LMFDB - Embedded newform 162.7.d.f.53.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,7,Mod(53,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("162.53");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	162.d (of order $6$, degree $2$, not 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:	$37.2687615464$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.4
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	162.53
Dual form			162.7.d.f.107.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.89898 - 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(180.591 + 104.264i) q^{5} +(-2.09808 - 3.63397i) q^{7} -181.019i q^{8} +O(q^{10})$	\(q+(4.89898 - 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(180.591 + 104.264i) q^{5} +(-2.09808 - 3.63397i) q^{7} -181.019i q^{8} +1179.62 q^{10} +(1958.91 - 1130.98i) q^{11} +(-1420.00 + 2459.52i) q^{13} +(-20.5569 - 11.8685i) q^{14} +(-512.000 - 886.810i) q^{16} -1965.86i q^{17} -281.295 q^{19} +(5778.91 - 3336.46i) q^{20} +(6397.77 - 11081.3i) q^{22} +(14501.0 + 8372.14i) q^{23} +(13929.6 + 24126.7i) q^{25} +16065.5i q^{26} -134.277 q^{28} +(-32141.8 + 18557.1i) q^{29} +(12354.2 - 21398.0i) q^{31} +(-5016.55 - 2896.31i) q^{32} +(-5560.29 - 9630.70i) q^{34} -875.017i q^{35} -17016.7 q^{37} +(-1378.06 + 795.623i) q^{38} +(18873.8 - 32690.5i) q^{40} +(100663. + 58117.9i) q^{41} +(15331.4 + 26554.8i) q^{43} -72382.5i q^{44} +94720.0 q^{46} +(67261.3 - 38833.3i) q^{47} +(58815.7 - 101872. i) q^{49} +(136481. + 78797.5i) q^{50} +(45440.1 + 78704.6i) q^{52} -138657. i q^{53} +471682. q^{55} +(-657.820 + 379.792i) q^{56} +(-104975. + 181821. i) q^{58} +(-132465. - 76478.8i) q^{59} +(8069.05 + 13976.0i) q^{61} -139771. i q^{62} -32768.0 q^{64} +(-512880. + 296111. i) q^{65} +(237334. - 411074. i) q^{67} +(-54479.4 - 31453.7i) q^{68} +(-2474.92 - 4286.69i) q^{70} +150338. i q^{71} +331690. q^{73} +(-83364.7 + 48130.6i) q^{74} +(-4500.73 + 7795.49i) q^{76} +(-8219.88 - 4745.75i) q^{77} +(448056. + 776056. i) q^{79} -213533. i q^{80} +657529. q^{82} +(-818472. + 472545. i) q^{83} +(204969. - 355016. i) q^{85} +(150217. + 86727.7i) q^{86} +(-204729. - 354600. i) q^{88} -790302. i q^{89} +11917.1 q^{91} +(464031. - 267909. i) q^{92} +(219674. - 380487. i) q^{94} +(-50799.4 - 29329.0i) q^{95} +(-696338. - 1.20609e6i) q^{97} -665424. