LMFDB - Embedded newform 336.5.bh.d.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,5,Mod(145,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 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("336.145");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	336.bh (of order $6$, degree $2$, 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:	$34.7323075962$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.2
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	336.145
Dual form			336.5.bh.d.241.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.50000 - 2.59808i) q^{3} +(-12.2574 - 7.07679i) q^{5} +(-12.1985 + 47.4573i) q^{7} +(13.5000 - 23.3827i) q^{9} +O(q^{10})$	\(q+(4.50000 - 2.59808i) q^{3} +(-12.2574 - 7.07679i) q^{5} +(-12.1985 + 47.4573i) q^{7} +(13.5000 - 23.3827i) q^{9} +(32.0147 + 55.4511i) q^{11} -228.919i q^{13} -73.5442 q^{15} +(-195.250 + 112.728i) q^{17} +(255.250 + 147.369i) q^{19} +(68.4045 + 245.251i) q^{21} +(354.749 - 614.444i) q^{23} +(-212.338 - 367.780i) q^{25} -140.296i q^{27} +740.397 q^{29} +(577.390 - 333.356i) q^{31} +(288.132 + 166.353i) q^{33} +(485.367 - 495.375i) q^{35} +(416.882 - 722.061i) q^{37} +(-594.749 - 1030.14i) q^{39} -2817.60i q^{41} -3066.41 q^{43} +(-330.949 + 191.073i) q^{45} +(531.502 + 306.863i) q^{47} +(-2103.39 - 1157.81i) q^{49} +(-585.749 + 1014.55i) q^{51} +(576.300 + 998.181i) q^{53} -906.246i q^{55} +1531.50 q^{57} +(3024.67 - 1746.30i) q^{59} +(1967.79 + 1136.11i) q^{61} +(945.000 + 925.907i) q^{63} +(-1620.01 + 2805.94i) q^{65} +(-4337.31 - 7512.44i) q^{67} -3686.66i q^{69} +353.591 q^{71} +(3524.68 - 2034.97i) q^{73} +(-1911.04 - 1103.34i) q^{75} +(-3022.09 + 842.913i) q^{77} +(3236.41 - 5605.63i) q^{79} +(-364.500 - 631.333i) q^{81} +8225.83i q^{83} +3191.00 q^{85} +(3331.79 - 1923.61i) q^{87} +(-13456.5 - 7769.13i) q^{89} +(10863.9 + 2792.47i) q^{91} +(1732.17 - 3000.21i) q^{93} +(-2085.79 - 3612.70i) q^{95} +1558.61i q^{97} +1728.79 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 18 q^{3} - 66 q^{5} + 70 q^{7} + 54 q^{9}+O(q^{10}) $ 4 * q + 18 * q^3 - 66 * q^5 + 70 * q^7 + 54 * q^9	$ 4 q + 18 q^{3} - 66 q^{5} + 70 q^{7} + 54 q^{9} + 162 q^{11} - 396 q^{15} - 204 q^{17} + 444 q^{19} + 630 q^{21} - 312 q^{23} - 476 q^{25} + 2724 q^{29} + 3786 q^{31} + 1458 q^{33} - 672 q^{35} + 1396 q^{37} - 648 q^{39} + 632 q^{43} - 1782 q^{45} + 7896 q^{47} - 98 q^{49} - 612 q^{51} - 1038 q^{53} + 2664 q^{57} + 966 q^{59} + 5088 q^{61} + 3780 q^{63} - 744 q^{65} - 14600 q^{67} + 9696 q^{71} + 22584 q^{73} - 4284 q^{75} - 3654 q^{77} - 3974 q^{79} - 1458 q^{81} + 1224 q^{85} + 12258 q^{87} - 33156 q^{89} + 18984 q^{91} + 11358 q^{93} - 3252 q^{95} + 8748 q^{99}+O(q^{100}) $ 4 * q + 18 * q^3 - 66 * q^5 + 70 * q^7 + 54 * q^9 + 162 * q^11 - 396 * q^15 - 204 * q^17 + 444 * q^19 + 630 * q^21 - 312 * q^23 - 476 * q^25 + 2724 * q^29 + 3786 * q^31 + 1458 * q^33 - 672 * q^35 + 1396 * q^37 - 648 * q^39 + 632 * q^43 - 1782 * q^45 + 7896 * q^47 - 98 * q^49 - 612 * q^51 - 1038 * q^53 + 2664 * q^57 + 966 * q^59 + 5088 * q^61 + 3780 * q^63 - 744 * q^65 - 14600 * q^67 + 9696 * q^71 + 22584 * q^73 - 4284 * q^75 - 3654 * q^77 - 3974 * q^79 - 1458 * q^81 + 1224 * q^85 + 12258 * q^87 - 33156 * q^89 + 18984 * q^91 + 11358 * q^93 - 3252 * q^95 + 8748 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	4.50000	−	2.59808i	0.500000	−	0.288675i
$3$	4.50000	−	2.59808i	0.500000	−	0.288675i
$4$		0			0
$5$	−12.2574	−	7.07679i	−0.490294	−	0.283072i	0.234402	−	0.972140i	$-0.424687\pi$
$5$	−12.2574	−	7.07679i	−0.490294	−	0.283072i	−0.724697	+	0.689068i	$0.758020\pi$
$6$		0			0
$7$	−12.1985	+	47.4573i	−0.248949	+	0.968517i
$7$	−12.1985	+	47.4573i	−0.248949	+	0.968517i
$8$		0			0
$9$	13.5000	−	23.3827i	0.166667	−	0.288675i
$10$		0			0
$11$	32.0147	+	55.4511i	0.264584	+	0.458274i	0.967455	−	0.253044i	$-0.0814319\pi$
$11$	32.0147	+	55.4511i	0.264584	+	0.458274i	−0.702870	+	0.711318i	$0.748099\pi$
$12$		0			0
$13$		−	228.919i		−	1.35455i	−0.735729	−	0.677276i	$-0.763161\pi$
$13$		−	228.919i		−	1.35455i	0.735729	−	0.677276i	$-0.236839\pi$
$14$		0			0
$15$	−73.5442			−0.326863
$16$		0			0
$17$	−195.250	+	112.728i	−0.675605	+	0.390061i	−0.798197	−	0.602397i	$-0.794213\pi$
$17$	−195.250	+	112.728i	−0.675605	+	0.390061i	0.122592	+	0.992457i	$0.460879\pi$
$18$		0			0
$19$	255.250	+	147.369i	0.707063	+	0.408223i	0.809973	−	0.586468i	$-0.199482\pi$
$19$	255.250	+	147.369i	0.707063	+	0.408223i	−0.102910	+	0.994691i	$0.532815\pi$
$20$		0			0
$21$	68.4045	+	245.251i	0.155112	+	0.556124i
$22$		0			0
$23$	354.749	−	614.444i	0.670604	−	1.16152i	−0.307129	−	0.951668i	$-0.599368\pi$
$23$	354.749	−	614.444i	0.670604	−	1.16152i	0.977733	−	0.209852i	$-0.0672982\pi$
$24$		0			0
$25$	−212.338	−	367.780i	−0.339741	−	0.588449i
$26$		0			0
$27$		−	140.296i		−	0.192450i
$28$		0			0
$29$	740.397			0.880377			0.440188	−	0.897905i	$-0.354912\pi$
$29$	740.397			0.880377			0.440188	+	0.897905i	$0.354912\pi$
$30$		0			0
$31$	577.390	−	333.356i	0.600822	−	0.346885i	−0.168543	−	0.985694i	$-0.553906\pi$
$31$	577.390	−	333.356i	0.600822	−	0.346885i	0.769365	+	0.638809i	$0.220573\pi$
$32$		0			0
$33$	288.132	+	166.353i	0.264584	+	0.152758i
$34$		0			0
$35$	485.367	−	495.375i	0.396218	−	0.404388i
$36$		0			0
$37$	416.882	−	722.061i	0.304516	−	0.527437i	−0.672638	−	0.739972i	$-0.734839\pi$
$37$	416.882	−	722.061i	0.304516	−	0.527437i	0.977153	+	0.212535i	$0.0681720\pi$
$38$		0			0
$39$	−594.749	−	1030.14i	−0.391025	−	0.677276i
$40$		0			0
$41$		−	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	$-0.811207\pi$
$43$	−3066.41			−1.65841			−0.829207	+	0.558942i	$0.811207\pi$
$44$		0			0
$45$	−330.949	+	191.073i	−0.163431	+	0.0943572i
$46$		0			0
$47$	531.502	+	306.863i	0.240608	+	0.138915i	0.615456	−	0.788171i	$-0.288972\pi$
$47$	531.502	+	306.863i	0.240608	+	0.138915i	−0.374848	+	0.927086i	$0.622305\pi$
$48$		0			0
$49$	−2103.39	−	1157.81i	−0.876049	−	0.482222i
$50$		0			0
$51$	−585.749	+	1014.55i	−0.225202	+	0.390061i
$52$		0			0
$53$	576.300	+	998.181i	0.205162	+	0.355351i	0.950184	−	0.311688i	$-0.100895\pi$
$53$	576.300	+	998.181i	0.205162	+	0.355351i	−0.745022	+	0.667040i	$0.767561\pi$
$54$		0			0
$55$		−	906.246i		−	0.299585i
$56$		0			0
$57$	1531.50			0.471375
$58$		0			0
$59$	3024.67	−	1746.30i	0.868909	−	0.501665i	0.00192348	−	0.999998i	$-0.499388\pi$
$59$	3024.67	−	1746.30i	0.868909	−	0.501665i	0.866986	+	0.498333i	$0.166054\pi$
$60$		0			0
