LMFDB - Embedded newform 1710.2.p.d.1063.8

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			1063.8
Root			$1.75036 + 1.75036i$ of defining polynomial
Character	$\chi$	$=$	1710.1063
Dual form			1710.2.p.d.37.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(0.253765 - 2.22162i) q^{5} +(-2.47539 + 2.47539i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(0.253765 - 2.22162i) q^{5} +(-2.47539 + 2.47539i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.75036 - 1.39149i) q^{10} -2.74367 q^{11} +(1.20178 - 1.20178i) q^{13} -3.50073 q^{14} -1.00000 q^{16} +(4.87121 - 4.87121i) q^{17} +(-1.94007 - 3.90335i) q^{19} +(2.22162 + 0.253765i) q^{20} +(-1.94007 - 1.94007i) q^{22} +(-0.0321428 - 0.0321428i) q^{23} +(-4.87121 - 1.12754i) q^{25} +1.69957 q^{26} +(-2.47539 - 2.47539i) q^{28} +6.50952 q^{29} -6.50952i q^{31} +(-0.707107 - 0.707107i) q^{32} +6.88893 q^{34} +(4.87121 + 6.12754i) q^{35} +(-4.58998 - 4.58998i) q^{37} +(1.38825 - 4.13192i) q^{38} +(1.39149 + 1.75036i) q^{40} -5.96665i q^{41} +(5.39582 + 5.39582i) q^{43} -2.74367i q^{44} -0.0454567i q^{46} +(-3.66743 + 3.66743i) q^{47} -5.25508i q^{49} +(-2.64717 - 4.24175i) q^{50} +(1.20178 + 1.20178i) q^{52} +(8.97544 - 8.97544i) q^{53} +(-0.696246 + 6.09540i) q^{55} -3.50073i q^{56} +(4.60292 + 4.60292i) q^{58} +4.42301 q^{59} -2.95077 q^{61} +(4.60292 - 4.60292i) q^{62} -1.00000i q^{64} +(-2.36493 - 2.97487i) q^{65} +(-7.00145 - 7.00145i) q^{67} +(4.87121 + 4.87121i) q^{68} +(-0.888360 + 7.77729i) q^{70} -5.56594i q^{71} +(-2.19205 - 2.19205i) q^{73} -6.49122i q^{74} +(3.90335 - 1.94007i) q^{76} +(6.79164 - 6.79164i) q^{77} +0.225823 q^{79} +(-0.253765 + 2.22162i) q^{80} +(4.21906 - 4.21906i) q^{82} +(3.87246 + 3.87246i) q^{83} +(-9.58584 - 12.0581i) q^{85} +7.63084i q^{86} +(1.94007 - 1.94007i) q^{88} -9.13628 q^{89} +5.94974i q^{91} +(0.0321428 - 0.0321428i) q^{92} -5.18653 q^{94} +(-9.16409 + 3.31956i) q^{95} +(8.76663 + 8.76663i) q^{97} +(3.71590 - 3.71590i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.253765	−	2.22162i	0.113487	−	0.993539i
$5$	0.253765	−	2.22162i	0.113487	−	0.993539i
$6$		0			0
$7$	−2.47539	+	2.47539i	−0.935608	+	0.935608i	−0.998049	−	0.0624406i	$-0.980112\pi$
$7$	−2.47539	+	2.47539i	−0.935608	+	0.935608i	0.0624406	+	0.998049i	$0.480112\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	1.75036	−	1.39149i	0.553513	−	0.440026i
$11$	−2.74367			−0.827247			−0.413624	−	0.910448i	$-0.635737\pi$
$11$	−2.74367			−0.827247			−0.413624	+	0.910448i	$0.635737\pi$
$12$		0			0
$13$	1.20178	−	1.20178i	0.333314	−	0.333314i	−0.520530	−	0.853844i	$-0.674265\pi$
$13$	1.20178	−	1.20178i	0.333314	−	0.333314i	0.853844	+	0.520530i	$0.174265\pi$
$14$	−3.50073			−0.935608
$15$		0			0
$16$	−1.00000			−0.250000
$17$	4.87121	−	4.87121i	1.18144	−	1.18144i	0.202070	−	0.979371i	$-0.435233\pi$
$17$	4.87121	−	4.87121i	1.18144	−	1.18144i	0.979371	−	0.202070i	$-0.0647669\pi$
$18$		0			0
$19$	−1.94007	−	3.90335i	−0.445082	−	0.895490i
$19$	−1.94007	−	3.90335i	−0.445082	−	0.895490i
$20$	2.22162	+	0.253765i	0.496770	+	0.0567435i
$21$		0			0
$22$	−1.94007	−	1.94007i	−0.413624	−	0.413624i
$23$	−0.0321428	−	0.0321428i	−0.00670223	−	0.00670223i	0.703748	−	0.710450i	$-0.251509\pi$
$23$	−0.0321428	−	0.0321428i	−0.00670223	−	0.00670223i	−0.710450	+	0.703748i	$0.751509\pi$
$24$		0			0
$25$	−4.87121	−	1.12754i	−0.974241	−	0.225508i
$26$	1.69957			0.333314
$27$		0			0
$28$	−2.47539	−	2.47539i	−0.467804	−	0.467804i
$29$	6.50952			1.20879			0.604394	−	0.796686i	$-0.293415\pi$
$29$	6.50952			1.20879			0.604394	+	0.796686i	$0.293415\pi$
$30$		0			0
$31$		−	6.50952i		−	1.16914i	−0.811342	−	0.584572i	$-0.801262\pi$
$31$		−	6.50952i		−	1.16914i	0.811342	−	0.584572i	$-0.198738\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$	6.88893			1.18144
$35$	4.87121	+	6.12754i	0.823384	+	1.03574i
$36$		0			0
$37$	−4.58998	−	4.58998i	−0.754589	−	0.754589i	0.220743	−	0.975332i	$-0.429152\pi$
$37$	−4.58998	−	4.58998i	−0.754589	−	0.754589i	−0.975332	+	0.220743i	$0.929152\pi$
$38$	1.38825	−	4.13192i	0.225204	−	0.670286i
$39$		0			0
$40$	1.39149	+	1.75036i	0.220013	+	0.276757i
$41$		−	5.96665i		−	0.931833i	−0.884829	−	0.465917i	$-0.845725\pi$
$41$		−	5.96665i		−	0.931833i	0.884829	−	0.465917i	$-0.154275\pi$
$42$		0			0
$43$	5.39582	+	5.39582i	0.822855	+	0.822855i	0.986517	−	0.163662i	$-0.0523305\pi$
$43$	5.39582	+	5.39582i	0.822855	+	0.822855i	−0.163662	+	0.986517i	$0.552331\pi$
$44$		−	2.74367i		−	0.413624i
$45$		0			0
$46$		−	0.0454567i		−	0.00670223i
$47$	−3.66743	+	3.66743i	−0.534950	+	0.534950i	−0.922041	−	0.387091i	$-0.873480\pi$
$47$	−3.66743	+	3.66743i	−0.534950	+	0.534950i	0.387091	+	0.922041i	$0.373480\pi$
$48$		0			0
$49$		−	5.25508i		−	0.750725i
$50$	−2.64717	−	4.24175i	−0.374367	−	0.599875i
$51$		0			0
$52$	1.20178	+	1.20178i	0.166657	+	0.166657i
$53$	8.97544	−	8.97544i	1.23287	−	1.23287i	0.270015	−	0.962856i	$-0.412971\pi$
$53$	8.97544	−	8.97544i	1.23287	−	1.23287i	0.962856	−	0.270015i	$-0.0870288\pi$
$54$		0			0
$55$	−0.696246	+	6.09540i	−0.0938818	+	0.821903i
$56$		−	3.50073i		−	0.467804i
$57$		0			0
$58$	4.60292	+	4.60292i	0.604394	+	0.604394i
$59$	4.42301			0.575826			0.287913	−	0.957657i	$-0.407039\pi$
$59$	4.42301			0.575826			0.287913	+	0.957657i	$0.407039\pi$
$60$		0			0
$61$	−2.95077			−0.377808			−0.188904	−	0.981996i	$-0.560493\pi$
$61$	−2.95077			−0.377808			−0.188904	+	0.981996i	$0.560493\pi$
$62$	4.60292	−	4.60292i	0.584572	−	0.584572i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−2.36493	−	2.97487i	−0.293334	−	0.368987i
$66$		0			0
$67$	−7.00145	−	7.00145i	−0.855363	−	0.855363i	0.135424	−	0.990788i	$-0.456760\pi$
$67$	−7.00145	−	7.00145i	−0.855363	−	0.855363i	−0.990788	+	0.135424i	$0.956760\pi$
$68$	4.87121	+	4.87121i	0.590721	+	0.590721i
$69$		0			0
$70$	−0.888360	+	7.77729i	−0.106179	+	0.929564i
$71$		−	5.56594i		−	0.660556i	−0.943884	−	0.330278i	$-0.892858\pi$
$71$		−	5.56594i		−	0.660556i	0.943884	−	0.330278i	$-0.107142\pi$
$72$		0			0
$73$	−2.19205	−	2.19205i	−0.256560	−	0.256560i	0.567094	−	0.823653i	$-0.308068\pi$
$73$	−2.19205	−	2.19205i	−0.256560	−	0.256560i	−0.823653	+	0.567094i	$0.808068\pi$
$74$		−	6.49122i		−	0.754589i
$75$		0			0
$76$	3.90335	−	1.94007i	0.447745	−	0.222541i
$77$	6.79164	−	6.79164i	0.773979	−	0.773979i
$78$		0			0
$79$	0.225823			0.0254070			0.0127035	−	0.999919i	$-0.495956\pi$
$79$	0.225823			0.0254070			0.0127035	+	0.999919i	$0.495956\pi$
$80$	−0.253765	+	2.22162i	−0.0283717	+	0.248385i
$81$		0			0
$82$	4.21906	−	4.21906i	0.465917	−	0.465917i
$83$	3.87246	+	3.87246i	0.425058	+	0.425058i	0.886941	−	0.461883i	$-0.152826\pi$
$83$	3.87246	+	3.87246i	0.425058	+	0.425058i	−0.461883	+	0.886941i	$0.652826\pi$
$84$		0			0
$85$	−9.58584	−	12.0581i	−1.03973	−	1.30789i
$86$			7.63084i			0.822855i