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 128 q^{4} + 4 q^{7}+O(q^{10}) $ 8 * q + 128 * q^4 + 4 * q^7	$ 8 q + 128 q^{4} + 4 q^{7} + 5280 q^{10} - 3836 q^{13} - 4096 q^{16} + 20488 q^{19} + 27072 q^{22} + 25700 q^{25} + 256 q^{28} + 40096 q^{31} - 60528 q^{34} - 40400 q^{37} + 84480 q^{40} - 184940 q^{43} + 325440 q^{46} + 470484 q^{49} + 122752 q^{52} + 1899720 q^{55} - 24624 q^{58} - 609056 q^{61} - 262144 q^{64} + 2008972 q^{67} - 8160 q^{70} + 1051648 q^{73} + 327808 q^{76} + 848716 q^{79} + 1411584 q^{82} + 987840 q^{85} - 866304 q^{88} + 70520 q^{91} + 1965408 q^{94} - 3621728 q^{97}+O(q^{100}) $ 8 * q + 128 * q^4 + 4 * q^7 + 5280 * q^10 - 3836 * q^13 - 4096 * q^16 + 20488 * q^19 + 27072 * q^22 + 25700 * q^25 + 256 * q^28 + 40096 * q^31 - 60528 * q^34 - 40400 * q^37 + 84480 * q^40 - 184940 * q^43 + 325440 * q^46 + 470484 * q^49 + 122752 * q^52 + 1899720 * q^55 - 24624 * q^58 - 609056 * q^61 - 262144 * q^64 + 2008972 * q^67 - 8160 * q^70 + 1051648 * q^73 + 327808 * q^76 + 848716 * q^79 + 1411584 * q^82 + 987840 * q^85 - 866304 * q^88 + 70520 * q^91 + 1965408 * q^94 - 3621728 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	4.89898	−	2.82843i	0.612372	−	0.353553i
$2$	4.89898	−	2.82843i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	16.0000	−	27.7128i	0.250000	−	0.433013i
$5$	180.591	+	104.264i	1.44473	+	0.834114i	0.998160	−	0.0606359i	$-0.0193128\pi$
$5$	180.591	+	104.264i	1.44473	+	0.834114i	0.446568	+	0.894750i	$0.352646\pi$
$6$		0			0
$7$	−2.09808	−	3.63397i	−0.00611684	−	0.0105947i	0.862951	−	0.505288i	$-0.168614\pi$
$7$	−2.09808	−	3.63397i	−0.00611684	−	0.0105947i	−0.869068	+	0.494693i	$0.835280\pi$
$8$		−	181.019i		−	0.353553i
$9$		0			0
$10$	1179.62			1.17962
$11$	1958.91	−	1130.98i	1.47176	−	0.849719i	0.472261	−	0.881459i	$-0.343438\pi$
$11$	1958.91	−	1130.98i	1.47176	−	0.849719i	0.999496	+	0.0317396i	$0.0101047\pi$
$12$		0			0
$13$	−1420.00	+	2459.52i	−0.646338	+	1.11949i	0.337653	+	0.941271i	$0.390367\pi$
$13$	−1420.00	+	2459.52i	−0.646338	+	1.11949i	−0.983991	+	0.178219i	$0.942966\pi$
$14$	−20.5569	−	11.8685i	−0.00749157	−	0.00432526i
$15$		0			0
$16$	−512.000	−	886.810i	−0.125000	−	0.216506i
$17$		−	1965.86i		−	0.400134i	−0.979782	−	0.200067i	$-0.935884\pi$
$17$		−	1965.86i		−	0.400134i	0.979782	−	0.200067i	$-0.0641160\pi$
$18$		0			0
$19$	−281.295			−0.0410111			−0.0205056	−	0.999790i	$-0.506528\pi$
$19$	−281.295			−0.0410111			−0.0205056	+	0.999790i	$0.506528\pi$
$20$	5778.91	−	3336.46i	0.722364	−	0.417057i
$21$		0			0
$22$	6397.77	−	11081.3i	0.600842	−	1.04069i
$23$	14501.0	+	8372.14i	1.19183	+	0.688102i	0.958721	−	0.284348i	$-0.0917773\pi$
$23$	14501.0	+	8372.14i	1.19183	+	0.688102i	0.233107	+	0.972451i	$0.425111\pi$
$24$		0			0
$25$	13929.6	+	24126.7i	0.891492	+	1.54411i
$26$			16065.5i			0.914059i
$27$		0			0
$28$	−134.277			−0.00611684
$29$	−32141.8	+	18557.1i	−1.31788	+	0.760878i	−0.983387	−	0.181520i	$-0.941898\pi$
$29$	−32141.8	+	18557.1i	−1.31788	+	0.760878i	−0.334492	+	0.942399i	$0.608565\pi$
