LMFDB - Embedded newform 126.3.s.a.53.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,3,Mod(53,126)]

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([3, 4]))

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

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

chi := DirichletCharacter("126.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	126.s (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:	$3.43325133094$
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:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.2
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	126.53
Dual form			126.3.s.a.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(3.67423 - 2.12132i) q^{5} +(-3.50000 - 6.06218i) q^{7} -2.82843i q^{8} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(3.67423 - 2.12132i) q^{5} +(-3.50000 - 6.06218i) q^{7} -2.82843i q^{8} +(3.00000 - 5.19615i) q^{10} +(11.0227 + 6.36396i) q^{11} -1.00000 q^{13} +(-8.57321 - 4.94975i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(14.6969 + 8.48528i) q^{17} +(-11.5000 - 19.9186i) q^{19} -8.48528i q^{20} +18.0000 q^{22} +(-14.6969 + 8.48528i) q^{23} +(-3.50000 + 6.06218i) q^{25} +(-1.22474 + 0.707107i) q^{26} -14.0000 q^{28} +33.9411i q^{29} +(-23.5000 + 40.7032i) q^{31} +(-4.89898 - 2.82843i) q^{32} +24.0000 q^{34} +(-25.7196 - 14.8492i) q^{35} +(27.5000 + 47.6314i) q^{37} +(-28.1691 - 16.2635i) q^{38} +(-6.00000 - 10.3923i) q^{40} -46.6690i q^{41} +23.0000 q^{43} +(22.0454 - 12.7279i) q^{44} +(-12.0000 + 20.7846i) q^{46} +(-3.67423 + 2.12132i) q^{47} +(-24.5000 + 42.4352i) q^{49} +9.89949i q^{50} +(-1.00000 + 1.73205i) q^{52} +(44.0908 + 25.4558i) q^{53} +54.0000 q^{55} +(-17.1464 + 9.89949i) q^{56} +(24.0000 + 41.5692i) q^{58} +(-73.4847 - 42.4264i) q^{59} +(-52.0000 - 90.0666i) q^{61} +66.4680i q^{62} -8.00000 q^{64} +(-3.67423 + 2.12132i) q^{65} +(48.5000 - 84.0045i) q^{67} +(29.3939 - 16.9706i) q^{68} -42.0000 q^{70} +97.5807i q^{71} +(-32.5000 + 56.2917i) q^{73} +(67.3610 + 38.8909i) q^{74} -46.0000 q^{76} -89.0955i q^{77} +(-56.5000 - 97.8609i) q^{79} +(-14.6969 - 8.48528i) q^{80} +(-33.0000 - 57.1577i) q^{82} -29.6985i q^{83} +72.0000 q^{85} +(28.1691 - 16.2635i) q^{86} +(18.0000 - 31.1769i) q^{88} +(117.576 - 67.8823i) q^{89} +(3.50000 + 6.06218i) q^{91} +33.9411i q^{92} +(-3.00000 + 5.19615i) q^{94} +(-84.5074 - 48.7904i) q^{95} +104.000 q^{97} +69.2965i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4} - 14 q^{7}+O(q^{10}) $ 4 * q + 4 * q^4 - 14 * q^7	$ 4 q + 4 q^{4} - 14 q^{7} + 12 q^{10} - 4 q^{13} - 8 q^{16} - 46 q^{19} + 72 q^{22} - 14 q^{25} - 56 q^{28} - 94 q^{31} + 96 q^{34} + 110 q^{37} - 24 q^{40} + 92 q^{43} - 48 q^{46} - 98 q^{49} - 4 q^{52} + 216 q^{55} + 96 q^{58} - 208 q^{61} - 32 q^{64} + 194 q^{67} - 168 q^{70} - 130 q^{73} - 184 q^{76} - 226 q^{79} - 132 q^{82} + 288 q^{85} + 72 q^{88} + 14 q^{91} - 12 q^{94} + 416 q^{97}+O(q^{100}) $ 4 * q + 4 * q^4 - 14 * q^7 + 12 * q^10 - 4 * q^13 - 8 * q^16 - 46 * q^19 + 72 * q^22 - 14 * q^25 - 56 * q^28 - 94 * q^31 + 96 * q^34 + 110 * q^37 - 24 * q^40 + 92 * q^43 - 48 * q^46 - 98 * q^49 - 4 * q^52 + 216 * q^55 + 96 * q^58 - 208 * q^61 - 32 * q^64 + 194 * q^67 - 168 * q^70 - 130 * q^73 - 184 * q^76 - 226 * q^79 - 132 * q^82 + 288 * q^85 + 72 * q^88 + 14 * q^91 - 12 * q^94 + 416 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$73$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	3.67423	−	2.12132i	0.734847	−	0.424264i	−0.0853458	−	0.996351i	$-0.527199\pi$
$5$	3.67423	−	2.12132i	0.734847	−	0.424264i	0.820193	+	0.572087i	$0.193866\pi$
$6$		0			0
$7$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$7$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	3.00000	−	5.19615i	0.300000	−	0.519615i
$11$	11.0227	+	6.36396i	1.00206	+	0.578542i	0.908858	−	0.417105i	$-0.136955\pi$
$11$	11.0227	+	6.36396i	1.00206	+	0.578542i	0.0932057	+	0.995647i	$0.470289\pi$
$12$		0			0
$13$	−1.00000			−0.0769231			−0.0384615	−	0.999260i	$-0.512246\pi$
$13$	−1.00000			−0.0769231			−0.0384615	+	0.999260i	$0.512246\pi$
$14$	−8.57321	−	4.94975i	−0.612372	−	0.353553i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	14.6969	+	8.48528i	0.864526	+	0.499134i	0.865525	−	0.500865i	$-0.166985\pi$
$17$	14.6969	+	8.48528i	0.864526	+	0.499134i	−0.000999453		1.00000i	$0.500318\pi$
$18$		0			0
$19$	−11.5000	−	19.9186i	−0.605263	−	1.04835i	−0.992010	−	0.126161i	$-0.959735\pi$
$19$	−11.5000	−	19.9186i	−0.605263	−	1.04835i	0.386747	−	0.922186i	$-0.373599\pi$
$20$		−	8.48528i		−	0.424264i
$21$		0			0
$22$	18.0000			0.818182
$23$	−14.6969	+	8.48528i	−0.638997	+	0.368925i	−0.784228	−	0.620473i	$-0.786941\pi$
$23$	−14.6969	+	8.48528i	−0.638997	+	0.368925i	0.145231	+	0.989398i	$0.453608\pi$
$24$		0			0
$25$	−3.50000	+	6.06218i	−0.140000	+	0.242487i
$26$	−1.22474	+	0.707107i	−0.0471056	+	0.0271964i
$27$		0			0
$28$	−14.0000			−0.500000
$29$			33.9411i			1.17038i	0.810895	+	0.585192i	$0.198981\pi$
$29$			33.9411i			1.17038i	−0.810895	+	0.585192i	$0.801019\pi$
$30$		0			0
$31$	−23.5000	+	40.7032i	−0.758065	+	1.31301i	0.185772	+	0.982593i	$0.440521\pi$
$31$	−23.5000	+	40.7032i	−0.758065	+	1.31301i	−0.943836	+	0.330413i	$0.892812\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$		0			0
$34$	24.0000			0.705882
$35$	−25.7196	−	14.8492i	−0.734847	−	0.424264i
$36$		0			0
$37$	27.5000	+	47.6314i	0.743243	+	1.28734i	0.951011	+	0.309157i	$0.100047\pi$
$37$	27.5000	+	47.6314i	0.743243	+	1.28734i	−0.207768	+	0.978178i	$0.566620\pi$
$38$	−28.1691	−	16.2635i	−0.741293	−	0.427986i
$39$		0			0
$40$	−6.00000	−	10.3923i	−0.150000	−	0.259808i
$41$		−	46.6690i		−	1.13827i	−0.822244	−	0.569135i	$-0.807278\pi$
$41$		−	46.6690i		−	1.13827i	0.822244	−	0.569135i	$-0.192722\pi$
$42$		0			0
$43$	23.0000			0.534884			0.267442	−	0.963574i	$-0.413822\pi$
$43$	23.0000			0.534884			0.267442	+	0.963574i	$0.413822\pi$
$44$	22.0454	−	12.7279i	0.501032	−	0.289271i
$45$		0			0
$46$	−12.0000	+	20.7846i	−0.260870	+	0.451839i
$47$	−3.67423	+	2.12132i	−0.0781752	+	0.0451345i	−0.538578	−	0.842576i	$-0.681038\pi$
$47$	−3.67423	+	2.12132i	−0.0781752	+	0.0451345i	0.460403	+	0.887710i	$0.347705\pi$
$48$		0			0
$49$	−24.5000	+	42.4352i	−0.500000	+	0.866025i
$50$			9.89949i			0.197990i
$51$		0			0
$52$	−1.00000	+	1.73205i	−0.0192308	+	0.0333087i
$53$	44.0908	+	25.4558i	0.831902	+	0.480299i	0.854504	−	0.519446i	$-0.173862\pi$
$53$	44.0908	+	25.4558i	0.831902	+	0.480299i	−0.0226013	+	0.999745i	$0.507195\pi$
$54$		0			0
$55$	54.0000			0.981818
$56$	−17.1464	+	9.89949i	−0.306186	+	0.176777i
$57$		0			0
$58$	24.0000	+	41.5692i	0.413793	+	0.716711i
$59$	−73.4847	−	42.4264i	−1.24550	−	0.719092i	−0.275294	−	0.961360i	$-0.588775\pi$
$59$	−73.4847	−	42.4264i	−1.24550	−	0.719092i	−0.970209	+	0.242268i	$0.922109\pi$
$60$		0			0
$61$	−52.0000	−	90.0666i	−0.852459	−	1.47650i	−0.878982	−	0.476854i	$-0.841777\pi$
$61$	−52.0000	−	90.0666i	−0.852459	−	1.47650i	0.0265234	−	0.999648i	$-0.491556\pi$
$62$			66.4680i			1.07207i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−3.67423	+	2.12132i	−0.0565267	+	0.0326357i
$66$		0			0
$67$	48.5000	−	84.0045i	0.723881	−	1.25380i	−0.235553	−	0.971862i	$-0.575690\pi$
$67$	48.5000	−	84.0045i	0.723881	−	1.25380i	0.959433	−	0.281936i	$-0.0909767\pi$
