LMFDB - Embedded newform 1638.2.cr.b.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(361,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 5]))

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

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

chi := DirichletCharacter("1638.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.cr (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
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} + 56 x^{18} + 1306 x^{16} + 16508 x^{14} + 123139 x^{12} + 552164 x^{10} + 1447090 x^{8} + \cdots + 576 $ x^20 + 56x^18 + 1306x^16 + 16508x^14 + 123139x^12 + 552164x^10 + 1447090x^8 + 2035844x^6 + 1263505x^4 + 215520*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.1
Root			$-2.55339i$ of defining polynomial
Character	$\chi$	$=$	1638.361
Dual form			1638.2.cr.b.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.21130 + 1.27669i) q^{5} +(-0.853651 + 2.50425i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.21130 + 1.27669i) q^{5} +(-0.853651 + 2.50425i) q^{7} -1.00000i q^{8} +2.55339 q^{10} -0.519243i q^{11} +(-1.57238 + 3.24463i) q^{13} +(1.99141 - 1.74192i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.434150 - 0.751971i) q^{17} -4.62695i q^{19} +(-2.21130 - 1.27669i) q^{20} +(-0.259622 + 0.449678i) q^{22} +(-4.26046 + 7.37933i) q^{23} +(0.759893 - 1.31617i) q^{25} +(2.98403 - 2.02374i) q^{26} +(-2.59557 + 0.512843i) q^{28} +(1.98376 + 3.43598i) q^{29} +(3.49539 + 2.01806i) q^{31} +(0.866025 - 0.500000i) q^{32} +0.868301i q^{34} +(-1.30949 - 6.62750i) q^{35} +(-5.12950 - 2.96152i) q^{37} +(-2.31347 + 4.00705i) q^{38} +(1.27669 + 2.21130i) q^{40} +(5.87598 - 3.39250i) q^{41} +(2.24805 - 3.89373i) q^{43} +(0.449678 - 0.259622i) q^{44} +(7.37933 - 4.26046i) q^{46} +(-2.81446 + 1.62493i) q^{47} +(-5.54256 - 4.27552i) q^{49} +(-1.31617 + 0.759893i) q^{50} +(-3.59612 + 0.260597i) q^{52} +(4.12845 - 7.15068i) q^{53} +(0.662914 + 1.14820i) q^{55} +(2.50425 + 0.853651i) q^{56} -3.96752i q^{58} +(1.21312 - 0.700397i) q^{59} -6.03817 q^{61} +(-2.01806 - 3.49539i) q^{62} -1.00000 q^{64} +(-0.665404 - 9.18229i) q^{65} -11.0230i q^{67} +(0.434150 - 0.751971i) q^{68} +(-2.17970 + 6.39433i) q^{70} +(-4.47375 - 2.58292i) q^{71} +(-10.3558 - 5.97895i) q^{73} +(2.96152 + 5.12950i) q^{74} +(4.00705 - 2.31347i) q^{76} +(1.30032 + 0.443252i) q^{77} +(5.47473 + 9.48251i) q^{79} -2.55339i q^{80} -6.78500 q^{82} -12.9984i q^{83} +(1.92007 + 1.10855i) q^{85} +(-3.89373 + 2.24805i) q^{86} -0.519243 q^{88} +(-6.95371 - 4.01473i) q^{89} +(-6.78311 - 6.70741i) q^{91} -8.52091 q^{92} +3.24986 q^{94} +(5.90719 + 10.2316i) q^{95} +(-13.0095 - 7.51106i) q^{97} +(2.66224 + 6.47398i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{4} - 6 q^{7}+O(q^{10}) $ 20 * q + 10 * q^4 - 6 * q^7	$ 20 q + 10 q^{4} - 6 q^{7} - 8 q^{10} + 8 q^{13} - 4 q^{14} - 10 q^{16} - 4 q^{17} - 10 q^{22} - 8 q^{23} + 6 q^{25} - 2 q^{26} - 6 q^{28} - 8 q^{29} - 12 q^{31} - 4 q^{35} - 6 q^{38} - 4 q^{40} + 18 q^{41} + 18 q^{43} - 6 q^{44} - 24 q^{46} - 6 q^{47} + 4 q^{49} - 12 q^{50} - 2 q^{52} - 18 q^{53} - 12 q^{55} - 2 q^{56} - 36 q^{59} + 12 q^{61} - 20 q^{64} + 4 q^{68} - 42 q^{70} + 6 q^{71} - 24 q^{73} + 18 q^{74} + 12 q^{76} + 34 q^{77} - 36 q^{82} - 36 q^{86} - 20 q^{88} - 18 q^{89} - 94 q^{91} - 16 q^{92} + 32 q^{94} - 40 q^{95} - 96 q^{97} + 12 q^{98}+O(q^{100}) $ 20 * q + 10 * q^4 - 6 * q^7 - 8 * q^10 + 8 * q^13 - 4 * q^14 - 10 * q^16 - 4 * q^17 - 10 * q^22 - 8 * q^23 + 6 * q^25 - 2 * q^26 - 6 * q^28 - 8 * q^29 - 12 * q^31 - 4 * q^35 - 6 * q^38 - 4 * q^40 + 18 * q^41 + 18 * q^43 - 6 * q^44 - 24 * q^46 - 6 * q^47 + 4 * q^49 - 12 * q^50 - 2 * q^52 - 18 * q^53 - 12 * q^55 - 2 * q^56 - 36 * q^59 + 12 * q^61 - 20 * q^64 + 4 * q^68 - 42 * q^70 + 6 * q^71 - 24 * q^73 + 18 * q^74 + 12 * q^76 + 34 * q^77 - 36 * q^82 - 36 * q^86 - 20 * q^88 - 18 * q^89 - 94 * q^91 - 16 * q^92 + 32 * q^94 - 40 * q^95 - 96 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.21130	+	1.27669i	−0.988923	+	0.570955i	−0.904952	−	0.425513i	$-0.860093\pi$
$5$	−2.21130	+	1.27669i	−0.988923	+	0.570955i	−0.0839705	+	0.996468i	$0.526760\pi$
$6$		0			0
$7$	−0.853651	+	2.50425i	−0.322650	+	0.946518i
$7$	−0.853651	+	2.50425i	−0.322650	+	0.946518i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	2.55339			0.807452
$11$		−	0.519243i		−	0.156558i	−0.996932	−	0.0782788i	$-0.975058\pi$
$11$		−	0.519243i		−	0.156558i	0.996932	−	0.0782788i	$-0.0249424\pi$
$12$		0			0
$13$	−1.57238	+	3.24463i	−0.436099	+	0.899899i
$13$	−1.57238	+	3.24463i	−0.436099	+	0.899899i
$14$	1.99141	−	1.74192i	0.532227	−	0.465548i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.434150	−	0.751971i	−0.105297	−	0.182380i	0.808563	−	0.588410i	$-0.200246\pi$
$17$	−0.434150	−	0.751971i	−0.105297	−	0.182380i	−0.913859	+	0.406031i	$0.866913\pi$
$18$		0			0
$19$		−	4.62695i		−	1.06149i	−0.847530	−	0.530747i	$-0.821911\pi$
$19$		−	4.62695i		−	1.06149i	0.847530	−	0.530747i	$-0.178089\pi$
$20$	−2.21130	−	1.27669i	−0.494461	−	0.285477i
$21$		0			0
$22$	−0.259622	+	0.449678i	−0.0553515	+	0.0958716i
$23$	−4.26046	+	7.37933i	−0.888367	+	1.53870i	−0.0465607	+	0.998915i	$0.514826\pi$
$23$	−4.26046	+	7.37933i	−0.888367	+	1.53870i	−0.841806	+	0.539780i	$0.818507\pi$
$24$		0			0
$25$	0.759893	−	1.31617i	0.151979	−	0.263235i
$26$	2.98403	−	2.02374i	0.585217	−	0.396889i
$27$		0			0
$28$	−2.59557	+	0.512843i	−0.490517	+	0.0969182i
$29$	1.98376	+	3.43598i	0.368375	+	0.638045i	0.989312	−	0.145816i	$-0.0465808\pi$
$29$	1.98376	+	3.43598i	0.368375	+	0.638045i	−0.620936	+	0.783861i	$0.713247\pi$
$30$		0			0
$31$	3.49539	+	2.01806i	0.627791	+	0.362455i	0.779896	−	0.625909i	$-0.215272\pi$
$31$	3.49539	+	2.01806i	0.627791	+	0.362455i	−0.152105	+	0.988364i	$0.548605\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$			0.868301i			0.148912i
$35$	−1.30949	−	6.62750i	−0.221344	−	1.12025i
$36$		0			0
$37$	−5.12950	−	2.96152i	−0.843285	−	0.486871i	0.0150948	−	0.999886i	$-0.495195\pi$
$37$	−5.12950	−	2.96152i	−0.843285	−	0.486871i	−0.858379	+	0.513015i	$0.828528\pi$
$38$	−2.31347	+	4.00705i	−0.375295	+	0.650030i
$39$		0			0
$40$	1.27669	+	2.21130i	0.201863	+	0.349637i
$41$	5.87598	−	3.39250i	0.917674	−	0.529819i	0.0347817	−	0.999395i	$-0.488926\pi$
$41$	5.87598	−	3.39250i	0.917674	−	0.529819i	0.882892	+	0.469576i	$0.155593\pi$
$42$		0			0
$43$	2.24805	−	3.89373i	0.342824	−	0.593789i	−0.642132	−	0.766594i	$-0.721950\pi$
$43$	2.24805	−	3.89373i	0.342824	−	0.593789i	0.984956	+	0.172805i	$0.0552831\pi$
$44$	0.449678	−	0.259622i	0.0677915	−	0.0391394i
$45$		0			0
$46$	7.37933	−	4.26046i	1.08802	−	0.628170i
$47$	−2.81446	+	1.62493i	−0.410531	+	0.237020i	−0.691018	−	0.722838i	$-0.742837\pi$
$47$	−2.81446	+	1.62493i	−0.410531	+	0.237020i	0.280487	+	0.959858i	$0.409504\pi$
$48$		0			0
$49$	−5.54256	−	4.27552i	−0.791794	−	0.610788i
$50$	−1.31617	+	0.759893i	−0.186135	+	0.107465i
$51$		0			0
$52$	−3.59612	+	0.260597i	−0.498692	+	0.0361383i
$53$	4.12845	−	7.15068i	0.567086	−	0.982222i	−0.429766	−	0.902940i	$-0.641404\pi$
$53$	4.12845	−	7.15068i	0.567086	−	0.982222i	0.996852	−	0.0792817i	$-0.0252627\pi$
$54$		0			0
$55$	0.662914	+	1.14820i	0.0893873	+	0.154823i
$56$	2.50425	+	0.853651i	0.334645	+	0.114074i
$57$		0			0
$58$		−	3.96752i		−	0.520962i
$59$	1.21312	−	0.700397i	0.157935	−	0.0911839i	−0.418949	−	0.908010i	$-0.637602\pi$
$59$	1.21312	−	0.700397i	0.157935	−	0.0911839i	0.576885	+	0.816826i	$0.304268\pi$
