LMFDB - Embedded newform 1710.2.n.i.1673.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(647,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("1710.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.n (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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} - 10 x^{18} + 56 x^{17} + 50 x^{16} - 336 x^{15} + 672 x^{14} - 776 x^{13} + 626 x^{12} + \cdots + 32 $ x^20 - 4x^19 - 10x^18 + 56x^17 + 50x^16 - 336x^15 + 672x^14 - 776x^13 + 626x^12 - 748x^11 + 514x^10 + 1340x^9 - 648x^8 - 2216x^7 + 3348x^6 - 2684x^5 + 1761x^4 - 728x^3 + 408x^2 - 96*x + 32
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1673.6
Root			$-3.06999 + 1.27163i$ of defining polynomial
Character	$\chi$	$=$	1710.1673
Dual form			1710.2.n.i.647.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-2.21129 + 0.331972i) q^{5} +(-1.82552 + 1.82552i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.79836 - 1.32888i) q^{10} -2.09952i q^{11} +(-1.64265 - 1.64265i) q^{13} -2.58168 q^{14} -1.00000 q^{16} +(-3.29353 - 3.29353i) q^{17} -1.00000i q^{19} +(-0.331972 - 2.21129i) q^{20} +(1.48459 - 1.48459i) q^{22} +(5.12494 - 5.12494i) q^{23} +(4.77959 - 1.46817i) q^{25} -2.32305i q^{26} +(-1.82552 - 1.82552i) q^{28} +9.48773 q^{29} +4.22425 q^{31} +(-0.707107 - 0.707107i) q^{32} -4.65775i q^{34} +(3.43074 - 4.64278i) q^{35} +(-1.64265 + 1.64265i) q^{37} +(0.707107 - 0.707107i) q^{38} +(1.32888 - 1.79836i) q^{40} +7.26473i q^{41} +(5.70884 + 5.70884i) q^{43} +2.09952 q^{44} +7.24776 q^{46} +(-9.10895 - 9.10895i) q^{47} +0.334925i q^{49} +(4.41783 + 2.34153i) q^{50} +(1.64265 - 1.64265i) q^{52} +(10.0145 - 10.0145i) q^{53} +(0.696982 + 4.64265i) q^{55} -2.58168i q^{56} +(6.70884 + 6.70884i) q^{58} -5.56868 q^{59} -13.7834 q^{61} +(2.98700 + 2.98700i) q^{62} -1.00000i q^{64} +(4.17768 + 3.08705i) q^{65} +(3.29353 - 3.29353i) q^{68} +(5.70884 - 0.857046i) q^{70} -0.853364i q^{71} +(-8.55918 - 8.55918i) q^{73} -2.32305 q^{74} +1.00000 q^{76} +(3.83273 + 3.83273i) q^{77} -1.45962i q^{79} +(2.21129 - 0.331972i) q^{80} +(-5.13694 + 5.13694i) q^{82} +(6.31562 - 6.31562i) q^{83} +(8.37630 + 6.18958i) q^{85} +8.07352i q^{86} +(1.48459 + 1.48459i) q^{88} +8.59262 q^{89} +5.99738 q^{91} +(5.12494 + 5.12494i) q^{92} -12.8820i q^{94} +(0.331972 + 2.21129i) q^{95} +(11.0176 - 11.0176i) q^{97} +(-0.236828 + 0.236828i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{10} - 12 q^{13} - 20 q^{16} - 16 q^{22} + 16 q^{31} - 12 q^{37} - 8 q^{46} + 12 q^{52} + 20 q^{58} - 16 q^{61} + 20 q^{73} + 20 q^{76} - 28 q^{82} - 8 q^{85} - 16 q^{88} + 32 q^{91} - 20 q^{97}+O(q^{100}) $ 20 * q + 4 * q^10 - 12 * q^13 - 20 * q^16 - 16 * q^22 + 16 * q^31 - 12 * q^37 - 8 * q^46 + 12 * q^52 + 20 * q^58 - 16 * q^61 + 20 * q^73 + 20 * q^76 - 28 * q^82 - 8 * q^85 - 16 * q^88 + 32 * q^91 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−2.21129	+	0.331972i	−0.988918	+	0.148462i
$5$	−2.21129	+	0.331972i	−0.988918	+	0.148462i
$6$		0			0
$7$	−1.82552	+	1.82552i	−0.689983	+	0.689983i	−0.962228	−	0.272245i	$-0.912234\pi$
$7$	−1.82552	+	1.82552i	−0.689983	+	0.689983i	0.272245	+	0.962228i	$0.412234\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−1.79836	−	1.32888i	−0.568690	−	0.420228i
$11$		−	2.09952i		−	0.633030i	−0.948588	−	0.316515i	$-0.897487\pi$
$11$		−	2.09952i		−	0.633030i	0.948588	−	0.316515i	$-0.102513\pi$
$12$		0			0
$13$	−1.64265	−	1.64265i	−0.455588	−	0.455588i	0.441616	−	0.897204i	$-0.354405\pi$
$13$	−1.64265	−	1.64265i	−0.455588	−	0.455588i	−0.897204	+	0.441616i	$0.854405\pi$
$14$	−2.58168			−0.689983
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−3.29353	−	3.29353i	−0.798798	−	0.798798i	0.184108	−	0.982906i	$-0.441060\pi$
$17$	−3.29353	−	3.29353i	−0.798798	−	0.798798i	−0.982906	+	0.184108i	$0.941060\pi$
$18$		0			0
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−0.331972	−	2.21129i	−0.0742312	−	0.494459i
$21$		0			0
$22$	1.48459	−	1.48459i	0.316515	−	0.316515i
$23$	5.12494	−	5.12494i	1.06862	−	1.06862i	0.0711590	−	0.997465i	$-0.477330\pi$
$23$	5.12494	−	5.12494i	1.06862	−	1.06862i	0.997465	−	0.0711590i	$-0.0226698\pi$
$24$		0			0
$25$	4.77959	−	1.46817i	0.955918	−	0.293634i
$26$		−	2.32305i		−	0.455588i
$27$		0			0
$28$	−1.82552	−	1.82552i	−0.344992	−	0.344992i
$29$	9.48773			1.76183			0.880914	−	0.473277i	$-0.156929\pi$
$29$	9.48773			1.76183			0.880914	+	0.473277i	$0.156929\pi$
$30$		0			0
$31$	4.22425			0.758698			0.379349	−	0.925254i	$-0.376148\pi$
$31$	4.22425			0.758698			0.379349	+	0.925254i	$0.376148\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$		−	4.65775i		−	0.798798i
$35$	3.43074	−	4.64278i	0.579900	−	0.784773i
$36$		0			0
$37$	−1.64265	+	1.64265i	−0.270050	+	0.270050i	−0.829120	−	0.559071i	$-0.811158\pi$
$37$	−1.64265	+	1.64265i	−0.270050	+	0.270050i	0.559071	+	0.829120i	$0.311158\pi$
$38$	0.707107	−	0.707107i	0.114708	−	0.114708i
$39$		0			0
$40$	1.32888	−	1.79836i	0.210114	−	0.284345i
$41$			7.26473i			1.13456i	0.823525	+	0.567280i	$0.192004\pi$
$41$			7.26473i			1.13456i	−0.823525	+	0.567280i	$0.807996\pi$
$42$		0			0
$43$	5.70884	+	5.70884i	0.870590	+	0.870590i	0.992537	−	0.121947i	$-0.0389137\pi$
$43$	5.70884	+	5.70884i	0.870590	+	0.870590i	−0.121947	+	0.992537i	$0.538914\pi$
$44$	2.09952			0.316515
$45$		0			0
$46$	7.24776			1.06862
$47$	−9.10895	−	9.10895i	−1.32868	−	1.32868i	−0.906525	−	0.422153i	$-0.861274\pi$
$47$	−9.10895	−	9.10895i	−1.32868	−	1.32868i	−0.422153	−	0.906525i	$-0.638726\pi$
$48$		0			0
$49$			0.334925i			0.0478465i
$50$	4.41783	+	2.34153i	0.624776	+	0.331142i
$51$		0			0
$52$	1.64265	−	1.64265i	0.227794	−	0.227794i
$53$	10.0145	−	10.0145i	1.37559	−	1.37559i	0.523675	−	0.851918i	$-0.324561\pi$
$53$	10.0145	−	10.0145i	1.37559	−	1.37559i	0.851918	−	0.523675i	$-0.175439\pi$
$54$		0			0
$55$	0.696982	+	4.64265i	0.0939811	+	0.626014i
$56$		−	2.58168i		−	0.344992i
$57$		0			0
$58$	6.70884	+	6.70884i	0.880914	+	0.880914i
$59$	−5.56868			−0.724980			−0.362490	−	0.931988i	$-0.618073\pi$
$59$	−5.56868			−0.724980			−0.362490	+	0.931988i	$0.618073\pi$
$60$		0			0
$61$	−13.7834			−1.76479			−0.882394	−	0.470512i	$-0.844069\pi$
$61$	−13.7834			−1.76479			−0.882394	+	0.470512i	$0.844069\pi$
$62$	2.98700	+	2.98700i	0.379349	+	0.379349i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	4.17768	+	3.08705i	0.518177	+	0.382902i
$66$		0			0
$67$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$67$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$68$	3.29353	−	3.29353i	0.399399	−	0.399399i
$69$		0			0
$70$	5.70884	−	0.857046i	0.682337	−	0.102437i
$71$		−	0.853364i		−	0.101276i	−0.998717	−	0.0506378i	$-0.983875\pi$
$71$		−	0.853364i		−	0.101276i	0.998717	−	0.0506378i	$-0.0161254\pi$
$72$		0			0
$73$	−8.55918	−	8.55918i	−1.00178	−	1.00178i	−0.999998	−	0.00177765i	$-0.999434\pi$
