LMFDB - Embedded newform 2070.2.j.g.323.1

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:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.1
Root			$-0.394157 + 1.35818i$ of defining polynomial
Character	$\chi$	$=$	2070.323
Dual form			2070.2.j.g.737.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.22126 - 0.256912i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.22126 - 0.256912i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.38900 + 1.75233i) q^{10} +3.34225i q^{11} +(3.50466 + 3.50466i) q^{13} +2.82843 q^{14} -1.00000 q^{16} +(-1.41421 - 1.41421i) q^{17} +0.778008i q^{19} +(0.256912 - 2.22126i) q^{20} +(2.36333 - 2.36333i) q^{22} +(0.707107 - 0.707107i) q^{23} +(4.86799 + 1.14134i) q^{25} -4.95634i q^{26} +(-2.00000 - 2.00000i) q^{28} -2.12792 q^{29} +2.72666 q^{31} +(0.707107 + 0.707107i) q^{32} +2.00000i q^{34} +(4.95634 - 3.92870i) q^{35} +(-4.36333 + 4.36333i) q^{37} +(0.550135 - 0.550135i) q^{38} +(-1.75233 + 1.38900i) q^{40} -4.64240i q^{41} +(-3.91934 - 3.91934i) q^{43} -3.34225 q^{44} -1.00000 q^{46} +(-7.27095 - 7.27095i) q^{47} -1.00000i q^{49} +(-2.63514 - 4.24924i) q^{50} +(-3.50466 + 3.50466i) q^{52} +(6.40687 - 6.40687i) q^{53} +(0.858664 - 7.42401i) q^{55} +2.82843i q^{56} +(1.50466 + 1.50466i) q^{58} +1.80078 q^{59} -2.05135 q^{61} +(-1.92804 - 1.92804i) q^{62} -1.00000i q^{64} +(-6.88438 - 8.68516i) q^{65} +(-10.1507 + 10.1507i) q^{67} +(1.41421 - 1.41421i) q^{68} +(-6.28267 - 0.726656i) q^{70} +10.2266i q^{71} +(3.28267 + 3.28267i) q^{73} +6.17068 q^{74} -0.778008 q^{76} +(-6.68450 - 6.68450i) q^{77} -5.55602i q^{79} +(2.22126 + 0.256912i) q^{80} +(-3.28267 + 3.28267i) q^{82} +(-9.36255 + 9.36255i) q^{83} +(2.77801 + 3.50466i) q^{85} +5.54279i q^{86} +(2.36333 + 2.36333i) q^{88} -9.21218 q^{89} -14.0187 q^{91} +(0.707107 + 0.707107i) q^{92} +10.2827i q^{94} +(0.199879 - 1.72816i) q^{95} +(0.778008 - 0.778008i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{7}+O(q^{10}) $ 12 * q - 24 * q^7	$ 12 q - 24 q^{7} + 4 q^{10} - 12 q^{16} + 20 q^{22} + 8 q^{25} - 24 q^{28} + 16 q^{31} - 44 q^{37} + 12 q^{43} - 12 q^{46} + 44 q^{55} - 24 q^{58} - 16 q^{61} - 4 q^{67} - 8 q^{70} - 28 q^{73} + 16 q^{76} + 28 q^{82} + 8 q^{85} + 20 q^{88} - 16 q^{97}+O(q^{100}) $ 12 * q - 24 * q^7 + 4 * q^10 - 12 * q^16 + 20 * q^22 + 8 * q^25 - 24 * q^28 + 16 * q^31 - 44 * q^37 + 12 * q^43 - 12 * q^46 + 44 * q^55 - 24 * q^58 - 16 * q^61 - 4 * q^67 - 8 * q^70 - 28 * q^73 + 16 * q^76 + 28 * q^82 + 8 * q^85 + 20 * q^88 - 16 * 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
$5$	−2.22126	−	0.256912i	−0.993378	−	0.114894i
$5$	−2.22126	−	0.256912i	−0.993378	−	0.114894i
$6$		0			0
$7$	−2.00000	+	2.00000i	−0.755929	+	0.755929i	−0.975579	−	0.219650i	$-0.929509\pi$
$7$	−2.00000	+	2.00000i	−0.755929	+	0.755929i	0.219650	+	0.975579i	$0.429509\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	1.38900	+	1.75233i	0.439242	+	0.554136i
$11$			3.34225i			1.00773i	0.863783	+	0.503863i	$0.168088\pi$
$11$			3.34225i			1.00773i	−0.863783	+	0.503863i	$0.831912\pi$
$12$		0			0
$13$	3.50466	+	3.50466i	0.972019	+	0.972019i	0.999619	−	0.0276000i	$-0.00878648\pi$
$13$	3.50466	+	3.50466i	0.972019	+	0.972019i	−0.0276000	+	0.999619i	$0.508786\pi$
$14$	2.82843			0.755929
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−1.41421	−	1.41421i	−0.342997	−	0.342997i	0.514496	−	0.857493i	$-0.327979\pi$
$17$	−1.41421	−	1.41421i	−0.342997	−	0.342997i	−0.857493	+	0.514496i	$0.827979\pi$
$18$		0			0
$19$			0.778008i			0.178487i	0.996010	+	0.0892436i	$0.0284450\pi$
$19$			0.778008i			0.178487i	−0.996010	+	0.0892436i	$0.971555\pi$
$20$	0.256912	−	2.22126i	0.0574472	−	0.496689i
$21$		0			0
$22$	2.36333	−	2.36333i	0.503863	−	0.503863i
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i
$24$		0			0
$25$	4.86799	+	1.14134i	0.973599	+	0.228267i
$26$		−	4.95634i		−	0.972019i
$27$		0			0
$28$	−2.00000	−	2.00000i	−0.377964	−	0.377964i
$29$	−2.12792			−0.395144			−0.197572	−	0.980288i	$-0.563306\pi$
$29$	−2.12792			−0.395144			−0.197572	+	0.980288i	$0.563306\pi$
$30$		0			0
$31$	2.72666			0.489722			0.244861	−	0.969558i	$-0.421258\pi$
$31$	2.72666			0.489722			0.244861	+	0.969558i	$0.421258\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$			2.00000i			0.342997i
$35$	4.95634	−	3.92870i	0.837775	−	0.664071i
$36$		0			0
$37$	−4.36333	+	4.36333i	−0.717327	+	0.717327i	−0.968057	−	0.250730i	$-0.919329\pi$
$37$	−4.36333	+	4.36333i	−0.717327	+	0.717327i	0.250730	+	0.968057i	$0.419329\pi$
$38$	0.550135	−	0.550135i	0.0892436	−	0.0892436i
$39$		0			0
$40$	−1.75233	+	1.38900i	−0.277068	+	0.219621i
$41$		−	4.64240i		−	0.725021i	−0.931980	−	0.362511i	$-0.881920\pi$
$41$		−	4.64240i		−	0.725021i	0.931980	−	0.362511i	$-0.118080\pi$
$42$		0			0
$43$	−3.91934	−	3.91934i	−0.597694	−	0.597694i	0.342004	−	0.939698i	$-0.388894\pi$
$43$	−3.91934	−	3.91934i	−0.597694	−	0.597694i	−0.939698	+	0.342004i	$0.888894\pi$
$44$	−3.34225			−0.503863
$45$		0			0
$46$	−1.00000			−0.147442
$47$	−7.27095	−	7.27095i	−1.06058	−	1.06058i	−0.998043	−	0.0625338i	$-0.980082\pi$
$47$	−7.27095	−	7.27095i	−1.06058	−	1.06058i	−0.0625338	−	0.998043i	$-0.519918\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	−2.63514	−	4.24924i	−0.372666	−	0.600933i
$51$		0			0
$52$	−3.50466	+	3.50466i	−0.486010	+	0.486010i
$53$	6.40687	−	6.40687i	0.880051	−	0.880051i	−0.113488	−	0.993539i	$-0.536202\pi$
$53$	6.40687	−	6.40687i	0.880051	−	0.880051i	0.993539	+	0.113488i	$0.0362024\pi$
$54$		0			0
$55$	0.858664	−	7.42401i	0.115782	−	1.00105i
$56$			2.82843i			0.377964i
$57$		0			0
$58$	1.50466	+	1.50466i	0.197572	+	0.197572i
$59$	1.80078			0.234442			0.117221	−	0.993106i	$-0.462601\pi$
$59$	1.80078			0.234442			0.117221	+	0.993106i	$0.462601\pi$
$60$		0			0
$61$	−2.05135			−0.262649			−0.131324	−	0.991339i	$-0.541923\pi$
$61$	−2.05135			−0.262649			−0.131324	+	0.991339i	$0.541923\pi$
$62$	−1.92804	−	1.92804i	−0.244861	−	0.244861i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−6.88438	−	8.68516i	−0.853902	−	1.07726i
$66$		0			0
$67$	−10.1507	+	10.1507i	−1.24010	+	1.24010i	−0.280143	+	0.959958i	$0.590382\pi$
$67$	−10.1507	+	10.1507i	−1.24010	+	1.24010i	−0.959958	+	0.280143i	$0.909618\pi$
$68$	1.41421	−	1.41421i	0.171499	−	0.171499i
$69$		0			0
$70$	−6.28267	−	0.726656i	−0.750923	−	0.0868521i
$71$			10.2266i			1.21368i	0.794825	+	0.606839i	$0.207563\pi$
$71$			10.2266i			1.21368i	−0.794825	+	0.606839i	$0.792437\pi$
$72$		0			0
$73$	3.28267	+	3.28267i	0.384208	+	0.384208i	0.872616	−	0.488408i	$-0.162422\pi$
$73$	3.28267	+	3.28267i	0.384208	+	0.384208i	−0.488408	+	0.872616i	$0.662422\pi$
$74$	6.17068			0.717327
$75$		0			0
$76$	−0.778008			−0.0892436
$77$	−6.68450	−	6.68450i	−0.761770	−	0.761770i
$78$		0			0
$79$		−	5.55602i		−	0.625101i	−0.949901	−	0.312550i	$-0.898817\pi$