$60$		0			0
$61$	−6.03817			−0.773108			−0.386554	−	0.922267i	$-0.626335\pi$
$61$	−6.03817			−0.773108			−0.386554	+	0.922267i	$0.626335\pi$
$62$	−2.01806	−	3.49539i	−0.256294	−	0.443915i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.665404	−	9.18229i	−0.0825332	−	1.13892i
$66$		0			0
$67$		−	11.0230i		−	1.34667i	−0.739336	−	0.673337i	$-0.764861\pi$
$67$		−	11.0230i		−	1.34667i	0.739336	−	0.673337i	$-0.235139\pi$
$68$	0.434150	−	0.751971i	0.0526485	−	0.0911898i
$69$		0			0
$70$	−2.17970	+	6.39433i	−0.260524	+	0.764268i
$71$	−4.47375	−	2.58292i	−0.530937	−	0.306536i	0.210461	−	0.977602i	$-0.432503\pi$
$71$	−4.47375	−	2.58292i	−0.530937	−	0.306536i	−0.741398	+	0.671066i	$0.765837\pi$
$72$		0			0
$73$	−10.3558	−	5.97895i	−1.21206	−	0.699783i	−0.248852	−	0.968542i	$-0.580053\pi$
$73$	−10.3558	−	5.97895i	−1.21206	−	0.699783i	−0.963208	+	0.268759i	$0.913387\pi$
$74$	2.96152	+	5.12950i	0.344269	+	0.596292i
$75$		0			0
$76$	4.00705	−	2.31347i	0.459640	−	0.265374i
$77$	1.30032	+	0.443252i	0.148185	+	0.0505133i
$78$		0			0
$79$	5.47473	+	9.48251i	0.615955	+	1.06687i	0.990216	+	0.139542i	$0.0445630\pi$
$79$	5.47473	+	9.48251i	0.615955	+	1.06687i	−0.374261	+	0.927323i	$0.622104\pi$
$80$		−	2.55339i		−	0.285477i
$81$		0			0
$82$	−6.78500			−0.749278
$83$		−	12.9984i		−	1.42676i	−0.700778	−	0.713379i	$-0.747164\pi$
$83$		−	12.9984i		−	1.42676i	0.700778	−	0.713379i	$-0.252836\pi$
$84$		0			0
$85$	1.92007	+	1.10855i	0.208261	+	0.120240i
$86$	−3.89373	+	2.24805i	−0.419872	+	0.242413i
$87$		0			0
$88$	−0.519243			−0.0553515
$89$	−6.95371	−	4.01473i	−0.737092	−	0.425560i	0.0839190	−	0.996473i	$-0.473256\pi$
$89$	−6.95371	−	4.01473i	−0.737092	−	0.425560i	−0.821011	+	0.570912i	$0.806590\pi$
$90$		0			0
$91$	−6.78311	−	6.70741i	−0.711063	−	0.703128i
$92$	−8.52091			−0.888367
$93$		0			0
$94$	3.24986			0.335197
$95$	5.90719	+	10.2316i	0.606065	+	1.04974i
$96$		0			0
$97$	−13.0095	−	7.51106i	−1.32092	−	0.762632i	−0.337043	−	0.941489i	$-0.609427\pi$
$97$	−13.0095	−	7.51106i	−1.32092	−	0.762632i	−0.983875	+	0.178857i	$0.942760\pi$
$98$	2.66224	+	6.47398i	0.268927	+	0.653971i
$99$		0			0
$100$	1.51979			0.151979
$101$	8.50066			0.845847			0.422923	−	0.906165i	$-0.361004\pi$
$101$	8.50066			0.845847			0.422923	+	0.906165i	$0.361004\pi$
$102$		0			0
$103$	−7.78135	−	13.4777i	−0.766719	−	1.32800i	−0.939333	−	0.343007i	$-0.888554\pi$
$103$	−7.78135	−	13.4777i	−0.766719	−	1.32800i	0.172613	−	0.984990i	$-0.444779\pi$
$104$	3.24463	+	1.57238i	0.318162	+	0.154184i
$105$		0			0
$106$	−7.15068	+	4.12845i	−0.694536	+	0.400990i
$107$	−1.37028	+	2.37339i	−0.132470	+	0.229444i	−0.924628	−	0.380871i	$-0.875624\pi$
$107$	−1.37028	+	2.37339i	−0.132470	+	0.229444i	0.792158	+	0.610316i	$0.208957\pi$
$108$		0			0
$109$	12.3004	+	7.10162i	1.17816	+	0.680212i	0.955588	−	0.294704i	$-0.0952212\pi$
$109$	12.3004	+	7.10162i	1.17816	+	0.680212i	0.222573	+	0.974916i	$0.428555\pi$
$110$		−	1.32583i		−	0.126413i
$111$		0			0
$112$	−1.74192	−	1.99141i	−0.164596	−	0.188171i
$113$	−9.29913	+	16.1066i	−0.874788	+	1.51518i	−0.0178004	+	0.999842i	$0.505666\pi$
$113$	−9.29913	+	16.1066i	−0.874788	+	1.51518i	−0.856988	+	0.515336i	$0.827667\pi$
$114$		0			0
$115$		−	21.7572i		−	2.02887i
$116$	−1.98376	+	3.43598i	−0.184188	+	0.319022i
$117$		0			0
$118$	−1.40079			−0.128954
$119$	2.25374	−	0.445302i	0.206600	−	0.0408207i
$120$		0			0
$121$	10.7304			0.975490
$122$	5.22921	+	3.01909i	0.473430	+	0.273335i
$123$		0			0
$124$			4.03613i			0.362455i
$125$		−	8.88633i		−	0.794818i
$126$		0			0
$127$	−5.67318	−	9.82624i	−0.503413	−	0.871938i	−0.999992	−	0.00394597i	$-0.998744\pi$
$127$	−5.67318	−	9.82624i	−0.503413	−	0.871938i	0.496579	−	0.867992i	$-0.334589\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−4.01489	+	8.28480i	−0.352129	+	0.726625i
$131$	1.43219	+	2.48062i	0.125131	+	0.216733i	0.921784	−	0.387704i	$-0.126732\pi$
$131$	1.43219	+	2.48062i	0.125131	+	0.216733i	−0.796653	+	0.604437i	$0.793398\pi$
$132$		0			0
$133$	11.5870	+	3.94980i	1.00472	+	0.342491i
$134$	−5.51150	+	9.54619i	−0.476121	+	0.824665i
$135$		0			0
$136$	−0.751971	+	0.434150i	−0.0644809	+	0.0372281i
$137$	8.49269	−	4.90326i	0.725579	−	0.418913i	−0.0912235	−	0.995830i	$-0.529078\pi$
$137$	8.49269	−	4.90326i	0.725579	−	0.418913i	0.816803	+	0.576917i	$0.195744\pi$
$138$		0			0
$139$	−3.49317	+	6.05035i	−0.296287	+	0.513184i	−0.975283	−	0.220957i	$-0.929082\pi$
$139$	−3.49317	+	6.05035i	−0.296287	+	0.513184i	0.678996	+	0.734142i	$0.262415\pi$
$140$	5.08484	−	4.44780i	0.429747	−	0.375908i
$141$		0			0
$142$	2.58292	+	4.47375i	0.216754	+	0.375429i
$143$	1.68475	+	0.816446i	0.140886	+	0.0682746i
$144$		0			0
$145$	−8.77338	−	5.06531i	−0.728590	−	0.420651i
$146$	5.97895	+	10.3558i	0.494821	+	0.857055i
$147$		0			0
$148$		−	5.92304i		−	0.486871i
$149$		−	0.633345i		−	0.0518856i	−0.999663	−	0.0259428i	$-0.991741\pi$
$149$		−	0.633345i		−	0.0518856i	0.999663	−	0.0259428i	$-0.00825878\pi$
$150$		0			0
$151$	3.43434	+	1.98282i	0.279483	+	0.161360i	0.633189	−	0.773997i	$-0.281745\pi$
$151$	3.43434	+	1.98282i	0.279483	+	0.161360i	−0.353706	+	0.935357i	$0.615079\pi$
$152$	−4.62695			−0.375295
$153$		0			0
$154$	−0.904480	−	1.03403i	−0.0728851	−	0.0833242i
$155$	−10.3058			−0.827782
$156$		0			0
$157$	−4.83448	+	8.37356i	−0.385833	+	0.668283i	−0.991884	−	0.127143i	$-0.959419\pi$
$157$	−4.83448	+	8.37356i	−0.385833	+	0.668283i	0.606051	+	0.795426i	$0.292753\pi$
$158$		−	10.9495i		−	0.871092i
$159$		0			0
$160$	−1.27669	+	2.21130i	−0.100931	+	0.174818i
$161$	−14.8428	−	16.9686i	−1.16977	−	1.33732i
$162$		0			0
$163$			23.7227i			1.85810i	0.369949	+	0.929052i	$0.379375\pi$
$163$			23.7227i			1.85810i	−0.369949	+	0.929052i	$0.620625\pi$
$164$	5.87598	+	3.39250i	0.458837	+	0.264910i
$165$		0			0
$166$	−6.49919	+	11.2569i	−0.504435	+	0.873707i
$167$	−3.53346	+	2.04005i	−0.273428	+	0.157864i	−0.630444	−	0.776234i	$-0.717127\pi$
$167$	−3.53346	+	2.04005i	−0.273428	+	0.157864i	0.357017	+	0.934098i	$0.383794\pi$
$168$		0			0
$169$	−8.05526	−	10.2036i	−0.619635	−	0.784890i
$170$	−1.10855	−	1.92007i	−0.0850222	−	0.147263i
$171$		0			0
$172$	4.49610			0.342824
$173$	−13.7809			−1.04774			−0.523869	−	0.851799i	$-0.675512\pi$
$173$	−13.7809			−1.04774			−0.523869	+	0.851799i	$0.675512\pi$
$174$		0			0
$175$	2.64735	+	3.02652i	0.200121	+	0.228783i
$176$	0.449678	+	0.259622i	0.0338957	+	0.0195697i
$177$		0			0
$178$	4.01473	+	6.95371i	0.300917	+	0.521203i
$179$	−3.85587			−0.288201			−0.144100	−	0.989563i	$-0.546029\pi$
$179$	−3.85587			−0.288201			−0.144100	+	0.989563i	$0.546029\pi$
$180$		0			0
$181$	−3.18446			−0.236699			−0.118349	−	0.992972i	$-0.537760\pi$
$181$	−3.18446			−0.236699			−0.118349	+	0.992972i	$0.537760\pi$
$182$	2.52064	+	9.20035i	0.186842	+	0.681975i
$183$		0			0
$184$	7.37933	+	4.26046i	0.544011	+	0.314085i
$185$	15.1238			1.11192
$186$		0			0
$187$	−0.390455	+	0.225430i	−0.0285529	+	0.0164850i
$188$	−2.81446	−	1.62493i	−0.205266	−	0.118510i
$189$		0			0
$190$		−	11.8144i		−	0.857105i
$191$	−13.4139			−0.970597			−0.485299	−	0.874349i	$-0.661289\pi$
$191$	−13.4139			−0.970597			−0.485299	+	0.874349i	$0.661289\pi$
$192$		0			0
$193$		−	5.98995i		−	0.431166i	−0.976486	−	0.215583i	$-0.930835\pi$
$193$		−	5.98995i		−	0.431166i	0.976486	−	0.215583i	$-0.0691652\pi$
$194$	7.51106	+	13.0095i	0.539262	+	0.934030i
$195$		0			0
$196$	0.931425	−	6.93776i	0.0665303	−	0.495554i