$73$	−8.55918	−	8.55918i	−1.00178	−	1.00178i	−0.00177765	−	0.999998i	$-0.500566\pi$
$74$	−2.32305			−0.270050
$75$		0			0
$76$	1.00000			0.114708
$77$	3.83273	+	3.83273i	0.436780	+	0.436780i
$78$		0			0
$79$		−	1.45962i		−	0.164221i	−0.996623	−	0.0821103i	$-0.973834\pi$
$79$		−	1.45962i		−	0.164221i	0.996623	−	0.0821103i	$-0.0261660\pi$
$80$	2.21129	−	0.331972i	0.247230	−	0.0371156i
$81$		0			0
$82$	−5.13694	+	5.13694i	−0.567280	+	0.567280i
$83$	6.31562	−	6.31562i	0.693230	−	0.693230i	−0.269712	−	0.962941i	$-0.586928\pi$
$83$	6.31562	−	6.31562i	0.693230	−	0.693230i	0.962941	+	0.269712i	$0.0869284\pi$
$84$		0			0
$85$	8.37630	+	6.18958i	0.908538	+	0.671355i
$86$			8.07352i			0.870590i
$87$		0			0
$88$	1.48459	+	1.48459i	0.158257	+	0.158257i
$89$	8.59262			0.910816			0.455408	−	0.890283i	$-0.349493\pi$
$89$	8.59262			0.910816			0.455408	+	0.890283i	$0.349493\pi$
$90$		0			0
$91$	5.99738			0.628697
$92$	5.12494	+	5.12494i	0.534312	+	0.534312i
$93$		0			0
$94$		−	12.8820i		−	1.32868i
$95$	0.331972	+	2.21129i	0.0340596	+	0.226873i
$96$		0			0
$97$	11.0176	−	11.0176i	1.11867	−	1.11867i	0.126735	−	0.991937i	$-0.459550\pi$
$97$	11.0176	−	11.0176i	1.11867	−	1.11867i	0.991937	−	0.126735i	$-0.0404499\pi$
$98$	−0.236828	+	0.236828i	−0.0239232	+	0.0239232i
$99$		0			0
$100$	1.46817	+	4.77959i	0.146817	+	0.477959i
$101$		−	14.5956i		−	1.45232i	−0.687527	−	0.726159i	$-0.741304\pi$
$101$		−	14.5956i		−	1.45232i	0.687527	−	0.726159i	$-0.258696\pi$
$102$		0			0
$103$	−5.69373	−	5.69373i	−0.561020	−	0.561020i	0.368577	−	0.929597i	$-0.379845\pi$
$103$	−5.69373	−	5.69373i	−0.561020	−	0.561020i	−0.929597	+	0.368577i	$0.879845\pi$
$104$	2.32305			0.227794
$105$		0			0
$106$	14.1626			1.37559
$107$	−11.2683	−	11.2683i	−1.08934	−	1.08934i	−0.995596	−	0.0937480i	$-0.970115\pi$
$107$	−11.2683	−	11.2683i	−1.08934	−	1.08934i	−0.0937480	−	0.995596i	$-0.529885\pi$
$108$		0			0
$109$			9.19081i			0.880320i	0.897919	+	0.440160i	$0.145078\pi$
$109$			9.19081i			0.880320i	−0.897919	+	0.440160i	$0.854922\pi$
$110$	−2.79001	+	3.77569i	−0.266017	+	0.359998i
$111$		0			0
$112$	1.82552	−	1.82552i	0.172496	−	0.172496i
$113$	3.32007	−	3.32007i	0.312326	−	0.312326i	−0.533484	−	0.845810i	$-0.679118\pi$
$113$	3.32007	−	3.32007i	0.312326	−	0.312326i	0.845810	+	0.533484i	$0.179118\pi$
$114$		0			0
$115$	−9.63138	+	13.0341i	−0.898131	+	1.21543i
$116$			9.48773i			0.880914i
$117$		0			0
$118$	−3.93765	−	3.93765i	−0.362490	−	0.362490i
$119$	12.0248			1.10231
$120$		0			0
$121$	6.59201			0.599273
$122$	−9.74636	−	9.74636i	−0.882394	−	0.882394i
$123$		0			0
$124$			4.22425i			0.379349i
$125$	−10.0817	+	4.83324i	−0.901731	+	0.432298i
$126$		0			0
$127$	−6.97903	+	6.97903i	−0.619289	+	0.619289i	−0.945349	−	0.326060i	$-0.894279\pi$
$127$	−6.97903	+	6.97903i	−0.619289	+	0.619289i	0.326060	+	0.945349i	$0.394279\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	0.771189	+	5.13694i	0.0676377	+	0.450540i
$131$		−	1.52919i		−	0.133606i	−0.997766	−	0.0668029i	$-0.978720\pi$
$131$		−	1.52919i		−	0.133606i	0.997766	−	0.0668029i	$-0.0212799\pi$
$132$		0			0
$133$	1.82552	+	1.82552i	0.158293	+	0.158293i
$134$		0			0
$135$		0			0
$136$	4.65775			0.399399
$137$	−8.70549	−	8.70549i	−0.743760	−	0.743760i	0.229539	−	0.973299i	$-0.426278\pi$
$137$	−8.70549	−	8.70549i	−0.743760	−	0.743760i	−0.973299	+	0.229539i	$0.926278\pi$
$138$		0			0
$139$		−	11.8451i		−	1.00469i	−0.864668	−	0.502344i	$-0.832471\pi$
$139$		−	11.8451i		−	1.00469i	0.864668	−	0.502344i	$-0.167529\pi$
$140$	4.64278	+	3.43074i	0.392387	+	0.289950i
$141$		0			0
$142$	0.603419	−	0.603419i	0.0506378	−	0.0506378i
$143$	−3.44877	+	3.44877i	−0.288401	+	0.288401i
$144$		0			0
$145$	−20.9801	+	3.14966i	−1.74230	+	0.261565i
$146$		−	12.1045i		−	1.00178i
$147$		0			0
$148$	−1.64265	−	1.64265i	−0.135025	−	0.135025i
$149$	−19.3650			−1.58644			−0.793221	−	0.608934i	$-0.791598\pi$
$149$	−19.3650			−1.58644			−0.793221	+	0.608934i	$0.791598\pi$
$150$		0			0
$151$	2.09187			0.170234			0.0851170	−	0.996371i	$-0.472874\pi$
$151$	2.09187			0.170234			0.0851170	+	0.996371i	$0.472874\pi$
$152$	0.707107	+	0.707107i	0.0573539	+	0.0573539i
$153$		0			0
$154$			5.42029i			0.436780i
$155$	−9.34104	+	1.40233i	−0.750290	+	0.112638i
$156$		0			0
$157$	0.0362263	−	0.0362263i	0.00289117	−	0.00289117i	−0.705660	−	0.708551i	$-0.749349\pi$
$157$	0.0362263	−	0.0362263i	0.00289117	−	0.00289117i	0.708551	+	0.705660i	$0.249349\pi$
$158$	1.03211	−	1.03211i	0.0821103	−	0.0821103i
$159$		0			0
$160$	1.79836	+	1.32888i	0.142173	+	0.105057i
$161$			18.7114i			1.47467i
$162$		0			0
$163$	14.6211	+	14.6211i	1.14521	+	1.14521i	0.987483	+	0.157727i	$0.0504166\pi$
$163$	14.6211	+	14.6211i	1.14521	+	1.14521i	0.157727	+	0.987483i	$0.449583\pi$
$164$	−7.26473			−0.567280
$165$		0			0
$166$	8.93164			0.693230
$167$	−8.05215	−	8.05215i	−0.623094	−	0.623094i	0.323227	−	0.946321i	$-0.395232\pi$
$167$	−8.05215	−	8.05215i	−0.623094	−	0.623094i	−0.946321	+	0.323227i	$0.895232\pi$
$168$		0			0
$169$		−	7.60342i		−	0.584878i
$170$	1.54624	+	10.2996i	0.118591	+	0.789946i
$171$		0			0
$172$	−5.70884	+	5.70884i	−0.435295	+	0.435295i
$173$	12.5516	−	12.5516i	0.954278	−	0.954278i	−0.0447212	−	0.999000i	$-0.514240\pi$
$173$	12.5516	−	12.5516i	0.954278	−	0.954278i	0.999000	+	0.0447212i	$0.0142400\pi$
$174$		0			0
$175$	−6.04507	+	11.4054i	−0.456965	+	0.862170i
$176$			2.09952i			0.158257i
$177$		0			0
$178$	6.07590	+	6.07590i	0.455408	+	0.455408i
$179$	−11.9025			−0.889638			−0.444819	−	0.895620i	$-0.646732\pi$
$179$	−11.9025			−0.889638			−0.444819	+	0.895620i	$0.646732\pi$
$180$		0			0
$181$	−4.82767			−0.358838			−0.179419	−	0.983773i	$-0.557422\pi$
$181$	−4.82767			−0.358838			−0.179419	+	0.983773i	$0.557422\pi$
$182$	4.24079	+	4.24079i	0.314348	+	0.314348i
$183$		0			0
$184$			7.24776i			0.534312i
$185$	3.08705	−	4.17768i	0.226965	−	0.307149i
$186$		0			0
$187$	−6.91484	+	6.91484i	−0.505663	+	0.505663i
$188$	9.10895	−	9.10895i	0.664339	−	0.664339i
$189$		0			0
$190$	−1.32888	+	1.79836i	−0.0964069	+	0.130466i
$191$		−	7.88988i		−	0.570892i	−0.958395	−	0.285446i	$-0.907858\pi$
$191$		−	7.88988i		−	0.570892i	0.958395	−	0.285446i	$-0.0921417\pi$
$192$		0			0
$193$	−1.49129	−	1.49129i	−0.107346	−	0.107346i	0.651394	−	0.758740i	$-0.274185\pi$
$193$	−1.49129	−	1.49129i	−0.107346	−	0.107346i	−0.758740	+	0.651394i	$0.774185\pi$
$194$	15.5813			1.11867
$195$		0			0
$196$	−0.334925			−0.0239232
$197$	−14.4190	−	14.4190i	−1.02731	−	1.02731i	−0.999616	−	0.0276953i	$-0.991183\pi$
$197$	−14.4190	−	14.4190i	−1.02731	−	1.02731i	−0.0276953	−	0.999616i	$-0.508817\pi$
$198$		0			0
$199$			2.84447i			0.201639i	0.994905	+	0.100820i	$0.0321465\pi$
$199$			2.84447i			0.201639i	−0.994905	+	0.100820i	$0.967853\pi$
$200$	−2.34153	+	4.41783i	−0.165571	+	0.312388i