$61$	1967.79	+	1136.11i	0.528834	+	0.305323i	0.740542	−	0.672010i	$-0.234569\pi$
$61$	1967.79	+	1136.11i	0.528834	+	0.305323i	−0.211707	+	0.977333i	$0.567902\pi$
$62$		0			0
$63$	945.000	+	925.907i	0.238095	+	0.233285i
$64$		0			0
$65$	−1620.01	+	2805.94i	−0.383435	+	0.664129i
$66$		0			0
$67$	−4337.31	−	7512.44i	−0.966208	−	1.67352i	−0.706334	−	0.707879i	$-0.749652\pi$
$67$	−4337.31	−	7512.44i	−0.966208	−	1.67352i	−0.259874	−	0.965642i	$-0.583681\pi$
$68$		0			0
$69$		−	3686.66i		−	0.774346i
$70$		0			0
$71$	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	−0.131401	−	0.991329i	$-0.541948\pi$
$73$	3524.68	−	2034.97i	0.661415	−	0.381868i	0.792816	+	0.609461i	$0.208614\pi$
$74$		0			0
$75$	−1911.04	−	1103.34i	−0.339741	−	0.196150i
$76$		0			0
$77$	−3022.09	+	842.913i	−0.509714	+	0.142168i
$78$		0			0
$79$	3236.41	−	5605.63i	0.518573	−	0.898194i	−0.481194	−	0.876614i	$-0.659797\pi$
$79$	3236.41	−	5605.63i	0.518573	−	0.898194i	0.999767	−	0.0215805i	$-0.00686981\pi$
$80$		0			0
$81$	−364.500	−	631.333i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			8225.83i			1.19405i	0.802222	+	0.597026i	$0.203651\pi$
$83$			8225.83i			1.19405i	−0.802222	+	0.597026i	$0.796349\pi$
$84$		0			0
$85$	3191.00			0.441660
$86$		0			0
$87$	3331.79	−	1923.61i	0.440188	−	0.254143i
$88$		0			0
$89$	−13456.5	−	7769.13i	−1.69884	−	0.980828i	−0.946860	−	0.321645i	$-0.895764\pi$
$89$	−13456.5	−	7769.13i	−1.69884	−	0.980828i	−0.751983	−	0.659183i	$-0.770902\pi$
$90$		0			0
$91$	10863.9	+	2792.47i	1.31191	+	0.337214i
$92$		0			0
$93$	1732.17	−	3000.21i	0.200274	−	0.346885i
$94$		0			0
$95$	−2085.79	−	3612.70i	−0.231113	−	0.400299i
$96$		0			0
$97$			1558.61i			0.165651i	0.996564	+	0.0828254i	$0.0263944\pi$
$97$			1558.61i			0.165651i	−0.996564	+	0.0828254i	$0.973606\pi$
$98$		0			0
$99$	1728.79			0.176390
$100$		0			0
$101$	13627.2	−	7867.66i	1.33587	−	0.771264i	0.349676	−	0.936871i	$-0.386292\pi$
$101$	13627.2	−	7867.66i	1.33587	−	0.771264i	0.986192	+	0.165607i	$0.0529583\pi$
$102$		0			0
$103$	−29.2099	−	16.8644i	−0.00275332	−	0.00158963i	0.498623	−	0.866819i	$-0.333839\pi$
$103$	−29.2099	−	16.8644i	−0.00275332	−	0.00158963i	−0.501376	+	0.865229i	$0.667173\pi$
$104$		0			0
$105$	897.127	−	3490.21i	0.0813721	−	0.316572i
$106$		0			0
$107$	−2723.23	+	4716.78i	−0.237858	+	0.411981i	−0.960099	−	0.279659i	$-0.909778\pi$
$107$	−2723.23	+	4716.78i	−0.237858	+	0.411981i	0.722242	+	0.691641i	$0.243112\pi$
$108$		0			0
$109$	−8348.89	−	14460.7i	−0.702709	−	1.21713i	−0.967512	−	0.252825i	$-0.918640\pi$
$109$	−8348.89	−	14460.7i	−0.702709	−	1.21713i	0.264803	−	0.964303i	$-0.414693\pi$
$110$		0			0
$111$		−	4332.37i		−	0.351625i
$112$		0			0
$113$	9455.64			0.740515			0.370258	−	0.928929i	$-0.379269\pi$
$113$	9455.64			0.740515			0.370258	+	0.928929i	$0.379269\pi$
$114$		0			0
$115$	−8696.58	+	5020.97i	−0.657586	+	0.379658i
$116$		0			0
$117$	−5352.74	−	3090.41i	−0.391025	−	0.225759i
$118$		0			0
$119$	−2967.99	−	10641.1i	−0.209589	−	0.751440i
$120$		0			0
$121$	5270.62	−	9128.97i	0.359990	−	0.623521i
$122$		0			0
$123$	−7320.35	−	12679.2i	−0.483862	−	0.838073i
$124$		0			0
$125$			14856.7i			0.950827i
$126$		0			0
$127$	2380.07			0.147564			0.0737822	−	0.997274i	$-0.476493\pi$
$127$	2380.07			0.147564			0.0737822	+	0.997274i	$0.476493\pi$
$128$		0			0
$129$	−13798.8	+	7966.76i	−0.829207	+	0.478743i
$130$		0			0
$131$	3758.37	+	2169.90i	0.219006	+	0.126443i	0.605490	−	0.795853i	$-0.292977\pi$
$131$	3758.37	+	2169.90i	0.219006	+	0.126443i	−0.386484	+	0.922296i	$0.626310\pi$
$132$		0			0
$133$	−10107.4	+	10315.8i	−0.571393	+	0.583176i
$134$		0			0
$135$	−992.846	+	1719.66i	−0.0544772	+	0.0943572i
$136$		0			0
$137$	15379.6	+	26638.2i	0.819414	+	1.41927i	0.906114	+	0.423033i	$0.139034\pi$
$137$	15379.6	+	26638.2i	0.819414	+	1.41927i	−0.0867001	+	0.996234i	$0.527632\pi$
$138$		0			0
$139$		−	27186.6i		−	1.40710i	−0.710644	−	0.703551i	$-0.751596\pi$
$139$		−	27186.6i		−	1.40710i	0.710644	−	0.703551i	$-0.248404\pi$
$140$		0			0
$141$	3189.01			0.160405
$142$		0			0
$143$	12693.8	−	7328.78i	0.620755	−	0.358393i
$144$		0			0
$145$	−9075.31	−	5239.63i	−0.431644	−	0.249210i
$146$		0			0
$147$	−12473.4	+	254.611i	−0.577230	+	0.0117827i
$148$		0			0
$149$	2913.46	−	5046.26i	0.131231	−	0.227299i	−0.792920	−	0.609325i	$-0.791440\pi$
$149$	2913.46	−	5046.26i	0.131231	−	0.227299i	0.924151	+	0.382027i	$0.124774\pi$
$150$		0			0
$151$	12593.4	+	21812.4i	0.552317	+	0.956642i	0.998107	+	0.0615039i	$0.0195897\pi$
$151$	12593.4	+	21812.4i	0.552317	+	0.956642i	−0.445789	+	0.895138i	$0.647077\pi$
$152$		0			0
$153$			6087.29i			0.260040i
$154$		0			0
$155$	−9436.37			−0.392773
$156$		0			0
$157$	20694.6	−	11948.0i	0.839571	−	0.484726i	−0.0175475	−	0.999846i	$-0.505586\pi$
$157$	20694.6	−	11948.0i	0.839571	−	0.484726i	0.857118	+	0.515120i	$0.172253\pi$
$158$		0			0
$159$	5186.70	+	2994.54i	0.205162	+	0.118450i
$160$		0			0
$161$	24832.5	+	24330.7i	0.958005	+	0.938650i
$162$		0			0
$163$	−21293.0	+	36880.5i	−0.801422	+	1.38810i	0.117259	+	0.993101i	$0.462589\pi$
$163$	−21293.0	+	36880.5i	−0.801422	+	1.38810i	−0.918680	+	0.395001i	$0.870744\pi$
$164$		0			0
$165$	−2354.50	−	4078.11i	−0.0864828	−	0.149793i
$166$		0			0
$167$			26356.3i			0.945043i	0.881319	+	0.472521i	$0.156656\pi$
$167$			26356.3i			0.945043i	−0.881319	+	0.472521i	$0.843344\pi$
$168$		0			0
$169$	−23843.0			−0.834809
$170$		0			0
$171$	6891.74	−	3978.95i	0.235688	−	0.136074i
$172$		0			0
$173$	24265.3	+	14009.6i	0.810763	+	0.468094i	0.847221	−	0.531241i	$-0.178274\pi$
$173$	24265.3	+	14009.6i	0.810763	+	0.468094i	−0.0364578	+	0.999335i	$0.511607\pi$
$174$		0			0
$175$	20044.1	−	5590.63i	0.654500	−	0.182551i
$176$		0			0
$177$	9074.02	−	15716.7i	0.289636	−	0.501665i
$178$		0			0
$179$	12699.2	+	21995.7i	0.396343	+	0.686487i	0.993272	−	0.115808i	$-0.0369457\pi$
$179$	12699.2	+	21995.7i	0.396343	+	0.686487i	−0.596928	+	0.802295i	$0.703612\pi$
$180$		0			0
$181$			44097.2i			1.34603i	0.739630	+	0.673014i	$0.235001\pi$
$181$			44097.2i			1.34603i	−0.739630	+	0.673014i	$0.764999\pi$
$182$		0			0
$183$	11806.8			0.352556
$184$		0			0
$185$	−10219.8	+	5900.38i	−0.298605	+	0.172400i
$186$		0			0
$187$	−12501.7	−	7217.88i	−0.357509	−	0.206408i
$188$		0			0
$189$	6658.08	+	1711.40i	0.186391	+	0.0479102i
$190$		0			0
$191$	−32279.6	+	55909.8i	−0.884832	+	1.53257i	−0.0389256	+	0.999242i	$0.512394\pi$
$191$	−32279.6	+	55909.8i	−0.884832	+	1.53257i	−0.845906	+	0.533332i	$0.820940\pi$
