LMFDB - Embedded newform 2070.2.j.j.323.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,2,Mod(323,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("2070.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2070.j (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:	$16.5290332184$
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} - 20 x^{18} + 187 x^{16} - 1012 x^{14} + 3533 x^{12} - 7896 x^{10} + 10837 x^{8} - 5668 x^{6} + \cdots + 3721 $ x^20 - 20x^18 + 187x^16 - 1012x^14 + 3533x^12 - 7896x^10 + 10837x^8 - 5668x^6 - 4125x^4 + 8700*x^2 + 3721
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.5
Root			$1.31011 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2070.323
Dual form			2070.2.j.j.737.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(1.85363 + 1.25063i) q^{5} +(-3.08825 + 3.08825i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(1.85363 + 1.25063i) q^{5} +(-3.08825 + 3.08825i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.426386 - 2.19504i) q^{10} -1.10820i q^{11} +(-2.55227 - 2.55227i) q^{13} +4.36745 q^{14} -1.00000 q^{16} +(-1.10820 - 1.10820i) q^{17} -7.95731i q^{19} +(-1.25063 + 1.85363i) q^{20} +(-0.783617 + 0.783617i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(1.87187 + 4.63639i) q^{25} +3.60945i q^{26} +(-3.08825 - 3.08825i) q^{28} -6.30046 q^{29} +3.74374 q^{31} +(0.707107 + 0.707107i) q^{32} +1.56723i q^{34} +(-9.58672 + 1.86222i) q^{35} +(4.56245 - 4.56245i) q^{37} +(-5.62667 + 5.62667i) q^{38} +(2.19504 - 0.426386i) q^{40} +4.15924i q^{41} +(-3.87187 - 3.87187i) q^{43} +1.10820 q^{44} +1.00000 q^{46} +(-6.32747 - 6.32747i) q^{47} -12.0746i q^{49} +(1.95481 - 4.60203i) q^{50} +(2.55227 - 2.55227i) q^{52} +(3.25022 - 3.25022i) q^{53} +(1.38595 - 2.05419i) q^{55} +4.36745i q^{56} +(4.45510 + 4.45510i) q^{58} +12.9339 q^{59} +13.0995 q^{61} +(-2.64722 - 2.64722i) q^{62} -1.00000i q^{64} +(-1.53902 - 7.92289i) q^{65} +(0.0854412 - 0.0854412i) q^{67} +(1.10820 - 1.10820i) q^{68} +(8.09562 + 5.46205i) q^{70} -2.39084i q^{71} +(2.36995 + 2.36995i) q^{73} -6.45228 q^{74} +7.95731 q^{76} +(3.42241 + 3.42241i) q^{77} -13.4194i q^{79} +(-1.85363 - 1.25063i) q^{80} +(2.94103 - 2.94103i) q^{82} +(-4.53963 + 4.53963i) q^{83} +(-0.668247 - 3.44014i) q^{85} +5.47565i q^{86} +(-0.783617 - 0.783617i) q^{88} -1.98703 q^{89} +15.7641 q^{91} +(-0.707107 - 0.707107i) q^{92} +8.94840i q^{94} +(9.95162 - 14.7499i) q^{95} +(1.85409 - 1.85409i) q^{97} +(-8.53804 + 8.53804i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 16 q^{7}+O(q^{10}) $ 20 * q - 16 * q^7	$ 20 q - 16 q^{7} + 12 q^{10} - 12 q^{13} - 20 q^{16} - 24 q^{25} - 16 q^{28} - 48 q^{31} - 60 q^{37} - 16 q^{43} + 20 q^{46} + 12 q^{52} - 32 q^{55} + 4 q^{58} + 104 q^{61} - 56 q^{67} - 8 q^{70} - 20 q^{73} + 40 q^{76} - 28 q^{82} - 40 q^{85} - 32 q^{91} - 44 q^{97}+O(q^{100}) $ 20 * q - 16 * q^7 + 12 * q^10 - 12 * q^13 - 20 * q^16 - 24 * q^25 - 16 * q^28 - 48 * q^31 - 60 * q^37 - 16 * q^43 + 20 * q^46 + 12 * q^52 - 32 * q^55 + 4 * q^58 + 104 * q^61 - 56 * q^67 - 8 * q^70 - 20 * q^73 + 40 * q^76 - 28 * q^82 - 40 * q^85 - 32 * q^91 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times$.

$n$	$461$	$1657$	$1891$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	1.85363	+	1.25063i	0.828967	+	0.559297i
$5$	1.85363	+	1.25063i	0.828967	+	0.559297i
$6$		0			0
$7$	−3.08825	+	3.08825i	−1.16725	+	1.16725i	−0.184398	+	0.982852i	$0.559034\pi$
$7$	−3.08825	+	3.08825i	−1.16725	+	1.16725i	−0.982852	+	0.184398i	$0.940966\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−0.426386	−	2.19504i	−0.134835	−	0.694132i
$11$		−	1.10820i		−	0.334135i	−0.985945	−	0.167068i	$-0.946570\pi$
$11$		−	1.10820i		−	0.334135i	0.985945	−	0.167068i	$-0.0534298\pi$
$12$		0			0
$13$	−2.55227	−	2.55227i	−0.707872	−	0.707872i	0.258215	−	0.966087i	$-0.416866\pi$
$13$	−2.55227	−	2.55227i	−0.707872	−	0.707872i	−0.966087	+	0.258215i	$0.916866\pi$
$14$	4.36745			1.16725
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−1.10820	−	1.10820i	−0.268778	−	0.268778i	0.559830	−	0.828608i	$-0.310867\pi$
$17$	−1.10820	−	1.10820i	−0.268778	−	0.268778i	−0.828608	+	0.559830i	$0.810867\pi$
$18$		0			0
$19$		−	7.95731i		−	1.82553i	−0.408483	−	0.912766i	$-0.633942\pi$
$19$		−	7.95731i		−	1.82553i	0.408483	−	0.912766i	$-0.366058\pi$
$20$	−1.25063	+	1.85363i	−0.279648	+	0.414484i
$21$		0			0
$22$	−0.783617	+	0.783617i	−0.167068	+	0.167068i
$23$	−0.707107	+	0.707107i	−0.147442	+	0.147442i
$23$	−0.707107	+	0.707107i	−0.147442	+	0.147442i
$24$		0			0
$25$	1.87187	+	4.63639i	0.374374	+	0.927278i
$26$			3.60945i			0.707872i
$27$		0			0
$28$	−3.08825	−	3.08825i	−0.583625	−	0.583625i
$29$	−6.30046			−1.16997			−0.584983	−	0.811045i	$-0.698899\pi$
$29$	−6.30046			−1.16997			−0.584983	+	0.811045i	$0.698899\pi$
$30$		0			0
$31$	3.74374			0.672395			0.336198	−	0.941791i	$-0.390859\pi$
$31$	3.74374			0.672395			0.336198	+	0.941791i	$0.390859\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$			1.56723i			0.268778i
$35$	−9.58672	+	1.86222i	−1.62045	+	0.314773i
$36$		0			0
$37$	4.56245	−	4.56245i	0.750062	−	0.750062i	−0.224428	−	0.974491i	$-0.572051\pi$
$37$	4.56245	−	4.56245i	0.750062	−	0.750062i	0.974491	+	0.224428i	$0.0720515\pi$
$38$	−5.62667	+	5.62667i	−0.912766	+	0.912766i
$39$		0			0
$40$	2.19504	−	0.426386i	0.347066	−	0.0674176i
$41$			4.15924i			0.649564i	0.945789	+	0.324782i	$0.105291\pi$
$41$			4.15924i			0.649564i	−0.945789	+	0.324782i	$0.894709\pi$
$42$		0			0
$43$	−3.87187	−	3.87187i	−0.590455	−	0.590455i	0.347300	−	0.937754i	$-0.387099\pi$
$43$	−3.87187	−	3.87187i	−0.590455	−	0.590455i	−0.937754	+	0.347300i	$0.887099\pi$
$44$	1.10820			0.167068
$45$		0			0
$46$	1.00000			0.147442
$47$	−6.32747	−	6.32747i	−0.922957	−	0.922957i	0.0742808	−	0.997237i	$-0.476334\pi$
$47$	−6.32747	−	6.32747i	−0.922957	−	0.922957i	−0.997237	+	0.0742808i	$0.976334\pi$
$48$		0			0
$49$		−	12.0746i		−	1.72494i
$50$	1.95481	−	4.60203i	0.276452	−	0.650826i
$51$		0			0
$52$	2.55227	−	2.55227i	0.353936	−	0.353936i
$53$	3.25022	−	3.25022i	0.446453	−	0.446453i	−0.447721	−	0.894173i	$-0.647764\pi$
$53$	3.25022	−	3.25022i	0.446453	−	0.446453i	0.894173	+	0.447721i	$0.147764\pi$
$54$		0			0
$55$	1.38595	−	2.05419i	0.186881	−	0.276987i
$56$			4.36745i			0.583625i
$57$		0			0
$58$	4.45510	+	4.45510i	0.584983	+	0.584983i
$59$	12.9339			1.68386			0.841928	−	0.539589i	$-0.181420\pi$
$59$	12.9339			1.68386			0.841928	+	0.539589i	$0.181420\pi$
$60$		0			0
$61$	13.0995			1.67722			0.838608	−	0.544736i	$-0.183370\pi$
$61$	13.0995			1.67722			0.838608	+	0.544736i	$0.183370\pi$
$62$	−2.64722	−	2.64722i	−0.336198	−	0.336198i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−1.53902	−	7.92289i	−0.190892	−	0.982713i
$66$		0			0
$67$	0.0854412	−	0.0854412i	0.0104383	−	0.0104383i	−0.701868	−	0.712307i	$-0.747651\pi$
$67$	0.0854412	−	0.0854412i	0.0104383	−	0.0104383i	0.712307	+	0.701868i	$0.247651\pi$
