LMFDB - Embedded newform 180.9.c.b.91.12

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			91.12
Character	$\chi$	$=$	180.91
Dual form			180.9.c.b.91.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.96713 + 13.2511i) q^{2} +(-95.1813 - 237.648i) q^{4} -279.508 q^{5} -3400.42i q^{7} +(4002.59 + 869.766i) q^{8} +(2506.39 - 3703.78i) q^{10} -3247.97i q^{11} +10010.8 q^{13} +(45059.1 + 30492.0i) q^{14} +(-47417.1 + 45239.3i) q^{16} +112504. q^{17} -62167.3i q^{19} +(26604.0 + 66424.6i) q^{20} +(43039.1 + 29125.0i) q^{22} +250249. i q^{23} +78125.0 q^{25} +(-89768.3 + 132654. i) q^{26} +(-808102. + 323656. i) q^{28} +420649. q^{29} +161412. i q^{31} +(-174273. - 1.03399e6i) q^{32} +(-1.00884e6 + 1.49079e6i) q^{34} +950445. i q^{35} +1.31491e6 q^{37} +(823782. + 557462. i) q^{38} +(-1.11876e6 - 243107. i) q^{40} -667494. q^{41} -2.96065e6i q^{43} +(-771874. + 309146. i) q^{44} +(-3.31607e6 - 2.24402e6i) q^{46} -3.08304e6i q^{47} -5.79803e6 q^{49} +(-700557. + 1.03524e6i) q^{50} +(-952843. - 2.37905e6i) q^{52} +5.63544e6 q^{53} +907836. i q^{55} +(2.95757e6 - 1.36105e7i) q^{56} +(-3.77201e6 + 5.57405e6i) q^{58} +3.54850e6i q^{59} -2.55655e7 q^{61} +(-2.13888e6 - 1.44740e6i) q^{62} +(1.52642e7 + 6.96263e6i) q^{64} -2.79811e6 q^{65} +3.28205e7i q^{67} +(-1.07083e7 - 2.67363e7i) q^{68} +(-1.25944e7 - 8.52276e6i) q^{70} -2.69401e7i q^{71} -1.96776e7 q^{73} +(-1.17909e7 + 1.74239e7i) q^{74} +(-1.47739e7 + 5.91716e6i) q^{76} -1.10445e7 q^{77} -1.49155e7i q^{79} +(1.32535e7 - 1.26448e7i) q^{80} +(5.98551e6 - 8.84501e6i) q^{82} -7.32854e7i q^{83} -3.14458e7 q^{85} +(3.92318e7 + 2.65485e7i) q^{86} +(2.82498e6 - 1.30003e7i) q^{88} +4.30098e7 q^{89} -3.40410e7i q^{91} +(5.94712e7 - 2.38190e7i) q^{92} +(4.08535e7 + 2.76460e7i) q^{94} +1.73763e7i q^{95} +1.35970e8 q^{97} +(5.19917e7 - 7.68301e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−8.96713	+	13.2511i	−0.560445	+	0.828191i
$2$	−8.96713	+	13.2511i	−0.560445	+	0.828191i
$3$		0			0
$3$		0			0
$4$	−95.1813	−	237.648i	−0.371802	−	0.928312i
$5$	−279.508			−0.447214
$5$	−279.508			−0.447214
$6$		0			0
$7$		−	3400.42i		−	1.41625i	−0.706087	−	0.708125i	$-0.749541\pi$
$7$		−	3400.42i		−	1.41625i	0.706087	−	0.708125i	$-0.250459\pi$
$8$	4002.59	+	869.766i	0.977195	+	0.212345i
$9$		0			0
$10$	2506.39	−	3703.78i	0.250639	−	0.370378i
$11$		−	3247.97i		−	0.221841i	−0.993829	−	0.110920i	$-0.964620\pi$
$11$		−	3247.97i		−	0.221841i	0.993829	−	0.110920i	$-0.0353799\pi$
$12$		0			0
$13$	10010.8			0.350507			0.175253	−	0.984523i	$-0.443926\pi$
$13$	10010.8			0.350507			0.175253	+	0.984523i	$0.443926\pi$
$14$	45059.1	+	30492.0i	1.17293	+	0.793731i
$15$		0			0
$16$	−47417.1	+	45239.3i	−0.723527	+	0.690296i
$17$	112504.			1.34701			0.673506	−	0.739182i	$-0.264788\pi$
$17$	112504.			1.34701			0.673506	+	0.739182i	$0.264788\pi$
$18$		0			0
$19$		−	62167.3i		−	0.477032i	−0.971139	−	0.238516i	$-0.923339\pi$
$19$		−	62167.3i		−	0.477032i	0.971139	−	0.238516i	$-0.0766609\pi$
$20$	26604.0	+	66424.6i	0.166275	+	0.415154i
$21$		0			0
$22$	43039.1	+	29125.0i	0.183727	+	0.124330i
$23$			250249.i			0.894255i	0.894470	+	0.447128i	$0.147553\pi$
$23$			250249.i			0.894255i	−0.894470	+	0.447128i	$0.852447\pi$
$24$		0			0
$25$	78125.0			0.200000
$26$	−89768.3	+	132654.i	−0.196440	+	0.290287i
$27$		0			0
$28$	−808102.	+	323656.i	−1.31472	+	0.526564i
$29$	420649.			0.594741			0.297371	−	0.954762i	$-0.403890\pi$
$29$	420649.			0.594741			0.297371	+	0.954762i	$0.403890\pi$
$30$		0			0
$31$			161412.i			0.174779i	0.996174	+	0.0873894i	$0.0278524\pi$
$31$			161412.i			0.174779i	−0.996174	+	0.0873894i	$0.972148\pi$
$32$	−174273.	−	1.03399e6i	−0.166200	−	0.986092i
$33$		0			0
$34$	−1.00884e6	+	1.49079e6i	−0.754927	+	1.11558i
$35$			950445.i			0.633366i
$36$		0			0
$37$	1.31491e6			0.701597			0.350798	−	0.936451i	$-0.385910\pi$
$37$	1.31491e6			0.701597			0.350798	+	0.936451i	$0.385910\pi$
$38$	823782.	+	557462.i	0.395074	+	0.267350i
$39$		0			0
$40$	−1.11876e6	−	243107.i	−0.437015	−	0.0949637i
$41$	−667494.			−0.236218			−0.118109	−	0.993001i	$-0.537683\pi$
$41$	−667494.			−0.236218			−0.118109	+	0.993001i	$0.537683\pi$
$42$		0			0
$43$		−	2.96065e6i		−	0.865991i	−0.901396	−	0.432995i	$-0.857457\pi$
$43$		−	2.96065e6i		−	0.865991i	0.901396	−	0.432995i	$-0.142543\pi$
$44$	−771874.	+	309146.i	−0.205938	+	0.0824808i
$45$		0			0
$46$	−3.31607e6	−	2.24402e6i	−0.740614	−	0.501181i
$47$		−	3.08304e6i		−	0.631811i	−0.948791	−	0.315906i	$-0.897692\pi$
$47$		−	3.08304e6i		−	0.631811i	0.948791	−	0.315906i	$-0.102308\pi$
$48$		0			0
$49$	−5.79803e6			−1.00576
$50$	−700557.	+	1.03524e6i	−0.112089	+	0.165638i
$51$		0			0
$52$	−952843.	−	2.37905e6i	−0.130319	−	0.325380i
$53$	5.63544e6			0.714208			0.357104	−	0.934065i	$-0.383764\pi$
$53$	5.63544e6			0.714208			0.357104	+	0.934065i	$0.383764\pi$
$54$		0			0
$55$			907836.i			0.0992103i
$56$	2.95757e6	−	1.36105e7i	0.300734	−	1.38395i
$57$		0			0
$58$	−3.77201e6	+	5.57405e6i	−0.333320	+	0.492559i
$59$			3.54850e6i			0.292845i	0.989222	+	0.146422i	$0.0467758\pi$
$59$			3.54850e6i			0.292845i	−0.989222	+	0.146422i	$0.953224\pi$
$60$		0			0
$61$	−2.55655e7			−1.84644			−0.923220	−	0.384271i	$-0.874453\pi$
$61$	−2.55655e7			−1.84644			−0.923220	+	0.384271i	$0.874453\pi$
$62$	−2.13888e6	−	1.44740e6i	−0.144750	−	0.0979540i
$63$		0			0
$64$	1.52642e7	+	6.96263e6i	0.909819	+	0.415005i
$65$	−2.79811e6			−0.156751
$66$		0			0
$67$			3.28205e7i			1.62872i	0.580362	+	0.814358i	$0.302911\pi$
$67$			3.28205e7i			1.62872i	−0.580362	+	0.814358i	$0.697089\pi$
$68$	−1.07083e7	−	2.67363e7i	−0.500822	−	1.25045i
$69$		0			0
$70$	−1.25944e7	−	8.52276e6i	−0.524549	−	0.354967i
$71$		−	2.69401e7i		−	1.06015i	−0.847952	−	0.530073i	$-0.822164\pi$
$71$		−	2.69401e7i		−	1.06015i	0.847952	−	0.530073i	$-0.177836\pi$
$72$		0			0
$73$	−1.96776e7			−0.692918			−0.346459	−	0.938065i	$-0.612616\pi$
$73$	−1.96776e7			−0.692918			−0.346459	+	0.938065i	$0.612616\pi$
$74$	−1.17909e7	+	1.74239e7i	−0.393207	+	0.581056i
$75$		0			0
$76$	−1.47739e7	+	5.91716e6i	−0.442835	+	0.177361i
$77$	−1.10445e7			−0.314182
$78$		0			0
$79$		−	1.49155e7i		−	0.382940i	−0.981498	−	0.191470i	$-0.938675\pi$
$79$		−	1.49155e7i		−	0.382940i	0.981498	−	0.191470i	$-0.0613255\pi$
$80$	1.32535e7	−	1.26448e7i	0.323571	−	0.308710i
$81$		0			0
$82$	5.98551e6	−	8.84501e6i	0.132387	−	0.195633i
$83$		−	7.32854e7i		−	1.54420i	−0.635498	−	0.772102i	$-0.719205\pi$
$83$		−	7.32854e7i		−	1.54420i	0.635498	−	0.772102i	$-0.280795\pi$
$84$		0			0
$85$	−3.14458e7			−0.602402
$86$	3.92318e7	+	2.65485e7i	0.717206	+	0.485341i
$87$		0			0
$88$	2.82498e6	−	1.30003e7i	0.0471068	−	0.216782i
$89$	4.30098e7			0.685501			0.342750	−	0.939427i	$-0.388642\pi$
$89$	4.30098e7			0.685501			0.342750	+	0.939427i	$0.388642\pi$
