LMFDB - Embedded newform 1710.2.p.d.37.5

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			37.5
Root			$-1.53190 + 1.53190i$ of defining polynomial
Character	$\chi$	$=$	1710.37
Dual form			1710.2.p.d.1063.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.23502 - 0.0685835i) q^{5} +(-2.16643 - 2.16643i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.23502 - 0.0685835i) q^{5} +(-2.16643 - 2.16643i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.53190 + 1.62889i) q^{10} +5.68402 q^{11} +(-3.92222 - 3.92222i) q^{13} +3.06380 q^{14} -1.00000 q^{16} +(-4.99059 - 4.99059i) q^{17} +(-4.01921 - 1.68699i) q^{19} +(-0.0685835 - 2.23502i) q^{20} +(-4.01921 + 4.01921i) q^{22} +(-4.30360 + 4.30360i) q^{23} +(4.99059 - 0.306570i) q^{25} +5.54686 q^{26} +(-2.16643 + 2.16643i) q^{28} -4.04446 q^{29} -4.04446i q^{31} +(0.707107 - 0.707107i) q^{32} +7.05776 q^{34} +(-4.99059 - 4.69343i) q^{35} +(-6.19934 + 6.19934i) q^{37} +(4.03490 - 1.64913i) q^{38} +(1.62889 + 1.53190i) q^{40} +6.38884i q^{41} +(-4.15703 + 4.15703i) q^{43} -5.68402i q^{44} -6.08621i q^{46} +(-3.24326 - 3.24326i) q^{47} +2.38686i q^{49} +(-3.31210 + 3.74566i) q^{50} +(-3.92222 + 3.92222i) q^{52} +(5.40818 + 5.40818i) q^{53} +(12.7039 - 0.389830i) q^{55} -3.06380i q^{56} +(2.85986 - 2.85986i) q^{58} -2.39487 q^{59} -2.33286 q^{61} +(2.85986 + 2.85986i) q^{62} +1.00000i q^{64} +(-9.03522 - 8.49722i) q^{65} +(6.12760 - 6.12760i) q^{67} +(-4.99059 + 4.99059i) q^{68} +(6.84764 - 0.210126i) q^{70} +6.51556i q^{71} +(-2.07682 + 2.07682i) q^{73} -8.76719i q^{74} +(-1.68699 + 4.01921i) q^{76} +(-12.3141 - 12.3141i) q^{77} -4.23844 q^{79} +(-2.23502 + 0.0685835i) q^{80} +(-4.51759 - 4.51759i) q^{82} +(5.30657 - 5.30657i) q^{83} +(-11.4963 - 10.8118i) q^{85} -5.87892i q^{86} +(4.01921 + 4.01921i) q^{88} -2.50829 q^{89} +16.9944i q^{91} +(4.30360 + 4.30360i) q^{92} +4.58666 q^{94} +(-9.09870 - 3.49481i) q^{95} +(-6.22010 + 6.22010i) q^{97} +(-1.68776 - 1.68776i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	2.23502	−	0.0685835i	0.999530	−	0.0306715i
$5$	2.23502	−	0.0685835i	0.999530	−	0.0306715i
$6$		0			0
$7$	−2.16643	−	2.16643i	−0.818835	−	0.818835i	0.167105	−	0.985939i	$-0.446558\pi$
$7$	−2.16643	−	2.16643i	−0.818835	−	0.818835i	−0.985939	+	0.167105i	$0.946558\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	−1.53190	+	1.62889i	−0.484429	+	0.515100i
$11$	5.68402			1.71380			0.856899	−	0.515485i	$-0.172388\pi$
$11$	5.68402			1.71380			0.856899	+	0.515485i	$0.172388\pi$
$12$		0			0
$13$	−3.92222	−	3.92222i	−1.08783	−	1.08783i	−0.995752	−	0.0920758i	$-0.970650\pi$
$13$	−3.92222	−	3.92222i	−1.08783	−	1.08783i	−0.0920758	−	0.995752i	$-0.529350\pi$
$14$	3.06380			0.818835
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−4.99059	−	4.99059i	−1.21040	−	1.21040i	−0.970896	−	0.239500i	$-0.923016\pi$
$17$	−4.99059	−	4.99059i	−1.21040	−	1.21040i	−0.239500	−	0.970896i	$-0.576984\pi$
$18$		0			0
$19$	−4.01921	−	1.68699i	−0.922070	−	0.387023i
$19$	−4.01921	−	1.68699i	−0.922070	−	0.387023i
$20$	−0.0685835	−	2.23502i	−0.0153357	−	0.499765i
$21$		0			0
$22$	−4.01921	+	4.01921i	−0.856899	+	0.856899i
$23$	−4.30360	+	4.30360i	−0.897363	+	0.897363i	−0.995202	−	0.0978397i	$-0.968807\pi$
$23$	−4.30360	+	4.30360i	−0.897363	+	0.897363i	0.0978397	+	0.995202i	$0.468807\pi$
$24$		0			0
$25$	4.99059	−	0.306570i	0.998119	−	0.0613141i
$26$	5.54686			1.08783
$27$		0			0
$28$	−2.16643	+	2.16643i	−0.409417	+	0.409417i
$29$	−4.04446			−0.751037			−0.375518	−	0.926815i	$-0.622535\pi$
$29$	−4.04446			−0.751037			−0.375518	+	0.926815i	$0.622535\pi$
$30$		0			0
$31$		−	4.04446i		−	0.726406i	−0.931710	−	0.363203i	$-0.881683\pi$
$31$		−	4.04446i		−	0.726406i	0.931710	−	0.363203i	$-0.118317\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	7.05776			1.21040
$35$	−4.99059	−	4.69343i	−0.843564	−	0.793334i
$36$		0			0
$37$	−6.19934	+	6.19934i	−1.01917	+	1.01917i	−0.0193530	+	0.999813i	$0.506161\pi$
$37$	−6.19934	+	6.19934i	−1.01917	+	1.01917i	−0.999813	+	0.0193530i	$0.993839\pi$
$38$	4.03490	−	1.64913i	0.654546	−	0.267524i
$39$		0			0
$40$	1.62889	+	1.53190i	0.257550	+	0.242215i
$41$			6.38884i			0.997769i	0.866669	+	0.498884i	$0.166257\pi$
$41$			6.38884i			0.997769i	−0.866669	+	0.498884i	$0.833743\pi$
$42$		0			0
$43$	−4.15703	+	4.15703i	−0.633940	+	0.633940i	−0.949054	−	0.315114i	$-0.897957\pi$
$43$	−4.15703	+	4.15703i	−0.633940	+	0.633940i	0.315114	+	0.949054i	$0.397957\pi$
$44$		−	5.68402i		−	0.856899i
$45$		0			0
$46$		−	6.08621i		−	0.897363i
$47$	−3.24326	−	3.24326i	−0.473077	−	0.473077i	0.429832	−	0.902909i	$-0.358573\pi$
$47$	−3.24326	−	3.24326i	−0.473077	−	0.473077i	−0.902909	+	0.429832i	$0.858573\pi$
$48$		0			0
$49$			2.38686i			0.340980i
$50$	−3.31210	+	3.74566i	−0.468402	+	0.529716i
$51$		0			0
$52$	−3.92222	+	3.92222i	−0.543914	+	0.543914i
$53$	5.40818	+	5.40818i	0.742871	+	0.742871i	0.973129	−	0.230259i	$-0.0739573\pi$
$53$	5.40818	+	5.40818i	0.742871	+	0.742871i	−0.230259	+	0.973129i	$0.573957\pi$
$54$		0			0
$55$	12.7039	−	0.389830i	1.71299	−	0.0525647i
$56$		−	3.06380i		−	0.409417i
$57$		0			0
$58$	2.85986	−	2.85986i	0.375518	−	0.375518i
$59$	−2.39487			−0.311786			−0.155893	−	0.987774i	$-0.549825\pi$
$59$	−2.39487			−0.311786			−0.155893	+	0.987774i	$0.549825\pi$
$60$		0			0
$61$	−2.33286			−0.298693			−0.149346	−	0.988785i	$-0.547717\pi$
$61$	−2.33286			−0.298693			−0.149346	+	0.988785i	$0.547717\pi$
$62$	2.85986	+	2.85986i	0.363203	+	0.363203i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−9.03522	−	8.49722i	−1.12068	−	1.05395i
$66$		0			0
$67$	6.12760	−	6.12760i	0.748605	−	0.748605i	−0.225612	−	0.974217i	$-0.572438\pi$
$67$	6.12760	−	6.12760i	0.748605	−	0.748605i	0.974217	+	0.225612i	$0.0724382\pi$
$68$	−4.99059	+	4.99059i	−0.605198	+	0.605198i
$69$		0			0
$70$	6.84764	−	0.210126i	0.818449	−	0.0251149i
$71$			6.51556i			0.773255i	0.922236	+	0.386628i	$0.126360\pi$
$71$			6.51556i			0.773255i	−0.922236	+	0.386628i	$0.873640\pi$
$72$		0			0
$73$	−2.07682	+	2.07682i	−0.243074	+	0.243074i	−0.818121	−	0.575047i	$-0.804984\pi$
$73$	−2.07682	+	2.07682i	−0.243074	+	0.243074i	0.575047	+	0.818121i	$0.304984\pi$
$74$		−	8.76719i		−	1.01917i
$75$		0			0
$76$	−1.68699	+	4.01921i	−0.193511	+	0.461035i
$77$	−12.3141	−	12.3141i	−1.40332	−	1.40332i
$78$		0			0
$79$	−4.23844			−0.476862			−0.238431	−	0.971159i	$-0.576633\pi$
$79$	−4.23844			−0.476862			−0.238431	+	0.971159i	$0.576633\pi$
$80$	−2.23502	+	0.0685835i	−0.249882	+	0.00766787i
$81$		0			0
$82$	−4.51759	−	4.51759i	−0.498884	−	0.498884i
$83$	5.30657	−	5.30657i	0.582472	−	0.582472i	−0.353110	−	0.935582i	$-0.614876\pi$
$83$	5.30657	−	5.30657i	0.582472	−	0.582472i	0.935582	+	0.353110i	$0.114876\pi$
$84$		0			0
$85$	−11.4963	−	10.8118i	−1.24695	−	1.17270i
$86$		−	5.87892i		−	0.633940i