$192$		0			0
$193$	−18337.3	−	31761.1i	−0.492290	−	0.852670i	0.507671	−	0.861551i	$-0.330507\pi$
$193$	−18337.3	−	31761.1i	−0.492290	−	0.852670i	−0.999961	+	0.00888055i	$0.997173\pi$
$194$		0			0
$195$			16835.7i			0.442753i
$196$		0			0
$197$	−73147.0			−1.88480			−0.942398	−	0.334494i	$-0.891434\pi$
$197$	−73147.0			−1.88480			−0.942398	+	0.334494i	$0.891434\pi$
$198$		0			0
$199$	1213.33	−	700.514i	0.0306387	−	0.0176893i	−0.484602	−	0.874735i	$-0.661036\pi$
$199$	1213.33	−	700.514i	0.0306387	−	0.0176893i	0.515241	+	0.857045i	$0.327702\pi$
$200$		0			0
$201$	−39035.8	−	22537.3i	−0.966208	−	0.557840i
$202$		0			0
$203$	−9031.72	+	35137.3i	−0.219169	+	0.852660i
$204$		0			0
$205$	−19939.6	+	34536.4i	−0.474469	+	0.821805i
$206$		0			0
$207$	−9578.23	−	16590.0i	−0.223535	−	0.387173i
$208$		0			0
$209$			18871.8i			0.432038i
$210$		0			0
$211$	−58231.7			−1.30796			−0.653980	−	0.756512i	$-0.726902\pi$
$211$	−58231.7			−1.30796			−0.653980	+	0.756512i	$0.726902\pi$
$212$		0			0
$213$	1591.16	−	918.657i	0.0350715	−	0.0202486i
$214$		0			0
$215$	37586.1	+	21700.3i	0.813111	+	0.469450i
$216$		0			0
$217$	8776.92	+	31467.8i	0.186390	+	0.668263i
$218$		0			0
$219$	10574.0	−	18314.8i	0.220472	−	0.381868i
$220$		0			0
$221$	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	$-0.210374\pi$
$224$		0			0
$225$	−11466.3			−0.226494
$226$		0			0
$227$	−21645.2	+	12496.8i	−0.420058	+	0.242520i	−0.695102	−	0.718911i	$-0.744641\pi$
$227$	−21645.2	+	12496.8i	−0.420058	+	0.242520i	0.275044	+	0.961432i	$0.411307\pi$
$228$		0			0
$229$	−16392.9	−	9464.44i	−0.312597	−	0.180478i	0.335491	−	0.942043i	$-0.391098\pi$
$229$	−16392.9	−	9464.44i	−0.312597	−	0.180478i	−0.648088	+	0.761565i	$0.724431\pi$
$230$		0			0
$231$	−11409.5	+	11644.7i	−0.213817	+	0.218226i
$232$		0			0
$233$	−3342.37	+	5789.15i	−0.0615662	+	0.106636i	−0.895166	−	0.445734i	$-0.852943\pi$
$233$	−3342.37	+	5789.15i	−0.0615662	+	0.106636i	0.833599	+	0.552369i	$0.186276\pi$
$234$		0			0
$235$	−4343.21	−	7522.66i	−0.0786457	−	0.136218i
$236$		0			0
$237$		−	33633.8i		−	0.598796i
$238$		0			0
$239$	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	−0.0332863	−	0.999446i	$-0.510597\pi$
$241$	47371.8	−	27350.1i	0.815616	−	0.470896i	0.848902	+	0.528550i	$0.177264\pi$
$242$		0			0
$243$	−3280.50	−	1894.00i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	17588.4	+	29077.0i	0.293019	+	0.484415i
$246$		0			0
$247$	33735.5	−	58431.6i	0.552959	−	0.957753i
$248$		0			0
$249$	21371.3	+	37016.2i	0.344693	+	0.597026i
$250$		0			0
$251$			108137.i			1.71643i	0.513286	+	0.858217i	$0.328428\pi$
$251$			108137.i			1.71643i	−0.513286	+	0.858217i	$0.671572\pi$
$252$		0			0
$253$	45428.8			0.709725
$254$		0			0
$255$	14359.5	−	8290.45i	0.220830	−	0.127496i
$256$		0			0
$257$	31078.3	+	17943.0i	0.470533	+	0.271663i	0.716463	−	0.697625i	$-0.245760\pi$
$257$	31078.3	+	17943.0i	0.470533	+	0.271663i	−0.245930	+	0.969288i	$0.579093\pi$
$258$		0			0
$259$	29181.8	+	28592.2i	0.435023	+	0.426233i
$260$		0			0
$261$	9995.36	−	17312.5i	0.146729	−	0.254143i
$262$		0			0
$263$	−32715.8	−	56665.4i	−0.472984	−	0.819232i	0.526538	−	0.850151i	$-0.323490\pi$
$263$	−32715.8	−	56665.4i	−0.472984	−	0.819232i	−0.999522	+	0.0309199i	$0.990156\pi$
$264$		0			0
$265$		−	16313.4i		−	0.232302i
$266$		0			0
$267$	−80739.2			−1.13256
$268$		0			0
$269$	−59938.7	+	34605.6i	−0.828329	+	0.478236i	−0.853280	−	0.521453i	$-0.825390\pi$
$269$	−59938.7	+	34605.6i	−0.828329	+	0.478236i	0.0249511	+	0.999689i	$0.492057\pi$
$270$		0			0
$271$	−5672.94	−	3275.27i	−0.0772449	−	0.0445973i	0.460880	−	0.887462i	$-0.347534\pi$
$271$	−5672.94	−	3275.27i	−0.0772449	−	0.0445973i	−0.538125	+	0.842865i	$0.680867\pi$
$272$		0			0
$273$	56142.5	−	15659.1i	0.753298	−	0.210108i
$274$		0			0
$275$	13595.9	−	23548.8i	0.179780	−	0.311389i
$276$		0			0
$277$	−39551.6	−	68505.4i	−0.515471	−	0.892823i	−0.999839	−	0.0179578i	$-0.994284\pi$
$277$	−39551.6	−	68505.4i	−0.515471	−	0.892823i	0.484367	−	0.874865i	$-0.339050\pi$
$278$		0			0
$279$		−	18001.2i		−	0.231257i
$280$		0			0
$281$	34363.1			0.435191			0.217596	−	0.976039i	$-0.430179\pi$
$281$	34363.1			0.435191			0.217596	+	0.976039i	$0.430179\pi$
$282$		0			0
$283$	−79598.4	+	45956.1i	−0.993874	+	0.573813i	−0.906430	−	0.422356i	$-0.861203\pi$
$283$	−79598.4	+	45956.1i	−0.993874	+	0.573813i	−0.0874439	+	0.996169i	$0.527870\pi$
$284$		0			0
$285$	−18772.1	−	10838.1i	−0.231113	−	0.133433i
$286$		0			0
$287$	133716.	+	34370.5i	1.62338	+	0.417274i
$288$		0			0
$289$	−16345.5	+	28311.3i	−0.195705	+	0.338972i
$290$		0			0
$291$	4049.38	+	7013.74i	0.0478193	+	0.0828254i
$292$		0			0
$293$			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
$296$		0			0
$297$	7779.58	−	4491.54i	0.0881948	−	0.0509193i
$298$		0			0
$299$	−140658.	−	81208.9i	−1.57334	−	0.908367i
$300$		0			0
$301$	37405.5	−	145523.i	0.412860	−	1.60620i
$302$		0			0
$303$	40881.6	−	70808.9i	0.445289	−	0.771264i
$304$		0			0
$305$	−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	$0.885439\pi$
$308$		0			0
$309$	−175.260			−0.00183555
$310$		0			0
$311$	82879.0	−	47850.2i	0.856888	−	0.494724i	−0.00608108	−	0.999982i	$-0.501936\pi$
$311$	82879.0	−	47850.2i	0.856888	−	0.494724i	0.862969	+	0.505257i	$0.168602\pi$
$312$		0			0
$313$	41486.1	+	23952.0i	0.423461	+	0.244486i	0.696557	−	0.717501i	$-0.254714\pi$
$313$	41486.1	+	23952.0i	0.423461	+	0.244486i	−0.273096	+	0.961987i	$0.588048\pi$
$314$		0			0
$315$	−5030.75	−	18036.7i	−0.0507005	−	0.181776i
$316$		0			0
$317$	17064.1	−	29555.9i	0.169811	−	0.294121i	−0.768543	−	0.639799i	$-0.779018\pi$
$317$	17064.1	−	29555.9i	0.169811	−	0.294121i	0.938353	+	0.345678i	$0.112351\pi$
$318$		0			0
$319$	23703.6	+	41055.8i	0.232934	+	0.403454i
$320$		0			0
$321$			28300.7i			0.274654i
$322$		0			0
$323$	−66450.0			−0.636927
$324$		0			0
$325$	−84192.0	+	48608.3i	−0.797084	+	0.460196i
$326$		0			0
$327$	−75140.0	−	43382.1i	−0.702709	−	0.405709i
$328$		0			0
$329$	−21046.4	+	21480.4i	−0.194440	+	0.198450i
$330$		0			0
$331$	66642.6	−	115428.i	0.608270	−	1.05355i	−0.383256	−	0.923642i	$-0.625197\pi$
$331$	66642.6	−	115428.i	0.608270	−	1.05355i	0.991526	−	0.129912i	$-0.0414694\pi$
$332$		0			0
$333$	−11255.8	−	19495.7i	−0.101505	−	0.175812i
$334$		0			0
$335$			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	$0.570267\pi$
$338$		0			0
$339$	42550.4	−	24566.5i	0.370258	−	0.213768i
$340$		0			0