$90$		0			0
$91$		−	3.40410e7i		−	0.496405i
$92$	5.94712e7	−	2.38190e7i	0.830148	−	0.332486i
$93$		0			0
$94$	4.08535e7	+	2.76460e7i	0.523261	+	0.354096i
$95$			1.73763e7i			0.213335i
$96$		0			0
$97$	1.35970e8			1.53587			0.767937	−	0.640525i	$-0.221283\pi$
$97$	1.35970e8			1.53587			0.767937	+	0.640525i	$0.221283\pi$
$98$	5.19917e7	−	7.68301e7i	0.563676	−	0.832966i
$99$		0			0
$100$	−7.43604e6	−	1.85662e7i	−0.0743604	−	0.185662i
$101$	5.95062e7			0.571843			0.285922	−	0.958253i	$-0.407700\pi$
$101$	5.95062e7			0.571843			0.285922	+	0.958253i	$0.407700\pi$
$102$		0			0
$103$		−	1.08021e8i		−	0.959755i	−0.877335	−	0.479878i	$-0.840681\pi$
$103$		−	1.08021e8i		−	0.959755i	0.877335	−	0.479878i	$-0.159319\pi$
$104$	4.00692e7	+	8.70708e6i	0.342513	+	0.0744284i
$105$		0			0
$106$	−5.05337e7	+	7.46756e7i	−0.400275	+	0.591501i
$107$		−	3.81332e7i		−	0.290917i	−0.989364	−	0.145458i	$-0.953534\pi$
$107$		−	3.81332e7i		−	0.290917i	0.989364	−	0.145458i	$-0.0464657\pi$
$108$		0			0
$109$	5.90318e7			0.418196			0.209098	−	0.977895i	$-0.432947\pi$
$109$	5.90318e7			0.418196			0.209098	+	0.977895i	$0.432947\pi$
$110$	−1.20298e7	−	8.14068e6i	−0.0821651	−	0.0556019i
$111$		0			0
$112$	1.53832e8	+	1.61238e8i	0.977632	+	1.02469i
$113$	1.37301e8			0.842094			0.421047	−	0.907039i	$-0.361663\pi$
$113$	1.37301e8			0.842094			0.421047	+	0.907039i	$0.361663\pi$
$114$		0			0
$115$		−	6.99468e7i		−	0.399923i
$116$	−4.00379e7	−	9.99664e7i	−0.221126	−	0.552105i
$117$		0			0
$118$	−4.70214e7	−	3.18199e7i	−0.242531	−	0.164123i
$119$		−	3.82560e8i		−	1.90771i
$120$		0			0
$121$	2.03810e8			0.950787
$122$	2.29249e8	−	3.38770e8i	1.03483	−	1.52921i
$123$		0			0
$124$	3.83592e7	−	1.53634e7i	0.162249	−	0.0649831i
$125$	−2.18366e7			−0.0894427
$126$		0			0
$127$		−	2.56554e8i		−	0.986197i	−0.869974	−	0.493098i	$-0.835864\pi$
$127$		−	2.56554e8i		−	0.986197i	0.869974	−	0.493098i	$-0.164136\pi$
$128$	−2.29139e8	+	1.39832e8i	−0.853608	+	0.520916i
$129$		0			0
$130$	2.50910e7	−	3.70779e7i	0.0878506	−	0.129820i
$131$		−	3.65845e8i		−	1.24226i	−0.783708	−	0.621129i	$-0.786674\pi$
$131$		−	3.65845e8i		−	1.24226i	0.783708	−	0.621129i	$-0.213326\pi$
$132$		0			0
$133$	−2.11395e8			−0.675597
$134$	−4.34906e8	−	2.94305e8i	−1.34889	−	0.912807i
$135$		0			0
$136$	4.50306e8	+	9.78520e7i	1.31629	+	0.286032i
$137$	−6.25242e8			−1.77487			−0.887433	−	0.460936i	$-0.847514\pi$
$137$	−6.25242e8			−1.77487			−0.887433	+	0.460936i	$0.847514\pi$
$138$		0			0
$139$			6.77999e7i			0.181623i	0.995868	+	0.0908113i	$0.0289460\pi$
$139$			6.77999e7i			0.181623i	−0.995868	+	0.0908113i	$0.971054\pi$
$140$	2.25871e8	−	9.04646e7i	0.587962	−	0.235487i
$141$		0			0
$142$	3.56985e8	+	2.41575e8i	0.878004	+	0.594154i
$143$		−	3.25149e7i		−	0.0777567i
$144$		0			0
$145$	−1.17575e8			−0.265976
$146$	1.76452e8	−	2.60750e8i	0.388343	−	0.573868i
$147$		0			0
$148$	−1.25154e8	−	3.12485e8i	−0.260855	−	0.651301i
$149$	7.15051e8			1.45075			0.725374	−	0.688355i	$-0.241667\pi$
$149$	7.15051e8			1.45075			0.725374	+	0.688355i	$0.241667\pi$
$150$		0			0
$151$			3.45928e8i			0.665392i	0.943034	+	0.332696i	$0.107958\pi$
$151$			3.45928e8i			0.665392i	−0.943034	+	0.332696i	$0.892042\pi$
$152$	5.40710e7	−	2.48830e8i	0.101295	−	0.466153i
$153$		0			0
$154$	9.90371e7	−	1.46351e8i	0.176082	−	0.260203i
$155$		−	4.51160e7i		−	0.0781635i
$156$		0			0
$157$	−1.15504e9			−1.90107			−0.950535	−	0.310618i	$-0.899464\pi$
$157$	−1.15504e9			−1.90107			−0.950535	+	0.310618i	$0.899464\pi$
$158$	1.97647e8	+	1.33750e8i	0.317148	+	0.214617i
$159$		0			0
$160$	4.87109e7	+	2.89010e8i	0.0743270	+	0.440994i
$161$	8.50952e8			1.26649
$162$		0			0
$163$		−	1.13292e9i		−	1.60490i	−0.596719	−	0.802451i	$-0.703529\pi$
$163$		−	1.13292e9i		−	1.60490i	0.596719	−	0.802451i	$-0.296471\pi$
$164$	6.35330e7	+	1.58629e8i	0.0878261	+	0.219284i
$165$		0			0
$166$	9.71109e8	+	6.57159e8i	1.27890	+	0.865443i
$167$			1.06381e9i			1.36772i	0.729613	+	0.683860i	$0.239700\pi$
$167$			1.06381e9i			1.36772i	−0.729613	+	0.683860i	$0.760300\pi$
$168$		0			0
$169$	−7.15514e8			−0.877145
$170$	2.81978e8	−	4.16690e8i	0.337613	−	0.498904i
$171$		0			0
$172$	−7.03592e8	+	2.81798e8i	−0.803910	+	0.321977i
$173$	2.72699e8			0.304438			0.152219	−	0.988347i	$-0.451358\pi$
$173$	2.72699e8			0.304438			0.152219	+	0.988347i	$0.451358\pi$
$174$		0			0
$175$		−	2.65658e8i		−	0.283250i
$176$	1.46936e8	+	1.54009e8i	0.153136	+	0.160508i
$177$		0			0
$178$	−3.85675e8	+	5.69926e8i	−0.384186	+	0.567726i
$179$		−	7.70098e8i		−	0.750125i	−0.927000	−	0.375063i	$-0.877621\pi$
$179$		−	7.70098e8i		−	0.750125i	0.927000	−	0.375063i	$-0.122379\pi$
$180$		0			0
$181$	2.38505e8			0.222220			0.111110	−	0.993808i	$-0.464559\pi$
$181$	2.38505e8			0.222220			0.111110	+	0.993808i	$0.464559\pi$
$182$	4.51079e8	+	3.05250e8i	0.411119	+	0.278208i
$183$		0			0
$184$	−2.17658e8	+	1.00164e9i	−0.189891	+	0.873861i
$185$	−3.67527e8			−0.313764
$186$		0			0
$187$		−	3.65409e8i		−	0.298822i
$188$	−7.32678e8	+	2.93448e8i	−0.586518	+	0.234909i
$189$		0			0
$190$	−2.30254e8	−	1.55815e8i	−0.176682	−	0.119563i
$191$			1.23415e9i			0.927333i	0.886010	+	0.463667i	$0.153466\pi$
$191$			1.23415e9i			0.927333i	−0.886010	+	0.463667i	$0.846534\pi$
$192$		0			0
$193$	−2.27280e9			−1.63806			−0.819032	−	0.573747i	$-0.805489\pi$
$193$	−2.27280e9			−1.63806			−0.819032	+	0.573747i	$0.805489\pi$
$194$	−1.21926e9	+	1.80174e9i	−0.860774	+	1.27200i
$195$		0			0
$196$	5.51864e8	+	1.37789e9i	0.373945	+	0.933664i
$197$	−2.68424e9			−1.78220			−0.891102	−	0.453804i	$-0.850067\pi$
$197$	−2.68424e9			−1.78220			−0.891102	+	0.453804i	$0.850067\pi$
$198$		0			0
$199$		−	2.82249e9i		−	1.79978i	−0.436117	−	0.899890i	$-0.643647\pi$
$199$		−	2.82249e9i		−	1.79978i	0.436117	−	0.899890i	$-0.356353\pi$
$200$	3.12702e8	+	6.79505e7i	0.195439	+	0.0424690i
$201$		0			0
$202$	−5.33600e8	+	7.88521e8i	−0.320487	+	0.473596i
$203$		−	1.43038e9i		−	0.842302i
$204$		0			0
$205$	1.86570e8			0.105640
$206$	1.43140e9	+	9.68641e8i	0.794861	+	0.537890i
$207$		0			0
$208$	−4.74684e8	+	4.52882e8i	−0.253601	+	0.241954i
$209$	−2.01918e8			−0.105825
$210$		0			0
$211$		−	2.17654e9i		−	1.09809i	−0.835794	−	0.549043i	$-0.814992\pi$
$211$		−	2.17654e9i		−	1.09809i	0.835794	−	0.549043i	$-0.185008\pi$
$212$	−5.36389e8	−	1.33925e9i	−0.265544	−	0.663008i
$213$		0			0
$214$	5.05306e8	+	3.41946e8i	0.240935	+	0.163043i
$215$			8.27527e8i			0.387283i
$216$		0			0
$217$	5.48868e8			0.247531
$218$	−5.29346e8	+	7.82234e8i	−0.234376	+	0.346346i
$219$		0			0
$220$	2.15745e8	−	8.64090e7i	0.0920981	−	0.0368866i
$221$	1.12626e9			0.472137
$222$		0			0
$223$		−	1.82816e9i		−	0.739256i	−0.929180	−	0.369628i	$-0.879485\pi$
$223$		−	1.82816e9i		−	0.739256i	0.929180	−	0.369628i	$-0.120515\pi$
