LMFDB - Embedded newform 81.3.f.a.44.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,3,Mod(8,81)]

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([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("81.8");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	81.f (of order $18$, 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:	$2.20709014132$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			44.4
Character	$\chi$	$=$	81.44
Dual form			81.3.f.a.35.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24712 + 1.48626i) q^{2} +(0.0409354 - 0.232156i) q^{4} +(1.47839 + 4.06185i) q^{5} +(1.54363 + 8.75434i) q^{7} +(7.11704 - 4.10903i) q^{8} +O(q^{10})$	\(q+(1.24712 + 1.48626i) q^{2} +(0.0409354 - 0.232156i) q^{4} +(1.47839 + 4.06185i) q^{5} +(1.54363 + 8.75434i) q^{7} +(7.11704 - 4.10903i) q^{8} +(-4.19322 + 7.26288i) q^{10} +(2.52275 - 6.93119i) q^{11} +(-12.4164 - 10.4186i) q^{13} +(-11.0861 + 13.2119i) q^{14} +(14.0968 + 5.13081i) q^{16} +(-9.06825 - 5.23555i) q^{17} +(-8.63742 - 14.9604i) q^{19} +(1.00350 - 0.176945i) q^{20} +(13.4477 - 4.89456i) q^{22} +(-12.9785 - 2.28846i) q^{23} +(4.83813 - 4.05967i) q^{25} -31.4473i q^{26} +2.09556 q^{28} +(26.8925 + 32.0493i) q^{29} +(6.43612 - 36.5011i) q^{31} +(-1.28832 - 3.53963i) q^{32} +(-3.52779 - 20.0071i) q^{34} +(-33.2767 + 19.2123i) q^{35} +(-31.9875 + 55.4041i) q^{37} +(11.4632 - 31.4949i) q^{38} +(27.2120 + 22.8336i) q^{40} +(16.3590 - 19.4958i) q^{41} +(-2.32975 - 0.847961i) q^{43} +(-1.50585 - 0.869403i) q^{44} +(-12.7845 - 22.1433i) q^{46} +(-45.9670 + 8.10521i) q^{47} +(-28.2107 + 10.2679i) q^{49} +(12.0674 + 2.12781i) q^{50} +(-2.92703 + 2.45607i) q^{52} +50.7217i q^{53} +31.8831 q^{55} +(46.9579 + 55.9622i) q^{56} +(-14.0953 + 79.9384i) q^{58} +(-1.43303 - 3.93723i) q^{59} +(6.31465 + 35.8121i) q^{61} +(62.2766 - 35.9554i) q^{62} +(33.6571 - 58.2957i) q^{64} +(23.9626 - 65.8366i) q^{65} +(13.2595 + 11.1260i) q^{67} +(-1.58668 + 1.89093i) q^{68} +(-70.0545 - 25.4977i) q^{70} +(51.5041 + 29.7359i) q^{71} +(26.3451 + 45.6310i) q^{73} +(-122.237 + 21.5537i) q^{74} +(-3.82674 + 1.39282i) q^{76} +(64.5722 + 11.3858i) q^{77} +(-1.19477 + 1.00253i) q^{79} +64.8443i q^{80} +49.3774 q^{82} +(-72.6820 - 86.6190i) q^{83} +(7.85961 - 44.5741i) q^{85} +(-1.64519 - 4.52012i) q^{86} +(-10.5259 - 59.6956i) q^{88} +(-41.4518 + 23.9322i) q^{89} +(72.0419 - 124.780i) q^{91} +(-1.06256 + 2.91936i) q^{92} +(-69.3726 - 58.2105i) q^{94} +(47.9976 - 57.2013i) q^{95} +(34.5497 + 12.5750i) q^{97} +(-50.4428 - 29.1232i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{2} - 6 q^{4} + 15 q^{5} - 6 q^{7} + 9 q^{8}+O(q^{10}) $ 30 * q + 6 * q^2 - 6 * q^4 + 15 * q^5 - 6 * q^7 + 9 * q^8	$ 30 q + 6 q^{2} - 6 q^{4} + 15 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 6 q^{11} - 6 q^{13} + 15 q^{14} - 18 q^{16} + 9 q^{17} - 3 q^{19} - 213 q^{20} - 42 q^{22} - 120 q^{23} - 15 q^{25} - 12 q^{28} + 168 q^{29} + 39 q^{31} + 360 q^{32} + 54 q^{34} + 252 q^{35} - 3 q^{37} + 84 q^{38} - 33 q^{40} - 228 q^{41} - 96 q^{43} - 639 q^{44} - 3 q^{46} - 399 q^{47} - 78 q^{49} - 303 q^{50} - 9 q^{52} - 12 q^{55} + 393 q^{56} + 129 q^{58} + 474 q^{59} + 138 q^{61} + 900 q^{62} - 51 q^{64} + 411 q^{65} + 354 q^{67} - 99 q^{68} + 489 q^{70} - 315 q^{71} - 66 q^{73} - 321 q^{74} + 258 q^{76} - 201 q^{77} + 30 q^{79} - 12 q^{82} + 33 q^{83} - 261 q^{85} + 258 q^{86} - 642 q^{88} - 72 q^{89} + 96 q^{91} + 3 q^{92} - 861 q^{94} - 681 q^{95} - 582 q^{97} - 882 q^{98}+O(q^{100}) $ 30 * q + 6 * q^2 - 6 * q^4 + 15 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 6 * q^11 - 6 * q^13 + 15 * q^14 - 18 * q^16 + 9 * q^17 - 3 * q^19 - 213 * q^20 - 42 * q^22 - 120 * q^23 - 15 * q^25 - 12 * q^28 + 168 * q^29 + 39 * q^31 + 360 * q^32 + 54 * q^34 + 252 * q^35 - 3 * q^37 + 84 * q^38 - 33 * q^40 - 228 * q^41 - 96 * q^43 - 639 * q^44 - 3 * q^46 - 399 * q^47 - 78 * q^49 - 303 * q^50 - 9 * q^52 - 12 * q^55 + 393 * q^56 + 129 * q^58 + 474 * q^59 + 138 * q^61 + 900 * q^62 - 51 * q^64 + 411 * q^65 + 354 * q^67 - 99 * q^68 + 489 * q^70 - 315 * q^71 - 66 * q^73 - 321 * q^74 + 258 * q^76 - 201 * q^77 + 30 * q^79 - 12 * q^82 + 33 * q^83 - 261 * q^85 + 258 * q^86 - 642 * q^88 - 72 * q^89 + 96 * q^91 + 3 * q^92 - 861 * q^94 - 681 * q^95 - 582 * q^97 - 882 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	1.24712	+	1.48626i	0.623559	+	0.743128i	0.981678	−	0.190547i	$-0.0610263\pi$
$2$	1.24712	+	1.48626i	0.623559	+	0.743128i	−0.358119	+	0.933676i	$0.616582\pi$
$3$		0			0
$3$		0			0
$4$	0.0409354	−	0.232156i	0.0102339	−	0.0580391i
$5$	1.47839	+	4.06185i	0.295679	+	0.812370i	0.995209	+	0.0977676i	$0.0311702\pi$
$5$	1.47839	+	4.06185i	0.295679	+	0.812370i	−0.699531	+	0.714602i	$0.746608\pi$
$6$		0			0
$7$	1.54363	+	8.75434i	0.220518	+	1.25062i	0.871070	+	0.491158i	$0.163426\pi$
$7$	1.54363	+	8.75434i	0.220518	+	1.25062i	−0.650552	+	0.759462i	$0.725463\pi$
$8$	7.11704	−	4.10903i	0.889630	−	0.513628i
$9$		0			0
$10$	−4.19322	+	7.26288i	−0.419322	+	0.726288i
$11$	2.52275	−	6.93119i	0.229341	−	0.630108i	−0.770634	−	0.637278i	$-0.780060\pi$
$11$	2.52275	−	6.93119i	0.229341	−	0.630108i	0.999974	+	0.00717020i	$0.00228236\pi$
$12$		0			0
$13$	−12.4164	−	10.4186i	−0.955111	−	0.801434i	0.0250395	−	0.999686i	$-0.492029\pi$
$13$	−12.4164	−	10.4186i	−0.955111	−	0.801434i	−0.980151	+	0.198253i	$0.936473\pi$
$14$	−11.0861	+	13.2119i	−0.791865	+	0.943708i
$15$		0			0
$16$	14.0968	+	5.13081i	0.881049	+	0.320675i
$17$	−9.06825	−	5.23555i	−0.533426	−	0.307974i	0.208984	−	0.977919i	$-0.432984\pi$
$17$	−9.06825	−	5.23555i	−0.533426	−	0.307974i	−0.742411	+	0.669945i	$0.766318\pi$
$18$		0			0
$19$	−8.63742	−	14.9604i	−0.454601	−	0.787392i	0.544064	−	0.839044i	$-0.316885\pi$
$19$	−8.63742	−	14.9604i	−0.454601	−	0.787392i	−0.998665	+	0.0516517i	$0.983551\pi$
$20$	1.00350	−	0.176945i	0.0501752	−	0.00884723i
$21$		0			0
$22$	13.4477	−	4.89456i	0.611259	−	0.222480i
$23$	−12.9785	−	2.28846i	−0.564282	−	0.0994981i	−0.115772	−	0.993276i	$-0.536934\pi$
$23$	−12.9785	−	2.28846i	−0.564282	−	0.0994981i	−0.448510	+	0.893778i	$0.648045\pi$
$24$		0			0
$25$	4.83813	−	4.05967i	0.193525	−	0.162387i
$26$		−	31.4473i		−	1.20951i
$27$		0			0
$28$	2.09556			0.0748416
$29$	26.8925	+	32.0493i	0.927329	+	1.10515i	0.994217	+	0.107387i	$0.0342484\pi$
$29$	26.8925	+	32.0493i	0.927329	+	1.10515i	−0.0668885	+	0.997760i	$0.521307\pi$
$30$		0			0
$31$	6.43612	−	36.5011i	0.207617	−	1.17745i	−0.685651	−	0.727930i	$-0.740483\pi$
$31$	6.43612	−	36.5011i	0.207617	−	1.17745i	0.893268	−	0.449524i	$-0.148406\pi$
$32$	−1.28832	−	3.53963i	−0.0402600	−	0.110613i
$33$		0			0
$34$	−3.52779	−	20.0071i	−0.103759	−	0.588444i
$35$	−33.2767	+	19.2123i	−0.950764	+	0.548924i
$36$		0			0
$37$	−31.9875	+	55.4041i	−0.864528	+	1.49741i	0.00298644	+	0.999996i	$0.499049\pi$
$37$	−31.9875	+	55.4041i	−0.864528	+	1.49741i	−0.867515	+	0.497411i	$0.834284\pi$
$38$	11.4632	−	31.4949i	0.301663	−	0.828812i
$39$		0			0
$40$	27.2120	+	22.8336i	0.680301	+	0.570840i
$41$	16.3590	−	19.4958i	0.398999	−	0.475508i	−0.528715	−	0.848799i	$-0.677326\pi$
$41$	16.3590	−	19.4958i	0.398999	−	0.475508i	0.927714	+	0.373291i	$0.121771\pi$
$42$		0			0
$43$	−2.32975	−	0.847961i	−0.0541803	−	0.0197200i	0.314788	−	0.949162i	$-0.398067\pi$
$43$	−2.32975	−	0.847961i	−0.0541803	−	0.0197200i	−0.368968	+	0.929442i	$0.620289\pi$
$44$	−1.50585	−	0.869403i	−0.0342239	−	0.0197592i
$45$		0			0
$46$	−12.7845	−	22.1433i	−0.277923	−	0.481377i
$47$	−45.9670	+	8.10521i	−0.978020	+	0.172451i	−0.639738	−	0.768593i	$-0.720957\pi$
$47$	−45.9670	+	8.10521i	−0.978020	+	0.172451i	−0.338282	+	0.941045i	$0.609846\pi$
$48$		0			0
$49$	−28.2107	+	10.2679i	−0.575729	+	0.209548i
$50$	12.0674	+	2.12781i	0.241349	+	0.0425563i
$51$		0			0
$52$	−2.92703	+	2.45607i	−0.0562890	+	0.0472320i
$53$			50.7217i			0.957013i	0.878084	+	0.478507i	$0.158822\pi$
$53$			50.7217i			0.957013i	−0.878084	+	0.478507i	$0.841178\pi$
$54$		0			0
$55$	31.8831			0.579692
$56$	46.9579	+	55.9622i	0.838533	+	0.999325i
