LMFDB - Embedded newform 1710.2.p.d.1063.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(37,1710)]

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([0, 1, 2]))

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

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

chi := DirichletCharacter("1710.37");

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.p (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} + 153x^{16} + 6416x^{12} + 78648x^{8} + 19120x^{4} + 16 $ x^20 + 153x^16 + 6416x^12 + 78648x^8 + 19120x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1063.1
Root			$0.498616 + 0.498616i$ of defining polynomial
Character	$\chi$	$=$	1710.1063
Dual form			1710.2.p.d.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-1.89390 - 1.18875i) q^{5} +(0.705149 - 0.705149i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-1.89390 - 1.18875i) q^{5} +(0.705149 - 0.705149i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.498616 + 2.17977i) q^{10} -1.32903 q^{11} +(-0.741383 + 0.741383i) q^{13} -0.997232 q^{14} -1.00000 q^{16} +(-2.17373 + 2.17373i) q^{17} +(0.939768 + 4.25639i) q^{19} +(1.18875 - 1.89390i) q^{20} +(0.939768 + 0.939768i) q^{22} +(1.08266 + 1.08266i) q^{23} +(2.17373 + 4.50276i) q^{25} +1.04847 q^{26} +(0.705149 + 0.705149i) q^{28} +5.95089 q^{29} -5.95089i q^{31} +(0.707107 + 0.707107i) q^{32} +3.07412 q^{34} +(-2.17373 + 0.497236i) q^{35} +(-1.33551 - 1.33551i) q^{37} +(2.34520 - 3.67424i) q^{38} +(-2.17977 + 0.498616i) q^{40} -0.531910i q^{41} +(1.53142 + 1.53142i) q^{43} -1.32903i q^{44} -1.53111i q^{46} +(-4.13113 + 4.13113i) q^{47} +6.00553i q^{49} +(1.64687 - 4.72100i) q^{50} +(-0.741383 - 0.741383i) q^{52} +(5.48557 - 5.48557i) q^{53} +(2.51706 + 1.57989i) q^{55} -0.997232i q^{56} +(-4.20791 - 4.20791i) q^{58} +3.53944 q^{59} +3.41030 q^{61} +(-4.20791 + 4.20791i) q^{62} -1.00000i q^{64} +(2.28543 - 0.522786i) q^{65} +(-1.99446 - 1.99446i) q^{67} +(-2.17373 - 2.17373i) q^{68} +(1.88866 + 1.18546i) q^{70} +8.71907i q^{71} +(-5.83628 - 5.83628i) q^{73} +1.88869i q^{74} +(-4.25639 + 0.939768i) q^{76} +(-0.937166 + 0.937166i) q^{77} +9.31319 q^{79} +(1.89390 + 1.18875i) q^{80} +(-0.376117 + 0.376117i) q^{82} +(9.50276 + 9.50276i) q^{83} +(6.70087 - 1.53281i) q^{85} -2.16575i q^{86} +(-0.939768 + 0.939768i) q^{88} +16.7874 q^{89} +1.04557i q^{91} +(-1.08266 + 1.08266i) q^{92} +5.84230 q^{94} +(3.27997 - 9.17833i) q^{95} +(1.11691 + 1.11691i) q^{97} +(4.24655 - 4.24655i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{5} - 4 q^{7}+O(q^{10}) $ 20 * q + 4 * q^5 - 4 * q^7	$ 20 q + 4 q^{5} - 4 q^{7} + 8 q^{11} - 20 q^{16} - 4 q^{17} - 44 q^{23} + 4 q^{25} + 8 q^{26} - 4 q^{28} - 4 q^{35} + 4 q^{38} + 52 q^{43} - 4 q^{47} + 16 q^{55} + 8 q^{58} + 32 q^{61} + 8 q^{62} - 4 q^{68} - 20 q^{73} + 20 q^{76} + 24 q^{77} - 4 q^{80} - 24 q^{82} + 116 q^{83} - 60 q^{85} + 44 q^{92} + 32 q^{95}+O(q^{100}) $ 20 * q + 4 * q^5 - 4 * q^7 + 8 * q^11 - 20 * q^16 - 4 * q^17 - 44 * q^23 + 4 * q^25 + 8 * q^26 - 4 * q^28 - 4 * q^35 + 4 * q^38 + 52 * q^43 - 4 * q^47 + 16 * q^55 + 8 * q^58 + 32 * q^61 + 8 * q^62 - 4 * q^68 - 20 * q^73 + 20 * q^76 + 24 * q^77 - 4 * q^80 - 24 * q^82 + 116 * q^83 - 60 * q^85 + 44 * q^92 + 32 * q^95

Display 100 coefficients 10 coefficients

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
$5$	−1.89390	−	1.18875i	−0.846979	−	0.531627i
$5$	−1.89390	−	1.18875i	−0.846979	−	0.531627i
$6$		0			0
$7$	0.705149	−	0.705149i	0.266521	−	0.266521i	−0.561175	−	0.827697i	$-0.689651\pi$
$7$	0.705149	−	0.705149i	0.266521	−	0.266521i	0.827697	+	0.561175i	$0.189651\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	0.498616	+	2.17977i	0.157676	+	0.689303i
$11$	−1.32903			−0.400718			−0.200359	−	0.979723i	$-0.564211\pi$
$11$	−1.32903			−0.400718			−0.200359	+	0.979723i	$0.564211\pi$
$12$		0			0
$13$	−0.741383	+	0.741383i	−0.205623	+	0.205623i	−0.802404	−	0.596781i	$-0.796446\pi$
$13$	−0.741383	+	0.741383i	−0.205623	+	0.205623i	0.596781	+	0.802404i	$0.296446\pi$
$14$	−0.997232			−0.266521
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−2.17373	+	2.17373i	−0.527208	+	0.527208i	−0.919739	−	0.392531i	$-0.871600\pi$
$17$	−2.17373	+	2.17373i	−0.527208	+	0.527208i	0.392531	+	0.919739i	$0.371600\pi$
$18$		0			0
$19$	0.939768	+	4.25639i	0.215597	+	0.976482i
$19$	0.939768	+	4.25639i	0.215597	+	0.976482i
$20$	1.18875	−	1.89390i	0.265813	−	0.423489i
$21$		0			0
$22$	0.939768	+	0.939768i	0.200359	+	0.200359i
$23$	1.08266	+	1.08266i	0.225749	+	0.225749i	0.810914	−	0.585165i	$-0.198970\pi$
$23$	1.08266	+	1.08266i	0.225749	+	0.225749i	−0.585165	+	0.810914i	$0.698970\pi$
$24$		0			0
$25$	2.17373	+	4.50276i	0.434746	+	0.900553i
$26$	1.04847			0.205623
$27$		0			0
$28$	0.705149	+	0.705149i	0.133261	+	0.133261i
$29$	5.95089			1.10505			0.552526	−	0.833496i	$-0.313664\pi$
$29$	5.95089			1.10505			0.552526	+	0.833496i	$0.313664\pi$
$30$		0			0
$31$		−	5.95089i		−	1.06881i	−0.845228	−	0.534406i	$-0.820536\pi$
$31$		−	5.95089i		−	1.06881i	0.845228	−	0.534406i	$-0.179464\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	3.07412			0.527208
$35$	−2.17373	+	0.497236i	−0.367428	+	0.0840481i
$36$		0			0
$37$	−1.33551	−	1.33551i	−0.219556	−	0.219556i	0.588755	−	0.808311i	$-0.299618\pi$
$37$	−1.33551	−	1.33551i	−0.219556	−	0.219556i	−0.808311	+	0.588755i	$0.799618\pi$
$38$	2.34520	−	3.67424i	0.380442	−	0.596040i
$39$		0			0
$40$	−2.17977	+	0.498616i	−0.344651	+	0.0788381i
$41$		−	0.531910i		−	0.0830704i	−0.999137	−	0.0415352i	$-0.986775\pi$
$41$		−	0.531910i		−	0.0830704i	0.999137	−	0.0415352i	$-0.0132249\pi$
$42$		0			0
$43$	1.53142	+	1.53142i	0.233539	+	0.233539i	0.814168	−	0.580629i	$-0.197193\pi$
$43$	1.53142	+	1.53142i	0.233539	+	0.233539i	−0.580629	+	0.814168i	$0.697193\pi$
$44$		−	1.32903i		−	0.200359i
$45$		0			0
$46$		−	1.53111i		−	0.225749i
$47$	−4.13113	+	4.13113i	−0.602587	+	0.602587i	−0.940998	−	0.338411i	$-0.890111\pi$
$47$	−4.13113	+	4.13113i	−0.602587	+	0.602587i	0.338411	+	0.940998i	$0.390111\pi$
$48$		0			0
$49$			6.00553i			0.857933i
$50$	1.64687	−	4.72100i	0.232903	−	0.667650i
$51$		0			0
$52$	−0.741383	−	0.741383i	−0.102811	−	0.102811i
$53$	5.48557	−	5.48557i	0.753501	−	0.753501i	−0.221630	−	0.975131i	$-0.571138\pi$
$53$	5.48557	−	5.48557i	0.753501	−	0.753501i	0.975131	+	0.221630i	$0.0711378\pi$
$54$		0			0
$55$	2.51706	+	1.57989i	0.339400	+	0.213032i
$56$		−	0.997232i		−	0.133261i
$57$		0			0
$58$	−4.20791	−	4.20791i	−0.552526	−	0.552526i
$59$	3.53944			0.460796			0.230398	−	0.973096i	$-0.425997\pi$
$59$	3.53944			0.460796			0.230398	+	0.973096i	$0.425997\pi$
$60$		0			0
$61$	3.41030			0.436644			0.218322	−	0.975877i	$-0.429942\pi$
$61$	3.41030			0.436644			0.218322	+	0.975877i	$0.429942\pi$
$62$	−4.20791	+	4.20791i	−0.534406	+	0.534406i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	2.28543	−	0.522786i	0.283473	−	0.0648436i
$66$		0			0
$67$	−1.99446	−	1.99446i	−0.243662	−	0.243662i	0.574701	−	0.818363i	$-0.305118\pi$
$67$	−1.99446	−	1.99446i	−0.243662	−	0.243662i	−0.818363	+	0.574701i	$0.805118\pi$