$224$	−3.51601e9	+	5.92602e8i	−1.39655	+	0.235381i
$225$		0			0
$226$	−1.23120e9	+	1.81939e9i	−0.471948	+	0.697415i
$227$			1.90754e9i			0.718406i	0.933259	+	0.359203i	$0.116951\pi$
$227$			1.90754e9i			0.718406i	−0.933259	+	0.359203i	$0.883049\pi$
$228$		0			0
$229$	−1.75323e9			−0.637526			−0.318763	−	0.947834i	$-0.603267\pi$
$229$	−1.75323e9			−0.637526			−0.318763	+	0.947834i	$0.603267\pi$
$230$	9.26869e8	+	6.27222e8i	0.331213	+	0.224135i
$231$		0			0
$232$	1.68369e9	+	3.65866e8i	0.581178	+	0.126290i
$233$	−1.21612e9			−0.412621			−0.206310	−	0.978487i	$-0.566146\pi$
$233$	−1.21612e9			−0.412621			−0.206310	+	0.978487i	$0.566146\pi$
$234$		0			0
$235$			8.61735e8i			0.282555i
$236$	8.43295e8	−	3.37751e8i	0.271851	−	0.108880i
$237$		0			0
$238$	5.06932e9	+	3.43046e9i	1.57995	+	1.06917i
$239$			4.76046e9i			1.45901i	0.683977	+	0.729504i	$0.260249\pi$
$239$			4.76046e9i			1.45901i	−0.683977	+	0.729504i	$0.739751\pi$
$240$		0			0
$241$	−4.34950e9			−1.28935			−0.644676	−	0.764456i	$-0.723008\pi$
$241$	−4.34950e9			−1.28935			−0.644676	+	0.764456i	$0.723008\pi$
$242$	−1.82759e9	+	2.70069e9i	−0.532864	+	0.787433i
$243$		0			0
$244$	2.43336e9	+	6.07559e9i	0.686510	+	1.71407i
$245$	1.62060e9			0.449792
$246$		0			0
$247$		−	6.22346e8i		−	0.167203i
$248$	−1.40391e8	+	6.46066e8i	−0.0371135	+	0.170793i
$249$		0			0
$250$	1.95812e8	−	2.89358e8i	0.0501278	−	0.0740757i
$251$		−	3.57234e9i		−	0.900032i	−0.893020	−	0.450016i	$-0.851418\pi$
$251$		−	3.57234e9i		−	0.900032i	0.893020	−	0.450016i	$-0.148582\pi$
$252$		0			0
$253$	8.12803e8			0.198382
$254$	3.39961e9	+	2.30055e9i	0.816759	+	0.552709i
$255$		0			0
$256$	2.01786e8	−	4.29022e9i	0.0469820	−	0.998896i
$257$	−5.45646e9			−1.25077			−0.625387	−	0.780315i	$-0.715059\pi$
$257$	−5.45646e9			−1.25077			−0.625387	+	0.780315i	$0.715059\pi$
$258$		0			0
$259$		−	4.47123e9i		−	0.993637i
$260$	2.66328e8	+	6.64965e8i	0.0582805	+	0.145514i
$261$		0			0
$262$	4.84784e9	+	3.28058e9i	1.02883	+	0.696218i
$263$			7.23083e9i			1.51135i	0.654946	+	0.755675i	$0.272691\pi$
$263$			7.23083e9i			1.51135i	−0.654946	+	0.755675i	$0.727309\pi$
$264$		0			0
$265$	−1.57515e9			−0.319404
$266$	1.89560e9	−	2.80120e9i	0.378635	−	0.559523i
$267$		0			0
$268$	7.79972e9	−	3.12389e9i	1.51196	−	0.605560i
$269$	−5.99517e9			−1.14496			−0.572482	−	0.819917i	$-0.694019\pi$
$269$	−5.99517e9			−1.14496			−0.572482	+	0.819917i	$0.694019\pi$
$270$		0			0
$271$		−	8.02363e9i		−	1.48763i	−0.668387	−	0.743813i	$-0.733015\pi$
$271$		−	8.02363e9i		−	1.48763i	0.668387	−	0.743813i	$-0.266985\pi$
$272$	−5.33460e9	+	5.08959e9i	−0.974599	+	0.929837i
$273$		0			0
$274$	5.60662e9	−	8.28512e9i	0.994716	−	1.46993i
$275$		−	2.53748e8i		−	0.0443682i
$276$		0			0
$277$	−2.75538e9			−0.468018			−0.234009	−	0.972234i	$-0.575185\pi$
$277$	−2.75538e9			−0.468018			−0.234009	+	0.972234i	$0.575185\pi$
$278$	−8.98420e8	−	6.07970e8i	−0.150418	−	0.101790i
$279$		0			0
$280$	−8.26665e8	+	3.80424e9i	−0.134492	+	0.618922i
$281$	1.12388e10			1.80258			0.901291	−	0.433215i	$-0.142621\pi$
$281$	1.12388e10			1.80258			0.901291	+	0.433215i	$0.142621\pi$
$282$		0			0
$283$		−	1.19605e9i		−	0.186467i	−0.995644	−	0.0932337i	$-0.970280\pi$
$283$		−	1.19605e9i		−	0.186467i	0.995644	−	0.0932337i	$-0.0297204\pi$
$284$	−6.40226e9	+	2.56419e9i	−0.984147	+	0.394164i
$285$		0			0
$286$	4.30857e8	+	2.91565e8i	0.0643975	+	0.0435784i
$287$			2.26976e9i			0.334543i
$288$		0			0
$289$	5.68134e9			0.814441
$290$	1.05431e9	−	1.55799e9i	0.149065	−	0.220279i
$291$		0			0
$292$	1.87294e9	+	4.67635e9i	0.257628	+	0.643244i
$293$	−8.81945e8			−0.119666			−0.0598330	−	0.998208i	$-0.519057\pi$
$293$	−8.81945e8			−0.119666			−0.0598330	+	0.998208i	$0.519057\pi$
$294$		0			0
$295$		−	9.91837e8i		−	0.130964i
$296$	5.26303e9	+	1.14366e9i	0.685597	+	0.148981i
$297$		0			0
$298$	−6.41195e9	+	9.47518e9i	−0.813065	+	1.20150i
$299$			2.50520e9i			0.313442i
$300$		0			0
$301$	−1.00674e10			−1.22646
$302$	−4.58391e9	−	3.10198e9i	−0.551072	−	0.372916i
$303$		0			0
$304$	2.81240e9	+	2.94779e9i	0.329293	+	0.345145i
$305$	7.14578e9			0.825754
$306$		0			0
$307$		−	4.49843e9i		−	0.506416i	−0.967412	−	0.253208i	$-0.918514\pi$
$307$		−	4.49843e9i		−	0.506416i	0.967412	−	0.253208i	$-0.0814857\pi$
$308$	1.05123e9	+	2.62469e9i	0.116814	+	0.291659i
$309$		0			0
$310$	5.97835e8	+	4.04561e8i	0.0647343	+	0.0438064i
$311$			5.01658e9i			0.536249i	0.963384	+	0.268125i	$0.0864039\pi$
$311$			5.01658e9i			0.536249i	−0.963384	+	0.268125i	$0.913596\pi$
$312$		0			0
$313$	1.33944e10			1.39555			0.697776	−	0.716316i	$-0.254173\pi$
$313$	1.33944e10			1.39555			0.697776	+	0.716316i	$0.254173\pi$
$314$	1.03574e10	−	1.53055e10i	1.06545	−	1.57445i
$315$		0			0
$316$	−3.54465e9	+	1.41968e9i	−0.355488	+	0.142378i
$317$	5.15443e9			0.510439			0.255219	−	0.966883i	$-0.417852\pi$
$317$	5.15443e9			0.510439			0.255219	+	0.966883i	$0.417852\pi$
$318$		0			0
$319$		−	1.36626e9i		−	0.131938i
$320$	−4.26648e9	−	1.94612e9i	−0.406883	−	0.185596i
$321$		0			0
$322$	−7.63059e9	+	1.12760e10i	−0.709798	+	1.04890i
$323$		−	6.99405e9i		−	0.642568i
$324$		0			0
$325$	7.82096e8			0.0701014
$326$	1.50124e10	+	1.01590e10i	1.32917	+	0.899459i
$327$		0			0
$328$	−2.67171e9	−	5.80564e8i	−0.230831	−	0.0501597i
$329$	−1.04836e10			−0.894803
$330$		0			0
$331$		−	5.31095e9i		−	0.442446i	−0.975223	−	0.221223i	$-0.928995\pi$
$331$		−	5.31095e9i		−	0.442446i	0.975223	−	0.221223i	$-0.0710048\pi$
$332$	−1.74161e10	+	6.97540e9i	−1.43350	+	0.574138i
$333$		0			0
$334$	−1.40966e10	−	9.53929e9i	−1.13273	−	0.766532i
$335$		−	9.17360e9i		−	0.728384i
$336$		0			0
$337$	−1.60185e10			−1.24195			−0.620973	−	0.783832i	$-0.713262\pi$
$337$	−1.60185e10			−1.24195			−0.620973	+	0.783832i	$0.713262\pi$
$338$	6.41611e9	−	9.48132e9i	0.491592	−	0.726444i
$339$		0			0
$340$	2.99305e9	+	7.47302e9i	0.223974	+	0.559217i
$341$	5.24262e8			0.0387731
$342$		0			0
$343$			1.13005e8i			0.00816433i
$344$	2.57507e9	−	1.18503e10i	0.183889	−	0.846242i
$345$		0			0
$346$	−2.44533e9	+	3.61355e9i	−0.170621	+	0.252133i
$347$		−	2.52648e10i		−	1.74260i	−0.490751	−	0.871300i	$-0.663278\pi$
$347$		−	2.52648e10i		−	1.74260i	0.490751	−	0.871300i	$-0.336722\pi$
$348$		0			0
$349$	−1.17048e10			−0.788970			−0.394485	−	0.918902i	$-0.629077\pi$
$349$	−1.17048e10			−0.788970			−0.394485	+	0.918902i	$0.629077\pi$
$350$	3.52024e9	+	2.38219e9i	0.234585	+	0.158746i
$351$		0			0
$352$	−3.35838e9	+	5.66035e8i	−0.218756	+	0.0368700i
$353$	−1.38652e10			−0.892947			−0.446474	−	0.894797i	$-0.647320\pi$
$353$	−1.38652e10			−0.892947			−0.446474	+	0.894797i	$0.647320\pi$
$354$		0			0
$355$			7.52999e9i			0.474112i
$356$	−4.09373e9	−	1.02212e10i	−0.254870	−	0.636358i
$357$		0			0
$358$	1.02046e10	+	6.90556e9i	0.621247	+	0.420404i