$57$		0			0
$58$	−14.0953	+	79.9384i	−0.243022	+	1.37825i
$59$	−1.43303	−	3.93723i	−0.0242887	−	0.0667327i	0.926956	−	0.375171i	$-0.122416\pi$
$59$	−1.43303	−	3.93723i	−0.0242887	−	0.0667327i	−0.951244	+	0.308438i	$0.900194\pi$
$60$		0			0
$61$	6.31465	+	35.8121i	0.103519	+	0.587084i	0.991802	+	0.127787i	$0.0407875\pi$
$61$	6.31465	+	35.8121i	0.103519	+	0.587084i	−0.888283	+	0.459297i	$0.848101\pi$
$62$	62.2766	−	35.9554i	1.00446	−	0.579926i
$63$		0			0
$64$	33.6571	−	58.2957i	0.525892	−	0.910871i
$65$	23.9626	−	65.8366i	0.368655	−	1.01287i
$66$		0			0
$67$	13.2595	+	11.1260i	0.197902	+	0.166060i	0.736354	−	0.676597i	$-0.236546\pi$
$67$	13.2595	+	11.1260i	0.197902	+	0.166060i	−0.538451	+	0.842657i	$0.680990\pi$
$68$	−1.58668	+	1.89093i	−0.0233335	+	0.0278078i
$69$		0			0
$70$	−70.0545	−	25.4977i	−1.00078	−	0.364253i
$71$	51.5041	+	29.7359i	0.725410	+	0.418815i	0.816740	−	0.577005i	$-0.195779\pi$
$71$	51.5041	+	29.7359i	0.725410	+	0.418815i	−0.0913309	+	0.995821i	$0.529112\pi$
$72$		0			0
$73$	26.3451	+	45.6310i	0.360892	+	0.625083i	0.988108	−	0.153762i	$-0.0491391\pi$
$73$	26.3451	+	45.6310i	0.360892	+	0.625083i	−0.627216	+	0.778845i	$0.715806\pi$
$74$	−122.237	+	21.5537i	−1.65185	+	0.291266i
$75$		0			0
$76$	−3.82674	+	1.39282i	−0.0503518	+	0.0183266i
$77$	64.5722	+	11.3858i	0.838600	+	0.147868i
$78$		0			0
$79$	−1.19477	+	1.00253i	−0.0151237	+	0.0126903i	−0.650318	−	0.759662i	$-0.725364\pi$
$79$	−1.19477	+	1.00253i	−0.0151237	+	0.0126903i	0.635194	+	0.772352i	$0.280920\pi$
$80$			64.8443i			0.810554i
$81$		0			0
$82$	49.3774			0.602163
$83$	−72.6820	−	86.6190i	−0.875686	−	1.04360i	−0.998689	−	0.0511958i	$-0.983697\pi$
$83$	−72.6820	−	86.6190i	−0.875686	−	1.04360i	0.123002	−	0.992406i	$-0.460748\pi$
$84$		0			0
$85$	7.85961	−	44.5741i	0.0924660	−	0.524401i
$86$	−1.64519	−	4.52012i	−0.0191301	−	0.0525595i
$87$		0			0
$88$	−10.5259	−	59.6956i	−0.119613	−	0.678359i
$89$	−41.4518	+	23.9322i	−0.465750	+	0.268901i	−0.714459	−	0.699677i	$-0.753327\pi$
$89$	−41.4518	+	23.9322i	−0.465750	+	0.268901i	0.248709	+	0.968578i	$0.419994\pi$
$90$		0			0
$91$	72.0419	−	124.780i	0.791670	−	1.37121i
$92$	−1.06256	+	2.91936i	−0.0115496	+	0.0317322i
$93$		0			0
$94$	−69.3726	−	58.2105i	−0.738007	−	0.619261i
$95$	47.9976	−	57.2013i	0.505238	−	0.602119i
$96$		0			0
$97$	34.5497	+	12.5750i	0.356182	+	0.129640i	0.513913	−	0.857843i	$-0.328196\pi$
$97$	34.5497	+	12.5750i	0.356182	+	0.129640i	−0.157731	+	0.987482i	$0.550418\pi$
$98$	−50.4428	−	29.1232i	−0.514722	−	0.297175i
$99$		0			0
$100$	−0.744428	−	1.28939i	−0.00744428	−	0.0128939i
$101$	−84.0022	+	14.8119i	−0.831705	+	0.146652i	−0.573260	−	0.819374i	$-0.694321\pi$
$101$	−84.0022	+	14.8119i	−0.831705	+	0.146652i	−0.258445	+	0.966026i	$0.583210\pi$
$102$		0			0
$103$	−21.8401	+	7.94915i	−0.212040	+	0.0771762i	−0.445856	−	0.895105i	$-0.647101\pi$
$103$	−21.8401	+	7.94915i	−0.212040	+	0.0771762i	0.233816	+	0.972281i	$0.424879\pi$
$104$	−131.179	−	23.1304i	−1.26134	−	0.222407i
$105$		0			0
$106$	−75.3855	+	63.2559i	−0.711184	+	0.596754i
$107$		−	95.7625i		−	0.894977i	−0.894290	−	0.447488i	$-0.852319\pi$
$107$		−	95.7625i		−	0.894977i	0.894290	−	0.447488i	$-0.147681\pi$
$108$		0			0
$109$	−102.160			−0.937249			−0.468625	−	0.883397i	$-0.655250\pi$
$109$	−102.160			−0.937249			−0.468625	+	0.883397i	$0.655250\pi$
$110$	39.7619	+	47.3864i	0.361472	+	0.430786i
$111$		0			0
$112$	−23.1567	+	131.328i	−0.206756	+	1.17257i
$113$	−5.57835	−	15.3264i	−0.0493660	−	0.135632i	0.912559	−	0.408944i	$-0.134103\pi$
$113$	−5.57835	−	15.3264i	−0.0493660	−	0.135632i	−0.961925	+	0.273312i	$0.911881\pi$
$114$		0			0
$115$	−9.89192	−	56.0999i	−0.0860167	−	0.487825i
$116$	8.54130	−	4.93132i	0.0736319	−	0.0425114i
$117$		0			0
$118$	4.06457	−	7.04005i	0.0344455	−	0.0596614i
$119$	31.8358	−	87.4682i	0.267528	−	0.735027i
$120$		0			0
$121$	51.0142	+	42.8060i	0.421605	+	0.353769i
$122$	−45.3509	+	54.0471i	−0.371729	+	0.443009i
$123$		0			0
$124$	−8.21049	−	2.98837i	−0.0662136	−	0.0240998i
$125$	117.228	+	67.6816i	0.937824	+	0.541453i
$126$		0			0
$127$	40.7309	+	70.5479i	0.320715	+	0.555495i	0.980636	−	0.195840i	$-0.0627433\pi$
$127$	40.7309	+	70.5479i	0.320715	+	0.555495i	−0.659920	+	0.751336i	$0.729410\pi$
$128$	113.779	−	20.0622i	0.888895	−	0.156736i
$129$		0			0
$130$	127.734	−	46.4915i	0.982571	−	0.357627i
$131$	143.243	+	25.2576i	1.09346	+	0.192806i	0.691159	−	0.722703i	$-0.257101\pi$
$131$	143.243	+	25.2576i	1.09346	+	0.192806i	0.402298	+	0.915509i	$0.368212\pi$
$132$		0			0
$133$	117.636	−	98.7082i	0.884480	−	0.742167i
$134$			33.5824i			0.250615i
$135$		0			0
$136$	−86.0521			−0.632736
$137$	120.843	+	144.016i	0.882069	+	1.05121i	0.998317	+	0.0579889i	$0.0184688\pi$
$137$	120.843	+	144.016i	0.882069	+	1.05121i	−0.116248	+	0.993220i	$0.537087\pi$
$138$		0			0
$139$	15.2570	−	86.5267i	0.109762	−	0.622494i	−0.879448	−	0.475995i	$-0.842088\pi$
$139$	15.2570	−	86.5267i	0.109762	−	0.622494i	0.989211	−	0.146500i	$-0.0468007\pi$
$140$	3.09807	+	8.51187i	0.0221291	+	0.0607991i
$141$		0			0
$142$	20.0365	+	113.632i	0.141102	+	0.800229i
$143$	−103.537	+	59.7772i	−0.724036	+	0.418022i
$144$		0			0
$145$	−90.4216	+	156.615i	−0.623597	+	1.08010i
$146$	−34.9640	+	96.0629i	−0.239480	+	0.657965i
$147$		0			0
$148$	11.5530	+	9.69410i	0.0780607	+	0.0655007i
$149$	−40.4096	+	48.1582i	−0.271205	+	0.323210i	−0.884407	−	0.466717i	$-0.845437\pi$
$149$	−40.4096	+	48.1582i	−0.271205	+	0.323210i	0.613202	+	0.789926i	$0.289881\pi$
$150$		0			0
$151$	108.435	+	39.4672i	0.718114	+	0.261372i	0.675125	−	0.737703i	$-0.264090\pi$
$151$	108.435	+	39.4672i	0.718114	+	0.261372i	0.0429892	+	0.999076i	$0.486312\pi$
$152$	−122.946	−	70.9828i	−0.808854	−	0.466992i
$153$		0			0
$154$	63.6068	+	110.170i	0.413031	+	0.715391i
$155$	157.777	−	27.8203i	1.01792	−	0.179486i
$156$		0			0
$157$	−49.1767	+	17.8989i	−0.313228	+	0.114006i	−0.493850	−	0.869547i	$-0.664411\pi$
$157$	−49.1767	+	17.8989i	−0.313228	+	0.114006i	0.180623	+	0.983552i	$0.442189\pi$
$158$	−2.98004	−	0.525462i	−0.0188610	−	0.00332571i
$159$		0			0
$160$	12.4728	−	10.4659i	0.0779549	−	0.0654120i
$161$		−	117.151i		−	0.727643i
$162$		0			0
$163$	−251.388			−1.54226			−0.771128	−	0.636681i	$-0.780307\pi$
$163$	−251.388			−1.54226			−0.771128	+	0.636681i	$0.780307\pi$
$164$	−3.85642	−	4.59591i	−0.0235148	−	0.0280238i
$165$		0			0
$166$	38.0951	−	216.048i	0.229489	−	1.30149i
$167$	2.89515	+	7.95437i	0.0173363	+	0.0476310i	0.948059	−	0.318095i	$-0.103043\pi$
$167$	2.89515	+	7.95437i	0.0173363	+	0.0476310i	−0.930723	+	0.365726i	$0.880821\pi$
$168$		0			0
$169$	16.2736	+	92.2924i	0.0962937	+	0.546109i
$170$	76.0504	−	43.9077i	0.447355	−	0.258281i
$171$		0			0
$172$	−0.292229	+	0.506155i	−0.00169901	+	0.00294276i
$173$	−66.7138	+	183.295i	−0.385629	+	1.05951i	0.583319	+	0.812243i	$0.301754\pi$
$173$	−66.7138	+	183.295i	−0.385629	+	1.05951i	−0.968948	+	0.247264i	$0.920468\pi$
$174$		0			0
$175$	43.0080	+	36.0880i	0.245760	+	0.206217i
$176$	71.1252	−	84.7637i	0.404120	−	0.481612i
$177$		0			0
$178$	−87.2646	−	31.7617i	−0.490251	−	0.178437i
$179$	−183.204	−	105.773i	−1.02349	−	0.590910i	−0.108374	−	0.994110i	$-0.534564\pi$
$179$	−183.204	−	105.773i	−1.02349	−	0.590910i	−0.915112	+	0.403200i	$0.867898\pi$
$180$		0			0
$181$	−43.8874	−	76.0153i	−0.242472	−	0.419974i	0.718946	−	0.695066i	$-0.244625\pi$
$181$	−43.8874	−	76.0153i	−0.242472	−	0.419974i	−0.961418	+	0.275092i	$0.911292\pi$
$182$	275.300	−	48.5429i	1.51264	−	0.266719i
$183$		0			0
$184$	−101.772	+	37.0419i	−0.553107	+	0.201315i
$185$	−272.333	−	48.0197i	−1.47207	−	0.259566i
$186$		0			0
$187$	−59.1655	+	49.6458i	−0.316393	+	0.265485i
$188$			11.0033i			0.0585283i
$189$		0			0
$190$	144.874			0.762497
$191$	−206.497	−	246.093i	−1.08113	−	1.28845i	−0.955056	−	0.296426i	$-0.904205\pi$
$191$	−206.497	−	246.093i	−1.08113	−	1.28845i	−0.126079	−	0.992020i	$-0.540239\pi$
$192$		0			0
$193$	10.7145	−	60.7650i	0.0555156	−	0.314845i	−0.944387	−	0.328838i	$-0.893343\pi$