$68$	−2.17373	−	2.17373i	−0.263604	−	0.263604i
$69$		0			0
$70$	1.88866	+	1.18546i	0.225738	+	0.141690i
$71$			8.71907i			1.03476i	0.855755	+	0.517381i	$0.173093\pi$
$71$			8.71907i			1.03476i	−0.855755	+	0.517381i	$0.826907\pi$
$72$		0			0
$73$	−5.83628	−	5.83628i	−0.683085	−	0.683085i	0.277609	−	0.960694i	$-0.410458\pi$
$73$	−5.83628	−	5.83628i	−0.683085	−	0.683085i	−0.960694	+	0.277609i	$0.910458\pi$
$74$			1.88869i			0.219556i
$75$		0			0
$76$	−4.25639	+	0.939768i	−0.488241	+	0.107799i
$77$	−0.937166	+	0.937166i	−0.106800	+	0.106800i
$78$		0			0
$79$	9.31319			1.04782			0.523908	−	0.851775i	$-0.324474\pi$
$79$	9.31319			1.04782			0.523908	+	0.851775i	$0.324474\pi$
$80$	1.89390	+	1.18875i	0.211745	+	0.132907i
$81$		0			0
$82$	−0.376117	+	0.376117i	−0.0415352	+	0.0415352i
$83$	9.50276	+	9.50276i	1.04306	+	1.04306i	0.999030	+	0.0440339i	$0.0140209\pi$
$83$	9.50276	+	9.50276i	1.04306	+	1.04306i	0.0440339	+	0.999030i	$0.485979\pi$
$84$		0			0
$85$	6.70087	−	1.53281i	0.726811	−	0.166256i
$86$		−	2.16575i		−	0.233539i
$87$		0			0
$88$	−0.939768	+	0.939768i	−0.100180	+	0.100180i
$89$	16.7874			1.77946			0.889729	−	0.456490i	$-0.150894\pi$
$89$	16.7874			1.77946			0.889729	+	0.456490i	$0.150894\pi$
$90$		0			0
$91$			1.04557i			0.109606i
$92$	−1.08266	+	1.08266i	−0.112875	+	0.112875i
$93$		0			0
$94$	5.84230			0.602587
$95$	3.27997	−	9.17833i	0.336517	−	0.941677i
$96$		0			0
$97$	1.11691	+	1.11691i	0.113405	+	0.113405i	0.761532	−	0.648127i	$-0.224447\pi$
$97$	1.11691	+	1.11691i	0.113405	+	0.113405i	−0.648127	+	0.761532i	$0.724447\pi$
$98$	4.24655	−	4.24655i	0.428966	−	0.428966i
$99$		0			0
$100$	−4.50276	+	2.17373i	−0.450276	+	0.217373i
$101$	15.7109			1.56329			0.781645	−	0.623723i	$-0.214381\pi$
$101$	15.7109			1.56329			0.781645	+	0.623723i	$0.214381\pi$
$102$		0			0
$103$	10.7950	−	10.7950i	1.06367	−	1.06367i	0.0658345	−	0.997831i	$-0.479029\pi$
$103$	10.7950	−	10.7950i	1.06367	−	1.06367i	0.997831	−	0.0658345i	$-0.0209710\pi$
$104$			1.04847i			0.102811i
$105$		0			0
$106$	−7.75776			−0.753501
$107$	2.65129	+	2.65129i	0.256309	+	0.256309i	0.823551	−	0.567242i	$-0.191990\pi$
$107$	2.65129	+	2.65129i	0.256309	+	0.256309i	−0.567242	+	0.823551i	$0.691990\pi$
$108$		0			0
$109$	−5.83596			−0.558984			−0.279492	−	0.960148i	$-0.590166\pi$
$109$	−5.83596			−0.558984			−0.279492	+	0.960148i	$0.590166\pi$
$110$	−0.662676	−	2.89698i	−0.0631837	−	0.276216i
$111$		0			0
$112$	−0.705149	+	0.705149i	−0.0666303	+	0.0666303i
$113$	0.463357	−	0.463357i	0.0435890	−	0.0435890i	−0.684976	−	0.728565i	$-0.740187\pi$
$113$	0.463357	−	0.463357i	0.0435890	−	0.0435890i	0.728565	+	0.684976i	$0.240187\pi$
$114$		0			0
$115$	−0.763434	−	3.33745i	−0.0711906	−	0.311219i
$116$			5.95089i			0.552526i
$117$		0			0
$118$	−2.50276	−	2.50276i	−0.230398	−	0.230398i
$119$			3.06561i			0.281024i
$120$		0			0
$121$	−9.23367			−0.839425
$122$	−2.41145	−	2.41145i	−0.218322	−	0.218322i
$123$		0			0
$124$	5.95089			0.534406
$125$	1.23584	−	11.1118i	0.110537	−	0.993872i
$126$		0			0
$127$	7.75499	+	7.75499i	0.688144	+	0.688144i	0.961821	−	0.273678i	$-0.0882402\pi$
$127$	7.75499	+	7.75499i	0.688144	+	0.688144i	−0.273678	+	0.961821i	$0.588240\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	−1.98571	−	1.24638i	−0.174158	−	0.109314i
$131$	13.2521			1.15784			0.578921	−	0.815384i	$-0.303474\pi$
$131$	13.2521			1.15784			0.578921	+	0.815384i	$0.303474\pi$
$132$		0			0
$133$	3.66407	+	2.33871i	0.317715	+	0.202792i
$134$			2.82060i			0.243662i
$135$		0			0
$136$			3.07412i			0.263604i
$137$	−4.42031	+	4.42031i	−0.377653	+	0.377653i	−0.870255	−	0.492602i	$-0.836046\pi$
$137$	−4.42031	+	4.42031i	−0.377653	+	0.377653i	0.492602	+	0.870255i	$0.336046\pi$
$138$		0			0
$139$			2.68665i			0.227879i	0.993488	+	0.113939i	$0.0363469\pi$
$139$			2.68665i			0.227879i	−0.993488	+	0.113939i	$0.963653\pi$
$140$	−0.497236	−	2.17373i	−0.0420241	−	0.183714i
$141$		0			0
$142$	6.16531	−	6.16531i	0.517381	−	0.517381i
$143$	0.985322	−	0.985322i	0.0823968	−	0.0823968i
$144$		0			0
$145$	−11.2704	−	7.07414i	−0.935956	−	0.587475i
$146$			8.25374i			0.683085i
$147$		0			0
$148$	1.33551	−	1.33551i	0.109778	−	0.109778i
$149$			14.1380i			1.15823i	0.815244	+	0.579117i	$0.196603\pi$
$149$			14.1380i			1.15823i	−0.815244	+	0.579117i	$0.803397\pi$
$150$		0			0
$151$			9.45030i			0.769054i	0.923114	+	0.384527i	$0.125635\pi$
$151$			9.45030i			0.769054i	−0.923114	+	0.384527i	$0.874365\pi$
$152$	3.67424	+	2.34520i	0.298020	+	0.190221i
$153$		0			0
$154$	1.32535			0.106800
$155$	−7.07414	+	11.2704i	−0.568208	+	0.905260i
$156$		0			0
$157$	13.7650	−	13.7650i	1.09857	−	1.09857i	0.103990	−	0.994578i	$-0.466839\pi$
$157$	13.7650	−	13.7650i	1.09857	−	1.09857i	0.994578	−	0.103990i	$-0.0331610\pi$
$158$	−6.58542	−	6.58542i	−0.523908	−	0.523908i
$159$		0			0
$160$	−0.498616	−	2.17977i	−0.0394190	−	0.172326i
$161$	1.52687			0.120334
$162$		0			0
$163$	0.792086	+	0.792086i	0.0620410	+	0.0620410i	0.737447	−	0.675406i	$-0.236031\pi$
$163$	0.792086	+	0.792086i	0.0620410	+	0.0620410i	−0.675406	+	0.737447i	$0.736031\pi$
$164$	0.531910			0.0415352
$165$		0			0
$166$		−	13.4389i		−	1.04306i
$167$	−11.1325	−	11.1325i	−0.861457	−	0.861457i	0.130051	−	0.991507i	$-0.458486\pi$
$167$	−11.1325	−	11.1325i	−0.861457	−	0.861457i	−0.991507	+	0.130051i	$0.958486\pi$
$168$		0			0
$169$			11.9007i			0.915439i
$170$	−5.82209	−	3.65437i	−0.446534	−	0.280278i
$171$		0			0
$172$	−1.53142	+	1.53142i	−0.116769	+	0.116769i
$173$	−5.42532	+	5.42532i	−0.412479	+	0.412479i	−0.882601	−	0.470122i	$-0.844210\pi$
$173$	−5.42532	+	5.42532i	−0.412479	+	0.412479i	0.470122	+	0.882601i	$0.344210\pi$
$174$		0			0
$175$	4.70793	+	1.64232i	0.355886	+	0.124147i
$176$	1.32903			0.100180
$177$		0			0
$178$	−11.8705	−	11.8705i	−0.889729	−	0.889729i
$179$	0.963050			0.0719817			0.0359909	−	0.999352i	$-0.488541\pi$
$179$	0.963050			0.0719817			0.0359909	+	0.999352i	$0.488541\pi$
$180$		0			0
$181$			20.4214i			1.51791i	0.651141	+	0.758956i	$0.274290\pi$
$181$			20.4214i			1.51791i	−0.651141	+	0.758956i	$0.725710\pi$
$182$	0.739331	−	0.739331i	0.0548028	−	0.0548028i
$183$		0			0
$184$	1.53111			0.112875
$185$	0.941732	+	4.11691i	0.0692375	+	0.302681i
$186$		0			0
$187$	2.88896	−	2.88896i	0.211262	−	0.211262i
$188$	−4.13113	−	4.13113i	−0.301294	−	0.301294i
$189$		0			0
$190$	−8.80935	+	4.17078i	−0.639097	+	0.302580i
$191$	7.34773			0.531663			0.265832	−	0.964019i	$-0.414353\pi$
$191$	7.34773			0.531663			0.265832	+	0.964019i	$0.414353\pi$
$192$		0			0
$193$	9.32428	−	9.32428i	0.671176	−	0.671176i	−0.286811	−	0.957987i	$-0.592595\pi$
$193$	9.32428	−	9.32428i	0.671176	−	0.671176i	0.957987	+	0.286811i	$0.0925952\pi$
$194$		−	1.57955i		−	0.113405i
$195$		0			0
$196$	−6.00553			−0.428966
$197$	−5.43012	+	5.43012i	−0.386880	+	0.386880i	−0.873573	−	0.486693i	$-0.838203\pi$
$197$	−5.43012	+	5.43012i	−0.386880	+	0.386880i	0.486693	+	0.873573i	$0.338203\pi$
$198$		0			0
$199$		−	23.4987i		−	1.66578i	−0.553440	−	0.832889i	$-0.686685\pi$
$199$		−	23.4987i		−	1.66578i	0.553440	−	0.832889i	$-0.313315\pi$