$79$		−	5.55602i		−	0.625101i	0.949901	−	0.312550i	$-0.101183\pi$
$80$	2.22126	+	0.256912i	0.248344	+	0.0287236i
$81$		0			0
$82$	−3.28267	+	3.28267i	−0.362511	+	0.362511i
$83$	−9.36255	+	9.36255i	−1.02767	+	1.02767i	−0.0280677	+	0.999606i	$0.508935\pi$
$83$	−9.36255	+	9.36255i	−1.02767	+	1.02767i	−0.999606	+	0.0280677i	$0.991065\pi$
$84$		0			0
$85$	2.77801	+	3.50466i	0.301317	+	0.380134i
$86$			5.54279i			0.597694i
$87$		0			0
$88$	2.36333	+	2.36333i	0.251932	+	0.251932i
$89$	−9.21218			−0.976489			−0.488244	−	0.872707i	$-0.662363\pi$
$89$	−9.21218			−0.976489			−0.488244	+	0.872707i	$0.662363\pi$
$90$		0			0
$91$	−14.0187			−1.46955
$92$	0.707107	+	0.707107i	0.0737210	+	0.0737210i
$93$		0			0
$94$			10.2827i			1.06058i
$95$	0.199879	−	1.72816i	0.0205072	−	0.177305i
$96$		0			0
$97$	0.778008	−	0.778008i	0.0789947	−	0.0789947i	−0.666505	−	0.745500i	$-0.732211\pi$
$97$	0.778008	−	0.778008i	0.0789947	−	0.0789947i	0.745500	+	0.666505i	$0.232211\pi$
$98$	−0.707107	+	0.707107i	−0.0714286	+	0.0714286i
$99$		0			0
$100$	−1.14134	+	4.86799i	−0.114134	+	0.486799i
$101$			11.6408i			1.15831i	0.815218	+	0.579154i	$0.196617\pi$
$101$			11.6408i			1.15831i	−0.815218	+	0.579154i	$0.803383\pi$
$102$		0			0
$103$	−13.2920	−	13.2920i	−1.30970	−	1.30970i	−0.921630	−	0.388070i	$-0.873142\pi$
$103$	−13.2920	−	13.2920i	−1.30970	−	1.30970i	−0.388070	−	0.921630i	$-0.626858\pi$
$104$	4.95634			0.486010
$105$		0			0
$106$	−9.06068			−0.880051
$107$	−11.7498	−	11.7498i	−1.13589	−	1.13589i	−0.989179	−	0.146715i	$-0.953130\pi$
$107$	−11.7498	−	11.7498i	−1.13589	−	1.13589i	−0.146715	−	0.989179i	$-0.546870\pi$
$108$		0			0
$109$			8.79667i			0.842568i	0.906929	+	0.421284i	$0.138420\pi$
$109$			8.79667i			0.842568i	−0.906929	+	0.421284i	$0.861580\pi$
$110$	−5.85673	+	4.64240i	−0.558418	+	0.442635i
$111$		0			0
$112$	2.00000	−	2.00000i	0.188982	−	0.188982i
$113$	7.47083	−	7.47083i	0.702796	−	0.702796i	−0.262214	−	0.965010i	$-0.584452\pi$
$113$	7.47083	−	7.47083i	0.702796	−	0.702796i	0.965010	+	0.262214i	$0.0844525\pi$
$114$		0			0
$115$	−1.75233	+	1.38900i	−0.163406	+	0.129525i
$116$		−	2.12792i		−	0.197572i
$117$		0			0
$118$	−1.27334	−	1.27334i	−0.117221	−	0.117221i
$119$	5.65685			0.518563
$120$		0			0
$121$	−0.170641			−0.0155128
$122$	1.45052	+	1.45052i	0.131324	+	0.131324i
$123$		0			0
$124$			2.72666i			0.244861i
$125$	−10.5199	−	3.78585i	−0.940924	−	0.338617i
$126$		0			0
$127$	−2.50466	+	2.50466i	−0.222253	+	0.222253i	−0.809447	−	0.587194i	$-0.800233\pi$
$127$	−2.50466	+	2.50466i	−0.222253	+	0.222253i	0.587194	+	0.809447i	$0.300233\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	−1.27334	+	11.0093i	−0.111680	+	0.965582i
$131$		−	13.1409i		−	1.14812i	−0.818812	−	0.574062i	$-0.805367\pi$
$131$		−	13.1409i		−	1.14812i	0.818812	−	0.574062i	$-0.194633\pi$
$132$		0			0
$133$	−1.55602	−	1.55602i	−0.134924	−	0.134924i
$134$	14.3552			1.24010
$135$		0			0
$136$	−2.00000			−0.171499
$137$	−8.17134	−	8.17134i	−0.698124	−	0.698124i	0.265881	−	0.964006i	$-0.414337\pi$
$137$	−8.17134	−	8.17134i	−0.698124	−	0.698124i	−0.964006	+	0.265881i	$0.914337\pi$
$138$		0			0
$139$		−	15.5747i		−	1.32103i	−0.750814	−	0.660513i	$-0.770339\pi$
$139$		−	15.5747i		−	1.32103i	0.750814	−	0.660513i	$-0.229661\pi$
$140$	3.92870	+	4.95634i	0.332035	+	0.418888i
$141$		0			0
$142$	7.23132	−	7.23132i	0.606839	−	0.606839i
$143$	−11.7135	+	11.7135i	−0.979529	+	0.979529i
$144$		0			0
$145$	4.72666	+	0.546687i	0.392527	+	0.0453999i
$146$		−	4.64240i		−	0.384208i
$147$		0			0
$148$	−4.36333	−	4.36333i	−0.358663	−	0.358663i
$149$	19.6849			1.61265			0.806326	−	0.591471i	$-0.201453\pi$
$149$	19.6849			1.61265			0.806326	+	0.591471i	$0.201453\pi$
$150$		0			0
$151$	3.73599			0.304030			0.152015	−	0.988378i	$-0.451424\pi$
$151$	3.73599			0.304030			0.152015	+	0.988378i	$0.451424\pi$
$152$	0.550135	+	0.550135i	0.0446218	+	0.0446218i
$153$		0			0
$154$			9.45331i			0.761770i
$155$	−6.05661	−	0.700510i	−0.486479	−	0.0562663i
$156$		0			0
$157$	16.0993	−	16.0993i	1.28487	−	1.28487i	0.347000	−	0.937865i	$-0.387200\pi$
$157$	16.0993	−	16.0993i	1.28487	−	1.28487i	0.937865	−	0.347000i	$-0.112800\pi$
$158$	−3.92870	+	3.92870i	−0.312550	+	0.312550i
$159$		0			0
$160$	−1.38900	−	1.75233i	−0.109810	−	0.138534i
$161$			2.82843i			0.222911i
$162$		0			0
$163$	−0.443984	−	0.443984i	−0.0347755	−	0.0347755i	0.689505	−	0.724281i	$-0.257828\pi$
$163$	−0.443984	−	0.443984i	−0.0347755	−	0.0347755i	−0.724281	+	0.689505i	$0.757828\pi$
$164$	4.64240			0.362511
$165$		0			0
$166$	13.2406			1.02767
$167$	5.78411	+	5.78411i	0.447588	+	0.447588i	0.894552	−	0.446964i	$-0.147495\pi$
$167$	5.78411	+	5.78411i	0.447588	+	0.447588i	−0.446964	+	0.894552i	$0.647495\pi$
$168$		0			0
$169$			11.5653i			0.889642i
$170$	0.513824	−	4.44252i	0.0394085	−	0.340726i
$171$		0			0
$172$	3.91934	−	3.91934i	0.298847	−	0.298847i
$173$	−16.9838	+	16.9838i	−1.29125	+	1.29125i	−0.357237	+	0.934014i	$0.616281\pi$
$173$	−16.9838	+	16.9838i	−1.29125	+	1.29125i	−0.934014	+	0.357237i	$0.883719\pi$
$174$		0			0
$175$	−12.0187	+	7.45331i	−0.908525	+	0.563418i
$176$		−	3.34225i		−	0.251932i
$177$		0			0
$178$	6.51399	+	6.51399i	0.488244	+	0.488244i
$179$	−15.7148			−1.17458			−0.587289	−	0.809377i	$-0.699805\pi$
$179$	−15.7148			−1.17458			−0.587289	+	0.809377i	$0.699805\pi$
$180$		0			0
$181$	−12.9580			−0.963159			−0.481579	−	0.876402i	$-0.659937\pi$
$181$	−12.9580			−0.963159			−0.481579	+	0.876402i	$0.659937\pi$
$182$	9.91269	+	9.91269i	0.734777	+	0.734777i
$183$		0			0
$184$		−	1.00000i		−	0.0737210i
$185$	10.8131	−	8.57110i	0.794993	−	0.630160i
$186$		0			0
$187$	4.72666	−	4.72666i	0.345647	−	0.345647i
$188$	7.27095	−	7.27095i	0.530288	−	0.530288i
$189$		0			0
$190$	−1.36333	+	1.08066i	−0.0989062	+	0.0783990i
$191$			1.80078i			0.130300i	0.997875	+	0.0651499i	$0.0207526\pi$
$191$			1.80078i			0.130300i	−0.997875	+	0.0651499i	$0.979247\pi$
$192$		0			0
$193$	−16.7360	−	16.7360i	−1.20468	−	1.20468i	−0.972726	−	0.231956i	$-0.925487\pi$
$193$	−16.7360	−	16.7360i	−1.20468	−	1.20468i	−0.231956	−	0.972726i	$-0.574513\pi$
$194$	−1.10027			−0.0789947
$195$		0			0
$196$	1.00000			0.0714286
$197$	−11.3269	−	11.3269i	−0.807008	−	0.807008i	0.177172	−	0.984180i	$-0.443305\pi$
$197$	−11.3269	−	11.3269i	−0.807008	−	0.807008i	−0.984180	+	0.177172i	$0.943305\pi$
$198$		0			0
$199$			1.45331i			0.103023i	0.998672	+	0.0515113i	$0.0164038\pi$
$199$			1.45331i			0.103023i	−0.998672	+	0.0515113i	$0.983596\pi$
$200$	4.24924	−	2.63514i	0.300466	−	0.186333i
$201$		0			0
$202$	8.23132	−	8.23132i	0.579154	−	0.579154i
$203$	4.25583	−	4.25583i	0.298701	−	0.298701i
$204$		0			0
$205$	−1.19269	+	10.3120i	−0.0833009	+	0.720220i
$206$			18.7977i			1.30970i
$207$		0			0
$208$	−3.50466	−	3.50466i	−0.243005	−	0.243005i
$209$	−2.60030			−0.179866
$210$		0			0
$211$	19.0093			1.30866			0.654328	−	0.756211i	$-0.272952\pi$