$68$	1.10820	−	1.10820i	0.134389	−	0.134389i
$69$		0			0
$70$	8.09562	+	5.46205i	0.967612	+	0.652839i
$71$		−	2.39084i		−	0.283741i	−0.989885	−	0.141870i	$-0.954688\pi$
$71$		−	2.39084i		−	0.283741i	0.989885	−	0.141870i	$-0.0453116\pi$
$72$		0			0
$73$	2.36995	+	2.36995i	0.277381	+	0.277381i	0.832063	−	0.554682i	$-0.187160\pi$
$73$	2.36995	+	2.36995i	0.277381	+	0.277381i	−0.554682	+	0.832063i	$0.687160\pi$
$74$	−6.45228			−0.750062
$75$		0			0
$76$	7.95731			0.912766
$77$	3.42241	+	3.42241i	0.390019	+	0.390019i
$78$		0			0
$79$		−	13.4194i		−	1.50980i	−0.655843	−	0.754898i	$-0.727686\pi$
$79$		−	13.4194i		−	1.50980i	0.655843	−	0.754898i	$-0.272314\pi$
$80$	−1.85363	−	1.25063i	−0.207242	−	0.139824i
$81$		0			0
$82$	2.94103	−	2.94103i	0.324782	−	0.324782i
$83$	−4.53963	+	4.53963i	−0.498289	+	0.498289i	−0.910905	−	0.412616i	$-0.864615\pi$
$83$	−4.53963	+	4.53963i	−0.498289	+	0.498289i	0.412616	+	0.910905i	$0.364615\pi$
$84$		0			0
$85$	−0.668247	−	3.44014i	−0.0724815	−	0.373135i
$86$			5.47565i			0.590455i
$87$		0			0
$88$	−0.783617	−	0.783617i	−0.0835338	−	0.0835338i
$89$	−1.98703			−0.210625			−0.105312	−	0.994439i	$-0.533584\pi$
$89$	−1.98703			−0.210625			−0.105312	+	0.994439i	$0.533584\pi$
$90$		0			0
$91$	15.7641			1.65253
$92$	−0.707107	−	0.707107i	−0.0737210	−	0.0737210i
$93$		0			0
$94$			8.94840i			0.922957i
$95$	9.95162	−	14.7499i	1.02101	−	1.51331i
$96$		0			0
$97$	1.85409	−	1.85409i	0.188255	−	0.188255i	−0.606687	−	0.794941i	$-0.707502\pi$
$97$	1.85409	−	1.85409i	0.188255	−	0.188255i	0.794941	+	0.606687i	$0.207502\pi$
$98$	−8.53804	+	8.53804i	−0.862472	+	0.862472i
$99$		0			0
$100$	−4.63639	+	1.87187i	−0.463639	+	0.187187i
$101$			4.75010i			0.472653i	0.971674	+	0.236326i	$0.0759434\pi$
$101$			4.75010i			0.472653i	−0.971674	+	0.236326i	$0.924057\pi$
$102$		0			0
$103$	−7.86841	−	7.86841i	−0.775297	−	0.775297i	0.203730	−	0.979027i	$-0.434694\pi$
$103$	−7.86841	−	7.86841i	−0.775297	−	0.775297i	−0.979027	+	0.203730i	$0.934694\pi$
$104$	−3.60945			−0.353936
$105$		0			0
$106$	−4.59651			−0.446453
$107$	5.84343	+	5.84343i	0.564906	+	0.564906i	0.930697	−	0.365791i	$-0.119201\pi$
$107$	5.84343	+	5.84343i	0.564906	+	0.564906i	−0.365791	+	0.930697i	$0.619201\pi$
$108$		0			0
$109$		−	16.5666i		−	1.58679i	−0.608707	−	0.793395i	$-0.708311\pi$
$109$		−	16.5666i		−	1.58679i	0.608707	−	0.793395i	$-0.291689\pi$
$110$	−2.43254	+	0.472522i	−0.231934	+	0.0450532i
$111$		0			0
$112$	3.08825	−	3.08825i	0.291812	−	0.291812i
$113$	1.82387	−	1.82387i	0.171575	−	0.171575i	−0.616096	−	0.787671i	$-0.711287\pi$
$113$	1.82387	−	1.82387i	0.171575	−	0.171575i	0.787671	+	0.616096i	$0.211287\pi$
$114$		0			0
$115$	−2.19504	+	0.426386i	−0.204688	+	0.0397607i
$116$		−	6.30046i		−	0.584983i
$117$		0			0
$118$	−9.14568	−	9.14568i	−0.841928	−	0.841928i
$119$	6.84481			0.627463
$120$		0			0
$121$	9.77189			0.888354
$122$	−9.26272	−	9.26272i	−0.838608	−	0.838608i
$123$		0			0
$124$			3.74374i			0.336198i
$125$	−2.32864	+	10.9351i	−0.208280	+	0.978069i
$126$		0			0
$127$	−4.15328	+	4.15328i	−0.368544	+	0.368544i	−0.866946	−	0.498402i	$-0.833920\pi$
$127$	−4.15328	+	4.15328i	−0.368544	+	0.368544i	0.498402	+	0.866946i	$0.333920\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	−4.51408	+	6.69058i	−0.395911	+	0.586803i
$131$			0.125728i			0.0109849i	0.999985	+	0.00549245i	$0.00174831\pi$
$131$			0.125728i			0.0109849i	−0.999985	+	0.00549245i	$0.998252\pi$
$132$		0			0
$133$	24.5742	+	24.5742i	2.13085	+	2.13085i
$134$	−0.120832			−0.0104383
$135$		0			0
$136$	−1.56723			−0.134389
$137$	10.2258	+	10.2258i	0.873645	+	0.873645i	0.992868	−	0.119223i	$-0.0380403\pi$
$137$	10.2258	+	10.2258i	0.873645	+	0.873645i	−0.119223	+	0.992868i	$0.538040\pi$
$138$		0			0
$139$		−	14.8803i		−	1.26213i	−0.775731	−	0.631064i	$-0.782618\pi$
$139$		−	14.8803i		−	1.26213i	0.775731	−	0.631064i	$-0.217382\pi$
$140$	−1.86222	−	9.58672i	−0.157386	−	0.810226i
$141$		0			0
$142$	−1.69058	+	1.69058i	−0.141870	+	0.141870i
$143$	−2.82843	+	2.82843i	−0.236525	+	0.236525i
$144$		0			0
$145$	−11.6787	−	7.87953i	−0.969864	−	0.654359i
$146$		−	3.35161i		−	0.277381i
$147$		0			0
$148$	4.56245	+	4.56245i	0.375031	+	0.375031i
$149$	−2.44724			−0.200486			−0.100243	−	0.994963i	$-0.531962\pi$
$149$	−2.44724			−0.200486			−0.100243	+	0.994963i	$0.531962\pi$
$150$		0			0
$151$	−22.0052			−1.79076			−0.895378	−	0.445307i	$-0.853094\pi$
$151$	−22.0052			−1.79076			−0.895378	+	0.445307i	$0.853094\pi$
$152$	−5.62667	−	5.62667i	−0.456383	−	0.456383i
$153$		0			0
$154$		−	4.84001i		−	0.390019i
$155$	6.93950	+	4.68202i	0.557394	+	0.376069i
$156$		0			0
$157$	−1.65225	+	1.65225i	−0.131864	+	0.131864i	−0.769958	−	0.638094i	$-0.779723\pi$
$157$	−1.65225	+	1.65225i	−0.131864	+	0.131864i	0.638094	+	0.769958i	$0.279723\pi$
$158$	−9.48892	+	9.48892i	−0.754898	+	0.754898i
$159$		0			0
$160$	0.426386	+	2.19504i	0.0337088	+	0.173533i
$161$		−	4.36745i		−	0.344203i
$162$		0			0
$163$	−3.60543	−	3.60543i	−0.282399	−	0.282399i	0.551666	−	0.834065i	$-0.313992\pi$
$163$	−3.60543	−	3.60543i	−0.282399	−	0.282399i	−0.834065	+	0.551666i	$0.813992\pi$
$164$	−4.15924			−0.324782
$165$		0			0
$166$	6.42001			0.498289
$167$	−17.0620	−	17.0620i	−1.32030	−	1.32030i	−0.913533	−	0.406765i	$-0.866657\pi$
$167$	−17.0620	−	17.0620i	−1.32030	−	1.32030i	−0.406765	−	0.913533i	$-0.633343\pi$
$168$		0			0
$169$			0.0281519i			0.00216553i
$170$	−1.96002	+	2.90507i	−0.150327	+	0.222808i
$171$		0			0
$172$	3.87187	−	3.87187i	0.295227	−	0.295227i
$173$	−12.9466	+	12.9466i	−0.984308	+	0.984308i	−0.999879	−	0.0155704i	$-0.995044\pi$
$173$	−12.9466	+	12.9466i	−0.984308	+	0.984308i	0.0155704	+	0.999879i	$0.495044\pi$
$174$		0			0
$175$	−20.0991	−	8.53754i	−1.51935	−	0.645377i
$176$			1.10820i			0.0835338i
$177$		0			0
$178$	1.40504	+	1.40504i	0.105312	+	0.105312i
$179$	9.01390			0.673731			0.336865	−	0.941553i	$-0.390633\pi$
$179$	9.01390			0.673731			0.336865	+	0.941553i	$0.390633\pi$
$180$		0			0
$181$	2.72272			0.202379			0.101189	−	0.994867i	$-0.467735\pi$
$181$	2.72272			0.202379			0.101189	+	0.994867i	$0.467735\pi$
$182$	−11.1469	−	11.1469i	−0.826263	−	0.826263i
$183$		0			0
$184$			1.00000i			0.0737210i
$185$	14.1630	−	2.75116i	1.04128	−	0.202270i
$186$		0			0
$187$	−1.22811	+	1.22811i	−0.0898083	+	0.0898083i
$188$	6.32747	−	6.32747i	0.461478	−	0.461478i
$189$		0			0
$190$	−17.4666	+	3.39289i	−1.26716	+	0.246146i
$191$		−	21.7099i		−	1.57087i	−0.618941	−	0.785437i	$-0.712438\pi$
$191$		−	21.7099i		−	1.57087i	0.618941	−	0.785437i	$-0.287562\pi$
$192$		0			0
$193$	10.5672	+	10.5672i	0.760646	+	0.760646i	0.976439	−	0.215793i	$-0.0692337\pi$
$193$	10.5672	+	10.5672i	0.760646	+	0.760646i	−0.215793	+	0.976439i	$0.569234\pi$
$194$	−2.62208			−0.188255
$195$		0			0
$196$	12.0746			0.862472
$197$	2.44764	+	2.44764i	0.174387	+	0.174387i	0.788904	−	0.614517i	$-0.210649\pi$
$197$	2.44764	+	2.44764i	0.174387	+	0.174387i	−0.614517	+	0.788904i	$0.710649\pi$