$341$	36970.0	+	21344.6i	0.317936	+	0.183561i
$342$		0			0
$343$	80605.0	−	85697.8i	0.685131	−	0.728420i
$344$		0			0
$345$	−26089.7	+	45188.8i	−0.219195	+	0.379658i
$346$		0			0
$347$	9384.77	+	16254.9i	0.0779408	+	0.134997i	0.902361	−	0.430980i	$-0.141832\pi$
$347$	9384.77	+	16254.9i	0.0779408	+	0.134997i	−0.824421	+	0.565978i	$0.808499\pi$
$348$		0			0
$349$		−	4574.17i		−	0.0375545i	−0.999824	−	0.0187772i	$-0.994023\pi$
$349$		−	4574.17i		−	0.0375545i	0.999824	−	0.0187772i	$-0.00597733\pi$
$350$		0			0
$351$	−32116.5			−0.260683
$352$		0			0
$353$	52734.9	−	30446.5i	0.423203	−	0.244336i	−0.273244	−	0.961945i	$-0.588097\pi$
$353$	52734.9	−	30446.5i	0.423203	−	0.244336i	0.696447	+	0.717608i	$0.254763\pi$
$354$		0			0
$355$	−4334.10	−	2502.29i	−0.0343908	−	0.0198555i
$356$		0			0
$357$	−41002.5	−	40174.0i	−0.321717	−	0.315217i
$358$		0			0
$359$	116059.	−	201020.i	0.900513	−	1.55973i	0.0736826	−	0.997282i	$-0.476525\pi$
$359$	116059.	−	201020.i	0.900513	−	1.55973i	0.826830	−	0.562452i	$-0.190142\pi$
$360$		0			0
$361$	−21725.5	−	37629.7i	−0.166708	−	0.288746i
$362$		0			0
$363$		−	54773.8i		−	0.415681i
$364$		0			0
$365$	−57604.4			−0.432384
$366$		0			0
$367$	125329.	−	72358.9i	0.930509	−	0.537229i	0.0435362	−	0.999052i	$-0.486138\pi$
$367$	125329.	−	72358.9i	0.930509	−	0.537229i	0.886972	+	0.461822i	$0.152804\pi$
$368$		0			0
$369$	−65883.1	−	38037.6i	−0.483862	−	0.279358i
$370$		0			0
$371$	−54401.0	+	15173.4i	−0.395238	+	0.110239i
$372$		0			0
$373$	74441.6	−	128937.i	0.535054	−	0.926741i	−0.464107	−	0.885779i	$-0.653625\pi$
$373$	74441.6	−	128937.i	0.535054	−	0.926741i	0.999161	−	0.0409616i	$-0.0130421\pi$
$374$		0			0
$375$	38598.8	+	66855.0i	0.274480	+	0.475414i
$376$		0			0
$377$		−	169491.i		−	1.19252i
$378$		0			0
$379$	−140667.			−0.979299			−0.489649	−	0.871919i	$-0.662875\pi$
$379$	−140667.			−0.979299			−0.489649	+	0.871919i	$0.662875\pi$
$380$		0			0
$381$	10710.3	−	6183.59i	0.0737822	−	0.0425982i
$382$		0			0
$383$	−25393.9	−	14661.2i	−0.173114	−	0.0999473i	0.410939	−	0.911663i	$-0.365201\pi$
$383$	−25393.9	−	14661.2i	−0.173114	−	0.0999473i	−0.584053	+	0.811715i	$0.698534\pi$
$384$		0			0
$385$	43008.0	+	11054.8i	0.290153	+	0.0745814i
$386$		0			0
$387$	−41396.5	+	71700.8i	−0.276402	+	0.478743i
$388$		0			0
$389$	−66209.9	−	114679.i	−0.437546	−	0.757852i	0.559954	−	0.828524i	$-0.310819\pi$
$389$	−66209.9	−	114679.i	−0.437546	−	0.757852i	−0.997500	+	0.0706723i	$0.977486\pi$
$390$		0			0
$391$			159960.i			1.04630i
$392$		0			0
$393$	22550.2			0.146004
$394$		0			0
$395$	−79339.7	+	45806.8i	−0.508507	+	0.293586i
$396$		0			0
$397$	29642.0	+	17113.8i	0.188073	+	0.108584i	0.591080	−	0.806613i	$-0.298702\pi$
$397$	29642.0	+	17113.8i	0.188073	+	0.108584i	−0.403007	+	0.915197i	$0.632035\pi$
$398$		0			0
$399$	−18682.0	+	72680.8i	−0.117348	+	0.456535i
$400$		0			0
$401$	89540.6	−	155089.i	0.556841	−	0.964477i	−0.440917	−	0.897548i	$-0.645347\pi$
$401$	89540.6	−	155089.i	0.556841	−	0.964477i	0.997758	−	0.0669288i	$-0.0213200\pi$
$402$		0			0
$403$	−76311.7	−	132176.i	−0.469873	−	0.813845i
$404$		0			0
$405$			10318.0i			0.0629048i
$406$		0			0
$407$	53385.5			0.322281
$408$		0			0
$409$	43099.3	−	24883.4i	0.257646	−	0.148752i	−0.365614	−	0.930767i	$-0.619141\pi$
$409$	43099.3	−	24883.4i	0.257646	−	0.148752i	0.623260	+	0.782014i	$0.285808\pi$
$410$		0			0
$411$	138416.	+	79914.7i	0.819414	+	0.473089i
$412$		0			0
$413$	45978.1	+	164845.i	0.269557	+	0.966442i
$414$		0			0
$415$	58212.4	−	100827.i	0.338002	−	0.585437i
$416$		0			0
$417$	−70633.0	−	122340.i	−0.406196	−	0.703551i
$418$		0			0
$419$			43951.2i			0.250347i	0.992135	+	0.125174i	$0.0399488\pi$
$419$			43951.2i			0.250347i	−0.992135	+	0.125174i	$0.960051\pi$
$420$		0			0
$421$	−218257.			−1.23141			−0.615707	−	0.787975i	$-0.711129\pi$
$421$	−218257.			−1.23141			−0.615707	+	0.787975i	$0.711129\pi$
$422$		0			0
$423$	14350.6	−	8285.30i	0.0802025	−	0.0463050i
$424$		0			0
$425$	82917.9	+	47872.7i	0.459061	+	0.265039i
$426$		0			0
$427$	−77920.6	+	79527.4i	−0.427363	+	0.436175i
$428$		0			0
$429$	38081.5	−	65959.0i	0.206918	−	0.358393i
$430$		0			0
$431$	−38369.8	−	66458.5i	−0.206555	−	0.357763i	0.744072	−	0.668099i	$-0.232892\pi$
$431$	−38369.8	−	66458.5i	−0.206555	−	0.357763i	−0.950627	+	0.310336i	$0.899558\pi$
$432$		0			0
$433$			216713.i			1.15587i	0.816083	+	0.577935i	$0.196141\pi$
$433$			216713.i			1.15587i	−0.816083	+	0.577935i	$0.803859\pi$
$434$		0			0
$435$	−54451.9			−0.287763
$436$		0			0
$437$	181099.	−	104558.i	0.948318	−	0.547512i
$438$		0			0
$439$	−20578.6	−	11881.0i	−0.106779	−	0.0616489i	0.445659	−	0.895203i	$-0.352969\pi$
$439$	−20578.6	−	11881.0i	−0.106779	−	0.0616489i	−0.552438	+	0.833554i	$0.686303\pi$
$440$		0			0
$441$	−55468.6	+	33552.5i	−0.285214	+	0.172523i
$442$		0			0
$443$	87432.4	−	151437.i	0.445517	−	0.771659i	−0.552571	−	0.833466i	$-0.686353\pi$
$443$	87432.4	−	151437.i	0.445517	−	0.771659i	0.998088	+	0.0618072i	$0.0196864\pi$
$444$		0			0
$445$	109961.	+	190458.i	0.555289	+	0.961788i
$446$		0			0
$447$		−	30277.6i		−	0.151532i
$448$		0			0
$449$	−195154.			−0.968023			−0.484011	−	0.875062i	$-0.660821\pi$
$449$	−195154.			−0.968023			−0.484011	+	0.875062i	$0.660821\pi$
$450$		0			0
$451$	156239.	−	90204.7i	0.768134	−	0.443482i
$452$		0			0
$453$	113340.	+	65437.2i	0.552317	+	0.318881i
$454$		0			0
$455$	−113401.	−	111110.i	−0.547764	−	0.536697i
$456$		0			0
$457$	−29236.1	+	50638.5i	−0.139987	+	0.242464i	−0.927491	−	0.373844i	$-0.878039\pi$
$457$	−29236.1	+	50638.5i	−0.139987	+	0.242464i	0.787505	+	0.616309i	$0.211373\pi$
$458$		0			0
$459$	15815.2	+	27392.8i	0.0750672	+	0.130020i
$460$		0			0
$461$			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	$-0.486801\pi$
$463$	17772.2			0.0829049			0.0414524	+	0.999140i	$0.486801\pi$
$464$		0			0
$465$	−42463.7	+	24516.4i	−0.196387	+	0.113384i
$466$		0			0
$467$	−56261.4	−	32482.5i	−0.257974	−	0.148942i	0.365436	−	0.930837i	$-0.380920\pi$
$467$	−56261.4	−	32482.5i	−0.257974	−	0.148942i	−0.623410	+	0.781895i	$0.714253\pi$
$468$		0			0
$469$	409429.	−	114197.i	1.86137	−	0.519168i
$470$		0			0
$471$	62083.7	−	107532.i	0.279857	−	0.484726i
$472$		0			0
$473$	−98170.2	−	170036.i	−0.438790	−	0.760007i
$474$		0			0
$475$		−	125168.i		−	0.554760i
$476$		0			0
$477$	31120.2			0.136775
$478$		0			0
$479$	−182677.	+	105468.i	−0.796181	+	0.459675i	−0.842134	−	0.539268i	$-0.818701\pi$
