LMFDB - Embedded newform 81.10.c.j.28.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,10,Mod(28,81)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("81.28"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(81, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	81.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$41.7179027293$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 83x^{6} + 5449x^{4} + 119520x^{2} + 2073600 $ x^8 + 83x^6 + 5449x^4 + 119520*x^2 + 2073600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{16} $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			28.1
Root			$3.81773 + 6.61251i$ of defining polynomial
Character	$\chi$	$=$	81.28
Dual form			81.10.c.j.55.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-22.2386 - 38.5183i) q^{2} +(-733.108 + 1269.78i) q^{4} +(525.311 - 909.865i) q^{5} +(-3295.93 - 5708.72i) q^{7} +42440.8 q^{8} -46728.6 q^{10} +(-7232.96 - 12527.8i) q^{11} +(-2501.75 + 4333.15i) q^{13} +(-146594. + 253908. i) q^{14} +(-568471. - 984621. i) q^{16} -444500. q^{17} -487431. q^{19} +(770219. + 1.33406e6i) q^{20} +(-321701. + 557203. i) q^{22} +(33652.3 - 58287.4i) q^{23} +(424660. + 735532. i) q^{25} +222541. q^{26} +9.66510e6 q^{28} +(1.70907e6 + 2.96019e6i) q^{29} +(-1.72962e6 + 2.99578e6i) q^{31} +(-1.44191e7 + 2.49747e7i) q^{32} +(9.88504e6 + 1.71214e7i) q^{34} -6.92555e6 q^{35} -3.94510e6 q^{37} +(1.08398e7 + 1.87750e7i) q^{38} +(2.22946e7 - 3.86154e7i) q^{40} +(8.80305e6 - 1.52473e7i) q^{41} +(-1.65115e7 - 2.85988e7i) q^{43} +2.12102e7 q^{44} -2.99351e6 q^{46} +(1.85636e7 + 3.21530e7i) q^{47} +(-1.54953e6 + 2.68387e6i) q^{49} +(1.88876e7 - 3.27144e7i) q^{50} +(-3.66810e6 - 6.35334e6i) q^{52} -7.86818e7 q^{53} -1.51982e7 q^{55} +(-1.39882e8 - 2.42283e8i) q^{56} +(7.60144e7 - 1.31661e8i) q^{58} +(-2.56527e7 + 4.44318e7i) q^{59} +(9.63615e6 + 1.66903e7i) q^{61} +1.53857e8 q^{62} +7.00529e8 q^{64} +(2.62839e6 + 4.55250e6i) q^{65} +(-1.07419e8 + 1.86055e8i) q^{67} +(3.25866e8 - 5.64417e8i) q^{68} +(1.54014e8 + 2.66761e8i) q^{70} +3.25802e8 q^{71} +1.57548e8 q^{73} +(8.77334e7 + 1.51959e8i) q^{74} +(3.57340e8 - 6.18931e8i) q^{76} +(-4.76787e7 + 8.25819e7i) q^{77} +(-1.79317e7 - 3.10586e7i) q^{79} -1.19450e9 q^{80} -7.83069e8 q^{82} +(-4.03992e6 - 6.99735e6i) q^{83} +(-2.33501e8 + 4.04435e8i) q^{85} +(-7.34386e8 + 1.27199e9i) q^{86} +(-3.06972e8 - 5.31692e8i) q^{88} +9.43654e8 q^{89} +3.29823e7 q^{91} +(4.93415e7 + 8.54620e7i) q^{92} +(8.25654e8 - 1.43008e9i) q^{94} +(-2.56053e8 + 4.43497e8i) q^{95} +(-4.83526e8 - 8.37491e8i) q^{97} +1.37838e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2236 q^{4} - 11852 q^{7} - 83520 q^{10} - 179684 q^{13} - 2348680 q^{16} + 2022856 q^{19} - 3473568 q^{22} - 2554060 q^{25} + 39587848 q^{28} - 889136 q^{31} + 43111008 q^{34} - 7610312 q^{37} + 133649280 q^{40}+ \cdots - 1935734516 q^{97}+O(q^{100}) $ 8 * q - 2236 * q^4 - 11852 * q^7 - 83520 * q^10 - 179684 * q^13 - 2348680 * q^16 + 2022856 * q^19 - 3473568 * q^22 - 2554060 * q^25 + 39587848 * q^28 - 889136 * q^31 + 43111008 * q^34 - 7610312 * q^37 + 133649280 * q^40 - 11585024 * q^43 + 26856000 * q^46 + 73622328 * q^49 + 44411860 * q^52 + 629444160 * q^55 + 407685888 * q^58 - 219882572 * q^61 + 3038570720 * q^64 - 390561236 * q^67 + 650481120 * q^70 + 2395899016 * q^73 + 2121017572 * q^76 - 49814324 * q^79 - 3534253056 * q^82 - 370444320 * q^85 + 653198976 * q^88 - 94034344 * q^91 + 4146926688 * q^94 - 1935734516 * q^97

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−22.2386	−	38.5183i	−0.982815	−	1.70229i	−0.651269	−	0.758847i	$-0.725763\pi$
$2$	−22.2386	−	38.5183i	−0.982815	−	1.70229i	−0.331546	−	0.943439i	$-0.607570\pi$
$3$		0			0
$3$		0			0
$4$	−733.108	+	1269.78i	−1.43185	+	2.48004i
$5$	525.311	−	909.865i	0.375882	−	0.651046i	−0.614577	−	0.788857i	$-0.710673\pi$
$5$	525.311	−	909.865i	0.375882	−	0.651046i	0.990459	+	0.137811i	$0.0440065\pi$
$6$		0			0
$7$	−3295.93	−	5708.72i	−0.518844	−	0.898665i	−0.999760	−	0.0218980i	$-0.993029\pi$
$7$	−3295.93	−	5708.72i	−0.518844	−	0.898665i	0.480916	−	0.876767i	$-0.340304\pi$
$8$	42440.8			3.66335
$9$		0			0
$10$	−46728.6			−1.47769
$11$	−7232.96	−	12527.8i	−0.148953	−	0.257994i	0.781888	−	0.623419i	$-0.214257\pi$
$11$	−7232.96	−	12527.8i	−0.148953	−	0.257994i	−0.930841	+	0.365425i	$0.880924\pi$
$12$		0			0
$13$	−2501.75	+	4333.15i	−0.0242940	+	0.0420784i	−0.877917	−	0.478813i	$-0.841067\pi$
$13$	−2501.75	+	4333.15i	−0.0242940	+	0.0420784i	0.853623	+	0.520892i	$0.174400\pi$
$14$	−146594.	+	253908.i	−1.01986	+	1.76644i
$15$		0			0
$16$	−568471.	−	984621.i	−2.16855	−	3.75603i
$17$	−444500.			−1.29078			−0.645389	−	0.763854i	$-0.723305\pi$
$17$	−444500.			−1.29078			−0.645389	+	0.763854i	$0.723305\pi$
$18$		0			0
$19$	−487431.			−0.858069			−0.429035	−	0.903288i	$-0.641146\pi$
$19$	−487431.			−0.858069			−0.429035	+	0.903288i	$0.641146\pi$
$20$	770219.	+	1.33406e6i	1.07641	+	1.86440i
$21$		0			0
$22$	−321701.	+	557203.i	−0.292786	+	0.507121i
$23$	33652.3	−	58287.4i	0.0250749	−	0.0434310i	−0.853216	−	0.521558i	$-0.825351\pi$
$23$	33652.3	−	58287.4i	0.0250749	−	0.0434310i	0.878291	+	0.478127i	$0.158684\pi$
$24$		0			0
$25$	424660.	+	735532.i	0.217426	+	0.376592i
$26$	222541.			0.0955059
$27$		0			0
$28$	9.66510e6			2.97163
$29$	1.70907e6	+	2.96019e6i	0.448712	+	0.777193i	0.998303	−	0.0582417i	$-0.0185494\pi$
$29$	1.70907e6	+	2.96019e6i	0.448712	+	0.777193i	−0.549590	+	0.835434i	$0.685216\pi$
$30$		0			0
$31$	−1.72962e6	+	2.99578e6i	−0.336374	+	0.582616i	−0.983748	−	0.179556i	$-0.942534\pi$
$31$	−1.72962e6	+	2.99578e6i	−0.336374	+	0.582616i	0.647374	+	0.762172i	$0.275867\pi$
$32$	−1.44191e7	+	2.49747e7i	−2.43089	+	4.21042i
$33$		0			0
$34$	9.88504e6	+	1.71214e7i	1.26860	+	2.19727i
$35$	−6.92555e6			−0.780097
$36$		0			0
$37$	−3.94510e6			−0.346059			−0.173030	−	0.984917i	$-0.555356\pi$
$37$	−3.94510e6			−0.346059			−0.173030	+	0.984917i	$0.555356\pi$
$38$	1.08398e7	+	1.87750e7i	0.843323	+	1.46068i
$39$		0			0
$40$	2.22946e7	−	3.86154e7i	1.37699	−	2.38501i
$41$	8.80305e6	−	1.52473e7i	0.486526	−	0.842687i	−0.513354	−	0.858177i	$-0.671597\pi$
$41$	8.80305e6	−	1.52473e7i	0.486526	−	0.842687i	0.999880	+	0.0154894i	$0.00493064\pi$
$42$		0			0
$43$	−1.65115e7	−	2.85988e7i	−0.736512	−	1.27568i	−0.954057	−	0.299625i	$-0.903138\pi$
$43$	−1.65115e7	−	2.85988e7i	−0.736512	−	1.27568i	0.217545	−	0.976050i	$-0.430195\pi$
$44$	2.12102e7			0.853113
$45$		0			0
$46$	−2.99351e6			−0.0985759
$47$	1.85636e7	+	3.21530e7i	0.554908	+	0.961129i	0.997911	+	0.0646087i	$0.0205799\pi$
$47$	1.85636e7	+	3.21530e7i	0.554908	+	0.961129i	−0.443003	+	0.896520i	$0.646087\pi$
$48$		0			0
$49$	−1.54953e6	+	2.68387e6i	−0.0383989	+	0.0665088i
$50$	1.88876e7	−	3.27144e7i	0.427379	−	0.740242i
$51$		0			0
$52$	−3.66810e6	−	6.35334e6i	−0.0695707	−	0.120500i
$53$	−7.86818e7			−1.36972			−0.684861	−	0.728673i	$-0.740137\pi$
$53$	−7.86818e7			−1.36972			−0.684861	+	0.728673i	$0.740137\pi$
$54$		0			0
$55$	−1.51982e7			−0.223955
$56$	−1.39882e8	−	2.42283e8i	−1.90071	−	3.29213i
$57$		0			0
$58$	7.60144e7	−	1.31661e8i	0.882003	−	1.52767i
$59$	−2.56527e7	+	4.44318e7i	−0.275613	+	0.477375i	−0.970290	−	0.241947i	$-0.922214\pi$
$59$	−2.56527e7	+	4.44318e7i	−0.275613	+	0.477375i	0.694677	+	0.719322i	$0.255547\pi$
$60$		0			0
$61$	9.63615e6	+	1.66903e7i	0.0891085	+	0.154340i	0.907135	−	0.420841i	$-0.138265\pi$
$61$	9.63615e6	+	1.66903e7i	0.0891085	+	0.154340i	−0.818026	+	0.575181i	$0.804932\pi$
$62$	1.53857e8			1.32237
$63$		0			0
$64$	7.00529e8			5.21935
$65$	2.62839e6	+	4.55250e6i	0.0182633	+	0.0316330i
$66$		0			0
