LMFDB - Embedded newform 81.10.e.a.10.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,10,Mod(10,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("81.10");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	81.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$41.7179027293$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			10.16
Character	$\chi$	$=$	81.10
Dual form			81.10.e.a.73.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50531 + 8.53705i) q^{2} +(410.507 - 149.412i) q^{4} +(-1797.12 - 1507.96i) q^{5} +(1.39853 + 0.509023i) q^{7} +(4112.68 + 7123.37i) q^{8} +(10168.3 - 17612.1i) q^{10} +(19727.7 - 16553.5i) q^{11} +(6493.07 - 36824.0i) q^{13} +(-2.24033 + 12.7056i) q^{14} +(116718. - 97938.4i) q^{16} +(96230.1 - 166676. i) q^{17} +(4946.96 + 8568.39i) q^{19} +(-963040. - 350518. i) q^{20} +(171015. + 143498. i) q^{22} +(-2.26265e6 + 823538. i) q^{23} +(616533. + 3.49653e6i) q^{25} +324143. q^{26} +650.162 q^{28} +(-501702. - 2.84529e6i) q^{29} +(-5.78701e6 + 2.10630e6i) q^{31} +(4.23791e6 + 3.55603e6i) q^{32} +(1.56777e6 + 570623. i) q^{34} +(-1745.74 - 3023.71i) q^{35} +(8.45078e6 - 1.46372e7i) q^{37} +(-65702.1 + 55130.6i) q^{38} +(3.35080e6 - 1.90033e7i) q^{40} +(-5.31407e6 + 3.01376e7i) q^{41} +(-2.68009e7 + 2.24886e7i) q^{43} +(5.62507e6 - 9.74291e6i) q^{44} +(-1.04366e7 - 1.80767e7i) q^{46} +(-2.42993e7 - 8.84423e6i) q^{47} +(-3.09127e7 - 2.59388e7i) q^{49} +(-2.89220e7 + 1.05267e7i) q^{50} +(-2.83652e6 - 1.60867e7i) q^{52} -7.34002e7 q^{53} -6.04152e7 q^{55} +(2125.75 + 12055.7i) q^{56} +(2.35352e7 - 8.56610e6i) q^{58} +(-1.86320e7 - 1.56341e7i) q^{59} +(-6.94530e6 - 2.52788e6i) q^{61} +(-2.66928e7 - 4.62334e7i) q^{62} +(1.50269e7 - 2.60273e7i) q^{64} +(-6.71981e7 + 5.63859e7i) q^{65} +(9.62082e6 - 5.45624e7i) q^{67} +(1.45998e7 - 8.27995e7i) q^{68} +(23185.7 - 19455.1i) q^{70} +(-4.15044e7 + 7.18877e7i) q^{71} +(-1.66337e7 - 2.88104e7i) q^{73} +(1.37679e8 + 5.01112e7i) q^{74} +(3.31099e6 + 2.77825e6i) q^{76} +(36016.0 - 13108.7i) q^{77} +(-1.07586e8 - 6.10150e8i) q^{79} -3.57445e8 q^{80} -2.65285e8 q^{82} +(4.60878e7 + 2.61377e8i) q^{83} +(-4.24278e8 + 1.54424e8i) q^{85} +(-2.32330e8 - 1.94948e8i) q^{86} +(1.99051e8 + 7.24485e7i) q^{88} +(-1.77344e7 - 3.07170e7i) q^{89} +(27825.1 - 48194.4i) q^{91} +(-8.05789e8 + 6.76137e8i) q^{92} +(3.89255e7 - 2.20758e8i) q^{94} +(4.03053e6 - 2.28583e7i) q^{95} +(-7.22738e8 + 6.06450e8i) q^{97} +(1.74908e8 - 3.02949e8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) $ 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	1.50531	+	8.53705i	0.0665260	+	0.377288i	0.999834	+	0.0182113i	$0.00579714\pi$
$2$	1.50531	+	8.53705i	0.0665260	+	0.377288i	−0.933308	+	0.359076i	$0.883092\pi$
$3$		0			0
$3$		0			0
$4$	410.507	−	149.412i	0.801772	−	0.291821i
$5$	−1797.12	−	1507.96i	−1.28591	−	1.07901i	−0.992400	−	0.123056i	$-0.960730\pi$
$5$	−1797.12	−	1507.96i	−1.28591	−	1.07901i	−0.293515	−	0.955954i	$-0.594825\pi$
$6$		0			0
$7$	1.39853	+	0.509023i	0.000220156	+	8.01303e-5i	0.342130	−	0.939653i	$-0.388852\pi$
$7$	1.39853	+	0.509023i	0.000220156	+	8.01303e-5i	−0.341910	+	0.939733i	$0.611074\pi$
$8$	4112.68	+	7123.37i	0.354993	+	0.614866i
$9$		0			0
$10$	10168.3	−	17612.1i	0.321551	−	0.556942i
$11$	19727.7	−	16553.5i	0.406265	−	0.340897i	−0.416644	−	0.909070i	$-0.636794\pi$
$11$	19727.7	−	16553.5i	0.406265	−	0.340897i	0.822909	+	0.568173i	$0.192349\pi$
$12$		0			0
$13$	6493.07	−	36824.0i	0.0630529	−	0.357591i	−0.936915	−	0.349558i	$-0.886332\pi$
$13$	6493.07	−	36824.0i	0.0630529	−	0.357591i	0.999968	−	0.00803312i	$-0.00255705\pi$
$14$	−2.24033	+	12.7056i	−1.55861e−5	+	8.83929e-5i
$15$		0			0
$16$	116718.	−	97938.4i	0.445246	−	0.373605i
$17$	96230.1	−	166676.i	0.279442	−	0.484007i	−0.691805	−	0.722085i	$-0.743184\pi$
$17$	96230.1	−	166676.i	0.279442	−	0.484007i	0.971246	+	0.238078i	$0.0765173\pi$
$18$		0			0
$19$	4946.96	+	8568.39i	0.00870859	+	0.0150837i	0.870347	−	0.492439i	$-0.163895\pi$
$19$	4946.96	+	8568.39i	0.00870859	+	0.0150837i	−0.861638	+	0.507523i	$0.830561\pi$
$20$	−963040.	−	350518.i	−1.34589	−	0.489864i
$21$		0			0
$22$	171015.	+	143498.i	0.155644	+	0.130600i
$23$	−2.26265e6	+	823538.i	−1.68594	+	0.613633i	−0.994105	−	0.108422i	$-0.965420\pi$
$23$	−2.26265e6	+	823538.i	−1.68594	+	0.613633i	−0.691837	+	0.722054i	$0.743198\pi$
$24$		0			0
$25$	616533.	+	3.49653e6i	0.315665	+	1.79022i
$26$	324143.			0.139109
$27$		0			0
$28$	650.162			0.000199899
$29$	−501702.	−	2.84529e6i	−0.131721	−	0.747026i	−0.977087	−	0.212839i	$-0.931729\pi$
$29$	−501702.	−	2.84529e6i	−0.131721	−	0.747026i	0.845366	−	0.534187i	$-0.179382\pi$
$30$		0			0
$31$	−5.78701e6	+	2.10630e6i	−1.12545	+	0.409631i	−0.836639	−	0.547755i	$-0.815483\pi$
$31$	−5.78701e6	+	2.10630e6i	−1.12545	+	0.409631i	−0.288813	+	0.957386i	$0.593261\pi$
$32$	4.23791e6	+	3.55603e6i	0.714458	+	0.599502i
$33$		0			0
$34$	1.56777e6	+	570623.i	0.201200	+	0.0732308i
$35$	−1745.74	−	3023.71i	−0.000196641	−	0.000340591i
$36$		0			0
$37$	8.45078e6	−	1.46372e7i	0.741292	−	1.28395i	−0.210616	−	0.977569i	$-0.567547\pi$
$37$	8.45078e6	−	1.46372e7i	0.741292	−	1.28395i	0.951907	−	0.306386i	$-0.0991198\pi$
$38$	−65702.1	+	55130.6i	−0.00511155	+	0.00428910i
$39$		0			0
$40$	3.35080e6	−	1.90033e7i	0.206956	−	1.17371i
$41$	−5.31407e6	+	3.01376e7i	−0.293697	+	1.66564i	0.378753	+	0.925498i	$0.376353\pi$
$41$	−5.31407e6	+	3.01376e7i	−0.293697	+	1.66564i	−0.672450	+	0.740142i	$0.734758\pi$
$42$		0			0
$43$	−2.68009e7	+	2.24886e7i	−1.19548	+	1.00312i	−0.195730	+	0.980658i	$0.562708\pi$
$43$	−2.68009e7	+	2.24886e7i	−1.19548	+	1.00312i	−0.999748	+	0.0224671i	$0.992848\pi$
$44$	5.62507e6	−	9.74291e6i	0.226251	−	0.391879i
$45$		0			0
$46$	−1.04366e7	−	1.80767e7i	−0.343675	−	0.595262i
$47$	−2.42993e7	−	8.84423e6i	−0.726363	−	0.264374i	−0.0477384	−	0.998860i	$-0.515201\pi$
$47$	−2.42993e7	−	8.84423e6i	−0.726363	−	0.264374i	−0.678624	+	0.734485i	$0.737424\pi$
$48$		0			0
$49$	−3.09127e7	−	2.59388e7i	−0.766044	−	0.642788i
$50$	−2.89220e7	+	1.05267e7i	−0.654429	+	0.238193i
$51$		0			0
$52$	−2.83652e6	−	1.60867e7i	−0.0537985	−	0.305107i
$53$	−7.34002e7			−1.27778			−0.638890	−	0.769298i	$-0.720606\pi$
$53$	−7.34002e7			−1.27778			−0.638890	+	0.769298i	$0.720606\pi$
$54$		0			0
$55$	−6.04152e7			−0.890254
$56$	2125.75	+	12055.7i	2.88845e−5	+	0.000163812i
$57$		0			0
$58$	2.35352e7	−	8.56610e6i	0.273081	−	0.0993933i
$59$	−1.86320e7	−	1.56341e7i	−0.200182	−	0.167973i	0.537186	−	0.843464i	$-0.319487\pi$
$59$	−1.86320e7	−	1.56341e7i	−0.200182	−	0.167973i	−0.737368	+	0.675491i	$0.763932\pi$
$60$		0			0
$61$	−6.94530e6	−	2.52788e6i	−0.0642254	−	0.0233761i	0.309708	−	0.950832i	$-0.399769\pi$
$61$	−6.94530e6	−	2.52788e6i	−0.0642254	−	0.0233761i	−0.373933	+	0.927456i	$0.621991\pi$
$62$	−2.66928e7	−	4.62334e7i	−0.229421	−	0.397368i
$63$		0			0
$64$	1.50269e7	−	2.60273e7i	0.111959	−	0.193918i
$65$	−6.71981e7	+	5.63859e7i	−0.466925	+	0.391797i
$66$		0			0
$67$	9.62082e6	−	5.45624e7i	0.0583278	−	0.330793i	−0.941655	−	0.336578i	$-0.890730\pi$
$67$	9.62082e6	−	5.45624e7i	0.0583278	−	0.330793i	0.999983	+	0.00578504i	$0.00184145\pi$
$68$	1.45998e7	−	8.27995e7i	0.0828050	−	0.469610i
$69$		0			0
$70$	23185.7	−	19455.1i	0.000115419	−	9.68482e-5i
$71$	−4.15044e7	+	7.18877e7i	−0.193835	+	0.335731i	−0.946518	−	0.322651i	$-0.895426\pi$
$71$	−4.15044e7	+	7.18877e7i	−0.193835	+	0.335731i	0.752683	+	0.658383i	$0.228759\pi$
$72$		0			0
$73$	−1.66337e7	−	2.88104e7i	−0.0685544	−	0.118740i	0.829711	−	0.558194i	$-0.188505\pi$
$73$	−1.66337e7	−	2.88104e7i	−0.0685544	−	0.118740i	−0.898265	+	0.439454i	$0.855172\pi$
$74$	1.37679e8	+	5.01112e7i	0.533735	+	0.194264i
$75$		0			0
$76$	3.31099e6	+	2.77825e6i	0.0113841	+	0.00955235i
$77$	36016.0	−	13108.7i	0.000116758	−	4.24964e-5i
$78$		0			0
$79$	−1.07586e8	−	6.10150e8i	−0.310766	−	1.76244i	−0.595038	−	0.803698i	$-0.702863\pi$
$79$	−1.07586e8	−	6.10150e8i	−0.310766	−	1.76244i	0.284272	−	0.958744i	$-0.408248\pi$
$80$	−3.57445e8			−0.975672
$81$		0			0
$82$	−2.65285e8			−0.647964