$30$		0			0
$31$	12354.2	−	21398.0i	0.414694	−	0.718272i	−0.580702	−	0.814116i	$-0.697222\pi$
$31$	12354.2	−	21398.0i	0.414694	−	0.718272i	0.995396	+	0.0958444i	$0.0305551\pi$
$32$	−5016.55	−	2896.31i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−5560.29	−	9630.70i	−0.141469	−	0.245031i
$35$		−	875.017i		−	0.0204086i
$36$		0			0
$37$	−17016.7			−0.335947			−0.167974	−	0.985791i	$-0.553722\pi$
$37$	−17016.7			−0.335947			−0.167974	+	0.985791i	$0.553722\pi$
$38$	−1378.06	+	795.623i	−0.0251141	+	0.0144996i
$39$		0			0
$40$	18873.8	−	32690.5i	0.294904	−	0.510788i
$41$	100663.	+	58117.9i	1.46056	+	0.843253i	0.999037	−	0.0438761i	$-0.0139707\pi$
$41$	100663.	+	58117.9i	1.46056	+	0.843253i	0.461521	+	0.887129i	$0.347304\pi$
$42$		0			0
$43$	15331.4	+	26554.8i	0.192831	+	0.333993i	0.946187	−	0.323619i	$-0.104900\pi$
$43$	15331.4	+	26554.8i	0.192831	+	0.333993i	−0.753356	+	0.657613i	$0.771566\pi$
$44$		−	72382.5i		−	0.849719i
$45$		0			0
$46$	94720.0			0.973124
$47$	67261.3	−	38833.3i	0.647846	−	0.374034i	−0.139785	−	0.990182i	$-0.544641\pi$
$47$	67261.3	−	38833.3i	0.647846	−	0.374034i	0.787630	+	0.616148i	$0.211308\pi$
$48$		0			0
$49$	58815.7	−	101872.i	0.499925	−	0.865896i
$50$	136481.	+	78797.5i	1.09185	+	0.630380i
$51$		0			0
$52$	45440.1	+	78704.6i	0.323169	+	0.559745i
$53$		−	138657.i		−	0.931354i	−0.884955	−	0.465677i	$-0.845811\pi$
$53$		−	138657.i		−	0.931354i	0.884955	−	0.465677i	$-0.154189\pi$
$54$		0			0
$55$	471682.			2.83505
$56$	−657.820	+	379.792i	−0.00374578	+	0.00216263i
$57$		0			0
$58$	−104975.	+	181821.i	−0.538022	+	0.931881i
$59$	−132465.	−	76478.8i	−0.644979	−	0.372379i	0.141551	−	0.989931i	$-0.454791\pi$
$59$	−132465.	−	76478.8i	−0.644979	−	0.372379i	−0.786530	+	0.617552i	$0.788124\pi$
$60$		0			0
$61$	8069.05	+	13976.0i	0.0355495	+	0.0615735i	0.883253	−	0.468897i	$-0.155349\pi$
$61$	8069.05	+	13976.0i	0.0355495	+	0.0615735i	−0.847703	+	0.530471i	$0.822015\pi$
$62$		−	139771.i		−	0.586467i
$63$		0			0
$64$	−32768.0			−0.125000
$65$	−512880.	+	296111.i	−1.86756	+	1.07824i
$66$		0			0
$67$	237334.	−	411074.i	0.789105	−	1.36677i	−0.137411	−	0.990514i	$-0.543878\pi$
$67$	237334.	−	411074.i	0.789105	−	1.36677i	0.926516	−	0.376255i	$-0.122788\pi$
$68$	−54479.4	−	31453.7i	−0.173263	−	0.100033i
$69$		0			0
$70$	−2474.92	−	4286.69i	−0.00721552	−	0.0124976i
$71$			150338.i			0.420043i	0.977697	+	0.210021i	$0.0673534\pi$
$71$			150338.i			0.420043i	−0.977697	+	0.210021i	$0.932647\pi$
$72$		0			0
$73$	331690.			0.852636			0.426318	−	0.904573i	$-0.359811\pi$
$73$	331690.			0.852636			0.426318	+	0.904573i	$0.359811\pi$
$74$	−83364.7	+	48130.6i	−0.205725	+	0.118775i
$75$		0			0