$211$	19.0093			1.30866			0.654328	+	0.756211i	$0.272952\pi$
$212$	6.40687	+	6.40687i	0.440026	+	0.440026i
$213$		0			0
$214$			16.6167i			1.13589i
$215$	7.69896	+	9.71281i	0.525064	+	0.662408i
$216$		0			0
$217$	−5.45331	+	5.45331i	−0.370195	+	0.370195i
$218$	6.22018	−	6.22018i	0.421284	−	0.421284i
$219$		0			0
$220$	7.42401	+	0.858664i	0.500527	+	0.0578911i
$221$		−	9.91269i		−	0.666800i
$222$		0			0
$223$	−1.21266	−	1.21266i	−0.0812059	−	0.0812059i	0.665337	−	0.746543i	$-0.268288\pi$
$223$	−1.21266	−	1.21266i	−0.0812059	−	0.0812059i	−0.746543	+	0.665337i	$0.768288\pi$
$224$	−2.82843			−0.188982
$225$		0			0
$226$	−10.5653			−0.702796
$227$	−8.52159	−	8.52159i	−0.565598	−	0.565598i	0.365294	−	0.930892i	$-0.380968\pi$
$227$	−8.52159	−	8.52159i	−0.565598	−	0.565598i	−0.930892	+	0.365294i	$0.880968\pi$
$228$		0			0
$229$			0.392633i			0.0259459i	0.999916	+	0.0129730i	$0.00412954\pi$
$229$			0.392633i			0.0259459i	−0.999916	+	0.0129730i	$0.995870\pi$
$230$	2.22126	+	0.256912i	0.146466	+	0.0169403i
$231$		0			0
$232$	−1.50466	+	1.50466i	−0.0987861	+	0.0987861i
$233$	−3.41487	+	3.41487i	−0.223716	+	0.223716i	−0.810061	−	0.586345i	$-0.800566\pi$
$233$	−3.41487	+	3.41487i	−0.223716	+	0.223716i	0.586345	+	0.810061i	$0.300566\pi$
$234$		0			0
$235$	14.2827	+	18.0187i	0.931699	+	1.17541i
$236$			1.80078i			0.117221i
$237$		0			0
$238$	−4.00000	−	4.00000i	−0.259281	−	0.259281i
$239$	8.82561			0.570881			0.285441	−	0.958396i	$-0.407860\pi$
$239$	8.82561			0.570881			0.285441	+	0.958396i	$0.407860\pi$
$240$		0			0
$241$	−11.0280			−0.710375			−0.355188	−	0.934795i	$-0.615583\pi$
$241$	−11.0280			−0.710375			−0.355188	+	0.934795i	$0.615583\pi$
$242$	0.120661	+	0.120661i	0.00775640	+	0.00775640i
$243$		0			0
$244$		−	2.05135i		−	0.131324i
$245$	−0.256912	+	2.22126i	−0.0164135	+	0.141911i
$246$		0			0
$247$	−2.72666	+	2.72666i	−0.173493	+	0.173493i
$248$	1.92804	−	1.92804i	0.122430	−	0.122430i
$249$		0			0
$250$	4.76166	+	10.1157i	0.301154	+	0.639771i
$251$			13.2549i			0.836644i	0.908299	+	0.418322i	$0.137382\pi$
$251$			13.2549i			0.836644i	−0.908299	+	0.418322i	$0.862618\pi$
$252$		0			0
$253$	2.36333	+	2.36333i	0.148581	+	0.148581i
$254$	3.54213			0.222253
$255$		0			0
$256$	1.00000			0.0625000
$257$	−9.51293	−	9.51293i	−0.593400	−	0.593400i	0.345148	−	0.938548i	$-0.387829\pi$
$257$	−9.51293	−	9.51293i	−0.593400	−	0.593400i	−0.938548	+	0.345148i	$0.887829\pi$
$258$		0			0
$259$		−	17.4533i		−	1.08450i
$260$	8.68516	−	6.88438i	0.538631	−	0.426951i
$261$		0			0
$262$	−9.29200	+	9.29200i	−0.574062	+	0.574062i
$263$	−9.98531	+	9.98531i	−0.615721	+	0.615721i	−0.944431	−	0.328710i	$-0.893386\pi$
$263$	−9.98531	+	9.98531i	−0.615721	+	0.615721i	0.328710	+	0.944431i	$0.393386\pi$
$264$		0			0
$265$	−15.8773	+	12.5853i	−0.975336	+	0.773110i
$266$			2.20054i			0.134924i
$267$		0			0
$268$	−10.1507	−	10.1507i	−0.620051	−	0.620051i
$269$	10.7584			0.655954			0.327977	−	0.944686i	$-0.393633\pi$
$269$	10.7584			0.655954			0.327977	+	0.944686i	$0.393633\pi$
$270$		0			0
$271$	−11.1120			−0.675008			−0.337504	−	0.941324i	$-0.609583\pi$
$271$	−11.1120			−0.675008			−0.337504	+	0.941324i	$0.609583\pi$
$272$	1.41421	+	1.41421i	0.0857493	+	0.0857493i
$273$		0			0
$274$			11.5560i			0.698124i
$275$	−3.81463	+	16.2701i	−0.230031	+	0.981121i
$276$		0			0
$277$	−6.33402	+	6.33402i	−0.380575	+	0.380575i	−0.871309	−	0.490735i	$-0.836728\pi$
$277$	−6.33402	+	6.33402i	−0.380575	+	0.380575i	0.490735	+	0.871309i	$0.336728\pi$
$278$	−11.0130	+	11.0130i	−0.660513	+	0.660513i
$279$		0			0
$280$	0.726656	−	6.28267i	0.0434260	−	0.375461i
$281$		−	12.6685i		−	0.755739i	−0.925859	−	0.377869i	$-0.876657\pi$
$281$		−	12.6685i		−	0.755739i	0.925859	−	0.377869i	$-0.123343\pi$
$282$		0			0
$283$	−2.41468	−	2.41468i	−0.143538	−	0.143538i	0.631686	−	0.775224i	$-0.282363\pi$
$283$	−2.41468	−	2.41468i	−0.143538	−	0.143538i	−0.775224	+	0.631686i	$0.782363\pi$
$284$	−10.2266			−0.606839
$285$		0			0
$286$	16.5653			0.979529
$287$	9.28480	+	9.28480i	0.548064	+	0.548064i
$288$		0			0
$289$		−	13.0000i		−	0.764706i
$290$	−2.95568	−	3.72882i	−0.173564	−	0.218964i
$291$		0			0
$292$	−3.28267	+	3.28267i	−0.192104	+	0.192104i
$293$	−13.6052	+	13.6052i	−0.794824	+	0.794824i	−0.982274	−	0.187450i	$-0.939978\pi$
$293$	−13.6052	+	13.6052i	−0.794824	+	0.794824i	0.187450	+	0.982274i	$0.439978\pi$
$294$		0			0
$295$	−4.00000	−	0.462642i	−0.232889	−	0.0269360i
$296$			6.17068i			0.358663i
$297$		0			0
$298$	−13.9193	−	13.9193i	−0.806326	−	0.806326i
$299$	4.95634			0.286633
$300$		0			0
$301$	15.6774			0.903629
$302$	−2.64174	−	2.64174i	−0.152015	−	0.152015i
$303$		0			0
$304$		−	0.778008i		−	0.0446218i
$305$	4.55658	+	0.527017i	0.260909	+	0.0301769i
$306$		0			0
$307$	−0.990671	+	0.990671i	−0.0565406	+	0.0565406i	−0.734812	−	0.678271i	$-0.762729\pi$
$307$	−0.990671	+	0.990671i	−0.0565406	+	0.0565406i	0.678271	+	0.734812i	$0.262729\pi$
$308$	6.68450	−	6.68450i	0.380885	−	0.380885i
$309$		0			0
$310$	3.78734	+	4.77801i	0.215106	+	0.271373i
$311$			15.6554i			0.887734i	0.896093	+	0.443867i	$0.146394\pi$
$311$			15.6554i			0.887734i	−0.896093	+	0.443867i	$0.853606\pi$
$312$		0			0
$313$	8.23132	+	8.23132i	0.465262	+	0.465262i	0.900375	−	0.435114i	$-0.143292\pi$
$313$	8.23132	+	8.23132i	0.465262	+	0.465262i	−0.435114	+	0.900375i	$0.643292\pi$
$314$	−22.7679			−1.28487
$315$		0			0
$316$	5.55602			0.312550
$317$	14.4825	+	14.4825i	0.813416	+	0.813416i	0.985144	−	0.171728i	$-0.0549350\pi$
$317$	14.4825	+	14.4825i	0.813416	+	0.813416i	−0.171728	+	0.985144i	$0.554935\pi$
$318$		0			0
$319$		−	7.11203i		−	0.398197i
$320$	−0.256912	+	2.22126i	−0.0143618	+	0.124172i
$321$		0			0
$322$	2.00000	−	2.00000i	0.111456	−	0.111456i
$323$	1.10027	−	1.10027i	0.0612206	−	0.0612206i
$324$		0			0
$325$	13.0607	+	21.0607i	0.724476	+	1.16824i
$326$			0.627889i			0.0347755i
$327$		0			0
$328$	−3.28267	−	3.28267i	−0.181255	−	0.181255i
$329$	29.0838			1.60344
$330$		0			0
$331$	6.44398			0.354193			0.177097	−	0.984193i	$-0.443329\pi$
$331$	6.44398			0.354193			0.177097	+	0.984193i	$0.443329\pi$
$332$	−9.36255	−	9.36255i	−0.513837	−	0.513837i
$333$		0			0
$334$		−	8.17997i		−	0.447588i
$335$	25.1551	−	19.9394i	1.37437	−	1.08941i
$336$		0			0
$337$	11.0607	−	11.0607i	0.602514	−	0.602514i	−0.338465	−	0.940979i	$-0.609908\pi$
$337$	11.0607	−	11.0607i	0.602514	−	0.602514i	0.940979	+	0.338465i	$0.109908\pi$
$338$	8.17793	−	8.17793i	0.444821	−	0.444821i
$339$		0			0
$340$	−3.50466	+	2.77801i	−0.190067	+	0.150659i
$341$			9.11317i			0.493506i
$342$		0			0
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$	−5.54279			−0.298847
$345$		0			0
$346$	24.0187			1.29125
$347$	−0.700510	−	0.700510i	−0.0376054	−	0.0376054i	0.688054	−	0.725659i	$-0.258465\pi$
$347$	−0.700510	−	0.700510i	−0.0376054	−	0.0376054i	−0.725659	+	0.688054i	$0.758465\pi$