$83$	4.60878e7	+	2.61377e8i	0.106594	+	0.604527i	0.990572	+	0.136997i	$0.0437449\pi$
$83$	4.60878e7	+	2.61377e8i	0.106594	+	0.604527i	−0.883977	+	0.467530i	$0.845144\pi$
$84$		0			0
$85$	−4.24278e8	+	1.54424e8i	−0.881587	+	0.320871i
$86$	−2.32330e8	−	1.94948e8i	−0.457997	−	0.384305i
$87$		0			0
$88$	1.99051e8	+	7.24485e7i	0.353828	+	0.128783i
$89$	−1.77344e7	−	3.07170e7i	−0.0299614	−	0.0518947i	0.850656	−	0.525723i	$-0.176205\pi$
$89$	−1.77344e7	−	3.07170e7i	−0.0299614	−	0.0518947i	−0.880617	+	0.473828i	$0.842872\pi$
$90$		0			0
$91$	27825.1	−	48194.4i	4.25353e−5	−	7.36734e-5i
$92$	−8.05789e8	+	6.76137e8i	−1.17267	+	0.983987i
$93$		0			0
$94$	3.89255e7	−	2.20758e8i	0.0514232	−	0.291636i
$95$	4.03053e6	−	2.28583e7i	0.00507699	−	0.0287930i
$96$		0			0
$97$	−7.22738e8	+	6.06450e8i	−0.828912	+	0.695540i	−0.955041	−	0.296474i	$-0.904189\pi$
$97$	−7.22738e8	+	6.06450e8i	−0.828912	+	0.695540i	0.126129	+	0.992014i	$0.459745\pi$
$98$	1.74908e8	−	3.02949e8i	0.191554	−	0.331781i
$99$		0			0
$100$	7.75516e8	+	1.34323e9i	0.775516	+	1.34323i
$101$	2.43869e8	+	8.87610e7i	0.233190	+	0.0848743i	0.455972	−	0.889994i	$-0.349292\pi$
$101$	2.43869e8	+	8.87610e7i	0.233190	+	0.0848743i	−0.222782	+	0.974868i	$0.571514\pi$
$102$		0			0
$103$	−1.09636e9	−	9.19954e8i	−0.959810	−	0.805376i	0.0211122	−	0.999777i	$-0.493279\pi$
$103$	−1.09636e9	−	9.19954e8i	−0.959810	−	0.805376i	−0.980922	+	0.194401i	$0.937724\pi$
$104$	2.89015e8	−	1.05193e8i	0.242254	−	0.0881732i
$105$		0			0
$106$	−1.10490e8	−	6.26621e8i	−0.0850055	−	0.482090i
$107$	2.55715e9			1.88595			0.942973	−	0.332870i	$-0.108017\pi$
$107$	2.55715e9			1.88595			0.942973	+	0.332870i	$0.108017\pi$
$108$		0			0
$109$	2.09335e9			1.42044			0.710219	−	0.703981i	$-0.248596\pi$
$109$	2.09335e9			1.42044			0.710219	+	0.703981i	$0.248596\pi$
$110$	−9.09437e7	−	5.15767e8i	−0.0592251	−	0.335882i
$111$		0			0
$112$	213087.	−	77557.4i	0.000127961	−	4.65739e-5i
$113$	6.39797e8	+	5.36853e8i	0.369138	+	0.309744i	0.808421	−	0.588605i	$-0.200323\pi$
$113$	6.39797e8	+	5.36853e8i	0.369138	+	0.309744i	−0.439282	+	0.898349i	$0.644767\pi$
$114$		0			0
$115$	5.30812e9	+	1.93200e9i	2.83009	+	1.03007i
$116$	−6.31074e8	−	1.09305e9i	−0.323608	−	0.560506i
$117$		0			0
$118$	1.05422e8	−	1.82597e8i	0.0500568	−	0.0867009i
$119$	219423.	−	184117.i	0.000100304	−	8.41654e-5i
$120$		0			0
$121$	−2.94289e8	+	1.66900e9i	−0.124807	+	0.707818i
$122$	1.11258e7	−	6.30976e7i	0.00454687	−	0.0257866i
$123$		0			0
$124$	−2.06090e9	+	1.72930e9i	−0.782817	+	0.656862i
$125$	1.87366e9	−	3.24528e9i	0.686431	−	1.18893i
$126$		0			0
$127$	−7.80368e7	−	1.35164e8i	−0.0266185	−	0.0461045i	0.852409	−	0.522875i	$-0.175141\pi$
$127$	−7.80368e7	−	1.35164e8i	−0.0266185	−	0.0461045i	−0.879028	+	0.476771i	$0.841807\pi$
$128$	2.90648e9	+	1.05787e9i	0.957024	+	0.348328i
$129$		0			0
$130$	−5.82523e8	−	4.88795e8i	−0.178883	−	0.150100i
$131$	−2.88604e9	+	1.05043e9i	−0.856212	+	0.311636i	−0.732570	−	0.680691i	$-0.761679\pi$
$131$	−2.88604e9	+	1.05043e9i	−0.856212	+	0.311636i	−0.123641	+	0.992327i	$0.539457\pi$
$132$		0			0
$133$	2556.97	+	14501.3i	7.08586e−7	+	4.01859e-6i
$134$	4.80284e8			0.128685
$135$		0			0
$136$	1.58306e9			0.396799
$137$	−3.23605e8	−	1.83526e9i	−0.0784825	−	0.445097i	−0.998574	−	0.0533921i	$-0.982997\pi$
$137$	−3.23605e8	−	1.83526e9i	−0.0784825	−	0.445097i	0.920091	−	0.391704i	$-0.128114\pi$
$138$		0			0
$139$	−2.05612e9	+	7.48366e8i	−0.467177	+	0.170039i	−0.564873	−	0.825178i	$-0.691075\pi$
$139$	−2.05612e9	+	7.48366e8i	−0.467177	+	0.170039i	0.0976961	+	0.995216i	$0.468853\pi$
$140$	−1.16842e6	−	980420.i	−0.000257053	−	0.000215693i
$141$		0			0
$142$	−6.76186e8	−	2.46111e8i	−0.139562	−	0.0507965i
$143$	−4.81474e8	−	8.33938e8i	−0.0962855	−	0.166771i
$144$		0			0
$145$	−3.38898e9	+	5.86988e9i	−0.636667	+	1.10274i
$146$	2.20917e8	−	1.85371e8i	0.0402384	−	0.0337640i
$147$		0			0
$148$	1.28213e9	−	7.27132e9i	0.219662	−	1.24576i
$149$	−4.21626e8	+	2.39116e9i	−0.0700793	+	0.397439i	0.929510	+	0.368796i	$0.120230\pi$
$149$	−4.21626e8	+	2.39116e9i	−0.0700793	+	0.397439i	−0.999590	+	0.0286435i	$0.990881\pi$
$150$		0			0
$151$	6.29590e9	−	5.28289e9i	0.985512	−	0.826943i	0.000600109	−	1.00000i	$-0.499809\pi$
$151$	6.29590e9	−	5.28289e9i	0.985512	−	0.826943i	0.984912	+	0.173057i	$0.0553645\pi$
$152$	−4.06906e7	+	7.04781e7i	−0.00618298	+	0.0107092i
$153$		0			0
$154$	166125.	+	287737.i	2.38008e−5	+	4.12242e-5i
$155$	1.35762e10	+	4.94133e9i	1.88923	+	0.687624i
$156$		0			0
$157$	4.94235e9	+	4.14712e9i	0.649209	+	0.544751i	0.906831	−	0.421495i	$-0.138494\pi$
$157$	4.94235e9	+	4.14712e9i	0.649209	+	0.544751i	−0.257622	+	0.966246i	$0.582939\pi$
$158$	5.04693e9	−	1.83693e9i	0.644273	−	0.234496i
$159$		0			0
$160$	−2.25367e9	−	1.27812e10i	−0.271864	−	1.54182i
$161$	−3.58359e6			−0.000420341
$162$		0			0
$163$	−7.51506e9			−0.833850			−0.416925	−	0.908941i	$-0.636892\pi$
$163$	−7.51506e9			−0.833850			−0.416925	+	0.908941i	$0.636892\pi$
$164$	2.32147e9	+	1.31657e10i	0.250591	+	1.42117i
$165$		0			0
$166$	−2.16201e9	+	7.86907e8i	−0.220989	+	0.0804335i
$167$	−1.39513e10	−	1.17065e10i	−1.38800	−	1.16467i	−0.966143	−	0.258008i	$-0.916934\pi$
$167$	−1.39513e10	−	1.17065e10i	−1.38800	−	1.16467i	−0.421858	−	0.906662i	$-0.638622\pi$
$168$		0			0
$169$	8.65112e9	+	3.14875e9i	0.815797	+	0.296926i
$170$	−1.95700e9	−	3.38962e9i	−0.179709	−	0.311265i
$171$		0			0
$172$	−7.64189e9	+	1.32361e10i	−0.665768	+	1.15314i
$173$	−8.57354e9	+	7.19405e9i	−0.727700	+	0.610613i	−0.929504	−	0.368813i	$-0.879764\pi$
$173$	−8.57354e9	+	7.19405e9i	−0.727700	+	0.610613i	0.201803	+	0.979426i	$0.435320\pi$
$174$		0			0
$175$	−917576.	+	5.20383e6i	−7.39556e−5	+	0.000419423i
$176$	6.81363e8	−	3.86420e9i	0.0535269	−	0.303566i
$177$		0			0
$178$	2.35536e8	−	1.97638e8i	0.0175860	−	0.0147564i
$179$	4.49668e9	−	7.78848e9i	0.327381	−	0.567040i	−0.654610	−	0.755966i	$-0.727167\pi$
$179$	4.49668e9	−	7.78848e9i	0.327381	−	0.567040i	0.981991	+	0.188926i	$0.0605006\pi$
$180$		0			0
$181$	1.03921e10	+	1.79997e10i	0.719699	+	1.24656i	0.961119	+	0.276135i	$0.0890536\pi$
$181$	1.03921e10	+	1.79997e10i	0.719699	+	1.24656i	−0.241420	+	0.970421i	$0.577613\pi$
$182$	453323.	+	164996.i	3.06258e−5	+	1.11469e-5i
$183$		0			0
$184$	−1.51719e10	−	1.27308e10i	−0.975800	−	0.818793i
$185$	−3.72594e10	+	1.35613e10i	−2.33864	+	0.851195i
$186$		0			0
$187$	−8.60665e8	−	4.88108e9i	−0.0514692	−	0.291896i
$188$	−1.12965e10			−0.659528
$189$		0			0
$190$	2.01209e8			0.0112010
$191$	−2.04507e9	−	1.15982e10i	−0.111188	−	0.630580i	−0.988567	−	0.150782i	$-0.951821\pi$
$191$	−2.04507e9	−	1.15982e10i	−0.111188	−	0.630580i	0.877379	−	0.479798i	$-0.159290\pi$
$192$		0			0
$193$	−2.54023e10	+	9.24567e9i	−1.31785	+	0.479657i	−0.902767	−	0.430129i	$-0.858468\pi$
$193$	−2.54023e10	+	9.24567e9i	−1.31785	+	0.479657i	−0.415078	+	0.909786i	$0.636246\pi$
$194$	−6.26523e9	−	5.25716e9i	−0.317563	−	0.266467i
$195$		0			0
$196$	−1.65655e10	−	6.02933e9i	−0.801772	−	0.291821i
$197$	1.49018e9	+	2.58107e9i	0.0704922	+	0.122096i	0.899117	−	0.437708i	$-0.144210\pi$
$197$	1.49018e9	+	2.58107e9i	0.0704922	+	0.122096i	−0.828625	+	0.559804i	$0.810876\pi$
$198$		0			0
$199$	6.90584e9	−	1.19613e10i	0.312160	−	0.540678i	−0.666669	−	0.745354i	$-0.732281\pi$
$199$	6.90584e9	−	1.19613e10i	0.312160	−	0.540678i	0.978830	+	0.204676i	$0.0656140\pi$
$200$	−2.23715e10	+	1.87719e10i	−0.988689	+	0.829609i
$201$		0			0
$202$	−3.90658e8	+	2.21553e9i	−0.0165088	+	0.0936261i
$203$	746675.	−	4.23460e6i	3.08603e−5	−	0.000175017i
$204$		0			0
$205$	5.49964e10	−	4.61475e10i	2.17491	−	1.82497i
$206$	6.20333e9	−	1.07445e10i	0.240006	−	0.415703i
$207$		0			0
$208$	−2.84863e9	−	4.93397e9i	−0.105524	−	0.182773i
$209$	2.39429e8	+	8.71452e7i	0.00867999	+	0.00315926i
$210$		0			0
$211$	−3.40840e10	−	2.85999e10i	−1.18380	−	0.993329i	−0.999946	−	0.0103758i	$-0.996697\pi$
$211$	−3.40840e10	−	2.85999e10i	−1.18380	−	0.993329i	−0.183857	−	0.982953i	$-0.558858\pi$
$212$	−3.01313e10	+	1.09669e10i	−1.02449	+	0.372883i
$213$		0			0