$193$	10.7145	−	60.7650i	0.0555156	−	0.314845i	0.999902	+	0.0139930i	$0.00445425\pi$
$194$	24.3977	+	67.0322i	0.125762	+	0.345527i
$195$		0			0
$196$	1.22893	+	6.96962i	0.00627006	+	0.0355593i
$197$	194.174	−	112.106i	0.985652	−	0.569067i	0.0816805	−	0.996659i	$-0.473971\pi$
$197$	194.174	−	112.106i	0.985652	−	0.569067i	0.903972	+	0.427592i	$0.140638\pi$
$198$		0			0
$199$	2.60375	−	4.50982i	0.0130842	−	0.0226624i	−0.859409	−	0.511288i	$-0.829168\pi$
$199$	2.60375	−	4.50982i	0.0130842	−	0.0226624i	0.872493	+	0.488626i	$0.162502\pi$
$200$	17.7519	−	48.7729i	0.0887593	−	0.243864i
$201$		0			0
$202$	−126.775	−	106.377i	−0.627598	−	0.526617i
$203$	−239.058	+	284.898i	−1.17763	+	1.40344i
$204$		0			0
$205$	103.374	+	37.6251i	0.504264	+	0.183537i
$206$	−39.0517	−	22.5465i	−0.189571	−	0.109449i
$207$		0			0
$208$	−121.576	−	210.576i	−0.584499	−	1.01238i
$209$	−125.484	+	22.1262i	−0.600400	+	0.105867i
$210$		0			0
$211$	21.6633	−	7.88481i	0.102670	−	0.0373688i	−0.290174	−	0.956974i	$-0.593713\pi$
$211$	21.6633	−	7.88481i	0.102670	−	0.0373688i	0.392844	+	0.919605i	$0.371491\pi$
$212$	11.7754	+	2.07631i	0.0555442	+	0.00979394i
$213$		0			0
$214$	142.328	−	119.427i	0.665083	−	0.558071i
$215$		−	10.7167i		−	0.0498452i
$216$		0			0
$217$	329.478			1.51833
$218$	−127.406	−	151.836i	−0.584430	−	0.696497i
$219$		0			0
$220$	1.30515	−	7.40186i	0.00593249	−	0.0336448i
$221$	58.0481	+	159.486i	0.262661	+	0.721655i
$222$		0			0
$223$	−32.6616	−	185.233i	−0.146464	−	0.830641i	−0.966180	−	0.257870i	$-0.916979\pi$
$223$	−32.6616	−	185.233i	−0.146464	−	0.830641i	0.819715	−	0.572771i	$-0.194132\pi$
$224$	28.9984	−	16.7422i	0.129457	−	0.0747421i
$225$		0			0
$226$	15.8221	−	27.4047i	0.0700093	−	0.121260i
$227$	−42.9222	+	117.928i	−0.189085	+	0.519505i	−0.997621	−	0.0689410i	$-0.978038\pi$
$227$	−42.9222	+	117.928i	−0.189085	+	0.519505i	0.808536	+	0.588446i	$0.200260\pi$
$228$		0			0
$229$	−100.359	−	84.2111i	−0.438248	−	0.367734i	0.396805	−	0.917903i	$-0.370119\pi$
$229$	−100.359	−	84.2111i	−0.438248	−	0.367734i	−0.835053	+	0.550169i	$0.814563\pi$
$230$	71.0425	−	84.6651i	0.308880	−	0.368109i
$231$		0			0
$232$	323.087	+	117.594i	1.39261	+	0.506870i
$233$	352.009	+	203.233i	1.51077	+	0.872243i	0.999921	+	0.0125723i	$0.00400199\pi$
$233$	352.009	+	203.233i	1.51077	+	0.872243i	0.510848	+	0.859671i	$0.329331\pi$
$234$		0			0
$235$	−100.879	−	174.728i	−0.429274	−	0.743524i
$236$	−0.972715	+	0.171516i	−0.00412167	+	0.000726762i
$237$		0			0
$238$	169.703	−	61.7670i	0.713039	−	0.259525i
$239$	189.404	+	33.3970i	0.792484	+	0.139736i	0.555214	−	0.831707i	$-0.312636\pi$
$239$	189.404	+	33.3970i	0.792484	+	0.139736i	0.237270	+	0.971444i	$0.423747\pi$
$240$		0			0
$241$	−265.638	+	222.896i	−1.10223	+	0.924881i	−0.997573	−	0.0696270i	$-0.977819\pi$
$241$	−265.638	+	222.896i	−1.10223	+	0.924881i	−0.104658	+	0.994508i	$0.533375\pi$
$242$			129.204i			0.533903i
$243$		0			0
$244$	8.57251			0.0351332
$245$	−83.4131	−	99.4079i	−0.340462	−	0.405746i
$246$		0			0
$247$	−48.6214	+	275.746i	−0.196848	+	1.11638i
$248$	−104.178	−	286.226i	−0.420071	−	1.15414i
$249$		0			0
$250$	45.6048	+	258.638i	0.182419	+	1.03455i
$251$	−370.198	+	213.734i	−1.47489	+	0.851530i	−0.999600	−	0.0282966i	$-0.990992\pi$
$251$	−370.198	+	213.734i	−1.47489	+	0.851530i	−0.475294	+	0.879827i	$0.657658\pi$
$252$		0			0
$253$	−48.6032	+	84.1831i	−0.192107	+	0.332740i
$254$	−54.0562	+	148.518i	−0.212820	+	0.584717i
$255$		0			0
$256$	−34.5496	−	28.9906i	−0.134960	−	0.113245i
$257$	182.597	−	217.611i	0.710495	−	0.846735i	−0.283176	−	0.959068i	$-0.591388\pi$
$257$	182.597	−	217.611i	0.710495	−	0.846735i	0.993671	+	0.112333i	$0.0358324\pi$
$258$		0			0
$259$	−534.403	−	194.507i	−2.06333	−	0.750991i
$260$	−14.3035	−	8.25811i	−0.0550133	−	0.0317620i
$261$		0			0
$262$	141.101	+	244.395i	0.538555	+	0.932805i
$263$	341.187	−	60.1605i	1.29729	−	0.228747i	0.517983	−	0.855391i	$-0.326683\pi$
$263$	341.187	−	60.1605i	1.29729	−	0.228747i	0.779306	+	0.626643i	$0.215572\pi$
$264$		0			0
$265$	−206.024	+	74.9866i	−0.777449	+	0.282968i
$266$	293.412	+	51.7364i	1.10305	+	0.194498i
$267$		0			0
$268$	3.12576	−	2.62282i	0.0116633	−	0.00978665i
$269$		−	297.900i		−	1.10743i	−0.832705	−	0.553717i	$-0.813209\pi$
$269$		−	297.900i		−	1.10743i	0.832705	−	0.553717i	$-0.186791\pi$
$270$		0			0
$271$	368.678			1.36044			0.680218	−	0.733010i	$-0.261885\pi$
$271$	368.678			1.36044			0.680218	+	0.733010i	$0.261885\pi$
$272$	−100.970	−	120.332i	−0.371215	−	0.442397i
$273$		0			0
$274$	−63.3382	+	359.209i	−0.231161	+	1.31098i
$275$	−15.9330	−	43.7755i	−0.0579381	−	0.159184i
$276$		0			0
$277$	−49.1193	−	278.569i	−0.177326	−	1.00566i	−0.935425	−	0.353525i	$-0.884983\pi$
$277$	−49.1193	−	278.569i	−0.177326	−	1.00566i	0.758099	−	0.652139i	$-0.226128\pi$
$278$	147.628	−	85.2331i	0.531036	−	0.306594i
$279$		0			0
$280$	−157.888	+	273.470i	−0.563886	+	0.976678i
$281$	−96.1506	+	264.172i	−0.342173	+	0.940112i	0.642590	+	0.766210i	$0.277860\pi$
$281$	−96.1506	+	264.172i	−0.342173	+	0.940112i	−0.984763	+	0.173902i	$0.944362\pi$
$282$		0			0
$283$	334.168	+	280.400i	1.18081	+	0.990814i	0.999973	+	0.00730054i	$0.00232386\pi$
$283$	334.168	+	280.400i	1.18081	+	0.990814i	0.180833	+	0.983514i	$0.442121\pi$
$284$	9.01172	−	10.7397i	0.0317314	−	0.0378160i
$285$		0			0
$286$	−217.967	−	79.3336i	−0.762123	−	0.277390i
$287$	195.925	+	113.118i	0.682667	+	0.394138i
$288$		0			0
$289$	−89.6779	−	155.327i	−0.310304	−	0.537463i
$290$	−345.536	+	60.9274i	−1.19150	+	0.210094i
$291$		0			0
$292$	11.6720	−	4.24826i	0.0399726	−	0.0145488i
$293$	−363.553	−	64.1042i	−1.24080	−	0.218786i	−0.485539	−	0.874215i	$-0.661377\pi$
$293$	−363.553	−	64.1042i	−1.24080	−	0.218786i	−0.755256	+	0.655429i	$0.772488\pi$
$294$		0			0
$295$	13.8739	−	11.6415i	0.0470300	−	0.0394629i
$296$			525.751i			1.77619i
$297$		0			0
$298$	−121.971			−0.409299
$299$	137.304	+	163.633i	0.459211	+	0.547266i
$300$		0			0
$301$	3.82707	−	21.7044i	0.0127145	−	0.0721076i
$302$	76.5731	+	210.383i	0.253553	+	0.696632i
$303$		0			0
$304$	−45.0006	−	255.211i	−0.148028	−	0.839510i
$305$	−136.128	+	78.5936i	−0.446321	+	0.257684i
$306$		0			0
$307$	183.104	−	317.145i	0.596429	−	1.03304i	−0.396915	−	0.917855i	$-0.629919\pi$
$307$	183.104	−	317.145i	0.596429	−	1.03304i	0.993344	−	0.115189i	$-0.0367475\pi$
$308$	5.28658	−	14.5248i	0.0171642	−	0.0471583i
$309$		0			0
$310$	238.115	+	199.802i	0.768112	+	0.644522i
$311$	306.742	−	365.561i	0.986308	−	1.17544i	0.00181732	−	0.999998i	$-0.499422\pi$
$311$	306.742	−	365.561i	0.986308	−	1.17544i	0.984491	−	0.175438i	$-0.0561340\pi$
$312$		0			0
$313$	95.0647	+	34.6007i	0.303721	+	0.110545i	0.489385	−	0.872068i	$-0.337221\pi$
$313$	95.0647	+	34.6007i	0.303721	+	0.110545i	−0.185664	+	0.982613i	$0.559444\pi$
$314$	−87.9315	−	50.7673i	−0.280037	−	0.161679i
$315$		0			0
$316$	0.183836	+	0.318413i	0.000581759	+	0.00100764i
$317$	364.896	−	64.3410i	1.15109	−	0.202968i	0.434639	−	0.900605i	$-0.356876\pi$
$317$	364.896	−	64.3410i	1.15109	−	0.202968i	0.716452	+	0.697636i	$0.245765\pi$
$318$		0			0
$319$	289.983	−	105.545i	0.909037	−	0.330862i
$320$	286.547	+	50.5260i	0.895459	+	0.157894i
$321$		0			0
$322$	174.116	−	146.101i	0.540732	−	0.453728i
$323$			180.887i			0.560021i
$324$		0			0
$325$	−102.369			−0.314980
$326$	−313.510	−	373.627i	−0.961687	−	1.14609i
$327$		0			0
$328$	36.3185	−	205.972i	0.110727	−	0.627964i
$329$	−141.912	−	389.899i	−0.431342	−	1.18510i
$330$		0			0
$331$	61.9327	+	351.238i	0.187108	+	1.06114i	0.923217	+	0.384279i	$0.125550\pi$
$331$	61.9327	+	351.238i	0.187108	+	1.06114i	−0.736109	+	0.676863i	$0.763339\pi$
$332$	−23.0844	+	13.3278i	−0.0695314	+	0.0401440i
$333$		0			0
$334$	−8.21164	+	14.2230i	−0.0245857	+	0.0425838i
$335$	−25.5895	+	70.3066i	−0.0763866	+	0.209870i
$336$		0			0
$337$	−307.364	−	257.909i	−0.912059	−	0.765309i	0.0604502	−	0.998171i	$-0.480746\pi$
$337$	−307.364	−	257.909i	−0.912059	−	0.765309i	−0.972510	+	0.232862i	$0.925191\pi$
$338$	−116.875	+	139.286i	−0.345784	+	0.412090i