$87$		0			0
$88$	1.94007	−	1.94007i	0.206812	−	0.206812i
$89$	−9.13628			−0.968444			−0.484222	−	0.874945i	$-0.660897\pi$
$89$	−9.13628			−0.968444			−0.484222	+	0.874945i	$0.660897\pi$
$90$		0			0
$91$			5.94974i			0.623703i
$92$	0.0321428	−	0.0321428i	0.00335112	−	0.00335112i
$93$		0			0
$94$	−5.18653			−0.534950
$95$	−9.16409	+	3.31956i	−0.940216	+	0.340580i
$96$		0			0
$97$	8.76663	+	8.76663i	0.890117	+	0.890117i	0.994534	−	0.104417i	$-0.0332976\pi$
$97$	8.76663	+	8.76663i	0.890117	+	0.890117i	−0.104417	+	0.994534i	$0.533298\pi$
$98$	3.71590	−	3.71590i	0.375363	−	0.375363i
$99$		0			0
$100$	1.12754	−	4.87121i	0.112754	−	0.487121i
$101$	−11.2650			−1.12091			−0.560455	−	0.828185i	$-0.689374\pi$
$101$	−11.2650			−1.12091			−0.560455	+	0.828185i	$0.689374\pi$
$102$		0			0
$103$	−0.762447	+	0.762447i	−0.0751262	+	0.0751262i	−0.743671	−	0.668545i	$-0.766917\pi$
$103$	−0.762447	+	0.762447i	−0.0751262	+	0.0751262i	0.668545	+	0.743671i	$0.266917\pi$
$104$			1.69957i			0.166657i
$105$		0			0
$106$	12.6932			1.23287
$107$	−13.5351	−	13.5351i	−1.30849	−	1.30849i	−0.922505	−	0.385985i	$-0.873861\pi$
$107$	−13.5351	−	13.5351i	−1.30849	−	1.30849i	−0.385985	−	0.922505i	$-0.626139\pi$
$108$		0			0
$109$	4.37207			0.418768			0.209384	−	0.977833i	$-0.432854\pi$
$109$	4.37207			0.418768			0.209384	+	0.977833i	$0.432854\pi$
$110$	−4.80242	+	3.81777i	−0.457892	+	0.364011i
$111$		0			0
$112$	2.47539	−	2.47539i	0.233902	−	0.233902i
$113$	6.95599	−	6.95599i	0.654365	−	0.654365i	−0.299676	−	0.954041i	$-0.596879\pi$
$113$	6.95599	−	6.95599i	0.654365	−	0.654365i	0.954041	+	0.299676i	$0.0968786\pi$
$114$		0			0
$115$	−0.0795658	+	0.0632524i	−0.00741955	+	0.00589832i
$116$			6.50952i			0.604394i
$117$		0			0
$118$	3.12754	+	3.12754i	0.287913	+	0.287913i
$119$			24.1162i			2.21073i
$120$		0			0
$121$	−3.47228			−0.315662
$122$	−2.08651	−	2.08651i	−0.188904	−	0.188904i
$123$		0			0
$124$	6.50952			0.584572
$125$	−3.74110	+	10.5359i	−0.334614	+	0.942355i
$126$		0			0
$127$	−13.7136	−	13.7136i	−1.21689	−	1.21689i	−0.968716	−	0.248173i	$-0.920170\pi$
$127$	−13.7136	−	13.7136i	−1.21689	−	1.21689i	−0.248173	−	0.968716i	$-0.579830\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	0.431292	−	3.77581i	0.0378268	−	0.331161i
$131$	−8.01380			−0.700169			−0.350085	−	0.936718i	$-0.613847\pi$
$131$	−8.01380			−0.700169			−0.350085	+	0.936718i	$0.613847\pi$
$132$		0			0
$133$	14.4647	+	4.85988i	1.25425	+	0.421405i
$134$		−	9.90155i		−	0.855363i
$135$		0			0
$136$			6.88893i			0.590721i
$137$	12.6299	−	12.6299i	1.07905	−	1.07905i	0.0824532	−	0.996595i	$-0.473725\pi$
$137$	12.6299	−	12.6299i	1.07905	−	1.07905i	0.996595	−	0.0824532i	$-0.0262755\pi$
$138$		0			0
$139$			10.3499i			0.877869i	0.898519	+	0.438934i	$0.144644\pi$
$139$			10.3499i			0.877869i	−0.898519	+	0.438934i	$0.855356\pi$
$140$	−6.12754	+	4.87121i	−0.517871	+	0.411692i
$141$		0			0
$142$	3.93571	−	3.93571i	0.330278	−	0.330278i
$143$	−3.29729	+	3.29729i	−0.275733	+	0.275733i
$144$		0			0
$145$	1.65189	−	14.4617i	0.137182	−	1.20098i
$146$		−	3.10002i		−	0.256560i
$147$		0			0
$148$	4.58998	−	4.58998i	0.377294	−	0.377294i
$149$			9.07466i			0.743425i	0.928348	+	0.371712i	$0.121229\pi$
$149$			9.07466i			0.743425i	−0.928348	+	0.371712i	$0.878771\pi$
$150$		0			0
$151$		−	1.75287i		−	0.142647i	−0.997453	−	0.0713234i	$-0.977278\pi$
$151$		−	1.75287i		−	0.142647i	0.997453	−	0.0713234i	$-0.0227222\pi$
$152$	4.13192	+	1.38825i	0.335143	+	0.112602i
$153$		0			0
$154$	9.60483			0.773979
$155$	−14.4617	−	1.65189i	−1.16159	−	0.132683i
$156$		0			0
$157$	7.20733	−	7.20733i	0.575207	−	0.575207i	−0.358372	−	0.933579i	$-0.616668\pi$
$157$	7.20733	−	7.20733i	0.575207	−	0.575207i	0.933579	+	0.358372i	$0.116668\pi$
$158$	0.159681	+	0.159681i	0.0127035	+	0.0127035i
$159$		0			0
$160$	−1.75036	+	1.39149i	−0.138378	+	0.110007i
$161$	0.159132			0.0125413
$162$		0			0
$163$	9.60292	+	9.60292i	0.752159	+	0.752159i	0.974882	−	0.222723i	$-0.0714945\pi$
$163$	9.60292	+	9.60292i	0.752159	+	0.752159i	−0.222723	+	0.974882i	$0.571494\pi$
$164$	5.96665			0.465917
$165$		0			0
$166$			5.47649i			0.425058i
$167$	12.9013	+	12.9013i	0.998336	+	0.998336i	0.999999	−	0.00166271i	$-0.000529259\pi$
$167$	12.9013	+	12.9013i	0.998336	+	0.998336i	−0.00166271	+	0.999999i	$0.500529\pi$
$168$		0			0
$169$			10.1114i			0.777804i
$170$	1.74817	−	15.3046i	0.134078	−	1.17381i
$171$		0			0
$172$	−5.39582	+	5.39582i	−0.411427	+	0.411427i
$173$	0.271593	−	0.271593i	0.0206488	−	0.0206488i	−0.696707	−	0.717356i	$-0.745352\pi$
$173$	0.271593	−	0.271593i	0.0206488	−	0.0206488i	0.717356	+	0.696707i	$0.245352\pi$
$174$		0			0
$175$	14.8492	−	9.26703i	1.12249	−	0.700521i
$176$	2.74367			0.206812
$177$		0			0
$178$	−6.46033	−	6.46033i	−0.484222	−	0.484222i
$179$	16.1543			1.20743			0.603715	−	0.797200i	$-0.293686\pi$
$179$	16.1543			1.20743			0.603715	+	0.797200i	$0.293686\pi$
$180$		0			0
$181$			16.1980i			1.20399i	0.798501	+	0.601994i	$0.205627\pi$
$181$			16.1980i			1.20399i	−0.798501	+	0.601994i	$0.794373\pi$
$182$	−4.20710	+	4.20710i	−0.311851	+	0.311851i
$183$		0			0
$184$	0.0454567			0.00335112
$185$	−11.3620	+	9.03243i	−0.835349	+	0.664078i
$186$		0			0
$187$	−13.3650	+	13.3650i	−0.977344	+	0.977344i
$188$	−3.66743	−	3.66743i	−0.267475	−	0.267475i
$189$		0			0
$190$	−8.82727	−	4.13270i	−0.640398	−	0.299818i
$191$	−14.6162			−1.05759			−0.528795	−	0.848750i	$-0.677356\pi$
$191$	−14.6162			−1.05759			−0.528795	+	0.848750i	$0.677356\pi$
$192$		0			0
$193$	−6.20432	+	6.20432i	−0.446597	+	0.446597i	−0.894221	−	0.447625i	$-0.852270\pi$
$193$	−6.20432	+	6.20432i	−0.446597	+	0.446597i	0.447625	+	0.894221i	$0.352270\pi$
$194$			12.3979i			0.890117i
$195$		0			0
$196$	5.25508			0.375363
$197$	9.77456	−	9.77456i	0.696408	−	0.696408i	−0.267226	−	0.963634i	$-0.586107\pi$
$197$	9.77456	−	9.77456i	0.696408	−	0.696408i	0.963634	+	0.267226i	$0.0861069\pi$
$198$		0			0
$199$			7.77253i			0.550980i	0.961304	+	0.275490i	$0.0888401\pi$
$199$			7.77253i			0.550980i	−0.961304	+	0.275490i	$0.911160\pi$
$200$	4.24175	−	2.64717i	0.299937	−	0.187183i
$201$		0			0
$202$	−7.96556	−	7.96556i	−0.560455	−	0.560455i
$203$	−16.1136	+	16.1136i	−1.13095	+	1.13095i
$204$		0			0
$205$	−13.2556	−	1.51412i	−0.925813	−	0.105751i
$206$	−1.07826			−0.0751262
$207$		0			0
$208$	−1.20178	+	1.20178i	−0.0833285	+	0.0833285i
$209$	5.32290	+	10.7095i	0.368193	+	0.740792i
$210$		0			0
$211$			7.91902i			0.545168i	0.962132	+	0.272584i	$0.0878783\pi$
$211$			7.91902i			0.545168i	−0.962132	+	0.272584i	$0.912122\pi$
$212$	8.97544	+	8.97544i	0.616436	+	0.616436i
$213$		0			0
$214$		−	19.1416i		−	1.30849i
$215$	13.3567	−	10.6182i	0.910922	−	0.724156i
$216$		0			0
$217$	16.1136	+	16.1136i	1.09386	+	1.09386i
$218$	3.09152	+	3.09152i	0.209384	+	0.209384i
$219$		0			0