$197$	3.78655	−	2.18617i	0.269781	−	0.155758i	−0.359007	−	0.933335i	$-0.616885\pi$
$197$	3.78655	−	2.18617i	0.269781	−	0.155758i	0.628788	+	0.777577i	$0.283551\pi$
$198$		0			0
$199$	−4.84755	−	8.39621i	−0.343634	−	0.595191i	0.641471	−	0.767148i	$-0.278325\pi$
$199$	−4.84755	−	8.39621i	−0.343634	−	0.595191i	−0.985105	+	0.171956i	$0.944991\pi$
$200$	−1.31617	−	0.759893i	−0.0930675	−	0.0537326i
$201$		0			0
$202$	−7.36178	−	4.25033i	−0.517973	−	0.299052i
$203$	−10.2980	+	2.03472i	−0.722778	+	0.142809i
$204$		0			0
$205$	−8.66236	+	15.0037i	−0.605006	+	1.04790i
$206$			15.5627i			1.08431i
$207$		0			0
$208$	−2.02374	−	2.98403i	−0.140321	−	0.206906i
$209$	−2.40251			−0.166185
$210$		0			0
$211$	3.54943	+	6.14780i	0.244353	+	0.423232i	0.961950	−	0.273227i	$-0.0880911\pi$
$211$	3.54943	+	6.14780i	0.244353	+	0.423232i	−0.717596	+	0.696459i	$0.754758\pi$
$212$	8.25690			0.567086
$213$		0			0
$214$	2.37339	−	1.37028i	0.162242	−	0.0936703i
$215$			11.4803i			0.782948i
$216$		0			0
$217$	−8.03759	+	7.03062i	−0.545627	+	0.477269i
$218$	−7.10162	−	12.3004i	−0.480982	−	0.833086i
$219$		0			0
$220$	−0.662914	+	1.14820i	−0.0446937	+	0.0774117i
$221$	3.12251	−	0.226276i	0.210043	−	0.0152210i
$222$		0			0
$223$	−5.20714	+	3.00634i	−0.348696	+	0.201320i	−0.664111	−	0.747634i	$-0.731190\pi$
$223$	−5.20714	+	3.00634i	−0.348696	+	0.201320i	0.315415	+	0.948954i	$0.397856\pi$
$224$	0.512843	+	2.59557i	0.0342657	+	0.173424i
$225$		0			0
$226$	16.1066	−	9.29913i	1.07139	−	0.618569i
$227$	−3.12015	+	1.80142i	−0.207092	+	0.119564i	−0.599959	−	0.800031i	$-0.704816\pi$
$227$	−3.12015	+	1.80142i	−0.207092	+	0.119564i	0.392867	+	0.919595i	$0.371483\pi$
$228$		0			0
$229$	23.8424	−	13.7654i	1.57555	−	0.909644i	0.580081	−	0.814559i	$-0.303021\pi$
$229$	23.8424	−	13.7654i	1.57555	−	0.909644i	0.995469	−	0.0950854i	$-0.0303124\pi$
$230$	−10.8786	+	18.8423i	−0.717313	+	1.24242i
$231$		0			0
$232$	3.43598	−	1.98376i	0.225583	−	0.130240i
$233$	5.84917	+	10.1311i	0.383192	+	0.663708i	0.991517	−	0.129981i	$-0.0414915\pi$
$233$	5.84917	+	10.1311i	0.383192	+	0.663708i	−0.608325	+	0.793688i	$0.708158\pi$
$234$		0			0
$235$	4.14908	−	7.18641i	0.270656	−	0.468790i
$236$	1.21312	+	0.700397i	0.0789676	+	0.0455920i
$237$		0			0
$238$	−2.17444	−	0.741226i	−0.140948	−	0.0480465i
$239$		−	16.4292i		−	1.06272i	−0.847147	−	0.531359i	$-0.821682\pi$
$239$		−	16.4292i		−	1.06272i	0.847147	−	0.531359i	$-0.178318\pi$
$240$		0			0
$241$	−12.4413	+	7.18297i	−0.801413	+	0.462696i	−0.843965	−	0.536398i	$-0.819784\pi$
$241$	−12.4413	+	7.18297i	−0.801413	+	0.462696i	0.0425522	+	0.999094i	$0.486451\pi$
$242$	−9.29279	−	5.36519i	−0.597363	−	0.344888i
$243$		0			0
$244$	−3.01909	−	5.22921i	−0.193277	−	0.334766i
$245$	17.7148	+	2.37829i	1.13176	+	0.151943i
$246$		0			0
$247$	15.0127	+	7.27530i	0.955237	+	0.462917i
$248$	2.01806	−	3.49539i	0.128147	−	0.221958i
$249$		0			0
$250$	−4.44317	+	7.69579i	−0.281011	+	0.486725i
$251$	9.52013	−	16.4893i	0.600905	−	1.04080i	−0.391779	−	0.920059i	$-0.628140\pi$
$251$	9.52013	−	16.4893i	0.600905	−	1.04080i	0.992684	−	0.120739i	$-0.0385264\pi$
$252$		0			0
$253$	3.83166	+	2.21221i	0.240895	+	0.139081i
$254$			11.3464i			0.711934i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.6666	−	20.2071i	0.727742	−	1.26049i	−0.230094	−	0.973168i	$-0.573903\pi$
$257$	11.6666	−	20.2071i	0.727742	−	1.26049i	0.957836	−	0.287317i	$-0.0927634\pi$
$258$		0			0
$259$	11.7952	−	10.3175i	0.732918	−	0.641096i
$260$	7.61939	−	5.16740i	0.472535	−	0.320469i
$261$		0			0
$262$		−	2.86438i		−	0.176962i
$263$	−20.6333			−1.27230			−0.636152	−	0.771564i	$-0.719475\pi$
$263$	−20.6333			−1.27230			−0.636152	+	0.771564i	$0.719475\pi$
$264$		0			0
$265$			21.0831i			1.29512i
$266$	−8.05977	−	9.21414i	−0.494176	−	0.564955i
$267$		0			0
$268$	9.54619	−	5.51150i	0.583127	−	0.336668i
$269$	−4.37116	−	7.57108i	−0.266515	−	0.461617i	0.701445	−	0.712724i	$-0.252539\pi$
$269$	−4.37116	−	7.57108i	−0.266515	−	0.461617i	−0.967959	+	0.251107i	$0.919205\pi$
$270$		0			0
$271$	8.76510	+	5.06054i	0.532442	+	0.307406i	0.742010	−	0.670388i	$-0.233873\pi$
$271$	8.76510	+	5.06054i	0.532442	+	0.307406i	−0.209568	+	0.977794i	$0.567206\pi$
$272$	0.868301			0.0526485
$273$		0			0
$274$	−9.80651			−0.592433
$275$	−0.683414	−	0.394569i	−0.0412114	−	0.0237934i
$276$		0			0
$277$	2.48866	+	4.31049i	0.149529	+	0.258992i	0.931054	−	0.364882i	$-0.118891\pi$
$277$	2.48866	+	4.31049i	0.149529	+	0.258992i	−0.781524	+	0.623875i	$0.785557\pi$
$278$	6.05035	−	3.49317i	0.362876	−	0.209507i
$279$		0			0
$280$	−6.62750	+	1.30949i	−0.396069	+	0.0782568i
$281$		−	27.2729i		−	1.62696i	−0.581591	−	0.813481i	$-0.697570\pi$
$281$		−	27.2729i		−	1.62696i	0.581591	−	0.813481i	$-0.302430\pi$
$282$		0			0
$283$	−9.80513			−0.582854			−0.291427	−	0.956593i	$-0.594130\pi$
$283$	−9.80513			−0.582854			−0.291427	+	0.956593i	$0.594130\pi$
$284$		−	5.16584i		−	0.306536i
$285$		0			0
$286$	−1.05082	−	1.54944i	−0.0621360	−	0.0916202i
$287$	3.47964	+	17.6109i	0.205396	+	1.03954i
$288$		0			0
$289$	8.12303	−	14.0695i	0.477825	−	0.827617i
$290$	5.06531	+	8.77338i	0.297445	+	0.515191i
$291$		0			0
$292$		−	11.9579i		−	0.699783i
$293$	−24.3101	−	14.0354i	−1.42021	−	0.819959i	−0.423895	−	0.905711i	$-0.639337\pi$
$293$	−24.3101	−	14.0354i	−1.42021	−	0.819959i	−0.996317	+	0.0857521i	$0.972671\pi$
$294$		0			0
$295$	−1.78838	+	3.09757i	−0.104124	+	0.180348i
$296$	−2.96152	+	5.12950i	−0.172135	+	0.298146i
$297$		0			0
$298$	−0.316672	+	0.548493i	−0.0183443	+	0.0317733i
$299$	−17.2441	−	25.4267i	−0.997255	−	1.47046i
$300$		0			0
$301$	7.83184	+	8.95357i	0.451420	+	0.516075i
$302$	−1.98282	−	3.43434i	−0.114098	−	0.197624i
$303$		0			0
$304$	4.00705	+	2.31347i	0.229820	+	0.132687i
$305$	13.3522	−	7.70889i	0.764544	−	0.441410i
$306$		0			0
$307$			27.0072i			1.54139i	0.637207	+	0.770693i	$0.280090\pi$
$307$			27.0072i			1.54139i	−0.637207	+	0.770693i	$0.719910\pi$
$308$	0.266290	+	1.34773i	0.0151733	+	0.0767942i
$309$		0			0
$310$	8.92509	+	5.15290i	0.506911	+	0.292665i
$311$	−12.0954	+	20.9499i	−0.685869	+	1.18796i	0.287294	+	0.957843i	$0.407244\pi$
$311$	−12.0954	+	20.9499i	−0.685869	+	1.18796i	−0.973163	+	0.230118i	$0.926089\pi$
$312$		0			0
$313$	11.8941	+	20.6011i	0.672293	+	1.16444i	0.977252	+	0.212080i	$0.0680236\pi$
$313$	11.8941	+	20.6011i	0.672293	+	1.16444i	−0.304960	+	0.952365i	$0.598643\pi$
$314$	8.37356	−	4.83448i	0.472548	−	0.272825i
$315$		0			0
$316$	−5.47473	+	9.48251i	−0.307977	+	0.533433i
$317$	7.55286	−	4.36064i	0.424211	−	0.244918i	−0.272667	−	0.962109i	$-0.587906\pi$
$317$	7.55286	−	4.36064i	0.424211	−	0.244918i	0.696877	+	0.717190i	$0.254572\pi$
$318$		0			0
$319$	1.78411	−	1.03005i	0.0998908	−	0.0576720i
$320$	2.21130	−	1.27669i	0.123615	−	0.0713693i
$321$		0			0
$322$	4.36989	+	22.1166i	0.243524	+	1.23251i
$323$	−3.47933	+	2.00879i	−0.193595	+	0.111772i
$324$		0			0
$325$	3.07566	+	4.53509i	0.170607	+	0.251562i
$326$	11.8613	−	20.5444i	0.656939	−	1.13785i
$327$		0			0
$328$	−3.39250	−	5.87598i	−0.187319	−	0.324447i
$329$	−1.66667	−	8.43524i	−0.0918863	−	0.465050i
$330$		0			0
$331$			12.0056i			0.659888i	0.944000	+	0.329944i	$0.107030\pi$
$331$			12.0056i			0.659888i	−0.944000	+	0.329944i	$0.892970\pi$
$332$	11.2569	−	6.49919i	0.617804	−	0.356689i
$333$		0			0
$334$	4.08009			0.223253
$335$	14.0730	+	24.3751i	0.768889	+	1.33176i
$336$		0			0
$337$	22.4347			1.22210			0.611049	−	0.791593i	$-0.290748\pi$