$214$	3.84931e9	+	2.18305e10i	0.125464	+	0.711544i
$215$	8.20765e10			2.61966
$216$		0			0
$217$	−9.16547e6			−0.000280599
$218$	3.15114e9	+	1.78710e10i	0.0944961	+	0.535914i
$219$		0			0
$220$	−2.48009e10	+	9.02678e9i	−0.713781	+	0.259795i
$221$	−5.51284e9	−	4.62582e9i	−0.155457	−	0.130444i
$222$		0			0
$223$	−2.75909e10	−	1.00423e10i	−0.747126	−	0.271932i	−0.0597301	−	0.998215i	$-0.519024\pi$
$223$	−2.75909e10	−	1.00423e10i	−0.747126	−	0.271932i	−0.687396	+	0.726283i	$0.741246\pi$
$224$	4.11674e6	+	7.13041e6i	0.000109254	+	0.000189234i
$225$		0			0
$226$	−3.62005e9	+	6.27011e9i	−0.0923052	+	0.159877i
$227$	3.85707e10	−	3.23647e10i	0.964142	−	0.809011i	−0.0174797	−	0.999847i	$-0.505564\pi$
$227$	3.85707e10	−	3.23647e10i	0.964142	−	0.809011i	0.981622	+	0.190836i	$0.0611198\pi$
$228$		0			0
$229$	6.72006e9	−	3.81114e10i	0.161478	−	0.915788i	−0.791144	−	0.611630i	$-0.790514\pi$
$229$	6.72006e9	−	3.81114e10i	0.161478	−	0.915788i	0.952622	−	0.304157i	$-0.0983749\pi$
$230$	−8.50318e9	+	4.82239e10i	−0.200358	+	1.13629i
$231$		0			0
$232$	1.82047e10	−	1.52756e10i	0.412561	−	0.346180i
$233$	1.36441e10	−	2.36323e10i	0.303280	−	0.525296i	−0.673597	−	0.739099i	$-0.735252\pi$
$233$	1.36441e10	−	2.36323e10i	0.303280	−	0.525296i	0.976877	+	0.213803i	$0.0685849\pi$
$234$		0			0
$235$	3.03320e10	+	5.25366e10i	0.648778	+	1.12372i
$236$	−9.98452e9	−	3.63407e9i	−0.209519	−	0.0762586i
$237$		0			0
$238$	1.90212e6	+	1.59607e6i	3.84274e−5	+	3.22444e-5i
$239$	4.53131e10	−	1.64926e10i	0.898325	−	0.326964i	0.148744	−	0.988876i	$-0.452477\pi$
$239$	4.53131e10	−	1.64926e10i	0.898325	−	0.326964i	0.749581	+	0.661912i	$0.230255\pi$
$240$		0			0
$241$	8.23009e9	+	4.66751e10i	0.157155	+	0.891269i	0.956789	+	0.290782i	$0.0939155\pi$
$241$	8.23009e9	+	4.66751e10i	0.157155	+	0.891269i	−0.799634	+	0.600487i	$0.794973\pi$
$242$	−1.46913e10			−0.275354
$243$		0			0
$244$	−3.22880e9			−0.0583158
$245$	1.64390e10	+	9.32303e10i	0.291493	+	1.65314i
$246$		0			0
$247$	3.47644e8	−	1.26532e8i	0.00594290	−	0.00216304i
$248$	−3.88041e10	−	3.25605e10i	−0.651396	−	0.546586i
$249$		0			0
$250$	3.05256e10	+	1.11104e10i	0.494235	+	0.179887i
$251$	−4.56111e10	−	7.90007e10i	−0.725335	−	1.25632i	−0.958836	−	0.283961i	$-0.908352\pi$
$251$	−4.56111e10	−	7.90007e10i	−0.725335	−	1.25632i	0.233501	−	0.972357i	$-0.424982\pi$
$252$		0			0
$253$	−3.10045e10	+	5.37014e10i	−0.475754	+	0.824030i
$254$	1.03643e9	−	8.69668e8i	0.0156238	−	0.0131100i
$255$		0			0
$256$	−1.98394e9	+	1.12515e10i	−0.0288701	+	0.163730i
$257$	1.52609e10	−	8.65490e10i	0.218214	−	1.23755i	−0.657029	−	0.753866i	$-0.728187\pi$
$257$	1.52609e10	−	8.65490e10i	0.218214	−	1.23755i	0.875242	−	0.483685i	$-0.160702\pi$
$258$		0			0
$259$	1.92693e7	−	1.61689e7i	0.000266084	−	0.000223271i
$260$	−1.91606e10	+	3.31871e10i	−0.260033	+	0.450390i
$261$		0			0
$262$	−1.33120e10	−	2.30570e10i	−0.174537	−	0.302306i
$263$	8.04215e10	+	2.92710e10i	1.03651	+	0.377257i	0.803554	−	0.595231i	$-0.202940\pi$
$263$	8.04215e10	+	2.92710e10i	1.03651	+	0.377257i	0.232951	+	0.972488i	$0.425162\pi$
$264$		0			0
$265$	1.31909e11	+	1.10685e11i	1.64312	+	1.37874i
$266$	−119949.	+	43657.9i	−1.46903e−6	+	5.34682e-7i
$267$		0			0
$268$	−4.20288e9	−	2.38357e10i	−0.0497669	−	0.282242i
$269$	−6.66859e10			−0.776513			−0.388257	−	0.921551i	$-0.626923\pi$
$269$	−6.66859e10			−0.776513			−0.388257	+	0.921551i	$0.626923\pi$
$270$		0			0
$271$	3.68301e10			0.414803			0.207401	−	0.978256i	$-0.433499\pi$
$271$	3.68301e10			0.414803			0.207401	+	0.978256i	$0.433499\pi$
$272$	−5.09210e9	−	2.88787e10i	−0.0564075	−	0.319903i
$273$		0			0
$274$	1.51805e10	−	5.52527e9i	0.162708	−	0.0592210i
$275$	7.00427e10	+	5.87728e10i	0.738526	+	0.619697i
$276$		0			0
$277$	1.80483e10	+	6.56906e9i	0.184195	+	0.0670416i	0.432471	−	0.901648i	$-0.357642\pi$
$277$	1.80483e10	+	6.56906e9i	0.184195	+	0.0670416i	−0.248276	+	0.968689i	$0.579864\pi$
$278$	−9.48393e9	−	1.64266e10i	−0.0952328	−	0.164948i
$279$		0			0
$280$	1.43593e7	−	2.48711e7i	0.000139612	−	0.000241815i
$281$	8.02625e10	−	6.73482e10i	0.767952	−	0.644388i	−0.172231	−	0.985057i	$-0.555098\pi$
$281$	8.02625e10	−	6.73482e10i	0.767952	−	0.644388i	0.940184	+	0.340668i	$0.110653\pi$
$282$		0			0
$283$	1.39118e10	−	7.88977e10i	0.128927	−	0.731182i	−0.849970	−	0.526830i	$-0.823380\pi$
$283$	1.39118e10	−	7.88977e10i	0.128927	−	0.731182i	0.978898	−	0.204352i	$-0.0655086\pi$
$284$	−6.29694e9	+	3.57117e10i	−0.0574377	+	0.325745i
$285$		0			0
$286$	6.39460e9	−	5.36570e9i	0.0565153	−	0.0474220i
$287$	−2.27726e7	+	3.94434e7i	−0.000198127	+	0.000343167i
$288$		0			0
$289$	4.07735e10	+	7.06217e10i	0.343825	+	0.595522i
$290$	−5.52129e10	−	2.00958e10i	−0.458405	−	0.166846i
$291$		0			0
$292$	−1.11329e10	−	9.34160e9i	−0.0896158	−	0.0751966i
$293$	6.18663e10	−	2.25175e10i	0.490399	−	0.178491i	−0.0849715	−	0.996383i	$-0.527080\pi$
$293$	6.18663e10	−	2.25175e10i	0.490399	−	0.178491i	0.575371	+	0.817893i	$0.304858\pi$
$294$		0			0
$295$	9.90831e9	+	5.61928e10i	0.0761729	+	0.431998i
$296$	1.39021e11			1.05261
$297$		0			0
$298$	−2.10481e10			−0.154611
$299$	1.56344e10	+	8.86673e10i	0.113126	+	0.641569i
$300$		0			0
$301$	−4.89291e7	+	1.78087e7i	−0.000343572	+	0.000125050i
$302$	5.45776e10	+	4.57960e10i	0.377557	+	0.316808i
$303$		0			0
$304$	1.41658e9	+	5.15592e8i	0.00951282	+	0.00346238i
$305$	8.66959e9	+	1.50162e10i	0.0573653	+	0.0993596i
$306$		0			0
$307$	2.44354e10	−	4.23234e10i	0.156999	−	0.271931i	−0.776786	−	0.629765i	$-0.783151\pi$
$307$	2.44354e10	−	4.23234e10i	0.156999	−	0.271931i	0.933785	+	0.357834i	$0.116485\pi$
$308$	1.28262e7	−	1.07625e7i	8.12120e−5	−	6.81449e-5i
$309$		0			0
$310$	−2.17480e10	+	1.23339e11i	−0.133749	+	0.758529i
$311$	6.03707e9	−	3.42379e10i	0.0365936	−	0.207532i	−0.961029	−	0.276448i	$-0.910843\pi$
$311$	6.03707e9	−	3.42379e10i	0.0365936	−	0.207532i	0.997623	+	0.0689154i	$0.0219538\pi$
$312$		0			0
$313$	−1.56901e11	+	1.31655e11i	−0.924007	+	0.775334i	−0.974732	−	0.223379i	$-0.928291\pi$
$313$	−1.56901e11	+	1.31655e11i	−0.924007	+	0.775334i	0.0507249	+	0.998713i	$0.483847\pi$
$314$	−2.79644e10	+	4.84358e10i	−0.162339	+	0.281179i
$315$		0			0
$316$	−1.35329e11	−	2.34396e11i	−0.763481	−	1.32239i
$317$	−1.93398e11	−	7.03911e10i	−1.07569	−	0.391518i	−0.257386	−	0.966309i	$-0.582861\pi$
$317$	−1.93398e11	−	7.03911e10i	−1.07569	−	0.391518i	−0.818300	+	0.574791i	$0.805083\pi$
$318$		0			0
$319$	−5.69970e10	−	4.78262e10i	−0.308173	−	0.258588i
$320$	−6.62533e10	+	2.41142e10i	−0.353210	+	0.128558i
$321$		0			0
$322$	−5.39442e6	−	3.05933e7i	−2.79636e−5	−	0.000158589i
$323$	1.90419e9			0.00973416
$324$		0			0
$325$	1.32760e11			0.660071
$326$	−1.13125e10	−	6.41564e10i	−0.0554727	−	0.314601i
$327$		0			0
$328$	−2.36536e11	+	8.60922e10i	−1.12841	+	0.410706i
$329$	−2.94814e7	−	2.47378e7i	−0.000138729	−	0.000116407i
$330$		0			0
$331$	5.33833e10	+	1.94299e10i	0.244444	+	0.0889704i	0.461337	−	0.887225i	$-0.347370\pi$
$331$	5.33833e10	+	1.94299e10i	0.244444	+	0.0889704i	−0.216893	+	0.976195i	$0.569592\pi$
$332$	5.79723e10	+	1.00411e11i	0.261878	+	0.453586i
$333$		0			0
$334$	7.89379e10	−	1.36725e11i	0.347078	−	0.601156i
$335$	−9.95678e10	+	8.35473e10i	−0.431934	+	0.362436i
$336$		0			0
$337$	5.14979e10	−	2.92059e11i	0.217498	−	1.23349i	−0.659021	−	0.752124i	$-0.729029\pi$
$337$	5.14979e10	−	2.92059e11i	0.217498	−	1.23349i	0.876519	−	0.481367i	$-0.159860\pi$
$338$	−1.38584e10	+	7.85948e10i	−0.0577547	+	0.327543i
$339$		0			0
$340$	−1.51096e11	+	1.26785e11i	−0.613195	+	0.514531i
$341$	−7.92979e10	+	1.37348e11i	−0.317590	+	0.550082i
$342$		0			0
$343$	−6.00577e7	−	1.04023e8i	−0.000234285	−	0.000405794i
$344$	−2.70419e11	−	9.84243e10i	−1.04117	−	0.378956i
$345$		0			0
$346$	−7.43218e10	−	6.23634e10i	−0.278788	−	0.233931i
$347$	2.12602e11	−	7.73808e10i	0.787199	−	0.286517i	0.0830277	−	0.996547i	$-0.473541\pi$
$347$	2.12602e11	−	7.73808e10i	0.787199	−	0.286517i	0.704171	+	0.710030i	$0.251319\pi$
$348$		0			0
$349$	−7.48865e10	−	4.24702e11i	−0.270202	−	1.53239i	−0.753800	−	0.657104i	$-0.771781\pi$