$67$	−1.07419e8	+	1.86055e8i	−0.651245	+	1.12799i	0.331575	+	0.943429i	$0.392420\pi$
$67$	−1.07419e8	+	1.86055e8i	−0.651245	+	1.12799i	−0.982821	+	0.184562i	$0.940913\pi$
$68$	3.25866e8	−	5.64417e8i	1.84820	−	3.20118i
$69$		0			0
$70$	1.54014e8	+	2.66761e8i	0.766691	+	1.32795i
$71$	3.25802e8			1.52157			0.760784	−	0.649006i	$-0.224815\pi$
$71$	3.25802e8			1.52157			0.760784	+	0.649006i	$0.224815\pi$
$72$		0			0
$73$	1.57548e8			0.649322			0.324661	−	0.945830i	$-0.394750\pi$
$73$	1.57548e8			0.649322			0.324661	+	0.945830i	$0.394750\pi$
$74$	8.77334e7	+	1.51959e8i	0.340112	+	0.589092i
$75$		0			0
$76$	3.57340e8	−	6.18931e8i	1.22863	−	2.12805i
$77$	−4.76787e7	+	8.25819e7i	−0.154567	+	0.267717i
$78$		0			0
$79$	−1.79317e7	−	3.10586e7i	−0.0517964	−	0.0897140i	0.838965	−	0.544186i	$-0.183161\pi$
$79$	−1.79317e7	−	3.10586e7i	−0.0517964	−	0.0897140i	−0.890761	+	0.454472i	$0.849828\pi$
$80$	−1.19450e9			−3.26047
$81$		0			0
$82$	−7.83069e8			−1.91266
$83$	−4.03992e6	−	6.99735e6i	−0.00934375	−	0.0161839i	0.861316	−	0.508070i	$-0.169641\pi$
$83$	−4.03992e6	−	6.99735e6i	−0.00934375	−	0.0161839i	−0.870659	+	0.491886i	$0.836308\pi$
$84$		0			0
$85$	−2.33501e8	+	4.04435e8i	−0.485180	+	0.840356i
$86$	−7.34386e8	+	1.27199e9i	−1.44771	+	2.50751i
$87$		0			0
$88$	−3.06972e8	−	5.31692e8i	−0.545667	−	0.945122i
$89$	9.43654e8			1.59425			0.797127	−	0.603812i	$-0.206352\pi$
$89$	9.43654e8			1.59425			0.797127	+	0.603812i	$0.206352\pi$
$90$		0			0
$91$	3.29823e7			0.0504191
$92$	4.93415e7	+	8.54620e7i	0.0718070	+	0.124373i
$93$		0			0
$94$	8.25654e8	−	1.43008e9i	1.09074	−	1.88922i
$95$	−2.56053e8	+	4.43497e8i	−0.322533	+	0.558643i
$96$		0			0
$97$	−4.83526e8	−	8.37491e8i	−0.554558	−	0.960522i	−0.997938	−	0.0641886i	$-0.979554\pi$
$97$	−4.83526e8	−	8.37491e8i	−0.554558	−	0.960522i	0.443380	−	0.896334i	$-0.353779\pi$
$98$	1.37838e8			0.150956
$99$		0			0
$100$	−1.24529e9			−1.24529
$101$	8.41991e8	+	1.45837e9i	0.805121	+	1.39451i	0.916209	+	0.400700i	$0.131233\pi$
$101$	8.41991e8	+	1.45837e9i	0.805121	+	1.39451i	−0.111088	+	0.993811i	$0.535434\pi$
$102$		0			0
$103$	−5.03057e7	+	8.71321e7i	−0.0440403	+	0.0762800i	−0.887205	−	0.461375i	$-0.847356\pi$
$103$	−5.03057e7	+	8.71321e7i	−0.0440403	+	0.0762800i	0.843165	+	0.537655i	$0.180690\pi$
$104$	−1.06176e8	+	1.83902e8i	−0.0889973	+	0.154148i
$105$		0			0
$106$	1.74977e9	+	3.03069e9i	1.34618	+	2.33166i
$107$	5.50494e8			0.406000			0.203000	−	0.979179i	$-0.434931\pi$
$107$	5.50494e8			0.406000			0.203000	+	0.979179i	$0.434931\pi$
$108$		0			0
$109$	1.31023e9			0.889055			0.444527	−	0.895765i	$-0.353372\pi$
$109$	1.31023e9			0.889055			0.444527	+	0.895765i	$0.353372\pi$
$110$	3.37986e8	+	5.85409e8i	0.220106	+	0.381235i
$111$		0			0
$112$	−3.74729e9	+	6.49049e9i	−2.25028	+	3.89759i
$113$	3.87701e7	−	6.71518e7i	0.0223689	−	0.0387440i	−0.854624	−	0.519247i	$-0.826213\pi$
$113$	3.87701e7	−	6.71518e7i	0.0223689	−	0.0387440i	0.876993	+	0.480503i	$0.159546\pi$
$114$		0			0
$115$	−3.53558e7	−	6.12380e7i	−0.0188504	−	0.0326498i
$116$	−5.01172e9			−2.56996
$117$		0			0
$118$	2.28192e9			1.08351
$119$	1.46504e9	+	2.53753e9i	0.669713	+	1.15998i
$120$		0			0
$121$	1.07434e9	−	1.86082e9i	0.455626	−	0.789168i
$122$	4.28588e8	−	7.42337e8i	0.175154	−	0.303376i
$123$		0			0
$124$	−2.53599e9	−	4.39246e9i	−0.963274	−	1.66844i
$125$	2.94431e9			1.07867
$126$		0			0
$127$	−1.89287e9			−0.645661			−0.322830	−	0.946457i	$-0.604634\pi$
$127$	−1.89287e9			−0.645661			−0.322830	+	0.946457i	$0.604634\pi$
$128$	−8.19617e9	−	1.41962e10i	−2.69877	−	4.67441i
$129$		0			0
$130$	1.16903e8	−	2.02482e8i	0.0358989	−	0.0621788i
$131$	2.31093e9	−	4.00265e9i	0.685593	−	1.18748i	−0.287657	−	0.957734i	$-0.592876\pi$
$131$	2.31093e9	−	4.00265e9i	0.685593	−	1.18748i	0.973250	−	0.229749i	$-0.0737904\pi$
$132$		0			0
$133$	1.60654e9	+	2.78261e9i	0.445204	+	0.771116i
$134$	9.55538e9			2.56022
$135$		0			0
$136$	−1.88649e10			−4.72857
$137$	3.41347e9	+	5.91231e9i	0.827854	+	1.43389i	0.899718	+	0.436471i	$0.143772\pi$
$137$	3.41347e9	+	5.91231e9i	0.827854	+	1.43389i	−0.0718644	+	0.997414i	$0.522895\pi$
$138$		0			0
$139$	−2.43834e9	+	4.22333e9i	−0.554023	+	0.959596i	0.443956	+	0.896049i	$0.353575\pi$
$139$	−2.43834e9	+	4.22333e9i	−0.554023	+	0.959596i	−0.997979	+	0.0635471i	$0.979759\pi$
$140$	5.07718e9	−	8.79393e9i	1.11698	−	1.93467i
$141$		0			0
$142$	−7.24537e9	−	1.25493e10i	−1.49542	−	2.59014i
$143$	7.23801e7			0.0144746
$144$		0			0
$145$	3.59117e9			0.674651
$146$	−3.50364e9	−	6.06849e9i	−0.638163	−	1.10533i
$147$		0			0
$148$	2.89219e9	−	5.00941e9i	0.495506	−	0.858241i
$149$	−3.82468e9	+	6.62455e9i	−0.635708	+	1.10108i	0.350657	+	0.936504i	$0.385958\pi$
$149$	−3.82468e9	+	6.62455e9i	−0.635708	+	1.10108i	−0.986365	+	0.164574i	$0.947375\pi$
$150$		0			0
$151$	2.09794e9	+	3.63374e9i	0.328396	+	0.568798i	0.982194	−	0.187871i	$-0.0601587\pi$
$151$	2.09794e9	+	3.63374e9i	0.328396	+	0.568798i	−0.653798	+	0.756669i	$0.726825\pi$
$152$	−2.06870e10			−3.14341
$153$		0			0
$154$	4.24122e9			0.607642
$155$	1.81717e9	+	3.14743e9i	0.252873	+	0.437990i
$156$		0			0
$157$	3.80239e8	−	6.58594e8i	0.0499469	−	0.0865106i	−0.839971	−	0.542631i	$-0.817428\pi$
$157$	3.80239e8	−	6.58594e8i	0.0499469	−	0.0865106i	0.889918	+	0.456121i	$0.150761\pi$
$158$	−7.97550e8	+	1.38140e9i	−0.101813	+	0.176344i
$159$		0			0
$160$	1.51491e10	+	2.62389e10i	1.82745	+	3.16524i
$161$	−4.43662e8			−0.0520398
$162$		0			0
$163$	−7.55113e9			−0.837853			−0.418926	−	0.908020i	$-0.637593\pi$
$163$	−7.55113e9			−0.837853			−0.418926	+	0.908020i	$0.637593\pi$
$164$	1.29072e10	+	2.23559e10i	1.39327	+	2.41321i
$165$		0			0
$166$	−1.79684e8	+	3.11222e8i	−0.0183664	+	0.0318115i
$167$	−4.02882e9	+	6.97812e9i	−0.400824	+	0.694248i	−0.993826	−	0.110954i	$-0.964609\pi$
$167$	−4.02882e9	+	6.97812e9i	−0.400824	+	0.694248i	0.593002	+	0.805201i	$0.297943\pi$
$168$		0			0
$169$	5.28973e9	+	9.16208e9i	0.498820	+	0.863981i
$170$	2.07709e10			1.90737
$171$		0			0
$172$	4.84190e10			4.21830
$173$	−2.06159e9	−	3.57078e9i	−0.174982	−	0.303079i	0.765173	−	0.643825i	$-0.222654\pi$
$173$	−2.06159e9	−	3.57078e9i	−0.174982	−	0.303079i	−0.940155	+	0.340747i	$0.889320\pi$
$174$		0			0
$175$	2.79930e9	−	4.84853e9i	0.225620	−	0.390786i
$176$	−8.22346e9	+	1.42434e10i	−0.646022	+	1.11894i
$177$		0			0
$178$	−2.09855e10	−	3.63480e10i	−1.56686	−	2.71388i
$179$	2.46170e10			1.79224			0.896120	−	0.443811i	$-0.146374\pi$
$179$	2.46170e10			1.79224			0.896120	+	0.443811i	$0.146374\pi$
$180$		0			0
$181$	−4.17661e9			−0.289248			−0.144624	−	0.989487i	$-0.546197\pi$
$181$	−4.17661e9			−0.289248			−0.144624	+	0.989487i	$0.546197\pi$
$182$	−7.33480e8	−	1.27043e9i	−0.0495527	−	0.0858278i
$183$		0			0
$184$	1.42823e9	−	2.47376e9i	0.0918581	−	0.159103i
$185$	−2.07240e9	+	3.58951e9i	−0.130077	+	0.225301i
$186$		0			0
$187$	3.21505e9	+	5.56862e9i	0.192265	+	0.333013i
$188$	−5.44364e10			−3.17818
$189$		0			0
$190$	2.27770e10			1.26796
$191$	−7.32150e9	−	1.26812e10i	−0.398061	−	0.689462i	0.595426	−	0.803411i	$-0.296983\pi$
$191$	−7.32150e9	−	1.26812e10i	−0.398061	−	0.689462i	−0.993487	+	0.113948i	$0.963650\pi$
$192$		0			0
$193$	−7.93330e9	+	1.37409e10i	−0.411572	+	0.712864i	−0.995062	−	0.0992567i	$-0.968354\pi$
$193$	−7.93330e9	+	1.37409e10i	−0.411572	+	0.712864i	0.583490	+	0.812120i	$0.301687\pi$
$194$	−2.15058e10	+	3.72492e10i	−1.09006	+	1.88803i
$195$		0			0
$196$	−2.27195e9	−	3.93514e9i	−0.109963	−	0.190462i
$197$	−4.01582e9			−0.189966			−0.0949832	−	0.995479i	$-0.530280\pi$
$197$	−4.01582e9			−0.189966			−0.0949832	+	0.995479i	$0.530280\pi$
$198$		0			0
$199$	−3.90309e10			−1.76429			−0.882144	−	0.470980i	$-0.843901\pi$
