LMFDB - Embedded newform 180.9.c.a.91.11

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 = [16,-6] 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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 15630052 x^{14} + 100431843210026 x^{12} + \cdots + 41\!\cdots\!25 $ x^16 + 15630052x^14 + 100431843210026x^12 + 340815019972466359600x^10 + 649371842679456980126645875x^8 + 673266389314517670870339888950000x^6 + 325232066696204458027621996847496406250x^4 + 40989992790937256917294995464570014826562500*x^2 + 414509653712510017117723543124903397237712890625
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{58}\cdot 3^{4}\cdot 5^{16} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.11
Root			$1770.35i$ of defining polynomial
Character	$\chi$	$=$	180.91
Dual form			180.9.c.a.91.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(7.35022 - 14.2118i) q^{2} +(-147.949 - 208.919i) q^{4} +279.508 q^{5} +3540.70i q^{7} +(-4056.56 + 567.011i) q^{8} +(2054.45 - 3972.31i) q^{10} -15969.8i q^{11} -24176.2 q^{13} +(50319.6 + 26024.9i) q^{14} +(-21758.4 + 61818.6i) q^{16} -43810.0 q^{17} +50919.1i q^{19} +(-41352.9 - 58394.7i) q^{20} +(-226960. - 117382. i) q^{22} -270875. i q^{23} +78125.0 q^{25} +(-177701. + 343587. i) q^{26} +(739720. - 523841. i) q^{28} +1.32588e6 q^{29} +1.18623e6i q^{31} +(718623. + 763605. i) q^{32} +(-322013. + 622618. i) q^{34} +989655. i q^{35} +2.97108e6 q^{37} +(723650. + 374266. i) q^{38} +(-1.13384e6 + 158484. i) q^{40} +4.92072e6 q^{41} -2.86229e6i q^{43} +(-3.33641e6 + 2.36272e6i) q^{44} +(-3.84961e6 - 1.99099e6i) q^{46} +12696.5i q^{47} -6.77174e6 q^{49} +(574236. - 1.11029e6i) q^{50} +(3.57684e6 + 5.05088e6i) q^{52} +5.50364e6 q^{53} -4.46371e6i q^{55} +(-2.00761e6 - 1.43631e7i) q^{56} +(9.74547e6 - 1.88430e7i) q^{58} +6.68863e6i q^{59} -2.50550e6 q^{61} +(1.68584e7 + 8.71902e6i) q^{62} +(1.61342e7 - 4.60023e6i) q^{64} -6.75746e6 q^{65} +3.86718e6i q^{67} +(6.48163e6 + 9.15275e6i) q^{68} +(1.40647e7 + 7.27418e6i) q^{70} -3.21701e7i q^{71} +1.91362e7 q^{73} +(2.18381e7 - 4.22243e7i) q^{74} +(1.06380e7 - 7.53341e6i) q^{76} +5.65444e7 q^{77} +5.33471e7i q^{79} +(-6.08166e6 + 1.72788e7i) q^{80} +(3.61683e7 - 6.99321e7i) q^{82} -6.22776e6i q^{83} -1.22453e7 q^{85} +(-4.06782e7 - 2.10385e7i) q^{86} +(9.05507e6 + 6.47827e7i) q^{88} -3.83322e7 q^{89} -8.56008e7i q^{91} +(-5.65909e7 + 4.00755e7i) q^{92} +(180440. + 93322.2i) q^{94} +1.42323e7i q^{95} +7.87237e7 q^{97} +(-4.97738e7 + 9.62384e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 52 q^{4} + 14184 q^{8} + 8750 q^{10} + 51392 q^{13} - 68472 q^{14} - 81424 q^{16} - 27552 q^{17} - 172500 q^{20} - 389120 q^{22} + 1250000 q^{25} - 1037124 q^{26} + 1288520 q^{28} - 2764896 q^{29}+ \cdots + 285387714 q^{98}+O(q^{100}) $ 16 * q - 6 * q^2 - 52 * q^4 + 14184 * q^8 + 8750 * q^10 + 51392 * q^13 - 68472 * q^14 - 81424 * q^16 - 27552 * q^17 - 172500 * q^20 - 389120 * q^22 + 1250000 * q^25 - 1037124 * q^26 + 1288520 * q^28 - 2764896 * q^29 + 4379904 * q^32 + 3793964 * q^34 + 9009472 * q^37 + 3087360 * q^38 + 385000 * q^40 + 8576448 * q^41 - 16921200 * q^44 - 7974152 * q^46 - 32803600 * q^49 - 468750 * q^50 + 6679352 * q^52 - 2452032 * q^53 - 34134768 * q^56 + 52156572 * q^58 + 8371712 * q^61 - 1290000 * q^62 - 47543872 * q^64 - 9060000 * q^65 - 16095192 * q^68 + 10500000 * q^70 + 61907232 * q^73 + 138210876 * q^74 + 2570400 * q^76 + 156997440 * q^77 - 37590000 * q^80 + 83921012 * q^82 - 106960000 * q^85 + 101724672 * q^86 + 44728480 * q^88 - 106647456 * q^89 + 13876200 * q^92 + 55264632 * q^94 + 171851232 * q^97 + 285387714 * q^98

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 $

$2$	7.35022	−	14.2118i	0.459389	−	0.888235i
$2$	7.35022	−	14.2118i	0.459389	−	0.888235i
$3$		0			0
$3$		0			0
$4$	−147.949	−	208.919i	−0.577924	−	0.816090i
$5$	279.508			0.447214
$5$	279.508			0.447214
$6$		0			0
$7$			3540.70i			1.47468i	0.675524	+	0.737338i	$0.263918\pi$
$7$			3540.70i			1.47468i	−0.675524	+	0.737338i	$0.736082\pi$
$8$	−4056.56	+	567.011i	−0.990372	+	0.138430i
$9$		0			0
$10$	2054.45	−	3972.31i	0.205445	−	0.397231i
$11$		−	15969.8i		−	1.09076i	−0.838188	−	0.545381i	$-0.816385\pi$
$11$		−	15969.8i		−	1.09076i	0.838188	−	0.545381i	$-0.183615\pi$
$12$		0			0
$13$	−24176.2			−0.846477			−0.423239	−	0.906018i	$-0.639107\pi$
$13$	−24176.2			−0.846477			−0.423239	+	0.906018i	$0.639107\pi$
$14$	50319.6	+	26024.9i	1.30986	+	0.677449i
$15$		0			0
$16$	−21758.4	+	61818.6i	−0.332007	+	0.943277i
$17$	−43810.0			−0.524539			−0.262269	−	0.964995i	$-0.584471\pi$
$17$	−43810.0			−0.524539			−0.262269	+	0.964995i	$0.584471\pi$
$18$		0			0
$19$			50919.1i			0.390721i	0.980732	+	0.195360i	$0.0625876\pi$
$19$			50919.1i			0.390721i	−0.980732	+	0.195360i	$0.937412\pi$
$20$	−41352.9	−	58394.7i	−0.258456	−	0.364967i
$21$		0			0
$22$	−226960.	−	117382.i	−0.968853	−	0.501083i
$23$		−	270875.i		−	0.967959i	−0.875079	−	0.483980i	$-0.839191\pi$
$23$		−	270875.i		−	0.967959i	0.875079	−	0.483980i	$-0.160809\pi$
$24$		0			0
$25$	78125.0			0.200000
$26$	−177701.	+	343587.i	−0.388862	+	0.751871i
$27$		0			0
$28$	739720.	−	523841.i	1.20347	−	0.852251i
$29$	1.32588e6			1.87461			0.937305	−	0.348511i	$-0.113313\pi$
$29$	1.32588e6			1.87461			0.937305	+	0.348511i	$0.113313\pi$
$30$		0			0
$31$			1.18623e6i			1.28446i	0.766512	+	0.642230i	$0.221991\pi$
$31$			1.18623e6i			1.28446i	−0.766512	+	0.642230i	$0.778009\pi$
$32$	718623.	+	763605.i	0.685332	+	0.728231i
$33$		0			0
$34$	−322013.	+	622618.i	−0.240967	+	0.465914i
$35$			989655.i			0.659495i
$36$		0			0
$37$	2.97108e6			1.58529			0.792643	−	0.609686i	$-0.208705\pi$
$37$	2.97108e6			1.58529			0.792643	+	0.609686i	$0.208705\pi$
$38$	723650.	+	374266.i	0.347052	+	0.179493i
$39$		0			0
$40$	−1.13384e6	+	158484.i	−0.442908	+	0.0619079i
$41$	4.92072e6			1.74138			0.870689	−	0.491834i	$-0.163673\pi$
$41$	4.92072e6			1.74138			0.870689	+	0.491834i	$0.163673\pi$
$42$		0			0
$43$		−	2.86229e6i		−	0.837221i	−0.908166	−	0.418611i	$-0.862517\pi$
$43$		−	2.86229e6i		−	0.837221i	0.908166	−	0.418611i	$-0.137483\pi$
$44$	−3.33641e6	+	2.36272e6i	−0.890160	+	0.630378i
$45$		0			0
$46$	−3.84961e6	−	1.99099e6i	−0.859776	−	0.444669i
$47$			12696.5i			0.00260192i	0.999999	+	0.00130096i	$0.000414108\pi$
$47$			12696.5i			0.00260192i	−0.999999	+	0.00130096i	$0.999586\pi$
$48$		0			0
$49$	−6.77174e6			−1.17467
$50$	574236.	−	1.11029e6i	0.0918777	−	0.177647i
$51$		0			0
$52$	3.57684e6	+	5.05088e6i	0.489200	+	0.690802i
$53$	5.50364e6			0.697504			0.348752	−	0.937215i	$-0.386606\pi$
$53$	5.50364e6			0.697504			0.348752	+	0.937215i	$0.386606\pi$
$54$		0			0
$55$		−	4.46371e6i		−	0.487803i
$56$	−2.00761e6	−	1.43631e7i	−0.204140	−	1.46048i
$57$		0			0
$58$	9.74547e6	−	1.88430e7i	0.861174	−	1.66509i
$59$			6.68863e6i			0.551987i	0.961159	+	0.275994i	$0.0890068\pi$
$59$			6.68863e6i			0.551987i	−0.961159	+	0.275994i	$0.910993\pi$
$60$		0			0
$61$	−2.50550e6			−0.180957			−0.0904784	−	0.995898i	$-0.528840\pi$
$61$	−2.50550e6			−0.180957			−0.0904784	+	0.995898i	$0.528840\pi$
$62$	1.68584e7	+	8.71902e6i	1.14090	+	0.590066i
$63$		0			0