$198$		0			0
$199$			5.89032i			0.417553i	0.977963	+	0.208777i	$0.0669482\pi$
$199$			5.89032i			0.417553i	−0.977963	+	0.208777i	$0.933052\pi$
$200$	4.60203	+	1.95481i	0.325413	+	0.138226i
$201$		0			0
$202$	3.35883	−	3.35883i	0.236326	−	0.236326i
$203$	19.4574	−	19.4574i	1.36564	−	1.36564i
$204$		0			0
$205$	−5.20165	+	7.70968i	−0.363299	+	0.538467i
$206$			11.1276i			0.775297i
$207$		0			0
$208$	2.55227	+	2.55227i	0.176968	+	0.176968i
$209$	−8.81830			−0.609975
$210$		0			0
$211$	−20.5443			−1.41432			−0.707162	−	0.707051i	$-0.750025\pi$
$211$	−20.5443			−1.41432			−0.707162	+	0.707051i	$0.750025\pi$
$212$	3.25022	+	3.25022i	0.223226	+	0.223226i
$213$		0			0
$214$		−	8.26386i		−	0.564906i
$215$	−2.33474	−	12.0193i	−0.159228	−	0.819707i
$216$		0			0
$217$	−11.5616	+	11.5616i	−0.784853	+	0.784853i
$218$	−11.7143	+	11.7143i	−0.793395	+	0.793395i
$219$		0			0
$220$	2.05419	+	1.38595i	0.138494	+	0.0934404i
$221$			5.65685i			0.380521i
$222$		0			0
$223$	−16.0089	−	16.0089i	−1.07204	−	1.07204i	−0.997195	−	0.0748413i	$-0.976155\pi$
$223$	−16.0089	−	16.0089i	−1.07204	−	1.07204i	−0.0748413	−	0.997195i	$-0.523845\pi$
$224$	−4.36745			−0.291812
$225$		0			0
$226$	−2.57934			−0.171575
$227$	5.02446	+	5.02446i	0.333485	+	0.333485i	0.853908	−	0.520423i	$-0.174226\pi$
$227$	5.02446	+	5.02446i	0.333485	+	0.333485i	−0.520423	+	0.853908i	$0.674226\pi$
$228$		0			0
$229$		−	11.7509i		−	0.776520i	−0.921550	−	0.388260i	$-0.873076\pi$
$229$		−	11.7509i		−	0.776520i	0.921550	−	0.388260i	$-0.126924\pi$
$230$	1.85363	+	1.25063i	0.122225	+	0.0824638i
$231$		0			0
$232$	−4.45510	+	4.45510i	−0.292492	+	0.292492i
$233$	16.0418	−	16.0418i	1.05093	−	1.05093i	0.0523010	−	0.998631i	$-0.483344\pi$
$233$	16.0418	−	16.0418i	1.05093	−	1.05093i	0.998631	−	0.0523010i	$-0.0166555\pi$
$234$		0			0
$235$	−3.81547	−	19.6421i	−0.248894	−	1.28131i
$236$			12.9339i			0.841928i
$237$		0			0
$238$	−4.84001	−	4.84001i	−0.313731	−	0.313731i
$239$	−15.8376			−1.02445			−0.512223	−	0.858852i	$-0.671178\pi$
$239$	−15.8376			−1.02445			−0.512223	+	0.858852i	$0.671178\pi$
$240$		0			0
$241$	−1.54557			−0.0995588			−0.0497794	−	0.998760i	$-0.515852\pi$
$241$	−1.54557			−0.0995588			−0.0497794	+	0.998760i	$0.515852\pi$
$242$	−6.90977	−	6.90977i	−0.444177	−	0.444177i
$243$		0			0
$244$			13.0995i			0.838608i
$245$	15.1008	−	22.3818i	0.964756	−	1.42992i
$246$		0			0
$247$	−20.3092	+	20.3092i	−1.29224	+	1.29224i
$248$	2.64722	−	2.64722i	0.168099	−	0.168099i
$249$		0			0
$250$	9.37891	−	6.08572i	0.593175	−	0.384895i
$251$			2.42064i			0.152789i	0.997078	+	0.0763946i	$0.0243409\pi$
$251$			2.42064i			0.152789i	−0.997078	+	0.0763946i	$0.975659\pi$
$252$		0			0
$253$	0.783617	+	0.783617i	0.0492655	+	0.0492655i
$254$	5.87362			0.368544
$255$		0			0
$256$	1.00000			0.0625000
$257$	−18.5298	−	18.5298i	−1.15586	−	1.15586i	−0.985357	−	0.170501i	$-0.945461\pi$
$257$	−18.5298	−	18.5298i	−1.15586	−	1.15586i	−0.170501	−	0.985357i	$-0.554539\pi$
$258$		0			0
$259$			28.1800i			1.75102i
$260$	7.92289	−	1.53902i	0.491357	−	0.0954461i
$261$		0			0
$262$	0.0889031	−	0.0889031i	0.00549245	−	0.00549245i
$263$	−14.2120	+	14.2120i	−0.876350	+	0.876350i	−0.993155	−	0.116805i	$-0.962735\pi$
$263$	−14.2120	+	14.2120i	−0.876350	+	0.876350i	0.116805	+	0.993155i	$0.462735\pi$
$264$		0			0
$265$	10.0895	−	1.95989i	0.619794	−	0.120395i
$266$		−	34.7531i		−	2.13085i
$267$		0			0
$268$	0.0854412	+	0.0854412i	0.00521915	+	0.00521915i
$269$	−25.2330			−1.53849			−0.769243	−	0.638956i	$-0.779366\pi$
$269$	−25.2330			−1.53849			−0.769243	+	0.638956i	$0.779366\pi$
$270$		0			0
$271$	16.2766			0.988735			0.494367	−	0.869253i	$-0.335400\pi$
$271$	16.2766			0.988735			0.494367	+	0.869253i	$0.335400\pi$
$272$	1.10820	+	1.10820i	0.0671946	+	0.0671946i
$273$		0			0
$274$		−	14.4614i		−	0.873645i
$275$	5.13805	−	2.07441i	0.309836	−	0.125091i
$276$		0			0
$277$	−12.8997	+	12.8997i	−0.775065	+	0.775065i	−0.978987	−	0.203922i	$-0.934631\pi$
$277$	−12.8997	+	12.8997i	−0.775065	+	0.775065i	0.203922	+	0.978987i	$0.434631\pi$
$278$	−10.5219	+	10.5219i	−0.631064	+	0.631064i
$279$		0			0
$280$	−5.46205	+	8.09562i	−0.326420	+	0.483806i
$281$			0.578255i			0.0344958i	0.999851	+	0.0172479i	$0.00549045\pi$
$281$			0.578255i			0.0344958i	−0.999851	+	0.0172479i	$0.994510\pi$
$282$		0			0
$283$	−11.6049	−	11.6049i	−0.689841	−	0.689841i	0.272356	−	0.962197i	$-0.412197\pi$
$283$	−11.6049	−	11.6049i	−0.689841	−	0.689841i	−0.962197	+	0.272356i	$0.912197\pi$
$284$	2.39084			0.141870
$285$		0			0
$286$	4.00000			0.236525
$287$	−12.8448	−	12.8448i	−0.758203	−	0.758203i
$288$		0			0
$289$		−	14.5438i		−	0.855517i
$290$	2.68643	+	13.8298i	0.157753	+	0.812112i
$291$		0			0
$292$	−2.36995	+	2.36995i	−0.138691	+	0.138691i
$293$	−4.23175	+	4.23175i	−0.247221	+	0.247221i	−0.819829	−	0.572608i	$-0.805932\pi$
$293$	−4.23175	+	4.23175i	−0.247221	+	0.247221i	0.572608	+	0.819829i	$0.305932\pi$
$294$		0			0
$295$	23.9747	+	16.1755i	1.39586	+	0.941776i
$296$		−	6.45228i		−	0.375031i
$297$		0			0
$298$	1.73046	+	1.73046i	0.100243	+	0.100243i
$299$	3.60945			0.208740
$300$		0			0
$301$	23.9146			1.37842
$302$	15.5600	+	15.5600i	0.895378	+	0.895378i
$303$		0			0
$304$			7.95731i			0.456383i
$305$	24.2815	+	16.3825i	1.39036	+	0.938061i
$306$		0			0
$307$	9.67562	−	9.67562i	0.552217	−	0.552217i	−0.374863	−	0.927080i	$-0.622310\pi$
$307$	9.67562	−	9.67562i	0.552217	−	0.552217i	0.927080	+	0.374863i	$0.122310\pi$
$308$	−3.42241	+	3.42241i	−0.195010	+	0.195010i
$309$		0			0
$310$	−1.59628	−	8.21765i	−0.0906626	−	0.466731i
$311$		−	15.6457i		−	0.887185i	−0.896229	−	0.443593i	$-0.853704\pi$
$311$		−	15.6457i		−	0.887185i	0.896229	−	0.443593i	$-0.146296\pi$
$312$		0			0
$313$	−1.21225	−	1.21225i	−0.0685205	−	0.0685205i	0.672016	−	0.740537i	$-0.265429\pi$
$313$	−1.21225	−	1.21225i	−0.0685205	−	0.0685205i	−0.740537	+	0.672016i	$0.765429\pi$
$314$	2.33663			0.131864
$315$		0			0
$316$	13.4194			0.754898
$317$	14.1728	+	14.1728i	0.796024	+	0.796024i	0.982466	−	0.186442i	$-0.0596957\pi$
$317$	14.1728	+	14.1728i	0.796024	+	0.796024i	−0.186442	+	0.982466i	$0.559696\pi$
$318$		0			0
$319$			6.98218i			0.390927i
$320$	1.25063	−	1.85363i	0.0699121	−	0.103621i
$321$		0			0
$322$	−3.08825	+	3.08825i	−0.172102	+	0.172102i
$323$	−8.81830	+	8.81830i	−0.490663	+	0.490663i
$324$		0			0
$325$	7.05580	−	16.6108i	0.391385	−	0.921403i
$326$			5.09884i			0.282399i
$327$		0			0
$328$	2.94103	+	2.94103i	0.162391	+	0.162391i
$329$	39.0817			2.15464
$330$		0			0
$331$	19.7203			1.08392			0.541962	−	0.840403i	$-0.317681\pi$
$331$	19.7203			1.08392			0.541962	+	0.840403i	$0.317681\pi$
$332$	−4.53963	−	4.53963i	−0.249145	−	0.249145i
$333$		0			0
$334$			24.1293i			1.32030i
$335$	0.265231	−	0.0515211i	0.0144911	−	0.00281490i
$336$		0			0
$337$	−10.7496	+	10.7496i	−0.585566	+	0.585566i	−0.936427	−	0.350862i	$-0.885889\pi$
$337$	−10.7496	+	10.7496i	−0.585566	+	0.585566i	0.350862	+	0.936427i	$0.385889\pi$
