LMFDB - Embedded newform 144.2.l.a.107.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,2,Mod(35,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("144.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	144.l (of order $4$, 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:	$1.14984578911$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 6x^12 - 12x^10 + 33x^8 - 48x^6 + 96x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.2
Root			$-1.36166 - 0.381939i$ of defining polynomial
Character	$\chi$	$=$	144.107
Dual form			144.2.l.a.35.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12697 - 0.854358i) q^{2} +(0.540143 + 1.92568i) q^{4} +(0.763878 - 0.763878i) q^{5} +1.33620 q^{7} +(1.03649 - 2.63167i) q^{8} +O(q^{10})$	\(q+(-1.12697 - 0.854358i) q^{2} +(0.540143 + 1.92568i) q^{4} +(0.763878 - 0.763878i) q^{5} +1.33620 q^{7} +(1.03649 - 2.63167i) q^{8} +(-1.51350 + 0.208245i) q^{10} +(1.95945 + 1.95945i) q^{11} +(4.18757 - 4.18757i) q^{13} +(-1.50587 - 1.14160i) q^{14} +(-3.41649 + 2.08029i) q^{16} -4.03243i q^{17} +(-4.26785 - 4.26785i) q^{19} +(1.88359 + 1.05838i) q^{20} +(-0.534176 - 3.88231i) q^{22} +8.86408i q^{23} +3.83298i q^{25} +(-8.29696 + 1.14160i) q^{26} +(0.721742 + 2.57310i) q^{28} +(1.23934 + 1.23934i) q^{29} +2.87835i q^{31} +(5.62761 + 0.574478i) q^{32} +(-3.44514 + 4.54445i) q^{34} +(1.02070 - 1.02070i) q^{35} +(0.434870 + 0.434870i) q^{37} +(1.16348 + 8.45604i) q^{38} +(-1.21852 - 2.80203i) q^{40} -7.81179 q^{41} +(-5.49678 + 5.49678i) q^{43} +(-2.71489 + 4.83165i) q^{44} +(7.57310 - 9.98959i) q^{46} -3.20723 q^{47} -5.21456 q^{49} +(3.27474 - 4.31967i) q^{50} +(10.3258 + 5.80203i) q^{52} +(4.06777 - 4.06777i) q^{53} +2.99355 q^{55} +(1.38497 - 3.51645i) q^{56} +(-0.337865 - 2.45555i) q^{58} +(-4.71811 - 4.71811i) q^{59} +(3.26785 - 3.26785i) q^{61} +(2.45915 - 3.24383i) q^{62} +(-5.85136 - 5.45542i) q^{64} -6.39758i q^{65} +(-5.44348 - 5.44348i) q^{67} +(7.76518 - 2.17809i) q^{68} +(-2.02234 + 0.278258i) q^{70} -3.76718i q^{71} +10.5357i q^{73} +(-0.118553 - 0.861623i) q^{74} +(5.91327 - 10.5238i) q^{76} +(2.61822 + 2.61822i) q^{77} +11.1995i q^{79} +(-1.02070 + 4.19887i) q^{80} +(8.80369 + 6.67407i) q^{82} +(9.73306 - 9.73306i) q^{83} +(-3.08029 - 3.08029i) q^{85} +(10.8909 - 1.49851i) q^{86} +(7.18757 - 3.12566i) q^{88} -1.64130 q^{89} +(5.59544 - 5.59544i) q^{91} +(-17.0694 + 4.78787i) q^{92} +(3.61446 + 2.74012i) q^{94} -6.52023 q^{95} -5.70272 q^{97} +(5.87667 + 4.45510i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{10} - 16 q^{16} + 16 q^{19} - 40 q^{22} - 24 q^{28} + 24 q^{34} + 72 q^{40} - 32 q^{43} + 40 q^{46} + 16 q^{49} + 24 q^{52} - 64 q^{55} + 24 q^{58} - 32 q^{61} - 48 q^{64} - 16 q^{67} - 72 q^{70} + 80 q^{82} - 32 q^{85} + 48 q^{88} + 48 q^{91} + 72 q^{94}+O(q^{100}) $ 16 * q - 8 * q^10 - 16 * q^16 + 16 * q^19 - 40 * q^22 - 24 * q^28 + 24 * q^34 + 72 * q^40 - 32 * q^43 + 40 * q^46 + 16 * q^49 + 24 * q^52 - 64 * q^55 + 24 * q^58 - 32 * q^61 - 48 * q^64 - 16 * q^67 - 72 * q^70 + 80 * q^82 - 32 * q^85 + 48 * q^88 + 48 * q^91 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

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 $

$2$	−1.12697	−	0.854358i	−0.796891	−	0.604123i
$2$	−1.12697	−	0.854358i	−0.796891	−	0.604123i
$3$		0			0
$3$		0			0
$4$	0.540143	+	1.92568i	0.270072	+	0.962840i
$5$	0.763878	−	0.763878i	0.341617	−	0.341617i	−0.515358	−	0.856975i	$-0.672341\pi$
$5$	0.763878	−	0.763878i	0.341617	−	0.341617i	0.856975	+	0.515358i	$0.172341\pi$
$6$		0			0
$7$	1.33620			0.505038			0.252519	−	0.967592i	$-0.418741\pi$
$7$	1.33620			0.505038			0.252519	+	0.967592i	$0.418741\pi$
$8$	1.03649	−	2.63167i	0.366456	−	0.930435i
$9$		0			0
$10$	−1.51350	+	0.208245i	−0.478610	+	0.0658530i
$11$	1.95945	+	1.95945i	0.590795	+	0.590795i	0.937846	−	0.347051i	$-0.112817\pi$
$11$	1.95945	+	1.95945i	0.590795	+	0.590795i	−0.347051	+	0.937846i	$0.612817\pi$
$12$		0			0
$13$	4.18757	−	4.18757i	1.16142	−	1.16142i	0.177257	−	0.984165i	$-0.443278\pi$
$13$	4.18757	−	4.18757i	1.16142	−	1.16142i	0.984165	−	0.177257i	$-0.0567224\pi$
$14$	−1.50587	−	1.14160i	−0.402460	−	0.305105i
$15$		0			0
$16$	−3.41649	+	2.08029i	−0.854123	+	0.520072i
$17$		−	4.03243i		−	0.978009i	−0.872281	−	0.489004i	$-0.837360\pi$
$17$		−	4.03243i		−	0.978009i	0.872281	−	0.489004i	$-0.162640\pi$
$18$		0			0
$19$	−4.26785	−	4.26785i	−0.979112	−	0.979112i	0.0206739	−	0.999786i	$-0.493419\pi$
$19$	−4.26785	−	4.26785i	−0.979112	−	0.979112i	−0.999786	+	0.0206739i	$0.993419\pi$
$20$	1.88359	+	1.05838i	0.421183	+	0.236661i
$21$		0			0
$22$	−0.534176	−	3.88231i	−0.113887	−	0.827712i
$23$			8.86408i			1.84829i	0.382044	+	0.924144i	$0.375220\pi$
$23$			8.86408i			1.84829i	−0.382044	+	0.924144i	$0.624780\pi$
$24$		0			0
$25$			3.83298i			0.766596i
$26$	−8.29696	+	1.14160i	−1.62717	+	0.223886i
$27$		0			0
$28$	0.721742	+	2.57310i	0.136396	+	0.486271i
$29$	1.23934	+	1.23934i	0.230140	+	0.230140i	0.812751	−	0.582611i	$-0.197969\pi$
$29$	1.23934	+	1.23934i	0.230140	+	0.230140i	−0.582611	+	0.812751i	$0.697969\pi$
$30$		0			0
$31$			2.87835i			0.516968i	0.966016	+	0.258484i	$0.0832229\pi$
$31$			2.87835i			0.516968i	−0.966016	+	0.258484i	$0.916777\pi$
$32$	5.62761	+	0.574478i	0.994830	+	0.101554i
$33$		0			0
$34$	−3.44514	+	4.54445i	−0.590837	+	0.779367i
$35$	1.02070	−	1.02070i	0.172529	−	0.172529i
$36$		0			0
$37$	0.434870	+	0.434870i	0.0714922	+	0.0714922i	0.741949	−	0.670457i	$-0.233902\pi$
$37$	0.434870	+	0.434870i	0.0714922	+	0.0714922i	−0.670457	+	0.741949i	$0.733902\pi$
$38$	1.16348	+	8.45604i	0.188742	+	1.37175i
$39$		0			0
$40$	−1.21852	−	2.80203i	−0.192665	−	0.443040i
$41$	−7.81179			−1.22000			−0.609998	−	0.792403i	$-0.708830\pi$
$41$	−7.81179			−1.22000			−0.609998	+	0.792403i	$0.708830\pi$
$42$		0			0
$43$	−5.49678	+	5.49678i	−0.838251	+	0.838251i	−0.988629	−	0.150378i	$-0.951951\pi$
$43$	−5.49678	+	5.49678i	−0.838251	+	0.838251i	0.150378	+	0.988629i	$0.451951\pi$
$44$	−2.71489	+	4.83165i	−0.409284	+	0.728398i
$45$		0			0
$46$	7.57310	−	9.98959i	1.11659	−	1.47289i
$47$	−3.20723			−0.467822			−0.233911	−	0.972258i	$-0.575152\pi$
$47$	−3.20723			−0.467822			−0.233911	+	0.972258i	$0.575152\pi$
$48$		0			0
$49$	−5.21456			−0.744937
$50$	3.27474	−	4.31967i	0.463118	−	0.610894i
$51$		0			0
$52$	10.3258	+	5.80203i	1.43193	+	0.804597i
$53$	4.06777	−	4.06777i	0.558751	−	0.558751i	−0.370201	−	0.928952i	$-0.620711\pi$
$53$	4.06777	−	4.06777i	0.558751	−	0.558751i	0.928952	+	0.370201i	$0.120711\pi$
$54$		0			0
$55$	2.99355			0.403651
$56$	1.38497	−	3.51645i	0.185074	−	0.469905i
$57$		0			0
$58$	−0.337865	−	2.45555i	−0.0443638	−	0.322430i
$59$	−4.71811	−	4.71811i	−0.614245	−	0.614245i	0.329804	−	0.944049i	$-0.393017\pi$
$59$	−4.71811	−	4.71811i	−0.614245	−	0.614245i	−0.944049	+	0.329804i	$0.893017\pi$
$60$		0			0
$61$	3.26785	−	3.26785i	0.418406	−	0.418406i	−0.466248	−	0.884654i	$-0.654395\pi$
$61$	3.26785	−	3.26785i	0.418406	−	0.418406i	0.884654	+	0.466248i	$0.154395\pi$
$62$	2.45915	−	3.24383i	0.312312	−	0.411967i
$63$		0			0
$64$	−5.85136	−	5.45542i	−0.731420	−	0.681927i
$65$		−	6.39758i		−	0.793522i
$66$		0			0
$67$	−5.44348	−	5.44348i	−0.665027	−	0.665027i	0.291533	−	0.956561i	$-0.405835\pi$
$67$	−5.44348	−	5.44348i	−0.665027	−	0.665027i	−0.956561	+	0.291533i	$0.905835\pi$