$337$	22.4347			1.22210			0.611049	+	0.791593i	$0.290748\pi$
$338$	1.87427	+	12.8642i	0.101947	+	0.699719i
$339$		0			0
$340$			2.21711i			0.120240i
$341$	1.04787	−	1.81496i	0.0567451	−	0.0982854i
$342$		0			0
$343$	15.4384	−	10.2302i	0.833594	−	0.552377i
$344$	−3.89373	−	2.24805i	−0.209936	−	0.121207i
$345$		0			0
$346$	11.9346	+	6.89043i	0.641606	+	0.370432i
$347$	14.6360	+	25.3503i	0.785701	+	1.36087i	0.928579	+	0.371134i	$0.121031\pi$
$347$	14.6360	+	25.3503i	0.785701	+	1.36087i	−0.142878	+	0.989740i	$0.545636\pi$
$348$		0			0
$349$	−22.1028	+	12.7610i	−1.18313	+	0.683083i	−0.956738	−	0.290952i	$-0.906028\pi$
$349$	−22.1028	+	12.7610i	−1.18313	+	0.683083i	−0.226397	+	0.974035i	$0.572695\pi$
$350$	−0.779411	−	3.94471i	−0.0416613	−	0.210854i
$351$		0			0
$352$	−0.259622	−	0.449678i	−0.0138379	−	0.0239679i
$353$			3.65680i			0.194632i	0.995254	+	0.0973158i	$0.0310257\pi$
$353$			3.65680i			0.194632i	−0.995254	+	0.0973158i	$0.968974\pi$
$354$		0			0
$355$	13.1904			0.700074
$356$		−	8.02946i		−	0.425560i
$357$		0			0
$358$	3.33928	+	1.92793i	0.176486	+	0.101894i
$359$	−29.7911	+	17.1999i	−1.57231	+	0.907775i	−0.576428	+	0.817148i	$0.695554\pi$
$359$	−29.7911	+	17.1999i	−1.57231	+	0.907775i	−0.995885	+	0.0906276i	$0.971113\pi$
$360$		0			0
$361$	−2.40862			−0.126770
$362$	2.75782	+	1.59223i	0.144948	+	0.0836857i
$363$		0			0
$364$	2.41723	−	9.22805i	0.126697	−	0.483681i
$365$	30.5331			1.59818
$366$		0			0
$367$	6.39203			0.333662			0.166831	−	0.985986i	$-0.446647\pi$
$367$	6.39203			0.333662			0.166831	+	0.985986i	$0.446647\pi$
$368$	−4.26046	−	7.37933i	−0.222092	−	0.384674i
$369$		0			0
$370$	−13.0976	−	7.56190i	−0.680912	−	0.393125i
$371$	14.3829	+	16.4429i	0.746721	+	0.853671i
$372$		0			0
$373$	18.2237			0.943588			0.471794	−	0.881709i	$-0.343607\pi$
$373$	18.2237			0.943588			0.471794	+	0.881709i	$0.343607\pi$
$374$	0.450859			0.0233134
$375$		0			0
$376$	1.62493	+	2.81446i	0.0837994	+	0.145145i
$377$	−14.2677	+	1.03392i	−0.734824	+	0.0532498i
$378$		0			0
$379$	−6.69334	+	3.86440i	−0.343814	+	0.198501i	−0.661957	−	0.749542i	$-0.730274\pi$
$379$	−6.69334	+	3.86440i	−0.343814	+	0.198501i	0.318143	+	0.948043i	$0.396941\pi$
$380$	−5.90719	+	10.2316i	−0.303033	+	0.524868i
$381$		0			0
$382$	11.6168	+	6.70696i	0.594367	+	0.343158i
$383$		−	9.81986i		−	0.501771i	−0.968017	−	0.250886i	$-0.919278\pi$
$383$		−	9.81986i		−	0.501771i	0.968017	−	0.250886i	$-0.0807218\pi$
$384$		0			0
$385$	−3.44128	+	0.679942i	−0.175384	+	0.0346530i
$386$	−2.99498	+	5.18745i	−0.152440	+	0.264034i
$387$		0			0
$388$		−	15.0221i		−	0.762632i
$389$	−4.70287	+	8.14562i	−0.238445	+	0.412999i	−0.960268	−	0.279078i	$-0.909971\pi$
$389$	−4.70287	+	8.14562i	−0.238445	+	0.412999i	0.721823	+	0.692078i	$0.243304\pi$
$390$		0			0
$391$	7.39871			0.374169
$392$	−4.27552	+	5.54256i	−0.215946	+	0.279942i
$393$		0			0
$394$	−4.37233			−0.220275
$395$	−24.2125	−	13.9791i	−1.21826	−	0.703365i
$396$		0			0
$397$			11.5422i			0.579288i	0.957134	+	0.289644i	$0.0935369\pi$
$397$			11.5422i			0.579288i	−0.957134	+	0.289644i	$0.906463\pi$
$398$			9.69511i			0.485972i
$399$		0			0
$400$	0.759893	+	1.31617i	0.0379947	+	0.0658087i
$401$	29.0665	+	16.7815i	1.45151	+	0.838030i	0.998567	−	0.0535085i	$-0.0170404\pi$
$401$	29.0665	+	16.7815i	1.45151	+	0.838030i	0.452944	+	0.891539i	$0.350374\pi$
$402$		0			0
$403$	−12.0439	+	8.16809i	−0.599952	+	0.406882i
$404$	4.25033	+	7.36178i	0.211462	+	0.366262i
$405$		0			0
$406$	9.93568	+	3.38688i	0.493100	+	0.168088i
$407$	−1.53775	+	2.66346i	−0.0762233	+	0.132023i
$408$		0			0
$409$	−15.8543	+	9.15349i	−0.783945	+	0.452611i	−0.837827	−	0.545937i	$-0.816174\pi$
$409$	−15.8543	+	9.15349i	−0.783945	+	0.452611i	0.0538817	+	0.998547i	$0.482841\pi$
$410$	15.0037	−	8.66236i	0.740978	−	0.427804i
$411$		0			0
$412$	7.78135	−	13.4777i	0.383360	−	0.663999i
$413$	0.718387	+	3.63586i	0.0353495	+	0.178909i
$414$		0			0
$415$	16.5950	+	28.7433i	0.814614	+	1.41095i
$416$	0.260597	+	3.59612i	0.0127768	+	0.176314i
$417$		0			0
$418$	2.08063	+	1.20125i	0.101767	+	0.0587553i
$419$	8.13046	+	14.0824i	0.397199	+	0.687969i	0.993379	−	0.114882i	$-0.0366489\pi$
$419$	8.13046	+	14.0824i	0.397199	+	0.687969i	−0.596180	+	0.802851i	$0.703316\pi$
$420$		0			0
$421$		−	20.7347i		−	1.01055i	−0.862959	−	0.505274i	$-0.831392\pi$
$421$		−	20.7347i		−	1.01055i	0.862959	−	0.505274i	$-0.168608\pi$
$422$		−	7.09887i		−	0.345567i
$423$		0			0
$424$	−7.15068	−	4.12845i	−0.347268	−	0.200495i
$425$	−1.31963			−0.0640115
$426$		0			0
$427$	5.15449	−	15.1211i	0.249443	−	0.731761i
$428$	−2.74056			−0.132470
$429$		0			0
$430$	5.74014	−	9.94221i	0.276814	−	0.479456i
$431$		−	27.1145i		−	1.30606i	−0.757332	−	0.653030i	$-0.773497\pi$
$431$		−	27.1145i		−	1.30606i	0.757332	−	0.653030i	$-0.226503\pi$
$432$		0			0
$433$	9.82893	−	17.0242i	0.472348	−	0.818131i	−0.527151	−	0.849772i	$-0.676740\pi$
$433$	9.82893	−	17.0242i	0.472348	−	0.818131i	0.999499	+	0.0316404i	$0.0100731\pi$
$434$	10.4761	−	2.06990i	0.502867	−	0.0993584i
$435$		0			0
$436$			14.2032i			0.680212i
$437$	34.1437	+	19.7129i	1.63332	+	0.942996i
$438$		0			0
$439$	8.75923	−	15.1714i	0.418055	−	0.724093i	−0.577688	−	0.816257i	$-0.696045\pi$
$439$	8.75923	−	15.1714i	0.418055	−	0.724093i	0.995744	+	0.0921642i	$0.0293785\pi$
$440$	1.14820	−	0.662914i	0.0547383	−	0.0316032i
$441$		0			0
$442$	−2.81732	−	1.36530i	−0.134006	−	0.0649405i
$443$	17.0463	+	29.5250i	0.809894	+	1.40278i	0.912937	+	0.408100i	$0.133809\pi$
$443$	17.0463	+	29.5250i	0.809894	+	1.40278i	−0.103044	+	0.994677i	$0.532858\pi$
$444$		0			0
$445$	20.5023			0.971903
$446$	6.01269			0.284709
$447$		0			0
$448$	0.853651	−	2.50425i	0.0403312	−	0.118315i
$449$	−24.4229	−	14.1006i	−1.15259	−	0.665447i	−0.203072	−	0.979164i	$-0.565093\pi$
$449$	−24.4229	−	14.1006i	−1.15259	−	0.665447i	−0.949517	+	0.313716i	$0.898426\pi$
$450$		0			0
$451$	−1.76153	−	3.05106i	−0.0829473	−	0.143669i
$452$	−18.5983			−0.874788
$453$		0			0
$454$	3.60284			0.169090
$455$	23.5628	+	6.17213i	1.10464	+	0.289354i
$456$		0			0
$457$	−19.8047	−	11.4342i	−0.926424	−	0.534871i	−0.0407450	−	0.999170i	$-0.512973\pi$
$457$	−19.8047	−	11.4342i	−0.926424	−	0.534871i	−0.885679	+	0.464299i	$0.846306\pi$
$458$	−27.5308			−1.28643
$459$		0			0
$460$	18.8423	−	10.8786i	0.878526	−	0.507217i
$461$	20.8622	+	12.0448i	0.971648	+	0.560981i	0.899738	−	0.436430i	$-0.143757\pi$
$461$	20.8622	+	12.0448i	0.971648	+	0.560981i	0.0719098	+	0.997411i	$0.477091\pi$
$462$		0			0
$463$			12.2189i			0.567860i	0.958845	+	0.283930i	$0.0916384\pi$
$463$			12.2189i			0.567860i	−0.958845	+	0.283930i	$0.908362\pi$
$464$	−3.96752			−0.184188
$465$		0			0
$466$		−	11.6983i		−	0.541915i
$467$	7.51520	+	13.0167i	0.347762	+	0.602341i	0.985852	−	0.167621i	$-0.0536084\pi$
$467$	7.51520	+	13.0167i	0.347762	+	0.602341i	−0.638090	+	0.769962i	$0.720275\pi$
$468$		0			0
$469$	27.6044	+	9.40979i	1.27465	+	0.434504i
$470$	−7.18641	+	4.14908i	−0.331484	+	0.191383i
$471$		0			0
$472$	−0.700397	−	1.21312i	−0.0322384	−	0.0558385i
$473$	−2.02179	−	1.16728i	−0.0929622	−	0.0536718i
$474$		0			0
$475$	−6.08986	−	3.51598i	−0.279422	−	0.161324i
$476$	1.51251	+	1.72914i	0.0693258	+	0.0792551i
$477$		0			0
$478$	−8.21461	+	14.2281i	−0.375727	+	0.650779i
$479$		−	0.906307i		−	0.0414102i	−0.999786	−	0.0207051i	$-0.993409\pi$
$479$		−	0.906307i		−	0.0414102i	0.999786	−	0.0207051i	$-0.00659111\pi$
$480$		0			0