$68$	29.3939	−	16.9706i	0.432263	−	0.249567i
$69$		0			0
$70$	−42.0000			−0.600000
$71$			97.5807i			1.37438i	0.726479	+	0.687188i	$0.241155\pi$
$71$			97.5807i			1.37438i	−0.726479	+	0.687188i	$0.758845\pi$
$72$		0			0
$73$	−32.5000	+	56.2917i	−0.445205	+	0.771119i	−0.998067	−	0.0621550i	$-0.980203\pi$
$73$	−32.5000	+	56.2917i	−0.445205	+	0.771119i	0.552861	+	0.833273i	$0.313536\pi$
$74$	67.3610	+	38.8909i	0.910283	+	0.525552i
$75$		0			0
$76$	−46.0000			−0.605263
$77$		−	89.0955i		−	1.15708i
$78$		0			0
$79$	−56.5000	−	97.8609i	−0.715190	−	1.23875i	−0.962886	−	0.269907i	$-0.913007\pi$
$79$	−56.5000	−	97.8609i	−0.715190	−	1.23875i	0.247696	−	0.968838i	$-0.420326\pi$
$80$	−14.6969	−	8.48528i	−0.183712	−	0.106066i
$81$		0			0
$82$	−33.0000	−	57.1577i	−0.402439	−	0.697045i
$83$		−	29.6985i		−	0.357813i	−0.983866	−	0.178907i	$-0.942744\pi$
$83$		−	29.6985i		−	0.357813i	0.983866	−	0.178907i	$-0.0572560\pi$
$84$		0			0
$85$	72.0000			0.847059
$86$	28.1691	−	16.2635i	0.327548	−	0.189110i
$87$		0			0
$88$	18.0000	−	31.1769i	0.204545	−	0.354283i
$89$	117.576	−	67.8823i	1.32107	−	0.762722i	0.337173	−	0.941443i	$-0.390529\pi$
$89$	117.576	−	67.8823i	1.32107	−	0.762722i	0.983900	+	0.178721i	$0.0571958\pi$
$90$		0			0
$91$	3.50000	+	6.06218i	0.0384615	+	0.0666173i
$92$			33.9411i			0.368925i
$93$		0			0
$94$	−3.00000	+	5.19615i	−0.0319149	+	0.0552782i
$95$	−84.5074	−	48.7904i	−0.889552	−	0.513583i
$96$		0			0
$97$	104.000			1.07216			0.536082	−	0.844166i	$-0.319904\pi$
$97$	104.000			1.07216			0.536082	+	0.844166i	$0.319904\pi$
$98$			69.2965i			0.707107i
$99$		0			0
$100$	7.00000	+	12.1244i	0.0700000	+	0.121244i
$101$	128.598	+	74.2462i	1.27325	+	0.735111i	0.975598	−	0.219564i	$-0.0704633\pi$
$101$	128.598	+	74.2462i	1.27325	+	0.735111i	0.297651	+	0.954675i	$0.403797\pi$
$102$		0			0
$103$	−59.5000	−	103.057i	−0.577670	−	1.00055i	−0.995746	−	0.0921416i	$-0.970629\pi$
$103$	−59.5000	−	103.057i	−0.577670	−	1.00055i	0.418076	−	0.908412i	$-0.362705\pi$
$104$			2.82843i			0.0271964i
$105$		0			0
$106$	72.0000			0.679245
$107$	−102.879	+	59.3970i	−0.961482	+	0.555112i	−0.896629	−	0.442783i	$-0.853991\pi$
$107$	−102.879	+	59.3970i	−0.961482	+	0.555112i	−0.0648531	+	0.997895i	$0.520658\pi$
$108$		0			0
$109$	24.5000	−	42.4352i	0.224771	−	0.389314i	−0.731480	−	0.681863i	$-0.761170\pi$
$109$	24.5000	−	42.4352i	0.224771	−	0.389314i	0.956251	+	0.292549i	$0.0945034\pi$
$110$	66.1362	−	38.1838i	0.601238	−	0.347125i
$111$		0			0
$112$	−14.0000	+	24.2487i	−0.125000	+	0.216506i
$113$		−	97.5807i		−	0.863546i	−0.901982	−	0.431773i	$-0.857888\pi$
$113$		−	97.5807i		−	0.863546i	0.901982	−	0.431773i	$-0.142112\pi$
$114$		0			0
$115$	−36.0000	+	62.3538i	−0.313043	+	0.542207i
$116$	58.7878	+	33.9411i	0.506791	+	0.292596i
$117$		0			0
$118$	−120.000			−1.01695
$119$		−	118.794i		−	0.998268i
$120$		0			0
$121$	20.5000	+	35.5070i	0.169421	+	0.293447i
$122$	−127.373	−	73.5391i	−1.04404	−	0.602780i
$123$		0			0
$124$	47.0000	+	81.4064i	0.379032	+	0.656503i
$125$			135.765i			1.08612i
$126$		0			0
$127$	113.000			0.889764			0.444882	−	0.895589i	$-0.353246\pi$
$127$	113.000			0.889764			0.444882	+	0.895589i	$0.353246\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−3.00000	+	5.19615i	−0.0230769	+	0.0399704i
$131$	18.3712	−	10.6066i	0.140238	−	0.0809664i	−0.428239	−	0.903665i	$-0.640866\pi$
$131$	18.3712	−	10.6066i	0.140238	−	0.0809664i	0.568477	+	0.822699i	$0.307533\pi$
$132$		0			0
$133$	−80.5000	+	139.430i	−0.605263	+	1.04835i
$134$		−	137.179i		−	1.02372i
$135$		0			0
$136$	24.0000	−	41.5692i	0.176471	−	0.305656i
$137$	−58.7878	−	33.9411i	−0.429108	−	0.247745i	0.269859	−	0.962900i	$-0.413023\pi$
$137$	−58.7878	−	33.9411i	−0.429108	−	0.247745i	−0.698966	+	0.715154i	$0.746356\pi$
$138$		0			0
$139$	−103.000			−0.741007			−0.370504	−	0.928831i	$-0.620815\pi$
$139$	−103.000			−0.741007			−0.370504	+	0.928831i	$0.620815\pi$
$140$	−51.4393	+	29.6985i	−0.367423	+	0.212132i
$141$		0			0
$142$	69.0000	+	119.512i	0.485915	+	0.841630i
$143$	−11.0227	−	6.36396i	−0.0770818	−	0.0445032i
$144$		0			0
$145$	72.0000	+	124.708i	0.496552	+	0.860053i
$146$			91.9239i			0.629616i
$147$		0			0
$148$	110.000			0.743243
$149$	−146.969	+	84.8528i	−0.986372	+	0.569482i	−0.904188	−	0.427135i	$-0.859523\pi$
$149$	−146.969	+	84.8528i	−0.986372	+	0.569482i	−0.0821839	+	0.996617i	$0.526189\pi$
$150$		0			0
$151$	−52.0000	+	90.0666i	−0.344371	+	0.596468i	−0.985239	−	0.171183i	$-0.945241\pi$
$151$	−52.0000	+	90.0666i	−0.344371	+	0.596468i	0.640868	+	0.767651i	$0.278574\pi$
$152$	−56.3383	+	32.5269i	−0.370646	+	0.213993i
$153$		0			0
$154$	−63.0000	−	109.119i	−0.409091	−	0.708566i
$155$			199.404i			1.28648i
$156$		0			0
$157$	−76.0000	+	131.636i	−0.484076	+	0.838445i	−0.999833	−	0.0182904i	$-0.994178\pi$
$157$	−76.0000	+	131.636i	−0.484076	+	0.838445i	0.515756	+	0.856735i	$0.327511\pi$
$158$	−138.396	−	79.9031i	−0.875925	−	0.505716i
$159$		0			0
$160$	−24.0000			−0.150000
$161$	102.879	+	59.3970i	0.638997	+	0.368925i
$162$		0			0
$163$	−28.0000	−	48.4974i	−0.171779	−	0.297530i	0.767263	−	0.641333i	$-0.221618\pi$
$163$	−28.0000	−	48.4974i	−0.171779	−	0.297530i	−0.939042	+	0.343803i	$0.888285\pi$
$164$	−80.8332	−	46.6690i	−0.492885	−	0.284567i
$165$		0			0
$166$	−21.0000	−	36.3731i	−0.126506	−	0.219115i
$167$		−	4.24264i		−	0.0254050i	−0.999919	−	0.0127025i	$-0.995957\pi$
$167$		−	4.24264i		−	0.0254050i	0.999919	−	0.0127025i	$-0.00404345\pi$
$168$		0			0
$169$	−168.000			−0.994083
$170$	88.1816	−	50.9117i	0.518715	−	0.299481i
$171$		0			0
$172$	23.0000	−	39.8372i	0.133721	−	0.231611i
$173$	−132.272	+	76.3675i	−0.764581	+	0.441431i	−0.830938	−	0.556365i	$-0.812196\pi$
$173$	−132.272	+	76.3675i	−0.764581	+	0.441431i	0.0663573	+	0.997796i	$0.478862\pi$
$174$		0			0
$175$	49.0000			0.280000
$176$		−	50.9117i		−	0.289271i
$177$		0			0
$178$	96.0000	−	166.277i	0.539326	−	0.934140i
$179$	−3.67423	−	2.12132i	−0.0205265	−	0.0118510i	0.489702	−	0.871890i	$-0.337106\pi$
$179$	−3.67423	−	2.12132i	−0.0205265	−	0.0118510i	−0.510228	+	0.860039i	$0.670439\pi$
$180$		0			0
$181$	−55.0000			−0.303867			−0.151934	−	0.988391i	$-0.548550\pi$
$181$	−55.0000			−0.303867			−0.151934	+	0.988391i	$0.548550\pi$
$182$	8.57321	+	4.94975i	0.0471056	+	0.0271964i
$183$		0			0
$184$	24.0000	+	41.5692i	0.130435	+	0.225920i
$185$	202.083	+	116.673i	1.09234	+	0.630663i
$186$		0			0
$187$	108.000	+	187.061i	0.577540	+	1.00033i
$188$			8.48528i			0.0451345i
$189$		0			0
$190$	−138.000			−0.726316
$191$	−55.1135	+	31.8198i	−0.288552	+	0.166596i	−0.637289	−	0.770625i	$-0.719944\pi$
$191$	−55.1135	+	31.8198i	−0.288552	+	0.166596i	0.348736	+	0.937221i	$0.386611\pi$
$192$		0			0
$193$	75.5000	−	130.770i	0.391192	−	0.677564i	−0.601415	−	0.798937i	$-0.705396\pi$
$193$	75.5000	−	130.770i	0.391192	−	0.677564i	0.992607	+	0.121373i	$0.0387296\pi$
$194$	127.373	−	73.5391i	0.656564	−	0.379068i
$195$		0			0
$196$	49.0000	+	84.8705i	0.250000	+	0.433013i
$197$			16.9706i			0.0861450i	0.999072	+	0.0430725i	$0.0137146\pi$
$197$			16.9706i			0.0861450i	−0.999072	+	0.0430725i	$0.986285\pi$
$198$		0			0
$199$	80.0000	−	138.564i	0.402010	−	0.696302i	−0.591958	−	0.805969i	$-0.701645\pi$
$199$	80.0000	−	138.564i	0.402010	−	0.696302i	0.993968	+	0.109667i	$0.0349784\pi$