$68$	7.76518	−	2.17809i	0.941666	−	0.264132i
$69$		0			0
$70$	−2.02234	+	0.278258i	−0.241716	+	0.0332582i
$71$		−	3.76718i		−	0.447082i	−0.974695	−	0.223541i	$-0.928238\pi$
$71$		−	3.76718i		−	0.447082i	0.974695	−	0.223541i	$-0.0717616\pi$
$72$		0			0
$73$			10.5357i			1.23311i	0.787312	+	0.616555i	$0.211472\pi$
$73$			10.5357i			1.23311i	−0.787312	+	0.616555i	$0.788528\pi$
$74$	−0.118553	−	0.861623i	−0.0137815	−	0.100162i
$75$		0			0
$76$	5.91327	−	10.5238i	0.678298	−	1.20716i
$77$	2.61822	+	2.61822i	0.298374	+	0.298374i
$78$		0			0
$79$			11.1995i			1.26004i	0.776578	+	0.630021i	$0.216954\pi$
$79$			11.1995i			1.26004i	−0.776578	+	0.630021i	$0.783046\pi$
$80$	−1.02070	+	4.19887i	−0.114117	+	0.469447i
$81$		0			0
$82$	8.80369	+	6.67407i	0.972205	+	0.737028i
$83$	9.73306	−	9.73306i	1.06834	−	1.06834i	0.0708558	−	0.997487i	$-0.477427\pi$
$83$	9.73306	−	9.73306i	1.06834	−	1.06834i	0.997487	−	0.0708558i	$-0.0225730\pi$
$84$		0			0
$85$	−3.08029	−	3.08029i	−0.334104	−	0.334104i
$86$	10.8909	−	1.49851i	1.17440	−	0.161588i
$87$		0			0
$88$	7.18757	−	3.12566i	0.766197	−	0.333196i
$89$	−1.64130			−0.173977			−0.0869886	−	0.996209i	$-0.527724\pi$
$89$	−1.64130			−0.173977			−0.0869886	+	0.996209i	$0.527724\pi$
$90$		0			0
$91$	5.59544	−	5.59544i	0.586562	−	0.586562i
$92$	−17.0694	+	4.78787i	−1.77961	+	0.499170i
$93$		0			0
$94$	3.61446	+	2.74012i	0.372803	+	0.282622i
$95$	−6.52023			−0.668962
$96$		0			0
$97$	−5.70272			−0.579024			−0.289512	−	0.957174i	$-0.593493\pi$
$97$	−5.70272			−0.579024			−0.289512	+	0.957174i	$0.593493\pi$
$98$	5.87667	+	4.45510i	0.593634	+	0.450033i
$99$		0			0
$100$	−7.38110	+	2.07036i	−0.738110	+	0.207036i
$101$	−6.68599	+	6.68599i	−0.665281	+	0.665281i	−0.956620	−	0.291339i	$-0.905899\pi$
$101$	−6.68599	+	6.68599i	−0.665281	+	0.665281i	0.291339	+	0.956620i	$0.405899\pi$
$102$		0			0
$103$	10.8784			1.07188			0.535938	−	0.844257i	$-0.319958\pi$
$103$	10.8784			1.07188			0.535938	+	0.844257i	$0.319958\pi$
$104$	−6.67990	−	15.3607i	−0.655018	−	1.50624i
$105$		0			0
$106$	−8.05961	+	1.10894i	−0.782818	+	0.107710i
$107$	−1.31755	−	1.31755i	−0.127372	−	0.127372i	0.640547	−	0.767919i	$-0.278708\pi$
$107$	−1.31755	−	1.31755i	−0.127372	−	0.127372i	−0.767919	+	0.640547i	$0.778708\pi$
$108$		0			0
$109$	−3.51516	+	3.51516i	−0.336691	+	0.336691i	−0.855120	−	0.518429i	$-0.826517\pi$
$109$	−3.51516	+	3.51516i	−0.336691	+	0.336691i	0.518429	+	0.855120i	$0.326517\pi$
$110$	−3.37366	−	2.55757i	−0.321666	−	0.243855i
$111$		0			0
$112$	−4.56513	+	2.77969i	−0.431364	+	0.262656i
$113$			16.3139i			1.53469i	0.641236	+	0.767344i	$0.278422\pi$
$113$			16.3139i			1.53469i	−0.641236	+	0.767344i	$0.721578\pi$
$114$		0			0
$115$	6.77107	+	6.77107i	0.631406	+	0.631406i
$116$	−1.71716	+	3.05600i	−0.159434	+	0.283742i
$117$		0			0
$118$	1.28623	+	9.34814i	0.118407	+	0.860566i
$119$		−	5.38815i		−	0.493931i
$120$		0			0
$121$		−	3.32115i		−	0.301922i
$122$	−6.47470	+	0.890869i	−0.586192	+	0.0806555i
$123$		0			0
$124$	−5.54279	+	1.55472i	−0.497757	+	0.139618i
$125$	6.74732	+	6.74732i	0.603499	+	0.603499i
$126$		0			0
$127$		−	20.7416i		−	1.84052i	−0.391303	−	0.920262i	$-0.627976\pi$
$127$		−	20.7416i		−	1.84052i	0.391303	−	0.920262i	$-0.372024\pi$
$128$	1.93345	+	11.1473i	0.170895	+	0.985289i
$129$		0			0
$130$	−5.46582	+	7.20991i	−0.479384	+	0.632351i
$131$	−9.43621	+	9.43621i	−0.824446	+	0.824446i	−0.986742	−	0.162296i	$-0.948110\pi$
$131$	−9.43621	+	9.43621i	−0.824446	+	0.824446i	0.162296	+	0.986742i	$0.448110\pi$
$132$		0			0
$133$	−5.70272	−	5.70272i	−0.494489	−	0.494489i
$134$	1.48398	+	10.7854i	0.128196	+	0.931713i
$135$		0			0
$136$	−10.6120	−	4.17959i	−0.909974	−	0.358397i
$137$	12.8211			1.09538			0.547692	−	0.836680i	$-0.315506\pi$
$137$	12.8211			1.09538			0.547692	+	0.836680i	$0.315506\pi$
$138$		0			0
$139$	1.44348	−	1.44348i	0.122435	−	0.122435i	−0.643235	−	0.765669i	$-0.722408\pi$
$139$	1.44348	−	1.44348i	0.122435	−	0.122435i	0.765669	+	0.643235i	$0.222408\pi$
$140$	2.51686	+	1.41421i	0.212713	+	0.119523i
$141$		0			0
$142$	−3.21852	+	4.24551i	−0.270092	+	0.356275i
$143$	16.4106			1.37232
$144$		0			0
$145$	1.89341			0.157239
$146$	9.00127	−	11.8735i	0.744950	−	0.982655i
$147$		0			0
$148$	−0.602529	+	1.07231i	−0.0495276	+	0.0881436i
$149$	−6.42073	+	6.42073i	−0.526007	+	0.526007i	−0.919379	−	0.393372i	$-0.871308\pi$
$149$	−6.42073	+	6.42073i	−0.526007	+	0.526007i	0.393372	+	0.919379i	$0.371308\pi$
$150$		0			0
$151$	0.205945			0.0167596			0.00837978	−	0.999965i	$-0.497333\pi$
$151$	0.205945			0.0167596			0.00837978	+	0.999965i	$0.497333\pi$
$152$	−15.6552	+	6.80797i	−1.26980	+	0.552199i
$153$		0			0
$154$	−0.713769	−	5.18757i	−0.0575171	−	0.418026i
$155$	2.19871	+	2.19871i	0.176605	+	0.176605i
$156$		0			0
$157$	−1.26785	+	1.26785i	−0.101186	+	0.101186i	−0.755887	−	0.654702i	$-0.772794\pi$
$157$	−1.26785	+	1.26785i	−0.101186	+	0.101186i	0.654702	+	0.755887i	$0.272794\pi$
$158$	9.56839	−	12.6216i	0.761220	−	1.00412i
$159$		0			0
$160$	4.73764	−	3.85997i	0.374543	−	0.305158i
$161$			11.8442i			0.933456i
$162$		0			0
$163$	0.169186	+	0.169186i	0.0132517	+	0.0132517i	0.713702	−	0.700450i	$-0.247017\pi$
$163$	0.169186	+	0.169186i	0.0132517	+	0.0132517i	−0.700450	+	0.713702i	$0.747017\pi$
$164$	−4.21949	−	15.0430i	−0.329486	−	1.17466i
$165$		0			0
$166$	−19.2844	+	2.65339i	−1.49676	+	0.205943i
$167$		−	10.4503i		−	0.808671i	−0.914611	−	0.404335i	$-0.867503\pi$
$167$		−	10.4503i		−	0.808671i	0.914611	−	0.404335i	$-0.132497\pi$
$168$		0			0
$169$		−	22.0714i		−	1.69780i
$170$	0.839735	+	6.10307i	0.0644048	+	0.468084i
$171$		0			0
$172$	−13.5541	−	7.61599i	−1.03349	−	0.580714i
$173$	0.974085	+	0.974085i	0.0740583	+	0.0740583i	0.743166	−	0.669107i	$-0.233323\pi$
$173$	0.974085	+	0.974085i	0.0740583	+	0.0740583i	−0.669107	+	0.743166i	$0.733323\pi$
$174$		0			0
$175$			5.12165i			0.387160i
$176$	−10.7706	−	2.61822i	−0.811867	−	0.197356i
$177$		0			0
$178$	1.84970	+	1.40226i	0.138641	+	0.105104i
$179$	6.59560	−	6.59560i	0.492979	−	0.492979i	−0.416265	−	0.909243i	$-0.636661\pi$
$179$	6.59560	−	6.59560i	0.492979	−	0.492979i	0.909243	+	0.416265i	$0.136661\pi$
$180$		0			0
$181$	10.1876	+	10.1876i	0.757236	+	0.757236i	0.975818	−	0.218583i	$-0.0701433\pi$
$181$	10.1876	+	10.1876i	0.757236	+	0.757236i	−0.218583	+	0.975818i	$0.570143\pi$
$182$	−11.0864	+	1.52541i	−0.821781	+	0.113071i
$183$		0			0
$184$	23.3273	+	9.18757i	1.71971	+	0.677316i
$185$	0.664376			0.0488459
$186$		0			0
$187$	7.90133	−	7.90133i	0.577803	−	0.577803i
$188$	−1.73236	−	6.17609i	−0.126345	−	0.450438i
$189$		0			0
$190$	7.34814	+	5.57062i	0.533090	+	0.404135i
$191$	−14.2297			−1.02962			−0.514812	−	0.857303i	$-0.672138\pi$
$191$	−14.2297			−1.02962			−0.514812	+	0.857303i	$0.672138\pi$
$192$		0			0
$193$	6.53570			0.470450			0.235225	−	0.971941i	$-0.424417\pi$
$193$	6.53570			0.470450			0.235225	+	0.971941i	$0.424417\pi$
$194$	6.42682	+	4.87217i	0.461419	+	0.349801i
$195$		0			0
$196$	−2.81661	−	10.0416i	−0.201186	−	0.717255i
$197$	9.07713	−	9.07713i	0.646718	−	0.646718i	−0.305480	−	0.952198i	$-0.598817\pi$
$197$	9.07713	−	9.07713i	0.646718	−	0.646718i	0.952198	+	0.305480i	$0.0988169\pi$
$198$		0			0
$199$	−10.0865			−0.715011			−0.357505	−	0.933911i	$-0.616373\pi$
$199$	−10.0865			−0.715011			−0.357505	+	0.933911i	$0.616373\pi$
$200$	10.0871	+	3.97286i	0.713268	+	0.280924i