$200$	4.72100	+	1.64687i	0.333825	+	0.116452i
$201$		0			0
$202$	−11.1093	−	11.1093i	−0.781645	−	0.781645i
$203$	4.19627	−	4.19627i	0.294520	−	0.294520i
$204$		0			0
$205$	−0.632310	+	1.00739i	−0.0441624	+	0.0703589i
$206$	−15.2665			−1.06367
$207$		0			0
$208$	0.741383	−	0.741383i	0.0514057	−	0.0514057i
$209$	−1.24898	−	5.65688i	−0.0863938	−	0.391294i
$210$		0			0
$211$			8.16488i			0.562094i	0.959694	+	0.281047i	$0.0906816\pi$
$211$			8.16488i			0.562094i	−0.959694	+	0.281047i	$0.909318\pi$
$212$	5.48557	+	5.48557i	0.376750	+	0.376750i
$213$		0			0
$214$		−	3.74948i		−	0.256309i
$215$	−1.07988	−	4.72083i	−0.0736470	−	0.321958i
$216$		0			0
$217$	−4.19627	−	4.19627i	−0.284861	−	0.284861i
$218$	4.12665	+	4.12665i	0.279492	+	0.279492i
$219$		0			0
$220$	−1.57989	+	2.51706i	−0.106516	+	0.169700i
$221$		−	3.22314i		−	0.216812i
$222$		0			0
$223$	0.212542	−	0.212542i	0.0142329	−	0.0142329i	−0.699955	−	0.714187i	$-0.746796\pi$
$223$	0.212542	−	0.212542i	0.0142329	−	0.0142329i	0.714187	+	0.699955i	$0.246796\pi$
$224$	0.997232			0.0666303
$225$		0			0
$226$	−0.655286			−0.0435890
$227$	−16.9240	−	16.9240i	−1.12328	−	1.12328i	−0.991244	−	0.132040i	$-0.957847\pi$
$227$	−16.9240	−	16.9240i	−1.12328	−	1.12328i	−0.132040	−	0.991244i	$-0.542153\pi$
$228$		0			0
$229$			7.59523i			0.501907i	0.967999	+	0.250953i	$0.0807441\pi$
$229$			7.59523i			0.501907i	−0.967999	+	0.250953i	$0.919256\pi$
$230$	−1.82011	+	2.89977i	−0.120014	+	0.191205i
$231$		0			0
$232$	4.20791	−	4.20791i	0.276263	−	0.276263i
$233$	−0.816115	−	0.816115i	−0.0534655	−	0.0534655i	0.679869	−	0.733334i	$-0.262037\pi$
$233$	−0.816115	−	0.816115i	−0.0534655	−	0.0534655i	−0.733334	+	0.679869i	$0.762037\pi$
$234$		0			0
$235$	12.7348	−	2.91306i	0.830730	−	0.190027i
$236$			3.53944i			0.230398i
$237$		0			0
$238$	2.16771	−	2.16771i	0.140512	−	0.140512i
$239$		−	4.21103i		−	0.272389i	−0.990682	−	0.136195i	$-0.956513\pi$
$239$		−	4.21103i		−	0.272389i	0.990682	−	0.136195i	$-0.0434872\pi$
$240$		0			0
$241$			24.8896i			1.60328i	0.597809	+	0.801638i	$0.296038\pi$
$241$			24.8896i			1.60328i	−0.597809	+	0.801638i	$0.703962\pi$
$242$	6.52919	+	6.52919i	0.419712	+	0.419712i
$243$		0			0
$244$			3.41030i			0.218322i
$245$	7.13909	−	11.3739i	0.456100	−	0.726651i
$246$		0			0
$247$	−3.85234	−	2.45889i	−0.245119	−	0.156455i
$248$	−4.20791	−	4.20791i	−0.267203	−	0.267203i
$249$		0			0
$250$	−8.73112	+	6.98338i	−0.552204	+	0.441668i
$251$	0.952848			0.0601432			0.0300716	−	0.999548i	$-0.490426\pi$
$251$	0.952848			0.0601432			0.0300716	+	0.999548i	$0.490426\pi$
$252$		0			0
$253$	−1.43888	−	1.43888i	−0.0904619	−	0.0904619i
$254$		−	10.9672i		−	0.688144i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−12.4298	−	12.4298i	−0.775349	−	0.775349i	0.203687	−	0.979036i	$-0.434708\pi$
$257$	−12.4298	−	12.4298i	−0.775349	−	0.775349i	−0.979036	+	0.203687i	$0.934708\pi$
$258$		0			0
$259$	−1.88346			−0.117033
$260$	0.522786	+	2.28543i	0.0324218	+	0.141736i
$261$		0			0
$262$	−9.37065	−	9.37065i	−0.578921	−	0.578921i
$263$	−3.37612	−	3.37612i	−0.208180	−	0.208180i	0.595313	−	0.803494i	$-0.297028\pi$
$263$	−3.37612	−	3.37612i	−0.208180	−	0.208180i	−0.803494	+	0.595313i	$0.797028\pi$
$264$		0			0
$265$	−16.9101	+	3.86814i	−1.03878	+	0.237618i
$266$	−0.937166	−	4.24460i	−0.0574613	−	0.260253i
$267$		0			0
$268$	1.99446	−	1.99446i	0.121831	−	0.121831i
$269$	−1.10025			−0.0670834			−0.0335417	−	0.999437i	$-0.510679\pi$
$269$	−1.10025			−0.0670834			−0.0335417	+	0.999437i	$0.510679\pi$
$270$		0			0
$271$	18.3193			1.11282			0.556409	−	0.830909i	$-0.312179\pi$
$271$	18.3193			1.11282			0.556409	+	0.830909i	$0.312179\pi$
$272$	2.17373	−	2.17373i	0.131802	−	0.131802i
$273$		0			0
$274$	6.25126			0.377653
$275$	−2.88896	−	5.98432i	−0.174211	−	0.360868i
$276$		0			0
$277$	−6.48039	+	6.48039i	−0.389369	+	0.389369i	−0.874462	−	0.485093i	$-0.838786\pi$
$277$	−6.48039	+	6.48039i	−0.389369	+	0.389369i	0.485093	+	0.874462i	$0.338786\pi$
$278$	1.89975	−	1.89975i	0.113939	−	0.113939i
$279$		0			0
$280$	−1.18546	+	1.88866i	−0.0708449	+	0.112869i
$281$		−	12.6675i		−	0.755678i	−0.925871	−	0.377839i	$-0.876667\pi$
$281$		−	12.6675i		−	0.755678i	0.925871	−	0.377839i	$-0.123333\pi$
$282$		0			0
$283$	11.2107	+	11.2107i	0.666406	+	0.666406i	0.956882	−	0.290476i	$-0.0938136\pi$
$283$	11.2107	+	11.2107i	0.666406	+	0.666406i	−0.290476	+	0.956882i	$0.593814\pi$
$284$	−8.71907			−0.517381
$285$		0			0
$286$	−1.39346			−0.0823968
$287$	−0.375076	−	0.375076i	−0.0221400	−	0.0221400i
$288$		0			0
$289$			7.54978i			0.444104i
$290$	2.96721	+	12.9715i	0.174240	+	0.761716i
$291$		0			0
$292$	5.83628	−	5.83628i	0.341542	−	0.341542i
$293$	−0.128802	+	0.128802i	−0.00752471	+	0.00752471i	−0.710859	−	0.703334i	$-0.751694\pi$
$293$	−0.128802	+	0.128802i	−0.00752471	+	0.00752471i	0.703334	+	0.710859i	$0.251694\pi$
$294$		0			0
$295$	−6.70336	−	4.20752i	−0.390285	−	0.244972i
$296$	−1.88869			−0.109778
$297$		0			0
$298$	9.99711	−	9.99711i	0.579117	−	0.579117i
$299$	−1.60532			−0.0928383
$300$		0			0
$301$	2.15976			0.124486
$302$	6.68237	−	6.68237i	0.384527	−	0.384527i
$303$		0			0
$304$	−0.939768	−	4.25639i	−0.0538994	−	0.244121i
$305$	−6.45877	−	4.05400i	−0.369828	−	0.232132i
$306$		0			0
$307$	15.7940	+	15.7940i	0.901413	+	0.901413i	0.995558	−	0.0941458i	$-0.0300120\pi$
$307$	15.7940	+	15.7940i	0.901413	+	0.901413i	−0.0941458	+	0.995558i	$0.530012\pi$
$308$	−0.937166	−	0.937166i	−0.0534000	−	0.0534000i
$309$		0			0
$310$	12.9715	−	2.96721i	0.736734	−	0.168526i
$311$	−14.6924			−0.833132			−0.416566	−	0.909105i	$-0.636767\pi$
$311$	−14.6924			−0.833132			−0.416566	+	0.909105i	$0.636767\pi$
$312$		0			0
$313$	−1.77069	−	1.77069i	−0.100086	−	0.100086i	0.655291	−	0.755377i	$-0.272546\pi$
$313$	−1.77069	−	1.77069i	−0.100086	−	0.100086i	−0.755377	+	0.655291i	$0.772546\pi$
$314$	−19.4667			−1.09857
$315$		0			0
$316$			9.31319i			0.523908i
$317$	4.63384	+	4.63384i	0.260262	+	0.260262i	0.825161	−	0.564898i	$-0.191085\pi$
$317$	4.63384	+	4.63384i	0.260262	+	0.260262i	−0.564898	+	0.825161i	$0.691085\pi$
$318$		0			0
$319$	−7.90892			−0.442815
$320$	−1.18875	+	1.89390i	−0.0664533	+	0.105872i
$321$		0			0
$322$	−1.07966	−	1.07966i	−0.0601670	−	0.0601670i
$323$	−11.2951	−	7.20944i	−0.628473	−	0.401144i
$324$		0			0
$325$	−4.94984	−	1.72670i	−0.274568	−	0.0957804i
$326$		−	1.12018i		−	0.0620410i
$327$		0			0
$328$	−0.376117	−	0.376117i	−0.0207676	−	0.0207676i
$329$			5.82613i			0.321205i
$330$		0			0
$331$			10.5075i			0.577544i	0.957398	+	0.288772i	$0.0932470\pi$
$331$			10.5075i			0.577544i	−0.957398	+	0.288772i	$0.906753\pi$
$332$	−9.50276	+	9.50276i	−0.521532	+	0.521532i
$333$		0			0
$334$			15.7437i			0.861457i
$335$	1.40639	+	6.14824i	0.0768395	+	0.335914i
$336$		0			0
$337$	−18.8126	−	18.8126i	−1.02479	−	1.02479i	−0.999685	−	0.0251053i	$-0.992008\pi$
$337$	−18.8126	−	18.8126i	−1.02479	−	1.02479i	−0.0251053	−	0.999685i	$-0.507992\pi$
$338$	8.41507	−	8.41507i	0.457719	−	0.457719i
$339$		0			0
$340$	1.53281	+	6.70087i	0.0831281	+	0.363406i