$348$		0			0
$349$		−	4.90663i		−	0.262646i	−0.991340	−	0.131323i	$-0.958078\pi$
$349$		−	4.90663i		−	0.262646i	0.991340	−	0.131323i	$-0.0419224\pi$
$350$	13.7688	+	3.22819i	0.735971	+	0.172554i
$351$		0			0
$352$	−2.36333	+	2.36333i	−0.125966	+	0.125966i
$353$	3.02831	−	3.02831i	0.161180	−	0.161180i	−0.621909	−	0.783090i	$-0.713643\pi$
$353$	3.02831	−	3.02831i	0.161180	−	0.161180i	0.783090	+	0.621909i	$0.213643\pi$
$354$		0			0
$355$	2.62734	−	22.7160i	0.139445	−	1.20564i
$356$		−	9.21218i		−	0.488244i
$357$		0			0
$358$	11.1120	+	11.1120i	0.587289	+	0.587289i
$359$	−1.80078			−0.0950415			−0.0475208	−	0.998870i	$-0.515132\pi$
$359$	−1.80078			−0.0950415			−0.0475208	+	0.998870i	$0.515132\pi$
$360$		0			0
$361$	18.3947			0.968142
$362$	9.16267	+	9.16267i	0.481579	+	0.481579i
$363$		0			0
$364$		−	14.0187i		−	0.734777i
$365$	−6.44831	−	8.13503i	−0.337520	−	0.425807i
$366$		0			0
$367$	17.1120	−	17.1120i	0.893241	−	0.893241i	−0.101586	−	0.994827i	$-0.532392\pi$
$367$	17.1120	−	17.1120i	0.893241	−	0.893241i	0.994827	+	0.101586i	$0.0323917\pi$
$368$	−0.707107	+	0.707107i	−0.0368605	+	0.0368605i
$369$		0			0
$370$	−13.7067	−	1.58532i	−0.712576	−	0.0824169i
$371$			25.6275i			1.33051i
$372$		0			0
$373$	−24.0993	−	24.0993i	−1.24782	−	1.24782i	−0.956683	−	0.291132i	$-0.905968\pi$
$373$	−24.0993	−	24.0993i	−1.24782	−	1.24782i	−0.291132	−	0.956683i	$-0.594032\pi$
$374$	−6.68450			−0.345647
$375$		0			0
$376$	−10.2827			−0.530288
$377$	−7.45763	−	7.45763i	−0.384088	−	0.384088i
$378$		0			0
$379$		−	13.4020i		−	0.688413i	−0.938894	−	0.344206i	$-0.888148\pi$
$379$		−	13.4020i		−	0.688413i	0.938894	−	0.344206i	$-0.111852\pi$
$380$	1.72816	+	0.199879i	0.0886526	+	0.0102536i
$381$		0			0
$382$	1.27334	−	1.27334i	0.0651499	−	0.0651499i
$383$	−0.0726218	+	0.0726218i	−0.00371080	+	0.00371080i	−0.708960	−	0.705249i	$-0.750835\pi$
$383$	−0.0726218	+	0.0726218i	−0.00371080	+	0.00371080i	0.705249	+	0.708960i	$0.250835\pi$
$384$		0			0
$385$	13.1307	+	16.5653i	0.669202	+	0.844248i
$386$			23.6683i			1.20468i
$387$		0			0
$388$	0.778008	+	0.778008i	0.0394974	+	0.0394974i
$389$	−9.07173			−0.459955			−0.229977	−	0.973196i	$-0.573865\pi$
$389$	−9.07173			−0.459955			−0.229977	+	0.973196i	$0.573865\pi$
$390$		0			0
$391$	−2.00000			−0.101144
$392$	−0.707107	−	0.707107i	−0.0357143	−	0.0357143i
$393$		0			0
$394$			16.0187i			0.807008i
$395$	−1.42741	+	12.3414i	−0.0718206	+	0.620961i
$396$		0			0
$397$	20.5327	−	20.5327i	1.03050	−	1.03050i	0.0309843	−	0.999520i	$-0.490136\pi$
$397$	20.5327	−	20.5327i	1.03050	−	1.03050i	0.999520	−	0.0309843i	$-0.00986419\pi$
$398$	1.02765	−	1.02765i	0.0515113	−	0.0515113i
$399$		0			0
$400$	−4.86799	−	1.14134i	−0.243400	−	0.0570668i
$401$			31.4662i			1.57135i	0.618641	+	0.785674i	$0.287684\pi$
$401$			31.4662i			1.57135i	−0.618641	+	0.785674i	$0.712316\pi$
$402$		0			0
$403$	9.55602	+	9.55602i	0.476019	+	0.476019i
$404$	−11.6408			−0.579154
$405$		0			0
$406$	−6.01866			−0.298701
$407$	−14.5833	−	14.5833i	−0.722869	−	0.722869i
$408$		0			0
$409$		−	34.0373i		−	1.68304i	−0.540228	−	0.841518i	$-0.681662\pi$
$409$		−	34.0373i		−	1.68304i	0.540228	−	0.841518i	$-0.318338\pi$
$410$	8.13503	−	6.44831i	0.401760	−	0.318459i
$411$		0			0
$412$	13.2920	−	13.2920i	0.654850	−	0.654850i
$413$	−3.60156	+	3.60156i	−0.177221	+	0.177221i
$414$		0			0
$415$	23.2020	−	18.3913i	1.13894	−	0.902794i
$416$			4.95634i			0.243005i
$417$		0			0
$418$	1.83869	+	1.83869i	0.0899332	+	0.0899332i
$419$	−16.4105			−0.801706			−0.400853	−	0.916142i	$-0.631286\pi$
$419$	−16.4105			−0.801706			−0.400853	+	0.916142i	$0.631286\pi$
$420$		0			0
$421$	14.2500			0.694501			0.347251	−	0.937772i	$-0.387115\pi$
$421$	14.2500			0.694501			0.347251	+	0.937772i	$0.387115\pi$
$422$	−13.4416	−	13.4416i	−0.654328	−	0.654328i
$423$		0			0
$424$		−	9.06068i		−	0.440026i
$425$	−5.27029	−	8.49847i	−0.255647	−	0.412237i
$426$		0			0
$427$	4.10270	−	4.10270i	0.198544	−	0.198544i
$428$	11.7498	−	11.7498i	0.567947	−	0.567947i
$429$		0			0
$430$	1.42401	−	12.3120i	0.0686718	−	0.593736i
$431$			19.4256i			0.935699i	0.883808	+	0.467850i	$0.154971\pi$
$431$			19.4256i			0.935699i	−0.883808	+	0.467850i	$0.845029\pi$
$432$		0			0
$433$	13.7687	+	13.7687i	0.661680	+	0.661680i	0.955776	−	0.294096i	$-0.0950184\pi$
$433$	13.7687	+	13.7687i	0.661680	+	0.661680i	−0.294096	+	0.955776i	$0.595018\pi$
$434$	7.71215			0.370195
$435$		0			0
$436$	−8.79667			−0.421284
$437$	0.550135	+	0.550135i	0.0263165	+	0.0263165i
$438$		0			0
$439$			19.5560i			0.933358i	0.884427	+	0.466679i	$0.154550\pi$
$439$			19.5560i			0.933358i	−0.884427	+	0.466679i	$0.845450\pi$
$440$	−4.64240	−	5.85673i	−0.221318	−	0.279209i
$441$		0			0
$442$	−7.00933	+	7.00933i	−0.333400	+	0.333400i
$443$	−25.4096	+	25.4096i	−1.20725	+	1.20725i	−0.235332	+	0.971915i	$0.575618\pi$
$443$	−25.4096	+	25.4096i	−1.20725	+	1.20725i	−0.971915	+	0.235332i	$0.924382\pi$
$444$		0			0
$445$	20.4626	+	2.36672i	0.970022	+	0.112193i
$446$			1.71497i			0.0812059i
$447$		0			0
$448$	2.00000	+	2.00000i	0.0944911	+	0.0944911i
$449$	−0.158436			−0.00747708			−0.00373854	−	0.999993i	$-0.501190\pi$
$449$	−0.158436			−0.00747708			−0.00373854	+	0.999993i	$0.501190\pi$
$450$		0			0
$451$	15.5161			0.730623
$452$	7.47083	+	7.47083i	0.351398	+	0.351398i
$453$		0			0
$454$			12.0514i			0.565598i
$455$	31.1391	+	3.60156i	1.45982	+	0.168844i
$456$		0			0
$457$	−2.79667	+	2.79667i	−0.130822	+	0.130822i	−0.769486	−	0.638664i	$-0.779488\pi$
$457$	−2.79667	+	2.79667i	−0.130822	+	0.130822i	0.638664	+	0.769486i	$0.279488\pi$
$458$	0.277633	−	0.277633i	0.0129730	−	0.0129730i
$459$		0			0
$460$	−1.38900	−	1.75233i	−0.0647626	−	0.0817029i
$461$		−	4.32846i		−	0.201596i	−0.994907	−	0.100798i	$-0.967860\pi$
$461$		−	4.32846i		−	0.201596i	0.994907	−	0.100798i	$-0.0321396\pi$
$462$		0			0
$463$	−4.22199	−	4.22199i	−0.196213	−	0.196213i	0.602162	−	0.798374i	$-0.294306\pi$
$463$	−4.22199	−	4.22199i	−0.196213	−	0.196213i	−0.798374	+	0.602162i	$0.794306\pi$
$464$	2.12792			0.0987861
$465$		0			0
$466$	4.82936			0.223716
$467$	−13.9191	−	13.9191i	−0.644101	−	0.644101i	0.307460	−	0.951561i	$-0.400521\pi$
$467$	−13.9191	−	13.9191i	−0.644101	−	0.644101i	−0.951561	+	0.307460i	$0.900521\pi$
$468$		0			0
$469$		−	40.6027i		−	1.87486i
$470$	2.64174	−	22.8405i	0.121854	−	1.05355i
$471$		0			0
$472$	1.27334	−	1.27334i	0.0586104	−	0.0586104i
$473$	13.0994	−	13.0994i	0.602312	−	0.602312i
$474$		0			0
$475$	−0.887968	+	3.78734i	−0.0407428	+	0.173775i
$476$			5.65685i			0.259281i
$477$		0			0
$478$	−6.24065	−	6.24065i	−0.285441	−	0.285441i
$479$	17.6248			0.805299			0.402650	−	0.915354i	$-0.368089\pi$
$479$	17.6248			0.805299			0.402650	+	0.915354i	$0.368089\pi$
$480$		0			0
$481$	−30.5840			−1.39451
$482$	7.79796	+	7.79796i	0.355188	+	0.355188i
$483$		0			0