$349$	−7.48865e10	−	4.24702e11i	−0.270202	−	1.53239i	0.483598	−	0.875290i	$-0.339330\pi$
$350$	−4.58066e7			−0.000163163
$351$		0			0
$352$	1.42469e11			0.494628
$353$	−7.06834e10	−	4.00865e11i	−0.242288	−	1.37408i	−0.826709	−	0.562630i	$-0.809789\pi$
$353$	−7.06834e10	−	4.00865e11i	−0.242288	−	1.37408i	0.584421	−	0.811450i	$-0.301322\pi$
$354$		0			0
$355$	1.82992e11	−	6.66038e10i	0.611513	−	0.222572i
$356$	−1.18696e10	−	9.95980e9i	−0.0391662	−	0.0328644i
$357$		0			0
$358$	7.32595e10	+	2.66643e10i	0.235717	+	0.0857939i
$359$	−1.06722e11	−	1.84848e11i	−0.339100	−	0.587339i	0.645163	−	0.764045i	$-0.276789\pi$
$359$	−1.06722e11	−	1.84848e11i	−0.339100	−	0.587339i	−0.984264	+	0.176706i	$0.943456\pi$
$360$		0			0
$361$	1.61295e11	−	2.79371e11i	0.499848	−	0.865763i
$362$	−1.38021e11	+	1.15813e11i	−0.422431	+	0.354462i
$363$		0			0
$364$	4.22155e6	−	2.39416e7i	1.26042e−5	−	7.14820e-5i
$365$	−1.35523e10	+	7.68587e10i	−0.0399663	+	0.226660i
$366$		0			0
$367$	−4.73437e11	+	3.97261e11i	−1.36228	+	1.14309i	−0.387005	+	0.922078i	$0.626490\pi$
$367$	−4.73437e11	+	3.97261e11i	−1.36228	+	1.14309i	−0.975272	+	0.221008i	$0.929065\pi$
$368$	−1.83437e11	+	3.17723e11i	−0.521402	+	0.903094i
$369$		0			0
$370$	−1.71861e11	−	2.97671e11i	−0.476726	−	0.825713i
$371$	−1.02652e8	−	3.73624e7i	−0.000281311	−	0.000102389i
$372$		0			0
$373$	4.67268e11	+	3.92085e11i	1.24990	+	1.04879i	0.996683	+	0.0813853i	$0.0259344\pi$
$373$	4.67268e11	+	3.92085e11i	1.24990	+	1.04879i	0.253221	+	0.967408i	$0.418510\pi$
$374$	4.03744e10	−	1.46951e10i	0.106705	−	0.0388374i
$375$		0			0
$376$	−3.69346e10	−	2.09467e11i	−0.0952990	−	0.540467i
$377$	−1.08033e11			−0.275435
$378$		0			0
$379$	−6.97076e11			−1.73542			−0.867708	−	0.497073i	$-0.834408\pi$
$379$	−6.97076e11			−1.73542			−0.867708	+	0.497073i	$0.834408\pi$
$380$	−1.76075e9	−	9.98571e9i	−0.00433183	−	0.0245670i
$381$		0			0
$382$	9.59358e10	−	3.49178e10i	0.230513	−	0.0838999i
$383$	3.21343e9	+	2.69639e9i	0.00763088	+	0.00640307i	0.646595	−	0.762833i	$-0.276192\pi$
$383$	3.21343e9	+	2.69639e9i	0.00763088	+	0.00640307i	−0.638964	+	0.769236i	$0.720637\pi$
$384$		0			0
$385$	−8.44925e7	−	3.07528e7i	−0.000195995	−	7.13363e-5i
$386$	−1.17169e11	−	2.02943e11i	−0.268639	−	0.465297i
$387$		0			0
$388$	−2.06078e11	+	3.56938e11i	−0.461625	+	0.799559i
$389$	2.73855e11	−	2.29791e11i	0.606383	−	0.508815i	−0.287107	−	0.957898i	$-0.592694\pi$
$389$	2.73855e11	−	2.29791e11i	0.606383	−	0.508815i	0.893490	+	0.449083i	$0.148249\pi$
$390$		0			0
$391$	−8.04717e10	+	4.56378e11i	−0.174120	+	0.987482i
$392$	5.76378e10	−	3.26880e11i	0.123288	−	0.699200i
$393$		0			0
$394$	−1.97915e10	+	1.66070e10i	−0.0413757	+	0.0347184i
$395$	−7.26739e11	+	1.25875e12i	−1.50207	+	2.60167i
$396$		0			0
$397$	5.96798e10	+	1.03369e11i	0.120579	+	0.208848i	0.919996	−	0.391928i	$-0.128192\pi$
$397$	5.96798e10	+	1.03369e11i	0.120579	+	0.208848i	−0.799417	+	0.600776i	$0.794858\pi$
$398$	1.12509e11	+	4.09501e10i	0.224758	+	0.0818052i
$399$		0			0
$400$	4.14405e11	+	3.47727e11i	0.809386	+	0.679155i
$401$	−2.55298e11	+	9.29209e10i	−0.493058	+	0.179458i	−0.576569	−	0.817048i	$-0.695609\pi$
$401$	−2.55298e11	+	9.29209e10i	−0.493058	+	0.179458i	0.0835110	+	0.996507i	$0.473387\pi$
$402$		0			0
$403$	3.99870e10	+	2.26778e11i	0.0755173	+	0.428280i
$404$	1.13372e11			0.211734
$405$		0			0
$406$	3.72750e7			6.80848e−5
$407$	−7.55823e10	−	4.28648e11i	−0.136535	−	0.774331i
$408$		0			0
$409$	5.48864e11	−	1.99770e11i	0.969863	−	0.353001i	0.191972	−	0.981400i	$-0.438512\pi$
$409$	5.48864e11	−	1.99770e11i	0.969863	−	0.353001i	0.777891	+	0.628399i	$0.216290\pi$
$410$	4.76750e11	+	4.00040e11i	0.833226	+	0.699160i
$411$		0			0
$412$	−5.87516e11	−	2.13838e11i	−1.00458	−	0.365635i
$413$	−1.80993e7	−	3.13489e7i	−3.06117e−5	−	5.30209e-5i
$414$		0			0
$415$	3.11321e11	−	5.39224e11i	0.515219	−	0.892386i
$416$	1.58464e11	−	1.32967e11i	0.259425	−	0.217683i
$417$		0			0
$418$	−3.83547e8	+	2.17520e9i	−0.000614504	+	0.00348503i
$419$	−3.25619e10	+	1.84668e11i	−0.0516115	+	0.292703i	−0.999678	−	0.0253683i	$-0.991924\pi$
$419$	−3.25619e10	+	1.84668e11i	−0.0516115	+	0.292703i	0.948067	+	0.318072i	$0.103035\pi$
$420$		0			0
$421$	4.28012e11	−	3.59145e11i	0.664029	−	0.557186i	−0.247263	−	0.968948i	$-0.579531\pi$
$421$	4.28012e11	−	3.59145e11i	0.664029	−	0.557186i	0.911291	+	0.411762i	$0.135087\pi$
$422$	1.92851e11	−	3.34028e11i	0.296017	−	0.512717i
$423$		0			0
$424$	−3.01872e11	−	5.22857e11i	−0.453603	−	0.785663i
$425$	6.42115e11	+	2.33711e11i	0.954690	+	0.347479i
$426$		0			0
$427$	−8.42647e6	−	7.07065e6i	−1.22665e−5	−	1.02928e-5i
$428$	1.04973e12	−	3.82070e11i	1.51210	−	0.550359i
$429$		0			0
$430$	1.23551e11	+	7.00691e11i	0.174276	+	0.988367i
$431$	7.29796e11			1.01872			0.509359	−	0.860554i	$-0.329883\pi$
$431$	7.29796e11			1.01872			0.509359	+	0.860554i	$0.329883\pi$
$432$		0			0
$433$	−1.19394e12			−1.63225			−0.816126	−	0.577874i	$-0.803882\pi$
$433$	−1.19394e12			−1.63225			−0.816126	+	0.577874i	$0.803882\pi$
$434$	−1.37969e7	−	7.82461e7i	−1.86671e−5	−	0.000105867i
$435$		0			0
$436$	8.59335e11	−	3.12772e11i	1.13887	−	0.414514i
$437$	−1.82497e10	−	1.53133e10i	−0.0239380	−	0.0200864i
$438$		0			0
$439$	−1.34402e10	−	4.89183e9i	−0.0172709	−	0.00628609i	0.333370	−	0.942796i	$-0.391814\pi$
$439$	−1.34402e10	−	4.89183e9i	−0.0172709	−	0.00628609i	−0.350641	+	0.936510i	$0.614036\pi$
$440$	−2.48468e11	−	4.30360e11i	−0.316034	−	0.547387i
$441$		0			0
$442$	3.11923e10	−	5.40266e10i	0.0388729	−	0.0673299i
$443$	−1.20975e11	+	1.01510e11i	−0.149237	+	0.125225i	−0.714350	−	0.699789i	$-0.753277\pi$
$443$	−1.20975e11	+	1.01510e11i	−0.149237	+	0.125225i	0.565112	+	0.825014i	$0.308833\pi$
$444$		0			0
$445$	−1.44491e10	+	8.19450e10i	−0.0174671	+	0.0990609i
$446$	4.41984e10	−	2.50661e11i	0.0528931	−	0.299972i
$447$		0			0
$448$	3.42640e7	−	2.87509e7i	4.01872e−5	−	3.37210e-5i
$449$	−3.72319e11	+	6.44875e11i	−0.432321	+	0.748802i	−0.997073	−	0.0764588i	$-0.975639\pi$
$449$	−3.72319e11	+	6.44875e11i	−0.432321	+	0.748802i	0.564752	+	0.825261i	$0.308972\pi$
$450$		0			0
$451$	3.94049e11	+	6.82513e11i	0.448493	+	0.776813i
$452$	3.42854e11	+	1.24789e11i	0.386355	+	0.140622i
$453$		0			0
$454$	3.34359e11	+	2.80561e11i	0.369371	+	0.309939i
$455$	−1.22680e8	+	4.46520e7i	−0.000134191	+	4.88416e-5i
$456$		0			0
$457$	1.33616e11	+	7.57775e11i	0.143297	+	0.812675i	0.968719	+	0.248160i	$0.0798258\pi$
$457$	1.33616e11	+	7.57775e11i	0.143297	+	0.812675i	−0.825422	+	0.564515i	$0.809063\pi$
$458$	3.35474e11			0.356258
$459$		0			0
$460$	2.46769e12			2.56969
$461$	−2.80527e11	−	1.59095e12i	−0.289281	−	1.64060i	−0.689579	−	0.724211i	$-0.742204\pi$
$461$	−2.80527e11	−	1.59095e12i	−0.289281	−	1.64060i	0.400297	−	0.916385i	$-0.368907\pi$
$462$		0			0
$463$	−1.13144e12	+	4.11809e11i	−1.14423	+	0.416467i	−0.843441	−	0.537222i	$-0.819474\pi$
$463$	−1.13144e12	+	4.11809e11i	−1.14423	+	0.416467i	−0.300794	+	0.953689i	$0.597252\pi$
$464$	−3.37221e11	−	2.82962e11i	−0.337741	−	0.283398i
$465$		0			0
$466$	2.22289e11	+	8.09065e10i	0.218364	+	0.0794779i
$467$	−4.93370e11	−	8.54542e11i	−0.480006	−	0.831395i	0.519731	−	0.854330i	$-0.326032\pi$
$467$	−4.93370e11	−	8.54542e11i	−0.480006	−	0.831395i	−0.999737	+	0.0229353i	$0.992699\pi$
$468$		0			0
$469$	4.12285e7	−	7.14099e7i	3.93478e−5	−	6.81523e-5i
$470$	−4.02848e11	+	3.38030e11i	−0.380804	+	0.319532i
$471$		0			0
$472$	3.47401e10	−	1.97021e11i	0.0322175	−	0.182715i
$473$	−1.56455e11	+	8.87299e11i	−0.143719	+	0.815070i
$474$		0			0
$475$	−2.69097e10	+	2.25799e10i	−0.0242542	+	0.0203517i
$476$	6.25651e7	−	1.08366e8i	5.58600e−5	−	9.67524e-5i
$477$		0			0
$478$	2.09009e11	+	3.62014e11i	0.183121	+	0.317175i
$479$	−4.86847e11	−	1.77198e11i	−0.422554	−	0.153797i	0.121986	−	0.992532i	$-0.461074\pi$
$479$	−4.86847e11	−	1.77198e11i	−0.422554	−	0.153797i	−0.544540	+	0.838735i	$0.683296\pi$
$480$		0			0
$481$	−4.84129e11	−	4.06232e11i	−0.412390	−	0.346036i
$482$	−3.86079e11	+	1.40521e11i	−0.325810	+	0.118585i
$483$		0			0