$200$	17.1464	+	9.89949i	0.0857321	+	0.0494975i
$201$		0			0
$202$	210.000			1.03960
$203$	205.757	−	118.794i	1.01358	−	0.585192i
$204$		0			0
$205$	−99.0000	−	171.473i	−0.482927	−	0.836454i
$206$	−145.745	−	84.1457i	−0.707498	−	0.408474i
$207$		0			0
$208$	2.00000	+	3.46410i	0.00961538	+	0.0166543i
$209$		−	292.742i		−	1.40068i
$210$		0			0
$211$	−208.000			−0.985782			−0.492891	−	0.870091i	$-0.664060\pi$
$211$	−208.000			−0.985782			−0.492891	+	0.870091i	$0.664060\pi$
$212$	88.1816	−	50.9117i	0.415951	−	0.240149i
$213$		0			0
$214$	−84.0000	+	145.492i	−0.392523	+	0.679870i
$215$	84.5074	−	48.7904i	0.393058	−	0.226932i
$216$		0			0
$217$	329.000			1.51613
$218$		−	69.2965i		−	0.317874i
$219$		0			0
$220$	54.0000	−	93.5307i	0.245455	−	0.425140i
$221$	−14.6969	−	8.48528i	−0.0665020	−	0.0383949i
$222$		0			0
$223$	−40.0000			−0.179372			−0.0896861	−	0.995970i	$-0.528586\pi$
$223$	−40.0000			−0.179372			−0.0896861	+	0.995970i	$0.528586\pi$
$224$			39.5980i			0.176777i
$225$		0			0
$226$	−69.0000	−	119.512i	−0.305310	−	0.528812i
$227$	194.734	+	112.430i	0.857861	+	0.495286i	0.863295	−	0.504699i	$-0.168397\pi$
$227$	194.734	+	112.430i	0.857861	+	0.495286i	−0.00543445	+	0.999985i	$0.501730\pi$
$228$		0			0
$229$	−188.500	−	326.492i	−0.823144	−	1.42573i	−0.903329	−	0.428947i	$-0.858885\pi$
$229$	−188.500	−	326.492i	−0.823144	−	1.42573i	0.0801853	−	0.996780i	$-0.474449\pi$
$230$			101.823i			0.442710i
$231$		0			0
$232$	96.0000			0.413793
$233$	297.613	−	171.827i	1.27731	−	0.737455i	0.300956	−	0.953638i	$-0.402694\pi$
$233$	297.613	−	171.827i	1.27731	−	0.737455i	0.976353	+	0.216183i	$0.0693609\pi$
$234$		0			0
$235$	−9.00000	+	15.5885i	−0.0382979	+	0.0663339i
$236$	−146.969	+	84.8528i	−0.622752	+	0.359546i
$237$		0			0
$238$	−84.0000	−	145.492i	−0.352941	−	0.611312i
$239$		−	12.7279i		−	0.0532549i	−0.999645	−	0.0266275i	$-0.991523\pi$
$239$		−	12.7279i		−	0.0532549i	0.999645	−	0.0266275i	$-0.00847678\pi$
$240$		0			0
$241$	65.0000	−	112.583i	0.269710	−	0.467151i	−0.699077	−	0.715046i	$-0.746406\pi$
$241$	65.0000	−	112.583i	0.269710	−	0.467151i	0.968787	+	0.247896i	$0.0797390\pi$
$242$	50.2145	+	28.9914i	0.207498	+	0.119799i
$243$		0			0
$244$	−208.000			−0.852459
$245$			207.889i			0.848528i
$246$		0			0
$247$	11.5000	+	19.9186i	0.0465587	+	0.0806420i
$248$	115.126	+	66.4680i	0.464218	+	0.268016i
$249$		0			0
$250$	96.0000	+	166.277i	0.384000	+	0.665108i
$251$		−	50.9117i		−	0.202835i	−0.994844	−	0.101418i	$-0.967662\pi$
$251$		−	50.9117i		−	0.202835i	0.994844	−	0.101418i	$-0.0323379\pi$
$252$		0			0
$253$	−216.000			−0.853755
$254$	138.396	−	79.9031i	0.544867	−	0.314579i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−407.840	+	235.467i	−1.58693	+	0.916212i	−0.593117	+	0.805117i	$0.702103\pi$
$257$	−407.840	+	235.467i	−1.58693	+	0.916212i	−0.993810	+	0.111096i	$0.964564\pi$
$258$		0			0
$259$	192.500	−	333.420i	0.743243	−	1.28734i
$260$			8.48528i			0.0326357i
$261$		0			0
$262$	15.0000	−	25.9808i	0.0572519	−	0.0991632i
$263$	88.1816	+	50.9117i	0.335291	+	0.193581i	0.658188	−	0.752854i	$-0.271323\pi$
$263$	88.1816	+	50.9117i	0.335291	+	0.193581i	−0.322897	+	0.946434i	$0.604657\pi$
$264$		0			0
$265$	216.000			0.815094
$266$			227.688i			0.855971i
$267$		0			0
$268$	−97.0000	−	168.009i	−0.361940	−	0.626899i
$269$	−246.174	−	142.128i	−0.915144	−	0.528359i	−0.0330613	−	0.999453i	$-0.510526\pi$
$269$	−246.174	−	142.128i	−0.915144	−	0.528359i	−0.882083	+	0.471095i	$0.843859\pi$
$270$		0			0
$271$	260.000	+	450.333i	0.959410	+	1.66175i	0.723938	+	0.689865i	$0.242330\pi$
$271$	260.000	+	450.333i	0.959410	+	1.66175i	0.235471	+	0.971881i	$0.424337\pi$
$272$		−	67.8823i		−	0.249567i
$273$		0			0
$274$	−96.0000			−0.350365
$275$	−77.1589	+	44.5477i	−0.280578	+	0.161992i
$276$		0			0
$277$	−56.5000	+	97.8609i	−0.203971	+	0.353288i	−0.949804	−	0.312844i	$-0.898718\pi$
$277$	−56.5000	+	97.8609i	−0.203971	+	0.353288i	0.745833	+	0.666133i	$0.232052\pi$
$278$	−126.149	+	72.8320i	−0.453772	+	0.261986i
$279$		0			0
$280$	−42.0000	+	72.7461i	−0.150000	+	0.259808i
$281$		−	458.205i		−	1.63062i	−0.579022	−	0.815312i	$-0.696566\pi$
$281$		−	458.205i		−	1.63062i	0.579022	−	0.815312i	$-0.303434\pi$
$282$		0			0
$283$	−44.5000	+	77.0763i	−0.157244	+	0.272354i	−0.933874	−	0.357603i	$-0.883594\pi$
$283$	−44.5000	+	77.0763i	−0.157244	+	0.272354i	0.776630	+	0.629957i	$0.216928\pi$
$284$	169.015	+	97.5807i	0.595123	+	0.343594i
$285$		0			0
$286$	−18.0000			−0.0629371
$287$	−282.916	+	163.342i	−0.985770	+	0.569135i
$288$		0			0
$289$	−0.500000	−	0.866025i	−0.00173010	−	0.00299663i
$290$	176.363	+	101.823i	0.608149	+	0.351115i
$291$		0			0
$292$	65.0000	+	112.583i	0.222603	+	0.385559i
$293$		−	67.8823i		−	0.231680i	−0.993268	−	0.115840i	$-0.963044\pi$
$293$		−	67.8823i		−	0.231680i	0.993268	−	0.115840i	$-0.0369560\pi$
$294$		0			0
$295$	−360.000			−1.22034
$296$	134.722	−	77.7817i	0.455142	−	0.262776i
$297$		0			0
$298$	−120.000	+	207.846i	−0.402685	+	0.697470i
$299$	14.6969	−	8.48528i	0.0491536	−	0.0283789i
$300$		0			0
$301$	−80.5000	−	139.430i	−0.267442	−	0.463223i
$302$			147.078i			0.487014i
$303$		0			0
$304$	−46.0000	+	79.6743i	−0.151316	+	0.262087i
$305$	−382.120	−	220.617i	−1.25285	−	0.723335i
$306$		0			0
$307$	233.000			0.758958			0.379479	−	0.925200i	$-0.376103\pi$
$307$	233.000			0.758958			0.379479	+	0.925200i	$0.376103\pi$
$308$	−154.318	−	89.0955i	−0.501032	−	0.289271i
$309$		0			0
$310$	141.000	+	244.219i	0.454839	+	0.787804i
$311$	216.780	+	125.158i	0.697041	+	0.402437i	0.806244	−	0.591582i	$-0.201497\pi$
$311$	216.780	+	125.158i	0.697041	+	0.402437i	−0.109203	+	0.994019i	$0.534830\pi$
$312$		0			0
$313$	75.5000	+	130.770i	0.241214	+	0.417795i	0.961060	−	0.276338i	$-0.0891211\pi$
$313$	75.5000	+	130.770i	0.241214	+	0.417795i	−0.719846	+	0.694133i	$0.755788\pi$
$314$			214.960i			0.684587i
$315$		0			0
$316$	−226.000			−0.715190
$317$	−352.727	+	203.647i	−1.11270	+	0.642419i	−0.939528	−	0.342472i	$-0.888736\pi$
$317$	−352.727	+	203.647i	−1.11270	+	0.642419i	−0.173174	+	0.984891i	$0.555402\pi$
$318$		0			0
$319$	−216.000	+	374.123i	−0.677116	+	1.17280i
$320$	−29.3939	+	16.9706i	−0.0918559	+	0.0530330i
$321$		0			0
$322$	168.000			0.521739
$323$		−	390.323i		−	1.20843i
$324$		0			0
$325$	3.50000	−	6.06218i	0.0107692	−	0.0186529i
$326$	−68.5857	−	39.5980i	−0.210386	−	0.121466i
$327$		0			0
$328$	−132.000			−0.402439
$329$	25.7196	+	14.8492i	0.0781752	+	0.0451345i
$330$		0			0
$331$	36.5000	+	63.2199i	0.110272	+	0.190997i	0.915880	−	0.401452i	$-0.131495\pi$
$331$	36.5000	+	63.2199i	0.110272	+	0.190997i	−0.805608	+	0.592449i	$0.798161\pi$
$332$	−51.4393	−	29.6985i	−0.154938	−	0.0894533i
$333$		0			0
$334$	−3.00000	−	5.19615i	−0.00898204	−	0.0155573i
$335$		−	411.536i		−	1.22847i
$336$		0			0
$337$	527.000			1.56380			0.781899	−	0.623405i	$-0.214251\pi$
$337$	527.000			1.56380			0.781899	+	0.623405i	$0.214251\pi$
$338$	−205.757	+	118.794i	−0.608749	+	0.351461i
$339$		0			0
$340$	72.0000	−	124.708i	0.211765	−	0.366787i
$341$	−518.067	+	299.106i	−1.51926	+	0.877144i
$342$		0			0
$343$	343.000			1.00000
$344$		−	65.0538i		−	0.189110i
$345$		0			0
$346$	−108.000	+	187.061i	−0.312139	+	0.540640i