$481$	17.6745	−	11.9867i	0.805890	−	0.546547i
$482$	14.3659			0.654351
$483$		0			0
$484$	5.36519	+	9.29279i	0.243872	+	0.422399i
$485$	38.3573			1.74171
$486$		0			0
$487$	−24.9033	+	14.3779i	−1.12848	+	0.651527i	−0.943552	−	0.331225i	$-0.892538\pi$
$487$	−24.9033	+	14.3779i	−1.12848	+	0.651527i	−0.184926	+	0.982752i	$0.559205\pi$
$488$			6.03817i			0.273335i
$489$		0			0
$490$	−14.1523	−	10.9170i	−0.639336	−	0.493182i
$491$	13.8621	+	24.0099i	0.625589	+	1.08355i	0.988427	+	0.151700i	$0.0484746\pi$
$491$	13.8621	+	24.0099i	0.625589	+	1.08355i	−0.362838	+	0.931852i	$0.618192\pi$
$492$		0			0
$493$	1.72250	−	2.98346i	0.0775776	−	0.134368i
$494$	−9.36375	−	13.8070i	−0.421295	−	0.621205i
$495$		0			0
$496$	−3.49539	+	2.01806i	−0.156948	+	0.0906138i
$497$	10.2873	−	8.99849i	0.461449	−	0.403637i
$498$		0			0
$499$	−3.50306	+	2.02249i	−0.156818	+	0.0905392i	−0.576356	−	0.817199i	$-0.695526\pi$
$499$	−3.50306	+	2.02249i	−0.156818	+	0.0905392i	0.419537	+	0.907738i	$0.362192\pi$
$500$	7.69579	−	4.44317i	0.344166	−	0.198704i
$501$		0			0
$502$	−16.4893	+	9.52013i	−0.735955	+	0.424904i
$503$	0.861181	−	1.49161i	0.0383982	−	0.0665076i	−0.846188	−	0.532885i	$-0.821108\pi$
$503$	0.861181	−	1.49161i	0.0383982	−	0.0665076i	0.884586	+	0.466377i	$0.154441\pi$
$504$		0			0
$505$	−18.7975	+	10.8527i	−0.836477	+	0.482940i
$506$	−2.21221	−	3.83166i	−0.0983448	−	0.170338i
$507$		0			0
$508$	5.67318	−	9.82624i	0.251707	−	0.435969i
$509$	−36.2224	−	20.9130i	−1.60553	−	0.926953i	−0.990354	−	0.138563i	$-0.955752\pi$
$509$	−36.2224	−	20.9130i	−1.60553	−	0.926953i	−0.615176	−	0.788390i	$-0.710915\pi$
$510$		0			0
$511$	23.8131	−	20.8297i	1.05343	−	0.921452i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−20.2071	+	11.6666i	−0.891298	+	0.514591i
$515$	34.4138	+	19.8688i	1.51645	+	0.875524i
$516$		0			0
$517$	0.843734	+	1.46139i	0.0371074	+	0.0642718i
$518$	−15.3737	+	3.03759i	−0.675480	+	0.133464i
$519$		0			0
$520$	−9.18229	+	0.665404i	−0.402670	+	0.0291799i
$521$	14.7751	−	25.5912i	0.647308	−	1.12117i	−0.336455	−	0.941700i	$-0.609228\pi$
$521$	14.7751	−	25.5912i	0.647308	−	1.12117i	0.983763	−	0.179471i	$-0.0574386\pi$
$522$		0			0
$523$	−5.43131	+	9.40731i	−0.237495	+	0.411353i	−0.959995	−	0.280018i	$-0.909660\pi$
$523$	−5.43131	+	9.40731i	−0.237495	+	0.411353i	0.722500	+	0.691371i	$0.242993\pi$
$524$	−1.43219	+	2.48062i	−0.0625655	+	0.108367i
$525$		0			0
$526$	17.8690	+	10.3167i	0.779124	+	0.449828i
$527$		−	3.50457i		−	0.152662i
$528$		0			0
$529$	−24.8030	−	42.9600i	−1.07839	−	1.86783i
$530$	10.5415	−	18.2585i	0.457895	−	0.793097i
$531$		0			0
$532$	2.37290	+	12.0096i	0.102878	+	0.520681i
$533$	1.76815	+	24.3997i	0.0765870	+	1.05687i
$534$		0			0
$535$		−	6.99770i		−	0.302537i
$536$	−11.0230			−0.476121
$537$		0			0
$538$			8.74233i			0.376909i
$539$	−2.22003	+	2.87794i	−0.0956235	+	0.123961i
$540$		0			0
$541$	−9.53428	+	5.50462i	−0.409911	+	0.236662i	−0.690751	−	0.723092i	$-0.742720\pi$
$541$	−9.53428	+	5.50462i	−0.409911	+	0.236662i	0.280841	+	0.959754i	$0.409387\pi$
$542$	−5.06054	−	8.76510i	−0.217369	−	0.376493i
$543$		0			0
$544$	−0.751971	−	0.434150i	−0.0322405	−	0.0186140i
$545$	−36.2664			−1.55348
$546$		0			0
$547$	−36.2418			−1.54959			−0.774793	−	0.632215i	$-0.782146\pi$
$547$	−36.2418			−1.54959			−0.774793	+	0.632215i	$0.782146\pi$
$548$	8.49269	+	4.90326i	0.362790	+	0.209457i
$549$		0			0
$550$	0.394569	+	0.683414i	0.0168245	+	0.0291409i
$551$	15.8981	−	9.17876i	0.677281	−	0.391028i
$552$		0			0
$553$	−28.4201	+	5.61535i	−1.20855	+	0.238789i
$554$		−	4.97733i		−	0.211466i
$555$		0			0
$556$	−6.98635			−0.296287
$557$		−	11.1046i		−	0.470519i	−0.971933	−	0.235260i	$-0.924406\pi$
$557$		−	11.1046i		−	0.470519i	0.971933	−	0.235260i	$-0.0755940\pi$
$558$		0			0
$559$	9.09895	+	13.4165i	0.384845	+	0.567458i
$560$	6.39433	+	2.17970i	0.270210	+	0.0921092i
$561$		0			0
$562$	−13.6364	+	23.6190i	−0.575218	+	0.996307i
$563$	5.15606	+	8.93055i	0.217302	+	0.376378i	0.953982	−	0.299863i	$-0.0969411\pi$
$563$	5.15606	+	8.93055i	0.217302	+	0.376378i	−0.736680	+	0.676241i	$0.763608\pi$
$564$		0			0
$565$		−	47.4886i		−	1.99786i
$566$	8.49149	+	4.90256i	0.356924	+	0.206070i
$567$		0			0
$568$	−2.58292	+	4.47375i	−0.108377	+	0.187714i
$569$	−16.9098	+	29.2886i	−0.708894	+	1.22784i	0.256373	+	0.966578i	$0.417472\pi$
$569$	−16.9098	+	29.2886i	−0.708894	+	1.22784i	−0.965268	+	0.261263i	$0.915861\pi$
$570$		0			0
$571$	6.09944	−	10.5645i	0.255254	−	0.442112i	−0.709711	−	0.704493i	$-0.751174\pi$
$571$	6.09944	−	10.5645i	0.255254	−	0.442112i	0.964964	+	0.262381i	$0.0845077\pi$
$572$	0.135313	+	1.86726i	0.00565772	+	0.0780741i
$573$		0			0
$574$	5.79202	−	16.9913i	0.241754	−	0.709205i
$575$	6.47498	+	11.2150i	0.270025	+	0.467698i
$576$		0			0
$577$	22.1116	+	12.7661i	0.920517	+	0.531460i	0.883800	−	0.467865i	$-0.154977\pi$
$577$	22.1116	+	12.7661i	0.920517	+	0.531460i	0.0367167	+	0.999326i	$0.488310\pi$
$578$	−14.0695	+	8.12303i	−0.585214	+	0.337873i
$579$		0			0
$580$		−	10.1306i		−	0.420651i
$581$	32.5512	+	11.0961i	1.35045	+	0.460343i
$582$		0			0
$583$	−3.71294	−	2.14367i	−0.153774	−	0.0887817i
$584$	−5.97895	+	10.3558i	−0.247411	+	0.428528i
$585$		0			0
$586$	14.0354	+	24.3101i	0.579799	+	1.00424i
$587$	−17.3456	+	10.0145i	−0.715928	+	0.413341i	−0.813252	−	0.581912i	$-0.802305\pi$
$587$	−17.3456	+	10.0145i	−0.715928	+	0.413341i	0.0973243	+	0.995253i	$0.468972\pi$
$588$		0			0
$589$	9.33747	−	16.1730i	0.384744	−	0.666396i
$590$	3.09757	−	1.78838i	0.127525	−	0.0736266i
$591$		0			0
$592$	5.12950	−	2.96152i	0.210821	−	0.121718i
$593$	3.62655	−	2.09379i	0.148924	−	0.0859816i	−0.423686	−	0.905809i	$-0.639264\pi$
$593$	3.62655	−	2.09379i	0.148924	−	0.0859816i	0.572611	+	0.819827i	$0.305931\pi$
$594$		0			0
$595$	−4.41517	+	3.86203i	−0.181004	+	0.158328i
$596$	0.548493	−	0.316672i	0.0224671	−	0.0129714i
$597$		0			0
$598$	2.22052	+	30.6422i	0.0908039	+	1.25305i
$599$	−13.7033	+	23.7348i	−0.559900	+	0.969776i	0.437604	+	0.899168i	$0.355827\pi$
$599$	−13.7033	+	23.7348i	−0.559900	+	0.969776i	−0.997504	+	0.0706079i	$0.977506\pi$
$600$		0			0
$601$	−12.7864	−	22.1467i	−0.521569	−	0.903383i	−0.999685	−	0.0250869i	$-0.992014\pi$
$601$	−12.7864	−	22.1467i	−0.521569	−	0.903383i	0.478117	−	0.878296i	$-0.341320\pi$
$602$	−2.30579	−	11.6699i	−0.0939770	−	0.475631i
$603$		0			0
$604$			3.96564i			0.161360i
$605$	−23.7281	+	13.6994i	−0.964684	+	0.556960i
$606$		0			0
$607$	−36.3560			−1.47564			−0.737822	−	0.674995i	$-0.764146\pi$
$607$	−36.3560			−1.47564			−0.737822	+	0.674995i	$0.764146\pi$
$608$	−2.31347	−	4.00705i	−0.0938237	−	0.162507i
$609$		0			0
$610$	−15.4178			−0.624248
$611$	−0.846903	−	11.6869i	−0.0342620	−	0.472801i
$612$		0			0
$613$		−	22.4164i		−	0.905391i	−0.891665	−	0.452696i	$-0.850462\pi$
$613$		−	22.4164i		−	0.905391i	0.891665	−	0.452696i	$-0.149538\pi$
$614$	13.5036	−	23.3890i	0.544962	−	0.943902i
$615$		0			0
$616$	0.443252	−	1.30032i	0.0178591	−	0.0523912i
$617$	9.38150	+	5.41641i	0.377685	+	0.218056i	0.676810	−	0.736157i	$-0.263362\pi$
$617$	9.38150	+	5.41641i	0.377685	+	0.218056i	−0.299126	+	0.954214i	$0.596695\pi$
$618$		0			0
$619$	35.7658	+	20.6494i	1.43755	+	0.829969i	0.997679	−	0.0680933i	$-0.0216916\pi$
$619$	35.7658	+	20.6494i	1.43755	+	0.829969i	0.439869	+	0.898062i	$0.355025\pi$
$620$	−5.15290	−	8.92509i	−0.206945	−	0.358440i
$621$		0			0
$622$	20.9499	−	12.0954i	0.840015	−	0.484983i
$623$	15.9899	−	13.9867i	0.640623	−	0.560364i