$64$	1.61342e7	−	4.60023e6i	0.961674	−	0.274195i
$65$	−6.75746e6			−0.378556
$66$		0			0
$67$			3.86718e6i			0.191909i	0.995386	+	0.0959546i	$0.0305904\pi$
$67$			3.86718e6i			0.191909i	−0.995386	+	0.0959546i	$0.969410\pi$
$68$	6.48163e6	+	9.15275e6i	0.303144	+	0.428071i
$69$		0			0
$70$	1.40647e7	+	7.27418e6i	0.585787	+	0.302965i
$71$		−	3.21701e7i		−	1.26596i	−0.774170	−	0.632978i	$-0.781832\pi$
$71$		−	3.21701e7i		−	1.26596i	0.774170	−	0.632978i	$-0.218168\pi$
$72$		0			0
$73$	1.91362e7			0.673853			0.336927	−	0.941531i	$-0.390613\pi$
$73$	1.91362e7			0.673853			0.336927	+	0.941531i	$0.390613\pi$
$74$	2.18381e7	−	4.22243e7i	0.728262	−	1.40811i
$75$		0			0
$76$	1.06380e7	−	7.53341e6i	0.318863	−	0.225807i
$77$	5.65444e7			1.60852
$78$		0			0
$79$			5.33471e7i			1.36963i	0.728718	+	0.684814i	$0.240116\pi$
$79$			5.33471e7i			1.36963i	−0.728718	+	0.684814i	$0.759884\pi$
$80$	−6.08166e6	+	1.72788e7i	−0.148478	+	0.421846i
$81$		0			0
$82$	3.61683e7	−	6.99321e7i	0.799969	−	1.54675i
$83$		−	6.22776e6i		−	0.131226i	−0.997845	−	0.0656129i	$-0.979100\pi$
$83$		−	6.22776e6i		−	0.131226i	0.997845	−	0.0656129i	$-0.0209003\pi$
$84$		0			0
$85$	−1.22453e7			−0.234581
$86$	−4.06782e7	−	2.10385e7i	−0.743650	−	0.384610i
$87$		0			0
$88$	9.05507e6	+	6.47827e7i	0.150995	+	1.08026i
$89$	−3.83322e7			−0.610947			−0.305473	−	0.952201i	$-0.598815\pi$
$89$	−3.83322e7			−0.610947			−0.305473	+	0.952201i	$0.598815\pi$
$90$		0			0
$91$		−	8.56008e7i		−	1.24828i
$92$	−5.65909e7	+	4.00755e7i	−0.789942	+	0.559407i
$93$		0			0
$94$	180440.	+	93322.2i	0.00231111	+	0.00119529i
$95$			1.42323e7i			0.174736i
$96$		0			0
$97$	7.87237e7			0.889239			0.444620	−	0.895720i	$-0.353339\pi$
$97$	7.87237e7			0.889239			0.444620	+	0.895720i	$0.353339\pi$
$98$	−4.97738e7	+	9.62384e7i	−0.539630	+	1.04338i
$99$		0			0
$100$	−1.15585e7	−	1.63218e7i	−0.115585	−	0.163218i
$101$	1.16450e7			0.111906			0.0559530	−	0.998433i	$-0.482180\pi$
$101$	1.16450e7			0.111906			0.0559530	+	0.998433i	$0.482180\pi$
$102$		0			0
$103$		−	6.88569e7i		−	0.611785i	−0.952066	−	0.305892i	$-0.901045\pi$
$103$		−	6.88569e7i		−	0.611785i	0.952066	−	0.305892i	$-0.0989547\pi$
$104$	9.80725e7	−	1.37082e7i	0.838328	−	0.117178i
$105$		0			0
$106$	4.04529e7	−	7.82164e7i	0.320425	−	0.619547i
$107$		−	7.69690e7i		−	0.587193i	−0.955929	−	0.293596i	$-0.905148\pi$
$107$		−	7.69690e7i		−	0.587193i	0.955929	−	0.293596i	$-0.0948521\pi$
$108$		0			0
$109$	−4.29484e6			−0.0304257			−0.0152129	−	0.999884i	$-0.504843\pi$
$109$	−4.29484e6			−0.0304257			−0.0152129	+	0.999884i	$0.504843\pi$
$110$	−6.34372e7	−	3.28092e7i	−0.433284	−	0.224091i
$111$		0			0
$112$	−2.18881e8	−	7.70399e7i	−1.39103	−	0.489603i
$113$	2.34309e8			1.43706			0.718530	−	0.695496i	$-0.244815\pi$
$113$	2.34309e8			1.43706			0.718530	+	0.695496i	$0.244815\pi$
$114$		0			0
$115$		−	7.57118e7i		−	0.432884i
$116$	−1.96161e8	−	2.77001e8i	−1.08338	−	1.52985i
$117$		0			0
$118$	9.50572e7	+	4.91629e7i	0.490294	+	0.253577i
$119$		−	1.55118e8i		−	0.773525i
$120$		0			0
$121$	−4.06770e7			−0.189761
$122$	−1.84160e7	+	3.56076e7i	−0.0831295	+	0.160732i
$123$		0			0
$124$	2.47825e8	−	1.75500e8i	1.04824	−	0.742321i
$125$	2.18366e7			0.0894427
$126$		0			0
$127$		−	2.94344e8i		−	1.13146i	−0.824589	−	0.565732i	$-0.808594\pi$
$127$		−	2.94344e8i		−	1.13146i	0.824589	−	0.565732i	$-0.191406\pi$
$128$	5.32125e7	−	2.63108e8i	0.198232	−	0.980155i
$129$		0			0
$130$	−4.96688e7	+	9.60355e7i	−0.173904	+	0.336247i
$131$			3.43317e8i			1.16576i	0.812558	+	0.582881i	$0.198075\pi$
$131$			3.43317e8i			1.16576i	−0.812558	+	0.582881i	$0.801925\pi$
$132$		0			0
$133$	−1.80289e8			−0.576186
$134$	5.49595e7	+	2.84246e7i	0.170461	+	0.0881609i
$135$		0			0
$136$	1.77718e8	−	2.48407e7i	0.519489	−	0.0726121i
$137$	−2.03539e8			−0.577784			−0.288892	−	0.957362i	$-0.593287\pi$
$137$	−2.03539e8			−0.577784			−0.288892	+	0.957362i	$0.593287\pi$
$138$		0			0
$139$			2.51305e8i			0.673197i	0.941648	+	0.336599i	$0.109277\pi$
$139$			2.51305e8i			0.673197i	−0.941648	+	0.336599i	$0.890723\pi$
$140$	2.06758e8	−	1.46418e8i	0.538208	−	0.381138i
$141$		0			0
$142$	−4.57193e8	−	2.36457e8i	−1.12447	−	0.581566i
$143$			3.86091e8i			0.923305i
$144$		0			0
$145$	3.70593e8			0.838351
$146$	1.40656e8	−	2.71960e8i	0.309560	−	0.598540i
$147$		0			0
$148$	−4.39567e8	−	6.20716e8i	−0.916175	−	1.29374i
$149$	−7.65026e8			−1.55214			−0.776070	−	0.630647i	$-0.782790\pi$
$149$	−7.65026e8			−1.55214			−0.776070	+	0.630647i	$0.782790\pi$
$150$		0			0
$151$		−	5.12585e8i		−	0.985958i	−0.870041	−	0.492979i	$-0.835908\pi$
$151$		−	5.12585e8i		−	0.985958i	0.870041	−	0.492979i	$-0.164092\pi$
$152$	−2.88717e7	−	2.06557e8i	−0.0540876	−	0.386959i
$153$		0			0
$154$	4.15613e8	−	8.03596e8i	0.738936	−	1.42874i
$155$			3.31560e8i			0.574428i
$156$		0			0
$157$	1.16971e9			1.92522			0.962610	−	0.270890i	$-0.0873179\pi$
$157$	1.16971e9			1.92522			0.962610	+	0.270890i	$0.0873179\pi$
$158$	7.58157e8	+	3.92113e8i	1.21655	+	0.629191i
$159$		0			0
$160$	2.00861e8	+	2.13434e8i	0.306490	+	0.325675i
$161$	9.59085e8			1.42743
$162$		0			0
$163$			8.79268e8i			1.24558i	0.782390	+	0.622789i	$0.214000\pi$
$163$			8.79268e8i			1.24558i	−0.782390	+	0.622789i	$0.786000\pi$
$164$	−7.28014e8	−	1.02803e9i	−1.00638	−	1.42112i
$165$		0			0
$166$	−8.85075e7	−	4.57754e7i	−0.116559	−	0.0602837i
$167$		−	4.63319e8i		−	0.595682i	−0.954616	−	0.297841i	$-0.903734\pi$
$167$		−	4.63319e8i		−	0.595682i	0.954616	−	0.297841i	$-0.0962665\pi$
$168$		0			0
$169$	−2.31240e8			−0.283476
$170$	−9.00054e7	+	1.74027e8i	−0.107764	+	0.208363i
$171$		0			0
$172$	−5.97988e8	+	4.23472e8i	−0.683248	+	0.483851i
$173$	−4.71680e8			−0.526579			−0.263289	−	0.964717i	$-0.584807\pi$
$173$	−4.71680e8			−0.526579			−0.263289	+	0.964717i	$0.584807\pi$
$174$		0			0
$175$			2.76617e8i			0.294935i
$176$	9.87233e8	+	3.47478e8i	1.02889	+	0.362140i
$177$		0			0
$178$	−2.81750e8	+	5.44768e8i	−0.280662	+	0.542664i
$179$			8.30768e8i			0.809222i	0.914489	+	0.404611i	$0.132593\pi$
$179$			8.30768e8i			0.809222i	−0.914489	+	0.404611i	$0.867407\pi$
$180$		0			0
$181$	6.19754e8			0.577437			0.288719	−	0.957414i	$-0.406771\pi$
$181$	6.19754e8			0.577437			0.288719	+	0.957414i	$0.406771\pi$
$182$	−1.21654e9	−	6.29184e8i	−1.10877	−	0.573446i
$183$		0			0
$184$	1.53589e8	+	1.09882e9i	0.133995	+	0.958640i
$185$	8.30442e8			0.708961
$186$		0			0
$187$			6.99639e8i			0.572147i
$188$	2.65255e6	−	1.87843e6i	0.00212340	−	0.00150371i
$189$		0			0
$190$	2.02266e8	+	1.04611e8i	0.155206	+	0.0802715i
$191$			4.24020e7i			0.0318605i	0.999873	+	0.0159303i	$0.00507097\pi$
$191$			4.24020e7i			0.0318605i	−0.999873	+	0.0159303i	$0.994929\pi$
$192$		0			0
$193$	4.21151e8			0.303535			0.151767	−	0.988416i	$-0.451504\pi$
$193$	4.21151e8			0.303535			0.151767	+	0.988416i	$0.451504\pi$
$194$	5.78636e8	−	1.11880e9i	0.408506	−	0.789854i
$195$		0			0
$196$	1.00187e9	+	1.41475e9i	0.678871	+	0.958637i
$197$	1.93944e9			1.28769			0.643846	−	0.765155i	$-0.277338\pi$
$197$	1.93944e9			1.28769			0.643846	+	0.765155i	$0.277338\pi$
$198$		0			0
$199$			2.11255e8i			0.134708i	0.997729	+	0.0673542i	$0.0214557\pi$