$201$		0			0
$202$	13.2472	−	1.82271i	0.932068	−	0.128245i
$203$	1.65601	+	1.65601i	0.116229	+	0.116229i
$204$		0			0
$205$	−5.96725	+	5.96725i	−0.416771	+	0.416771i
$206$	−12.2596	−	9.29401i	−0.854169	−	0.647545i
$207$		0			0
$208$	−5.59544	+	23.0181i	−0.387974	+	1.59602i
$209$		−	16.7252i		−	1.15691i
$210$		0			0
$211$	17.9792	+	17.9792i	1.23774	+	1.23774i	0.960923	+	0.276815i	$0.0892789\pi$
$211$	17.9792	+	17.9792i	1.23774	+	1.23774i	0.276815	+	0.960923i	$0.410721\pi$
$212$	10.0304	+	5.63605i	0.688891	+	0.387085i
$213$		0			0
$214$	0.359185	+	2.61050i	0.0245534	+	0.178450i
$215$			8.39773i			0.572721i
$216$		0			0
$217$			3.84607i			0.261088i
$218$	6.96470	−	0.958288i	0.471709	−	0.0649035i
$219$		0			0
$220$	1.61695	+	5.76463i	0.109015	+	0.388651i
$221$	−16.8861	−	16.8861i	−1.13588	−	1.13588i
$222$		0			0
$223$		−	4.00861i		−	0.268437i	−0.990952	−	0.134218i	$-0.957148\pi$
$223$		−	4.00861i		−	0.268437i	0.990952	−	0.134218i	$-0.0428523\pi$
$224$	7.51963	+	0.767620i	0.502427	+	0.0512888i
$225$		0			0
$226$	13.9380	−	18.3854i	0.927139	−	1.22298i
$227$	−13.7915	+	13.7915i	−0.915373	+	0.915373i	−0.996688	−	0.0813152i	$-0.974088\pi$
$227$	−13.7915	+	13.7915i	−0.915373	+	0.915373i	0.0813152	+	0.996688i	$0.474088\pi$
$228$		0			0
$229$	3.47840	+	3.47840i	0.229859	+	0.229859i	0.812634	−	0.582775i	$-0.198033\pi$
$229$	3.47840	+	3.47840i	0.229859	+	0.229859i	−0.582775	+	0.812634i	$0.698033\pi$
$230$	−1.84590	−	13.4158i	−0.121715	−	0.884609i
$231$		0			0
$232$	4.54611	−	1.97697i	0.298467	−	0.129794i
$233$	3.23973			0.212241			0.106121	−	0.994353i	$-0.466157\pi$
$233$	3.23973			0.212241			0.106121	+	0.994353i	$0.466157\pi$
$234$		0			0
$235$	−2.44993	+	2.44993i	−0.159816	+	0.159816i
$236$	6.53711	−	11.6340i	0.425530	−	0.757310i
$237$		0			0
$238$	−4.60342	+	6.07231i	−0.298395	+	0.393610i
$239$	24.2484			1.56850			0.784249	−	0.620446i	$-0.213048\pi$
$239$	24.2484			1.56850			0.784249	+	0.620446i	$0.213048\pi$
$240$		0			0
$241$	16.5596			1.06670			0.533348	−	0.845896i	$-0.320934\pi$
$241$	16.5596			1.06670			0.533348	+	0.845896i	$0.320934\pi$
$242$	−2.83745	+	3.74285i	−0.182398	+	0.240599i
$243$		0			0
$244$	8.05795	+	4.52773i	0.515857	+	0.289858i
$245$	−3.98329	+	3.98329i	−0.254483	+	0.254483i
$246$		0			0
$247$	−35.7438			−2.27432
$248$	7.57487	+	2.98340i	0.481005	+	0.189446i
$249$		0			0
$250$	−1.83943	−	13.3687i	−0.116336	−	0.845510i
$251$	−11.3957	−	11.3957i	−0.719287	−	0.719287i	0.249172	−	0.968459i	$-0.419842\pi$
$251$	−11.3957	−	11.3957i	−0.719287	−	0.719287i	−0.968459	+	0.249172i	$0.919842\pi$
$252$		0			0
$253$	−17.3687	+	17.3687i	−1.09196	+	1.09196i
$254$	−17.7208	+	23.3753i	−1.11190	+	1.46670i
$255$		0			0
$256$	7.34482	−	14.2146i	0.459051	−	0.888410i
$257$			3.54316i			0.221016i	0.993875	+	0.110508i	$0.0352478\pi$
$257$			3.54316i			0.221016i	−0.993875	+	0.110508i	$0.964752\pi$
$258$		0			0
$259$	0.581076	+	0.581076i	0.0361063	+	0.0361063i
$260$	12.3197	−	3.45561i	0.764035	−	0.214308i
$261$		0			0
$262$	18.6963	−	2.57246i	1.15506	−	0.158927i
$263$		−	21.0534i		−	1.29821i	−0.760701	−	0.649103i	$-0.775145\pi$
$263$		−	21.0534i		−	1.29821i	0.760701	−	0.649103i	$-0.224855\pi$
$264$		0			0
$265$		−	6.21456i		−	0.381757i
$266$	1.55465	+	11.2990i	0.0953219	+	0.692786i
$267$		0			0
$268$	7.54215	−	13.4227i	0.460710	−	0.819920i
$269$	−20.4077	−	20.4077i	−1.24428	−	1.24428i	−0.958208	−	0.286072i	$-0.907650\pi$
$269$	−20.4077	−	20.4077i	−1.24428	−	1.24428i	−0.286072	−	0.958208i	$-0.592350\pi$
$270$		0			0
$271$		−	5.06279i		−	0.307543i	−0.988106	−	0.153771i	$-0.950858\pi$
$271$		−	5.06279i		−	0.307543i	0.988106	−	0.153771i	$-0.0491419\pi$
$272$	8.38862	+	13.7768i	0.508635	+	0.835339i
$273$		0			0
$274$	−14.4491	−	10.9539i	−0.872902	−	0.661747i
$275$	−7.51052	+	7.51052i	−0.452901	+	0.452901i
$276$		0			0
$277$	−5.86642	−	5.86642i	−0.352479	−	0.352479i	0.508552	−	0.861031i	$-0.330181\pi$
$277$	−5.86642	−	5.86642i	−0.352479	−	0.352479i	−0.861031	+	0.508552i	$0.830181\pi$
$278$	−2.86002	+	0.393517i	−0.171533	+	0.0236016i
$279$		0			0
$280$	−1.62819	−	3.74408i	−0.0973030	−	0.223752i
$281$	4.77316			0.284743			0.142371	−	0.989813i	$-0.454527\pi$
$281$	4.77316			0.284743			0.142371	+	0.989813i	$0.454527\pi$
$282$		0			0
$283$	−10.0779	+	10.0779i	−0.599066	+	0.599066i	−0.940064	−	0.340998i	$-0.889235\pi$
$283$	−10.0779	+	10.0779i	−0.599066	+	0.599066i	0.340998	+	0.940064i	$0.389235\pi$
$284$	7.25438	−	2.03481i	0.430468	−	0.120744i
$285$		0			0
$286$	−18.4943	−	14.0205i	−1.09359	−	0.829052i
$287$	−10.4381			−0.616144
$288$		0			0
$289$	0.739481			0.0434989
$290$	−2.13383	−	1.61765i	−0.125303	−	0.0949919i
$291$		0			0
$292$	−20.2884	+	5.69079i	−1.18729	+	0.333028i
$293$	11.7829	−	11.7829i	0.688364	−	0.688364i	−0.273506	−	0.961870i	$-0.588183\pi$
$293$	11.7829	−	11.7829i	0.688364	−	0.688364i	0.961870	+	0.273506i	$0.0881834\pi$
$294$		0			0
$295$	−7.20811			−0.419673
$296$	1.59517	−	0.693694i	0.0927177	−	0.0403202i
$297$		0			0
$298$	12.7216	−	1.75039i	0.736943	−	0.101398i
$299$	37.1189	+	37.1189i	2.14664	+	2.14664i
$300$		0			0
$301$	−7.34482	+	7.34482i	−0.423348	+	0.423348i
$302$	−0.232095	−	0.175951i	−0.0133555	−	0.0101248i
$303$		0			0
$304$	23.4594	+	5.70272i	1.34549	+	0.327074i
$305$		−	4.99248i		−	0.285869i
$306$		0			0
$307$	−4.31322	−	4.31322i	−0.246169	−	0.246169i	0.573228	−	0.819396i	$-0.305691\pi$
$307$	−4.31322	−	4.31322i	−0.246169	−	0.246169i	−0.819396	+	0.573228i	$0.805691\pi$
$308$	−3.62764	+	6.45607i	−0.206704	+	0.367869i
$309$		0			0
$310$	−0.599404	−	4.35638i	−0.0340438	−	0.247426i
$311$			27.4434i			1.55617i	0.628156	+	0.778087i	$0.283810\pi$
$311$			27.4434i			1.55617i	−0.628156	+	0.778087i	$0.716190\pi$
$312$		0			0
$313$		−	18.8568i		−	1.06585i	−0.846162	−	0.532926i	$-0.821092\pi$
$313$		−	18.8568i		−	1.06585i	0.846162	−	0.532926i	$-0.178908\pi$
$314$	2.51204	−	0.345637i	0.141762	−	0.0195054i
$315$		0			0
$316$	−21.5667	+	6.04933i	−1.21322	+	0.340302i
$317$	−0.154552	−	0.154552i	−0.00868053	−	0.00868053i	0.702753	−	0.711434i	$-0.251954\pi$
$317$	−0.154552	−	0.154552i	−0.00868053	−	0.00868053i	−0.711434	+	0.702753i	$0.751954\pi$
$318$		0			0
$319$			4.85685i			0.271931i
$320$	−8.63700	+	0.302453i	−0.482823	+	0.0169076i
$321$		0			0
$322$	10.1192	−	13.3481i	0.563922	−	0.743863i
$323$	−17.2098	+	17.2098i	−0.957580	+	0.957580i
$324$		0			0
$325$	16.0509	+	16.0509i	0.890342	+	0.890342i
$326$	−0.0461227	−	0.335213i	−0.00255450	−	0.0185657i
$327$		0			0
$328$	−8.09687	+	20.5580i	−0.447075	+	1.13513i
$329$	−4.28551			−0.236268
$330$		0			0
$331$	−16.3132	+	16.3132i	−0.896656	+	0.896656i	−0.995139	−	0.0984829i	$-0.968601\pi$
$331$	−16.3132	+	16.3132i	−0.896656	+	0.896656i	0.0984829	+	0.995139i	$0.468601\pi$
$332$	24.0000	+	13.4855i	1.31717	+	0.740114i
$333$		0			0
$334$	−8.92833	+	11.7773i	−0.488536	+	0.644423i
$335$	−8.31631			−0.454369
$336$		0			0
$337$	1.89341			0.103141			0.0515704	−	0.998669i	$-0.483577\pi$
$337$	1.89341			0.103141			0.0515704	+	0.998669i	$0.483577\pi$
$338$	−18.8569	+	24.8739i	−1.02568	+	1.35296i
$339$		0			0
$340$	4.26785	−	7.59544i	0.231457	−	0.411921i
$341$	−5.63998	+	5.63998i	−0.305422	+	0.305422i
$342$		0			0
$343$	−16.3211			−0.881259
$344$	8.76832	+	20.1631i	0.472756	+	1.08712i
$345$		0			0
$346$	−0.265551	−	1.92999i	−0.0142761	−	0.103757i