$359$		−	1.15769e10i		−	0.696970i	−0.937314	−	0.348485i	$-0.886696\pi$
$359$		−	1.15769e10i		−	0.696970i	0.937314	−	0.348485i	$-0.113304\pi$
$360$		0			0
$361$	1.31188e10			0.772441
$362$	−2.13870e9	+	3.16044e9i	−0.124542	+	0.184040i
$363$		0			0
$364$	−8.08977e9	+	3.24006e9i	−0.460819	+	0.184564i
$365$	5.50007e9			0.309882
$366$		0			0
$367$			1.61343e10i			0.889374i	0.895686	+	0.444687i	$0.146685\pi$
$367$			1.61343e10i			0.889374i	−0.895686	+	0.444687i	$0.853315\pi$
$368$	−1.13211e10	−	1.18661e10i	−0.617301	−	0.647017i
$369$		0			0
$370$	3.29566e9	−	4.87013e9i	0.175847	−	0.259856i
$371$		−	1.91629e10i		−	1.01150i
$372$		0			0
$373$	−2.16378e10			−1.11783			−0.558917	−	0.829223i	$-0.688783\pi$
$373$	−2.16378e10			−1.11783			−0.558917	+	0.829223i	$0.688783\pi$
$374$	4.84206e9	+	3.27667e9i	0.247482	+	0.167474i
$375$		0			0
$376$	2.68152e9	−	1.23401e10i	0.134162	−	0.617403i
$377$	4.21104e9			0.208461
$378$		0			0
$379$		−	1.87414e10i		−	0.908333i	−0.890917	−	0.454167i	$-0.849937\pi$
$379$		−	1.87414e10i		−	0.908333i	0.890917	−	0.454167i	$-0.150063\pi$
$380$	4.12944e9	−	1.65390e9i	0.198042	−	0.0793184i
$381$		0			0
$382$	−1.63539e10	−	1.10668e10i	−0.768010	−	0.519720i
$383$			1.99044e9i			0.0925028i	0.998930	+	0.0462514i	$0.0147275\pi$
$383$			1.99044e9i			0.0925028i	−0.998930	+	0.0462514i	$0.985272\pi$
$384$		0			0
$385$	3.08702e9			0.140507
$386$	2.03804e10	−	3.01170e10i	0.918046	−	1.35663i
$387$		0			0
$388$	−1.29418e10	−	3.23129e10i	−0.571041	−	1.42577i
$389$	−3.00115e9			−0.131066			−0.0655329	−	0.997850i	$-0.520875\pi$
$389$	−3.00115e9			−0.131066			−0.0655329	+	0.997850i	$0.520875\pi$
$390$		0			0
$391$			2.81540e10i			1.20457i
$392$	−2.32071e10	−	5.04293e9i	−0.982828	−	0.213569i
$393$		0			0
$394$	2.40700e10	−	3.55691e10i	0.998828	−	1.47601i
$395$			4.16902e9i			0.171256i
$396$		0			0
$397$	−1.03885e10			−0.418205			−0.209102	−	0.977894i	$-0.567054\pi$
$397$	−1.03885e10			−0.418205			−0.209102	+	0.977894i	$0.567054\pi$
$398$	3.74009e10	+	2.53096e10i	1.49056	+	1.00868i
$399$		0			0
$400$	−3.70446e9	+	3.53432e9i	−0.144705	+	0.138059i
$401$	3.29629e10			1.27482			0.637408	−	0.770526i	$-0.280007\pi$
$401$	3.29629e10			1.27482			0.637408	+	0.770526i	$0.280007\pi$
$402$		0			0
$403$			1.61587e9i			0.0612612i
$404$	−5.66388e9	−	1.41415e10i	−0.212612	−	0.530849i
$405$		0			0
$406$	1.89541e10	+	1.28264e10i	0.697587	+	0.472064i
$407$		−	4.27078e9i		−	0.155643i
$408$		0			0
$409$	7.57826e9			0.270817			0.135409	−	0.990790i	$-0.456765\pi$
$409$	7.57826e9			0.270817			0.135409	+	0.990790i	$0.456765\pi$
$410$	−1.67300e9	+	2.47226e9i	−0.0592053	+	0.0874899i
$411$		0			0
$412$	−2.56710e10	+	1.02816e10i	−0.890952	+	0.356839i
$413$	1.20664e10			0.414741
$414$		0			0
$415$			2.04839e10i			0.690589i
$416$	−1.74462e9	−	1.03511e10i	−0.0582543	−	0.345632i
$417$		0			0
$418$	1.81062e9	−	2.67562e9i	0.0593092	−	0.0876435i
$419$			3.55051e10i			1.15195i	0.817466	+	0.575976i	$0.195378\pi$
$419$			3.55051e10i			1.15195i	−0.817466	+	0.575976i	$0.804622\pi$
$420$		0			0
$421$	4.49522e10			1.43095			0.715473	−	0.698641i	$-0.246211\pi$
$421$	4.49522e10			1.43095			0.715473	+	0.698641i	$0.246211\pi$
$422$	2.88415e10	+	1.95173e10i	0.909426	+	0.615418i
$423$		0			0
$424$	2.25564e10	+	4.90152e9i	0.697920	+	0.151659i
$425$	8.78936e9			0.269402
$426$		0			0
$427$			8.69335e10i			2.61502i
$428$	−9.06228e9	+	3.62957e9i	−0.270061	+	0.108163i
$429$		0			0
$430$	−1.09656e10	−	7.42054e9i	−0.320744	−	0.217051i
$431$		−	1.83961e10i		−	0.533109i	−0.963820	−	0.266554i	$-0.914115\pi$
$431$		−	1.83961e10i		−	0.533109i	0.963820	−	0.266554i	$-0.0858852\pi$
$432$		0			0
$433$	2.23500e10			0.635809			0.317904	−	0.948123i	$-0.397021\pi$
$433$	2.23500e10			0.635809			0.317904	+	0.948123i	$0.397021\pi$
$434$	−4.92177e9	+	7.27308e9i	−0.138727	+	0.205003i
$435$		0			0
$436$	−5.61872e9	−	1.40288e10i	−0.155486	−	0.388217i
$437$	1.55573e10			0.426588
$438$		0			0
$439$		−	2.10747e10i		−	0.567417i	−0.958911	−	0.283709i	$-0.908435\pi$
$439$		−	2.10747e10i		−	0.567417i	0.958911	−	0.283709i	$-0.0915648\pi$
$440$	−7.89605e8	+	3.63369e9i	−0.0210668	+	0.0969477i
$441$		0			0
$442$	−1.00993e10	+	1.49241e10i	−0.264607	+	0.391020i
$443$		−	4.03550e10i		−	1.04781i	−0.851776	−	0.523905i	$-0.824475\pi$
$443$		−	4.03550e10i		−	1.04781i	0.851776	−	0.523905i	$-0.175525\pi$
$444$		0			0
$445$	−1.20216e10			−0.306565
$446$	2.42251e10	+	1.63933e10i	0.612245	+	0.414312i
$447$		0			0
$448$	2.36759e10	−	5.19047e10i	0.587751	−	1.28853i
$449$	3.54510e9			0.0872255			0.0436127	−	0.999049i	$-0.486113\pi$
$449$	3.54510e9			0.0872255			0.0436127	+	0.999049i	$0.486113\pi$
$450$		0			0
$451$			2.16800e9i			0.0524027i
$452$	−1.30685e10	−	3.26293e10i	−0.313092	−	0.781726i
$453$		0			0
$454$	−2.52769e10	−	1.71051e10i	−0.594977	−	0.402627i
$455$			9.51474e9i			0.221999i
$456$		0			0
$457$	6.52065e10			1.49495			0.747474	−	0.664291i	$-0.231266\pi$
$457$	6.52065e10			1.49495			0.747474	+	0.664291i	$0.231266\pi$
$458$	1.57215e10	−	2.32322e10i	0.357299	−	0.527994i
$459$		0			0
$460$	−1.66227e10	+	6.65762e9i	−0.371253	+	0.148692i
$461$	−5.21597e10			−1.15487			−0.577433	−	0.816438i	$-0.695945\pi$
$461$	−5.21597e10			−1.15487			−0.577433	+	0.816438i	$0.695945\pi$
$462$		0			0
$463$		−	5.93407e10i		−	1.29130i	−0.763632	−	0.645652i	$-0.776586\pi$
$463$		−	5.93407e10i		−	1.29130i	0.763632	−	0.645652i	$-0.223414\pi$
$464$	−1.99459e10	+	1.90299e10i	−0.430311	+	0.410548i
$465$		0			0
$466$	1.09051e10	−	1.61148e10i	0.231251	−	0.341729i
$467$			4.59693e10i			0.966497i	0.875483	+	0.483248i	$0.160543\pi$
$467$			4.59693e10i			0.966497i	−0.875483	+	0.483248i	$0.839457\pi$
$468$		0			0
$469$	1.11603e11			2.30667
$470$	−1.14189e10	−	7.72729e9i	−0.234009	−	0.158356i
$471$		0			0
$472$	−3.08637e9	+	1.42032e10i	−0.0621842	+	0.286166i
$473$	−9.61611e9			−0.192112
$474$		0			0
$475$		−	4.85682e9i		−	0.0954064i
$476$	−9.09145e10	+	3.64125e10i	−1.77095	+	0.709289i
$477$		0			0
$478$	−6.30812e10	−	4.26877e10i	−1.20834	−	0.817694i
$479$		−	6.32809e8i		−	0.0120207i	−0.999982	−	0.00601036i	$-0.998087\pi$
$479$		−	6.32809e8i		−	0.0120207i	0.999982	−	0.00601036i	$-0.00191317\pi$
$480$		0			0
$481$	1.31633e10			0.245914
$482$	3.90026e10	−	5.76356e10i	0.722612	−	1.06783i
$483$		0			0
$484$	−1.93989e10	−	4.84349e10i	−0.353504	−	0.882627i
$485$	−3.80047e10			−0.686864
$486$		0			0
$487$			9.69788e10i			1.72409i	0.506828	+	0.862047i	$0.330818\pi$
$487$			9.69788e10i			1.72409i	−0.506828	+	0.862047i	$0.669182\pi$
$488$	−1.02328e11	−	2.22360e10i	−1.80433	−	0.392083i
$489$		0			0
$490$	−1.45321e10	+	2.14747e10i	−0.252084	+	0.372514i
$491$			6.96030e10i			1.19757i	0.800909	+	0.598787i	$0.204350\pi$
$491$			6.96030e10i			1.19757i	−0.800909	+	0.598787i	$0.795650\pi$