$201$		0			0
$202$	10.3207	−	10.3207i	0.726159	−	0.726159i
$203$	−17.3201	+	17.3201i	−1.21563	+	1.21563i
$204$		0			0
$205$	−2.41169	−	16.0644i	−0.168440	−	1.12199i
$206$		−	8.05215i		−	0.561020i
$207$		0			0
$208$	1.64265	+	1.64265i	0.113897	+	0.113897i
$209$	−2.09952			−0.145227
$210$		0			0
$211$	−10.7289			−0.738607			−0.369304	−	0.929309i	$-0.620404\pi$
$211$	−10.7289			−0.738607			−0.369304	+	0.929309i	$0.620404\pi$
$212$	10.0145	+	10.0145i	0.687797	+	0.687797i
$213$		0			0
$214$		−	15.9357i		−	1.08934i
$215$	−14.5191	−	10.7287i	−0.990192	−	0.731692i
$216$		0			0
$217$	−7.71148	+	7.71148i	−0.523489	+	0.523489i
$218$	−6.49888	+	6.49888i	−0.440160	+	0.440160i
$219$		0			0
$220$	−4.64265	+	0.696982i	−0.313007	+	0.0469905i
$221$			10.8202i			0.727846i
$222$		0			0
$223$	13.0260	+	13.0260i	0.872288	+	0.872288i	0.992721	−	0.120433i	$-0.0384283\pi$
$223$	13.0260	+	13.0260i	0.872288	+	0.872288i	−0.120433	+	0.992721i	$0.538428\pi$
$224$	2.58168			0.172496
$225$		0			0
$226$	4.69529			0.312326
$227$	20.4647	+	20.4647i	1.35829	+	1.35829i	0.876029	+	0.482259i	$0.160184\pi$
$227$	20.4647	+	20.4647i	1.35829	+	1.35829i	0.482259	+	0.876029i	$0.339816\pi$
$228$		0			0
$229$		−	1.89472i		−	0.125206i	−0.998038	−	0.0626032i	$-0.980060\pi$
$229$		−	1.89472i		−	0.125206i	0.998038	−	0.0626032i	$-0.0199403\pi$
$230$	−16.0269	+	2.40605i	−1.05678	+	0.158650i
$231$		0			0
$232$	−6.70884	+	6.70884i	−0.440457	+	0.440457i
$233$	2.12791	−	2.12791i	0.139404	−	0.139404i	−0.633961	−	0.773365i	$-0.718572\pi$
$233$	2.12791	−	2.12791i	0.139404	−	0.139404i	0.773365	+	0.633961i	$0.218572\pi$
$234$		0			0
$235$	23.1664	+	17.1186i	1.51121	+	1.11669i
$236$		−	5.56868i		−	0.362490i
$237$		0			0
$238$	8.50284	+	8.50284i	0.551157	+	0.551157i
$239$	14.0763			0.910521			0.455260	−	0.890358i	$-0.349546\pi$
$239$	14.0763			0.910521			0.455260	+	0.890358i	$0.349546\pi$
$240$		0			0
$241$	11.1960			0.721200			0.360600	−	0.932720i	$-0.382572\pi$
$241$	11.1960			0.721200			0.360600	+	0.932720i	$0.382572\pi$
$242$	4.66125	+	4.66125i	0.299637	+	0.299637i
$243$		0			0
$244$		−	13.7834i		−	0.882394i
$245$	−0.111186	−	0.740616i	−0.00710340	−	0.0473162i
$246$		0			0
$247$	−1.64265	+	1.64265i	−0.104519	+	0.104519i
$248$	−2.98700	+	2.98700i	−0.189675	+	0.189675i
$249$		0			0
$250$	−10.5464	−	3.71119i	−0.667014	−	0.234716i
$251$			21.3245i			1.34599i	0.739647	+	0.672995i	$0.234992\pi$
$251$			21.3245i			1.34599i	−0.739647	+	0.672995i	$0.765008\pi$
$252$		0			0
$253$	−10.7599	−	10.7599i	−0.676471	−	0.676471i
$254$	−9.86983			−0.619289
$255$		0			0
$256$	1.00000			0.0625000
$257$	19.5098	+	19.5098i	1.21699	+	1.21699i	0.968681	+	0.248309i	$0.0798749\pi$
$257$	19.5098	+	19.5098i	1.21699	+	1.21699i	0.248309	+	0.968681i	$0.420125\pi$
$258$		0			0
$259$		−	5.99738i		−	0.372659i
$260$	−3.08705	+	4.17768i	−0.191451	+	0.259089i
$261$		0			0
$262$	1.08130	−	1.08130i	0.0668029	−	0.0668029i
$263$	6.06124	−	6.06124i	0.373752	−	0.373752i	−0.495090	−	0.868842i	$-0.664865\pi$
$263$	6.06124	−	6.06124i	0.373752	−	0.373752i	0.868842	+	0.495090i	$0.164865\pi$
$264$		0			0
$265$	−18.8204	+	25.4694i	−1.15613	+	1.56457i
$266$			2.58168i			0.158293i
$267$		0			0
$268$		0			0
$269$	−9.04067			−0.551219			−0.275610	−	0.961270i	$-0.588880\pi$
$269$	−9.04067			−0.551219			−0.275610	+	0.961270i	$0.588880\pi$
$270$		0			0
$271$	12.5180			0.760417			0.380209	−	0.924901i	$-0.375852\pi$
$271$	12.5180			0.760417			0.380209	+	0.924901i	$0.375852\pi$
$272$	3.29353	+	3.29353i	0.199700	+	0.199700i
$273$		0			0
$274$		−	12.3114i		−	0.743760i
$275$	−3.08246	−	10.0349i	−0.185879	−	0.605124i
$276$		0			0
$277$	9.58199	−	9.58199i	0.575726	−	0.575726i	−0.357997	−	0.933723i	$-0.616540\pi$
$277$	9.58199	−	9.58199i	0.575726	−	0.575726i	0.933723	+	0.357997i	$0.116540\pi$
$278$	8.37574	−	8.37574i	0.502344	−	0.502344i
$279$		0			0
$280$	0.857046	+	5.70884i	0.0512183	+	0.341168i
$281$			4.36612i			0.260461i	0.991484	+	0.130230i	$0.0415717\pi$
$281$			4.36612i			0.260461i	−0.991484	+	0.130230i	$0.958428\pi$
$282$		0			0
$283$	−18.6452	−	18.6452i	−1.10834	−	1.10834i	−0.993369	−	0.114972i	$-0.963322\pi$
$283$	−18.6452	−	18.6452i	−1.10834	−	1.10834i	−0.114972	−	0.993369i	$-0.536678\pi$
$284$	0.853364			0.0506378
$285$		0			0
$286$	−4.87730			−0.288401
$287$	−13.2619	−	13.2619i	−0.782828	−	0.782828i
$288$		0			0
$289$			4.69467i			0.276157i
$290$	−17.0623	−	12.6080i	−1.00193	−	0.740369i
$291$		0			0
$292$	8.55918	−	8.55918i	0.500888	−	0.500888i
$293$	−17.8949	+	17.8949i	−1.04543	+	1.04543i	−0.0465116	+	0.998918i	$0.514810\pi$
$293$	−17.8949	+	17.8949i	−1.04543	+	1.04543i	−0.998918	+	0.0465116i	$0.985190\pi$
$294$		0			0
$295$	12.3140	−	1.84865i	0.716946	−	0.107632i
$296$		−	2.32305i		−	0.135025i
$297$		0			0
$298$	−13.6931	−	13.6931i	−0.793221	−	0.793221i
$299$	−16.8369			−0.973705
$300$		0			0
$301$	−20.8432			−1.20138
$302$	1.47917	+	1.47917i	0.0851170	+	0.0851170i
$303$		0			0
$304$			1.00000i			0.0573539i
$305$	30.4791	−	4.57571i	1.74523	−	0.262005i
$306$		0			0
$307$	−12.5089	+	12.5089i	−0.713923	+	0.713923i	−0.967353	−	0.253431i	$-0.918441\pi$
$307$	−12.5089	+	12.5089i	−0.713923	+	0.713923i	0.253431	+	0.967353i	$0.418441\pi$
$308$	−3.83273	+	3.83273i	−0.218390	+	0.218390i
$309$		0			0
$310$	−7.59671	−	5.61351i	−0.431464	−	0.318826i
$311$			30.0324i			1.70298i	0.524369	+	0.851491i	$0.324301\pi$
$311$			30.0324i			1.70298i	−0.524369	+	0.851491i	$0.675699\pi$
$312$		0			0
$313$	−2.49454	−	2.49454i	−0.141000	−	0.141000i	0.633084	−	0.774083i	$-0.281789\pi$
$313$	−2.49454	−	2.49454i	−0.141000	−	0.141000i	−0.774083	+	0.633084i	$0.781789\pi$
$314$	0.0512317			0.00289117
$315$		0			0
$316$	1.45962			0.0821103
$317$	−14.4465	−	14.4465i	−0.811398	−	0.811398i	0.173446	−	0.984843i	$-0.444510\pi$
$317$	−14.4465	−	14.4465i	−0.811398	−	0.811398i	−0.984843	+	0.173446i	$0.944510\pi$
$318$		0			0
$319$		−	19.9197i		−	1.11529i
$320$	0.331972	+	2.21129i	0.0185578	+	0.123615i
$321$		0			0
$322$	−13.2310	+	13.2310i	−0.737333	+	0.737333i
$323$	−3.29353	+	3.29353i	−0.183257	+	0.183257i
$324$		0			0
$325$	−10.2629	−	5.43949i	−0.569281	−	0.301729i
$326$			20.6773i			1.14521i
$327$		0			0
$328$	−5.13694	−	5.13694i	−0.283640	−	0.283640i
$329$	33.2572			1.83353
$330$		0			0
$331$	17.8028			0.978533			0.489267	−	0.872134i	$-0.337265\pi$
$331$	17.8028			0.978533			0.489267	+	0.872134i	$0.337265\pi$
$332$	6.31562	+	6.31562i	0.346615	+	0.346615i
$333$		0			0
$334$		−	11.3875i		−	0.623094i
$335$		0			0
$336$		0			0
$337$	8.82883	−	8.82883i	0.480937	−	0.480937i	−0.424494	−	0.905431i	$-0.639548\pi$
$337$	8.82883	−	8.82883i	0.480937	−	0.480937i	0.905431	+	0.424494i	$0.139548\pi$
$338$	5.37643	−	5.37643i	0.292439	−	0.292439i
$339$		0			0
$340$	−6.18958	+	8.37630i	−0.335677	+	0.454269i
$341$		−	8.86891i		−	0.480279i
