LMFDB - Embedded newform 126.5.n.b.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,5,Mod(19,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("126.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	126.n (of order $6$, degree $2$, 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:	$13.0246153486$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	126.73
Dual form			126.5.n.b.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41421 + 2.44949i) q^{2} +(-4.00000 + 6.92820i) q^{4} +(12.2574 - 7.07679i) q^{5} +(12.1985 + 47.4573i) q^{7} -22.6274 q^{8} +(34.6690 + 20.0162i) q^{10} +(32.0147 - 55.4511i) q^{11} +228.919i q^{13} +(-98.9949 + 96.9948i) q^{14} +(-32.0000 - 55.4256i) q^{16} +(195.250 + 112.728i) q^{17} +(-255.250 + 147.369i) q^{19} +113.229i q^{20} +181.103 q^{22} +(354.749 + 614.444i) q^{23} +(-212.338 + 367.780i) q^{25} +(-560.735 + 323.741i) q^{26} +(-377.588 - 105.316i) q^{28} -740.397 q^{29} +(-577.390 - 333.356i) q^{31} +(90.5097 - 156.767i) q^{32} +637.683i q^{34} +(485.367 + 495.375i) q^{35} +(416.882 + 722.061i) q^{37} +(-721.955 - 416.821i) q^{38} +(-277.352 + 160.129i) q^{40} -2817.60i q^{41} +3066.41 q^{43} +(256.118 + 443.609i) q^{44} +(-1003.38 + 1737.91i) q^{46} +(531.502 - 306.863i) q^{47} +(-2103.39 + 1157.81i) q^{49} -1201.17 q^{50} +(-1586.00 - 915.677i) q^{52} +(-576.300 + 998.181i) q^{53} -906.246i q^{55} +(-276.020 - 1073.84i) q^{56} +(-1047.08 - 1813.59i) q^{58} +(3024.67 + 1746.30i) q^{59} +(1967.79 - 1136.11i) q^{61} -1885.75i q^{62} +512.000 q^{64} +(1620.01 + 2805.94i) q^{65} +(4337.31 - 7512.44i) q^{67} +(-1562.00 + 901.820i) q^{68} +(-527.005 + 1889.47i) q^{70} +353.591 q^{71} +(3524.68 + 2034.97i) q^{73} +(-1179.12 + 2042.30i) q^{74} -2357.90i q^{76} +(3022.09 + 842.913i) q^{77} +(-3236.41 - 5605.63i) q^{79} +(-784.471 - 452.915i) q^{80} +(6901.69 - 3984.69i) q^{82} -8225.83i q^{83} +3191.00 q^{85} +(4336.55 + 7511.13i) q^{86} +(-724.410 + 1254.72i) q^{88} +(13456.5 - 7769.13i) q^{89} +(-10863.9 + 2792.47i) q^{91} -5675.99 q^{92} +(1503.32 + 867.939i) q^{94} +(-2085.79 + 3612.70i) q^{95} -1558.61i q^{97} +(-5810.70 - 3514.84i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{4} + 66 q^{5} - 70 q^{7} - 48 q^{10} + 162 q^{11} - 128 q^{16} + 204 q^{17} - 444 q^{19} - 192 q^{22} - 312 q^{23} - 476 q^{25} - 1632 q^{26} - 560 q^{28} - 2724 q^{29} - 3786 q^{31} - 672 q^{35}+ \cdots - 23520 q^{98}+O(q^{100}) $ 4 * q - 16 * q^4 + 66 * q^5 - 70 * q^7 - 48 * q^10 + 162 * q^11 - 128 * q^16 + 204 * q^17 - 444 * q^19 - 192 * q^22 - 312 * q^23 - 476 * q^25 - 1632 * q^26 - 560 * q^28 - 2724 * q^29 - 3786 * q^31 - 672 * q^35 + 1396 * q^37 - 1632 * q^38 + 384 * q^40 - 632 * q^43 + 1296 * q^44 - 4896 * q^46 + 7896 * q^47 - 98 * q^49 - 2112 * q^50 - 1728 * q^52 + 1038 * q^53 - 2688 * q^56 - 336 * q^58 + 966 * q^59 + 5088 * q^61 + 2048 * q^64 + 744 * q^65 + 14600 * q^67 - 1632 * q^68 + 5376 * q^70 + 9696 * q^71 + 22584 * q^73 - 768 * q^74 + 3654 * q^77 + 3974 * q^79 - 4224 * q^80 + 18816 * q^82 + 1224 * q^85 + 18240 * q^86 + 768 * q^88 + 33156 * q^89 - 18984 * q^91 + 4992 * q^92 - 16320 * q^94 - 3252 * q^95 - 23520 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.41421	+	2.44949i	0.353553	+	0.612372i
$2$	1.41421	+	2.44949i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−4.00000	+	6.92820i	−0.250000	+	0.433013i
$5$	12.2574	−	7.07679i	0.490294	−	0.283072i	−0.234402	−	0.972140i	$-0.575313\pi$
$5$	12.2574	−	7.07679i	0.490294	−	0.283072i	0.724697	+	0.689068i	$0.241980\pi$
$6$		0			0
$7$	12.1985	+	47.4573i	0.248949	+	0.968517i
$7$	12.1985	+	47.4573i	0.248949	+	0.968517i
$8$	−22.6274			−0.353553
$9$		0			0
$10$	34.6690	+	20.0162i	0.346690	+	0.200162i
$11$	32.0147	−	55.4511i	0.264584	−	0.458274i	−0.702870	−	0.711318i	$-0.748099\pi$
$11$	32.0147	−	55.4511i	0.264584	−	0.458274i	0.967455	+	0.253044i	$0.0814319\pi$
$12$		0			0
$13$			228.919i			1.35455i	0.735729	+	0.677276i	$0.236839\pi$
$13$			228.919i			1.35455i	−0.735729	+	0.677276i	$0.763161\pi$
$14$	−98.9949	+	96.9948i	−0.505076	+	0.494872i
$15$		0			0
$16$	−32.0000	−	55.4256i	−0.125000	−	0.216506i
$17$	195.250	+	112.728i	0.675605	+	0.390061i	0.798197	−	0.602397i	$-0.205787\pi$
$17$	195.250	+	112.728i	0.675605	+	0.390061i	−0.122592	+	0.992457i	$0.539121\pi$
$18$		0			0
$19$	−255.250	+	147.369i	−0.707063	+	0.408223i	−0.809973	−	0.586468i	$-0.800518\pi$
$19$	−255.250	+	147.369i	−0.707063	+	0.408223i	0.102910	+	0.994691i	$0.467185\pi$
$20$			113.229i			0.283072i
$21$		0			0
$22$	181.103			0.374179
$23$	354.749	+	614.444i	0.670604	+	1.16152i	0.977733	+	0.209852i	$0.0672982\pi$
$23$	354.749	+	614.444i	0.670604	+	1.16152i	−0.307129	+	0.951668i	$0.599368\pi$
$24$		0			0
$25$	−212.338	+	367.780i	−0.339741	+	0.588449i
$26$	−560.735	+	323.741i	−0.829490	+	0.478906i
$27$		0			0
$28$	−377.588	−	105.316i	−0.481617	−	0.134331i
$29$	−740.397			−0.880377			−0.440188	−	0.897905i	$-0.645088\pi$
$29$	−740.397			−0.880377			−0.440188	+	0.897905i	$0.645088\pi$
$30$		0			0
$31$	−577.390	−	333.356i	−0.600822	−	0.346885i	0.168543	−	0.985694i	$-0.446094\pi$
$31$	−577.390	−	333.356i	−0.600822	−	0.346885i	−0.769365	+	0.638809i	$0.779427\pi$
$32$	90.5097	−	156.767i	0.0883883	−	0.153093i
$33$		0			0
$34$			637.683i			0.551629i
$35$	485.367	+	495.375i	0.396218	+	0.404388i
$36$		0			0
$37$	416.882	+	722.061i	0.304516	+	0.527437i	0.977153	−	0.212535i	$-0.0681720\pi$
$37$	416.882	+	722.061i	0.304516	+	0.527437i	−0.672638	+	0.739972i	$0.734839\pi$
$38$	−721.955	−	416.821i	−0.499969	−	0.288657i
$39$		0			0
$40$	−277.352	+	160.129i	−0.173345	+	0.100081i
$41$		−	2817.60i		−	1.67615i	−0.545558	−	0.838073i	$-0.683682\pi$
$41$		−	2817.60i		−	1.67615i	0.545558	−	0.838073i	$-0.316318\pi$
$42$		0			0
$43$	3066.41			1.65841			0.829207	−	0.558942i	$-0.188793\pi$
$43$	3066.41			1.65841			0.829207	+	0.558942i	$0.188793\pi$
$44$	256.118	+	443.609i	0.132292	+	0.229137i
$45$		0			0
$46$	−1003.38	+	1737.91i	−0.474188	+	0.821318i
$47$	531.502	−	306.863i	0.240608	−	0.138915i	−0.374848	−	0.927086i	$-0.622305\pi$
$47$	531.502	−	306.863i	0.240608	−	0.138915i	0.615456	+	0.788171i	$0.288972\pi$
$48$		0			0
$49$	−2103.39	+	1157.81i	−0.876049	+	0.482222i
$50$	−1201.17			−0.480466
$51$		0			0
$52$	−1586.00	−	915.677i	−0.586538	−	0.338638i
$53$	−576.300	+	998.181i	−0.205162	+	0.355351i	−0.950184	−	0.311688i	$-0.899105\pi$
$53$	−576.300	+	998.181i	−0.205162	+	0.355351i	0.745022	+	0.667040i	$0.232439\pi$
$54$		0			0
$55$		−	906.246i		−	0.299585i
$56$	−276.020	−	1073.84i	−0.0880166	−	0.342422i
$57$		0			0
$58$	−1047.08	−	1813.59i	−0.311260	−	0.539119i
$59$	3024.67	+	1746.30i	0.868909	+	0.501665i	0.866986	−	0.498333i	$-0.166054\pi$
$59$	3024.67	+	1746.30i	0.868909	+	0.501665i	0.00192348	+	0.999998i	$0.499388\pi$
$60$		0			0
$61$	1967.79	−	1136.11i	0.528834	−	0.305323i	−0.211707	−	0.977333i	$-0.567902\pi$
$61$	1967.79	−	1136.11i	0.528834	−	0.305323i	0.740542	+	0.672010i	$0.234569\pi$
$62$		−	1885.75i		−	0.490569i
$63$		0			0
$64$	512.000			0.125000
$65$	1620.01	+	2805.94i	0.383435	+	0.664129i
$66$		0			0
$67$	4337.31	−	7512.44i	0.966208	−	1.67352i	0.259874	−	0.965642i	$-0.416319\pi$
$67$	4337.31	−	7512.44i	0.966208	−	1.67352i	0.706334	−	0.707879i	$-0.250348\pi$
$68$	−1562.00	+	901.820i	−0.337802	+	0.195030i
$69$		0			0
$70$	−527.005	+	1889.47i	−0.107552	+	0.385606i
