LMFDB - Embedded newform 1710.2.n.i.647.7

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			647.7
Root			$0.897013 + 0.371555i$ of defining polynomial
Character	$\chi$	$=$	1710.647
Dual form			1710.2.n.i.1673.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.16531 + 1.90842i) q^{5} +(2.34049 + 2.34049i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.525458 + 2.17345i) q^{10} +2.48235i q^{11} +(0.107294 - 0.107294i) q^{13} +3.30996 q^{14} -1.00000 q^{16} +(-4.48794 + 4.48794i) q^{17} +1.00000i q^{19} +(1.90842 + 1.16531i) q^{20} +(1.75529 + 1.75529i) q^{22} +(-4.05307 - 4.05307i) q^{23} +(-2.28411 - 4.44779i) q^{25} -0.151737i q^{26} +(2.34049 - 2.34049i) q^{28} -4.04058 q^{29} -5.61241 q^{31} +(-0.707107 + 0.707107i) q^{32} +6.34690i q^{34} +(-7.19403 + 1.73924i) q^{35} +(0.107294 + 0.107294i) q^{37} +(0.707107 + 0.707107i) q^{38} +(2.17345 - 0.525458i) q^{40} +0.250062i q^{41} +(-3.85712 + 3.85712i) q^{43} +2.48235 q^{44} -5.73190 q^{46} +(-3.34779 + 3.34779i) q^{47} +3.95582i q^{49} +(-4.76017 - 1.52995i) q^{50} +(-0.107294 - 0.107294i) q^{52} +(3.82456 + 3.82456i) q^{53} +(-4.73737 - 2.89271i) q^{55} -3.30996i q^{56} +(-2.85712 + 2.85712i) q^{58} +7.27853 q^{59} +10.1806 q^{61} +(-3.96857 + 3.96857i) q^{62} +1.00000i q^{64} +(0.0797315 + 0.329794i) q^{65} +(4.48794 + 4.48794i) q^{68} +(-3.85712 + 6.31678i) q^{70} +8.45272i q^{71} +(5.56823 - 5.56823i) q^{73} +0.151737 q^{74} +1.00000 q^{76} +(-5.80993 + 5.80993i) q^{77} +15.3376i q^{79} +(1.16531 - 1.90842i) q^{80} +(0.176821 + 0.176821i) q^{82} +(-0.00476373 - 0.00476373i) q^{83} +(-3.33503 - 13.7947i) q^{85} +5.45479i q^{86} +(1.75529 - 1.75529i) q^{88} -7.88373 q^{89} +0.502244 q^{91} +(-4.05307 + 4.05307i) q^{92} +4.73450i q^{94} +(-1.90842 - 1.16531i) q^{95} +(-5.19120 - 5.19120i) q^{97} +(2.79719 + 2.79719i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

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

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
$5$	−1.16531	+	1.90842i	−0.521142	+	0.853470i
$5$	−1.16531	+	1.90842i	−0.521142	+	0.853470i
$6$		0			0
$7$	2.34049	+	2.34049i	0.884623	+	0.884623i	0.994000	−	0.109377i	$-0.0348855\pi$
$7$	2.34049	+	2.34049i	0.884623	+	0.884623i	−0.109377	+	0.994000i	$0.534886\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	0.525458	+	2.17345i	0.166164	+	0.687306i
$11$			2.48235i			0.748458i	0.927336	+	0.374229i	$0.122093\pi$
$11$			2.48235i			0.748458i	−0.927336	+	0.374229i	$0.877907\pi$
$12$		0			0
$13$	0.107294	−	0.107294i	0.0297581	−	0.0297581i	−0.692071	−	0.721829i	$-0.743302\pi$
$13$	0.107294	−	0.107294i	0.0297581	−	0.0297581i	0.721829	+	0.692071i	$0.243302\pi$
$14$	3.30996			0.884623
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−4.48794	+	4.48794i	−1.08849	+	1.08849i	−0.0928004	+	0.995685i	$0.529582\pi$
$17$	−4.48794	+	4.48794i	−1.08849	+	1.08849i	−0.995685	+	0.0928004i	$0.970418\pi$
$18$		0			0
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	1.90842	+	1.16531i	0.426735	+	0.260571i
$21$		0			0
$22$	1.75529	+	1.75529i	0.374229	+	0.374229i
$23$	−4.05307	−	4.05307i	−0.845123	−	0.845123i	0.144397	−	0.989520i	$-0.453876\pi$
$23$	−4.05307	−	4.05307i	−0.845123	−	0.845123i	−0.989520	+	0.144397i	$0.953876\pi$
$24$		0			0
$25$	−2.28411	−	4.44779i	−0.456823	−	0.889558i
$26$		−	0.151737i		−	0.0297581i
$27$		0			0
$28$	2.34049	−	2.34049i	0.442312	−	0.442312i
$29$	−4.04058			−0.750316			−0.375158	−	0.926961i	$-0.622412\pi$
$29$	−4.04058			−0.750316			−0.375158	+	0.926961i	$0.622412\pi$
$30$		0			0
$31$	−5.61241			−1.00802			−0.504009	−	0.863698i	$-0.668142\pi$
$31$	−5.61241			−1.00802			−0.504009	+	0.863698i	$0.668142\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$			6.34690i			1.08849i
$35$	−7.19403	+	1.73924i	−1.21601	+	0.293986i
$36$		0			0
$37$	0.107294	+	0.107294i	0.0176391	+	0.0176391i	0.715871	−	0.698232i	$-0.246030\pi$
$37$	0.107294	+	0.107294i	0.0176391	+	0.0176391i	−0.698232	+	0.715871i	$0.746030\pi$
$38$	0.707107	+	0.707107i	0.114708	+	0.114708i
$39$		0			0
$40$	2.17345	−	0.525458i	0.343653	−	0.0830822i
$41$			0.250062i			0.0390531i	0.999809	+	0.0195266i	$0.00621589\pi$
$41$			0.250062i			0.0390531i	−0.999809	+	0.0195266i	$0.993784\pi$
$42$		0			0
$43$	−3.85712	+	3.85712i	−0.588205	+	0.588205i	−0.937145	−	0.348940i	$-0.886542\pi$
$43$	−3.85712	+	3.85712i	−0.588205	+	0.588205i	0.348940	+	0.937145i	$0.386542\pi$
$44$	2.48235			0.374229
$45$		0			0
$46$	−5.73190			−0.845123
$47$	−3.34779	+	3.34779i	−0.488326	+	0.488326i	−0.907778	−	0.419452i	$-0.862222\pi$
$47$	−3.34779	+	3.34779i	−0.488326	+	0.488326i	0.419452	+	0.907778i	$0.362222\pi$
$48$		0			0
$49$			3.95582i			0.565117i
$50$	−4.76017	−	1.52995i	−0.673190	−	0.216367i
$51$		0			0
$52$	−0.107294	−	0.107294i	−0.0148791	−	0.0148791i
$53$	3.82456	+	3.82456i	0.525344	+	0.525344i	0.919180	−	0.393837i	$-0.128852\pi$
$53$	3.82456	+	3.82456i	0.525344	+	0.525344i	−0.393837	+	0.919180i	$0.628852\pi$
$54$		0			0
$55$	−4.73737	−	2.89271i	−0.638786	−	0.390052i
$56$		−	3.30996i		−	0.442312i
$57$		0			0
$58$	−2.85712	+	2.85712i	−0.375158	+	0.375158i
$59$	7.27853			0.947584			0.473792	−	0.880637i	$-0.342885\pi$
$59$	7.27853			0.947584			0.473792	+	0.880637i	$0.342885\pi$
$60$		0			0
$61$	10.1806			1.30350			0.651749	−	0.758435i	$-0.274036\pi$
$61$	10.1806			1.30350			0.651749	+	0.758435i	$0.274036\pi$
$62$	−3.96857	+	3.96857i	−0.504009	+	0.504009i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	0.0797315	+	0.329794i	0.00988948	+	0.0409059i
$66$		0			0
$67$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$67$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$68$	4.48794	+	4.48794i	0.544243	+	0.544243i
$69$		0			0
$70$	−3.85712	+	6.31678i	−0.461014	+	0.755000i
$71$			8.45272i			1.00315i	0.865113	+	0.501577i	$0.167246\pi$
$71$			8.45272i			1.00315i	−0.865113	+	0.501577i	$0.832754\pi$
$72$		0			0
$73$	5.56823	−	5.56823i	0.651712	−	0.651712i	−0.301693	−	0.953405i	$-0.597552\pi$
$73$	5.56823	−	5.56823i	0.651712	−	0.651712i	0.953405	+	0.301693i	$0.0975518\pi$
$74$	0.151737			0.0176391
$75$		0			0
$76$	1.00000			0.114708
$77$	−5.80993	+	5.80993i	−0.662103	+	0.662103i
$78$		0			0
$79$			15.3376i			1.72561i	0.505535	+	0.862806i	$0.331295\pi$
$79$			15.3376i			1.72561i	−0.505535	+	0.862806i	$0.668705\pi$
$80$	1.16531	−	1.90842i	0.130285	−	0.213368i
$81$		0			0
$82$	0.176821	+	0.176821i	0.0195266	+	0.0195266i
$83$	−0.00476373	−	0.00476373i	−0.000522887	−	0.000522887i	0.706845	−	0.707368i	$-0.250118\pi$
$83$	−0.00476373	−	0.00476373i	−0.000522887	−	0.000522887i	−0.707368	+	0.706845i	$0.750118\pi$
$84$		0			0
$85$	−3.33503	−	13.7947i	−0.361735	−	1.49624i
$86$			5.45479i			0.588205i
$87$		0			0
$88$	1.75529	−	1.75529i	0.187114	−	0.187114i