$624$		0			0
$625$	15.1446	+	26.2312i	0.605784	+	1.04925i
$626$		−	23.7881i		−	0.950765i
$627$		0			0
$628$	−9.66896			−0.385833
$629$			5.14298i			0.205064i
$630$		0			0
$631$	4.11495	+	2.37577i	0.163814	+	0.0945779i	0.579666	−	0.814854i	$-0.303183\pi$
$631$	4.11495	+	2.37577i	0.163814	+	0.0945779i	−0.415852	+	0.909432i	$0.636517\pi$
$632$	9.48251	−	5.47473i	0.377194	−	0.217773i
$633$		0			0
$634$	−8.72129			−0.346367
$635$	25.0902	+	14.4858i	0.995674	+	0.574853i
$636$		0			0
$637$	22.5875	−	11.2608i	0.894948	−	0.446171i
$638$	−2.06011			−0.0815605
$639$		0			0
$640$	−2.55339			−0.100931
$641$	4.00654	+	6.93952i	0.158249	+	0.274095i	0.934237	−	0.356652i	$-0.116082\pi$
$641$	4.00654	+	6.93952i	0.158249	+	0.274095i	−0.775989	+	0.630747i	$0.782749\pi$
$642$		0			0
$643$	−41.7271	−	24.0911i	−1.64556	−	0.950062i	−0.978809	−	0.204777i	$-0.934353\pi$
$643$	−41.7271	−	24.0911i	−1.64556	−	0.950062i	−0.666747	−	0.745284i	$-0.732314\pi$
$644$	7.27389	−	21.3385i	0.286631	−	0.840855i
$645$		0			0
$646$	4.01758			0.158070
$647$	−26.2164			−1.03067			−0.515337	−	0.856988i	$-0.672333\pi$
$647$	−26.2164			−1.03067			−0.515337	+	0.856988i	$0.672333\pi$
$648$		0			0
$649$	−0.363676	−	0.629906i	−0.0142755	−	0.0247260i
$650$	−0.396051	−	5.46534i	−0.0155344	−	0.214368i
$651$		0			0
$652$	−20.5444	+	11.8613i	−0.804583	+	0.464526i
$653$	13.5659	−	23.4968i	0.530874	−	0.919501i	−0.468477	−	0.883476i	$-0.655197\pi$
$653$	13.5659	−	23.4968i	0.530874	−	0.919501i	0.999351	−	0.0360253i	$-0.0114697\pi$
$654$		0			0
$655$	−6.33399	−	3.65693i	−0.247490	−	0.142888i
$656$			6.78500i			0.264910i
$657$		0			0
$658$	−2.77425	+	8.13847i	−0.108151	+	0.317271i
$659$	18.6795	−	32.3538i	0.727649	−	1.26033i	−0.230225	−	0.973137i	$-0.573946\pi$
$659$	18.6795	−	32.3538i	0.727649	−	1.26033i	0.957874	−	0.287188i	$-0.0927205\pi$
$660$		0			0
$661$			12.5245i			0.487148i	0.969882	+	0.243574i	$0.0783199\pi$
$661$			12.5245i			0.487148i	−0.969882	+	0.243574i	$0.921680\pi$
$662$	6.00281	−	10.3972i	0.233306	−	0.404097i
$663$		0			0
$664$	−12.9984			−0.504435
$665$	−30.6651	+	6.05892i	−1.18914	+	0.234955i
$666$		0			0
$667$	−33.8069			−1.30901
$668$	−3.53346	−	2.04005i	−0.136714	−	0.0789318i
$669$		0			0
$670$		−	28.1460i		−	1.08737i
$671$			3.13528i			0.121036i
$672$		0			0
$673$	−0.488082	−	0.845383i	−0.0188142	−	0.0325871i	0.856465	−	0.516205i	$-0.172656\pi$
$673$	−0.488082	−	0.845383i	−0.0188142	−	0.0325871i	−0.875279	+	0.483618i	$0.839322\pi$
$674$	−19.4291	−	11.2174i	−0.748379	−	0.432077i
$675$		0			0
$676$	4.80892	−	12.0778i	0.184958	−	0.464532i
$677$	−11.9057	−	20.6213i	−0.457574	−	0.792541i	0.541258	−	0.840856i	$-0.317948\pi$
$677$	−11.9057	−	20.6213i	−0.457574	−	0.792541i	−0.998832	+	0.0483154i	$0.984615\pi$
$678$		0			0
$679$	29.9152	−	26.1673i	1.14804	−	1.00421i
$680$	1.10855	−	1.92007i	0.0425111	−	0.0736314i
$681$		0			0
$682$	−1.81496	+	1.04787i	−0.0694983	+	0.0401249i
$683$	−36.8982	+	21.3032i	−1.41187	+	0.815144i	−0.995565	−	0.0940804i	$-0.970009\pi$
$683$	−36.8982	+	21.3032i	−1.41187	+	0.815144i	−0.416306	+	0.909224i	$0.636676\pi$
$684$		0			0
$685$	−12.5199	+	21.6851i	−0.478361	+	0.828546i
$686$	−18.4851	+	1.14040i	−0.705765	+	0.0435406i
$687$		0			0
$688$	2.24805	+	3.89373i	0.0857061	+	0.148447i
$689$	16.7098	+	24.6389i	0.636595	+	0.938666i
$690$		0			0
$691$	−33.4779	−	19.3285i	−1.27356	−	0.735289i	−0.297903	−	0.954596i	$-0.596287\pi$
$691$	−33.4779	−	19.3285i	−1.27356	−	0.735289i	−0.975656	+	0.219307i	$0.929620\pi$
$692$	−6.89043	−	11.9346i	−0.261935	−	0.453684i
$693$		0			0
$694$		−	29.2720i		−	1.11115i
$695$		−	17.8388i		−	0.676666i
$696$		0			0
$697$	−5.10212	−	2.94571i	−0.193257	−	0.111577i
$698$	25.5221			0.966025
$699$		0			0
$700$	−1.29737	+	3.80593i	−0.0490359	+	0.143851i
$701$	12.0226			0.454087			0.227044	−	0.973885i	$-0.427094\pi$
$701$	12.0226			0.454087			0.227044	+	0.973885i	$0.427094\pi$
$702$		0			0
$703$	−13.7028	+	23.7339i	−0.516810	+	0.895142i
$704$			0.519243i			0.0195697i
$705$		0			0
$706$	1.82840	−	3.16688i	0.0688127	−	0.119187i
$707$	−7.25659	+	21.2878i	−0.272912	+	0.800610i
$708$		0			0
$709$		−	31.4330i		−	1.18049i	−0.807224	−	0.590245i	$-0.799031\pi$
$709$		−	31.4330i		−	1.18049i	0.807224	−	0.590245i	$-0.200969\pi$
$710$	−11.4232	−	6.59520i	−0.428706	−	0.247513i
$711$		0			0
$712$	−4.01473	+	6.95371i	−0.150458	+	0.260601i
$713$	−29.7839	+	17.1958i	−1.11542	+	0.643986i
$714$		0			0
$715$	−4.76784	+	0.345507i	−0.178307	+	0.0129212i
$716$	−1.92793	−	3.33928i	−0.0720502	−	0.124795i
$717$		0			0
$718$	34.3998			1.28379
$719$	−51.3353			−1.91448			−0.957241	−	0.289290i	$-0.906581\pi$
$719$	−51.3353			−1.91448			−0.957241	+	0.289290i	$0.906581\pi$
$720$		0			0
$721$	40.3941	−	7.98122i	1.50436	−	0.297236i
$722$	2.08593	+	1.20431i	0.0776303	+	0.0448199i
$723$		0			0
$724$	−1.59223	−	2.75782i	−0.0591747	−	0.102494i
$725$	6.02979			0.223941
$726$		0			0
$727$	−10.6652			−0.395549			−0.197774	−	0.980248i	$-0.563371\pi$
$727$	−10.6652			−0.395549			−0.197774	+	0.980248i	$0.563371\pi$
$728$	−6.70741	+	6.78311i	−0.248593	+	0.251399i
$729$		0			0
$730$	−26.4425	−	15.2666i	−0.978680	−	0.565041i
$731$	−3.90396			−0.144393
$732$		0			0
$733$	1.58513	−	0.915174i	0.0585481	−	0.0338027i	−0.470440	−	0.882432i	$-0.655905\pi$
$733$	1.58513	−	0.915174i	0.0585481	−	0.0338027i	0.528988	+	0.848629i	$0.322572\pi$
$734$	−5.53566	−	3.19602i	−0.204325	−	0.117967i
$735$		0			0
$736$			8.52091i			0.314085i
$737$	−5.72361			−0.210832
$738$		0			0
$739$			44.8463i			1.64970i	0.565353	+	0.824849i	$0.308740\pi$
$739$			44.8463i			1.64970i	−0.565353	+	0.824849i	$0.691260\pi$
$740$	7.56190	+	13.0976i	0.277981	+	0.481477i
$741$		0			0
$742$	−4.23449	−	21.4314i	−0.155453	−	0.786770i
$743$	−31.7298	+	18.3192i	−1.16405	+	0.672066i	−0.952272	−	0.305251i	$-0.901260\pi$
$743$	−31.7298	+	18.3192i	−1.16405	+	0.672066i	−0.211781	+	0.977317i	$0.567926\pi$
$744$		0			0
$745$	0.808587	+	1.40051i	0.0296244	+	0.0513109i
$746$	−15.7822	−	9.11185i	−0.577827	−	0.333609i
$747$		0			0
$748$	−0.390455	−	0.225430i	−0.0142765	−	0.00824252i
$749$	−4.77383	−	5.45757i	−0.174432	−	0.199415i
$750$		0			0
$751$	−18.8234	+	32.6031i	−0.686877	+	1.18971i	0.285966	+	0.958240i	$0.407686\pi$
$751$	−18.8234	+	32.6031i	−0.686877	+	1.18971i	−0.972843	+	0.231466i	$0.925648\pi$
$752$		−	3.24986i		−	0.118510i
$753$		0			0
$754$	12.8732	+	6.23845i	0.468813	+	0.227191i
$755$	−10.1258			−0.368516
$756$		0			0
$757$	−0.733508	−	1.27047i	−0.0266598	−	0.0461761i	0.852388	−	0.522910i	$-0.175154\pi$
$757$	−0.733508	−	1.27047i	−0.0266598	−	0.0461761i	−0.879047	+	0.476734i	$0.841820\pi$
$758$	7.72880			0.280723
$759$		0			0
$760$	10.2316	−	5.90719i	0.371138	−	0.214276i
$761$			14.4443i			0.523605i	0.965121	+	0.261803i	$0.0843169\pi$
$761$			14.4443i			0.523605i	−0.965121	+	0.261803i	$0.915683\pi$
$762$		0			0
$763$	−28.2845	+	24.7409i	−1.02397	+	0.895681i
$764$	−6.70696	−	11.6168i	−0.242649	−	0.420281i
$765$		0			0
$766$	−4.90993	+	8.50425i	−0.177403	+	0.307271i
$767$	0.365042	+	5.03742i	0.0131809	+	0.181891i
$768$		0			0
$769$	−36.5814	+	21.1203i	−1.31916	+	0.761617i	−0.983593	−	0.180400i	$-0.942261\pi$
$769$	−36.5814	+	21.1203i	−1.31916	+	0.761617i	−0.335566	+	0.942017i	$0.608928\pi$
$770$	3.32021	+	1.13179i	0.119652	+	0.0407871i
$771$		0			0
$772$	5.18745	−	2.99498i	0.186700	−	0.107792i
$773$	5.95780	−	3.43974i	0.214287	−	0.123719i	−0.389015	−	0.921231i	$-0.627185\pi$