$338$	0.0199064	−	0.0199064i	0.00108277	−	0.00108277i
$339$		0			0
$340$	3.44014	−	0.668247i	0.186568	−	0.0362408i
$341$		−	4.14882i		−	0.224671i
$342$		0			0
$343$	15.6717	+	15.6717i	0.846191	+	0.846191i
$344$	−5.47565			−0.295227
$345$		0			0
$346$	18.3092			0.984308
$347$	−2.65585	−	2.65585i	−0.142574	−	0.142574i	0.632217	−	0.774791i	$-0.282145\pi$
$347$	−2.65585	−	2.65585i	−0.142574	−	0.142574i	−0.774791	+	0.632217i	$0.782145\pi$
$348$		0			0
$349$		−	7.28234i		−	0.389815i	−0.980822	−	0.194907i	$-0.937559\pi$
$349$		−	7.28234i		−	0.389815i	0.980822	−	0.194907i	$-0.0624407\pi$
$350$	8.17529	+	20.2492i	0.436988	+	1.08236i
$351$		0			0
$352$	0.783617	−	0.783617i	0.0417669	−	0.0417669i
$353$	14.4162	−	14.4162i	0.767299	−	0.767299i	−0.210331	−	0.977630i	$-0.567454\pi$
$353$	14.4162	−	14.4162i	0.767299	−	0.767299i	0.977630	+	0.210331i	$0.0674541\pi$
$354$		0			0
$355$	2.99005	−	4.43173i	0.158695	−	0.235212i
$356$		−	1.98703i		−	0.105312i
$357$		0			0
$358$	−6.37379	−	6.37379i	−0.336865	−	0.336865i
$359$	−27.4379			−1.44812			−0.724059	−	0.689739i	$-0.757725\pi$
$359$	−27.4379			−1.44812			−0.724059	+	0.689739i	$0.757725\pi$
$360$		0			0
$361$	−44.3188			−2.33257
$362$	−1.92526	−	1.92526i	−0.101189	−	0.101189i
$363$		0			0
$364$			15.7641i			0.826263i
$365$	1.42908	+	7.35691i	0.0748015	+	0.385078i
$366$		0			0
$367$	−4.15460	+	4.15460i	−0.216868	+	0.216868i	−0.807177	−	0.590309i	$-0.799006\pi$
$367$	−4.15460	+	4.15460i	−0.216868	+	0.216868i	0.590309	+	0.807177i	$0.299006\pi$
$368$	0.707107	−	0.707107i	0.0368605	−	0.0368605i
$369$		0			0
$370$	−11.9601	−	8.06939i	−0.621777	−	0.419508i
$371$			20.0750i			1.04224i
$372$		0			0
$373$	−7.45229	−	7.45229i	−0.385865	−	0.385865i	0.487345	−	0.873210i	$-0.337966\pi$
$373$	−7.45229	−	7.45229i	−0.385865	−	0.385865i	−0.873210	+	0.487345i	$0.837966\pi$
$374$	1.73681			0.0898083
$375$		0			0
$376$	−8.94840			−0.461478
$377$	16.0805	+	16.0805i	0.828187	+	0.828187i
$378$		0			0
$379$			38.7341i			1.98964i	0.101668	+	0.994818i	$0.467582\pi$
$379$			38.7341i			1.98964i	−0.101668	+	0.994818i	$0.532418\pi$
$380$	14.7499	+	9.95162i	0.756653	+	0.510507i
$381$		0			0
$382$	−15.3512	+	15.3512i	−0.785437	+	0.785437i
$383$	−20.6426	+	20.6426i	−1.05479	+	1.05479i	−0.0563772	+	0.998410i	$0.517955\pi$
$383$	−20.6426	+	20.6426i	−1.05479	+	1.05479i	−0.998410	+	0.0563772i	$0.982045\pi$
$384$		0			0
$385$	2.06372	+	10.6240i	0.105177	+	0.541450i
$386$		−	14.9443i		−	0.760646i
$387$		0			0
$388$	1.85409	+	1.85409i	0.0941273	+	0.0941273i
$389$	18.0487			0.915107			0.457553	−	0.889182i	$-0.348726\pi$
$389$	18.0487			0.915107			0.457553	+	0.889182i	$0.348726\pi$
$390$		0			0
$391$	1.56723			0.0792584
$392$	−8.53804	−	8.53804i	−0.431236	−	0.431236i
$393$		0			0
$394$		−	3.46149i		−	0.174387i
$395$	16.7826	−	24.8745i	0.844424	−	1.25157i
$396$		0			0
$397$	17.5389	−	17.5389i	0.880250	−	0.880250i	−0.113310	−	0.993560i	$-0.536145\pi$
$397$	17.5389	−	17.5389i	0.880250	−	0.880250i	0.993560	+	0.113310i	$0.0361452\pi$
$398$	4.16508	−	4.16508i	0.208777	−	0.208777i
$399$		0			0
$400$	−1.87187	−	4.63639i	−0.0935935	−	0.231819i
$401$			36.2950i			1.81248i	0.422760	+	0.906242i	$0.361061\pi$
$401$			36.2950i			1.81248i	−0.422760	+	0.906242i	$0.638939\pi$
$402$		0			0
$403$	−9.55503	−	9.55503i	−0.475970	−	0.475970i
$404$	−4.75010			−0.236326
$405$		0			0
$406$	−27.5170			−1.36564
$407$	−5.05611	−	5.05611i	−0.250622	−	0.250622i
$408$		0			0
$409$		−	35.7342i		−	1.76694i	−0.468487	−	0.883471i	$-0.655201\pi$
$409$		−	35.7342i		−	1.76694i	0.468487	−	0.883471i	$-0.344799\pi$
$410$	9.12969	−	1.77344i	0.450883	−	0.0875841i
$411$		0			0
$412$	7.86841	−	7.86841i	0.387649	−	0.387649i
$413$	−39.9433	+	39.9433i	−1.96548	+	1.96548i
$414$		0			0
$415$	−14.0922	+	2.73740i	−0.691757	+	0.134374i
$416$		−	3.60945i		−	0.176968i
$417$		0			0
$418$	6.23548	+	6.23548i	0.304987	+	0.304987i
$419$	22.7578			1.11179			0.555894	−	0.831253i	$-0.312376\pi$
$419$	22.7578			1.11179			0.555894	+	0.831253i	$0.312376\pi$
$420$		0			0
$421$	0.261330			0.0127364			0.00636822	−	0.999980i	$-0.497973\pi$
$421$	0.261330			0.0127364			0.00636822	+	0.999980i	$0.497973\pi$
$422$	14.5270	+	14.5270i	0.707162	+	0.707162i
$423$		0			0
$424$		−	4.59651i		−	0.223226i
$425$	3.06364	−	7.21246i	0.148609	−	0.349856i
$426$		0			0
$427$	−40.4545	+	40.4545i	−1.95773	+	1.95773i
$428$	−5.84343	+	5.84343i	−0.282453	+	0.282453i
$429$		0			0
$430$	−6.84799	+	10.1498i	−0.330239	+	0.489468i
$431$			14.2837i			0.688023i	0.938965	+	0.344011i	$0.111786\pi$
$431$			14.2837i			0.688023i	−0.938965	+	0.344011i	$0.888214\pi$
$432$		0			0
$433$	1.70752	+	1.70752i	0.0820580	+	0.0820580i	0.746944	−	0.664886i	$-0.231520\pi$
$433$	1.70752	+	1.70752i	0.0820580	+	0.0820580i	−0.664886	+	0.746944i	$0.731520\pi$
$434$	16.3506			0.784853
$435$		0			0
$436$	16.5666			0.793395
$437$	5.62667	+	5.62667i	0.269160	+	0.269160i
$438$		0			0
$439$			32.5652i			1.55425i	0.629345	+	0.777126i	$0.283323\pi$
$439$			32.5652i			1.55425i	−0.629345	+	0.777126i	$0.716677\pi$
$440$	−0.472522	−	2.43254i	−0.0225266	−	0.115967i
$441$		0			0
$442$	4.00000	−	4.00000i	0.190261	−	0.190261i
$443$	−2.27042	+	2.27042i	−0.107871	+	0.107871i	−0.758982	−	0.651111i	$-0.774303\pi$
$443$	−2.27042	+	2.27042i	−0.107871	+	0.107871i	0.651111	+	0.758982i	$0.274303\pi$
$444$		0			0
$445$	−3.68321	−	2.48503i	−0.174601	−	0.117802i
$446$			22.6400i			1.07204i
$447$		0			0
$448$	3.08825	+	3.08825i	0.145906	+	0.145906i
$449$	29.5592			1.39499			0.697493	−	0.716591i	$-0.254299\pi$
$449$	29.5592			1.39499			0.697493	+	0.716591i	$0.254299\pi$
$450$		0			0
$451$	4.60927			0.217042
$452$	1.82387	+	1.82387i	0.0857877	+	0.0857877i
$453$		0			0
$454$		−	7.10566i		−	0.333485i
$455$	29.2208	+	19.7150i	1.36989	+	0.924253i
$456$		0			0
$457$	−24.6819	+	24.6819i	−1.15457	+	1.15457i	−0.168945	+	0.985625i	$0.554036\pi$
$457$	−24.6819	+	24.6819i	−1.15457	+	1.15457i	−0.985625	+	0.168945i	$0.945964\pi$
$458$	−8.30912	+	8.30912i	−0.388260	+	0.388260i
$459$		0			0
$460$	−0.426386	−	2.19504i	−0.0198804	−	0.102344i
$461$		−	29.3487i		−	1.36691i	−0.729995	−	0.683453i	$-0.760478\pi$
$461$		−	29.3487i		−	1.36691i	0.729995	−	0.683453i	$-0.239522\pi$
$462$		0			0
$463$	10.4243	+	10.4243i	0.484457	+	0.484457i	0.906552	−	0.422095i	$-0.138705\pi$
$463$	10.4243	+	10.4243i	0.484457	+	0.484457i	−0.422095	+	0.906552i	$0.638705\pi$
$464$	6.30046			0.292492
$465$		0			0
$466$	−22.6865			−1.05093
$467$	−12.1339	−	12.1339i	−0.561489	−	0.561489i	0.368241	−	0.929730i	$-0.379960\pi$
$467$	−12.1339	−	12.1339i	−0.561489	−	0.561489i	−0.929730	+	0.368241i	$0.879960\pi$
$468$		0			0
$469$			0.527728i			0.0243682i
$470$	−11.1911	+	16.5870i	−0.516207	+	0.765101i
$471$		0			0
$472$	9.14568	−	9.14568i	0.420964	−	0.420964i
$473$	−4.29081	+	4.29081i	−0.197292	+	0.197292i
$474$		0			0
$475$	36.8932	−	14.8950i	1.69278	−	0.683431i
$476$			6.84481i			0.313731i
$477$		0			0
$478$	11.1988	+	11.1988i	0.512223	+	0.512223i