$89$	−7.88373			−0.835674			−0.417837	−	0.908522i	$-0.637212\pi$
$89$	−7.88373			−0.835674			−0.417837	+	0.908522i	$0.637212\pi$
$90$		0			0
$91$	0.502244			0.0526495
$92$	−4.05307	+	4.05307i	−0.422561	+	0.422561i
$93$		0			0
$94$			4.73450i			0.488326i
$95$	−1.90842	−	1.16531i	−0.195800	−	0.119558i
$96$		0			0
$97$	−5.19120	−	5.19120i	−0.527087	−	0.527087i	0.392616	−	0.919703i	$-0.371570\pi$
$97$	−5.19120	−	5.19120i	−0.527087	−	0.527087i	−0.919703	+	0.392616i	$0.871570\pi$
$98$	2.79719	+	2.79719i	0.282559	+	0.282559i
$99$		0			0
$100$	−4.44779	+	2.28411i	−0.444779	+	0.228411i
$101$		−	0.641823i		−	0.0638637i	−0.999490	−	0.0319319i	$-0.989834\pi$
$101$		−	0.641823i		−	0.0638637i	0.999490	−	0.0319319i	$-0.0101660\pi$
$102$		0			0
$103$	7.31132	−	7.31132i	0.720406	−	0.720406i	−0.248282	−	0.968688i	$-0.579866\pi$
$103$	7.31132	−	7.31132i	0.720406	−	0.720406i	0.968688	+	0.248282i	$0.0798660\pi$
$104$	−0.151737			−0.0148791
$105$		0			0
$106$	5.40875			0.525344
$107$	−8.14827	+	8.14827i	−0.787723	+	0.787723i	−0.981121	−	0.193397i	$-0.938049\pi$
$107$	−8.14827	+	8.14827i	−0.787723	+	0.787723i	0.193397	+	0.981121i	$0.438049\pi$
$108$		0			0
$109$			5.59959i			0.536343i	0.963371	+	0.268172i	$0.0864194\pi$
$109$			5.59959i			0.536343i	−0.963371	+	0.268172i	$0.913581\pi$
$110$	−5.39528	+	1.30437i	−0.514419	+	0.124367i
$111$		0			0
$112$	−2.34049	−	2.34049i	−0.221156	−	0.221156i
$113$	11.2177	+	11.2177i	1.05527	+	1.05527i	0.998380	+	0.0568918i	$0.0181190\pi$
$113$	11.2177	+	11.2177i	1.05527	+	1.05527i	0.0568918	+	0.998380i	$0.481881\pi$
$114$		0			0
$115$	12.4580	−	3.01187i	1.16172	−	0.280859i
$116$			4.04058i			0.375158i
$117$		0			0
$118$	5.14670	−	5.14670i	0.473792	−	0.473792i
$119$	−21.0080			−1.92580
$120$		0			0
$121$	4.83792			0.439811
$122$	7.19880	−	7.19880i	0.651749	−	0.651749i
$123$		0			0
$124$			5.61241i			0.504009i
$125$	11.1499	+	0.823998i	0.997280	+	0.0737006i
$126$		0			0
$127$	9.52591	+	9.52591i	0.845288	+	0.845288i	0.989541	−	0.144253i	$-0.0460780\pi$
$127$	9.52591	+	9.52591i	0.845288	+	0.845288i	−0.144253	+	0.989541i	$0.546078\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	0.289578	+	0.176821i	0.0253977	+	0.0155082i
$131$		−	4.66072i		−	0.407209i	−0.979053	−	0.203605i	$-0.934734\pi$
$131$		−	4.66072i		−	0.407209i	0.979053	−	0.203605i	$-0.0652657\pi$
$132$		0			0
$133$	−2.34049	+	2.34049i	−0.202947	+	0.202947i
$134$		0			0
$135$		0			0
$136$	6.34690			0.544243
$137$	−7.89391	+	7.89391i	−0.674422	+	0.674422i	−0.958732	−	0.284310i	$-0.908235\pi$
$137$	−7.89391	+	7.89391i	−0.674422	+	0.674422i	0.284310	+	0.958732i	$0.408235\pi$
$138$		0			0
$139$		−	13.2018i		−	1.11976i	−0.828573	−	0.559881i	$-0.810847\pi$
$139$		−	13.2018i		−	1.11976i	0.828573	−	0.559881i	$-0.189153\pi$
$140$	1.73924	+	7.19403i	0.146993	+	0.608007i
$141$		0			0
$142$	5.97698	+	5.97698i	0.501577	+	0.501577i
$143$	0.266343	+	0.266343i	0.0222727	+	0.0222727i
$144$		0			0
$145$	4.70852	−	7.71111i	0.391021	−	0.640373i
$146$		−	7.87467i		−	0.651712i
$147$		0			0
$148$	0.107294	−	0.107294i	0.00881955	−	0.00881955i
$149$	−11.4660			−0.939328			−0.469664	−	0.882845i	$-0.655625\pi$
$149$	−11.4660			−0.939328			−0.469664	+	0.882845i	$0.655625\pi$
$150$		0			0
$151$	7.88724			0.641855			0.320927	−	0.947104i	$-0.396005\pi$
$151$	7.88724			0.641855			0.320927	+	0.947104i	$0.396005\pi$
$152$	0.707107	−	0.707107i	0.0573539	−	0.0573539i
$153$		0			0
$154$			8.21648i			0.662103i
$155$	6.54018	−	10.7108i	0.525320	−	0.860314i
$156$		0			0
$157$	6.76844	+	6.76844i	0.540180	+	0.540180i	0.923582	−	0.383402i	$-0.125248\pi$
$157$	6.76844	+	6.76844i	0.540180	+	0.540180i	−0.383402	+	0.923582i	$0.625248\pi$
$158$	10.8453	+	10.8453i	0.862806	+	0.862806i
$159$		0			0
$160$	−0.525458	−	2.17345i	−0.0415411	−	0.171826i
$161$		−	18.9724i		−	1.49523i
$162$		0			0
$163$	3.78577	−	3.78577i	0.296525	−	0.296525i	−0.543126	−	0.839651i	$-0.682760\pi$
$163$	3.78577	−	3.78577i	0.296525	−	0.296525i	0.839651	+	0.543126i	$0.182760\pi$
$164$	0.250062			0.0195266
$165$		0			0
$166$	−0.00673693			−0.000522887
$167$	10.3398	−	10.3398i	0.800115	−	0.800115i	−0.182998	−	0.983113i	$-0.558580\pi$
$167$	10.3398	−	10.3398i	0.800115	−	0.800115i	0.983113	+	0.182998i	$0.0585802\pi$
$168$		0			0
$169$			12.9770i			0.998229i
$170$	−12.1125	−	7.39610i	−0.928990	−	0.567255i
$171$		0			0
$172$	3.85712	+	3.85712i	0.294103	+	0.294103i
$173$	−13.1428	−	13.1428i	−0.999232	−	0.999232i	0.000767569	−	1.00000i	$-0.499756\pi$
$173$	−13.1428	−	13.1428i	−0.999232	−	0.999232i	−1.00000		0.000767569i	$0.999756\pi$
$174$		0			0
$175$	5.06406	−	15.7560i	0.382807	−	1.19104i
$176$		−	2.48235i		−	0.187114i
$177$		0			0
$178$	−5.57464	+	5.57464i	−0.417837	+	0.417837i
$179$	19.0397			1.42310			0.711548	−	0.702638i	$-0.247994\pi$
$179$	19.0397			1.42310			0.711548	+	0.702638i	$0.247994\pi$
$180$		0			0
$181$	−0.364567			−0.0270981			−0.0135490	−	0.999908i	$-0.504313\pi$
$181$	−0.364567			−0.0270981			−0.0135490	+	0.999908i	$0.504313\pi$
$182$	0.355140	−	0.355140i	0.0263247	−	0.0263247i
$183$		0			0
$184$			5.73190i			0.422561i
$185$	−0.329794	+	0.0797315i	−0.0242469	+	0.00586198i
$186$		0			0
$187$	−11.1406	−	11.1406i	−0.814685	−	0.814685i
$188$	3.34779	+	3.34779i	0.244163	+	0.244163i
$189$		0			0
$190$	−2.17345	+	0.525458i	−0.157679	+	0.0381207i
$191$		−	11.3178i		−	0.818925i	−0.912327	−	0.409462i	$-0.865716\pi$
$191$		−	11.3178i		−	0.818925i	0.912327	−	0.409462i	$-0.134284\pi$
$192$		0			0
$193$	−11.7832	+	11.7832i	−0.848172	+	0.848172i	−0.989905	−	0.141733i	$-0.954733\pi$
$193$	−11.7832	+	11.7832i	−0.848172	+	0.848172i	0.141733	+	0.989905i	$0.454733\pi$
$194$	−7.34147			−0.527087
$195$		0			0
$196$	3.95582			0.282559
$197$	0.772516	−	0.772516i	0.0550395	−	0.0550395i	−0.679051	−	0.734091i	$-0.737609\pi$
$197$	0.772516	−	0.772516i	0.0550395	−	0.0550395i	0.734091	+	0.679051i	$0.237609\pi$
$198$		0			0
$199$			14.7828i			1.04793i	0.851741	+	0.523963i	$0.175547\pi$
$199$			14.7828i			1.04793i	−0.851741	+	0.523963i	$0.824453\pi$
$200$	−1.52995	+	4.76017i	−0.108184	+	0.336595i
$201$		0			0
$202$	−0.453837	−	0.453837i	−0.0319319	−	0.0319319i
$203$	−9.45695	−	9.45695i	−0.663748	−	0.663748i
$204$		0			0
$205$	−0.477223	−	0.291399i	−0.0333307	−	0.0203522i
$206$		−	10.3398i		−	0.720406i
$207$		0			0
$208$	−0.107294	+	0.107294i	−0.00743953	+	0.00743953i
$209$	−2.48235			−0.171708
$210$		0			0
$211$	4.43055			0.305012			0.152506	−	0.988303i	$-0.451266\pi$
$211$	4.43055			0.305012			0.152506	+	0.988303i	$0.451266\pi$
$212$	3.82456	−	3.82456i	0.262672	−	0.262672i
$213$		0			0
$214$			11.5234i			0.787723i
$215$	−2.86626	−	11.8557i	−0.195478	−	0.808554i
$216$		0			0
$217$	−13.1358	−	13.1358i	−0.891717	−	0.891717i
$218$	3.95951	+	3.95951i	0.268172	+	0.268172i