$342$		0			0
$343$	−13.3901	−	13.3901i	−0.722996	−	0.722996i
$344$	−8.07352			−0.435295
$345$		0			0
$346$	17.7506			0.954278
$347$	3.97699	+	3.97699i	0.213496	+	0.213496i	0.805751	−	0.592255i	$-0.201762\pi$
$347$	3.97699	+	3.97699i	0.213496	+	0.213496i	−0.592255	+	0.805751i	$0.701762\pi$
$348$		0			0
$349$		−	16.3895i		−	0.877308i	−0.898656	−	0.438654i	$-0.855455\pi$
$349$		−	16.3895i		−	0.877308i	0.898656	−	0.438654i	$-0.144545\pi$
$350$	−12.3394	+	3.79035i	−0.659567	+	0.202603i
$351$		0			0
$352$	−1.48459	+	1.48459i	−0.0791287	+	0.0791287i
$353$	2.24748	−	2.24748i	0.119621	−	0.119621i	−0.644762	−	0.764383i	$-0.723044\pi$
$353$	2.24748	−	2.24748i	0.119621	−	0.119621i	0.764383	+	0.644762i	$0.223044\pi$
$354$		0			0
$355$	0.283293	+	1.88703i	0.0150356	+	0.100153i
$356$			8.59262i			0.455408i
$357$		0			0
$358$	−8.41637	−	8.41637i	−0.444819	−	0.444819i
$359$	−15.4071			−0.813158			−0.406579	−	0.913616i	$-0.633278\pi$
$359$	−15.4071			−0.813158			−0.406579	+	0.913616i	$0.633278\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	−3.41368	−	3.41368i	−0.179419	−	0.179419i
$363$		0			0
$364$			5.99738i			0.314348i
$365$	21.7682	+	16.0854i	1.13940	+	0.841948i
$366$		0			0
$367$	−7.28985	+	7.28985i	−0.380527	+	0.380527i	−0.871292	−	0.490765i	$-0.836717\pi$
$367$	−7.28985	+	7.28985i	−0.380527	+	0.380527i	0.490765	+	0.871292i	$0.336717\pi$
$368$	−5.12494	+	5.12494i	−0.267156	+	0.267156i
$369$		0			0
$370$	5.13694	−	0.771189i	0.267057	−	0.0400922i
$371$			36.5633i			1.89827i
$372$		0			0
$373$	−5.96016	−	5.96016i	−0.308605	−	0.308605i	0.535763	−	0.844368i	$-0.320024\pi$
$373$	−5.96016	−	5.96016i	−0.308605	−	0.308605i	−0.844368	+	0.535763i	$0.820024\pi$
$374$	−9.77906			−0.505663
$375$		0			0
$376$	12.8820			0.664339
$377$	−15.5850	−	15.5850i	−0.802668	−	0.802668i
$378$		0			0
$379$			18.4581i			0.948128i	0.880490	+	0.474064i	$0.157213\pi$
$379$			18.4581i			0.948128i	−0.880490	+	0.474064i	$0.842787\pi$
$380$	−2.21129	+	0.331972i	−0.113437	+	0.0170298i
$381$		0			0
$382$	5.57899	−	5.57899i	0.285446	−	0.285446i
$383$	3.44149	−	3.44149i	0.175852	−	0.175852i	−0.613693	−	0.789545i	$-0.710317\pi$
$383$	3.44149	−	3.44149i	0.175852	−	0.175852i	0.789545	+	0.613693i	$0.210317\pi$
$384$		0			0
$385$	−9.74762	−	7.20291i	−0.496785	−	0.367094i
$386$		−	2.10901i		−	0.107346i
$387$		0			0
$388$	11.0176	+	11.0176i	0.559336	+	0.559336i
$389$	13.9339			0.706475			0.353238	−	0.935534i	$-0.385081\pi$
$389$	13.9339			0.706475			0.353238	+	0.935534i	$0.385081\pi$
$390$		0			0
$391$	−33.7583			−1.70723
$392$	−0.236828	−	0.236828i	−0.0119616	−	0.0119616i
$393$		0			0
$394$		−	20.3916i		−	1.02731i
$395$	0.484554	+	3.22765i	0.0243806	+	0.162401i
$396$		0			0
$397$	−3.29740	+	3.29740i	−0.165492	+	0.165492i	−0.784994	−	0.619503i	$-0.787334\pi$
$397$	−3.29740	+	3.29740i	−0.165492	+	0.165492i	0.619503	+	0.784994i	$0.287334\pi$
$398$	−2.01135	+	2.01135i	−0.100820	+	0.100820i
$399$		0			0
$400$	−4.77959	+	1.46817i	−0.238979	+	0.0734086i
$401$			17.5402i			0.875918i	0.898995	+	0.437959i	$0.144298\pi$
$401$			17.5402i			0.875918i	−0.898995	+	0.437959i	$0.855702\pi$
$402$		0			0
$403$	−6.93896	−	6.93896i	−0.345654	−	0.345654i
$404$	14.5956			0.726159
$405$		0			0
$406$	−24.4943			−1.21563
$407$	3.44877	+	3.44877i	0.170949	+	0.170949i
$408$		0			0
$409$		−	14.2981i		−	0.706995i	−0.935435	−	0.353498i	$-0.884992\pi$
$409$		−	14.2981i		−	0.706995i	0.935435	−	0.353498i	$-0.115008\pi$
$410$	9.65394	−	13.0646i	0.476774	−	0.645214i
$411$		0			0
$412$	5.69373	−	5.69373i	0.280510	−	0.280510i
$413$	10.1658	−	10.1658i	0.500224	−	0.500224i
$414$		0			0
$415$	−11.8690	+	16.0623i	−0.582629	+	0.788466i
$416$			2.32305i			0.113897i
$417$		0			0
$418$	−1.48459	−	1.48459i	−0.0726135	−	0.0726135i
$419$	7.08174			0.345966			0.172983	−	0.984925i	$-0.444659\pi$
$419$	7.08174			0.345966			0.172983	+	0.984925i	$0.444659\pi$
$420$		0			0
$421$	6.84570			0.333639			0.166820	−	0.985987i	$-0.446650\pi$
$421$	6.84570			0.333639			0.166820	+	0.985987i	$0.446650\pi$
$422$	−7.58647	−	7.58647i	−0.369304	−	0.369304i
$423$		0			0
$424$			14.1626i			0.687797i
$425$	−20.5772	−	10.9063i	−0.998140	−	0.529031i
$426$		0			0
$427$	25.1620	−	25.1620i	1.21767	−	1.21767i
$428$	11.2683	−	11.2683i	0.544672	−	0.544672i
$429$		0			0
$430$	−2.68018	−	17.8529i	−0.129250	−	0.860942i
$431$			18.5138i			0.891780i	0.895088	+	0.445890i	$0.147113\pi$
$431$			18.5138i			0.891780i	−0.895088	+	0.445890i	$0.852887\pi$
$432$		0			0
$433$	4.67392	+	4.67392i	0.224614	+	0.224614i	0.810438	−	0.585824i	$-0.199229\pi$
$433$	4.67392	+	4.67392i	0.224614	+	0.224614i	−0.585824	+	0.810438i	$0.699229\pi$
$434$	−10.9057			−0.523489
$435$		0			0
$436$	−9.19081			−0.440160
$437$	−5.12494	−	5.12494i	−0.245159	−	0.245159i
$438$		0			0
$439$		−	32.4355i		−	1.54806i	−0.633146	−	0.774032i	$-0.718237\pi$
$439$		−	32.4355i		−	1.54806i	0.633146	−	0.774032i	$-0.281763\pi$
$440$	−3.77569	−	2.79001i	−0.179999	−	0.133008i
$441$		0			0
$442$	−7.65105	+	7.65105i	−0.363923	+	0.363923i
$443$	−2.39842	+	2.39842i	−0.113952	+	0.113952i	−0.761784	−	0.647831i	$-0.775676\pi$
$443$	−2.39842	+	2.39842i	−0.113952	+	0.113952i	0.647831	+	0.761784i	$0.275676\pi$
$444$		0			0
$445$	−19.0008	+	2.85251i	−0.900722	+	0.135222i
$446$			18.4216i			0.872288i
$447$		0			0
$448$	1.82552	+	1.82552i	0.0862479	+	0.0862479i
$449$	27.3174			1.28919			0.644595	−	0.764525i	$-0.277026\pi$
$449$	27.3174			1.28919			0.644595	+	0.764525i	$0.277026\pi$
$450$		0			0
$451$	15.2525			0.718211
$452$	3.32007	+	3.32007i	0.156163	+	0.156163i
$453$		0			0
$454$			28.9414i			1.35829i
$455$	−13.2619	+	1.99096i	−0.621729	+	0.0933378i
$456$		0			0
$457$	4.28791	−	4.28791i	0.200580	−	0.200580i	−0.599669	−	0.800249i	$-0.704701\pi$
$457$	4.28791	−	4.28791i	0.200580	−	0.200580i	0.800249	+	0.599669i	$0.204701\pi$
$458$	1.33977	−	1.33977i	0.0626032	−	0.0626032i
$459$		0			0
$460$	−13.0341	−	9.63138i	−0.607716	−	0.449066i
$461$			26.0363i			1.21263i	0.795224	+	0.606316i	$0.207353\pi$
$461$			26.0363i			1.21263i	−0.795224	+	0.606316i	$0.792647\pi$
$462$		0			0
$463$	−7.86306	−	7.86306i	−0.365427	−	0.365427i	0.500379	−	0.865806i	$-0.333194\pi$
$463$	−7.86306	−	7.86306i	−0.365427	−	0.365427i	−0.865806	+	0.500379i	$0.833194\pi$
$464$	−9.48773			−0.440457
$465$		0			0
$466$	3.00932			0.139404
$467$	4.57597	+	4.57597i	0.211751	+	0.211751i	0.805011	−	0.593260i	$-0.202159\pi$
$467$	4.57597	+	4.57597i	0.211751	+	0.211751i	−0.593260	+	0.805011i	$0.702159\pi$
$468$		0			0
$469$		0			0
$470$	4.27647	+	28.4858i	0.197259	+	1.31395i
$471$		0			0
$472$	3.93765	−	3.93765i	0.181245	−	0.181245i
$473$	11.9858	−	11.9858i	0.551109	−	0.551109i
$474$		0			0
$475$	−1.46817	−	4.77959i	−0.0673643	−	0.219303i
$476$			12.0248i			0.551157i
$477$		0			0
$478$	9.95345	+	9.95345i	0.455260	+	0.455260i