$199$	−3.90309e10			−1.76429			−0.882144	+	0.470980i	$0.843901\pi$
$200$	1.80229e10	+	3.12166e10i	0.796507	+	1.37959i
$201$		0			0
$202$	3.74493e10	−	6.48642e10i	1.58257	−	2.74109i
$203$	1.12659e10	−	1.95132e10i	0.465624	−	0.806484i
$204$		0			0
$205$	−9.24867e9	−	1.60192e10i	−0.365752	−	0.633502i
$206$	4.47491e9			0.173134
$207$		0			0
$208$	5.68869e9			0.210730
$209$	3.52557e9	+	6.10647e9i	0.127812	+	0.221377i
$210$		0			0
$211$	−1.35050e10	+	2.33913e10i	−0.469054	+	0.812425i	−0.999374	−	0.0353723i	$-0.988738\pi$
$211$	−1.35050e10	+	2.33913e10i	−0.469054	+	0.812425i	0.530320	+	0.847797i	$0.322072\pi$
$212$	5.76822e10	−	9.99086e10i	1.96124	−	3.39697i
$213$		0			0
$214$	−1.22422e10	−	2.12041e10i	−0.399023	−	0.691128i
$215$	−3.46948e10			−1.10737
$216$		0			0
$217$	2.28028e10			0.698102
$218$	−2.91377e10	−	5.04679e10i	−0.873776	−	1.51343i
$219$		0			0
$220$	1.11419e10	−	1.92984e10i	0.320670	−	0.555416i
$221$	1.11203e9	−	1.92608e9i	0.0313581	−	0.0543138i
$222$		0			0
$223$	2.86518e10	+	4.96264e10i	0.775854	+	1.34382i	0.934313	+	0.356453i	$0.116014\pi$
$223$	2.86518e10	+	4.96264e10i	0.775854	+	1.34382i	−0.158459	+	0.987366i	$0.550653\pi$
$224$	1.90098e11			5.04500
$225$		0			0
$226$	−3.44877e9			−0.0879379
$227$	−1.75028e10	−	3.03158e10i	−0.437514	−	0.757797i	0.559983	−	0.828504i	$-0.310808\pi$
$227$	−1.75028e10	−	3.03158e10i	−0.437514	−	0.757797i	−0.997497	+	0.0707073i	$0.977474\pi$
$228$		0			0
$229$	−3.23765e10	+	5.60778e10i	−0.777984	+	1.34751i	0.155118	+	0.987896i	$0.450424\pi$
$229$	−3.23765e10	+	5.60778e10i	−0.777984	+	1.34751i	−0.933102	+	0.359611i	$0.882909\pi$
$230$	−1.57252e9	+	2.72369e9i	−0.0370529	+	0.0641775i
$231$		0			0
$232$	7.25342e10	+	1.25633e11i	1.64379	+	2.84713i
$233$	−5.91061e10			−1.31380			−0.656902	−	0.753976i	$-0.728134\pi$
$233$	−5.91061e10			−1.31380			−0.656902	+	0.753976i	$0.728134\pi$
$234$		0			0
$235$	3.90066e10			0.834319
$236$	−3.76124e10	−	6.51466e10i	−0.789273	−	1.36706i
$237$		0			0
$238$	6.51608e10	−	1.12862e11i	1.31641	−	2.28008i
$239$	2.02351e10	−	3.50482e10i	0.401158	−	0.694825i	−0.592708	−	0.805417i	$-0.701941\pi$
$239$	2.02351e10	−	3.50482e10i	0.401158	−	0.694825i	0.993866	+	0.110592i	$0.0352746\pi$
$240$		0			0
$241$	−1.68545e9	−	2.91928e9i	−0.0321839	−	0.0557441i	0.849485	−	0.527613i	$-0.176913\pi$
$241$	−1.68545e9	−	2.91928e9i	−0.0321839	−	0.0557441i	−0.881669	+	0.471869i	$0.843580\pi$
$242$	−9.55674e10			−1.79119
$243$		0			0
$244$	−2.82573e10			−0.510361
$245$	1.62797e9	+	2.81973e9i	0.0288669	+	0.0499989i
$246$		0			0
$247$	1.21943e9	−	2.11211e9i	0.0208459	−	0.0361061i
$248$	−7.34063e10	+	1.27143e11i	−1.23225	+	2.13433i
$249$		0			0
$250$	−6.54772e10	−	1.13410e11i	−1.06013	−	1.83620i
$251$	−4.69295e10			−0.746301			−0.373151	−	0.927771i	$-0.621723\pi$
$251$	−4.69295e10			−0.746301			−0.373151	+	0.927771i	$0.621723\pi$
$252$		0			0
$253$	−9.73621e8			−0.0149399
$254$	4.20947e10	+	7.29102e10i	0.634565	+	1.09910i
$255$		0			0
$256$	−1.85207e11	+	3.20788e11i	−2.69511	+	4.66808i
$257$	8.74728e9	−	1.51507e10i	0.125076	−	0.216638i	−0.796687	−	0.604393i	$-0.793416\pi$
$257$	8.74728e9	−	1.51507e10i	0.125076	−	0.216638i	0.921763	+	0.387755i	$0.126749\pi$
$258$		0			0
$259$	1.30028e10	+	2.25215e10i	0.179551	+	0.310991i
$260$	−7.70757e9			−0.104601
$261$		0			0
$262$	−2.05567e11			−2.69525
$263$	−5.03147e10	−	8.71475e10i	−0.648476	−	1.12319i	−0.983487	−	0.180979i	$-0.942073\pi$
$263$	−5.03147e10	−	8.71475e10i	−0.648476	−	1.12319i	0.335011	−	0.942214i	$-0.391260\pi$
$264$		0			0
$265$	−4.13324e10	+	7.15898e10i	−0.514854	+	0.891753i
$266$	7.14543e10	−	1.23763e11i	0.875107	−	1.51573i
$267$		0			0
$268$	−1.57500e11	−	2.72797e11i	−1.86497	−	3.23023i
$269$	2.18445e10			0.254365			0.127182	−	0.991879i	$-0.459407\pi$
$269$	2.18445e10			0.254365			0.127182	+	0.991879i	$0.459407\pi$
$270$		0			0
$271$	5.19462e10			0.585049			0.292524	−	0.956258i	$-0.405505\pi$
$271$	5.19462e10			0.585049			0.292524	+	0.956258i	$0.405505\pi$
$272$	2.52685e11	+	4.37664e11i	2.79911	+	4.84820i
$273$		0			0
$274$	1.51821e11	−	2.62962e11i	1.62726	−	2.81849i
$275$	6.14309e9	−	1.06401e10i	0.0647724	−	0.112189i
$276$		0			0
$277$	4.18852e9	+	7.25473e9i	0.0427466	+	0.0740393i	0.886607	−	0.462523i	$-0.153056\pi$
$277$	4.18852e9	+	7.25473e9i	0.0427466	+	0.0740393i	−0.843861	+	0.536563i	$0.819723\pi$
$278$	2.16901e11			2.17801
$279$		0			0
$280$	−2.93926e11			−2.85777
$281$	−4.08163e10	−	7.06959e10i	−0.390530	−	0.676419i	0.601989	−	0.798504i	$-0.294375\pi$
$281$	−4.08163e10	−	7.06959e10i	−0.390530	−	0.676419i	−0.992520	+	0.122086i	$0.961042\pi$
$282$		0			0
$283$	3.05738e10	−	5.29553e10i	0.283341	−	0.490762i	−0.688864	−	0.724890i	$-0.741890\pi$
$283$	3.05738e10	−	5.29553e10i	0.283341	−	0.490762i	0.972206	+	0.234129i	$0.0752237\pi$
$284$	−2.38848e11	+	4.13697e11i	−2.17866	+	3.77355i
$285$		0			0
$286$	−1.60963e9	−	2.78796e9i	−0.0142259	−	0.0246399i
$287$	−1.16057e11			−1.00972
$288$		0			0
$289$	7.89921e10			0.666106
$290$	−7.98624e10	−	1.38326e11i	−0.663058	−	1.14845i
$291$		0			0
$292$	−1.15500e11	+	2.00051e11i	−0.929732	+	1.61034i
$293$	−8.67297e10	+	1.50220e11i	−0.687486	+	1.19076i	0.285163	+	0.958479i	$0.407952\pi$
$293$	−8.67297e10	+	1.50220e11i	−0.687486	+	1.19076i	−0.972649	+	0.232281i	$0.925381\pi$
$294$		0			0
$295$	2.69513e10	+	4.66810e10i	0.207196	+	0.358873i
$296$	−1.67433e11			−1.26774
$297$		0			0
$298$	3.40222e11			2.49913
$299$	1.68379e8	+	2.91641e8i	0.00121834	+	0.00211022i
$300$		0			0
$301$	−1.08842e11	+	1.88520e11i	−0.764270	+	1.32375i
$302$	9.33105e10	−	1.61619e11i	0.645505	−	1.11805i
$303$		0			0
$304$	2.77091e11	+	4.79935e11i	1.86076	+	3.22294i
$305$	2.02479e10			0.133977
$306$		0			0
$307$	−1.89397e11			−1.21689			−0.608443	−	0.793598i	$-0.708205\pi$
$307$	−1.89397e11			−1.21689			−0.608443	+	0.793598i	$0.708205\pi$
$308$	−6.99072e10	−	1.21083e11i	−0.442633	−	0.766663i
$309$		0			0
$310$	8.08226e10	−	1.39989e11i	0.497056	−	0.860926i
$311$	−7.38382e10	+	1.27892e11i	−0.447569	+	0.775212i	−0.998227	−	0.0595190i	$-0.981043\pi$
$311$	−7.38382e10	+	1.27892e11i	−0.447569	+	0.775212i	0.550659	+	0.834731i	$0.314377\pi$
$312$		0			0
$313$	−2.32124e9	−	4.02051e9i	−0.0136701	−	0.0236773i	0.859109	−	0.511792i	$-0.171018\pi$
$313$	−2.32124e9	−	4.02051e9i	−0.0136701	−	0.0236773i	−0.872780	+	0.488115i	$0.837685\pi$
$314$	−3.38239e10			−0.196354
$315$		0			0
$316$	5.25835e10			0.296659
$317$	−8.81821e10	−	1.52736e11i	−0.490471	−	0.849521i	0.509468	−	0.860489i	$-0.329842\pi$
$317$	−8.81821e10	−	1.52736e11i	−0.490471	−	0.849521i	−0.999940	+	0.0109679i	$0.996509\pi$
$318$		0			0
$319$	2.47232e10	−	4.28219e10i	0.133674	−	0.231530i
$320$	3.67996e11	−	6.37387e11i	1.96186	−	3.39804i
$321$		0			0
$322$	9.86641e9	+	1.70891e10i	0.0511456	+	0.0885867i
$323$	2.16663e11			1.10758
$324$		0			0
$325$	−4.24956e9			−0.0211285
$326$	1.67926e11	+	2.90857e11i	0.823454	+	1.42626i
$327$		0			0
$328$	3.73609e11	−	6.47109e11i	1.78232	−	3.08706i
$329$	1.22369e11	−	2.11948e11i	0.575822	−	0.997353i
$330$		0			0
$331$	1.54928e11	+	2.68344e11i	0.709423	+	1.22876i	0.965072	+	0.261987i	$0.0843776\pi$
$331$	1.54928e11	+	2.68344e11i	0.709423	+	1.22876i	−0.255649	+	0.966770i	$0.582289\pi$
$332$	1.18468e10			0.0535155
$333$		0			0
$334$	3.58381e11			1.57574
$335$	1.12857e11	+	1.95474e11i	0.489583	+	0.847982i
$336$		0			0
$337$	−1.56829e11	+	2.71636e11i	−0.662356	+	1.14723i	0.317639	+	0.948212i	$0.397110\pi$
$337$	−1.56829e11	+	2.71636e11i	−0.662356	+	1.14723i	−0.979995	+	0.199023i	$0.936223\pi$
$338$	2.35272e11	−	4.07503e11i	0.980495	−	1.69827i
$339$		0			0
$340$	−3.42362e11	−	5.92989e11i	−1.38941	−	2.40653i