$219$		0			0
$220$	−2.89271	+	4.73737i	−0.195026	+	0.319393i
$221$			0.963062i			0.0647825i
$222$		0			0
$223$	−9.76490	+	9.76490i	−0.653906	+	0.653906i	−0.953931	−	0.300025i	$-0.903005\pi$
$223$	−9.76490	+	9.76490i	−0.653906	+	0.653906i	0.300025	+	0.953931i	$0.403005\pi$
$224$	−3.30996			−0.221156
$225$		0			0
$226$	15.8642			1.05527
$227$	−15.6881	+	15.6881i	−1.04126	+	1.04126i	−0.0421470	+	0.999111i	$0.513420\pi$
$227$	−15.6881	+	15.6881i	−1.04126	+	1.04126i	−0.999111	+	0.0421470i	$0.986580\pi$
$228$		0			0
$229$		−	23.9430i		−	1.58220i	−0.611687	−	0.791100i	$-0.709509\pi$
$229$		−	23.9430i		−	1.58220i	0.611687	−	0.791100i	$-0.290491\pi$
$230$	6.67943	−	10.9389i	0.440429	−	0.721287i
$231$		0			0
$232$	2.85712	+	2.85712i	0.187579	+	0.187579i
$233$	13.0996	+	13.0996i	0.858184	+	0.858184i	0.991124	−	0.132940i	$-0.0424418\pi$
$233$	13.0996	+	13.0996i	0.858184	+	0.858184i	−0.132940	+	0.991124i	$0.542442\pi$
$234$		0			0
$235$	−2.48778	−	10.2902i	−0.162285	−	0.671259i
$236$		−	7.27853i		−	0.473792i
$237$		0			0
$238$	−14.8549	+	14.8549i	−0.962899	+	0.962899i
$239$	20.4712			1.32417			0.662087	−	0.749427i	$-0.269671\pi$
$239$	20.4712			1.32417			0.662087	+	0.749427i	$0.269671\pi$
$240$		0			0
$241$	7.39592			0.476413			0.238207	−	0.971214i	$-0.423440\pi$
$241$	7.39592			0.476413			0.238207	+	0.971214i	$0.423440\pi$
$242$	3.42093	−	3.42093i	0.219906	−	0.219906i
$243$		0			0
$244$		−	10.1806i		−	0.651749i
$245$	−7.54936	−	4.60975i	−0.482311	−	0.294506i
$246$		0			0
$247$	0.107294	+	0.107294i	0.00682698	+	0.00682698i
$248$	3.96857	+	3.96857i	0.252005	+	0.252005i
$249$		0			0
$250$	8.46685	−	7.30154i	0.535490	−	0.461790i
$251$		−	7.36327i		−	0.464765i	−0.972624	−	0.232383i	$-0.925348\pi$
$251$		−	7.36327i		−	0.464765i	0.972624	−	0.232383i	$-0.0746522\pi$
$252$		0			0
$253$	10.0611	−	10.0611i	0.632539	−	0.632539i
$254$	13.4717			0.845288
$255$		0			0
$256$	1.00000			0.0625000
$257$	10.0781	−	10.0781i	0.628652	−	0.628652i	−0.319077	−	0.947729i	$-0.603373\pi$
$257$	10.0781	−	10.0781i	0.628652	−	0.628652i	0.947729	+	0.319077i	$0.103373\pi$
$258$		0			0
$259$			0.502244i			0.0312079i
$260$	0.329794	−	0.0797315i	0.0204529	−	0.00494474i
$261$		0			0
$262$	−3.29563	−	3.29563i	−0.203605	−	0.203605i
$263$	−16.4372	−	16.4372i	−1.01356	−	1.01356i	−0.999907	−	0.0136562i	$-0.995653\pi$
$263$	−16.4372	−	16.4372i	−1.01356	−	1.01356i	−0.0136562	−	0.999907i	$-0.504347\pi$
$264$		0			0
$265$	−11.7557	+	2.84207i	−0.722144	+	0.174587i
$266$			3.30996i			0.202947i
$267$		0			0
$268$		0			0
$269$	−1.22760			−0.0748482			−0.0374241	−	0.999299i	$-0.511915\pi$
$269$	−1.22760			−0.0748482			−0.0374241	+	0.999299i	$0.511915\pi$
$270$		0			0
$271$	27.2376			1.65457			0.827284	−	0.561783i	$-0.189885\pi$
$271$	27.2376			1.65457			0.827284	+	0.561783i	$0.189885\pi$
$272$	4.48794	−	4.48794i	0.272121	−	0.272121i
$273$		0			0
$274$			11.1637i			0.674422i
$275$	11.0410	−	5.66998i	0.665796	−	0.341913i
$276$		0			0
$277$	−17.8556	−	17.8556i	−1.07284	−	1.07284i	−0.997130	−	0.0757076i	$-0.975878\pi$
$277$	−17.8556	−	17.8556i	−1.07284	−	1.07284i	−0.0757076	−	0.997130i	$-0.524122\pi$
$278$	−9.33508	−	9.33508i	−0.559881	−	0.559881i
$279$		0			0
$280$	6.31678	+	3.85712i	0.377500	+	0.230507i
$281$			2.03023i			0.121113i	0.998165	+	0.0605566i	$0.0192876\pi$
$281$			2.03023i			0.121113i	−0.998165	+	0.0605566i	$0.980712\pi$
$282$		0			0
$283$	2.75270	−	2.75270i	0.163631	−	0.163631i	−0.620542	−	0.784173i	$-0.713087\pi$
$283$	2.75270	−	2.75270i	0.163631	−	0.163631i	0.784173	+	0.620542i	$0.213087\pi$
$284$	8.45272			0.501577
$285$		0			0
$286$	0.376665			0.0222727
$287$	−0.585269	+	0.585269i	−0.0345473	+	0.0345473i
$288$		0			0
$289$		−	23.2832i		−	1.36960i
$290$	−2.12315	−	8.78200i	−0.124676	−	0.515697i
$291$		0			0
$292$	−5.56823	−	5.56823i	−0.325856	−	0.325856i
$293$	21.6748	+	21.6748i	1.26625	+	1.26625i	0.948008	+	0.318247i	$0.103094\pi$
$293$	21.6748	+	21.6748i	1.26625	+	1.26625i	0.318247	+	0.948008i	$0.396906\pi$
$294$		0			0
$295$	−8.48173	+	13.8905i	−0.493825	+	0.808735i
$296$		−	0.151737i		−	0.00881955i
$297$		0			0
$298$	−8.10766	+	8.10766i	−0.469664	+	0.469664i
$299$	−0.869743			−0.0502985
$300$		0			0
$301$	−18.0551			−1.04068
$302$	5.57712	−	5.57712i	0.320927	−	0.320927i
$303$		0			0
$304$		−	1.00000i		−	0.0573539i
$305$	−11.8636	+	19.4289i	−0.679307	+	1.11250i
$306$		0			0
$307$	−6.59198	−	6.59198i	−0.376224	−	0.376224i	0.493514	−	0.869738i	$-0.335712\pi$
$307$	−6.59198	−	6.59198i	−0.376224	−	0.376224i	−0.869738	+	0.493514i	$0.835712\pi$
$308$	5.80993	+	5.80993i	0.331052	+	0.331052i
$309$		0			0
$310$	−2.94908	−	12.1983i	−0.167497	−	0.692817i
$311$		−	23.7065i		−	1.34427i	−0.740428	−	0.672135i	$-0.765377\pi$
$311$		−	23.7065i		−	1.34427i	0.740428	−	0.672135i	$-0.234623\pi$
$312$		0			0
$313$	−20.3571	+	20.3571i	−1.15065	+	1.15065i	−0.164231	+	0.986422i	$0.552514\pi$
$313$	−20.3571	+	20.3571i	−1.15065	+	1.15065i	−0.986422	+	0.164231i	$0.947486\pi$
$314$	9.57201			0.540180
$315$		0			0
$316$	15.3376			0.862806
$317$	−20.3368	+	20.3368i	−1.14223	+	1.14223i	−0.154184	+	0.988042i	$0.549275\pi$
$317$	−20.3368	+	20.3368i	−1.14223	+	1.14223i	−0.988042	+	0.154184i	$0.950725\pi$
$318$		0			0
$319$		−	10.0301i		−	0.561580i
$320$	−1.90842	−	1.16531i	−0.106684	−	0.0651427i
$321$		0			0
$322$	−13.4155	−	13.4155i	−0.747616	−	0.747616i
$323$	−4.48794	−	4.48794i	−0.249716	−	0.249716i
$324$		0			0
$325$	−0.722296	−	0.232150i	−0.0400657	−	0.0128774i
$326$		−	5.35389i		−	0.296525i
$327$		0			0
$328$	0.176821	−	0.176821i	0.00976328	−	0.00976328i
$329$	−15.6710			−0.863969
$330$		0			0
$331$	−13.8303			−0.760180			−0.380090	−	0.924949i	$-0.624107\pi$
$331$	−13.8303			−0.760180			−0.380090	+	0.924949i	$0.624107\pi$
$332$	−0.00476373	+	0.00476373i	−0.000261444	+	0.000261444i
$333$		0			0
$334$		−	14.6226i		−	0.800115i
$335$		0			0
$336$		0			0
$337$	20.3251	+	20.3251i	1.10718	+	1.10718i	0.993520	+	0.113660i	$0.0362574\pi$
$337$	20.3251	+	20.3251i	1.10718	+	1.10718i	0.113660	+	0.993520i	$0.463743\pi$
$338$	9.17611	+	9.17611i	0.499114	+	0.499114i
$339$		0			0
$340$	−13.7947	+	3.33503i	−0.748122	+	0.180867i
$341$		−	13.9320i		−	0.754459i
$342$		0			0
$343$	7.12488	−	7.12488i	0.384707	−	0.384707i
$344$	5.45479			0.294103
$345$		0			0
$346$	−18.5868			−0.999232
$347$	1.66858	−	1.66858i	0.0895739	−	0.0895739i	−0.660900	−	0.750474i	$-0.729825\pi$
$347$	1.66858	−	1.66858i	0.0895739	−	0.0895739i	0.750474	+	0.660900i	$0.229825\pi$
$348$		0			0
$349$			3.29409i			0.176329i	0.996106	+	0.0881644i	$0.0281001\pi$
$349$			3.29409i			0.176329i	−0.996106	+	0.0881644i	$0.971900\pi$
$350$	−7.56032	−	14.7220i	−0.404116	−	0.786924i
$351$		0			0
$352$	−1.75529	−	1.75529i	−0.0935572	−	0.0935572i