$479$	23.6217			1.07930			0.539652	−	0.841888i	$-0.318556\pi$
$479$	23.6217			1.07930			0.539652	+	0.841888i	$0.318556\pi$
$480$		0			0
$481$	5.39658			0.246063
$482$	7.91680	+	7.91680i	0.360600	+	0.360600i
$483$		0			0
$484$			6.59201i			0.299637i
$485$	−20.7056	+	28.0207i	−0.940194	+	1.27236i
$486$		0			0
$487$	−14.9536	+	14.9536i	−0.677612	+	0.677612i	−0.959459	−	0.281847i	$-0.909053\pi$
$487$	−14.9536	+	14.9536i	−0.677612	+	0.677612i	0.281847	+	0.959459i	$0.409053\pi$
$488$	9.74636	−	9.74636i	0.441197	−	0.441197i
$489$		0			0
$490$	0.445074	−	0.602315i	0.0201064	−	0.0272098i
$491$		−	37.3226i		−	1.68435i	−0.539207	−	0.842173i	$-0.681276\pi$
$491$		−	37.3226i		−	1.68435i	0.539207	−	0.842173i	$-0.318724\pi$
$492$		0			0
$493$	−31.2481	−	31.2481i	−1.40734	−	1.40734i
$494$	−2.32305			−0.104519
$495$		0			0
$496$	−4.22425			−0.189675
$497$	1.55784	+	1.55784i	0.0698785	+	0.0698785i
$498$		0			0
$499$			24.7116i			1.10624i	0.833101	+	0.553121i	$0.186563\pi$
$499$			24.7116i			1.10624i	−0.833101	+	0.553121i	$0.813437\pi$
$500$	−4.83324	−	10.0817i	−0.216149	−	0.450865i
$501$		0			0
$502$	−15.0787	+	15.0787i	−0.672995	+	0.672995i
$503$	−19.3802	+	19.3802i	−0.864120	+	0.864120i	−0.991814	−	0.127693i	$-0.959243\pi$
$503$	−19.3802	+	19.3802i	−0.864120	+	0.864120i	0.127693	+	0.991814i	$0.459243\pi$
$504$		0			0
$505$	4.84534	+	32.2751i	0.215615	+	1.43622i
$506$		−	15.2168i		−	0.676471i
$507$		0			0
$508$	−6.97903	−	6.97903i	−0.309644	−	0.309644i
$509$	−31.1709			−1.38163			−0.690813	−	0.723034i	$-0.742747\pi$
$509$	−31.1709			−1.38163			−0.690813	+	0.723034i	$0.742747\pi$
$510$		0			0
$511$	31.2500			1.38242
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$			27.5911i			1.21699i
$515$	14.4806	+	10.7003i	0.638093	+	0.471513i
$516$		0			0
$517$	−19.1244	+	19.1244i	−0.841092	+	0.841092i
$518$	4.24079	−	4.24079i	0.186330	−	0.186330i
$519$		0			0
$520$	−5.13694	+	0.771189i	−0.225270	+	0.0338189i
$521$		−	3.18272i		−	0.139438i	−0.997567	−	0.0697188i	$-0.977790\pi$
$521$		−	3.18272i		−	0.139438i	0.997567	−	0.0697188i	$-0.0222102\pi$
$522$		0			0
$523$	8.17601	+	8.17601i	0.357512	+	0.357512i	0.862895	−	0.505383i	$-0.168649\pi$
$523$	8.17601	+	8.17601i	0.357512	+	0.357512i	−0.505383	+	0.862895i	$0.668649\pi$
$524$	1.52919			0.0668029
$525$		0			0
$526$	8.57189			0.373752
$527$	−13.9127	−	13.9127i	−0.606047	−	0.606047i
$528$		0			0
$529$		−	29.5300i		−	1.28391i
$530$	−31.3176	+	4.70159i	−1.36035	+	0.204224i
$531$		0			0
$532$	−1.82552	+	1.82552i	−0.0791465	+	0.0791465i
$533$	11.9334	−	11.9334i	0.516893	−	0.516893i
$534$		0			0
$535$	28.6581	+	21.1766i	1.23900	+	0.915545i
$536$		0			0
$537$		0			0
$538$	−6.39272	−	6.39272i	−0.275610	−	0.275610i
$539$	0.703183			0.0302882
$540$		0			0
$541$	36.1737			1.55523			0.777614	−	0.628742i	$-0.216430\pi$
$541$	36.1737			1.55523			0.777614	+	0.628742i	$0.216430\pi$
$542$	8.85160	+	8.85160i	0.380209	+	0.380209i
$543$		0			0
$544$			4.65775i			0.199700i
$545$	−3.05109	−	20.3235i	−0.130694	−	0.870564i
$546$		0			0
$547$	−8.84018	+	8.84018i	−0.377979	+	0.377979i	−0.870372	−	0.492394i	$-0.836122\pi$
$547$	−8.84018	+	8.84018i	−0.377979	+	0.377979i	0.492394	+	0.870372i	$0.336122\pi$
$548$	8.70549	−	8.70549i	0.371880	−	0.371880i
$549$		0			0
$550$	4.91609	−	9.27534i	0.209623	−	0.395502i
$551$		−	9.48773i		−	0.404191i
$552$		0			0
$553$	2.66458	+	2.66458i	0.113309	+	0.113309i
$554$	13.5510			0.575726
$555$		0			0
$556$	11.8451			0.502344
$557$	−10.8373	−	10.8373i	−0.459190	−	0.459190i	0.439200	−	0.898390i	$-0.355262\pi$
$557$	−10.8373	−	10.8373i	−0.459190	−	0.459190i	−0.898390	+	0.439200i	$0.855262\pi$
$558$		0			0
$559$		−	18.7552i		−	0.793261i
$560$	−3.43074	+	4.64278i	−0.144975	+	0.196193i
$561$		0			0
$562$	−3.08731	+	3.08731i	−0.130230	+	0.130230i
$563$	−3.71984	+	3.71984i	−0.156772	+	0.156772i	−0.781135	−	0.624362i	$-0.785359\pi$
$563$	−3.71984	+	3.71984i	−0.156772	+	0.156772i	0.624362	+	0.781135i	$0.285359\pi$
$564$		0			0
$565$	−6.23946	+	8.44380i	−0.262496	+	0.355233i
$566$		−	26.3683i		−	1.10834i
$567$		0			0
$568$	0.603419	+	0.603419i	0.0253189	+	0.0253189i
$569$	24.0334			1.00753			0.503767	−	0.863839i	$-0.331947\pi$
$569$	24.0334			1.00753			0.503767	+	0.863839i	$0.331947\pi$
$570$		0			0
$571$	−2.37267			−0.0992930			−0.0496465	−	0.998767i	$-0.515809\pi$
$571$	−2.37267			−0.0992930			−0.0496465	+	0.998767i	$0.515809\pi$
$572$	−3.44877	−	3.44877i	−0.144200	−	0.144200i
$573$		0			0
$574$		−	18.7552i		−	0.782828i
$575$	16.9708	−	32.0194i	0.707732	−	1.33530i
$576$		0			0
$577$	10.3672	−	10.3672i	0.431593	−	0.431593i	−0.457577	−	0.889170i	$-0.651283\pi$
$577$	10.3672	−	10.3672i	0.431593	−	0.431593i	0.889170	+	0.457577i	$0.151283\pi$
$578$	−3.31964	+	3.31964i	−0.138079	+	0.138079i
$579$		0			0
$580$	−3.14966	−	20.9801i	−0.130783	−	0.871152i
$581$			23.0586i			0.956633i
$582$		0			0
$583$	−21.0256	−	21.0256i	−0.870791	−	0.870791i
$584$	12.1045			0.500888
$585$		0			0
$586$	−25.3072			−1.04543
$587$	21.0872	+	21.0872i	0.870360	+	0.870360i	0.992511	−	0.122152i	$-0.0389794\pi$
$587$	21.0872	+	21.0872i	0.870360	+	0.870360i	−0.122152	+	0.992511i	$0.538979\pi$
$588$		0			0
$589$		−	4.22425i		−	0.174057i
$590$	10.0145	+	7.40009i	0.412289	+	0.304657i
$591$		0			0
$592$	1.64265	−	1.64265i	0.0675124	−	0.0675124i
$593$	2.52768	−	2.52768i	0.103799	−	0.103799i	−0.653300	−	0.757099i	$-0.726616\pi$
$593$	2.52768	−	2.52768i	0.103799	−	0.103799i	0.757099	+	0.653300i	$0.226616\pi$
$594$		0			0
$595$	−26.5904	+	3.99191i	−1.09010	+	0.163652i
$596$		−	19.3650i		−	0.793221i
$597$		0			0
$598$	−11.9055	−	11.9055i	−0.486853	−	0.486853i
$599$	4.86149			0.198635			0.0993175	−	0.995056i	$-0.468334\pi$
$599$	4.86149			0.198635			0.0993175	+	0.995056i	$0.468334\pi$
$600$		0			0
$601$	15.6846			0.639790			0.319895	−	0.947453i	$-0.396352\pi$
$601$	15.6846			0.639790			0.319895	+	0.947453i	$0.396352\pi$
$602$	−14.7384	−	14.7384i	−0.600692	−	0.600692i
$603$		0			0
$604$			2.09187i			0.0851170i
$605$	−14.5768	+	2.18836i	−0.592632	+	0.0889696i
$606$		0			0
$607$	2.15135	−	2.15135i	0.0873208	−	0.0873208i	−0.662097	−	0.749418i	$-0.730333\pi$
$607$	2.15135	−	2.15135i	0.0873208	−	0.0873208i	0.749418	+	0.662097i	$0.230333\pi$
$608$	−0.707107	+	0.707107i	−0.0286770	+	0.0286770i
$609$		0			0
$610$	24.7875	+	18.3165i	1.00362	+	0.741613i
$611$			29.9256i			1.21066i
$612$		0			0
$613$	−25.6148	−	25.6148i	−1.03457	−	1.03457i	−0.999381	−	0.0351923i	$-0.988796\pi$
$613$	−25.6148	−	25.6148i	−1.03457	−	1.03457i	−0.0351923	−	0.999381i	$-0.511204\pi$
$614$	−17.6903			−0.713923
$615$		0			0
$616$	−5.42029			−0.218390
$617$	−4.42755	−	4.42755i	−0.178246	−	0.178246i	0.612345	−	0.790591i	$-0.290226\pi$
$617$	−4.42755	−	4.42755i	−0.178246	−	0.178246i	−0.790591	+	0.612345i	$0.790226\pi$
$618$		0			0
$619$			26.6804i			1.07238i	0.844098	+	0.536189i	$0.180136\pi$