$341$	5.00409e10			0.200415
$342$		0			0
$343$	−2.45577e11			−0.957996
$344$	−7.00763e11	−	1.21376e12i	−2.69810	−	4.67325i
$345$		0			0
$346$	−9.16936e10	+	1.58818e11i	−0.343951	+	0.595740i
$347$	4.05420e10	−	7.02209e10i	0.150115	−	0.260006i	−0.781155	−	0.624337i	$-0.785369\pi$
$347$	4.05420e10	−	7.02209e10i	0.150115	−	0.260006i	0.931269	+	0.364331i	$0.118702\pi$
$348$		0			0
$349$	−1.34389e11	−	2.32768e11i	−0.484896	−	0.839864i	0.514954	−	0.857218i	$-0.327809\pi$
$349$	−1.34389e11	−	2.32768e11i	−0.484896	−	0.839864i	−0.999849	+	0.0173540i	$0.994476\pi$
$350$	−2.49010e11			−0.886972
$351$		0			0
$352$	4.17172e11			1.44835
$353$	1.96480e11	+	3.40313e11i	0.673491	+	1.16652i	0.976907	+	0.213663i	$0.0685395\pi$
$353$	1.96480e11	+	3.40313e11i	0.673491	+	1.16652i	−0.303416	+	0.952858i	$0.598127\pi$
$354$		0			0
$355$	1.71147e11	−	2.96436e11i	0.571929	−	0.990611i
$356$	−6.91800e11	+	1.19823e12i	−2.28274	+	3.95381i
$357$		0			0
$358$	−5.47447e11	−	9.48206e11i	−1.76144	−	3.05091i
$359$	2.48781e11			0.790484			0.395242	−	0.918577i	$-0.370661\pi$
$359$	2.48781e11			0.790484			0.395242	+	0.918577i	$0.370661\pi$
$360$		0			0
$361$	−8.50984e10			−0.263718
$362$	9.28819e10	+	1.60876e11i	0.284277	+	0.492383i
$363$		0			0
$364$	−2.41796e10	+	4.18803e10i	−0.0721927	+	0.125041i
$365$	8.27617e10	−	1.43347e11i	0.244068	−	0.422739i
$366$		0			0
$367$	1.62624e11	+	2.81673e11i	0.467937	+	0.810491i	0.999329	−	0.0366351i	$-0.0116639\pi$
$367$	1.62624e11	+	2.81673e11i	0.467937	+	0.810491i	−0.531391	+	0.847126i	$0.678331\pi$
$368$	−7.65214e10			−0.217504
$369$		0			0
$370$	1.84349e11			0.511368
$371$	2.59330e11	+	4.49172e11i	0.710673	+	1.23092i
$372$		0			0
$373$	1.77616e11	−	3.07640e11i	0.475108	−	0.822912i	−0.524485	−	0.851420i	$-0.675742\pi$
$373$	1.77616e11	−	3.07640e11i	0.475108	−	0.822912i	0.999594	+	0.0285077i	$0.00907553\pi$
$374$	1.42996e11	−	2.47677e11i	0.377922	−	0.654580i
$375$		0			0
$376$	7.87853e11	+	1.36460e12i	2.03282	+	3.52095i
$377$	−1.71026e10			−0.0436040
$378$		0			0
$379$	−4.17590e11			−1.03962			−0.519809	−	0.854283i	$-0.673997\pi$
$379$	−4.17590e11			−1.03962			−0.519809	+	0.854283i	$0.673997\pi$
$380$	−3.75429e11	−	6.50262e11i	−0.923637	−	1.59979i
$381$		0			0
$382$	−3.25639e11	+	5.64024e11i	−0.782441	+	1.35523i
$383$	4.19861e9	−	7.27221e9i	0.00997038	−	0.0172692i	−0.860997	−	0.508610i	$-0.830160\pi$
$383$	4.19861e9	−	7.27221e9i	0.00997038	−	0.0172692i	0.870968	+	0.491341i	$0.163493\pi$
$384$		0			0
$385$	5.00922e10	+	8.67623e10i	0.116198	+	0.201260i
$386$	7.05701e11			1.61800
$387$		0			0
$388$	1.41791e12			3.17618
$389$	2.23902e11	+	3.87809e11i	0.495774	+	0.858706i	0.999988	−	0.00487245i	$-0.00155095\pi$
$389$	2.23902e11	+	3.87809e11i	0.495774	+	0.858706i	−0.504214	+	0.863579i	$0.668218\pi$
$390$		0			0
$391$	−1.49584e10	+	2.59087e10i	−0.0323661	+	0.0560597i
$392$	−6.57635e10	+	1.13906e11i	−0.140669	+	0.243645i
$393$		0			0
$394$	8.93062e10	+	1.54683e11i	0.186702	+	0.323377i
$395$	−3.76788e10			−0.0778773
$396$		0			0
$397$	8.93449e11			1.80515			0.902573	−	0.430537i	$-0.141676\pi$
$397$	8.93449e11			1.80515			0.902573	+	0.430537i	$0.141676\pi$
$398$	8.67991e11	+	1.50340e12i	1.73397	+	3.00332i
$399$		0			0
$400$	4.82814e11	−	8.36258e11i	0.942996	−	1.63332i
$401$	−1.10853e10	+	1.92004e10i	−0.0214092	+	0.0370817i	−0.876531	−	0.481345i	$-0.840149\pi$
$401$	−1.10853e10	+	1.92004e10i	−0.0214092	+	0.0370817i	0.855122	+	0.518426i	$0.173482\pi$
$402$		0			0
$403$	−8.65412e9	−	1.49894e10i	−0.0163437	−	0.0283081i
$404$	−2.46908e12			−4.61126
$405$		0			0
$406$	−1.00215e12			−1.83049
$407$	2.85347e10	+	4.94236e10i	0.0515465	+	0.0892812i
$408$		0			0
$409$	−2.39862e11	+	4.15453e11i	−0.423844	+	0.734120i	−0.996312	−	0.0858078i	$-0.972653\pi$
$409$	−2.39862e11	+	4.15453e11i	−0.423844	+	0.734120i	0.572468	+	0.819927i	$0.305986\pi$
$410$	−4.11355e11	+	7.12487e11i	−0.718934	+	1.24523i
$411$		0			0
$412$	−7.37590e10	−	1.27754e11i	−0.126118	−	0.218443i
$413$	3.38198e11			0.572000
$414$		0			0
$415$	−8.48885e9			−0.0140486
$416$	−7.21461e10	−	1.24961e11i	−0.118112	−	0.204575i
$417$		0			0
$418$	1.56807e11	−	2.71598e11i	0.251231	−	0.435144i
$419$	−4.17661e11	+	7.23411e11i	−0.662005	+	1.14663i	0.318083	+	0.948063i	$0.396961\pi$
$419$	−4.17661e11	+	7.23411e11i	−0.662005	+	1.14663i	−0.980088	+	0.198563i	$0.936373\pi$
$420$		0			0
$421$	−1.03140e11	−	1.78644e11i	−0.160014	−	0.277153i	0.774859	−	0.632134i	$-0.217821\pi$
$421$	−1.03140e11	−	1.78644e11i	−0.160014	−	0.277153i	−0.934874	+	0.354981i	$0.884487\pi$
$422$	1.20133e12			1.84397
$423$		0			0
$424$	−3.33932e12			−5.01778
$425$	−1.88761e11	−	3.26944e11i	−0.280648	−	0.486097i
$426$		0			0
$427$	6.35202e10	−	1.10020e11i	0.0924669	−	0.160157i
$428$	−4.03572e11	+	6.99007e11i	−0.581332	+	1.00690i
$429$		0			0
$430$	7.71562e11	+	1.33638e12i	1.08834	+	1.88505i
$431$	3.46311e11			0.483414			0.241707	−	0.970349i	$-0.422293\pi$
$431$	3.46311e11			0.483414			0.241707	+	0.970349i	$0.422293\pi$
$432$		0			0
$433$	−7.41282e9			−0.0101342			−0.00506708	−	0.999987i	$-0.501613\pi$
$433$	−7.41282e9			−0.0101342			−0.00506708	+	0.999987i	$0.501613\pi$
$434$	−5.07101e11	−	8.78325e11i	−0.686105	−	1.18837i
$435$		0			0
$436$	−9.60541e11	+	1.66370e12i	−1.27299	+	2.20489i
$437$	−1.64032e10	+	2.84111e10i	−0.0215160	+	0.0372668i
$438$		0			0
$439$	−4.79907e11	−	8.31224e11i	−0.616690	−	1.06814i	−0.990085	−	0.140466i	$-0.955140\pi$
$439$	−4.79907e11	−	8.31224e11i	−0.616690	−	1.06814i	0.373396	−	0.927672i	$-0.378193\pi$
$440$	−6.45024e11			−0.820425
$441$		0			0
$442$	−9.89194e10			−0.123277
$443$	−1.44256e11	−	2.49858e11i	−0.177958	−	0.308232i	0.763223	−	0.646135i	$-0.223616\pi$
$443$	−1.44256e11	−	2.49858e11i	−0.177958	−	0.308232i	−0.941181	+	0.337903i	$0.890282\pi$
$444$		0			0
$445$	4.95711e11	−	8.58597e11i	0.599251	−	1.03793i
$446$	1.27435e12	−	2.20724e12i	1.52504	−	2.64145i
$447$		0			0
$448$	−2.30890e12	−	3.99913e12i	−2.70803	−	4.69045i
$449$	1.00029e12			1.16150			0.580749	−	0.814083i	$-0.302760\pi$
$449$	1.00029e12			1.16150			0.580749	+	0.814083i	$0.302760\pi$
$450$		0			0
$451$	−2.54688e11			−0.289878
$452$	5.68454e10	+	9.84591e10i	0.0640578	+	0.110951i
$453$		0			0
$454$	−7.78476e11	+	1.34836e12i	−0.859991	+	1.48955i
$455$	1.73260e10	−	3.00095e10i	0.0189516	−	0.0328252i
$456$		0			0
$457$	−1.41927e11	−	2.45826e11i	−0.152210	−	0.263636i	0.779830	−	0.625992i	$-0.215306\pi$
$457$	−1.41927e11	−	2.45826e11i	−0.152210	−	0.263636i	−0.932040	+	0.362356i	$0.881972\pi$
$458$	2.88003e12			3.05846
$459$		0			0
$460$	1.03678e11			0.107964
$461$	3.22910e8	+	5.59296e8i	0.000332987	+	0.000576750i	0.866192	−	0.499712i	$-0.166561\pi$
$461$	3.22910e8	+	5.59296e8i	0.000332987	+	0.000576750i	−0.865859	+	0.500288i	$0.833227\pi$
$462$		0			0
$463$	2.41535e11	−	4.18352e11i	0.244268	−	0.423084i	−0.717658	−	0.696396i	$-0.754786\pi$
$463$	2.41535e11	−	4.18352e11i	0.244268	−	0.423084i	0.961926	+	0.273312i	$0.0881190\pi$
$464$	1.94311e12	−	3.36557e12i	1.94611	−	3.37076i
$465$		0			0
$466$	1.31444e12	+	2.27667e12i	1.29123	+	2.23647i
$467$	−7.10128e11			−0.690893			−0.345447	−	0.938438i	$-0.612273\pi$
$467$	−7.10128e11			−0.690893			−0.345447	+	0.938438i	$0.612273\pi$
$468$		0			0
$469$	1.41618e12			1.35158
$470$	−8.67450e11	−	1.50247e12i	−0.819982	−	1.42025i
$471$		0			0
$472$	−1.08872e12	+	1.88572e12i	−1.00967	+	1.74879i
$473$	−2.38855e11	+	4.13708e11i	−0.219411	+	0.380031i
$474$		0			0
$475$	−2.06992e11	−	3.58521e11i	−0.186566	−	0.323142i
$476$	−4.29613e12			−3.83572
$477$		0			0
$478$	−1.80000e12			−1.57706
$479$	−7.73097e9	−	1.33904e10i	−0.00671002	−	0.0116221i	0.862651	−	0.505800i	$-0.168803\pi$