$71$	353.591			0.0701431			0.0350715	−	0.999385i	$-0.488834\pi$
$71$	353.591			0.0701431			0.0350715	+	0.999385i	$0.488834\pi$
$72$		0			0
$73$	3524.68	+	2034.97i	0.661415	+	0.381868i	0.792816	−	0.609461i	$-0.208614\pi$
$73$	3524.68	+	2034.97i	0.661415	+	0.381868i	−0.131401	+	0.991329i	$0.541948\pi$
$74$	−1179.12	+	2042.30i	−0.215325	+	0.372954i
$75$		0			0
$76$		−	2357.90i		−	0.408223i
$77$	3022.09	+	842.913i	0.509714	+	0.142168i
$78$		0			0
$79$	−3236.41	−	5605.63i	−0.518573	−	0.898194i	−0.999767	−	0.0215805i	$-0.993130\pi$
$79$	−3236.41	−	5605.63i	−0.518573	−	0.898194i	0.481194	−	0.876614i	$-0.340203\pi$
$80$	−784.471	−	452.915i	−0.122574	−	0.0707679i
$81$		0			0
$82$	6901.69	−	3984.69i	1.02643	−	0.592607i
$83$		−	8225.83i		−	1.19405i	−0.802222	−	0.597026i	$-0.796349\pi$
$83$		−	8225.83i		−	1.19405i	0.802222	−	0.597026i	$-0.203651\pi$
$84$		0			0
$85$	3191.00			0.441660
$86$	4336.55	+	7511.13i	0.586338	+	1.01557i
$87$		0			0
$88$	−724.410	+	1254.72i	−0.0935447	+	0.162024i
$89$	13456.5	−	7769.13i	1.69884	−	0.980828i	0.751983	−	0.659183i	$-0.229098\pi$
$89$	13456.5	−	7769.13i	1.69884	−	0.980828i	0.946860	−	0.321645i	$-0.104236\pi$
$90$		0			0
$91$	−10863.9	+	2792.47i	−1.31191	+	0.337214i
$92$	−5675.99			−0.670604
$93$		0			0
$94$	1503.32	+	867.939i	0.170135	+	0.0982276i
$95$	−2085.79	+	3612.70i	−0.231113	+	0.400299i
$96$		0			0
$97$		−	1558.61i		−	0.165651i	−0.996564	−	0.0828254i	$-0.973606\pi$
$97$		−	1558.61i		−	0.165651i	0.996564	−	0.0828254i	$-0.0263944\pi$
$98$	−5810.70	−	3514.84i	−0.605030	−	0.365977i
$99$		0			0
$100$	−1698.70	−	2942.24i	−0.169870	−	0.294224i
$101$	−13627.2	−	7867.66i	−1.33587	−	0.771264i	−0.349676	−	0.936871i	$-0.613708\pi$
$101$	−13627.2	−	7867.66i	−1.33587	−	0.771264i	−0.986192	+	0.165607i	$0.947042\pi$
$102$		0			0
$103$	29.2099	−	16.8644i	0.00275332	−	0.00158963i	−0.498623	−	0.866819i	$-0.666161\pi$
$103$	29.2099	−	16.8644i	0.00275332	−	0.00158963i	0.501376	+	0.865229i	$0.332827\pi$
$104$		−	5179.85i		−	0.478906i
$105$		0			0
$106$	−3260.05			−0.290143
$107$	−2723.23	−	4716.78i	−0.237858	−	0.411981i	0.722242	−	0.691641i	$-0.243112\pi$
$107$	−2723.23	−	4716.78i	−0.237858	−	0.411981i	−0.960099	+	0.279659i	$0.909778\pi$
$108$		0			0
$109$	−8348.89	+	14460.7i	−0.702709	+	1.21713i	0.264803	+	0.964303i	$0.414693\pi$
$109$	−8348.89	+	14460.7i	−0.702709	+	1.21713i	−0.967512	+	0.252825i	$0.918640\pi$
$110$	2219.84	−	1281.62i	0.183458	−	0.105919i
$111$		0			0
$112$	2240.00	−	2194.74i	0.178571	−	0.174964i
$113$	−9455.64			−0.740515			−0.370258	−	0.928929i	$-0.620731\pi$
$113$	−9455.64			−0.740515			−0.370258	+	0.928929i	$0.620731\pi$
$114$		0			0
$115$	8696.58	+	5020.97i	0.657586	+	0.379658i
$116$	2961.59	−	5129.62i	0.220094	−	0.381214i
$117$		0			0
$118$			9878.54i			0.709461i
$119$	−2967.99	+	10641.1i	−0.209589	+	0.751440i
$120$		0			0
$121$	5270.62	+	9128.97i	0.359990	+	0.623521i
$122$	5565.76	+	3213.39i	0.373942	+	0.215896i
$123$		0			0
$124$	4619.12	−	2666.85i	0.300411	−	0.173442i
$125$			14856.7i			0.950827i
$126$		0			0
$127$	−2380.07			−0.147564			−0.0737822	−	0.997274i	$-0.523507\pi$
$127$	−2380.07			−0.147564			−0.0737822	+	0.997274i	$0.523507\pi$
$128$	724.077	+	1254.14i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−4582.09	+	7936.41i	−0.271129	+	0.469610i
$131$	3758.37	−	2169.90i	0.219006	−	0.126443i	−0.386484	−	0.922296i	$-0.626310\pi$
$131$	3758.37	−	2169.90i	0.219006	−	0.126443i	0.605490	+	0.795853i	$0.292977\pi$
$132$		0			0
$133$	−10107.4	−	10315.8i	−0.571393	−	0.583176i
$134$	24535.5			1.36642
$135$		0			0
$136$	−4418.00	−	2550.73i	−0.238862	−	0.137907i
$137$	−15379.6	+	26638.2i	−0.819414	+	1.41927i	0.0867001	+	0.996234i	$0.472368\pi$
$137$	−15379.6	+	26638.2i	−0.819414	+	1.41927i	−0.906114	+	0.423033i	$0.860966\pi$
$138$		0			0
$139$		−	27186.6i		−	1.40710i	−0.710644	−	0.703551i	$-0.751596\pi$
$139$		−	27186.6i		−	1.40710i	0.710644	−	0.703551i	$-0.248404\pi$
$140$	−5373.53	+	1381.22i	−0.274160	+	0.0704703i
$141$		0			0
$142$	500.054	+	866.118i	0.0247993	+	0.0429537i
$143$	12693.8	+	7328.78i	0.620755	+	0.358393i
$144$		0			0
$145$	−9075.31	+	5239.63i	−0.431644	+	0.249210i
$146$			11511.6i			0.540043i
$147$		0			0
$148$	−6670.12			−0.304516
$149$	−2913.46	−	5046.26i	−0.131231	−	0.227299i	0.792920	−	0.609325i	$-0.208560\pi$
$149$	−2913.46	−	5046.26i	−0.131231	−	0.227299i	−0.924151	+	0.382027i	$0.875226\pi$
$150$		0			0
$151$	−12593.4	+	21812.4i	−0.552317	+	0.956642i	0.445789	+	0.895138i	$0.352923\pi$
$151$	−12593.4	+	21812.4i	−0.552317	+	0.956642i	−0.998107	+	0.0615039i	$0.980410\pi$
$152$	5775.64	−	3334.57i	0.249985	−	0.144329i
$153$		0			0
$154$	2209.18	+	8594.64i	0.0931513	+	0.362399i
$155$	−9436.37			−0.392773
$156$		0			0
$157$	20694.6	+	11948.0i	0.839571	+	0.484726i	0.857118	−	0.515120i	$-0.172253\pi$
$157$	20694.6	+	11948.0i	0.839571	+	0.484726i	−0.0175475	+	0.999846i	$0.505586\pi$
$158$	9153.96	−	15855.1i	0.366686	−	0.635119i
$159$		0			0
$160$		−	2562.07i		−	0.100081i
$161$	−24832.5	+	24330.7i	−0.958005	+	0.938650i
$162$		0			0
$163$	21293.0	+	36880.5i	0.801422	+	1.38810i	0.918680	+	0.395001i	$0.129256\pi$
$163$	21293.0	+	36880.5i	0.801422	+	1.38810i	−0.117259	+	0.993101i	$0.537411\pi$
$164$	19520.9	+	11270.4i	0.725793	+	0.419037i
$165$		0			0
$166$	20149.1	−	11633.1i	0.731205	−	0.422161i
$167$		−	26356.3i		−	0.945043i	−0.881319	−	0.472521i	$-0.843344\pi$
$167$		−	26356.3i		−	0.945043i	0.881319	−	0.472521i	$-0.156656\pi$
$168$		0			0
$169$	−23843.0			−0.834809
$170$	4512.75	+	7816.31i	0.156150	+	0.270461i
$171$		0			0
$172$	−12265.6	+	21244.7i	−0.414603	+	0.718114i
$173$	−24265.3	+	14009.6i	−0.810763	+	0.468094i	−0.847221	−	0.531241i	$-0.821726\pi$
$173$	−24265.3	+	14009.6i	−0.810763	+	0.468094i	0.0364578	+	0.999335i	$0.488393\pi$
$174$		0			0
$175$	−20044.1	−	5590.63i	−0.654500	−	0.182551i
$176$	−4097.88			−0.132292
$177$		0			0
$178$	38060.8	+	21974.4i	1.20126	+	0.693550i
$179$	12699.2	−	21995.7i	0.396343	−	0.686487i	−0.596928	−	0.802295i	$-0.703612\pi$
$179$	12699.2	−	21995.7i	0.396343	−	0.686487i	0.993272	+	0.115808i	$0.0369457\pi$
$180$		0			0
$181$		−	44097.2i		−	1.34603i	−0.739630	−	0.673014i	$-0.764999\pi$
$181$		−	44097.2i		−	1.34603i	0.739630	−	0.673014i	$-0.235001\pi$
$182$	−22204.0	−	22661.8i	−0.670329	−	0.684152i
$183$		0			0
$184$	−8027.06	−	13903.3i	−0.237094	−	0.410659i
$185$	10219.8	+	5900.38i	0.298605	+	0.172400i
$186$		0			0
$187$	12501.7	−	7217.88i	0.357509	−	0.206408i
$188$			4909.81i			0.138915i
$189$		0			0
$190$	−11799.0			−0.326843
$191$	−32279.6	−	55909.8i	−0.884832	−	1.53257i	−0.845906	−	0.533332i	$-0.820940\pi$
$191$	−32279.6	−	55909.8i	−0.884832	−	1.53257i	−0.0389256	−	0.999242i	$-0.512394\pi$
$192$		0			0
$193$	−18337.3	+	31761.1i	−0.492290	+	0.852670i	−0.999961	−	0.00888055i	$-0.997173\pi$
$193$	−18337.3	+	31761.1i	−0.492290	+	0.852670i	0.507671	+	0.861551i	$0.330507\pi$
$194$	3817.80	−	2204.20i	0.101440	−	0.0585664i
$195$		0			0
$196$	392.000	−	19204.0i	0.0102041	−	0.499896i
$197$	73147.0			1.88480			0.942398	−	0.334494i	$-0.108566\pi$
$197$	73147.0			1.88480			0.942398	+	0.334494i	$0.108566\pi$
$198$		0			0
$199$	−1213.33	−	700.514i	−0.0306387	−	0.0176893i	0.484602	−	0.874735i	$-0.338964\pi$
$199$	−1213.33	−	700.514i	−0.0306387	−	0.0176893i	−0.515241	+	0.857045i	$0.672298\pi$
