + 2500000 * q^25 + 976324 * q^28 - 6117428 * q^34 + 5152064 * q^37 - 96250 * q^40 - 10391752 * q^46 - 11002976 * q^49 + 13976584 * q^52 - 36333948 * q^58 - 7802048 * q^61 + 116259994 * q^64 - 49897500 * q^70 - 94303680 * q^73 + 248840592 * q^76 - 428557904 * q^82 + 106960000 * q^85 + 510719924 * q^88 - 692727576 * q^94 + 80579520 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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