$199$			2.11255e8i			0.134708i	−0.997729	+	0.0673542i	$0.978544\pi$
$200$	−3.16919e8	+	4.42977e7i	−0.198074	+	0.0276861i
$201$		0			0
$202$	8.55931e7	−	1.65496e8i	0.0514083	−	0.0993989i
$203$			4.69452e9i			2.76444i
$204$		0			0
$205$	1.37538e9			0.778768
$206$	−9.78578e8	−	5.06113e8i	−0.543409	−	0.281047i
$207$		0			0
$208$	5.26036e8	−	1.49454e9i	0.281036	−	0.798463i
$209$	8.13170e8			0.426183
$210$		0			0
$211$			2.01406e9i			1.01611i	0.861324	+	0.508056i	$0.169636\pi$
$211$			2.01406e9i			1.01611i	−0.861324	+	0.508056i	$0.830364\pi$
$212$	−8.14256e8	−	1.14982e9i	−0.403104	−	0.569226i
$213$		0			0
$214$	−1.09387e9	−	5.65739e8i	−0.521565	−	0.269750i
$215$		−	8.00035e8i		−	0.374417i
$216$		0			0
$217$	−4.20007e9			−1.89416
$218$	−3.15680e7	+	6.10373e7i	−0.0139772	+	0.0270252i
$219$		0			0
$220$	−9.32554e8	+	6.60399e8i	−0.398092	+	0.281913i
$221$	1.05916e9			0.444010
$222$		0			0
$223$		−	9.06863e8i		−	0.366710i	−0.983047	−	0.183355i	$-0.941304\pi$
$223$		−	9.06863e8i		−	0.366710i	0.983047	−	0.183355i	$-0.0586957\pi$
$224$	−2.70370e9	+	2.54443e9i	−1.07390	+	1.01064i
$225$		0			0
$226$	1.72222e9	−	3.32994e9i	0.660169	−	1.27645i
$227$		−	9.31268e7i		−	0.0350729i	−0.999846	−	0.0175364i	$-0.994418\pi$
$227$		−	9.31268e7i		−	0.0350729i	0.999846	−	0.0175364i	$-0.00558230\pi$
$228$		0			0
$229$	−5.17840e8			−0.188301			−0.0941507	−	0.995558i	$-0.530014\pi$
$229$	−5.17840e8			−0.188301			−0.0941507	+	0.995558i	$0.530014\pi$
$230$	−1.07600e9	−	5.56498e8i	−0.384503	−	0.198862i
$231$		0			0
$232$	−5.37850e9	+	7.51786e8i	−1.85656	+	0.259503i
$233$	1.20417e9			0.408569			0.204284	−	0.978912i	$-0.434513\pi$
$233$	1.20417e9			0.408569			0.204284	+	0.978912i	$0.434513\pi$
$234$		0			0
$235$			3.54879e6i			0.00116361i
$236$	1.39738e9	−	9.89573e8i	0.450471	−	0.319007i
$237$		0			0
$238$	−2.20450e9	−	1.14015e9i	−0.687072	−	0.355349i
$239$			2.12088e9i			0.650018i	0.945711	+	0.325009i	$0.105367\pi$
$239$			2.12088e9i			0.650018i	−0.945711	+	0.325009i	$0.894633\pi$
$240$		0			0
$241$	−6.85448e8			−0.203192			−0.101596	−	0.994826i	$-0.532395\pi$
$241$	−6.85448e8			−0.203192			−0.101596	+	0.994826i	$0.532395\pi$
$242$	−2.98984e8	+	5.78092e8i	−0.0871740	+	0.168552i
$243$		0			0
$244$	3.70685e8	+	5.23447e8i	0.104579	+	0.147677i
$245$	−1.89276e9			−0.525329
$246$		0			0
$247$		−	1.23103e9i		−	0.330736i
$248$	−6.72603e8	−	4.81200e9i	−0.177808	−	1.27209i
$249$		0			0
$250$	1.60504e8	−	3.10337e8i	0.0410890	−	0.0794462i
$251$			4.44219e9i			1.11919i	0.828768	+	0.559593i	$0.189042\pi$
$251$			4.44219e9i			1.11919i	−0.828768	+	0.559593i	$0.810958\pi$
$252$		0			0
$253$	−4.32582e9			−1.05581
$254$	−4.18315e9	−	2.16350e9i	−1.00501	−	0.519782i
$255$		0			0
$256$	−3.34811e9	−	2.69015e9i	−0.779543	−	0.626349i
$257$	−1.71181e9			−0.392395			−0.196198	−	0.980564i	$-0.562859\pi$
$257$	−1.71181e9			−0.392395			−0.196198	+	0.980564i	$0.562859\pi$
$258$		0			0
$259$			1.05197e10i			2.33778i
$260$	9.99758e8	+	1.41176e9i	0.218777	+	0.308936i
$261$		0			0
$262$	4.87914e9	+	2.52345e9i	1.03547	+	0.535538i
$263$		−	2.50597e9i		−	0.523785i	−0.965097	−	0.261892i	$-0.915653\pi$
$263$		−	2.50597e9i		−	0.523785i	0.965097	−	0.261892i	$-0.0843465\pi$
$264$		0			0
$265$	1.53831e9			0.311933
$266$	−1.32516e9	+	2.56223e9i	−0.264693	+	0.511789i
$267$		0			0
$268$	8.07929e8	−	5.72145e8i	0.156615	−	0.110909i
$269$	−3.62847e8			−0.0692970			−0.0346485	−	0.999400i	$-0.511031\pi$
$269$	−3.62847e8			−0.0692970			−0.0346485	+	0.999400i	$0.511031\pi$
$270$		0			0
$271$			1.05662e10i			1.95903i	0.201368	+	0.979516i	$0.435461\pi$
$271$			1.05662e10i			1.95903i	−0.201368	+	0.979516i	$0.564539\pi$
$272$	9.53236e8	−	2.70827e9i	0.174151	−	0.494785i
$273$		0			0
$274$	−1.49606e9	+	2.89265e9i	−0.265428	+	0.513209i
$275$		−	1.24764e9i		−	0.218152i
$276$		0			0
$277$	−1.36227e9			−0.231390			−0.115695	−	0.993285i	$-0.536909\pi$
$277$	−1.36227e9			−0.231390			−0.115695	+	0.993285i	$0.536909\pi$
$278$	3.57149e9	+	1.84715e9i	0.597958	+	0.309259i
$279$		0			0
$280$	−5.61145e8	−	4.01460e9i	−0.0912942	−	0.653146i
$281$	3.01499e9			0.483572			0.241786	−	0.970330i	$-0.422267\pi$
$281$	3.01499e9			0.483572			0.241786	+	0.970330i	$0.422267\pi$
$282$		0			0
$283$		−	1.38220e9i		−	0.215490i	−0.994179	−	0.107745i	$-0.965637\pi$
$283$		−	1.38220e9i		−	0.215490i	0.994179	−	0.107745i	$-0.0343629\pi$
$284$	−6.72094e9	+	4.75952e9i	−1.03313	+	0.731627i
$285$		0			0
$286$	5.48703e9	+	2.83785e9i	0.820112	+	0.424156i
$287$			1.74228e10i			2.56797i
$288$		0			0
$289$	−5.05644e9			−0.724859
$290$	2.72394e9	−	5.26679e9i	0.385129	−	0.744653i
$291$		0			0
$292$	−2.83118e9	−	3.99793e9i	−0.389436	−	0.549925i
$293$	−5.86750e9			−0.796127			−0.398064	−	0.917358i	$-0.630318\pi$
$293$	−5.86750e9			−0.796127			−0.398064	+	0.917358i	$0.630318\pi$
$294$		0			0
$295$			1.86953e9i			0.246856i
$296$	−1.20524e10	+	1.68463e9i	−1.57002	+	0.219452i
$297$		0			0
$298$	−5.62310e9	+	1.08724e10i	−0.713035	+	1.37867i
$299$			6.54873e9i			0.819355i
$300$		0			0
$301$	1.01345e10			1.23463
$302$	−7.28474e9	−	3.76761e9i	−0.875762	−	0.452938i
$303$		0			0
$304$	−3.14775e9	−	1.10792e9i	−0.368558	−	0.129722i
$305$	−7.00308e8			−0.0809263
$306$		0			0
$307$			5.79386e9i			0.652250i	0.945327	+	0.326125i	$0.105743\pi$
$307$			5.79386e9i			0.652250i	−0.945327	+	0.326125i	$0.894257\pi$
$308$	−8.36567e9	−	1.18132e10i	−0.929603	−	1.31270i
$309$		0			0
$310$	4.71206e9	+	2.43704e9i	0.510227	+	0.263886i
$311$		−	8.37260e9i		−	0.894991i	−0.894286	−	0.447496i	$-0.852316\pi$
$311$		−	8.37260e9i		−	0.894991i	0.894286	−	0.447496i	$-0.147684\pi$
$312$		0			0
$313$	1.22771e10			1.27914			0.639572	−	0.768731i	$-0.279111\pi$
$313$	1.22771e10			1.27914			0.639572	+	0.768731i	$0.279111\pi$
$314$	8.59764e9	−	1.66237e10i	0.884424	−	1.71005i
$315$		0			0
$316$	1.11452e10	−	7.89263e9i	1.11774	−	0.791541i
$317$	1.38443e10			1.37099			0.685495	−	0.728077i	$-0.259586\pi$
$317$	1.38443e10			1.37099			0.685495	+	0.728077i	$0.259586\pi$
$318$		0			0
$319$		−	2.11740e10i		−	2.04475i
$320$	4.50965e9	−	1.28580e9i	0.430074	−	0.122624i
$321$		0			0
$322$	7.04948e9	−	1.36303e10i	0.655743	−	1.26789i
$323$		−	2.23077e9i		−	0.204948i
$324$		0			0
$325$	−1.88877e9			−0.169295
$326$	1.24959e10	+	6.46281e9i	1.10637	+	0.572204i
$327$		0			0
$328$	−1.99612e10	+	2.79010e9i	−1.72461	+	0.241060i
$329$	−4.49546e7			−0.00383699
$330$		0			0
$331$		−	7.71740e9i		−	0.642923i	−0.946923	−	0.321462i	$-0.895826\pi$
$331$		−	7.71740e9i		−	0.642923i	0.946923	−	0.321462i	$-0.104174\pi$
$332$	−1.30110e9	+	9.21389e8i	−0.107092	+	0.0758386i
$333$		0			0
$334$	−6.58458e9	−	3.40549e9i	−0.529105	−	0.273649i
$335$			1.08091e9i			0.0858244i
$336$		0			0
$337$	−1.47787e10			−1.14582			−0.572910	−	0.819618i	$-0.694186\pi$
$337$	−1.47787e10			−1.14582			−0.572910	+	0.819618i	$0.694186\pi$
$338$	−1.69966e9	+	3.28633e9i	−0.130226	+	0.251793i
$339$		0			0
$340$	1.81167e9	+	2.55827e9i	0.135570	+	0.191439i
$341$	1.89438e10			1.40104
$342$		0			0
$343$		−	3.56527e9i		−	0.257582i
$344$	1.62295e9	+	1.16111e10i	0.115897	+	0.829161i
$345$		0			0
$346$	−3.46695e9	+	6.70341e9i	−0.241904	+	0.467726i