$200$	4804.66	−	8321.92i	0.120117	−	0.208048i
$201$		0			0
$202$		−	44506.2i		−	1.09073i
$203$	−9031.72	−	35137.3i	−0.219169	−	0.852660i
$204$		0			0
$205$	−19939.6	−	34536.4i	−0.474469	−	0.821805i
$206$	82.6182	+	47.6996i	0.00194689	+	0.00112404i
$207$		0			0
$208$	12688.0	−	7325.41i	0.293269	−	0.169319i
$209$			18871.8i			0.432038i
$210$		0			0
$211$	58231.7			1.30796			0.653980	−	0.756512i	$-0.273098\pi$
$211$	58231.7			1.30796			0.653980	+	0.756512i	$0.273098\pi$
$212$	−4610.40	−	7985.45i	−0.102581	−	0.177676i
$213$		0			0
$214$	7702.46	−	13341.1i	0.168191	−	0.291315i
$215$	37586.1	−	21700.3i	0.813111	−	0.469450i
$216$		0			0
$217$	8776.92	−	31467.8i	0.186390	−	0.668263i
$218$	−47228.4			−0.993781
$219$		0			0
$220$	6278.65	+	3624.98i	0.129724	+	0.0748963i
$221$	−25805.5	+	44696.4i	−0.528357	+	0.915141i
$222$		0			0
$223$		−	61050.9i		−	1.22767i	−0.789434	−	0.613836i	$-0.789626\pi$
$223$		−	61050.9i		−	1.22767i	0.789434	−	0.613836i	$-0.210374\pi$
$224$	8543.84	+	2383.02i	0.170277	+	0.0474933i
$225$		0			0
$226$	−13372.3	−	23161.5i	−0.261812	−	0.453471i
$227$	−21645.2	−	12496.8i	−0.420058	−	0.242520i	0.275044	−	0.961432i	$-0.411307\pi$
$227$	−21645.2	−	12496.8i	−0.420058	−	0.242520i	−0.695102	+	0.718911i	$0.744641\pi$
$228$		0			0
$229$	−16392.9	+	9464.44i	−0.312597	+	0.180478i	−0.648088	−	0.761565i	$-0.724431\pi$
$229$	−16392.9	+	9464.44i	−0.312597	+	0.180478i	0.335491	+	0.942043i	$0.391098\pi$
$230$			28402.9i			0.536917i
$231$		0			0
$232$	16753.3			0.311260
$233$	3342.37	+	5789.15i	0.0615662	+	0.106636i	0.895166	−	0.445734i	$-0.147057\pi$
$233$	3342.37	+	5789.15i	0.0615662	+	0.106636i	−0.833599	+	0.552369i	$0.813724\pi$
$234$		0			0
$235$	4343.21	−	7522.66i	0.0786457	−	0.136218i
$236$	−24197.4	+	13970.4i	−0.434455	+	0.250832i
$237$		0			0
$238$	−30262.7	+	7778.77i	−0.534262	+	0.137327i
$239$	96461.0			1.68871			0.844356	−	0.535782i	$-0.179983\pi$
$239$	96461.0			1.68871			0.844356	+	0.535782i	$0.179983\pi$
$240$		0			0
$241$	47371.8	+	27350.1i	0.815616	+	0.470896i	0.848902	−	0.528550i	$-0.177264\pi$
$241$	47371.8	+	27350.1i	0.815616	+	0.470896i	−0.0332863	+	0.999446i	$0.510597\pi$
$242$	−14907.6	+	25820.6i	−0.254551	+	0.440896i
$243$		0			0
$244$			18177.7i			0.305323i
$245$	−17588.4	+	29077.0i	−0.293019	+	0.484415i
$246$		0			0
$247$	−33735.5	−	58431.6i	−0.552959	−	0.957753i
$248$	13064.9	+	7542.99i	0.212423	+	0.122642i
$249$		0			0
$250$	−36391.3	+	21010.5i	−0.582260	+	0.336168i
$251$		−	108137.i		−	1.71643i	−0.513286	−	0.858217i	$-0.671572\pi$
$251$		−	108137.i		−	1.71643i	0.513286	−	0.858217i	$-0.328428\pi$
$252$		0			0
$253$	45428.8			0.709725
$254$	−3365.92	−	5829.95i	−0.0521719	−	0.0903643i
$255$		0			0
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	−31078.3	+	17943.0i	−0.470533	+	0.271663i	−0.716463	−	0.697625i	$-0.754240\pi$
$257$	−31078.3	+	17943.0i	−0.470533	+	0.271663i	0.245930	+	0.969288i	$0.420907\pi$
$258$		0			0
$259$	−29181.8	+	28592.2i	−0.435023	+	0.426233i
$260$	−25920.2			−0.383435
$261$		0			0
$262$	10630.3	+	6137.39i	0.154861	+	0.0894090i
$263$	−32715.8	+	56665.4i	−0.472984	+	0.819232i	−0.999522	−	0.0309199i	$-0.990156\pi$
$263$	−32715.8	+	56665.4i	−0.472984	+	0.819232i	0.526538	+	0.850151i	$0.323490\pi$
$264$		0			0
$265$			16313.4i			0.232302i
$266$	10974.5	−	39346.7i	0.155103	−	0.556089i
$267$		0			0
$268$	34698.5	+	60099.5i	0.483104	+	0.836761i
$269$	59938.7	+	34605.6i	0.828329	+	0.478236i	0.853280	−	0.521453i	$-0.174610\pi$
$269$	59938.7	+	34605.6i	0.828329	+	0.478236i	−0.0249511	+	0.999689i	$0.507943\pi$
$270$		0			0
$271$	5672.94	−	3275.27i	0.0772449	−	0.0445973i	−0.460880	−	0.887462i	$-0.652466\pi$
$271$	5672.94	−	3275.27i	0.0772449	−	0.0445973i	0.538125	+	0.842865i	$0.319133\pi$
$272$		−	14429.1i		−	0.195030i
$273$		0			0
$274$	−87000.1			−1.15883
$275$	13595.9	+	23548.8i	0.179780	+	0.311389i
$276$		0			0
$277$	−39551.6	+	68505.4i	−0.515471	+	0.892823i	0.484367	+	0.874865i	$0.339050\pi$
$277$	−39551.6	+	68505.4i	−0.515471	+	0.892823i	−0.999839	+	0.0179578i	$0.994284\pi$
$278$	66593.4	−	38447.7i	0.861671	−	0.497486i
$279$		0			0
$280$	−10982.6	−	11209.1i	−0.140084	−	0.142973i
$281$	−34363.1			−0.435191			−0.217596	−	0.976039i	$-0.569821\pi$
$281$	−34363.1			−0.435191			−0.217596	+	0.976039i	$0.569821\pi$
$282$		0			0
$283$	79598.4	+	45956.1i	0.993874	+	0.573813i	0.906430	−	0.422356i	$-0.138797\pi$
$283$	79598.4	+	45956.1i	0.993874	+	0.573813i	0.0874439	+	0.996169i	$0.472130\pi$
$284$	−1414.37	+	2449.75i	−0.0175358	+	0.0303729i
$285$		0			0
$286$			41457.8i			0.506844i
$287$	133716.	−	34370.5i	1.62338	−	0.417274i
$288$		0			0
$289$	−16345.5	−	28311.3i	−0.195705	−	0.338972i
$290$	−25668.9	−	14819.9i	−0.305218	−	0.176218i
$291$		0			0
$292$	−28197.4	+	16279.8i	−0.330707	+	0.190934i
$293$			23218.2i			0.270453i	0.990815	+	0.135227i	$0.0431763\pi$
$293$			23218.2i			0.270453i	−0.990815	+	0.135227i	$0.956824\pi$
$294$		0			0
$295$	49432.7			0.568028
$296$	−9432.97	−	16338.4i	−0.107663	−	0.186477i
$297$		0			0
$298$	8240.51	−	14273.0i	0.0927943	−	0.160724i
$299$	−140658.	+	81208.9i	−1.57334	+	0.908367i
$300$		0			0
$301$	37405.5	+	145523.i	0.412860	+	1.60620i
$302$	−71239.0			−0.781095
$303$		0			0
$304$	16336.0	+	9431.59i	0.176766	+	0.102056i
$305$	16080.0	−	27851.3i	0.172856	−	0.299396i
$306$		0			0
$307$			66385.9i			0.704367i	0.935931	+	0.352183i	$0.114561\pi$
$307$			66385.9i			0.704367i	−0.935931	+	0.352183i	$0.885439\pi$
$308$	−17928.2	+	17566.0i	−0.188989	+	0.185171i
$309$		0			0
$310$	−13345.0	−	23114.3i	−0.138866	−	0.240523i
$311$	82879.0	+	47850.2i	0.856888	+	0.494724i	0.862969	−	0.505257i	$-0.168602\pi$
$311$	82879.0	+	47850.2i	0.856888	+	0.494724i	−0.00608108	+	0.999982i	$0.501936\pi$
$312$		0			0
$313$	41486.1	−	23952.0i	0.423461	−	0.244486i	−0.273096	−	0.961987i	$-0.588048\pi$
$313$	41486.1	−	23952.0i	0.423461	−	0.244486i	0.696557	+	0.717501i	$0.254714\pi$
$314$			67588.2i			0.685507i
$315$		0			0
$316$	51782.6			0.518573
$317$	−17064.1	−	29555.9i	−0.169811	−	0.294121i	0.768543	−	0.639799i	$-0.220982\pi$
$317$	−17064.1	−	29555.9i	−0.169811	−	0.294121i	−0.938353	+	0.345678i	$0.887649\pi$
$318$		0			0
$319$	−23703.6	+	41055.8i	−0.232934	+	0.403454i
$320$	6275.77	−	3623.32i	0.0612868	−	0.0353839i
$321$		0			0
$322$	−94716.3	−	26418.0i	−0.913509	−	0.254793i
$323$	−66450.0			−0.636927
$324$		0			0
$325$	−84192.0	−	48608.3i	−0.797084	−	0.460196i
$326$	−60225.6	+	104314.i	−0.566691	+	0.981537i
$327$		0			0
$328$			63755.1i			0.592607i
$329$	21046.4	+	21480.4i	0.194440	+	0.198450i
$330$		0			0
$331$	−66642.6	−	115428.i	−0.608270	−	1.05355i	−0.991526	−	0.129912i	$-0.958531\pi$
$331$	−66642.6	−	115428.i	−0.608270	−	1.05355i	0.383256	−	0.923642i	$-0.374803\pi$
$332$	56990.2	+	32903.3i	0.517040	+	0.298513i
$333$		0			0
$334$	64559.5	−	37273.4i	0.578718	−	0.334123i
$335$		−	122777.i		−	1.09402i
$336$		0			0
$337$	−49734.4			−0.437922			−0.218961	−	0.975734i	$-0.570267\pi$
$337$	−49734.4			−0.437922			−0.218961	+	0.975734i	$0.570267\pi$
$338$	−33719.0	−	58403.1i	−0.295149	−	0.511214i
$339$		0			0
$340$	−12764.0	+	22107.9i	−0.110415	+	0.191245i
$341$	−36970.0	+	21344.6i	−0.317936	+	0.183561i
$342$		0			0
$343$	−80605.0	−	85697.8i	−0.685131	−	0.728420i
$344$	−69384.9			−0.586338
$345$		0			0
$346$	−68632.7	−	39625.1i	−0.573296	−	0.330993i