$347$	367.423	+	212.132i	1.05886	+	0.611332i	0.925116	−	0.379685i	$-0.123968\pi$
$347$	367.423	+	212.132i	1.05886	+	0.611332i	0.133741	+	0.991016i	$0.457301\pi$
$348$		0			0
$349$	−112.000			−0.320917			−0.160458	−	0.987043i	$-0.551297\pi$
$349$	−112.000			−0.320917			−0.160458	+	0.987043i	$0.551297\pi$
$350$	60.0125	−	34.6482i	0.171464	−	0.0989949i
$351$		0			0
$352$	−36.0000	−	62.3538i	−0.102273	−	0.177142i
$353$	268.219	+	154.856i	0.759828	+	0.438687i	0.829234	−	0.558902i	$-0.188777\pi$
$353$	268.219	+	154.856i	0.759828	+	0.438687i	−0.0694063	+	0.997588i	$0.522110\pi$
$354$		0			0
$355$	207.000	+	358.535i	0.583099	+	1.00996i
$356$		−	271.529i		−	0.762722i
$357$		0			0
$358$	−6.00000			−0.0167598
$359$	440.908	−	254.558i	1.22816	−	0.709076i	0.261512	−	0.965200i	$-0.415779\pi$
$359$	440.908	−	254.558i	1.22816	−	0.709076i	0.966644	+	0.256124i	$0.0824454\pi$
$360$		0			0
$361$	−84.0000	+	145.492i	−0.232687	+	0.403026i
$362$	−67.3610	+	38.8909i	−0.186080	+	0.107433i
$363$		0			0
$364$	14.0000			0.0384615
$365$			275.772i			0.755539i
$366$		0			0
$367$	159.500	−	276.262i	0.434605	−	0.752758i	−0.562658	−	0.826689i	$-0.690221\pi$
$367$	159.500	−	276.262i	0.434605	−	0.752758i	0.997263	+	0.0739317i	$0.0235547\pi$
$368$	58.7878	+	33.9411i	0.159749	+	0.0922313i
$369$		0			0
$370$	330.000			0.891892
$371$		−	356.382i		−	0.960598i
$372$		0			0
$373$	−104.500	−	180.999i	−0.280161	−	0.485253i	0.691263	−	0.722603i	$-0.257054\pi$
$373$	−104.500	−	180.999i	−0.280161	−	0.485253i	−0.971424	+	0.237350i	$0.923721\pi$
$374$	264.545	+	152.735i	0.707339	+	0.408383i
$375$		0			0
$376$	6.00000	+	10.3923i	0.0159574	+	0.0276391i
$377$		−	33.9411i		−	0.0900295i
$378$		0			0
$379$	−433.000			−1.14248			−0.571240	−	0.820783i	$-0.693537\pi$
$379$	−433.000			−1.14248			−0.571240	+	0.820783i	$0.693537\pi$
$380$	−169.015	+	97.5807i	−0.444776	+	0.256791i
$381$		0			0
$382$	−45.0000	+	77.9423i	−0.117801	+	0.204037i
$383$	338.030	−	195.161i	0.882584	−	0.509560i	0.0110743	−	0.999939i	$-0.496475\pi$
$383$	338.030	−	195.161i	0.882584	−	0.509560i	0.871509	+	0.490379i	$0.163142\pi$
$384$		0			0
$385$	−189.000	−	327.358i	−0.490909	−	0.850279i
$386$		−	213.546i		−	0.553229i
$387$		0			0
$388$	104.000	−	180.133i	0.268041	−	0.464261i
$389$	−319.658	−	184.555i	−0.821744	−	0.474434i	0.0292735	−	0.999571i	$-0.490681\pi$
$389$	−319.658	−	184.555i	−0.821744	−	0.474434i	−0.851018	+	0.525137i	$0.824014\pi$
$390$		0			0
$391$	−288.000			−0.736573
$392$	120.025	+	69.2965i	0.306186	+	0.176777i
$393$		0			0
$394$	12.0000	+	20.7846i	0.0304569	+	0.0527528i
$395$	−415.189	−	239.709i	−1.05111	−	0.606859i
$396$		0			0
$397$	−56.5000	−	97.8609i	−0.142317	−	0.246501i	0.786052	−	0.618161i	$-0.212122\pi$
$397$	−56.5000	−	97.8609i	−0.142317	−	0.246501i	−0.928369	+	0.371660i	$0.878789\pi$
$398$		−	226.274i		−	0.568528i
$399$		0			0
$400$	28.0000			0.0700000
$401$	308.636	−	178.191i	0.769665	−	0.444366i	−0.0630900	−	0.998008i	$-0.520096\pi$
$401$	308.636	−	178.191i	0.769665	−	0.444366i	0.832755	+	0.553641i	$0.186762\pi$
$402$		0			0
$403$	23.5000	−	40.7032i	0.0583127	−	0.101000i
$404$	257.196	−	148.492i	0.636625	−	0.367556i
$405$		0			0
$406$	168.000	−	290.985i	0.413793	−	0.716711i
$407$			700.036i			1.71999i
$408$		0			0
$409$	159.500	−	276.262i	0.389976	−	0.675457i	−0.602470	−	0.798141i	$-0.705817\pi$
$409$	159.500	−	276.262i	0.389976	−	0.675457i	0.992446	+	0.122684i	$0.0391501\pi$
$410$	−242.499	−	140.007i	−0.591462	−	0.341481i
$411$		0			0
$412$	−238.000			−0.577670
$413$			593.970i			1.43818i
$414$		0			0
$415$	−63.0000	−	109.119i	−0.151807	−	0.262938i
$416$	4.89898	+	2.82843i	0.0117764	+	0.00679910i
$417$		0			0
$418$	−207.000	−	358.535i	−0.495215	−	0.857738i
$419$			767.918i			1.83274i	0.400333	+	0.916370i	$0.368895\pi$
$419$			767.918i			1.83274i	−0.400333	+	0.916370i	$0.631105\pi$
$420$		0			0
$421$	65.0000			0.154394			0.0771971	−	0.997016i	$-0.475403\pi$
$421$	65.0000			0.154394			0.0771971	+	0.997016i	$0.475403\pi$
$422$	−254.747	+	147.078i	−0.603666	+	0.348527i
$423$		0			0
$424$	72.0000	−	124.708i	0.169811	−	0.294122i
$425$	−102.879	+	59.3970i	−0.242067	+	0.139758i
$426$		0			0
$427$	−364.000	+	630.466i	−0.852459	+	1.47650i
$428$			237.588i			0.555112i
$429$		0			0
$430$	69.0000	−	119.512i	0.160465	−	0.277934i
$431$	415.189	+	239.709i	0.963314	+	0.556170i	0.897192	−	0.441642i	$-0.145604\pi$
$431$	415.189	+	239.709i	0.963314	+	0.556170i	0.0661229	+	0.997811i	$0.478937\pi$
$432$		0			0
$433$	−367.000			−0.847575			−0.423788	−	0.905762i	$-0.639300\pi$
$433$	−367.000			−0.847575			−0.423788	+	0.905762i	$0.639300\pi$
$434$	402.941	−	232.638i	0.928436	−	0.536033i
$435$		0			0
$436$	−49.0000	−	84.8705i	−0.112385	−	0.194657i
$437$	338.030	+	195.161i	0.773523	+	0.446594i
$438$		0			0
$439$	−268.000	−	464.190i	−0.610478	−	1.05738i	−0.991160	−	0.132673i	$-0.957644\pi$
$439$	−268.000	−	464.190i	−0.610478	−	1.05738i	0.380681	−	0.924706i	$-0.375689\pi$
$440$		−	152.735i		−	0.347125i
$441$		0			0
$442$	−24.0000			−0.0542986
$443$	73.4847	−	42.4264i	0.165880	−	0.0957707i	−0.414762	−	0.909930i	$-0.636135\pi$
$443$	73.4847	−	42.4264i	0.165880	−	0.0957707i	0.580642	+	0.814159i	$0.302802\pi$
$444$		0			0
$445$	288.000	−	498.831i	0.647191	−	1.12097i
$446$	−48.9898	+	28.2843i	−0.109843	+	0.0634176i
$447$		0			0
$448$	28.0000	+	48.4974i	0.0625000	+	0.108253i
$449$		−	615.183i		−	1.37012i	−0.728488	−	0.685059i	$-0.759776\pi$
$449$		−	615.183i		−	1.37012i	0.728488	−	0.685059i	$-0.240224\pi$
$450$		0			0
$451$	297.000	−	514.419i	0.658537	−	1.14062i
$452$	−169.015	−	97.5807i	−0.373927	−	0.215887i
$453$		0			0
$454$	318.000			0.700441
$455$	25.7196	+	14.8492i	0.0565267	+	0.0326357i
$456$		0			0
$457$	231.500	+	400.970i	0.506565	+	0.877396i	0.999971	+	0.00759675i	$0.00241814\pi$
$457$	231.500	+	400.970i	0.506565	+	0.877396i	−0.493407	+	0.869799i	$0.664249\pi$
$458$	−461.729	−	266.579i	−1.00814	−	0.582051i
$459$		0			0
$460$	72.0000	+	124.708i	0.156522	+	0.271104i
$461$			271.529i			0.589000i	0.955651	+	0.294500i	$0.0951531\pi$
$461$			271.529i			0.589000i	−0.955651	+	0.294500i	$0.904847\pi$
$462$		0			0
$463$	47.0000			0.101512			0.0507559	−	0.998711i	$-0.483837\pi$
$463$	47.0000			0.101512			0.0507559	+	0.998711i	$0.483837\pi$
$464$	117.576	−	67.8823i	0.253395	−	0.146298i
$465$		0			0
$466$	243.000	−	420.888i	0.521459	−	0.903194i
$467$	642.991	−	371.231i	1.37685	−	0.794927i	0.385075	−	0.922885i	$-0.374176\pi$
$467$	642.991	−	371.231i	1.37685	−	0.794927i	0.991780	+	0.127958i	$0.0408423\pi$
$468$		0			0
$469$	−679.000			−1.44776
$470$			25.4558i			0.0541614i
$471$		0			0
$472$	−120.000	+	207.846i	−0.254237	+	0.440352i
$473$	253.522	+	146.371i	0.535988	+	0.309453i
$474$		0			0
$475$	161.000			0.338947
$476$	−205.757	−	118.794i	−0.432263	−	0.249567i
$477$		0			0
$478$	−9.00000	−	15.5885i	−0.0188285	−	0.0326118i
$479$	−367.423	−	212.132i	−0.767064	−	0.442864i	0.0647625	−	0.997901i	$-0.479371\pi$
$479$	−367.423	−	212.132i	−0.767064	−	0.442864i	−0.831826	+	0.555036i	$0.812704\pi$
$480$		0			0
$481$	−27.5000	−	47.6314i	−0.0571726	−	0.0990258i
$482$		−	183.848i		−	0.381427i
$483$		0			0
$484$	82.0000			0.169421
$485$	382.120	−	220.617i	0.787877	−	0.454881i
$486$		0			0
$487$	−119.500	+	206.980i	−0.245380	+	0.425010i	−0.962238	−	0.272208i	$-0.912246\pi$