$347$		−	2.69899e10i		−	1.86158i	−0.365549	−	0.930792i	$-0.619119\pi$
$347$		−	2.69899e10i		−	1.86158i	0.365549	−	0.930792i	$-0.380881\pi$
$348$		0			0
$349$	2.02677e10			1.36617			0.683083	−	0.730340i	$-0.260639\pi$
$349$	2.02677e10			1.36617			0.683083	+	0.730340i	$0.260639\pi$
$350$	3.93122e9	+	2.03320e9i	0.261972	+	0.135490i
$351$		0			0
$352$	1.21947e10	−	1.14763e10i	0.794326	−	0.747534i
$353$	−9.41747e9			−0.606506			−0.303253	−	0.952910i	$-0.598073\pi$
$353$	−9.41747e9			−0.606506			−0.303253	+	0.952910i	$0.598073\pi$
$354$		0			0
$355$		−	8.99181e9i		−	0.566153i
$356$	5.67119e9	+	8.00832e9i	0.353081	+	0.498588i
$357$		0			0
$358$	1.18067e10	+	6.10633e9i	0.718780	+	0.371747i
$359$		−	3.30369e9i		−	0.198894i	−0.995043	−	0.0994469i	$-0.968293\pi$
$359$		−	3.30369e9i		−	0.198894i	0.995043	−	0.0994469i	$-0.0317073\pi$
$360$		0			0
$361$	1.43908e10			0.847337
$362$	4.55533e9	−	8.80780e9i	0.265268	−	0.512900i
$363$		0			0
$364$	−1.78836e10	+	1.26645e10i	−1.01871	+	0.721412i
$365$	5.34874e9			0.301356
$366$		0			0
$367$		−	1.14531e10i		−	0.631335i	−0.948870	−	0.315667i	$-0.897772\pi$
$367$		−	1.14531e10i		−	0.631335i	0.948870	−	0.315667i	$-0.102228\pi$
$368$	1.67451e10	+	5.89380e9i	0.913053	+	0.321369i
$369$		0			0
$370$	6.10393e9	−	1.18021e10i	0.325689	−	0.629725i
$371$			1.94867e10i			1.02859i
$372$		0			0
$373$	2.26449e10			1.16986			0.584932	−	0.811083i	$-0.301121\pi$
$373$	2.26449e10			1.16986			0.584932	+	0.811083i	$0.301121\pi$
$374$	9.94311e9	+	5.14250e9i	0.508201	+	0.262838i
$375$		0			0
$376$	−7.19907e6	−	5.15043e7i	−0.000360184	−	0.00257687i
$377$	−3.20547e10			−1.58681
$378$		0			0
$379$			5.61760e9i			0.272266i	0.990691	+	0.136133i	$0.0434675\pi$
$379$			5.61760e9i			0.272266i	−0.990691	+	0.136133i	$0.956533\pi$
$380$	2.97340e9	−	2.10565e9i	0.142600	−	0.100984i
$381$		0			0
$382$	6.02607e8	+	3.11664e8i	0.0282996	+	0.0146364i
$383$			4.10535e9i			0.190790i	0.995440	+	0.0953950i	$0.0304114\pi$
$383$			4.10535e9i			0.190790i	−0.995440	+	0.0953950i	$0.969589\pi$
$384$		0			0
$385$	1.58046e10			0.719352
$386$	3.09555e9	−	5.98530e9i	0.139440	−	0.269610i
$387$		0			0
$388$	−1.16471e10	−	1.64469e10i	−0.513913	−	0.725699i
$389$	1.37663e9			0.0601199			0.0300599	−	0.999548i	$-0.490430\pi$
$389$	1.37663e9			0.0601199			0.0300599	+	0.999548i	$0.490430\pi$
$390$		0			0
$391$			1.18670e10i			0.507732i
$392$	2.74700e10	−	3.83965e9i	1.16336	−	0.162610i
$393$		0			0
$394$	1.42553e10	−	2.75629e10i	0.591551	−	1.14377i
$395$			1.49110e10i			0.612516i
$396$		0			0
$397$	−3.04208e10			−1.22464			−0.612321	−	0.790610i	$-0.709764\pi$
$397$	−3.04208e10			−1.22464			−0.612321	+	0.790610i	$0.709764\pi$
$398$	3.00231e9	+	1.55277e9i	0.119653	+	0.0618835i
$399$		0			0
$400$	−1.69988e9	+	4.82958e9i	−0.0664014	+	0.188655i
$401$	1.95473e10			0.755977			0.377989	−	0.925810i	$-0.376616\pi$
$401$	1.95473e10			0.755977			0.377989	+	0.925810i	$0.376616\pi$
$402$		0			0
$403$		−	2.86785e10i		−	1.08727i
$404$	−1.72286e9	−	2.43286e9i	−0.0646732	−	0.0913254i
$405$		0			0
$406$	6.67175e10	+	3.45058e10i	2.45548	+	1.26995i
$407$		−	4.74477e10i		−	1.72917i
$408$		0			0
$409$	−4.37475e10			−1.56336			−0.781681	−	0.623678i	$-0.785638\pi$
$409$	−4.37475e10			−1.56336			−0.781681	+	0.623678i	$0.785638\pi$
$410$	1.01094e10	−	1.95466e10i	0.357757	−	0.691729i
$411$		0			0
$412$	−1.43855e10	+	1.01873e10i	−0.499271	+	0.353565i
$413$	−2.36824e10			−0.814002
$414$		0			0
$415$		−	1.74071e9i		−	0.0586860i
$416$	−1.73736e10	−	1.84611e10i	−0.580118	−	0.616431i
$417$		0			0
$418$	5.97697e9	−	1.15566e10i	0.195784	−	0.378551i
$419$			1.93115e10i			0.626555i	0.949662	+	0.313277i	$0.101427\pi$
$419$			1.93115e10i			0.626555i	−0.949662	+	0.313277i	$0.898573\pi$
$420$		0			0
$421$	−3.65545e10			−1.16362			−0.581812	−	0.813323i	$-0.697656\pi$
$421$	−3.65545e10			−1.16362			−0.581812	+	0.813323i	$0.697656\pi$
$422$	2.86233e10	+	1.48038e10i	0.902547	+	0.466791i
$423$		0			0
$424$	−2.23259e10	+	3.12062e9i	−0.690788	+	0.0965557i
$425$	−3.42266e9			−0.104908
$426$		0			0
$427$		−	8.87121e9i		−	0.266853i
$428$	−1.60803e10	+	1.13875e10i	−0.479202	+	0.339353i
$429$		0			0
$430$	−1.13699e10	−	5.88043e9i	−0.332570	−	0.172003i
$431$		−	3.98669e10i		−	1.15532i	−0.816276	−	0.577662i	$-0.803965\pi$
$431$		−	3.98669e10i		−	1.15532i	0.816276	−	0.577662i	$-0.196035\pi$
$432$		0			0
$433$	3.21564e10			0.914779			0.457389	−	0.889266i	$-0.348785\pi$
$433$	3.21564e10			0.914779			0.457389	+	0.889266i	$0.348785\pi$
$434$	−3.08714e10	+	5.96904e10i	−0.870157	+	1.68246i
$435$		0			0
$436$	6.35416e8	+	8.97275e8i	0.0175838	+	0.0248302i
$437$	1.37927e10			0.378201
$438$		0			0
$439$			2.72016e10i			0.732379i	0.930540	+	0.366189i	$0.119338\pi$
$439$			2.72016e10i			0.732379i	−0.930540	+	0.366189i	$0.880662\pi$
$440$	2.53097e9	+	1.81073e10i	0.0675268	+	0.483107i
$441$		0			0
$442$	7.78507e9	−	1.50526e10i	0.203973	−	0.394386i
$443$			1.32228e10i			0.343327i	0.985156	+	0.171663i	$0.0549142\pi$
$443$			1.32228e10i			0.343327i	−0.985156	+	0.171663i	$0.945086\pi$
$444$		0			0
$445$	−1.07142e10			−0.273224
$446$	−1.28881e10	−	6.66564e9i	−0.325724	−	0.168462i
$447$		0			0
$448$	1.62880e10	+	5.71264e10i	0.404349	+	1.41816i
$449$	−2.82958e10			−0.696203			−0.348102	−	0.937457i	$-0.613174\pi$
$449$	−2.82958e10			−0.696203			−0.348102	+	0.937457i	$0.613174\pi$
$450$		0			0
$451$		−	7.85831e10i		−	1.89943i
$452$	−3.46657e10	−	4.89516e10i	−0.830512	−	1.17277i
$453$		0			0
$454$	−1.32350e9	−	6.84502e8i	−0.0311530	−	0.0161121i
$455$		−	2.39261e10i		−	0.558248i
$456$		0			0
$457$	7.89688e10			1.81047			0.905234	−	0.424914i	$-0.139696\pi$
$457$	7.89688e10			1.81047			0.905234	+	0.424914i	$0.139696\pi$
$458$	−3.80623e9	+	7.35942e9i	−0.0865035	+	0.167256i
$459$		0			0
$460$	−1.58176e10	+	1.12015e10i	−0.353273	+	0.250174i
$461$	−2.63713e10			−0.583885			−0.291943	−	0.956436i	$-0.594302\pi$
$461$	−2.63713e10			−0.583885			−0.291943	+	0.956436i	$0.594302\pi$
$462$		0			0
$463$			2.74281e10i			0.596858i	0.954432	+	0.298429i	$0.0964627\pi$
$463$			2.74281e10i			0.596858i	−0.954432	+	0.298429i	$0.903537\pi$
$464$	−2.88489e10	+	8.19638e10i	−0.622383	+	1.76828i
$465$		0			0
$466$	8.85093e9	−	1.71134e10i	0.187692	−	0.362905i
$467$		−	8.24023e10i		−	1.73249i	−0.499616	−	0.866247i	$-0.666525\pi$
$467$		−	8.24023e10i		−	1.73249i	0.499616	−	0.866247i	$-0.333475\pi$
$468$		0			0
$469$	−1.36925e10			−0.283004
$470$	5.04345e7	+	2.60843e7i	0.00103356	+	0.000534550i
$471$		0			0
$472$	−3.79252e9	−	2.71328e10i	−0.0764118	−	0.546673i
$473$	−4.57104e10			−0.913209
$474$		0			0
$475$			3.97805e9i			0.0781441i
$476$	−3.24071e10	+	2.29495e10i	−0.631266	+	0.447039i
$477$		0			0
$478$	3.01415e10	+	1.55890e10i	0.577369	+	0.298611i
$479$		−	1.28142e10i		−	0.243415i	−0.992566	−	0.121708i	$-0.961163\pi$
$479$		−	1.28142e10i		−	0.243415i	0.992566	−	0.121708i	$-0.0388370\pi$
$480$		0			0
$481$	−7.18296e10			−1.34191
$482$	−5.03819e9	+	9.74143e9i	−0.0933441	+	0.180482i
$483$		0			0
$484$	6.01810e9	+	8.49820e9i	0.109668	+	0.154862i
$485$	2.20039e10			0.397680
$486$		0			0
$487$			2.27188e10i			0.403895i	0.979396	+	0.201948i	$0.0647271\pi$