$347$	9384.77	−	16254.9i	0.0779408	−	0.134997i	−0.824421	−	0.565978i	$-0.808499\pi$
$347$	9384.77	−	16254.9i	0.0779408	−	0.134997i	0.902361	+	0.430980i	$0.141832\pi$
$348$		0			0
$349$			4574.17i			0.0375545i	0.999824	+	0.0187772i	$0.00597733\pi$
$349$			4574.17i			0.0375545i	−0.999824	+	0.0187772i	$0.994023\pi$
$350$	−14652.4	−	57004.1i	−0.119611	−	0.465340i
$351$		0			0
$352$	−5795.28	−	10037.7i	−0.0467724	−	0.0810121i
$353$	−52734.9	−	30446.5i	−0.423203	−	0.244336i	0.273244	−	0.961945i	$-0.411903\pi$
$353$	−52734.9	−	30446.5i	−0.423203	−	0.244336i	−0.696447	+	0.717608i	$0.745237\pi$
$354$		0			0
$355$	4334.10	−	2502.29i	0.0343908	−	0.0198555i
$356$			124306.i			0.980828i
$357$		0			0
$358$	71837.7			0.560514
$359$	116059.	+	201020.i	0.900513	+	1.55973i	0.826830	+	0.562452i	$0.190142\pi$
$359$	116059.	+	201020.i	0.900513	+	1.55973i	0.0736826	+	0.997282i	$0.476525\pi$
$360$		0			0
$361$	−21725.5	+	37629.7i	−0.166708	+	0.288746i
$362$	108016.	−	62362.9i	0.824271	−	0.475893i
$363$		0			0
$364$	24108.8	−	86437.1i	0.181959	−	0.652375i
$365$	57604.4			0.432384
$366$		0			0
$367$	−125329.	−	72358.9i	−0.930509	−	0.537229i	−0.0435362	−	0.999052i	$-0.513862\pi$
$367$	−125329.	−	72358.9i	−0.930509	−	0.537229i	−0.886972	+	0.461822i	$0.847196\pi$
$368$	22704.0	−	39324.4i	0.167651	−	0.290380i
$369$		0			0
$370$			33377.6i			0.243810i
$371$	−54401.0	−	15173.4i	−0.395238	−	0.110239i
$372$		0			0
$373$	74441.6	+	128937.i	0.535054	+	0.926741i	0.999161	+	0.0409616i	$0.0130421\pi$
$373$	74441.6	+	128937.i	0.535054	+	0.926741i	−0.464107	+	0.885779i	$0.653625\pi$
$374$	35360.2	+	20415.2i	0.252797	+	0.145952i
$375$		0			0
$376$	−12026.5	+	6943.52i	−0.0850676	+	0.0491138i
$377$		−	169491.i		−	1.19252i
$378$		0			0
$379$	140667.			0.979299			0.489649	−	0.871919i	$-0.337125\pi$
$379$	140667.			0.979299			0.489649	+	0.871919i	$0.337125\pi$
$380$	−16686.3	−	28901.6i	−0.115556	−	0.200149i
$381$		0			0
$382$	91300.4	−	158137.i	0.625671	−	1.08369i
$383$	−25393.9	+	14661.2i	−0.173114	+	0.0999473i	−0.584053	−	0.811715i	$-0.698534\pi$
$383$	−25393.9	+	14661.2i	−0.173114	+	0.0999473i	0.410939	+	0.911663i	$0.365201\pi$
$384$		0			0
$385$	43008.0	−	11054.8i	0.290153	−	0.0745814i
$386$	−103731.			−0.696202
$387$		0			0
$388$	10798.4	+	6234.43i	0.0717289	+	0.0414127i
$389$	66209.9	−	114679.i	0.437546	−	0.757852i	−0.559954	−	0.828524i	$-0.689181\pi$
$389$	66209.9	−	114679.i	0.437546	−	0.757852i	0.997500	+	0.0706723i	$0.0225145\pi$
$390$		0			0
$391$			159960.i			1.04630i
$392$	47594.4	−	26198.4i	0.309730	−	0.170491i
$393$		0			0
$394$	103446.	+	179173.i	0.666376	+	1.15420i
$395$	−79339.7	−	45806.8i	−0.508507	−	0.293586i
$396$		0			0
$397$	29642.0	−	17113.8i	0.188073	−	0.108584i	−0.403007	−	0.915197i	$-0.632035\pi$
$397$	29642.0	−	17113.8i	0.188073	−	0.108584i	0.591080	+	0.806613i	$0.298702\pi$
$398$		−	3962.70i		−	0.0250164i
$399$		0			0
$400$	27179.3			0.169870
$401$	−89540.6	−	155089.i	−0.556841	−	0.964477i	−0.997758	−	0.0669288i	$-0.978680\pi$
$401$	−89540.6	−	155089.i	−0.556841	−	0.964477i	0.440917	−	0.897548i	$-0.354653\pi$
$402$		0			0
$403$	76311.7	−	132176.i	0.469873	−	0.813845i
$404$	109018.	−	62941.3i	0.667934	−	0.385632i
$405$		0			0
$406$	73295.6	−	71814.7i	0.444657	−	0.435674i
$407$	53385.5			0.322281
$408$		0			0
$409$	43099.3	+	24883.4i	0.257646	+	0.148752i	0.623260	−	0.782014i	$-0.285808\pi$
$409$	43099.3	+	24883.4i	0.257646	+	0.148752i	−0.365614	+	0.930767i	$0.619141\pi$
$410$	56397.6	−	97683.6i	0.335501	−	0.581104i
$411$		0			0
$412$			269.830i			0.00158963i
$413$	−45978.1	+	164845.i	−0.269557	+	0.966442i
$414$		0			0
$415$	−58212.4	−	100827.i	−0.338002	−	0.585437i
$416$	35887.0	+	20719.4i	0.207372	+	0.119727i
$417$		0			0
$418$	−46226.4	+	26688.8i	−0.264568	+	0.152748i
$419$		−	43951.2i		−	0.250347i	−0.992135	−	0.125174i	$-0.960051\pi$
$419$		−	43951.2i		−	0.250347i	0.992135	−	0.125174i	$-0.0399488\pi$
$420$		0			0
$421$	−218257.			−1.23141			−0.615707	−	0.787975i	$-0.711129\pi$
$421$	−218257.			−1.23141			−0.615707	+	0.787975i	$0.711129\pi$
$422$	82352.0	+	142638.i	0.462433	+	0.800958i
$423$		0			0
$424$	13040.2	−	22586.3i	0.0725357	−	0.125636i
$425$	−82917.9	+	47872.7i	−0.459061	+	0.265039i
$426$		0			0
$427$	77920.6	+	79527.4i	0.427363	+	0.436175i
$428$	43571.7			0.237858
$429$		0			0
$430$	106309.	+	61377.8i	0.574956	+	0.331951i
$431$	−38369.8	+	66458.5i	−0.206555	+	0.357763i	−0.950627	−	0.310336i	$-0.899558\pi$
$431$	−38369.8	+	66458.5i	−0.206555	+	0.357763i	0.744072	+	0.668099i	$0.232892\pi$
$432$		0			0
$433$		−	216713.i		−	1.15587i	−0.816083	−	0.577935i	$-0.803859\pi$
$433$		−	216713.i		−	1.15587i	0.816083	−	0.577935i	$-0.196141\pi$
$434$	89492.6	−	23003.3i	0.475125	−	0.122127i
$435$		0			0
$436$	−66791.1	−	115686.i	−0.351354	−	0.608564i
$437$	−181099.	−	104558.i	−0.948318	−	0.547512i
$438$		0			0
$439$	20578.6	−	11881.0i	0.106779	−	0.0616489i	−0.445659	−	0.895203i	$-0.647031\pi$
$439$	20578.6	−	11881.0i	0.106779	−	0.0616489i	0.552438	+	0.833554i	$0.313697\pi$
$440$			20506.0i			0.105919i
$441$		0			0
$442$	−145978.			−0.747210
$443$	87432.4	+	151437.i	0.445517	+	0.771659i	0.998088	−	0.0618072i	$-0.0196864\pi$
$443$	87432.4	+	151437.i	0.445517	+	0.771659i	−0.552571	+	0.833466i	$0.686353\pi$
$444$		0			0
$445$	109961.	−	190458.i	0.555289	−	0.961788i
$446$	149544.	−	86339.0i	0.751793	−	0.434048i
$447$		0			0
$448$	6245.62	+	24298.1i	0.0311186	+	0.121065i
$449$	195154.			0.968023			0.484011	−	0.875062i	$-0.339179\pi$
$449$	195154.			0.968023			0.484011	+	0.875062i	$0.339179\pi$
$450$		0			0
$451$	−156239.	−	90204.7i	−0.768134	−	0.443482i
$452$	37822.6	−	65510.6i	0.185129	−	0.320653i
$453$		0			0
$454$		−	70692.8i		−	0.342976i
$455$	−113401.	+	111110.i	−0.547764	+	0.536697i
$456$		0			0
$457$	−29236.1	−	50638.5i	−0.139987	−	0.242464i	0.787505	−	0.616309i	$-0.211373\pi$
$457$	−29236.1	−	50638.5i	−0.139987	−	0.242464i	−0.927491	+	0.373844i	$0.878039\pi$
$458$	−46366.1	−	26769.5i	−0.221039	−	0.127617i
$459$		0			0
$460$	−69572.6	+	40167.8i	−0.328793	+	0.189829i
$461$			307243.i			1.44571i	0.691002	+	0.722853i	$0.257169\pi$
$461$			307243.i			1.44571i	−0.691002	+	0.722853i	$0.742831\pi$
$462$		0			0
$463$	−17772.2			−0.0829049			−0.0414524	−	0.999140i	$-0.513199\pi$
$463$	−17772.2			−0.0829049			−0.0414524	+	0.999140i	$0.513199\pi$
$464$	23692.7	+	41037.0i	0.110047	+	0.190607i
$465$		0			0
$466$	−9453.65	+	16374.2i	−0.0435339	+	0.0754029i
$467$	−56261.4	+	32482.5i	−0.257974	+	0.148942i	−0.623410	−	0.781895i	$-0.714253\pi$
$467$	−56261.4	+	32482.5i	−0.257974	+	0.148942i	0.365436	+	0.930837i	$0.380920\pi$
$468$		0			0
$469$	409429.	+	114197.i	1.86137	+	0.519168i
$470$	24568.9			0.111222
$471$		0			0
$472$	−68440.5	−	39514.2i	−0.307206	−	0.177365i
$473$	98170.2	−	170036.i	0.438790	−	0.760007i
$474$		0			0
$475$		−	125168.i		−	0.554760i
$476$	−61852.0	−	63127.4i	−0.272986	−	0.278615i
$477$		0			0
$478$	136416.	+	236280.i	0.597050	+	1.03412i
$479$	−182677.	−	105468.i	−0.796181	−	0.459675i	0.0459530	−	0.998944i	$-0.485368\pi$
$479$	−182677.	−	105468.i	−0.796181	−	0.459675i	−0.842134	+	0.539268i	$0.818701\pi$
$480$		0			0
$481$	−165294.	+	95432.3i	−0.714440	+	0.412482i
$482$			154716.i			0.665948i
$483$		0			0
$484$	−84329.8			−0.359990
$485$	−11029.9	−	19104.4i	−0.0468910	−	0.0812177i
$486$		0			0