$347$	−19.7630	−	19.7630i	−1.06093	−	1.06093i	−0.998019	−	0.0629131i	$-0.979961\pi$
$347$	−19.7630	−	19.7630i	−1.06093	−	1.06093i	−0.0629131	−	0.998019i	$-0.520039\pi$
$348$		0			0
$349$	18.1008	−	18.1008i	0.968915	−	0.968915i	−0.0306158	−	0.999531i	$-0.509747\pi$
$349$	18.1008	−	18.1008i	0.968915	−	0.968915i	0.999531	+	0.0306158i	$0.00974685\pi$
$350$	4.37572	−	5.77197i	0.233892	−	0.308525i
$351$		0			0
$352$	9.90133	+	12.1527i	0.527743	+	0.647738i
$353$		−	19.3695i		−	1.03093i	−0.856910	−	0.515466i	$-0.827619\pi$
$353$		−	19.3695i		−	1.03093i	0.856910	−	0.515466i	$-0.172381\pi$
$354$		0			0
$355$	−2.87766	−	2.87766i	−0.152730	−	0.152730i
$356$	−0.886536	−	3.16061i	−0.0469863	−	0.167512i
$357$		0			0
$358$	−13.0681	+	1.79807i	−0.690670	+	0.0950308i
$359$		−	7.09236i		−	0.374321i	−0.982329	−	0.187160i	$-0.940072\pi$
$359$		−	7.09236i		−	0.374321i	0.982329	−	0.187160i	$-0.0599284\pi$
$360$		0			0
$361$			17.4291i			0.917322i
$362$	−2.77729	−	20.1850i	−0.145971	−	1.06090i
$363$		0			0
$364$	13.7974	+	7.75270i	0.723179	+	0.406352i
$365$	8.04799	+	8.04799i	0.421251	+	0.421251i
$366$		0			0
$367$		−	1.65735i		−	0.0865130i	−0.999064	−	0.0432565i	$-0.986227\pi$
$367$		−	1.65735i		−	0.0865130i	0.999064	−	0.0432565i	$-0.0137733\pi$
$368$	−18.4398	−	30.2840i	−0.961242	−	1.57867i
$369$		0			0
$370$	−0.748734	−	0.567615i	−0.0389248	−	0.0295089i
$371$	5.43537	−	5.43537i	0.282190	−	0.282190i
$372$		0			0
$373$	−3.48241	−	3.48241i	−0.180312	−	0.180312i	0.611180	−	0.791492i	$-0.290695\pi$
$373$	−3.48241	−	3.48241i	−0.180312	−	0.180312i	−0.791492	+	0.611180i	$0.790695\pi$
$374$	−15.6552	+	2.15403i	−0.809510	+	0.111382i
$375$		0			0
$376$	−3.32427	+	8.44036i	−0.171436	+	0.435278i
$377$	10.3797			0.534579
$378$		0			0
$379$	19.1548	−	19.1548i	0.983917	−	0.983917i	−0.0159558	−	0.999873i	$-0.505079\pi$
$379$	19.1548	−	19.1548i	0.983917	−	0.983917i	0.999873	+	0.0159558i	$0.00507910\pi$
$380$	−3.52186	−	12.5559i	−0.180668	−	0.644103i
$381$		0			0
$382$	16.0365	+	12.1573i	0.820498	+	0.622019i
$383$	15.2907			0.781319			0.390660	−	0.920535i	$-0.372247\pi$
$383$	15.2907			0.781319			0.390660	+	0.920535i	$0.372247\pi$
$384$		0			0
$385$	4.00000			0.203859
$386$	−7.36557	−	5.58383i	−0.374898	−	0.284210i
$387$		0			0
$388$	−3.08029	−	10.9816i	−0.156378	−	0.557507i
$389$	−22.7144	+	22.7144i	−1.15166	+	1.15166i	−0.165445	+	0.986219i	$0.552906\pi$
$389$	−22.7144	+	22.7144i	−1.15166	+	1.15166i	−0.986219	+	0.165445i	$0.947094\pi$
$390$		0			0
$391$	35.7438			1.80764
$392$	−5.40486	+	13.7230i	−0.272987	+	0.693116i
$393$		0			0
$394$	−17.9848	+	2.47457i	−0.906062	+	0.124667i
$395$	8.55505	+	8.55505i	0.430451	+	0.430451i
$396$		0			0
$397$	7.45854	−	7.45854i	0.374334	−	0.374334i	−0.494719	−	0.869053i	$-0.664729\pi$
$397$	7.45854	−	7.45854i	0.374334	−	0.374334i	0.869053	+	0.494719i	$0.164729\pi$
$398$	11.3672	+	8.61746i	0.569786	+	0.431954i
$399$		0			0
$400$	−7.97370	−	13.0953i	−0.398685	−	0.654767i
$401$			11.5911i			0.578834i	0.957203	+	0.289417i	$0.0934615\pi$
$401$			11.5911i			0.578834i	−0.957203	+	0.289417i	$0.906539\pi$
$402$		0			0
$403$	12.0533	+	12.0533i	0.600417	+	0.600417i
$404$	−16.4865	−	9.26369i	−0.820233	−	0.460886i
$405$		0			0
$406$	−0.451456	−	3.28112i	−0.0224054	−	0.162839i
$407$			1.70421i			0.0844745i
$408$		0			0
$409$		−	12.4659i		−	0.616398i	−0.951322	−	0.308199i	$-0.900274\pi$
$409$		−	12.4659i		−	0.616398i	0.951322	−	0.308199i	$-0.0997262\pi$
$410$	11.8231	−	1.62677i	0.583902	−	0.0803404i
$411$		0			0
$412$	5.87587	+	20.9482i	0.289483	+	1.03205i
$413$	−6.30435	−	6.30435i	−0.310217	−	0.310217i
$414$		0			0
$415$		−	14.8697i		−	0.729927i
$416$	25.9716	−	21.1603i	1.27336	−	1.03747i
$417$		0			0
$418$	−14.2894	+	18.8489i	−0.698915	+	0.921931i
$419$	14.4096	−	14.4096i	0.703953	−	0.703953i	−0.261304	−	0.965257i	$-0.584152\pi$
$419$	14.4096	−	14.4096i	0.703953	−	0.703953i	0.965257	+	0.261304i	$0.0841525\pi$
$420$		0			0
$421$	−5.83630	−	5.83630i	−0.284444	−	0.284444i	0.550434	−	0.834878i	$-0.314462\pi$
$421$	−5.83630	−	5.83630i	−0.284444	−	0.284444i	−0.834878	+	0.550434i	$0.814462\pi$
$422$	−4.90141	−	35.6228i	−0.238597	−	1.73409i
$423$		0			0
$424$	−6.48880	−	14.9212i	−0.315124	−	0.724640i
$425$	15.4562			0.749738
$426$		0			0
$427$	4.36652	−	4.36652i	0.211311	−	0.211311i
$428$	1.82551	−	3.24884i	0.0882395	−	0.157039i
$429$		0			0
$430$	7.17467	−	9.46403i	0.345993	−	0.456396i
$431$	18.4510			0.888755			0.444377	−	0.895840i	$-0.353425\pi$
$431$	18.4510			0.888755			0.444377	+	0.895840i	$0.353425\pi$
$432$		0			0
$433$	6.58166			0.316295			0.158147	−	0.987416i	$-0.449448\pi$
$433$	6.58166			0.316295			0.158147	+	0.987416i	$0.449448\pi$
$434$	3.28592	−	4.33442i	0.157729	−	0.208059i
$435$		0			0
$436$	−8.66776	−	4.87038i	−0.415110	−	0.233249i
$437$	37.8306	−	37.8306i	1.80968	−	1.80968i
$438$		0			0
$439$	3.68747			0.175993			0.0879966	−	0.996121i	$-0.471954\pi$
$439$	3.68747			0.175993			0.0879966	+	0.996121i	$0.471954\pi$
$440$	3.10280	−	7.87804i	0.147920	−	0.375571i
$441$		0			0
$442$	4.60342	+	33.4569i	0.218962	+	1.59138i
$443$	−3.31861	−	3.31861i	−0.157672	−	0.157672i	0.623862	−	0.781534i	$-0.285563\pi$
$443$	−3.31861	−	3.31861i	−0.157672	−	0.157672i	−0.781534	+	0.623862i	$0.785563\pi$
$444$		0			0
$445$	−1.25375	+	1.25375i	−0.0594335	+	0.0594335i
$446$	−3.42479	+	4.51760i	−0.162169	+	0.213915i
$447$		0			0
$448$	−7.81861	−	7.28955i	−0.369395	−	0.344399i
$449$			20.3555i			0.960635i	0.877095	+	0.480318i	$0.159479\pi$
$449$			20.3555i			0.960635i	−0.877095	+	0.480318i	$0.840521\pi$
$450$		0			0
$451$	−15.3068	−	15.3068i	−0.720768	−	0.720768i
$452$	−31.4155	+	8.81187i	−1.47766	+	0.414475i
$453$		0			0
$454$	27.3255	−	3.75978i	1.28245	−	0.176455i
$455$		−	8.54847i		−	0.400758i
$456$		0			0
$457$			10.0239i			0.468897i	0.972129	+	0.234448i	$0.0753284\pi$
$457$			10.0239i			0.468897i	−0.972129	+	0.234448i	$0.924672\pi$
$458$	−0.948267	−	6.89186i	−0.0443096	−	0.322036i
$459$		0			0
$460$	−9.38158	+	16.6963i	−0.437418	+	0.778468i
$461$	16.4043	+	16.4043i	0.764026	+	0.764026i	0.977048	−	0.213021i	$-0.0683304\pi$
$461$	16.4043	+	16.4043i	0.764026	+	0.764026i	−0.213021	+	0.977048i	$0.568330\pi$
$462$		0			0
$463$			0.997833i			0.0463732i	0.999731	+	0.0231866i	$0.00738119\pi$
$463$			0.997833i			0.0463732i	−0.999731	+	0.0231866i	$0.992619\pi$
$464$	−6.81239	−	1.65601i	−0.316257	−	0.0768786i
$465$		0			0
$466$	−3.65109	−	2.76789i	−0.169133	−	0.128220i
$467$	9.73306	−	9.73306i	0.450392	−	0.450392i	−0.445092	−	0.895485i	$-0.646829\pi$
$467$	9.73306	−	9.73306i	0.450392	−	0.450392i	0.895485	+	0.445092i	$0.146829\pi$
$468$		0			0
$469$	−7.27361	−	7.27361i	−0.335864	−	0.335864i
$470$	4.85413	−	0.667890i	0.223904	−	0.0308075i
$471$		0			0
$472$	−17.3068	+	7.52620i	−0.796609	+	0.346422i
$473$	−21.5413			−0.990469
$474$		0			0
$475$	16.3586	−	16.3586i	0.750584	−	0.750584i
$476$	10.3759	−	2.91038i	0.475577	−	0.133397i
$477$		0			0
$478$	−27.3273	−	20.7168i	−1.24992	−	0.947565i
$479$	−37.0669			−1.69363			−0.846816	−	0.531886i	$-0.821483\pi$
$479$	−37.0669			−1.69363			−0.846816	+	0.531886i	$0.821483\pi$
$480$		0			0
$481$	3.64210			0.166065
$482$	−18.6622	−	14.1478i	−0.850041	−	0.644415i
$483$		0			0
$484$	6.39546	−	1.79389i	0.290703	−	0.0815406i
$485$	−4.35618	+	4.35618i	−0.197804	+	0.197804i
$486$		0			0