$487$			2.27188e10i			0.403895i	−0.979396	+	0.201948i	$0.935273\pi$
$488$	1.01637e10	−	1.42064e9i	0.179215	−	0.0250499i
$489$		0			0
$490$	−1.39122e10	+	2.68995e10i	−0.241330	+	0.466615i
$491$		−	8.70411e10i		−	1.49761i	−0.662791	−	0.748805i	$-0.730628\pi$
$491$		−	8.70411e10i		−	1.49761i	0.662791	−	0.748805i	$-0.269372\pi$
$492$		0			0
$493$	−5.80866e10			−0.983305
$494$	−1.74951e10	−	9.04835e9i	−0.293772	−	0.151936i
$495$		0			0
$496$	−7.33308e10	−	2.58104e10i	−1.21160	−	0.426449i
$497$	1.13904e11			1.86688
$498$		0			0
$499$			1.34972e10i			0.217691i	0.994059	+	0.108846i	$0.0347154\pi$
$499$			1.34972e10i			0.217691i	−0.994059	+	0.108846i	$0.965285\pi$
$500$	−3.23070e9	−	4.56208e9i	−0.0516911	−	0.0729933i
$501$		0			0
$502$	6.31313e10	+	3.26510e10i	0.994100	+	0.514141i
$503$			4.13249e10i			0.645565i	0.946473	+	0.322782i	$0.104618\pi$
$503$			4.13249e10i			0.645565i	−0.946473	+	0.322782i	$0.895382\pi$
$504$		0			0
$505$	3.25487e9			0.0500459
$506$	−3.17957e10	+	6.14776e10i	−0.485028	+	0.937810i
$507$		0			0
$508$	−6.14942e10	+	4.35479e10i	−0.923377	+	0.653901i
$509$	3.37390e9			0.0502645			0.0251322	−	0.999684i	$-0.491999\pi$
$509$	3.37390e9			0.0502645			0.0251322	+	0.999684i	$0.491999\pi$
$510$		0			0
$511$			6.77557e10i			0.993715i
$512$	−6.28411e10	+	2.78094e10i	−0.914458	+	0.404680i
$513$		0			0
$514$	−1.25822e10	+	2.43279e10i	−0.180262	+	0.348539i
$515$		−	1.92461e10i		−	0.273598i
$516$		0			0
$517$	2.02761e8			0.00283807
$518$	1.49504e11	+	7.73221e10i	2.07650	+	1.07395i
$519$		0			0
$520$	2.74121e10	−	3.83156e9i	0.374912	−	0.0524037i
$521$	−1.24497e11			−1.68969			−0.844847	−	0.535007i	$-0.820309\pi$
$521$	−1.24497e11			−1.68969			−0.844847	+	0.535007i	$0.820309\pi$
$522$		0			0
$523$			4.47960e10i			0.598733i	0.954138	+	0.299366i	$0.0967753\pi$
$523$			4.47960e10i			0.598733i	−0.954138	+	0.299366i	$0.903225\pi$
$524$	7.17254e10	−	5.07932e10i	0.951367	−	0.673722i
$525$		0			0
$526$	−3.56142e10	−	1.84194e10i	−0.465244	−	0.240621i
$527$		−	5.19686e10i		−	0.673749i
$528$		0			0
$529$	4.93792e9			0.0630553
$530$	1.13069e10	−	2.18622e10i	0.143298	−	0.277070i
$531$		0			0
$532$	2.66735e10	+	3.76658e10i	0.332992	+	0.470220i
$533$	−1.18964e11			−1.47404
$534$		0			0
$535$		−	2.15135e10i		−	0.262601i
$536$	−2.19274e9	−	1.56875e10i	−0.0265661	−	0.190061i
$537$		0			0
$538$	−2.66700e9	+	5.15670e9i	−0.0318342	+	0.0615520i
$539$			1.08144e11i			1.28129i
$540$		0			0
$541$	−8.68526e10			−1.01390			−0.506948	−	0.861977i	$-0.669226\pi$
$541$	−8.68526e10			−1.01390			−0.506948	+	0.861977i	$0.669226\pi$
$542$	1.50164e11	+	7.76638e10i	1.74008	+	0.899957i
$543$		0			0
$544$	−3.14829e10	−	3.34536e10i	−0.359483	−	0.381985i
$545$	−1.20044e9			−0.0136068
$546$		0			0
$547$		−	1.65768e11i		−	1.85162i	−0.377993	−	0.925808i	$-0.623386\pi$
$547$		−	1.65768e11i		−	1.85162i	0.377993	−	0.925808i	$-0.376614\pi$
$548$	3.01133e10	+	4.25232e10i	0.333916	+	0.471524i
$549$		0			0
$550$	−1.77312e10	−	9.17045e9i	−0.193771	−	0.100217i
$551$			6.75124e10i			0.732448i
$552$		0			0
$553$	−1.88886e11			−2.01976
$554$	−1.00130e10	+	1.93603e10i	−0.106298	+	0.205529i
$555$		0			0
$556$	5.25025e10	−	3.71803e10i	0.549390	−	0.389057i
$557$	9.73769e10			1.01166			0.505831	−	0.862633i	$-0.331186\pi$
$557$	9.73769e10			1.01166			0.505831	+	0.862633i	$0.331186\pi$
$558$		0			0
$559$			6.91995e10i			0.708689i
$560$	−6.11791e10	−	2.15333e10i	−0.622087	−	0.218957i
$561$		0			0
$562$	2.21608e10	−	4.28484e10i	0.222147	−	0.429525i
$563$			1.96004e9i			0.0195088i	0.999952	+	0.00975440i	$0.00310497\pi$
$563$			1.96004e9i			0.0195088i	−0.999952	+	0.00975440i	$0.996895\pi$
$564$		0			0
$565$	6.54913e10			0.642673
$566$	−1.96435e10	−	1.01595e10i	−0.191405	−	0.0989934i
$567$		0			0
$568$	1.82408e10	+	1.30500e11i	0.175247	+	1.25377i
$569$	−7.88598e10			−0.752327			−0.376164	−	0.926553i	$-0.622757\pi$
$569$	−7.88598e10			−0.752327			−0.376164	+	0.926553i	$0.622757\pi$
$570$		0			0
$571$			5.71331e10i			0.537457i	0.963216	+	0.268728i	$0.0866034\pi$
$571$			5.71331e10i			0.537457i	−0.963216	+	0.268728i	$0.913397\pi$
$572$	8.06617e10	−	5.71216e10i	0.753500	−	0.533601i
$573$		0			0
$574$	2.47608e11	+	1.28061e11i	2.28096	+	1.17970i
$575$		−	2.11621e10i		−	0.193592i
$576$		0			0
$577$	1.51459e11			1.36644			0.683221	−	0.730212i	$-0.260579\pi$
$577$	1.51459e11			1.36644			0.683221	+	0.730212i	$0.260579\pi$
$578$	−3.71659e10	+	7.18610e10i	−0.332992	+	0.643845i
$579$		0			0
$580$	−5.48288e10	−	7.74241e10i	−0.484503	−	0.684170i
$581$	2.20506e10			0.193516
$582$		0			0
$583$		−	8.78922e10i		−	0.760810i
$584$	−7.76274e10	+	1.08505e10i	−0.667365	+	0.0932817i
$585$		0			0
$586$	−4.31274e10	+	8.33875e10i	−0.365732	+	0.707148i
$587$			1.33645e11i			1.12564i	0.826580	+	0.562819i	$0.190283\pi$
$587$			1.33645e11i			1.12564i	−0.826580	+	0.562819i	$0.809717\pi$
$588$		0			0
$589$	−6.04015e10			−0.501865
$590$	2.65693e10	+	1.37414e10i	0.219266	+	0.113403i
$591$		0			0
$592$	−6.46460e10	+	1.83668e11i	−0.526326	+	1.49536i
$593$	1.58419e11			1.28112			0.640558	−	0.767910i	$-0.278703\pi$
$593$	1.58419e11			1.28112			0.640558	+	0.767910i	$0.278703\pi$
$594$		0			0
$595$		−	4.33568e10i		−	0.345931i
$596$	1.13185e11	+	1.59829e11i	0.897020	+	1.26669i
$597$		0			0
$598$	9.30690e10	+	4.81346e10i	0.727781	+	0.376403i
$599$			4.31245e10i			0.334978i	0.985874	+	0.167489i	$0.0535659\pi$
$599$			4.31245e10i			0.334978i	−0.985874	+	0.167489i	$0.946434\pi$
$600$		0			0
$601$	4.15092e10			0.318160			0.159080	−	0.987266i	$-0.449147\pi$
$601$	4.15092e10			0.318160			0.159080	+	0.987266i	$0.449147\pi$
$602$	7.44909e10	−	1.44029e11i	0.567175	−	1.09664i
$603$		0			0
$604$	−1.07089e11	+	7.58363e10i	−0.804630	+	0.569809i
$605$	−1.13696e10			−0.0848637
$606$		0			0
$607$			2.83174e10i			0.208592i	0.994546	+	0.104296i	$0.0332590\pi$
$607$			2.83174e10i			0.208592i	−0.994546	+	0.104296i	$0.966741\pi$
$608$	−3.88821e10	+	3.65916e10i	−0.284535	+	0.267773i
$609$		0			0
$610$	−5.14742e9	+	9.95262e9i	−0.0371766	+	0.0718816i
$611$		−	3.06954e8i		−	0.00220246i
$612$		0			0
$613$	2.40024e11			1.69986			0.849928	−	0.526899i	$-0.176645\pi$
$613$	2.40024e11			1.69986			0.849928	+	0.526899i	$0.176645\pi$
$614$	8.23410e10	+	4.25861e10i	0.579352	+	0.299636i
$615$		0			0
$616$	−2.29376e11	+	3.20613e10i	−1.59303	+	0.222668i
$617$	1.16795e10			0.0805904			0.0402952	−	0.999188i	$-0.487170\pi$
$617$	1.16795e10			0.0805904			0.0402952	+	0.999188i	$0.487170\pi$
$618$		0			0
$619$			2.19401e11i			1.49443i	0.664583	+	0.747215i	$0.268609\pi$
$619$			2.19401e11i			1.49443i	−0.664583	+	0.747215i	$0.731391\pi$
$620$	6.92693e10	−	4.90539e10i	0.468785	−	0.331976i
$621$		0			0
$622$	−1.18989e11	−	6.15404e10i	−0.794963	−	0.411149i
$623$		−	1.35723e11i		−	0.900948i
$624$		0			0
$625$	6.10352e9			0.0400000
$626$	9.02396e10	−	1.74480e11i	0.587624	−	1.13618i
$627$		0			0
$628$	−1.73057e11	−	2.44375e11i	−1.11263	−	1.57115i
$629$	−1.30163e11			−0.831544
$630$		0			0
$631$			2.35335e10i			0.148446i	0.997242	+	0.0742230i	$0.0236477\pi$
$631$			2.35335e10i			0.148446i	−0.997242	+	0.0742230i	$0.976352\pi$
$632$	−3.02484e10	−	2.16406e11i	−0.189598	−	1.35644i