$479$	32.2536			1.47370			0.736851	−	0.676055i	$-0.236312\pi$
$479$	32.2536			1.47370			0.736851	+	0.676055i	$0.236312\pi$
$480$		0			0
$481$	−23.2892			−1.06190
$482$	1.09288	+	1.09288i	0.0497794	+	0.0497794i
$483$		0			0
$484$			9.77189i			0.444177i
$485$	5.75558	−	1.11802i	0.261347	−	0.0507667i
$486$		0			0
$487$	9.93521	−	9.93521i	0.450207	−	0.450207i	−0.445216	−	0.895423i	$-0.646873\pi$
$487$	9.93521	−	9.93521i	0.450207	−	0.450207i	0.895423	+	0.445216i	$0.146873\pi$
$488$	9.26272	−	9.26272i	0.419304	−	0.419304i
$489$		0			0
$490$	−26.5042	+	5.14845i	−1.19734	+	0.232583i
$491$		−	12.6998i		−	0.573132i	−0.958061	−	0.286566i	$-0.907486\pi$
$491$		−	12.6998i		−	0.573132i	0.958061	−	0.286566i	$-0.0925138\pi$
$492$		0			0
$493$	6.98218	+	6.98218i	0.314462	+	0.314462i
$494$	28.7215			1.29224
$495$		0			0
$496$	−3.74374			−0.168099
$497$	7.38353	+	7.38353i	0.331196	+	0.331196i
$498$		0			0
$499$		−	37.9477i		−	1.69877i	−0.527773	−	0.849385i	$-0.676973\pi$
$499$		−	37.9477i		−	1.69877i	0.527773	−	0.849385i	$-0.323027\pi$
$500$	−10.9351	−	2.32864i	−0.489035	−	0.104140i
$501$		0			0
$502$	1.71165	−	1.71165i	0.0763946	−	0.0763946i
$503$	−12.3759	+	12.3759i	−0.551816	+	0.551816i	−0.926965	−	0.375149i	$-0.877592\pi$
$503$	−12.3759	+	12.3759i	−0.551816	+	0.551816i	0.375149	+	0.926965i	$0.377592\pi$
$504$		0			0
$505$	−5.94060	+	8.80492i	−0.264353	+	0.391814i
$506$		−	1.10820i		−	0.0492655i
$507$		0			0
$508$	−4.15328	−	4.15328i	−0.184272	−	0.184272i
$509$	−25.9750			−1.15132			−0.575660	−	0.817689i	$-0.695255\pi$
$509$	−25.9750			−1.15132			−0.575660	+	0.817689i	$0.695255\pi$
$510$		0			0
$511$	−14.6380			−0.647546
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$			26.2051i			1.15586i
$515$	−4.74466	−	24.4255i	−0.209075	−	1.07632i
$516$		0			0
$517$	−7.01211	+	7.01211i	−0.308392	+	0.308392i
$518$	19.9263	−	19.9263i	0.875510	−	0.875510i
$519$		0			0
$520$	−6.69058	−	4.51408i	−0.293401	−	0.197955i
$521$			34.6906i			1.51982i	0.650027	+	0.759911i	$0.274757\pi$
$521$			34.6906i			1.51982i	−0.650027	+	0.759911i	$0.725243\pi$
$522$		0			0
$523$	15.5419	+	15.5419i	0.679598	+	0.679598i	0.959909	−	0.280311i	$-0.0904376\pi$
$523$	15.5419	+	15.5419i	0.679598	+	0.679598i	−0.280311	+	0.959909i	$0.590438\pi$
$524$	−0.125728			−0.00549245
$525$		0			0
$526$	20.0988			0.876350
$527$	−4.14882	−	4.14882i	−0.180725	−	0.180725i
$528$		0			0
$529$		−	1.00000i		−	0.0434783i
$530$	−8.52022	−	5.74852i	−0.370095	−	0.249700i
$531$		0			0
$532$	−24.5742	+	24.5742i	−1.06543	+	1.06543i
$533$	10.6155	−	10.6155i	0.459808	−	0.459808i
$534$		0			0
$535$	3.52360	+	18.1395i	0.152338	+	0.784239i
$536$		−	0.120832i		−	0.00521915i
$537$		0			0
$538$	17.8425	+	17.8425i	0.769243	+	0.769243i
$539$	−13.3811			−0.576365
$540$		0			0
$541$	41.6475			1.79057			0.895283	−	0.445498i	$-0.146973\pi$
$541$	41.6475			1.79057			0.895283	+	0.445498i	$0.146973\pi$
$542$	−11.5093	−	11.5093i	−0.494367	−	0.494367i
$543$		0			0
$544$		−	1.56723i		−	0.0671946i
$545$	20.7186	−	30.7083i	0.887487	−	1.31540i
$546$		0			0
$547$	1.06634	−	1.06634i	0.0455936	−	0.0455936i	−0.683942	−	0.729536i	$-0.739736\pi$
$547$	1.06634	−	1.06634i	0.0455936	−	0.0455936i	0.729536	+	0.683942i	$0.239736\pi$
$548$	−10.2258	+	10.2258i	−0.436822	+	0.436822i
$549$		0			0
$550$	−5.09998	−	2.16632i	−0.217464	−	0.0923724i
$551$			50.1348i			2.13581i
$552$		0			0
$553$	41.4424	+	41.4424i	1.76231	+	1.76231i
$554$	18.2429			0.775065
$555$		0			0
$556$	14.8803			0.631064
$557$	3.96379	+	3.96379i	0.167951	+	0.167951i	0.786078	−	0.618127i	$-0.212108\pi$
$557$	3.96379	+	3.96379i	0.167951	+	0.167951i	−0.618127	+	0.786078i	$0.712108\pi$
$558$		0			0
$559$			19.7641i			0.835932i
$560$	9.58672	−	1.86222i	0.405113	−	0.0786932i
$561$		0			0
$562$	0.408888	−	0.408888i	0.0172479	−	0.0172479i
$563$	8.82368	−	8.82368i	0.371874	−	0.371874i	−0.496286	−	0.868159i	$-0.665303\pi$
$563$	8.82368	−	8.82368i	0.371874	−	0.371874i	0.868159	+	0.496286i	$0.165303\pi$
$564$		0			0
$565$	5.66176	−	1.09980i	0.238192	−	0.0462688i
$566$			16.4118i			0.689841i
$567$		0			0
$568$	−1.69058	−	1.69058i	−0.0709352	−	0.0709352i
$569$	7.43475			0.311681			0.155841	−	0.987782i	$-0.450191\pi$
$569$	7.43475			0.311681			0.155841	+	0.987782i	$0.450191\pi$
$570$		0			0
$571$	16.0631			0.672218			0.336109	−	0.941823i	$-0.390889\pi$
$571$	16.0631			0.672218			0.336109	+	0.941823i	$0.390889\pi$
$572$	−2.82843	−	2.82843i	−0.118262	−	0.118262i
$573$		0			0
$574$			18.1653i			0.758203i
$575$	−4.60203	−	1.95481i	−0.191918	−	0.0815213i
$576$		0			0
$577$	29.9207	−	29.9207i	1.24561	−	1.24561i	0.287977	−	0.957637i	$-0.407017\pi$
$577$	29.9207	−	29.9207i	1.24561	−	1.24561i	0.957637	−	0.287977i	$-0.0929828\pi$
$578$	−10.2840	+	10.2840i	−0.427758	+	0.427758i
$579$		0			0
$580$	7.87953	−	11.6787i	0.327179	−	0.484932i
$581$		−	28.0390i		−	1.16326i
$582$		0			0
$583$	−3.60190	−	3.60190i	−0.149176	−	0.149176i
$584$	3.35161			0.138691
$585$		0			0
$586$	5.98460			0.247221
$587$	20.5169	+	20.5169i	0.846821	+	0.846821i	0.989735	−	0.142914i	$-0.0456472\pi$
$587$	20.5169	+	20.5169i	0.846821	+	0.846821i	−0.142914	+	0.989735i	$0.545647\pi$
$588$		0			0
$589$		−	29.7901i		−	1.22748i
$590$	−5.51486	−	28.3905i	−0.227043	−	1.16882i
$591$		0			0
$592$	−4.56245	+	4.56245i	−0.187516	+	0.187516i
$593$	−2.71761	+	2.71761i	−0.111599	+	0.111599i	−0.760701	−	0.649102i	$-0.775145\pi$
$593$	−2.71761	+	2.71761i	−0.111599	+	0.111599i	0.649102	+	0.760701i	$0.275145\pi$
$594$		0			0
$595$	12.6877	+	8.56030i	0.520146	+	0.350938i
$596$		−	2.44724i		−	0.100243i
$597$		0			0
$598$	−2.55227	−	2.55227i	−0.104370	−	0.104370i
$599$	−19.0438			−0.778109			−0.389054	−	0.921215i	$-0.627198\pi$
$599$	−19.0438			−0.778109			−0.389054	+	0.921215i	$0.627198\pi$
$600$		0			0
$601$	21.0798			0.859862			0.429931	−	0.902862i	$-0.358538\pi$
$601$	21.0798			0.859862			0.429931	+	0.902862i	$0.358538\pi$
$602$	−16.9102	−	16.9102i	−0.689208	−	0.689208i
$603$		0			0
$604$		−	22.0052i		−	0.895378i
$605$	18.1134	+	12.2210i	0.736416	+	0.496853i
$606$		0			0
$607$	−7.74186	+	7.74186i	−0.314233	+	0.314233i	−0.846547	−	0.532314i	$-0.821322\pi$
$607$	−7.74186	+	7.74186i	−0.314233	+	0.314233i	0.532314	+	0.846547i	$0.321322\pi$
$608$	5.62667	−	5.62667i	0.228192	−	0.228192i
$609$		0			0
$610$	−5.58544	−	28.7538i	−0.226148	−	1.16421i
$611$			32.2988i			1.30667i
$612$		0			0
$613$	−12.8900	−	12.8900i	−0.520623	−	0.520623i	0.397136	−	0.917760i	$-0.370004\pi$
$613$	−12.8900	−	12.8900i	−0.520623	−	0.520623i	−0.917760	+	0.397136i	$0.870004\pi$
$614$	−13.6834			−0.552217
$615$		0			0
$616$	4.84001			0.195010
$617$	−23.2475	−	23.2475i	−0.935908	−	0.935908i	0.0621580	−	0.998066i	$-0.480202\pi$
$617$	−23.2475	−	23.2475i	−0.935908	−	0.935908i	−0.998066	+	0.0621580i	$0.980202\pi$
$618$		0			0
$619$		−	37.9833i		−	1.52668i	−0.645998	−	0.763339i	$-0.723559\pi$
$619$		−	37.9833i		−	1.52668i	0.645998	−	0.763339i	$-0.276441\pi$