$341$			7.90892i			0.428292i
$342$		0			0
$343$	9.17084	+	9.17084i	0.495179	+	0.495179i
$344$	2.16575			0.116769
$345$		0			0
$346$	7.67256			0.412479
$347$	−16.9775	+	16.9775i	−0.911399	+	0.911399i	−0.996382	−	0.0849832i	$-0.972916\pi$
$347$	−16.9775	+	16.9775i	−0.911399	+	0.911399i	0.0849832	+	0.996382i	$0.472916\pi$
$348$		0			0
$349$			16.3106i			0.873086i	0.899683	+	0.436543i	$0.143797\pi$
$349$			16.3106i			0.873086i	−0.899683	+	0.436543i	$0.856203\pi$
$350$	−2.16771	−	4.49030i	−0.115869	−	0.240017i
$351$		0			0
$352$	−0.939768	−	0.939768i	−0.0500898	−	0.0500898i
$353$	−7.93890	−	7.93890i	−0.422545	−	0.422545i	0.463534	−	0.886079i	$-0.346581\pi$
$353$	−7.93890	−	7.93890i	−0.422545	−	0.422545i	−0.886079	+	0.463534i	$0.846581\pi$
$354$		0			0
$355$	10.3648	−	16.5131i	0.550107	−	0.876422i
$356$			16.7874i			0.889729i
$357$		0			0
$358$	−0.680979	−	0.680979i	−0.0359909	−	0.0359909i
$359$		−	26.2304i		−	1.38439i	−0.721712	−	0.692193i	$-0.756645\pi$
$359$		−	26.2304i		−	1.38439i	0.721712	−	0.692193i	$-0.243355\pi$
$360$		0			0
$361$	−17.2337	+	8.00003i	−0.907035	+	0.421054i
$362$	14.4401	−	14.4401i	0.758956	−	0.758956i
$363$		0			0
$364$	−1.04557			−0.0548028
$365$	4.11545	+	17.9912i	0.215412	+	0.941704i
$366$		0			0
$367$	−1.62269	+	1.62269i	−0.0847040	+	0.0847040i	−0.748189	−	0.663485i	$-0.769077\pi$
$367$	−1.62269	+	1.62269i	−0.0847040	+	0.0847040i	0.663485	+	0.748189i	$0.269077\pi$
$368$	−1.08266	−	1.08266i	−0.0564373	−	0.0564373i
$369$		0			0
$370$	2.24519	−	3.57700i	0.116722	−	0.185959i
$371$		−	7.73629i		−	0.401648i
$372$		0			0
$373$	9.00900	−	9.00900i	0.466468	−	0.466468i	−0.434300	−	0.900768i	$-0.643004\pi$
$373$	9.00900	−	9.00900i	0.466468	−	0.466468i	0.900768	+	0.434300i	$0.143004\pi$
$374$	−4.08561			−0.211262
$375$		0			0
$376$			5.84230i			0.301294i
$377$	−4.41189	+	4.41189i	−0.227224	+	0.227224i
$378$		0			0
$379$	4.49635			0.230962			0.115481	−	0.993310i	$-0.463159\pi$
$379$	4.49635			0.230962			0.115481	+	0.993310i	$0.463159\pi$
$380$	9.17833	+	3.27997i	0.470839	+	0.168259i
$381$		0			0
$382$	−5.19563	−	5.19563i	−0.265832	−	0.265832i
$383$	−22.5064	+	22.5064i	−1.15003	+	1.15003i	−0.163478	+	0.986547i	$0.552271\pi$
$383$	−22.5064	+	22.5064i	−1.15003	+	1.15003i	−0.986547	+	0.163478i	$0.947729\pi$
$384$		0			0
$385$	2.88896	−	0.660842i	0.147235	−	0.0336796i
$386$	−13.1865			−0.671176
$387$		0			0
$388$	−1.11691	+	1.11691i	−0.0567025	+	0.0567025i
$389$			26.1672i			1.32673i	0.748297	+	0.663364i	$0.230872\pi$
$389$			26.1672i			1.32673i	−0.748297	+	0.663364i	$0.769128\pi$
$390$		0			0
$391$	−4.70681			−0.238033
$392$	4.24655	+	4.24655i	0.214483	+	0.214483i
$393$		0			0
$394$	7.67935			0.386880
$395$	−17.6383	−	11.0711i	−0.887478	−	0.557047i
$396$		0			0
$397$	−15.5911	+	15.5911i	−0.782497	+	0.782497i	−0.980252	−	0.197754i	$-0.936635\pi$
$397$	−15.5911	+	15.5911i	−0.782497	+	0.782497i	0.197754	+	0.980252i	$0.436635\pi$
$398$	−16.6161	+	16.6161i	−0.832889	+	0.832889i
$399$		0			0
$400$	−2.17373	−	4.50276i	−0.108687	−	0.225138i
$401$			13.8440i			0.691337i	0.938357	+	0.345668i	$0.112348\pi$
$401$			13.8440i			0.691337i	−0.938357	+	0.345668i	$0.887652\pi$
$402$		0			0
$403$	4.41189	+	4.41189i	0.219772	+	0.219772i
$404$			15.7109i			0.781645i
$405$		0			0
$406$	−5.93441			−0.294520
$407$	1.77493	+	1.77493i	0.0879801	+	0.0879801i
$408$		0			0
$409$	−9.17657			−0.453752			−0.226876	−	0.973924i	$-0.572851\pi$
$409$	−9.17657			−0.453752			−0.226876	+	0.973924i	$0.572851\pi$
$410$	1.15944	−	0.265219i	0.0572606	−	0.0130982i
$411$		0			0
$412$	10.7950	+	10.7950i	0.531833	+	0.531833i
$413$	2.49584	−	2.49584i	0.122812	−	0.122812i
$414$		0			0
$415$	−6.70087	−	29.2937i	−0.328933	−	1.43797i
$416$	−1.04847			−0.0514057
$417$		0			0
$418$	−3.11685	+	4.88318i	−0.152450	+	0.238844i
$419$		−	21.8535i		−	1.06762i	−0.845606	−	0.533808i	$-0.820761\pi$
$419$		−	21.8535i		−	1.06762i	0.845606	−	0.533808i	$-0.179239\pi$
$420$		0			0
$421$			29.4223i			1.43396i	0.697095	+	0.716978i	$0.254475\pi$
$421$			29.4223i			1.43396i	−0.697095	+	0.716978i	$0.745525\pi$
$422$	5.77344	−	5.77344i	0.281047	−	0.281047i
$423$		0			0
$424$		−	7.75776i		−	0.376750i
$425$	−14.5129	−	5.06269i	−0.703980	−	0.245577i
$426$		0			0
$427$	2.40477	−	2.40477i	0.116375	−	0.116375i
$428$	−2.65129	+	2.65129i	−0.128155	+	0.128155i
$429$		0			0
$430$	−2.57454	+	4.10172i	−0.124155	+	0.197803i
$431$			36.4149i			1.75404i	0.480452	+	0.877021i	$0.340473\pi$
$431$			36.4149i			1.75404i	−0.480452	+	0.877021i	$0.659527\pi$
$432$		0			0
$433$	16.4903	−	16.4903i	0.792475	−	0.792475i	−0.189421	−	0.981896i	$-0.560661\pi$
$433$	16.4903	−	16.4903i	0.792475	−	0.792475i	0.981896	+	0.189421i	$0.0606610\pi$
$434$			5.93441i			0.284861i
$435$		0			0
$436$		−	5.83596i		−	0.279492i
$437$	−3.59076	+	5.62565i	−0.171769	+	0.269111i
$438$		0			0
$439$	13.3446			0.636903			0.318452	−	0.947939i	$-0.396837\pi$
$439$	13.3446			0.636903			0.318452	+	0.947939i	$0.396837\pi$
$440$	2.89698	−	0.662676i	0.138108	−	0.0315919i
$441$		0			0
$442$	−2.27910	+	2.27910i	−0.108406	+	0.108406i
$443$	17.4215	+	17.4215i	0.827720	+	0.827720i	0.987201	−	0.159481i	$-0.0509820\pi$
$443$	17.4215	+	17.4215i	0.827720	+	0.827720i	−0.159481	+	0.987201i	$0.550982\pi$
$444$		0			0
$445$	−31.7936	−	19.9560i	−1.50716	−	0.946007i
$446$	−0.300580			−0.0142329
$447$		0			0
$448$	−0.705149	−	0.705149i	−0.0333152	−	0.0333152i
$449$	−39.0761			−1.84412			−0.922058	−	0.387051i	$-0.873494\pi$
$449$	−39.0761			−1.84412			−0.922058	+	0.387051i	$0.873494\pi$
$450$		0			0
$451$			0.706926i			0.0332878i
$452$	0.463357	+	0.463357i	0.0217945	+	0.0217945i
$453$		0			0
$454$			23.9341i			1.12328i
$455$	1.24293	−	1.98021i	0.0582693	−	0.0928337i
$456$		0			0
$457$	−25.9258	+	25.9258i	−1.21276	+	1.21276i	−0.242643	+	0.970116i	$0.578014\pi$
$457$	−25.9258	+	25.9258i	−1.21276	+	1.21276i	−0.970116	+	0.242643i	$0.921986\pi$
$458$	5.37064	−	5.37064i	0.250953	−	0.250953i
$459$		0			0
$460$	3.33745	−	0.763434i	0.155610	−	0.0355953i
$461$	16.3202			0.760108			0.380054	−	0.924964i	$-0.375905\pi$
$461$	16.3202			0.760108			0.380054	+	0.924964i	$0.375905\pi$
$462$		0			0
$463$	−4.26074	−	4.26074i	−0.198013	−	0.198013i	0.601135	−	0.799148i	$-0.294716\pi$
$463$	−4.26074	−	4.26074i	−0.198013	−	0.198013i	−0.799148	+	0.601135i	$0.794716\pi$
$464$	−5.95089			−0.276263
$465$		0			0
$466$			1.15416i			0.0534655i
$467$	24.0643	−	24.0643i	1.11356	−	1.11356i	0.120897	−	0.992665i	$-0.461423\pi$
$467$	24.0643	−	24.0643i	1.11356	−	1.11356i	0.992665	−	0.120897i	$-0.0385771\pi$
$468$		0			0
$469$	−2.81279			−0.129883
$470$	−11.0647	−	6.94505i	−0.510379	−	0.320351i
$471$		0			0
$472$	2.50276	−	2.50276i	0.115199	−	0.115199i
$473$	−2.03530	−	2.03530i	−0.0935833	−	0.0935833i
$474$		0			0
$475$	−17.1227	+	13.4838i	−0.785644	+	0.618679i
$476$	−3.06561			−0.140512
$477$		0			0
$478$	−2.97765	+	2.97765i	−0.136195	+	0.136195i
$479$			19.7176i			0.900920i	0.892797	+	0.450460i	$0.148740\pi$
$479$			19.7176i			0.900920i	−0.892797	+	0.450460i	$0.851260\pi$
$480$		0			0
$481$	1.98024			0.0902914