$76$	−4500.73	+	7795.49i	−0.0102528	+	0.0177583i
$77$	−8219.88	−	4745.75i	−0.0180050	−	0.0103952i
$78$		0			0
$79$	448056.	+	776056.i	0.908764	+	1.57403i	0.815783	+	0.578357i	$0.196306\pi$
$79$	448056.	+	776056.i	0.908764	+	1.57403i	0.0929805	+	0.995668i	$0.470361\pi$
$80$		−	213533.i		−	0.417057i
$81$		0			0
$82$	657529.			1.19254
$83$	−818472.	+	472545.i	−1.43143	+	0.826435i	−0.997230	−	0.0743823i	$-0.976301\pi$
$83$	−818472.	+	472545.i	−1.43143	+	0.826435i	−0.434198	+	0.900817i	$0.642968\pi$
$84$		0			0
$85$	204969.	−	355016.i	0.333757	−	0.578084i
$86$	150217.	+	86727.7i	0.236169	+	0.136352i
$87$		0			0
$88$	−204729.	−	354600.i	−0.300421	−	0.520345i
$89$		−	790302.i		−	1.12105i	−0.828139	−	0.560523i	$-0.810600\pi$
$89$		−	790302.i		−	1.12105i	0.828139	−	0.560523i	$-0.189400\pi$
$90$		0			0
$91$	11917.1			0.0158142
$92$	464031.	−	267909.i	0.595914	−	0.344051i
$93$		0			0
$94$	219674.	−	380487.i	0.264482	−	0.458096i
$95$	−50799.4	−	29329.0i	−0.0592499	−	0.0342080i
$96$		0			0
$97$	−696338.	−	1.20609e6i	−0.762965	−	1.32149i	−0.941316	−	0.337527i	$-0.890409\pi$
$97$	−696338.	−	1.20609e6i	−0.762965	−	1.32149i	0.178351	−	0.983967i	$-0.442924\pi$
$98$		−	665424.i		−	0.707001i
$99$		0			0
$100$	891492.			0.891492
$101$	−113927.	+	65775.9i	−0.110577	+	0.0638414i	−0.554268	−	0.832338i	$-0.687002\pi$
$101$	−113927.	+	65775.9i	−0.110577	+	0.0638414i	0.443692	+	0.896179i	$0.353669\pi$
$102$		0			0
$103$	−967305.	+	1.67542e6i	−0.885221	+	1.53325i	−0.0397603	+	0.999209i	$0.512659\pi$
$103$	−967305.	+	1.67542e6i	−0.885221	+	1.53325i	−0.845460	+	0.534038i	$0.820674\pi$
$104$	445220.	+	257048.i	0.395799	+	0.228515i
$105$		0			0
$106$	−392182.	−	679279.i	−0.329283	−	0.570336i
$107$			621916.i			0.507669i	0.967248	+	0.253834i	$0.0816918\pi$
$107$			621916.i			0.507669i	−0.967248	+	0.253834i	$0.918308\pi$
$108$		0			0
$109$	−1.34578e6			−1.03919			−0.519594	−	0.854413i	$-0.673917\pi$
$109$	−1.34578e6			−1.03919			−0.519594	+	0.854413i	$0.673917\pi$
$110$	2.31076e6	−	1.33412e6i	1.73611	−	1.00234i
$111$		0			0
$112$	−2148.43	+	3721.19i	−0.00152921	+	0.00264867i
$113$	1.07329e6	+	619662.i	0.743841	+	0.429457i	0.823464	−	0.567368i	$-0.192038\pi$
$113$	1.07329e6	+	619662.i	0.743841	+	0.429457i	−0.0796229	+	0.996825i	$0.525372\pi$
$114$		0			0
$115$	1.74583e6	+	3.02387e6i	1.14791	+	1.98824i
$116$			1.18765e6i			0.760878i
$117$		0			0
$118$	−865259.			−0.526623
$119$	−7143.88	+	4124.52i	−0.00423929	+	0.00244755i
$120$		0			0
$121$	1.67243e6	−	2.89674e6i	0.944046	−	1.63514i
$122$	79060.2	+	45645.5i	0.0435390	+	0.0251373i
$123$		0			0
$124$	−395333.	−	684737.i	−0.207347	−	0.359136i
$125$			2.55116e6i			1.30620i
$126$		0			0