$87$		0			0
$88$	4.01921	+	4.01921i	0.428449	+	0.428449i
$89$	−2.50829			−0.265879			−0.132939	−	0.991124i	$-0.542442\pi$
$89$	−2.50829			−0.265879			−0.132939	+	0.991124i	$0.542442\pi$
$90$		0			0
$91$			16.9944i			1.78150i
$92$	4.30360	+	4.30360i	0.448681	+	0.448681i
$93$		0			0
$94$	4.58666			0.473077
$95$	−9.09870	−	3.49481i	−0.933507	−	0.358559i
$96$		0			0
$97$	−6.22010	+	6.22010i	−0.631555	+	0.631555i	−0.948458	−	0.316903i	$-0.897357\pi$
$97$	−6.22010	+	6.22010i	−0.631555	+	0.631555i	0.316903	+	0.948458i	$0.397357\pi$
$98$	−1.68776	−	1.68776i	−0.170490	−	0.170490i
$99$		0			0
$100$	−0.306570	−	4.99059i	−0.0306570	−	0.499059i
$101$	−3.42891			−0.341189			−0.170595	−	0.985341i	$-0.554569\pi$
$101$	−3.42891			−0.341189			−0.170595	+	0.985341i	$0.554569\pi$
$102$		0			0
$103$	−13.0842	−	13.0842i	−1.28922	−	1.28922i	−0.935260	−	0.353961i	$-0.884835\pi$
$103$	−13.0842	−	13.0842i	−1.28922	−	1.28922i	−0.353961	−	0.935260i	$-0.615165\pi$
$104$		−	5.54686i		−	0.543914i
$105$		0			0
$106$	−7.64832			−0.742871
$107$	5.02931	−	5.02931i	0.486202	−	0.486202i	−0.420903	−	0.907106i	$-0.638287\pi$
$107$	5.02931	−	5.02931i	0.486202	−	0.486202i	0.907106	+	0.420903i	$0.138287\pi$
$108$		0			0
$109$	5.95528			0.570412			0.285206	−	0.958466i	$-0.407938\pi$
$109$	5.95528			0.570412			0.285206	+	0.958466i	$0.407938\pi$
$110$	−8.70735	+	9.25865i	−0.830213	+	0.882778i
$111$		0			0
$112$	2.16643	+	2.16643i	0.204709	+	0.204709i
$113$	−0.0413876	−	0.0413876i	−0.00389342	−	0.00389342i	0.705157	−	0.709051i	$-0.250876\pi$
$113$	−0.0413876	−	0.0413876i	−0.00389342	−	0.00389342i	−0.709051	+	0.705157i	$0.750876\pi$
$114$		0			0
$115$	−9.32346	+	9.91377i	−0.869417	+	0.924464i
$116$			4.04446i			0.375518i
$117$		0			0
$118$	1.69343	−	1.69343i	0.155893	−	0.155893i
$119$			21.6236i			1.98223i
$120$		0			0
$121$	21.3081			1.93710
$122$	1.64958	−	1.64958i	0.149346	−	0.149346i
$123$		0			0
$124$	−4.04446			−0.363203
$125$	11.1330	−	1.02746i	0.995768	−	0.0918990i
$126$		0			0
$127$	10.0379	−	10.0379i	0.890717	−	0.890717i	−0.103873	−	0.994591i	$-0.533124\pi$
$127$	10.0379	−	10.0379i	0.890717	−	0.890717i	0.994591	+	0.103873i	$0.0331236\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	12.3973	−	0.380423i	1.08732	−	0.0333653i
$131$	−4.64290			−0.405652			−0.202826	−	0.979215i	$-0.565013\pi$
$131$	−4.64290			−0.405652			−0.202826	+	0.979215i	$0.565013\pi$
$132$		0			0
$133$	5.05259	+	12.3621i	0.438115	+	1.07193i
$134$			8.66573i			0.748605i
$135$		0			0
$136$		−	7.05776i		−	0.605198i
$137$	2.26545	+	2.26545i	0.193550	+	0.193550i	0.797228	−	0.603678i	$-0.206299\pi$
$137$	2.26545	+	2.26545i	0.193550	+	0.193550i	−0.603678	+	0.797228i	$0.706299\pi$
$138$		0			0
$139$		−	17.4266i		−	1.47810i	−0.673649	−	0.739051i	$-0.735274\pi$
$139$		−	17.4266i		−	1.47810i	0.673649	−	0.739051i	$-0.264726\pi$
$140$	−4.69343	+	4.99059i	−0.396667	+	0.421782i
$141$		0			0
$142$	−4.60720	−	4.60720i	−0.386628	−	0.386628i
$143$	−22.2940	−	22.2940i	−1.86432	−	1.86432i
$144$		0			0
$145$	−9.03942	+	0.277383i	−0.750683	+	0.0230354i
$146$		−	2.93707i		−	0.243074i
$147$		0			0
$148$	6.19934	+	6.19934i	0.509583	+	0.509583i
$149$			1.79836i			0.147327i	0.997283	+	0.0736637i	$0.0234691\pi$
$149$			1.79836i			0.147327i	−0.997283	+	0.0736637i	$0.976531\pi$
$150$		0			0
$151$		−	8.62201i		−	0.701649i	−0.936441	−	0.350825i	$-0.885901\pi$
$151$		−	8.62201i		−	0.701649i	0.936441	−	0.350825i	$-0.114099\pi$
$152$	−1.64913	−	4.03490i	−0.133762	−	0.327273i
$153$		0			0
$154$	17.4147			1.40332
$155$	−0.277383	−	9.03942i	−0.0222799	−	0.726064i
$156$		0			0
$157$	7.79308	+	7.79308i	0.621956	+	0.621956i	0.946031	−	0.324076i	$-0.105053\pi$
$157$	7.79308	+	7.79308i	0.621956	+	0.621956i	−0.324076	+	0.946031i	$0.605053\pi$
$158$	2.99703	−	2.99703i	0.238431	−	0.238431i
$159$		0			0
$160$	1.53190	−	1.62889i	0.121107	−	0.128775i
$161$	18.6469			1.46958
$162$		0			0
$163$	7.85986	−	7.85986i	0.615632	−	0.615632i	−0.328776	−	0.944408i	$-0.606636\pi$
$163$	7.85986	−	7.85986i	0.615632	−	0.615632i	0.944408	+	0.328776i	$0.106636\pi$
$164$	6.38884			0.498884
$165$		0			0
$166$			7.50462i			0.582472i
$167$	17.5764	−	17.5764i	1.36010	−	1.36010i	0.486323	−	0.873779i	$-0.338338\pi$
$167$	17.5764	−	17.5764i	1.36010	−	1.36010i	0.873779	−	0.486323i	$-0.161662\pi$
$168$		0			0
$169$			17.7676i			1.36674i
$170$	15.7742	−	0.484046i	1.20983	−	0.0371246i
$171$		0			0
$172$	4.15703	+	4.15703i	0.316970	+	0.316970i
$173$	−0.108645	−	0.108645i	−0.00826009	−	0.00826009i	0.702965	−	0.711225i	$-0.251859\pi$
$173$	−0.108645	−	0.108645i	−0.00826009	−	0.00826009i	−0.711225	+	0.702965i	$0.751859\pi$
$174$		0			0
$175$	−11.4759	−	10.1476i	−0.867500	−	0.767088i
$176$	−5.68402			−0.428449
$177$		0			0
$178$	1.77363	−	1.77363i	0.132939	−	0.132939i
$179$	9.54798			0.713649			0.356825	−	0.934171i	$-0.383859\pi$
$179$	9.54798			0.713649			0.356825	+	0.934171i	$0.383859\pi$
$180$		0			0
$181$		−	19.4384i		−	1.44484i	−0.691453	−	0.722421i	$-0.743029\pi$
$181$		−	19.4384i		−	1.44484i	0.691453	−	0.722421i	$-0.256971\pi$
$182$	−12.0169	−	12.0169i	−0.890751	−	0.890751i
$183$		0			0
$184$	−6.08621			−0.448681
$185$	−13.4305	+	14.2808i	−0.987427	+	1.04995i
$186$		0			0
$187$	−28.3666	−	28.3666i	−2.07437	−	2.07437i
$188$	−3.24326	+	3.24326i	−0.236539	+	0.236539i
$189$		0			0
$190$	8.90495	−	3.96255i	0.646033	−	0.287474i
$191$	−25.1526			−1.81998			−0.909991	−	0.414628i	$-0.863912\pi$
$191$	−25.1526			−1.81998			−0.909991	+	0.414628i	$0.863912\pi$
$192$		0			0
$193$	1.23637	+	1.23637i	0.0889961	+	0.0889961i	0.750203	−	0.661207i	$-0.229956\pi$
$193$	1.23637	+	1.23637i	0.0889961	+	0.0889961i	−0.661207	+	0.750203i	$0.729956\pi$
$194$		−	8.79655i		−	0.631555i
$195$		0			0
$196$	2.38686			0.170490
$197$	−5.67759	−	5.67759i	−0.404511	−	0.404511i	0.475308	−	0.879819i	$-0.342337\pi$
$197$	−5.67759	−	5.67759i	−0.404511	−	0.404511i	−0.879819	+	0.475308i	$0.842337\pi$
$198$		0			0
$199$		−	3.89894i		−	0.276389i	−0.990405	−	0.138194i	$-0.955870\pi$
$199$		−	3.89894i		−	0.276389i	0.990405	−	0.138194i	$-0.0441299\pi$
$200$	3.74566	+	3.31210i	0.264858	+	0.234201i
$201$		0			0
$202$	2.42461	−	2.42461i	0.170595	−	0.170595i
$203$	8.76204	+	8.76204i	0.614975	+	0.614975i
$204$		0			0
$205$	0.438169	+	14.2792i	0.0306030	+	0.997299i
$206$	18.5038			1.28922
$207$		0			0
$208$	3.92222	+	3.92222i	0.271957	+	0.271957i
$209$	−22.8453	−	9.58891i	−1.58024	−	0.663279i
$210$		0			0
$211$		−	18.9376i		−	1.30372i	−0.758341	−	0.651858i	$-0.773990\pi$
$211$		−	18.9376i		−	1.30372i	0.758341	−	0.651858i	$-0.226010\pi$
$212$	5.40818	−	5.40818i	0.371435	−	0.371435i
$213$		0			0
$214$			7.11253i			0.486202i
$215$	−9.00591	+	9.57612i	−0.614198	+	0.653086i
$216$		0			0
$217$	−8.76204	+	8.76204i	−0.594806	+	0.594806i
$218$	−4.21102	+	4.21102i	−0.285206	+	0.285206i