$487$	114444.	−	198223.i	0.482542	−	0.835787i	−0.517257	−	0.855830i	$-0.673047\pi$
$487$	114444.	−	198223.i	0.482542	−	0.835787i	0.999799	+	0.0200431i	$0.00638033\pi$
$488$	−44526.1	+	25707.1i	−0.186971	+	0.107948i
$489$		0			0
$490$	−96097.7	−	1961.59i	−0.400240	−	0.00816987i
$491$	−140350.			−0.582169			−0.291085	−	0.956697i	$-0.594016\pi$
$491$	−140350.			−0.582169			−0.291085	+	0.956697i	$0.594016\pi$
$492$		0			0
$493$	−144562.	−	83463.1i	−0.594787	−	0.343400i
$494$	95418.3	−	165269.i	0.391001	−	0.677234i
$495$		0			0
$496$			42669.6i			0.173442i
$497$	4313.28	+	16780.5i	0.0174620	+	0.0679348i
$498$		0			0
$499$	172663.	+	299062.i	0.693424	+	1.20105i	0.970709	+	0.240258i	$0.0772322\pi$
$499$	172663.	+	299062.i	0.693424	+	1.20105i	−0.277285	+	0.960788i	$0.589434\pi$
$500$	−102930.	−	59426.7i	−0.411720	−	0.237707i
$501$		0			0
$502$	264881.	−	152929.i	1.05110	−	0.606851i
$503$		−	58979.0i		−	0.233110i	−0.993184	−	0.116555i	$-0.962815\pi$
$503$		−	58979.0i		−	0.233110i	0.993184	−	0.116555i	$-0.0371851\pi$
$504$		0			0
$505$	−222711.			−0.873291
$506$	64246.0	+	111277.i	0.250926	+	0.434616i
$507$		0			0
$508$	9520.26	−	16489.6i	0.0368911	−	0.0638972i
$509$	−20653.6	+	11924.3i	−0.0797186	+	0.0460255i	−0.539329	−	0.842095i	$-0.681322\pi$
$509$	−20653.6	+	11924.3i	−0.0797186	+	0.0460255i	0.459611	+	0.888120i	$0.347989\pi$
$510$		0			0
$511$	−53578.7	+	192095.i	−0.205187	+	0.735657i
$512$	−11585.2			−0.0441942
$513$		0			0
$514$	−87902.6	−	50750.6i	−0.332717	−	0.192094i
$515$	238.691	−	413.425i	0.000899957	−	0.00155877i
$516$		0			0
$517$		−	39296.5i		−	0.147019i
$518$	−111305.	−	31045.0i	−0.414817	−	0.115700i
$519$		0			0
$520$	−36656.7	−	63491.3i	−0.135565	−	0.234805i
$521$	−417171.	−	240854.i	−1.53688	−	0.887315i	−0.999019	−	0.0442788i	$-0.985901\pi$
$521$	−417171.	−	240854.i	−1.53688	−	0.887315i	−0.537856	−	0.843037i	$-0.680766\pi$
$522$		0			0
$523$	−399593.	+	230705.i	−1.46088	+	0.843438i	−0.999052	−	0.0435320i	$-0.986139\pi$
$523$	−399593.	+	230705.i	−1.46088	+	0.843438i	−0.461826	+	0.886970i	$0.652806\pi$
$524$			34718.3i			0.126443i
$525$		0			0
$526$	−185068.			−0.668900
$527$	−75156.9	−	130176.i	−0.270612	−	0.468714i
$528$		0			0
$529$	−111774.	+	193598.i	−0.399419	+	0.691813i
$530$	−39959.6	+	23070.7i	−0.142255	+	0.0821312i
$531$		0			0
$532$	111899.	−	28762.8i	0.395371	−	0.101627i
$533$	645003.			2.27043
$534$		0			0
$535$	−66759.3	−	38543.5i	−0.233240	−	0.134661i
$536$	−98142.1	+	169987.i	−0.341606	+	0.591679i
$537$		0			0
$538$			195759.i			0.676328i
$539$	−3137.44	+	153703.i	−0.0107994	+	0.529059i
$540$		0			0
$541$	254098.	+	440111.i	0.868174	+	1.50372i	0.863861	+	0.503731i	$0.168040\pi$
$541$	254098.	+	440111.i	0.868174	+	1.50372i	0.00431302	+	0.999991i	$0.498627\pi$
$542$	16045.5	+	9263.87i	0.0546204	+	0.0315351i
$543$		0			0
$544$	35344.0	−	20405.9i	0.119431	−	0.0689536i
$545$			236333.i			0.795668i
$546$		0			0
$547$	40170.8			0.134257			0.0671283	−	0.997744i	$-0.478616\pi$
$547$	40170.8			0.134257			0.0671283	+	0.997744i	$0.478616\pi$
$548$	−123037.	−	213106.i	−0.409707	−	0.709634i
$549$		0			0
$550$	−38455.0	+	66606.0i	−0.127124	+	0.220185i
$551$	188986.	−	109111.i	0.622482	−	0.359390i
$552$		0			0
$553$	226549.	−	221972.i	0.740818	−	0.725851i
$554$	−223738.			−0.728987
$555$		0			0
$556$	188355.	+	108747.i	0.609293	+	0.351776i
$557$	−39230.2	+	67948.7i	−0.126447	+	0.219013i	−0.922298	−	0.386480i	$-0.873691\pi$
$557$	−39230.2	+	67948.7i	−0.126447	+	0.219013i	0.795850	+	0.605493i	$0.207024\pi$
$558$		0			0
$559$			701959.i			2.24641i
$560$	11924.8	−	42753.8i	0.0380254	−	0.136332i
$561$		0			0
$562$	−48596.8	−	84172.2i	−0.153863	−	0.266499i
$563$	355612.	+	205312.i	1.12191	+	0.647737i	0.941889	−	0.335926i	$-0.109049\pi$
$563$	355612.	+	205312.i	1.12191	+	0.647737i	0.180024	+	0.983662i	$0.442382\pi$
$564$		0			0
$565$	−115901.	+	66915.6i	−0.363071	+	0.209619i
$566$			259967.i			0.811495i
$567$		0			0
$568$	−8000.86			−0.0247993
$569$	−74404.3	−	128872.i	−0.229812	−	0.398047i	0.727940	−	0.685641i	$-0.240478\pi$
$569$	−74404.3	−	128872.i	−0.229812	−	0.398047i	−0.957752	+	0.287594i	$0.907145\pi$
$570$		0			0
$571$	−36146.3	+	62607.3i	−0.110864	+	0.192023i	−0.916119	−	0.400906i	$-0.868695\pi$
$571$	−36146.3	+	62607.3i	−0.110864	+	0.192023i	0.805255	+	0.592929i	$0.202029\pi$
$572$	−101551.	+	58630.3i	−0.310378	+	0.179197i
$573$		0			0
$574$	273293.	+	278928.i	0.829477	+	0.846582i
$575$	−301307.			−0.911326
$576$		0			0
$577$	−482666.	−	278667.i	−1.44976	−	0.837018i	−0.451290	−	0.892377i	$-0.649036\pi$
$577$	−482666.	−	278667.i	−1.44976	−	0.837018i	−0.998466	+	0.0553596i	$0.982369\pi$
$578$	46232.1	−	80076.3i	0.138385	−	0.239689i
$579$		0			0
$580$		−	83834.1i		−	0.249210i
$581$	390376.	−	100343.i	1.15646	−	0.297258i
$582$		0			0
$583$	36900.2	+	63913.0i	0.108565	+	0.188041i
$584$	−79754.4	−	46046.2i	−0.233845	−	0.135011i
$585$		0			0
$586$	−56872.6	+	32835.4i	−0.165618	+	0.0956197i
$587$		−	308119.i		−	0.894217i	−0.894480	−	0.447109i	$-0.852454\pi$
$587$		−	308119.i		−	0.894217i	0.894480	−	0.447109i	$-0.147546\pi$
$588$		0			0
$589$	196505.			0.566426
$590$	69908.3	+	121085.i	0.200828	+	0.347845i
$591$		0			0
$592$	26680.5	−	46211.9i	0.0761290	−	0.131859i
$593$	200805.	−	115935.i	0.571038	−	0.329689i	−0.186526	−	0.982450i	$-0.559723\pi$
$593$	200805.	−	115935.i	0.571038	−	0.329689i	0.757564	+	0.652761i	$0.226389\pi$
$594$		0			0
$595$	38925.3	+	151436.i	0.109951	+	0.427755i
$596$	46615.3			0.131231
$597$		0			0
$598$	−397841.	−	229693.i	−1.11252	−	0.642312i
$599$	−167042.	+	289325.i	−0.465555	+	0.806365i	−0.999226	−	0.0393269i	$-0.987479\pi$
$599$	−167042.	+	289325.i	−0.465555	+	0.806365i	0.533671	+	0.845692i	$0.320812\pi$
$600$		0			0
$601$		−	645072.i		−	1.78591i	−0.450147	−	0.892955i	$-0.648628\pi$
$601$		−	645072.i		−	1.78591i	0.450147	−	0.892955i	$-0.351372\pi$
$602$	−303559.	+	297426.i	−0.837625	+	0.820702i
$603$		0			0
$604$	−100747.	−	174499.i	−0.276159	−	0.478321i
$605$	129208.	+	74598.1i	0.353002	+	0.203806i
$606$		0			0
$607$	120643.	−	69653.0i	0.327433	−	0.189044i	−0.327268	−	0.944932i	$-0.606128\pi$
$607$	120643.	−	69653.0i	0.327433	−	0.189044i	0.654701	+	0.755888i	$0.272795\pi$
$608$			53353.1i			0.144329i
$609$		0			0
$610$	90962.0			0.244456
$611$	70246.8	+	121671.i	0.188167	+	0.325915i
$612$		0			0
$613$	203665.	−	352759.i	0.541997	−	0.938765i	−0.456793	−	0.889573i	$-0.651002\pi$
$613$	203665.	−	352759.i	0.541997	−	0.938765i	0.998789	−	0.0491924i	$-0.0156647\pi$
$614$	−162611.	+	93883.8i	−0.431335	+	0.249031i
$615$		0			0
$616$	−68382.1	−	19072.9i	−0.180211	−	0.0502639i
$617$	−276504.			−0.726325			−0.363163	−	0.931726i	$-0.618303\pi$
$617$	−276504.			−0.726325			−0.363163	+	0.931726i	$0.618303\pi$
$618$		0			0
$619$	193904.	+	111950.i	0.506064	+	0.292176i	0.731214	−	0.682148i	$-0.238954\pi$
$619$	193904.	+	111950.i	0.506064	+	0.292176i	−0.225150	+	0.974324i	$0.572287\pi$
$620$	37745.5	−	65377.1i	0.0981933	−	0.170076i
$621$		0			0
$622$			270682.i			0.699646i
$623$	532852.	+	543839.i	1.37287	+	1.40118i
$624$		0			0
$625$	−27573.7	−	47759.1i	−0.0705888	−	0.122263i
$626$	117340.	+	67746.5i	0.299432	+	0.172877i
$627$		0			0
$628$	−165557.	+	95584.2i	−0.419785	+	0.242363i
$629$			187976.i			0.475119i
$630$		0			0
$631$	299528.			0.752278			0.376139	−	0.926563i	$-0.377251\pi$