$127$	−1.65297e6			−0.806962			−0.403481	−	0.914988i	$-0.632200\pi$
$127$	−1.65297e6			−0.806962			−0.403481	+	0.914988i	$0.632200\pi$
$128$	−160530.	+	92681.9i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−1.67506e6	+	2.90129e6i	−0.762430	+	1.32057i
$131$	−2.30472e6	−	1.33063e6i	−1.02519	−	0.591893i	−0.109586	−	0.993977i	$-0.534952\pi$
$131$	−2.30472e6	−	1.33063e6i	−1.02519	−	0.591893i	−0.915602	+	0.402085i	$0.868286\pi$
$132$		0			0
$133$	590.179	+	1022.22i	0.000250859	+	0.000434500i
$134$		−	2.68512e6i		−	1.11596i
$135$		0			0
$136$	−355858.			−0.141469
$137$	−2.26046e6	+	1.30508e6i	−0.879092	+	0.507544i	−0.870359	−	0.492418i	$-0.836113\pi$
$137$	−2.26046e6	+	1.30508e6i	−0.879092	+	0.507544i	−0.00873327	+	0.999962i	$0.502780\pi$
$138$		0			0
$139$	350661.	−	607362.i	0.130570	−	0.226153i	−0.793327	−	0.608796i	$-0.791653\pi$
$139$	350661.	−	607362.i	0.130570	−	0.226153i	0.923896	+	0.382643i	$0.124986\pi$
$140$	−24249.2	−	14000.3i	−0.00883717	−	0.00510214i
$141$		0			0
$142$	425220.	+	736503.i	0.148508	+	0.257223i
$143$			6.42396e6i			2.19682i
$144$		0			0
$145$	−7.73935e6			−2.53864
$146$	1.62494e6	−	938160.i	0.522131	−	0.301452i
$147$		0			0
$148$	−272268.	+	471582.i	−0.0839868	+	0.145469i
$149$	−4.09928e6	−	2.36672e6i	−1.23922	−	0.715464i	−0.270285	−	0.962780i	$-0.587118\pi$
$149$	−4.09928e6	−	2.36672e6i	−1.23922	−	0.715464i	−0.968935	+	0.247316i	$0.920451\pi$
$150$		0			0
$151$	−1.86865e6	−	3.23659e6i	−0.542746	−	0.940063i	−0.998745	−	0.0500829i	$-0.984051\pi$
$151$	−1.86865e6	−	3.23659e6i	−0.542746	−	0.940063i	0.455999	−	0.889980i	$-0.349282\pi$
$152$			50919.9i			0.0144996i
$153$		0			0
$154$	−53692.0			−0.0147010
$155$	4.46210e6	−	2.57619e6i	1.19824	−	0.691805i
$156$		0			0
$157$	−1.60331e6	+	2.77701e6i	−0.414303	+	0.717594i	−0.995355	−	0.0962723i	$-0.969308\pi$
$157$	−1.60331e6	+	2.77701e6i	−0.414303	+	0.717594i	0.581052	+	0.813867i	$0.302641\pi$
$158$	4.39004e6	+	2.53459e6i	1.11300	+	0.642593i
$159$		0			0
$160$	−603963.	−	1.04609e6i	−0.147452	−	0.255394i
$161$		−	70261.6i		−	0.0168361i
$162$		0			0
$163$	−964418.			−0.222691			−0.111345	−	0.993782i	$-0.535516\pi$
$163$	−964418.			−0.222691			−0.111345	+	0.993782i	$0.535516\pi$
$164$	3.22122e6	−	1.85977e6i	0.730279	−	0.421627i
$165$		0			0
$166$	−2.67312e6	+	4.62998e6i	−0.584378	+	1.01217i
$167$	−896330.	−	517496.i	−0.192450	−	0.111111i	0.400679	−	0.916219i	$-0.368774\pi$
$167$	−896330.	−	517496.i	−0.192450	−	0.111111i	−0.593129	+	0.805107i	$0.702108\pi$
$168$		0			0
$169$	−1.61942e6	−	2.80491e6i	−0.335504	−	0.581111i
$170$		−	2.31896e6i		−	0.472004i
$171$		0			0
$172$	981212.			0.192831
$173$	−561701.	+	324298.i	−0.108484	+	0.0626334i	−0.553260	−	0.833008i	$-0.686617\pi$