$220$	−6.09540	−	0.696246i	−0.410951	−	0.0469409i
$221$		−	11.7082i		−	0.787582i
$222$		0			0
$223$	14.3643	−	14.3643i	0.961907	−	0.961907i	−0.0373940	−	0.999301i	$-0.511906\pi$
$223$	14.3643	−	14.3643i	0.961907	−	0.961907i	0.999301	+	0.0373940i	$0.0119057\pi$
$224$	3.50073			0.233902
$225$		0			0
$226$	9.83726			0.654365
$227$	−15.0385	−	15.0385i	−0.998139	−	0.998139i	0.00185921	−	0.999998i	$-0.499408\pi$
$227$	−15.0385	−	15.0385i	−0.998139	−	0.998139i	−0.999998	+	0.00185921i	$0.999408\pi$
$228$		0			0
$229$			2.69570i			0.178137i	0.996026	+	0.0890683i	$0.0283890\pi$
$229$			2.69570i			0.178137i	−0.996026	+	0.0890683i	$0.971611\pi$
$230$	−0.100988	−	0.0115353i	−0.00665893	−	0.000760616i
$231$		0			0
$232$	−4.60292	+	4.60292i	−0.302197	+	0.302197i
$233$	12.4775	+	12.4775i	0.817426	+	0.817426i	0.985734	−	0.168309i	$-0.0538306\pi$
$233$	12.4775	+	12.4775i	0.817426	+	0.817426i	−0.168309	+	0.985734i	$0.553831\pi$
$234$		0			0
$235$	7.21698	+	9.07831i	0.470784	+	0.592204i
$236$			4.42301i			0.287913i
$237$		0			0
$238$	−17.0528	+	17.0528i	−1.10537	+	1.10537i
$239$		−	27.2150i		−	1.76039i	−0.474613	−	0.880195i	$-0.657412\pi$
$239$		−	27.2150i		−	1.76039i	0.474613	−	0.880195i	$-0.342588\pi$
$240$		0			0
$241$			25.1111i			1.61755i	0.588120	+	0.808774i	$0.299868\pi$
$241$			25.1111i			1.61755i	−0.588120	+	0.808774i	$0.700132\pi$
$242$	−2.45527	−	2.45527i	−0.157831	−	0.157831i
$243$		0			0
$244$		−	2.95077i		−	0.188904i
$245$	−11.6748	−	1.33355i	−0.745875	−	0.0851975i
$246$		0			0
$247$	−7.02251	−	2.35944i	−0.446831	−	0.150127i
$248$	4.60292	+	4.60292i	0.292286	+	0.292286i
$249$		0			0
$250$	−10.0953	+	4.80461i	−0.638485	+	0.303870i
$251$	2.30195			0.145298			0.0726489	−	0.997358i	$-0.476855\pi$
$251$	2.30195			0.145298			0.0726489	+	0.997358i	$0.476855\pi$
$252$		0			0
$253$	0.0881891	+	0.0881891i	0.00554440	+	0.00554440i
$254$		−	19.3940i		−	1.21689i
$255$		0			0
$256$	1.00000			0.0625000
$257$	15.7752	+	15.7752i	0.984032	+	0.984032i	0.999874	−	0.0158429i	$-0.00504315\pi$
$257$	15.7752	+	15.7752i	0.984032	+	0.984032i	−0.0158429	+	0.999874i	$0.505043\pi$
$258$		0			0
$259$	22.7240			1.41200
$260$	2.97487	−	2.36493i	0.184494	−	0.146667i
$261$		0			0
$262$	−5.66661	−	5.66661i	−0.350085	−	0.350085i
$263$	1.21906	+	1.21906i	0.0751702	+	0.0751702i	0.743692	−	0.668522i	$-0.233073\pi$
$263$	1.21906	+	1.21906i	0.0751702	+	0.0751702i	−0.668522	+	0.743692i	$0.733073\pi$
$264$		0			0
$265$	−17.6624	−	22.2177i	−1.08499	−	1.36482i
$266$	6.79164	+	13.6646i	0.416422	+	0.837828i
$267$		0			0
$268$	7.00145	−	7.00145i	0.427682	−	0.427682i
$269$	−7.58430			−0.462423			−0.231211	−	0.972904i	$-0.574269\pi$
$269$	−7.58430			−0.462423			−0.231211	+	0.972904i	$0.574269\pi$
$270$		0			0
$271$	−25.6741			−1.55959			−0.779795	−	0.626036i	$-0.784676\pi$
$271$	−25.6741			−1.55959			−0.779795	+	0.626036i	$0.784676\pi$
$272$	−4.87121	+	4.87121i	−0.295360	+	0.295360i
$273$		0			0
$274$	17.8614			1.07905
$275$	13.3650	+	3.09359i	0.805939	+	0.186551i
$276$		0			0
$277$	−21.7414	+	21.7414i	−1.30631	+	1.30631i	−0.382257	+	0.924056i	$0.624853\pi$
$277$	−21.7414	+	21.7414i	−1.30631	+	1.30631i	−0.924056	+	0.382257i	$0.875147\pi$
$278$	−7.31850	+	7.31850i	−0.438934	+	0.438934i
$279$		0			0
$280$	−7.77729	−	0.888360i	−0.464782	−	0.0530897i
$281$		−	21.9050i		−	1.30674i	−0.757037	−	0.653372i	$-0.773354\pi$
$281$		−	21.9050i		−	1.30674i	0.757037	−	0.653372i	$-0.226646\pi$
$282$		0			0
$283$	15.7217	+	15.7217i	0.934557	+	0.934557i	0.997986	−	0.0634298i	$-0.0202039\pi$
$283$	15.7217	+	15.7217i	0.934557	+	0.934557i	−0.0634298	+	0.997986i	$0.520204\pi$
$284$	5.56594			0.330278
$285$		0			0
$286$	−4.66307			−0.275733
$287$	14.7698	+	14.7698i	0.871831	+	0.871831i
$288$		0			0
$289$		−	30.4573i		−	1.79161i
$290$	11.3940	−	9.05790i	0.669080	−	0.531898i
$291$		0			0
$292$	2.19205	−	2.19205i	0.128280	−	0.128280i
$293$	−8.25768	+	8.25768i	−0.482419	+	0.482419i	−0.905903	−	0.423484i	$-0.860807\pi$
$293$	−8.25768	+	8.25768i	−0.482419	+	0.482419i	0.423484	+	0.905903i	$0.360807\pi$
$294$		0			0
$295$	1.12240	−	9.82625i	0.0653488	−	0.572106i
$296$	6.49122			0.377294
$297$		0			0
$298$	−6.41675	+	6.41675i	−0.371712	+	0.371712i
$299$	−0.0772571			−0.00446790
$300$		0			0
$301$	−26.7135			−1.53974
$302$	1.23947	−	1.23947i	0.0713234	−	0.0713234i
$303$		0			0
$304$	1.94007	+	3.90335i	0.111270	+	0.223872i
$305$	−0.748802	+	6.55550i	−0.0428763	+	0.375367i
$306$		0			0
$307$	22.1239	+	22.1239i	1.26268	+	1.26268i	0.949790	+	0.312887i	$0.101296\pi$
$307$	22.1239	+	22.1239i	1.26268	+	1.26268i	0.312887	+	0.949790i	$0.398704\pi$
$308$	6.79164	+	6.79164i	0.386990	+	0.386990i
$309$		0			0
$310$	−9.05790	−	11.3940i	−0.514454	−	0.647137i
$311$	−3.22108			−0.182651			−0.0913254	−	0.995821i	$-0.529110\pi$
$311$	−3.22108			−0.182651			−0.0913254	+	0.995821i	$0.529110\pi$
$312$		0			0
$313$	−14.9801	−	14.9801i	−0.846724	−	0.846724i	0.142999	−	0.989723i	$-0.454326\pi$
$313$	−14.9801	−	14.9801i	−0.846724	−	0.846724i	−0.989723	+	0.142999i	$0.954326\pi$
$314$	10.1927			0.575207
$315$		0			0
$316$			0.225823i			0.0127035i
$317$	−13.3317	−	13.3317i	−0.748782	−	0.748782i	0.225468	−	0.974251i	$-0.427609\pi$
$317$	−13.3317	−	13.3317i	−0.748782	−	0.748782i	−0.974251	+	0.225468i	$0.927609\pi$
$318$		0			0
$319$	−17.8600			−0.999966
$320$	−2.22162	−	0.253765i	−0.124192	−	0.0141859i
$321$		0			0
$322$	0.112523	+	0.112523i	0.00627066	+	0.00627066i
$323$	−28.4645	−	9.56356i	−1.58381	−	0.532131i
$324$		0			0
$325$	−7.20918	+	4.49907i	−0.399893	+	0.249563i
$326$			13.5806i			0.752159i
$327$		0			0
$328$	4.21906	+	4.21906i	0.232958	+	0.232958i
$329$		−	18.1566i		−	1.00101i
$330$		0			0
$331$		−	6.73163i		−	0.370004i	−0.982738	−	0.185002i	$-0.940771\pi$
$331$		−	6.73163i		−	0.370004i	0.982738	−	0.185002i	$-0.0592292\pi$
$332$	−3.87246	+	3.87246i	−0.212529	+	0.212529i
$333$		0			0
$334$			18.2453i			0.998336i
$335$	−17.3313	+	13.7779i	−0.946910	+	0.752765i
$336$		0			0
$337$	−14.1501	−	14.1501i	−0.770806	−	0.770806i	0.207441	−	0.978247i	$-0.433486\pi$
$337$	−14.1501	−	14.1501i	−0.770806	−	0.770806i	−0.978247	+	0.207441i	$0.933486\pi$
$338$	−7.14987	+	7.14987i	−0.388902	+	0.388902i
$339$		0			0
$340$	12.0581	−	9.58584i	0.653943	−	0.519865i
$341$			17.8600i			0.967171i
$342$		0			0
$343$	−4.31936	−	4.31936i	−0.233224	−	0.233224i
$344$	−7.63084			−0.411427
$345$		0			0
$346$	0.384091			0.0206488
$347$	−6.84109	+	6.84109i	−0.367249	+	0.367249i	−0.866473	−	0.499224i	$-0.833618\pi$
$347$	−6.84109	+	6.84109i	−0.367249	+	0.367249i	0.499224	+	0.866473i	$0.333618\pi$
$348$		0			0
$349$			33.2298i			1.77875i	0.457181	+	0.889374i	$0.348859\pi$
$349$			33.2298i			1.77875i	−0.457181	+	0.889374i	$0.651141\pi$
$350$	17.0528	+	3.94720i	0.911508	+	0.210987i
$351$		0			0
$352$	1.94007	+	1.94007i	0.103406	+	0.103406i