$620$	−4.68202	+	6.93950i	−0.188034	+	0.278697i
$621$		0			0
$622$	−11.0632	+	11.0632i	−0.443593	+	0.443593i
$623$	6.13645	−	6.13645i	0.245852	−	0.245852i
$624$		0			0
$625$	−17.9922	+	17.3574i	−0.719688	+	0.694297i
$626$			1.71438i			0.0685205i
$627$		0			0
$628$	−1.65225	−	1.65225i	−0.0659319	−	0.0659319i
$629$	−10.1122			−0.403201
$630$		0			0
$631$	−9.85775			−0.392431			−0.196215	−	0.980561i	$-0.562865\pi$
$631$	−9.85775			−0.392431			−0.196215	+	0.980561i	$0.562865\pi$
$632$	−9.48892	−	9.48892i	−0.377449	−	0.377449i
$633$		0			0
$634$		−	20.0434i		−	0.796024i
$635$	−12.8928	+	2.50443i	−0.511636	+	0.0993853i
$636$		0			0
$637$	−30.8176	+	30.8176i	−1.22104	+	1.22104i
$638$	4.93715	−	4.93715i	0.195464	−	0.195464i
$639$		0			0
$640$	−2.19504	+	0.426386i	−0.0867665	+	0.0168544i
$641$			44.7416i			1.76719i	0.468253	+	0.883594i	$0.344884\pi$
$641$			44.7416i			1.76719i	−0.468253	+	0.883594i	$0.655116\pi$
$642$		0			0
$643$	6.28923	+	6.28923i	0.248023	+	0.248023i	0.820159	−	0.572136i	$-0.193885\pi$
$643$	6.28923	+	6.28923i	0.248023	+	0.248023i	−0.572136	+	0.820159i	$0.693885\pi$
$644$	4.36745			0.172102
$645$		0			0
$646$	12.4710			0.490663
$647$	−9.27300	−	9.27300i	−0.364559	−	0.364559i	0.500929	−	0.865488i	$-0.332992\pi$
$647$	−9.27300	−	9.27300i	−0.364559	−	0.364559i	−0.865488	+	0.500929i	$0.832992\pi$
$648$		0			0
$649$		−	14.3334i		−	0.562636i
$650$	−16.7348	+	6.75642i	−0.656394	+	0.265009i
$651$		0			0
$652$	3.60543	−	3.60543i	0.141199	−	0.141199i
$653$	26.6242	−	26.6242i	1.04189	−	1.04189i	0.0428031	−	0.999084i	$-0.486371\pi$
$653$	26.6242	−	26.6242i	1.04189	−	1.04189i	0.999084	−	0.0428031i	$-0.0136288\pi$
$654$		0			0
$655$	−0.157239	+	0.233053i	−0.00614382	+	0.00910613i
$656$		−	4.15924i		−	0.162391i
$657$		0			0
$658$	−27.6349	−	27.6349i	−1.07732	−	1.07732i
$659$	−13.1521			−0.512331			−0.256166	−	0.966633i	$-0.582459\pi$
$659$	−13.1521			−0.512331			−0.256166	+	0.966633i	$0.582459\pi$
$660$		0			0
$661$	−20.4920			−0.797045			−0.398522	−	0.917159i	$-0.630477\pi$
$661$	−20.4920			−0.797045			−0.398522	+	0.917159i	$0.630477\pi$
$662$	−13.9443	−	13.9443i	−0.541962	−	0.541962i
$663$		0			0
$664$			6.42001i			0.249145i
$665$	14.8183	+	76.2845i	0.574628	+	2.95819i
$666$		0			0
$667$	4.45510	−	4.45510i	0.172502	−	0.172502i
$668$	17.0620	−	17.0620i	0.660149	−	0.660149i
$669$		0			0
$670$	−0.223978	−	0.151116i	−0.00865301	−	0.00583811i
$671$		−	14.5168i		−	0.560417i
$672$		0			0
$673$	−10.6709	−	10.6709i	−0.411332	−	0.411332i	0.470870	−	0.882202i	$-0.343940\pi$
$673$	−10.6709	−	10.6709i	−0.411332	−	0.411332i	−0.882202	+	0.470870i	$0.843940\pi$
$674$	15.2022			0.585566
$675$		0			0
$676$	−0.0281519			−0.00108277
$677$	−13.7900	−	13.7900i	−0.529993	−	0.529993i	0.390577	−	0.920570i	$-0.372275\pi$
$677$	−13.7900	−	13.7900i	−0.529993	−	0.529993i	−0.920570	+	0.390577i	$0.872275\pi$
$678$		0			0
$679$			11.4518i			0.439480i
$680$	−2.90507	−	1.96002i	−0.111404	−	0.0751634i
$681$		0			0
$682$	−2.93366	+	2.93366i	−0.112335	+	0.112335i
$683$	31.3149	−	31.3149i	1.19823	−	1.19823i	0.223534	−	0.974696i	$-0.428240\pi$
$683$	31.3149	−	31.3149i	1.19823	−	1.19823i	0.974696	−	0.223534i	$-0.0717595\pi$
$684$		0			0
$685$	6.16614	+	31.7433i	0.235596	+	1.21285i
$686$		−	22.1631i		−	0.846191i
$687$		0			0
$688$	3.87187	+	3.87187i	0.147614	+	0.147614i
$689$	−16.5909			−0.632063
$690$		0			0
$691$	−34.8286			−1.32494			−0.662471	−	0.749088i	$-0.730492\pi$
$691$	−34.8286			−1.32494			−0.662471	+	0.749088i	$0.730492\pi$
$692$	−12.9466	−	12.9466i	−0.492154	−	0.492154i
$693$		0			0
$694$			3.75594i			0.142574i
$695$	18.6097	−	27.5825i	0.705905	−	1.04626i
$696$		0			0
$697$	4.60927	−	4.60927i	0.174589	−	0.174589i
$698$	−5.14939	+	5.14939i	−0.194907	+	0.194907i
$699$		0			0
$700$	8.53754	−	20.0991i	0.322689	−	0.759676i
$701$			11.9697i			0.452090i	0.974117	+	0.226045i	$0.0725797\pi$
$701$			11.9697i			0.452090i	−0.974117	+	0.226045i	$0.927420\pi$
$702$		0			0
$703$	−36.3048	−	36.3048i	−1.36926	−	1.36926i
$704$	−1.10820			−0.0417669
$705$		0			0
$706$	−20.3877			−0.767299
$707$	−14.6695	−	14.6695i	−0.551704	−	0.551704i
$708$		0			0
$709$			2.35453i			0.0884261i	0.999022	+	0.0442130i	$0.0140780\pi$
$709$			2.35453i			0.0884261i	−0.999022	+	0.0442130i	$0.985922\pi$
$710$	−5.24799	+	1.01942i	−0.196954	+	0.0382583i
$711$		0			0
$712$	−1.40504	+	1.40504i	−0.0526562	+	0.0526562i
$713$	−2.64722	+	2.64722i	−0.0991393	+	0.0991393i
$714$		0			0
$715$	−8.78015	+	1.70555i	−0.328359	+	0.0637838i
$716$			9.01390i			0.336865i
$717$		0			0
$718$	19.4015	+	19.4015i	0.724059	+	0.724059i
$719$	9.59308			0.357761			0.178881	−	0.983871i	$-0.442752\pi$
$719$	9.59308			0.357761			0.178881	+	0.983871i	$0.442752\pi$
$720$		0			0
$721$	48.5993			1.80993
$722$	31.3381	+	31.3381i	1.16628	+	1.16628i
$723$		0			0
$724$			2.72272i			0.101189i
$725$	−11.7936	−	29.2114i	−0.438005	−	1.08488i
$726$		0			0
$727$	23.1915	−	23.1915i	0.860124	−	0.860124i	−0.131228	−	0.991352i	$-0.541892\pi$
$727$	23.1915	−	23.1915i	0.860124	−	0.860124i	0.991352	+	0.131228i	$0.0418920\pi$
$728$	11.1469	−	11.1469i	0.413132	−	0.413132i
$729$		0			0
$730$	4.19161	−	6.21264i	0.155138	−	0.229940i
$731$			8.58162i			0.317403i
$732$		0			0
$733$	−3.04410	−	3.04410i	−0.112436	−	0.112436i	0.648650	−	0.761087i	$-0.275334\pi$
$733$	−3.04410	−	3.04410i	−0.112436	−	0.112436i	−0.761087	+	0.648650i	$0.775334\pi$
$734$	5.87549			0.216868
$735$		0			0
$736$	−1.00000			−0.0368605
$737$	−0.0946860	−	0.0946860i	−0.00348780	−	0.00348780i
$738$		0			0
$739$			15.1345i			0.556730i	0.960475	+	0.278365i	$0.0897925\pi$
$739$			15.1345i			0.556730i	−0.960475	+	0.278365i	$0.910207\pi$
$740$	2.75116	+	14.1630i	0.101135	+	0.520642i
$741$		0			0
$742$	14.1952	−	14.1952i	0.521122	−	0.521122i
$743$	12.7074	−	12.7074i	0.466188	−	0.466188i	−0.434489	−	0.900677i	$-0.643071\pi$
$743$	12.7074	−	12.7074i	0.466188	−	0.466188i	0.900677	+	0.434489i	$0.143071\pi$
$744$		0			0
$745$	−4.53627	−	3.06058i	−0.166196	−	0.112131i
$746$			10.5391i			0.385865i
$747$		0			0
$748$	−1.22811	−	1.22811i	−0.0449041	−	0.0449041i
$749$	−36.0920			−1.31877
$750$		0			0
$751$	−4.67001			−0.170411			−0.0852055	−	0.996363i	$-0.527155\pi$
$751$	−4.67001			−0.170411			−0.0852055	+	0.996363i	$0.527155\pi$
$752$	6.32747	+	6.32747i	0.230739	+	0.230739i
$753$		0			0
$754$		−	22.7412i		−	0.828187i
$755$	−40.7894	−	27.5202i	−1.48448	−	1.00156i
$756$		0			0
$757$	−5.30627	+	5.30627i	−0.192860	+	0.192860i	−0.796931	−	0.604071i	$-0.793544\pi$
$757$	−5.30627	+	5.30627i	−0.192860	+	0.192860i	0.604071	+	0.796931i	$0.293544\pi$
$758$	27.3891	−	27.3891i	0.994818	−	0.994818i
$759$		0			0
$760$	−3.39289	−	17.4666i	−0.123073	−	0.633580i
$761$			31.4820i			1.14122i	0.821220	+	0.570611i	$0.193294\pi$
$761$			31.4820i			1.14122i	−0.821220	+	0.570611i	$0.806706\pi$
$762$		0			0
$763$	51.1618	+	51.1618i	1.85218	+	1.85218i
$764$	21.7099			0.785437
$765$		0			0
$766$	29.1930			1.05479
$767$	−33.0109	−	33.0109i	−1.19195	−	1.19195i