$173$	−561701.	+	324298.i	−0.108484	+	0.0626334i	0.444776	+	0.895642i	$0.353283\pi$
$174$		0			0
$175$	58450.6	−	101239.i	0.0109062	−	0.0188901i
$176$	−2.00592e6	−	1.15812e6i	−0.367939	−	0.212430i
$177$		0			0
$178$	−2.23531e6	−	3.87168e6i	−0.396349	−	0.686497i
$179$		−	4.65189e6i		−	0.811092i	−0.914075	−	0.405546i	$-0.867081\pi$
$179$		−	4.65189e6i		−	0.811092i	0.914075	−	0.405546i	$-0.132919\pi$
$180$		0			0
$181$	3.43720e6			0.579654			0.289827	−	0.957079i	$-0.406402\pi$
$181$	3.43720e6			0.579654			0.289827	+	0.957079i	$0.406402\pi$
$182$	58381.6	−	33706.7i	0.00968416	−	0.00559115i
$183$		0			0
$184$	1.51552e6	−	2.62496e6i	0.243281	−	0.421375i
$185$	−3.07307e6	−	1.77424e6i	−0.485352	−	0.280218i
$186$		0			0
$187$	−2.22334e6	−	3.85094e6i	−0.340001	−	0.588900i
$188$		−	2.48533e6i		−	0.374034i
$189$		0			0
$190$	−331820.			−0.0483774
$191$	−1.01766e7	+	5.87547e6i	−1.46050	+	0.843222i	−0.999034	−	0.0439335i	$-0.986011\pi$
$191$	−1.01766e7	+	5.87547e6i	−1.46050	+	0.843222i	−0.461470	+	0.887156i	$0.652678\pi$
$192$		0			0
$193$	−3.47800e6	+	6.02407e6i	−0.483790	+	0.837950i	−0.999827	−	0.0186172i	$-0.994074\pi$
$193$	−3.47800e6	+	6.02407e6i	−0.483790	+	0.837950i	0.516036	+	0.856567i	$0.327407\pi$
$194$	−6.82269e6	−	3.93908e6i	−0.934438	−	0.539498i
$195$		0			0
$196$	−1.88210e6	−	3.25990e6i	−0.249963	−	0.432948i
$197$		−	409645.i		−	0.0535807i	−0.999641	−	0.0267904i	$-0.991471\pi$
$197$		−	409645.i		−	0.0535807i	0.999641	−	0.0267904i	$-0.00852866\pi$
$198$		0			0
$199$	−3.24847e6			−0.412212			−0.206106	−	0.978530i	$-0.566079\pi$
$199$	−3.24847e6			−0.412212			−0.206106	+	0.978530i	$0.566079\pi$
$200$	4.36740e6	−	2.52152e6i	0.545925	−	0.315190i
$201$		0			0
$202$	−372084.	+	644469.i	−0.0451427	+	0.0781894i
$203$	134872.	+	77868.2i	0.0161225	+	0.00930834i
$204$		0			0
$205$	1.21192e7	+	2.09911e7i	1.40674	+	2.43654i
$206$			1.09438e7i			1.25189i
$207$		0			0
$208$	2.90817e6			0.323169
$209$	−551032.	+	318138.i	−0.0603584	+	0.0348480i
$210$		0			0
$211$	2.49743e6	−	4.32568e6i	0.265856	−	0.460476i	−0.701932	−	0.712244i	$-0.747679\pi$
$211$	2.49743e6	−	4.32568e6i	0.265856	−	0.460476i	0.967788	+	0.251768i	$0.0810121\pi$
$212$	−3.84258e6	−	2.21852e6i	−0.403288	−	0.232839i
$213$		0			0
$214$	1.75904e6	+	3.04676e6i	0.179488	+	0.310882i
$215$			6.39408e6i			0.643373i
$216$		0			0
$217$	−103680.			−0.0101465
$218$	−6.59294e6	+	3.80644e6i	−0.636370	+	0.367408i
$219$		0			0
$220$	7.54691e6	−	1.30716e7i	0.708763	−	1.22761i
$221$	4.83506e6	+	2.79152e6i	0.447946	+	0.258622i
$222$		0			0
$223$	−2.84462e6	−	4.92703e6i	−0.256513	−	0.444294i	0.708792	−	0.705417i	$-0.249240\pi$