$482$	17.5996	−	17.5996i	0.801638	−	0.801638i
$483$		0			0
$484$		−	9.23367i		−	0.419712i
$485$	−0.787588	−	3.44305i	−0.0357625	−	0.156341i
$486$		0			0
$487$	−23.8855	−	23.8855i	−1.08236	−	1.08236i	−0.996289	−	0.0860674i	$-0.972570\pi$
$487$	−23.8855	−	23.8855i	−1.08236	−	1.08236i	−0.0860674	−	0.996289i	$-0.527430\pi$
$488$	2.41145	−	2.41145i	0.109161	−	0.109161i
$489$		0			0
$490$	−13.0907	+	2.99445i	−0.591375	+	0.135276i
$491$	−21.2521			−0.959094			−0.479547	−	0.877516i	$-0.659199\pi$
$491$	−21.2521			−0.959094			−0.479547	+	0.877516i	$0.659199\pi$
$492$		0			0
$493$	−12.9356	+	12.9356i	−0.582592	+	0.582592i
$494$	0.985322	+	4.46271i	0.0443317	+	0.200787i
$495$		0			0
$496$			5.95089i			0.267203i
$497$	6.14824	+	6.14824i	0.275786	+	0.275786i
$498$		0			0
$499$		−	39.2906i		−	1.75889i	−0.476002	−	0.879444i	$-0.657915\pi$
$499$		−	39.2906i		−	1.75889i	0.476002	−	0.879444i	$-0.342085\pi$
$500$	11.1118	+	1.23584i	0.496936	+	0.0552684i
$501$		0			0
$502$	−0.673765	−	0.673765i	−0.0300716	−	0.0300716i
$503$	−7.92010	−	7.92010i	−0.353140	−	0.353140i	0.508137	−	0.861276i	$-0.330334\pi$
$503$	−7.92010	−	7.92010i	−0.353140	−	0.353140i	−0.861276	+	0.508137i	$0.830334\pi$
$504$		0			0
$505$	−29.7549	−	18.6764i	−1.32407	−	0.831087i
$506$			2.03489i			0.0904619i
$507$		0			0
$508$	−7.75499	+	7.75499i	−0.344072	+	0.344072i
$509$	−19.7948			−0.877389			−0.438695	−	0.898636i	$-0.644559\pi$
$509$	−19.7948			−0.877389			−0.438695	+	0.898636i	$0.644559\pi$
$510$		0			0
$511$	−8.23090			−0.364113
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$			17.5784i			0.775349i
$515$	−33.2773	+	7.61210i	−1.46637	+	0.335429i
$516$		0			0
$517$	5.49040	−	5.49040i	0.241468	−	0.241468i
$518$	1.33181	+	1.33181i	0.0585164	+	0.0585164i
$519$		0			0
$520$	1.24638	−	1.98571i	0.0546572	−	0.0870790i
$521$		−	32.9001i		−	1.44138i	−0.693257	−	0.720691i	$-0.743825\pi$
$521$		−	32.9001i		−	1.44138i	0.693257	−	0.720691i	$-0.256175\pi$
$522$		0			0
$523$	−5.26214	+	5.26214i	−0.230098	+	0.230098i	−0.812733	−	0.582636i	$-0.802021\pi$
$523$	−5.26214	+	5.26214i	−0.230098	+	0.230098i	0.582636	+	0.812733i	$0.302021\pi$
$524$			13.2521i			0.578921i
$525$		0			0
$526$			4.77455i			0.208180i
$527$	12.9356	+	12.9356i	0.563485	+	0.563485i
$528$		0			0
$529$		−	20.6557i		−	0.898075i
$530$	14.6924	+	9.22206i	0.638199	+	0.400581i
$531$		0			0
$532$	−2.33871	+	3.66407i	−0.101396	+	0.158857i
$533$	0.394349	+	0.394349i	0.0170812	+	0.0170812i
$534$		0			0
$535$	−1.86955	−	8.17300i	−0.0808278	−	0.353350i
$536$	−2.82060			−0.121831
$537$		0			0
$538$	0.777994	+	0.777994i	0.0335417	+	0.0335417i
$539$		−	7.98154i		−	0.343789i
$540$		0			0
$541$	−3.97998			−0.171113			−0.0855563	−	0.996333i	$-0.527267\pi$
$541$	−3.97998			−0.171113			−0.0855563	+	0.996333i	$0.527267\pi$
$542$	−12.9537	−	12.9537i	−0.556409	−	0.556409i
$543$		0			0
$544$	−3.07412			−0.131802
$545$	11.0527	+	6.93752i	0.473447	+	0.297171i
$546$		0			0
$547$	17.5769	+	17.5769i	0.751533	+	0.751533i	0.974765	−	0.223232i	$-0.0716608\pi$
$547$	17.5769	+	17.5769i	0.751533	+	0.751533i	−0.223232	+	0.974765i	$0.571661\pi$
$548$	−4.42031	−	4.42031i	−0.188826	−	0.188826i
$549$		0			0
$550$	−2.18875	+	6.27436i	−0.0933286	+	0.267539i
$551$	5.59245	+	25.3293i	0.238246	+	1.07906i
$552$		0			0
$553$	6.56719	−	6.56719i	0.279265	−	0.279265i
$554$	9.16466			0.389369
$555$		0			0
$556$	−2.68665			−0.113939
$557$	−10.5795	+	10.5795i	−0.448267	+	0.448267i	−0.894778	−	0.446511i	$-0.852666\pi$
$557$	−10.5795	+	10.5795i	−0.448267	+	0.448267i	0.446511	+	0.894778i	$0.352666\pi$
$558$		0			0
$559$	−2.27073			−0.0960418
$560$	2.17373	−	0.497236i	0.0918570	−	0.0210120i
$561$		0			0
$562$	−8.95726	+	8.95726i	−0.377839	+	0.377839i
$563$	1.06530	−	1.06530i	0.0448971	−	0.0448971i	−0.684302	−	0.729199i	$-0.739893\pi$
$563$	1.06530	−	1.06530i	0.0448971	−	0.0448971i	0.729199	+	0.684302i	$0.239893\pi$
$564$		0			0
$565$	−1.42837	+	0.326736i	−0.0600920	+	0.0137459i
$566$		−	15.8543i		−	0.666406i
$567$		0			0
$568$	6.16531	+	6.16531i	0.258691	+	0.258691i
$569$	17.2827			0.724528			0.362264	−	0.932076i	$-0.382004\pi$
$569$	17.2827			0.724528			0.362264	+	0.932076i	$0.382004\pi$
$570$		0			0
$571$	10.3420			0.432798			0.216399	−	0.976305i	$-0.430569\pi$
$571$	10.3420			0.432798			0.216399	+	0.976305i	$0.430569\pi$
$572$	0.985322	+	0.985322i	0.0411984	+	0.0411984i
$573$		0			0
$574$			0.530438i			0.0221400i
$575$	−2.52154	+	7.22835i	−0.105155	+	0.301443i
$576$		0			0
$577$	−25.5328	+	25.5328i	−1.06294	+	1.06294i	−0.0650631	+	0.997881i	$0.520725\pi$
$577$	−25.5328	+	25.5328i	−1.06294	+	1.06294i	−0.997881	+	0.0650631i	$0.979275\pi$
$578$	5.33850	−	5.33850i	0.222052	−	0.222052i
$579$		0			0
$580$	7.07414	−	11.2704i	0.293738	−	0.467978i
$581$	13.4017			0.555998
$582$		0			0
$583$	−7.29049	+	7.29049i	−0.301941	+	0.301941i
$584$	−8.25374			−0.341542
$585$		0			0
$586$	0.182154			0.00752471
$587$	25.3120	−	25.3120i	1.04474	−	1.04474i	0.0457889	−	0.998951i	$-0.485420\pi$
$587$	25.3120	−	25.3120i	1.04474	−	1.04474i	0.998951	−	0.0457889i	$-0.0145801\pi$
$588$		0			0
$589$	25.3293	−	5.59245i	1.04368	−	0.230433i
$590$	1.76482	+	7.71516i	0.0726566	+	0.317628i
$591$		0			0
$592$	1.33551	+	1.33551i	0.0548890	+	0.0548890i
$593$	9.66808	+	9.66808i	0.397020	+	0.397020i	0.877181	−	0.480160i	$-0.159422\pi$
$593$	9.66808	+	9.66808i	0.397020	+	0.397020i	−0.480160	+	0.877181i	$0.659422\pi$
$594$		0			0
$595$	3.64426	−	5.80597i	0.149400	−	0.238022i
$596$	−14.1380			−0.579117
$597$		0			0
$598$	1.13514	+	1.13514i	0.0464192	+	0.0464192i
$599$	28.5298			1.16569			0.582847	−	0.812582i	$-0.301939\pi$
$599$	28.5298			1.16569			0.582847	+	0.812582i	$0.301939\pi$
$600$		0			0
$601$			24.3760i			0.994317i	0.867660	+	0.497159i	$0.165623\pi$
$601$			24.3760i			0.994317i	−0.867660	+	0.497159i	$0.834377\pi$
$602$	−1.52718	−	1.52718i	−0.0622431	−	0.0622431i
$603$		0			0
$604$	−9.45030			−0.384527
$605$	17.4877	+	10.9766i	0.710975	+	0.446261i
$606$		0			0
$607$	−27.0140	−	27.0140i	−1.09647	−	1.09647i	−0.994821	−	0.101646i	$-0.967589\pi$
$607$	−27.0140	−	27.0140i	−1.09647	−	1.09647i	−0.101646	−	0.994821i	$-0.532411\pi$
$608$	−2.34520	+	3.67424i	−0.0951106	+	0.149010i
$609$		0			0
$610$	1.70043	+	7.43365i	0.0688484	+	0.300980i
$611$		−	6.12550i		−	0.247811i
$612$		0			0
$613$	17.2695	+	17.2695i	0.697508	+	0.697508i	0.963872	−	0.266364i	$-0.0858224\pi$
$613$	17.2695	+	17.2695i	0.697508	+	0.697508i	−0.266364	+	0.963872i	$0.585822\pi$
$614$		−	22.3361i		−	0.901413i
$615$		0			0
$616$			1.32535i			0.0534000i
$617$	−34.2253	+	34.2253i	−1.37786	+	1.37786i	−0.529625	+	0.848232i	$0.677667\pi$
$617$	−34.2253	+	34.2253i	−1.37786	+	1.37786i	−0.848232	+	0.529625i	$0.822333\pi$
$618$		0			0
$619$		−	34.9000i		−	1.40275i	−0.712792	−	0.701375i	$-0.752570\pi$
$619$		−	34.9000i		−	1.40275i	0.712792	−	0.701375i	$-0.247430\pi$
$620$	−11.2704	−	7.07414i	−0.452630	−	0.284104i
$621$		0			0
$622$	10.3891	+	10.3891i	0.416566	+	0.416566i
$623$	11.8376	−	11.8376i	0.474263	−	0.474263i
$624$		0			0
$625$	−15.5498	+	19.5756i	−0.621991	+	0.783024i