$773$	5.95780	−	3.43974i	0.214287	−	0.123719i	0.603302	+	0.797513i	$0.293851\pi$
$774$		0			0
$775$	5.31225	−	3.06703i	0.190822	−	0.110171i
$776$	−7.51106	+	13.0095i	−0.269631	+	0.467015i
$777$		0			0
$778$	8.14562	−	4.70287i	0.292035	−	0.168606i
$779$	−15.6969	−	27.1878i	−0.562400	−	0.974106i
$780$		0			0
$781$	−1.34116	+	2.32296i	−0.0479906	+	0.0831222i
$782$	−6.40747	−	3.69936i	−0.229131	−	0.132289i
$783$		0			0
$784$	6.47398	−	2.66224i	0.231214	−	0.0950800i
$785$		−	24.6886i		−	0.881174i
$786$		0			0
$787$	−26.3386	+	15.2066i	−0.938871	+	0.542057i	−0.889606	−	0.456729i	$-0.849021\pi$
$787$	−26.3386	+	15.2066i	−0.938871	+	0.542057i	−0.0492644	+	0.998786i	$0.515688\pi$
$788$	3.78655	+	2.18617i	0.134890	+	0.0778790i
$789$		0			0
$790$	13.9791	+	24.2125i	0.497354	+	0.861442i
$791$	−32.3967	−	37.0367i	−1.15189	−	1.31688i
$792$		0			0
$793$	9.49428	−	19.5916i	0.337152	−	0.695719i
$794$	5.77112	−	9.99586i	0.204809	−	0.354740i
$795$		0			0
$796$	4.84755	−	8.39621i	0.171817	−	0.297596i
$797$	−8.31093	+	14.3949i	−0.294388	+	0.509895i	−0.974842	−	0.222895i	$-0.928449\pi$
$797$	−8.31093	+	14.3949i	−0.294388	+	0.509895i	0.680454	+	0.732791i	$0.261782\pi$
$798$		0			0
$799$	2.44380	+	1.41093i	0.0864554	+	0.0499150i
$800$		−	1.51979i		−	0.0537326i
$801$		0			0
$802$	−16.7815	−	29.0665i	−0.592577	−	1.02637i
$803$	−3.10453	+	5.37720i	−0.109556	+	0.189757i
$804$		0			0
$805$	54.4855	+	18.5730i	1.92036	+	0.654614i
$806$	14.5144	−	1.05180i	0.511248	−	0.0370481i
$807$		0			0
$808$		−	8.50066i		−	0.299052i
$809$	−33.8116			−1.18875			−0.594376	−	0.804187i	$-0.702601\pi$
$809$	−33.8116			−1.18875			−0.594376	+	0.804187i	$0.702601\pi$
$810$		0			0
$811$		−	34.4041i		−	1.20809i	−0.796950	−	0.604045i	$-0.793555\pi$
$811$		−	34.4041i		−	1.20809i	0.796950	−	0.604045i	$-0.206445\pi$
$812$	−6.91111	−	7.90097i	−0.242533	−	0.277270i
$813$		0			0
$814$	2.66346	−	1.53775i	0.0933541	−	0.0538980i
$815$	−30.2866	−	52.4579i	−1.06089	−	1.83752i
$816$		0			0
$817$	−18.0161	−	10.4016i	−0.630303	−	0.363906i
$818$	18.3070			0.640088
$819$		0			0
$820$	−17.3247			−0.605006
$821$	−13.2427	−	7.64567i	−0.462173	−	0.266836i	0.250785	−	0.968043i	$-0.419311\pi$
$821$	−13.2427	−	7.64567i	−0.462173	−	0.266836i	−0.712957	+	0.701207i	$0.752645\pi$
$822$		0			0
$823$	7.14846	+	12.3815i	0.249180	+	0.431592i	0.963298	−	0.268433i	$-0.0865057\pi$
$823$	7.14846	+	12.3815i	0.249180	+	0.431592i	−0.714119	+	0.700025i	$0.753172\pi$
$824$	−13.4777	+	7.78135i	−0.469518	+	0.271076i
$825$		0			0
$826$	1.19579	−	3.50794i	0.0416068	−	0.122057i
$827$		−	40.6945i		−	1.41509i	−0.706670	−	0.707543i	$-0.749804\pi$
$827$		−	40.6945i		−	1.41509i	0.706670	−	0.707543i	$-0.250196\pi$
$828$		0			0
$829$	31.9196			1.10861			0.554306	−	0.832313i	$-0.312984\pi$
$829$	31.9196			1.10861			0.554306	+	0.832313i	$0.312984\pi$
$830$		−	33.1899i		−	1.15204i
$831$		0			0
$832$	1.57238	−	3.24463i	0.0545124	−	0.112487i
$833$	−0.808757	+	6.02406i	−0.0280218	+	0.208721i
$834$		0			0
$835$	5.20903	−	9.02230i	0.180266	−	0.312230i
$836$	−1.20125	−	2.08063i	−0.0415463	−	0.0719602i
$837$		0			0
$838$		−	16.2609i		−	0.561724i
$839$	−13.8203	−	7.97917i	−0.477131	−	0.275471i	0.242089	−	0.970254i	$-0.422167\pi$
$839$	−13.8203	−	7.97917i	−0.477131	−	0.275471i	−0.719220	+	0.694782i	$0.755501\pi$
$840$		0			0
$841$	6.62937	−	11.4824i	0.228599	−	0.395945i
$842$	−10.3674	+	17.9568i	−0.357282	+	0.618831i
$843$		0			0
$844$	−3.54943	+	6.14780i	−0.122177	+	0.211616i
$845$	30.8394	+	12.2790i	1.06091	+	0.422412i
$846$		0			0
$847$	−9.16001	+	26.8716i	−0.314742	+	0.923319i
$848$	4.12845	+	7.15068i	0.141772	+	0.245555i
$849$		0			0
$850$	1.14283	+	0.659816i	0.0391989	+	0.0226315i
$851$	43.7080	−	25.2348i	1.49829	−	0.865039i
$852$		0			0
$853$		−	21.8333i		−	0.747559i	−0.927518	−	0.373779i	$-0.878062\pi$
$853$		−	21.8333i		−	0.747559i	0.927518	−	0.373779i	$-0.121938\pi$
$854$	−12.0245	+	10.5180i	−0.411469	+	0.359919i
$855$		0			0
$856$	2.37339	+	1.37028i	0.0811208	+	0.0468351i
$857$	27.3267	−	47.3312i	0.933461	−	1.61680i	0.156106	−	0.987740i	$-0.450106\pi$
$857$	27.3267	−	47.3312i	0.933461	−	1.61680i	0.777355	−	0.629062i	$-0.216561\pi$
$858$		0			0
$859$	−19.0946	−	33.0728i	−0.651500	−	1.12843i	−0.982759	−	0.184891i	$-0.940807\pi$
$859$	−19.0946	−	33.0728i	−0.651500	−	1.12843i	0.331259	−	0.943540i	$-0.392527\pi$
$860$	−9.94221	+	5.74014i	−0.339027	+	0.195737i
$861$		0			0
$862$	−13.5573	+	23.4819i	−0.461762	+	0.799796i
$863$	−5.85315	+	3.37932i	−0.199244	+	0.115033i	−0.596303	−	0.802760i	$-0.703364\pi$
$863$	−5.85315	+	3.37932i	−0.199244	+	0.115033i	0.397059	+	0.917793i	$0.370031\pi$
$864$		0			0
$865$	30.4736	−	17.5939i	1.03613	−	0.598211i
$866$	−17.0242	+	9.82893i	−0.578506	+	0.334001i
$867$		0			0
$868$	−10.1075	−	3.44545i	−0.343070	−	0.116946i
$869$	4.92372	−	2.84271i	0.167026	−	0.0964325i
$870$		0			0
$871$	35.7655	+	17.3323i	1.21187	+	0.587283i
$872$	7.10162	−	12.3004i	0.240491	−	0.416543i
$873$		0			0
$874$	−19.7129	−	34.1437i	−0.666799	−	1.15493i
$875$	22.2536	+	7.58583i	0.752310	+	0.256448i
$876$		0			0
$877$			19.3908i			0.654781i	0.944889	+	0.327390i	$0.106169\pi$
$877$			19.3908i			0.654781i	−0.944889	+	0.327390i	$0.893831\pi$
$878$	−15.1714	+	8.75923i	−0.512011	+	0.295610i
$879$		0			0
$880$	−1.32583			−0.0446937
$881$	−28.6313	−	49.5909i	−0.964615	−	1.67076i	−0.710647	−	0.703549i	$-0.751598\pi$
$881$	−28.6313	−	49.5909i	−0.964615	−	1.67076i	−0.253968	−	0.967213i	$-0.581736\pi$
$882$		0			0
$883$	27.5353			0.926637			0.463318	−	0.886192i	$-0.346659\pi$
$883$	27.5353			0.926637			0.463318	+	0.886192i	$0.346659\pi$
$884$	1.75722	+	2.59104i	0.0591017	+	0.0871461i
$885$		0			0
$886$		−	34.0926i		−	1.14536i
$887$	3.16134	−	5.47560i	0.106147	−	0.183853i	−0.808059	−	0.589102i	$-0.799482\pi$
$887$	3.16134	−	5.47560i	0.106147	−	0.183853i	0.914206	+	0.405249i	$0.132815\pi$
$888$		0			0
$889$	29.4503	−	5.81890i	0.987731	−	0.195160i
$890$	−17.7555	−	10.2512i	−0.595166	−	0.343620i
$891$		0			0
$892$	−5.20714	−	3.00634i	−0.174348	−	0.100660i
$893$	7.51846	+	13.0224i	0.251596	+	0.435777i
$894$		0			0
$895$	8.52647	−	4.92276i	0.285008	−	0.164550i
$896$	−1.99141	+	1.74192i	−0.0665283	+	0.0581935i
$897$		0			0
$898$	14.1006	+	24.4229i	0.470542	+	0.815003i
$899$			16.0134i			0.534078i
$900$		0			0
$901$	−7.16947			−0.238850
$902$			3.52306i			0.117305i
$903$		0			0
$904$	16.1066	+	9.29913i	0.535696	+	0.309284i
$905$	7.04179	−	4.06558i	0.234077	−	0.135144i
$906$		0			0
$907$	−43.0540			−1.42959			−0.714793	−	0.699337i	$-0.753479\pi$
$907$	−43.0540			−1.42959			−0.714793	+	0.699337i	$0.753479\pi$
$908$	−3.12015	−	1.80142i	−0.103546	−	0.0597822i
$909$		0			0
$910$	−17.3199	−	17.1266i	−0.574150	−	0.567742i
$911$	−21.4332			−0.710114			−0.355057	−	0.934845i	$-0.615539\pi$
$911$	−21.4332			−0.710114			−0.355057	+	0.934845i	$0.615539\pi$
$912$		0			0
$913$	−6.74932			−0.223370
$914$	11.4342	+	19.8047i	0.378211	+	0.655080i
$915$		0			0
$916$	23.8424	+	13.7654i	0.787775	+	0.454822i
$917$	−7.43470	+	1.46898i	−0.245515	+	0.0485098i
$918$		0			0
$919$	−45.8381			−1.51206			−0.756030	−	0.654537i	$-0.772864\pi$
$919$	−45.8381			−1.51206			−0.756030	+	0.654537i	$0.772864\pi$
$920$	−21.7572			−0.717313
$921$		0			0
$922$	−12.0448	−	20.8622i	−0.396674	−	0.687059i
$923$	15.4151	−	10.4543i	0.507393	−	0.344109i
$924$		0			0
$925$	−7.79574	+	4.50088i	−0.256322	+	0.147988i
$926$	6.10945	−	10.5819i	0.200769	−	0.347742i
$927$		0			0