$353$	17.7359	+	17.7359i	0.943985	+	0.943985i	0.998512	−	0.0545275i	$-0.0173653\pi$
$353$	17.7359	+	17.7359i	0.943985	+	0.943985i	−0.0545275	+	0.998512i	$0.517365\pi$
$354$		0			0
$355$	−16.1313	−	9.85002i	−0.856162	−	0.522785i
$356$			7.88373i			0.417837i
$357$		0			0
$358$	13.4631	−	13.4631i	0.711548	−	0.711548i
$359$	−0.977134			−0.0515711			−0.0257856	−	0.999667i	$-0.508209\pi$
$359$	−0.977134			−0.0515711			−0.0257856	+	0.999667i	$0.508209\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	−0.257788	+	0.257788i	−0.0135490	+	0.0135490i
$363$		0			0
$364$		−	0.502244i		−	0.0263247i
$365$	4.13781	+	17.1152i	0.216583	+	0.895851i
$366$		0			0
$367$	−14.1082	−	14.1082i	−0.736444	−	0.736444i	0.235444	−	0.971888i	$-0.424346\pi$
$367$	−14.1082	−	14.1082i	−0.736444	−	0.736444i	−0.971888	+	0.235444i	$0.924346\pi$
$368$	4.05307	+	4.05307i	0.211281	+	0.211281i
$369$		0			0
$370$	−0.176821	+	0.289578i	−0.00919246	+	0.0150544i
$371$			17.9027i			0.929463i
$372$		0			0
$373$	−20.5032	+	20.5032i	−1.06162	+	1.06162i	−0.0636452	+	0.997973i	$0.520273\pi$
$373$	−20.5032	+	20.5032i	−1.06162	+	1.06162i	−0.997973	+	0.0636452i	$0.979727\pi$
$374$	−15.7553			−0.814685
$375$		0			0
$376$	4.73450			0.244163
$377$	−0.433531	+	0.433531i	−0.0223280	+	0.0223280i
$378$		0			0
$379$		−	28.1712i		−	1.44706i	−0.690295	−	0.723528i	$-0.742519\pi$
$379$		−	28.1712i		−	1.44706i	0.690295	−	0.723528i	$-0.257481\pi$
$380$	−1.16531	+	1.90842i	−0.0597790	+	0.0978998i
$381$		0			0
$382$	−8.00287	−	8.00287i	−0.409462	−	0.409462i
$383$	19.7414	+	19.7414i	1.00874	+	1.00874i	0.999961	+	0.00877950i	$0.00279464\pi$
$383$	19.7414	+	19.7414i	1.00874	+	1.00874i	0.00877950	+	0.999961i	$0.497205\pi$
$384$		0			0
$385$	−4.31742	−	17.8581i	−0.220036	−	0.910135i
$386$			16.6639i			0.848172i
$387$		0			0
$388$	−5.19120	+	5.19120i	−0.263543	+	0.263543i
$389$	37.3644			1.89445			0.947225	−	0.320570i	$-0.103875\pi$
$389$	37.3644			1.89445			0.947225	+	0.320570i	$0.103875\pi$
$390$		0			0
$391$	36.3798			1.83981
$392$	2.79719	−	2.79719i	0.141279	−	0.141279i
$393$		0			0
$394$		−	1.09250i		−	0.0550395i
$395$	−29.2705	−	17.8730i	−1.47276	−	0.899288i
$396$		0			0
$397$	−17.0923	−	17.0923i	−0.857839	−	0.857839i	0.133244	−	0.991083i	$-0.457460\pi$
$397$	−17.0923	−	17.0923i	−0.857839	−	0.857839i	−0.991083	+	0.133244i	$0.957460\pi$
$398$	10.4530	+	10.4530i	0.523963	+	0.523963i
$399$		0			0
$400$	2.28411	+	4.44779i	0.114206	+	0.222389i
$401$		−	15.9215i		−	0.795083i	−0.917584	−	0.397542i	$-0.869863\pi$
$401$		−	15.9215i		−	0.795083i	0.917584	−	0.397542i	$-0.130137\pi$
$402$		0			0
$403$	−0.602180	+	0.602180i	−0.0299967	+	0.0299967i
$404$	−0.641823			−0.0319319
$405$		0			0
$406$	−13.3741			−0.663748
$407$	−0.266343	+	0.266343i	−0.0132021	+	0.0132021i
$408$		0			0
$409$			38.2602i			1.89184i	0.324395	+	0.945922i	$0.394839\pi$
$409$			38.2602i			1.89184i	−0.324395	+	0.945922i	$0.605161\pi$
$410$	−0.543498	+	0.131397i	−0.0268414	+	0.00648924i
$411$		0			0
$412$	−7.31132	−	7.31132i	−0.360203	−	0.360203i
$413$	17.0354	+	17.0354i	0.838255	+	0.838255i
$414$		0			0
$415$	0.0146424	−	0.00353997i	0.000718767	−	0.000173771i
$416$			0.151737i			0.00743953i
$417$		0			0
$418$	−1.75529	+	1.75529i	−0.0858540	+	0.0858540i
$419$	16.9480			0.827966			0.413983	−	0.910285i	$-0.364137\pi$
$419$	16.9480			0.827966			0.413983	+	0.910285i	$0.364137\pi$
$420$		0			0
$421$	−25.6208			−1.24868			−0.624340	−	0.781153i	$-0.714632\pi$
$421$	−25.6208			−1.24868			−0.624340	+	0.781153i	$0.714632\pi$
$422$	3.13287	−	3.13287i	0.152506	−	0.152506i
$423$		0			0
$424$		−	5.40875i		−	0.262672i
$425$	30.2124	+	9.71043i	1.46552	+	0.471025i
$426$		0			0
$427$	23.8277	+	23.8277i	1.15310	+	1.15310i
$428$	8.14827	+	8.14827i	0.393862	+	0.393862i
$429$		0			0
$430$	−10.4100	−	6.35651i	−0.502016	−	0.306538i
$431$		−	37.2026i		−	1.79199i	−0.444068	−	0.895993i	$-0.646465\pi$
$431$		−	37.2026i		−	1.79199i	0.444068	−	0.895993i	$-0.353535\pi$
$432$		0			0
$433$	−8.87668	+	8.87668i	−0.426586	+	0.426586i	−0.887464	−	0.460878i	$-0.847535\pi$
$433$	−8.87668	+	8.87668i	−0.426586	+	0.426586i	0.460878	+	0.887464i	$0.347535\pi$
$434$	−18.5768			−0.891717
$435$		0			0
$436$	5.59959			0.268172
$437$	4.05307	−	4.05307i	0.193885	−	0.193885i
$438$		0			0
$439$			1.46971i			0.0701456i	0.999385	+	0.0350728i	$0.0111663\pi$
$439$			1.46971i			0.0701456i	−0.999385	+	0.0350728i	$0.988834\pi$
$440$	1.30437	+	5.39528i	0.0621835	+	0.257210i
$441$		0			0
$442$	0.680987	+	0.680987i	0.0323913	+	0.0323913i
$443$	−0.644785	−	0.644785i	−0.0306347	−	0.0306347i	0.691624	−	0.722258i	$-0.256896\pi$
$443$	−0.644785	−	0.644785i	−0.0306347	−	0.0306347i	−0.722258	+	0.691624i	$0.756896\pi$
$444$		0			0
$445$	9.18698	−	15.0455i	0.435504	−	0.713223i
$446$			13.8096i			0.653906i
$447$		0			0
$448$	−2.34049	+	2.34049i	−0.110578	+	0.110578i
$449$	−11.1942			−0.528285			−0.264142	−	0.964484i	$-0.585089\pi$
$449$	−11.1942			−0.528285			−0.264142	+	0.964484i	$0.585089\pi$
$450$		0			0
$451$	−0.620742			−0.0292296
$452$	11.2177	−	11.2177i	0.527636	−	0.527636i
$453$		0			0
$454$			22.1864i			1.04126i
$455$	−0.585269	+	0.958491i	−0.0274378	+	0.0449347i
$456$		0			0
$457$	6.28317	+	6.28317i	0.293914	+	0.293914i	0.838624	−	0.544710i	$-0.183360\pi$
$457$	6.28317	+	6.28317i	0.293914	+	0.293914i	−0.544710	+	0.838624i	$0.683360\pi$
$458$	−16.9303	−	16.9303i	−0.791100	−	0.791100i
$459$		0			0
$460$	−3.01187	−	12.4580i	−0.140429	−	0.580858i
$461$		−	30.8581i		−	1.43721i	−0.695420	−	0.718603i	$-0.744782\pi$
$461$		−	30.8581i		−	1.43721i	0.695420	−	0.718603i	$-0.255218\pi$
$462$		0			0
$463$	−13.1768	+	13.1768i	−0.612379	+	0.612379i	−0.943565	−	0.331187i	$-0.892551\pi$
$463$	−13.1768	+	13.1768i	−0.612379	+	0.612379i	0.331187	+	0.943565i	$0.392551\pi$
$464$	4.04058			0.187579
$465$		0			0
$466$	18.5256			0.858184
$467$	−6.31117	+	6.31117i	−0.292046	+	0.292046i	−0.837888	−	0.545842i	$-0.816210\pi$
$467$	−6.31117	+	6.31117i	−0.292046	+	0.292046i	0.545842	+	0.837888i	$0.316210\pi$
$468$		0			0
$469$		0			0
$470$	−9.03539	−	5.51714i	−0.416772	−	0.254487i
$471$		0			0
$472$	−5.14670	−	5.14670i	−0.236896	−	0.236896i
$473$	−9.57473	−	9.57473i	−0.440247	−	0.440247i
$474$		0			0
$475$	4.44779	−	2.28411i	0.204079	−	0.104802i
$476$			21.0080i			0.962899i
$477$		0			0
$478$	14.4754	−	14.4754i	0.662087	−	0.662087i
$479$	40.6014			1.85512			0.927562	−	0.373670i	$-0.121901\pi$
$479$	40.6014			1.85512			0.927562	+	0.373670i	$0.121901\pi$
$480$		0			0
$481$	0.0230242			0.00104981
$482$	5.22971	−	5.22971i	0.238207	−	0.238207i
$483$		0			0
$484$		−	4.83792i		−	0.219906i
$485$	15.9563	−	3.85763i	0.724540	−	0.175166i
$486$		0			0
$487$	21.3018	+	21.3018i	0.965275	+	0.965275i	0.999417	−	0.0341417i	$-0.0108698\pi$