$633$		0			0
$634$	1.01759e11	−	1.96752e11i	0.629817	−	1.21776i
$635$		−	8.22718e10i		−	0.506006i
$636$		0			0
$637$	1.63715e11			0.994332
$638$	−3.00920e11	−	1.55634e11i	−1.81622	−	0.939336i
$639$		0			0
$640$	1.48734e10	−	7.35410e10i	0.0886521	−	0.438339i
$641$	8.47231e10			0.501845			0.250923	−	0.968007i	$-0.419266\pi$
$641$	8.47231e10			0.501845			0.250923	+	0.968007i	$0.419266\pi$
$642$		0			0
$643$		−	2.37102e11i		−	1.38705i	−0.720435	−	0.693523i	$-0.756058\pi$
$643$		−	2.37102e11i		−	1.38705i	0.720435	−	0.693523i	$-0.243942\pi$
$644$	−1.41895e11	−	2.00371e11i	−0.824944	−	1.16491i
$645$		0			0
$646$	−3.17031e10	−	1.63966e10i	−0.182042	−	0.0941508i
$647$		−	2.88712e11i		−	1.64758i	−0.566892	−	0.823792i	$-0.691854\pi$
$647$		−	2.88712e11i		−	1.64758i	0.566892	−	0.823792i	$-0.308146\pi$
$648$		0			0
$649$	1.06816e11			0.602086
$650$	−1.38829e10	+	2.68427e10i	−0.0777724	+	0.150374i
$651$		0			0
$652$	1.83696e11	−	1.30086e11i	1.01650	−	0.719850i
$653$	−7.01205e10			−0.385649			−0.192824	−	0.981233i	$-0.561765\pi$
$653$	−7.01205e10			−0.385649			−0.192824	+	0.981233i	$0.561765\pi$
$654$		0			0
$655$			9.59600e10i			0.521345i
$656$	−1.07067e11	+	3.04192e11i	−0.578149	+	1.64260i
$657$		0			0
$658$	−3.30426e8	+	6.38884e8i	−0.00176267	+	0.00340815i
$659$			1.30280e11i			0.690774i	0.938460	+	0.345387i	$0.112252\pi$
$659$			1.30280e11i			0.690774i	−0.938460	+	0.345387i	$0.887748\pi$
$660$		0			0
$661$	−9.13098e10			−0.478312			−0.239156	−	0.970981i	$-0.576871\pi$
$661$	−9.13098e10			−0.478312			−0.239156	+	0.970981i	$0.576871\pi$
$662$	−1.09678e11	−	5.67246e10i	−0.571067	−	0.295352i
$663$		0			0
$664$	3.53121e9	+	2.52633e10i	0.0181656	+	0.129962i
$665$	−5.03923e10			−0.257678
$666$		0			0
$667$		−	3.59146e11i		−	1.81454i
$668$	−9.67962e10	+	6.85474e10i	−0.486130	+	0.344259i
$669$		0			0
$670$	1.53617e10	+	7.94493e9i	0.0762323	+	0.0394267i
$671$			4.00124e10i			0.197381i
$672$		0			0
$673$	−2.19105e11			−1.06805			−0.534026	−	0.845468i	$-0.679321\pi$
$673$	−2.19105e11			−1.06805			−0.534026	+	0.845468i	$0.679321\pi$
$674$	−1.08627e11	+	2.10031e11i	−0.526377	+	1.01776i
$675$		0			0
$676$	3.42117e10	+	4.83105e10i	0.163828	+	0.231342i
$677$	8.12354e10			0.386715			0.193357	−	0.981128i	$-0.438062\pi$
$677$	8.12354e10			0.386715			0.193357	+	0.981128i	$0.438062\pi$
$678$		0			0
$679$			2.78737e11i			1.31134i
$680$	4.96737e10	−	6.94320e9i	0.232322	−	0.0324731i
$681$		0			0
$682$	1.39241e11	−	2.69225e11i	0.643622	−	1.24445i
$683$			2.91761e11i			1.34074i	0.742028	+	0.670369i	$0.233864\pi$
$683$			2.91761e11i			1.34074i	−0.742028	+	0.670369i	$0.766136\pi$
$684$		0			0
$685$	−5.68909e10			−0.258393
$686$	−5.06688e10	−	2.62055e10i	−0.228794	−	0.118330i
$687$		0			0
$688$	1.76943e11	+	6.22789e10i	0.789732	+	0.277963i
$689$	−1.33057e11			−0.590421
$690$		0			0
$691$		−	1.35594e11i		−	0.594743i	−0.954762	−	0.297371i	$-0.903890\pi$
$691$		−	1.35594e11i		−	0.594743i	0.954762	−	0.297371i	$-0.0961100\pi$
$692$	6.97845e10	+	9.85430e10i	0.304323	+	0.429736i
$693$		0			0
$694$	−3.83574e11	−	1.98381e11i	−1.65353	−	0.855191i
$695$			7.02420e10i			0.301063i
$696$		0			0
$697$	−2.15577e11			−0.913420
$698$	1.48972e11	−	2.88040e11i	0.627601	−	1.21348i
$699$		0			0
$700$	5.77906e10	−	4.09251e10i	0.240694	−	0.170450i
$701$	−1.48441e11			−0.614725			−0.307363	−	0.951592i	$-0.599446\pi$
$701$	−1.48441e11			−0.614725			−0.307363	+	0.951592i	$0.599446\pi$
$702$		0			0
$703$			1.51285e11i			0.619404i
$704$	−7.34650e10	−	2.57661e11i	−0.299082	−	1.04896i
$705$		0			0
$706$	−6.92204e10	+	1.33839e11i	−0.278622	+	0.538720i
$707$			4.12314e10i			0.165025i
$708$		0			0
$709$	4.79726e11			1.89849			0.949245	−	0.314536i	$-0.101849\pi$
$709$	4.79726e11			1.89849			0.949245	+	0.314536i	$0.101849\pi$
$710$	−1.27789e11	−	6.60917e10i	−0.502877	−	0.260084i
$711$		0			0
$712$	1.55497e11	−	2.17347e10i	0.605064	−	0.0845735i
$713$	3.21318e11			1.24330
$714$		0			0
$715$			1.07916e11i			0.412915i
$716$	1.73563e11	−	1.22911e11i	0.660399	−	0.467669i
$717$		0			0
$718$	−4.69512e10	−	2.42828e10i	−0.176664	−	0.0913695i
$719$			4.02314e11i			1.50539i	0.658368	+	0.752696i	$0.271247\pi$
$719$			4.02314e11i			1.50539i	−0.658368	+	0.752696i	$0.728753\pi$
$720$		0			0
$721$	2.43801e11			0.902184
$722$	1.05776e11	−	2.04519e11i	0.389257	−	0.752635i
$723$		0			0
$724$	−9.16917e10	−	1.29478e11i	−0.333715	−	0.471241i
$725$	1.03584e11			0.374922
$726$		0			0
$727$			3.49293e11i			1.25041i	0.780461	+	0.625204i	$0.214984\pi$
$727$			3.49293e11i			1.25041i	−0.780461	+	0.625204i	$0.785016\pi$
$728$	4.85366e10	+	3.47245e11i	0.172800	+	1.23626i
$729$		0			0
$730$	3.93144e10	−	7.60151e10i	0.138440	−	0.267675i
$731$			1.25397e11i			0.439155i
$732$		0			0
$733$	−1.75651e11			−0.608464			−0.304232	−	0.952598i	$-0.598400\pi$
$733$	−1.75651e11			−0.608464			−0.304232	+	0.952598i	$0.598400\pi$
$734$	−1.62769e11	−	8.41829e10i	−0.560774	−	0.290028i
$735$		0			0
$736$	2.06841e11	−	1.94657e11i	0.704898	−	0.663373i
$737$	6.17583e10			0.209327
$738$		0			0
$739$		−	1.85701e11i		−	0.622640i	−0.950305	−	0.311320i	$-0.899229\pi$
$739$		−	1.85701e11i		−	0.622640i	0.950305	−	0.311320i	$-0.100771\pi$
$740$	−1.22863e11	−	1.73495e11i	−0.409726	−	0.578576i
$741$		0			0
$742$	2.76941e11	+	1.43232e11i	0.913632	+	0.472523i
$743$		−	2.85901e11i		−	0.938126i	−0.883165	−	0.469063i	$-0.844592\pi$
$743$		−	2.85901e11i		−	0.938126i	0.883165	−	0.469063i	$-0.155408\pi$
$744$		0			0
$745$	−2.13831e11			−0.694138
$746$	1.66445e11	−	3.21824e11i	0.537422	−	1.03911i
$747$		0			0
$748$	1.46168e11	−	1.03511e11i	0.466924	−	0.330658i
$749$	2.72524e11			0.865919
$750$		0			0
$751$		−	6.18679e11i		−	1.94494i	−0.233031	−	0.972469i	$-0.574864\pi$
$751$		−	6.18679e11i		−	1.94494i	0.233031	−	0.972469i	$-0.425136\pi$
$752$	−7.84881e8	−	2.76256e8i	−0.00245433	−	0.000863854i
$753$		0			0
$754$	−2.35609e11	+	4.55554e11i	−0.728964	+	1.40946i
$755$		−	1.43272e11i		−	0.440934i
$756$		0			0
$757$	9.34034e10			0.284433			0.142216	−	0.989836i	$-0.454577\pi$
$757$	9.34034e10			0.284433			0.142216	+	0.989836i	$0.454577\pi$
$758$	7.98360e10	+	4.12905e10i	0.241836	+	0.125076i
$759$		0			0
$760$	−8.06988e9	−	5.77343e10i	−0.0241887	−	0.173053i
$761$	3.21388e11			0.958276			0.479138	−	0.877740i	$-0.340949\pi$
$761$	3.21388e11			0.958276			0.479138	+	0.877740i	$0.340949\pi$
$762$		0			0
$763$		−	1.52067e10i		−	0.0448681i
$764$	8.85859e9	−	6.27332e9i	0.0260011	−	0.0184130i
$765$		0			0
$766$	5.83443e10	+	3.01752e10i	0.169466	+	0.0876467i
$767$		−	1.61706e11i		−	0.467245i
$768$		0			0
$769$	2.44957e10			0.0700461			0.0350231	−	0.999387i	$-0.488850\pi$
$769$	2.44957e10			0.0700461			0.0350231	+	0.999387i	$0.488850\pi$
$770$	1.16168e11	−	2.24612e11i	0.330462	−	0.638954i
$771$		0			0
$772$	−6.23087e10	−	8.79865e10i	−0.175420	−	0.247712i
$773$	−1.61194e11			−0.451472			−0.225736	−	0.974189i	$-0.572479\pi$
$773$	−1.61194e11			−0.451472			−0.225736	+	0.974189i	$0.572479\pi$
$774$		0			0
$775$			9.26739e10i			0.256892i
$776$	−3.19348e11	+	4.46372e10i	−0.880678	+	0.123098i
$777$		0			0
$778$	1.01185e10	−	1.95643e10i	0.0276184	−	0.0534006i