$631$	299528.			0.752278			0.376139	+	0.926563i	$0.377251\pi$
$632$	73231.7	+	126841.i	0.183343	+	0.317560i
$633$		0			0
$634$	48264.6	−	83596.7i	0.120074	−	0.207975i
$635$	−29173.3	+	16843.2i	−0.0723500	+	0.0417713i
$636$		0			0
$637$	−265046.	−	481507.i	−0.653194	−	1.18665i
$638$	−134088.			−0.329418
$639$		0			0
$640$	17750.6	+	10248.3i	0.0433363	+	0.0250202i
$641$	288942.	−	500462.i	0.703226	−	1.21802i	−0.264102	−	0.964495i	$-0.585076\pi$
$641$	288942.	−	500462.i	0.703226	−	1.21802i	0.967328	−	0.253528i	$-0.0815911\pi$
$642$		0			0
$643$			135320.i			0.327295i	0.986519	+	0.163647i	$0.0523259\pi$
$643$			135320.i			0.327295i	−0.986519	+	0.163647i	$0.947674\pi$
$644$	−69238.5	−	269367.i	−0.166946	−	0.649491i
$645$		0			0
$646$	−93974.4	−	162768.i	−0.225188	−	0.390037i
$647$	−188880.	−	109050.i	−0.451209	−	0.260506i	0.257132	−	0.966376i	$-0.417223\pi$
$647$	−188880.	−	109050.i	−0.451209	−	0.260506i	−0.708341	+	0.705871i	$0.750556\pi$
$648$		0			0
$649$	193668.	−	111814.i	0.459800	−	0.265465i
$650$		−	274970.i		−	0.650816i
$651$		0			0
$652$	−340688.			−0.801422
$653$	72127.2	+	124928.i	0.169150	+	0.292977i	0.938121	−	0.346307i	$-0.112564\pi$
$653$	72127.2	+	124928.i	0.169150	+	0.292977i	−0.768971	+	0.639284i	$0.779231\pi$
$654$		0			0
$655$	30711.8	−	53194.4i	0.0715851	−	0.123989i
$656$	−156167.	+	90163.3i	−0.362896	+	0.209518i
$657$		0			0
$658$	−22851.9	+	81930.8i	−0.0527802	+	0.189232i
$659$	159392.			0.367024			0.183512	−	0.983017i	$-0.441253\pi$
$659$	159392.			0.367024			0.183512	+	0.983017i	$0.441253\pi$
$660$		0			0
$661$	305674.	+	176481.i	0.699609	+	0.403919i	0.807202	−	0.590276i	$-0.200981\pi$
$661$	305674.	+	176481.i	0.699609	+	0.403919i	−0.107593	+	0.994195i	$0.534314\pi$
$662$	188494.	−	326481.i	0.430112	−	0.744975i
$663$		0			0
$664$			186129.i			0.422161i
$665$	−196892.	−	54916.7i	−0.445231	−	0.124183i
$666$		0			0
$667$	−262655.	−	454932.i	−0.590384	−	1.02258i
$668$	182602.	+	105425.i	0.409216	+	0.236261i
$669$		0			0
$670$	300741.	−	173633.i	0.669950	−	0.386796i
$671$		−	145488.i		−	0.323135i
$672$		0			0
$673$	504858.			1.11465			0.557326	−	0.830294i	$-0.311827\pi$
$673$	504858.			1.11465			0.557326	+	0.830294i	$0.311827\pi$
$674$	−70335.1	−	121824.i	−0.154829	−	0.268172i
$675$		0			0
$676$	95371.9	−	165189.i	0.208702	−	0.361483i
$677$	169486.	−	97853.0i	0.369792	−	0.213500i	−0.303576	−	0.952807i	$-0.598180\pi$
$677$	169486.	−	97853.0i	0.369792	−	0.213500i	0.673368	+	0.739308i	$0.264847\pi$
$678$		0			0
$679$	73967.4	−	19012.7i	0.160436	−	0.0412385i
$680$	−72204.0			−0.156150
$681$		0			0
$682$	−104567.	−	60371.7i	−0.224815	−	0.129797i
$683$	−117221.	+	203032.i	−0.251283	+	0.435235i	−0.963879	−	0.266340i	$-0.914186\pi$
$683$	−117221.	+	203032.i	−0.251283	+	0.435235i	0.712596	+	0.701574i	$0.247519\pi$
$684$		0			0
$685$			435352.i			0.927812i
$686$	95923.3	−	318636.i	0.203834	−	0.677091i
$687$		0			0
$688$	−98125.0	−	169958.i	−0.207302	−	0.359057i
$689$	−228503.	−	131926.i	−0.481341	−	0.277902i
$690$		0			0
$691$	−77344.0	+	44654.6i	−0.161983	+	0.0935212i	−0.578800	−	0.815469i	$-0.696479\pi$
$691$	−77344.0	+	44654.6i	−0.161983	+	0.0935212i	0.416817	+	0.908990i	$0.363146\pi$
$692$		−	224153.i		−	0.468094i
$693$		0			0
$694$	53088.3			0.110225
$695$	−192394.	−	333236.i	−0.398311	−	0.689895i
$696$		0			0
$697$	317621.	−	550136.i	0.653799	−	1.13241i
$698$	−11204.4	+	6468.85i	−0.0229973	+	0.0132775i
$699$		0			0
$700$	118909.	−	116507.i	0.242672	−	0.237769i
$701$	−122213.			−0.248704			−0.124352	−	0.992238i	$-0.539685\pi$
$701$	−122213.			−0.248704			−0.124352	+	0.992238i	$0.539685\pi$
$702$		0			0
$703$	−212818.	−	122871.i	−0.430624	−	0.248621i
$704$	16391.5	−	28391.0i	0.0330731	−	0.0572842i
$705$		0			0
$706$		−	172231.i		−	0.345544i
$707$	207147.	−	742683.i	0.414419	−	1.48582i
$708$		0			0
$709$	−42009.9	−	72763.3i	−0.0835717	−	0.144750i	0.821210	−	0.570626i	$-0.193299\pi$
$709$	−42009.9	−	72763.3i	−0.0835717	−	0.144750i	−0.904782	+	0.425876i	$0.859966\pi$
$710$	12258.7	+	7077.55i	0.0243179	+	0.0140400i
$711$		0			0
$712$	−304487.	+	175795.i	−0.600632	+	0.346775i
$713$		−	473032.i		−	0.930489i
$714$		0			0
$715$	207457.			0.405804
$716$	101594.	+	175966.i	0.198172	+	0.343243i
$717$		0			0
$718$	−328264.	+	568570.i	−0.636759	+	1.10290i
$719$	−657416.	+	379560.i	−1.27169	+	0.734213i	−0.975307	−	0.220855i	$-0.929115\pi$
$719$	−657416.	+	379560.i	−1.27169	+	0.734213i	−0.296388	+	0.955068i	$0.595782\pi$
$720$		0			0
$721$	1156.65	+	1180.51i	0.00222502	+	0.00227090i
$722$	−122898.			−0.235760
$723$		0			0
$724$	305515.	+	176389.i	0.582847	+	0.336507i
$725$	157214.	−	272303.i	0.299100	−	0.518057i
$726$		0			0
$727$		−	92384.1i		−	0.174795i	−0.996174	−	0.0873974i	$-0.972145\pi$
$727$		−	92384.1i		−	0.174795i	0.996174	−	0.0873974i	$-0.0278550\pi$
$728$	245822.	−	63186.3i	0.463829	−	0.119223i
$729$		0			0
$730$	81464.9	+	141101.i	0.152871	+	0.264780i
$731$	598715.	+	345668.i	1.12043	+	0.646882i
$732$		0			0
$733$	2903.50	−	1676.34i	0.00540399	−	0.00312000i	−0.497296	−	0.867581i	$-0.665674\pi$
$733$	2903.50	−	1676.34i	0.00540399	−	0.00312000i	0.502700	+	0.864461i	$0.332340\pi$
$734$		−	409324.i		−	0.759757i
$735$		0			0
$736$	128433.			0.237094
$737$	−277715.	−	481017.i	−0.511287	−	0.885575i
$738$		0			0
$739$	13592.8	−	23543.4i	0.0248897	−	0.0431103i	−0.853312	−	0.521400i	$-0.825410\pi$
$739$	13592.8	−	23543.4i	0.0248897	−	0.0431103i	0.878202	+	0.478290i	$0.158743\pi$
$740$	−81758.0	+	47203.0i	−0.149302	+	0.0861998i
$741$		0			0
$742$	−39767.6	−	154713.i	−0.0722307	−	0.281008i
$743$	−773801.			−1.40169			−0.700845	−	0.713314i	$-0.747193\pi$
$743$	−773801.			−1.40169			−0.700845	+	0.713314i	$0.747193\pi$
$744$		0			0
$745$	−71422.6	−	41235.9i	−0.128684	−	0.0742955i
$746$	−210553.	+	364688.i	−0.378340	+	0.655305i
$747$		0			0
$748$			115486.i			0.206408i
$749$	190626.	−	186775.i	0.339797	−	0.332931i
$750$		0			0
$751$	−98922.2	−	171338.i	−0.175394	−	0.303791i	0.764904	−	0.644145i	$-0.222786\pi$
$751$	−98922.2	−	171338.i	−0.175394	−	0.303791i	−0.940297	+	0.340354i	$0.889453\pi$
$752$	−34016.1	−	19639.2i	−0.0601519	−	0.0347287i
$753$		0			0
$754$	415167.	−	239697.i	0.730264	−	0.421618i
$755$			356483.i			0.625381i
$756$		0			0
$757$	−770706.			−1.34492			−0.672461	−	0.740132i	$-0.734763\pi$
$757$	−770706.			−1.34492			−0.672461	+	0.740132i	$0.734763\pi$
$758$	198934.	+	344564.i	0.346234	+	0.599696i
$759$		0			0
$760$	47196.1	−	81746.0i	0.0817107	−	0.141527i
$761$	131757.	−	76069.9i	0.227512	−	0.131354i	−0.381912	−	0.924199i	$-0.624734\pi$
$761$	131757.	−	76069.9i	0.227512	−	0.131354i	0.609424	+	0.792845i	$0.291401\pi$
$762$		0			0
$763$	−788109.	−	219817.i	−1.35375	−	0.377583i
$764$	516473.			0.884832
$765$		0			0
$766$	−71824.8	−	41468.0i	−0.122410	−	0.0706734i
$767$	−399760.	+	692405.i	−0.679531	+	1.17698i
$768$		0			0
$769$			961897.i			1.62658i	0.581857	+	0.813291i	$0.302326\pi$
$769$			961897.i			1.62658i	−0.581857	+	0.813291i	$0.697674\pi$
$770$	87901.2	+	89713.7i	0.148256	+	0.151313i
$771$		0			0
$772$	−146698.	−	254089.i	−0.246145	−	0.426335i
$773$	130829.	+	75534.4i	0.218951	+	0.126411i	0.605464	−	0.795872i	$-0.292987\pi$
$773$	130829.	+	75534.4i	0.218951	+	0.126411i	−0.386514	+	0.922284i	$0.626321\pi$
$774$		0			0
$775$	245204.	−	141569.i	0.408248	−	0.235702i