$487$	21.3018	+	21.3018i	0.965275	+	0.965275i	−0.0341417	+	0.999417i	$0.510870\pi$
$488$	−7.19880	−	7.19880i	−0.325874	−	0.325874i
$489$		0			0
$490$	−8.59779	+	2.07862i	−0.388408	+	0.0939024i
$491$		−	40.2353i		−	1.81579i	−0.419194	−	0.907897i	$-0.637687\pi$
$491$		−	40.2353i		−	1.81579i	0.419194	−	0.907897i	$-0.362313\pi$
$492$		0			0
$493$	18.1339	−	18.1339i	0.816708	−	0.816708i
$494$	0.151737			0.00682698
$495$		0			0
$496$	5.61241			0.252005
$497$	−19.7835	+	19.7835i	−0.887413	+	0.887413i
$498$		0			0
$499$			20.1365i			0.901433i	0.892667	+	0.450716i	$0.148831\pi$
$499$			20.1365i			0.901433i	−0.892667	+	0.450716i	$0.851169\pi$
$500$	0.823998	−	11.1499i	0.0368503	−	0.498640i
$501$		0			0
$502$	−5.20662	−	5.20662i	−0.232383	−	0.232383i
$503$	−0.126633	−	0.126633i	−0.00564630	−	0.00564630i	0.704278	−	0.709924i	$-0.251271\pi$
$503$	−0.126633	−	0.126633i	−0.00564630	−	0.00564630i	−0.709924	+	0.704278i	$0.751271\pi$
$504$		0			0
$505$	1.22487	+	0.747921i	0.0545058	+	0.0332821i
$506$		−	14.2286i		−	0.632539i
$507$		0			0
$508$	9.52591	−	9.52591i	0.422644	−	0.422644i
$509$	−3.80325			−0.168576			−0.0842880	−	0.996441i	$-0.526862\pi$
$509$	−3.80325			−0.168576			−0.0842880	+	0.996441i	$0.526862\pi$
$510$		0			0
$511$	26.0648			1.15304
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	14.2525i		−	0.628652i
$515$	5.43311	+	22.4730i	0.239411	+	0.990278i
$516$		0			0
$517$	−8.31041	−	8.31041i	−0.365491	−	0.365491i
$518$	0.355140	+	0.355140i	0.0156040	+	0.0156040i
$519$		0			0
$520$	0.176821	−	0.289578i	0.00775409	−	0.0126988i
$521$		−	26.0863i		−	1.14286i	−0.820650	−	0.571431i	$-0.806388\pi$
$521$		−	26.0863i		−	1.14286i	0.820650	−	0.571431i	$-0.193612\pi$
$522$		0			0
$523$	19.4645	−	19.4645i	0.851124	−	0.851124i	−0.139147	−	0.990272i	$-0.544436\pi$
$523$	19.4645	−	19.4645i	0.851124	−	0.851124i	0.990272	+	0.139147i	$0.0444361\pi$
$524$	−4.66072			−0.203605
$525$		0			0
$526$	−23.2458			−1.01356
$527$	25.1881	−	25.1881i	1.09721	−	1.09721i
$528$		0			0
$529$			9.85471i			0.428466i
$530$	−6.30285	+	10.3221i	−0.273778	+	0.448365i
$531$		0			0
$532$	2.34049	+	2.34049i	0.101473	+	0.101473i
$533$	0.0268303	+	0.0268303i	0.00116215	+	0.00116215i
$534$		0			0
$535$	−6.05506	−	25.0456i	−0.261783	−	1.08281i
$536$		0			0
$537$		0			0
$538$	−0.868046	+	0.868046i	−0.0374241	+	0.0374241i
$539$	−9.81974			−0.422966
$540$		0			0
$541$	−39.5875			−1.70200			−0.850999	−	0.525167i	$-0.824003\pi$
$541$	−39.5875			−1.70200			−0.850999	+	0.525167i	$0.824003\pi$
$542$	19.2599	−	19.2599i	0.827284	−	0.827284i
$543$		0			0
$544$		−	6.34690i		−	0.272121i
$545$	−10.6864	−	6.52524i	−0.457753	−	0.279511i
$546$		0			0
$547$	8.19294	+	8.19294i	0.350305	+	0.350305i	0.860223	−	0.509918i	$-0.170324\pi$
$547$	8.19294	+	8.19294i	0.350305	+	0.350305i	−0.509918	+	0.860223i	$0.670324\pi$
$548$	7.89391	+	7.89391i	0.337211	+	0.337211i
$549$		0			0
$550$	3.79787	−	11.8164i	0.161942	−	0.503854i
$551$		−	4.04058i		−	0.172134i
$552$		0			0
$553$	−35.8975	+	35.8975i	−1.52652	+	1.52652i
$554$	−25.2516			−1.07284
$555$		0			0
$556$	−13.2018			−0.559881
$557$	8.41488	−	8.41488i	0.356550	−	0.356550i	−0.505990	−	0.862540i	$-0.668873\pi$
$557$	8.41488	−	8.41488i	0.356550	−	0.356550i	0.862540	+	0.505990i	$0.168873\pi$
$558$		0			0
$559$			0.827695i			0.0350078i
$560$	7.19403	−	1.73924i	0.304003	−	0.0734964i
$561$		0			0
$562$	1.43559	+	1.43559i	0.0605566	+	0.0605566i
$563$	1.10342	+	1.10342i	0.0465036	+	0.0465036i	0.729976	−	0.683473i	$-0.239531\pi$
$563$	1.10342	+	1.10342i	0.0465036	+	0.0465036i	−0.683473	+	0.729976i	$0.739531\pi$
$564$		0			0
$565$	−34.4801	+	8.33598i	−1.45059	+	0.350697i
$566$		−	3.89290i		−	0.163631i
$567$		0			0
$568$	5.97698	−	5.97698i	0.250788	−	0.250788i
$569$	30.4270			1.27557			0.637783	−	0.770217i	$-0.279852\pi$
$569$	30.4270			1.27557			0.637783	+	0.770217i	$0.279852\pi$
$570$		0			0
$571$	−2.44148			−0.102173			−0.0510864	−	0.998694i	$-0.516268\pi$
$571$	−2.44148			−0.102173			−0.0510864	+	0.998694i	$0.516268\pi$
$572$	0.266343	−	0.266343i	0.0111363	−	0.0111363i
$573$		0			0
$574$			0.827695i			0.0345473i
$575$	−8.76951	+	27.2849i	−0.365714	+	1.13786i
$576$		0			0
$577$	4.56598	+	4.56598i	0.190084	+	0.190084i	0.795732	−	0.605648i	$-0.207086\pi$
$577$	4.56598	+	4.56598i	0.190084	+	0.190084i	−0.605648	+	0.795732i	$0.707086\pi$
$578$	−16.4637	−	16.4637i	−0.684800	−	0.684800i
$579$		0			0
$580$	−7.71111	−	4.70852i	−0.320186	−	0.195511i
$581$		−	0.0222990i		−	0.000925117i
$582$		0			0
$583$	−9.49391	+	9.49391i	−0.393198	+	0.393198i
$584$	−7.87467			−0.325856
$585$		0			0
$586$	30.6528			1.26625
$587$	−16.5210	+	16.5210i	−0.681895	+	0.681895i	−0.960427	−	0.278532i	$-0.910152\pi$
$587$	−16.5210	+	16.5210i	−0.681895	+	0.681895i	0.278532	+	0.960427i	$0.410152\pi$
$588$		0			0
$589$		−	5.61241i		−	0.231255i
$590$	3.82456	+	15.8195i	0.157455	+	0.651280i
$591$		0			0
$592$	−0.107294	−	0.107294i	−0.00440977	−	0.00440977i
$593$	0.778495	+	0.778495i	0.0319689	+	0.0319689i	0.722911	−	0.690942i	$-0.242804\pi$
$593$	0.778495	+	0.778495i	0.0319689	+	0.0319689i	−0.690942	+	0.722911i	$0.742804\pi$
$594$		0			0
$595$	24.4808	−	40.0920i	1.00361	−	1.64361i
$596$			11.4660i			0.469664i
$597$		0			0
$598$	−0.615001	+	0.615001i	−0.0251493	+	0.0251493i
$599$	27.5622			1.12616			0.563081	−	0.826401i	$-0.309616\pi$
$599$	27.5622			1.12616			0.563081	+	0.826401i	$0.309616\pi$
$600$		0			0
$601$	−18.9758			−0.774037			−0.387019	−	0.922072i	$-0.626495\pi$
$601$	−18.9758			−0.774037			−0.387019	+	0.922072i	$0.626495\pi$
$602$	−12.7669	+	12.7669i	−0.520340	+	0.520340i
$603$		0			0
$604$		−	7.88724i		−	0.320927i
$605$	−5.63767	+	9.23278i	−0.229204	+	0.375366i
$606$		0			0
$607$	−9.89047	−	9.89047i	−0.401442	−	0.401442i	0.477299	−	0.878741i	$-0.341616\pi$
$607$	−9.89047	−	9.89047i	−0.401442	−	0.401442i	−0.878741	+	0.477299i	$0.841616\pi$
$608$	−0.707107	−	0.707107i	−0.0286770	−	0.0286770i
$609$		0			0
$610$	5.34950	+	22.1271i	0.216595	+	0.895901i
$611$			0.718399i			0.0290633i
$612$		0			0
$613$	−10.5506	+	10.5506i	−0.426134	+	0.426134i	−0.887309	−	0.461175i	$-0.847428\pi$
$613$	−10.5506	+	10.5506i	−0.426134	+	0.426134i	0.461175	+	0.887309i	$0.347428\pi$
$614$	−9.32246			−0.376224
$615$		0			0
$616$	8.21648			0.331052
$617$	−22.8595	+	22.8595i	−0.920290	+	0.920290i	−0.997050	−	0.0767599i	$-0.975543\pi$
$617$	−22.8595	+	22.8595i	−0.920290	+	0.920290i	0.0767599	+	0.997050i	$0.475543\pi$
$618$		0			0
$619$			36.6303i			1.47230i	0.676821	+	0.736148i	$0.263357\pi$
$619$			36.6303i			1.47230i	−0.676821	+	0.736148i	$0.736643\pi$
$620$	−10.7108	−	6.54018i	−0.430157	−	0.262660i
$621$		0			0
$622$	−16.7630	−	16.7630i	−0.672135	−	0.672135i
$623$	−18.4518	−	18.4518i	−0.739257	−	0.739257i