$339$		0			0
$340$	−10.0264	−	3.64932i	−0.0294895	−	0.0107333i
$341$	−236.759	−	136.693i	−0.694308	−	0.400859i
$342$		0			0
$343$	84.3548	+	146.107i	0.245932	+	0.425967i
$344$	−20.0652	+	3.53804i	−0.0583292	+	0.0102850i
$345$		0			0
$346$	−355.623	+	129.436i	−1.02781	+	0.374093i
$347$	−56.4104	−	9.94668i	−0.162566	−	0.0286648i	0.0917726	−	0.995780i	$-0.470747\pi$
$347$	−56.4104	−	9.94668i	−0.162566	−	0.0286648i	−0.254339	+	0.967115i	$0.581858\pi$
$348$		0			0
$349$	287.357	−	241.121i	0.823371	−	0.690890i	−0.130388	−	0.991463i	$-0.541622\pi$
$349$	287.357	−	241.121i	0.823371	−	0.690890i	0.953759	+	0.300573i	$0.0971778\pi$
$350$			108.927i			0.311220i
$351$		0			0
$352$	−27.7839			−0.0789316
$353$	141.432	+	168.552i	0.400658	+	0.477485i	0.928220	−	0.372031i	$-0.121338\pi$
$353$	141.432	+	168.552i	0.400658	+	0.477485i	−0.527563	+	0.849516i	$0.676894\pi$
$354$		0			0
$355$	−44.6395	+	253.163i	−0.125745	+	0.713136i
$356$	3.85917	+	10.6030i	0.0108404	+	0.0297836i
$357$		0			0
$358$	−71.2712	−	404.199i	−0.199082	−	1.12905i
$359$	174.426	−	100.705i	0.485866	−	0.280515i	−0.236992	−	0.971512i	$-0.576162\pi$
$359$	174.426	−	100.705i	0.485866	−	0.280515i	0.722858	+	0.690997i	$0.242828\pi$
$360$		0			0
$361$	31.2901	−	54.1960i	0.0866761	−	0.150127i
$362$	58.2454	−	160.028i	0.160899	−	0.442066i
$363$		0			0
$364$	−26.0195	−	21.8329i	−0.0714821	−	0.0599806i
$365$	−146.398	+	174.470i	−0.401091	+	0.478001i
$366$		0			0
$367$	−149.564	−	54.4369i	−0.407532	−	0.148330i	0.130116	−	0.991499i	$-0.458465\pi$
$367$	−149.564	−	54.4369i	−0.407532	−	0.148330i	−0.537648	+	0.843169i	$0.680687\pi$
$368$	−171.213	−	98.8500i	−0.465253	−	0.268614i
$369$		0			0
$370$	−268.262	−	464.643i	−0.725032	−	1.25579i
$371$	−444.035	+	78.2954i	−1.19686	+	0.211039i
$372$		0			0
$373$	48.5332	−	17.6646i	0.130116	−	0.0473583i	−0.276142	−	0.961117i	$-0.589056\pi$
$373$	48.5332	−	17.6646i	0.130116	−	0.0473583i	0.406257	+	0.913759i	$0.366834\pi$
$374$	−147.573	−	26.0211i	−0.394579	−	0.0695750i
$375$		0			0
$376$	−293.844	+	246.565i	−0.781501	+	0.655757i
$377$		−	678.122i		−	1.79873i
$378$		0			0
$379$	147.231			0.388472			0.194236	−	0.980955i	$-0.437777\pi$
$379$	147.231			0.388472			0.194236	+	0.980955i	$0.437777\pi$
$380$	−11.3148	−	13.4845i	−0.0297759	−	0.0354855i
$381$		0			0
$382$	108.232	−	613.814i	0.283330	−	1.60684i
$383$	38.8997	+	106.876i	0.101566	+	0.279049i	0.980059	−	0.198704i	$-0.0636733\pi$
$383$	38.8997	+	106.876i	0.101566	+	0.279049i	−0.878494	+	0.477754i	$0.841451\pi$
$384$		0			0
$385$	49.2155	+	279.115i	0.127833	+	0.724975i
$386$	103.675	−	59.8566i	0.268587	−	0.155069i
$387$		0			0
$388$	4.33368	−	7.50616i	0.0111693	−	0.0193458i
$389$	123.951	−	340.552i	0.318639	−	0.875454i	−0.672195	−	0.740374i	$-0.734649\pi$
$389$	123.951	−	340.552i	0.318639	−	0.875454i	0.990835	−	0.135080i	$-0.0431292\pi$
$390$		0			0
$391$	105.711	+	88.7018i	0.270360	+	0.226859i
$392$	−158.586	+	188.996i	−0.404556	+	0.482132i
$393$		0			0
$394$	408.776	+	148.782i	1.03750	+	0.377620i
$395$	−5.83848	−	3.37085i	−0.0147810	−	0.00853379i
$396$		0			0
$397$	368.516	+	638.289i	0.928252	+	1.60778i	0.786246	+	0.617914i	$0.212022\pi$
$397$	368.516	+	638.289i	0.928252	+	1.60778i	0.142006	+	0.989866i	$0.454645\pi$
$398$	9.94994	−	1.75444i	0.0249998	−	0.00440815i
$399$		0			0
$400$	89.0314	−	32.4048i	0.222579	−	0.0810119i
$401$	−217.940	−	38.4287i	−0.543491	−	0.0958322i	−0.104839	−	0.994489i	$-0.533433\pi$
$401$	−217.940	−	38.4287i	−0.543491	−	0.0958322i	−0.438652	+	0.898657i	$0.644544\pi$
$402$		0			0
$403$	−460.205	+	386.158i	−1.14195	+	0.958208i
$404$			20.1080i			0.0497722i
$405$		0			0
$406$	−721.566			−1.77726
$407$	303.320	+	361.482i	0.745257	+	0.888163i
$408$		0			0
$409$	77.3060	−	438.424i	0.189012	−	1.07194i	−0.731679	−	0.681650i	$-0.761263\pi$
$409$	77.3060	−	438.424i	0.189012	−	1.07194i	0.920691	−	0.390292i	$-0.127626\pi$
$410$	72.9992	+	200.564i	0.178047	+	0.489179i
$411$		0			0
$412$	0.951411	+	5.39572i	0.00230925	+	0.0130964i
$413$	32.2558	−	18.6229i	0.0781012	−	0.0450917i
$414$		0			0
$415$	244.381	−	423.280i	0.588870	−	1.01995i
$416$	−20.8817	+	57.3721i	−0.0501965	+	0.137914i
$417$		0			0
$418$	−189.378	−	158.907i	−0.453058	−	0.380161i
$419$	−371.014	+	442.157i	−0.885475	+	1.05527i	0.112624	+	0.993638i	$0.464074\pi$
$419$	−371.014	+	442.157i	−0.885475	+	1.05527i	−0.998099	+	0.0616300i	$0.980370\pi$
$420$		0			0
$421$	315.735	+	114.918i	0.749964	+	0.272964i	0.688591	−	0.725150i	$-0.258230\pi$
$421$	315.735	+	114.918i	0.749964	+	0.272964i	0.0613732	+	0.998115i	$0.480452\pi$
$422$	38.7356	+	22.3640i	0.0917905	+	0.0529953i
$423$		0			0
$424$	208.417	+	360.989i	0.491549	+	0.851388i
$425$	−65.1280	+	11.4838i	−0.153242	+	0.0270207i
$426$		0			0
$427$	−303.764	+	110.561i	−0.711392	+	0.258925i
$428$	−22.2319	−	3.92008i	−0.0519436	−	0.00915906i
$429$		0			0
$430$	15.9278	−	13.3650i	0.0370414	−	0.0310814i
$431$		−	113.799i		−	0.264034i	−0.991247	−	0.132017i	$-0.957855\pi$
$431$		−	113.799i		−	0.264034i	0.991247	−	0.132017i	$-0.0421454\pi$
$432$		0			0
$433$	−204.214			−0.471625			−0.235812	−	0.971799i	$-0.575775\pi$
$433$	−204.214			−0.471625			−0.235812	+	0.971799i	$0.575775\pi$
$434$	410.897	+	489.689i	0.946768	+	1.12831i
$435$		0			0
$436$	−4.18197	+	23.7171i	−0.00959168	+	0.0543971i
$437$	77.8642	+	213.930i	0.178179	+	0.489543i
$438$		0			0
$439$	70.1264	+	397.706i	0.159741	+	0.905937i	0.954322	+	0.298779i	$0.0965794\pi$
$439$	70.1264	+	397.706i	0.159741	+	0.905937i	−0.794581	+	0.607158i	$0.792309\pi$
$440$	226.913	−	131.008i	0.515712	−	0.297746i
$441$		0			0
$442$	−164.644	+	285.172i	−0.372498	+	0.645185i
$443$	226.287	−	621.719i	0.510806	−	1.40343i	−0.369593	−	0.929194i	$-0.620503\pi$
$443$	226.287	−	621.719i	0.510806	−	1.40343i	0.880399	−	0.474234i	$-0.157275\pi$
$444$		0			0
$445$	−158.491	−	132.990i	−0.356160	−	0.298853i
$446$	234.571	−	279.551i	0.525944	−	0.626796i
$447$		0			0
$448$	562.295	+	204.659i	1.25512	+	0.456827i
$449$	403.851	+	233.164i	0.899446	+	0.519295i	0.877020	−	0.480453i	$-0.159528\pi$
$449$	403.851	+	233.164i	0.899446	+	0.519295i	0.0224253	+	0.999749i	$0.492861\pi$
$450$		0			0
$451$	−93.8599	−	162.570i	−0.208115	−	0.360466i
$452$	−3.78647	+	0.667658i	−0.00837716	+	0.00147712i
$453$		0			0
$454$	−228.800	+	83.2764i	−0.503965	+	0.183428i
$455$	613.345	+	108.149i	1.34801	+	0.237691i
$456$		0			0
$457$	654.268	−	548.996i	1.43166	−	1.20130i	0.486935	−	0.873438i	$-0.338115\pi$
$457$	654.268	−	548.996i	1.43166	−	1.20130i	0.944724	−	0.327866i	$-0.106330\pi$
$458$		−	254.180i		−	0.554979i
$459$		0			0
$460$	−13.4289			−0.0291932
$461$	52.6518	+	62.7480i	0.114212	+	0.136113i	0.820121	−	0.572190i	$-0.193906\pi$
$461$	52.6518	+	62.7480i	0.114212	+	0.136113i	−0.705909	+	0.708302i	$0.749461\pi$
$462$		0			0
$463$	−113.673	+	644.671i	−0.245514	+	1.39238i	0.573783	+	0.819007i	$0.305475\pi$
$463$	−113.673	+	644.671i	−0.245514	+	1.39238i	−0.819297	+	0.573370i	$0.805636\pi$
$464$	214.659	+	589.772i	0.462628	+	1.27106i
$465$		0			0
$466$	136.941	+	776.631i	0.293865	+	1.66659i
$467$	−113.391	+	65.4664i	−0.242808	+	0.140185i	−0.616466	−	0.787381i	$-0.711436\pi$
$467$	−113.391	+	65.4664i	−0.242808	+	0.140185i	0.373659	+	0.927566i	$0.378103\pi$
$468$		0			0
$469$	−76.9332	+	133.252i	−0.164037	+	0.284120i
$470$	133.883	−	367.839i	0.284856	−	0.782637i
$471$		0			0
$472$	−26.3772	−	22.1331i	−0.0558838	−	0.0468921i
$473$	−11.7548	+	14.0088i	−0.0248515	+	0.0296169i
$474$		0			0
$475$	−102.523	−	37.3155i	−0.215839	−	0.0785589i
$476$	−19.0031	−	10.9714i	−0.0399225	−	0.0230493i
$477$		0			0
$478$	186.572	+	323.152i	0.390318	+	0.676051i
$479$	155.272	−	27.3786i	0.324158	−	0.0571578i	−0.00920134	−	0.999958i	$-0.502929\pi$
$479$	155.272	−	27.3786i	0.324158	−	0.0571578i	0.333359	+	0.942800i	$0.391818\pi$
$480$		0			0
$481$	974.406	−	354.655i	2.02579	−	0.737328i
$482$	−662.563	−	116.828i	−1.37461	−	0.242381i
$483$		0			0
$484$	12.0260	−	10.0910i	0.0248471	−	0.0208492i
$485$			158.926i			0.327683i