$484$		−	0.170641i		−	0.00775640i
$485$	−1.92804	+	1.52828i	−0.0875477	+	0.0693955i
$486$		0			0
$487$	−12.6074	+	12.6074i	−0.571294	+	0.571294i	−0.932490	−	0.361196i	$-0.882369\pi$
$487$	−12.6074	+	12.6074i	−0.571294	+	0.571294i	0.361196	+	0.932490i	$0.382369\pi$
$488$	−1.45052	+	1.45052i	−0.0656622	+	0.0656622i
$489$		0			0
$490$	1.75233	−	1.38900i	0.0791623	−	0.0627488i
$491$			7.22950i			0.326263i	0.986604	+	0.163131i	$0.0521595\pi$
$491$			7.22950i			0.326263i	−0.986604	+	0.163131i	$0.947841\pi$
$492$		0			0
$493$	3.00933	+	3.00933i	0.135533	+	0.135533i
$494$	3.85607			0.173493
$495$		0			0
$496$	−2.72666			−0.122430
$497$	−20.4533	−	20.4533i	−0.917454	−	0.917454i
$498$		0			0
$499$			29.4533i			1.31851i	0.751919	+	0.659256i	$0.229129\pi$
$499$			29.4533i			1.31851i	−0.751919	+	0.659256i	$0.770871\pi$
$500$	3.78585	−	10.5199i	0.169308	−	0.470462i
$501$		0			0
$502$	9.37266	−	9.37266i	0.418322	−	0.418322i
$503$	−19.8980	+	19.8980i	−0.887208	+	0.887208i	−0.994254	−	0.107046i	$-0.965861\pi$
$503$	−19.8980	+	19.8980i	−0.887208	+	0.887208i	0.107046	+	0.994254i	$0.465861\pi$
$504$		0			0
$505$	2.99067	−	25.8573i	0.133083	−	1.15064i
$506$		−	3.34225i		−	0.148581i
$507$		0			0
$508$	−2.50466	−	2.50466i	−0.111127	−	0.111127i
$509$	34.6680			1.53663			0.768317	−	0.640070i	$-0.221095\pi$
$509$	34.6680			1.53663			0.768317	+	0.640070i	$0.221095\pi$
$510$		0			0
$511$	−13.1307			−0.580867
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$			13.4533i			0.593400i
$515$	26.1101	+	32.9399i	1.15055	+	1.45150i
$516$		0			0
$517$	24.3013	−	24.3013i	1.06877	−	1.06877i
$518$	−12.3414	+	12.3414i	−0.542248	+	0.542248i
$519$		0			0
$520$	−11.0093	−	1.27334i	−0.482791	−	0.0558398i
$521$		−	7.55664i		−	0.331062i	−0.986205	−	0.165531i	$-0.947066\pi$
$521$		−	7.55664i		−	0.331062i	0.986205	−	0.165531i	$-0.0529339\pi$
$522$		0			0
$523$	16.3820	+	16.3820i	0.716334	+	0.716334i	0.967853	−	0.251518i	$-0.0809299\pi$
$523$	16.3820	+	16.3820i	0.716334	+	0.716334i	−0.251518	+	0.967853i	$0.580930\pi$
$524$	13.1409			0.574062
$525$		0			0
$526$	14.1214			0.615721
$527$	−3.85607	−	3.85607i	−0.167973	−	0.167973i
$528$		0			0
$529$		−	1.00000i		−	0.0434783i
$530$	20.1261	+	2.32780i	0.874223	+	0.101113i
$531$		0			0
$532$	1.55602	−	1.55602i	0.0674618	−	0.0674618i
$533$	16.2701	−	16.2701i	0.704734	−	0.704734i
$534$		0			0
$535$	23.0807	+	29.1180i	0.997864	+	1.25888i
$536$			14.3552i			0.620051i
$537$		0			0
$538$	−7.60737	−	7.60737i	−0.327977	−	0.327977i
$539$	3.34225			0.143961
$540$		0			0
$541$	22.0373			0.947458			0.473729	−	0.880671i	$-0.342908\pi$
$541$	22.0373			0.947458			0.473729	+	0.880671i	$0.342908\pi$
$542$	7.85739	+	7.85739i	0.337504	+	0.337504i
$543$		0			0
$544$		−	2.00000i		−	0.0857493i
$545$	2.25997	−	19.5397i	0.0968064	−	0.836988i
$546$		0			0
$547$	−5.83869	+	5.83869i	−0.249644	+	0.249644i	−0.820825	−	0.571180i	$-0.806486\pi$
$547$	−5.83869	+	5.83869i	−0.249644	+	0.249644i	0.571180	+	0.820825i	$0.306486\pi$
$548$	8.17134	−	8.17134i	0.349062	−	0.349062i
$549$		0			0
$550$	14.2020	−	8.80731i	0.605576	−	0.375545i
$551$		−	1.65554i		−	0.0705282i
$552$		0			0
$553$	11.1120	+	11.1120i	0.472532	+	0.472532i
$554$	8.95766			0.380575
$555$		0			0
$556$	15.5747			0.660513
$557$	16.5326	+	16.5326i	0.700510	+	0.700510i	0.964520	−	0.264010i	$-0.0850452\pi$
$557$	16.5326	+	16.5326i	0.700510	+	0.700510i	−0.264010	+	0.964520i	$0.585045\pi$
$558$		0			0
$559$		−	27.4720i		−	1.16194i
$560$	−4.95634	+	3.92870i	−0.209444	+	0.166018i
$561$		0			0
$562$	−8.95798	+	8.95798i	−0.377869	+	0.377869i
$563$	28.2329	−	28.2329i	1.18987	−	1.18987i	0.212773	−	0.977102i	$-0.431750\pi$
$563$	28.2329	−	28.2329i	1.18987	−	1.18987i	0.977102	−	0.212773i	$-0.0682496\pi$
$564$		0			0
$565$	−18.5140	+	14.6753i	−0.778890	+	0.617395i
$566$			3.41487i			0.143538i
$567$		0			0
$568$	7.23132	+	7.23132i	0.303419	+	0.303419i
$569$	−12.4404			−0.521527			−0.260764	−	0.965403i	$-0.583974\pi$
$569$	−12.4404			−0.521527			−0.260764	+	0.965403i	$0.583974\pi$
$570$		0			0
$571$	−27.9486			−1.16961			−0.584807	−	0.811172i	$-0.698830\pi$
$571$	−27.9486			−1.16961			−0.584807	+	0.811172i	$0.698830\pi$
$572$	−11.7135	−	11.7135i	−0.489765	−	0.489765i
$573$		0			0
$574$		−	13.1307i		−	0.548064i
$575$	4.24924	−	2.63514i	0.177205	−	0.109893i
$576$		0			0
$577$	29.5840	−	29.5840i	1.23160	−	1.23160i	0.268248	−	0.963350i	$-0.413555\pi$
$577$	29.5840	−	29.5840i	1.23160	−	1.23160i	0.963350	−	0.268248i	$-0.0864448\pi$
$578$	−9.19239	+	9.19239i	−0.382353	+	0.382353i
$579$		0			0
$580$	−0.546687	+	4.72666i	−0.0226999	+	0.196264i
$581$		−	37.4502i		−	1.55370i
$582$		0			0
$583$	21.4134	+	21.4134i	0.886851	+	0.886851i
$584$	4.64240			0.192104
$585$		0			0
$586$	19.2406			0.794824
$587$	−5.65685	−	5.65685i	−0.233483	−	0.233483i	0.580662	−	0.814145i	$-0.302794\pi$
$587$	−5.65685	−	5.65685i	−0.233483	−	0.233483i	−0.814145	+	0.580662i	$0.802794\pi$
$588$		0			0
$589$			2.12136i			0.0874091i
$590$	2.50129	+	3.15556i	0.102976	+	0.129913i
$591$		0			0
$592$	4.36333	−	4.36333i	0.179332	−	0.179332i
$593$	3.85607	−	3.85607i	0.158350	−	0.158350i	−0.623485	−	0.781835i	$-0.714284\pi$
$593$	3.85607	−	3.85607i	0.158350	−	0.158350i	0.781835	+	0.623485i	$0.214284\pi$
$594$		0			0
$595$	−12.5653	−	1.45331i	−0.515129	−	0.0595800i
$596$			19.6849i			0.806326i
$597$		0			0
$598$	−3.50466	−	3.50466i	−0.143316	−	0.143316i
$599$	0.604432			0.0246964			0.0123482	−	0.999924i	$-0.496069\pi$
$599$	0.604432			0.0246964			0.0123482	+	0.999924i	$0.496069\pi$
$600$		0			0
$601$	−12.8294			−0.523320			−0.261660	−	0.965160i	$-0.584270\pi$
$601$	−12.8294			−0.523320			−0.261660	+	0.965160i	$0.584270\pi$
$602$	−11.0856	−	11.0856i	−0.451814	−	0.451814i
$603$		0			0
$604$			3.73599i			0.152015i
$605$	0.379037	+	0.0438396i	0.0154101	+	0.00178233i
$606$		0			0
$607$	11.0514	−	11.0514i	0.448561	−	0.448561i	−0.446315	−	0.894876i	$-0.647264\pi$
$607$	11.0514	−	11.0514i	0.448561	−	0.448561i	0.894876	+	0.446315i	$0.147264\pi$
$608$	−0.550135	+	0.550135i	−0.0223109	+	0.0223109i
$609$		0			0
$610$	−2.84934	−	3.59465i	−0.115366	−	0.145543i
$611$		−	50.9645i		−	2.06180i
$612$		0			0
$613$	30.2534	+	30.2534i	1.22192	+	1.22192i	0.966948	+	0.254974i	$0.0820670\pi$
$613$	30.2534	+	30.2534i	1.22192	+	1.22192i	0.254974	+	0.966948i	$0.417933\pi$
$614$	1.40102			0.0565406
$615$		0			0
$616$	−9.45331			−0.380885
$617$	−9.59874	−	9.59874i	−0.386431	−	0.386431i	0.486981	−	0.873412i	$-0.338098\pi$
$617$	−9.59874	−	9.59874i	−0.386431	−	0.386431i	−0.873412	+	0.486981i	$0.838098\pi$
$618$		0			0
$619$			38.1659i			1.53402i	0.641636	+	0.767009i	$0.278256\pi$
$619$			38.1659i			1.53402i	−0.641636	+	0.767009i	$0.721744\pi$
$620$	0.700510	−	6.05661i	0.0281332	−	0.243239i
$621$		0			0
$622$	11.0700	−	11.0700i	0.443867	−	0.443867i
$623$	18.4244	−	18.4244i	0.738156	−	0.738156i