$624$		0			0
$625$	−14.5656	+	20.3185i	−0.582626	+	0.812741i
$626$			28.7893i			1.15065i
$627$		0			0
$628$	6.76844	−	6.76844i	0.270090	−	0.270090i
$629$	−0.963062			−0.0383998
$630$		0			0
$631$	40.8481			1.62614			0.813069	−	0.582167i	$-0.197795\pi$
$631$	40.8481			1.62614			0.813069	+	0.582167i	$0.197795\pi$
$632$	10.8453	−	10.8453i	0.431403	−	0.431403i
$633$		0			0
$634$			28.7605i			1.14223i
$635$	−29.2800	+	7.07879i	−1.16194	+	0.280913i
$636$		0			0
$637$	0.424437	+	0.424437i	0.0168168	+	0.0168168i
$638$	−7.09238	−	7.09238i	−0.280790	−	0.280790i
$639$		0			0
$640$	−2.17345	+	0.525458i	−0.0859132	+	0.0207705i
$641$			0.0715441i			0.00282582i	0.999999	+	0.00141291i	$0.000449744\pi$
$641$			0.0715441i			0.00282582i	−0.999999	+	0.00141291i	$0.999550\pi$
$642$		0			0
$643$	−1.02615	+	1.02615i	−0.0404676	+	0.0404676i	−0.727051	−	0.686583i	$-0.759110\pi$
$643$	−1.02615	+	1.02615i	−0.0404676	+	0.0404676i	0.686583	+	0.727051i	$0.259110\pi$
$644$	−18.9724			−0.747616
$645$		0			0
$646$	−6.34690			−0.249716
$647$	−17.8251	+	17.8251i	−0.700778	+	0.700778i	−0.964578	−	0.263800i	$-0.915024\pi$
$647$	−17.8251	+	17.8251i	−0.700778	+	0.700778i	0.263800	+	0.964578i	$0.415024\pi$
$648$		0			0
$649$			18.0679i			0.709226i
$650$	−0.674895	+	0.346585i	−0.0264716	+	0.0135942i
$651$		0			0
$652$	−3.78577	−	3.78577i	−0.148262	−	0.148262i
$653$	−24.0428	−	24.0428i	−0.940867	−	0.940867i	0.0574801	−	0.998347i	$-0.481693\pi$
$653$	−24.0428	−	24.0428i	−0.940867	−	0.940867i	−0.998347	+	0.0574801i	$0.981693\pi$
$654$		0			0
$655$	8.89460	+	5.43117i	0.347541	+	0.212214i
$656$		−	0.250062i		−	0.00976328i
$657$		0			0
$658$	−11.0811	+	11.0811i	−0.431985	+	0.431985i
$659$	47.4254			1.84743			0.923716	−	0.383077i	$-0.125136\pi$
$659$	47.4254			1.84743			0.923716	+	0.383077i	$0.125136\pi$
$660$		0			0
$661$	−15.3029			−0.595214			−0.297607	−	0.954688i	$-0.596188\pi$
$661$	−15.3029			−0.595214			−0.297607	+	0.954688i	$0.596188\pi$
$662$	−9.77948	+	9.77948i	−0.380090	+	0.380090i
$663$		0			0
$664$			0.00673693i			0.000261444i
$665$	−1.73924	−	7.19403i	−0.0674450	−	0.278973i
$666$		0			0
$667$	16.3767	+	16.3767i	0.634110	+	0.634110i
$668$	−10.3398	−	10.3398i	−0.400058	−	0.400058i
$669$		0			0
$670$		0			0
$671$			25.2719i			0.975612i
$672$		0			0
$673$	−12.2854	+	12.2854i	−0.473568	+	0.473568i	−0.903067	−	0.429499i	$-0.858690\pi$
$673$	−12.2854	+	12.2854i	−0.473568	+	0.473568i	0.429499	+	0.903067i	$0.358690\pi$
$674$	28.7441			1.10718
$675$		0			0
$676$	12.9770			0.499114
$677$	26.8800	−	26.8800i	1.03308	−	1.03308i	0.0336477	−	0.999434i	$-0.489288\pi$
$677$	26.8800	−	26.8800i	1.03308	−	1.03308i	0.999434	−	0.0336477i	$-0.0107124\pi$
$678$		0			0
$679$		−	24.3000i		−	0.932547i
$680$	−7.39610	+	12.1125i	−0.283627	+	0.464495i
$681$		0			0
$682$	−9.85140	−	9.85140i	−0.377230	−	0.377230i
$683$	−8.29913	−	8.29913i	−0.317557	−	0.317557i	0.530271	−	0.847828i	$-0.322090\pi$
$683$	−8.29913	−	8.29913i	−0.317557	−	0.317557i	−0.847828	+	0.530271i	$0.822090\pi$
$684$		0			0
$685$	−5.86604	−	24.2637i	−0.224130	−	0.927069i
$686$		−	10.0761i		−	0.384707i
$687$		0			0
$688$	3.85712	−	3.85712i	0.147051	−	0.147051i
$689$	0.820708			0.0312665
$690$		0			0
$691$	1.85848			0.0706998			0.0353499	−	0.999375i	$-0.488745\pi$
$691$	1.85848			0.0706998			0.0353499	+	0.999375i	$0.488745\pi$
$692$	−13.1428	+	13.1428i	−0.499616	+	0.499616i
$693$		0			0
$694$		−	2.35973i		−	0.0895739i
$695$	25.1945	+	15.3842i	0.955683	+	0.583554i
$696$		0			0
$697$	−1.12226	−	1.12226i	−0.0425088	−	0.0425088i
$698$	2.32928	+	2.32928i	0.0881644	+	0.0881644i
$699$		0			0
$700$	−15.7560	−	5.06406i	−0.595520	−	0.191404i
$701$			17.0065i			0.642325i	0.947024	+	0.321163i	$0.104074\pi$
$701$			17.0065i			0.642325i	−0.947024	+	0.321163i	$0.895926\pi$
$702$		0			0
$703$	−0.107294	+	0.107294i	−0.00404669	+	0.00404669i
$704$	−2.48235			−0.0935572
$705$		0			0
$706$	25.0823			0.943985
$707$	1.50218	−	1.50218i	0.0564954	−	0.0564954i
$708$		0			0
$709$			27.4933i			1.03253i	0.856428	+	0.516266i	$0.172678\pi$
$709$			27.4933i			1.03253i	−0.856428	+	0.516266i	$0.827322\pi$
$710$	−18.3716	+	4.44155i	−0.689473	+	0.166688i
$711$		0			0
$712$	5.57464	+	5.57464i	0.208918	+	0.208918i
$713$	22.7475	+	22.7475i	0.851900	+	0.851900i
$714$		0			0
$715$	−0.818664	+	0.197922i	−0.0306163	+	0.00740185i
$716$		−	19.0397i		−	0.711548i
$717$		0			0
$718$	−0.690938	+	0.690938i	−0.0257856	+	0.0257856i
$719$	−24.3240			−0.907131			−0.453566	−	0.891223i	$-0.649848\pi$
$719$	−24.3240			−0.907131			−0.453566	+	0.891223i	$0.649848\pi$
$720$		0			0
$721$	34.2242			1.27458
$722$	−0.707107	+	0.707107i	−0.0263158	+	0.0263158i
$723$		0			0
$724$			0.364567i			0.0135490i
$725$	9.22914	+	17.9716i	0.342762	+	0.667450i
$726$		0			0
$727$	19.7688	+	19.7688i	0.733184	+	0.733184i	0.971249	−	0.238065i	$-0.0765132\pi$
$727$	19.7688	+	19.7688i	0.733184	+	0.733184i	−0.238065	+	0.971249i	$0.576513\pi$
$728$	−0.355140	−	0.355140i	−0.0131624	−	0.0131624i
$729$		0			0
$730$	15.0282	+	9.17641i	0.556217	+	0.339634i
$731$		−	34.6210i		−	1.28051i
$732$		0			0
$733$	29.4875	−	29.4875i	1.08915	−	1.08915i	0.0935309	−	0.995616i	$-0.470185\pi$
$733$	29.4875	−	29.4875i	1.08915	−	1.08915i	0.995616	−	0.0935309i	$-0.0298154\pi$
$734$	−19.9521			−0.736444
$735$		0			0
$736$	5.73190			0.211281
$737$		0			0
$738$		0			0
$739$		−	35.9052i		−	1.32079i	−0.750917	−	0.660396i	$-0.770388\pi$
$739$		−	35.9052i		−	1.32079i	0.750917	−	0.660396i	$-0.229612\pi$
$740$	0.0797315	+	0.329794i	0.00293099	+	0.0121235i
$741$		0			0
$742$	12.6591	+	12.6591i	0.464731	+	0.464731i
$743$	−10.5627	−	10.5627i	−0.387510	−	0.387510i	0.486289	−	0.873798i	$-0.338350\pi$
$743$	−10.5627	−	10.5627i	−0.387510	−	0.387510i	−0.873798	+	0.486289i	$0.838350\pi$
$744$		0			0
$745$	13.3614	−	21.8818i	0.489523	−	0.801688i
$746$			28.9960i			1.06162i
$747$		0			0
$748$	−11.1406	+	11.1406i	−0.407342	+	0.407342i
$749$	−38.1420			−1.39368
$750$		0			0
$751$	32.2193			1.17570			0.587850	−	0.808970i	$-0.299975\pi$
$751$	32.2193			1.17570			0.587850	+	0.808970i	$0.299975\pi$
$752$	3.34779	−	3.34779i	0.122081	−	0.122081i
$753$		0			0
$754$			0.613106i			0.0223280i
$755$	−9.19107	+	15.0522i	−0.334497	+	0.547804i
$756$		0			0
$757$	−24.1074	−	24.1074i	−0.876198	−	0.876198i	0.116941	−	0.993139i	$-0.462691\pi$
$757$	−24.1074	−	24.1074i	−0.876198	−	0.876198i	−0.993139	+	0.116941i	$0.962691\pi$
$758$	−19.9200	−	19.9200i	−0.723528	−	0.723528i
$759$		0			0
$760$	0.525458	+	2.17345i	0.0190604	+	0.0788394i
$761$			26.0724i			0.945122i	0.881298	+	0.472561i	$0.156670\pi$
$761$			26.0724i			0.945122i	−0.881298	+	0.472561i	$0.843330\pi$
$762$		0			0
$763$	−13.1058	+	13.1058i	−0.474462	+	0.474462i
$764$	−11.3178			−0.409462
$765$		0			0
$766$	27.9186			1.00874