$484$	1.28561e11	+	7.29107e11i	0.106489	+	0.603931i
$485$	2.21335e12			1.81640
$486$		0			0
$487$	3.80821e11			0.306790			0.153395	−	0.988165i	$-0.450979\pi$
$487$	3.80821e11			0.306790			0.153395	+	0.988165i	$0.450979\pi$
$488$	−1.05568e10	−	5.98704e10i	−0.00842639	−	0.0477884i
$489$		0			0
$490$	−7.71165e11	+	2.80681e11i	−0.604317	+	0.219954i
$491$	8.55989e11	+	7.18260e11i	0.664663	+	0.557718i	0.911480	−	0.411344i	$-0.134940\pi$
$491$	8.55989e11	+	7.18260e11i	0.664663	+	0.557718i	−0.246817	+	0.969062i	$0.579385\pi$
$492$		0			0
$493$	−5.22519e11	−	1.90181e11i	−0.398374	−	0.144996i
$494$	1.60352e9	+	2.77738e9i	0.00121145	+	0.00209828i
$495$		0			0
$496$	−4.69164e11	+	8.12615e11i	−0.348062	+	0.602861i
$497$	−9.46377e7	+	7.94104e7i	−6.95761e−5	+	5.83813e-5i
$498$		0			0
$499$	5.74714e10	−	3.25937e11i	0.0414954	−	0.235332i	−0.957005	−	0.290070i	$-0.906321\pi$
$499$	5.74714e10	−	3.25937e11i	0.0414954	−	0.235332i	0.998501	+	0.0547383i	$0.0174325\pi$
$500$	2.84268e11	−	1.61216e12i	0.203405	−	1.15357i
$501$		0			0
$502$	6.05774e11	−	5.08305e11i	0.425739	−	0.357238i
$503$	4.66379e11	−	8.07793e11i	0.324850	−	0.562657i	−0.656632	−	0.754211i	$-0.728019\pi$
$503$	4.66379e11	−	8.07793e11i	0.324850	−	0.562657i	0.981482	+	0.191554i	$0.0613527\pi$
$504$		0			0
$505$	−3.04414e11	−	5.27260e11i	−0.208282	−	0.360756i
$506$	−5.05123e11	−	1.83850e11i	−0.342547	−	0.124677i
$507$		0			0
$508$	−5.22299e10	−	4.38261e10i	−0.0347962	−	0.0291975i
$509$	−1.16127e12	+	4.22666e11i	−0.766835	+	0.279105i	−0.695672	−	0.718360i	$-0.744893\pi$
$509$	−1.16127e12	+	4.22666e11i	−0.766835	+	0.279105i	−0.0711628	+	0.997465i	$0.522671\pi$
$510$		0			0
$511$	−8.59755e6	−	4.87591e7i	−5.57803e−6	−	3.16346e-5i
$512$	1.48458e12			0.954750
$513$		0			0
$514$	7.61845e11			0.481429
$515$	5.83032e11	+	3.30654e12i	0.365224	+	2.07129i
$516$		0			0
$517$	−6.25773e11	+	2.27763e11i	−0.385221	+	0.140209i
$518$	1.67041e8	+	1.40164e8i	0.000101939	+	8.55367e-5i
$519$		0			0
$520$	−6.78023e11	−	2.46780e11i	−0.406658	−	0.148011i
$521$	−6.35588e11	−	1.10087e12i	−0.377925	−	0.654586i	0.612835	−	0.790211i	$-0.290029\pi$
$521$	−6.35588e11	−	1.10087e12i	−0.377925	−	0.654586i	−0.990760	+	0.135625i	$0.956696\pi$
$522$		0			0
$523$	3.43395e10	−	5.94777e10i	0.0200695	−	0.0347613i	−0.855816	−	0.517280i	$-0.826945\pi$
$523$	3.43395e10	−	5.94777e10i	0.0200695	−	0.0347613i	0.875886	+	0.482519i	$0.160278\pi$
$524$	−1.02779e12	+	8.62420e11i	−0.595545	+	0.499721i
$525$		0			0
$526$	−1.28829e11	+	7.30624e11i	−0.0733799	+	0.416158i
$527$	−2.05816e11	+	1.16724e12i	−0.116234	+	0.659195i
$528$		0			0
$529$	3.06162e12	−	2.56900e12i	1.69981	−	1.42631i
$530$	−7.46357e11	+	1.29273e12i	−0.410871	+	0.711649i
$531$		0			0
$532$	3.21633e6	+	5.57084e6i	1.74084e−6	+	3.01522e-6i
$533$	1.07528e12	+	3.91371e11i	0.577099	+	0.210047i
$534$		0			0
$535$	−4.59551e12	−	3.85609e12i	−2.42516	−	2.03495i
$536$	4.28235e11	−	1.55865e11i	0.224100	−	0.0815656i
$537$		0			0
$538$	−1.00383e11	−	5.69301e11i	−0.0516583	−	0.292969i
$539$	−1.03921e12			−0.530342
$540$		0			0
$541$	−2.31050e12			−1.15963			−0.579815	−	0.814749i	$-0.696875\pi$
$541$	−2.31050e12			−1.15963			−0.579815	+	0.814749i	$0.696875\pi$
$542$	5.54408e10	+	3.14421e11i	0.0275952	+	0.156500i
$543$		0			0
$544$	1.00052e12	−	3.64159e11i	0.489812	−	0.178277i
$545$	−3.76200e12	−	3.15669e12i	−1.82656	−	1.53267i
$546$		0			0
$547$	−3.97960e11	−	1.44846e11i	−0.190063	−	0.0691772i	0.245235	−	0.969464i	$-0.421135\pi$
$547$	−3.97960e11	−	1.44846e11i	−0.190063	−	0.0691772i	−0.435298	+	0.900286i	$0.643357\pi$
$548$	−4.07053e11	−	7.05036e11i	−0.192814	−	0.333963i
$549$		0			0
$550$	−3.96310e11	+	6.86429e11i	−0.184673	+	0.319863i
$551$	2.18977e10	−	1.83743e10i	0.0101208	−	0.00849238i
$552$		0			0
$553$	1.60118e8	−	9.08077e8i	7.28079e−5	−	0.000412914i
$554$	−2.89120e10	+	1.63968e11i	−0.0130402	+	0.0739546i
$555$		0			0
$556$	−7.32237e11	+	6.14419e11i	−0.324949	+	0.272664i
$557$	−1.70837e12	+	2.95898e12i	−0.752027	+	1.30255i	0.194812	+	0.980841i	$0.437590\pi$
$557$	−1.70837e12	+	2.95898e12i	−0.752027	+	1.30255i	−0.946839	+	0.321708i	$0.895743\pi$
$558$		0			0
$559$	6.54102e11	+	1.13294e12i	0.283330	+	0.490742i
$560$	−4.99897e8	−	1.81948e8i	−0.000214800	−	7.81809e-5i
$561$		0			0
$562$	6.95775e11	+	5.83824e11i	0.294209	+	0.246870i
$563$	−1.34674e12	+	4.90172e11i	−0.564931	+	0.205618i	−0.608668	−	0.793425i	$-0.708296\pi$
$563$	−1.34674e12	+	4.90172e11i	−0.564931	+	0.205618i	0.0437371	+	0.999043i	$0.486074\pi$
$564$		0			0
$565$	−3.40237e11	−	1.92958e12i	−0.140464	−	0.796608i
$566$	6.94495e11			0.284443
$567$		0			0
$568$	−6.82777e11			−0.275240
$569$	5.97232e11	+	3.38707e12i	0.238857	+	1.35463i	0.834337	+	0.551255i	$0.185851\pi$
$569$	5.97232e11	+	3.38707e12i	0.238857	+	1.35463i	−0.595479	+	0.803371i	$0.703038\pi$
$570$		0			0
$571$	1.62120e12	−	5.90069e11i	0.638226	−	0.232295i	−0.00258173	−	0.999997i	$-0.500822\pi$
$571$	1.62120e12	−	5.90069e11i	0.638226	−	0.232295i	0.640808	+	0.767701i	$0.278600\pi$
$572$	−3.22249e11	−	2.70399e11i	−0.125866	−	0.105615i
$573$		0			0
$574$	−3.71010e8	−	1.35036e8i	−0.000142653	−	5.19215e-5i
$575$	−4.27452e12	−	7.40369e12i	−1.63073	−	2.82451i
$576$		0			0
$577$	−1.91628e12	+	3.31910e12i	−0.719728	+	1.24661i	0.241380	+	0.970431i	$0.422400\pi$
$577$	−1.91628e12	+	3.31910e12i	−0.719728	+	1.24661i	−0.961108	+	0.276174i	$0.910933\pi$
$578$	−5.41524e11	+	4.54392e11i	−0.201810	+	0.169339i
$579$		0			0
$580$	−5.14167e11	+	2.91598e12i	−0.188659	+	1.06994i
$581$	−6.85917e7	+	3.89003e8i	−2.49735e−5	+	0.000141632i
$582$		0			0
$583$	−1.44802e12	+	1.21503e12i	−0.519118	+	0.435591i
$584$	1.36818e11	−	2.36976e11i	0.0486727	−	0.0843036i
$585$		0			0
$586$	2.85361e11	+	4.94260e11i	0.0999667	+	0.173147i
$587$	−7.41947e11	−	2.70047e11i	−0.257930	−	0.0938788i	0.209819	−	0.977740i	$-0.432713\pi$
$587$	−7.41947e11	−	2.70047e11i	−0.257930	−	0.0938788i	−0.467749	+	0.883861i	$0.654935\pi$
$588$		0			0
$589$	−4.66758e10	−	3.91656e10i	−0.0159799	−	0.0134087i
$590$	−4.64805e11	+	1.69175e11i	−0.157920	+	0.0574782i
$591$		0			0
$592$	−4.47180e11	−	2.53609e12i	−0.149636	−	0.848626i
$593$	1.82644e12			0.606539			0.303270	−	0.952905i	$-0.401922\pi$
$593$	1.82644e12			0.606539			0.303270	+	0.952905i	$0.401922\pi$
$594$		0			0
$595$	−6.71971e8			−0.000219798
$596$	1.84189e11	+	1.04459e12i	0.0597936	+	0.339107i
$597$		0			0
$598$	−7.33422e11	+	2.66944e11i	−0.234530	+	0.0853620i
$599$	2.46238e12	+	2.06618e12i	0.781509	+	0.655764i	0.943628	−	0.331007i	$-0.107388\pi$
$599$	2.46238e12	+	2.06618e12i	0.781509	+	0.655764i	−0.162119	+	0.986771i	$0.551833\pi$
$600$		0			0
$601$	4.02548e12	+	1.46515e12i	1.25858	+	0.458087i	0.883294	−	0.468820i	$-0.155321\pi$
$601$	4.02548e12	+	1.46515e12i	1.25858	+	0.458087i	0.375291	+	0.926907i	$0.377543\pi$
$602$	−2.25688e8	−	3.90902e8i	−7.00364e−5	−	0.000121307i
$603$		0			0
$604$	1.79519e12	−	3.10935e12i	0.548837	−	0.950613i
$605$	3.04566e12	−	2.55561e12i	0.924235	−	0.775525i
$606$		0			0
$607$	8.96564e11	−	5.08467e12i	0.268060	−	1.52024i	−0.492117	−	0.870529i	$-0.663777\pi$
$607$	8.96564e11	−	5.08467e12i	0.268060	−	1.52024i	0.760177	−	0.649715i	$-0.225112\pi$
$608$	−9.50467e9	+	5.39036e10i	−0.00282079	+	0.0159975i
$609$		0			0
$610$	−1.15143e11	+	9.66167e10i	−0.0336709	+	0.0282532i
$611$	−4.83457e11	+	8.37373e11i	−0.140337	+	0.243071i
$612$		0			0
$613$	2.55599e12	+	4.42711e12i	0.731118	+	1.26633i	0.956406	+	0.292041i	$0.0943343\pi$
$613$	2.55599e12	+	4.42711e12i	0.731118	+	1.26633i	−0.225288	+	0.974292i	$0.572332\pi$
$614$	3.98100e11	+	1.44896e11i	0.113041	+	0.0411434i
$615$		0			0
$616$	2.41501e8	+	2.02643e8i	6.75779e−5	+	5.67046e-5i
$617$	−3.56688e12	+	1.29824e12i	−0.990843	+	0.360638i	−0.786047	−	0.618167i	$-0.787876\pi$
$617$	−3.56688e12	+	1.29824e12i	−0.990843	+	0.360638i	−0.204797	+	0.978805i	$0.565653\pi$
$618$		0			0
$619$	−1.54659e11	−	8.77115e11i	−0.0423416	−	0.240131i	0.956290	−	0.292418i	$-0.0944600\pi$
$619$	−1.54659e11	−	8.77115e11i	−0.0423416	−	0.240131i	−0.998632	+	0.0522872i	$0.983349\pi$