$219$		0			0
$220$	−0.389830	−	12.7039i	−0.0262823	−	0.856495i
$221$			39.1484i			2.63341i
$222$		0			0
$223$	−9.26030	−	9.26030i	−0.620116	−	0.620116i	0.325445	−	0.945561i	$-0.394486\pi$
$223$	−9.26030	−	9.26030i	−0.620116	−	0.620116i	−0.945561	+	0.325445i	$0.894486\pi$
$224$	−3.06380			−0.204709
$225$		0			0
$226$	0.0585309			0.00389342
$227$	2.63934	−	2.63934i	0.175179	−	0.175179i	−0.614071	−	0.789251i	$-0.710469\pi$
$227$	2.63934	−	2.63934i	0.175179	−	0.175179i	0.789251	+	0.614071i	$0.210469\pi$
$228$		0			0
$229$		−	4.94601i		−	0.326841i	−0.986556	−	0.163421i	$-0.947747\pi$
$229$		−	4.94601i		−	0.326841i	0.986556	−	0.163421i	$-0.0522528\pi$
$230$	−0.417413	−	13.6028i	−0.0275234	−	0.896940i
$231$		0			0
$232$	−2.85986	−	2.85986i	−0.187759	−	0.187759i
$233$	18.1200	−	18.1200i	1.18708	−	1.18708i	0.209210	−	0.977871i	$-0.432911\pi$
$233$	18.1200	−	18.1200i	1.18708	−	1.18708i	0.977871	−	0.209210i	$-0.0670893\pi$
$234$		0			0
$235$	−7.47116	−	7.02629i	−0.487365	−	0.458345i
$236$			2.39487i			0.155893i
$237$		0			0
$238$	−15.2902	−	15.2902i	−0.991114	−	0.991114i
$239$		−	6.98300i		−	0.451693i	−0.974163	−	0.225846i	$-0.927485\pi$
$239$		−	6.98300i		−	0.451693i	0.974163	−	0.225846i	$-0.0725147\pi$
$240$		0			0
$241$		−	7.54947i		−	0.486304i	−0.969988	−	0.243152i	$-0.921819\pi$
$241$		−	7.54947i		−	0.486304i	0.969988	−	0.243152i	$-0.0781814\pi$
$242$	−15.0671	+	15.0671i	−0.968550	+	0.968550i
$243$		0			0
$244$			2.33286i			0.149346i
$245$	0.163699	+	5.33467i	0.0104584	+	0.340819i
$246$		0			0
$247$	9.14747	+	22.3810i	0.582039	+	1.42407i
$248$	2.85986	−	2.85986i	0.181601	−	0.181601i
$249$		0			0
$250$	−7.14571	+	8.59877i	−0.451935	+	0.543834i
$251$	20.0566			1.26596			0.632981	−	0.774168i	$-0.281831\pi$
$251$	20.0566			1.26596			0.632981	+	0.774168i	$0.281831\pi$
$252$		0			0
$253$	−24.4618	+	24.4618i	−1.53790	+	1.53790i
$254$			14.1957i			0.890717i
$255$		0			0
$256$	1.00000			0.0625000
$257$	8.66176	−	8.66176i	0.540306	−	0.540306i	−0.383313	−	0.923619i	$-0.625217\pi$
$257$	8.66176	−	8.66176i	0.540306	−	0.540306i	0.923619	+	0.383313i	$0.125217\pi$
$258$		0			0
$259$	26.8609			1.66906
$260$	−8.49722	+	9.03522i	−0.526975	+	0.560341i
$261$		0			0
$262$	3.28303	−	3.28303i	0.202826	−	0.202826i
$263$	−7.51759	+	7.51759i	−0.463554	+	0.463554i	−0.899819	−	0.436264i	$-0.856301\pi$
$263$	−7.51759	+	7.51759i	−0.463554	+	0.463554i	0.436264	+	0.899819i	$0.356301\pi$
$264$		0			0
$265$	12.4583	+	11.7165i	0.765306	+	0.719736i
$266$	−12.3141	−	5.16861i	−0.755023	−	0.316908i
$267$		0			0
$268$	−6.12760	−	6.12760i	−0.374303	−	0.374303i
$269$	20.3832			1.24278			0.621391	−	0.783500i	$-0.286568\pi$
$269$	20.3832			1.24278			0.621391	+	0.783500i	$0.286568\pi$
$270$		0			0
$271$	−20.5647			−1.24921			−0.624607	−	0.780939i	$-0.714741\pi$
$271$	−20.5647			−1.24921			−0.624607	+	0.780939i	$0.714741\pi$
$272$	4.99059	+	4.99059i	0.302599	+	0.302599i
$273$		0			0
$274$	−3.20383			−0.193550
$275$	28.3666	−	1.74255i	1.71057	−	0.105080i
$276$		0			0
$277$	16.5022	+	16.5022i	0.991518	+	0.991518i	0.999964	−	0.00844603i	$-0.00268849\pi$
$277$	16.5022	+	16.5022i	0.991518	+	0.991518i	−0.00844603	+	0.999964i	$0.502688\pi$
$278$	12.3224	+	12.3224i	0.739051	+	0.739051i
$279$		0			0
$280$	−0.210126	−	6.84764i	−0.0125574	−	0.409225i
$281$		−	16.7009i		−	0.996293i	−0.867093	−	0.498147i	$-0.834014\pi$
$281$		−	16.7009i		−	0.996293i	0.867093	−	0.498147i	$-0.165986\pi$
$282$		0			0
$283$	−9.16938	+	9.16938i	−0.545063	+	0.545063i	−0.925009	−	0.379946i	$-0.875943\pi$
$283$	−9.16938	+	9.16938i	−0.545063	+	0.545063i	0.379946	+	0.925009i	$0.375943\pi$
$284$	6.51556			0.386628
$285$		0			0
$286$	31.5284			1.86432
$287$	13.8410	−	13.8410i	0.817007	−	0.817007i
$288$		0			0
$289$			32.8120i			1.93012i
$290$	6.19570	−	6.58798i	0.363824	−	0.386859i
$291$		0			0
$292$	2.07682	+	2.07682i	0.121537	+	0.121537i
$293$	−11.7298	−	11.7298i	−0.685260	−	0.685260i	0.275921	−	0.961180i	$-0.411017\pi$
$293$	−11.7298	−	11.7298i	−0.685260	−	0.685260i	−0.961180	+	0.275921i	$0.911017\pi$
$294$		0			0
$295$	−5.35258	+	0.164249i	−0.311639	+	0.00956293i
$296$	−8.76719			−0.509583
$297$		0			0
$298$	−1.27163	−	1.27163i	−0.0736637	−	0.0736637i
$299$	33.7593			1.95235
$300$		0			0
$301$	18.0118			1.03818
$302$	6.09668	+	6.09668i	0.350825	+	0.350825i
$303$		0			0
$304$	4.01921	+	1.68699i	0.230518	+	0.0967557i
$305$	−5.21399	+	0.159996i	−0.298552	+	0.00916135i
$306$		0			0
$307$	7.51719	−	7.51719i	0.429029	−	0.429029i	−0.459269	−	0.888297i	$-0.651889\pi$
$307$	7.51719	−	7.51719i	0.429029	−	0.429029i	0.888297	+	0.459269i	$0.151889\pi$
$308$	−12.3141	+	12.3141i	−0.701658	+	0.701658i
$309$		0			0
$310$	6.58798	+	6.19570i	0.374172	+	0.351892i
$311$	17.0941			0.969318			0.484659	−	0.874703i	$-0.338944\pi$
$311$	17.0941			0.969318			0.484659	+	0.874703i	$0.338944\pi$
$312$		0			0
$313$	−4.46822	+	4.46822i	−0.252559	+	0.252559i	−0.822019	−	0.569460i	$-0.807152\pi$
$313$	−4.46822	+	4.46822i	−0.252559	+	0.252559i	0.569460	+	0.822019i	$0.307152\pi$
$314$	−11.0211			−0.621956
$315$		0			0
$316$			4.23844i			0.238431i
$317$	−20.3285	+	20.3285i	−1.14176	+	1.14176i	−0.153632	+	0.988128i	$0.549097\pi$
$317$	−20.3285	+	20.3285i	−1.14176	+	1.14176i	−0.988128	+	0.153632i	$0.950903\pi$
$318$		0			0
$319$	−22.9888			−1.28712
$320$	0.0685835	+	2.23502i	0.00383393	+	0.124941i
$321$		0			0
$322$	−13.1854	+	13.1854i	−0.734791	+	0.734791i
$323$	11.6391	+	28.4773i	0.647619	+	1.58452i
$324$		0			0
$325$	−20.7766	−	18.3718i	−1.15248	−	1.01908i
$326$			11.1155i			0.615632i
$327$		0			0
$328$	−4.51759	+	4.51759i	−0.249442	+	0.249442i
$329$			14.0526i			0.774744i
$330$		0			0
$331$		−	21.9956i		−	1.20898i	−0.796611	−	0.604492i	$-0.793376\pi$
$331$		−	21.9956i		−	1.20898i	0.796611	−	0.604492i	$-0.206624\pi$
$332$	−5.30657	−	5.30657i	−0.291236	−	0.291236i
$333$		0			0
$334$			24.8568i			1.36010i
$335$	13.2750	−	14.1155i	0.725292	−	0.771214i
$336$		0			0
$337$	−4.20829	+	4.20829i	−0.229240	+	0.229240i	−0.812375	−	0.583135i	$-0.801826\pi$
$337$	−4.20829	+	4.20829i	−0.229240	+	0.229240i	0.583135	+	0.812375i	$0.301826\pi$
$338$	−12.5636	−	12.5636i	−0.683369	−	0.683369i
$339$		0			0
$340$	−10.8118	+	11.4963i	−0.586351	+	0.623476i
$341$		−	22.9888i		−	1.24491i
$342$		0			0
$343$	−9.99406	+	9.99406i	−0.539628	+	0.539628i
$344$	−5.87892			−0.316970
$345$		0			0
$346$	0.153647			0.00826009
$347$	18.8707	+	18.8707i	1.01303	+	1.01303i	0.999914	+	0.0131194i	$0.00417616\pi$
$347$	18.8707	+	18.8707i	1.01303	+	1.01303i	0.0131194	+	0.999914i	$0.495824\pi$
$348$		0			0
$349$			3.34923i			0.179280i	0.995974	+	0.0896401i	$0.0285717\pi$
$349$			3.34923i			0.179280i	−0.995974	+	0.0896401i	$0.971428\pi$
$350$	15.2902	−	0.939270i	0.817294	−	0.0502061i
$351$		0			0
$352$	4.01921	−	4.01921i	0.214225	−	0.214225i