$479$	−182677.	+	105468.i	−0.796181	+	0.459675i	0.0459530	+	0.998944i	$0.485368\pi$
$480$		0			0
$481$	−165294.	−	95432.3i	−0.714440	−	0.412482i
$482$		0			0
$483$	174959.	+	44971.7i	0.749967	+	0.192773i
$484$		0			0
$485$	11029.9	−	19104.4i	0.0468910	−	0.0812177i
$486$		0			0
$487$	−114444.	−	198223.i	−0.482542	−	0.835787i	0.517257	−	0.855830i	$-0.326953\pi$
$487$	−114444.	−	198223.i	−0.482542	−	0.835787i	−0.999799	+	0.0200431i	$0.993620\pi$
$488$		0			0
$489$			221283.i			0.925402i
$490$		0			0
$491$	−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
$494$		0			0
$495$	−21190.5	−	12234.3i	−0.0864828	−	0.0499309i
$496$		0			0
$497$	−4313.28	+	16780.5i	−0.0174620	+	0.0679348i
$498$		0			0
$499$	−172663.	+	299062.i	−0.693424	+	1.20105i	0.277285	+	0.960788i	$0.410566\pi$
$499$	−172663.	+	299062.i	−0.693424	+	1.20105i	−0.970709	+	0.240258i	$0.922768\pi$
$500$		0			0
$501$	68475.7	+	118603.i	0.272810	+	0.472521i
$502$		0			0
$503$			58979.0i			0.233110i	0.993184	+	0.116555i	$0.0371851\pi$
$503$			58979.0i			0.233110i	−0.993184	+	0.116555i	$0.962815\pi$
$504$		0			0
$505$	−222711.			−0.873291
$506$		0			0
$507$	−107293.	+	61945.9i	−0.417404	+	0.240988i
$508$		0			0
$509$	20653.6	+	11924.3i	0.0797186	+	0.0460255i	0.539329	−	0.842095i	$-0.318678\pi$
$509$	20653.6	+	11924.3i	0.0797186	+	0.0460255i	−0.459611	+	0.888120i	$0.652011\pi$
$510$		0			0
$511$	53578.7	+	192095.i	0.205187	+	0.735657i
$512$		0			0
$513$	20675.2	−	35810.6i	0.0785626	−	0.136074i
$514$		0			0
$515$	238.691	+	413.425i	0.000899957	+	0.00155877i
$516$		0			0
$517$			39296.5i			0.147019i
$518$		0			0
$519$	145592.			0.540509
$520$		0			0
$521$	417171.	−	240854.i	1.53688	−	0.887315i	0.537856	−	0.843037i	$-0.319234\pi$
$521$	417171.	−	240854.i	1.53688	−	0.887315i	0.999019	−	0.0442788i	$-0.0140990\pi$
$522$		0			0
$523$	399593.	+	230705.i	1.46088	+	0.843438i	0.999052	−	0.0435320i	$-0.0138610\pi$
$523$	399593.	+	230705.i	1.46088	+	0.843438i	0.461826	+	0.886970i	$0.347194\pi$
$524$		0			0
$525$	75673.4	−	77233.9i	0.274552	−	0.280214i
$526$		0			0
$527$	−75156.9	+	130176.i	−0.270612	+	0.468714i
$528$		0			0
$529$	−111774.	−	193598.i	−0.399419	−	0.691813i
$530$		0			0
$531$		−	94299.9i		−	0.334443i
$532$		0			0
$533$	−645003.			−2.27043
$534$		0			0
$535$	66759.3	−	38543.5i	0.233240	−	0.134661i
$536$		0			0
$537$	114293.	+	65987.2i	0.396343	+	0.228829i
$538$		0			0
$539$	−3137.44	−	153703.i	−0.0107994	−	0.529059i
$540$		0			0
$541$	254098.	−	440111.i	0.868174	−	1.50372i	0.00431302	−	0.999991i	$-0.498627\pi$
$541$	254098.	−	440111.i	0.868174	−	1.50372i	0.863861	−	0.503731i	$-0.168040\pi$
$542$		0			0
$543$	114568.	+	198438.i	0.388565	+	0.673014i
$544$		0			0
$545$			236333.i			0.795668i
$546$		0			0
$547$	−40170.8			−0.134257			−0.0671283	−	0.997744i	$-0.521384\pi$
$547$	−40170.8			−0.134257			−0.0671283	+	0.997744i	$0.521384\pi$
$548$		0			0
$549$	53130.4	−	30674.9i	0.176278	−	0.101774i
$550$		0			0
$551$	188986.	+	109111.i	0.622482	+	0.359390i
$552$		0			0
$553$	226549.	+	221972.i	0.740818	+	0.725851i
$554$		0			0
$555$	−30659.3	+	53103.4i	−0.0995350	+	0.172400i
$556$		0			0
$557$	39230.2	+	67948.7i	0.126447	+	0.219013i	0.922298	−	0.386480i	$-0.126309\pi$
$557$	39230.2	+	67948.7i	0.126447	+	0.219013i	−0.795850	+	0.605493i	$0.792976\pi$
$558$		0			0
$559$			701959.i			2.24641i
$560$		0			0
$561$	−75010.4			−0.238339
$562$		0			0
$563$	355612.	−	205312.i	1.12191	−	0.647737i	0.180024	−	0.983662i	$-0.442382\pi$
$563$	355612.	−	205312.i	1.12191	−	0.647737i	0.941889	+	0.335926i	$0.109049\pi$
$564$		0			0
$565$	−115901.	−	66915.6i	−0.363071	−	0.209619i
$566$		0			0
$567$	34407.7	−	9596.89i	0.107026	−	0.0298514i
$568$		0			0
$569$	74404.3	−	128872.i	0.229812	−	0.398047i	−0.727940	−	0.685641i	$-0.759522\pi$
$569$	74404.3	−	128872.i	0.229812	−	0.398047i	0.957752	+	0.287594i	$0.0928554\pi$
$570$		0			0
$571$	36146.3	+	62607.3i	0.110864	+	0.192023i	0.916119	−	0.400906i	$-0.131305\pi$
$571$	36146.3	+	62607.3i	0.110864	+	0.192023i	−0.805255	+	0.592929i	$0.797971\pi$
$572$		0			0
$573$			335459.i			1.02172i
$574$		0			0
$575$	−301307.			−0.911326
$576$		0			0
$577$	−482666.	+	278667.i	−1.44976	+	0.837018i	−0.998466	−	0.0553596i	$-0.982369\pi$
$577$	−482666.	+	278667.i	−1.44976	+	0.837018i	−0.451290	+	0.892377i	$0.649036\pi$
$578$		0			0
$579$	−165036.	−	95283.4i	−0.492290	−	0.284223i
$580$		0			0
$581$	−390376.	−	100343.i	−1.15646	−	0.297258i
$582$		0			0
$583$	−36900.2	+	63913.0i	−0.108565	+	0.188041i
$584$		0			0
$585$	43740.3	+	75760.5i	0.127812	+	0.221376i
$586$		0			0
$587$			308119.i			0.894217i	0.894480	+	0.447109i	$0.147546\pi$
$587$			308119.i			0.894217i	−0.894480	+	0.447109i	$0.852454\pi$
$588$		0			0
$589$	196505.			0.566426
$590$		0			0
$591$	−329162.	+	190042.i	−0.942398	+	0.544094i
$592$		0			0
$593$	−200805.	−	115935.i	−0.571038	−	0.329689i	0.186526	−	0.982450i	$-0.440277\pi$
$593$	−200805.	−	115935.i	−0.571038	−	0.329689i	−0.757564	+	0.652761i	$0.773611\pi$
$594$		0			0
$595$	−38925.3	+	151436.i	−0.109951	+	0.427755i
$596$		0			0
$597$	3639.98	−	6304.62i	0.0102129	−	0.0176893i
$598$		0			0
$599$	−167042.	−	289325.i	−0.465555	−	0.806365i	0.533671	−	0.845692i	$-0.320812\pi$
$599$	−167042.	−	289325.i	−0.465555	−	0.806365i	−0.999226	+	0.0393269i	$0.987479\pi$
$600$		0			0
$601$			645072.i			1.78591i	0.450147	+	0.892955i	$0.351372\pi$
$601$			645072.i			1.78591i	−0.450147	+	0.892955i	$0.648628\pi$
$602$		0			0
$603$	−234215.			−0.644139
$604$		0			0
$605$	−129208.	+	74598.1i	−0.353002	+	0.203806i
$606$		0			0
$607$	−120643.	−	69653.0i	−0.327433	−	0.189044i	0.327268	−	0.944932i	$-0.393872\pi$
$607$	−120643.	−	69653.0i	−0.327433	−	0.189044i	−0.654701	+	0.755888i	$0.727205\pi$
$608$		0			0
$609$	50646.5	+	181583.i	0.136557	+	0.489598i
$610$		0			0
$611$	70246.8	−	121671.i	0.188167	−	0.325915i
$612$		0			0
$613$	203665.	+	352759.i	0.541997	+	0.938765i	0.998789	+	0.0491924i	$0.0156647\pi$
$613$	203665.	+	352759.i	0.541997	+	0.938765i	−0.456793	+	0.889573i	$0.651002\pi$
$614$		0			0
$615$			207218.i			0.547870i
$616$		0			0
$617$	276504.			0.726325			0.363163	−	0.931726i	$-0.381697\pi$
$617$	276504.			0.726325			0.363163	+	0.931726i	$0.381697\pi$
$618$		0			0
$619$	−193904.	+	111950.i	−0.506064	+	0.292176i	−0.731214	−	0.682148i	$-0.761046\pi$
$619$	−193904.	+	111950.i	−0.506064	+	0.292176i	0.225150	+	0.974324i	$0.427713\pi$
$620$		0			0
$621$	−86204.1	−	49770.0i	−0.223535	−	0.129058i
$622$		0			0
$623$	532852.	−	543839.i	1.37287	−	1.40118i