$620$	6.31142e12			1.71540
$621$		0			0
$622$	3.01378e11			0.0807338
$623$	−9.16651e6	−	5.19859e7i	−2.43785e−6	−	1.38258e-5i
$624$		0			0
$625$	−1.74466e12	+	6.35004e11i	−0.457352	+	0.166462i
$626$	−1.36013e12	−	1.14129e12i	−0.353994	−	0.297037i
$627$		0			0
$628$	2.64850e12	+	9.63976e11i	0.679488	+	0.247313i
$629$	−1.62644e12	−	2.81708e12i	−0.414295	−	0.717581i
$630$		0			0
$631$	3.64375e11	−	6.31117e11i	0.0914991	−	0.158481i	−0.816643	−	0.577143i	$-0.804167\pi$
$631$	3.64375e11	−	6.31117e11i	0.0914991	−	0.158481i	0.908142	+	0.418662i	$0.137501\pi$
$632$	3.90386e12	−	3.27573e12i	0.973346	−	0.816734i
$633$		0			0
$634$	3.09808e11	−	1.75701e12i	0.0761537	−	0.431889i
$635$	−6.35804e10	+	3.60582e11i	−0.0155182	+	0.0880081i
$636$		0			0
$637$	−1.15589e12	+	9.69907e11i	−0.278156	+	0.233401i
$638$	3.22496e11	−	5.58580e11i	0.0770604	−	0.133473i
$639$		0			0
$640$	−3.62807e12	−	6.28399e12i	−0.854801	−	1.48056i
$641$	3.41738e12	+	1.24383e12i	0.799526	+	0.291004i	0.709290	−	0.704917i	$-0.249016\pi$
$641$	3.41738e12	+	1.24383e12i	0.799526	+	0.291004i	0.0902361	+	0.995920i	$0.471238\pi$
$642$		0			0
$643$	−2.27459e12	−	1.90861e12i	−0.524751	−	0.440319i	0.341533	−	0.939870i	$-0.389054\pi$
$643$	−2.27459e12	−	1.90861e12i	−0.524751	−	0.440319i	−0.866284	+	0.499551i	$0.833498\pi$
$644$	−1.47109e9	+	5.35433e8i	−0.000337018	+	0.000122664i
$645$		0			0
$646$	2.86640e9	+	1.62561e10i	0.000647575	+	0.00367258i
$647$	6.86393e12			1.53994			0.769969	−	0.638081i	$-0.220271\pi$
$647$	6.86393e12			1.53994			0.769969	+	0.638081i	$0.220271\pi$
$648$		0			0
$649$	−6.26367e11			−0.138589
$650$	1.99845e11	+	1.13337e12i	0.0439119	+	0.249037i
$651$		0			0
$652$	−3.08499e12	+	1.12284e12i	−0.668558	+	0.243335i
$653$	1.77818e12	+	1.49207e12i	0.382707	+	0.321129i	0.813764	−	0.581195i	$-0.197415\pi$
$653$	1.77818e12	+	1.49207e12i	0.382707	+	0.321129i	−0.431057	+	0.902325i	$0.641859\pi$
$654$		0			0
$655$	6.77057e12	+	2.46429e12i	1.43727	+	0.523125i
$656$	2.33138e12	+	4.03806e12i	0.491525	+	0.851346i
$657$		0			0
$658$	1.66809e8	−	2.88922e8i	3.46900e−5	−	6.00848e-5i
$659$	−5.69977e12	+	4.78268e12i	−1.17726	+	0.987841i	−0.177269	+	0.984162i	$0.556726\pi$
$659$	−5.69977e12	+	4.78268e12i	−1.17726	+	0.987841i	−0.999993	+	0.00367819i	$0.998829\pi$
$660$		0			0
$661$	−6.75544e11	+	3.83120e12i	−0.137641	+	0.780600i	0.835343	+	0.549728i	$0.185269\pi$
$661$	−6.75544e11	+	3.83120e12i	−0.137641	+	0.780600i	−0.972984	+	0.230872i	$0.925842\pi$
$662$	−8.55157e10	+	4.84984e11i	−0.0173055	+	0.0981446i
$663$		0			0
$664$	−1.67234e12	+	1.40326e12i	−0.333863	+	0.280144i
$665$	1.72722e7	−	2.99164e7i	3.42492e−6	−	5.93214e-6i
$666$		0			0
$667$	3.47838e12	+	6.02473e12i	0.680473	+	1.17861i
$668$	−7.47620e12	−	2.72111e12i	−1.45274	−	0.528753i
$669$		0			0
$670$	−8.63128e11	−	7.24250e11i	−0.165477	−	0.138852i
$671$	−1.78860e11	+	6.50999e10i	−0.0340614	+	0.0123973i
$672$		0			0
$673$	−3.31614e11	−	1.88068e12i	−0.0623111	−	0.353384i	−0.999983	−	0.00586154i	$-0.998134\pi$
$673$	−3.31614e11	−	1.88068e12i	−0.0623111	−	0.353384i	0.937672	−	0.347522i	$-0.112977\pi$
$674$	2.57084e12			0.479850
$675$		0			0
$676$	4.02181e12			0.740733
$677$	−9.03957e11	−	5.12659e12i	−0.165386	−	0.937950i	−0.948666	−	0.316281i	$-0.897566\pi$
$677$	−9.03957e11	−	5.12659e12i	−0.165386	−	0.937950i	0.783280	−	0.621670i	$-0.213545\pi$
$678$		0			0
$679$	−1.31947e9	+	4.80247e8i	−0.000238224	+	8.67064e-5i
$680$	−2.84494e12	−	2.38719e12i	−0.510250	−	0.428151i
$681$		0			0
$682$	−1.29191e12	−	4.70218e11i	−0.228667	−	0.0832281i
$683$	−2.44647e12	−	4.23742e12i	−0.430177	−	0.745089i	0.566711	−	0.823917i	$-0.308216\pi$
$683$	−2.44647e12	−	4.23742e12i	−0.430177	−	0.745089i	−0.996888	+	0.0788276i	$0.974882\pi$
$684$		0			0
$685$	−2.18594e12	+	3.78616e12i	−0.379342	+	0.657040i
$686$	7.97643e8	−	6.69302e8i	0.000137515	−	0.000115389i
$687$		0			0
$688$	−9.25660e11	+	5.24968e12i	−0.157508	+	0.893274i
$689$	−4.76593e11	+	2.70289e12i	−0.0805677	+	0.456922i
$690$		0			0
$691$	1.33693e12	−	1.12182e12i	0.223079	−	0.187186i	−0.524398	−	0.851473i	$-0.675710\pi$
$691$	1.33693e12	−	1.12182e12i	0.223079	−	0.187186i	0.747477	+	0.664288i	$0.231265\pi$
$692$	−2.44462e12	+	4.23421e12i	−0.405260	+	0.701931i
$693$		0			0
$694$	9.80635e11	+	1.69851e12i	0.160468	+	0.277940i
$695$	4.82360e12	+	1.75565e12i	0.784223	+	0.285434i
$696$		0			0
$697$	4.51182e12	+	3.78587e12i	0.724110	+	0.607601i
$698$	3.51298e12	−	1.27862e12i	0.560178	−	0.203888i
$699$		0			0
$700$	4.00846e8	+	2.27331e9i	6.31010e−5	+	0.000357864i
$701$	4.01526e12			0.628034			0.314017	−	0.949417i	$-0.398325\pi$
$701$	4.01526e12			0.628034			0.314017	+	0.949417i	$0.398325\pi$
$702$		0			0
$703$	1.67223e11			0.0258224
$704$	−1.34398e11	−	7.62207e11i	−0.0206212	−	0.116949i
$705$		0			0
$706$	3.31580e12	−	1.20685e12i	0.502305	−	0.182824i
$707$	2.95877e8	+	2.48270e8i	4.45373e−5	+	3.73712e-5i
$708$		0			0
$709$	−3.46475e11	−	1.26107e11i	−0.0514949	−	0.0187426i	0.316144	−	0.948711i	$-0.397612\pi$
$709$	−3.46475e11	−	1.26107e11i	−0.0514949	−	0.0187426i	−0.367639	+	0.929969i	$0.619834\pi$
$710$	8.44060e11	+	1.46195e12i	0.124655	+	0.215909i
$711$		0			0
$712$	1.45872e11	−	2.52658e11i	0.0212722	−	0.0368446i
$713$	1.13594e13	−	9.53165e12i	1.64608	−	1.38123i
$714$		0			0
$715$	−3.92280e11	+	2.22473e12i	−0.0561331	+	0.318347i
$716$	6.82225e11	−	3.86909e12i	0.0970105	−	0.550174i
$717$		0			0
$718$	1.41740e12	−	1.18934e12i	0.199037	−	0.167012i
$719$	−2.83079e12	+	4.90308e12i	−0.395028	+	0.684209i	−0.993105	−	0.117230i	$-0.962599\pi$
$719$	−2.83079e12	+	4.90308e12i	−0.395028	+	0.684209i	0.598077	+	0.801439i	$0.295932\pi$
$720$		0			0
$721$	−1.06501e9	−	1.84466e9i	−0.000146773	−	0.000254218i
$722$	2.62780e12	+	9.56442e11i	0.359894	+	0.130991i
$723$		0			0
$724$	6.95543e12	+	5.83630e12i	0.940806	+	0.789430i
$725$	9.63933e12	−	3.50843e12i	1.29576	−	0.471620i
$726$		0			0
$727$	3.04318e11	+	1.72587e12i	0.0404039	+	0.229142i	0.998322	−	0.0578982i	$-0.0184399\pi$
$727$	3.04318e11	+	1.72587e12i	0.0404039	+	0.229142i	−0.957919	+	0.287040i	$0.907329\pi$
$728$	4.57742e8			6.03990e−5
$729$		0			0
$730$	−6.76547e11			−0.0881749
$731$	1.16925e12	+	6.63114e12i	0.151453	+	0.858934i
$732$		0			0
$733$	1.07759e13	−	3.92211e12i	1.37875	−	0.501825i	0.456953	−	0.889491i	$-0.348941\pi$
$733$	1.07759e13	−	3.92211e12i	1.37875	−	0.501825i	0.921800	+	0.387666i	$0.126719\pi$
$734$	−4.10411e12	−	3.44375e12i	−0.521899	−	0.437925i
$735$		0			0
$736$	−1.25174e13	−	4.55598e12i	−1.57241	−	0.572310i
$737$	−7.13403e11	−	1.23565e12i	−0.0890699	−	0.154274i
$738$		0			0
$739$	1.24608e11	−	2.15828e11i	0.0153690	−	0.0266199i	−0.858239	−	0.513251i	$-0.828441\pi$
$739$	1.24608e11	−	2.15828e11i	0.0153690	−	0.0266199i	0.873608	+	0.486631i	$0.161774\pi$
$740$	−1.32690e13	+	1.11340e13i	−1.62666	+	1.36493i
$741$		0			0
$742$	1.64441e8	−	9.32590e8i	1.99155e−5	−	0.000112947i
$743$	1.47075e12	−	8.34102e12i	0.177047	−	1.00408i	−0.758708	−	0.651431i	$-0.774169\pi$
$743$	1.47075e12	−	8.34102e12i	0.177047	−	1.00408i	0.935755	−	0.352652i	$-0.114720\pi$
$744$		0			0
$745$	4.36350e12	−	3.66141e12i	0.518957	−	0.435457i
$746$	−2.64386e12	+	4.57930e12i	−0.312546	+	0.541345i
$747$		0			0
$748$	−1.08260e12	−	1.87512e12i	−0.126448	−	0.219014i
$749$	3.57625e9	+	1.30165e9i	0.000415202	+	0.000151121i
$750$		0			0
$751$	−2.54579e12	−	2.13617e12i	−0.292040	−	0.245051i	0.484982	−	0.874524i	$-0.338826\pi$
$751$	−2.54579e12	−	2.13617e12i	−0.292040	−	0.245051i	−0.777022	+	0.629473i	$0.783271\pi$
$752$	−3.70237e12	+	1.34755e12i	−0.422182	+	0.153662i
$753$		0			0
$754$	−1.62623e11	−	9.22280e11i	−0.0183236	−	0.103918i
$755$	−1.92809e13			−2.15956
$756$		0			0
$757$	−3.39854e12			−0.376150			−0.188075	−	0.982155i	$-0.560225\pi$
$757$	−3.39854e12			−0.376150			−0.188075	+	0.982155i	$0.560225\pi$
$758$	−1.04932e12	−	5.95097e12i	−0.115450	−	0.654751i
$759$		0			0
$760$	1.79404e11	−	6.52978e10i	0.0195062	−	0.00709966i
$761$	8.93034e12	+	7.49344e12i	0.965243	+	0.809935i	0.981798	−	0.189928i	$-0.0608253\pi$