$353$	−21.8457	+	21.8457i	−1.16273	+	1.16273i	−0.178852	+	0.983876i	$0.557238\pi$
$353$	−21.8457	+	21.8457i	−1.16273	+	1.16273i	−0.983876	+	0.178852i	$0.942762\pi$
$354$		0			0
$355$	0.446860	+	14.5624i	0.0237169	+	0.772891i
$356$			2.50829i			0.132939i
$357$		0			0
$358$	−6.75144	+	6.75144i	−0.356825	+	0.356825i
$359$		−	5.22092i		−	0.275550i	−0.990464	−	0.137775i	$-0.956005\pi$
$359$		−	5.22092i		−	0.275550i	0.990464	−	0.137775i	$-0.0439950\pi$
$360$		0			0
$361$	13.3081	+	13.5608i	0.700427	+	0.713724i
$362$	13.7450	+	13.7450i	0.722421	+	0.722421i
$363$		0			0
$364$	16.9944			0.890751
$365$	−4.49930	+	4.78417i	−0.235504	+	0.250415i
$366$		0			0
$367$	3.73845	+	3.73845i	0.195146	+	0.195146i	0.797915	−	0.602770i	$-0.205936\pi$
$367$	3.73845	+	3.73845i	0.195146	+	0.195146i	−0.602770	+	0.797915i	$0.705936\pi$
$368$	4.30360	−	4.30360i	0.224341	−	0.224341i
$369$		0			0
$370$	−0.601285	−	19.5948i	−0.0312593	−	1.01869i
$371$		−	23.4329i		−	1.21658i
$372$		0			0
$373$	16.6782	+	16.6782i	0.863566	+	0.863566i	0.991750	−	0.128185i	$-0.0409150\pi$
$373$	16.6782	+	16.6782i	0.863566	+	0.863566i	−0.128185	+	0.991750i	$0.540915\pi$
$374$	40.1165			2.07437
$375$		0			0
$376$		−	4.58666i		−	0.236539i
$377$	15.8632	+	15.8632i	0.816998	+	0.816998i
$378$		0			0
$379$	20.7405			1.06537			0.532683	−	0.846315i	$-0.321184\pi$
$379$	20.7405			1.06537			0.532683	+	0.846315i	$0.321184\pi$
$380$	−3.49481	+	9.09870i	−0.179280	+	0.466753i
$381$		0			0
$382$	17.7856	−	17.7856i	0.909991	−	0.909991i
$383$	0.963152	+	0.963152i	0.0492148	+	0.0492148i	0.731286	−	0.682071i	$-0.238921\pi$
$383$	0.963152	+	0.963152i	0.0492148	+	0.0492148i	−0.682071	+	0.731286i	$0.738921\pi$
$384$		0			0
$385$	−28.3666	−	26.6776i	−1.44570	−	1.35961i
$386$	−1.74850			−0.0889961
$387$		0			0
$388$	6.22010	+	6.22010i	0.315778	+	0.315778i
$389$			37.2714i			1.88974i	0.327452	+	0.944868i	$0.393810\pi$
$389$			37.2714i			1.88974i	−0.327452	+	0.944868i	$0.606190\pi$
$390$		0			0
$391$	42.9550			2.17233
$392$	−1.68776	+	1.68776i	−0.0852450	+	0.0852450i
$393$		0			0
$394$	8.02932			0.404511
$395$	−9.47298	+	0.290687i	−0.476637	+	0.0146260i
$396$		0			0
$397$	10.2595	+	10.2595i	0.514910	+	0.514910i	0.916027	−	0.401117i	$-0.131378\pi$
$397$	10.2595	+	10.2595i	0.514910	+	0.514910i	−0.401117	+	0.916027i	$0.631378\pi$
$398$	2.75697	+	2.75697i	0.138194	+	0.138194i
$399$		0			0
$400$	−4.99059	+	0.306570i	−0.249530	+	0.0153285i
$401$			7.24755i			0.361925i	0.983490	+	0.180963i	$0.0579213\pi$
$401$			7.24755i			0.361925i	−0.983490	+	0.180963i	$0.942079\pi$
$402$		0			0
$403$	−15.8632	+	15.8632i	−0.790204	+	0.790204i
$404$			3.42891i			0.170595i
$405$		0			0
$406$	−12.3914			−0.614975
$407$	−35.2372	+	35.2372i	−1.74664	+	1.74664i
$408$		0			0
$409$	4.10739			0.203097			0.101549	−	0.994831i	$-0.467620\pi$
$409$	4.10739			0.203097			0.101549	+	0.994831i	$0.467620\pi$
$410$	−10.4067	−	9.78705i	−0.513951	−	0.483348i
$411$		0			0
$412$	−13.0842	+	13.0842i	−0.644611	+	0.644611i
$413$	5.18833	+	5.18833i	0.255301	+	0.255301i
$414$		0			0
$415$	11.4963	−	12.2242i	0.564332	−	0.600063i
$416$	−5.54686			−0.271957
$417$		0			0
$418$	22.9344	−	9.37367i	1.12176	−	0.458481i
$419$			11.2890i			0.551504i	0.961229	+	0.275752i	$0.0889268\pi$
$419$			11.2890i			0.551504i	−0.961229	+	0.275752i	$0.911073\pi$
$420$		0			0
$421$			4.87088i			0.237392i	0.992931	+	0.118696i	$0.0378714\pi$
$421$			4.87088i			0.237392i	−0.992931	+	0.118696i	$0.962129\pi$
$422$	13.3909	+	13.3909i	0.651858	+	0.651858i
$423$		0			0
$424$			7.64832i			0.371435i
$425$	−26.4360	−	23.3760i	−1.28233	−	1.13390i
$426$		0			0
$427$	5.05399	+	5.05399i	0.244580	+	0.244580i
$428$	−5.02931	−	5.02931i	−0.243101	−	0.243101i
$429$		0			0
$430$	−0.403197	−	13.1395i	−0.0194439	−	0.633642i
$431$			7.08729i			0.341383i	0.985325	+	0.170691i	$0.0546001\pi$
$431$			7.08729i			0.341383i	−0.985325	+	0.170691i	$0.945400\pi$
$432$		0			0
$433$	−21.2804	−	21.2804i	−1.02267	−	1.02267i	−0.999737	−	0.0229344i	$-0.992699\pi$
$433$	−21.2804	−	21.2804i	−1.02267	−	1.02267i	−0.0229344	−	0.999737i	$-0.507301\pi$
$434$		−	12.3914i		−	0.594806i
$435$		0			0
$436$		−	5.95528i		−	0.285206i
$437$	24.5572	−	10.0369i	1.17473	−	0.480131i
$438$		0			0
$439$	−27.9747			−1.33516			−0.667580	−	0.744538i	$-0.732670\pi$
$439$	−27.9747			−1.33516			−0.667580	+	0.744538i	$0.732670\pi$
$440$	9.25865	+	8.70735i	0.441389	+	0.415107i
$441$		0			0
$442$	−27.6821	−	27.6821i	−1.31670	−	1.31670i
$443$	11.9554	−	11.9554i	0.568019	−	0.568019i	−0.363554	−	0.931573i	$-0.618437\pi$
$443$	11.9554	−	11.9554i	0.568019	−	0.568019i	0.931573	+	0.363554i	$0.118437\pi$
$444$		0			0
$445$	−5.60608	+	0.172028i	−0.265753	+	0.00815489i
$446$	13.0960			0.620116
$447$		0			0
$448$	2.16643	−	2.16643i	0.102354	−	0.102354i
$449$	−0.799279			−0.0377203			−0.0188602	−	0.999822i	$-0.506004\pi$
$449$	−0.799279			−0.0377203			−0.0188602	+	0.999822i	$0.506004\pi$
$450$		0			0
$451$			36.3143i			1.70997i
$452$	−0.0413876	+	0.0413876i	−0.00194671	+	0.00194671i
$453$		0			0
$454$			3.73260i			0.175179i
$455$	1.16554	+	37.9829i	0.0546413	+	1.78066i
$456$		0			0
$457$	−19.9638	−	19.9638i	−0.933866	−	0.933866i	0.0640788	−	0.997945i	$-0.479589\pi$
$457$	−19.9638	−	19.9638i	−0.933866	−	0.933866i	−0.997945	+	0.0640788i	$0.979589\pi$
$458$	3.49735	+	3.49735i	0.163421	+	0.163421i
$459$		0			0
$460$	9.91377	+	9.32346i	0.462232	+	0.434708i
$461$	16.7900			0.781989			0.390995	−	0.920393i	$-0.372131\pi$
$461$	16.7900			0.781989			0.390995	+	0.920393i	$0.372131\pi$
$462$		0			0
$463$	13.2413	−	13.2413i	0.615377	−	0.615377i	−0.328965	−	0.944342i	$-0.606700\pi$
$463$	13.2413	−	13.2413i	0.615377	−	0.615377i	0.944342	+	0.328965i	$0.106700\pi$
$464$	4.04446			0.187759
$465$		0			0
$466$			25.6256i			1.18708i
$467$	−18.9064	−	18.9064i	−0.874885	−	0.874885i	0.118115	−	0.993000i	$-0.462315\pi$
$467$	−18.9064	−	18.9064i	−0.874885	−	0.874885i	−0.993000	+	0.118115i	$0.962315\pi$
$468$		0			0
$469$	−26.5500			−1.22597
$470$	10.2512	−	0.314569i	0.472855	−	0.0145100i
$471$		0			0
$472$	−1.69343	−	1.69343i	−0.0779464	−	0.0779464i
$473$	−23.6286	+	23.6286i	−1.08645	+	1.08645i
$474$		0			0
$475$	−20.5754	−	7.18692i	−0.944065	−	0.329759i
$476$	21.6236			0.991114
$477$		0			0
$478$	4.93773	+	4.93773i	0.225846	+	0.225846i
$479$			6.59491i			0.301329i	0.988585	+	0.150665i	$0.0481413\pi$
$479$			6.59491i			0.301329i	−0.988585	+	0.150665i	$0.951859\pi$
$480$		0			0
$481$	48.6304			2.21735
$482$	5.33828	+	5.33828i	0.243152	+	0.243152i
$483$		0			0
$484$		−	21.3081i		−	0.968550i
$485$	−13.4754	+	14.3286i	−0.611887	+	0.650629i
$486$		0			0
$487$	3.62733	−	3.62733i	0.164370	−	0.164370i	−0.620129	−	0.784499i	$-0.712920\pi$
$487$	3.62733	−	3.62733i	0.164370	−	0.164370i	0.784499	+	0.620129i	$0.212920\pi$