$624$		0			0
$625$	−27573.7	+	47759.1i	−0.0705888	+	0.122263i
$626$		0			0
$627$	49030.5	+	84923.3i	0.124719	+	0.216019i
$628$		0			0
$629$			187976.i			0.475119i
$630$		0			0
$631$	−299528.			−0.752278			−0.376139	−	0.926563i	$-0.622749\pi$
$631$	−299528.			−0.752278			−0.376139	+	0.926563i	$0.622749\pi$
$632$		0			0
$633$	−262042.	+	151290.i	−0.653980	+	0.377575i
$634$		0			0
$635$	−29173.3	−	16843.2i	−0.0723500	−	0.0417713i
$636$		0			0
$637$	−265046.	+	481507.i	−0.653194	+	1.18665i
$638$		0			0
$639$	4773.48	−	8267.92i	0.0116905	−	0.0202486i
$640$		0			0
$641$	−288942.	−	500462.i	−0.703226	−	1.21802i	−0.967328	−	0.253528i	$-0.918409\pi$
$641$	−288942.	−	500462.i	−0.703226	−	1.21802i	0.264102	−	0.964495i	$-0.414924\pi$
$642$		0			0
$643$			135320.i			0.327295i	0.986519	+	0.163647i	$0.0523259\pi$
$643$			135320.i			0.327295i	−0.986519	+	0.163647i	$0.947674\pi$
$644$		0			0
$645$	225516.			0.542074
$646$		0			0
$647$	−188880.	+	109050.i	−0.451209	+	0.260506i	−0.708341	−	0.705871i	$-0.750556\pi$
$647$	−188880.	+	109050.i	−0.451209	+	0.260506i	0.257132	+	0.966376i	$0.417223\pi$
$648$		0			0
$649$	193668.	+	111814.i	0.459800	+	0.265465i
$650$		0			0
$651$	121252.	+	118802.i	0.286106	+	0.280325i
$652$		0			0
$653$	−72127.2	+	124928.i	−0.169150	+	0.292977i	−0.938121	−	0.346307i	$-0.887436\pi$
$653$	−72127.2	+	124928.i	−0.169150	+	0.292977i	0.768971	+	0.639284i	$0.220769\pi$
$654$		0			0
$655$	−30711.8	−	53194.4i	−0.0715851	−	0.123989i
$656$		0			0
$657$		−	109889.i		−	0.254579i
$658$		0			0
$659$	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	−0.107593	−	0.994195i	$-0.534314\pi$
$661$	305674.	−	176481.i	0.699609	−	0.403919i	0.807202	+	0.590276i	$0.200981\pi$
$662$		0			0
$663$	232249.	+	134089.i	0.528357	+	0.305047i
$664$		0			0
$665$	196892.	−	54916.7i	0.445231	−	0.124183i
$666$		0			0
$667$	262655.	−	454932.i	0.590384	−	1.02258i
$668$		0			0
$669$	−158615.	−	274729.i	−0.354398	−	0.613836i
$670$		0			0
$671$			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	$0.311827\pi$
$674$		0			0
$675$	−51598.2	+	29790.2i	−0.113247	+	0.0653832i
$676$		0			0
$677$	−169486.	−	97853.0i	−0.369792	−	0.213500i	0.303576	−	0.952807i	$-0.401820\pi$
$677$	−169486.	−	97853.0i	−0.369792	−	0.213500i	−0.673368	+	0.739308i	$0.735153\pi$
$678$		0			0
$679$	−73967.4	−	19012.7i	−0.160436	−	0.0412385i
$680$		0			0
$681$	−64935.5	+	112472.i	−0.140019	+	0.242520i
$682$		0			0
$683$	−117221.	−	203032.i	−0.251283	−	0.435235i	0.712596	−	0.701574i	$-0.247519\pi$
$683$	−117221.	−	203032.i	−0.251283	−	0.435235i	−0.963879	+	0.266340i	$0.914186\pi$
$684$		0			0
$685$		−	435352.i		−	0.927812i
$686$		0			0
$687$	−98357.4			−0.208398
$688$		0			0
$689$	228503.	−	131926.i	0.481341	−	0.277902i
$690$		0			0
$691$	77344.0	+	44654.6i	0.161983	+	0.0935212i	0.578800	−	0.815469i	$-0.303521\pi$
$691$	77344.0	+	44654.6i	0.161983	+	0.0935212i	−0.416817	+	0.908990i	$0.636854\pi$
$692$		0			0
$693$	−21088.7	+	82044.0i	−0.0439120	+	0.170836i
$694$		0			0
$695$	−192394.	+	333236.i	−0.398311	+	0.689895i
$696$		0			0
$697$	317621.	+	550136.i	0.653799	+	1.13241i
$698$		0			0
$699$			34734.9i			0.0710905i
$700$		0			0
$701$	122213.			0.248704			0.124352	−	0.992238i	$-0.460315\pi$
$701$	122213.			0.248704			0.124352	+	0.992238i	$0.460315\pi$
$702$		0			0
$703$	212818.	−	122871.i	0.430624	−	0.248621i
$704$		0			0
$705$	−39088.9	−	22568.0i	−0.0786457	−	0.0454061i
$706$		0			0
$707$	207147.	+	742683.i	0.414419	+	1.48582i
$708$		0			0
$709$	−42009.9	+	72763.3i	−0.0835717	+	0.144750i	−0.904782	−	0.425876i	$-0.859966\pi$
$709$	−42009.9	+	72763.3i	−0.0835717	+	0.144750i	0.821210	+	0.570626i	$0.193299\pi$
$710$		0			0
$711$	−87383.1	−	151352.i	−0.172858	−	0.299398i
$712$		0			0
$713$		−	473032.i		−	0.930489i
$714$		0			0
$715$	−207457.			−0.405804
$716$		0			0
$717$	434074.	−	250613.i	0.844356	−	0.487489i
$718$		0			0
$719$	−657416.	−	379560.i	−1.27169	−	0.734213i	−0.296388	−	0.955068i	$-0.595782\pi$
$719$	−657416.	−	379560.i	−1.27169	−	0.734213i	−0.975307	+	0.220855i	$0.929115\pi$
$720$		0			0
$721$	1156.65	−	1180.51i	0.00222502	−	0.00227090i
$722$		0			0
$723$	142115.	−	246151.i	0.271872	−	0.470896i
$724$		0			0
$725$	−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	$-0.0278550\pi$
$728$		0			0
$729$	−19683.0			−0.0370370
$730$		0			0
$731$	598715.	−	345668.i	1.12043	−	0.646882i
$732$		0			0
$733$	2903.50	+	1676.34i	0.00540399	+	0.00312000i	0.502700	−	0.864461i	$-0.332340\pi$
$733$	2903.50	+	1676.34i	0.00540399	+	0.00312000i	−0.497296	+	0.867581i	$0.665674\pi$
$734$		0			0
$735$	154692.	+	85150.5i	0.286348	+	0.157620i
$736$		0			0
$737$	277715.	−	481017.i	0.511287	−	0.885575i
$738$		0			0
$739$	−13592.8	−	23543.4i	−0.0248897	−	0.0431103i	0.853312	−	0.521400i	$-0.174590\pi$
$739$	−13592.8	−	23543.4i	−0.0248897	−	0.0431103i	−0.878202	+	0.478290i	$0.841257\pi$
$740$		0			0
$741$		−	350589.i		−	0.638502i
$742$		0			0
$743$	−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
$746$		0			0
$747$	192342.	+	111049.i	0.344693	+	0.199009i
$748$		0			0
$749$	−190626.	−	186775.i	−0.339797	−	0.332931i
$750$		0			0
$751$	98922.2	−	171338.i	0.175394	−	0.303791i	−0.764904	−	0.644145i	$-0.777214\pi$
$751$	98922.2	−	171338.i	0.175394	−	0.303791i	0.940297	+	0.340354i	$0.110547\pi$
$752$		0			0
$753$	280948.	+	486617.i	0.495492	+	0.858217i
$754$		0			0
$755$		−	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	$0.734763\pi$
$758$		0			0
$759$	204430.	−	118027.i	0.354863	−	0.204880i
$760$		0			0
$761$	−131757.	−	76069.9i	−0.227512	−	0.131354i	0.381912	−	0.924199i	$-0.375266\pi$
$761$	−131757.	−	76069.9i	−0.227512	−	0.131354i	−0.609424	+	0.792845i	$0.708599\pi$
$762$		0			0
$763$	788109.	−	219817.i	1.35375	−	0.377583i
$764$		0			0
$765$	43078.4	−	74614.0i	0.0736100	−	0.127496i
$766$		0			0
$767$	−399760.	−	692405.i	−0.679531	−	1.17698i
$768$		0			0
$769$		−	961897.i		−	1.62658i	−0.581857	−	0.813291i	$-0.697674\pi$
$769$		−	961897.i		−	1.62658i	0.581857	−	0.813291i	$-0.302326\pi$
$770$		0			0
$771$	186470.			0.313689
$772$		0			0
$773$	−130829.	+	75534.4i	−0.218951	+	0.126411i	−0.605464	−	0.795872i	$-0.707013\pi$
$773$	−130829.	+	75534.4i	−0.218951	+	0.126411i	0.386514	+	0.922284i	$0.373679\pi$
$774$		0			0
$775$	−245204.	−	141569.i	−0.408248	−	0.235702i
$776$		0			0
$777$	205603.	+	52848.3i	0.340554	+	0.0875365i
$778$		0			0
$779$	415226.	−	719192.i	0.684242	−	1.18514i
$780$		0			0
$781$	11320.1	+	19607.0i	0.0185588	+	0.0321447i