$487$	33.1866			1.50383			0.751914	−	0.659261i	$-0.229131\pi$
$487$	33.1866			1.50383			0.751914	+	0.659261i	$0.229131\pi$
$488$	−5.21280	−	11.9870i	−0.235972	−	0.542627i
$489$		0			0
$490$	7.89221	−	1.08591i	0.356534	−	0.0490563i
$491$	−10.2580	−	10.2580i	−0.462936	−	0.462936i	0.436681	−	0.899617i	$-0.356154\pi$
$491$	−10.2580	−	10.2580i	−0.462936	−	0.462936i	−0.899617	+	0.436681i	$0.856154\pi$
$492$		0			0
$493$	4.99757	−	4.99757i	0.225079	−	0.225079i
$494$	40.2824	+	30.5380i	1.81239	+	1.37397i
$495$		0			0
$496$	−5.98780	−	9.83387i	−0.268860	−	0.441554i
$497$		−	5.03372i		−	0.225793i
$498$		0			0
$499$	4.19733	+	4.19733i	0.187898	+	0.187898i	0.794787	−	0.606889i	$-0.207583\pi$
$499$	4.19733	+	4.19733i	0.187898	+	0.187898i	−0.606889	+	0.794787i	$0.707583\pi$
$500$	−9.34866	+	16.6377i	−0.418085	+	0.744060i
$501$		0			0
$502$	3.10664	+	22.5786i	0.138656	+	1.00773i
$503$			21.0655i			0.939266i	0.882862	+	0.469633i	$0.155614\pi$
$503$			21.0655i			0.939266i	−0.882862	+	0.469633i	$0.844386\pi$
$504$		0			0
$505$			10.2146i			0.454542i
$506$	34.4131	−	4.73498i	1.52985	−	0.210496i
$507$		0			0
$508$	39.9418	−	11.2035i	1.77213	−	0.497073i
$509$	22.6424	+	22.6424i	1.00361	+	1.00361i	0.999993	+	0.00361481i	$0.00115063\pi$
$509$	22.6424	+	22.6424i	1.00361	+	1.00361i	0.00361481	+	0.999993i	$0.498849\pi$
$510$		0			0
$511$			14.0779i			0.622768i
$512$	−20.4218	+	9.74434i	−0.902522	+	0.430643i
$513$		0			0
$514$	3.02713	−	3.99305i	0.133521	−	0.176126i
$515$	8.30973	−	8.30973i	0.366171	−	0.366171i
$516$		0			0
$517$	−6.28439	−	6.28439i	−0.276387	−	0.276387i
$518$	−0.158411	−	1.15130i	−0.00696016	−	0.0505854i
$519$		0			0
$520$	−16.8363	−	6.63105i	−0.738321	−	0.290791i
$521$	−38.3351			−1.67949			−0.839746	−	0.542980i	$-0.817296\pi$
$521$	−38.3351			−1.67949			−0.839746	+	0.542980i	$0.817296\pi$
$522$		0			0
$523$	−5.39811	+	5.39811i	−0.236043	+	0.236043i	−0.815209	−	0.579166i	$-0.803378\pi$
$523$	−5.39811	+	5.39811i	−0.236043	+	0.236043i	0.579166	+	0.815209i	$0.303378\pi$
$524$	−23.2680	−	13.0742i	−1.01647	−	0.571150i
$525$		0			0
$526$	−17.9871	+	23.7266i	−0.784275	+	1.03453i
$527$	11.6068			0.505599
$528$		0			0
$529$	−55.5719			−2.41617
$530$	−5.30946	+	7.00365i	−0.230628	+	0.304219i
$531$		0			0
$532$	7.90133	−	14.0619i	0.342566	−	0.609661i
$533$	−32.7124	+	32.7124i	−1.41693	+	1.41693i
$534$		0			0
$535$	−2.01289			−0.0870249
$536$	−19.9676	+	8.68331i	−0.862468	+	0.375062i
$537$		0			0
$538$	5.56347	+	40.4345i	0.239858	+	1.74325i
$539$	−10.2176	−	10.2176i	−0.440105	−	0.440105i
$540$		0			0
$541$	5.51516	−	5.51516i	0.237115	−	0.237115i	−0.578539	−	0.815654i	$-0.696377\pi$
$541$	5.51516	−	5.51516i	0.237115	−	0.237115i	0.815654	+	0.578539i	$0.196377\pi$
$542$	−4.32544	+	5.70564i	−0.185794	+	0.245078i
$543$		0			0
$544$	2.31654	−	22.6930i	0.0993210	−	0.972952i
$545$			5.37030i			0.230038i
$546$		0			0
$547$	−23.2535	−	23.2535i	−0.994247	−	0.994247i	0.00573636	−	0.999984i	$-0.498174\pi$
$547$	−23.2535	−	23.2535i	−0.994247	−	0.994247i	−0.999984	+	0.00573636i	$0.998174\pi$
$548$	6.92525	+	24.6894i	0.295832	+	1.05468i
$549$		0			0
$550$	14.8808	−	2.04749i	0.634521	−	0.0873052i
$551$		−	10.5787i		−	0.450666i
$552$		0			0
$553$			14.9648i			0.636369i
$554$	1.59928	+	11.6233i	0.0679469	+	0.493828i
$555$		0			0
$556$	3.55938	+	2.00000i	0.150951	+	0.0848189i
$557$	26.9066	+	26.9066i	1.14007	+	1.14007i	0.988437	+	0.151635i	$0.0484537\pi$
$557$	26.9066	+	26.9066i	1.14007	+	1.14007i	0.151635	+	0.988437i	$0.451546\pi$
$558$		0			0
$559$			46.0362i			1.94712i
$560$	−1.36386	+	5.61054i	−0.0576336	+	0.237089i
$561$		0			0
$562$	−5.37922	−	4.07799i	−0.226909	−	0.172019i
$563$	21.4144	−	21.4144i	0.902508	−	0.902508i	−0.0931446	−	0.995653i	$-0.529692\pi$
$563$	21.4144	−	21.4144i	0.902508	−	0.902508i	0.995653	+	0.0931446i	$0.0296919\pi$
$564$		0			0
$565$	12.4619	+	12.4619i	0.524275	+	0.524275i
$566$	19.9676	−	2.74738i	0.839300	−	0.115481i
$567$		0			0
$568$	−9.91396	−	3.90465i	−0.415980	−	0.163836i
$569$	−1.54807			−0.0648986			−0.0324493	−	0.999473i	$-0.510331\pi$
$569$	−1.54807			−0.0648986			−0.0324493	+	0.999473i	$0.510331\pi$
$570$		0			0
$571$	−12.3384	+	12.3384i	−0.516345	+	0.516345i	−0.916463	−	0.400119i	$-0.868969\pi$
$571$	−12.3384	+	12.3384i	−0.516345	+	0.516345i	0.400119	+	0.916463i	$0.368969\pi$
$572$	8.86408	+	31.6016i	0.370626	+	1.32133i
$573$		0			0
$574$	11.7635	+	8.91792i	0.491000	+	0.372227i
$575$	−33.9759			−1.41689
$576$		0			0
$577$	−24.9648			−1.03930			−0.519650	−	0.854380i	$-0.673937\pi$
$577$	−24.9648			−1.03930			−0.519650	+	0.854380i	$0.673937\pi$
$578$	−0.833376	−	0.631782i	−0.0346639	−	0.0262787i
$579$		0			0
$580$	1.02271	+	3.64611i	0.0424659	+	0.151396i
$581$	13.0054	−	13.0054i	0.539553	−	0.539553i
$582$		0			0
$583$	15.9411			0.660215
$584$	27.7265	+	10.9202i	1.14733	+	0.451881i
$585$		0			0
$586$	−23.3458	+	3.21221i	−0.964408	+	0.132695i
$587$	−3.99426	−	3.99426i	−0.164861	−	0.164861i	0.619855	−	0.784716i	$-0.287191\pi$
$587$	−3.99426	−	3.99426i	−0.164861	−	0.164861i	−0.784716	+	0.619855i	$0.787191\pi$
$588$		0			0
$589$	12.2844	−	12.2844i	0.506169	−	0.506169i
$590$	8.12336	+	6.15831i	0.334433	+	0.253534i
$591$		0			0
$592$	−2.39038	−	0.581076i	−0.0982442	−	0.0238821i
$593$			21.0442i			0.864183i	0.901830	+	0.432092i	$0.142224\pi$
$593$			21.0442i			0.864183i	−0.901830	+	0.432092i	$0.857776\pi$
$594$		0			0
$595$	−4.11589	−	4.11589i	−0.168735	−	0.168735i
$596$	−15.8324	−	8.89616i	−0.648520	−	0.364401i
$597$		0			0
$598$	−10.1192	−	73.5449i	−0.413805	−	3.00748i
$599$		−	12.7718i		−	0.521840i	−0.965360	−	0.260920i	$-0.915974\pi$
$599$		−	12.7718i		−	0.521840i	0.965360	−	0.260920i	$-0.0840259\pi$
$600$		0			0
$601$			44.2967i			1.80690i	0.428691	+	0.903451i	$0.358975\pi$
$601$			44.2967i			1.80690i	−0.428691	+	0.903451i	$0.641025\pi$
$602$	14.5525	−	2.00232i	0.593117	−	0.0816083i
$603$		0			0
$604$	0.111240	+	0.396584i	0.00452628	+	0.0161368i
$605$	−2.53695	−	2.53695i	−0.103142	−	0.103142i
$606$		0			0
$607$		−	26.8784i		−	1.09096i	−0.838124	−	0.545479i	$-0.816348\pi$
$607$		−	26.8784i		−	1.09096i	0.838124	−	0.545479i	$-0.183652\pi$
$608$	−21.5660	−	26.4696i	−0.874617	−	1.07348i
$609$		0			0
$610$	−4.26537	+	5.62640i	−0.172700	+	0.227806i
$611$	−13.4305	+	13.4305i	−0.543339	+	0.543339i
$612$		0			0
$613$	−27.6602	−	27.6602i	−1.11719	−	1.11719i	−0.992153	−	0.125033i	$-0.960096\pi$
$613$	−27.6602	−	27.6602i	−1.11719	−	1.11719i	−0.125033	−	0.992153i	$-0.539904\pi$
$614$	1.17585	+	8.54593i	0.0474536	+	0.344886i
$615$		0			0
$616$	9.60406	−	4.17652i	0.386958	−	0.168277i
$617$	19.6148			0.789661			0.394831	−	0.918754i	$-0.370803\pi$
$617$	19.6148			0.789661			0.394831	+	0.918754i	$0.370803\pi$
$618$		0			0
$619$	−11.7854	+	11.7854i	−0.473697	+	0.473697i	−0.903109	−	0.429412i	$-0.858721\pi$
$619$	−11.7854	+	11.7854i	−0.473697	+	0.473697i	0.429412	+	0.903109i	$0.358721\pi$
$620$	−3.04640	+	5.42163i	−0.122346	+	0.217738i
$621$		0			0
$622$	23.4465	−	30.9281i	0.940120	−	1.24010i
$623$	−2.19311			−0.0878651
$624$		0			0
$625$	−8.85665			−0.354266
$626$	−16.1105	+	21.2512i	−0.643905	+	0.849368i
$627$		0			0
$628$	−3.12630	−	1.75666i	−0.124753	−	0.0700982i
$629$	1.75359	−	1.75359i	0.0699200	−	0.0699200i
$630$		0			0
$631$	18.8195			0.749193			0.374596	−	0.927188i	$-0.377781\pi$
$631$	18.8195			0.749193			0.374596	+	0.927188i	$0.377781\pi$