$487$	−119.500	+	206.980i	−0.245380	+	0.425010i	0.716858	+	0.697219i	$0.245579\pi$
$488$	−254.747	+	147.078i	−0.522022	+	0.301390i
$489$		0			0
$490$	147.000	+	254.611i	0.300000	+	0.519615i
$491$			203.647i			0.414759i	0.978261	+	0.207380i	$0.0664935\pi$
$491$			203.647i			0.414759i	−0.978261	+	0.207380i	$0.933506\pi$
$492$		0			0
$493$	−288.000	+	498.831i	−0.584178	+	1.01183i
$494$	28.1691	+	16.2635i	0.0570225	+	0.0329220i
$495$		0			0
$496$	188.000			0.379032
$497$	591.552	−	341.533i	1.19025	−	0.687188i
$498$		0			0
$499$	24.5000	+	42.4352i	0.0490982	+	0.0850406i	0.889530	−	0.456877i	$-0.151032\pi$
$499$	24.5000	+	42.4352i	0.0490982	+	0.0850406i	−0.840432	+	0.541917i	$0.817699\pi$
$500$	235.151	+	135.765i	0.470302	+	0.271529i
$501$		0			0
$502$	−36.0000	−	62.3538i	−0.0717131	−	0.124211i
$503$			589.727i			1.17242i	0.810159	+	0.586210i	$0.199381\pi$
$503$			589.727i			1.17242i	−0.810159	+	0.586210i	$0.800619\pi$
$504$		0			0
$505$	630.000			1.24752
$506$	−264.545	+	152.735i	−0.522816	+	0.301848i
$507$		0			0
$508$	113.000	−	195.722i	0.222441	−	0.385279i
$509$	−209.431	+	120.915i	−0.411457	+	0.237555i	−0.691415	−	0.722457i	$-0.743013\pi$
$509$	−209.431	+	120.915i	−0.411457	+	0.237555i	0.279959	+	0.960012i	$0.409679\pi$
$510$		0			0
$511$	455.000			0.890411
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	−333.000	+	576.773i	−0.647860	+	1.12213i
$515$	−437.234	−	252.437i	−0.848998	−	0.490169i
$516$		0			0
$517$	−54.0000			−0.104449
$518$		−	544.472i		−	1.05110i
$519$		0			0
$520$	6.00000	+	10.3923i	0.0115385	+	0.0199852i
$521$	−734.847	−	424.264i	−1.41045	−	0.814326i	−0.415024	−	0.909811i	$-0.636227\pi$
$521$	−734.847	−	424.264i	−1.41045	−	0.814326i	−0.995431	+	0.0954841i	$0.969560\pi$
$522$		0			0
$523$	195.500	+	338.616i	0.373805	+	0.647449i	0.990147	−	0.140029i	$-0.0447196\pi$
$523$	195.500	+	338.616i	0.373805	+	0.647449i	−0.616342	+	0.787478i	$0.711386\pi$
$524$		−	42.4264i		−	0.0809664i
$525$		0			0
$526$	144.000			0.273764
$527$	−690.756	+	398.808i	−1.31073	+	0.756752i
$528$		0			0
$529$	−120.500	+	208.712i	−0.227788	+	0.394541i
$530$	264.545	−	152.735i	0.499141	−	0.288179i
$531$		0			0
$532$	161.000	+	278.860i	0.302632	+	0.524173i
$533$			46.6690i			0.0875592i
$534$		0			0
$535$	−252.000	+	436.477i	−0.471028	+	0.815844i
$536$	−237.601	−	137.179i	−0.443285	−	0.255930i
$537$		0			0
$538$	−402.000			−0.747212
$539$	−540.112	+	311.834i	−1.00206	+	0.578542i
$540$		0			0
$541$	36.5000	+	63.2199i	0.0674677	+	0.116857i	0.897786	−	0.440432i	$-0.145175\pi$
$541$	36.5000	+	63.2199i	0.0674677	+	0.116857i	−0.830318	+	0.557289i	$0.811841\pi$
$542$	636.867	+	367.696i	1.17503	+	0.678405i
$543$		0			0
$544$	−48.0000	−	83.1384i	−0.0882353	−	0.152828i
$545$		−	207.889i		−	0.381448i
$546$		0			0
$547$	32.0000			0.0585009			0.0292505	−	0.999572i	$-0.490688\pi$
$547$	32.0000			0.0585009			0.0292505	+	0.999572i	$0.490688\pi$
$548$	−117.576	+	67.8823i	−0.214554	+	0.123873i
$549$		0			0
$550$	−63.0000	+	109.119i	−0.114545	+	0.198399i
$551$	676.059	−	390.323i	1.22697	−	0.708390i
$552$		0			0
$553$	−395.500	+	685.026i	−0.715190	+	1.23875i
$554$			159.806i			0.288459i
$555$		0			0
$556$	−103.000	+	178.401i	−0.185252	+	0.320866i
$557$	40.4166	+	23.3345i	0.0725612	+	0.0418932i	0.535842	−	0.844319i	$-0.319994\pi$
$557$	40.4166	+	23.3345i	0.0725612	+	0.0418932i	−0.463280	+	0.886212i	$0.653328\pi$
$558$		0			0
$559$	−23.0000			−0.0411449
$560$			118.794i			0.212132i
$561$		0			0
$562$	−324.000	−	561.184i	−0.576512	−	0.998549i
$563$	−767.915	−	443.356i	−1.36397	−	0.787488i	−0.373820	−	0.927501i	$-0.621952\pi$
$563$	−767.915	−	443.356i	−1.36397	−	0.787488i	−0.990150	+	0.140013i	$0.955286\pi$
$564$		0			0
$565$	−207.000	−	358.535i	−0.366372	−	0.634574i
$566$			125.865i			0.222376i
$567$		0			0
$568$	276.000			0.485915
$569$	−275.568	+	159.099i	−0.484302	+	0.279612i	−0.722207	−	0.691677i	$-0.756872\pi$
$569$	−275.568	+	159.099i	−0.484302	+	0.279612i	0.237906	+	0.971288i	$0.423539\pi$
$570$		0			0
$571$	267.500	−	463.324i	0.468476	−	0.811425i	−0.530875	−	0.847450i	$-0.678136\pi$
$571$	267.500	−	463.324i	0.468476	−	0.811425i	0.999351	+	0.0360256i	$0.0114698\pi$
$572$	−22.0454	+	12.7279i	−0.0385409	+	0.0222516i
$573$		0			0
$574$	−231.000	+	400.104i	−0.402439	+	0.697045i
$575$		−	118.794i		−	0.206598i
$576$		0			0
$577$	−452.500	+	783.753i	−0.784229	+	1.35832i	0.145230	+	0.989398i	$0.453608\pi$
$577$	−452.500	+	783.753i	−0.784229	+	1.35832i	−0.929459	+	0.368926i	$0.879726\pi$
$578$	−1.22474	−	0.707107i	−0.00211894	−	0.00122337i
$579$		0			0
$580$	288.000			0.496552
$581$	−180.037	+	103.945i	−0.309875	+	0.178907i
$582$		0			0
$583$	324.000	+	561.184i	0.555746	+	0.962581i
$584$	159.217	+	91.9239i	0.272632	+	0.157404i
$585$		0			0
$586$	−48.0000	−	83.1384i	−0.0819113	−	0.141874i
$587$			576.999i			0.982963i	0.870888	+	0.491481i	$0.163544\pi$
$587$			576.999i			0.982963i	−0.870888	+	0.491481i	$0.836456\pi$
$588$		0			0
$589$	1081.00			1.83531
$590$	−440.908	+	254.558i	−0.747302	+	0.431455i
$591$		0			0
$592$	110.000	−	190.526i	0.185811	−	0.321834i
$593$	481.325	−	277.893i	0.811677	−	0.468622i	−0.0358606	−	0.999357i	$-0.511417\pi$
$593$	481.325	−	277.893i	0.811677	−	0.468622i	0.847538	+	0.530735i	$0.178084\pi$
$594$		0			0
$595$	−252.000	−	436.477i	−0.423529	−	0.733574i
$596$			339.411i			0.569482i
$597$		0			0
$598$	12.0000	−	20.7846i	0.0200669	−	0.0347569i
$599$	−176.363	−	101.823i	−0.294429	−	0.169989i	0.345508	−	0.938416i	$-0.387707\pi$
$599$	−176.363	−	101.823i	−0.294429	−	0.169989i	−0.639938	+	0.768427i	$0.721040\pi$
$600$		0			0
$601$	143.000			0.237937			0.118968	−	0.992898i	$-0.462041\pi$
$601$	143.000			0.237937			0.118968	+	0.992898i	$0.462041\pi$
$602$	−197.184	−	113.844i	−0.327548	−	0.189110i
$603$		0			0
$604$	104.000	+	180.133i	0.172185	+	0.298234i
$605$	150.644	+	86.9741i	0.248998	+	0.143759i
$606$		0			0
$607$	−299.500	−	518.749i	−0.493410	−	0.854612i	0.506561	−	0.862204i	$-0.330917\pi$
$607$	−299.500	−	518.749i	−0.493410	−	0.854612i	−0.999971	+	0.00759259i	$0.997583\pi$
$608$			130.108i			0.213993i
$609$		0			0
$610$	−624.000			−1.02295
$611$	3.67423	−	2.12132i	0.00601348	−	0.00347188i
$612$		0			0
$613$	152.000	−	263.272i	0.247961	−	0.429481i	−0.714999	−	0.699125i	$-0.753573\pi$
$613$	152.000	−	263.272i	0.247961	−	0.429481i	0.962960	+	0.269645i	$0.0869062\pi$
$614$	285.366	−	164.756i	0.464765	−	0.268332i
$615$		0			0
$616$	−252.000			−0.409091
$617$		−	292.742i		−	0.474461i	−0.971453	−	0.237230i	$-0.923760\pi$
$617$		−	292.742i		−	0.474461i	0.971453	−	0.237230i	$-0.0762396\pi$
$618$		0			0
$619$	171.500	−	297.047i	0.277060	−	0.479882i	−0.693593	−	0.720367i	$-0.743973\pi$
$619$	171.500	−	297.047i	0.277060	−	0.479882i	0.970653	+	0.240486i	$0.0773067\pi$
$620$	345.378	+	199.404i	0.557061	+	0.321620i
$621$		0			0
$622$	354.000			0.569132
$623$	−823.029	−	475.176i	−1.32107	−	0.762722i
$624$		0			0
$625$	200.500	+	347.276i	0.320800	+	0.555642i
$626$	184.936	+	106.773i	0.295426	+	0.170564i
$627$		0			0
$628$	152.000	+	263.272i	0.242038	+	0.419222i
$629$			933.381i			1.48391i
$630$		0			0
$631$	272.000			0.431062			0.215531	−	0.976497i	$-0.430852\pi$
$631$	272.000			0.431062			0.215531	+	0.976497i	$0.430852\pi$
$632$	−276.792	+	159.806i	−0.437963	+	0.252858i