$761$	8.93034e12	+	7.49344e12i	0.965243	+	0.809935i	−0.0165548	+	0.999863i	$0.505270\pi$
$762$		0			0
$763$	2.92761e9	+	1.06556e9i	0.000312718	+	0.000113820i
$764$	−2.57243e12	−	4.45558e12i	−0.273164	−	0.473134i
$765$		0			0
$766$	−1.81820e10	+	3.14921e10i	−0.00190815	+	0.00330501i
$767$	−6.96691e11	+	5.84593e11i	−0.0726877	+	0.0609922i
$768$		0			0
$769$	1.20658e12	−	6.84286e12i	0.124419	−	0.705618i	−0.857232	−	0.514931i	$-0.827818\pi$
$769$	1.20658e12	−	6.84286e12i	0.124419	−	0.705618i	0.981651	−	0.190686i	$-0.0610714\pi$
$770$	1.35350e8	−	7.67609e8i	1.38756e−5	−	7.86922e-5i
$771$		0			0
$772$	−9.04640e12	+	7.59083e12i	−0.916638	+	0.769151i
$773$	−2.42267e12	+	4.19620e12i	−0.244055	+	0.422715i	−0.961865	−	0.273523i	$-0.911811\pi$
$773$	−2.42267e12	+	4.19620e12i	−0.244055	+	0.422715i	0.717811	+	0.696238i	$0.245144\pi$
$774$		0			0
$775$	−1.09326e13	−	1.89359e13i	−1.08860	−	1.88550i
$776$	−7.29236e12	−	2.65420e12i	−0.721922	−	0.262758i
$777$		0			0
$778$	2.37397e12	+	1.99200e12i	0.232310	+	0.194931i
$779$	−2.84519e11	+	1.03557e11i	−0.0276817	+	0.0100753i
$780$		0			0
$781$	3.71208e11	+	2.10522e12i	0.0357016	+	0.202474i
$782$	−4.01725e12			−0.384148
$783$		0			0
$784$	−6.14848e12			−0.581227
$785$	−2.62829e12	−	1.49058e13i	−0.247035	−	1.40101i
$786$		0			0
$787$	−1.19846e13	+	4.36205e12i	−1.11362	+	0.405326i	−0.832322	−	0.554293i	$-0.812989\pi$
$787$	−1.19846e13	+	4.36205e12i	−1.11362	+	0.405326i	−0.281303	+	0.959619i	$0.590767\pi$
$788$	9.97374e11	+	8.36896e11i	0.0921489	+	0.0773221i
$789$		0			0
$790$	−1.18400e13	−	4.30939e12i	−1.08150	−	0.393636i
$791$	6.21505e8	+	1.07648e9i	5.64482e−5	+	9.77712e-5i
$792$		0			0
$793$	−1.38183e11	+	2.39340e11i	−0.0124087	+	0.0214925i
$794$	−7.92625e11	+	6.65091e11i	−0.0707743	+	0.0593867i
$795$		0			0
$796$	1.04774e12	−	5.94201e12i	0.0925004	−	0.524596i
$797$	−1.74728e12	+	9.90932e12i	−0.153391	+	0.869924i	0.806851	+	0.590755i	$0.201170\pi$
$797$	−1.74728e12	+	9.90932e12i	−0.153391	+	0.869924i	−0.960242	+	0.279169i	$0.909941\pi$
$798$		0			0
$799$	−3.81244e12	+	3.19902e12i	−0.330935	+	0.277688i
$800$	−9.82095e12	+	1.70104e13i	−0.847713	+	1.46828i
$801$		0			0
$802$	−1.17757e12	−	2.03962e12i	−0.100509	−	0.174086i
$803$	−8.05058e11	−	2.93017e11i	−0.0683293	−	0.0248698i
$804$		0			0
$805$	6.44014e9	+	5.40392e9i	0.000540523	+	0.000453552i
$806$	−1.87582e12	+	6.82742e11i	−0.156561	+	0.0569835i
$807$		0			0
$808$	3.70677e11	+	2.10222e12i	0.0305946	+	0.173511i
$809$	1.95680e13			1.60612			0.803060	−	0.595899i	$-0.203204\pi$
$809$	1.95680e13			1.60612			0.803060	+	0.595899i	$0.203204\pi$
$810$		0			0
$811$	2.53301e12			0.205609			0.102805	−	0.994702i	$-0.467218\pi$
$811$	2.53301e12			0.205609			0.102805	+	0.994702i	$0.467218\pi$
$812$	−3.26187e8	−	1.84990e9i	−2.63308e−5	−	0.000149330i
$813$		0			0
$814$	3.54562e12	−	1.29050e12i	0.283062	−	0.103026i
$815$	1.35055e13	+	1.13324e13i	1.07226	+	0.899733i
$816$		0			0
$817$	−3.25275e11	−	1.18390e11i	−0.0255418	−	0.00929644i
$818$	2.53166e12	+	4.38496e12i	0.197704	+	0.342433i
$819$		0			0
$820$	1.56814e13	−	2.71610e13i	1.21122	−	2.09790i
$821$	1.97188e12	−	1.65460e12i	0.151473	−	0.127101i	−0.563902	−	0.825842i	$-0.690700\pi$
$821$	1.97188e12	−	1.65460e12i	0.151473	−	0.127101i	0.715375	+	0.698741i	$0.246256\pi$
$822$		0			0
$823$	1.19721e12	−	6.78969e12i	0.0909640	−	0.515883i	−0.904946	−	0.425527i	$-0.860089\pi$
$823$	1.19721e12	−	6.78969e12i	0.0909640	−	0.515883i	0.995910	−	0.0903553i	$-0.0288003\pi$
$824$	2.04420e12	−	1.15933e13i	0.154473	−	0.876058i
$825$		0			0
$826$	2.40382e8	−	2.01705e8i	1.79677e−5	−	1.50767e-5i
$827$	4.34391e12	−	7.52388e12i	0.322928	−	0.559328i	−0.658163	−	0.752876i	$-0.728666\pi$
$827$	4.34391e12	−	7.52388e12i	0.322928	−	0.559328i	0.981091	+	0.193548i	$0.0619994\pi$
$828$		0			0
$829$	−1.27609e13	−	2.21025e13i	−0.938393	−	1.62535i	−0.768468	−	0.639888i	$-0.778981\pi$
$829$	−1.27609e13	−	2.21025e13i	−0.938393	−	1.62535i	−0.169925	−	0.985457i	$-0.554353\pi$
$830$	5.07202e12	+	1.84606e12i	0.370962	+	0.135019i
$831$		0			0
$832$	−8.60860e11	−	7.22347e11i	−0.0622841	−	0.0522626i
$833$	−7.29809e12	+	2.65629e12i	−0.525178	+	0.191149i
$834$		0			0
$835$	7.41913e12	+	4.20760e13i	0.528158	+	2.99533i
$836$	1.11308e11			0.00788132
$837$		0			0
$838$	−1.62553e12			−0.113867
$839$	−3.57823e12	−	2.02932e13i	−0.249310	−	1.41391i	−0.810267	−	0.586061i	$-0.800678\pi$
$839$	−3.57823e12	−	2.02932e13i	−0.249310	−	1.41391i	0.560957	−	0.827845i	$-0.310433\pi$
$840$		0			0
$841$	5.78828e12	−	2.10676e12i	0.398995	−	0.145222i
$842$	3.71033e12	+	3.11333e12i	0.254395	+	0.213462i
$843$		0			0
$844$	−1.82649e13	−	6.64788e12i	−1.23902	−	0.450965i
$845$	−1.07989e13	−	1.87043e13i	−0.728659	−	1.26207i
$846$		0			0
$847$	−1.26113e9	+	2.18434e9i	−8.41948e−5	+	0.000145830i
$848$	−8.56716e12	+	7.18870e12i	−0.568926	+	0.477385i
$849$		0			0
$850$	−1.02862e12	+	5.83357e12i	−0.0675878	+	0.383309i
$851$	−7.06690e12	+	4.00784e13i	−0.461898	+	2.61955i
$852$		0			0
$853$	1.01071e13	−	8.48090e12i	0.653669	−	0.548493i	−0.254513	−	0.967069i	$-0.581915\pi$
$853$	1.01071e13	−	8.48090e12i	0.653669	−	0.548493i	0.908182	+	0.418576i	$0.137471\pi$
$854$	4.76780e7	−	8.25807e7i	3.06731e−6	−	5.31273e-6i
$855$		0			0
$856$	1.05167e13	+	1.82155e13i	0.669498	+	1.15960i
$857$	−1.23209e13	−	4.48445e12i	−0.780243	−	0.283985i	−0.0789691	−	0.996877i	$-0.525163\pi$
$857$	−1.23209e13	−	4.48445e12i	−0.780243	−	0.283985i	−0.701274	+	0.712892i	$0.747385\pi$
$858$		0			0
$859$	1.04932e13	+	8.80483e12i	0.657564	+	0.551762i	0.909356	−	0.416019i	$-0.136575\pi$
$859$	1.04932e13	+	8.80483e12i	0.657564	+	0.551762i	−0.251791	+	0.967782i	$0.581020\pi$
$860$	3.36930e13	−	1.22633e13i	2.10037	−	0.764474i
$861$		0			0
$862$	1.09857e12	+	6.23030e12i	0.0677712	+	0.384350i
$863$	−1.95087e13			−1.19724			−0.598619	−	0.801034i	$-0.704284\pi$
$863$	−1.95087e13			−1.19724			−0.598619	+	0.801034i	$0.704284\pi$
$864$		0			0
$865$	2.62560e13			1.59462
$866$	−1.79725e12	−	1.01927e13i	−0.108587	−	0.615828i
$867$		0			0
$868$	−3.76249e9	+	1.36944e9i	−0.000224976	+	8.18847e-5i
$869$	−1.22226e13	−	1.02559e13i	−0.727065	−	0.610080i
$870$		0			0
$871$	−1.94674e12	−	7.08555e11i	−0.114611	−	0.0417150i
$872$	8.60928e12	+	1.49117e13i	0.504246	+	0.873380i
$873$		0			0
$874$	1.03259e11	−	1.78849e11i	0.00598584	−	0.0103678i
$875$	4.27230e9	−	3.58489e9i	0.000246391	−	0.000206747i
$876$		0			0
$877$	5.82049e11	−	3.30096e12i	0.0332247	−	0.188427i	−0.963678	−	0.267065i	$-0.913946\pi$
$877$	5.82049e11	−	3.30096e12i	0.0332247	−	0.188427i	0.996903	+	0.0786384i	$0.0250572\pi$
$878$	2.15301e10	−	1.22103e11i	0.00122270	−	0.00693429i
$879$		0			0
$880$	−7.05157e12	+	5.91697e12i	−0.396382	+	0.332604i
$881$	−1.87831e12	+	3.25333e12i	−0.105045	+	0.181944i	−0.913757	−	0.406262i	$-0.866832\pi$
$881$	−1.87831e12	+	3.25333e12i	−0.105045	+	0.181944i	0.808711	+	0.588206i	$0.200165\pi$
$882$		0			0
$883$	9.03604e12	+	1.56509e13i	0.500213	+	0.866394i	1.00000		0.000245952i	$7.82889e-5\pi$
$883$	9.03604e12	+	1.56509e13i	0.500213	+	0.866394i	−0.499787	+	0.866148i	$0.666588\pi$
$884$	−2.95422e12	−	1.07525e12i	−0.162707	−	0.0592206i
$885$		0			0
$886$	−1.04870e12	−	8.79963e11i	−0.0571741	−	0.0479747i
$887$	−6.74841e12	+	2.45622e12i	−0.366054	+	0.133233i	−0.518497	−	0.855080i	$-0.673508\pi$
$887$	−6.74841e12	+	2.45622e12i	−0.366054	+	0.133233i	0.152443	+	0.988312i	$0.451286\pi$
$888$		0			0
$889$	−4.03354e7	−	2.28753e8i	−2.16585e−6	−	1.22831e-5i
$890$	−7.21318e11			−0.0385365
$891$		0			0
$892$	−1.28267e13			−0.678380
$893$	−4.44270e10	−	2.51958e11i	−0.00233784	−	0.0132586i
$894$		0			0
$895$	−1.98258e13	+	7.21601e12i	−1.03283	+	0.375918i
$896$	3.52632e9	+	2.95894e9i	0.000182783	+	0.000153373i
$897$		0			0
$898$	−6.06578e12	−	2.20776e12i	−0.311274	−	0.113295i
$899$	8.89640e12	+	1.54090e13i	0.454251	+	0.786785i
$900$		0			0
$901$	−7.06331e12	+	1.22340e13i	−0.357065	+	0.618454i
$902$	−5.23347e12	+	4.39141e12i	−0.263245	+	0.220889i
$903$		0			0
$904$	−1.19293e12	+	6.76542e12i	−0.0594094	+	0.336928i