$486$		0			0
$487$	−698.201			−1.43368			−0.716839	−	0.697239i	$-0.754412\pi$
$487$	−698.201			−1.43368			−0.716839	+	0.697239i	$0.754412\pi$
$488$	192.095	+	228.930i	0.393637	+	0.469118i
$489$		0			0
$490$	43.7197	−	247.947i	0.0892238	−	0.506013i
$491$	−14.4407	−	39.6755i	−0.0294108	−	0.0808056i	0.924118	−	0.382107i	$-0.124801\pi$
$491$	−14.4407	−	39.6755i	−0.0294108	−	0.0808056i	−0.953529	+	0.301301i	$0.902579\pi$
$492$		0			0
$493$	−76.0724	−	431.428i	−0.154305	−	0.875108i
$494$	−470.466	+	271.623i	−0.952359	+	0.549845i
$495$		0			0
$496$	278.009	−	481.525i	0.560501	−	0.970816i
$497$	−180.815	+	496.785i	−0.363813	+	0.999568i
$498$		0			0
$499$	−367.980	−	308.772i	−0.737435	−	0.618781i	0.194713	−	0.980860i	$-0.437623\pi$
$499$	−367.980	−	308.772i	−0.737435	−	0.618781i	−0.932147	+	0.362079i	$0.882067\pi$
$500$	20.5115	−	24.4446i	0.0410230	−	0.0488893i
$501$		0			0
$502$	−779.345	−	283.658i	−1.55248	−	0.565056i
$503$	−73.7969	−	42.6067i	−0.146714	−	0.0847051i	0.424846	−	0.905266i	$-0.360328\pi$
$503$	−73.7969	−	42.6067i	−0.146714	−	0.0847051i	−0.571560	+	0.820560i	$0.693661\pi$
$504$		0			0
$505$	−184.352	−	319.307i	−0.365053	−	0.632290i
$506$	−185.732	+	32.7495i	−0.367059	+	0.0647223i
$507$		0			0
$508$	18.0455	−	6.56802i	0.0355226	−	0.0129292i
$509$	−391.247	−	68.9874i	−0.768658	−	0.135535i	−0.224450	−	0.974486i	$-0.572059\pi$
$509$	−391.247	−	68.9874i	−0.768658	−	0.135535i	−0.544208	+	0.838950i	$0.683170\pi$
$510$		0			0
$511$	−358.803	+	301.071i	−0.702158	+	0.589180i
$512$		−	549.639i		−	1.07351i
$513$		0			0
$514$	551.146			1.07227
$515$	−64.5765	−	76.9593i	−0.125391	−	0.149435i
$516$		0			0
$517$	−59.7842	+	339.053i	−0.115637	+	0.655809i
$518$	−377.376	−	1036.83i	−0.728525	−	2.00161i
$519$		0			0
$520$	−99.9817	−	567.025i	−0.192273	−	1.09043i
$521$	19.7109	−	11.3801i	0.0378328	−	0.0218428i	−0.480964	−	0.876740i	$-0.659713\pi$
$521$	19.7109	−	11.3801i	0.0378328	−	0.0218428i	0.518797	+	0.854897i	$0.326380\pi$
$522$		0			0
$523$	−380.270	+	658.647i	−0.727093	+	1.25936i	0.231013	+	0.972951i	$0.425796\pi$
$523$	−380.270	+	658.647i	−0.727093	+	1.25936i	−0.958107	+	0.286412i	$0.907537\pi$
$524$	11.7274	−	32.2208i	0.0223806	−	0.0614901i
$525$		0			0
$526$	514.914	+	432.065i	0.978925	+	0.821415i
$527$	−249.468	+	297.304i	−0.473373	+	0.564144i
$528$		0			0
$529$	−333.893	−	121.527i	−0.631178	−	0.229730i
$530$	−368.385	−	212.687i	−0.695067	−	0.401297i
$531$		0			0
$532$	−18.1003	−	31.3506i	−0.0340231	−	0.0589297i
$533$	−406.240	+	71.6311i	−0.762177	+	0.134392i
$534$		0			0
$535$	388.973	−	141.575i	0.727052	−	0.264625i
$536$	140.085	+	24.7008i	0.261353	+	0.0460836i
$537$		0			0
$538$	442.755	−	371.516i	0.822966	−	0.690550i
$539$			221.437i			0.410830i
$540$		0			0
$541$	−158.844			−0.293612			−0.146806	−	0.989165i	$-0.546899\pi$
$541$	−158.844			−0.293612			−0.146806	+	0.989165i	$0.546899\pi$
$542$	459.785	+	547.950i	0.848312	+	1.01098i
$543$		0			0
$544$	−6.84912	+	38.8433i	−0.0125903	+	0.0714031i
$545$	−151.033	−	414.959i	−0.277124	−	0.761393i
$546$		0			0
$547$	−114.270	−	648.057i	−0.208903	−	1.18475i	−0.891179	−	0.453653i	$-0.850121\pi$
$547$	−114.270	−	648.057i	−0.208903	−	1.18475i	0.682276	−	0.731095i	$-0.260990\pi$
$548$	38.3809	−	22.1592i	0.0700382	−	0.0404366i
$549$		0			0
$550$	45.1914	−	78.2737i	0.0821661	−	0.142316i
$551$	247.189	−	679.147i	0.448620	−	1.23257i
$552$		0			0
$553$	−10.6208	−	8.91190i	−0.0192058	−	0.0161155i
$554$	352.768	−	420.412i	0.636765	−	0.758867i
$555$		0			0
$556$	−19.4632	−	7.08401i	−0.0350057	−	0.0127410i
$557$	−817.907	−	472.219i	−1.46842	−	0.847790i	−0.469041	−	0.883176i	$-0.655400\pi$
$557$	−817.907	−	472.219i	−1.46842	−	0.847790i	−0.999374	+	0.0353864i	$0.988734\pi$
$558$		0			0
$559$	20.0927	+	34.8015i	0.0359439	+	0.0622567i
$560$	−567.669	+	100.095i	−1.01370	+	0.178742i
$561$		0			0
$562$	−512.538	+	186.549i	−0.911989	+	0.331937i
$563$	1042.20	+	183.769i	1.85116	+	0.326410i	0.984892	−	0.173168i	$-0.0554002\pi$
$563$	1042.20	+	183.769i	1.85116	+	0.326410i	0.866269	+	0.499577i	$0.166511\pi$
$564$		0			0
$565$	54.0066	−	45.3169i	0.0955868	−	0.0802069i
$566$			846.352i			1.49532i
$567$		0			0
$568$	488.742			0.860462
$569$	−114.850	−	136.873i	−0.201845	−	0.240550i	0.655621	−	0.755090i	$-0.272407\pi$
$569$	−114.850	−	136.873i	−0.201845	−	0.240550i	−0.857466	+	0.514540i	$0.827963\pi$
$570$		0			0
$571$	104.611	−	593.280i	0.183207	−	1.03902i	−0.745030	−	0.667030i	$-0.767565\pi$
$571$	104.611	−	593.280i	0.183207	−	1.03902i	0.928237	−	0.371988i	$-0.121324\pi$
$572$	9.63932	+	26.4838i	0.0168520	+	0.0463004i
$573$		0			0
$574$	76.2202	+	432.266i	0.132788	+	0.753077i
$575$	−72.0819	+	41.6165i	−0.125360	+	0.0723766i
$576$		0			0
$577$	87.1430	−	150.936i	0.151028	−	0.261588i	−0.780578	−	0.625059i	$-0.785075\pi$
$577$	87.1430	−	150.936i	0.151028	−	0.261588i	0.931606	+	0.363471i	$0.118408\pi$
$578$	119.017	−	326.995i	0.205911	−	0.565736i
$579$		0			0
$580$	32.6577	+	27.4031i	0.0563064	+	0.0472466i
$581$	646.098	−	769.990i	1.11205	−	1.32528i
$582$		0			0
$583$	351.562	+	127.958i	0.603022	+	0.219482i
$584$	374.998	+	216.505i	0.642121	+	0.370728i
$585$		0			0
$586$	−358.118	−	620.279i	−0.611123	−	1.05850i
$587$	−1005.60	+	177.314i	−1.71311	+	0.302068i	−0.942244	−	0.334928i	$-0.891288\pi$
$587$	−1005.60	+	177.314i	−1.71311	+	0.302068i	−0.770867	+	0.636996i	$0.780177\pi$
$588$		0			0
$589$	−601.664	+	218.988i	−1.02150	+	0.371796i
$590$	34.6046	+	6.10173i	0.0586519	+	0.0103419i
$591$		0			0
$592$	−735.189	+	616.897i	−1.24187	+	1.04206i
$593$			848.172i			1.43031i	0.698967	+	0.715153i	$0.253643\pi$
$593$			848.172i			1.43031i	−0.698967	+	0.715153i	$0.746357\pi$
$594$		0			0
$595$	402.349			0.676216
$596$	9.52606	+	11.3527i	0.0159833	+	0.0190482i
$597$		0			0
$598$	−71.9658	+	408.138i	−0.120344	+	0.682505i
$599$	108.727	+	298.725i	0.181514	+	0.498706i	0.996762	−	0.0804060i	$-0.0256217\pi$
$599$	108.727	+	298.725i	0.181514	+	0.498706i	−0.815248	+	0.579112i	$0.803399\pi$
$600$		0			0
$601$	−94.5670	−	536.316i	−0.157349	−	0.892372i	−0.956606	−	0.291383i	$-0.905885\pi$
$601$	−94.5670	−	536.316i	−0.157349	−	0.892372i	0.799257	−	0.600989i	$-0.205227\pi$
$602$	37.0311	−	21.3799i	0.0615134	−	0.0355148i
$603$		0			0
$604$	13.6014	−	23.5583i	0.0225189	−	0.0390039i
$605$	−98.4526	+	270.496i	−0.162732	+	0.447101i
$606$		0			0
$607$	326.292	+	273.792i	0.537549	+	0.451057i	0.870699	−	0.491817i	$-0.163667\pi$
$607$	326.292	+	273.792i	0.537549	+	0.451057i	−0.333150	+	0.942874i	$0.608111\pi$
$608$	−41.8266	+	49.8470i	−0.0687938	+	0.0819853i
$609$		0			0
$610$	−286.578	−	104.306i	−0.469800	−	0.170993i
$611$	655.192	+	378.275i	1.07233	+	0.619108i
$612$		0			0
$613$	−43.8571	−	75.9627i	−0.0715450	−	0.123920i	0.828034	−	0.560679i	$-0.189460\pi$
$613$	−43.8571	−	75.9627i	−0.0715450	−	0.123920i	−0.899579	+	0.436759i	$0.856126\pi$
$614$	699.710	−	123.378i	1.13959	−	0.200941i
$615$		0			0
$616$	506.348	−	184.295i	0.821993	−	0.299181i
$617$	−679.824	−	119.871i	−1.10182	−	0.194281i	−0.406975	−	0.913439i	$-0.633416\pi$
$617$	−679.824	−	119.871i	−1.10182	−	0.194281i	−0.694846	+	0.719159i	$0.744528\pi$
$618$		0			0
$619$	531.346	−	445.852i	0.858393	−	0.720278i	−0.103228	−	0.994658i	$-0.532917\pi$
$619$	531.346	−	445.852i	0.858393	−	0.720278i	0.961621	+	0.274380i	$0.0884727\pi$
$620$		−	37.7678i		−	0.0609158i
$621$		0			0
$622$	925.860			1.48852
$623$	−273.497	−	325.941i	−0.438999	−	0.523179i
$624$		0			0
$625$	−74.1857	+	420.728i	−0.118697	+	0.673165i
$626$	67.1313	+	184.442i	0.107239	+	0.294635i
$627$		0			0
$628$	2.14227	+	12.1494i	0.00341125	+	0.0193462i
$629$	580.142	−	334.945i	0.922324	−	0.532504i
$630$		0			0
$631$	−58.9015	+	102.020i	−0.0933463	+	0.161681i	−0.908917	−	0.416977i	$-0.863090\pi$
$631$	−58.9015	+	102.020i	−0.0933463	+	0.161681i	0.815571	+	0.578657i	$0.196423\pi$
$632$	−4.38381	+	12.0444i	−0.00693640	+	0.0190576i
$633$		0			0
$634$	550.695	+	462.088i	0.868604	+	0.728846i
$635$	−226.339	+	269.740i	−0.356439	+	0.424788i
$636$		0			0