$782$		0			0
$783$		−	103875.i		−	0.169429i
$784$		0			0
$785$	−338215.			−0.548849
$786$		0			0
$787$	172244.	−	99445.4i	0.278097	−	0.160559i	−0.354465	−	0.935069i	$-0.615337\pi$
$787$	172244.	−	99445.4i	0.278097	−	0.160559i	0.632561	+	0.774510i	$0.282004\pi$
$788$		0			0
$789$	−294442.	−	169996.i	−0.472984	−	0.273077i
$790$		0			0
$791$	−115344.	+	448739.i	−0.184350	+	0.717202i
$792$		0			0
$793$	260076.	−	450465.i	0.413575	−	0.716333i
$794$		0			0
$795$	−42383.5	−	73410.4i	−0.0670599	−	0.116151i
$796$		0			0
$797$			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
$800$		0			0
$801$	−363326.	+	209767.i	−0.566281	+	0.326943i
$802$		0			0
$803$	225683.	+	130298.i	0.350000	+	0.202073i
$804$		0			0
$805$	−132197.	−	473965.i	−0.204000	−	0.731399i
$806$		0			0
$807$	−179816.	+	311451.i	−0.276110	+	0.478236i
$808$		0			0
$809$	46144.3	+	79924.3i	0.0705052	+	0.122119i	0.899123	−	0.437696i	$-0.144206\pi$
$809$	46144.3	+	79924.3i	0.0705052	+	0.122119i	−0.828618	+	0.559815i	$0.810872\pi$
$810$		0			0
$811$		−	617125.i		−	0.938277i	−0.883125	−	0.469139i	$-0.844564\pi$
$811$		−	617125.i		−	0.938277i	0.883125	−	0.469139i	$-0.155436\pi$
$812$		0			0
$813$	−34037.6			−0.0514966
$814$		0			0
$815$	521991.	−	301372.i	0.785865	−	0.453719i
$816$		0			0
$817$	−782700.	−	451892.i	−1.17260	−	0.677003i
$818$		0			0
$819$	211958.	−	216329.i	0.315996	−	0.322512i
$820$		0			0
$821$	−153533.	+	265927.i	−0.227780	+	0.394526i	−0.957150	−	0.289593i	$-0.906480\pi$
$821$	−153533.	+	265927.i	−0.227780	+	0.394526i	0.729370	+	0.684119i	$0.239813\pi$
$822$		0			0
$823$	423429.	+	733401.i	0.625146	+	1.08278i	0.988513	+	0.151138i	$0.0482937\pi$
$823$	423429.	+	733401.i	0.625146	+	1.08278i	−0.363367	+	0.931646i	$0.618373\pi$
$824$		0			0
$825$		−	141293.i		−	0.207592i
$826$		0			0
$827$	−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	0.322479	−	0.946577i	$-0.395484\pi$
$829$	895803.	−	517192.i	1.30348	−	0.752563i	0.980999	+	0.194013i	$0.0621506\pi$
$830$		0			0
$831$	−355964.	−	205516.i	−0.515471	−	0.297608i
$832$		0			0
$833$	541205.	−	11047.3i	0.779959	−	0.0159208i
$834$		0			0
$835$	186518.	−	323059.i	0.267515	−	0.463349i
$836$		0			0
$837$	−46768.6	−	81005.6i	−0.0667580	−	0.115628i
$838$		0			0
$839$			307258.i			0.436495i	0.975893	+	0.218248i	$0.0700340\pi$
$839$			307258.i			0.436495i	−0.975893	+	0.218248i	$0.929966\pi$
$840$		0			0
$841$	−159093.			−0.224937
$842$		0			0
$843$	154634.	−	89278.1i	0.217596	−	0.125629i
$844$		0			0
$845$	292252.	+	168732.i	0.409302	+	0.236311i
$846$		0			0
$847$	368943.	+	361489.i	0.514272	+	0.503881i
$848$		0			0
$849$	−238795.	+	413605.i	−0.331291	+	0.573813i
$850$		0			0
$851$	−295777.	−	512302.i	−0.408419	−	0.707402i
$852$		0			0
$853$		−	70737.4i		−	0.0972190i	−0.998818	−	0.0486095i	$-0.984521\pi$
$853$		−	70737.4i		−	0.0972190i	0.998818	−	0.0486095i	$-0.0154790\pi$
$854$		0			0
$855$	−112633.			−0.154075
$856$		0			0
$857$	285670.	−	164932.i	0.388958	−	0.224565i	−0.292751	−	0.956189i	$-0.594571\pi$
$857$	285670.	−	164932.i	0.388958	−	0.224565i	0.681709	+	0.731624i	$0.261237\pi$
$858$		0			0
$859$	60589.3	+	34981.2i	0.0821125	+	0.0474077i	0.540494	−	0.841348i	$-0.318237\pi$
$859$	60589.3	+	34981.2i	0.0821125	+	0.0474077i	−0.458382	+	0.888756i	$0.651571\pi$
$860$		0			0
$861$	691018.	−	192737.i	0.932145	−	0.259991i
$862$		0			0
$863$	−386112.	+	668765.i	−0.518431	+	0.897949i	0.481339	+	0.876534i	$0.340150\pi$
$863$	−386112.	+	668765.i	−0.518431	+	0.897949i	−0.999771	+	0.0214151i	$0.993183\pi$
$864$		0			0
$865$	−198286.	−	343441.i	−0.265008	−	0.459008i
$866$		0			0
$867$			169868.i			0.225981i
$868$		0			0
$869$	414451.			0.548825
$870$		0			0
$871$	−1.71974e6	+	992893.i	−2.26687	+	1.30878i
$872$		0			0
$873$	36444.4	+	21041.2i	0.0478193	+	0.0276085i
$874$		0			0
$875$	−705058.	−	181229.i	−0.920892	−	0.236707i
$876$		0			0
$877$	−121260.	+	210028.i	−0.157659	+	0.273073i	−0.934024	−	0.357211i	$-0.883728\pi$
$877$	−121260.	+	210028.i	−0.157659	+	0.273073i	0.776365	+	0.630283i	$0.217061\pi$
$878$		0			0
$879$	60322.5	+	104482.i	0.0780732	+	0.135227i
$880$		0			0
$881$		−	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	$-0.404283\pi$
$883$	461877.			0.592387			0.296193	+	0.955128i	$0.404283\pi$
$884$		0			0
$885$	−222447.	+	128430.i	−0.284014	+	0.163976i
$886$		0			0
$887$	186391.	+	107613.i	0.236907	+	0.136778i	0.613754	−	0.789497i	$-0.289658\pi$
$887$	186391.	+	107613.i	0.236907	+	0.136778i	−0.376847	+	0.926275i	$0.622992\pi$
$888$		0			0
$889$	−29033.2	+	112952.i	−0.0367359	+	0.142919i
$890$		0			0
$891$	23338.7	−	40423.9i	0.0293983	−	0.0509193i
$892$		0			0
$893$	90443.9	+	156653.i	0.113417	+	0.196443i
$894$		0			0
$895$		−	359479.i		−	0.448774i
$896$		0			0
$897$	−843948.			−1.04889
$898$		0			0
$899$	427498.	−	246816.i	0.528950	−	0.305389i
$900$		0			0
$901$	−225045.	−	129930.i	−0.277217	−	0.160051i
$902$		0			0
$903$	−209756.	−	752038.i	−0.257240	−	0.922283i
$904$		0			0
$905$	312067.	−	540516.i	0.381022	−	0.659950i
$906$		0			0
$907$	549134.	+	951128.i	0.667519	+	1.15618i	0.978596	+	0.205793i	$0.0659773\pi$
$907$	549134.	+	951128.i	0.667519	+	1.15618i	−0.311076	+	0.950385i	$0.600689\pi$
$908$		0			0
$909$		−	424854.i		−	0.514176i
$910$		0			0
$911$	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
$914$		0			0
$915$	−144720.	−	83553.9i	−0.172856	−	0.0997987i
$916$		0			0
$917$	−148824.	+	151893.i	−0.176984	+	0.180633i
$918$		0			0
$919$	258264.	−	447326.i	0.305797	−	0.529656i	−0.671642	−	0.740876i	$-0.734411\pi$
$919$	258264.	−	447326.i	0.305797	−	0.529656i	0.977438	+	0.211221i	$0.0677438\pi$
$920$		0			0
$921$	172476.	+	298736.i	0.203333	+	0.352183i
$922$		0			0
$923$		−	80943.8i		−	0.0950124i
$924$		0			0
$925$	−354080.			−0.413826
$926$		0			0
$927$	−788.669	+	455.338i	−0.000917773	+	0.000529876i
$928$		0			0
$929$	1.07335e6	+	619697.i	1.24368	+	0.718039i	0.969841	−	0.243737i	$-0.0783734\pi$
$929$	1.07335e6	+	619697.i	1.24368	+	0.718039i	0.273838	+	0.961776i	$0.411707\pi$
$930$		0			0
$931$	−366265.	−	605506.i	−0.422568	−	0.698585i
$932$		0			0
$933$	248637.	−	430652.i	0.285629	−	0.494724i
$934$		0			0
$935$	102159.	+	176944.i	0.116856	+	0.202401i
$936$		0			0
$937$			1.15260e6i			1.31281i	0.754411	+	0.656403i	$0.227923\pi$
$937$			1.15260e6i			1.31281i	−0.754411	+	0.656403i	$0.772077\pi$
$938$		0			0
$939$	248917.			0.282308
$940$		0			0
$941$	93104.2	−	53753.7i	0.105145	−	0.0607057i	−0.446505	−	0.894781i	$-0.647332\pi$