$479$	−7.73097e9	−	1.33904e10i	−0.00671002	−	0.0116221i	−0.869361	+	0.494178i	$0.835469\pi$
$480$		0			0
$481$	9.86964e9	−	1.70947e10i	0.00840715	−	0.0145616i
$482$	−7.49638e10	+	1.29841e11i	−0.0632616	+	0.109572i
$483$		0			0
$484$	1.57522e12	+	2.72836e12i	1.30478	+	2.25994i
$485$	−1.01601e12			−0.833793
$486$		0			0
$487$	−5.65405e11			−0.455490			−0.227745	−	0.973721i	$-0.573135\pi$
$487$	−5.65405e11			−0.455490			−0.227745	+	0.973721i	$0.573135\pi$
$488$	4.08966e11	+	7.08349e11i	0.326436	+	0.565403i
$489$		0			0
$490$	7.24076e10	−	1.25414e11i	0.0567416	−	0.0982794i
$491$	1.86366e11	−	3.22796e11i	0.144711	−	0.250646i	−0.784554	−	0.620060i	$-0.787108\pi$
$491$	1.86366e11	−	3.22796e11i	0.144711	−	0.250646i	0.929265	+	0.369414i	$0.120442\pi$
$492$		0			0
$493$	−7.59680e11	−	1.31580e12i	−0.579188	−	1.00318i
$494$	−1.08473e11			−0.0819506
$495$		0			0
$496$	3.93295e12			2.91777
$497$	−1.07382e12	−	1.85991e12i	−0.789456	−	1.36738i
$498$		0			0
$499$	1.78807e11	−	3.09703e11i	0.129102	−	0.223611i	−0.794227	−	0.607621i	$-0.792124\pi$
$499$	1.78807e11	−	3.09703e11i	0.129102	−	0.223611i	0.923329	+	0.384010i	$0.125457\pi$
$500$	−2.15850e12	+	3.73863e12i	−1.54449	+	2.67514i
$501$		0			0
$502$	1.04365e12	+	1.80765e12i	0.733476	+	1.27042i
$503$	−1.08145e12			−0.753267			−0.376633	−	0.926362i	$-0.622918\pi$
$503$	−1.08145e12			−0.753267			−0.376633	+	0.926362i	$0.622918\pi$
$504$		0			0
$505$	1.76923e12			1.21052
$506$	2.16519e10	+	3.75023e10i	0.0146832	+	0.0254320i
$507$		0			0
$508$	1.38768e12	−	2.40353e12i	0.924490	−	1.60126i
$509$	3.48650e11	−	6.03880e11i	0.230229	−	0.398768i	−0.727646	−	0.685952i	$-0.759386\pi$
$509$	3.48650e11	−	6.03880e11i	0.230229	−	0.398768i	0.957875	+	0.287184i	$0.0927192\pi$
$510$		0			0
$511$	−5.19267e11	−	8.99398e11i	−0.336897	−	0.583523i
$512$	8.08206e12			5.19765
$513$		0			0
$514$	−7.78108e11			−0.491706
$515$	5.28523e10	+	9.15428e10i	0.0331079	+	0.0573445i
$516$		0			0
$517$	2.68539e11	−	4.65123e11i	0.165310	−	0.286326i
$518$	5.78327e11	−	1.00169e12i	0.352931	−	0.611294i
$519$		0			0
$520$	1.11551e11	+	1.93212e11i	0.0669049	+	0.115883i
$521$	−1.96135e12			−1.16623			−0.583116	−	0.812389i	$-0.698167\pi$
$521$	−1.96135e12			−1.16623			−0.583116	+	0.812389i	$0.698167\pi$
$522$		0			0
$523$	−6.03647e10			−0.0352797			−0.0176399	−	0.999844i	$-0.505615\pi$
$523$	−6.03647e10			−0.0352797			−0.0176399	+	0.999844i	$0.505615\pi$
$524$	3.38833e12	+	5.86875e12i	1.96334	+	3.40060i
$525$		0			0
$526$	−2.23785e12	+	3.87607e12i	−1.27466	+	2.20778i
$527$	7.68814e11	−	1.33162e12i	0.434183	−	0.752028i
$528$		0			0
$529$	8.98311e11	+	1.55592e12i	0.498743	+	0.863847i
$530$	3.67669e12			2.02402
$531$		0			0
$532$	−4.71107e12			−2.54987
$533$	4.40460e10	+	7.62899e10i	0.0236393	+	0.0409444i
$534$		0			0
$535$	2.89181e11	−	5.00876e11i	0.152608	−	0.264325i
$536$	−4.55895e12	+	7.89633e12i	−2.38574	+	4.13223i
$537$		0			0
$538$	−4.85790e11	−	8.41413e11i	−0.249993	−	0.433001i
$539$	4.48308e10			0.0228785
$540$		0			0
$541$	−1.58437e12			−0.795185			−0.397592	−	0.917562i	$-0.630154\pi$
$541$	−1.58437e12			−0.795185			−0.397592	+	0.917562i	$0.630154\pi$
$542$	−1.15521e12	−	2.00088e12i	−0.574995	−	0.995920i
$543$		0			0
$544$	6.40930e12	−	1.11012e13i	3.13773	−	5.43471i
$545$	6.88278e11	−	1.19213e12i	0.334179	−	0.578816i
$546$		0			0
$547$	−7.36182e11	−	1.27510e12i	−0.351595	−	0.608980i	0.634934	−	0.772566i	$-0.281027\pi$
$547$	−7.36182e11	−	1.27510e12i	−0.351595	−	0.608980i	−0.986529	+	0.163586i	$0.947694\pi$
$548$	−1.00098e13			−4.74146
$549$		0			0
$550$	−5.46454e11			−0.254637
$551$	−8.33053e11	−	1.44289e12i	−0.385026	−	0.666885i
$552$		0			0
$553$	−1.18203e11	+	2.04734e11i	−0.0537485	+	0.0930952i
$554$	1.86293e11	−	3.22669e11i	0.0840240	−	0.145534i
$555$		0			0
$556$	−3.57513e12	−	6.19231e12i	−1.58656	−	2.74800i
$557$	−1.23459e12			−0.543470			−0.271735	−	0.962372i	$-0.587597\pi$
$557$	−1.23459e12			−0.543470			−0.271735	+	0.962372i	$0.587597\pi$
$558$		0			0
$559$	1.65231e11			0.0715711
$560$	3.93698e12	+	6.81905e12i	1.69168	+	2.93007i
$561$		0			0
$562$	−1.81539e12	+	3.14435e12i	−0.767638	+	1.32959i
$563$	−1.61399e11	+	2.79551e11i	−0.0677037	+	0.117266i	−0.897890	−	0.440220i	$-0.854901\pi$
$563$	−1.61399e11	+	2.79551e11i	−0.0677037	+	0.117266i	0.830186	+	0.557486i	$0.188234\pi$
$564$		0			0
$565$	−4.07327e10	−	7.05511e10i	−0.0168161	−	0.0291263i
$566$	−2.71967e12			−1.11389
$567$		0			0
$568$	1.38273e13			5.57404
$569$	7.58978e11	+	1.31459e12i	0.303546	+	0.525756i	0.976936	−	0.213530i	$-0.0684962\pi$
$569$	7.58978e11	+	1.31459e12i	0.303546	+	0.525756i	−0.673391	+	0.739287i	$0.735163\pi$
$570$		0			0
$571$	−3.02035e11	+	5.23139e11i	−0.118903	+	0.205947i	−0.919333	−	0.393480i	$-0.871271\pi$
$571$	−3.02035e11	+	5.23139e11i	−0.118903	+	0.205947i	0.800430	+	0.599426i	$0.204605\pi$
$572$	−5.30624e10	+	9.19068e10i	−0.0207255	+	0.0358976i
$573$		0			0
$574$	2.58094e12	+	4.47032e12i	0.992373	+	1.71884i
$575$	5.71630e10			0.0218077
$576$		0			0
$577$	−4.16132e12			−1.56293			−0.781466	−	0.623948i	$-0.785528\pi$
$577$	−4.16132e12			−1.56293			−0.781466	+	0.623948i	$0.785528\pi$
$578$	−1.75667e12	−	3.04265e12i	−0.654660	−	1.13390i
$579$		0			0
$580$	−2.63271e12	+	4.55999e12i	−0.966001	+	1.67316i
$581$	−2.66306e10	+	4.61256e10i	−0.00969591	+	0.0167938i
$582$		0			0
$583$	5.69102e11	+	9.85713e11i	0.204024	+	0.353380i
$584$	6.68646e12			2.37869
$585$		0			0
$586$	7.71498e12			2.70269
$587$	−6.48959e11	−	1.12403e12i	−0.225604	−	0.390757i	0.730897	−	0.682488i	$-0.239102\pi$
$587$	−6.48959e11	−	1.12403e12i	−0.225604	−	0.390757i	−0.956500	+	0.291731i	$0.905769\pi$
$588$		0			0
$589$	8.43069e11	−	1.46024e12i	0.288632	−	0.499925i
$590$	1.19872e12	−	2.07624e12i	0.407270	−	0.705412i
$591$		0			0
$592$	2.24268e12	+	3.88443e12i	0.750446	+	1.29981i
$593$	6.89642e11			0.229022			0.114511	−	0.993422i	$-0.463470\pi$
$593$	6.89642e11			0.229022			0.114511	+	0.993422i	$0.463470\pi$
$594$		0			0
$595$	3.07841e12			1.00693
$596$	−5.60781e12	−	9.71302e12i	−1.82048	−	3.15316i
$597$		0			0
$598$	7.48901e9	−	1.29713e10i	0.00239480	−	0.00414791i
$599$	3.40832e11	−	5.90339e11i	0.108173	−	0.187362i	−0.806857	−	0.590747i	$-0.798833\pi$
$599$	3.40832e11	−	5.90339e11i	0.108173	−	0.187362i	0.915030	+	0.403385i	$0.132167\pi$
$600$		0			0
$601$	2.36698e12	+	4.09974e12i	0.740049	+	1.28180i	0.952473	+	0.304624i	$0.0985309\pi$
$601$	2.36698e12	+	4.09974e12i	0.740049	+	1.28180i	−0.212424	+	0.977178i	$0.568136\pi$
$602$	9.68195e12			3.00454
$603$		0			0
$604$	−6.15208e12			−1.88086
$605$	−1.12873e12	−	1.95501e12i	−0.342523	−	0.593267i
$606$		0			0
$607$	1.69211e12	−	2.93082e12i	0.505917	−	0.876273i	−0.494060	−	0.869428i	$-0.664488\pi$
$607$	1.69211e12	−	2.93082e12i	0.505917	−	0.876273i	0.999977	−	0.00684543i	$-0.00217898\pi$
$608$	7.02834e12	−	1.21734e13i	2.08587	−	3.61283i
$609$		0			0
$610$	−4.50284e11	−	7.79915e11i	−0.131675	−	0.228067i
$611$	−1.85765e11			−0.0539237
$612$		0			0
$613$	−2.77900e12			−0.794906			−0.397453	−	0.917622i	$-0.630106\pi$
$613$	−2.77900e12			−0.794906			−0.397453	+	0.917622i	$0.630106\pi$
$614$	4.21191e12	+	7.29525e12i	1.19597	+	2.07149i
$615$		0			0
$616$	−2.02352e12	+	3.50484e12i	−0.566232	+	0.980743i
$617$	−2.85307e12	+	4.94166e12i	−0.792554	+	1.37274i	0.131827	+	0.991273i	$0.457916\pi$
$617$	−2.85307e12	+	4.94166e12i	−0.792554	+	1.37274i	−0.924381	+	0.381470i	$0.875418\pi$
$618$		0			0
$619$	−2.85011e12	−	4.93653e12i	−0.780285	−	1.35149i	−0.931776	−	0.363035i	$-0.881741\pi$
$619$	−2.85011e12	−	4.93653e12i	−0.780285	−	1.35149i	0.151490	−	0.988459i	$-0.451593\pi$
$620$	−5.32873e12			−1.44831
$621$		0			0
$622$	6.56823e12			1.75951