$637$	457.254	+	166.427i	0.717825	+	0.261267i
$638$	518.510	+	299.362i	0.812711	+	0.469219i
$639$		0			0
$640$	249.699	+	432.491i	0.390155	+	0.675768i
$641$	−361.107	+	63.6729i	−0.563349	+	0.0993337i	−0.448068	−	0.893999i	$-0.647888\pi$
$641$	−361.107	+	63.6729i	−0.563349	+	0.0993337i	−0.115281	+	0.993333i	$0.536777\pi$
$642$		0			0
$643$	−902.678	+	328.548i	−1.40385	+	0.510961i	−0.929320	−	0.369276i	$-0.879606\pi$
$643$	−902.678	+	328.548i	−1.40385	+	0.510961i	−0.474534	+	0.880237i	$0.657383\pi$
$644$	−27.1973	−	4.79561i	−0.0422318	−	0.00744660i
$645$		0			0
$646$	−268.844	+	225.587i	−0.416167	+	0.349206i
$647$		−	181.832i		−	0.281039i	−0.990078	−	0.140519i	$-0.955123\pi$
$647$		−	181.832i		−	0.281039i	0.990078	−	0.140519i	$-0.0448772\pi$
$648$		0			0
$649$	−30.9049			−0.0476192
$650$	−127.666	−	152.146i	−0.196409	−	0.234071i
$651$		0			0
$652$	−10.2907	+	58.3612i	−0.0157832	+	0.0895111i
$653$	301.244	+	827.662i	0.461324	+	1.26748i	0.924491	+	0.381205i	$0.124491\pi$
$653$	301.244	+	827.662i	0.461324	+	1.26748i	−0.463167	+	0.886271i	$0.653287\pi$
$654$		0			0
$655$	109.177	+	619.171i	0.166682	+	0.945300i
$656$	330.638	−	190.894i	0.504021	−	0.290997i
$657$		0			0
$658$	402.509	−	697.167i	0.611717	−	1.05952i
$659$	21.8046	−	59.9077i	0.0330874	−	0.0909070i	−0.922049	−	0.387073i	$-0.873486\pi$
$659$	21.8046	−	59.9077i	0.0330874	−	0.0909070i	0.955136	+	0.296166i	$0.0957083\pi$
$660$		0			0
$661$	−351.302	−	294.777i	−0.531471	−	0.445957i	0.337138	−	0.941455i	$-0.390541\pi$
$661$	−351.302	−	294.777i	−0.531471	−	0.445957i	−0.868609	+	0.495498i	$0.834985\pi$
$662$	−444.792	+	530.083i	−0.671892	+	0.800730i
$663$		0			0
$664$	−873.200	−	317.819i	−1.31506	−	0.478643i
$665$	574.850	+	331.890i	0.864436	+	0.499082i
$666$		0			0
$667$	−275.681	−	477.493i	−0.413315	−	0.715882i
$668$	1.96517	−	0.346513i	0.00294187	−	0.000518732i
$669$		0			0
$670$	−136.407	+	49.6480i	−0.203592	+	0.0741015i
$671$	264.151	+	46.5770i	0.393668	+	0.0694142i
$672$		0			0
$673$	−840.742	+	705.467i	−1.24925	+	1.04824i	−0.252503	+	0.967596i	$0.581254\pi$
$673$	−840.742	+	705.467i	−1.24925	+	1.04824i	−0.996743	+	0.0806456i	$0.974302\pi$
$674$		−	778.465i		−	1.15499i
$675$		0			0
$676$	22.0924			0.0326811
$677$	−315.404	−	375.883i	−0.465884	−	0.555219i	0.481031	−	0.876704i	$-0.340263\pi$
$677$	−315.404	−	375.883i	−0.465884	−	0.555219i	−0.946915	+	0.321485i	$0.895818\pi$
$678$		0			0
$679$	−56.7545	+	321.871i	−0.0835854	+	0.474036i
$680$	−127.219	−	349.531i	−0.187087	−	0.514016i
$681$		0			0
$682$	−92.1056	−	522.357i	−0.135052	−	0.765919i
$683$	−684.465	+	395.176i	−1.00215	+	0.578589i	−0.908882	−	0.417053i	$-0.863063\pi$
$683$	−684.465	+	395.176i	−1.00215	+	0.578589i	−0.0932631	+	0.995642i	$0.529730\pi$
$684$		0			0
$685$	−406.316	+	703.760i	−0.593162	+	1.02739i
$686$	−111.952	+	307.585i	−0.163195	+	0.448375i
$687$		0			0
$688$	−28.4913	−	23.9070i	−0.0414118	−	0.0347486i
$689$	528.451	−	629.783i	0.766983	−	0.914054i
$690$		0			0
$691$	202.870	+	73.8387i	0.293589	+	0.106858i	0.484616	−	0.874727i	$-0.338959\pi$
$691$	202.870	+	73.8387i	0.293589	+	0.106858i	−0.191027	+	0.981585i	$0.561182\pi$
$692$	39.8221	+	22.9913i	0.0575464	+	0.0332244i
$693$		0			0
$694$	−55.5671	−	96.2451i	−0.0800679	−	0.138682i
$695$	374.014	−	65.9488i	0.538150	−	0.0948904i
$696$		0			0
$697$	−250.419	+	91.1449i	−0.359281	+	0.130767i
$698$	716.735	+	126.380i	1.02684	+	0.181060i
$699$		0			0
$700$	10.1386	−	8.50730i	0.0144837	−	0.0121533i
$701$			503.242i			0.717891i	0.933358	+	0.358946i	$0.116864\pi$
$701$			503.242i			0.717891i	−0.933358	+	0.358946i	$0.883136\pi$
$702$		0			0
$703$	1105.16			1.57206
$704$	−319.151	−	380.349i	−0.453339	−	0.540268i
$705$		0			0
$706$	−74.1294	+	420.409i	−0.104999	+	0.595480i
$707$	−259.336	−	712.520i	−0.366812	−	1.00781i
$708$		0			0
$709$	223.809	+	1269.28i	0.315668	+	1.79024i	0.568447	+	0.822720i	$0.307544\pi$
$709$	223.809	+	1269.28i	0.315668	+	1.79024i	−0.252779	+	0.967524i	$0.581345\pi$
$710$	−431.936	+	249.379i	−0.608361	+	0.351237i
$711$		0			0
$712$	−196.676	+	340.653i	−0.276230	+	0.478445i
$713$	−167.062	+	459.000i	−0.234309	+	0.643758i
$714$		0			0
$715$	−395.874	−	332.178i	−0.553671	−	0.464585i
$716$	−32.0554	+	38.2021i	−0.0447701	+	0.0533549i
$717$		0			0
$718$	367.203	+	133.651i	0.511424	+	0.186143i
$719$	−497.326	−	287.131i	−0.691691	−	0.399348i	0.112554	−	0.993646i	$-0.464097\pi$
$719$	−497.326	−	287.131i	−0.691691	−	0.399348i	−0.804245	+	0.594298i	$0.797430\pi$
$720$		0			0
$721$	−103.302	−	178.925i	−0.143277	−	0.248162i
$722$	119.572	−	21.0837i	0.165612	−	0.0292018i
$723$		0			0
$724$	−19.4440	+	7.07703i	−0.0268563	+	0.00977491i
$725$	260.219	+	45.8836i	0.358923	+	0.0632878i
$726$		0			0
$727$	427.936	−	359.081i	0.588633	−	0.493922i	−0.299136	−	0.954210i	$-0.596699\pi$
$727$	427.936	−	359.081i	0.588633	−	0.493922i	0.887769	+	0.460289i	$0.152254\pi$
$728$		−	1184.09i		−	1.62650i
$729$		0			0
$730$	−441.884			−0.605320
$731$	16.6872	+	19.8871i	0.0228279	+	0.0272053i
$732$		0			0
$733$	195.824	−	1110.57i	0.267155	−	1.51511i	−0.495674	−	0.868509i	$-0.665079\pi$
$733$	195.824	−	1110.57i	0.267155	−	1.51511i	0.762829	−	0.646601i	$-0.223810\pi$
$734$	−105.617	−	290.180i	−0.143892	−	0.395341i
$735$		0			0
$736$	8.62014	+	48.8872i	0.0117121	+	0.0664229i
$737$	110.567	−	63.8358i	0.150023	−	0.0866157i
$738$		0			0
$739$	−163.517	+	283.219i	−0.221268	+	0.383247i	−0.955193	−	0.295983i	$-0.904353\pi$
$739$	−163.517	+	283.219i	−0.221268	+	0.383247i	0.733926	+	0.679230i	$0.237686\pi$
$740$	−22.2962	+	61.2582i	−0.0301299	+	0.0827813i
$741$		0			0
$742$	−670.131	−	562.307i	−0.903141	−	0.757826i
$743$	−239.908	+	285.911i	−0.322891	+	0.384806i	−0.902934	−	0.429780i	$-0.858591\pi$
$743$	−239.908	+	285.911i	−0.322891	+	0.384806i	0.580043	+	0.814586i	$0.303036\pi$
$744$		0			0
$745$	−255.353	−	92.9408i	−0.342755	−	0.124753i
$746$	86.7808	+	50.1029i	0.116328	+	0.0671621i
$747$		0			0
$748$	9.10361	+	15.7679i	0.0121706	+	0.0210801i
$749$	838.337	−	147.821i	1.11928	−	0.197358i
$750$		0			0
$751$	1084.18	−	394.608i	1.44364	−	0.525443i	0.502835	−	0.864383i	$-0.332290\pi$
$751$	1084.18	−	394.608i	1.44364	−	0.525443i	0.940808	+	0.338940i	$0.110068\pi$
$752$	−689.572	−	121.590i	−0.916984	−	0.161689i
$753$		0			0
$754$	1007.86	−	845.698i	1.33669	−	1.12161i
$755$			498.796i			0.660657i
$756$		0			0
$757$	−372.849			−0.492535			−0.246268	−	0.969202i	$-0.579204\pi$
$757$	−372.849			−0.492535			−0.246268	+	0.969202i	$0.579204\pi$
$758$	183.614	+	218.823i	0.242235	+	0.288685i
$759$		0			0
$760$	106.559	−	604.328i	0.140210	−	0.795168i
$761$	395.241	+	1085.91i	0.519370	+	1.42696i	0.871216	+	0.490900i	$0.163332\pi$
$761$	395.241	+	1085.91i	0.519370	+	1.42696i	−0.351846	+	0.936058i	$0.614446\pi$
$762$		0			0
$763$	−157.697	−	894.345i	−0.206680	−	1.17214i
$764$	−65.5851	+	37.8656i	−0.0858444	+	0.0495623i
$765$		0			0
$766$	−110.333	+	191.102i	−0.144037	+	0.249480i
$767$	−23.2274	+	63.8167i	−0.0302834	+	0.0832030i
$768$		0			0
$769$	813.852	+	682.903i	1.05833	+	0.888041i	0.993944	−	0.109885i	$-0.0350482\pi$
$769$	813.852	+	682.903i	1.05833	+	0.888041i	0.0643812	+	0.997925i	$0.479493\pi$
$770$	−353.459	+	421.236i	−0.459038	+	0.547060i
$771$		0			0
$772$	−13.6684	−	4.97488i	−0.0177052	−	0.00644415i
$773$	−808.848	−	466.989i	−1.04638	−	0.604125i	−0.124743	−	0.992189i	$-0.539811\pi$
$773$	−808.848	−	466.989i	−1.04638	−	0.604125i	−0.921632	+	0.388064i	$0.873144\pi$
$774$		0			0
$775$	−117.044	−	202.725i	−0.151024	−	0.261581i
$776$	297.563	−	52.4683i	0.383457	−	0.0676138i
$777$		0			0
$778$	660.728	−	240.485i	0.849265	−	0.309107i
$779$	−432.966	−	76.3435i	−0.555797	−	0.0980020i
$780$		0			0
$781$	336.037	−	281.968i	0.430265	−	0.361035i
$782$			267.735i			0.342372i
$783$		0			0
$784$	−450.363			−0.574443
$785$	−145.405	−	173.287i	−0.185229	−	0.220748i
$786$		0			0
$787$	142.512	−	808.227i	0.181083	−	1.02697i	−0.749803	−	0.661661i	$-0.769852\pi$
$787$	142.512	−	808.227i	0.181083	−	1.02697i	0.930886	−	0.365310i	$-0.119037\pi$