$941$	93104.2	−	53753.7i	0.105145	−	0.0607057i	0.551650	+	0.834075i	$0.313998\pi$
$942$		0			0
$943$	−1.73126e6	−	999543.i	−1.94688	−	1.12403i
$944$		0			0
$945$	−69499.2	−	68095.1i	−0.0778245	−	0.0762521i
$946$		0			0
$947$	−206307.	+	357335.i	−0.230046	+	0.398451i	−0.957821	−	0.287364i	$-0.907221\pi$
$947$	−206307.	+	357335.i	−0.230046	+	0.398451i	0.727775	+	0.685815i	$0.240554\pi$
$948$		0			0
$949$	−465845.	−	806867.i	−0.517260	−	0.895920i
$950$		0			0
$951$		−	177335.i		−	0.196080i
$952$		0			0
$953$	1.43052e6			1.57510			0.787550	−	0.616251i	$-0.211349\pi$
$953$	1.43052e6			1.57510			0.787550	+	0.616251i	$0.211349\pi$
$954$		0			0
$955$	791324.	−	456871.i	0.867656	−	0.500942i
$956$		0			0
$957$	213332.	+	123168.i	0.232934	+	0.134485i
$958$		0			0
$959$	−1.45179e6	+	404928.i	−1.57858	+	0.440292i
$960$		0			0
$961$	−239507.	+	414839.i	−0.259342	+	0.449193i
$962$		0			0
$963$	73527.3	+	127353.i	0.0792859	+	0.137327i
$964$		0			0
$965$			519077.i			0.557413i
$966$		0			0
$967$	344533.			0.368449			0.184225	−	0.982884i	$-0.441023\pi$
$967$	344533.			0.368449			0.184225	+	0.982884i	$0.441023\pi$
$968$		0			0
$969$	−299025.	+	172642.i	−0.318463	+	0.183865i
$970$		0			0
$971$	1.25848e6	+	726581.i	1.33477	+	0.770630i	0.986027	−	0.166588i	$-0.0532751\pi$
$971$	1.25848e6	+	726581.i	1.33477	+	0.770630i	0.348744	+	0.937218i	$0.386608\pi$
$972$		0			0
$973$	1.29020e6	+	331636.i	1.36280	+	0.350296i
$974$		0			0
$975$	−252576.	+	437474.i	−0.265695	+	0.460196i
$976$		0			0
$977$	−772853.	−	1.33862e6i	−0.809669	−	1.40239i	−0.913093	−	0.407751i	$-0.866313\pi$
$977$	−772853.	−	1.33862e6i	−0.809669	−	1.40239i	0.103424	−	0.994637i	$-0.467020\pi$
$978$		0			0
$979$		−	994907.i		−	1.03805i
$980$		0			0
$981$	−450840.			−0.468473
$982$		0			0
$983$	−116280.	+	67134.0i	−0.120336	+	0.0694761i	−0.558960	−	0.829195i	$-0.688799\pi$
$983$	−116280.	+	67134.0i	−0.120336	+	0.0694761i	0.438624	+	0.898671i	$0.355466\pi$
$984$		0			0
$985$	896589.	+	517646.i	0.924105	+	0.533532i
$986$		0			0
$987$	−38901.1	+	151342.i	−0.0399326	+	0.155355i
$988$		0			0
$989$	−1.08781e6	+	1.88414e6i	−1.11214	+	1.92628i
$990$		0			0
$991$	−395596.	−	685192.i	−0.402814	−	0.697694i	0.591251	−	0.806488i	$-0.298634\pi$
$991$	−395596.	−	685192.i	−0.402814	−	0.697694i	−0.994064	+	0.108794i	$0.965301\pi$
$992$		0			0
$993$		−	692571.i		−	0.702369i
$994$		0			0
$995$	−19829.5			−0.0200293
$996$		0			0
$997$	582624.	−	336378.i	0.586136	−	0.338406i	−0.177432	−	0.984133i	$-0.556779\pi$
$997$	582624.	−	336378.i	0.586136	−	0.338406i	0.763568	+	0.645727i	$0.223446\pi$
$998$		0			0
$999$	−101302.	−	58487.0i	−0.101505	−	0.0586041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.5.bh.d.145.2		4
4.3	odd	2		42.5.g.a.19.1	✓	4
7.3	odd	6	inner	336.5.bh.d.241.2		4
12.11	even	2		126.5.n.b.19.2		4
28.3	even	6		42.5.g.a.31.1	yes	4
28.11	odd	6		294.5.g.c.31.1		4
28.19	even	6		294.5.c.a.97.4		4
28.23	odd	6		294.5.c.a.97.3		4
28.27	even	2		294.5.g.c.19.1		4
84.23	even	6		882.5.c.a.685.1		4
84.47	odd	6		882.5.c.a.685.2		4
84.59	odd	6		126.5.n.b.73.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.5.g.a.19.1	✓	4	4.3	odd	2
42.5.g.a.31.1	yes	4	28.3	even	6
126.5.n.b.19.2		4	12.11	even	2
126.5.n.b.73.2		4	84.59	odd	6
294.5.c.a.97.3		4	28.23	odd	6
294.5.c.a.97.4		4	28.19	even	6
294.5.g.c.19.1		4	28.27	even	2
294.5.g.c.31.1		4	28.11	odd	6
336.5.bh.d.145.2		4	1.1	even	1	trivial
336.5.bh.d.241.2		4	7.3	odd	6	inner
882.5.c.a.685.1		4	84.23	even	6
882.5.c.a.685.2		4	84.47	odd	6

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	336.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.50000 - 2.59808i) q^{3} +(-12.2574 - 7.07679i) q^{5} +(-12.1985 + 47.4573i) q^{7} +(13.5000 - 23.3827i) q^{9} +O(q^{10})\)	\(q+(4.50000 - 2.59808i) q^{3} +(-12.2574 - 7.07679i) q^{5} +(-12.1985 + 47.4573i) q^{7} +(13.5000 - 23.3827i) q^{9} +(32.0147 + 55.4511i) q^{11} -228.919i q^{13} -73.5442 q^{15} +(-195.250 + 112.728i) q^{17} +(255.250 + 147.369i) q^{19} +(68.4045 + 245.251i) q^{21} +(354.749 - 614.444i) q^{23} +(-212.338 - 367.780i) q^{25} -140.296i q^{27} +740.397 q^{29} +(577.390 - 333.356i) q^{31} +(288.132 + 166.353i) q^{33} +(485.367 - 495.375i) q^{35} +(416.882 - 722.061i) q^{37} +(-594.749 - 1030.14i) q^{39} -2817.60i q^{41} -3066.41 q^{43} +(-330.949 + 191.073i) q^{45} +(531.502 + 306.863i) q^{47} +(-2103.39 - 1157.81i) q^{49} +(-585.749 + 1014.55i) q^{51} +(576.300 + 998.181i) q^{53} -906.246i q^{55} +1531.50 q^{57} +(3024.67 - 1746.30i) q^{59} +(1967.79 + 1136.11i) q^{61} +(945.000 + 925.907i) q^{63} +(-1620.01 + 2805.94i) q^{65} +(-4337.31 - 7512.44i) q^{67} -3686.66i q^{69} +353.591 q^{71} +(3524.68 - 2034.97i) q^{73} +(-1911.04 - 1103.34i) q^{75} +(-3022.09 + 842.913i) q^{77} +(3236.41 - 5605.63i) q^{79} +(-364.500 - 631.333i) q^{81} +8225.83i q^{83} +3191.00 q^{85} +(3331.79 - 1923.61i) q^{87} +(-13456.5 - 7769.13i) q^{89} +(10863.9 + 2792.47i) q^{91} +(1732.17 - 3000.21i) q^{93} +(-2085.79 - 3612.70i) q^{95} +1558.61i q^{97} +1728.79 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 18 q^{3} - 66 q^{5} + 70 q^{7} + 54 q^{9}+O(q^{10}) \) 4 * q + 18 * q^3 - 66 * q^5 + 70 * q^7 + 54 * q^9	\( 4 q + 18 q^{3} - 66 q^{5} + 70 q^{7} + 54 q^{9} + 162 q^{11} - 396 q^{15} - 204 q^{17} + 444 q^{19} + 630 q^{21} - 312 q^{23} - 476 q^{25} + 2724 q^{29} + 3786 q^{31} + 1458 q^{33} - 672 q^{35} + 1396 q^{37} - 648 q^{39} + 632 q^{43} - 1782 q^{45} + 7896 q^{47} - 98 q^{49} - 612 q^{51} - 1038 q^{53} + 2664 q^{57} + 966 q^{59} + 5088 q^{61} + 3780 q^{63} - 744 q^{65} - 14600 q^{67} + 9696 q^{71} + 22584 q^{73} - 4284 q^{75} - 3654 q^{77} - 3974 q^{79} - 1458 q^{81} + 1224 q^{85} + 12258 q^{87} - 33156 q^{89} + 18984 q^{91} + 11358 q^{93} - 3252 q^{95} + 8748 q^{99}+O(q^{100}) \) 4 * q + 18 * q^3 - 66 * q^5 + 70 * q^7 + 54 * q^9 + 162 * q^11 - 396 * q^15 - 204 * q^17 + 444 * q^19 + 630 * q^21 - 312 * q^23 - 476 * q^25 + 2724 * q^29 + 3786 * q^31 + 1458 * q^33 - 672 * q^35 + 1396 * q^37 - 648 * q^39 + 632 * q^43 - 1782 * q^45 + 7896 * q^47 - 98 * q^49 - 612 * q^51 - 1038 * q^53 + 2664 * q^57 + 966 * q^59 + 5088 * q^61 + 3780 * q^63 - 744 * q^65 - 14600 * q^67 + 9696 * q^71 + 22584 * q^73 - 4284 * q^75 - 3654 * q^77 - 3974 * q^79 - 1458 * q^81 + 1224 * q^85 + 12258 * q^87 - 33156 * q^89 + 18984 * q^91 + 11358 * q^93 - 3252 * q^95 + 8748 * q^99

Introduction

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