$632$	29.4734	+	11.6082i	1.17239	+	0.461750i
$633$		0			0
$634$	0.0421335	+	0.306220i	0.00167333	+	0.0121615i
$635$	−15.8441	−	15.8441i	−0.628753	−	0.628753i
$636$		0			0
$637$	−21.8363	+	21.8363i	−0.865186	+	0.865186i
$638$	4.14949	−	5.47354i	0.164280	−	0.216700i
$639$		0			0
$640$	9.99208	+	7.03823i	0.394972	+	0.278211i
$641$		−	17.9718i		−	0.709845i	−0.934896	−	0.354923i	$-0.884507\pi$
$641$		−	17.9718i		−	0.709845i	0.934896	−	0.354923i	$-0.115493\pi$
$642$		0			0
$643$	−9.92589	−	9.92589i	−0.391439	−	0.391439i	0.483761	−	0.875200i	$-0.339270\pi$
$643$	−9.92589	−	9.92589i	−0.391439	−	0.391439i	−0.875200	+	0.483761i	$0.839270\pi$
$644$	−22.8082	+	6.39758i	−0.898769	+	0.252100i
$645$		0			0
$646$	34.0984	−	4.69168i	1.34158	−	0.184591i
$647$			13.6801i			0.537820i	0.963165	+	0.268910i	$0.0866635\pi$
$647$			13.6801i			0.537820i	−0.963165	+	0.268910i	$0.913337\pi$
$648$		0			0
$649$		−	18.4897i		−	0.725786i
$650$	−4.37572	−	31.8021i	−0.171630	−	1.24738i
$651$		0			0
$652$	−0.234413	+	0.417182i	−0.00918033	+	0.0163381i
$653$	−31.1940	−	31.1940i	−1.22071	−	1.22071i	−0.967378	−	0.253336i	$-0.918472\pi$
$653$	−31.1940	−	31.1940i	−1.22071	−	1.22071i	−0.253336	−	0.967378i	$-0.581528\pi$
$654$		0			0
$655$			14.4162i			0.563288i
$656$	26.6889	−	16.2508i	1.04203	−	0.634486i
$657$		0			0
$658$	4.82966	+	3.66136i	0.188280	+	0.142735i
$659$	27.2397	−	27.2397i	1.06111	−	1.06111i	0.0631026	−	0.998007i	$-0.479900\pi$
$659$	27.2397	−	27.2397i	1.06111	−	1.06111i	0.998007	−	0.0631026i	$-0.0200995\pi$
$660$		0			0
$661$	−12.0770	−	12.0770i	−0.469740	−	0.469740i	0.432091	−	0.901830i	$-0.357776\pi$
$661$	−12.0770	−	12.0770i	−0.469740	−	0.469740i	−0.901830	+	0.432091i	$0.857776\pi$
$662$	32.3219	−	4.44725i	1.25623	−	0.172847i
$663$		0			0
$664$	−15.5259	−	35.7025i	−0.602523	−	1.38552i
$665$	−8.71237			−0.337851
$666$		0			0
$667$	−10.9856	+	10.9856i	−0.425365	+	0.425365i
$668$	20.1240	−	5.64467i	0.778621	−	0.218399i
$669$		0			0
$670$	9.37227	+	7.10511i	0.362082	+	0.274494i
$671$	12.8064			0.494384
$672$		0			0
$673$	11.0108			0.424434			0.212217	−	0.977223i	$-0.431932\pi$
$673$	11.0108			0.424434			0.212217	+	0.977223i	$0.431932\pi$
$674$	−2.13383	−	1.61765i	−0.0821920	−	0.0623097i
$675$		0			0
$676$	42.5025	−	11.9217i	1.63471	−	0.458528i
$677$	−5.26708	+	5.26708i	−0.202430	+	0.202430i	−0.801040	−	0.598610i	$-0.795720\pi$
$677$	−5.26708	+	5.26708i	−0.202430	+	0.202430i	0.598610	+	0.801040i	$0.295720\pi$
$678$		0			0
$679$	−7.62000			−0.292429
$680$	−11.2990	+	4.91360i	−0.433297	+	0.188428i
$681$		0			0
$682$	11.1747	−	1.53755i	0.427900	−	0.0588758i
$683$	−16.0080	−	16.0080i	−0.612528	−	0.612528i	0.331076	−	0.943604i	$-0.392588\pi$
$683$	−16.0080	−	16.0080i	−0.612528	−	0.612528i	−0.943604	+	0.331076i	$0.892588\pi$
$684$		0			0
$685$	9.79379	−	9.79379i	0.374201	−	0.374201i
$686$	18.3935	+	13.9441i	0.702268	+	0.532389i
$687$		0			0
$688$	7.34482	−	30.2146i	0.280019	−	1.15192i
$689$		−	34.0681i		−	1.29789i
$690$		0			0
$691$	7.63348	+	7.63348i	0.290391	+	0.290391i	0.837235	−	0.546843i	$-0.184171\pi$
$691$	7.63348	+	7.63348i	0.290391	+	0.290391i	−0.546843	+	0.837235i	$0.684171\pi$
$692$	−1.34963	+	2.40192i	−0.0513053	+	0.0913074i
$693$		0			0
$694$	5.38770	+	39.1570i	0.204514	+	1.48638i
$695$		−	2.20529i		−	0.0836514i
$696$		0			0
$697$			31.5005i			1.19317i
$698$	−35.8638	+	4.93458i	−1.35746	+	0.186777i
$699$		0			0
$700$	−9.86265	+	2.76642i	−0.372773	+	0.104561i
$701$	18.3494	+	18.3494i	0.693049	+	0.693049i	0.962902	−	0.269853i	$-0.0869750\pi$
$701$	18.3494	+	18.3494i	0.693049	+	0.693049i	−0.269853	+	0.962902i	$0.586975\pi$
$702$		0			0
$703$		−	3.71192i		−	0.139998i
$704$	−0.775831	−	22.1550i	−0.0292402	−	0.834999i
$705$		0			0
$706$	−16.5485	+	21.8289i	−0.622810	+	0.821541i
$707$	−8.93385	+	8.93385i	−0.335992	+	0.335992i
$708$		0			0
$709$	19.8774	+	19.8774i	0.746511	+	0.746511i	0.973822	−	0.227311i	$-0.0729934\pi$
$709$	19.8774	+	19.8774i	0.746511	+	0.746511i	−0.227311	+	0.973822i	$0.572993\pi$
$710$	0.784497	+	5.70161i	0.0294416	+	0.213977i
$711$		0			0
$712$	−1.70119	+	4.31935i	−0.0637550	+	0.161875i
$713$	−25.5140			−0.955505
$714$		0			0
$715$	12.5357	−	12.5357i	0.468809	−	0.468809i
$716$	16.2636	+	9.13845i	0.607799	+	0.341520i
$717$		0			0
$718$	−6.05942	+	7.99291i	−0.226136	+	0.298293i
$719$	16.1176			0.601083			0.300542	−	0.953769i	$-0.402833\pi$
$719$	16.1176			0.601083			0.300542	+	0.953769i	$0.402833\pi$
$720$		0			0
$721$	14.5357			0.541338
$722$	14.8907	−	19.6422i	0.554175	−	0.731006i
$723$		0			0
$724$	−14.1153	+	25.1207i	−0.524589	+	0.933605i
$725$	−4.75038	+	4.75038i	−0.176425	+	0.176425i
$726$		0			0
$727$	16.4536			0.610229			0.305115	−	0.952316i	$-0.401305\pi$
$727$	16.4536			0.610229			0.305115	+	0.952316i	$0.401305\pi$
$728$	−8.92571	−	20.5250i	−0.330809	−	0.760707i
$729$		0			0
$730$	−2.19401	−	15.9457i	−0.0812040	−	0.590179i
$731$	22.1654	+	22.1654i	0.819816	+	0.819816i
$732$		0			0
$733$	24.5995	−	24.5995i	0.908602	−	0.908602i	−0.0875578	−	0.996159i	$-0.527906\pi$
$733$	24.5995	−	24.5995i	0.908602	−	0.908602i	0.996159	+	0.0875578i	$0.0279063\pi$
$734$	−1.41597	+	1.86779i	−0.0522644	+	0.0689414i
$735$		0			0
$736$	−5.09222	+	49.8836i	−0.187702	+	1.83873i
$737$		−	21.3324i		−	0.785790i
$738$		0			0
$739$	3.06707	+	3.06707i	0.112824	+	0.112824i	0.761265	−	0.648441i	$-0.224579\pi$
$739$	3.06707	+	3.06707i	0.112824	+	0.112824i	−0.648441	+	0.761265i	$0.724579\pi$
$740$	0.358858	+	1.27937i	0.0131919	+	0.0470308i
$741$		0			0
$742$	−10.7693	+	1.48177i	−0.395353	+	0.0543975i
$743$			1.16681i			0.0428061i	0.999771	+	0.0214031i	$0.00681333\pi$
$743$			1.16681i			0.0428061i	−0.999771	+	0.0214031i	$0.993187\pi$
$744$		0			0
$745$			9.80931i			0.359385i
$746$	0.949361	+	6.89981i	0.0347586	+	0.252620i
$747$		0			0
$748$	19.4833	+	10.9476i	0.712380	+	0.400284i
$749$	−1.76051	−	1.76051i	−0.0643278	−	0.0643278i
$750$		0			0
$751$			2.12809i			0.0776552i	0.999246	+	0.0388276i	$0.0123623\pi$
$751$			2.12809i			0.0776552i	−0.999246	+	0.0388276i	$0.987638\pi$
$752$	10.9575	−	6.67195i	0.399577	−	0.243301i
$753$		0			0
$754$	−11.6976	−	8.86795i	−0.426002	−	0.322952i
$755$	0.157317	−	0.157317i	0.00572534	−	0.00572534i
$756$		0			0
$757$	19.1573	+	19.1573i	0.696282	+	0.696282i	0.963607	−	0.267324i	$-0.0861395\pi$
$757$	19.1573	+	19.1573i	0.696282	+	0.696282i	−0.267324	+	0.963607i	$0.586140\pi$
$758$	−37.9521	+	5.22191i	−1.37848	+	0.189668i
$759$		0			0
$760$	−6.75818	+	17.1591i	−0.245145	+	0.622426i
$761$	10.2848			0.372824			0.186412	−	0.982472i	$-0.440314\pi$
$761$	10.2848			0.372824			0.186412	+	0.982472i	$0.440314\pi$
$762$		0			0
$763$	−4.69697	+	4.69697i	−0.170042	+	0.170042i
$764$	−7.68607	−	27.4018i	−0.278072	−	0.991363i
$765$		0			0
$766$	−17.2322	−	13.0638i	−0.622626	−	0.472013i
$767$	−39.5147			−1.42679
$768$		0			0
$769$	−15.2860			−0.551226			−0.275613	−	0.961269i	$-0.588881\pi$
$769$	−15.2860			−0.551226			−0.275613	+	0.961269i	$0.588881\pi$
$770$	−4.50790	−	3.41743i	−0.162453	−	0.123156i
$771$		0			0
$772$	3.53022	+	12.5857i	0.127055	+	0.452968i
$773$	23.6903	−	23.6903i	0.852081	−	0.852081i	−0.138308	−	0.990389i	$-0.544166\pi$
$773$	23.6903	−	23.6903i	0.852081	−	0.852081i	0.990389	+	0.138308i	$0.0441664\pi$
$774$		0			0
$775$	−11.0327			−0.396305
$776$	−5.91084	+	15.0077i	−0.212187	+	0.538744i