$492$		0			0
$493$	4.73246e10			0.801123
$494$	8.24674e9	+	5.58065e9i	0.138476	+	0.0937081i
$495$		0			0
$496$	−7.30216e9	−	7.65368e9i	−0.120649	−	0.126457i
$497$	−9.16076e10			−1.50143
$498$		0			0
$499$			3.12582e9i			0.0504153i	0.999682	+	0.0252077i	$0.00802470\pi$
$499$			3.12582e9i			0.0504153i	−0.999682	+	0.0252077i	$0.991975\pi$
$500$	2.07844e9	+	5.18942e9i	0.0332550	+	0.0830308i
$501$		0			0
$502$	4.73373e10	+	3.20336e10i	0.745399	+	0.504419i
$503$		−	1.46398e10i		−	0.228699i	−0.993441	−	0.114349i	$-0.963522\pi$
$503$		−	1.46398e10i		−	0.228699i	0.993441	−	0.114349i	$-0.0364783\pi$
$504$		0			0
$505$	−1.66325e10			−0.255736
$506$	−7.28850e9	+	1.07705e10i	−0.111182	+	0.164299i
$507$		0			0
$508$	−6.09695e10	+	2.44191e10i	−0.915498	+	0.366670i
$509$	1.11039e11			1.65427			0.827133	−	0.562006i	$-0.189970\pi$
$509$	1.11039e11			1.65427			0.827133	+	0.562006i	$0.189970\pi$
$510$		0			0
$511$			6.69122e10i			0.981345i
$512$	5.50406e10	+	4.11449e10i	0.800946	+	0.598737i
$513$		0			0
$514$	4.89288e10	−	7.23039e10i	0.700990	−	1.03588i
$515$			3.01929e10i			0.429216i
$516$		0			0
$517$	−1.00136e10			−0.140162
$518$	5.92485e10	+	4.00941e10i	0.822921	+	0.556879i
$519$		0			0
$520$	−1.11997e10	−	2.43370e9i	−0.153177	−	0.0332854i
$521$	−1.19216e10			−0.161802			−0.0809011	−	0.996722i	$-0.525780\pi$
$521$	−1.19216e10			−0.161802			−0.0809011	+	0.996722i	$0.525780\pi$
$522$		0			0
$523$			6.62945e10i			0.886075i	0.896503	+	0.443037i	$0.146099\pi$
$523$			6.62945e10i			0.886075i	−0.896503	+	0.443037i	$0.853901\pi$
$524$	−8.69423e10	+	3.48216e10i	−1.15320	+	0.461874i
$525$		0			0
$526$	−9.58162e10	−	6.48398e10i	−1.25169	−	0.847030i
$527$			1.81595e10i			0.235429i
$528$		0			0
$529$	1.56863e10			0.200308
$530$	1.41246e10	−	2.08725e10i	0.179008	−	0.264527i
$531$		0			0
$532$	2.01208e10	+	5.02375e10i	0.251188	+	0.627165i
$533$	−6.68217e9			−0.0827959
$534$		0			0
$535$			1.06586e10i			0.130102i
$536$	−2.85461e10	+	1.31367e11i	−0.345850	+	1.59157i
$537$		0			0
$538$	5.37594e10	−	7.94423e10i	0.641690	−	0.948250i
$539$			1.88319e10i			0.223120i
$540$		0			0
$541$	−9.57709e10			−1.11801			−0.559003	−	0.829165i	$-0.688816\pi$
$541$	−9.57709e10			−1.11801			−0.559003	+	0.829165i	$0.688816\pi$
$542$	1.06322e11	+	7.19490e10i	1.23204	+	0.833734i
$543$		0			0
$544$	−1.96064e10	−	1.16328e11i	−0.223874	−	1.32828i
$545$	−1.64999e10			−0.187023
$546$		0			0
$547$			9.71054e10i			1.08466i	0.840165	+	0.542331i	$0.182458\pi$
$547$			9.71054e10i			1.08466i	−0.840165	+	0.542331i	$0.817542\pi$
$548$	5.95113e10	+	1.48587e11i	0.659899	+	1.64763i
$549$		0			0
$550$	3.36243e9	+	2.27539e9i	0.0367453	+	0.0248659i
$551$		−	2.61506e10i		−	0.283711i
$552$		0			0
$553$	−5.07191e10			−0.542339
$554$	2.47079e10	−	3.65117e10i	0.262299	−	0.387609i
$555$		0			0
$556$	1.61125e10	−	6.45328e9i	0.168602	−	0.0675276i
$557$	3.57282e10			0.371185			0.185592	−	0.982627i	$-0.440580\pi$
$557$	3.57282e10			0.371185			0.185592	+	0.982627i	$0.440580\pi$
$558$		0			0
$559$		−	2.96386e10i		−	0.303536i
$560$	−4.29974e10	−	4.50673e10i	−0.437210	−	0.458258i
$561$		0			0
$562$	−1.00780e11	+	1.48926e11i	−1.01025	+	1.49288i
$563$			1.20784e11i			1.20219i	0.799176	+	0.601097i	$0.205270\pi$
$563$			1.20784e11i			1.20219i	−0.799176	+	0.601097i	$0.794730\pi$
$564$		0			0
$565$	−3.83769e10			−0.376596
$566$	1.58489e10	+	1.07251e10i	0.154431	+	0.104505i
$567$		0			0
$568$	2.34316e10	−	1.07830e11i	0.225117	−	1.03597i
$569$	6.84831e10			0.653332			0.326666	−	0.945140i	$-0.394075\pi$
$569$	6.84831e10			0.653332			0.326666	+	0.945140i	$0.394075\pi$
$570$		0			0
$571$		−	1.76672e10i		−	0.166197i	−0.996541	−	0.0830987i	$-0.973518\pi$
$571$		−	1.76672e10i		−	0.166197i	0.996541	−	0.0830987i	$-0.0264817\pi$
$572$	−7.72709e9	+	3.09481e9i	−0.0721825	+	0.0289101i
$573$		0			0
$574$	−3.00767e10	−	2.03532e10i	−0.277066	−	0.187493i
$575$			1.95507e10i			0.178851i
$576$		0			0
$577$	−1.86231e11			−1.68016			−0.840078	−	0.542466i	$-0.817491\pi$
$577$	−1.86231e11			−1.68016			−0.840078	+	0.542466i	$0.817491\pi$
$578$	−5.09453e10	+	7.52838e10i	−0.456450	+	0.674513i
$579$		0			0
$580$	1.11909e10	+	2.79415e10i	0.0988905	+	0.246909i
$581$	−2.49201e11			−2.18698
$582$		0			0
$583$		−	1.83038e10i		−	0.158441i
$584$	−7.87615e10	−	1.71149e10i	−0.677116	−	0.147138i
$585$		0			0
$586$	7.90851e9	−	1.16867e10i	0.0670663	−	0.0991064i
$587$			1.32669e11i			1.11742i	0.829362	+	0.558711i	$0.188704\pi$
$587$			1.32669e11i			1.11742i	−0.829362	+	0.558711i	$0.811296\pi$
$588$		0			0
$589$	1.00345e10			0.0833751
$590$	1.31429e10	+	8.89393e9i	0.108463	+	0.0733982i
$591$		0			0
$592$	−6.23489e10	+	5.94853e10i	−0.507624	+	0.484310i
$593$	7.14055e10			0.577448			0.288724	−	0.957412i	$-0.406769\pi$
$593$	7.14055e10			0.577448			0.288724	+	0.957412i	$0.406769\pi$
$594$		0			0
$595$			1.06929e11i			0.853152i
$596$	−6.80594e10	−	1.69930e11i	−0.539390	−	1.34675i
$597$		0			0
$598$	−3.31966e10	−	2.24645e10i	−0.259590	−	0.175667i
$599$		−	6.39499e10i		−	0.496744i	−0.968665	−	0.248372i	$-0.920105\pi$
$599$		−	6.39499e10i		−	0.496744i	0.968665	−	0.248372i	$-0.0798955\pi$
$600$		0			0
$601$	1.55828e11			1.19439			0.597196	−	0.802095i	$-0.296282\pi$
$601$	1.55828e11			1.19439			0.597196	+	0.802095i	$0.296282\pi$
$602$	9.02761e10	−	1.33404e11i	0.687364	−	1.01574i
$603$		0			0
$604$	8.22090e10	−	3.29259e10i	0.617692	−	0.247394i
$605$	−5.69665e10			−0.425205
$606$		0			0
$607$			1.36790e11i			1.00762i	0.863813	+	0.503812i	$0.168070\pi$
$607$			1.36790e11i			1.00762i	−0.863813	+	0.503812i	$0.831930\pi$
$608$	−6.42805e10	+	1.08341e10i	−0.470397	+	0.0792828i
$609$		0			0
$610$	−6.40771e10	+	9.46892e10i	−0.462790	+	0.683882i
$611$		−	3.08638e10i		−	0.221454i
$612$		0			0
$613$	6.10843e10			0.432601			0.216301	−	0.976327i	$-0.430601\pi$
$613$	6.10843e10			0.432601			0.216301	+	0.976327i	$0.430601\pi$
$614$	5.96089e10	+	4.03380e10i	0.419409	+	0.283818i
$615$		0			0
$616$	−4.42064e10	−	9.60610e9i	−0.307017	−	0.0667151i
$617$	4.69649e10			0.324066			0.162033	−	0.986785i	$-0.448195\pi$
$617$	4.69649e10			0.324066			0.162033	+	0.986785i	$0.448195\pi$
$618$		0			0
$619$		−	2.24452e11i		−	1.52884i	−0.644721	−	0.764418i	$-0.723026\pi$
$619$		−	2.24452e11i		−	1.52884i	0.644721	−	0.764418i	$-0.276974\pi$
$620$	−1.07217e10	+	4.29420e9i	−0.0725601	+	0.0290613i
$621$		0			0
$622$	−6.64751e10	−	4.49843e10i	−0.444117	−	0.300538i
$623$		−	1.46251e11i		−	0.970840i
$624$		0			0
$625$	6.10352e9			0.0400000
$626$	−1.20109e11	+	1.77490e11i	−0.782130	+	1.15578i
$627$		0			0
$628$	1.09938e11	+	2.74493e11i	0.706821	+	1.76479i
$629$	1.47932e11			0.945059
$630$		0			0
$631$		−	1.29989e11i		−	0.819950i	−0.912097	−	0.409975i	$-0.865537\pi$
$631$		−	1.29989e11i		−	0.819950i	0.912097	−	0.409975i	$-0.134463\pi$