$768$		0			0
$769$			7.30478i			0.263417i	0.991288	+	0.131708i	$0.0420463\pi$
$769$			7.30478i			0.263417i	−0.991288	+	0.131708i	$0.957954\pi$
$770$	6.05304	−	8.97158i	0.218137	−	0.323313i
$771$		0			0
$772$	−10.5672	+	10.5672i	−0.380323	+	0.380323i
$773$	−11.7702	+	11.7702i	−0.423346	+	0.423346i	−0.886354	−	0.463008i	$-0.846770\pi$
$773$	−11.7702	+	11.7702i	−0.423346	+	0.423346i	0.463008	+	0.886354i	$0.346770\pi$
$774$		0			0
$775$	7.00779	+	17.3574i	0.251727	+	0.623497i
$776$		−	2.62208i		−	0.0941273i
$777$		0			0
$778$	−12.7624	−	12.7624i	−0.457553	−	0.457553i
$779$	33.0963			1.18580
$780$		0			0
$781$	−2.64953			−0.0948078
$782$	−1.10820	−	1.10820i	−0.0396292	−	0.0396292i
$783$		0			0
$784$			12.0746i			0.431236i
$785$	−5.12900	+	0.996308i	−0.183062	+	0.0355597i
$786$		0			0
$787$	−8.17730	+	8.17730i	−0.291489	+	0.291489i	−0.837668	−	0.546179i	$-0.816082\pi$
$787$	−8.17730	+	8.17730i	−0.291489	+	0.291489i	0.546179	+	0.837668i	$0.316082\pi$
$788$	−2.44764	+	2.44764i	−0.0871937	+	0.0871937i
$789$		0			0
$790$	−29.4560	+	5.72183i	−1.04800	+	0.203574i
$791$			11.2652i			0.400543i
$792$		0			0
$793$	−33.4334	−	33.4334i	−1.18725	−	1.18725i
$794$	−24.8037			−0.880250
$795$		0			0
$796$	−5.89032			−0.208777
$797$	−19.1263	−	19.1263i	−0.677490	−	0.677490i	0.281942	−	0.959432i	$-0.409021\pi$
$797$	−19.1263	−	19.1263i	−0.677490	−	0.677490i	−0.959432	+	0.281942i	$0.909021\pi$
$798$		0			0
$799$			14.0242i			0.496141i
$800$	−1.95481	+	4.60203i	−0.0691130	+	0.162706i
$801$		0			0
$802$	25.6644	−	25.6644i	0.906242	−	0.906242i
$803$	2.62638	−	2.62638i	0.0926828	−	0.0926828i
$804$		0			0
$805$	5.46205	−	8.09562i	0.192512	−	0.285333i
$806$			13.5128i			0.475970i
$807$		0			0
$808$	3.35883	+	3.35883i	0.118163	+	0.118163i
$809$	−32.6423			−1.14764			−0.573820	−	0.818981i	$-0.694539\pi$
$809$	−32.6423			−1.14764			−0.573820	+	0.818981i	$0.694539\pi$
$810$		0			0
$811$	−24.3856			−0.856294			−0.428147	−	0.903709i	$-0.640833\pi$
$811$	−24.3856			−0.856294			−0.428147	+	0.903709i	$0.640833\pi$
$812$	19.4574	+	19.4574i	0.682822	+	0.682822i
$813$		0			0
$814$			7.15042i			0.250622i
$815$	−2.17408	−	11.1922i	−0.0761546	−	0.392044i
$816$		0			0
$817$	−30.8097	+	30.8097i	−1.07789	+	1.07789i
$818$	−25.2679	+	25.2679i	−0.883471	+	0.883471i
$819$		0			0
$820$	−7.70968	−	5.20165i	−0.269234	−	0.181650i
$821$			27.6947i			0.966551i	0.875468	+	0.483275i	$0.160553\pi$
$821$			27.6947i			0.966551i	−0.875468	+	0.483275i	$0.839447\pi$
$822$		0			0
$823$	8.48297	+	8.48297i	0.295698	+	0.295698i	0.839326	−	0.543628i	$-0.182950\pi$
$823$	8.48297	+	8.48297i	0.295698	+	0.295698i	−0.543628	+	0.839326i	$0.682950\pi$
$824$	−11.1276			−0.387649
$825$		0			0
$826$	56.4884			1.96548
$827$	23.1817	+	23.1817i	0.806108	+	0.806108i	0.984042	−	0.177934i	$-0.0569415\pi$
$827$	23.1817	+	23.1817i	0.806108	+	0.806108i	−0.177934	+	0.984042i	$0.556942\pi$
$828$		0			0
$829$			47.4679i			1.64863i	0.566133	+	0.824314i	$0.308439\pi$
$829$			47.4679i			1.64863i	−0.566133	+	0.824314i	$0.691561\pi$
$830$	11.9003	+	8.02903i	0.413065	+	0.278692i
$831$		0			0
$832$	−2.55227	+	2.55227i	−0.0884840	+	0.0884840i
$833$	−13.3811	+	13.3811i	−0.463627	+	0.463627i
$834$		0			0
$835$	−10.2884	−	52.9648i	−0.356045	−	1.83292i
$836$		−	8.81830i		−	0.304987i
$837$		0			0
$838$	−16.0922	−	16.0922i	−0.555894	−	0.555894i
$839$	38.1279			1.31632			0.658161	−	0.752878i	$-0.271335\pi$
$839$	38.1279			1.31632			0.658161	+	0.752878i	$0.271335\pi$
$840$		0			0
$841$	10.6959			0.368823
$842$	−0.184788	−	0.184788i	−0.00636822	−	0.00636822i
$843$		0			0
$844$		−	20.5443i		−	0.707162i
$845$	−0.0352075	+	0.0521831i	−0.00121117	+	0.00179515i
$846$		0			0
$847$	−30.1781	+	30.1781i	−1.03693	+	1.03693i
$848$	−3.25022	+	3.25022i	−0.111613	+	0.111613i
$849$		0			0
$850$	−7.26630	+	2.93366i	−0.249232	+	0.100624i
$851$			6.45228i			0.221181i
$852$		0			0
$853$	−34.1724	−	34.1724i	−1.17004	−	1.17004i	−0.982199	−	0.187843i	$-0.939850\pi$
$853$	−34.1724	−	34.1724i	−1.17004	−	1.17004i	−0.187843	−	0.982199i	$-0.560150\pi$
$854$	57.2113			1.95773
$855$		0			0
$856$	8.26386			0.282453
$857$	−9.46775	−	9.46775i	−0.323412	−	0.323412i	0.526662	−	0.850075i	$-0.323443\pi$
$857$	−9.46775	−	9.46775i	−0.323412	−	0.323412i	−0.850075	+	0.526662i	$0.823443\pi$
$858$		0			0
$859$			5.52135i			0.188386i	0.995554	+	0.0941930i	$0.0300271\pi$
$859$			5.52135i			0.188386i	−0.995554	+	0.0941930i	$0.969973\pi$
$860$	12.0193	−	2.33474i	0.409853	−	0.0796141i
$861$		0			0
$862$	10.1001	−	10.1001i	0.344011	−	0.344011i
$863$	−14.2872	+	14.2872i	−0.486341	+	0.486341i	−0.907150	−	0.420808i	$-0.861747\pi$
$863$	−14.2872	+	14.2872i	−0.486341	+	0.486341i	0.420808	+	0.907150i	$0.361747\pi$
$864$		0			0
$865$	−40.1894	+	7.80679i	−1.36648	+	0.265439i
$866$		−	2.41479i		−	0.0820580i
$867$		0			0
$868$	−11.5616	−	11.5616i	−0.392427	−	0.392427i
$869$	−14.8713			−0.504476
$870$		0			0
$871$	−0.436138			−0.0147780
$872$	−11.7143	−	11.7143i	−0.396698	−	0.396698i
$873$		0			0
$874$		−	7.95731i		−	0.269160i
$875$	−26.5791	−	40.9619i	−0.898536	−	1.38477i
$876$		0			0
$877$	30.2973	−	30.2973i	1.02307	−	1.02307i	0.0233412	−	0.999728i	$-0.492570\pi$
$877$	30.2973	−	30.2973i	1.02307	−	1.02307i	0.999728	−	0.0233412i	$-0.00743040\pi$
$878$	23.0271	−	23.0271i	0.777126	−	0.777126i
$879$		0			0
$880$	−1.38595	+	2.05419i	−0.0467202	+	0.0692468i
$881$			13.6379i			0.459474i	0.973253	+	0.229737i	$0.0737865\pi$
$881$			13.6379i			0.459474i	−0.973253	+	0.229737i	$0.926213\pi$
$882$		0			0
$883$	32.8929	+	32.8929i	1.10694	+	1.10694i	0.993551	+	0.113385i	$0.0361692\pi$
$883$	32.8929	+	32.8929i	1.10694	+	1.10694i	0.113385	+	0.993551i	$0.463831\pi$
$884$	−5.65685			−0.190261
$885$		0			0
$886$	3.21085			0.107871
$887$	7.35218	+	7.35218i	0.246862	+	0.246862i	0.819682	−	0.572819i	$-0.194150\pi$
$887$	7.35218	+	7.35218i	0.246862	+	0.246862i	−0.572819	+	0.819682i	$0.694150\pi$
$888$		0			0
$889$		−	25.6527i		−	0.860365i
$890$	0.847242	+	4.36161i	0.0283996	+	0.146201i
$891$		0			0
$892$	16.0089	−	16.0089i	0.536018	−	0.536018i
$893$	−50.3497	+	50.3497i	−1.68489	+	1.68489i
$894$		0			0
$895$	16.7084	+	11.2730i	0.558501	+	0.376816i
$896$		−	4.36745i		−	0.145906i
$897$		0			0
$898$	−20.9015	−	20.9015i	−0.697493	−	0.697493i
$899$	−23.5873			−0.786680
$900$		0			0
$901$	−7.20380			−0.239994
$902$	−3.25925	−	3.25925i	−0.108521	−	0.108521i
$903$		0			0
$904$		−	2.57934i		−	0.0857877i
$905$	5.04692	+	3.40511i	0.167765	+	0.113190i
$906$		0			0
$907$	−30.4804	+	30.4804i	−1.01209	+	1.01209i	−0.0121594	+	0.999926i	$0.503871\pi$
$907$	−30.4804	+	30.4804i	−1.01209	+	1.01209i	−0.999926	+	0.0121594i	$0.996129\pi$
$908$	−5.02446	+	5.02446i	−0.166743	+	0.166743i
$909$		0			0
$910$	−6.72160	−	34.6028i	−0.222819	−	1.14707i
$911$			19.2942i			0.639245i	0.947545	+	0.319622i	$0.103556\pi$
$911$			19.2942i			0.639245i	−0.947545	+	0.319622i	$0.896444\pi$
$912$		0			0
$913$	5.03082	+	5.03082i	0.166496	+	0.166496i