$626$			2.50414i			0.100086i
$627$		0			0
$628$	13.7650	+	13.7650i	0.549284	+	0.549284i
$629$	5.80607			0.231503
$630$		0			0
$631$	33.8489			1.34750			0.673752	−	0.738957i	$-0.264682\pi$
$631$	33.8489			1.34750			0.673752	+	0.738957i	$0.264682\pi$
$632$	6.58542	−	6.58542i	0.261954	−	0.261954i
$633$		0			0
$634$		−	6.55324i		−	0.260262i
$635$	−5.46842	−	23.9060i	−0.217008	−	0.948679i
$636$		0			0
$637$	−4.45240	−	4.45240i	−0.176410	−	0.176410i
$638$	5.59245	+	5.59245i	0.221407	+	0.221407i
$639$		0			0
$640$	2.17977	−	0.498616i	0.0861628	−	0.0197095i
$641$			38.3389i			1.51429i	0.653245	+	0.757147i	$0.273407\pi$
$641$			38.3389i			1.51429i	−0.653245	+	0.757147i	$0.726593\pi$
$642$		0			0
$643$	−21.8777	−	21.8777i	−0.862773	−	0.862773i	0.128886	−	0.991659i	$-0.458860\pi$
$643$	−21.8777	−	21.8777i	−0.862773	−	0.862773i	−0.991659	+	0.128886i	$0.958860\pi$
$644$			1.52687i			0.0601670i
$645$		0			0
$646$	2.88896	+	13.0847i	0.113665	+	0.514809i
$647$	11.5954	−	11.5954i	0.455863	−	0.455863i	−0.441432	−	0.897295i	$-0.645529\pi$
$647$	11.5954	−	11.5954i	0.455863	−	0.455863i	0.897295	+	0.441432i	$0.145529\pi$
$648$		0			0
$649$	−4.70403			−0.184649
$650$	2.27910	+	4.72103i	0.0893937	+	0.185174i
$651$		0			0
$652$	−0.792086	+	0.792086i	−0.0310205	+	0.0310205i
$653$	11.6996	+	11.6996i	0.457842	+	0.457842i	0.897946	−	0.440105i	$-0.145059\pi$
$653$	11.6996	+	11.6996i	0.457842	+	0.457842i	−0.440105	+	0.897946i	$0.645059\pi$
$654$		0			0
$655$	−25.0982	−	15.7535i	−0.980668	−	0.615539i
$656$			0.531910i			0.0207676i
$657$		0			0
$658$	4.11969	−	4.11969i	0.160602	−	0.160602i
$659$	44.6662			1.73995			0.869974	−	0.493097i	$-0.164135\pi$
$659$	44.6662			1.73995			0.869974	+	0.493097i	$0.164135\pi$
$660$		0			0
$661$		−	46.5099i		−	1.80902i	−0.426447	−	0.904512i	$-0.640235\pi$
$661$		−	46.5099i		−	1.80902i	0.426447	−	0.904512i	$-0.359765\pi$
$662$	7.42992	−	7.42992i	0.288772	−	0.288772i
$663$		0			0
$664$	13.4389			0.521532
$665$	−4.15923	−	8.78496i	−0.161288	−	0.340666i
$666$		0			0
$667$	6.44276	+	6.44276i	0.249465	+	0.249465i
$668$	11.1325	−	11.1325i	0.430728	−	0.430728i
$669$		0			0
$670$	3.35299	−	5.34194i	0.129537	−	0.206377i
$671$	−4.53240			−0.174971
$672$		0			0
$673$	17.8598	−	17.8598i	0.688446	−	0.688446i	−0.273443	−	0.961888i	$-0.588162\pi$
$673$	17.8598	−	17.8598i	0.688446	−	0.688446i	0.961888	+	0.273443i	$0.0881624\pi$
$674$			26.6051i			1.02479i
$675$		0			0
$676$	−11.9007			−0.457719
$677$	−20.6616	−	20.6616i	−0.794092	−	0.794092i	0.188065	−	0.982157i	$-0.439778\pi$
$677$	−20.6616	−	20.6616i	−0.794092	−	0.794092i	−0.982157	+	0.188065i	$0.939778\pi$
$678$		0			0
$679$	1.57518			0.0604497
$680$	3.65437	−	5.82209i	0.140139	−	0.223267i
$681$		0			0
$682$	5.59245	−	5.59245i	0.214146	−	0.214146i
$683$	23.8243	−	23.8243i	0.911610	−	0.911610i	−0.0847893	−	0.996399i	$-0.527022\pi$
$683$	23.8243	−	23.8243i	0.911610	−	0.911610i	0.996399	+	0.0847893i	$0.0270217\pi$
$684$		0			0
$685$	13.6263	−	3.11698i	0.520634	−	0.119094i
$686$		−	12.9695i		−	0.495179i
$687$		0			0
$688$	−1.53142	−	1.53142i	−0.0583847	−	0.0583847i
$689$			8.13381i			0.309874i
$690$		0			0
$691$	−4.34746			−0.165385			−0.0826927	−	0.996575i	$-0.526352\pi$
$691$	−4.34746			−0.165385			−0.0826927	+	0.996575i	$0.526352\pi$
$692$	−5.42532	−	5.42532i	−0.206240	−	0.206240i
$693$		0			0
$694$	24.0098			0.911399
$695$	3.19376	−	5.08825i	0.121146	−	0.193008i
$696$		0			0
$697$	1.15623	+	1.15623i	0.0437953	+	0.0437953i
$698$	11.5333	−	11.5333i	0.436543	−	0.436543i
$699$		0			0
$700$	−1.64232	+	4.70793i	−0.0620737	+	0.177943i
$701$	1.61462			0.0609832			0.0304916	−	0.999535i	$-0.490293\pi$
$701$	1.61462			0.0609832			0.0304916	+	0.999535i	$0.490293\pi$
$702$		0			0
$703$	4.42937	−	6.93950i	0.167057	−	0.261728i
$704$			1.32903i			0.0500898i
$705$		0			0
$706$			11.2273i			0.422545i
$707$	11.0785	−	11.0785i	0.416650	−	0.416650i
$708$		0			0
$709$			45.1909i			1.69718i	0.529052	+	0.848589i	$0.322548\pi$
$709$			45.1909i			1.69718i	−0.529052	+	0.848589i	$0.677452\pi$
$710$	−19.0055	+	4.34746i	−0.713265	+	0.163157i
$711$		0			0
$712$	11.8705	−	11.8705i	0.444864	−	0.444864i
$713$	6.44276	−	6.44276i	0.241283	−	0.241283i
$714$		0			0
$715$	−3.03741	+	0.694799i	−0.113593	+	0.0259840i
$716$			0.963050i			0.0359909i
$717$		0			0
$718$	−18.5477	+	18.5477i	−0.692193	+	0.692193i
$719$		−	8.72035i		−	0.325214i	−0.986691	−	0.162607i	$-0.948010\pi$
$719$		−	8.72035i		−	0.325214i	0.986691	−	0.162607i	$-0.0519903\pi$
$720$		0			0
$721$		−	15.2242i		−	0.566979i
$722$	17.8429	+	6.52917i	0.664045	+	0.242991i
$723$		0			0
$724$	−20.4214			−0.758956
$725$	12.9356	+	26.7955i	0.480418	+	0.995158i
$726$		0			0
$727$	16.9674	−	16.9674i	0.629286	−	0.629286i	−0.318602	−	0.947889i	$-0.603213\pi$
$727$	16.9674	−	16.9674i	0.629286	−	0.629286i	0.947889	+	0.318602i	$0.103213\pi$
$728$	0.739331	+	0.739331i	0.0274014	+	0.0274014i
$729$		0			0
$730$	9.81166	−	15.6318i	0.363146	−	0.578558i
$731$	−6.65778			−0.246247
$732$		0			0
$733$	25.1664	+	25.1664i	0.929541	+	0.929541i	0.997676	−	0.0681355i	$-0.0217050\pi$
$733$	25.1664	+	25.1664i	0.929541	+	0.929541i	−0.0681355	+	0.997676i	$0.521705\pi$
$734$	2.29484			0.0847040
$735$		0			0
$736$			1.53111i			0.0564373i
$737$	2.65071	+	2.65071i	0.0976400	+	0.0976400i
$738$		0			0
$739$		−	14.7543i		−	0.542747i	−0.962474	−	0.271373i	$-0.912522\pi$
$739$		−	14.7543i		−	0.542747i	0.962474	−	0.271373i	$-0.0874778\pi$
$740$	−4.11691	+	0.941732i	−0.151341	+	0.0346188i
$741$		0			0
$742$	−5.47038	+	5.47038i	−0.200824	+	0.200824i
$743$	8.61240	−	8.61240i	0.315958	−	0.315958i	−0.531254	−	0.847213i	$-0.678279\pi$
$743$	8.61240	−	8.61240i	0.315958	−	0.315958i	0.847213	+	0.531254i	$0.178279\pi$
$744$		0			0
$745$	16.8066	−	26.7761i	0.615748	−	0.981000i
$746$	−12.7407			−0.466468
$747$		0			0
$748$	2.88896	+	2.88896i	0.105631	+	0.105631i
$749$	3.73910			0.136624
$750$		0			0
$751$		−	44.6100i		−	1.62784i	−0.580974	−	0.813922i	$-0.697328\pi$
$751$		−	44.6100i		−	1.62784i	0.580974	−	0.813922i	$-0.302672\pi$
$752$	4.13113	−	4.13113i	0.150647	−	0.150647i
$753$		0			0
$754$	6.23935			0.227224
$755$	11.2341	−	17.8979i	0.408850	−	0.651373i
$756$		0			0
$757$	2.38067	−	2.38067i	0.0865268	−	0.0865268i	−0.662519	−	0.749045i	$-0.730512\pi$
$757$	2.38067	−	2.38067i	0.0865268	−	0.0865268i	0.749045	+	0.662519i	$0.230512\pi$
$758$	−3.17940	−	3.17940i	−0.115481	−	0.115481i
$759$		0			0
$760$	−4.17078	−	8.80935i	−0.151290	−	0.319549i
$761$	−4.25052			−0.154081			−0.0770406	−	0.997028i	$-0.524547\pi$
$761$	−4.25052			−0.154081			−0.0770406	+	0.997028i	$0.524547\pi$
$762$		0			0
$763$	−4.11522	+	4.11522i	−0.148981	+	0.148981i
$764$			7.34773i			0.265832i
$765$		0			0
$766$	31.8289			1.15003
$767$	−2.62408	+	2.62408i	−0.0947502	+	0.0947502i
$768$		0			0
$769$		−	3.40202i		−	0.122680i	−0.998117	−	0.0613400i	$-0.980463\pi$
$769$		−	3.40202i		−	0.122680i	0.998117	−	0.0613400i	$-0.0195374\pi$
$770$	−2.51009	−	1.57552i	−0.0904573	−	0.0567777i
$771$		0			0
$772$	9.32428	+	9.32428i	0.335588	+	0.335588i