$488$	−1.64958	−	1.64958i	−0.0746732	−	0.0746732i
$489$		0			0
$490$	−3.88793	−	3.65643i	−0.175639	−	0.165181i
$491$	−3.35710			−0.151504			−0.0757519	−	0.997127i	$-0.524136\pi$
$491$	−3.35710			−0.151504			−0.0757519	+	0.997127i	$0.524136\pi$
$492$		0			0
$493$	20.1842	+	20.1842i	0.909052	+	0.909052i
$494$	−22.2940	−	9.35751i	−1.00305	−	0.421014i
$495$		0			0
$496$			4.04446i			0.181601i
$497$	14.1155	−	14.1155i	0.633168	−	0.633168i
$498$		0			0
$499$			13.9250i			0.623367i	0.950186	+	0.311684i	$0.100893\pi$
$499$			13.9250i			0.623367i	−0.950186	+	0.311684i	$0.899107\pi$
$500$	−1.02746	−	11.1330i	−0.0459495	−	0.497884i
$501$		0			0
$502$	−14.1822	+	14.1822i	−0.632981	+	0.632981i
$503$	−18.2263	+	18.2263i	−0.812668	+	0.812668i	−0.985033	−	0.172365i	$-0.944859\pi$
$503$	−18.2263	+	18.2263i	−0.812668	+	0.812668i	0.172365	+	0.985033i	$0.444859\pi$
$504$		0			0
$505$	−7.66367	+	0.235167i	−0.341029	+	0.0104648i
$506$		−	34.5941i		−	1.53790i
$507$		0			0
$508$	−10.0379	−	10.0379i	−0.445359	−	0.445359i
$509$	−31.4996			−1.39619			−0.698097	−	0.716003i	$-0.745970\pi$
$509$	−31.4996			−1.39619			−0.698097	+	0.716003i	$0.745970\pi$
$510$		0			0
$511$	8.99859			0.398074
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			12.2496i			0.540306i
$515$	−30.1407	−	28.3460i	−1.32816	−	1.24907i
$516$		0			0
$517$	−18.4347	−	18.4347i	−0.810759	−	0.810759i
$518$	−18.9935	+	18.9935i	−0.834528	+	0.834528i
$519$		0			0
$520$	−0.380423	−	12.3973i	−0.0166826	−	0.543658i
$521$		−	32.9541i		−	1.44375i	−0.692026	−	0.721873i	$-0.743281\pi$
$521$		−	32.9541i		−	1.44375i	0.692026	−	0.721873i	$-0.256719\pi$
$522$		0			0
$523$	30.6631	+	30.6631i	1.34080	+	1.34080i	0.895260	+	0.445544i	$0.146990\pi$
$523$	30.6631	+	30.6631i	1.34080	+	1.34080i	0.445544	+	0.895260i	$0.353010\pi$
$524$			4.64290i			0.202826i
$525$		0			0
$526$		−	10.6315i		−	0.463554i
$527$	−20.1842	+	20.1842i	−0.879239	+	0.879239i
$528$		0			0
$529$		−	14.0419i		−	0.610519i
$530$	−17.0941	+	0.524549i	−0.742521	+	0.0227849i
$531$		0			0
$532$	12.3621	−	5.05259i	0.535965	−	0.219058i
$533$	25.0584	−	25.0584i	1.08540	−	1.08540i
$534$		0			0
$535$	10.8957	−	11.5855i	0.471061	−	0.500886i
$536$	8.66573			0.374303
$537$		0			0
$538$	−14.4131	+	14.4131i	−0.621391	+	0.621391i
$539$			13.5670i			0.584370i
$540$		0			0
$541$	−5.86517			−0.252163			−0.126082	−	0.992020i	$-0.540240\pi$
$541$	−5.86517			−0.252163			−0.126082	+	0.992020i	$0.540240\pi$
$542$	14.5414	−	14.5414i	0.624607	−	0.624607i
$543$		0			0
$544$	−7.05776			−0.302599
$545$	13.3101	−	0.408434i	0.570144	−	0.0174954i
$546$		0			0
$547$	27.3401	−	27.3401i	1.16898	−	1.16898i	0.186527	−	0.982450i	$-0.440277\pi$
$547$	27.3401	−	27.3401i	1.16898	−	1.16898i	0.982450	−	0.186527i	$-0.0597231\pi$
$548$	2.26545	−	2.26545i	0.0967752	−	0.0967752i
$549$		0			0
$550$	−18.8261	+	21.2904i	−0.802746	+	0.907826i
$551$	16.2555	+	6.82297i	0.692508	+	0.290668i
$552$		0			0
$553$	9.18229	+	9.18229i	0.390471	+	0.390471i
$554$	−23.3376			−0.991518
$555$		0			0
$556$	−17.4266			−0.739051
$557$	−30.4617	−	30.4617i	−1.29070	−	1.29070i	−0.934353	−	0.356350i	$-0.884021\pi$
$557$	−30.4617	−	30.4617i	−1.29070	−	1.29070i	−0.356350	−	0.934353i	$-0.615979\pi$
$558$		0			0
$559$	32.6095			1.37924
$560$	4.99059	+	4.69343i	0.210891	+	0.198334i
$561$		0			0
$562$	11.8093	+	11.8093i	0.498147	+	0.498147i
$563$	−9.62507	−	9.62507i	−0.405648	−	0.405648i	0.474570	−	0.880218i	$-0.342604\pi$
$563$	−9.62507	−	9.62507i	−0.405648	−	0.405648i	−0.880218	+	0.474570i	$0.842604\pi$
$564$		0			0
$565$	−0.0953405	−	0.0896635i	−0.00401100	−	0.00377217i
$566$		−	12.9675i		−	0.545063i
$567$		0			0
$568$	−4.60720	+	4.60720i	−0.193314	+	0.193314i
$569$	−12.8721			−0.539627			−0.269814	−	0.962913i	$-0.586962\pi$
$569$	−12.8721			−0.539627			−0.269814	+	0.962913i	$0.586962\pi$
$570$		0			0
$571$	6.13588			0.256778			0.128389	−	0.991724i	$-0.459019\pi$
$571$	6.13588			0.256778			0.128389	+	0.991724i	$0.459019\pi$
$572$	−22.2940	+	22.2940i	−0.932158	+	0.932158i
$573$		0			0
$574$			19.5741i			0.817007i
$575$	−20.1582	+	22.7969i	−0.840653	+	0.950695i
$576$		0			0
$577$	−18.5088	−	18.5088i	−0.770532	−	0.770532i	0.207667	−	0.978200i	$-0.433413\pi$
$577$	−18.5088	−	18.5088i	−0.770532	−	0.770532i	−0.978200	+	0.207667i	$0.933413\pi$
$578$	−23.2016	−	23.2016i	−0.965060	−	0.965060i
$579$		0			0
$580$	0.277383	+	9.03942i	0.0115177	+	0.375342i
$581$	−22.9927			−0.953896
$582$		0			0
$583$	30.7402	+	30.7402i	1.27313	+	1.27313i
$584$	−2.93707			−0.121537
$585$		0			0
$586$	16.5884			0.685260
$587$	−25.9416	−	25.9416i	−1.07072	−	1.07072i	−0.997301	−	0.0734236i	$-0.976607\pi$
$587$	−25.9416	−	25.9416i	−1.07072	−	1.07072i	−0.0734236	−	0.997301i	$-0.523393\pi$
$588$		0			0
$589$	−6.82297	+	16.2555i	−0.281136	+	0.669797i
$590$	3.66870	−	3.90098i	0.151038	−	0.160601i
$591$		0			0
$592$	6.19934	−	6.19934i	0.254791	−	0.254791i
$593$	−5.30063	+	5.30063i	−0.217671	+	0.217671i	−0.807516	−	0.589845i	$-0.799189\pi$
$593$	−5.30063	+	5.30063i	−0.217671	+	0.217671i	0.589845	+	0.807516i	$0.299189\pi$
$594$		0			0
$595$	1.48302	+	48.3290i	0.0607979	+	1.98130i
$596$	1.79836			0.0736637
$597$		0			0
$598$	−23.8714	+	23.8714i	−0.976176	+	0.976176i
$599$	8.38430			0.342573			0.171287	−	0.985221i	$-0.445208\pi$
$599$	8.38430			0.342573			0.171287	+	0.985221i	$0.445208\pi$
$600$		0			0
$601$			11.8588i			0.483731i	0.970310	+	0.241866i	$0.0777594\pi$
$601$			11.8588i			0.483731i	−0.970310	+	0.241866i	$0.922241\pi$
$602$	−12.7363	+	12.7363i	−0.519092	+	0.519092i
$603$		0			0
$604$	−8.62201			−0.350825
$605$	47.6240	−	1.46138i	1.93619	−	0.0594137i
$606$		0			0
$607$	−11.1795	+	11.1795i	−0.453763	+	0.453763i	−0.896601	−	0.442838i	$-0.853972\pi$
$607$	−11.1795	+	11.1795i	−0.453763	+	0.453763i	0.442838	+	0.896601i	$0.353972\pi$
$608$	−4.03490	+	1.64913i	−0.163637	+	0.0668809i
$609$		0			0
$610$	3.57371	−	3.79998i	0.144695	−	0.153857i
$611$			25.4415i			1.02925i
$612$		0			0
$613$	27.8634	−	27.8634i	1.12539	−	1.12539i	0.134477	−	0.990917i	$-0.457065\pi$
$613$	27.8634	−	27.8634i	1.12539	−	1.12539i	0.990917	−	0.134477i	$-0.0429355\pi$
$614$			10.6309i			0.429029i
$615$		0			0
$616$		−	17.4147i		−	0.701658i
$617$	9.90590	+	9.90590i	0.398797	+	0.398797i	0.877808	−	0.479012i	$-0.159005\pi$
$617$	9.90590	+	9.90590i	0.398797	+	0.398797i	−0.479012	+	0.877808i	$0.659005\pi$
$618$		0			0
$619$		−	13.1404i		−	0.528156i	−0.964501	−	0.264078i	$-0.914932\pi$
$619$		−	13.1404i		−	0.528156i	0.964501	−	0.264078i	$-0.0850676\pi$
$620$	−9.03942	+	0.277383i	−0.363032	+	0.0111400i
$621$		0			0
$622$	−12.0874	+	12.0874i	−0.484659	+	0.484659i
$623$	5.43405	+	5.43405i	0.217711	+	0.217711i
$624$		0			0
$625$	24.8120	−	3.05994i	0.992481	−	0.122397i
$626$		−	6.31902i		−	0.252559i
$627$		0			0
$628$	7.79308	−	7.79308i	0.310978	−	0.310978i