$767$	0.780946	−	0.780946i	0.0281983	−	0.0281983i
$768$		0			0
$769$			39.5504i			1.42622i	0.701050	+	0.713112i	$0.252715\pi$
$769$			39.5504i			1.42622i	−0.701050	+	0.713112i	$0.747285\pi$
$770$	−15.6805	−	9.57473i	−0.565085	−	0.345049i
$771$		0			0
$772$	11.7832	+	11.7832i	0.424086	+	0.424086i
$773$	−19.2419	−	19.2419i	−0.692083	−	0.692083i	0.270607	−	0.962690i	$-0.412776\pi$
$773$	−19.2419	−	19.2419i	−0.692083	−	0.692083i	−0.962690	+	0.270607i	$0.912776\pi$
$774$		0			0
$775$	12.8194	+	24.9628i	0.460486	+	0.896690i
$776$			7.34147i			0.263543i
$777$		0			0
$778$	26.4206	−	26.4206i	0.947225	−	0.947225i
$779$	−0.250062			−0.00895940
$780$		0			0
$781$	−20.9826			−0.750818
$782$	25.7244	−	25.7244i	0.919904	−	0.919904i
$783$		0			0
$784$		−	3.95582i		−	0.141279i
$785$	−20.8043	+	5.02969i	−0.742538	+	0.179517i
$786$		0			0
$787$	16.3492	+	16.3492i	0.582785	+	0.582785i	0.935668	−	0.352882i	$-0.114798\pi$
$787$	16.3492	+	16.3492i	0.582785	+	0.582785i	−0.352882	+	0.935668i	$0.614798\pi$
$788$	−0.772516	−	0.772516i	−0.0275197	−	0.0275197i
$789$		0			0
$790$	−33.3355	+	8.05925i	−1.18602	+	0.286735i
$791$			52.5099i			1.86704i
$792$		0			0
$793$	1.09233	−	1.09233i	0.0387896	−	0.0387896i
$794$	−24.1722			−0.857839
$795$		0			0
$796$	14.7828			0.523963
$797$	27.9196	−	27.9196i	0.988963	−	0.988963i	−0.0109771	−	0.999940i	$-0.503494\pi$
$797$	27.9196	−	27.9196i	0.988963	−	0.988963i	0.999940	+	0.0109771i	$0.00349420\pi$
$798$		0			0
$799$		−	30.0494i		−	1.06307i
$800$	4.76017	+	1.52995i	0.168298	+	0.0540918i
$801$		0			0
$802$	−11.2582	−	11.2582i	−0.397542	−	0.397542i
$803$	13.8223	+	13.8223i	0.487779	+	0.487779i
$804$		0			0
$805$	36.2072	+	22.1086i	1.27614	+	0.779227i
$806$			0.851611i			0.0299967i
$807$		0			0
$808$	−0.453837	+	0.453837i	−0.0159659	+	0.0159659i
$809$	32.2712			1.13459			0.567297	−	0.823513i	$-0.307989\pi$
$809$	32.2712			1.13459			0.567297	+	0.823513i	$0.307989\pi$
$810$		0			0
$811$	2.47485			0.0869039			0.0434519	−	0.999056i	$-0.486164\pi$
$811$	2.47485			0.0869039			0.0434519	+	0.999056i	$0.486164\pi$
$812$	−9.45695	+	9.45695i	−0.331874	+	0.331874i
$813$		0			0
$814$			0.376665i			0.0132021i
$815$	2.81324	+	11.6364i	0.0985436	+	0.407606i
$816$		0			0
$817$	−3.85712	−	3.85712i	−0.134944	−	0.134944i
$818$	27.0540	+	27.0540i	0.945922	+	0.945922i
$819$		0			0
$820$	−0.291399	+	0.477223i	−0.0101761	+	0.0166653i
$821$			53.2663i			1.85901i	0.368812	+	0.929504i	$0.379765\pi$
$821$			53.2663i			1.85901i	−0.368812	+	0.929504i	$0.620235\pi$
$822$		0			0
$823$	−21.8689	+	21.8689i	−0.762302	+	0.762302i	−0.976738	−	0.214436i	$-0.931209\pi$
$823$	−21.8689	+	21.8689i	−0.762302	+	0.762302i	0.214436	+	0.976738i	$0.431209\pi$
$824$	−10.3398			−0.360203
$825$		0			0
$826$	24.0916			0.838255
$827$	25.0863	−	25.0863i	0.872335	−	0.872335i	−0.120391	−	0.992727i	$-0.538415\pi$
$827$	25.0863	−	25.0863i	0.872335	−	0.872335i	0.992727	+	0.120391i	$0.0384149\pi$
$828$		0			0
$829$		−	28.5272i		−	0.990791i	−0.868668	−	0.495395i	$-0.835023\pi$
$829$		−	28.5272i		−	0.990791i	0.868668	−	0.495395i	$-0.164977\pi$
$830$	0.00785060	−	0.0128569i	0.000272498	−	0.000446269i
$831$		0			0
$832$	0.107294	+	0.107294i	0.00371976	+	0.00371976i
$833$	−17.7535	−	17.7535i	−0.615122	−	0.615122i
$834$		0			0
$835$	7.68358	+	31.7816i	0.265901	+	1.09985i
$836$			2.48235i			0.0858540i
$837$		0			0
$838$	11.9841	−	11.9841i	0.413983	−	0.413983i
$839$	41.8793			1.44583			0.722917	−	0.690935i	$-0.242801\pi$
$839$	41.8793			1.44583			0.722917	+	0.690935i	$0.242801\pi$
$840$		0			0
$841$	−12.6737			−0.437025
$842$	−18.1166	+	18.1166i	−0.624340	+	0.624340i
$843$		0			0
$844$		−	4.43055i		−	0.152506i
$845$	−24.7655	−	15.1222i	−0.851959	−	0.520219i
$846$		0			0
$847$	11.3231	+	11.3231i	0.389067	+	0.389067i
$848$	−3.82456	−	3.82456i	−0.131336	−	0.131336i
$849$		0			0
$850$	28.2297	−	14.4971i	0.968270	−	0.497245i
$851$		−	0.869743i		−	0.0298144i
$852$		0			0
$853$	−5.31646	+	5.31646i	−0.182032	+	0.182032i	−0.792241	−	0.610209i	$-0.791086\pi$
$853$	−5.31646	+	5.31646i	−0.182032	+	0.182032i	0.610209	+	0.792241i	$0.291086\pi$
$854$	33.6975			1.15310
$855$		0			0
$856$	11.5234			0.393862
$857$	−38.1661	+	38.1661i	−1.30373	+	1.30373i	−0.377873	+	0.925858i	$0.623344\pi$
$857$	−38.1661	+	38.1661i	−1.30373	+	1.30373i	−0.925858	+	0.377873i	$0.876656\pi$
$858$		0			0
$859$		−	13.3449i		−	0.455321i	−0.973741	−	0.227660i	$-0.926892\pi$
$859$		−	13.3449i		−	0.455321i	0.973741	−	0.227660i	$-0.0731076\pi$
$860$	−11.8557	+	2.86626i	−0.404277	+	0.0977388i
$861$		0			0
$862$	−26.3062	−	26.3062i	−0.895993	−	0.895993i
$863$	−21.0034	−	21.0034i	−0.714965	−	0.714965i	0.252605	−	0.967570i	$-0.418713\pi$
$863$	−21.0034	−	21.0034i	−0.714965	−	0.714965i	−0.967570	+	0.252605i	$0.918713\pi$
$864$		0			0
$865$	40.3975	−	9.76658i	1.37356	−	0.332074i
$866$			12.5535i			0.426586i
$867$		0			0
$868$	−13.1358	+	13.1358i	−0.445858	+	0.445858i
$869$	−38.0733			−1.29155
$870$		0			0
$871$		0			0
$872$	3.95951	−	3.95951i	0.134086	−	0.134086i
$873$		0			0
$874$		−	5.73190i		−	0.193885i
$875$	24.1678	+	28.0249i	0.817020	+	0.947415i
$876$		0			0
$877$	28.8550	+	28.8550i	0.974364	+	0.974364i	0.999680	−	0.0253157i	$-0.00805910\pi$
$877$	28.8550	+	28.8550i	0.974364	+	0.974364i	−0.0253157	+	0.999680i	$0.508059\pi$
$878$	1.03924	+	1.03924i	0.0350728	+	0.0350728i
$879$		0			0
$880$	4.73737	+	2.89271i	0.159697	+	0.0975131i
$881$		−	13.6670i		−	0.460454i	−0.973137	−	0.230227i	$-0.926053\pi$
$881$		−	13.6670i		−	0.460454i	0.973137	−	0.230227i	$-0.0739468\pi$
$882$		0			0
$883$	−20.8357	+	20.8357i	−0.701177	+	0.701177i	−0.964663	−	0.263486i	$-0.915128\pi$
$883$	−20.8357	+	20.8357i	−0.701177	+	0.701177i	0.263486	+	0.964663i	$0.415128\pi$
$884$	0.963062			0.0323913
$885$		0			0
$886$	−0.911863			−0.0306347
$887$	−4.77598	+	4.77598i	−0.160362	+	0.160362i	−0.782727	−	0.622365i	$-0.786172\pi$
$887$	−4.77598	+	4.77598i	−0.160362	+	0.160362i	0.622365	+	0.782727i	$0.286172\pi$
$888$		0			0
$889$			44.5907i			1.49552i
$890$	−4.14257	−	17.1349i	−0.138859	−	0.574364i
$891$		0			0
$892$	9.76490	+	9.76490i	0.326953	+	0.326953i
$893$	−3.34779	−	3.34779i	−0.112030	−	0.112030i
$894$		0			0
$895$	−22.1871	+	36.3357i	−0.741634	+	1.21457i
$896$			3.30996i			0.110578i
$897$		0			0
$898$	−7.91546	+	7.91546i	−0.264142	+	0.264142i
$899$	22.6774			0.756333
$900$		0			0
$901$	−34.3288			−1.14366
$902$	−0.438931	+	0.438931i	−0.0146148	+	0.0146148i
$903$		0			0
$904$		−	15.8642i		−	0.527636i
$905$	0.424833	−	0.695746i	0.0141219	−	0.0231274i
$906$		0			0
$907$	16.2953	+	16.2953i	0.541076	+	0.541076i	0.923844	−	0.382768i	$-0.125029\pi$
$907$	16.2953	+	16.2953i	0.541076	+	0.541076i	−0.382768	+	0.923844i	$0.625029\pi$
$908$	15.6881	+	15.6881i	0.520629	+	0.520629i