$776$			35267.3i			0.0585664i
$777$		0			0
$778$	374540.			0.618783
$779$	415226.	+	719192.i	0.684242	+	1.18514i
$780$		0			0
$781$	11320.1	−	19607.0i	0.0185588	−	0.0321447i
$782$	−391821.	+	226218.i	−0.640728	+	0.369924i
$783$		0			0
$784$	131481.	+	79531.9i	0.213910	+	0.129392i
$785$	338215.			0.548849
$786$		0			0
$787$	−172244.	−	99445.4i	−0.278097	−	0.160559i	0.354465	−	0.935069i	$-0.384663\pi$
$787$	−172244.	−	99445.4i	−0.278097	−	0.160559i	−0.632561	+	0.774510i	$0.717996\pi$
$788$	−292588.	+	506777.i	−0.471199	+	0.816140i
$789$		0			0
$790$		−	259123.i		−	0.415194i
$791$	−115344.	−	448739.i	−0.184350	−	0.717202i
$792$		0			0
$793$	260076.	+	450465.i	0.413575	+	0.716333i
$794$	83840.2	+	48405.1i	0.132988	+	0.0767804i
$795$		0			0
$796$	9706.60	−	5604.11i	0.0153194	−	0.00884465i
$797$			990756.i			1.55973i	0.625947	+	0.779866i	$0.284713\pi$
$797$			990756.i			1.55973i	−0.625947	+	0.779866i	$0.715287\pi$
$798$		0			0
$799$	138368.			0.216741
$800$	38437.3	+	66575.4i	0.0600583	+	0.104024i
$801$		0			0
$802$	253259.	−	438657.i	0.393746	−	0.681988i
$803$	225683.	−	130298.i	0.350000	−	0.202073i
$804$		0			0
$805$	−132197.	+	473965.i	−0.204000	+	0.731399i
$806$	431684.			0.664501
$807$		0			0
$808$	308348.	+	178025.i	0.472301	+	0.272683i
$809$	−46144.3	+	79924.3i	−0.0705052	+	0.122119i	−0.899123	−	0.437696i	$-0.855794\pi$
$809$	−46144.3	+	79924.3i	−0.0705052	+	0.122119i	0.828618	+	0.559815i	$0.189128\pi$
$810$		0			0
$811$		−	617125.i		−	0.938277i	−0.883125	−	0.469139i	$-0.844564\pi$
$811$		−	617125.i		−	0.938277i	0.883125	−	0.469139i	$-0.155436\pi$
$812$	279565.	+	77975.4i	0.424005	+	0.118262i
$813$		0			0
$814$	75498.5	+	130767.i	0.113943	+	0.197356i
$815$	521991.	+	301372.i	0.785865	+	0.453719i
$816$		0			0
$817$	−782700.	+	451892.i	−1.17260	+	0.677003i
$818$			140762.i			0.210367i
$819$		0			0
$820$	319033.			0.474469
$821$	153533.	+	265927.i	0.227780	+	0.394526i	0.957150	−	0.289593i	$-0.0935201\pi$
$821$	153533.	+	265927.i	0.227780	+	0.394526i	−0.729370	+	0.684119i	$0.760187\pi$
$822$		0			0
$823$	−423429.	+	733401.i	−0.625146	+	1.08278i	0.363367	+	0.931646i	$0.381627\pi$
$823$	−423429.	+	733401.i	−0.625146	+	1.08278i	−0.988513	+	0.151138i	$0.951706\pi$
$824$	−660.946	+	381.597i	−0.000973445	+	0.000562019i
$825$		0			0
$826$	−468809.	+	120503.i	−0.687125	+	0.176619i
$827$	−294059.			−0.429956			−0.214978	−	0.976619i	$-0.568968\pi$
$827$	−294059.			−0.429956			−0.214978	+	0.976619i	$0.568968\pi$
$828$		0			0
$829$	895803.	+	517192.i	1.30348	+	0.752563i	0.980999	−	0.194013i	$-0.0621506\pi$
$829$	895803.	+	517192.i	1.30348	+	0.752563i	0.322479	+	0.946577i	$0.395484\pi$
$830$	164650.	−	285182.i	0.239004	−	0.413967i
$831$		0			0
$832$			117207.i			0.169319i
$833$	−541205.	−	11047.3i	−0.779959	−	0.0159208i
$834$		0			0
$835$	−186518.	−	323059.i	−0.267515	−	0.463349i
$836$	−130748.	−	75487.4i	−0.187078	−	0.108009i
$837$		0			0
$838$	107658.	−	62156.4i	0.153306	−	0.0885111i
$839$		−	307258.i		−	0.436495i	−0.975893	−	0.218248i	$-0.929966\pi$
$839$		−	307258.i		−	0.436495i	0.975893	−	0.218248i	$-0.0700340\pi$
$840$		0			0
$841$	−159093.			−0.224937
$842$	−308662.	−	534618.i	−0.435370	−	0.754084i
$843$		0			0
$844$	−232927.	+	403441.i	−0.326990	+	0.566363i
$845$	−292252.	+	168732.i	−0.409302	+	0.236311i
$846$		0			0
$847$	−368943.	+	361489.i	−0.514272	+	0.503881i
$848$	73766.4			0.102581
$849$		0			0
$850$	−234527.	−	135404.i	−0.324605	−	0.187411i
$851$	−295777.	+	512302.i	−0.408419	+	0.707402i
$852$		0			0
$853$			70737.4i			0.0972190i	0.998818	+	0.0486095i	$0.0154790\pi$
$853$			70737.4i			0.0972190i	−0.998818	+	0.0486095i	$0.984521\pi$
$854$	−84605.2	+	303335.i	−0.116006	+	0.415916i
$855$		0			0
$856$	61619.7	+	106728.i	0.0840954	+	0.145657i
$857$	−285670.	−	164932.i	−0.388958	−	0.224565i	0.292751	−	0.956189i	$-0.405429\pi$
$857$	−285670.	−	164932.i	−0.388958	−	0.224565i	−0.681709	+	0.731624i	$0.738763\pi$
$858$		0			0
$859$	−60589.3	+	34981.2i	−0.0821125	+	0.0474077i	−0.540494	−	0.841348i	$-0.681763\pi$
$859$	−60589.3	+	34981.2i	−0.0821125	+	0.0474077i	0.458382	+	0.888756i	$0.348429\pi$
$860$			347205.i			0.469450i
$861$		0			0
$862$	−217052.			−0.292113
$863$	−386112.	−	668765.i	−0.518431	−	0.897949i	−0.999771	−	0.0214151i	$-0.993183\pi$
$863$	−386112.	−	668765.i	−0.518431	−	0.897949i	0.481339	−	0.876534i	$-0.340150\pi$
$864$		0			0
$865$	−198286.	+	343441.i	−0.265008	+	0.459008i
$866$	530836.	−	306478.i	0.707823	−	0.408662i
$867$		0			0
$868$	182908.	+	186680.i	0.242769	+	0.247775i
$869$	−414451.			−0.548825
$870$		0			0
$871$	1.71974e6	+	992893.i	2.26687	+	1.30878i
$872$	188914.	−	327208.i	0.248445	−	0.430320i
$873$		0			0
$874$		−	591468.i		−	0.774299i
$875$	−705058.	+	181229.i	−0.920892	+	0.236707i
$876$		0			0
$877$	−121260.	−	210028.i	−0.157659	−	0.273073i	0.776365	−	0.630283i	$-0.217061\pi$
$877$	−121260.	−	210028.i	−0.157659	−	0.273073i	−0.934024	+	0.357211i	$0.883728\pi$
$878$	58204.9	+	33604.6i	0.0755042	+	0.0435923i
$879$		0			0
$880$	−50229.2	+	28999.9i	−0.0648621	+	0.0374482i
$881$		−	646528.i		−	0.832982i	−0.909140	−	0.416491i	$-0.863260\pi$
$881$		−	646528.i		−	0.832982i	0.909140	−	0.416491i	$-0.136740\pi$
$882$		0			0
$883$	−461877.			−0.592387			−0.296193	−	0.955128i	$-0.595717\pi$
$883$	−461877.			−0.592387			−0.296193	+	0.955128i	$0.595717\pi$
$884$	−206444.	−	357571.i	−0.264179	−	0.457571i
$885$		0			0
$886$	−247296.	+	428329.i	−0.315028	+	0.545645i
$887$	186391.	−	107613.i	0.236907	−	0.136778i	−0.376847	−	0.926275i	$-0.622992\pi$
$887$	186391.	−	107613.i	0.236907	−	0.136778i	0.613754	+	0.789497i	$0.289658\pi$
$888$		0			0
$889$	−29033.2	−	112952.i	−0.0367359	−	0.142919i
$890$	622034.			0.785297
$891$		0			0
$892$	422973.	+	244204.i	0.531598	+	0.306918i
$893$	−90443.9	+	156653.i	−0.113417	+	0.196443i
$894$		0			0
$895$		−	359479.i		−	0.448774i
$896$	−50685.4	+	49661.4i	−0.0631345	+	0.0618590i
$897$		0			0
$898$	275990.	+	478029.i	0.342248	+	0.592791i
$899$	427498.	+	246816.i	0.528950	+	0.305389i
$900$		0			0
$901$	−225045.	+	129930.i	−0.277217	+	0.160051i
$902$		−	510275.i		−	0.627179i
$903$		0			0
$904$	213957.			0.261812
$905$	−312067.	−	540516.i	−0.381022	−	0.659950i
$906$		0			0
$907$	−549134.	+	951128.i	−0.667519	+	1.15618i	0.311076	+	0.950385i	$0.399311\pi$
$907$	−549134.	+	951128.i	−0.667519	+	1.15618i	−0.978596	+	0.205793i	$0.934023\pi$
$908$	173161.	−	99974.7i	0.210029	−	0.121260i
$909$		0			0
$910$	−432535.	−	120641.i	−0.522322	−	0.145685i
$911$	1.32312e6			1.59427			0.797133	−	0.603803i	$-0.206349\pi$
$911$	1.32312e6			1.59427			0.797133	+	0.603803i	$0.206349\pi$
$912$		0			0
$913$	−456131.	−	263348.i	−0.547203	−	0.315928i
$914$	82692.2	−	143227.i	0.0989857	−	0.171448i
$915$		0			0
$916$		−	151431.i		−	0.180478i
$917$	148824.	+	151893.i	0.176984	+	0.180633i
$918$		0			0
$919$	−258264.	−	447326.i	−0.305797	−	0.529656i	0.671642	−	0.740876i	$-0.265589\pi$
$919$	−258264.	−	447326.i	−0.305797	−	0.529656i	−0.977438	+	0.211221i	$0.932256\pi$
$920$	−196781.	−	113612.i	−0.232492	−	0.134229i
$921$		0			0
$922$	−752588.	+	434507.i	−0.885310	+	0.511134i
$923$			80943.8i			0.0950124i
$924$		0			0
$925$	−354080.			−0.413826
$926$	−25133.7	−	43532.9i	−0.0293113	−	0.0507687i
$927$		0			0
$928$	−67013.1	+	116070.i	−0.0778151	+	0.134780i