$629$	61.8768			2.46719
$630$		0			0
$631$	−1.22727			−0.0488569			−0.0244284	−	0.999702i	$-0.507777\pi$
$631$	−1.22727			−0.0488569			−0.0244284	+	0.999702i	$0.507777\pi$
$632$	−2.99703	−	2.99703i	−0.119215	−	0.119215i
$633$		0			0
$634$		−	28.7488i		−	1.14176i
$635$	21.7464	−	23.1232i	0.862979	−	0.917618i
$636$		0			0
$637$	9.36178	−	9.36178i	0.370927	−	0.370927i
$638$	16.2555	−	16.2555i	0.643562	−	0.643562i
$639$		0			0
$640$	−1.62889	−	1.53190i	−0.0643876	−	0.0605536i
$641$			36.0180i			1.42263i	0.702875	+	0.711313i	$0.251899\pi$
$641$			36.0180i			1.42263i	−0.702875	+	0.711313i	$0.748101\pi$
$642$		0			0
$643$	−2.37113	+	2.37113i	−0.0935082	+	0.0935082i	−0.752314	−	0.658805i	$-0.771062\pi$
$643$	−2.37113	+	2.37113i	−0.0935082	+	0.0935082i	0.658805	+	0.752314i	$0.271062\pi$
$644$		−	18.6469i		−	0.734791i
$645$		0			0
$646$	−28.3666	−	11.9064i	−1.11607	−	0.468451i
$647$	1.07039	+	1.07039i	0.0420812	+	0.0420812i	0.727834	−	0.685753i	$-0.240527\pi$
$647$	1.07039	+	1.07039i	0.0420812	+	0.0420812i	−0.685753	+	0.727834i	$0.740527\pi$
$648$		0			0
$649$	−13.6125			−0.534337
$650$	27.6821	−	1.70050i	1.08578	−	0.0666992i
$651$		0			0
$652$	−7.85986	−	7.85986i	−0.307816	−	0.307816i
$653$	17.2204	−	17.2204i	0.673887	−	0.673887i	−0.284723	−	0.958610i	$-0.591901\pi$
$653$	17.2204	−	17.2204i	0.673887	−	0.673887i	0.958610	+	0.284723i	$0.0919015\pi$
$654$		0			0
$655$	−10.3770	+	0.318426i	−0.405461	+	0.0124419i
$656$		−	6.38884i		−	0.249442i
$657$		0			0
$658$	−9.93668	−	9.93668i	−0.387372	−	0.387372i
$659$	−33.5146			−1.30555			−0.652773	−	0.757554i	$-0.726394\pi$
$659$	−33.5146			−1.30555			−0.652773	+	0.757554i	$0.726394\pi$
$660$		0			0
$661$		−	38.1923i		−	1.48551i	−0.669564	−	0.742754i	$-0.733519\pi$
$661$		−	38.1923i		−	1.48551i	0.669564	−	0.742754i	$-0.266481\pi$
$662$	15.5532	+	15.5532i	0.604492	+	0.604492i
$663$		0			0
$664$	7.50462			0.291236
$665$	12.1405	+	27.2830i	0.470787	+	1.05799i
$666$		0			0
$667$	17.4057	−	17.4057i	0.673952	−	0.673952i
$668$	−17.5764	−	17.5764i	−0.680051	−	0.680051i
$669$		0			0
$670$	0.594326	+	19.3680i	0.0229608	+	0.748253i
$671$	−13.2601			−0.511899
$672$		0			0
$673$	12.1639	+	12.1639i	0.468885	+	0.468885i	0.901553	−	0.432668i	$-0.142428\pi$
$673$	12.1639	+	12.1639i	0.468885	+	0.468885i	−0.432668	+	0.901553i	$0.642428\pi$
$674$		−	5.95143i		−	0.229240i
$675$		0			0
$676$	17.7676			0.683369
$677$	27.8121	−	27.8121i	1.06891	−	1.06891i	0.0714633	−	0.997443i	$-0.477233\pi$
$677$	27.8121	−	27.8121i	1.06891	−	1.06891i	0.997443	−	0.0714633i	$-0.0227669\pi$
$678$		0			0
$679$	26.9508			1.03428
$680$	−0.484046	−	15.7742i	−0.0185623	−	0.604914i
$681$		0			0
$682$	16.2555	+	16.2555i	0.622456	+	0.622456i
$683$	17.1745	+	17.1745i	0.657166	+	0.657166i	0.954709	−	0.297543i	$-0.0961671\pi$
$683$	17.1745	+	17.1745i	0.657166	+	0.657166i	−0.297543	+	0.954709i	$0.596167\pi$
$684$		0			0
$685$	5.21869	+	4.90794i	0.199396	+	0.187523i
$686$		−	14.1337i		−	0.539628i
$687$		0			0
$688$	4.15703	−	4.15703i	0.158485	−	0.158485i
$689$		−	42.4241i		−	1.61623i
$690$		0			0
$691$	−9.98119			−0.379702			−0.189851	−	0.981813i	$-0.560801\pi$
$691$	−9.98119			−0.379702			−0.189851	+	0.981813i	$0.560801\pi$
$692$	−0.108645	+	0.108645i	−0.00413005	+	0.00413005i
$693$		0			0
$694$	−26.6872			−1.01303
$695$	−1.19518	−	38.9487i	−0.0453356	−	1.47741i
$696$		0			0
$697$	31.8841	−	31.8841i	1.20770	−	1.20770i
$698$	−2.36826	−	2.36826i	−0.0896401	−	0.0896401i
$699$		0			0
$700$	−10.1476	+	11.4759i	−0.383544	+	0.433750i
$701$	−8.14987			−0.307816			−0.153908	−	0.988085i	$-0.549186\pi$
$701$	−8.14987			−0.307816			−0.153908	+	0.988085i	$0.549186\pi$
$702$		0			0
$703$	35.3747	−	14.4582i	1.33418	−	0.545302i
$704$			5.68402i			0.214225i
$705$		0			0
$706$		−	30.8944i		−	1.16273i
$707$	7.42850	+	7.42850i	0.279378	+	0.279378i
$708$		0			0
$709$		−	24.1408i		−	0.906626i	−0.891351	−	0.453313i	$-0.850242\pi$
$709$		−	24.1408i		−	0.906626i	0.891351	−	0.453313i	$-0.149758\pi$
$710$	−10.6131	−	9.98119i	−0.398304	−	0.374587i
$711$		0			0
$712$	−1.77363	−	1.77363i	−0.0664696	−	0.0664696i
$713$	17.4057	+	17.4057i	0.651849	+	0.651849i
$714$		0			0
$715$	−51.3564	−	48.2984i	−1.92062	−	1.80626i
$716$		−	9.54798i		−	0.356825i
$717$		0			0
$718$	3.69175	+	3.69175i	0.137775	+	0.137775i
$719$		−	12.6723i		−	0.472595i	−0.971681	−	0.236298i	$-0.924066\pi$
$719$		−	12.6723i		−	0.472595i	0.971681	−	0.236298i	$-0.0759340\pi$
$720$		0			0
$721$			56.6919i			2.11132i
$722$	−18.9992	−	0.178653i	−0.707076	−	0.00664878i
$723$		0			0
$724$	−19.4384			−0.722421
$725$	−20.1842	+	1.23991i	−0.749624	+	0.0460491i
$726$		0			0
$727$	12.3201	+	12.3201i	0.456926	+	0.456926i	0.897645	−	0.440719i	$-0.145276\pi$
$727$	12.3201	+	12.3201i	0.456926	+	0.456926i	−0.440719	+	0.897645i	$0.645276\pi$
$728$	−12.0169	+	12.0169i	−0.445375	+	0.445375i
$729$		0			0
$730$	−0.201435	−	6.56440i	−0.00745543	−	0.242959i
$731$	41.4920			1.53464
$732$		0			0
$733$	−1.44833	+	1.44833i	−0.0534954	+	0.0534954i	−0.733348	−	0.679853i	$-0.762044\pi$
$733$	−1.44833	+	1.44833i	−0.0534954	+	0.0534954i	0.679853	+	0.733348i	$0.262044\pi$
$734$	−5.28697			−0.195146
$735$		0			0
$736$			6.08621i			0.224341i
$737$	34.8294	−	34.8294i	1.28296	−	1.28296i
$738$		0			0
$739$		−	8.64709i		−	0.318088i	−0.987271	−	0.159044i	$-0.949159\pi$
$739$		−	8.64709i		−	0.318088i	0.987271	−	0.159044i	$-0.0508412\pi$
$740$	14.2808	+	13.4305i	0.524973	+	0.493713i
$741$		0			0
$742$	16.5696	+	16.5696i	0.608288	+	0.608288i
$743$	18.4885	+	18.4885i	0.678277	+	0.678277i	0.959610	−	0.281333i	$-0.0907767\pi$
$743$	18.4885	+	18.4885i	0.678277	+	0.678277i	−0.281333	+	0.959610i	$0.590777\pi$
$744$		0			0
$745$	0.123338	+	4.01936i	0.00451875	+	0.147258i
$746$	−23.5866			−0.863566
$747$		0			0
$748$	−28.3666	+	28.3666i	−1.03719	+	1.03719i
$749$	−21.7913			−0.796238
$750$		0			0
$751$		−	7.72319i		−	0.281823i	−0.990022	−	0.140912i	$-0.954997\pi$
$751$		−	7.72319i		−	0.281823i	0.990022	−	0.140912i	$-0.0450033\pi$
$752$	3.24326	+	3.24326i	0.118269	+	0.118269i
$753$		0			0
$754$	−22.4340			−0.816998
$755$	−0.591328	−	19.2703i	−0.0215206	−	0.701319i
$756$		0			0
$757$	−16.2864	−	16.2864i	−0.591937	−	0.591937i	0.346217	−	0.938154i	$-0.387466\pi$
$757$	−16.2864	−	16.2864i	−0.591937	−	0.591937i	−0.938154	+	0.346217i	$0.887466\pi$
$758$	−14.6657	+	14.6657i	−0.532683	+	0.532683i
$759$		0			0
$760$	−3.96255	−	8.90495i	−0.143737	−	0.323017i
$761$	−0.887475			−0.0321709			−0.0160855	−	0.999871i	$-0.505120\pi$
$761$	−0.887475			−0.0321709			−0.0160855	+	0.999871i	$0.505120\pi$
$762$		0			0
$763$	−12.9017	−	12.9017i	−0.467073	−	0.467073i
$764$			25.1526i			0.909991i
$765$		0			0
$766$	−1.36210			−0.0492148
$767$	9.39321	+	9.39321i	0.339169	+	0.339169i
$768$		0			0
$769$			1.13134i			0.0407972i	0.999792	+	0.0203986i	$0.00649352\pi$