$623$	−3.11022e12	−	5.38706e12i	−0.827170	−	1.43270i
$624$		0			0
$625$	7.17264e11	−	1.24234e12i	0.188026	−	0.325671i
$626$	−1.03242e11	+	1.78821e11i	−0.0268703	+	0.0465408i
$627$		0			0
$628$	5.57513e11	+	9.65641e11i	0.143033	+	0.247741i
$629$	1.75360e12			0.446685
$630$		0			0
$631$	−7.58053e11			−0.190356			−0.0951782	−	0.995460i	$-0.530342\pi$
$631$	−7.58053e11			−0.190356			−0.0951782	+	0.995460i	$0.530342\pi$
$632$	−7.61035e11	−	1.31815e12i	−0.189748	−	0.328654i
$633$		0			0
$634$	−3.92209e12	+	6.79325e12i	−0.964086	+	1.66985i
$635$	−9.94346e11	+	1.72226e12i	−0.242692	+	0.420355i
$636$		0			0
$637$	−7.75308e9	−	1.34287e10i	−0.00186572	−	0.00323153i
$638$	−2.19924e12			−0.525507
$639$		0			0
$640$	−1.72222e13			−4.05768
$641$	1.53875e12	+	2.66519e12i	0.360003	+	0.623544i	0.987961	−	0.154703i	$-0.0494422\pi$
$641$	1.53875e12	+	2.66519e12i	0.360003	+	0.623544i	−0.627958	+	0.778248i	$0.716109\pi$
$642$		0			0
$643$	−1.05213e12	+	1.82234e12i	−0.242727	+	0.420416i	−0.961490	−	0.274839i	$-0.911375\pi$
$643$	−1.05213e12	+	1.82234e12i	−0.242727	+	0.420416i	0.718763	+	0.695255i	$0.244709\pi$
$644$	3.25252e11	−	5.63354e11i	0.0745133	−	0.129061i
$645$		0			0
$646$	−4.81828e12	−	8.34550e12i	−1.08854	−	1.88541i
$647$	−1.41884e12			−0.318319			−0.159160	−	0.987253i	$-0.550878\pi$
$647$	−1.41884e12			−0.318319			−0.159160	+	0.987253i	$0.550878\pi$
$648$		0			0
$649$	7.42180e11			0.164213
$650$	9.45042e10	+	1.63686e11i	0.0207654	+	0.0359668i
$651$		0			0
$652$	5.53579e12	−	9.58827e12i	1.19968	−	2.07791i
$653$	−1.70144e11	+	2.94698e11i	−0.0366191	+	0.0634262i	−0.883754	−	0.467952i	$-0.844992\pi$
$653$	−1.70144e11	+	2.94698e11i	−0.0366191	+	0.0634262i	0.847135	+	0.531378i	$0.178326\pi$
$654$		0			0
$655$	−2.42792e12	−	4.20527e12i	−0.515404	−	0.892706i
$656$	−2.00171e13			−4.22022
$657$		0			0
$658$	−1.08852e13			−2.26371
$659$	2.31012e12	+	4.00125e12i	0.477145	+	0.826440i	0.999657	−	0.0261924i	$-0.00833826\pi$
$659$	2.31012e12	+	4.00125e12i	0.477145	+	0.826440i	−0.522512	+	0.852632i	$0.675005\pi$
$660$		0			0
$661$	2.31748e12	−	4.01400e12i	0.472183	−	0.817845i	−0.527311	−	0.849673i	$-0.676800\pi$
$661$	2.31748e12	−	4.01400e12i	0.472183	−	0.817845i	0.999493	+	0.0318281i	$0.0101329\pi$
$662$	6.89077e12	−	1.19352e13i	1.39446	−	2.41528i
$663$		0			0
$664$	−1.71457e11	−	2.96973e11i	−0.0342295	−	0.0592872i
$665$	3.37573e12			0.669377
$666$		0			0
$667$	2.30056e11			0.0450057
$668$	−5.90712e12	−	1.02314e13i	−1.14784	−	1.98812i
$669$		0			0
$670$	5.01955e12	−	8.69411e12i	0.962339	−	1.66682i
$671$	1.39396e11	−	2.41440e11i	0.0265459	−	0.0459789i
$672$		0			0
$673$	5.02585e12	+	8.70503e12i	0.944370	+	1.63570i	0.757009	+	0.653405i	$0.226660\pi$
$673$	5.02585e12	+	8.70503e12i	0.944370	+	1.63570i	0.187361	+	0.982291i	$0.440007\pi$
$674$	1.39506e13			2.60390
$675$		0			0
$676$	−1.55118e13			−2.85694
$677$	4.41589e12	+	7.64855e12i	0.807922	+	1.39936i	0.914300	+	0.405037i	$0.132741\pi$
$677$	4.41589e12	+	7.64855e12i	0.807922	+	1.39936i	−0.106378	+	0.994326i	$0.533925\pi$
$678$		0			0
$679$	−3.18734e12	+	5.52063e12i	−0.575458	+	0.996723i
$680$	−9.90995e12	+	1.71645e13i	−1.77738	+	3.07852i
$681$		0			0
$682$	−1.11284e12	−	1.92749e12i	−0.196971	−	0.341164i
$683$	1.10788e13			1.94805			0.974027	−	0.226430i	$-0.0727055\pi$
$683$	1.10788e13			1.94805			0.974027	+	0.226430i	$0.0727055\pi$
$684$		0			0
$685$	7.17253e12			1.24470
$686$	5.46128e12	+	9.45921e12i	0.941534	+	1.63078i
$687$		0			0
$688$	−1.87727e13	+	3.25152e13i	−3.19432	+	5.53272i
$689$	1.96842e11	−	3.40940e11i	0.0332760	−	0.0576357i
$690$		0			0
$691$	3.16465e11	+	5.48134e11i	0.0528050	+	0.0914609i	0.891220	−	0.453572i	$-0.149850\pi$
$691$	3.16465e11	+	5.48134e11i	0.0528050	+	0.0914609i	−0.838415	+	0.545033i	$0.816517\pi$
$692$	6.04547e12			1.00220
$693$		0			0
$694$	−3.60639e12			−0.590140
$695$	2.56177e12	+	4.43712e12i	0.416494	+	0.721389i
$696$		0			0
$697$	−3.91295e12	+	6.77743e12i	−0.627996	+	1.08772i
$698$	−5.97723e12	+	1.03529e13i	−0.953126	+	1.65086i
$699$		0			0
$700$	4.10438e12	+	7.10899e12i	0.646109	+	1.11909i
$701$	−3.84382e12			−0.601219			−0.300609	−	0.953747i	$-0.597190\pi$
$701$	−3.84382e12			−0.601219			−0.300609	+	0.953747i	$0.597190\pi$
$702$		0			0
$703$	1.92297e12			0.296943
$704$	−5.06690e12	−	8.77613e12i	−0.777437	−	1.34656i
$705$		0			0
$706$	8.73887e12	−	1.51362e13i	1.32384	−	2.29295i
$707$	5.55029e12	−	9.61338e12i	0.835465	−	1.44707i
$708$		0			0
$709$	3.07967e12	+	5.33415e12i	0.457716	+	0.792788i	0.998840	−	0.0481550i	$-0.0153341\pi$
$709$	3.07967e12	+	5.33415e12i	0.457716	+	0.792788i	−0.541123	+	0.840943i	$0.682001\pi$
$710$	−1.52243e13			−2.24840
$711$		0			0
$712$	4.00494e13			5.84031
$713$	1.16411e11	+	2.01630e11i	0.0168691	+	0.0292181i
$714$		0			0
$715$	3.80220e10	−	6.58561e10i	0.00544074	−	0.00942364i
$716$	−1.80469e13	+	3.12582e13i	−2.56622	+	4.44483i
$717$		0			0
$718$	−5.53254e12	−	9.58265e12i	−0.776900	−	1.34563i
$719$	−6.51194e12			−0.908721			−0.454361	−	0.890818i	$-0.650132\pi$
$719$	−6.51194e12			−0.908721			−0.454361	+	0.890818i	$0.650132\pi$
$720$		0			0
$721$	6.63217e11			0.0914001
$722$	1.89247e12	+	3.27785e12i	0.259186	+	0.448923i
$723$		0			0
$724$	3.06191e12	−	5.30338e12i	0.414160	−	0.717347i
$725$	−1.45154e12	+	2.51415e12i	−0.195123	+	0.337963i
$726$		0			0
$727$	−1.02893e12	−	1.78215e12i	−0.136609	−	0.236614i	0.789602	−	0.613620i	$-0.210287\pi$
$727$	−1.02893e12	−	1.78215e12i	−0.136609	−	0.236614i	−0.926211	+	0.377006i	$0.876954\pi$
$728$	1.39980e12			0.184703
$729$		0			0
$730$	−7.36200e12			−0.959496
$731$	7.33938e12	+	1.27122e13i	0.950673	+	1.64661i
$732$		0			0
$733$	−3.98122e12	+	6.89568e12i	−0.509388	+	0.882286i	0.490553	+	0.871411i	$0.336795\pi$
$733$	−3.98122e12	+	6.89568e12i	−0.509388	+	0.882286i	−0.999941	+	0.0108743i	$0.996539\pi$
$734$	7.23306e12	−	1.25280e13i	0.919792	−	1.59313i
$735$		0			0
$736$	9.70473e11	+	1.68091e12i	0.121908	+	0.211151i
$737$	3.10783e12			0.388019
$738$		0			0
$739$	−4.20258e12			−0.518341			−0.259171	−	0.965832i	$-0.583449\pi$
$739$	−4.20258e12			−0.518341			−0.259171	+	0.965832i	$0.583449\pi$
$740$	−3.03859e12	−	5.26300e12i	−0.372503	−	0.645194i
$741$		0			0
$742$	1.15342e13	−	1.99779e13i	1.39692	−	2.41954i
$743$	−2.73405e12	+	4.73551e12i	−0.329122	+	0.570056i	−0.982338	−	0.187116i	$-0.940086\pi$
$743$	−2.73405e12	+	4.73551e12i	−0.329122	+	0.570056i	0.653216	+	0.757172i	$0.273419\pi$
$744$		0			0
$745$	4.01830e12	+	6.95989e12i	0.477902	+	0.827750i
$746$	−1.57997e13			−1.86777
$747$		0			0
$748$	−9.42791e12			−1.10118
$749$	−1.81439e12	−	3.14262e12i	−0.210651	−	0.364858i
$750$		0			0
$751$	−3.73761e12	+	6.47374e12i	−0.428760	+	0.742635i	−0.996763	−	0.0803918i	$-0.974383\pi$
$751$	−3.73761e12	+	6.47374e12i	−0.428760	+	0.742635i	0.568003	+	0.823026i	$0.307716\pi$
$752$	2.11057e13	−	3.65562e13i	2.40669	−	4.16851i
$753$		0			0
$754$	3.80338e11	+	6.58764e11i	0.0428547	+	0.0742265i
$755$	4.40829e12			0.493752
$756$		0			0
$757$	1.40395e12			0.155389			0.0776947	−	0.996977i	$-0.475244\pi$
$757$	1.40395e12			0.155389			0.0776947	+	0.996977i	$0.475244\pi$
$758$	9.28661e12	+	1.60849e13i	1.02175	+	1.76973i
$759$		0			0
$760$	−1.08671e13	+	1.88224e13i	−1.18155	+	2.04650i
$761$	3.97524e12	−	6.88531e12i	0.429667	−	0.744205i	−0.567177	−	0.823596i	$-0.691964\pi$
$761$	3.97524e12	−	6.88531e12i	0.429667	−	0.744205i	0.996844	+	0.0793912i	$0.0252976\pi$
$762$		0			0
$763$	−4.31843e12	−	7.47974e12i	−0.461281	−	0.798962i
$764$	2.14698e13			2.27986
$765$		0			0
$766$	−3.73485e11			−0.0391961
$767$	−1.28353e11	−	2.22314e11i	−0.0133914	−	0.0231947i
$768$		0			0