$788$	−18.0776	−	49.6677i	−0.0229411	−	0.0630301i
$789$		0			0
$790$	−2.27132	−	12.8813i	−0.00287509	−	0.0163055i
$791$	125.562	−	72.4931i	0.158738	−	0.0916473i
$792$		0			0
$793$	294.708	−	510.450i	0.371637	−	0.643694i
$794$	−489.078	+	1343.73i	−0.615967	+	1.69236i
$795$		0			0
$796$	−0.940399	−	0.789088i	−0.00118141	−	0.000991317i
$797$	−22.0398	+	26.2660i	−0.0276534	+	0.0329561i	−0.779694	−	0.626161i	$-0.784625\pi$
$797$	−22.0398	+	26.2660i	−0.0276534	+	0.0329561i	0.752040	+	0.659117i	$0.229070\pi$
$798$		0			0
$799$	459.275	+	167.162i	0.574812	+	0.209215i
$800$	−20.6028	−	11.8950i	−0.0257535	−	0.0148688i
$801$		0			0
$802$	−214.682	−	371.840i	−0.267683	−	0.463641i
$803$	382.739	−	67.4873i	0.476637	−	0.0840439i
$804$		0			0
$805$	475.848	−	173.195i	0.591116	−	0.215148i
$806$	−1147.86	−	202.399i	−1.42414	−	0.251115i
$807$		0			0
$808$	−536.985	+	450.584i	−0.664585	+	0.557653i
$809$		−	521.511i		−	0.644636i	−0.946631	−	0.322318i	$-0.895538\pi$
$809$		−	521.511i		−	0.644636i	0.946631	−	0.322318i	$-0.104462\pi$
$810$		0			0
$811$	−684.645			−0.844199			−0.422099	−	0.906550i	$-0.638707\pi$
$811$	−684.645			−0.844199			−0.422099	+	0.906550i	$0.638707\pi$
$812$	56.3550	+	67.1613i	0.0694028	+	0.0827110i
$813$		0			0
$814$	−158.980	+	901.622i	−0.195307	+	1.10764i
$815$	−371.650	−	1021.10i	−0.456012	−	1.25288i
$816$		0			0
$817$	7.43718	+	42.1783i	0.00910303	+	0.0516259i
$818$	748.021	−	431.870i	0.914451	−	0.527958i
$819$		0			0
$820$	12.9666	−	22.4588i	0.0158129	−	0.0273887i
$821$	463.561	−	1273.62i	0.564630	−	1.55131i	−0.248140	−	0.968724i	$-0.579819\pi$
$821$	463.561	−	1273.62i	0.564630	−	1.55131i	0.812770	−	0.582585i	$-0.197959\pi$
$822$		0			0
$823$	−498.544	−	418.328i	−0.605765	−	0.508297i	0.287528	−	0.957772i	$-0.407167\pi$
$823$	−498.544	−	418.328i	−0.605765	−	0.508297i	−0.893293	+	0.449475i	$0.851611\pi$
$824$	−122.774	+	146.316i	−0.148997	+	0.177568i
$825$		0			0
$826$	67.9051	+	24.7154i	0.0822096	+	0.0299218i
$827$	−1042.15	−	601.688i	−1.26016	−	0.727555i	−0.287056	−	0.957914i	$-0.592677\pi$
$827$	−1042.15	−	601.688i	−1.26016	−	0.727555i	−0.973106	+	0.230359i	$0.926010\pi$
$828$		0			0
$829$	753.210	+	1304.60i	0.908577	+	1.57370i	0.816043	+	0.577992i	$0.196163\pi$
$829$	753.210	+	1304.60i	0.908577	+	1.57370i	0.0925344	+	0.995709i	$0.470503\pi$
$830$	933.875	−	164.667i	1.12515	−	0.198394i
$831$		0			0
$832$	−1025.26	+	373.165i	−1.23229	+	0.448516i
$833$	309.580	+	54.5873i	0.371645	+	0.0655310i
$834$		0			0
$835$	−28.0293	+	23.5194i	−0.0335680	+	0.0281669i
$836$			30.0376i			0.0359301i
$837$		0			0
$838$	−1119.86			−1.33635
$839$	−38.2178	−	45.5462i	−0.0455516	−	0.0542863i	0.742788	−	0.669527i	$-0.233503\pi$
$839$	−38.2178	−	45.5462i	−0.0455516	−	0.0542863i	−0.788339	+	0.615241i	$0.789059\pi$
$840$		0			0
$841$	−157.909	+	895.549i	−0.187764	+	1.06486i
$842$	222.961	+	612.579i	0.264799	+	0.727529i
$843$		0			0
$844$	−0.943711	−	5.35205i	−0.00111814	−	0.00634129i
$845$	−350.819	+	202.546i	−0.415171	+	0.239699i
$846$		0			0
$847$	−295.992	+	512.672i	−0.349459	+	0.605280i
$848$	−260.243	+	715.013i	−0.306891	+	0.843175i
$849$		0			0
$850$	−98.2901	−	82.4752i	−0.115635	−	0.0970297i
$851$	541.940	−	645.858i	0.636827	−	0.758941i
$852$		0			0
$853$	330.344	+	120.235i	0.387273	+	0.140956i	0.528316	−	0.849048i	$-0.322823\pi$
$853$	330.344	+	120.235i	0.387273	+	0.140956i	−0.141043	+	0.990003i	$0.545046\pi$
$854$	−543.152	−	313.589i	−0.636009	−	0.367200i
$855$		0			0
$856$	−393.491	−	681.546i	−0.459685	−	0.796198i
$857$	1219.40	−	215.013i	1.42287	−	0.250890i	0.591363	−	0.806405i	$-0.298590\pi$
$857$	1219.40	−	215.013i	1.42287	−	0.250890i	0.831507	+	0.555515i	$0.187479\pi$
$858$		0			0
$859$	249.859	−	90.9414i	0.290872	−	0.105869i	−0.192463	−	0.981304i	$-0.561647\pi$
$859$	249.859	−	90.9414i	0.290872	−	0.105869i	0.483335	+	0.875435i	$0.339425\pi$
$860$	−2.48796	−	0.438694i	−0.00289297	−	0.000510109i
$861$		0			0
$862$	169.134	−	141.921i	0.196211	−	0.164641i
$863$		−	297.514i		−	0.344744i	−0.985032	−	0.172372i	$-0.944857\pi$
$863$		−	297.514i		−	0.344744i	0.985032	−	0.172372i	$-0.0551431\pi$
$864$		0			0
$865$	−843.145			−0.974734
$866$	−254.678	−	303.514i	−0.294086	−	0.350478i
$867$		0			0
$868$	13.4873	−	76.4904i	0.0155384	−	0.0881225i
$869$	3.93463	+	10.8103i	0.00452777	+	0.0124400i
$870$		0			0
$871$	−48.7176	−	276.291i	−0.0559329	−	0.317211i
$872$	−727.078	+	419.779i	−0.833805	+	0.481398i
$873$		0			0
$874$	−220.849	+	382.522i	−0.252688	+	0.437669i
$875$	−411.552	+	1130.73i	−0.470345	+	1.29226i
$876$		0			0
$877$	−276.515	−	232.024i	−0.315296	−	0.264565i	0.471381	−	0.881930i	$-0.343756\pi$
$877$	−276.515	−	232.024i	−0.315296	−	0.264565i	−0.786677	+	0.617365i	$0.788200\pi$
$878$	−503.638	+	600.213i	−0.573620	+	0.683613i
$879$		0			0
$880$	449.448	+	163.586i	0.510737	+	0.185893i
$881$	782.766	+	451.930i	0.888497	+	0.512974i	0.873451	−	0.486913i	$-0.161877\pi$
$881$	782.766	+	451.930i	0.888497	+	0.512974i	0.0150464	+	0.999887i	$0.495210\pi$
$882$		0			0
$883$	462.202	+	800.558i	0.523445	+	0.906634i	0.999628	+	0.0272872i	$0.00868687\pi$
$883$	462.202	+	800.558i	0.523445	+	0.906634i	−0.476182	+	0.879347i	$0.657980\pi$
$884$	39.4019	−	6.94761i	0.0445722	−	0.00785929i
$885$		0			0
$886$	1206.24	−	439.036i	1.36144	−	0.495525i
$887$	−275.138	−	48.5142i	−0.310189	−	0.0546947i	0.0163867	−	0.999866i	$-0.494784\pi$
$887$	−275.138	−	48.5142i	−0.310189	−	0.0546947i	−0.326576	+	0.945171i	$0.605895\pi$
$888$		0			0
$889$	−554.727	+	465.471i	−0.623990	+	0.523590i
$890$		−	401.412i		−	0.451025i
$891$		0			0
$892$	−44.3400			−0.0497086
$893$	518.293	+	617.678i	0.580396	+	0.691689i
$894$		0			0
$895$	158.786	−	900.521i	0.177415	−	1.00617i
$896$	351.263	+	965.087i	0.392035	+	1.07711i
$897$		0			0
$898$	157.109	+	891.009i	0.174954	+	0.992215i
$899$	1342.92	−	775.333i	1.49379	−	0.862440i
$900$		0			0
$901$	265.556	−	459.957i	0.294735	−	0.510496i
$902$	124.567	−	342.244i	0.138100	−	0.379428i
$903$		0			0
$904$	−102.678	−	86.1571i	−0.113582	−	0.0953065i
$905$	243.880	−	290.645i	0.269480	−	0.321154i
$906$		0			0
$907$	555.388	+	202.145i	0.612335	+	0.222872i	0.629525	−	0.776981i	$-0.283250\pi$
$907$	555.388	+	202.145i	0.612335	+	0.222872i	−0.0171896	+	0.999852i	$0.505472\pi$
$908$	25.6206	+	14.7921i	0.0282166	+	0.0162908i
$909$		0			0
$910$	604.176	+	1046.46i	0.663930	+	1.14996i
$911$	372.493	−	65.6805i	0.408883	−	0.0720972i	0.0345765	−	0.999402i	$-0.488992\pi$
$911$	372.493	−	65.6805i	0.408883	−	0.0720972i	0.374307	+	0.927305i	$0.377881\pi$
$912$		0			0
$913$	−783.731	+	285.255i	−0.858413	+	0.312437i
$914$	1631.90	+	287.748i	1.78545	+	0.314823i
$915$		0			0
$916$	−23.6584	+	19.8517i	−0.0258279	+	0.0216722i
$917$			1292.98i			1.41002i
$918$		0			0
$919$	86.9159			0.0945766			0.0472883	−	0.998881i	$-0.484942\pi$
$919$	86.9159			0.0945766			0.0472883	+	0.998881i	$0.484942\pi$
$920$	−300.917	−	358.619i	−0.327084	−	0.389803i
$921$		0			0
$922$	−27.5966	+	156.508i	−0.0299313	+	0.169749i
$923$	−329.690	−	905.816i	−0.357194	−	0.981383i
$924$		0			0
$925$	70.1624	+	397.911i	0.0758513	+	0.430174i
$926$	−1099.91	+	635.033i	−1.18781	+	0.685781i
$927$		0			0
$928$	78.7963	−	136.479i	0.0849098	−	0.147068i
$929$	−231.271	+	635.412i	−0.248946	+	0.683975i	0.750779	+	0.660553i	$0.229678\pi$
$929$	−231.271	+	635.412i	−0.248946	+	0.683975i	−0.999726	+	0.0234215i	$0.992544\pi$
$930$		0			0
$931$	397.280	+	333.357i	0.426724	+	0.358064i
$932$	61.5914	−	73.4018i	0.0660852	−	0.0787573i
$933$		0			0
$934$	−238.712	−	86.8841i	−0.255580	−	0.0930236i
$935$	−289.124	−	166.926i	−0.309223	−	0.178530i
$936$		0			0
$937$	168.348	+	291.587i	0.179667	+	0.311192i	0.941766	−	0.336268i	$-0.109165\pi$
$937$	168.348	+	291.587i	0.179667	+	0.311192i	−0.762100	+	0.647460i	$0.775831\pi$
$938$	−293.992	+	51.8387i	−0.313424	+	0.0552651i
$939$		0			0
$940$	−44.6938	+	16.2672i	−0.0475466	+	0.0173055i
$941$	−232.277	−	40.9567i	−0.246841	−	0.0435247i	0.0488587	−	0.998806i	$-0.484442\pi$
$941$	−232.277	−	40.9567i	−0.246841	−	0.0435247i	−0.295699	+	0.955281i	$0.595553\pi$