$353$	−25.3639	−	25.3639i	−1.34999	−	1.34999i	−0.885668	−	0.464318i	$-0.846299\pi$
$353$	−25.3639	−	25.3639i	−1.34999	−	1.34999i	−0.464318	−	0.885668i	$-0.653701\pi$
$354$		0			0
$355$	−12.3654	−	1.41244i	−0.656288	−	0.0749645i
$356$		−	9.13628i		−	0.484222i
$357$		0			0
$358$	11.4228	+	11.4228i	0.603715	+	0.603715i
$359$			9.12994i			0.481860i	0.970543	+	0.240930i	$0.0774524\pi$
$359$			9.12994i			0.481860i	−0.970543	+	0.240930i	$0.922548\pi$
$360$		0			0
$361$	−11.4723	+	15.1455i	−0.603804	+	0.797133i
$362$	−11.4537	+	11.4537i	−0.601994	+	0.601994i
$363$		0			0
$364$	−5.94974			−0.311851
$365$	−5.42616	+	4.31363i	−0.284018	+	0.225786i
$366$		0			0
$367$	12.9778	−	12.9778i	0.677435	−	0.677435i	−0.281984	−	0.959419i	$-0.590993\pi$
$367$	12.9778	−	12.9778i	0.677435	−	0.677435i	0.959419	+	0.281984i	$0.0909926\pi$
$368$	0.0321428	+	0.0321428i	0.00167556	+	0.00167556i
$369$		0			0
$370$	−14.4210	−	1.64724i	−0.749713	−	0.0856360i
$371$			44.4354i			2.30697i
$372$		0			0
$373$	−6.92570	+	6.92570i	−0.358599	+	0.358599i	−0.863296	−	0.504697i	$-0.831604\pi$
$373$	−6.92570	+	6.92570i	−0.358599	+	0.358599i	0.504697	+	0.863296i	$0.331604\pi$
$374$	−18.9009			−0.977344
$375$		0			0
$376$		−	5.18653i		−	0.267475i
$377$	7.82301	−	7.82301i	0.402906	−	0.402906i
$378$		0			0
$379$	−22.4882			−1.15514			−0.577570	−	0.816341i	$-0.695999\pi$
$379$	−22.4882			−1.15514			−0.577570	+	0.816341i	$0.695999\pi$
$380$	−3.31956	−	9.16409i	−0.170290	−	0.470108i
$381$		0			0
$382$	−10.3352	−	10.3352i	−0.528795	−	0.528795i
$383$	14.9680	−	14.9680i	0.764830	−	0.764830i	−0.212361	−	0.977191i	$-0.568115\pi$
$383$	14.9680	−	14.9680i	0.764830	−	0.764830i	0.977191	+	0.212361i	$0.0681153\pi$
$384$		0			0
$385$	−13.3650	−	16.8119i	−0.681142	−	0.856816i
$386$	−8.77423			−0.446597
$387$		0			0
$388$	−8.76663	+	8.76663i	−0.445058	+	0.445058i
$389$			10.1897i			0.516639i	0.966060	+	0.258319i	$0.0831687\pi$
$389$			10.1897i			0.516639i	−0.966060	+	0.258319i	$0.916831\pi$
$390$		0			0
$391$	−0.313148			−0.0158366
$392$	3.71590	+	3.71590i	0.187681	+	0.187681i
$393$		0			0
$394$	13.8233			0.696408
$395$	0.0573058	−	0.501693i	0.00288337	−	0.0252429i
$396$		0			0
$397$	14.9493	−	14.9493i	0.750284	−	0.750284i	−0.224248	−	0.974532i	$-0.571993\pi$
$397$	14.9493	−	14.9493i	0.750284	−	0.750284i	0.974532	+	0.224248i	$0.0719927\pi$
$398$	−5.49601	+	5.49601i	−0.275490	+	0.275490i
$399$		0			0
$400$	4.87121	+	1.12754i	0.243560	+	0.0563769i
$401$		−	17.1894i		−	0.858400i	−0.903210	−	0.429200i	$-0.858796\pi$
$401$		−	17.1894i		−	0.858400i	0.903210	−	0.429200i	$-0.141204\pi$
$402$		0			0
$403$	−7.82301	−	7.82301i	−0.389692	−	0.389692i
$404$		−	11.2650i		−	0.560455i
$405$		0			0
$406$	−22.7880			−1.13095
$407$	12.5934	+	12.5934i	0.624231	+	0.624231i
$408$		0			0
$409$	23.9489			1.18420			0.592099	−	0.805865i	$-0.298299\pi$
$409$	23.9489			1.18420			0.592099	+	0.805865i	$0.298299\pi$
$410$	−8.30250	−	10.4438i	−0.410031	−	0.515782i
$411$		0			0
$412$	−0.762447	−	0.762447i	−0.0375631	−	0.0375631i
$413$	−10.9487	+	10.9487i	−0.538748	+	0.538748i
$414$		0			0
$415$	9.58584	−	7.62045i	0.470550	−	0.374073i
$416$	−1.69957			−0.0833285
$417$		0			0
$418$	−3.80890	+	11.3366i	−0.186299	+	0.554492i
$419$		−	21.4134i		−	1.04611i	−0.852298	−	0.523056i	$-0.824792\pi$
$419$		−	21.4134i		−	1.04611i	0.852298	−	0.523056i	$-0.175208\pi$
$420$		0			0
$421$		−	1.72609i		−	0.0841246i	−0.999115	−	0.0420623i	$-0.986607\pi$
$421$		−	1.72609i		−	0.0841246i	0.999115	−	0.0420623i	$-0.0133928\pi$
$422$	−5.59960	+	5.59960i	−0.272584	+	0.272584i
$423$		0			0
$424$			12.6932i			0.616436i
$425$	−29.2211	+	18.2362i	−1.41743	+	0.884585i
$426$		0			0
$427$	7.30430	−	7.30430i	0.353480	−	0.353480i
$428$	13.5351	−	13.5351i	0.654245	−	0.654245i
$429$		0			0
$430$	16.9528	+	1.93644i	0.817539	+	0.0933833i
$431$			29.5770i			1.42467i	0.701838	+	0.712337i	$0.252363\pi$
$431$			29.5770i			1.42467i	−0.701838	+	0.712337i	$0.747637\pi$
$432$		0			0
$433$	18.7711	−	18.7711i	0.902081	−	0.902081i	−0.0935354	−	0.995616i	$-0.529817\pi$
$433$	18.7711	−	18.7711i	0.902081	−	0.902081i	0.995616	+	0.0935354i	$0.0298168\pi$
$434$			22.7880i			1.09386i
$435$		0			0
$436$			4.37207i			0.209384i
$437$	−0.0631054	+	0.187824i	−0.00301874	+	0.00898482i
$438$		0			0
$439$	−8.66125			−0.413379			−0.206690	−	0.978407i	$-0.566269\pi$
$439$	−8.66125			−0.413379			−0.206690	+	0.978407i	$0.566269\pi$
$440$	−3.81777	−	4.80242i	−0.182005	−	0.228946i
$441$		0			0
$442$	8.27898	−	8.27898i	0.393791	−	0.393791i
$443$	19.5669	+	19.5669i	0.929652	+	0.929652i	0.997683	−	0.0680315i	$-0.0216718\pi$
$443$	19.5669	+	19.5669i	0.929652	+	0.929652i	−0.0680315	+	0.997683i	$0.521672\pi$
$444$		0			0
$445$	−2.31847	+	20.2974i	−0.109906	+	0.962187i
$446$	20.3142			0.961907
$447$		0			0
$448$	2.47539	+	2.47539i	0.116951	+	0.116951i
$449$	21.3429			1.00724			0.503618	−	0.863927i	$-0.332002\pi$
$449$	21.3429			1.00724			0.503618	+	0.863927i	$0.332002\pi$
$450$		0			0
$451$			16.3705i			0.770857i
$452$	6.95599	+	6.95599i	0.327182	+	0.327182i
$453$		0			0
$454$		−	21.2676i		−	0.998139i
$455$	13.2181	+	1.50983i	0.619673	+	0.0707821i
$456$		0			0
$457$	21.3371	−	21.3371i	0.998110	−	0.998110i	−0.00188859	−	0.999998i	$-0.500601\pi$
$457$	21.3371	−	21.3371i	0.998110	−	0.998110i	0.999998	+	0.00188859i	$0.000601157\pi$
$458$	−1.90615	+	1.90615i	−0.0890683	+	0.0890683i
$459$		0			0
$460$	−0.0632524	−	0.0795658i	−0.00294916	−	0.00370977i
$461$	−0.603474			−0.0281066			−0.0140533	−	0.999901i	$-0.504473\pi$
$461$	−0.603474			−0.0281066			−0.0140533	+	0.999901i	$0.504473\pi$
$462$		0			0
$463$	−13.8679	−	13.8679i	−0.644495	−	0.644495i	0.307162	−	0.951657i	$-0.400621\pi$
$463$	−13.8679	−	13.8679i	−0.644495	−	0.644495i	−0.951657	+	0.307162i	$0.900621\pi$
$464$	−6.50952			−0.302197
$465$		0			0
$466$			17.6458i			0.817426i
$467$	−5.10843	+	5.10843i	−0.236390	+	0.236390i	−0.815353	−	0.578964i	$-0.803457\pi$
$467$	−5.10843	+	5.10843i	−0.236390	+	0.236390i	0.578964	+	0.815353i	$0.303457\pi$
$468$		0			0
$469$	34.6626			1.60057
$470$	−1.31616	+	11.5225i	−0.0607098	+	0.531494i
$471$		0			0
$472$	−3.12754	+	3.12754i	−0.143957	+	0.143957i
$473$	−14.8043	−	14.8043i	−0.680705	−	0.680705i
$474$		0			0
$475$	5.04929	+	21.2015i	0.231677	+	0.972793i
$476$	−24.1162			−1.10537
$477$		0			0
$478$	19.2439	−	19.2439i	0.880195	−	0.880195i
$479$			0.676761i			0.0309220i	0.999880	+	0.0154610i	$0.00492158\pi$
$479$			0.676761i			0.0309220i	−0.999880	+	0.0154610i	$0.995078\pi$
$480$		0			0
$481$	−11.0323			−0.503030
$482$	−17.7562	+	17.7562i	−0.808774	+	0.808774i
$483$		0			0
$484$		−	3.47228i		−	0.157831i
$485$	21.7008	−	17.2515i	0.985383	−	0.783350i
$486$		0			0
$487$	2.31334	+	2.31334i	0.104828	+	0.104828i	0.757575	−	0.652748i	$-0.226384\pi$