$773$	−21.7310	+	21.7310i	−0.781611	+	0.781611i	−0.980103	−	0.198491i	$-0.936396\pi$
$773$	−21.7310	+	21.7310i	−0.781611	+	0.781611i	0.198491	+	0.980103i	$0.436396\pi$
$774$		0			0
$775$	26.7955	−	12.9356i	0.962521	−	0.464662i
$776$	1.57955			0.0567025
$777$		0			0
$778$	18.5030	−	18.5030i	0.663364	−	0.663364i
$779$	2.26402	−	0.499872i	0.0811168	−	0.0179098i
$780$		0			0
$781$		−	11.5879i		−	0.414648i
$782$	3.32821	+	3.32821i	0.119017	+	0.119017i
$783$		0			0
$784$		−	6.00553i		−	0.214483i
$785$	−42.4328	+	9.70640i	−1.51449	+	0.346436i
$786$		0			0
$787$	−8.02221	−	8.02221i	−0.285961	−	0.285961i	0.549520	−	0.835481i	$-0.314811\pi$
$787$	−8.02221	−	8.02221i	−0.285961	−	0.285961i	−0.835481	+	0.549520i	$0.814811\pi$
$788$	−5.43012	−	5.43012i	−0.193440	−	0.193440i
$789$		0			0
$790$	4.64370	+	20.3006i	0.165216	+	0.722262i
$791$		−	0.653472i		−	0.0232348i
$792$		0			0
$793$	−2.52834	+	2.52834i	−0.0897839	+	0.0897839i
$794$	22.0492			0.782497
$795$		0			0
$796$	23.4987			0.832889
$797$	29.0862	+	29.0862i	1.03029	+	1.03029i	0.999527	+	0.0307591i	$0.00979247\pi$
$797$	29.0862	+	29.0862i	1.03029	+	1.03029i	0.0307591	+	0.999527i	$0.490208\pi$
$798$		0			0
$799$		−	17.9599i		−	0.635377i
$800$	−1.64687	+	4.72100i	−0.0582258	+	0.166912i
$801$		0			0
$802$	9.78919	−	9.78919i	0.345668	−	0.345668i
$803$	7.75660	+	7.75660i	0.273725	+	0.273725i
$804$		0			0
$805$	−2.89174	−	1.81507i	−0.101920	−	0.0639728i
$806$		−	6.23935i		−	0.219772i
$807$		0			0
$808$	11.1093	−	11.1093i	0.390823	−	0.390823i
$809$		−	26.9228i		−	0.946556i	−0.880913	−	0.473278i	$-0.843071\pi$
$809$		−	26.9228i		−	0.946556i	0.880913	−	0.473278i	$-0.156929\pi$
$810$		0			0
$811$			38.9518i			1.36778i	0.729584	+	0.683891i	$0.239714\pi$
$811$			38.9518i			1.36778i	−0.729584	+	0.683891i	$0.760286\pi$
$812$	4.19627	+	4.19627i	0.147260	+	0.147260i
$813$		0			0
$814$		−	2.51013i		−	0.0879801i
$815$	−0.558539	−	2.44173i	−0.0195648	−	0.0855300i
$816$		0			0
$817$	−5.07913	+	7.95748i	−0.177696	+	0.278397i
$818$	6.48881	+	6.48881i	0.226876	+	0.226876i
$819$		0			0
$820$	−1.00739	−	0.632310i	−0.0351794	−	0.0220812i
$821$	−27.0500			−0.944053			−0.472026	−	0.881584i	$-0.656477\pi$
$821$	−27.0500			−0.944053			−0.472026	+	0.881584i	$0.656477\pi$
$822$		0			0
$823$	−7.85319	−	7.85319i	−0.273745	−	0.273745i	0.556861	−	0.830606i	$-0.312006\pi$
$823$	−7.85319	−	7.85319i	−0.273745	−	0.273745i	−0.830606	+	0.556861i	$0.812006\pi$
$824$		−	15.2665i		−	0.531833i
$825$		0			0
$826$	−3.52965			−0.122812
$827$	−13.3020	−	13.3020i	−0.462557	−	0.462557i	0.436936	−	0.899493i	$-0.356064\pi$
$827$	−13.3020	−	13.3020i	−0.462557	−	0.462557i	−0.899493	+	0.436936i	$0.856064\pi$
$828$		0			0
$829$	53.6495			1.86332			0.931662	−	0.363326i	$-0.118359\pi$
$829$	53.6495			1.86332			0.931662	+	0.363326i	$0.118359\pi$
$830$	−15.9756	+	25.4520i	−0.554520	+	0.883453i
$831$		0			0
$832$	0.741383	+	0.741383i	0.0257028	+	0.0257028i
$833$	−13.0544	−	13.0544i	−0.452309	−	0.452309i
$834$		0			0
$835$	7.85006	+	34.3176i	0.271662	+	1.18761i
$836$	5.65688	−	1.24898i	0.195647	−	0.0431969i
$837$		0			0
$838$	−15.4528	+	15.4528i	−0.533808	+	0.533808i
$839$	32.8129			1.13283			0.566413	−	0.824122i	$-0.308331\pi$
$839$	32.8129			1.13283			0.566413	+	0.824122i	$0.308331\pi$
$840$		0			0
$841$	6.41308			0.221141
$842$	20.8047	−	20.8047i	0.716978	−	0.716978i
$843$		0			0
$844$	−8.16488			−0.281047
$845$	14.1470	−	22.5388i	0.486671	−	0.775357i
$846$		0			0
$847$	−6.51112	+	6.51112i	−0.223725	+	0.223725i
$848$	−5.48557	+	5.48557i	−0.188375	+	0.188375i
$849$		0			0
$850$	6.68232	+	13.8420i	0.229202	+	0.474778i
$851$		−	2.89179i		−	0.0991292i
$852$		0			0
$853$	23.9591	+	23.9591i	0.820342	+	0.820342i	0.986157	−	0.165815i	$-0.0530253\pi$
$853$	23.9591	+	23.9591i	0.820342	+	0.820342i	−0.165815	+	0.986157i	$0.553025\pi$
$854$	−3.40086			−0.116375
$855$		0			0
$856$	3.74948			0.128155
$857$	−24.8412	−	24.8412i	−0.848560	−	0.848560i	0.141394	−	0.989953i	$-0.454842\pi$
$857$	−24.8412	−	24.8412i	−0.848560	−	0.848560i	−0.989953	+	0.141394i	$0.954842\pi$
$858$		0			0
$859$			20.5100i			0.699792i	0.936789	+	0.349896i	$0.113783\pi$
$859$			20.5100i			0.699792i	−0.936789	+	0.349896i	$0.886217\pi$
$860$	4.72083	−	1.07988i	0.160979	−	0.0368235i
$861$		0			0
$862$	25.7492	−	25.7492i	0.877021	−	0.877021i
$863$	36.4695	−	36.4695i	1.24144	−	1.24144i	0.282033	−	0.959405i	$-0.408991\pi$
$863$	36.4695	−	36.4695i	1.24144	−	1.24144i	0.959405	−	0.282033i	$-0.0910088\pi$
$864$		0			0
$865$	16.7244	−	3.82566i	0.568646	−	0.130076i
$866$	−23.3209			−0.792475
$867$		0			0
$868$	4.19627	−	4.19627i	0.142431	−	0.142431i
$869$	−12.3775			−0.419879
$870$		0			0
$871$	2.95732			0.100205
$872$	−4.12665	+	4.12665i	−0.139746	+	0.139746i
$873$		0			0
$874$	6.51698	−	1.43888i	0.220440	−	0.0486710i
$875$	−6.96405	−	8.70695i	−0.235428	−	0.294349i
$876$		0			0
$877$	4.63012	+	4.63012i	0.156348	+	0.156348i	0.780946	−	0.624598i	$-0.214737\pi$
$877$	4.63012	+	4.63012i	0.156348	+	0.156348i	−0.624598	+	0.780946i	$0.714737\pi$
$878$	−9.43606	−	9.43606i	−0.318452	−	0.318452i
$879$		0			0
$880$	−2.51706	−	1.57989i	−0.0848500	−	0.0532581i
$881$	−24.1826			−0.814731			−0.407365	−	0.913265i	$-0.633552\pi$
$881$	−24.1826			−0.814731			−0.407365	+	0.913265i	$0.633552\pi$
$882$		0			0
$883$	4.73940	+	4.73940i	0.159494	+	0.159494i	0.782342	−	0.622849i	$-0.214025\pi$
$883$	4.73940	+	4.73940i	0.159494	+	0.159494i	−0.622849	+	0.782342i	$0.714025\pi$
$884$	3.22314			0.108406
$885$		0			0
$886$		−	24.6377i		−	0.827720i
$887$	17.0631	+	17.0631i	0.572921	+	0.572921i	0.932944	−	0.360022i	$-0.117231\pi$
$887$	17.0631	+	17.0631i	0.572921	+	0.572921i	−0.360022	+	0.932944i	$0.617231\pi$
$888$		0			0
$889$	10.9368			0.366810
$890$	8.37045	+	36.5925i	0.280578	+	1.22658i
$891$		0			0
$892$	0.212542	+	0.212542i	0.00711644	+	0.00711644i
$893$	−21.4660	−	13.7014i	−0.718332	−	0.458499i
$894$		0			0
$895$	−1.82392	−	1.14483i	−0.0609670	−	0.0382674i
$896$			0.997232i			0.0333152i
$897$		0			0
$898$	27.6310	+	27.6310i	0.922058	+	0.922058i
$899$		−	35.4131i		−	1.18109i
$900$		0			0
$901$			23.8483i			0.794502i
$902$	0.499872	−	0.499872i	0.0166439	−	0.0166439i
$903$		0			0
$904$		−	0.655286i		−	0.0217945i
$905$	24.2760	−	38.6762i	0.806963	−	1.28564i
$906$		0			0
$907$	40.9598	+	40.9598i	1.36005	+	1.36005i	0.873845	+	0.486204i	$0.161619\pi$
$907$	40.9598	+	40.9598i	1.36005	+	1.36005i	0.486204	+	0.873845i	$0.338381\pi$
$908$	16.9240	−	16.9240i	0.561642	−	0.561642i
$909$		0			0
$910$	−2.27910	+	0.521339i	−0.0755515	+	0.0172822i
$911$			30.8795i			1.02308i	0.859259	+	0.511541i	$0.170925\pi$
$911$			30.8795i			1.02308i	−0.859259	+	0.511541i	$0.829075\pi$
$912$		0			0
$913$	−12.6295	−	12.6295i	−0.417975	−	0.417975i
$914$	36.6647			1.21276
$915$		0			0
$916$	−7.59523			−0.250953
$917$	9.34471	−	9.34471i	0.308590	−	0.308590i
$918$		0			0
$919$		−	7.02277i		−	0.231660i	−0.993269	−	0.115830i	$-0.963047\pi$
$919$		−	7.02277i		−	0.231660i	0.993269	−	0.115830i	$-0.0369528\pi$
$920$	−2.89977	−	1.82011i	−0.0956024	−	0.0600071i
$921$		0			0
$922$	−11.5401	−	11.5401i	−0.380054	−	0.380054i