$624$		0			0
$625$	22.3947	+	11.1120i	0.895788	+	0.444481i
$626$		−	11.6408i		−	0.465262i
$627$		0			0
$628$	16.0993	+	16.0993i	0.642433	+	0.642433i
$629$	12.3414			0.492082
$630$		0			0
$631$	−35.4720			−1.41212			−0.706058	−	0.708154i	$-0.749528\pi$
$631$	−35.4720			−1.41212			−0.706058	+	0.708154i	$0.749528\pi$
$632$	−3.92870	−	3.92870i	−0.156275	−	0.156275i
$633$		0			0
$634$		−	20.4813i		−	0.813416i
$635$	6.20699	−	4.92003i	0.246317	−	0.195246i
$636$		0			0
$637$	3.50466	−	3.50466i	0.138860	−	0.138860i
$638$	−5.02897	+	5.02897i	−0.199099	+	0.199099i
$639$		0			0
$640$	1.75233	−	1.38900i	0.0692670	−	0.0549052i
$641$			42.0068i			1.65917i	0.558381	+	0.829584i	$0.311423\pi$
$641$			42.0068i			1.65917i	−0.558381	+	0.829584i	$0.688577\pi$
$642$		0			0
$643$	−35.2814	−	35.2814i	−1.39136	−	1.39136i	−0.822285	−	0.569075i	$-0.807301\pi$
$643$	−35.2814	−	35.2814i	−1.39136	−	1.39136i	−0.569075	−	0.822285i	$-0.692699\pi$
$644$	−2.82843			−0.111456
$645$		0			0
$646$	−1.55602			−0.0612206
$647$	31.0797	+	31.0797i	1.22187	+	1.22187i	0.966967	+	0.254900i	$0.0820425\pi$
$647$	31.0797	+	31.0797i	1.22187	+	1.22187i	0.254900	+	0.966967i	$0.417957\pi$
$648$		0			0
$649$			6.01866i			0.236253i
$650$	5.65685	−	24.1274i	0.221880	−	0.946356i
$651$		0			0
$652$	0.443984	−	0.443984i	0.0173878	−	0.0173878i
$653$	−15.5827	+	15.5827i	−0.609800	+	0.609800i	−0.942894	−	0.333094i	$-0.891907\pi$
$653$	−15.5827	+	15.5827i	−0.609800	+	0.609800i	0.333094	+	0.942894i	$0.391907\pi$
$654$		0			0
$655$	−3.37605	+	29.1893i	−0.131913	+	1.14052i
$656$			4.64240i			0.181255i
$657$		0			0
$658$	−20.5653	−	20.5653i	−0.801721	−	0.801721i
$659$	34.5540			1.34603			0.673016	−	0.739628i	$-0.264999\pi$
$659$	34.5540			1.34603			0.673016	+	0.739628i	$0.264999\pi$
$660$		0			0
$661$	−20.4367			−0.794897			−0.397448	−	0.917625i	$-0.630104\pi$
$661$	−20.4367			−0.794897			−0.397448	+	0.917625i	$0.630104\pi$
$662$	−4.55658	−	4.55658i	−0.177097	−	0.177097i
$663$		0			0
$664$			13.2406i			0.513837i
$665$	3.05656	+	3.85607i	0.118528	+	0.149532i
$666$		0			0
$667$	−1.50466	+	1.50466i	−0.0582608	+	0.0582608i
$668$	−5.78411	+	5.78411i	−0.223794	+	0.223794i
$669$		0			0
$670$	−31.8867	−	3.68802i	−1.23189	−	0.142481i
$671$		−	6.85613i		−	0.264678i
$672$		0			0
$673$	−22.4720	−	22.4720i	−0.866231	−	0.866231i	0.125822	−	0.992053i	$-0.459843\pi$
$673$	−22.4720	−	22.4720i	−0.866231	−	0.866231i	−0.992053	+	0.125822i	$0.959843\pi$
$674$	−15.6422			−0.602514
$675$		0			0
$676$	−11.5653			−0.444821
$677$	−21.0892	−	21.0892i	−0.810524	−	0.810524i	0.174188	−	0.984712i	$-0.444270\pi$
$677$	−21.0892	−	21.0892i	−0.810524	−	0.810524i	−0.984712	+	0.174188i	$0.944270\pi$
$678$		0			0
$679$			3.11203i			0.119429i
$680$	4.44252	+	0.513824i	0.170363	+	0.0197042i
$681$		0			0
$682$	6.44398	−	6.44398i	0.246753	−	0.246753i
$683$	7.85739	−	7.85739i	0.300655	−	0.300655i	−0.540615	−	0.841270i	$-0.681808\pi$
$683$	7.85739	−	7.85739i	0.300655	−	0.300655i	0.841270	+	0.540615i	$0.181808\pi$
$684$		0			0
$685$	16.0514	+	20.2500i	0.613291	+	0.773712i
$686$			16.9706i			0.647939i
$687$		0			0
$688$	3.91934	+	3.91934i	0.149424	+	0.149424i
$689$	44.9078			1.71085
$690$		0			0
$691$	20.0373			0.762255			0.381128	−	0.924522i	$-0.375536\pi$
$691$	20.0373			0.762255			0.381128	+	0.924522i	$0.375536\pi$
$692$	−16.9838	−	16.9838i	−0.645626	−	0.645626i
$693$		0			0
$694$			0.990671i			0.0376054i
$695$	−4.00132	+	34.5954i	−0.151779	+	1.31228i
$696$		0			0
$697$	−6.56534	+	6.56534i	−0.248680	+	0.248680i
$698$	−3.46951	+	3.46951i	−0.131323	+	0.131323i
$699$		0			0
$700$	−7.45331	−	12.0187i	−0.281709	−	0.454263i
$701$		−	30.2519i		−	1.14260i	−0.820742	−	0.571299i	$-0.806440\pi$
$701$		−	30.2519i		−	1.14260i	0.820742	−	0.571299i	$-0.193560\pi$
$702$		0			0
$703$	−3.39470	−	3.39470i	−0.128034	−	0.128034i
$704$	3.34225			0.125966
$705$		0			0
$706$	−4.28267			−0.161180
$707$	−23.2817	−	23.2817i	−0.875598	−	0.875598i
$708$		0			0
$709$		−	18.4767i		−	0.693906i	−0.937882	−	0.346953i	$-0.887216\pi$
$709$		−	18.4767i		−	0.693906i	0.937882	−	0.346953i	$-0.112784\pi$
$710$	−17.9205	+	14.2048i	−0.672543	+	0.533098i
$711$		0			0
$712$	−6.51399	+	6.51399i	−0.244122	+	0.244122i
$713$	1.92804	−	1.92804i	0.0722056	−	0.0722056i
$714$		0			0
$715$	29.0280	−	23.0093i	1.08559	−	0.860500i
$716$		−	15.7148i		−	0.587289i
$717$		0			0
$718$	1.27334	+	1.27334i	0.0475208	+	0.0475208i
$719$	−27.9703			−1.04312			−0.521559	−	0.853215i	$-0.674649\pi$
$719$	−27.9703			−1.04312			−0.521559	+	0.853215i	$0.674649\pi$
$720$		0			0
$721$	53.1680			1.98008
$722$	−13.0070	−	13.0070i	−0.484071	−	0.484071i
$723$		0			0
$724$		−	12.9580i		−	0.481579i
$725$	−10.3587	−	2.42867i	−0.384712	−	0.0901985i
$726$		0			0
$727$	−8.35994	+	8.35994i	−0.310053	+	0.310053i	−0.844930	−	0.534877i	$-0.820358\pi$
$727$	−8.35994	+	8.35994i	−0.310053	+	0.310053i	0.534877	+	0.844930i	$0.320358\pi$
$728$	−9.91269	+	9.91269i	−0.367389	+	0.367389i
$729$		0			0
$730$	−1.19269	+	10.3120i	−0.0441433	+	0.381663i
$731$			11.0856i			0.410015i
$732$		0			0
$733$	29.0573	+	29.0573i	1.07326	+	1.07326i	0.997096	+	0.0761599i	$0.0242659\pi$
$733$	29.0573	+	29.0573i	1.07326	+	1.07326i	0.0761599	+	0.997096i	$0.475734\pi$
$734$	−24.2001			−0.893241
$735$		0			0
$736$	1.00000			0.0368605
$737$	−33.9261	−	33.9261i	−1.24968	−	1.24968i
$738$		0			0
$739$			12.4626i			0.458446i	0.973374	+	0.229223i	$0.0736185\pi$
$739$			12.4626i			0.458446i	−0.973374	+	0.229223i	$0.926382\pi$
$740$	8.57110	+	10.8131i	0.315080	+	0.397497i
$741$		0			0
$742$	18.1214	−	18.1214i	0.665256	−	0.665256i
$743$	−0.0726218	+	0.0726218i	−0.00266424	+	0.00266424i	−0.708438	−	0.705773i	$-0.750600\pi$
$743$	−0.0726218	+	0.0726218i	−0.00266424	+	0.00266424i	0.705773	+	0.708438i	$0.250600\pi$
$744$		0			0
$745$	−43.7253	−	5.05729i	−1.60197	−	0.185285i
$746$			34.0816i			1.24782i
$747$		0			0
$748$	4.72666	+	4.72666i	0.172824	+	0.172824i
$749$	46.9991			1.71731
$750$		0			0
$751$	−24.9907			−0.911923			−0.455961	−	0.890000i	$-0.650704\pi$
$751$	−24.9907			−0.911923			−0.455961	+	0.890000i	$0.650704\pi$
$752$	7.27095	+	7.27095i	0.265144	+	0.265144i
$753$		0			0
$754$			10.5467i			0.384088i
$755$	−8.29859	−	0.959819i	−0.302017	−	0.0349314i
$756$		0			0
$757$	7.70668	−	7.70668i	0.280104	−	0.280104i	−0.553046	−	0.833150i	$-0.686535\pi$
$757$	7.70668	−	7.70668i	0.280104	−	0.280104i	0.833150	+	0.553046i	$0.186535\pi$
$758$	−9.47662	+	9.47662i	−0.344206	+	0.344206i
$759$		0			0
$760$	−1.08066	−	1.36333i	−0.0391995	−	0.0494531i
$761$		−	38.6099i		−	1.39961i	−0.714335	−	0.699804i	$-0.753271\pi$
$761$		−	38.6099i		−	1.39961i	0.714335	−	0.699804i	$-0.246729\pi$
$762$		0			0
$763$	−17.5933	−	17.5933i	−0.636921	−	0.636921i
$764$	−1.80078			−0.0651499
$765$		0			0
$766$	0.102703			0.00371080
$767$	6.31113	+	6.31113i	0.227882	+	0.227882i
$768$		0			0