$619$			26.6804i			1.07238i	−0.844098	+	0.536189i	$0.819864\pi$
$620$	−1.40233	−	9.34104i	−0.0563191	−	0.375145i
$621$		0			0
$622$	−21.2361	+	21.2361i	−0.851491	+	0.851491i
$623$	−15.6860	+	15.6860i	−0.628448	+	0.628448i
$624$		0			0
$625$	20.6889	−	14.0345i	0.827558	−	0.561380i
$626$		−	3.52782i		−	0.141000i
$627$		0			0
$628$	0.0362263	+	0.0362263i	0.00144559	+	0.00144559i
$629$	10.8202			0.431430
$630$		0			0
$631$	−44.2590			−1.76192			−0.880962	−	0.473186i	$-0.843104\pi$
$631$	−44.2590			−1.76192			−0.880962	+	0.473186i	$0.843104\pi$
$632$	1.03211	+	1.03211i	0.0410551	+	0.0410551i
$633$		0			0
$634$		−	20.4305i		−	0.811398i
$635$	13.1158	−	17.7495i	0.520485	−	0.704367i
$636$		0			0
$637$	0.550164	−	0.550164i	0.0217983	−	0.0217983i
$638$	14.0854	−	14.0854i	0.557645	−	0.557645i
$639$		0			0
$640$	−1.32888	+	1.79836i	−0.0525285	+	0.0710863i
$641$		−	9.64240i		−	0.380852i	−0.981702	−	0.190426i	$-0.939013\pi$
$641$		−	9.64240i		−	0.380852i	0.981702	−	0.190426i	$-0.0609869\pi$
$642$		0			0
$643$	8.17076	+	8.17076i	0.322223	+	0.322223i	0.849619	−	0.527396i	$-0.176832\pi$
$643$	8.17076	+	8.17076i	0.322223	+	0.322223i	−0.527396	+	0.849619i	$0.676832\pi$
$644$	−18.7114			−0.737333
$645$		0			0
$646$	−4.65775			−0.183257
$647$	6.20608	+	6.20608i	0.243986	+	0.243986i	0.818497	−	0.574511i	$-0.194808\pi$
$647$	6.20608	+	6.20608i	0.243986	+	0.243986i	−0.574511	+	0.818497i	$0.694808\pi$
$648$		0			0
$649$			11.6916i			0.458934i
$650$	−3.41064	−	11.1032i	−0.133776	−	0.435505i
$651$		0			0
$652$	−14.6211	+	14.6211i	−0.572605	+	0.572605i
$653$	−14.3615	+	14.3615i	−0.562008	+	0.562008i	−0.929877	−	0.367870i	$-0.880087\pi$
$653$	−14.3615	+	14.3615i	−0.562008	+	0.562008i	0.367870	+	0.929877i	$0.380087\pi$
$654$		0			0
$655$	0.507647	+	3.38147i	0.0198354	+	0.132125i
$656$		−	7.26473i		−	0.283640i
$657$		0			0
$658$	23.5164	+	23.5164i	0.916765	+	0.916765i
$659$	−49.6826			−1.93536			−0.967680	−	0.252182i	$-0.918852\pi$
$659$	−49.6826			−1.93536			−0.967680	+	0.252182i	$0.918852\pi$
$660$		0			0
$661$	33.7100			1.31117			0.655584	−	0.755122i	$-0.272422\pi$
$661$	33.7100			1.31117			0.655584	+	0.755122i	$0.272422\pi$
$662$	12.5885	+	12.5885i	0.489267	+	0.489267i
$663$		0			0
$664$			8.93164i			0.346615i
$665$	−4.64278	−	3.43074i	−0.180039	−	0.133038i
$666$		0			0
$667$	48.6241	−	48.6241i	1.88273	−	1.88273i
$668$	8.05215	−	8.05215i	0.311547	−	0.311547i
$669$		0			0
$670$		0			0
$671$			28.9386i			1.11716i
$672$		0			0
$673$	−7.48868	−	7.48868i	−0.288667	−	0.288667i	0.547886	−	0.836553i	$-0.315433\pi$
$673$	−7.48868	−	7.48868i	−0.288667	−	0.288667i	−0.836553	+	0.547886i	$0.815433\pi$
$674$	12.4859			0.480937
$675$		0			0
$676$	7.60342			0.292439
$677$	−34.8468	−	34.8468i	−1.33927	−	1.33927i	−0.896766	−	0.442504i	$-0.854090\pi$
$677$	−34.8468	−	34.8468i	−1.33927	−	1.33927i	−0.442504	−	0.896766i	$-0.645910\pi$
$678$		0			0
$679$			40.2259i			1.54373i
$680$	−10.2996	+	1.54624i	−0.394973	+	0.0592957i
$681$		0			0
$682$	6.27127	−	6.27127i	0.240139	−	0.240139i
$683$	0.0313944	−	0.0313944i	0.00120127	−	0.00120127i	−0.706506	−	0.707707i	$-0.749730\pi$
$683$	0.0313944	−	0.0313944i	0.00120127	−	0.00120127i	0.707707	+	0.706506i	$0.249730\pi$
$684$		0			0
$685$	22.1403	+	16.3604i	0.845938	+	0.625097i
$686$		−	18.9364i		−	0.722996i
$687$		0			0
$688$	−5.70884	−	5.70884i	−0.217647	−	0.217647i
$689$	−32.9005			−1.25341
$690$		0			0
$691$	17.8533			0.679170			0.339585	−	0.940575i	$-0.389713\pi$
$691$	17.8533			0.679170			0.339585	+	0.940575i	$0.389713\pi$
$692$	12.5516	+	12.5516i	0.477139	+	0.477139i
$693$		0			0
$694$			5.62431i			0.213496i
$695$	3.93224	+	26.1929i	0.149158	+	0.993553i
$696$		0			0
$697$	23.9266	−	23.9266i	0.906285	−	0.906285i
$698$	11.5891	−	11.5891i	0.438654	−	0.438654i
$699$		0			0
$700$	−11.4054	−	6.04507i	−0.431085	−	0.228482i
$701$		−	32.4158i		−	1.22433i	−0.790730	−	0.612165i	$-0.790299\pi$
$701$		−	32.4158i		−	1.22433i	0.790730	−	0.612165i	$-0.209701\pi$
$702$		0			0
$703$	1.64265	+	1.64265i	0.0619536	+	0.0619536i
$704$	−2.09952			−0.0791287
$705$		0			0
$706$	3.17842			0.119621
$707$	26.6446	+	26.6446i	1.00208	+	1.00208i
$708$		0			0
$709$			5.58539i			0.209764i	0.994485	+	0.104882i	$0.0334464\pi$
$709$			5.58539i			0.209764i	−0.994485	+	0.104882i	$0.966554\pi$
$710$	−1.13402	+	1.53465i	−0.0425588	+	0.0575945i
$711$		0			0
$712$	−6.07590	+	6.07590i	−0.227704	+	0.227704i
$713$	21.6490	−	21.6490i	0.810763	−	0.810763i
$714$		0			0
$715$	6.48134	−	8.77113i	0.242388	−	0.328022i
$716$		−	11.9025i		−	0.444819i
$717$		0			0
$718$	−10.8945	−	10.8945i	−0.406579	−	0.406579i
$719$	−28.8576			−1.07621			−0.538104	−	0.842878i	$-0.680859\pi$
$719$	−28.8576			−1.07621			−0.538104	+	0.842878i	$0.680859\pi$
$720$		0			0
$721$	20.7881			0.774189
$722$	−0.707107	−	0.707107i	−0.0263158	−	0.0263158i
$723$		0			0
$724$		−	4.82767i		−	0.179419i
$725$	45.3475	−	13.9296i	1.68416	−	0.517333i
$726$		0			0
$727$	20.3720	−	20.3720i	0.755555	−	0.755555i	−0.219955	−	0.975510i	$-0.570591\pi$
$727$	20.3720	−	20.3720i	0.755555	−	0.755555i	0.975510	+	0.219955i	$0.0705910\pi$
$728$	−4.24079	+	4.24079i	−0.157174	+	0.157174i
$729$		0			0
$730$	4.01836	+	26.7665i	0.148726	+	0.990674i
$731$		−	37.6045i		−	1.39085i
$732$		0			0
$733$	−11.7713	−	11.7713i	−0.434784	−	0.434784i	0.455468	−	0.890252i	$-0.349472\pi$
$733$	−11.7713	−	11.7713i	−0.434784	−	0.434784i	−0.890252	+	0.455468i	$0.849472\pi$
$734$	−10.3094			−0.380527
$735$		0			0
$736$	−7.24776			−0.267156
$737$		0			0
$738$		0			0
$739$			30.7303i			1.13043i	0.824943	+	0.565216i	$0.191207\pi$
$739$			30.7303i			1.13043i	−0.824943	+	0.565216i	$0.808793\pi$
$740$	4.17768	+	3.08705i	0.153575	+	0.113482i
$741$		0			0
$742$	−25.8542	+	25.8542i	−0.949136	+	0.949136i
$743$	−33.6074	+	33.6074i	−1.23294	+	1.23294i	−0.270105	+	0.962831i	$0.587058\pi$
$743$	−33.6074	+	33.6074i	−1.23294	+	1.23294i	−0.962831	+	0.270105i	$0.912942\pi$
$744$		0			0
$745$	42.8216	−	6.42864i	1.56886	−	0.235527i
$746$		−	8.42894i		−	0.308605i
$747$		0			0
$748$	−6.91484	−	6.91484i	−0.252831	−	0.252831i
$749$	41.1410			1.50326
$750$		0			0
$751$	39.7645			1.45103			0.725513	−	0.688208i	$-0.241603\pi$
$751$	39.7645			1.45103			0.725513	+	0.688208i	$0.241603\pi$
$752$	9.10895	+	9.10895i	0.332169	+	0.332169i
$753$		0			0
$754$		−	22.0405i		−	0.802668i
$755$	−4.62573	+	0.694442i	−0.168347	+	0.0252733i
$756$		0			0
$757$	4.66245	−	4.66245i	0.169460	−	0.169460i	−0.617282	−	0.786742i	$-0.711766\pi$
$757$	4.66245	−	4.66245i	0.169460	−	0.169460i	0.786742	+	0.617282i	$0.211766\pi$
$758$	−13.0518	+	13.0518i	−0.474064	+	0.474064i
$759$		0			0
$760$	−1.79836	−	1.32888i	−0.0652332	−	0.0482034i
$761$			19.9340i			0.722607i	0.932448	+	0.361303i	$0.117668\pi$
$761$			19.9340i			0.722607i	−0.932448	+	0.361303i	$0.882332\pi$