$779$			2.50558e11i			0.680392i
$780$		0			0
$781$	−5.13751e11			−1.38086
$782$	1.68651e11	+	8.72252e10i	0.450986	+	0.233246i
$783$		0			0
$784$	1.47342e11	−	4.18620e11i	0.389999	−	1.10804i
$785$	3.26945e11			0.860985
$786$		0			0
$787$			4.76190e11i			1.24131i	0.784083	+	0.620657i	$0.213134\pi$
$787$			4.76190e11i			1.24131i	−0.784083	+	0.620657i	$0.786866\pi$
$788$	−2.86938e11	−	4.05187e11i	−0.744189	−	1.05087i
$789$		0			0
$790$	2.11911e11	+	1.09599e11i	0.544059	+	0.281383i
$791$			8.29617e11i			2.11920i
$792$		0			0
$793$	6.05735e10			0.153176
$794$	−2.23600e11	+	4.32334e11i	−0.562586	+	1.08777i
$795$		0			0
$796$	4.41352e10	−	3.12549e10i	0.109934	−	0.0778512i
$797$	1.59422e11			0.395107			0.197553	−	0.980292i	$-0.436700\pi$
$797$	1.59422e11			0.395107			0.197553	+	0.980292i	$0.436700\pi$
$798$		0			0
$799$		−	5.56235e8i		−	0.00136481i
$800$	5.61424e10	+	5.96567e10i	0.137066	+	0.145646i
$801$		0			0
$802$	1.43677e11	−	2.77801e11i	0.347287	−	0.671486i
$803$		−	3.05603e11i		−	0.735013i
$804$		0			0
$805$	2.68072e11			0.638364
$806$	−4.07572e11	−	2.10793e11i	−0.965748	−	0.499478i
$807$		0			0
$808$	−4.72386e10	+	6.60283e9i	−0.110829	+	0.0154912i
$809$	4.86253e11			1.13519			0.567594	−	0.823308i	$-0.307874\pi$
$809$	4.86253e11			1.13519			0.567594	+	0.823308i	$0.307874\pi$
$810$		0			0
$811$			3.39760e11i			0.785396i	0.919667	+	0.392698i	$0.128458\pi$
$811$			3.39760e11i			0.785396i	−0.919667	+	0.392698i	$0.871542\pi$
$812$	9.80776e11	−	6.94548e11i	2.25603	−	1.59764i
$813$		0			0
$814$	−6.74315e11	−	3.48751e11i	−1.53591	−	0.794360i
$815$			2.45763e11i			0.557039i
$816$		0			0
$817$	1.45745e11			0.327120
$818$	−3.21553e11	+	6.21729e11i	−0.718191	+	1.38863i
$819$		0			0
$820$	−2.03486e11	−	2.87344e11i	−0.450069	−	0.635545i
$821$	−6.74268e11			−1.48409			−0.742044	−	0.670351i	$-0.766144\pi$
$821$	−6.74268e11			−1.48409			−0.742044	+	0.670351i	$0.766144\pi$
$822$		0			0
$823$		−	3.11660e11i		−	0.679332i	−0.940546	−	0.339666i	$-0.889686\pi$
$823$		−	3.11660e11i		−	0.679332i	0.940546	−	0.339666i	$-0.110314\pi$
$824$	3.90426e10	+	2.79322e11i	0.0846896	+	0.605894i
$825$		0			0
$826$	−1.74071e11	+	3.36569e11i	−0.373943	+	0.723026i
$827$			3.10210e11i			0.663183i	0.943423	+	0.331592i	$0.107586\pi$
$827$			3.10210e11i			0.663183i	−0.943423	+	0.331592i	$0.892414\pi$
$828$		0			0
$829$	−3.09076e11			−0.654406			−0.327203	−	0.944954i	$-0.606106\pi$
$829$	−3.09076e11			−0.654406			−0.327203	+	0.944954i	$0.606106\pi$
$830$	−2.47386e10	−	1.27946e10i	−0.0521270	−	0.0269597i
$831$		0			0
$832$	−3.90065e11	+	1.11216e11i	−0.814035	+	0.232100i
$833$	2.96670e11			0.616160
$834$		0			0
$835$		−	1.29502e11i		−	0.266397i
$836$	−1.20307e11	−	1.69887e11i	−0.246302	−	0.347804i
$837$		0			0
$838$	2.74450e11	+	1.41943e11i	0.556528	+	0.287832i
$839$		−	5.22492e11i		−	1.05446i	−0.849722	−	0.527232i	$-0.823230\pi$
$839$		−	5.22492e11i		−	1.05446i	0.849722	−	0.527232i	$-0.176770\pi$
$840$		0			0
$841$	1.25770e12			2.51416
$842$	−2.68684e11	+	5.19504e11i	−0.534556	+	1.03357i
$843$		0			0
$844$	4.20775e11	−	2.97977e11i	0.829240	−	0.587236i
$845$	−6.46336e10			−0.126774
$846$		0			0
$847$		−	1.44025e11i		−	0.279836i
$848$	−1.19750e11	+	3.40227e11i	−0.231576	+	0.657939i
$849$		0			0
$850$	−2.51573e10	+	4.86420e10i	−0.0481934	+	0.0931828i
$851$		−	8.04790e11i		−	1.53449i
$852$		0			0
$853$	−5.25270e11			−0.992171			−0.496086	−	0.868274i	$-0.665230\pi$
$853$	−5.25270e11			−0.992171			−0.496086	+	0.868274i	$0.665230\pi$
$854$	−1.26076e11	−	6.52053e10i	−0.237028	−	0.122589i
$855$		0			0
$856$	4.36422e10	+	3.12230e11i	0.0812853	+	0.581539i
$857$	−3.18270e11			−0.590028			−0.295014	−	0.955493i	$-0.595324\pi$
$857$	−3.18270e11			−0.590028			−0.295014	+	0.955493i	$0.595324\pi$
$858$		0			0
$859$			8.61467e11i			1.58222i	0.611676	+	0.791108i	$0.290496\pi$
$859$			8.61467e11i			1.58222i	−0.611676	+	0.791108i	$0.709504\pi$
$860$	−1.67143e11	+	1.18364e11i	−0.305558	+	0.216385i
$861$		0			0
$862$	−5.66579e11	−	2.93031e11i	−1.02620	−	0.530742i
$863$			1.40931e11i			0.254075i	0.991898	+	0.127038i	$0.0405469\pi$
$863$			1.40931e11i			0.254075i	−0.991898	+	0.127038i	$0.959453\pi$
$864$		0			0
$865$	−1.31839e11			−0.235493
$866$	2.36357e11	−	4.57000e11i	0.420239	−	0.812539i
$867$		0			0
$868$	6.21394e11	+	8.77474e11i	1.09468	+	1.54581i
$869$	8.51945e11			1.49394
$870$		0			0
$871$		−	9.34940e10i		−	0.162447i
$872$	1.74223e10	−	2.43522e9i	0.0301328	−	0.00421185i
$873$		0			0
$874$	1.01379e11	−	1.96018e11i	0.173741	−	0.335932i
$875$			7.73168e10i			0.131899i
$876$		0			0
$877$	−4.00362e11			−0.676790			−0.338395	−	0.941004i	$-0.609884\pi$
$877$	−4.00362e11			−0.676790			−0.338395	+	0.941004i	$0.609884\pi$
$878$	3.86582e11	+	1.99937e11i	0.650525	+	0.336447i
$879$		0			0
$880$	2.75940e11	+	9.71231e10i	0.460134	+	0.161954i
$881$	−4.94890e11			−0.821496			−0.410748	−	0.911749i	$-0.634732\pi$
$881$	−4.94890e11			−0.821496			−0.410748	+	0.911749i	$0.634732\pi$
$882$		0			0
$883$			7.88039e11i			1.29630i	0.761513	+	0.648149i	$0.224457\pi$
$883$			7.88039e11i			1.29630i	−0.761513	+	0.648149i	$0.775543\pi$
$884$	−1.56701e11	−	2.21279e11i	−0.256604	−	0.362353i
$885$		0			0
$886$	1.87919e11	+	9.71903e10i	0.304955	+	0.157720i
$887$			2.78785e10i			0.0450375i	0.999746	+	0.0225188i	$0.00716855\pi$
$887$			2.78785e10i			0.0450375i	−0.999746	+	0.0225188i	$0.992831\pi$
$888$		0			0
$889$	1.04218e12			1.66854
$890$	−7.87514e10	+	1.52267e11i	−0.125516	+	0.242687i
$891$		0			0
$892$	−1.89461e11	+	1.34169e11i	−0.299268	+	0.211930i
$893$	−6.46496e8			−0.00101662
$894$		0			0
$895$			2.32207e11i			0.361895i
$896$	9.31587e11	+	1.88410e11i	1.44541	+	0.292328i
$897$		0			0
$898$	−2.07980e11	+	4.02133e11i	−0.319828	+	0.618392i
$899$			1.57279e12i			2.40786i
$900$		0			0
$901$	−2.41114e11			−0.365868
$902$	−1.11680e12	−	5.77603e11i	−1.68714	−	0.872576i
$903$		0			0
$904$	−9.50489e11	+	1.32856e11i	−1.42322	+	0.198933i
$905$	1.73226e11			0.258238
$906$		0			0
$907$		−	5.94476e11i		−	0.878426i	−0.898383	−	0.439213i	$-0.855257\pi$
$907$		−	5.94476e11i		−	0.878426i	0.898383	−	0.439213i	$-0.144743\pi$
$908$	−1.94560e10	+	1.37780e10i	−0.0286226	+	0.0202695i
$909$		0			0
$910$	−3.40033e11	−	1.75862e11i	−0.495856	−	0.256453i
$911$		−	5.11180e11i		−	0.742165i	−0.928600	−	0.371082i	$-0.878987\pi$
$911$		−	5.11180e11i		−	0.742165i	0.928600	−	0.371082i	$-0.121013\pi$
$912$		0			0
$913$	−9.94564e10			−0.143136
$914$	5.80438e11	−	1.12229e12i	0.831708	−	1.60812i
$915$		0			0
$916$	7.66137e10	+	1.08187e11i	0.108824	+	0.153671i
$917$	−1.21558e12			−1.71912
$918$		0			0
$919$			7.89745e11i			1.10720i	0.832784	+	0.553598i	$0.186746\pi$
$919$			7.89745e11i			1.10720i	−0.832784	+	0.553598i	$0.813254\pi$
$920$	4.29294e10	+	3.07130e11i	0.0599244	+	0.428717i
$921$		0			0
$922$	−1.93835e11	+	3.74783e11i	−0.268230	+	0.518628i
$923$			7.77751e11i			1.07160i
$924$		0			0
$925$	2.32116e11			0.317057
$926$	3.89801e11	+	2.01602e11i	0.530151	+	0.274190i
$927$		0			0
$928$	9.52804e11	+	1.01245e12i	1.28473	+	1.36515i
$929$	−1.28241e12			−1.72172			−0.860862	−	0.508839i	$-0.830075\pi$
$929$	−1.28241e12			−1.72172			−0.860862	+	0.508839i	$0.830075\pi$