$942$		0			0
$943$	−256.930	+	215.590i	−0.272460	+	0.228621i
$944$		−	62.8549i		−	0.0665836i
$945$		0			0
$946$	−35.4802			−0.0375055
$947$	−411.104	−	489.935i	−0.434112	−	0.517355i	0.503992	−	0.863708i	$-0.331864\pi$
$947$	−411.104	−	489.935i	−0.434112	−	0.517355i	−0.938104	+	0.346354i	$0.887420\pi$
$948$		0			0
$949$	148.301	−	841.055i	0.156271	−	0.886254i
$950$	−72.3984	−	198.913i	−0.0762088	−	0.209382i
$951$		0			0
$952$	−132.832	−	753.330i	−0.139530	−	0.791313i
$953$	742.976	−	428.957i	0.779618	−	0.450112i	−0.0566772	−	0.998393i	$-0.518051\pi$
$953$	742.976	−	428.957i	0.779618	−	0.450112i	0.836295	+	0.548280i	$0.184717\pi$
$954$		0			0
$955$	694.310	−	1202.58i	0.727027	−	1.25925i
$956$	15.5066	−	42.6041i	0.0162203	−	0.0445650i
$957$		0			0
$958$	234.334	+	196.629i	0.244607	+	0.205250i
$959$	−1074.22	+	1280.21i	−1.12015	+	1.33494i
$960$		0			0
$961$	−387.860	−	141.169i	−0.403600	−	0.146898i
$962$	1742.31	+	1005.92i	1.81113	+	1.04566i
$963$		0			0
$964$	40.8728	+	70.7938i	0.0423992	+	0.0734376i
$965$	262.659	−	46.3138i	0.272185	−	0.0479936i
$966$		0			0
$967$	−538.010	+	195.820i	−0.556371	+	0.202502i	−0.604875	−	0.796321i	$-0.706777\pi$
$967$	−538.010	+	195.820i	−0.556371	+	0.202502i	0.0485042	+	0.998823i	$0.484555\pi$
$968$	538.962	+	95.0335i	0.556779	+	0.0981751i
$969$		0			0
$970$	−236.205	+	198.200i	−0.243511	+	0.204330i
$971$		−	140.513i		−	0.144710i	−0.997379	−	0.0723548i	$-0.976949\pi$
$971$		−	140.513i		−	0.144710i	0.997379	−	0.0723548i	$-0.0230514\pi$
$972$		0			0
$973$	781.035			0.802708
$974$	−870.739	−	1037.71i	−0.893983	−	1.06541i
$975$		0			0
$976$	−94.7290	+	537.235i	−0.0970584	+	0.550446i
$977$	528.635	+	1452.41i	0.541079	+	1.48660i	0.845453	+	0.534050i	$0.179331\pi$
$977$	528.635	+	1452.41i	0.541079	+	1.48660i	−0.304373	+	0.952553i	$0.598447\pi$
$978$		0			0
$979$	61.3063	+	347.685i	0.0626213	+	0.355143i
$980$	−26.4927	+	15.2956i	−0.0270334	+	0.0156077i
$981$		0			0
$982$	40.9588	−	70.9427i	0.0417095	−	0.0722430i
$983$	−359.214	+	986.932i	−0.365426	+	1.00400i	0.611654	+	0.791126i	$0.290505\pi$
$983$	−359.214	+	986.932i	−0.365426	+	1.00400i	−0.977080	+	0.212874i	$0.931718\pi$
$984$		0			0
$985$	742.423	+	622.967i	0.753729	+	0.632454i
$986$	546.342	−	651.105i	0.554099	−	0.660350i
$987$		0			0
$988$	62.0258	+	22.5755i	0.0627791	+	0.0228497i
$989$	28.2961	+	16.3368i	0.0286109	+	0.0165185i
$990$		0			0
$991$	−255.730	−	442.938i	−0.258053	−	0.446961i	0.707667	−	0.706546i	$-0.249748\pi$
$991$	−255.730	−	442.938i	−0.258053	−	0.446961i	−0.965720	+	0.259585i	$0.916414\pi$
$992$	−137.492	+	24.2435i	−0.138601	+	0.0244390i
$993$		0			0
$994$	−963.848	+	350.812i	−0.969666	+	0.352930i
$995$	22.1676	+	3.90874i	0.0222790	+	0.00392839i
$996$		0			0
$997$	250.278	−	210.008i	0.251031	−	0.210640i	−0.508585	−	0.861012i	$-0.669831\pi$
$997$	250.278	−	210.008i	0.251031	−	0.210640i	0.759616	+	0.650371i	$0.225387\pi$
$998$		−	931.987i		−	0.933855i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.3.f.a.44.4		30
3.2	odd	2		27.3.f.a.5.2	✓	30
9.2	odd	6		243.3.f.d.53.2		30
9.4	even	3		243.3.f.b.215.2		30
9.5	odd	6		243.3.f.c.215.4		30
9.7	even	3		243.3.f.a.53.4		30
12.11	even	2		432.3.bc.a.113.1		30
27.2	odd	18		243.3.f.a.188.4		30
27.4	even	9		729.3.b.a.728.22		30
27.7	even	9		243.3.f.c.26.4		30
27.11	odd	18	inner	81.3.f.a.35.4		30
27.16	even	9		27.3.f.a.11.2	yes	30
27.20	odd	18		243.3.f.b.26.2		30
27.23	odd	18		729.3.b.a.728.9		30
27.25	even	9		243.3.f.d.188.2		30
108.43	odd	18		432.3.bc.a.65.1		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.5.2	✓	30	3.2	odd	2
27.3.f.a.11.2	yes	30	27.16	even	9
81.3.f.a.35.4		30	27.11	odd	18	inner
81.3.f.a.44.4		30	1.1	even	1	trivial
243.3.f.a.53.4		30	9.7	even	3
243.3.f.a.188.4		30	27.2	odd	18
243.3.f.b.26.2		30	27.20	odd	18
243.3.f.b.215.2		30	9.4	even	3
243.3.f.c.26.4		30	27.7	even	9
243.3.f.c.215.4		30	9.5	odd	6
243.3.f.d.53.2		30	9.2	odd	6
243.3.f.d.188.2		30	27.25	even	9
432.3.bc.a.65.1		30	108.43	odd	18
432.3.bc.a.113.1		30	12.11	even	2
729.3.b.a.728.9		30	27.23	odd	18
729.3.b.a.728.22		30	27.4	even	9

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.24712 + 1.48626i) q^{2} +(0.0409354 - 0.232156i) q^{4} +(1.47839 + 4.06185i) q^{5} +(1.54363 + 8.75434i) q^{7} +(7.11704 - 4.10903i) q^{8} +O(q^{10})\)	\(q+(1.24712 + 1.48626i) q^{2} +(0.0409354 - 0.232156i) q^{4} +(1.47839 + 4.06185i) q^{5} +(1.54363 + 8.75434i) q^{7} +(7.11704 - 4.10903i) q^{8} +(-4.19322 + 7.26288i) q^{10} +(2.52275 - 6.93119i) q^{11} +(-12.4164 - 10.4186i) q^{13} +(-11.0861 + 13.2119i) q^{14} +(14.0968 + 5.13081i) q^{16} +(-9.06825 - 5.23555i) q^{17} +(-8.63742 - 14.9604i) q^{19} +(1.00350 - 0.176945i) q^{20} +(13.4477 - 4.89456i) q^{22} +(-12.9785 - 2.28846i) q^{23} +(4.83813 - 4.05967i) q^{25} -31.4473i q^{26} +2.09556 q^{28} +(26.8925 + 32.0493i) q^{29} +(6.43612 - 36.5011i) q^{31} +(-1.28832 - 3.53963i) q^{32} +(-3.52779 - 20.0071i) q^{34} +(-33.2767 + 19.2123i) q^{35} +(-31.9875 + 55.4041i) q^{37} +(11.4632 - 31.4949i) q^{38} +(27.2120 + 22.8336i) q^{40} +(16.3590 - 19.4958i) q^{41} +(-2.32975 - 0.847961i) q^{43} +(-1.50585 - 0.869403i) q^{44} +(-12.7845 - 22.1433i) q^{46} +(-45.9670 + 8.10521i) q^{47} +(-28.2107 + 10.2679i) q^{49} +(12.0674 + 2.12781i) q^{50} +(-2.92703 + 2.45607i) q^{52} +50.7217i q^{53} +31.8831 q^{55} +(46.9579 + 55.9622i) q^{56} +(-14.0953 + 79.9384i) q^{58} +(-1.43303 - 3.93723i) q^{59} +(6.31465 + 35.8121i) q^{61} +(62.2766 - 35.9554i) q^{62} +(33.6571 - 58.2957i) q^{64} +(23.9626 - 65.8366i) q^{65} +(13.2595 + 11.1260i) q^{67} +(-1.58668 + 1.89093i) q^{68} +(-70.0545 - 25.4977i) q^{70} +(51.5041 + 29.7359i) q^{71} +(26.3451 + 45.6310i) q^{73} +(-122.237 + 21.5537i) q^{74} +(-3.82674 + 1.39282i) q^{76} +(64.5722 + 11.3858i) q^{77} +(-1.19477 + 1.00253i) q^{79} +64.8443i q^{80} +49.3774 q^{82} +(-72.6820 - 86.6190i) q^{83} +(7.85961 - 44.5741i) q^{85} +(-1.64519 - 4.52012i) q^{86} +(-10.5259 - 59.6956i) q^{88} +(-41.4518 + 23.9322i) q^{89} +(72.0419 - 124.780i) q^{91} +(-1.06256 + 2.91936i) q^{92} +(-69.3726 - 58.2105i) q^{94} +(47.9976 - 57.2013i) q^{95} +(34.5497 + 12.5750i) q^{97} +(-50.4428 - 29.1232i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{2} - 6 q^{4} + 15 q^{5} - 6 q^{7} + 9 q^{8}+O(q^{10}) \) 30 * q + 6 * q^2 - 6 * q^4 + 15 * q^5 - 6 * q^7 + 9 * q^8	\( 30 q + 6 q^{2} - 6 q^{4} + 15 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 6 q^{11} - 6 q^{13} + 15 q^{14} - 18 q^{16} + 9 q^{17} - 3 q^{19} - 213 q^{20} - 42 q^{22} - 120 q^{23} - 15 q^{25} - 12 q^{28} + 168 q^{29} + 39 q^{31} + 360 q^{32} + 54 q^{34} + 252 q^{35} - 3 q^{37} + 84 q^{38} - 33 q^{40} - 228 q^{41} - 96 q^{43} - 639 q^{44} - 3 q^{46} - 399 q^{47} - 78 q^{49} - 303 q^{50} - 9 q^{52} - 12 q^{55} + 393 q^{56} + 129 q^{58} + 474 q^{59} + 138 q^{61} + 900 q^{62} - 51 q^{64} + 411 q^{65} + 354 q^{67} - 99 q^{68} + 489 q^{70} - 315 q^{71} - 66 q^{73} - 321 q^{74} + 258 q^{76} - 201 q^{77} + 30 q^{79} - 12 q^{82} + 33 q^{83} - 261 q^{85} + 258 q^{86} - 642 q^{88} - 72 q^{89} + 96 q^{91} + 3 q^{92} - 861 q^{94} - 681 q^{95} - 582 q^{97} - 882 q^{98}+O(q^{100}) \) 30 * q + 6 * q^2 - 6 * q^4 + 15 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 6 * q^11 - 6 * q^13 + 15 * q^14 - 18 * q^16 + 9 * q^17 - 3 * q^19 - 213 * q^20 - 42 * q^22 - 120 * q^23 - 15 * q^25 - 12 * q^28 + 168 * q^29 + 39 * q^31 + 360 * q^32 + 54 * q^34 + 252 * q^35 - 3 * q^37 + 84 * q^38 - 33 * q^40 - 228 * q^41 - 96 * q^43 - 639 * q^44 - 3 * q^46 - 399 * q^47 - 78 * q^49 - 303 * q^50 - 9 * q^52 - 12 * q^55 + 393 * q^56 + 129 * q^58 + 474 * q^59 + 138 * q^61 + 900 * q^62 - 51 * q^64 + 411 * q^65 + 354 * q^67 - 99 * q^68 + 489 * q^70 - 315 * q^71 - 66 * q^73 - 321 * q^74 + 258 * q^76 - 201 * q^77 + 30 * q^79 - 12 * q^82 + 33 * q^83 - 261 * q^85 + 258 * q^86 - 642 * q^88 - 72 * q^89 + 96 * q^91 + 3 * q^92 - 861 * q^94 - 681 * q^95 - 582 * q^97 - 882 * q^98

Introduction

L-functions

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