$487$	2.31334	+	2.31334i	0.104828	+	0.104828i	−0.652748	+	0.757575i	$0.726384\pi$
$488$	2.08651	−	2.08651i	0.0944519	−	0.0944519i
$489$		0			0
$490$	−7.31236	−	9.19829i	−0.330339	−	0.415536i
$491$	0.0138034			0.000622939			0.000311469	−	1.00000i	$-0.499901\pi$
$491$	0.0138034			0.000622939			0.000311469		1.00000i	$0.499901\pi$
$492$		0			0
$493$	31.7092	−	31.7092i	1.42811	−	1.42811i
$494$	−3.29729	−	6.63403i	−0.148352	−	0.298479i
$495$		0			0
$496$			6.50952i			0.292286i
$497$	13.7779	+	13.7779i	0.618021	+	0.618021i
$498$		0			0
$499$		−	19.0461i		−	0.852619i	−0.904577	−	0.426309i	$-0.859813\pi$
$499$		−	19.0461i		−	0.852619i	0.904577	−	0.426309i	$-0.140187\pi$
$500$	−10.5359	−	3.74110i	−0.471178	−	0.167307i
$501$		0			0
$502$	1.62772	+	1.62772i	0.0726489	+	0.0726489i
$503$	15.5475	+	15.5475i	0.693230	+	0.693230i	0.962941	−	0.269711i	$-0.0869282\pi$
$503$	15.5475	+	15.5475i	0.693230	+	0.693230i	−0.269711	+	0.962941i	$0.586928\pi$
$504$		0			0
$505$	−2.85866	+	25.0266i	−0.127209	+	1.11367i
$506$			0.124718i			0.00554440i
$507$		0			0
$508$	13.7136	−	13.7136i	0.608444	−	0.608444i
$509$	4.08859			0.181224			0.0906118	−	0.995886i	$-0.471118\pi$
$509$	4.08859			0.181224			0.0906118	+	0.995886i	$0.471118\pi$
$510$		0			0
$511$	10.8523			0.480078
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$			22.3095i			0.984032i
$515$	1.50039	+	1.88735i	0.0661150	+	0.0831667i
$516$		0			0
$517$	10.0622	−	10.0622i	0.442536	−	0.442536i
$518$	16.0683	+	16.0683i	0.705999	+	0.705999i
$519$		0			0
$520$	3.77581	+	0.431292i	0.165580	+	0.0189134i
$521$			29.8730i			1.30876i	0.756166	+	0.654380i	$0.227070\pi$
$521$			29.8730i			1.30876i	−0.756166	+	0.654380i	$0.772930\pi$
$522$		0			0
$523$	20.1935	−	20.1935i	0.883001	−	0.883001i	−0.110837	−	0.993839i	$-0.535353\pi$
$523$	20.1935	−	20.1935i	0.883001	−	0.883001i	0.993839	+	0.110837i	$0.0353532\pi$
$524$		−	8.01380i		−	0.350085i
$525$		0			0
$526$			1.72400i			0.0751702i
$527$	−31.7092	−	31.7092i	−1.38127	−	1.38127i
$528$		0			0
$529$		−	22.9979i		−	0.999910i
$530$	3.22108	−	28.1995i	0.139915	−	1.22491i
$531$		0			0
$532$	−4.85988	+	14.4647i	−0.210703	+	0.627125i
$533$	−7.17060	−	7.17060i	−0.310593	−	0.310593i
$534$		0			0
$535$	−33.5047	+	26.6352i	−1.44853	+	1.15154i
$536$	9.90155			0.427682
$537$		0			0
$538$	−5.36291	−	5.36291i	−0.231211	−	0.231211i
$539$			14.4182i			0.621035i
$540$		0			0
$541$	−25.3583			−1.09024			−0.545120	−	0.838358i	$-0.683516\pi$
$541$	−25.3583			−1.09024			−0.545120	+	0.838358i	$0.683516\pi$
$542$	−18.1543	−	18.1543i	−0.779795	−	0.779795i
$543$		0			0
$544$	−6.88893			−0.295360
$545$	1.10948	−	9.71308i	0.0475247	−	0.416063i
$546$		0			0
$547$	13.3457	+	13.3457i	0.570622	+	0.570622i	0.932302	−	0.361680i	$-0.117797\pi$
$547$	13.3457	+	13.3457i	0.570622	+	0.570622i	−0.361680	+	0.932302i	$0.617797\pi$
$548$	12.6299	+	12.6299i	0.539524	+	0.539524i
$549$		0			0
$550$	7.26297	+	11.6380i	0.309694	+	0.496245i
$551$	−12.6289	−	25.4089i	−0.538009	−	1.08246i
$552$		0			0
$553$	−0.558998	+	0.558998i	−0.0237710	+	0.0237710i
$554$	−30.7470			−1.30631
$555$		0			0
$556$	−10.3499			−0.438934
$557$	8.05867	−	8.05867i	0.341457	−	0.341457i	−0.515458	−	0.856915i	$-0.672378\pi$
$557$	8.05867	−	8.05867i	0.341457	−	0.341457i	0.856915	+	0.515458i	$0.172378\pi$
$558$		0			0
$559$	12.9692			0.548538
$560$	−4.87121	−	6.12754i	−0.205846	−	0.258936i
$561$		0			0
$562$	15.4892	−	15.4892i	0.653372	−	0.653372i
$563$	28.6648	−	28.6648i	1.20808	−	1.20808i	0.236430	−	0.971648i	$-0.424022\pi$
$563$	28.6648	−	28.6648i	1.20808	−	1.20808i	0.971648	−	0.236430i	$-0.0759775\pi$
$564$		0			0
$565$	−13.6884	−	17.2188i	−0.575875	−	0.724399i
$566$			22.2338i			0.934557i
$567$		0			0
$568$	3.93571	+	3.93571i	0.165139	+	0.165139i
$569$	−8.54540			−0.358242			−0.179121	−	0.983827i	$-0.557325\pi$
$569$	−8.54540			−0.358242			−0.179121	+	0.983827i	$0.557325\pi$
$570$		0			0
$571$	45.4169			1.90064			0.950320	−	0.311275i	$-0.100756\pi$
$571$	45.4169			1.90064			0.950320	+	0.311275i	$0.100756\pi$
$572$	−3.29729	−	3.29729i	−0.137867	−	0.137867i
$573$		0			0
$574$			20.8876i			0.871831i
$575$	0.120332	+	0.192816i	0.00501819	+	0.00804100i
$576$		0			0
$577$	12.1650	−	12.1650i	0.506437	−	0.506437i	−0.406994	−	0.913431i	$-0.633423\pi$
$577$	12.1650	−	12.1650i	0.506437	−	0.506437i	0.913431	+	0.406994i	$0.133423\pi$
$578$	21.5366	−	21.5366i	0.895803	−	0.895803i
$579$		0			0
$580$	14.4617	+	1.65189i	0.600489	+	0.0685908i
$581$	−19.1717			−0.795375
$582$		0			0
$583$	−24.6256	+	24.6256i	−1.01989	+	1.01989i
$584$	3.10002			0.128280
$585$		0			0
$586$	−11.6781			−0.482419
$587$	5.32968	−	5.32968i	0.219980	−	0.219980i	−0.588510	−	0.808490i	$-0.700285\pi$
$587$	5.32968	−	5.32968i	0.219980	−	0.219980i	0.808490	+	0.588510i	$0.200285\pi$
$588$		0			0
$589$	−25.4089	+	12.6289i	−1.04696	+	0.520365i
$590$	7.74186	−	6.15455i	0.318728	−	0.253379i
$591$		0			0
$592$	4.58998	+	4.58998i	0.188647	+	0.188647i
$593$	1.80818	+	1.80818i	0.0742529	+	0.0742529i	0.743258	−	0.669005i	$-0.233280\pi$
$593$	1.80818	+	1.80818i	0.0742529	+	0.0742529i	−0.669005	+	0.743258i	$0.733280\pi$
$594$		0			0
$595$	53.5772	+	6.11985i	2.19645	+	0.250889i
$596$	−9.07466			−0.371712
$597$		0			0
$598$	−0.0546290	−	0.0546290i	−0.00223395	−	0.00223395i
$599$	25.3131			1.03426			0.517132	−	0.855906i	$-0.327000\pi$
$599$	25.3131			1.03426			0.517132	+	0.855906i	$0.327000\pi$
$600$		0			0
$601$			18.5367i			0.756126i	0.925780	+	0.378063i	$0.123410\pi$
$601$			18.5367i			0.756126i	−0.925780	+	0.378063i	$0.876590\pi$
$602$	−18.8893	−	18.8893i	−0.769870	−	0.769870i
$603$		0			0
$604$	1.75287			0.0713234
$605$	−0.881142	+	7.71409i	−0.0358235	+	0.313622i
$606$		0			0
$607$	11.5164	+	11.5164i	0.467435	+	0.467435i	0.901083	−	0.433647i	$-0.142774\pi$
$607$	11.5164	+	11.5164i	0.467435	+	0.467435i	−0.433647	+	0.901083i	$0.642774\pi$
$608$	−1.38825	+	4.13192i	−0.0563010	+	0.167571i
$609$		0			0
$610$	−5.16492	+	4.10596i	−0.209122	+	0.166245i
$611$			8.81490i			0.356613i
$612$		0			0
$613$	−7.66890	−	7.66890i	−0.309744	−	0.309744i	0.535066	−	0.844810i	$-0.320287\pi$
$613$	−7.66890	−	7.66890i	−0.309744	−	0.309744i	−0.844810	+	0.535066i	$0.820287\pi$
$614$			31.2879i			1.26268i
$615$		0			0
$616$			9.60483i			0.386990i
$617$	−33.2792	+	33.2792i	−1.33977	+	1.33977i	−0.443492	+	0.896278i	$0.646260\pi$
$617$	−33.2792	+	33.2792i	−1.33977	+	1.33977i	−0.896278	+	0.443492i	$0.853740\pi$
$618$		0			0
$619$			3.87513i			0.155755i	0.996963	+	0.0778774i	$0.0248143\pi$
$619$			3.87513i			0.155755i	−0.996963	+	0.0778774i	$0.975186\pi$
$620$	1.65189	−	14.4617i	0.0663413	−	0.580795i
$621$		0			0
$622$	−2.27765	−	2.27765i	−0.0913254	−	0.0913254i
$623$	22.6158	−	22.6158i	0.906084	−	0.906084i
$624$		0			0
$625$	22.4573	+	10.9849i	0.898293	+	0.439398i
$626$		−	21.1850i		−	0.846724i
$627$		0			0