$769$			31.4906i			1.13558i	0.823173	+	0.567791i	$0.192202\pi$
$769$			31.4906i			1.13558i	−0.823173	+	0.567791i	$0.807798\pi$
$770$	2.42867	−	20.9983i	0.0875231	−	0.756725i
$771$		0			0
$772$	16.7360	−	16.7360i	0.602341	−	0.602341i
$773$	2.73269	−	2.73269i	0.0982879	−	0.0982879i	−0.656253	−	0.754541i	$-0.727860\pi$
$773$	2.73269	−	2.73269i	0.0982879	−	0.0982879i	0.754541	+	0.656253i	$0.227860\pi$
$774$		0			0
$775$	13.2733	+	3.11203i	0.476793	+	0.111787i
$776$		−	1.10027i		−	0.0394974i
$777$		0			0
$778$	6.41468	+	6.41468i	0.229977	+	0.229977i
$779$	3.61182			0.129407
$780$		0			0
$781$	−34.1800			−1.22306
$782$	1.41421	+	1.41421i	0.0505722	+	0.0505722i
$783$		0			0
$784$			1.00000i			0.0357143i
$785$	−39.8969	+	31.6247i	−1.42398	+	1.12873i
$786$		0			0
$787$	−24.4333	+	24.4333i	−0.870954	+	0.870954i	−0.992576	−	0.121622i	$-0.961190\pi$
$787$	−24.4333	+	24.4333i	−0.870954	+	0.870954i	0.121622	+	0.992576i	$0.461190\pi$
$788$	11.3269	−	11.3269i	0.403504	−	0.403504i
$789$		0			0
$790$	9.73599	−	7.71733i	0.346391	−	0.274570i
$791$			29.8833i			1.06253i
$792$		0			0
$793$	−7.18930	−	7.18930i	−0.255299	−	0.255299i
$794$	−29.0376			−1.03050
$795$		0			0
$796$	−1.45331			−0.0515113
$797$	26.6782	+	26.6782i	0.944992	+	0.944992i	0.998564	−	0.0535723i	$-0.0170607\pi$
$797$	26.6782	+	26.6782i	0.944992	+	0.944992i	−0.0535723	+	0.998564i	$0.517061\pi$
$798$		0			0
$799$			20.5653i			0.727550i
$800$	2.63514	+	4.24924i	0.0931664	+	0.150233i
$801$		0			0
$802$	22.2500	−	22.2500i	0.785674	−	0.785674i
$803$	−10.9715	+	10.9715i	−0.387176	+	0.387176i
$804$		0			0
$805$	0.726656	−	6.28267i	0.0256113	−	0.221435i
$806$		−	13.5142i		−	0.476019i
$807$		0			0
$808$	8.23132	+	8.23132i	0.289577	+	0.289577i
$809$	−14.3835			−0.505695			−0.252848	−	0.967506i	$-0.581367\pi$
$809$	−14.3835			−0.505695			−0.252848	+	0.967506i	$0.581367\pi$
$810$		0			0
$811$	−30.2241			−1.06131			−0.530655	−	0.847588i	$-0.678054\pi$
$811$	−30.2241			−1.06131			−0.530655	+	0.847588i	$0.678054\pi$
$812$	4.25583	+	4.25583i	0.149350	+	0.149350i
$813$		0			0
$814$			20.6240i			0.722869i
$815$	0.872140	+	1.10027i	0.0305497	+	0.0385408i
$816$		0			0
$817$	3.04928	−	3.04928i	0.106681	−	0.106681i
$818$	−24.0680	+	24.0680i	−0.841518	+	0.841518i
$819$		0			0
$820$	−10.3120	−	1.19269i	−0.360110	−	0.0416505i
$821$			31.4398i			1.09726i	0.836066	+	0.548629i	$0.184850\pi$
$821$			31.4398i			1.09726i	−0.836066	+	0.548629i	$0.815150\pi$
$822$		0			0
$823$	9.24998	+	9.24998i	0.322434	+	0.322434i	0.849700	−	0.527266i	$-0.176783\pi$
$823$	9.24998	+	9.24998i	0.322434	+	0.322434i	−0.527266	+	0.849700i	$0.676783\pi$
$824$	−18.7977			−0.654850
$825$		0			0
$826$	5.09337			0.177221
$827$	13.8051	+	13.8051i	0.480049	+	0.480049i	0.905147	−	0.425098i	$-0.139760\pi$
$827$	13.8051	+	13.8051i	0.480049	+	0.480049i	−0.425098	+	0.905147i	$0.639760\pi$
$828$		0			0
$829$		−	4.70122i		−	0.163280i	−0.996662	−	0.0816401i	$-0.973984\pi$
$829$		−	4.70122i		−	0.163280i	0.996662	−	0.0816401i	$-0.0260158\pi$
$830$	−29.4109	−	3.40168i	−1.02087	−	0.118074i
$831$		0			0
$832$	3.50466	−	3.50466i	0.121502	−	0.121502i
$833$	−1.41421	+	1.41421i	−0.0489996	+	0.0489996i
$834$		0			0
$835$	−11.3620	−	14.3340i	−0.393199	−	0.496049i
$836$		−	2.60030i		−	0.0899332i
$837$		0			0
$838$	11.6040	+	11.6040i	0.400853	+	0.400853i
$839$	−18.9070			−0.652742			−0.326371	−	0.945242i	$-0.605826\pi$
$839$	−18.9070			−0.652742			−0.326371	+	0.945242i	$0.605826\pi$
$840$		0			0
$841$	−24.4720			−0.843861
$842$	−10.0763	−	10.0763i	−0.347251	−	0.347251i
$843$		0			0
$844$			19.0093i			0.654328i
$845$	2.97127	−	25.6896i	0.102215	−	0.883750i
$846$		0			0
$847$	0.341281	−	0.341281i	0.0117266	−	0.0117266i
$848$	−6.40687	+	6.40687i	−0.220013	+	0.220013i
$849$		0			0
$850$	−2.28267	+	9.73599i	−0.0782950	+	0.333942i
$851$			6.17068i			0.211528i
$852$		0			0
$853$	20.9580	+	20.9580i	0.717587	+	0.717587i	0.968111	−	0.250523i	$-0.0806026\pi$
$853$	20.9580	+	20.9580i	0.717587	+	0.717587i	−0.250523	+	0.968111i	$0.580603\pi$
$854$	−5.80210			−0.198544
$855$		0			0
$856$	−16.6167			−0.567947
$857$	−18.1981	−	18.1981i	−0.621635	−	0.621635i	0.324314	−	0.945949i	$-0.394866\pi$
$857$	−18.1981	−	18.1981i	−0.621635	−	0.621635i	−0.945949	+	0.324314i	$0.894866\pi$
$858$		0			0
$859$			22.1214i			0.754771i	0.926056	+	0.377386i	$0.123177\pi$
$859$			22.1214i			0.754771i	−0.926056	+	0.377386i	$0.876823\pi$
$860$	−9.71281	+	7.69896i	−0.331204	+	0.262532i
$861$		0			0
$862$	13.7360	−	13.7360i	0.467850	−	0.467850i
$863$	−29.7975	+	29.7975i	−1.01432	+	1.01432i	−0.0144224	+	0.999896i	$0.504591\pi$
$863$	−29.7975	+	29.7975i	−1.01432	+	1.01432i	−0.999896	+	0.0144224i	$0.995409\pi$
$864$		0			0
$865$	42.0887	−	33.3620i	1.43106	−	1.13434i
$866$		−	19.4719i		−	0.661680i
$867$		0			0
$868$	−5.45331	−	5.45331i	−0.185098	−	0.185098i
$869$	18.5696			0.629930
$870$		0			0
$871$	−71.1493			−2.41080
$872$	6.22018	+	6.22018i	0.210642	+	0.210642i
$873$		0			0
$874$		−	0.778008i		−	0.0263165i
$875$	28.6114	−	13.4680i	0.967242	−	0.455302i
$876$		0			0
$877$	−3.89004	+	3.89004i	−0.131357	+	0.131357i	−0.769729	−	0.638371i	$-0.779608\pi$
$877$	−3.89004	+	3.89004i	−0.131357	+	0.131357i	0.638371	+	0.769729i	$0.279608\pi$
$878$	13.8282	−	13.8282i	0.466679	−	0.466679i
$879$		0			0
$880$	−0.858664	+	7.42401i	−0.0289456	+	0.250263i
$881$			10.6132i			0.357568i	0.983888	+	0.178784i	$0.0572163\pi$
$881$			10.6132i			0.357568i	−0.983888	+	0.178784i	$0.942784\pi$
$882$		0			0
$883$	−2.28267	−	2.28267i	−0.0768180	−	0.0768180i	0.667654	−	0.744472i	$-0.267299\pi$
$883$	−2.28267	−	2.28267i	−0.0768180	−	0.0768180i	−0.744472	+	0.667654i	$0.767299\pi$
$884$	9.91269			0.333400
$885$		0			0
$886$	35.9346			1.20725
$887$	15.3565	+	15.3565i	0.515620	+	0.515620i	0.916243	−	0.400623i	$-0.131206\pi$
$887$	15.3565	+	15.3565i	0.515620	+	0.515620i	−0.400623	+	0.916243i	$0.631206\pi$
$888$		0			0
$889$		−	10.0187i		−	0.336015i
$890$	−12.7958	−	16.1428i	−0.428915	−	0.541108i
$891$		0			0
$892$	1.21266	−	1.21266i	0.0406030	−	0.0406030i
$893$	5.65685	−	5.65685i	0.189299	−	0.189299i
$894$		0			0
$895$	34.9066	+	4.03731i	1.16680	+	0.134953i
$896$		−	2.82843i		−	0.0944911i
$897$		0			0
$898$	0.112032	+	0.112032i	0.00373854	+	0.00373854i
$899$	−5.80210			−0.193511
$900$		0			0
$901$	−18.1214			−0.603710
$902$	−10.9715	−	10.9715i	−0.365311	−	0.365311i
$903$		0			0
$904$		−	10.5653i		−	0.351398i
$905$	28.7830	+	3.32906i	0.956781	+	0.110662i
$906$		0			0
$907$	−32.2207	+	32.2207i	−1.06987	+	1.06987i	−0.0725016	+	0.997368i	$0.523098\pi$
$907$	−32.2207	+	32.2207i	−1.06987	+	1.06987i	−0.997368	+	0.0725016i	$0.976902\pi$
$908$	8.52159	−	8.52159i	0.282799	−	0.282799i
$909$		0			0
$910$	−19.4720	−	24.5653i	−0.645490	−	0.814333i
$911$			13.9404i			0.461866i	0.972970	+	0.230933i	$0.0741778\pi$
$911$			13.9404i			0.461866i	−0.972970	+	0.230933i	$0.925822\pi$