$777$		0			0
$778$	45.0047	−	6.19230i	1.61350	−	0.222005i
$779$	33.3396	+	33.3396i	1.19451	+	1.19451i
$780$		0			0
$781$	7.38158	−	7.38158i	0.264134	−	0.264134i
$782$	−40.2824	−	30.5380i	−1.44049	−	1.09204i
$783$		0			0
$784$	17.8155	−	10.8478i	0.636267	−	0.387420i
$785$			1.93697i			0.0691333i
$786$		0			0
$787$	−29.3220	−	29.3220i	−1.04522	−	1.04522i	−0.998928	−	0.0462895i	$-0.985260\pi$
$787$	−29.3220	−	29.3220i	−1.04522	−	1.04522i	−0.0462895	−	0.998928i	$-0.514740\pi$
$788$	22.3826	+	12.5767i	0.797347	+	0.448026i
$789$		0			0
$790$	−2.33224	−	16.9504i	−0.0829775	−	0.603068i
$791$			21.7988i			0.775075i
$792$		0			0
$793$		−	27.3687i		−	0.971890i
$794$	−14.7779	+	2.03332i	−0.524446	+	0.0721598i
$795$		0			0
$796$	−5.44814	−	19.4233i	−0.193104	−	0.688441i
$797$	−3.41153	−	3.41153i	−0.120843	−	0.120843i	0.644099	−	0.764942i	$-0.277232\pi$
$797$	−3.41153	−	3.41153i	−0.120843	−	0.120843i	−0.764942	+	0.644099i	$0.777232\pi$
$798$		0			0
$799$			12.9329i			0.457534i
$800$	−2.20196	+	21.5705i	−0.0778512	+	0.762633i
$801$		0			0
$802$	9.90299	−	13.0629i	0.349687	−	0.461268i
$803$	−20.6441	+	20.6441i	−0.728516	+	0.728516i
$804$		0			0
$805$	9.04754	+	9.04754i	0.318884	+	0.318884i
$806$	−3.28592	−	23.8816i	−0.115742	−	0.841193i
$807$		0			0
$808$	10.6653	+	24.5253i	0.375205	+	0.862797i
$809$	−9.15877			−0.322005			−0.161003	−	0.986954i	$-0.551473\pi$
$809$	−9.15877			−0.322005			−0.161003	+	0.986954i	$0.551473\pi$
$810$		0			0
$811$	−8.91014	+	8.91014i	−0.312877	+	0.312877i	−0.846023	−	0.533146i	$-0.821010\pi$
$811$	−8.91014	+	8.91014i	−0.312877	+	0.312877i	0.533146	+	0.846023i	$0.321010\pi$
$812$	−2.29447	+	4.08344i	−0.0805201	+	0.143301i
$813$		0			0
$814$	1.45601	−	1.92060i	0.0510330	−	0.0673170i
$815$	0.258474			0.00905397
$816$		0			0
$817$	46.9189			1.64148
$818$	−10.6503	+	14.0487i	−0.372380	+	0.491202i
$819$		0			0
$820$	−14.7142	−	8.26785i	−0.513842	−	0.288726i
$821$	27.0618	−	27.0618i	0.944464	−	0.944464i	−0.0540734	−	0.998537i	$-0.517221\pi$
$821$	27.0618	−	27.0618i	0.944464	−	0.944464i	0.998537	+	0.0540734i	$0.0172205\pi$
$822$		0			0
$823$	11.6286			0.405348			0.202674	−	0.979246i	$-0.435037\pi$
$823$	11.6286			0.405348			0.202674	+	0.979246i	$0.435037\pi$
$824$	11.2753	−	28.6282i	0.392795	−	0.997311i
$825$		0			0
$826$	1.71867	+	12.4910i	0.0598001	+	0.434618i
$827$	8.57283	+	8.57283i	0.298107	+	0.298107i	0.840272	−	0.542165i	$-0.182395\pi$
$827$	8.57283	+	8.57283i	0.298107	+	0.298107i	−0.542165	+	0.840272i	$0.682395\pi$
$828$		0			0
$829$	19.5629	−	19.5629i	0.679447	−	0.679447i	−0.280428	−	0.959875i	$-0.590476\pi$
$829$	19.5629	−	19.5629i	0.679447	−	0.679447i	0.959875	+	0.280428i	$0.0904763\pi$
$830$	−12.7041	+	16.7578i	−0.440965	+	0.581672i
$831$		0			0
$832$	−47.3479	+	1.65804i	−1.64149	+	0.0574822i
$833$			21.0274i			0.728555i
$834$		0			0
$835$	−7.98277	−	7.98277i	−0.276255	−	0.276255i
$836$	32.2075	−	9.03403i	1.11392	−	0.312448i
$837$		0			0
$838$	−28.5501	+	3.92828i	−0.986248	+	0.135700i
$839$			14.8018i			0.511015i	0.966807	+	0.255508i	$0.0822426\pi$
$839$			14.8018i			0.511015i	−0.966807	+	0.255508i	$0.917757\pi$
$840$		0			0
$841$		−	25.9281i		−	0.894071i
$842$	1.59107	+	11.5637i	0.0548319	+	0.398510i
$843$		0			0
$844$	−24.9108	+	44.3335i	−0.857466	+	1.52602i
$845$	−16.8599	−	16.8599i	−0.579997	−	0.579997i
$846$		0			0
$847$		−	4.43773i		−	0.152482i
$848$	−5.43537	+	22.3596i	−0.186651	+	0.767833i
$849$		0			0
$850$	−17.4188	−	13.2052i	−0.597460	−	0.452934i
$851$	−3.85473	+	3.85473i	−0.132138	+	0.132138i
$852$		0			0
$853$	−27.2550	−	27.2550i	−0.933192	−	0.933192i	0.0647119	−	0.997904i	$-0.479387\pi$
$853$	−27.2550	−	27.2550i	−0.933192	−	0.933192i	−0.997904	+	0.0647119i	$0.979387\pi$
$854$	−8.65153	+	1.19038i	−0.296049	+	0.0407341i
$855$		0			0
$856$	−4.83298	+	2.10172i	−0.165188	+	0.0718353i
$857$	28.7462			0.981951			0.490976	−	0.871173i	$-0.336640\pi$
$857$	28.7462			0.981951			0.490976	+	0.871173i	$0.336640\pi$
$858$		0			0
$859$	29.2578	−	29.2578i	0.998264	−	0.998264i	−0.00173461	−	0.999998i	$-0.500552\pi$
$859$	29.2578	−	29.2578i	0.998264	−	0.998264i	0.999998	+	0.00173461i	$0.000552144\pi$
$860$	−16.1713	+	4.53598i	−0.551438	+	0.154676i
$861$		0			0
$862$	−20.7938	−	15.7638i	−0.708241	−	0.536917i
$863$	40.6816			1.38482			0.692408	−	0.721506i	$-0.256550\pi$
$863$	40.6816			1.38482			0.692408	+	0.721506i	$0.256550\pi$
$864$		0			0
$865$	1.48816			0.0505991
$866$	−7.41737	−	5.62310i	−0.252052	−	0.191081i
$867$		0			0
$868$	−7.40630	+	2.07743i	−0.251386	+	0.0705125i
$869$	−21.9448	+	21.9448i	−0.744427	+	0.744427i
$870$		0			0
$871$	−45.5899			−1.54475
$872$	5.60729	+	12.8942i	0.189887	+	0.436652i
$873$		0			0
$874$	−74.9550	+	10.3132i	−2.53539	+	0.348850i
$875$	9.01580	+	9.01580i	0.304790	+	0.304790i
$876$		0			0
$877$	−28.9577	+	28.9577i	−0.977831	+	0.977831i	−0.999760	−	0.0219281i	$-0.993020\pi$
$877$	−28.9577	+	28.9577i	−0.977831	+	0.977831i	0.0219281	+	0.999760i	$0.493020\pi$
$878$	−4.15568	−	3.15042i	−0.140247	−	0.106321i
$879$		0			0
$880$	−10.2274	+	6.22745i	−0.344767	+	0.209927i
$881$			17.2311i			0.580531i	0.956946	+	0.290266i	$0.0937437\pi$
$881$			17.2311i			0.580531i	−0.956946	+	0.290266i	$0.906256\pi$
$882$		0			0
$883$	24.8129	+	24.8129i	0.835019	+	0.835019i	0.988198	−	0.153179i	$-0.0489512\pi$
$883$	24.8129	+	24.8129i	0.835019	+	0.835019i	−0.153179	+	0.988198i	$0.548951\pi$
$884$	23.3963	−	41.6381i	0.786902	−	1.40044i
$885$		0			0
$886$	0.904706	+	6.57527i	0.0303942	+	0.220901i
$887$			39.0606i			1.31153i	0.754967	+	0.655763i	$0.227653\pi$
$887$			39.0606i			1.31153i	−0.754967	+	0.655763i	$0.772347\pi$
$888$		0			0
$889$		−	27.7151i		−	0.929534i
$890$	2.48410	−	0.341793i	0.0832672	−	0.0114569i
$891$		0			0
$892$	7.71931	−	2.16522i	0.258462	−	0.0724971i
$893$	13.6880	+	13.6880i	0.458050	+	0.458050i
$894$		0			0
$895$		−	10.0765i		−	0.336819i
$896$	2.58349	+	14.8950i	0.0863083	+	0.497608i
$897$		0			0
$898$	17.3909	−	22.9401i	0.580342	−	0.765522i
$899$	−3.56727	+	3.56727i	−0.118975	+	0.118975i
$900$		0			0
$901$	−16.4030	−	16.4030i	−0.546463	−	0.546463i
$902$	4.17287	+	30.3278i	0.138941	+	1.00981i
$903$		0			0
$904$	42.9329	+	16.9093i	1.42793	+	0.562395i
$905$	15.5641			0.517369
$906$		0			0
$907$	0.366518	−	0.366518i	0.0121700	−	0.0121700i	−0.700996	−	0.713166i	$-0.747261\pi$
$907$	0.366518	−	0.366518i	0.0121700	−	0.0121700i	0.713166	+	0.700996i	$0.247261\pi$
$908$	−34.0074	−	19.1086i	−1.12857	−	0.634142i
$909$		0			0
$910$	−7.30346	+	9.63391i	−0.242107	+	0.319361i
$911$	18.8950			0.626018			0.313009	−	0.949750i	$-0.398663\pi$
$911$	18.8950			0.626018			0.313009	+	0.949750i	$0.398663\pi$
$912$		0			0
$913$	38.1428			1.26234
$914$	8.56398	−	11.2966i	0.283271	−	0.373660i
$915$		0			0
$916$	−4.81945	+	8.57711i	−0.159239	+	0.283396i
$917$	−12.6087	+	12.6087i	−0.416376	+	0.416376i
$918$		0			0
$919$	−54.5805			−1.80045			−0.900223	−	0.435429i	$-0.856597\pi$
$919$	−54.5805			−1.80045			−0.900223	+	0.435429i	$0.856597\pi$
$920$	24.8374	−	10.8010i	0.818865	−	0.356100i
$921$		0			0
$922$	−4.47208	−	32.5024i	−0.147280	−	1.07041i
$923$	−15.7753	−	15.7753i	−0.519250	−	0.519250i
$924$		0			0
$925$	−1.66685	+	1.66685i	−0.0548057	+	0.0548057i
$926$	0.852507	−	1.12453i	0.0280151	−	0.0369544i
$927$		0			0
$928$	6.26256	+	7.68651i	0.205579	+	0.252322i