$762$		0			0
$763$	−16.7780	−	16.7780i	−0.607406	−	0.607406i
$764$	7.88988			0.285446
$765$		0			0
$766$	4.86700			0.175852
$767$	9.14738	+	9.14738i	0.330293	+	0.330293i
$768$		0			0
$769$		−	45.7105i		−	1.64836i	−0.566325	−	0.824182i	$-0.691635\pi$
$769$		−	45.7105i		−	1.64836i	0.566325	−	0.824182i	$-0.308365\pi$
$770$	−1.79939	−	11.9858i	−0.0648454	−	0.431939i
$771$		0			0
$772$	1.49129	−	1.49129i	0.0536728	−	0.0536728i
$773$	−11.3039	+	11.3039i	−0.406574	+	0.406574i	−0.880542	−	0.473968i	$-0.842821\pi$
$773$	−11.3039	+	11.3039i	−0.406574	+	0.406574i	0.473968	+	0.880542i	$0.342821\pi$
$774$		0			0
$775$	20.1902	−	6.20193i	0.725253	−	0.222780i
$776$			15.5813i			0.559336i
$777$		0			0
$778$	9.85274	+	9.85274i	0.353238	+	0.353238i
$779$	7.26473			0.260286
$780$		0			0
$781$	−1.79166			−0.0641105
$782$	−23.8707	−	23.8707i	−0.853615	−	0.853615i
$783$		0			0
$784$		−	0.334925i		−	0.0119616i
$785$	−0.0680806	+	0.0921328i	−0.00242990	+	0.00328836i
$786$		0			0
$787$	−21.8619	+	21.8619i	−0.779292	+	0.779292i	−0.979710	−	0.200418i	$-0.935770\pi$
$787$	−21.8619	+	21.8619i	−0.779292	+	0.779292i	0.200418	+	0.979710i	$0.435770\pi$
$788$	14.4190	−	14.4190i	0.513656	−	0.513656i
$789$		0			0
$790$	−1.93966	+	2.62492i	−0.0690100	+	0.0933906i
$791$			12.1217i			0.430999i
$792$		0			0
$793$	22.6413	+	22.6413i	0.804017	+	0.804017i
$794$	−4.66323			−0.165492
$795$		0			0
$796$	−2.84447			−0.100820
$797$	−13.3091	−	13.3091i	−0.471433	−	0.471433i	0.430945	−	0.902378i	$-0.358180\pi$
$797$	−13.3091	−	13.3091i	−0.471433	−	0.471433i	−0.902378	+	0.430945i	$0.858180\pi$
$798$		0			0
$799$			60.0012i			2.12269i
$800$	−4.41783	−	2.34153i	−0.156194	−	0.0827854i
$801$		0			0
$802$	−12.4028	+	12.4028i	−0.437959	+	0.437959i
$803$	−17.9702	+	17.9702i	−0.634154	+	0.634154i
$804$		0			0
$805$	−6.21166	−	41.3763i	−0.218932	−	1.45832i
$806$		−	9.81317i		−	0.345654i
$807$		0			0
$808$	10.3207	+	10.3207i	0.363080	+	0.363080i
$809$	27.0517			0.951089			0.475544	−	0.879692i	$-0.342251\pi$
$809$	27.0517			0.951089			0.475544	+	0.879692i	$0.342251\pi$
$810$		0			0
$811$	21.6005			0.758496			0.379248	−	0.925295i	$-0.376183\pi$
$811$	21.6005			0.758496			0.379248	+	0.925295i	$0.376183\pi$
$812$	−17.3201	−	17.3201i	−0.607816	−	0.607816i
$813$		0			0
$814$			4.87730i			0.170949i
$815$	−37.1852	−	27.4776i	−1.30254	−	0.962498i
$816$		0			0
$817$	5.70884	−	5.70884i	0.199727	−	0.199727i
$818$	10.1103	−	10.1103i	0.353498	−	0.353498i
$819$		0			0
$820$	16.0644	−	2.41169i	0.560994	−	0.0842198i
$821$			3.62159i			0.126394i	0.998001	+	0.0631972i	$0.0201297\pi$
$821$			3.62159i			0.126394i	−0.998001	+	0.0631972i	$0.979870\pi$
$822$		0			0
$823$	19.7193	+	19.7193i	0.687372	+	0.687372i	0.961650	−	0.274278i	$-0.0884390\pi$
$823$	19.7193	+	19.7193i	0.687372	+	0.687372i	−0.274278	+	0.961650i	$0.588439\pi$
$824$	8.05215			0.280510
$825$		0			0
$826$	14.3765			0.500224
$827$	20.6069	+	20.6069i	0.716572	+	0.716572i	0.967902	−	0.251329i	$-0.0808677\pi$
$827$	20.6069	+	20.6069i	0.716572	+	0.716572i	−0.251329	+	0.967902i	$0.580868\pi$
$828$		0			0
$829$		−	38.1819i		−	1.32611i	−0.748570	−	0.663055i	$-0.769259\pi$
$829$		−	38.1819i		−	1.32611i	0.748570	−	0.663055i	$-0.230741\pi$
$830$	−19.7504	+	2.96505i	−0.685547	+	0.102919i
$831$		0			0
$832$	−1.64265	+	1.64265i	−0.0569486	+	0.0569486i
$833$	1.10309	−	1.10309i	0.0382197	−	0.0382197i
$834$		0			0
$835$	20.4787	+	15.1325i	0.708695	+	0.523683i
$836$		−	2.09952i		−	0.0726135i
$837$		0			0
$838$	5.00755	+	5.00755i	0.172983	+	0.172983i
$839$	48.7158			1.68186			0.840928	−	0.541147i	$-0.182010\pi$
$839$	48.7158			1.68186			0.840928	+	0.541147i	$0.182010\pi$
$840$		0			0
$841$	61.0171			2.10404
$842$	4.84064	+	4.84064i	0.166820	+	0.166820i
$843$		0			0
$844$		−	10.7289i		−	0.369304i
$845$	2.52412	+	16.8133i	0.0868324	+	0.578397i
$846$		0			0
$847$	−12.0339	+	12.0339i	−0.413489	+	0.413489i
$848$	−10.0145	+	10.0145i	−0.343898	+	0.343898i
$849$		0			0
$850$	−6.83838	−	22.2622i	−0.234555	−	0.763586i
$851$			16.8369i			0.577163i
$852$		0			0
$853$	−11.2720	−	11.2720i	−0.385945	−	0.385945i	0.487294	−	0.873238i	$-0.337984\pi$
$853$	−11.2720	−	11.2720i	−0.385945	−	0.385945i	−0.873238	+	0.487294i	$0.837984\pi$
$854$	35.5844			1.21767
$855$		0			0
$856$	15.9357			0.544672
$857$	8.44951	+	8.44951i	0.288630	+	0.288630i	0.836538	−	0.547908i	$-0.184576\pi$
$857$	8.44951	+	8.44951i	0.288630	+	0.288630i	−0.547908	+	0.836538i	$0.684576\pi$
$858$		0			0
$859$			48.2324i			1.64567i	0.568282	+	0.822834i	$0.307608\pi$
$859$			48.2324i			1.64567i	−0.568282	+	0.822834i	$0.692392\pi$
$860$	10.7287	−	14.5191i	0.365846	−	0.495096i
$861$		0			0
$862$	−13.0913	+	13.0913i	−0.445890	+	0.445890i
$863$	3.19558	−	3.19558i	0.108779	−	0.108779i	−0.650622	−	0.759401i	$-0.725492\pi$
$863$	3.19558	−	3.19558i	0.108779	−	0.108779i	0.759401	+	0.650622i	$0.225492\pi$
$864$		0			0
$865$	−23.5884	+	31.9219i	−0.802029	+	1.08538i
$866$			6.60992i			0.224614i
$867$		0			0
$868$	−7.71148	−	7.71148i	−0.261745	−	0.261745i
$869$	−3.06451			−0.103956
$870$		0			0
$871$		0			0
$872$	−6.49888	−	6.49888i	−0.220080	−	0.220080i
$873$		0			0
$874$		−	7.24776i		−	0.245159i
$875$	9.58111	−	27.2275i	0.323901	−	0.920457i
$876$		0			0
$877$	13.8213	−	13.8213i	0.466711	−	0.466711i	−0.434136	−	0.900847i	$-0.642946\pi$
$877$	13.8213	−	13.8213i	0.466711	−	0.466711i	0.900847	+	0.434136i	$0.142946\pi$
$878$	22.9354	−	22.9354i	0.774032	−	0.774032i
$879$		0			0
$880$	−0.696982	−	4.64265i	−0.0234953	−	0.156504i
$881$			13.9308i			0.469341i	0.972075	+	0.234670i	$0.0754011\pi$
$881$			13.9308i			0.469341i	−0.972075	+	0.234670i	$0.924599\pi$
$882$		0			0
$883$	−8.79801	−	8.79801i	−0.296076	−	0.296076i	0.543398	−	0.839475i	$-0.317137\pi$
$883$	−8.79801	−	8.79801i	−0.296076	−	0.296076i	−0.839475	+	0.543398i	$0.817137\pi$
$884$	−10.8202			−0.363923
$885$		0			0
$886$	−3.39188			−0.113952
$887$	−19.4915	−	19.4915i	−0.654461	−	0.654461i	0.299603	−	0.954064i	$-0.403146\pi$
$887$	−19.4915	−	19.4915i	−0.654461	−	0.654461i	−0.954064	+	0.299603i	$0.903146\pi$
$888$		0			0
$889$		−	25.4808i		−	0.854597i
$890$	−15.4526	−	11.4185i	−0.517972	−	0.382750i
$891$		0			0
$892$	−13.0260	+	13.0260i	−0.436144	+	0.436144i
$893$	−9.10895	+	9.10895i	−0.304820	+	0.304820i
$894$		0			0
$895$	26.3200	−	3.95131i	0.879779	−	0.132078i
$896$			2.58168i			0.0862479i
$897$		0			0
$898$	19.3163	+	19.3163i	0.644595	+	0.644595i
$899$	40.0786			1.33670
$900$		0			0
$901$	−65.9659			−2.19764
$902$	10.7851	+	10.7851i	0.359105	+	0.359105i
$903$		0			0
$904$			4.69529i			0.156163i
$905$	10.6754	−	1.60265i	0.354861	−	0.0532740i
$906$		0			0
$907$	−12.0103	+	12.0103i	−0.398795	+	0.398795i	−0.877808	−	0.479013i	$-0.840995\pi$
$907$	−12.0103	+	12.0103i	−0.398795	+	0.398795i	0.479013	+	0.877808i	$0.340995\pi$
$908$	−20.4647	+	20.4647i	−0.679144	+	0.679144i