$628$	7.20733	+	7.20733i	0.287604	+	0.287604i
$629$	−44.7175			−1.78300
$630$		0			0
$631$	1.80965			0.0720412			0.0360206	−	0.999351i	$-0.488532\pi$
$631$	1.80965			0.0720412			0.0360206	+	0.999351i	$0.488532\pi$
$632$	−0.159681	+	0.159681i	−0.00635176	+	0.00635176i
$633$		0			0
$634$		−	18.8539i		−	0.748782i
$635$	−33.9466	+	26.9865i	−1.34713	+	1.07093i
$636$		0			0
$637$	−6.31545	−	6.31545i	−0.250227	−	0.250227i
$638$	−12.6289	−	12.6289i	−0.499983	−	0.499983i
$639$		0			0
$640$	−1.39149	−	1.75036i	−0.0550033	−	0.0691892i
$641$		−	6.61503i		−	0.261278i	−0.991430	−	0.130639i	$-0.958297\pi$
$641$		−	6.61503i		−	0.261278i	0.991430	−	0.130639i	$-0.0417029\pi$
$642$		0			0
$643$	−30.3608	−	30.3608i	−1.19731	−	1.19731i	−0.974968	−	0.222347i	$-0.928628\pi$
$643$	−30.3608	−	30.3608i	−1.19731	−	1.19731i	−0.222347	−	0.974968i	$-0.571372\pi$
$644$			0.159132i			0.00627066i
$645$		0			0
$646$	−13.3650	−	26.8899i	−0.525838	−	1.05797i
$647$	−5.83884	+	5.83884i	−0.229549	+	0.229549i	−0.812504	−	0.582956i	$-0.801896\pi$
$647$	−5.83884	+	5.83884i	−0.229549	+	0.229549i	0.582956	+	0.812504i	$0.301896\pi$
$648$		0			0
$649$	−12.1353			−0.476351
$650$	−8.27898	−	1.91633i	−0.324728	−	0.0751648i
$651$		0			0
$652$	−9.60292	+	9.60292i	−0.376080	+	0.376080i
$653$	19.7797	+	19.7797i	0.774039	+	0.774039i	0.978810	−	0.204771i	$-0.0656449\pi$
$653$	19.7797	+	19.7797i	0.774039	+	0.774039i	−0.204771	+	0.978810i	$0.565645\pi$
$654$		0			0
$655$	−2.03362	+	17.8036i	−0.0794601	+	0.695646i
$656$			5.96665i			0.232958i
$657$		0			0
$658$	12.8387	−	12.8387i	0.500503	−	0.500503i
$659$	8.44761			0.329072			0.164536	−	0.986371i	$-0.447387\pi$
$659$	8.44761			0.329072			0.164536	+	0.986371i	$0.447387\pi$
$660$		0			0
$661$			23.8283i			0.926814i	0.886146	+	0.463407i	$0.153373\pi$
$661$			23.8283i			0.926814i	−0.886146	+	0.463407i	$0.846627\pi$
$662$	4.75998	−	4.75998i	0.185002	−	0.185002i
$663$		0			0
$664$	−5.47649			−0.212529
$665$	14.4675	−	30.9019i	0.561024	−	1.19832i
$666$		0			0
$667$	−0.209234	−	0.209234i	−0.00810157	−	0.00810157i
$668$	−12.9013	+	12.9013i	−0.499168	+	0.499168i
$669$		0			0
$670$	−21.9975	−	2.51266i	−0.849837	−	0.0970726i
$671$	8.09594			0.312540
$672$		0			0
$673$	31.9422	−	31.9422i	1.23128	−	1.23128i	0.267812	−	0.963471i	$-0.413700\pi$
$673$	31.9422	−	31.9422i	1.23128	−	1.23128i	0.963471	−	0.267812i	$-0.0863005\pi$
$674$		−	20.0113i		−	0.770806i
$675$		0			0
$676$	−10.1114			−0.388902
$677$	−11.7115	−	11.7115i	−0.450111	−	0.450111i	0.445280	−	0.895391i	$-0.353104\pi$
$677$	−11.7115	−	11.7115i	−0.450111	−	0.450111i	−0.895391	+	0.445280i	$0.853104\pi$
$678$		0			0
$679$	−43.4016			−1.66560
$680$	15.3046	+	1.74817i	0.586904	+	0.0670391i
$681$		0			0
$682$	−12.6289	+	12.6289i	−0.483586	+	0.483586i
$683$	−3.55375	+	3.55375i	−0.135981	+	0.135981i	−0.771821	−	0.635840i	$-0.780654\pi$
$683$	−3.55375	+	3.55375i	−0.135981	+	0.135981i	0.635840	+	0.771821i	$0.280654\pi$
$684$		0			0
$685$	−24.8539	−	31.2640i	−0.949619	−	1.19453i
$686$		−	6.10850i		−	0.233224i
$687$		0			0
$688$	−5.39582	−	5.39582i	−0.205714	−	0.205714i
$689$		−	21.5730i		−	0.821867i
$690$		0			0
$691$	9.74241			0.370619			0.185309	−	0.982680i	$-0.440671\pi$
$691$	9.74241			0.370619			0.185309	+	0.982680i	$0.440671\pi$
$692$	0.271593	+	0.271593i	0.0103244	+	0.0103244i
$693$		0			0
$694$	−9.67476			−0.367249
$695$	22.9936	+	2.62644i	0.872197	+	0.0996267i
$696$		0			0
$697$	−29.0648	−	29.0648i	−1.10091	−	1.10091i
$698$	−23.4970	+	23.4970i	−0.889374	+	0.889374i
$699$		0			0
$700$	9.26703	+	14.8492i	0.350261	+	0.561247i
$701$	10.3224			0.389873			0.194936	−	0.980816i	$-0.437550\pi$
$701$	10.3224			0.389873			0.194936	+	0.980816i	$0.437550\pi$
$702$		0			0
$703$	−9.01143	+	26.8212i	−0.339873	+	1.01158i
$704$			2.74367i			0.103406i
$705$		0			0
$706$		−	35.8700i		−	1.34999i
$707$	27.8852	−	27.8852i	1.04873	−	1.04873i
$708$		0			0
$709$			10.3223i			0.387663i	0.981035	+	0.193831i	$0.0620915\pi$
$709$			10.3223i			0.387663i	−0.981035	+	0.193831i	$0.937909\pi$
$710$	−7.74492	−	9.74241i	−0.290662	−	0.365626i
$711$		0			0
$712$	6.46033	−	6.46033i	0.242111	−	0.242111i
$713$	−0.209234	+	0.209234i	−0.00783587	+	0.00783587i
$714$		0			0
$715$	6.48859	+	8.16206i	0.242660	+	0.305244i
$716$			16.1543i			0.603715i
$717$		0			0
$718$	−6.45584	+	6.45584i	−0.240930	+	0.240930i
$719$			34.9029i			1.30166i	0.759224	+	0.650830i	$0.225579\pi$
$719$			34.9029i			1.30166i	−0.759224	+	0.650830i	$0.774421\pi$
$720$		0			0
$721$		−	3.77470i		−	0.140577i
$722$	−18.8216	+	2.59737i	−0.700468	+	0.0966642i
$723$		0			0
$724$	−16.1980			−0.601994
$725$	−31.7092	−	7.33973i	−1.17765	−	0.272591i
$726$		0			0
$727$	12.8595	−	12.8595i	0.476932	−	0.476932i	−0.427217	−	0.904149i	$-0.640506\pi$
$727$	12.8595	−	12.8595i	0.476932	−	0.476932i	0.904149	+	0.427217i	$0.140506\pi$
$728$	−4.20710	−	4.20710i	−0.155926	−	0.155926i
$729$		0			0
$730$	−6.88707	−	0.786675i	−0.254902	−	0.0291162i
$731$	52.5683			1.94431
$732$		0			0
$733$	11.1047	+	11.1047i	0.410162	+	0.410162i	0.881795	−	0.471633i	$-0.156335\pi$
$733$	11.1047	+	11.1047i	0.410162	+	0.410162i	−0.471633	+	0.881795i	$0.656335\pi$
$734$	18.3534			0.677435
$735$		0			0
$736$			0.0454567i			0.00167556i
$737$	19.2097	+	19.2097i	0.707597	+	0.707597i
$738$		0			0
$739$			18.1001i			0.665823i	0.942958	+	0.332911i	$0.108031\pi$
$739$			18.1001i			0.665823i	−0.942958	+	0.332911i	$0.891969\pi$
$740$	−9.03243	−	11.3620i	−0.332039	−	0.417675i
$741$		0			0
$742$	−31.4205	+	31.4205i	−1.15348	+	1.15348i
$743$	26.9208	−	26.9208i	0.987630	−	0.987630i	−0.0122949	−	0.999924i	$-0.503914\pi$
$743$	26.9208	−	26.9208i	0.987630	−	0.987630i	0.999924	+	0.0122949i	$0.00391368\pi$
$744$		0			0
$745$	20.1605	+	2.30283i	0.738622	+	0.0843690i
$746$	−9.79442			−0.358599
$747$		0			0
$748$	−13.3650	−	13.3650i	−0.488672	−	0.488672i
$749$	67.0093			2.44847
$750$		0			0
$751$			9.91849i			0.361931i	0.983489	+	0.180965i	$0.0579222\pi$
$751$			9.91849i			0.361931i	−0.983489	+	0.180965i	$0.942078\pi$
$752$	3.66743	−	3.66743i	0.133737	−	0.133737i
$753$		0			0
$754$	11.0634			0.402906
$755$	−3.89422	−	0.444817i	−0.141725	−	0.0161886i
$756$		0			0
$757$	3.01763	−	3.01763i	0.109678	−	0.109678i	−0.650138	−	0.759816i	$-0.725289\pi$
$757$	3.01763	−	3.01763i	0.109678	−	0.109678i	0.759816	+	0.650138i	$0.225289\pi$
$758$	−15.9015	−	15.9015i	−0.577570	−	0.577570i
$759$		0			0
$760$	4.13270	−	8.82727i	0.149909	−	0.320199i
$761$	11.1416			0.403881			0.201941	−	0.979398i	$-0.435275\pi$
$761$	11.1416			0.403881			0.201941	+	0.979398i	$0.435275\pi$
$762$		0			0
$763$	−10.8226	+	10.8226i	−0.391803	+	0.391803i
$764$		−	14.6162i		−	0.528795i
$765$		0			0
$766$	21.1680			0.764830
$767$	5.31548	−	5.31548i	0.191931	−	0.191931i
$768$		0			0
$769$		−	32.8840i		−	1.18583i	−0.805266	−	0.592913i	$-0.797978\pi$