$912$		0			0
$913$	−31.2920	−	31.2920i	−1.03561	−	1.03561i
$914$	3.95508			0.130822
$915$		0			0
$916$	−0.392633			−0.0129730
$917$	26.2817	+	26.2817i	0.867900	+	0.867900i
$918$		0			0
$919$			20.3599i			0.671612i	0.941931	+	0.335806i	$0.109009\pi$
$919$			20.3599i			0.671612i	−0.941931	+	0.335806i	$0.890991\pi$
$920$	−0.256912	+	2.22126i	−0.00847013	+	0.0732328i
$921$		0			0
$922$	−3.06068	+	3.06068i	−0.100798	+	0.100798i
$923$	−35.8409	+	35.8409i	−1.17972	+	1.17972i
$924$		0			0
$925$	−26.2207	+	16.2606i	−0.862130	+	0.534646i
$926$			5.97080i			0.196213i
$927$		0			0
$928$	−1.50466	−	1.50466i	−0.0493930	−	0.0493930i
$929$	−31.2975			−1.02684			−0.513419	−	0.858138i	$-0.671621\pi$
$929$	−31.2975			−1.02684			−0.513419	+	0.858138i	$0.671621\pi$
$930$		0			0
$931$	0.778008			0.0254982
$932$	−3.41487	−	3.41487i	−0.111858	−	0.111858i
$933$		0			0
$934$			19.6846i			0.644101i
$935$	−11.7135	+	9.28480i	−0.383071	+	0.303645i
$936$		0			0
$937$	−33.7287	+	33.7287i	−1.10187	+	1.10187i	−0.107684	+	0.994185i	$0.534344\pi$
$937$	−33.7287	+	33.7287i	−1.10187	+	1.10187i	−0.994185	+	0.107684i	$0.965656\pi$
$938$	−28.7104	+	28.7104i	−0.937428	+	0.937428i
$939$		0			0
$940$	−18.0187	+	14.2827i	−0.587704	+	0.465849i
$941$			12.4452i			0.405701i	0.979210	+	0.202850i	$0.0650205\pi$
$941$			12.4452i			0.405701i	−0.979210	+	0.202850i	$0.934980\pi$
$942$		0			0
$943$	−3.28267	−	3.28267i	−0.106899	−	0.106899i
$944$	−1.80078			−0.0586104
$945$		0			0
$946$	−18.5254			−0.602312
$947$	−24.4282	−	24.4282i	−0.793810	−	0.793810i	0.188302	−	0.982111i	$-0.439702\pi$
$947$	−24.4282	−	24.4282i	−0.793810	−	0.793810i	−0.982111	+	0.188302i	$0.939702\pi$
$948$		0			0
$949$			23.0093i			0.746914i
$950$	3.30594	−	2.05016i	0.107259	−	0.0665161i
$951$		0			0
$952$	4.00000	−	4.00000i	0.129641	−	0.129641i
$953$	25.5417	−	25.5417i	0.827375	−	0.827375i	−0.159778	−	0.987153i	$-0.551078\pi$
$953$	25.5417	−	25.5417i	0.827375	−	0.827375i	0.987153	+	0.159778i	$0.0510777\pi$
$954$		0			0
$955$	0.462642	−	4.00000i	0.0149707	−	0.129437i
$956$			8.82561i			0.285441i
$957$		0			0
$958$	−12.4626	−	12.4626i	−0.402650	−	0.402650i
$959$	32.6853			1.05546
$960$		0			0
$961$	−23.5653			−0.760172
$962$	21.6262	+	21.6262i	0.697255	+	0.697255i
$963$		0			0
$964$		−	11.0280i		−	0.355188i
$965$	32.8753	+	41.4746i	1.05829	+	1.33512i
$966$		0			0
$967$	−11.9766	+	11.9766i	−0.385143	+	0.385143i	−0.872951	−	0.487808i	$-0.837797\pi$
$967$	−11.9766	+	11.9766i	−0.385143	+	0.385143i	0.487808	+	0.872951i	$0.337797\pi$
$968$	−0.120661	+	0.120661i	−0.00387820	+	0.00387820i
$969$		0			0
$970$	2.44398	+	0.282672i	0.0784716	+	0.00907606i
$971$			49.5220i			1.58924i	0.607109	+	0.794618i	$0.292329\pi$
$971$			49.5220i			1.58924i	−0.607109	+	0.794618i	$0.707671\pi$
$972$		0			0
$973$	31.1493	+	31.1493i	0.998602	+	0.998602i
$974$	17.8295			0.571294
$975$		0			0
$976$	2.05135			0.0656622
$977$	−8.75299	−	8.75299i	−0.280033	−	0.280033i	0.553089	−	0.833122i	$-0.313449\pi$
$977$	−8.75299	−	8.75299i	−0.280033	−	0.280033i	−0.833122	+	0.553089i	$0.813449\pi$
$978$		0			0
$979$		−	30.7894i		−	0.984034i
$980$	−2.22126	−	0.256912i	−0.0709556	−	0.00820675i
$981$		0			0
$982$	5.11203	−	5.11203i	0.163131	−	0.163131i
$983$	26.6551	−	26.6551i	0.850166	−	0.850166i	−0.139987	−	0.990153i	$-0.544706\pi$
$983$	26.6551	−	26.6551i	0.850166	−	0.850166i	0.990153	+	0.139987i	$0.0447061\pi$
$984$		0			0
$985$	22.2500	+	28.0700i	0.708943	+	0.894385i
$986$		−	4.25583i		−	0.135533i
$987$		0			0
$988$	−2.72666	−	2.72666i	−0.0867465	−	0.0867465i
$989$	−5.54279			−0.176250
$990$		0			0
$991$	−51.4134			−1.63320			−0.816600	−	0.577205i	$-0.804144\pi$
$991$	−51.4134			−1.63320			−0.816600	+	0.577205i	$0.804144\pi$
$992$	1.92804	+	1.92804i	0.0612152	+	0.0612152i
$993$		0			0
$994$			28.9253i			0.917454i
$995$	0.373373	−	3.22819i	0.0118367	−	0.102340i
$996$		0			0
$997$	−11.7873	+	11.7873i	−0.373309	+	0.373309i	−0.868681	−	0.495372i	$-0.835032\pi$
$997$	−11.7873	+	11.7873i	−0.373309	+	0.373309i	0.495372	+	0.868681i	$0.335032\pi$
$998$	20.8266	−	20.8266i	0.659256	−	0.659256i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.j.g.323.1	✓	12
3.2	odd	2	inner	2070.2.j.g.323.6	yes	12
5.2	odd	4	inner	2070.2.j.g.737.6	yes	12
15.2	even	4	inner	2070.2.j.g.737.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.j.g.323.1	✓	12	1.1	even	1	trivial
2070.2.j.g.323.6	yes	12	3.2	odd	2	inner
2070.2.j.g.737.1	yes	12	15.2	even	4	inner
2070.2.j.g.737.6	yes	12	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.22126 - 0.256912i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.22126 - 0.256912i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.38900 + 1.75233i) q^{10} +3.34225i q^{11} +(3.50466 + 3.50466i) q^{13} +2.82843 q^{14} -1.00000 q^{16} +(-1.41421 - 1.41421i) q^{17} +0.778008i q^{19} +(0.256912 - 2.22126i) q^{20} +(2.36333 - 2.36333i) q^{22} +(0.707107 - 0.707107i) q^{23} +(4.86799 + 1.14134i) q^{25} -4.95634i q^{26} +(-2.00000 - 2.00000i) q^{28} -2.12792 q^{29} +2.72666 q^{31} +(0.707107 + 0.707107i) q^{32} +2.00000i q^{34} +(4.95634 - 3.92870i) q^{35} +(-4.36333 + 4.36333i) q^{37} +(0.550135 - 0.550135i) q^{38} +(-1.75233 + 1.38900i) q^{40} -4.64240i q^{41} +(-3.91934 - 3.91934i) q^{43} -3.34225 q^{44} -1.00000 q^{46} +(-7.27095 - 7.27095i) q^{47} -1.00000i q^{49} +(-2.63514 - 4.24924i) q^{50} +(-3.50466 + 3.50466i) q^{52} +(6.40687 - 6.40687i) q^{53} +(0.858664 - 7.42401i) q^{55} +2.82843i q^{56} +(1.50466 + 1.50466i) q^{58} +1.80078 q^{59} -2.05135 q^{61} +(-1.92804 - 1.92804i) q^{62} -1.00000i q^{64} +(-6.88438 - 8.68516i) q^{65} +(-10.1507 + 10.1507i) q^{67} +(1.41421 - 1.41421i) q^{68} +(-6.28267 - 0.726656i) q^{70} +10.2266i q^{71} +(3.28267 + 3.28267i) q^{73} +6.17068 q^{74} -0.778008 q^{76} +(-6.68450 - 6.68450i) q^{77} -5.55602i q^{79} +(2.22126 + 0.256912i) q^{80} +(-3.28267 + 3.28267i) q^{82} +(-9.36255 + 9.36255i) q^{83} +(2.77801 + 3.50466i) q^{85} +5.54279i q^{86} +(2.36333 + 2.36333i) q^{88} -9.21218 q^{89} -14.0187 q^{91} +(0.707107 + 0.707107i) q^{92} +10.2827i q^{94} +(0.199879 - 1.72816i) q^{95} +(0.778008 - 0.778008i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{7}+O(q^{10}) \) 12 * q - 24 * q^7	\( 12 q - 24 q^{7} + 4 q^{10} - 12 q^{16} + 20 q^{22} + 8 q^{25} - 24 q^{28} + 16 q^{31} - 44 q^{37} + 12 q^{43} - 12 q^{46} + 44 q^{55} - 24 q^{58} - 16 q^{61} - 4 q^{67} - 8 q^{70} - 28 q^{73} + 16 q^{76} + 28 q^{82} + 8 q^{85} + 20 q^{88} - 16 q^{97}+O(q^{100}) \) 12 * q - 24 * q^7 + 4 * q^10 - 12 * q^16 + 20 * q^22 + 8 * q^25 - 24 * q^28 + 16 * q^31 - 44 * q^37 + 12 * q^43 - 12 * q^46 + 44 * q^55 - 24 * q^58 - 16 * q^61 - 4 * q^67 - 8 * q^70 - 28 * q^73 + 16 * q^76 + 28 * q^82 + 8 * q^85 + 20 * q^88 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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