$928$	3.43598	+	1.98376i	0.112791	+	0.0651202i
$929$			18.9937i			0.623163i	0.950219	+	0.311581i	$0.100859\pi$
$929$			18.9937i			0.623163i	−0.950219	+	0.311581i	$0.899141\pi$
$930$		0			0
$931$	−19.7826	+	25.6451i	−0.648348	+	0.840485i
$932$	−5.84917	+	10.1311i	−0.191596	+	0.331854i
$933$		0			0
$934$		−	15.0304i		−	0.491810i
$935$	0.575609	−	0.996984i	0.0188244	−	0.0326049i
$936$		0			0
$937$	30.7500			1.00456			0.502280	−	0.864705i	$-0.332495\pi$
$937$	30.7500			1.00456			0.502280	+	0.864705i	$0.332495\pi$
$938$	−19.2012	−	21.9513i	−0.626941	−	0.716735i
$939$		0			0
$940$	8.29815			0.270656
$941$	−19.1978	−	11.0838i	−0.625830	−	0.361323i	0.153305	−	0.988179i	$-0.451008\pi$
$941$	−19.1978	−	11.0838i	−0.625830	−	0.361323i	−0.779135	+	0.626856i	$0.784341\pi$
$942$		0			0
$943$			57.8144i			1.88270i
$944$			1.40079i			0.0455920i
$945$		0			0
$946$	1.16728	+	2.02179i	0.0379517	+	0.0657342i
$947$	36.6168	+	21.1407i	1.18989	+	0.686981i	0.958281	−	0.285829i	$-0.0922690\pi$
$947$	36.6168	+	21.1407i	1.18989	+	0.686981i	0.231605	+	0.972810i	$0.425602\pi$
$948$		0			0
$949$	35.6828	−	24.1997i	1.15831	−	0.785556i
$950$	3.51598	+	6.08986i	0.114074	+	0.197581i
$951$		0			0
$952$	−0.445302	−	2.25374i	−0.0144323	−	0.0730440i
$953$	−11.3076	+	19.5853i	−0.366289	+	0.634431i	−0.988982	−	0.148035i	$-0.952705\pi$
$953$	−11.3076	+	19.5853i	−0.366289	+	0.634431i	0.622693	+	0.782466i	$0.286039\pi$
$954$		0			0
$955$	29.6622	−	17.1255i	0.959845	−	0.554167i
$956$	14.2281	−	8.21461i	0.460170	−	0.265679i
$957$		0			0
$958$	−0.453153	+	0.784884i	−0.0146407	+	0.0253585i
$959$	5.02920	+	25.4535i	0.162401	+	0.821936i
$960$		0			0
$961$	−7.35483	−	12.7389i	−0.237253	−	0.410934i
$962$	−21.3000	+	1.54352i	−0.686738	+	0.0497652i
$963$		0			0
$964$	−12.4413	−	7.18297i	−0.400706	−	0.231348i
$965$	7.64733	+	13.2456i	0.246176	+	0.426390i
$966$		0			0
$967$			24.8036i			0.797629i	0.917032	+	0.398815i	$0.130578\pi$
$967$			24.8036i			0.797629i	−0.917032	+	0.398815i	$0.869422\pi$
$968$		−	10.7304i		−	0.344888i
$969$		0			0
$970$	−33.2184	−	19.1786i	−1.06658	−	0.615789i
$971$	−41.4030			−1.32868			−0.664342	−	0.747429i	$-0.731288\pi$
$971$	−41.4030			−1.32868			−0.664342	+	0.747429i	$0.731288\pi$
$972$		0			0
$973$	−12.1697	−	13.9127i	−0.390141	−	0.446020i
$974$	28.7559			0.921398
$975$		0			0
$976$	3.01909	−	5.22921i	0.0966386	−	0.167383i
$977$			19.3117i			0.617836i	0.951089	+	0.308918i	$0.0999669\pi$
$977$			19.3117i			0.617836i	−0.951089	+	0.308918i	$0.900033\pi$
$978$		0			0
$979$	−2.08462	+	3.61067i	−0.0666247	+	0.115397i
$980$	6.79773	+	16.5306i	0.217146	+	0.528050i
$981$		0			0
$982$		−	27.7243i		−	0.884717i
$983$	9.97803	+	5.76082i	0.318250	+	0.183742i	0.650612	−	0.759410i	$-0.274512\pi$
$983$	9.97803	+	5.76082i	0.318250	+	0.183742i	−0.332362	+	0.943152i	$0.607846\pi$
$984$		0			0
$985$	−5.58213	+	9.66854i	−0.177862	+	0.308065i
$986$	−2.98346	+	1.72250i	−0.0950128	+	0.0548557i
$987$		0			0
$988$	1.20577	+	16.6391i	0.0383605	+	0.529359i
$989$	19.1554	+	33.1782i	0.609107	+	1.05500i
$990$		0			0
$991$	−11.2763			−0.358204			−0.179102	−	0.983830i	$-0.557319\pi$
$991$	−11.2763			−0.358204			−0.179102	+	0.983830i	$0.557319\pi$
$992$	4.03613			0.128147
$993$		0			0
$994$	−13.4083	+	2.64927i	−0.425286	+	0.0840296i
$995$	21.4388	+	12.3777i	0.679655	+	0.392399i
$996$		0			0
$997$	10.6829	+	18.5034i	0.338332	+	0.586007i	0.984119	−	0.177510i	$-0.0568041\pi$
$997$	10.6829	+	18.5034i	0.338332	+	0.586007i	−0.645788	+	0.763517i	$0.723471\pi$
$998$	4.04498			0.128042
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.cr.b.361.1		20
3.2	odd	2		546.2.bd.b.361.10	yes	20
7.2	even	3		1638.2.dt.b.1297.10		20
13.4	even	6		1638.2.dt.b.1369.5		20
21.2	odd	6		546.2.bm.b.205.1	yes	20
39.17	odd	6		546.2.bm.b.277.6	yes	20
91.30	even	6	inner	1638.2.cr.b.667.1		20
273.212	odd	6		546.2.bd.b.121.10	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.b.121.10	✓	20	273.212	odd	6
546.2.bd.b.361.10	yes	20	3.2	odd	2
546.2.bm.b.205.1	yes	20	21.2	odd	6
546.2.bm.b.277.6	yes	20	39.17	odd	6
1638.2.cr.b.361.1		20	1.1	even	1	trivial
1638.2.cr.b.667.1		20	91.30	even	6	inner
1638.2.dt.b.1297.10		20	7.2	even	3
1638.2.dt.b.1369.5		20	13.4	even	6

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.cr (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.21130 + 1.27669i) q^{5} +(-0.853651 + 2.50425i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.21130 + 1.27669i) q^{5} +(-0.853651 + 2.50425i) q^{7} -1.00000i q^{8} +2.55339 q^{10} -0.519243i q^{11} +(-1.57238 + 3.24463i) q^{13} +(1.99141 - 1.74192i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.434150 - 0.751971i) q^{17} -4.62695i q^{19} +(-2.21130 - 1.27669i) q^{20} +(-0.259622 + 0.449678i) q^{22} +(-4.26046 + 7.37933i) q^{23} +(0.759893 - 1.31617i) q^{25} +(2.98403 - 2.02374i) q^{26} +(-2.59557 + 0.512843i) q^{28} +(1.98376 + 3.43598i) q^{29} +(3.49539 + 2.01806i) q^{31} +(0.866025 - 0.500000i) q^{32} +0.868301i q^{34} +(-1.30949 - 6.62750i) q^{35} +(-5.12950 - 2.96152i) q^{37} +(-2.31347 + 4.00705i) q^{38} +(1.27669 + 2.21130i) q^{40} +(5.87598 - 3.39250i) q^{41} +(2.24805 - 3.89373i) q^{43} +(0.449678 - 0.259622i) q^{44} +(7.37933 - 4.26046i) q^{46} +(-2.81446 + 1.62493i) q^{47} +(-5.54256 - 4.27552i) q^{49} +(-1.31617 + 0.759893i) q^{50} +(-3.59612 + 0.260597i) q^{52} +(4.12845 - 7.15068i) q^{53} +(0.662914 + 1.14820i) q^{55} +(2.50425 + 0.853651i) q^{56} -3.96752i q^{58} +(1.21312 - 0.700397i) q^{59} -6.03817 q^{61} +(-2.01806 - 3.49539i) q^{62} -1.00000 q^{64} +(-0.665404 - 9.18229i) q^{65} -11.0230i q^{67} +(0.434150 - 0.751971i) q^{68} +(-2.17970 + 6.39433i) q^{70} +(-4.47375 - 2.58292i) q^{71} +(-10.3558 - 5.97895i) q^{73} +(2.96152 + 5.12950i) q^{74} +(4.00705 - 2.31347i) q^{76} +(1.30032 + 0.443252i) q^{77} +(5.47473 + 9.48251i) q^{79} -2.55339i q^{80} -6.78500 q^{82} -12.9984i q^{83} +(1.92007 + 1.10855i) q^{85} +(-3.89373 + 2.24805i) q^{86} -0.519243 q^{88} +(-6.95371 - 4.01473i) q^{89} +(-6.78311 - 6.70741i) q^{91} -8.52091 q^{92} +3.24986 q^{94} +(5.90719 + 10.2316i) q^{95} +(-13.0095 - 7.51106i) q^{97} +(2.66224 + 6.47398i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{4} - 6 q^{7}+O(q^{10}) \) 20 * q + 10 * q^4 - 6 * q^7	\( 20 q + 10 q^{4} - 6 q^{7} - 8 q^{10} + 8 q^{13} - 4 q^{14} - 10 q^{16} - 4 q^{17} - 10 q^{22} - 8 q^{23} + 6 q^{25} - 2 q^{26} - 6 q^{28} - 8 q^{29} - 12 q^{31} - 4 q^{35} - 6 q^{38} - 4 q^{40} + 18 q^{41} + 18 q^{43} - 6 q^{44} - 24 q^{46} - 6 q^{47} + 4 q^{49} - 12 q^{50} - 2 q^{52} - 18 q^{53} - 12 q^{55} - 2 q^{56} - 36 q^{59} + 12 q^{61} - 20 q^{64} + 4 q^{68} - 42 q^{70} + 6 q^{71} - 24 q^{73} + 18 q^{74} + 12 q^{76} + 34 q^{77} - 36 q^{82} - 36 q^{86} - 20 q^{88} - 18 q^{89} - 94 q^{91} - 16 q^{92} + 32 q^{94} - 40 q^{95} - 96 q^{97} + 12 q^{98}+O(q^{100}) \) 20 * q + 10 * q^4 - 6 * q^7 - 8 * q^10 + 8 * q^13 - 4 * q^14 - 10 * q^16 - 4 * q^17 - 10 * q^22 - 8 * q^23 + 6 * q^25 - 2 * q^26 - 6 * q^28 - 8 * q^29 - 12 * q^31 - 4 * q^35 - 6 * q^38 - 4 * q^40 + 18 * q^41 + 18 * q^43 - 6 * q^44 - 24 * q^46 - 6 * q^47 + 4 * q^49 - 12 * q^50 - 2 * q^52 - 18 * q^53 - 12 * q^55 - 2 * q^56 - 36 * q^59 + 12 * q^61 - 20 * q^64 + 4 * q^68 - 42 * q^70 + 6 * q^71 - 24 * q^73 + 18 * q^74 + 12 * q^76 + 34 * q^77 - 36 * q^82 - 36 * q^86 - 20 * q^88 - 18 * q^89 - 94 * q^91 - 16 * q^92 + 32 * q^94 - 40 * q^95 - 96 * q^97 + 12 * q^98

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