$633$		0			0
$634$	−288.000	+	498.831i	−0.454259	+	0.786799i
$635$	415.189	−	239.709i	0.653840	−	0.377495i
$636$		0			0
$637$	24.5000	−	42.4352i	0.0384615	−	0.0666173i
$638$			610.940i			0.957587i
$639$		0			0
$640$	−24.0000	+	41.5692i	−0.0375000	+	0.0649519i
$641$	367.423	+	212.132i	0.573204	+	0.330939i	0.758428	−	0.651757i	$-0.225968\pi$
$641$	367.423	+	212.132i	0.573204	+	0.330939i	−0.185224	+	0.982696i	$0.559301\pi$
$642$		0			0
$643$	−679.000			−1.05599			−0.527994	−	0.849248i	$-0.677056\pi$
$643$	−679.000			−1.05599			−0.527994	+	0.849248i	$0.677056\pi$
$644$	205.757	−	118.794i	0.319499	−	0.184463i
$645$		0			0
$646$	−276.000	−	478.046i	−0.427245	−	0.740009i
$647$	−834.051	−	481.540i	−1.28911	−	0.744265i	−0.310611	−	0.950537i	$-0.600534\pi$
$647$	−834.051	−	481.540i	−1.28911	−	0.744265i	−0.978495	+	0.206272i	$0.933867\pi$
$648$		0			0
$649$	−540.000	−	935.307i	−0.832049	−	1.44115i
$650$		−	9.89949i		−	0.0152300i
$651$		0			0
$652$	−112.000			−0.171779
$653$	775.264	−	447.599i	1.18723	−	0.685450i	0.229557	−	0.973295i	$-0.426272\pi$
$653$	775.264	−	447.599i	1.18723	−	0.685450i	0.957677	+	0.287846i	$0.0929390\pi$
$654$		0			0
$655$	45.0000	−	77.9423i	0.0687023	−	0.118996i
$656$	−161.666	+	93.3381i	−0.246443	+	0.142284i
$657$		0			0
$658$	42.0000			0.0638298
$659$			16.9706i			0.0257520i	0.999917	+	0.0128760i	$0.00409867\pi$
$659$			16.9706i			0.0257520i	−0.999917	+	0.0128760i	$0.995901\pi$
$660$		0			0
$661$	216.500	−	374.989i	0.327534	−	0.567306i	−0.654488	−	0.756072i	$-0.727116\pi$
$661$	216.500	−	374.989i	0.327534	−	0.567306i	0.982022	+	0.188767i	$0.0604491\pi$
$662$	89.4064	+	51.6188i	0.135055	+	0.0779740i
$663$		0			0
$664$	−84.0000			−0.126506
$665$			683.065i			1.02717i
$666$		0			0
$667$	−288.000	−	498.831i	−0.431784	−	0.747872i
$668$	−7.34847	−	4.24264i	−0.0110007	−	0.00635126i
$669$		0			0
$670$	−291.000	−	504.027i	−0.434328	−	0.752279i
$671$		−	1323.70i		−	1.97273i
$672$		0			0
$673$	737.000			1.09510			0.547548	−	0.836774i	$-0.315561\pi$
$673$	737.000			1.09510			0.547548	+	0.836774i	$0.315561\pi$
$674$	645.441	−	372.645i	0.957627	−	0.552886i
$675$		0			0
$676$	−168.000	+	290.985i	−0.248521	+	0.430450i
$677$	117.576	−	67.8823i	0.173671	−	0.100269i	−0.410644	−	0.911796i	$-0.634696\pi$
$677$	117.576	−	67.8823i	0.173671	−	0.100269i	0.584316	+	0.811526i	$0.301363\pi$
$678$		0			0
$679$	−364.000	−	630.466i	−0.536082	−	0.928522i
$680$		−	203.647i		−	0.299481i
$681$		0			0
$682$	−423.000	+	732.657i	−0.620235	+	1.07428i
$683$	1102.27	+	636.396i	1.61387	+	0.931766i	0.988463	+	0.151464i	$0.0483988\pi$
$683$	1102.27	+	636.396i	1.61387	+	0.931766i	0.625403	+	0.780302i	$0.284935\pi$
$684$		0			0
$685$	−288.000			−0.420438
$686$	420.087	−	242.538i	0.612372	−	0.353553i
$687$		0			0
$688$	−46.0000	−	79.6743i	−0.0668605	−	0.115806i
$689$	−44.0908	−	25.4558i	−0.0639925	−	0.0369461i
$690$		0			0
$691$	123.500	+	213.908i	0.178726	+	0.309563i	0.941445	−	0.337168i	$-0.109469\pi$
$691$	123.500	+	213.908i	0.178726	+	0.309563i	−0.762718	+	0.646731i	$0.776136\pi$
$692$			305.470i			0.441431i
$693$		0			0
$694$	600.000			0.864553
$695$	−378.446	+	218.496i	−0.544527	+	0.314383i
$696$		0			0
$697$	396.000	−	685.892i	0.568149	−	0.984063i
$698$	−137.171	+	79.1960i	−0.196521	+	0.113461i
$699$		0			0
$700$	49.0000	−	84.8705i	0.0700000	−	0.121244i
$701$		−	322.441i		−	0.459972i	−0.973194	−	0.229986i	$-0.926132\pi$
$701$		−	322.441i		−	0.459972i	0.973194	−	0.229986i	$-0.0738681\pi$
$702$		0			0
$703$	632.500	−	1095.52i	0.899716	−	1.55835i
$704$	−88.1816	−	50.9117i	−0.125258	−	0.0723177i
$705$		0			0
$706$	438.000			0.620397
$707$		−	1039.45i		−	1.47022i
$708$		0			0
$709$	524.000	+	907.595i	0.739069	+	1.28011i	0.952915	+	0.303238i	$0.0980677\pi$
$709$	524.000	+	907.595i	0.739069	+	1.28011i	−0.213846	+	0.976867i	$0.568599\pi$
$710$	507.044	+	292.742i	0.714147	+	0.412313i
$711$		0			0
$712$	−192.000	−	332.554i	−0.269663	−	0.467070i
$713$		−	797.616i		−	1.11868i
$714$		0			0
$715$	−54.0000			−0.0755245
$716$	−7.34847	+	4.24264i	−0.0102632	+	0.00592548i
$717$		0			0
$718$	360.000	−	623.538i	0.501393	−	0.868438i
$719$	−216.780	+	125.158i	−0.301502	+	0.174072i	−0.643117	−	0.765768i	$-0.722359\pi$
$719$	−216.780	+	125.158i	−0.301502	+	0.174072i	0.341616	+	0.939840i	$0.389026\pi$
$720$		0			0
$721$	−416.500	+	721.399i	−0.577670	+	1.00055i
$722$			237.588i			0.329069i
$723$		0			0
$724$	−55.0000	+	95.2628i	−0.0759669	+	0.131578i
$725$	−205.757	−	118.794i	−0.283803	−	0.163854i
$726$		0			0
$727$	641.000			0.881706			0.440853	−	0.897579i	$-0.354676\pi$
$727$	641.000			0.881706			0.440853	+	0.897579i	$0.354676\pi$
$728$	17.1464	−	9.89949i	0.0235528	−	0.0135982i
$729$		0			0
$730$	195.000	+	337.750i	0.267123	+	0.462671i
$731$	338.030	+	195.161i	0.462421	+	0.266979i
$732$		0			0
$733$	12.5000	+	21.6506i	0.0170532	+	0.0295370i	0.874426	−	0.485159i	$-0.161238\pi$
$733$	12.5000	+	21.6506i	0.0170532	+	0.0295370i	−0.857373	+	0.514696i	$0.827905\pi$
$734$		−	451.134i		−	0.614624i
$735$		0			0
$736$	96.0000			0.130435
$737$	1069.20	−	617.304i	1.45075	−	0.837591i
$738$		0			0
$739$	267.500	−	463.324i	0.361976	−	0.626960i	−0.626310	−	0.779574i	$-0.715436\pi$
$739$	267.500	−	463.324i	0.361976	−	0.626960i	0.988286	+	0.152614i	$0.0487690\pi$
$740$	404.166	−	233.345i	0.546170	−	0.315331i
$741$		0			0
$742$	−252.000	−	436.477i	−0.339623	−	0.588244i
$743$			937.624i			1.26194i	0.775806	+	0.630971i	$0.217344\pi$
$743$			937.624i			1.26194i	−0.775806	+	0.630971i	$0.782656\pi$
$744$		0			0
$745$	−360.000	+	623.538i	−0.483221	+	0.836964i
$746$	−255.972	−	147.785i	−0.343126	−	0.198104i
$747$		0			0
$748$	432.000			0.577540
$749$	720.150	+	415.779i	0.961482	+	0.555112i
$750$		0			0
$751$	−20.5000	−	35.5070i	−0.0272969	−	0.0472797i	0.852054	−	0.523454i	$-0.175357\pi$
$751$	−20.5000	−	35.5070i	−0.0272969	−	0.0472797i	−0.879351	+	0.476174i	$0.842023\pi$
$752$	14.6969	+	8.48528i	0.0195438	+	0.0112836i
$753$		0			0
$754$	−24.0000	−	41.5692i	−0.0318302	−	0.0551316i
$755$			441.235i			0.584417i
$756$		0			0
$757$	−1114.00			−1.47160			−0.735799	−	0.677200i	$-0.763193\pi$
$757$	−1114.00			−1.47160			−0.735799	+	0.677200i	$0.763193\pi$
$758$	−530.315	+	306.177i	−0.699623	+	0.403928i
$759$		0			0
$760$	−138.000	+	239.023i	−0.181579	+	0.314504i
$761$	−249.848	+	144.250i	−0.328315	+	0.189553i	−0.655093	−	0.755548i	$-0.727371\pi$
$761$	−249.848	+	144.250i	−0.328315	+	0.189553i	0.326778	+	0.945101i	$0.394037\pi$
$762$		0			0
$763$	−343.000			−0.449541
$764$			127.279i			0.166596i
$765$		0			0
$766$	276.000	−	478.046i	0.360313	−	0.624081i
$767$	73.4847	+	42.4264i	0.0958079	+	0.0553147i
$768$		0			0
$769$	1127.00			1.46554			0.732770	−	0.680477i	$-0.238227\pi$
$769$	1127.00			1.46554			0.732770	+	0.680477i	$0.238227\pi$
$770$	−462.954	−	267.286i	−0.601238	−	0.347125i
$771$		0			0
$772$	−151.000	−	261.540i	−0.195596	−	0.338782i
$773$	187.386	+	108.187i	0.242414	+	0.139958i	0.616286	−	0.787523i	$-0.288637\pi$
$773$	187.386	+	108.187i	0.242414	+	0.139958i	−0.373872	+	0.927480i	$0.621970\pi$
$774$		0			0
$775$	−164.500	−	284.922i	−0.212258	−	0.367642i
$776$		−	294.156i		−	0.379068i
$777$		0			0
$778$	−522.000			−0.670951
$779$	−929.581	+	536.694i	−1.19330	+	0.688953i
$780$		0			0