$632$	1.29730e10	−	5.97008e10i	0.0813155	−	0.374207i
$633$		0			0
$634$	−4.62204e10	+	6.83017e10i	−0.286073	+	0.422741i
$635$			7.17090e10i			0.441041i
$636$		0			0
$637$	−5.80431e10			−0.352527
$638$	1.81044e10	+	1.22514e10i	0.109270	+	0.0739440i
$639$		0			0
$640$	6.40462e10	−	3.90844e10i	0.381745	−	0.232961i
$641$	−4.05626e10			−0.240267			−0.120133	−	0.992758i	$-0.538332\pi$
$641$	−4.05626e10			−0.240267			−0.120133	+	0.992758i	$0.538332\pi$
$642$		0			0
$643$		−	1.82815e11i		−	1.06947i	−0.845020	−	0.534734i	$-0.820412\pi$
$643$		−	1.82815e11i		−	1.06947i	0.845020	−	0.534734i	$-0.179588\pi$
$644$	−8.09947e10	−	2.02227e11i	−0.470883	−	1.17570i
$645$		0			0
$646$	9.26786e10	+	6.27166e10i	0.532169	+	0.360124i
$647$		−	2.84680e11i		−	1.62458i	−0.583257	−	0.812288i	$-0.698222\pi$
$647$		−	2.84680e11i		−	1.62458i	0.583257	−	0.812288i	$-0.301778\pi$
$648$		0			0
$649$	1.15254e10			0.0649649
$650$	−7.01315e9	+	1.03636e10i	−0.0392880	+	0.0580573i
$651$		0			0
$652$	−2.69236e11	+	1.07833e11i	−1.48985	+	0.596705i
$653$	−1.87627e11			−1.03191			−0.515956	−	0.856615i	$-0.672563\pi$
$653$	−1.87627e11			−1.03191			−0.515956	+	0.856615i	$0.672563\pi$
$654$		0			0
$655$			1.02257e11i			0.555555i
$656$	3.16506e10	−	3.01970e10i	0.170910	−	0.163060i
$657$		0			0
$658$	9.40079e10	−	1.38919e11i	0.501488	−	0.741068i
$659$			1.58299e11i			0.839340i	0.907677	+	0.419670i	$0.137854\pi$
$659$			1.58299e11i			0.839340i	−0.907677	+	0.419670i	$0.862146\pi$
$660$		0			0
$661$	2.01282e10			0.105438			0.0527191	−	0.998609i	$-0.483211\pi$
$661$	2.01282e10			0.105438			0.0527191	+	0.998609i	$0.483211\pi$
$662$	7.03757e10	+	4.76239e10i	0.366430	+	0.247967i
$663$		0			0
$664$	6.37411e10	−	2.93331e11i	0.327905	−	1.50899i
$665$	5.90866e10			0.302136
$666$		0			0
$667$			1.05267e11i			0.531850i
$668$	2.52812e11	−	1.01255e11i	1.26967	−	0.508521i
$669$		0			0
$670$	1.21560e11	+	8.22608e10i	0.603242	+	0.408220i
$671$			8.30361e10i			0.409616i
$672$		0			0
$673$	2.47762e11			1.20775			0.603873	−	0.797081i	$-0.293624\pi$
$673$	2.47762e11			1.20775			0.603873	+	0.797081i	$0.293624\pi$
$674$	1.43640e11	−	2.12262e11i	0.696043	−	1.02857i
$675$		0			0
$676$	6.81035e10	+	1.70040e11i	0.326124	+	0.814264i
$677$	3.43092e11			1.63326			0.816631	−	0.577160i	$-0.195839\pi$
$677$	3.43092e11			1.63326			0.816631	+	0.577160i	$0.195839\pi$
$678$		0			0
$679$		−	4.62354e11i		−	2.17518i
$680$	−1.25864e11	−	2.73505e10i	−0.588664	−	0.127917i
$681$		0			0
$682$	−4.70112e9	+	6.94702e9i	−0.0217302	+	0.0321115i
$683$		−	4.32070e11i		−	1.98551i	−0.120173	−	0.992753i	$-0.538345\pi$
$683$		−	4.32070e11i		−	1.98551i	0.120173	−	0.992753i	$-0.461655\pi$
$684$		0			0
$685$	1.74760e11			0.793744
$686$	−1.49743e9	−	1.01333e9i	−0.00676163	−	0.00457566i
$687$		0			0
$688$	1.33938e11	+	1.40385e11i	0.597790	+	0.626568i
$689$	5.64155e10			0.250335
$690$		0			0
$691$		−	3.00386e11i		−	1.31755i	−0.752340	−	0.658775i	$-0.771075\pi$
$691$		−	3.00386e11i		−	1.31755i	0.752340	−	0.658775i	$-0.228925\pi$
$692$	−2.59559e10	−	6.48064e10i	−0.113191	−	0.282614i
$693$		0			0
$694$	3.34785e11	+	2.26552e11i	1.44321	+	0.976632i
$695$		−	1.89506e10i		−	0.0812241i
$696$		0			0
$697$	−7.50957e10			−0.318188
$698$	1.04958e11	−	1.55100e11i	0.442175	−	0.653418i
$699$		0			0
$700$	−6.31330e10	+	2.52856e10i	−0.262944	+	0.105313i
$701$	−2.08736e10			−0.0864419			−0.0432210	−	0.999066i	$-0.513762\pi$
$701$	−2.08736e10			−0.0864419			−0.0432210	+	0.999066i	$0.513762\pi$
$702$		0			0
$703$		−	8.17441e10i		−	0.334684i
$704$	2.26144e10	−	4.95778e10i	0.0920651	−	0.201835i
$705$		0			0
$706$	1.24331e11	−	1.83728e11i	0.500448	−	0.739531i
$707$		−	2.02346e11i		−	0.809873i
$708$		0			0
$709$	−1.84965e11			−0.731990			−0.365995	−	0.930617i	$-0.619271\pi$
$709$	−1.84965e11			−0.731990			−0.365995	+	0.930617i	$0.619271\pi$
$710$	−9.97803e10	−	6.75224e10i	−0.392655	−	0.265714i
$711$		0			0
$712$	1.72151e11	+	3.74085e10i	0.669868	+	0.145563i
$713$	−4.03932e10			−0.156297
$714$		0			0
$715$			9.08819e9i			0.0347739i
$716$	−1.83012e11	+	7.32989e10i	−0.696350	+	0.278898i
$717$		0			0
$718$	1.53406e11	+	1.03811e11i	0.577225	+	0.390614i
$719$			5.08281e11i			1.90190i	0.309340	+	0.950952i	$0.399892\pi$
$719$			5.08281e11i			1.90190i	−0.309340	+	0.950952i	$0.600108\pi$
$720$		0			0
$721$	−3.67317e11			−1.35925
$722$	−1.17638e11	+	1.73838e11i	−0.432911	+	0.639729i
$723$		0			0
$724$	−2.27012e10	−	5.66801e10i	−0.0826217	−	0.206289i
$725$	3.28632e10			0.118948
$726$		0			0
$727$		−	2.10234e10i		−	0.0752603i	−0.999292	−	0.0376302i	$-0.988019\pi$
$727$		−	2.10234e10i		−	0.0752603i	0.999292	−	0.0376302i	$-0.0119809\pi$
$728$	2.96077e10	−	1.36252e11i	0.105409	−	0.485085i
$729$		0			0
$730$	−4.93198e10	+	7.28817e10i	−0.173672	+	0.256642i
$731$		−	3.33084e11i		−	1.16650i
$732$		0			0
$733$	−1.59159e11			−0.551333			−0.275667	−	0.961253i	$-0.588899\pi$
$733$	−1.59159e11			−0.551333			−0.275667	+	0.961253i	$0.588899\pi$
$734$	−2.13796e11	−	1.44678e11i	−0.736572	−	0.498446i
$735$		0			0
$736$	2.58756e11	−	4.36118e10i	0.881818	−	0.148625i
$737$	1.06600e11			0.361316
$738$		0			0
$739$		−	6.68063e9i		−	0.0223996i	−0.999937	−	0.0111998i	$-0.996435\pi$
$739$		−	6.68063e9i		−	0.0223996i	0.999937	−	0.0111998i	$-0.00356508\pi$
$740$	3.49817e10	+	8.73421e10i	0.116658	+	0.291271i
$741$		0			0
$742$	2.53928e11	+	1.71836e11i	0.837713	+	0.566889i
$743$		−	1.99197e11i		−	0.653623i	−0.945090	−	0.326811i	$-0.894026\pi$
$743$		−	1.99197e11i		−	0.653623i	0.945090	−	0.326811i	$-0.105974\pi$
$744$		0			0
$745$	−1.99863e11			−0.648794
$746$	1.94029e11	−	2.86724e11i	0.626485	−	0.925781i
$747$		0			0
$748$	−8.68387e10	+	3.47801e10i	−0.277400	+	0.111103i
$749$	−1.29669e11			−0.412011
$750$		0			0
$751$			1.77629e11i			0.558410i	0.960231	+	0.279205i	$0.0900710\pi$
$751$			1.77629e11i			0.558410i	−0.960231	+	0.279205i	$0.909929\pi$
$752$	1.39474e11	+	1.46189e11i	0.436137	+	0.457133i
$753$		0			0
$754$	−3.77610e10	+	5.58008e10i	−0.116831	+	0.172645i
$755$		−	9.66898e10i		−	0.297572i
$756$		0			0
$757$	−3.22894e11			−0.983278			−0.491639	−	0.870799i	$-0.663602\pi$
$757$	−3.22894e11			−0.983278			−0.491639	+	0.870799i	$0.663602\pi$
$758$	2.48343e11	+	1.68057e11i	0.752274	+	0.509071i
$759$		0			0
$760$	−1.51133e10	+	6.95501e10i	−0.0453007	+	0.208470i
$761$	1.07849e11			0.321572			0.160786	−	0.986989i	$-0.448597\pi$
$761$	1.07849e11			0.321572			0.160786	+	0.986989i	$0.448597\pi$
$762$		0			0
$763$		−	2.00733e11i		−	0.592270i
$764$	2.93294e11	−	1.17468e11i	0.860855	−	0.344784i
$765$		0			0
$766$	−2.63755e10	−	1.78486e10i	−0.0766100	−	0.0518427i
$767$			3.55235e10i			0.102644i
$768$		0			0
$769$	9.94734e9			0.0284447			0.0142224	−	0.999899i	$-0.495473\pi$
$769$	9.94734e9			0.0284447			0.0142224	+	0.999899i	$0.495473\pi$