$909$		0			0
$910$	−10.7854	−	7.96979i	−0.357534	−	0.264196i
$911$		−	30.3411i		−	1.00525i	−0.864506	−	0.502623i	$-0.832369\pi$
$911$		−	30.3411i		−	1.00525i	0.864506	−	0.502623i	$-0.167631\pi$
$912$		0			0
$913$	−13.2598	−	13.2598i	−0.438835	−	0.438835i
$914$	6.06402			0.200580
$915$		0			0
$916$	1.89472			0.0626032
$917$	2.79157	+	2.79157i	0.0921857	+	0.0921857i
$918$		0			0
$919$			54.6727i			1.80349i	0.432272	+	0.901743i	$0.357712\pi$
$919$			54.6727i			1.80349i	−0.432272	+	0.901743i	$0.642288\pi$
$920$	−2.40605	−	16.0269i	−0.0793252	−	0.528391i
$921$		0			0
$922$	−18.4104	+	18.4104i	−0.606316	+	0.606316i
$923$	−1.40178	+	1.40178i	−0.0461400	+	0.0461400i
$924$		0			0
$925$	−5.43949	+	10.2629i	−0.178849	+	0.337441i
$926$		−	11.1200i		−	0.365427i
$927$		0			0
$928$	−6.70884	−	6.70884i	−0.220228	−	0.220228i
$929$	15.0006			0.492153			0.246077	−	0.969250i	$-0.420859\pi$
$929$	15.0006			0.492153			0.246077	+	0.969250i	$0.420859\pi$
$930$		0			0
$931$	0.334925			0.0109767
$932$	2.12791	+	2.12791i	0.0697021	+	0.0697021i
$933$		0			0
$934$			6.47140i			0.211751i
$935$	12.9952	−	17.5862i	0.424987	−	0.575131i
$936$		0			0
$937$	−15.4325	+	15.4325i	−0.504157	+	0.504157i	−0.912727	−	0.408570i	$-0.866028\pi$
$937$	−15.4325	+	15.4325i	−0.504157	+	0.504157i	0.408570	+	0.912727i	$0.366028\pi$
$938$		0			0
$939$		0			0
$940$	−17.1186	+	23.1664i	−0.558347	+	0.755606i
$941$		−	44.9592i		−	1.46563i	−0.680428	−	0.732815i	$-0.738206\pi$
$941$		−	44.9592i		−	1.46563i	0.680428	−	0.732815i	$-0.261794\pi$
$942$		0			0
$943$	37.2313	+	37.2313i	1.21242	+	1.21242i
$944$	5.56868			0.181245
$945$		0			0
$946$	16.9505			0.551109
$947$	−28.0152	−	28.0152i	−0.910372	−	0.910372i	0.0859292	−	0.996301i	$-0.472614\pi$
$947$	−28.0152	−	28.0152i	−0.910372	−	0.910372i	−0.996301	+	0.0859292i	$0.972614\pi$
$948$		0			0
$949$			28.1194i			0.912795i
$950$	2.34153	−	4.41783i	0.0759691	−	0.143333i
$951$		0			0
$952$	−8.50284	+	8.50284i	−0.275579	+	0.275579i
$953$	14.5780	−	14.5780i	0.472227	−	0.472227i	−0.430408	−	0.902635i	$-0.641630\pi$
$953$	14.5780	−	14.5780i	0.472227	−	0.472227i	0.902635	+	0.430408i	$0.141630\pi$
$954$		0			0
$955$	2.61922	+	17.4468i	0.0847560	+	0.564565i
$956$			14.0763i			0.455260i
$957$		0			0
$958$	16.7031	+	16.7031i	0.539652	+	0.539652i
$959$	31.7841			1.02636
$960$		0			0
$961$	−13.1557			−0.424377
$962$	3.81596	+	3.81596i	0.123031	+	0.123031i
$963$		0			0
$964$			11.1960i			0.360600i
$965$	3.79274	+	2.80261i	0.122093	+	0.0902192i
$966$		0			0
$967$	−5.38393	+	5.38393i	−0.173136	+	0.173136i	−0.788356	−	0.615220i	$-0.789067\pi$
$967$	−5.38393	+	5.38393i	−0.173136	+	0.173136i	0.615220	+	0.788356i	$0.289067\pi$
$968$	−4.66125	+	4.66125i	−0.149818	+	0.149818i
$969$		0			0
$970$	−34.4547	+	5.17255i	−1.10627	+	0.166081i
$971$		−	47.0342i		−	1.50940i	−0.656070	−	0.754700i	$-0.727782\pi$
$971$		−	47.0342i		−	1.50940i	0.656070	−	0.754700i	$-0.272218\pi$
$972$		0			0
$973$	21.6235	+	21.6235i	0.693217	+	0.693217i
$974$	−21.1476			−0.677612
$975$		0			0
$976$	13.7834			0.441197
$977$	−26.0939	−	26.0939i	−0.834816	−	0.834816i	0.153355	−	0.988171i	$-0.450992\pi$
$977$	−26.0939	−	26.0939i	−0.834816	−	0.834816i	−0.988171	+	0.153355i	$0.950992\pi$
$978$		0			0
$979$		−	18.0404i		−	0.576574i
$980$	0.740616	−	0.111186i	0.0236581	−	0.00355170i
$981$		0			0
$982$	26.3911	−	26.3911i	0.842173	−	0.842173i
$983$	−7.67835	+	7.67835i	−0.244901	+	0.244901i	−0.818874	−	0.573973i	$-0.805401\pi$
$983$	−7.67835	+	7.67835i	−0.244901	+	0.244901i	0.573973	+	0.818874i	$0.305401\pi$
$984$		0			0
$985$	36.6713	+	27.0979i	1.16844	+	0.863410i
$986$		−	44.1915i		−	1.40734i
$987$		0			0
$988$	−1.64265	−	1.64265i	−0.0522596	−	0.0522596i
$989$	58.5149			1.86067
$990$		0			0
$991$	−16.9894			−0.539685			−0.269842	−	0.962904i	$-0.586972\pi$
$991$	−16.9894			−0.539685			−0.269842	+	0.962904i	$0.586972\pi$
$992$	−2.98700	−	2.98700i	−0.0948373	−	0.0948373i
$993$		0			0
$994$			2.20311i			0.0698785i
$995$	−0.944285	−	6.28995i	−0.0299359	−	0.199405i
$996$		0			0
$997$	3.67554	−	3.67554i	0.116406	−	0.116406i	−0.646505	−	0.762910i	$-0.723770\pi$
$997$	3.67554	−	3.67554i	0.116406	−	0.116406i	0.762910	+	0.646505i	$0.223770\pi$
$998$	−17.4737	+	17.4737i	−0.553121	+	0.553121i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.n.i.1673.6	yes	20
3.2	odd	2	inner	1710.2.n.i.1673.5	yes	20
5.2	odd	4	inner	1710.2.n.i.647.5	✓	20
15.2	even	4	inner	1710.2.n.i.647.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1710.2.n.i.647.5	✓	20	5.2	odd	4	inner
1710.2.n.i.647.6	yes	20	15.2	even	4	inner
1710.2.n.i.1673.5	yes	20	3.2	odd	2	inner
1710.2.n.i.1673.6	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-2.21129 + 0.331972i) q^{5} +(-1.82552 + 1.82552i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.79836 - 1.32888i) q^{10} -2.09952i q^{11} +(-1.64265 - 1.64265i) q^{13} -2.58168 q^{14} -1.00000 q^{16} +(-3.29353 - 3.29353i) q^{17} -1.00000i q^{19} +(-0.331972 - 2.21129i) q^{20} +(1.48459 - 1.48459i) q^{22} +(5.12494 - 5.12494i) q^{23} +(4.77959 - 1.46817i) q^{25} -2.32305i q^{26} +(-1.82552 - 1.82552i) q^{28} +9.48773 q^{29} +4.22425 q^{31} +(-0.707107 - 0.707107i) q^{32} -4.65775i q^{34} +(3.43074 - 4.64278i) q^{35} +(-1.64265 + 1.64265i) q^{37} +(0.707107 - 0.707107i) q^{38} +(1.32888 - 1.79836i) q^{40} +7.26473i q^{41} +(5.70884 + 5.70884i) q^{43} +2.09952 q^{44} +7.24776 q^{46} +(-9.10895 - 9.10895i) q^{47} +0.334925i q^{49} +(4.41783 + 2.34153i) q^{50} +(1.64265 - 1.64265i) q^{52} +(10.0145 - 10.0145i) q^{53} +(0.696982 + 4.64265i) q^{55} -2.58168i q^{56} +(6.70884 + 6.70884i) q^{58} -5.56868 q^{59} -13.7834 q^{61} +(2.98700 + 2.98700i) q^{62} -1.00000i q^{64} +(4.17768 + 3.08705i) q^{65} +(3.29353 - 3.29353i) q^{68} +(5.70884 - 0.857046i) q^{70} -0.853364i q^{71} +(-8.55918 - 8.55918i) q^{73} -2.32305 q^{74} +1.00000 q^{76} +(3.83273 + 3.83273i) q^{77} -1.45962i q^{79} +(2.21129 - 0.331972i) q^{80} +(-5.13694 + 5.13694i) q^{82} +(6.31562 - 6.31562i) q^{83} +(8.37630 + 6.18958i) q^{85} +8.07352i q^{86} +(1.48459 + 1.48459i) q^{88} +8.59262 q^{89} +5.99738 q^{91} +(5.12494 + 5.12494i) q^{92} -12.8820i q^{94} +(0.331972 + 2.21129i) q^{95} +(11.0176 - 11.0176i) q^{97} +(-0.236828 + 0.236828i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{10} - 12 q^{13} - 20 q^{16} - 16 q^{22} + 16 q^{31} - 12 q^{37} - 8 q^{46} + 12 q^{52} + 20 q^{58} - 16 q^{61} + 20 q^{73} + 20 q^{76} - 28 q^{82} - 8 q^{85} - 16 q^{88} + 32 q^{91} - 20 q^{97}+O(q^{100}) \) 20 * q + 4 * q^10 - 12 * q^13 - 20 * q^16 - 16 * q^22 + 16 * q^31 - 12 * q^37 - 8 * q^46 + 12 * q^52 + 20 * q^58 - 16 * q^61 + 20 * q^73 + 20 * q^76 - 28 * q^82 - 8 * q^85 - 16 * q^88 + 32 * q^91 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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