$769$			1.13134i			0.0407972i	−0.999792	+	0.0203986i	$0.993506\pi$
$770$	38.9221	−	1.19436i	1.40266	−	0.0430418i
$771$		0			0
$772$	1.23637	−	1.23637i	0.0444980	−	0.0444980i
$773$	6.34620	+	6.34620i	0.228257	+	0.228257i	0.811964	−	0.583707i	$-0.198398\pi$
$773$	6.34620	+	6.34620i	0.228257	+	0.228257i	−0.583707	+	0.811964i	$0.698398\pi$
$774$		0			0
$775$	−1.23991	−	20.1842i	−0.0445389	−	0.725039i
$776$	−8.79655			−0.315778
$777$		0			0
$778$	−26.3549	−	26.3549i	−0.944868	−	0.944868i
$779$	10.7779	−	25.6781i	0.386159	−	0.920013i
$780$		0			0
$781$			37.0346i			1.32520i
$782$	−30.3738	+	30.3738i	−1.08616	+	1.08616i
$783$		0			0
$784$		−	2.38686i		−	0.0852450i
$785$	17.9521	+	16.8832i	0.640739	+	0.602587i
$786$		0			0
$787$	2.61114	−	2.61114i	0.0930770	−	0.0930770i	−0.659035	−	0.752112i	$-0.729035\pi$
$787$	2.61114	−	2.61114i	0.0930770	−	0.0930770i	0.752112	+	0.659035i	$0.229035\pi$
$788$	−5.67759	+	5.67759i	−0.202256	+	0.202256i
$789$		0			0
$790$	6.49286	−	6.90395i	0.231006	−	0.245632i
$791$			0.179327i			0.00637613i
$792$		0			0
$793$	9.15001	+	9.15001i	0.324926	+	0.324926i
$794$	−14.5091			−0.514910
$795$		0			0
$796$	−3.89894			−0.138194
$797$	−37.6179	+	37.6179i	−1.33249	+	1.33249i	−0.429360	+	0.903133i	$0.641261\pi$
$797$	−37.6179	+	37.6179i	−1.33249	+	1.33249i	−0.903133	+	0.429360i	$0.858739\pi$
$798$		0			0
$799$			32.3715i			1.14522i
$800$	3.31210	−	3.74566i	0.117101	−	0.132429i
$801$		0			0
$802$	−5.12479	−	5.12479i	−0.180963	−	0.180963i
$803$	−11.8047	+	11.8047i	−0.416579	+	0.416579i
$804$		0			0
$805$	41.6762	−	1.27887i	1.46889	−	0.0450743i
$806$		−	22.4340i		−	0.790204i
$807$		0			0
$808$	−2.42461	−	2.42461i	−0.0852973	−	0.0852973i
$809$		−	36.3150i		−	1.27677i	−0.769718	−	0.638384i	$-0.779603\pi$
$809$		−	36.3150i		−	1.27677i	0.769718	−	0.638384i	$-0.220397\pi$
$810$		0			0
$811$			33.7689i			1.18579i	0.805281	+	0.592893i	$0.202014\pi$
$811$			33.7689i			1.18579i	−0.805281	+	0.592893i	$0.797986\pi$
$812$	8.76204	−	8.76204i	0.307487	−	0.307487i
$813$		0			0
$814$		−	49.8329i		−	1.74664i
$815$	17.0279	−	18.1060i	0.596460	−	0.634225i
$816$		0			0
$817$	23.7208	−	9.69509i	0.829887	−	0.339188i
$818$	−2.90436	+	2.90436i	−0.101549	+	0.101549i
$819$		0			0
$820$	14.2792	−	0.438169i	0.498650	−	0.0153015i
$821$	−35.2486			−1.23019			−0.615093	−	0.788454i	$-0.710882\pi$
$821$	−35.2486			−1.23019			−0.615093	+	0.788454i	$0.710882\pi$
$822$		0			0
$823$	−1.01419	+	1.01419i	−0.0353525	+	0.0353525i	−0.724562	−	0.689210i	$-0.757958\pi$
$823$	−1.01419	+	1.01419i	−0.0353525	+	0.0353525i	0.689210	+	0.724562i	$0.257958\pi$
$824$		−	18.5038i		−	0.644611i
$825$		0			0
$826$	−7.33740			−0.255301
$827$	−26.2979	+	26.2979i	−0.914469	+	0.914469i	−0.996620	−	0.0821507i	$-0.973821\pi$
$827$	−26.2979	+	26.2979i	−0.914469	+	0.914469i	0.0821507	+	0.996620i	$0.473821\pi$
$828$		0			0
$829$	−24.6910			−0.857555			−0.428777	−	0.903410i	$-0.641056\pi$
$829$	−24.6910			−0.857555			−0.428777	+	0.903410i	$0.641056\pi$
$830$	0.514693	+	16.7730i	0.0178653	+	0.582198i
$831$		0			0
$832$	3.92222	−	3.92222i	0.135978	−	0.135978i
$833$	11.9118	−	11.9118i	0.412721	−	0.412721i
$834$		0			0
$835$	38.0781	−	40.4890i	1.31775	−	1.40118i
$836$	−9.58891	+	22.8453i	−0.331639	+	0.790121i
$837$		0			0
$838$	−7.98253	−	7.98253i	−0.275752	−	0.275752i
$839$	27.5645			0.951632			0.475816	−	0.879545i	$-0.342153\pi$
$839$	27.5645			0.951632			0.475816	+	0.879545i	$0.342153\pi$
$840$		0			0
$841$	−12.6424			−0.435944
$842$	−3.44423	−	3.44423i	−0.118696	−	0.118696i
$843$		0			0
$844$	−18.9376			−0.651858
$845$	1.21856	+	39.7109i	0.0419199	+	1.36610i
$846$		0			0
$847$	−46.1626	−	46.1626i	−1.58616	−	1.58616i
$848$	−5.40818	−	5.40818i	−0.185718	−	0.185718i
$849$		0			0
$850$	35.2224	−	2.16370i	1.20812	−	0.0742144i
$851$		−	53.3590i		−	1.82912i
$852$		0			0
$853$	−24.5359	+	24.5359i	−0.840094	+	0.840094i	−0.988871	−	0.148777i	$-0.952466\pi$
$853$	−24.5359	+	24.5359i	−0.840094	+	0.840094i	0.148777	+	0.988871i	$0.452466\pi$
$854$	−7.14743			−0.244580
$855$		0			0
$856$	7.11253			0.243101
$857$	−21.4801	+	21.4801i	−0.733747	+	0.733747i	−0.971360	−	0.237613i	$-0.923635\pi$
$857$	−21.4801	+	21.4801i	−0.733747	+	0.733747i	0.237613	+	0.971360i	$0.423635\pi$
$858$		0			0
$859$		−	28.6835i		−	0.978668i	−0.872096	−	0.489334i	$-0.837240\pi$
$859$		−	28.6835i		−	0.978668i	0.872096	−	0.489334i	$-0.162760\pi$
$860$	9.57612	+	9.00591i	0.326543	+	0.307099i
$861$		0			0
$862$	−5.01147	−	5.01147i	−0.170691	−	0.170691i
$863$	−10.4760	−	10.4760i	−0.356607	−	0.356607i	0.505954	−	0.862561i	$-0.331141\pi$
$863$	−10.4760	−	10.4760i	−0.356607	−	0.356607i	−0.862561	+	0.505954i	$0.831141\pi$
$864$		0			0
$865$	−0.250273	−	0.235371i	−0.00850955	−	0.00800286i
$866$	30.0950			1.02267
$867$		0			0
$868$	8.76204	+	8.76204i	0.297403	+	0.297403i
$869$	−24.0914			−0.817244
$870$		0			0
$871$	−48.0675			−1.62871
$872$	4.21102	+	4.21102i	0.142603	+	0.142603i
$873$		0			0
$874$	−10.2674	+	24.4618i	−0.347300	+	0.827431i
$875$	−26.3449	−	21.8930i	−0.890620	−	0.740119i
$876$		0			0
$877$	−41.3628	+	41.3628i	−1.39672	+	1.39672i	−0.587488	+	0.809233i	$0.699883\pi$
$877$	−41.3628	+	41.3628i	−1.39672	+	1.39672i	−0.809233	+	0.587488i	$0.800117\pi$
$878$	19.7811	−	19.7811i	0.667580	−	0.667580i
$879$		0			0
$880$	−12.7039	+	0.389830i	−0.428248	+	0.0131412i
$881$	−24.8371			−0.836785			−0.418392	−	0.908266i	$-0.637406\pi$
$881$	−24.8371			−0.836785			−0.418392	+	0.908266i	$0.637406\pi$
$882$		0			0
$883$	39.3033	−	39.3033i	1.32266	−	1.32266i	0.411049	−	0.911613i	$-0.365163\pi$
$883$	39.3033	−	39.3033i	1.32266	−	1.32266i	0.911613	−	0.411049i	$-0.134837\pi$
$884$	39.1484			1.31670
$885$		0			0
$886$			16.9075i			0.568019i
$887$	0.809857	−	0.809857i	0.0271923	−	0.0271923i	−0.693380	−	0.720572i	$-0.743879\pi$
$887$	0.809857	−	0.809857i	0.0271923	−	0.0271923i	0.720572	+	0.693380i	$0.243879\pi$
$888$		0			0
$889$	−43.4928			−1.45870
$890$	3.84245	−	4.08574i	0.128799	−	0.136954i
$891$		0			0
$892$	−9.26030	+	9.26030i	−0.310058	+	0.310058i
$893$	7.56398	+	18.5067i	0.253119	+	0.619302i
$894$		0			0
$895$	21.3399	−	0.654834i	0.713313	−	0.0218887i
$896$			3.06380i			0.102354i
$897$		0			0
$898$	0.565176	−	0.565176i	0.0188602	−	0.0188602i
$899$			16.3576i			0.545557i
$900$		0			0
$901$		−	53.9800i		−	1.79834i
$902$	−25.6781	−	25.6781i	−0.854987	−	0.854987i
$903$		0			0
$904$		−	0.0585309i		−	0.00194671i
$905$	−1.33315	−	43.4451i	−0.0443154	−	1.44416i
$906$		0			0
$907$	−11.4153	+	11.4153i	−0.379038	+	0.379038i	−0.870755	−	0.491717i	$-0.836369\pi$
$907$	−11.4153	+	11.4153i	−0.379038	+	0.379038i	0.491717	+	0.870755i	$0.336369\pi$
$908$	−2.63934	−	2.63934i	−0.0875897	−	0.0875897i
$909$		0			0
$910$	−27.6821	−	26.0338i	−0.917652	−	0.863011i
$911$		−	23.8379i		−	0.789786i	−0.918727	−	0.394893i	$-0.870782\pi$