$770$	−2.76817e10	+	4.09063e10i	−0.0787463	+	0.116366i
$771$		0			0
$772$	2.16328e11	+	5.40125e11i	0.609036	+	1.52064i
$773$	−1.84650e11			−0.517169			−0.258585	−	0.965989i	$-0.583256\pi$
$773$	−1.84650e11			−0.517169			−0.258585	+	0.965989i	$0.583256\pi$
$774$		0			0
$775$			1.26103e10i			0.0349558i
$776$	5.44231e11	+	1.18262e11i	1.50085	+	0.326135i
$777$		0			0
$778$	2.69117e10	−	3.97684e10i	0.0734552	−	0.108547i
$779$			4.14963e10i			0.112683i
$780$		0			0
$781$	−8.75007e10			−0.235184
$782$	−3.73070e11	−	2.52460e11i	−0.997616	−	0.675097i
$783$		0			0
$784$	2.74926e11	−	2.62299e11i	0.727698	−	0.694276i
$785$	3.22843e11			0.850184
$786$		0			0
$787$			1.78058e11i			0.464154i	0.972697	+	0.232077i	$0.0745522\pi$
$787$			1.78058e11i			0.464154i	−0.972697	+	0.232077i	$0.925448\pi$
$788$	2.55490e11	+	6.37905e11i	0.662626	+	1.65444i
$789$		0			0
$790$	−5.52440e10	−	3.73841e10i	−0.141833	−	0.0959796i
$791$		−	4.66881e11i		−	1.19262i
$792$		0			0
$793$	−2.55932e11			−0.647190
$794$	9.31546e10	−	1.37658e11i	0.234381	−	0.346354i
$795$		0			0
$796$	−6.70758e11	+	2.68648e11i	−1.67076	+	0.669161i
$797$	−1.67735e10			−0.0415711			−0.0207855	−	0.999784i	$-0.506617\pi$
$797$	−1.67735e10			−0.0415711			−0.0207855	+	0.999784i	$0.506617\pi$
$798$		0			0
$799$		−	3.46853e11i		−	0.851058i
$800$	−1.36151e10	−	8.07807e10i	−0.0332400	−	0.197218i
$801$		0			0
$802$	−2.95582e11	+	4.36793e11i	−0.714465	+	1.05579i
$803$			6.39124e10i			0.153717i
$804$		0			0
$805$	−2.37848e11			−0.566391
$806$	−2.14120e10	−	1.44897e10i	−0.0507360	−	0.0343336i
$807$		0			0
$808$	2.38179e11	+	5.17565e10i	0.558802	+	0.121428i
$809$	1.32788e11			0.310003			0.155002	−	0.987914i	$-0.450462\pi$
$809$	1.32788e11			0.310003			0.155002	+	0.987914i	$0.450462\pi$
$810$		0			0
$811$		−	5.70355e11i		−	1.31845i	−0.751948	−	0.659223i	$-0.770885\pi$
$811$		−	5.70355e11i		−	1.31845i	0.751948	−	0.659223i	$-0.229115\pi$
$812$	−3.39927e11	+	1.36146e11i	−0.781919	+	0.313170i
$813$		0			0
$814$	5.65923e10	+	3.82966e10i	0.128902	+	0.0872293i
$815$			3.16660e11i			0.717734i
$816$		0			0
$817$	−1.84056e11			−0.413105
$818$	−6.79552e10	+	1.00420e11i	−0.151778	+	0.224288i
$819$		0			0
$820$	−1.77580e10	−	4.43381e10i	−0.0392770	−	0.0980666i
$821$	−2.69201e11			−0.592522			−0.296261	−	0.955107i	$-0.595740\pi$
$821$	−2.69201e11			−0.592522			−0.296261	+	0.955107i	$0.595740\pi$
$822$		0			0
$823$		−	2.40740e11i		−	0.524745i	−0.964967	−	0.262372i	$-0.915495\pi$
$823$		−	2.40740e11i		−	0.524745i	0.964967	−	0.262372i	$-0.0845049\pi$
$824$	9.39533e10	−	4.32365e11i	0.203799	−	0.937868i
$825$		0			0
$826$	−1.08201e11	+	1.59893e11i	−0.232440	+	0.343485i
$827$		−	6.45140e11i		−	1.37921i	−0.724183	−	0.689607i	$-0.757783\pi$
$827$		−	6.45140e11i		−	1.37921i	0.724183	−	0.689607i	$-0.242217\pi$
$828$		0			0
$829$	7.67879e11			1.62583			0.812914	−	0.582383i	$-0.197880\pi$
$829$	7.67879e11			1.62583			0.812914	+	0.582383i	$0.197880\pi$
$830$	−2.71433e11	−	1.83682e11i	−0.571940	−	0.387038i
$831$		0			0
$832$	1.52808e11	+	6.97017e10i	0.318898	+	0.145462i
$833$	−6.52301e11			−1.35478
$834$		0			0
$835$		−	2.97343e11i		−	0.611663i
$836$	1.92188e10	+	4.79853e10i	0.0393460	+	0.0982388i
$837$		0			0
$838$	−4.70480e11	−	3.18379e11i	−0.954037	−	0.645606i
$839$			8.20188e11i			1.65526i	0.561276	+	0.827629i	$0.310311\pi$
$839$			8.20188e11i			1.65526i	−0.561276	+	0.827629i	$0.689689\pi$
$840$		0			0
$841$	−3.23301e11			−0.646283
$842$	−4.03092e11	+	5.95665e11i	−0.801967	+	1.18510i
$843$		0			0
$844$	−5.17250e11	+	2.07166e11i	−1.01937	+	0.408271i
$845$	1.99992e11			0.392271
$846$		0			0
$847$		−	6.93037e11i		−	1.34655i
$848$	−2.67216e11	+	2.54943e11i	−0.516749	+	0.493015i
$849$		0			0
$850$	−7.88153e10	+	1.16468e11i	−0.150985	+	0.223117i
$851$			3.29054e11i			0.627407i
$852$		0			0
$853$	−3.26117e11			−0.615995			−0.307998	−	0.951387i	$-0.599659\pi$
$853$	−3.26117e11			−0.615995			−0.307998	+	0.951387i	$0.599659\pi$
$854$	−1.15196e12	−	7.79543e11i	−2.16574	−	1.46558i
$855$		0			0
$856$	3.31670e10	−	1.52632e11i	0.0617748	−	0.284282i
$857$	−1.19858e11			−0.222199			−0.111099	−	0.993809i	$-0.535437\pi$
$857$	−1.19858e11			−0.222199			−0.111099	+	0.993809i	$0.535437\pi$
$858$		0			0
$859$			1.54336e11i			0.283461i	0.989905	+	0.141731i	$0.0452667\pi$
$859$			1.54336e11i			0.283461i	−0.989905	+	0.141731i	$0.954733\pi$
$860$	1.96660e11	−	7.87651e10i	0.359519	−	0.143992i
$861$		0			0
$862$	2.43767e11	+	1.64960e11i	0.441516	+	0.298778i
$863$		−	1.10902e10i		−	0.0199938i	−0.999950	−	0.00999689i	$-0.996818\pi$
$863$		−	1.10902e10i		−	0.0199938i	0.999950	−	0.00999689i	$-0.00318216\pi$
$864$		0			0
$865$	−7.62218e10			−0.136149
$866$	−2.00416e11	+	2.96162e11i	−0.356336	+	0.526571i
$867$		0			0
$868$	−5.22419e10	−	1.30437e11i	−0.0920323	−	0.229786i
$869$	−4.84453e10			−0.0849518
$870$		0			0
$871$			3.28560e11i			0.570876i
$872$	2.36280e11	+	5.13439e10i	0.408659	+	0.0888020i
$873$		0			0
$874$	−1.39504e11	+	2.06151e11i	−0.239079	+	0.353297i
$875$			7.42535e10i			0.126673i
$876$		0			0
$877$	5.82209e11			0.984193			0.492097	−	0.870541i	$-0.336231\pi$
$877$	5.82209e11			0.984193			0.492097	+	0.870541i	$0.336231\pi$
$878$	2.79262e11	+	1.88979e11i	0.469930	+	0.318006i
$879$		0			0
$880$	−4.10698e10	−	4.30469e10i	−0.0684845	−	0.0717813i
$881$	1.83965e11			0.305373			0.152686	−	0.988275i	$-0.451208\pi$
$881$	1.83965e11			0.305373			0.152686	+	0.988275i	$0.451208\pi$
$882$		0			0
$883$		−	9.18672e9i		−	0.0151118i	−0.999971	−	0.00755592i	$-0.997595\pi$
$883$		−	9.18672e9i		−	0.0151118i	0.999971	−	0.00755592i	$-0.00240515\pi$
$884$	−1.07198e11	−	2.67652e11i	−0.175541	−	0.438290i
$885$		0			0
$886$	5.34747e11	+	3.61869e11i	0.867788	+	0.587241i
$887$			6.69182e11i			1.08106i	0.841325	+	0.540530i	$0.181776\pi$
$887$			6.69182e11i			1.08106i	−0.841325	+	0.540530i	$0.818224\pi$
$888$		0			0
$889$	−8.72390e11			−1.39670
$890$	1.07799e11	−	1.59299e11i	0.171813	−	0.253895i
$891$		0			0
$892$	−4.34458e11	+	1.74007e11i	−0.686260	+	0.274857i
$893$	−1.91664e11			−0.301394
$894$		0			0
$895$			2.15249e11i			0.335466i
$896$	4.75489e11	+	7.79167e11i	0.737748	+	1.20892i
$897$		0			0
$898$	−3.17894e10	+	4.69764e10i	−0.0488851	+	0.0722394i
$899$			6.78978e10i			0.103948i
$900$		0			0
$901$	6.34009e11			0.962047
$902$	−2.87283e10	−	1.94408e10i	−0.0433995	−	0.0293689i
$903$		0			0
$904$	5.49560e11	+	1.19420e11i	0.822890	+	0.178815i
$905$	−6.66641e10			−0.0993797
$906$		0			0
$907$			9.42968e11i			1.39337i	0.717375	+	0.696687i	$0.245343\pi$
$907$			9.42968e11i			1.39337i	−0.717375	+	0.696687i	$0.754657\pi$
$908$	4.53322e11	−	1.81562e11i	0.666905	−	0.267105i
$909$		0			0
$910$	−1.26080e11	−	8.53199e10i	−0.183858	−	0.124418i
$911$			5.62696e11i			0.816959i	0.912767	+	0.408480i	$0.133941\pi$