$929$	−1.07335e6	+	619697.i	−1.24368	+	0.718039i	−0.969841	−	0.243737i	$-0.921627\pi$
$929$	−1.07335e6	+	619697.i	−1.24368	+	0.718039i	−0.273838	+	0.961776i	$0.588293\pi$
$930$		0			0
$931$	366265.	−	605506.i	0.422568	−	0.698585i
$932$	−53477.9			−0.0615662
$933$		0			0
$934$	−159131.	−	91874.5i	−0.182415	−	0.105318i
$935$	102159.	−	176944.i	0.116856	−	0.202401i
$936$		0			0
$937$		−	1.15260e6i		−	1.31281i	−0.754411	−	0.656403i	$-0.772077\pi$
$937$		−	1.15260e6i		−	1.31281i	0.754411	−	0.656403i	$-0.227923\pi$
$938$	299296.	+	1.16439e6i	0.340170	+	1.32340i
$939$		0			0
$940$	34745.7	+	60181.3i	0.0393228	+	0.0681092i
$941$	−93104.2	−	53753.7i	−0.105145	−	0.0607057i	0.446505	−	0.894781i	$-0.352668\pi$
$941$	−93104.2	−	53753.7i	−0.105145	−	0.0607057i	−0.551650	+	0.834075i	$0.686002\pi$
$942$		0			0
$943$	1.73126e6	−	999543.i	1.94688	−	1.12403i
$944$		−	223526.i		−	0.250832i
$945$		0			0
$946$	555334.			0.620543
$947$	−206307.	−	357335.i	−0.230046	−	0.398451i	0.727775	−	0.685815i	$-0.240554\pi$
$947$	−206307.	−	357335.i	−0.230046	−	0.398451i	−0.957821	+	0.287364i	$0.907221\pi$
$948$		0			0
$949$	−465845.	+	806867.i	−0.517260	+	0.895920i
$950$	306597.	−	177014.i	0.339720	−	0.196137i
$951$		0			0
$952$	67158.0	−	240781.i	0.0741010	−	0.265674i
$953$	−1.43052e6			−1.57510			−0.787550	−	0.616251i	$-0.788651\pi$
$953$	−1.43052e6			−1.57510			−0.787550	+	0.616251i	$0.788651\pi$
$954$		0			0
$955$	−791324.	−	456871.i	−0.867656	−	0.500942i
$956$	−385844.	+	668301.i	−0.422178	+	0.731234i
$957$		0			0
$958$		−	596619.i		−	0.650079i
$959$	−1.45179e6	−	404928.i	−1.57858	−	0.440292i
$960$		0			0
$961$	−239507.	−	414839.i	−0.259342	−	0.449193i
$962$	−467521.	−	269923.i	−0.505186	−	0.291669i
$963$		0			0
$964$	−378974.	+	218801.i	−0.407808	+	0.235448i
$965$			519077.i			0.557413i
$966$		0			0
$967$	−344533.			−0.368449			−0.184225	−	0.982884i	$-0.558977\pi$
$967$	−344533.			−0.368449			−0.184225	+	0.982884i	$0.558977\pi$
$968$	−119260.	−	206565.i	−0.127276	−	0.220448i
$969$		0			0
$970$	31197.4	−	54035.5i	0.0331570	−	0.0574296i
$971$	1.25848e6	−	726581.i	1.33477	−	0.770630i	0.348744	−	0.937218i	$-0.386608\pi$
$971$	1.25848e6	−	726581.i	1.33477	−	0.770630i	0.986027	+	0.166588i	$0.0532751\pi$
$972$		0			0
$973$	1.29020e6	−	331636.i	1.36280	−	0.350296i
$974$	647393.			0.682417
$975$		0			0
$976$	−125939.	−	72710.8i	−0.132209	−	0.0763307i
$977$	772853.	−	1.33862e6i	0.809669	−	1.40239i	−0.103424	−	0.994637i	$-0.532980\pi$
$977$	772853.	−	1.33862e6i	0.809669	−	1.40239i	0.913093	−	0.407751i	$-0.133687\pi$
$978$		0			0
$979$		−	994907.i		−	1.03805i
$980$	−131098.	−	238164.i	−0.136503	−	0.247985i
$981$		0			0
$982$	−198485.	−	343786.i	−0.205828	−	0.356504i
$983$	−116280.	−	67134.0i	−0.120336	−	0.0694761i	0.438624	−	0.898671i	$-0.355466\pi$
$983$	−116280.	−	67134.0i	−0.120336	−	0.0694761i	−0.558960	+	0.829195i	$0.688799\pi$
$984$		0			0
$985$	896589.	−	517646.i	0.924105	−	0.533532i
$986$		−	472139.i		−	0.485641i
$987$		0			0
$988$	539768.			0.552959
$989$	1.08781e6	+	1.88414e6i	1.11214	+	1.92628i
$990$		0			0
$991$	395596.	−	685192.i	0.402814	−	0.697694i	−0.591251	−	0.806488i	$-0.701366\pi$
$991$	395596.	−	685192.i	0.402814	−	0.697694i	0.994064	+	0.108794i	$0.0346990\pi$
$992$	−104519.	+	60344.0i	−0.106211	+	0.0613212i
$993$		0			0
$994$	−35003.8	+	34296.5i	−0.0354276	+	0.0347118i
$995$	−19829.5			−0.0200293
$996$		0			0
$997$	582624.	+	336378.i	0.586136	+	0.338406i	0.763568	−	0.645727i	$-0.223446\pi$
$997$	582624.	+	336378.i	0.586136	+	0.338406i	−0.177432	+	0.984133i	$0.556779\pi$
$998$	−488366.	+	845874.i	−0.490325	+	0.849268i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.5.n.b.73.2		4
3.2	odd	2		42.5.g.a.31.1	yes	4
7.3	odd	6		882.5.c.a.685.1		4
7.4	even	3		882.5.c.a.685.2		4
7.5	odd	6	inner	126.5.n.b.19.2		4
12.11	even	2		336.5.bh.d.241.2		4
21.2	odd	6		294.5.g.c.19.1		4
21.5	even	6		42.5.g.a.19.1	✓	4
21.11	odd	6		294.5.c.a.97.4		4
21.17	even	6		294.5.c.a.97.3		4
21.20	even	2		294.5.g.c.31.1		4
84.47	odd	6		336.5.bh.d.145.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.5.g.a.19.1	✓	4	21.5	even	6
42.5.g.a.31.1	yes	4	3.2	odd	2
126.5.n.b.19.2		4	7.5	odd	6	inner
126.5.n.b.73.2		4	1.1	even	1	trivial
294.5.c.a.97.3		4	21.17	even	6
294.5.c.a.97.4		4	21.11	odd	6
294.5.g.c.19.1		4	21.2	odd	6
294.5.g.c.31.1		4	21.20	even	2
336.5.bh.d.145.2		4	84.47	odd	6
336.5.bh.d.241.2		4	12.11	even	2
882.5.c.a.685.1		4	7.3	odd	6
882.5.c.a.685.2		4	7.4	even	3

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	126.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41421 + 2.44949i) q^{2} +(-4.00000 + 6.92820i) q^{4} +(12.2574 - 7.07679i) q^{5} +(12.1985 + 47.4573i) q^{7} -22.6274 q^{8} +(34.6690 + 20.0162i) q^{10} +(32.0147 - 55.4511i) q^{11} +228.919i q^{13} +(-98.9949 + 96.9948i) q^{14} +(-32.0000 - 55.4256i) q^{16} +(195.250 + 112.728i) q^{17} +(-255.250 + 147.369i) q^{19} +113.229i q^{20} +181.103 q^{22} +(354.749 + 614.444i) q^{23} +(-212.338 + 367.780i) q^{25} +(-560.735 + 323.741i) q^{26} +(-377.588 - 105.316i) q^{28} -740.397 q^{29} +(-577.390 - 333.356i) q^{31} +(90.5097 - 156.767i) q^{32} +637.683i q^{34} +(485.367 + 495.375i) q^{35} +(416.882 + 722.061i) q^{37} +(-721.955 - 416.821i) q^{38} +(-277.352 + 160.129i) q^{40} -2817.60i q^{41} +3066.41 q^{43} +(256.118 + 443.609i) q^{44} +(-1003.38 + 1737.91i) q^{46} +(531.502 - 306.863i) q^{47} +(-2103.39 + 1157.81i) q^{49} -1201.17 q^{50} +(-1586.00 - 915.677i) q^{52} +(-576.300 + 998.181i) q^{53} -906.246i q^{55} +(-276.020 - 1073.84i) q^{56} +(-1047.08 - 1813.59i) q^{58} +(3024.67 + 1746.30i) q^{59} +(1967.79 - 1136.11i) q^{61} -1885.75i q^{62} +512.000 q^{64} +(1620.01 + 2805.94i) q^{65} +(4337.31 - 7512.44i) q^{67} +(-1562.00 + 901.820i) q^{68} +(-527.005 + 1889.47i) q^{70} +353.591 q^{71} +(3524.68 + 2034.97i) q^{73} +(-1179.12 + 2042.30i) q^{74} -2357.90i q^{76} +(3022.09 + 842.913i) q^{77} +(-3236.41 - 5605.63i) q^{79} +(-784.471 - 452.915i) q^{80} +(6901.69 - 3984.69i) q^{82} -8225.83i q^{83} +3191.00 q^{85} +(4336.55 + 7511.13i) q^{86} +(-724.410 + 1254.72i) q^{88} +(13456.5 - 7769.13i) q^{89} +(-10863.9 + 2792.47i) q^{91} -5675.99 q^{92} +(1503.32 + 867.939i) q^{94} +(-2085.79 + 3612.70i) q^{95} -1558.61i q^{97} +(-5810.70 - 3514.84i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{4} + 66 q^{5} - 70 q^{7} - 48 q^{10} + 162 q^{11} - 128 q^{16} + 204 q^{17} - 444 q^{19} - 192 q^{22} - 312 q^{23} - 476 q^{25} - 1632 q^{26} - 560 q^{28} - 2724 q^{29} - 3786 q^{31} - 672 q^{35}+ \cdots - 23520 q^{98}+O(q^{100}) \) 4 * q - 16 * q^4 + 66 * q^5 - 70 * q^7 - 48 * q^10 + 162 * q^11 - 128 * q^16 + 204 * q^17 - 444 * q^19 - 192 * q^22 - 312 * q^23 - 476 * q^25 - 1632 * q^26 - 560 * q^28 - 2724 * q^29 - 3786 * q^31 - 672 * q^35 + 1396 * q^37 - 1632 * q^38 + 384 * q^40 - 632 * q^43 + 1296 * q^44 - 4896 * q^46 + 7896 * q^47 - 98 * q^49 - 2112 * q^50 - 1728 * q^52 + 1038 * q^53 - 2688 * q^56 - 336 * q^58 + 966 * q^59 + 5088 * q^61 + 2048 * q^64 + 744 * q^65 + 14600 * q^67 - 1632 * q^68 + 5376 * q^70 + 9696 * q^71 + 22584 * q^73 - 768 * q^74 + 3654 * q^77 + 3974 * q^79 - 4224 * q^80 + 18816 * q^82 + 1224 * q^85 + 18240 * q^86 + 768 * q^88 + 33156 * q^89 - 18984 * q^91 + 4992 * q^92 - 16320 * q^94 - 3252 * q^95 - 23520 * q^98

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