$781$	−621.000	+	1075.60i	−0.795134	+	1.37721i
$782$	−352.727	+	203.647i	−0.451057	+	0.260418i
$783$		0			0
$784$	196.000			0.250000
$785$			644.881i			0.821505i
$786$		0			0
$787$	−85.0000	+	147.224i	−0.108005	+	0.187070i	−0.914962	−	0.403540i	$-0.867780\pi$
$787$	−85.0000	+	147.224i	−0.108005	+	0.187070i	0.806957	+	0.590610i	$0.201113\pi$
$788$	29.3939	+	16.9706i	0.0373019	+	0.0215362i
$789$		0			0
$790$	−678.000			−0.858228
$791$	−591.552	+	341.533i	−0.747853	+	0.431773i
$792$		0			0
$793$	52.0000	+	90.0666i	0.0655738	+	0.113577i
$794$	−138.396	−	79.9031i	−0.174302	−	0.100634i
$795$		0			0
$796$	−160.000	−	277.128i	−0.201005	−	0.348151i
$797$		−	1170.97i		−	1.46922i	−0.678489	−	0.734610i	$-0.737365\pi$
$797$		−	1170.97i		−	1.46922i	0.678489	−	0.734610i	$-0.262635\pi$
$798$		0			0
$799$	−72.0000			−0.0901126
$800$	34.2929	−	19.7990i	0.0428661	−	0.0247487i
$801$		0			0
$802$	252.000	−	436.477i	0.314214	−	0.544235i
$803$	−716.476	+	413.657i	−0.892249	+	0.515140i
$804$		0			0
$805$	504.000			0.626087
$806$		−	66.4680i		−	0.0824665i
$807$		0			0
$808$	210.000	−	363.731i	0.259901	−	0.450162i
$809$	290.265	+	167.584i	0.358794	+	0.207150i	0.668552	−	0.743666i	$-0.266915\pi$
$809$	290.265	+	167.584i	0.358794	+	0.207150i	−0.309757	+	0.950816i	$0.600248\pi$
$810$		0			0
$811$	−1114.00			−1.37361			−0.686806	−	0.726840i	$-0.740988\pi$
$811$	−1114.00			−1.37361			−0.686806	+	0.726840i	$0.740988\pi$
$812$		−	475.176i		−	0.585192i
$813$		0			0
$814$	495.000	+	857.365i	0.608108	+	1.05327i
$815$	−205.757	−	118.794i	−0.252463	−	0.145759i
$816$		0			0
$817$	−264.500	−	458.127i	−0.323745	−	0.560743i
$818$		−	451.134i		−	0.551509i
$819$		0			0
$820$	−396.000			−0.482927
$821$	−84.5074	+	48.7904i	−0.102932	+	0.0594280i	−0.550582	−	0.834781i	$-0.685594\pi$
$821$	−84.5074	+	48.7904i	−0.102932	+	0.0594280i	0.447650	+	0.894209i	$0.352261\pi$
$822$		0			0
$823$	−796.000	+	1378.71i	−0.967193	+	1.67523i	−0.263590	+	0.964635i	$0.584907\pi$
$823$	−796.000	+	1378.71i	−0.967193	+	1.67523i	−0.703603	+	0.710593i	$0.748427\pi$
$824$	−291.489	+	168.291i	−0.353749	+	0.204237i
$825$		0			0
$826$	420.000	+	727.461i	0.508475	+	0.880704i
$827$			1022.48i			1.23637i	0.786033	+	0.618184i	$0.212131\pi$
$827$			1022.48i			1.23637i	−0.786033	+	0.618184i	$0.787869\pi$
$828$		0			0
$829$	−191.500	+	331.688i	−0.231001	+	0.400106i	−0.958103	−	0.286424i	$-0.907533\pi$
$829$	−191.500	+	331.688i	−0.231001	+	0.400106i	0.727102	+	0.686530i	$0.240867\pi$
$830$	−154.318	−	89.0955i	−0.185925	−	0.107344i
$831$		0			0
$832$	8.00000			0.00961538
$833$	−720.150	+	415.779i	−0.864526	+	0.499134i
$834$		0			0
$835$	−9.00000	−	15.5885i	−0.0107784	−	0.0186688i
$836$	−507.044	−	292.742i	−0.606512	−	0.350170i
$837$		0			0
$838$	543.000	+	940.504i	0.647971	+	1.12232i
$839$			576.999i			0.687722i	0.939020	+	0.343861i	$0.111735\pi$
$839$			576.999i			0.687722i	−0.939020	+	0.343861i	$0.888265\pi$
$840$		0			0
$841$	−311.000			−0.369798
$842$	79.6084	−	45.9619i	0.0945468	−	0.0545866i
$843$		0			0
$844$	−208.000	+	360.267i	−0.246445	+	0.426856i
$845$	−617.271	+	356.382i	−0.730499	+	0.421754i
$846$		0			0
$847$	143.500	−	248.549i	0.169421	−	0.293447i
$848$		−	203.647i		−	0.240149i
$849$		0			0
$850$	−84.0000	+	145.492i	−0.0988235	+	0.171167i
$851$	−808.332	−	466.690i	−0.949861	−	0.548402i
$852$		0			0
$853$	527.000			0.617819			0.308910	−	0.951091i	$-0.400036\pi$
$853$	527.000			0.617819			0.308910	+	0.951091i	$0.400036\pi$
$854$			1029.55i			1.20556i
$855$		0			0
$856$	168.000	+	290.985i	0.196262	+	0.339935i
$857$	1146.36	+	661.852i	1.33764	+	0.772289i	0.986458	−	0.164016i	$-0.0524449\pi$
$857$	1146.36	+	661.852i	1.33764	+	0.772289i	0.351187	+	0.936305i	$0.385778\pi$
$858$		0			0
$859$	707.000	+	1224.56i	0.823050	+	1.42556i	0.903400	+	0.428798i	$0.141063\pi$
$859$	707.000	+	1224.56i	0.823050	+	1.42556i	−0.0803504	+	0.996767i	$0.525604\pi$
$860$		−	195.161i		−	0.226932i
$861$		0			0
$862$	678.000			0.786543
$863$	1186.78	−	685.186i	1.37518	−	0.793959i	0.383603	−	0.923498i	$-0.374683\pi$
$863$	1186.78	−	685.186i	1.37518	−	0.793959i	0.991574	+	0.129539i	$0.0413499\pi$
$864$		0			0
$865$	−324.000	+	561.184i	−0.374566	+	0.648768i
$866$	−449.481	+	259.508i	−0.519032	+	0.299663i
$867$		0			0
$868$	329.000	−	569.845i	0.379032	−	0.656503i
$869$		−	1438.26i		−	1.65507i
$870$		0			0
$871$	−48.5000	+	84.0045i	−0.0556831	+	0.0964460i
$872$	−120.025	−	69.2965i	−0.137643	−	0.0794684i
$873$		0			0
$874$	552.000			0.631579
$875$	823.029	−	475.176i	0.940604	−	0.543058i
$876$		0			0
$877$	−112.000	−	193.990i	−0.127708	−	0.221197i	0.795080	−	0.606504i	$-0.207429\pi$
$877$	−112.000	−	193.990i	−0.127708	−	0.221197i	−0.922788	+	0.385307i	$0.874095\pi$
$878$	−656.463	−	379.009i	−0.747680	−	0.431673i
$879$		0			0
$880$	−108.000	−	187.061i	−0.122727	−	0.212570i
$881$			1612.20i			1.82997i	0.403488	+	0.914985i	$0.367798\pi$
$881$			1612.20i			1.82997i	−0.403488	+	0.914985i	$0.632202\pi$
$882$		0			0
$883$	329.000			0.372593			0.186297	−	0.982494i	$-0.440351\pi$
$883$	329.000			0.372593			0.186297	+	0.982494i	$0.440351\pi$
$884$	−29.3939	+	16.9706i	−0.0332510	+	0.0191975i
$885$		0			0
$886$	60.0000	−	103.923i	0.0677201	−	0.117295i
$887$	47.7650	−	27.5772i	0.0538501	−	0.0310904i	−0.472833	−	0.881152i	$-0.656769\pi$
$887$	47.7650	−	27.5772i	0.0538501	−	0.0310904i	0.526683	+	0.850062i	$0.323435\pi$
$888$		0			0
$889$	−395.500	−	685.026i	−0.444882	−	0.770558i
$890$		−	814.587i		−	0.915266i
$891$		0			0
$892$	−40.0000	+	69.2820i	−0.0448430	+	0.0776704i
$893$	84.5074	+	48.7904i	0.0946331	+	0.0546365i
$894$		0			0
$895$	−18.0000			−0.0201117
$896$	68.5857	+	39.5980i	0.0765466	+	0.0441942i
$897$		0			0
$898$	−435.000	−	753.442i	−0.484410	−	0.839022i
$899$	−1381.51	−	797.616i	−1.53672	−	0.887226i
$900$		0			0
$901$	432.000	+	748.246i	0.479467	+	0.830462i
$902$		−	840.043i		−	0.931311i
$903$		0			0
$904$	−276.000			−0.305310
$905$	−202.083	+	116.673i	−0.223296	+	0.128920i
$906$		0			0
$907$	−155.500	+	269.334i	−0.171444	+	0.296950i	−0.938925	−	0.344122i	$-0.888177\pi$
$907$	−155.500	+	269.334i	−0.171444	+	0.296950i	0.767481	+	0.641072i	$0.221510\pi$
$908$	389.469	−	224.860i	0.428930	−	0.247643i
$909$		0			0
$910$	42.0000			0.0461538
$911$			356.382i			0.391198i	0.980684	+	0.195599i	$0.0626652\pi$
$911$			356.382i			0.391198i	−0.980684	+	0.195599i	$0.937335\pi$
$912$		0			0
$913$	189.000	−	327.358i	0.207010	−	0.358552i
$914$	567.057	+	327.390i	0.620412	+	0.358195i
$915$		0			0
$916$	−754.000			−0.823144
$917$	−128.598	−	74.2462i	−0.140238	−	0.0809664i
$918$		0			0
$919$	72.5000	+	125.574i	0.0788901	+	0.136642i	0.902771	−	0.430121i	$-0.141529\pi$
$919$	72.5000	+	125.574i	0.0788901	+	0.136642i	−0.823881	+	0.566762i	$0.808196\pi$
$920$	176.363	+	101.823i	0.191699	+	0.110678i
$921$		0			0
$922$	192.000	+	332.554i	0.208243	+	0.360687i
$923$		−	97.5807i		−	0.105721i
$924$		0			0
$925$	−385.000			−0.416216
$926$	57.5630	−	33.2340i	0.0621631	−	0.0358899i
$927$		0			0
$928$	96.0000	−	166.277i	0.103448	−	0.179178i
$929$	−268.219	+	154.856i	−0.288718	+	0.166691i	−0.637364	−	0.770563i	$-0.719975\pi$
$929$	−268.219	+	154.856i	−0.288718	+	0.166691i	0.348645	+	0.937255i	$0.386642\pi$
$930$		0			0
$931$	1127.00			1.21053
$932$		−	687.308i		−	0.737455i