$909$		0			0
$910$	0.263908	+	1.09160i	0.00874846	+	0.0361863i
$911$			34.4249i			1.14055i	0.821455	+	0.570273i	$0.193163\pi$
$911$			34.4249i			1.14055i	−0.821455	+	0.570273i	$0.806837\pi$
$912$		0			0
$913$	0.0118253	−	0.0118253i	0.000391359	−	0.000391359i
$914$	8.88574			0.293914
$915$		0			0
$916$	−23.9430			−0.791100
$917$	10.9084	−	10.9084i	0.360227	−	0.360227i
$918$		0			0
$919$			8.94023i			0.294911i	0.989069	+	0.147455i	$0.0471083\pi$
$919$			8.94023i			0.294911i	−0.989069	+	0.147455i	$0.952892\pi$
$920$	−10.9389	−	6.67943i	−0.360644	−	0.220214i
$921$		0			0
$922$	−21.8200	−	21.8200i	−0.718603	−	0.718603i
$923$	0.906930	+	0.906930i	0.0298520	+	0.0298520i
$924$		0			0
$925$	0.232150	−	0.722296i	0.00763305	−	0.0237489i
$926$			18.6348i			0.612379i
$927$		0			0
$928$	2.85712	−	2.85712i	0.0937896	−	0.0937896i
$929$	−31.6023			−1.03684			−0.518419	−	0.855127i	$-0.673479\pi$
$929$	−31.6023			−1.03684			−0.518419	+	0.855127i	$0.673479\pi$
$930$		0			0
$931$	−3.95582			−0.129647
$932$	13.0996	−	13.0996i	0.429092	−	0.429092i
$933$		0			0
$934$			8.92534i			0.292046i
$935$	34.2433	−	8.27872i	1.11988	−	0.270743i
$936$		0			0
$937$	29.7784	+	29.7784i	0.972817	+	0.972817i	0.999640	−	0.0268237i	$-0.00853926\pi$
$937$	29.7784	+	29.7784i	0.972817	+	0.972817i	−0.0268237	+	0.999640i	$0.508539\pi$
$938$		0			0
$939$		0			0
$940$	−10.2902	+	2.48778i	−0.335629	+	0.0811424i
$941$			20.9352i			0.682469i	0.939978	+	0.341234i	$0.110845\pi$
$941$			20.9352i			0.682469i	−0.939978	+	0.341234i	$0.889155\pi$
$942$		0			0
$943$	1.01352	−	1.01352i	0.0330047	−	0.0330047i
$944$	−7.27853			−0.236896
$945$		0			0
$946$	−13.5407			−0.440247
$947$	−10.6944	+	10.6944i	−0.347522	+	0.347522i	−0.859186	−	0.511664i	$-0.829029\pi$
$947$	−10.6944	+	10.6944i	−0.347522	+	0.347522i	0.511664	+	0.859186i	$0.329029\pi$
$948$		0			0
$949$		−	1.19488i		−	0.0387874i
$950$	1.52995	−	4.76017i	0.0496381	−	0.154440i
$951$		0			0
$952$	14.8549	+	14.8549i	0.481450	+	0.481450i
$953$	15.6764	+	15.6764i	0.507809	+	0.507809i	0.913853	−	0.406045i	$-0.133092\pi$
$953$	15.6764	+	15.6764i	0.507809	+	0.507809i	−0.406045	+	0.913853i	$0.633092\pi$
$954$		0			0
$955$	21.5990	+	13.1887i	0.698928	+	0.426776i
$956$		−	20.4712i		−	0.662087i
$957$		0			0
$958$	28.7095	−	28.7095i	0.927562	−	0.927562i
$959$	−36.9513			−1.19322
$960$		0			0
$961$	0.499132			0.0161010
$962$	0.0162806	−	0.0162806i	0.000524906	−	0.000524906i
$963$		0			0
$964$		−	7.39592i		−	0.238207i
$965$	−8.75619	−	36.2183i	−0.281872	−	1.16591i
$966$		0			0
$967$	−25.7922	−	25.7922i	−0.829421	−	0.829421i	0.158015	−	0.987437i	$-0.449490\pi$
$967$	−25.7922	−	25.7922i	−0.829421	−	0.829421i	−0.987437	+	0.158015i	$0.949490\pi$
$968$	−3.42093	−	3.42093i	−0.109953	−	0.109953i
$969$		0			0
$970$	8.55507	−	14.0106i	0.274687	−	0.449853i
$971$		−	16.6081i		−	0.532979i	−0.963838	−	0.266489i	$-0.914136\pi$
$971$		−	16.6081i		−	0.532979i	0.963838	−	0.266489i	$-0.0858638\pi$
$972$		0			0
$973$	30.8987	−	30.8987i	0.990567	−	0.990567i
$974$	30.1252			0.965275
$975$		0			0
$976$	−10.1806			−0.325874
$977$	−19.4710	+	19.4710i	−0.622934	+	0.622934i	−0.946281	−	0.323347i	$-0.895192\pi$
$977$	−19.4710	+	19.4710i	−0.622934	+	0.622934i	0.323347	+	0.946281i	$0.395192\pi$
$978$		0			0
$979$		−	19.5702i		−	0.625467i
$980$	−4.60975	+	7.54936i	−0.147253	+	0.241155i
$981$		0			0
$982$	−28.4506	−	28.4506i	−0.907897	−	0.907897i
$983$	−17.5775	−	17.5775i	−0.560636	−	0.560636i	0.368852	−	0.929488i	$-0.379751\pi$
$983$	−17.5775	−	17.5775i	−0.560636	−	0.560636i	−0.929488	+	0.368852i	$0.879751\pi$
$984$		0			0
$985$	0.574064	+	2.37450i	0.0182912	+	0.0756579i
$986$		−	25.6452i		−	0.816708i
$987$		0			0
$988$	0.107294	−	0.107294i	0.00341349	−	0.00341349i
$989$	31.2663			0.994212
$990$		0			0
$991$	28.8400			0.916132			0.458066	−	0.888918i	$-0.348542\pi$
$991$	28.8400			0.916132			0.458066	+	0.888918i	$0.348542\pi$
$992$	3.96857	−	3.96857i	0.126002	−	0.126002i
$993$		0			0
$994$			27.9781i			0.887413i
$995$	−28.2118	−	17.2265i	−0.894374	−	0.546118i
$996$		0			0
$997$	−24.0560	−	24.0560i	−0.761860	−	0.761860i	0.214798	−	0.976658i	$-0.431091\pi$
$997$	−24.0560	−	24.0560i	−0.761860	−	0.761860i	−0.976658	+	0.214798i	$0.931091\pi$
$998$	14.2386	+	14.2386i	0.450716	+	0.450716i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.n.i.647.7	yes	20
3.2	odd	2	inner	1710.2.n.i.647.4	✓	20
5.3	odd	4	inner	1710.2.n.i.1673.4	yes	20
15.8	even	4	inner	1710.2.n.i.1673.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1710.2.n.i.647.4	✓	20	3.2	odd	2	inner
1710.2.n.i.647.7	yes	20	1.1	even	1	trivial
1710.2.n.i.1673.4	yes	20	5.3	odd	4	inner
1710.2.n.i.1673.7	yes	20	15.8	even	4	inner

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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.16531 + 1.90842i) q^{5} +(2.34049 + 2.34049i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.525458 + 2.17345i) q^{10} +2.48235i q^{11} +(0.107294 - 0.107294i) q^{13} +3.30996 q^{14} -1.00000 q^{16} +(-4.48794 + 4.48794i) q^{17} +1.00000i q^{19} +(1.90842 + 1.16531i) q^{20} +(1.75529 + 1.75529i) q^{22} +(-4.05307 - 4.05307i) q^{23} +(-2.28411 - 4.44779i) q^{25} -0.151737i q^{26} +(2.34049 - 2.34049i) q^{28} -4.04058 q^{29} -5.61241 q^{31} +(-0.707107 + 0.707107i) q^{32} +6.34690i q^{34} +(-7.19403 + 1.73924i) q^{35} +(0.107294 + 0.107294i) q^{37} +(0.707107 + 0.707107i) q^{38} +(2.17345 - 0.525458i) q^{40} +0.250062i q^{41} +(-3.85712 + 3.85712i) q^{43} +2.48235 q^{44} -5.73190 q^{46} +(-3.34779 + 3.34779i) q^{47} +3.95582i q^{49} +(-4.76017 - 1.52995i) q^{50} +(-0.107294 - 0.107294i) q^{52} +(3.82456 + 3.82456i) q^{53} +(-4.73737 - 2.89271i) q^{55} -3.30996i q^{56} +(-2.85712 + 2.85712i) q^{58} +7.27853 q^{59} +10.1806 q^{61} +(-3.96857 + 3.96857i) q^{62} +1.00000i q^{64} +(0.0797315 + 0.329794i) q^{65} +(4.48794 + 4.48794i) q^{68} +(-3.85712 + 6.31678i) q^{70} +8.45272i q^{71} +(5.56823 - 5.56823i) q^{73} +0.151737 q^{74} +1.00000 q^{76} +(-5.80993 + 5.80993i) q^{77} +15.3376i q^{79} +(1.16531 - 1.90842i) q^{80} +(0.176821 + 0.176821i) q^{82} +(-0.00476373 - 0.00476373i) q^{83} +(-3.33503 - 13.7947i) q^{85} +5.45479i q^{86} +(1.75529 - 1.75529i) q^{88} -7.88373 q^{89} +0.502244 q^{91} +(-4.05307 + 4.05307i) q^{92} +4.73450i q^{94} +(-1.90842 - 1.16531i) q^{95} +(-5.19120 - 5.19120i) q^{97} +(2.79719 + 2.79719i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{10} - 12 q^{13} - 20 q^{16} - 16 q^{22} + 16 q^{31} - 12 q^{37} - 8 q^{46} + 12 q^{52} + 20 q^{58} - 16 q^{61} + 20 q^{73} + 20 q^{76} - 28 q^{82} - 8 q^{85} - 16 q^{88} + 32 q^{91} - 20 q^{97}+O(q^{100}) \) 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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