$914$	34.9055			1.15457
$915$		0			0
$916$	11.7509			0.388260
$917$	−0.388280	−	0.388280i	−0.0128221	−	0.0128221i
$918$		0			0
$919$		−	44.0851i		−	1.45423i	−0.686515	−	0.727116i	$-0.740860\pi$
$919$		−	44.0851i		−	1.45423i	0.686515	−	0.727116i	$-0.259140\pi$
$920$	−1.25063	+	1.85363i	−0.0412319	+	0.0611123i
$921$		0			0
$922$	−20.7527	+	20.7527i	−0.683453	+	0.683453i
$923$	−6.10207	+	6.10207i	−0.200852	+	0.200852i
$924$		0			0
$925$	29.6936	+	12.6130i	0.976320	+	0.414712i
$926$		−	14.7422i		−	0.484457i
$927$		0			0
$928$	−4.45510	−	4.45510i	−0.146246	−	0.146246i
$929$	−20.4079			−0.669562			−0.334781	−	0.942296i	$-0.608662\pi$
$929$	−20.4079			−0.669562			−0.334781	+	0.942296i	$0.608662\pi$
$930$		0			0
$931$	−96.0814			−3.14894
$932$	16.0418	+	16.0418i	0.525466	+	0.525466i
$933$		0			0
$934$			17.1599i			0.561489i
$935$	−3.81236	+	0.740552i	−0.124678	+	0.0242186i
$936$		0			0
$937$	39.1021	−	39.1021i	1.27741	−	1.27741i	0.335299	−	0.942112i	$-0.391163\pi$
$937$	39.1021	−	39.1021i	1.27741	−	1.27741i	0.942112	−	0.335299i	$-0.108837\pi$
$938$	0.373160	−	0.373160i	0.0121841	−	0.0121841i
$939$		0			0
$940$	19.6421	−	3.81547i	0.640654	−	0.124447i
$941$			47.0848i			1.53492i	0.641097	+	0.767460i	$0.278480\pi$
$941$			47.0848i			1.53492i	−0.641097	+	0.767460i	$0.721520\pi$
$942$		0			0
$943$	−2.94103	−	2.94103i	−0.0957730	−	0.0957730i
$944$	−12.9339			−0.420964
$945$		0			0
$946$	6.06812			0.197292
$947$	−12.9557	−	12.9557i	−0.421005	−	0.421005i	0.464545	−	0.885550i	$-0.346218\pi$
$947$	−12.9557	−	12.9557i	−0.421005	−	0.421005i	−0.885550	+	0.464545i	$0.846218\pi$
$948$		0			0
$949$		−	12.0975i		−	0.392701i
$950$	−36.6198	−	15.5550i	−1.18810	−	0.504672i
$951$		0			0
$952$	4.84001	−	4.84001i	0.156866	−	0.156866i
$953$	27.0525	−	27.0525i	0.876318	−	0.876318i	−0.116834	−	0.993151i	$-0.537274\pi$
$953$	27.0525	−	27.0525i	0.876318	−	0.876318i	0.993151	+	0.116834i	$0.0372745\pi$
$954$		0			0
$955$	27.1510	−	40.2421i	0.878586	−	1.30220i
$956$		−	15.8376i		−	0.512223i
$957$		0			0
$958$	−22.8067	−	22.8067i	−0.736851	−	0.736851i
$959$	−63.1594			−2.03952
$960$		0			0
$961$	−16.9844			−0.547885
$962$	16.4680	+	16.4680i	0.530948	+	0.530948i
$963$		0			0
$964$		−	1.54557i		−	0.0497794i
$965$	6.37206	+	32.8034i	0.205124	+	1.05598i
$966$		0			0
$967$	8.85145	−	8.85145i	0.284644	−	0.284644i	−0.550314	−	0.834958i	$-0.685492\pi$
$967$	8.85145	−	8.85145i	0.284644	−	0.284644i	0.834958	+	0.550314i	$0.185492\pi$
$968$	6.90977	−	6.90977i	0.222088	−	0.222088i
$969$		0			0
$970$	−4.86037	−	3.27925i	−0.156057	−	0.105290i
$971$			44.1980i			1.41838i	0.705016	+	0.709191i	$0.250940\pi$
$971$			44.1980i			1.41838i	−0.705016	+	0.709191i	$0.749060\pi$
$972$		0			0
$973$	45.9540	+	45.9540i	1.47322	+	1.47322i
$974$	−14.0505			−0.450207
$975$		0			0
$976$	−13.0995			−0.419304
$977$	−32.5914	−	32.5914i	−1.04269	−	1.04269i	−0.999047	−	0.0436453i	$-0.986103\pi$
$977$	−32.5914	−	32.5914i	−1.04269	−	1.04269i	−0.0436453	−	0.999047i	$-0.513897\pi$
$978$		0			0
$979$			2.20203i			0.0703771i
$980$	22.3818	+	15.1008i	0.714961	+	0.482378i
$981$		0			0
$982$	−8.98008	+	8.98008i	−0.286566	+	0.286566i
$983$	31.9835	−	31.9835i	1.02012	−	1.02012i	0.0203217	−	0.999793i	$-0.493531\pi$
$983$	31.9835	−	31.9835i	1.02012	−	1.02012i	0.999793	−	0.0203217i	$-0.00646903\pi$
$984$		0			0
$985$	1.47593	+	7.59811i	0.0470271	+	0.242096i
$986$		−	9.87430i		−	0.314462i
$987$		0			0
$988$	−20.3092	−	20.3092i	−0.646122	−	0.646122i
$989$	5.47565			0.174116
$990$		0			0
$991$	49.6342			1.57668			0.788341	−	0.615239i	$-0.210940\pi$
$991$	49.6342			1.57668			0.788341	+	0.615239i	$0.210940\pi$
$992$	2.64722	+	2.64722i	0.0840494	+	0.0840494i
$993$		0			0
$994$		−	10.4419i		−	0.331196i
$995$	−7.36658	+	10.9184i	−0.233536	+	0.346138i
$996$		0			0
$997$	10.0016	−	10.0016i	0.316752	−	0.316752i	−0.530766	−	0.847518i	$-0.678096\pi$
$997$	10.0016	−	10.0016i	0.316752	−	0.316752i	0.847518	+	0.530766i	$0.178096\pi$
$998$	−26.8330	+	26.8330i	−0.849385	+	0.849385i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.j.j.323.5	✓	20
3.2	odd	2	inner	2070.2.j.j.323.6	yes	20
5.2	odd	4	inner	2070.2.j.j.737.6	yes	20
15.2	even	4	inner	2070.2.j.j.737.5	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.j.j.323.5	✓	20	1.1	even	1	trivial
2070.2.j.j.323.6	yes	20	3.2	odd	2	inner
2070.2.j.j.737.5	yes	20	15.2	even	4	inner
2070.2.j.j.737.6	yes	20	5.2	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:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(1.85363 + 1.25063i) q^{5} +(-3.08825 + 3.08825i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(1.85363 + 1.25063i) q^{5} +(-3.08825 + 3.08825i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.426386 - 2.19504i) q^{10} -1.10820i q^{11} +(-2.55227 - 2.55227i) q^{13} +4.36745 q^{14} -1.00000 q^{16} +(-1.10820 - 1.10820i) q^{17} -7.95731i q^{19} +(-1.25063 + 1.85363i) q^{20} +(-0.783617 + 0.783617i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(1.87187 + 4.63639i) q^{25} +3.60945i q^{26} +(-3.08825 - 3.08825i) q^{28} -6.30046 q^{29} +3.74374 q^{31} +(0.707107 + 0.707107i) q^{32} +1.56723i q^{34} +(-9.58672 + 1.86222i) q^{35} +(4.56245 - 4.56245i) q^{37} +(-5.62667 + 5.62667i) q^{38} +(2.19504 - 0.426386i) q^{40} +4.15924i q^{41} +(-3.87187 - 3.87187i) q^{43} +1.10820 q^{44} +1.00000 q^{46} +(-6.32747 - 6.32747i) q^{47} -12.0746i q^{49} +(1.95481 - 4.60203i) q^{50} +(2.55227 - 2.55227i) q^{52} +(3.25022 - 3.25022i) q^{53} +(1.38595 - 2.05419i) q^{55} +4.36745i q^{56} +(4.45510 + 4.45510i) q^{58} +12.9339 q^{59} +13.0995 q^{61} +(-2.64722 - 2.64722i) q^{62} -1.00000i q^{64} +(-1.53902 - 7.92289i) q^{65} +(0.0854412 - 0.0854412i) q^{67} +(1.10820 - 1.10820i) q^{68} +(8.09562 + 5.46205i) q^{70} -2.39084i q^{71} +(2.36995 + 2.36995i) q^{73} -6.45228 q^{74} +7.95731 q^{76} +(3.42241 + 3.42241i) q^{77} -13.4194i q^{79} +(-1.85363 - 1.25063i) q^{80} +(2.94103 - 2.94103i) q^{82} +(-4.53963 + 4.53963i) q^{83} +(-0.668247 - 3.44014i) q^{85} +5.47565i q^{86} +(-0.783617 - 0.783617i) q^{88} -1.98703 q^{89} +15.7641 q^{91} +(-0.707107 - 0.707107i) q^{92} +8.94840i q^{94} +(9.95162 - 14.7499i) q^{95} +(1.85409 - 1.85409i) q^{97} +(-8.53804 + 8.53804i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 16 q^{7}+O(q^{10}) \) 20 * q - 16 * q^7	\( 20 q - 16 q^{7} + 12 q^{10} - 12 q^{13} - 20 q^{16} - 24 q^{25} - 16 q^{28} - 48 q^{31} - 60 q^{37} - 16 q^{43} + 20 q^{46} + 12 q^{52} - 32 q^{55} + 4 q^{58} + 104 q^{61} - 56 q^{67} - 8 q^{70} - 20 q^{73} + 40 q^{76} - 28 q^{82} - 40 q^{85} - 32 q^{91} - 44 q^{97}+O(q^{100}) \) 20 * q - 16 * q^7 + 12 * q^10 - 12 * q^13 - 20 * q^16 - 24 * q^25 - 16 * q^28 - 48 * q^31 - 60 * q^37 - 16 * q^43 + 20 * q^46 + 12 * q^52 - 32 * q^55 + 4 * q^58 + 104 * q^61 - 56 * q^67 - 8 * q^70 - 20 * q^73 + 40 * q^76 - 28 * q^82 - 40 * q^85 - 32 * q^91 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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