$911$			5.62696e11i			0.816959i	−0.912767	+	0.408480i	$0.866059\pi$
$912$		0			0
$913$	−2.38029e11			−0.342568
$914$	−5.84715e11	+	8.64056e11i	−0.837837	+	1.23810i
$915$		0			0
$916$	1.66875e11	+	4.16653e11i	0.237033	+	0.591824i
$917$	−1.24403e12			−1.75935
$918$		0			0
$919$			6.08421e11i			0.852986i	0.904491	+	0.426493i	$0.140251\pi$
$919$			6.08421e11i			0.852986i	−0.904491	+	0.426493i	$0.859749\pi$
$920$	6.08373e10	−	2.79968e11i	0.0849217	−	0.390803i
$921$		0			0
$922$	4.67723e11	−	6.91171e11i	0.647239	−	0.956450i
$923$		−	2.69693e11i		−	0.371589i
$924$		0			0
$925$	1.02727e11			0.140319
$926$	7.86327e11	+	5.32116e11i	1.06945	+	0.723706i
$927$		0			0
$928$	−7.33080e10	−	4.34948e11i	−0.0988461	−	0.586470i
$929$	1.00111e12			1.34407			0.672033	−	0.740521i	$-0.265421\pi$
$929$	1.00111e12			1.34407			0.672033	+	0.740521i	$0.265421\pi$
$930$		0			0
$931$			3.60448e11i			0.479782i
$932$	1.15751e11	+	2.89007e11i	0.153413	+	0.383041i
$933$		0			0
$934$	−6.09142e11	−	4.12213e11i	−0.800444	−	0.541669i
$935$			1.02135e11i			0.133637i
$936$		0			0
$937$	4.79132e11			0.621579			0.310790	−	0.950479i	$-0.399407\pi$
$937$	4.79132e11			0.621579			0.310790	+	0.950479i	$0.399407\pi$
$938$	−1.00076e12	+	1.47886e12i	−1.29276	+	1.91036i
$939$		0			0
$940$	2.04790e11	−	8.20211e10i	0.262299	−	0.105054i
$941$	8.64017e11			1.10195			0.550977	−	0.834520i	$-0.314255\pi$
$941$	8.64017e11			1.10195			0.550977	+	0.834520i	$0.314255\pi$
$942$		0			0
$943$		−	1.67040e11i		−	0.211239i
$944$	−1.60532e11	−	1.68260e11i	−0.202150	−	0.211881i
$945$		0			0
$946$	8.62289e10	−	1.27424e11i	0.107668	−	0.159106i
$947$			1.43328e12i			1.78209i	0.453913	+	0.891046i	$0.350028\pi$
$947$			1.43328e12i			1.78209i	−0.453913	+	0.891046i	$0.649972\pi$
$948$		0			0
$949$	−1.96989e11			−0.242872
$950$	6.43580e10	+	4.35517e10i	0.0790148	+	0.0534701i
$951$		0			0
$952$	3.32737e11	−	1.53123e12i	0.405092	−	1.86420i
$953$	2.67647e10			0.0324483			0.0162241	−	0.999868i	$-0.494835\pi$
$953$	2.67647e10			0.0324483			0.0162241	+	0.999868i	$0.494835\pi$
$954$		0			0
$955$		−	3.44957e11i		−	0.414716i
$956$	1.13131e12	−	4.53107e11i	1.35441	−	0.542462i
$957$		0			0
$958$	8.38539e9	+	5.67448e9i	0.00995546	+	0.00673696i
$959$			2.12608e12i			2.51365i
$960$		0			0
$961$	8.26837e11			0.969452
$962$	−1.18037e11	+	1.74428e11i	−0.137822	+	0.203664i
$963$		0			0
$964$	4.13991e11	+	1.03365e12i	0.479384	+	1.19692i
$965$	6.35266e11			0.732565
$966$		0			0
$967$		−	2.12221e11i		−	0.242707i	−0.992609	−	0.121353i	$-0.961277\pi$
$967$		−	2.12221e11i		−	0.242707i	0.992609	−	0.121353i	$-0.0387234\pi$
$968$	8.15766e11	+	1.77267e11i	0.929104	+	0.201895i
$969$		0			0
$970$	3.40793e11	−	5.03603e11i	0.384950	−	0.568855i
$971$		−	1.21235e12i		−	1.36380i	−0.731447	−	0.681898i	$-0.761155\pi$
$971$		−	1.21235e12i		−	1.36380i	0.731447	−	0.681898i	$-0.238845\pi$
$972$		0			0
$973$	2.30548e11			0.257223
$974$	−1.28507e12	−	8.69621e11i	−1.42788	−	0.966261i
$975$		0			0
$976$	1.21224e12	−	1.15657e12i	1.33595	−	1.27459i
$977$	−7.92142e11			−0.869410			−0.434705	−	0.900573i	$-0.643147\pi$
$977$	−7.92142e11			−0.869410			−0.434705	+	0.900573i	$0.643147\pi$
$978$		0			0
$979$		−	1.39695e11i		−	0.152072i
$980$	−1.54251e11	−	3.85132e11i	−0.167233	−	0.417547i
$981$		0			0
$982$	−9.22314e11	−	6.24139e11i	−0.991820	−	0.671175i
$983$		−	1.50765e12i		−	1.61468i	−0.590085	−	0.807341i	$-0.700906\pi$
$983$		−	1.50765e12i		−	1.61468i	0.590085	−	0.807341i	$-0.299094\pi$
$984$		0			0
$985$	7.50269e11			0.797026
$986$	−4.24366e11	+	6.27101e11i	−0.448986	+	0.663484i
$987$		0			0
$988$	−1.47899e11	+	5.92357e10i	−0.155217	+	0.0621664i
$989$	7.40900e11			0.774417
$990$		0			0
$991$			1.63098e12i			1.69104i	0.533942	+	0.845521i	$0.320710\pi$
$991$			1.63098e12i			1.69104i	−0.533942	+	0.845521i	$0.679290\pi$
$992$	1.66899e11	−	2.81298e10i	0.172348	−	0.0290483i
$993$		0			0
$994$	8.21457e11	−	1.21390e12i	0.841471	−	1.24347i
$995$			7.88909e11i			0.804886i
$996$		0			0
$997$	−4.58651e11			−0.464197			−0.232098	−	0.972692i	$-0.574559\pi$
$997$	−4.58651e11			−0.464197			−0.232098	+	0.972692i	$0.574559\pi$
$998$	−4.14205e10	−	2.80297e10i	−0.0417535	−	0.0282550i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.9.c.b.91.12	yes	32
3.2	odd	2	inner	180.9.c.b.91.21	yes	32
4.3	odd	2	inner	180.9.c.b.91.11	✓	32
12.11	even	2	inner	180.9.c.b.91.22	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.9.c.b.91.11	✓	32	4.3	odd	2	inner
180.9.c.b.91.12	yes	32	1.1	even	1	trivial
180.9.c.b.91.21	yes	32	3.2	odd	2	inner
180.9.c.b.91.22	yes	32	12.11	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 $\F_{q}$
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)

\(f(q)\)	\(=\)	\(q+(-8.96713 + 13.2511i) q^{2} +(-95.1813 - 237.648i) q^{4} -279.508 q^{5} -3400.42i q^{7} +(4002.59 + 869.766i) q^{8} +(2506.39 - 3703.78i) q^{10} -3247.97i q^{11} +10010.8 q^{13} +(45059.1 + 30492.0i) q^{14} +(-47417.1 + 45239.3i) q^{16} +112504. q^{17} -62167.3i q^{19} +(26604.0 + 66424.6i) q^{20} +(43039.1 + 29125.0i) q^{22} +250249. i q^{23} +78125.0 q^{25} +(-89768.3 + 132654. i) q^{26} +(-808102. + 323656. i) q^{28} +420649. q^{29} +161412. i q^{31} +(-174273. - 1.03399e6i) q^{32} +(-1.00884e6 + 1.49079e6i) q^{34} +950445. i q^{35} +1.31491e6 q^{37} +(823782. + 557462. i) q^{38} +(-1.11876e6 - 243107. i) q^{40} -667494. q^{41} -2.96065e6i q^{43} +(-771874. + 309146. i) q^{44} +(-3.31607e6 - 2.24402e6i) q^{46} -3.08304e6i q^{47} -5.79803e6 q^{49} +(-700557. + 1.03524e6i) q^{50} +(-952843. - 2.37905e6i) q^{52} +5.63544e6 q^{53} +907836. i q^{55} +(2.95757e6 - 1.36105e7i) q^{56} +(-3.77201e6 + 5.57405e6i) q^{58} +3.54850e6i q^{59} -2.55655e7 q^{61} +(-2.13888e6 - 1.44740e6i) q^{62} +(1.52642e7 + 6.96263e6i) q^{64} -2.79811e6 q^{65} +3.28205e7i q^{67} +(-1.07083e7 - 2.67363e7i) q^{68} +(-1.25944e7 - 8.52276e6i) q^{70} -2.69401e7i q^{71} -1.96776e7 q^{73} +(-1.17909e7 + 1.74239e7i) q^{74} +(-1.47739e7 + 5.91716e6i) q^{76} -1.10445e7 q^{77} -1.49155e7i q^{79} +(1.32535e7 - 1.26448e7i) q^{80} +(5.98551e6 - 8.84501e6i) q^{82} -7.32854e7i q^{83} -3.14458e7 q^{85} +(3.92318e7 + 2.65485e7i) q^{86} +(2.82498e6 - 1.30003e7i) q^{88} +4.30098e7 q^{89} -3.40410e7i q^{91} +(5.94712e7 - 2.38190e7i) q^{92} +(4.08535e7 + 2.76460e7i) q^{94} +1.73763e7i q^{95} +1.35970e8 q^{97} +(5.19917e7 - 7.68301e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 610 q^{4} - 8750 q^{10} - 51392 q^{13} + 11986 q^{16} - 758068 q^{22} + 2500000 q^{25} + 976324 q^{28} - 6117428 q^{34} + 5152064 q^{37} - 96250 q^{40} - 10391752 q^{46} - 11002976 q^{49} + 13976584 q^{52}+ \cdots + 80579520 q^{97}+O(q^{100}) \) 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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