$911$		−	23.8379i		−	0.789786i	0.918727	−	0.394893i	$-0.129218\pi$
$912$		0			0
$913$	30.1627	−	30.1627i	0.998238	−	0.998238i
$914$	28.2330			0.933866
$915$		0			0
$916$	−4.94601			−0.163421
$917$	10.0585	+	10.0585i	0.332162	+	0.332162i
$918$		0			0
$919$			10.0575i			0.331766i	0.986145	+	0.165883i	$0.0530474\pi$
$919$			10.0575i			0.331766i	−0.986145	+	0.165883i	$0.946953\pi$
$920$	−13.6028	+	0.417413i	−0.448470	+	0.0137617i
$921$		0			0
$922$	−11.8723	+	11.8723i	−0.390995	+	0.390995i
$923$	25.5555	−	25.5555i	0.841168	−	0.841168i
$924$		0			0
$925$	−29.0379	+	32.8389i	−0.954759	+	1.07974i
$926$			18.7261i			0.615377i
$927$		0			0
$928$	−2.85986	+	2.85986i	−0.0938796	+	0.0938796i
$929$			25.9657i			0.851906i	0.904745	+	0.425953i	$0.140061\pi$
$929$			25.9657i			0.851906i	−0.904745	+	0.425953i	$0.859939\pi$
$930$		0			0
$931$	4.02662	−	9.59329i	0.131967	−	0.314407i
$932$	−18.1200	−	18.1200i	−0.593540	−	0.593540i
$933$		0			0
$934$	26.7377			0.874885
$935$	−65.3454	−	61.4544i	−2.13702	−	2.00977i
$936$		0			0
$937$	−15.1765	−	15.1765i	−0.495794	−	0.495794i	0.414332	−	0.910126i	$-0.364015\pi$
$937$	−15.1765	−	15.1765i	−0.495794	−	0.495794i	−0.910126	+	0.414332i	$0.864015\pi$
$938$	18.7737	−	18.7737i	0.612984	−	0.612984i
$939$		0			0
$940$	−7.02629	+	7.47116i	−0.229172	+	0.243682i
$941$			3.32842i			0.108503i	0.998527	+	0.0542517i	$0.0172773\pi$
$941$			3.32842i			0.108503i	−0.998527	+	0.0542517i	$0.982723\pi$
$942$		0			0
$943$	−27.4950	−	27.4950i	−0.895360	−	0.895360i
$944$	2.39487			0.0779464
$945$		0			0
$946$		−	33.4159i		−	1.08645i
$947$	−17.1510	−	17.1510i	−0.557332	−	0.557332i	0.371215	−	0.928547i	$-0.378941\pi$
$947$	−17.1510	−	17.1510i	−0.557332	−	0.557332i	−0.928547	+	0.371215i	$0.878941\pi$
$948$		0			0
$949$	16.2915			0.528845
$950$	19.6309	−	9.46710i	0.636912	−	0.307153i
$951$		0			0
$952$	−15.2902	+	15.2902i	−0.495557	+	0.495557i
$953$	17.4495	+	17.4495i	0.565246	+	0.565246i	0.930793	−	0.365547i	$-0.119118\pi$
$953$	17.4495	+	17.4495i	0.565246	+	0.565246i	−0.365547	+	0.930793i	$0.619118\pi$
$954$		0			0
$955$	−56.2166	+	1.72506i	−1.81913	+	0.0558215i
$956$	−6.98300			−0.225846
$957$		0			0
$958$	−4.66330	−	4.66330i	−0.150665	−	0.150665i
$959$		−	9.81588i		−	0.316971i
$960$		0			0
$961$	14.6424			0.472335
$962$	−34.3869	+	34.3869i	−1.10868	+	1.10868i
$963$		0			0
$964$	−7.54947			−0.243152
$965$	2.84811	+	2.67852i	0.0916838	+	0.0862245i
$966$		0			0
$967$	12.3387	+	12.3387i	0.396786	+	0.396786i	0.877098	−	0.480311i	$-0.159476\pi$
$967$	12.3387	+	12.3387i	0.396786	+	0.396786i	−0.480311	+	0.877098i	$0.659476\pi$
$968$	15.0671	+	15.0671i	0.484275	+	0.484275i
$969$		0			0
$970$	−0.603298	−	19.6604i	−0.0193707	−	0.631258i
$971$		−	34.0584i		−	1.09298i	−0.837464	−	0.546492i	$-0.815963\pi$
$971$		−	34.0584i		−	1.09298i	0.837464	−	0.546492i	$-0.184037\pi$
$972$		0			0
$973$	−37.7535	+	37.7535i	−1.21032	+	1.21032i
$974$			5.12982i			0.164370i
$975$		0			0
$976$	2.33286			0.0746732
$977$	28.7226	−	28.7226i	0.918916	−	0.918916i	−0.0780344	−	0.996951i	$-0.524864\pi$
$977$	28.7226	−	28.7226i	0.918916	−	0.918916i	0.996951	+	0.0780344i	$0.0248644\pi$
$978$		0			0
$979$	−14.2572			−0.455662
$980$	5.33467	−	0.163699i	0.170410	−	0.00522918i
$981$		0			0
$982$	2.37383	−	2.37383i	0.0757519	−	0.0757519i
$983$	22.6513	+	22.6513i	0.722464	+	0.722464i	0.969107	−	0.246642i	$-0.0793273\pi$
$983$	22.6513	+	22.6513i	0.722464	+	0.722464i	−0.246642	+	0.969107i	$0.579327\pi$
$984$		0			0
$985$	−13.0789	−	12.3001i	−0.416728	−	0.391914i
$986$	−28.5448			−0.909052
$987$		0			0
$988$	22.3810	−	9.14747i	0.712034	−	0.291020i
$989$		−	35.7803i		−	1.13775i
$990$		0			0
$991$		−	33.5419i		−	1.06549i	−0.846275	−	0.532746i	$-0.821160\pi$
$991$		−	33.5419i		−	1.06549i	0.846275	−	0.532746i	$-0.178840\pi$
$992$	−2.85986	−	2.85986i	−0.0908007	−	0.0908007i
$993$		0			0
$994$			19.9624i			0.633168i
$995$	−0.267403	−	8.71420i	−0.00847725	−	0.276259i
$996$		0			0
$997$	−5.19281	−	5.19281i	−0.164458	−	0.164458i	0.620080	−	0.784538i	$-0.287100\pi$
$997$	−5.19281	−	5.19281i	−0.164458	−	0.164458i	−0.784538	+	0.620080i	$0.787100\pi$
$998$	−9.84644	−	9.84644i	−0.311684	−	0.311684i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.p.d.37.5		20
3.2	odd	2		570.2.m.a.37.6	yes	20
5.3	odd	4	inner	1710.2.p.d.1063.10		20
15.8	even	4		570.2.m.a.493.1	yes	20
19.18	odd	2	inner	1710.2.p.d.37.10		20
57.56	even	2		570.2.m.a.37.1	✓	20
95.18	even	4	inner	1710.2.p.d.1063.5		20
285.113	odd	4		570.2.m.a.493.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.m.a.37.1	✓	20	57.56	even	2
570.2.m.a.37.6	yes	20	3.2	odd	2
570.2.m.a.493.1	yes	20	15.8	even	4
570.2.m.a.493.6	yes	20	285.113	odd	4
1710.2.p.d.37.5		20	1.1	even	1	trivial
1710.2.p.d.37.10		20	19.18	odd	2	inner
1710.2.p.d.1063.5		20	95.18	even	4	inner
1710.2.p.d.1063.10		20	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.23502 - 0.0685835i) q^{5} +(-2.16643 - 2.16643i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.23502 - 0.0685835i) q^{5} +(-2.16643 - 2.16643i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.53190 + 1.62889i) q^{10} +5.68402 q^{11} +(-3.92222 - 3.92222i) q^{13} +3.06380 q^{14} -1.00000 q^{16} +(-4.99059 - 4.99059i) q^{17} +(-4.01921 - 1.68699i) q^{19} +(-0.0685835 - 2.23502i) q^{20} +(-4.01921 + 4.01921i) q^{22} +(-4.30360 + 4.30360i) q^{23} +(4.99059 - 0.306570i) q^{25} +5.54686 q^{26} +(-2.16643 + 2.16643i) q^{28} -4.04446 q^{29} -4.04446i q^{31} +(0.707107 - 0.707107i) q^{32} +7.05776 q^{34} +(-4.99059 - 4.69343i) q^{35} +(-6.19934 + 6.19934i) q^{37} +(4.03490 - 1.64913i) q^{38} +(1.62889 + 1.53190i) q^{40} +6.38884i q^{41} +(-4.15703 + 4.15703i) q^{43} -5.68402i q^{44} -6.08621i q^{46} +(-3.24326 - 3.24326i) q^{47} +2.38686i q^{49} +(-3.31210 + 3.74566i) q^{50} +(-3.92222 + 3.92222i) q^{52} +(5.40818 + 5.40818i) q^{53} +(12.7039 - 0.389830i) q^{55} -3.06380i q^{56} +(2.85986 - 2.85986i) q^{58} -2.39487 q^{59} -2.33286 q^{61} +(2.85986 + 2.85986i) q^{62} +1.00000i q^{64} +(-9.03522 - 8.49722i) q^{65} +(6.12760 - 6.12760i) q^{67} +(-4.99059 + 4.99059i) q^{68} +(6.84764 - 0.210126i) q^{70} +6.51556i q^{71} +(-2.07682 + 2.07682i) q^{73} -8.76719i q^{74} +(-1.68699 + 4.01921i) q^{76} +(-12.3141 - 12.3141i) q^{77} -4.23844 q^{79} +(-2.23502 + 0.0685835i) q^{80} +(-4.51759 - 4.51759i) q^{82} +(5.30657 - 5.30657i) q^{83} +(-11.4963 - 10.8118i) q^{85} -5.87892i q^{86} +(4.01921 + 4.01921i) q^{88} -2.50829 q^{89} +16.9944i q^{91} +(4.30360 + 4.30360i) q^{92} +4.58666 q^{94} +(-9.09870 - 3.49481i) q^{95} +(-6.22010 + 6.22010i) q^{97} +(-1.68776 - 1.68776i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{5} - 4 q^{7}+O(q^{10}) \) 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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