$933$		0			0
$934$	525.000	−	909.327i	0.562099	−	0.973583i
$935$	793.635	+	458.205i	0.848807	+	0.490059i
$936$		0			0
$937$	−487.000			−0.519744			−0.259872	−	0.965643i	$-0.583680\pi$
$937$	−487.000			−0.519744			−0.259872	+	0.965643i	$0.583680\pi$
$938$	−831.602	+	480.126i	−0.886569	+	0.511861i
$939$		0			0
$940$	18.0000	+	31.1769i	0.0191489	+	0.0331669i
$941$	1190.45	+	687.308i	1.26509	+	0.730401i	0.974055	−	0.226310i	$-0.0726663\pi$
$941$	1190.45	+	687.308i	1.26509	+	0.730401i	0.291037	+	0.956712i	$0.406000\pi$
$942$		0			0
$943$	396.000	+	685.892i	0.419936	+	0.727351i
$944$			339.411i			0.359546i
$945$		0			0
$946$	414.000			0.437632
$947$	−165.341	+	95.4594i	−0.174594	+	0.100802i	−0.584750	−	0.811213i	$-0.698808\pi$
$947$	−165.341	+	95.4594i	−0.174594	+	0.100802i	0.410156	+	0.912015i	$0.365474\pi$
$948$		0			0
$949$	32.5000	−	56.2917i	0.0342466	−	0.0593168i
$950$	197.184	−	113.844i	0.207562	−	0.119836i
$951$		0			0
$952$	−336.000			−0.352941
$953$		−	1035.20i		−	1.08626i	−0.839649	−	0.543129i	$-0.817239\pi$
$953$		−	1035.20i		−	1.08626i	0.839649	−	0.543129i	$-0.182761\pi$
$954$		0			0
$955$	−135.000	+	233.827i	−0.141361	+	0.244845i
$956$	−22.0454	−	12.7279i	−0.0230600	−	0.0133137i
$957$		0			0
$958$	−600.000			−0.626305
$959$			475.176i			0.495491i
$960$		0			0
$961$	−624.000	−	1080.80i	−0.649324	−	1.12466i
$962$	−67.3610	−	38.8909i	−0.0700218	−	0.0404271i
$963$		0			0
$964$	−130.000	−	225.167i	−0.134855	−	0.233575i
$965$		−	640.639i		−	0.663874i
$966$		0			0
$967$	−1681.00			−1.73837			−0.869183	−	0.494490i	$-0.835355\pi$
$967$	−1681.00			−1.73837			−0.869183	+	0.494490i	$0.835355\pi$
$968$	100.429	−	57.9828i	0.103749	−	0.0598995i
$969$		0			0
$970$	312.000	−	540.400i	0.321649	−	0.557113i
$971$	1043.48	−	602.455i	1.07465	−	0.620448i	0.145200	−	0.989402i	$-0.453617\pi$
$971$	1043.48	−	602.455i	1.07465	−	0.620448i	0.929448	+	0.368954i	$0.120284\pi$
$972$		0			0
$973$	360.500	+	624.404i	0.370504	+	0.641731i
$974$			337.997i			0.347020i
$975$		0			0
$976$	−208.000	+	360.267i	−0.213115	+	0.369126i
$977$	−1017.76	−	587.606i	−1.04172	−	0.601439i	−0.121402	−	0.992603i	$-0.538739\pi$
$977$	−1017.76	−	587.606i	−1.04172	−	0.601439i	−0.920321	+	0.391165i	$0.872072\pi$
$978$		0			0
$979$	1728.00			1.76507
$980$	360.075	+	207.889i	0.367423	+	0.212132i
$981$		0			0
$982$	144.000	+	249.415i	0.146640	+	0.253987i
$983$	1660.75	+	958.837i	1.68948	+	0.975419i	0.954917	+	0.296873i	$0.0959439\pi$
$983$	1660.75	+	958.837i	1.68948	+	0.975419i	0.734558	+	0.678546i	$0.237389\pi$
$984$		0			0
$985$	36.0000	+	62.3538i	0.0365482	+	0.0633034i
$986$			814.587i			0.826153i
$987$		0			0
$988$	46.0000			0.0465587
$989$	−338.030	+	195.161i	−0.341789	+	0.197332i
$990$		0			0
$991$	312.500	−	541.266i	0.315338	−	0.546182i	−0.664171	−	0.747580i	$-0.731215\pi$
$991$	312.500	−	541.266i	0.315338	−	0.546182i	0.979509	+	0.201399i	$0.0645488\pi$
$992$	230.252	−	132.936i	0.232109	−	0.134008i
$993$		0			0
$994$	483.000	−	836.581i	0.485915	−	0.841630i
$995$		−	678.823i		−	0.682234i
$996$		0			0
$997$	471.500	−	816.662i	0.472919	−	0.819119i	−0.526601	−	0.850113i	$-0.676534\pi$
$997$	471.500	−	816.662i	0.472919	−	0.819119i	0.999520	+	0.0309934i	$0.00986707\pi$
$998$	60.0125	+	34.6482i	0.0601328	+	0.0347177i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.s.a.53.2	yes	4
3.2	odd	2	inner	126.3.s.a.53.1	✓	4
4.3	odd	2		1008.3.dc.b.305.2		4
7.2	even	3	inner	126.3.s.a.107.1	yes	4
7.3	odd	6		882.3.b.e.197.2		2
7.4	even	3		882.3.b.b.197.2		2
7.5	odd	6		882.3.s.a.863.1		4
7.6	odd	2		882.3.s.a.557.2		4
12.11	even	2		1008.3.dc.b.305.1		4
21.2	odd	6	inner	126.3.s.a.107.2	yes	4
21.5	even	6		882.3.s.a.863.2		4
21.11	odd	6		882.3.b.b.197.1		2
21.17	even	6		882.3.b.e.197.1		2
21.20	even	2		882.3.s.a.557.1		4
28.23	odd	6		1008.3.dc.b.737.1		4
84.23	even	6		1008.3.dc.b.737.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.s.a.53.1	✓	4	3.2	odd	2	inner
126.3.s.a.53.2	yes	4	1.1	even	1	trivial
126.3.s.a.107.1	yes	4	7.2	even	3	inner
126.3.s.a.107.2	yes	4	21.2	odd	6	inner
882.3.b.b.197.1		2	21.11	odd	6
882.3.b.b.197.2		2	7.4	even	3
882.3.b.e.197.1		2	21.17	even	6
882.3.b.e.197.2		2	7.3	odd	6
882.3.s.a.557.1		4	21.20	even	2
882.3.s.a.557.2		4	7.6	odd	2
882.3.s.a.863.1		4	7.5	odd	6
882.3.s.a.863.2		4	21.5	even	6
1008.3.dc.b.305.1		4	12.11	even	2
1008.3.dc.b.305.2		4	4.3	odd	2
1008.3.dc.b.737.1		4	28.23	odd	6
1008.3.dc.b.737.2		4	84.23	even	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	126.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(3.67423 - 2.12132i) q^{5} +(-3.50000 - 6.06218i) q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(3.67423 - 2.12132i) q^{5} +(-3.50000 - 6.06218i) q^{7} -2.82843i q^{8} +(3.00000 - 5.19615i) q^{10} +(11.0227 + 6.36396i) q^{11} -1.00000 q^{13} +(-8.57321 - 4.94975i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(14.6969 + 8.48528i) q^{17} +(-11.5000 - 19.9186i) q^{19} -8.48528i q^{20} +18.0000 q^{22} +(-14.6969 + 8.48528i) q^{23} +(-3.50000 + 6.06218i) q^{25} +(-1.22474 + 0.707107i) q^{26} -14.0000 q^{28} +33.9411i q^{29} +(-23.5000 + 40.7032i) q^{31} +(-4.89898 - 2.82843i) q^{32} +24.0000 q^{34} +(-25.7196 - 14.8492i) q^{35} +(27.5000 + 47.6314i) q^{37} +(-28.1691 - 16.2635i) q^{38} +(-6.00000 - 10.3923i) q^{40} -46.6690i q^{41} +23.0000 q^{43} +(22.0454 - 12.7279i) q^{44} +(-12.0000 + 20.7846i) q^{46} +(-3.67423 + 2.12132i) q^{47} +(-24.5000 + 42.4352i) q^{49} +9.89949i q^{50} +(-1.00000 + 1.73205i) q^{52} +(44.0908 + 25.4558i) q^{53} +54.0000 q^{55} +(-17.1464 + 9.89949i) q^{56} +(24.0000 + 41.5692i) q^{58} +(-73.4847 - 42.4264i) q^{59} +(-52.0000 - 90.0666i) q^{61} +66.4680i q^{62} -8.00000 q^{64} +(-3.67423 + 2.12132i) q^{65} +(48.5000 - 84.0045i) q^{67} +(29.3939 - 16.9706i) q^{68} -42.0000 q^{70} +97.5807i q^{71} +(-32.5000 + 56.2917i) q^{73} +(67.3610 + 38.8909i) q^{74} -46.0000 q^{76} -89.0955i q^{77} +(-56.5000 - 97.8609i) q^{79} +(-14.6969 - 8.48528i) q^{80} +(-33.0000 - 57.1577i) q^{82} -29.6985i q^{83} +72.0000 q^{85} +(28.1691 - 16.2635i) q^{86} +(18.0000 - 31.1769i) q^{88} +(117.576 - 67.8823i) q^{89} +(3.50000 + 6.06218i) q^{91} +33.9411i q^{92} +(-3.00000 + 5.19615i) q^{94} +(-84.5074 - 48.7904i) q^{95} +104.000 q^{97} +69.2965i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4} - 14 q^{7}+O(q^{10}) \) 4 * q + 4 * q^4 - 14 * q^7	\( 4 q + 4 q^{4} - 14 q^{7} + 12 q^{10} - 4 q^{13} - 8 q^{16} - 46 q^{19} + 72 q^{22} - 14 q^{25} - 56 q^{28} - 94 q^{31} + 96 q^{34} + 110 q^{37} - 24 q^{40} + 92 q^{43} - 48 q^{46} - 98 q^{49} - 4 q^{52} + 216 q^{55} + 96 q^{58} - 208 q^{61} - 32 q^{64} + 194 q^{67} - 168 q^{70} - 130 q^{73} - 184 q^{76} - 226 q^{79} - 132 q^{82} + 288 q^{85} + 72 q^{88} + 14 q^{91} - 12 q^{94} + 416 q^{97}+O(q^{100}) \) 4 * q + 4 * q^4 - 14 * q^7 + 12 * q^10 - 4 * q^13 - 8 * q^16 - 46 * q^19 + 72 * q^22 - 14 * q^25 - 56 * q^28 - 94 * q^31 + 96 * q^34 + 110 * q^37 - 24 * q^40 + 92 * q^43 - 48 * q^46 - 98 * q^49 - 4 * q^52 + 216 * q^55 + 96 * q^58 - 208 * q^61 - 32 * q^64 + 194 * q^67 - 168 * q^70 - 130 * q^73 - 184 * q^76 - 226 * q^79 - 132 * q^82 + 288 * q^85 + 72 * q^88 + 14 * q^91 - 12 * q^94 + 416 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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