$769$	3.47949e12	−	6.02666e12i	0.358796	−	0.621453i	−0.628964	−	0.777434i	$-0.716521\pi$
$769$	3.47949e12	−	6.02666e12i	0.358796	−	0.621453i	0.987760	+	0.155982i	$0.0498541\pi$
$770$	2.22796e12	−	3.85894e12i	0.228402	−	0.395603i
$771$		0			0
$772$	−1.16319e13	−	2.01471e13i	−1.17862	−	2.04143i
$773$	1.22597e13			1.23501			0.617506	−	0.786566i	$-0.288143\pi$
$773$	1.22597e13			1.23501			0.617506	+	0.786566i	$0.288143\pi$
$774$		0			0
$775$	−2.93799e12			−0.292545
$776$	−2.05212e13	−	3.55438e13i	−2.03154	−	3.51873i
$777$		0			0
$778$	9.95851e12	−	1.72486e13i	0.974509	−	1.68790i
$779$	−4.29088e12	+	7.43203e12i	−0.417473	+	0.723084i
$780$		0			0
$781$	−2.35651e12	−	4.08160e12i	−0.226642	−	0.392555i
$782$	1.33062e12			0.127240
$783$		0			0
$784$	3.52346e12			0.333079
$785$	−3.99488e11	−	6.91933e11i	−0.0375483	−	0.0650355i
$786$		0			0
$787$	−5.99070e12	+	1.03762e13i	−0.556662	+	0.964167i	0.441110	+	0.897453i	$0.354585\pi$
$787$	−5.99070e12	+	1.03762e13i	−0.556662	+	0.964167i	−0.997772	+	0.0667139i	$0.978749\pi$
$788$	2.94403e12	−	5.09921e12i	0.272004	−	0.471124i
$789$		0			0
$790$	8.37924e11	+	1.45133e12i	0.0765390	+	0.132569i
$791$	−5.11135e11			−0.0464238
$792$		0			0
$793$	−9.64288e10			−0.00865919
$794$	−1.98690e13	−	3.44142e13i	−1.77413	−	3.07288i
$795$		0			0
$796$	2.86139e13	−	4.95606e13i	2.52620	−	4.37550i
$797$	1.45080e12	−	2.51285e12i	0.127363	−	0.220599i	−0.795291	−	0.606228i	$-0.792682\pi$
$797$	1.45080e12	−	2.51285e12i	0.127363	−	0.220599i	0.922654	+	0.385628i	$0.126015\pi$
$798$		0			0
$799$	−8.25150e12	−	1.42920e13i	−0.716263	−	1.24060i
$800$	−2.44929e13			−2.11415
$801$		0			0
$802$	9.86089e11			0.0841650
$803$	−1.13954e12	−	1.97374e12i	−0.0967183	−	0.167521i
$804$		0			0
$805$	−2.33061e11	+	4.03673e11i	−0.0195608	+	0.0338804i
$806$	−3.84910e11	+	6.66684e11i	−0.0321257	+	0.0556433i
$807$		0			0
$808$	3.57348e13	+	6.18944e13i	2.94944	+	5.10858i
$809$	−1.25435e13			−1.02956			−0.514779	−	0.857323i	$-0.672126\pi$
$809$	−1.25435e13			−1.02956			−0.514779	+	0.857323i	$0.672126\pi$
$810$		0			0
$811$	−1.31788e13			−1.06975			−0.534874	−	0.844932i	$-0.679641\pi$
$811$	−1.31788e13			−1.06975			−0.534874	+	0.844932i	$0.679641\pi$
$812$	1.65183e13	+	2.86105e13i	1.33341	+	2.30953i
$813$		0			0
$814$	1.26914e12	−	2.19822e12i	0.101321	−	0.175494i
$815$	−3.96669e12	+	6.87051e12i	−0.314934	+	0.545481i
$816$		0			0
$817$	8.04824e12	+	1.39400e13i	0.631978	+	1.09462i
$818$	2.13367e13			1.66624
$819$		0			0
$820$	2.71211e13			2.09481
$821$	−6.97251e12	−	1.20767e13i	−0.535606	−	0.927696i	−0.999134	−	0.0416139i	$-0.986750\pi$
$821$	−6.97251e12	−	1.20767e13i	−0.535606	−	0.927696i	0.463528	−	0.886082i	$-0.346583\pi$
$822$		0			0
$823$	−9.05731e12	+	1.56877e13i	−0.688177	+	1.19196i	0.284250	+	0.958750i	$0.408255\pi$
$823$	−9.05731e12	+	1.56877e13i	−0.688177	+	1.19196i	−0.972427	+	0.233207i	$0.925078\pi$
$824$	−2.13501e12	+	3.69795e12i	−0.161335	+	0.279440i
$825$		0			0
$826$	−7.52105e12	−	1.30268e13i	−0.562171	−	0.973708i
$827$	9.15727e12			0.680756			0.340378	−	0.940289i	$-0.389445\pi$
$827$	9.15727e12			0.680756			0.340378	+	0.940289i	$0.389445\pi$
$828$		0			0
$829$	1.41975e13			1.04404			0.522020	−	0.852933i	$-0.325179\pi$
$829$	1.41975e13			1.04404			0.522020	+	0.852933i	$0.325179\pi$
$830$	1.88780e11	+	3.26976e11i	0.0138072	+	0.0239147i
$831$		0			0
$832$	−1.75255e12	+	3.03550e12i	−0.126799	+	0.219622i
$833$	6.88767e11	−	1.19298e12i	0.0495644	−	0.0858481i
$834$		0			0
$835$	4.23276e12	+	7.33136e12i	0.301325	+	0.521910i
$836$	−1.03385e13			−0.732030
$837$		0			0
$838$	3.71528e13			2.60251
$839$	−1.13179e13	−	1.96031e13i	−0.788561	−	1.36583i	−0.926848	−	0.375436i	$-0.877493\pi$
$839$	−1.13179e13	−	1.96031e13i	−0.788561	−	1.36583i	0.138287	−	0.990392i	$-0.455840\pi$
$840$		0			0
$841$	1.41175e12	−	2.44523e12i	0.0973143	−	0.168553i
$842$	−4.58739e12	+	7.94559e12i	−0.314529	+	0.544781i
$843$		0			0
$844$	−1.98012e13	−	3.42967e13i	−1.34323	−	2.32654i
$845$	1.11150e13			0.749989
$846$		0			0
$847$	−1.41638e13			−0.945596
$848$	4.47283e13	+	7.74718e13i	2.97031	+	5.14472i
$849$		0			0
$850$	−8.39555e12	+	1.45415e13i	−0.551651	+	0.955487i
$851$	−1.32762e11	+	2.29950e11i	−0.00867740	+	0.0150297i
$852$		0			0
$853$	1.37739e13	+	2.38571e13i	0.890813	+	1.54293i	0.838903	+	0.544281i	$0.183198\pi$
$853$	1.37739e13	+	2.38571e13i	0.890813	+	1.54293i	0.0519103	+	0.998652i	$0.483469\pi$
$854$	−5.65039e12			−0.363511
$855$		0			0
$856$	2.33634e13			1.48732
$857$	5.97538e12	+	1.03497e13i	0.378401	+	0.655409i	0.990830	−	0.135116i	$-0.0431408\pi$
$857$	5.97538e12	+	1.03497e13i	0.378401	+	0.655409i	−0.612429	+	0.790526i	$0.709807\pi$
$858$		0			0
$859$	8.43166e12	−	1.46041e13i	0.528377	−	0.915176i	−0.471076	−	0.882093i	$-0.656134\pi$
$859$	8.43166e12	−	1.46041e13i	0.528377	−	0.915176i	0.999453	−	0.0330829i	$-0.0105326\pi$
$860$	2.54350e13	−	4.40547e13i	1.58558	−	2.74631i
$861$		0			0
$862$	−7.70147e12	−	1.33393e13i	−0.475107	−	0.822909i
$863$	−2.70257e13			−1.65855			−0.829275	−	0.558840i	$-0.811247\pi$
$863$	−2.70257e13			−1.65855			−0.829275	+	0.558840i	$0.811247\pi$
$864$		0			0
$865$	−4.33190e12			−0.263091
$866$	1.64851e11	+	2.85530e11i	0.00996001	+	0.0172512i
$867$		0			0
$868$	−1.67169e13	+	2.89545e13i	−0.999579	+	1.73132i
$869$	−2.59398e11	+	4.49291e11i	−0.0154304	+	0.0267263i
$870$		0			0
$871$	−5.37470e11	−	9.30926e11i	−0.0316427	−	0.0548067i
$872$	5.56072e13			3.25692
$873$		0			0
$874$	1.45913e12			0.0845849
$875$	−9.70424e12	−	1.68082e13i	−0.559661	−	0.969362i
$876$		0			0
$877$	−7.36962e12	+	1.27646e13i	−0.420675	+	0.728631i	−0.996006	−	0.0892904i	$-0.971540\pi$
$877$	−7.36962e12	+	1.27646e13i	−0.420675	+	0.728631i	0.575331	+	0.817921i	$0.304873\pi$
$878$	−2.13449e13	+	3.69704e13i	−1.21218	+	2.09957i
$879$		0			0
$880$	8.63974e12	+	1.49645e13i	0.485656	+	0.841181i
$881$	−2.25153e13			−1.25918			−0.629589	−	0.776928i	$-0.716777\pi$
$881$	−2.25153e13			−1.25918			−0.629589	+	0.776928i	$0.716777\pi$
$882$		0			0
$883$	−2.11103e13			−1.16861			−0.584307	−	0.811533i	$-0.698634\pi$
$883$	−2.11103e13			−1.16861			−0.584307	+	0.811533i	$0.698634\pi$
$884$	1.63047e12	+	2.82406e12i	0.0898003	+	0.155539i
$885$		0			0
$886$	−6.41609e12	+	1.11130e13i	−0.349799	+	0.605870i
$887$	−2.36351e12	+	4.09372e12i	−0.128204	+	0.222056i	−0.922981	−	0.384846i	$-0.874255\pi$
$887$	−2.36351e12	+	4.09372e12i	−0.128204	+	0.222056i	0.794777	+	0.606902i	$0.207588\pi$
$888$		0			0
$889$	6.23877e12	+	1.08059e13i	0.334997	+	0.580232i
$890$	−4.40956e13			−2.35581
$891$		0			0
$892$	−8.40195e13			−4.44363
$893$	−9.04846e12	−	1.56724e13i	−0.476149	−	0.824715i
$894$		0			0
$895$	1.29316e13	−	2.23981e13i	0.673671	−	1.16683i
$896$	−5.40281e13	+	9.35794e13i	−2.80049	+	4.85058i
$897$		0			0
$898$	−2.22451e13	−	3.85296e13i	−1.14154	−	1.97720i
$899$	−1.18241e13			−0.603740
$900$		0			0
$901$	3.49740e13			1.76801
$902$	5.66390e12	+	9.81017e12i	0.284896	+	0.493454i
$903$		0			0
$904$	1.64543e12	−	2.84998e12i	0.0819450	−	0.141933i
$905$	−2.19402e12	+	3.80015e12i	−0.108723	+	0.188314i
$906$		0			0
$907$	−6.64325e12	−	1.15064e13i	−0.325948	−	0.564558i	0.655756	−	0.754973i	$-0.272350\pi$
$907$	−6.64325e12	−	1.15064e13i	−0.325948	−	0.564558i	−0.981704	+	0.190415i	$0.939017\pi$
$908$	5.13259e13			2.50582
$909$		0			0
$910$	−1.54122e12			−0.0745038
$911$	1.04554e13	+	1.81093e13i	0.502930	+	0.871100i	0.999994	+	0.00338636i	$0.00107791\pi$
$911$	1.04554e13	+	1.81093e13i	0.502930	+	0.871100i	−0.497064	+	0.867714i	$0.665589\pi$
$912$		0			0
$913$	−5.84411e10	+	1.01223e11i	−0.00278356	+	0.00482126i
$914$	−6.31253e12	+	1.09336e13i	−0.299189	+	0.518210i
$915$		0			0
$916$	−4.74710e13	−	8.22221e13i	−2.22791	−	3.85886i