$905$	8.46697e12	−	4.80186e13i	0.419575	−	2.37953i
$906$		0			0
$907$	−1.29188e13	+	1.08401e13i	−0.633853	+	0.531866i	−0.902124	−	0.431478i	$-0.857992\pi$
$907$	−1.29188e13	+	1.08401e13i	−0.633853	+	0.531866i	0.268271	+	0.963344i	$0.413548\pi$
$908$	1.09979e13	−	1.90489e13i	0.536936	−	0.930000i
$909$		0			0
$910$	−5.65868e8	−	9.80113e8i	−2.73545e−5	−	4.73794e-5i
$911$	−3.44752e10	−	1.25480e10i	−0.00165834	−	0.000603587i	0.341191	−	0.939994i	$-0.389170\pi$
$911$	−3.44752e10	−	1.25480e10i	−0.00165834	−	0.000603587i	−0.342849	+	0.939390i	$0.611392\pi$
$912$		0			0
$913$	5.23591e12	+	4.39345e12i	0.249387	+	0.209261i
$914$	−6.26802e12	+	2.28137e12i	−0.297079	+	0.108128i
$915$		0			0
$916$	−2.93568e12	−	1.66491e13i	−0.137778	−	0.781376i
$917$	−4.57090e9			−0.000213472
$918$		0			0
$919$	−1.36567e13			−0.631576			−0.315788	−	0.948830i	$-0.602269\pi$
$919$	−1.36567e13			−0.631576			−0.315788	+	0.948830i	$0.602269\pi$
$920$	8.06827e12	+	4.57574e13i	0.371309	+	2.10580i
$921$		0			0
$922$	1.31597e13	−	4.78974e12i	0.599732	−	0.218285i
$923$	2.37770e12	+	1.99513e12i	0.107833	+	0.0904823i
$924$		0			0
$925$	5.63895e13	+	2.05241e13i	2.53257	+	0.921779i
$926$	−5.21879e12	−	9.03921e12i	−0.233249	−	0.404000i
$927$		0			0
$928$	7.99177e12	−	1.38422e13i	0.353734	−	0.612686i
$929$	1.33618e13	−	1.12118e13i	0.588563	−	0.493863i	−0.299184	−	0.954196i	$-0.596714\pi$
$929$	1.33618e13	−	1.12118e13i	0.588563	−	0.493863i	0.887747	+	0.460333i	$0.152270\pi$
$930$		0			0
$931$	6.93300e10	−	3.93190e11i	0.00302446	−	0.0171526i
$932$	2.07005e12	−	1.17398e13i	0.0898689	−	0.509672i
$933$		0			0
$934$	6.55259e12	−	5.49827e12i	0.281742	−	0.236410i
$935$	−5.81376e12	+	1.00697e13i	−0.248774	+	0.430889i
$936$		0			0
$937$	6.24436e12	+	1.08155e13i	0.264643	+	0.458374i	0.967470	−	0.252986i	$-0.0814127\pi$
$937$	6.24436e12	+	1.08155e13i	0.264643	+	0.458374i	−0.702827	+	0.711360i	$0.748079\pi$
$938$	6.71691e8	+	2.44476e8i	2.83307e−5	+	1.03115e-5i
$939$		0			0
$940$	2.03011e13	+	1.70347e13i	0.848097	+	0.711637i
$941$	2.49594e13	−	9.08449e12i	1.03772	−	0.377700i	0.233706	−	0.972307i	$-0.424915\pi$
$941$	2.49594e13	−	9.08449e12i	1.03772	−	0.377700i	0.804017	+	0.594607i	$0.202692\pi$
$942$		0			0
$943$	−1.27956e13	−	7.25672e13i	−0.526934	−	2.98839i
$944$	−3.70588e12			−0.151886
$945$		0			0
$946$	−7.81043e12			−0.317077
$947$	1.92499e12	+	1.09172e13i	0.0777776	+	0.441098i	0.998683	+	0.0513117i	$0.0163402\pi$
$947$	1.92499e12	+	1.09172e13i	0.0777776	+	0.441098i	−0.920905	+	0.389787i	$0.872549\pi$
$948$		0			0
$949$	−1.16892e12	+	4.25452e11i	−0.0467828	+	0.0170275i
$950$	−2.33273e11	−	1.95739e11i	−0.00929199	−	0.00779690i
$951$		0			0
$952$	2.21395e9	+	8.05812e8i	8.73578e−5	+	3.17956e-5i
$953$	1.04225e13	+	1.80524e13i	0.409313	+	0.708951i	0.994813	−	0.101722i	$-0.0324351\pi$
$953$	1.04225e13	+	1.80524e13i	0.409313	+	0.708951i	−0.585500	+	0.810672i	$0.699102\pi$
$954$		0			0
$955$	−1.38144e13	+	2.39272e13i	−0.537424	+	0.930845i
$956$	1.61372e13	−	1.35407e13i	0.624837	−	0.524301i
$957$		0			0
$958$	7.79889e11	−	4.42297e12i	0.0299149	−	0.169656i
$959$	4.81617e8	−	2.73138e9i	1.83873e−5	−	0.000104280i
$960$		0			0
$961$	8.79911e12	−	7.38333e12i	0.332800	−	0.279252i
$962$	2.73926e12	−	4.74454e12i	0.103121	−	0.178610i
$963$		0			0
$964$	1.03524e13	+	1.79308e13i	0.386094	+	0.668734i
$965$	5.95931e13	+	2.16901e13i	2.21219	+	0.805172i
$966$		0			0
$967$	−9.79572e12	−	8.21958e12i	−0.360261	−	0.302295i	0.444634	−	0.895712i	$-0.353334\pi$
$967$	−9.79572e12	−	8.21958e12i	−0.360261	−	0.302295i	−0.804895	+	0.593418i	$0.797778\pi$
$968$	−1.30992e13	+	4.76772e12i	−0.479519	+	0.174531i
$969$		0			0
$970$	3.33178e12	+	1.88955e13i	0.120838	+	0.685307i
$971$	1.82419e13			0.658543			0.329271	−	0.944235i	$-0.393197\pi$
$971$	1.82419e13			0.658543			0.329271	+	0.944235i	$0.393197\pi$
$972$		0			0
$973$	−3.25648e9			−0.000116477
$974$	5.73254e11	+	3.25109e12i	0.0204095	+	0.115748i
$975$		0			0
$976$	−1.05822e12	+	3.85161e11i	−0.0373295	+	0.0135868i
$977$	1.43968e13	+	1.20804e13i	0.505524	+	0.424185i	0.859551	−	0.511050i	$-0.170743\pi$
$977$	1.43968e13	+	1.20804e13i	0.505524	+	0.424185i	−0.354027	+	0.935235i	$0.615188\pi$
$978$		0			0
$979$	−8.58334e11	−	3.12408e11i	−0.0298631	−	0.0108693i
$980$	2.06781e13	+	3.58155e13i	0.716133	+	1.24038i
$981$		0			0
$982$	−4.84329e12	+	8.38882e12i	−0.166203	+	0.287872i
$983$	8.36983e12	−	7.02312e12i	0.285908	−	0.239905i	−0.488542	−	0.872540i	$-0.662471\pi$
$983$	8.36983e12	−	7.02312e12i	0.285908	−	0.239905i	0.774450	+	0.632635i	$0.218027\pi$
$984$		0			0
$985$	1.21412e12	−	6.88563e12i	0.0410960	−	0.233067i
$986$	8.37033e11	−	4.74705e12i	0.0282031	−	0.159948i
$987$		0			0
$988$	1.23805e11	−	1.03885e11i	0.00413363	−	0.00346853i
$989$	4.21209e13	−	7.29555e13i	1.39996	−	2.42479i
$990$		0			0
$991$	−6.44728e12	−	1.11670e13i	−0.212347	−	0.367795i	0.740102	−	0.672495i	$-0.234777\pi$
$991$	−6.44728e12	−	1.11670e13i	−0.212347	−	0.367795i	−0.952448	+	0.304700i	$0.901444\pi$
$992$	−3.20149e13	−	1.16525e13i	−1.04966	−	0.382046i
$993$		0			0
$994$	−8.20390e8	−	6.88389e8i	−2.66552e−5	−	2.23663e-5i
$995$	−3.04478e13	+	1.10821e13i	−0.984809	+	0.358441i
$996$		0			0
$997$	−2.59413e12	−	1.47121e13i	−0.0831503	−	0.471569i	−0.997740	−	0.0671867i	$-0.978598\pi$
$997$	−2.59413e12	−	1.47121e13i	−0.0831503	−	0.471569i	0.914590	−	0.404382i	$-0.132513\pi$
$998$	2.86905e12			0.0915483
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.e.a.10.16		156
3.2	odd	2		27.10.e.a.13.11	✓	156
27.2	odd	18		27.10.e.a.25.11	yes	156
27.25	even	9	inner	81.10.e.a.73.16		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.13.11	✓	156	3.2	odd	2
27.10.e.a.25.11	yes	156	27.2	odd	18
81.10.e.a.10.16		156	1.1	even	1	trivial
81.10.e.a.73.16		156	27.25	even	9	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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50531 + 8.53705i) q^{2} +(410.507 - 149.412i) q^{4} +(-1797.12 - 1507.96i) q^{5} +(1.39853 + 0.509023i) q^{7} +(4112.68 + 7123.37i) q^{8} +(10168.3 - 17612.1i) q^{10} +(19727.7 - 16553.5i) q^{11} +(6493.07 - 36824.0i) q^{13} +(-2.24033 + 12.7056i) q^{14} +(116718. - 97938.4i) q^{16} +(96230.1 - 166676. i) q^{17} +(4946.96 + 8568.39i) q^{19} +(-963040. - 350518. i) q^{20} +(171015. + 143498. i) q^{22} +(-2.26265e6 + 823538. i) q^{23} +(616533. + 3.49653e6i) q^{25} +324143. q^{26} +650.162 q^{28} +(-501702. - 2.84529e6i) q^{29} +(-5.78701e6 + 2.10630e6i) q^{31} +(4.23791e6 + 3.55603e6i) q^{32} +(1.56777e6 + 570623. i) q^{34} +(-1745.74 - 3023.71i) q^{35} +(8.45078e6 - 1.46372e7i) q^{37} +(-65702.1 + 55130.6i) q^{38} +(3.35080e6 - 1.90033e7i) q^{40} +(-5.31407e6 + 3.01376e7i) q^{41} +(-2.68009e7 + 2.24886e7i) q^{43} +(5.62507e6 - 9.74291e6i) q^{44} +(-1.04366e7 - 1.80767e7i) q^{46} +(-2.42993e7 - 8.84423e6i) q^{47} +(-3.09127e7 - 2.59388e7i) q^{49} +(-2.89220e7 + 1.05267e7i) q^{50} +(-2.83652e6 - 1.60867e7i) q^{52} -7.34002e7 q^{53} -6.04152e7 q^{55} +(2125.75 + 12055.7i) q^{56} +(2.35352e7 - 8.56610e6i) q^{58} +(-1.86320e7 - 1.56341e7i) q^{59} +(-6.94530e6 - 2.52788e6i) q^{61} +(-2.66928e7 - 4.62334e7i) q^{62} +(1.50269e7 - 2.60273e7i) q^{64} +(-6.71981e7 + 5.63859e7i) q^{65} +(9.62082e6 - 5.45624e7i) q^{67} +(1.45998e7 - 8.27995e7i) q^{68} +(23185.7 - 19455.1i) q^{70} +(-4.15044e7 + 7.18877e7i) q^{71} +(-1.66337e7 - 2.88104e7i) q^{73} +(1.37679e8 + 5.01112e7i) q^{74} +(3.31099e6 + 2.77825e6i) q^{76} +(36016.0 - 13108.7i) q^{77} +(-1.07586e8 - 6.10150e8i) q^{79} -3.57445e8 q^{80} -2.65285e8 q^{82} +(4.60878e7 + 2.61377e8i) q^{83} +(-4.24278e8 + 1.54424e8i) q^{85} +(-2.32330e8 - 1.94948e8i) q^{86} +(1.99051e8 + 7.24485e7i) q^{88} +(-1.77344e7 - 3.07170e7i) q^{89} +(27825.1 - 48194.4i) q^{91} +(-8.05789e8 + 6.76137e8i) q^{92} +(3.89255e7 - 2.20758e8i) q^{94} +(4.03053e6 - 2.28583e7i) q^{95} +(-7.22738e8 + 6.06450e8i) q^{97} +(1.74908e8 - 3.02949e8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) \) 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Introduction

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