$930$		0			0
$931$		−	3.44811e11i		−	0.458968i
$932$	−1.78156e11	−	2.51575e11i	−0.236122	−	0.333429i
$933$		0			0
$934$	−1.17108e12	−	6.05675e11i	−1.53886	−	0.795888i
$935$			1.95555e11i			0.255872i
$936$		0			0
$937$	−4.16365e11			−0.540152			−0.270076	−	0.962839i	$-0.587049\pi$
$937$	−4.16365e11			−0.540152			−0.270076	+	0.962839i	$0.587049\pi$
$938$	−1.00643e11	+	1.94595e11i	−0.130009	+	0.251374i
$939$		0			0
$940$	7.41409e8	−	5.25038e8i	0.000949613	−	0.000672480i
$941$	1.33006e12			1.69634			0.848171	−	0.529723i	$-0.177704\pi$
$941$	1.33006e12			1.69634			0.848171	+	0.529723i	$0.177704\pi$
$942$		0			0
$943$		−	1.33290e12i		−	1.68558i
$944$	−4.13482e11	−	1.45534e11i	−0.520677	−	0.183264i
$945$		0			0
$946$	−3.35981e11	+	6.49625e11i	−0.419518	+	0.811145i
$947$		−	1.36285e11i		−	0.169453i	−0.996404	−	0.0847265i	$-0.972998\pi$
$947$		−	1.36285e11i		−	0.169453i	0.996404	−	0.0847265i	$-0.0270017\pi$
$948$		0			0
$949$	−4.62642e11			−0.570401
$950$	5.65352e10	+	2.92396e10i	0.0694104	+	0.0358985i
$951$		0			0
$952$	8.79536e10	+	6.29246e11i	0.107079	+	0.766078i
$953$	−1.22326e12			−1.48302			−0.741509	−	0.670943i	$-0.765889\pi$
$953$	−1.22326e12			−1.48302			−0.741509	+	0.670943i	$0.765889\pi$
$954$		0			0
$955$			1.18517e10i			0.0142485i
$956$	4.43093e11	−	3.13782e11i	0.530473	−	0.375661i
$957$		0			0
$958$	−1.82112e11	−	9.41868e10i	−0.216210	−	0.111822i
$959$		−	7.20671e11i		−	0.852045i
$960$		0			0
$961$	−5.54240e11			−0.649837
$962$	−5.27963e11	+	1.02083e12i	−0.616457	+	1.19193i
$963$		0			0
$964$	1.01411e11	+	1.43203e11i	0.117430	+	0.165823i
$965$	1.17715e11			0.135745
$966$		0			0
$967$		−	7.99217e10i		−	0.0914027i	−0.998955	−	0.0457014i	$-0.985448\pi$
$967$		−	7.99217e10i		−	0.0914027i	0.998955	−	0.0457014i	$-0.0145523\pi$
$968$	1.65009e11	−	2.30643e10i	0.187934	−	0.0262687i
$969$		0			0
$970$	1.61734e11	−	3.12715e11i	0.182690	−	0.353233i
$971$			3.43166e11i			0.386036i	0.981195	+	0.193018i	$0.0618276\pi$
$971$			3.43166e11i			0.386036i	−0.981195	+	0.193018i	$0.938172\pi$
$972$		0			0
$973$	−8.89796e11			−0.992748
$974$	3.22874e11	+	1.66988e11i	0.358754	+	0.185545i
$975$		0			0
$976$	5.45156e10	−	1.54886e11i	0.0600789	−	0.170692i
$977$	2.96831e11			0.325785			0.162893	−	0.986644i	$-0.447918\pi$
$977$	2.96831e11			0.325785			0.162893	+	0.986644i	$0.447918\pi$
$978$		0			0
$979$			6.12158e11i			0.666397i
$980$	2.80031e11	+	3.95434e11i	0.303600	+	0.428716i
$981$		0			0
$982$	−1.23701e12	−	6.39771e11i	−1.33023	−	0.687984i
$983$		−	9.12247e11i		−	0.977009i	−0.872561	−	0.488504i	$-0.837543\pi$
$983$		−	9.12247e11i		−	0.977009i	0.872561	−	0.488504i	$-0.162457\pi$
$984$		0			0
$985$	5.42091e11			0.575873
$986$	−4.26949e11	+	8.25513e11i	−0.451719	+	0.873407i
$987$		0			0
$988$	−2.57186e11	+	1.82130e11i	−0.269911	+	0.191140i
$989$	−7.75323e11			−0.810396
$990$		0			0
$991$			9.63646e11i			0.999132i	0.866276	+	0.499566i	$0.166507\pi$
$991$			9.63646e11i			0.999132i	−0.866276	+	0.499566i	$0.833493\pi$
$992$	−9.05808e11	+	8.52449e11i	−0.935383	+	0.880281i
$993$		0			0
$994$	8.37223e11	−	1.61878e12i	0.857621	−	1.65822i
$995$			5.90475e10i			0.0602434i
$996$		0			0
$997$	−1.13678e12			−1.15052			−0.575261	−	0.817970i	$-0.695100\pi$
$997$	−1.13678e12			−1.15052			−0.575261	+	0.817970i	$0.695100\pi$
$998$	1.91819e11	+	9.92073e10i	0.193361	+	0.100005i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.9.c.a.91.11		16
3.2	odd	2		20.9.b.a.11.6	yes	16
4.3	odd	2	inner	180.9.c.a.91.12		16
12.11	even	2		20.9.b.a.11.5	✓	16
15.2	even	4		100.9.d.c.99.5		32
15.8	even	4		100.9.d.c.99.28		32
15.14	odd	2		100.9.b.d.51.11		16
24.5	odd	2		320.9.b.d.191.14		16
24.11	even	2		320.9.b.d.191.3		16
60.23	odd	4		100.9.d.c.99.6		32
60.47	odd	4		100.9.d.c.99.27		32
60.59	even	2		100.9.b.d.51.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.5	✓	16	12.11	even	2
20.9.b.a.11.6	yes	16	3.2	odd	2
100.9.b.d.51.11		16	15.14	odd	2
100.9.b.d.51.12		16	60.59	even	2
100.9.d.c.99.5		32	15.2	even	4
100.9.d.c.99.6		32	60.23	odd	4
100.9.d.c.99.27		32	60.47	odd	4
100.9.d.c.99.28		32	15.8	even	4
180.9.c.a.91.11		16	1.1	even	1	trivial
180.9.c.a.91.12		16	4.3	odd	2	inner
320.9.b.d.191.3		16	24.11	even	2
320.9.b.d.191.14		16	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

\(f(q)\)	\(=\)	\(q+(7.35022 - 14.2118i) q^{2} +(-147.949 - 208.919i) q^{4} +279.508 q^{5} +3540.70i q^{7} +(-4056.56 + 567.011i) q^{8} +(2054.45 - 3972.31i) q^{10} -15969.8i q^{11} -24176.2 q^{13} +(50319.6 + 26024.9i) q^{14} +(-21758.4 + 61818.6i) q^{16} -43810.0 q^{17} +50919.1i q^{19} +(-41352.9 - 58394.7i) q^{20} +(-226960. - 117382. i) q^{22} -270875. i q^{23} +78125.0 q^{25} +(-177701. + 343587. i) q^{26} +(739720. - 523841. i) q^{28} +1.32588e6 q^{29} +1.18623e6i q^{31} +(718623. + 763605. i) q^{32} +(-322013. + 622618. i) q^{34} +989655. i q^{35} +2.97108e6 q^{37} +(723650. + 374266. i) q^{38} +(-1.13384e6 + 158484. i) q^{40} +4.92072e6 q^{41} -2.86229e6i q^{43} +(-3.33641e6 + 2.36272e6i) q^{44} +(-3.84961e6 - 1.99099e6i) q^{46} +12696.5i q^{47} -6.77174e6 q^{49} +(574236. - 1.11029e6i) q^{50} +(3.57684e6 + 5.05088e6i) q^{52} +5.50364e6 q^{53} -4.46371e6i q^{55} +(-2.00761e6 - 1.43631e7i) q^{56} +(9.74547e6 - 1.88430e7i) q^{58} +6.68863e6i q^{59} -2.50550e6 q^{61} +(1.68584e7 + 8.71902e6i) q^{62} +(1.61342e7 - 4.60023e6i) q^{64} -6.75746e6 q^{65} +3.86718e6i q^{67} +(6.48163e6 + 9.15275e6i) q^{68} +(1.40647e7 + 7.27418e6i) q^{70} -3.21701e7i q^{71} +1.91362e7 q^{73} +(2.18381e7 - 4.22243e7i) q^{74} +(1.06380e7 - 7.53341e6i) q^{76} +5.65444e7 q^{77} +5.33471e7i q^{79} +(-6.08166e6 + 1.72788e7i) q^{80} +(3.61683e7 - 6.99321e7i) q^{82} -6.22776e6i q^{83} -1.22453e7 q^{85} +(-4.06782e7 - 2.10385e7i) q^{86} +(9.05507e6 + 6.47827e7i) q^{88} -3.83322e7 q^{89} -8.56008e7i q^{91} +(-5.65909e7 + 4.00755e7i) q^{92} +(180440. + 93322.2i) q^{94} +1.42323e7i q^{95} +7.87237e7 q^{97} +(-4.97738e7 + 9.62384e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 52 q^{4} + 14184 q^{8} + 8750 q^{10} + 51392 q^{13} - 68472 q^{14} - 81424 q^{16} - 27552 q^{17} - 172500 q^{20} - 389120 q^{22} + 1250000 q^{25} - 1037124 q^{26} + 1288520 q^{28} - 2764896 q^{29}+ \cdots + 285387714 q^{98}+O(q^{100}) \) 16 * q - 6 * q^2 - 52 * q^4 + 14184 * q^8 + 8750 * q^10 + 51392 * q^13 - 68472 * q^14 - 81424 * q^16 - 27552 * q^17 - 172500 * q^20 - 389120 * q^22 + 1250000 * q^25 - 1037124 * q^26 + 1288520 * q^28 - 2764896 * q^29 + 4379904 * q^32 + 3793964 * q^34 + 9009472 * q^37 + 3087360 * q^38 + 385000 * q^40 + 8576448 * q^41 - 16921200 * q^44 - 7974152 * q^46 - 32803600 * q^49 - 468750 * q^50 + 6679352 * q^52 - 2452032 * q^53 - 34134768 * q^56 + 52156572 * q^58 + 8371712 * q^61 - 1290000 * q^62 - 47543872 * q^64 - 9060000 * q^65 - 16095192 * q^68 + 10500000 * q^70 + 61907232 * q^73 + 138210876 * q^74 + 2570400 * q^76 + 156997440 * q^77 - 37590000 * q^80 + 83921012 * q^82 - 106960000 * q^85 + 101724672 * q^86 + 44728480 * q^88 - 106647456 * q^89 + 13876200 * q^92 + 55264632 * q^94 + 171851232 * q^97 + 285387714 * q^98

Introduction

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