$923$	−6.46417	−	6.46417i	−0.212771	−	0.212771i
$924$		0			0
$925$	3.11044	−	8.91651i	0.102271	−	0.293173i
$926$			6.02559i			0.198013i
$927$		0			0
$928$	4.20791	+	4.20791i	0.138132	+	0.138132i
$929$			6.87722i			0.225634i	0.993616	+	0.112817i	$0.0359874\pi$
$929$			6.87722i			0.225634i	−0.993616	+	0.112817i	$0.964013\pi$
$930$		0			0
$931$	−25.5619	+	5.64380i	−0.837756	+	0.184968i
$932$	0.816115	−	0.816115i	0.0267327	−	0.0267327i
$933$		0			0
$934$	−34.0320			−1.11356
$935$	−8.90567	+	2.03715i	−0.291247	+	0.0666219i
$936$		0			0
$937$	−29.1041	+	29.1041i	−0.950788	+	0.950788i	−0.998845	−	0.0480562i	$-0.984697\pi$
$937$	−29.1041	+	29.1041i	−0.950788	+	0.950788i	0.0480562	+	0.998845i	$0.484697\pi$
$938$	1.98894	+	1.98894i	0.0649413	+	0.0649413i
$939$		0			0
$940$	2.91306	+	12.7348i	0.0950136	+	0.415365i
$941$		−	56.1970i		−	1.83197i	−0.401213	−	0.915985i	$-0.631411\pi$
$941$		−	56.1970i		−	1.83197i	0.401213	−	0.915985i	$-0.368589\pi$
$942$		0			0
$943$	0.575875	−	0.575875i	0.0187531	−	0.0187531i
$944$	−3.53944			−0.115199
$945$		0			0
$946$			2.87835i			0.0935833i
$947$	4.56166	−	4.56166i	0.148234	−	0.148234i	−0.629095	−	0.777329i	$-0.716574\pi$
$947$	4.56166	−	4.56166i	0.148234	−	0.148234i	0.777329	+	0.629095i	$0.216574\pi$
$948$		0			0
$949$	8.65384			0.280915
$950$	21.6421	+	2.57310i	0.702161	+	0.0834823i
$951$		0			0
$952$	2.16771	+	2.16771i	0.0702560	+	0.0702560i
$953$	2.55998	−	2.55998i	0.0829258	−	0.0829258i	−0.664427	−	0.747353i	$-0.731324\pi$
$953$	2.55998	−	2.55998i	0.0829258	−	0.0829258i	0.747353	+	0.664427i	$0.231324\pi$
$954$		0			0
$955$	−13.9159	−	8.73464i	−0.450308	−	0.282646i
$956$	4.21103			0.136195
$957$		0			0
$958$	13.9424	−	13.9424i	0.450460	−	0.450460i
$959$			6.23396i			0.201305i
$960$		0			0
$961$	−4.41308			−0.142357
$962$	−1.40024	−	1.40024i	−0.0451457	−	0.0451457i
$963$		0			0
$964$	−24.8896			−0.801638
$965$	−28.7435	+	6.57501i	−0.925287	+	0.211657i
$966$		0			0
$967$	28.9011	−	28.9011i	0.929398	−	0.929398i	−0.0682690	−	0.997667i	$-0.521748\pi$
$967$	28.9011	−	28.9011i	0.929398	−	0.929398i	0.997667	+	0.0682690i	$0.0217476\pi$
$968$	−6.52919	+	6.52919i	−0.209856	+	0.209856i
$969$		0			0
$970$	−1.87769	+	2.99151i	−0.0602891	+	0.0960516i
$971$		−	7.01480i		−	0.225116i	−0.993645	−	0.112558i	$-0.964096\pi$
$971$		−	7.01480i		−	0.225116i	0.993645	−	0.112558i	$-0.0359044\pi$
$972$		0			0
$973$	1.89449	+	1.89449i	0.0607345	+	0.0607345i
$974$			33.7792i			1.08236i
$975$		0			0
$976$	−3.41030			−0.109161
$977$	−22.3335	−	22.3335i	−0.714512	−	0.714512i	0.252964	−	0.967476i	$-0.418595\pi$
$977$	−22.3335	−	22.3335i	−0.714512	−	0.714512i	−0.967476	+	0.252964i	$0.918595\pi$
$978$		0			0
$979$	−22.3109			−0.713061
$980$	11.3739	+	7.13909i	0.363325	+	0.228050i
$981$		0			0
$982$	15.0275	+	15.0275i	0.479547	+	0.479547i
$983$	4.61128	−	4.61128i	0.147077	−	0.147077i	−0.629734	−	0.776811i	$-0.716836\pi$
$983$	4.61128	−	4.61128i	0.147077	−	0.147077i	0.776811	+	0.629734i	$0.216836\pi$
$984$		0			0
$985$	16.7392	−	3.82905i	0.533355	−	0.122004i
$986$	18.2938			0.582592
$987$		0			0
$988$	2.45889	−	3.85234i	0.0782276	−	0.122559i
$989$			3.31599i			0.105442i
$990$		0			0
$991$		−	30.5890i		−	0.971691i	−0.874045	−	0.485845i	$-0.838512\pi$
$991$		−	30.5890i		−	0.971691i	0.874045	−	0.485845i	$-0.161488\pi$
$992$	4.20791	−	4.20791i	0.133601	−	0.133601i
$993$		0			0
$994$		−	8.69493i		−	0.275786i
$995$	−27.9341	+	44.5042i	−0.885572	+	1.41088i
$996$		0			0
$997$	10.7588	−	10.7588i	0.340735	−	0.340735i	−0.515909	−	0.856644i	$-0.672546\pi$
$997$	10.7588	−	10.7588i	0.340735	−	0.340735i	0.856644	+	0.515909i	$0.172546\pi$
$998$	−27.7826	+	27.7826i	−0.879444	+	0.879444i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.p.d.1063.1		20
3.2	odd	2		570.2.m.a.493.10	yes	20
5.2	odd	4	inner	1710.2.p.d.37.6		20
15.2	even	4		570.2.m.a.37.5	✓	20
19.18	odd	2	inner	1710.2.p.d.1063.6		20
57.56	even	2		570.2.m.a.493.5	yes	20
95.37	even	4	inner	1710.2.p.d.37.1		20
285.227	odd	4		570.2.m.a.37.10	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.m.a.37.5	✓	20	15.2	even	4
570.2.m.a.37.10	yes	20	285.227	odd	4
570.2.m.a.493.5	yes	20	57.56	even	2
570.2.m.a.493.10	yes	20	3.2	odd	2
1710.2.p.d.37.1		20	95.37	even	4	inner
1710.2.p.d.37.6		20	5.2	odd	4	inner
1710.2.p.d.1063.1		20	1.1	even	1	trivial
1710.2.p.d.1063.6		20	19.18	odd	2	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.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-1.89390 - 1.18875i) q^{5} +(0.705149 - 0.705149i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-1.89390 - 1.18875i) q^{5} +(0.705149 - 0.705149i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.498616 + 2.17977i) q^{10} -1.32903 q^{11} +(-0.741383 + 0.741383i) q^{13} -0.997232 q^{14} -1.00000 q^{16} +(-2.17373 + 2.17373i) q^{17} +(0.939768 + 4.25639i) q^{19} +(1.18875 - 1.89390i) q^{20} +(0.939768 + 0.939768i) q^{22} +(1.08266 + 1.08266i) q^{23} +(2.17373 + 4.50276i) q^{25} +1.04847 q^{26} +(0.705149 + 0.705149i) q^{28} +5.95089 q^{29} -5.95089i q^{31} +(0.707107 + 0.707107i) q^{32} +3.07412 q^{34} +(-2.17373 + 0.497236i) q^{35} +(-1.33551 - 1.33551i) q^{37} +(2.34520 - 3.67424i) q^{38} +(-2.17977 + 0.498616i) q^{40} -0.531910i q^{41} +(1.53142 + 1.53142i) q^{43} -1.32903i q^{44} -1.53111i q^{46} +(-4.13113 + 4.13113i) q^{47} +6.00553i q^{49} +(1.64687 - 4.72100i) q^{50} +(-0.741383 - 0.741383i) q^{52} +(5.48557 - 5.48557i) q^{53} +(2.51706 + 1.57989i) q^{55} -0.997232i q^{56} +(-4.20791 - 4.20791i) q^{58} +3.53944 q^{59} +3.41030 q^{61} +(-4.20791 + 4.20791i) q^{62} -1.00000i q^{64} +(2.28543 - 0.522786i) q^{65} +(-1.99446 - 1.99446i) q^{67} +(-2.17373 - 2.17373i) q^{68} +(1.88866 + 1.18546i) q^{70} +8.71907i q^{71} +(-5.83628 - 5.83628i) q^{73} +1.88869i q^{74} +(-4.25639 + 0.939768i) q^{76} +(-0.937166 + 0.937166i) q^{77} +9.31319 q^{79} +(1.89390 + 1.18875i) q^{80} +(-0.376117 + 0.376117i) q^{82} +(9.50276 + 9.50276i) q^{83} +(6.70087 - 1.53281i) q^{85} -2.16575i q^{86} +(-0.939768 + 0.939768i) q^{88} +16.7874 q^{89} +1.04557i q^{91} +(-1.08266 + 1.08266i) q^{92} +5.84230 q^{94} +(3.27997 - 9.17833i) q^{95} +(1.11691 + 1.11691i) q^{97} +(4.24655 - 4.24655i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{5} - 4 q^{7}+O(q^{10}) \) 20 * q + 4 * q^5 - 4 * q^7	\( 20 q + 4 q^{5} - 4 q^{7} + 8 q^{11} - 20 q^{16} - 4 q^{17} - 44 q^{23} + 4 q^{25} + 8 q^{26} - 4 q^{28} - 4 q^{35} + 4 q^{38} + 52 q^{43} - 4 q^{47} + 16 q^{55} + 8 q^{58} + 32 q^{61} + 8 q^{62} - 4 q^{68} - 20 q^{73} + 20 q^{76} + 24 q^{77} - 4 q^{80} - 24 q^{82} + 116 q^{83} - 60 q^{85} + 44 q^{92} + 32 q^{95}+O(q^{100}) \) 20 * q + 4 * q^5 - 4 * q^7 + 8 * q^11 - 20 * q^16 - 4 * q^17 - 44 * q^23 + 4 * q^25 + 8 * q^26 - 4 * q^28 - 4 * q^35 + 4 * q^38 + 52 * q^43 - 4 * q^47 + 16 * q^55 + 8 * q^58 + 32 * q^61 + 8 * q^62 - 4 * q^68 - 20 * q^73 + 20 * q^76 + 24 * q^77 - 4 * q^80 - 24 * q^82 + 116 * q^83 - 60 * q^85 + 44 * q^92 + 32 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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