$769$		−	32.8840i		−	1.18583i	0.805266	−	0.592913i	$-0.202022\pi$
$770$	2.43737	−	21.3383i	0.0878366	−	0.768979i
$771$		0			0
$772$	−6.20432	−	6.20432i	−0.223298	−	0.223298i
$773$	−31.2573	+	31.2573i	−1.12425	+	1.12425i	−0.133152	+	0.991096i	$0.542510\pi$
$773$	−31.2573	+	31.2573i	−1.12425	+	1.12425i	−0.991096	+	0.133152i	$0.957490\pi$
$774$		0			0
$775$	−7.33973	+	31.7092i	−0.263651	+	1.13903i
$776$	−12.3979			−0.445058
$777$		0			0
$778$	−7.20521	+	7.20521i	−0.258319	+	0.258319i
$779$	−23.2899	+	11.5757i	−0.834447	+	0.414742i
$780$		0			0
$781$			15.2711i			0.546443i
$782$	−0.221429	−	0.221429i	−0.00791829	−	0.00791829i
$783$		0			0
$784$			5.25508i			0.187681i
$785$	−14.1830	−	17.8409i	−0.506213	−	0.636770i
$786$		0			0
$787$	−2.28524	−	2.28524i	−0.0814600	−	0.0814600i	0.665203	−	0.746663i	$-0.268345\pi$
$787$	−2.28524	−	2.28524i	−0.0814600	−	0.0814600i	−0.746663	+	0.665203i	$0.768345\pi$
$788$	9.77456	+	9.77456i	0.348204	+	0.348204i
$789$		0			0
$790$	0.395271	−	0.314229i	0.0140631	−	0.0111798i
$791$			34.4375i			1.22446i
$792$		0			0
$793$	−3.54618	+	3.54618i	−0.125929	+	0.125929i
$794$	21.1415			0.750284
$795$		0			0
$796$	−7.77253			−0.275490
$797$	20.1327	+	20.1327i	0.713137	+	0.713137i	0.967190	−	0.254054i	$-0.0817639\pi$
$797$	20.1327	+	20.1327i	0.713137	+	0.713137i	−0.254054	+	0.967190i	$0.581764\pi$
$798$		0			0
$799$			35.7296i			1.26402i
$800$	2.64717	+	4.24175i	0.0935917	+	0.149969i
$801$		0			0
$802$	12.1548	−	12.1548i	0.429200	−	0.429200i
$803$	6.01425	+	6.01425i	0.212238	+	0.212238i
$804$		0			0
$805$	0.0403820	−	0.353530i	0.00142328	−	0.0124603i
$806$		−	11.0634i		−	0.389692i
$807$		0			0
$808$	7.96556	−	7.96556i	0.280227	−	0.280227i
$809$			19.9089i			0.699958i	0.936758	+	0.349979i	$0.113811\pi$
$809$			19.9089i			0.699958i	−0.936758	+	0.349979i	$0.886189\pi$
$810$		0			0
$811$		−	27.5845i		−	0.968623i	−0.874896	−	0.484312i	$-0.839070\pi$
$811$		−	27.5845i		−	0.968623i	0.874896	−	0.484312i	$-0.160930\pi$
$812$	−16.1136	−	16.1136i	−0.565476	−	0.565476i
$813$		0			0
$814$			17.8097i			0.624231i
$815$	23.7709	−	18.8972i	0.832660	−	0.661939i
$816$		0			0
$817$	10.5935	−	31.5300i	0.370620	−	1.10310i
$818$	16.9345	+	16.9345i	0.592099	+	0.592099i
$819$		0			0
$820$	1.51412	−	13.2556i	0.0528755	−	0.462907i
$821$	16.0769			0.561089			0.280545	−	0.959841i	$-0.409485\pi$
$821$	16.0769			0.561089			0.280545	+	0.959841i	$0.409485\pi$
$822$		0			0
$823$	0.761023	+	0.761023i	0.0265276	+	0.0265276i	0.720246	−	0.693719i	$-0.244029\pi$
$823$	0.761023	+	0.761023i	0.0265276	+	0.0265276i	−0.693719	+	0.720246i	$0.744029\pi$
$824$		−	1.07826i		−	0.0375631i
$825$		0			0
$826$	−15.4837			−0.538748
$827$	−20.8201	−	20.8201i	−0.723984	−	0.723984i	0.245430	−	0.969414i	$-0.421071\pi$
$827$	−20.8201	−	20.8201i	−0.723984	−	0.723984i	−0.969414	+	0.245430i	$0.921071\pi$
$828$		0			0
$829$	−31.8887			−1.10754			−0.553771	−	0.832669i	$-0.686812\pi$
$829$	−31.8887			−1.10754			−0.553771	+	0.832669i	$0.686812\pi$
$830$	12.1667	+	1.38974i	0.422312	+	0.0482385i
$831$		0			0
$832$	−1.20178	−	1.20178i	−0.0416642	−	0.0416642i
$833$	−25.5986	−	25.5986i	−0.886938	−	0.886938i
$834$		0			0
$835$	31.9358	−	25.3880i	1.10518	−	0.878588i
$836$	−10.7095	+	5.32290i	−0.370396	+	0.184096i
$837$		0			0
$838$	15.1416	−	15.1416i	0.523056	−	0.523056i
$839$	−39.4110			−1.36062			−0.680310	−	0.732924i	$-0.738155\pi$
$839$	−39.4110			−1.36062			−0.680310	+	0.732924i	$0.738155\pi$
$840$		0			0
$841$	13.3738			0.461166
$842$	1.22053	−	1.22053i	0.0420623	−	0.0420623i
$843$		0			0
$844$	−7.91902			−0.272584
$845$	22.4638	+	2.56593i	0.772779	+	0.0882706i
$846$		0			0
$847$	8.59523	−	8.59523i	0.295336	−	0.295336i
$848$	−8.97544	+	8.97544i	−0.308218	+	0.308218i
$849$		0			0
$850$	−33.5574	−	7.76753i	−1.15101	−	0.266424i
$851$			0.295070i			0.0101149i
$852$		0			0
$853$	29.3272	+	29.3272i	1.00414	+	1.00414i	0.999991	+	0.00415191i	$0.00132160\pi$
$853$	29.3272	+	29.3272i	1.00414	+	1.00414i	0.00415191	+	0.999991i	$0.498678\pi$
$854$	10.3298			0.353480
$855$		0			0
$856$	19.1416			0.654245
$857$	−22.6621	−	22.6621i	−0.774121	−	0.774121i	0.204703	−	0.978824i	$-0.434377\pi$
$857$	−22.6621	−	22.6621i	−0.774121	−	0.774121i	−0.978824	+	0.204703i	$0.934377\pi$
$858$		0			0
$859$		−	9.13130i		−	0.311556i	−0.987792	−	0.155778i	$-0.950212\pi$
$859$		−	9.13130i		−	0.311556i	0.987792	−	0.155778i	$-0.0497884\pi$
$860$	10.6182	+	13.3567i	0.362078	+	0.455461i
$861$		0			0
$862$	−20.9141	+	20.9141i	−0.712337	+	0.712337i
$863$	31.2115	−	31.2115i	1.06245	−	1.06245i	0.0645382	−	0.997915i	$-0.479443\pi$
$863$	31.2115	−	31.2115i	1.06245	−	1.06245i	0.997915	−	0.0645382i	$-0.0205574\pi$
$864$		0			0
$865$	−0.534456	−	0.672298i	−0.0181721	−	0.0228588i
$866$	26.5463			0.902081
$867$		0			0
$868$	−16.1136	+	16.1136i	−0.546930	+	0.546930i
$869$	−0.619583			−0.0210179
$870$		0			0
$871$	−16.8284			−0.570209
$872$	−3.09152	+	3.09152i	−0.104692	+	0.104692i
$873$		0			0
$874$	−0.177434	+	0.0881891i	−0.00600178	+	0.00298304i
$875$	−16.8196	−	35.3410i	−0.568607	−	1.19474i
$876$		0			0
$877$	−15.7226	−	15.7226i	−0.530916	−	0.530916i	0.389929	−	0.920845i	$-0.372500\pi$
$877$	−15.7226	−	15.7226i	−0.530916	−	0.530916i	−0.920845	+	0.389929i	$0.872500\pi$
$878$	−6.12443	−	6.12443i	−0.206690	−	0.206690i
$879$		0			0
$880$	0.696246	−	6.09540i	0.0234705	−	0.205476i
$881$	12.7472			0.429464			0.214732	−	0.976673i	$-0.431112\pi$
$881$	12.7472			0.429464			0.214732	+	0.976673i	$0.431112\pi$
$882$		0			0
$883$	26.1600	+	26.1600i	0.880352	+	0.880352i	0.993570	−	0.113218i	$-0.0361158\pi$
$883$	26.1600	+	26.1600i	0.880352	+	0.880352i	−0.113218	+	0.993570i	$0.536116\pi$
$884$	11.7082			0.393791
$885$		0			0
$886$			27.6718i			0.929652i
$887$	3.63787	+	3.63787i	0.122148	+	0.122148i	0.765538	−	0.643390i	$-0.222473\pi$
$887$	3.63787	+	3.63787i	0.122148	+	0.122148i	−0.643390	+	0.765538i	$0.722473\pi$
$888$		0			0
$889$	67.8931			2.27706
$890$	−15.9918	+	12.7130i	−0.536047	+	0.426141i
$891$		0			0
$892$	14.3643	+	14.3643i	0.480953	+	0.480953i
$893$	21.4303	+	7.20021i	0.717139	+	0.240946i
$894$		0			0
$895$	4.09940	−	35.8888i	0.137028	−	1.19963i
$896$			3.50073i			0.116951i
$897$		0			0
$898$	15.0917	+	15.0917i	0.503618	+	0.503618i
$899$		−	42.3738i		−	1.41325i
$900$		0			0
$901$		−	87.4424i		−	2.91313i
$902$	−11.5757	+	11.5757i	−0.385428	+	0.385428i
$903$		0			0
$904$			9.83726i			0.327182i
$905$	35.9858	+	4.11048i	1.19621	+	0.136637i
$906$		0			0
$907$	27.2643	+	27.2643i	0.905298	+	0.905298i	0.995888	−	0.0905904i	$-0.0288754\pi$
$907$	27.2643	+	27.2643i	0.905298	+	0.905298i	−0.0905904	+	0.995888i	$0.528875\pi$
$908$	15.0385	−	15.0385i	0.499070	−	0.499070i
$909$		0			0
$910$	8.27898	+	10.4142i	0.274445	+	0.345228i
$911$			1.42099i			0.0470796i	0.999723	+	0.0235398i	$0.00749364\pi$