$929$		−	21.2118i		−	0.695938i	−0.937506	−	0.347969i	$-0.886871\pi$
$929$		−	21.2118i		−	0.695938i	0.937506	−	0.347969i	$-0.113129\pi$
$930$		0			0
$931$	22.2550	+	22.2550i	0.729377	+	0.729377i
$932$	1.74992	+	6.23868i	0.0573204	+	0.204355i
$933$		0			0
$934$	−19.2844	+	2.65339i	−0.631006	+	0.0868215i
$935$		−	12.0713i		−	0.394774i
$936$		0			0
$937$		−	15.7395i		−	0.514186i	−0.966387	−	0.257093i	$-0.917235\pi$
$937$		−	15.7395i		−	0.514186i	0.966387	−	0.257093i	$-0.0827647\pi$
$938$	1.98290	+	14.4114i	0.0647440	+	0.470550i
$939$		0			0
$940$	−6.04109	−	3.39447i	−0.197039	−	0.110715i
$941$	−1.43393	−	1.43393i	−0.0467447	−	0.0467447i	0.683348	−	0.730093i	$-0.260523\pi$
$941$	−1.43393	−	1.43393i	−0.0467447	−	0.0467447i	−0.730093	+	0.683348i	$0.760523\pi$
$942$		0			0
$943$		−	69.2443i		−	2.25491i
$944$	25.9344	+	6.30435i	0.844092	+	0.205189i
$945$		0			0
$946$	24.2765	+	18.4040i	0.789296	+	0.598365i
$947$	−28.5461	+	28.5461i	−0.927623	+	0.927623i	−0.997552	−	0.0699288i	$-0.977723\pi$
$947$	−28.5461	+	28.5461i	−0.927623	+	0.927623i	0.0699288	+	0.997552i	$0.477723\pi$
$948$		0			0
$949$	44.1189	+	44.1189i	1.43216	+	1.43216i
$950$	−32.4118	+	4.45962i	−1.05158	+	0.144689i
$951$		0			0
$952$	−14.1798	−	5.58479i	−0.459571	−	0.181004i
$953$	−14.6986			−0.476136			−0.238068	−	0.971249i	$-0.576514\pi$
$953$	−14.6986			−0.476136			−0.238068	+	0.971249i	$0.576514\pi$
$954$		0			0
$955$	−10.8697	+	10.8697i	−0.351737	+	0.351737i
$956$	13.0976	+	46.6947i	0.423607	+	1.51021i
$957$		0			0
$958$	41.7735	+	31.6684i	1.34964	+	1.02316i
$959$	17.1317			0.553210
$960$		0			0
$961$	22.7151			0.732745
$962$	−4.10455	−	3.11166i	−0.132336	−	0.100324i
$963$		0			0
$964$	8.94454	+	31.8884i	0.288084	+	1.02706i
$965$	4.99248	−	4.99248i	0.160714	−	0.160714i
$966$		0			0
$967$	−7.34054			−0.236056			−0.118028	−	0.993010i	$-0.537657\pi$
$967$	−7.34054			−0.236056			−0.118028	+	0.993010i	$0.537657\pi$
$968$	−8.74015	−	3.44235i	−0.280919	−	0.110641i
$969$		0			0
$970$	8.63105	−	1.18757i	0.277126	−	0.0381304i
$971$	3.48251	+	3.48251i	0.111759	+	0.111759i	0.760775	−	0.649016i	$-0.224819\pi$
$971$	3.48251	+	3.48251i	0.111759	+	0.111759i	−0.649016	+	0.760775i	$0.724819\pi$
$972$		0			0
$973$	1.92879	−	1.92879i	0.0618341	−	0.0618341i
$974$	−37.4005	−	28.3533i	−1.19839	−	0.908497i
$975$		0			0
$976$	−4.36652	+	17.9627i	−0.139769	+	0.574970i
$977$			9.95013i			0.318333i	0.987252	+	0.159166i	$0.0508806\pi$
$977$			9.95013i			0.318333i	−0.987252	+	0.159166i	$0.949119\pi$
$978$		0			0
$979$	−3.21603	−	3.21603i	−0.102785	−	0.102785i
$980$	−9.82208	−	5.51899i	−0.313755	−	0.176298i
$981$		0			0
$982$	2.79649	+	20.3245i	0.0892395	+	0.648580i
$983$			18.7648i			0.598505i	0.954174	+	0.299253i	$0.0967373\pi$
$983$			18.7648i			0.598505i	−0.954174	+	0.299253i	$0.903263\pi$
$984$		0			0
$985$		−	13.8676i		−	0.441859i
$986$	−9.90184	+	1.36242i	−0.315339	+	0.0433882i
$987$		0			0
$988$	−19.3068	−	68.8312i	−0.614230	−	2.18981i
$989$	−48.7239	−	48.7239i	−1.54933	−	1.54933i
$990$		0			0
$991$			3.18227i			0.101088i	0.998722	+	0.0505441i	$0.0160955\pi$
$991$			3.18227i			0.101088i	−0.998722	+	0.0505441i	$0.983904\pi$
$992$	−1.65355	+	16.1982i	−0.0525003	+	0.514295i
$993$		0			0
$994$	−4.30060	+	5.67287i	−0.136407	+	0.179933i
$995$	−7.70483	+	7.70483i	−0.244259	+	0.244259i
$996$		0			0
$997$	26.9944	+	26.9944i	0.854923	+	0.854923i	0.990735	−	0.135812i	$-0.0433643\pi$
$997$	26.9944	+	26.9944i	0.854923	+	0.854923i	−0.135812	+	0.990735i	$0.543364\pi$
$998$	−1.14426	−	8.31631i	−0.0362209	−	0.263248i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.2.l.a.107.2	yes	16
3.2	odd	2	inner	144.2.l.a.107.7	yes	16
4.3	odd	2		576.2.l.a.143.6		16
8.3	odd	2		1152.2.l.b.287.3		16
8.5	even	2		1152.2.l.a.287.3		16
12.11	even	2		576.2.l.a.143.3		16
16.3	odd	4	inner	144.2.l.a.35.7	yes	16
16.5	even	4		1152.2.l.b.863.6		16
16.11	odd	4		1152.2.l.a.863.6		16
16.13	even	4		576.2.l.a.431.3		16
24.5	odd	2		1152.2.l.a.287.6		16
24.11	even	2		1152.2.l.b.287.6		16
48.5	odd	4		1152.2.l.b.863.3		16
48.11	even	4		1152.2.l.a.863.3		16
48.29	odd	4		576.2.l.a.431.6		16
48.35	even	4	inner	144.2.l.a.35.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.l.a.35.2	✓	16	48.35	even	4	inner
144.2.l.a.35.7	yes	16	16.3	odd	4	inner
144.2.l.a.107.2	yes	16	1.1	even	1	trivial
144.2.l.a.107.7	yes	16	3.2	odd	2	inner
576.2.l.a.143.3		16	12.11	even	2
576.2.l.a.143.6		16	4.3	odd	2
576.2.l.a.431.3		16	16.13	even	4
576.2.l.a.431.6		16	48.29	odd	4
1152.2.l.a.287.3		16	8.5	even	2
1152.2.l.a.287.6		16	24.5	odd	2
1152.2.l.a.863.3		16	48.11	even	4
1152.2.l.a.863.6		16	16.11	odd	4
1152.2.l.b.287.3		16	8.3	odd	2
1152.2.l.b.287.6		16	24.11	even	2
1152.2.l.b.863.3		16	48.5	odd	4
1152.2.l.b.863.6		16	16.5	even	4

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12697 - 0.854358i) q^{2} +(0.540143 + 1.92568i) q^{4} +(0.763878 - 0.763878i) q^{5} +1.33620 q^{7} +(1.03649 - 2.63167i) q^{8} +O(q^{10})\)	\(q+(-1.12697 - 0.854358i) q^{2} +(0.540143 + 1.92568i) q^{4} +(0.763878 - 0.763878i) q^{5} +1.33620 q^{7} +(1.03649 - 2.63167i) q^{8} +(-1.51350 + 0.208245i) q^{10} +(1.95945 + 1.95945i) q^{11} +(4.18757 - 4.18757i) q^{13} +(-1.50587 - 1.14160i) q^{14} +(-3.41649 + 2.08029i) q^{16} -4.03243i q^{17} +(-4.26785 - 4.26785i) q^{19} +(1.88359 + 1.05838i) q^{20} +(-0.534176 - 3.88231i) q^{22} +8.86408i q^{23} +3.83298i q^{25} +(-8.29696 + 1.14160i) q^{26} +(0.721742 + 2.57310i) q^{28} +(1.23934 + 1.23934i) q^{29} +2.87835i q^{31} +(5.62761 + 0.574478i) q^{32} +(-3.44514 + 4.54445i) q^{34} +(1.02070 - 1.02070i) q^{35} +(0.434870 + 0.434870i) q^{37} +(1.16348 + 8.45604i) q^{38} +(-1.21852 - 2.80203i) q^{40} -7.81179 q^{41} +(-5.49678 + 5.49678i) q^{43} +(-2.71489 + 4.83165i) q^{44} +(7.57310 - 9.98959i) q^{46} -3.20723 q^{47} -5.21456 q^{49} +(3.27474 - 4.31967i) q^{50} +(10.3258 + 5.80203i) q^{52} +(4.06777 - 4.06777i) q^{53} +2.99355 q^{55} +(1.38497 - 3.51645i) q^{56} +(-0.337865 - 2.45555i) q^{58} +(-4.71811 - 4.71811i) q^{59} +(3.26785 - 3.26785i) q^{61} +(2.45915 - 3.24383i) q^{62} +(-5.85136 - 5.45542i) q^{64} -6.39758i q^{65} +(-5.44348 - 5.44348i) q^{67} +(7.76518 - 2.17809i) q^{68} +(-2.02234 + 0.278258i) q^{70} -3.76718i q^{71} +10.5357i q^{73} +(-0.118553 - 0.861623i) q^{74} +(5.91327 - 10.5238i) q^{76} +(2.61822 + 2.61822i) q^{77} +11.1995i q^{79} +(-1.02070 + 4.19887i) q^{80} +(8.80369 + 6.67407i) q^{82} +(9.73306 - 9.73306i) q^{83} +(-3.08029 - 3.08029i) q^{85} +(10.8909 - 1.49851i) q^{86} +(7.18757 - 3.12566i) q^{88} -1.64130 q^{89} +(5.59544 - 5.59544i) q^{91} +(-17.0694 + 4.78787i) q^{92} +(3.61446 + 2.74012i) q^{94} -6.52023 q^{95} -5.70272 q^{97} +(5.87667 + 4.45510i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{10} - 16 q^{16} + 16 q^{19} - 40 q^{22} - 24 q^{28} + 24 q^{34} + 72 q^{40} - 32 q^{43} + 40 q^{46} + 16 q^{49} + 24 q^{52} - 64 q^{55} + 24 q^{58} - 32 q^{61} - 48 q^{64} - 16 q^{67} - 72 q^{70} + 80 q^{82} - 32 q^{85} + 48 q^{88} + 48 q^{91} + 72 q^{94}+O(q^{100}) \) 16 * q - 8 * q^10 - 16 * q^16 + 16 * q^19 - 40 * q^22 - 24 * q^28 + 24 * q^34 + 72 * q^40 - 32 * q^43 + 40 * q^46 + 16 * q^49 + 24 * q^52 - 64 * q^55 + 24 * q^58 - 32 * q^61 - 48 * q^64 - 16 * q^67 - 72 * q^70 + 80 * q^82 - 32 * q^85 + 48 * q^88 + 48 * q^91 + 72 * q^94

Introduction

L-functions

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