$917$	−3.04667e13			−1.42286
$918$		0			0
$919$	−1.12670e13			−0.521060			−0.260530	−	0.965466i	$-0.583897\pi$
$919$	−1.12670e13			−0.521060			−0.260530	+	0.965466i	$0.583897\pi$
$920$	−1.50053e12	−	2.59899e12i	−0.0690556	−	0.119608i
$921$		0			0
$922$	1.43621e10	−	2.48759e10i	0.000654529	−	0.00113368i
$923$	−8.15074e11	+	1.41175e12i	−0.0369649	+	0.0640250i
$924$		0			0
$925$	−1.67533e12	−	2.90175e12i	−0.0752422	−	0.130323i
$926$	−2.14856e13			−0.960281
$927$		0			0
$928$	−9.85731e13			−4.36307
$929$	−1.24126e13	−	2.14992e13i	−0.546752	−	0.947003i	−0.998494	−	0.0548543i	$-0.982531\pi$
$929$	−1.24126e13	−	2.14992e13i	−0.546752	−	0.947003i	0.451742	−	0.892149i	$-0.350803\pi$
$930$		0			0
$931$	7.55291e11	−	1.30820e12i	0.0329489	−	0.0570692i
$932$	4.33312e13	−	7.50518e13i	1.88117	−	3.25829i
$933$		0			0
$934$	1.57922e13	+	2.73530e13i	0.679020	+	1.17610i
$935$	6.75560e12			0.289076
$936$		0			0
$937$	2.05299e13			0.870081			0.435040	−	0.900411i	$-0.356734\pi$
$937$	2.05299e13			0.870081			0.435040	+	0.900411i	$0.356734\pi$
$938$	−3.14939e13	−	5.45490e13i	−1.32835	−	2.30078i
$939$		0			0
$940$	−2.85960e13	+	4.95298e13i	−1.19462	+	2.06915i
$941$	1.44919e13	−	2.51006e13i	0.602519	−	1.04359i	−0.389919	−	0.920849i	$-0.627497\pi$
$941$	1.44919e13	−	2.51006e13i	0.602519	−	1.04359i	0.992438	−	0.122745i	$-0.0391697\pi$
$942$		0			0
$943$	−5.92485e11	−	1.02621e12i	−0.0243992	−	0.0422606i
$944$	5.83313e13			2.39072
$945$		0			0
$946$	2.12471e13			0.862562
$947$	1.39104e13	+	2.40935e13i	0.562036	+	0.973475i	0.997319	+	0.0731809i	$0.0233150\pi$
$947$	1.39104e13	+	2.40935e13i	0.562036	+	0.973475i	−0.435283	+	0.900294i	$0.643352\pi$
$948$		0			0
$949$	−3.94145e11	+	6.82679e11i	−0.0157746	+	0.0273224i
$950$	−9.20643e12	+	1.59460e13i	−0.366720	+	0.635178i
$951$		0			0
$952$	6.21775e13	+	1.07695e14i	2.45339	+	4.24940i
$953$	2.85882e13			1.12271			0.561357	−	0.827573i	$-0.310279\pi$
$953$	2.85882e13			1.12271			0.561357	+	0.827573i	$0.310279\pi$
$954$		0			0
$955$	−1.53842e13			−0.598496
$956$	2.96690e13	+	5.13883e13i	1.14880	+	1.98977i
$957$		0			0
$958$	−3.43851e11	+	5.95568e11i	−0.0131894	+	0.0228448i
$959$	2.25011e13	−	3.89731e13i	0.859055	−	1.48793i
$960$		0			0
$961$	7.23667e12	+	1.25343e13i	0.273706	+	0.474072i
$962$	−8.77947e11			−0.0330507
$963$		0			0
$964$	4.94246e12			0.184330
$965$	8.33489e12	+	1.44365e13i	0.309405	+	0.535905i
$966$		0			0
$967$	2.57467e13	−	4.45947e13i	0.946898	−	1.64008i	0.194993	−	0.980805i	$-0.437532\pi$
$967$	2.57467e13	−	4.45947e13i	0.946898	−	1.64008i	0.751906	−	0.659271i	$-0.229135\pi$
$968$	4.55960e13	−	7.89745e13i	1.66912	−	2.89100i
$969$		0			0
$970$	2.25945e13	+	3.91348e13i	0.819464	+	1.41935i
$971$	−3.75474e13			−1.35548			−0.677740	−	0.735301i	$-0.737041\pi$
$971$	−3.75474e13			−1.35548			−0.677740	+	0.735301i	$0.737041\pi$
$972$		0			0
$973$	3.21464e13			1.14981
$974$	1.25738e13	+	2.17784e13i	0.447663	+	0.775374i
$975$		0			0
$976$	1.09557e13	−	1.89759e13i	0.386472	−	0.669389i
$977$	1.62693e13	−	2.81792e13i	0.571271	−	0.989470i	−0.425165	−	0.905116i	$-0.639784\pi$
$977$	1.62693e13	−	2.81792e13i	0.571271	−	0.989470i	0.996436	−	0.0843544i	$-0.0268828\pi$
$978$		0			0
$979$	−6.82540e12	−	1.18219e13i	−0.237469	−	0.411308i
$980$	−4.77392e12			−0.165332
$981$		0			0
$982$	−1.65781e13			−0.568895
$983$	−2.81683e13	−	4.87889e13i	−0.962209	−	1.66660i	−0.716932	−	0.697143i	$-0.754454\pi$
$983$	−2.81683e13	−	4.87889e13i	−0.962209	−	1.66660i	−0.245277	−	0.969453i	$-0.578879\pi$
$984$		0			0
$985$	−2.10956e12	+	3.65386e12i	−0.0714049	+	0.123677i
$986$	−3.37884e13	+	5.85232e13i	−1.13847	+	1.97189i
$987$		0			0
$988$	1.78795e12	+	3.09682e12i	0.0596964	+	0.103397i
$989$	−2.22260e12			−0.0738718
$990$		0			0
$991$	−2.09674e13			−0.690578			−0.345289	−	0.938496i	$-0.612219\pi$
$991$	−2.09674e13			−0.690578			−0.345289	+	0.938496i	$0.612219\pi$
$992$	−4.98791e13	−	8.63932e13i	−1.63537	−	2.83255i
$993$		0			0
$994$	−4.77605e13	+	8.27236e13i	−1.55178	+	2.68776i
$995$	−2.05033e13	+	3.55128e13i	−0.663164	+	1.14863i
$996$		0			0
$997$	−2.42890e13	−	4.20698e13i	−0.778541	−	1.34847i	−0.932782	−	0.360440i	$-0.882627\pi$
$997$	−2.42890e13	−	4.20698e13i	−0.778541	−	1.34847i	0.154241	−	0.988033i	$-0.450707\pi$
$998$	−1.59057e13			−0.507533
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.c.j.28.1		8
3.2	odd	2	inner	81.10.c.j.28.4		8
9.2	odd	6	inner	81.10.c.j.55.4		8
9.4	even	3		27.10.a.d.1.4	yes	4
9.5	odd	6		27.10.a.d.1.1	✓	4
9.7	even	3	inner	81.10.c.j.55.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.a.d.1.1	✓	4	9.5	odd	6
27.10.a.d.1.4	yes	4	9.4	even	3
81.10.c.j.28.1		8	1.1	even	1	trivial
81.10.c.j.28.4		8	3.2	odd	2	inner
81.10.c.j.55.1		8	9.7	even	3	inner
81.10.c.j.55.4		8	9.2	odd	6	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.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-22.2386 - 38.5183i) q^{2} +(-733.108 + 1269.78i) q^{4} +(525.311 - 909.865i) q^{5} +(-3295.93 - 5708.72i) q^{7} +42440.8 q^{8} -46728.6 q^{10} +(-7232.96 - 12527.8i) q^{11} +(-2501.75 + 4333.15i) q^{13} +(-146594. + 253908. i) q^{14} +(-568471. - 984621. i) q^{16} -444500. q^{17} -487431. q^{19} +(770219. + 1.33406e6i) q^{20} +(-321701. + 557203. i) q^{22} +(33652.3 - 58287.4i) q^{23} +(424660. + 735532. i) q^{25} +222541. q^{26} +9.66510e6 q^{28} +(1.70907e6 + 2.96019e6i) q^{29} +(-1.72962e6 + 2.99578e6i) q^{31} +(-1.44191e7 + 2.49747e7i) q^{32} +(9.88504e6 + 1.71214e7i) q^{34} -6.92555e6 q^{35} -3.94510e6 q^{37} +(1.08398e7 + 1.87750e7i) q^{38} +(2.22946e7 - 3.86154e7i) q^{40} +(8.80305e6 - 1.52473e7i) q^{41} +(-1.65115e7 - 2.85988e7i) q^{43} +2.12102e7 q^{44} -2.99351e6 q^{46} +(1.85636e7 + 3.21530e7i) q^{47} +(-1.54953e6 + 2.68387e6i) q^{49} +(1.88876e7 - 3.27144e7i) q^{50} +(-3.66810e6 - 6.35334e6i) q^{52} -7.86818e7 q^{53} -1.51982e7 q^{55} +(-1.39882e8 - 2.42283e8i) q^{56} +(7.60144e7 - 1.31661e8i) q^{58} +(-2.56527e7 + 4.44318e7i) q^{59} +(9.63615e6 + 1.66903e7i) q^{61} +1.53857e8 q^{62} +7.00529e8 q^{64} +(2.62839e6 + 4.55250e6i) q^{65} +(-1.07419e8 + 1.86055e8i) q^{67} +(3.25866e8 - 5.64417e8i) q^{68} +(1.54014e8 + 2.66761e8i) q^{70} +3.25802e8 q^{71} +1.57548e8 q^{73} +(8.77334e7 + 1.51959e8i) q^{74} +(3.57340e8 - 6.18931e8i) q^{76} +(-4.76787e7 + 8.25819e7i) q^{77} +(-1.79317e7 - 3.10586e7i) q^{79} -1.19450e9 q^{80} -7.83069e8 q^{82} +(-4.03992e6 - 6.99735e6i) q^{83} +(-2.33501e8 + 4.04435e8i) q^{85} +(-7.34386e8 + 1.27199e9i) q^{86} +(-3.06972e8 - 5.31692e8i) q^{88} +9.43654e8 q^{89} +3.29823e7 q^{91} +(4.93415e7 + 8.54620e7i) q^{92} +(8.25654e8 - 1.43008e9i) q^{94} +(-2.56053e8 + 4.43497e8i) q^{95} +(-4.83526e8 - 8.37491e8i) q^{97} +1.37838e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2236 q^{4} - 11852 q^{7} - 83520 q^{10} - 179684 q^{13} - 2348680 q^{16} + 2022856 q^{19} - 3473568 q^{22} - 2554060 q^{25} + 39587848 q^{28} - 889136 q^{31} + 43111008 q^{34} - 7610312 q^{37} + 133649280 q^{40}+ \cdots - 1935734516 q^{97}+O(q^{100}) \) 8 * q - 2236 * q^4 - 11852 * q^7 - 83520 * q^10 - 179684 * q^13 - 2348680 * q^16 + 2022856 * q^19 - 3473568 * q^22 - 2554060 * q^25 + 39587848 * q^28 - 889136 * q^31 + 43111008 * q^34 - 7610312 * q^37 + 133649280 * q^40 - 11585024 * q^43 + 26856000 * q^46 + 73622328 * q^49 + 44411860 * q^52 + 629444160 * q^55 + 407685888 * q^58 - 219882572 * q^61 + 3038570720 * q^64 - 390561236 * q^67 + 650481120 * q^70 + 2395899016 * q^73 + 2121017572 * q^76 - 49814324 * q^79 - 3534253056 * q^82 - 370444320 * q^85 + 653198976 * q^88 - 94034344 * q^91 + 4146926688 * q^94 - 1935734516 * q^97

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