$911$			1.42099i			0.0470796i	−0.999723	+	0.0235398i	$0.992506\pi$
$912$		0			0
$913$	−10.6248	−	10.6248i	−0.351628	−	0.351628i
$914$	30.1753			0.998110
$915$		0			0
$916$	−2.69570			−0.0890683
$917$	19.8373	−	19.8373i	0.655084	−	0.655084i
$918$		0			0
$919$			38.9380i			1.28445i	0.766518	+	0.642223i	$0.221988\pi$
$919$			38.9380i			1.28445i	−0.766518	+	0.642223i	$0.778012\pi$
$920$	0.0115353	−	0.100988i	0.000380308	−	0.00332947i
$921$		0			0
$922$	−0.426720	−	0.426720i	−0.0140533	−	0.0140533i
$923$	−6.68904	−	6.68904i	−0.220172	−	0.220172i
$924$		0			0
$925$	17.1834	+	27.5341i	0.564986	+	0.905317i
$926$		−	19.6121i		−	0.644495i
$927$		0			0
$928$	−4.60292	−	4.60292i	−0.151098	−	0.151098i
$929$		−	23.8414i		−	0.782211i	−0.920346	−	0.391106i	$-0.872093\pi$
$929$		−	23.8414i		−	0.782211i	0.920346	−	0.391106i	$-0.127907\pi$
$930$		0			0
$931$	−20.5124	+	10.1952i	−0.672267	+	0.334134i
$932$	−12.4775	+	12.4775i	−0.408713	+	0.408713i
$933$		0			0
$934$	−7.22441			−0.236390
$935$	26.3004	+	33.0835i	0.860114	+	1.08195i
$936$		0			0
$937$	−13.2718	+	13.2718i	−0.433572	+	0.433572i	−0.889842	−	0.456270i	$-0.849185\pi$
$937$	−13.2718	+	13.2718i	−0.433572	+	0.433572i	0.456270	+	0.889842i	$0.349185\pi$
$938$	24.5102	+	24.5102i	0.800285	+	0.800285i
$939$		0			0
$940$	−9.07831	+	7.21698i	−0.296102	+	0.235392i
$941$		−	27.1173i		−	0.884000i	−0.897015	−	0.442000i	$-0.854269\pi$
$941$		−	27.1173i		−	0.884000i	0.897015	−	0.442000i	$-0.145731\pi$
$942$		0			0
$943$	−0.191785	+	0.191785i	−0.00624536	+	0.00624536i
$944$	−4.42301			−0.143957
$945$		0			0
$946$		−	20.9365i		−	0.680705i
$947$	12.0469	−	12.0469i	0.391473	−	0.391473i	−0.483739	−	0.875212i	$-0.660722\pi$
$947$	12.0469	−	12.0469i	0.391473	−	0.391473i	0.875212	+	0.483739i	$0.160722\pi$
$948$		0			0
$949$	−5.26872			−0.171030
$950$	−11.4214	+	18.5621i	−0.370558	+	0.602235i
$951$		0			0
$952$	−17.0528	−	17.0528i	−0.552683	−	0.552683i
$953$	33.0593	−	33.0593i	1.07090	−	1.07090i	0.0736082	−	0.997287i	$-0.476549\pi$
$953$	33.0593	−	33.0593i	1.07090	−	1.07090i	0.997287	−	0.0736082i	$-0.0234514\pi$
$954$		0			0
$955$	−3.70907	+	32.4716i	−0.120023	+	1.05076i
$956$	27.2150			0.880195
$957$		0			0
$958$	−0.478542	+	0.478542i	−0.0154610	+	0.0154610i
$959$			62.5279i			2.01913i
$960$		0			0
$961$	−11.3738			−0.366898
$962$	−7.80102	−	7.80102i	−0.251515	−	0.251515i
$963$		0			0
$964$	−25.1111			−0.808774
$965$	12.2092	+	15.3581i	0.393028	+	0.494394i
$966$		0			0
$967$	4.66093	−	4.66093i	0.149885	−	0.149885i	−0.628181	−	0.778067i	$-0.716200\pi$
$967$	4.66093	−	4.66093i	0.149885	−	0.149885i	0.778067	+	0.628181i	$0.216200\pi$
$968$	2.45527	−	2.45527i	0.0789155	−	0.0789155i
$969$		0			0
$970$	27.5434	+	3.14615i	0.884366	+	0.101017i
$971$		−	11.8515i		−	0.380332i	−0.981752	−	0.190166i	$-0.939097\pi$
$971$		−	11.8515i		−	0.380332i	0.981752	−	0.190166i	$-0.0609026\pi$
$972$		0			0
$973$	−25.6201	−	25.6201i	−0.821341	−	0.821341i
$974$			3.27156i			0.104828i
$975$		0			0
$976$	2.95077			0.0944519
$977$	26.7920	+	26.7920i	0.857153	+	0.857153i	0.991002	−	0.133849i	$-0.0427336\pi$
$977$	26.7920	+	26.7920i	0.857153	+	0.857153i	−0.133849	+	0.991002i	$0.542734\pi$
$978$		0			0
$979$	25.0669			0.801143
$980$	1.33355	−	11.6748i	0.0425988	−	0.372938i
$981$		0			0
$982$	0.00976048	+	0.00976048i	0.000311469	+	0.000311469i
$983$	−11.6066	+	11.6066i	−0.370193	+	0.370193i	−0.867547	−	0.497354i	$-0.834305\pi$
$983$	−11.6066	+	11.6066i	−0.370193	+	0.370193i	0.497354	+	0.867547i	$0.334305\pi$
$984$		0			0
$985$	−19.2349	−	24.1958i	−0.612876	−	0.770942i
$986$	44.8436			1.42811
$987$		0			0
$988$	2.35944	−	7.02251i	0.0750636	−	0.223416i
$989$		−	0.346873i		−	0.0110299i
$990$		0			0
$991$		−	58.1707i		−	1.84785i	−0.382568	−	0.923927i	$-0.624960\pi$
$991$		−	58.1707i		−	1.84785i	0.382568	−	0.923927i	$-0.375040\pi$
$992$	−4.60292	+	4.60292i	−0.146143	+	0.146143i
$993$		0			0
$994$			19.4848i			0.618021i
$995$	17.2676	+	1.97239i	0.547420	+	0.0625291i
$996$		0			0
$997$	−21.5242	+	21.5242i	−0.681678	+	0.681678i	−0.960378	−	0.278701i	$-0.910096\pi$
$997$	−21.5242	+	21.5242i	−0.681678	+	0.681678i	0.278701	+	0.960378i	$0.410096\pi$
$998$	13.4676	−	13.4676i	0.426309	−	0.426309i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.p.d.1063.8		20
3.2	odd	2		570.2.m.a.493.3	yes	20
5.2	odd	4	inner	1710.2.p.d.37.3		20
15.2	even	4		570.2.m.a.37.8	yes	20
19.18	odd	2	inner	1710.2.p.d.1063.3		20
57.56	even	2		570.2.m.a.493.8	yes	20
95.37	even	4	inner	1710.2.p.d.37.8		20
285.227	odd	4		570.2.m.a.37.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.m.a.37.3	✓	20	285.227	odd	4
570.2.m.a.37.8	yes	20	15.2	even	4
570.2.m.a.493.3	yes	20	3.2	odd	2
570.2.m.a.493.8	yes	20	57.56	even	2
1710.2.p.d.37.3		20	5.2	odd	4	inner
1710.2.p.d.37.8		20	95.37	even	4	inner
1710.2.p.d.1063.3		20	19.18	odd	2	inner
1710.2.p.d.1063.8		20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(0.253765 - 2.22162i) q^{5} +(-2.47539 + 2.47539i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(0.253765 - 2.22162i) q^{5} +(-2.47539 + 2.47539i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.75036 - 1.39149i) q^{10} -2.74367 q^{11} +(1.20178 - 1.20178i) q^{13} -3.50073 q^{14} -1.00000 q^{16} +(4.87121 - 4.87121i) q^{17} +(-1.94007 - 3.90335i) q^{19} +(2.22162 + 0.253765i) q^{20} +(-1.94007 - 1.94007i) q^{22} +(-0.0321428 - 0.0321428i) q^{23} +(-4.87121 - 1.12754i) q^{25} +1.69957 q^{26} +(-2.47539 - 2.47539i) q^{28} +6.50952 q^{29} -6.50952i q^{31} +(-0.707107 - 0.707107i) q^{32} +6.88893 q^{34} +(4.87121 + 6.12754i) q^{35} +(-4.58998 - 4.58998i) q^{37} +(1.38825 - 4.13192i) q^{38} +(1.39149 + 1.75036i) q^{40} -5.96665i q^{41} +(5.39582 + 5.39582i) q^{43} -2.74367i q^{44} -0.0454567i q^{46} +(-3.66743 + 3.66743i) q^{47} -5.25508i q^{49} +(-2.64717 - 4.24175i) q^{50} +(1.20178 + 1.20178i) q^{52} +(8.97544 - 8.97544i) q^{53} +(-0.696246 + 6.09540i) q^{55} -3.50073i q^{56} +(4.60292 + 4.60292i) q^{58} +4.42301 q^{59} -2.95077 q^{61} +(4.60292 - 4.60292i) q^{62} -1.00000i q^{64} +(-2.36493 - 2.97487i) q^{65} +(-7.00145 - 7.00145i) q^{67} +(4.87121 + 4.87121i) q^{68} +(-0.888360 + 7.77729i) q^{70} -5.56594i q^{71} +(-2.19205 - 2.19205i) q^{73} -6.49122i q^{74} +(3.90335 - 1.94007i) q^{76} +(6.79164 - 6.79164i) q^{77} +0.225823 q^{79} +(-0.253765 + 2.22162i) q^{80} +(4.21906 - 4.21906i) q^{82} +(3.87246 + 3.87246i) q^{83} +(-9.58584 - 12.0581i) q^{85} +7.63084i q^{86} +(1.94007 - 1.94007i) q^{88} -9.13628 q^{89} +5.94974i q^{91} +(0.0321428 - 0.0321428i) q^{92} -5.18653 q^{94} +(-9.16409 + 3.31956i) q^{95} +(8.76663 + 8.76663i) q^{97} +(3.71590 - 3.71590i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{5} - 4 q^{7}+O(q^{10}) \) 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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