$223$	−2.84462e6	−	4.92703e6i	−0.256513	−	0.444294i	−0.965305	+	0.261123i	$0.915907\pi$
$224$			24306.7i			0.00216263i
$225$		0			0
$226$	7.01068e6			0.607344
$227$	−1.00514e7	+	5.80319e6i	−0.859310	+	0.496123i	−0.863781	−	0.503867i	$-0.831910\pi$
$227$	−1.00514e7	+	5.80319e6i	−0.859310	+	0.496123i	0.00447105	+	0.999990i	$0.498577\pi$
$228$		0			0
$229$	1.72845e6	−	2.99376e6i	0.143930	−	0.249294i	−0.785043	−	0.619441i	$-0.787359\pi$
$229$	1.72845e6	−	2.99376e6i	0.143930	−	0.249294i	0.928973	+	0.370147i	$0.120693\pi$
$230$	1.71056e7	+	9.87591e6i	1.40590	+	0.811696i
$231$		0			0
$232$	3.35919e6	+	5.81828e6i	0.269011	+	0.465941i
$233$		−	1.27739e7i		−	1.00985i	−0.863164	−	0.504924i	$-0.831520\pi$
$233$		−	1.27739e7i		−	1.00985i	0.863164	−	0.504924i	$-0.168480\pi$
$234$		0			0
$235$	1.61957e7			1.24795
$236$	−4.23889e6	+	2.44732e6i	−0.322490	+	0.186189i
$237$		0			0
$238$	−23331.8	+	40411.9i	−0.00173068	+	0.00299763i
$239$	1.11918e7	+	6.46157e6i	0.819795	+	0.473309i	0.850346	−	0.526225i	$-0.176393\pi$
$239$	1.11918e7	+	6.46157e6i	0.819795	+	0.473309i	−0.0305510	+	0.999533i	$0.509726\pi$
$240$		0			0
$241$	−3.64016e6	−	6.30494e6i	−0.260057	−	0.450433i	0.706200	−	0.708013i	$-0.250408\pi$
$241$	−3.64016e6	−	6.30494e6i	−0.260057	−	0.450433i	−0.966257	+	0.257580i	$0.917075\pi$
$242$		−	1.89214e7i		−	1.33508i
$243$		0			0
$244$	516419.			0.0355495
$245$	2.12432e7	−	1.22647e7i	1.44451	−	0.833989i
$246$		0			0
$247$	399440.	−	691851.i	0.0265070	−	0.0459115i
$248$	−3.87346e6	−	2.23634e6i	−0.253947	−	0.146617i
$249$		0			0
$250$	7.21578e6	+	1.24981e7i	0.461810	+	0.799879i
$251$		−	1.71927e7i		−	1.08723i	−0.839334	−	0.543616i	$-0.817055\pi$
$251$		−	1.71927e7i		−	1.08723i	0.839334	−	0.543616i	$-0.182945\pi$
$252$		0			0
$253$	3.78748e7			2.33878
$254$	−8.09785e6	+	4.67529e6i	−0.494161	+	0.285304i
$255$		0			0
$256$	−524288.	+	908093.i	−0.0312500	+	0.0541266i
$257$	6.93783e6	+	4.00556e6i	0.408718	+	0.235974i	0.690239	−	0.723582i	$-0.257505\pi$
$257$	6.93783e6	+	4.00556e6i	0.408718	+	0.235974i	−0.281521	+	0.959555i	$0.590839\pi$
$258$		0			0
$259$	35702.4	+	61838.4i	0.00205494	+	0.00355925i
$260$			1.89511e7i			1.07824i
$261$		0			0
$262$	−1.50543e7			−0.837062
$263$	1.45674e7	−	8.41046e6i	0.800780	−	0.462331i	−0.0429637	−	0.999077i	$-0.513680\pi$
$263$	1.45674e7	−	8.41046e6i	0.800780	−	0.462331i	0.843744	+	0.536746i	$0.180347\pi$
$264$		0			0
$265$	1.44570e7	−	2.50402e7i	0.776856	−	1.34555i
$266$	5782.55	+	3338.56i	0.000307238	+	0.000177384i
$267$		0			0
$268$	−7.59467e6	−	1.31544e7i	−0.394552	−	0.683385i
$269$		−	3.33514e6i		−	0.171339i	−0.996324	−	0.0856697i	$-0.972697\pi$
$269$		−	3.33514e6i		−	0.171339i	0.996324	−	0.0856697i	$-0.0273030\pi$
$270$		0			0
$271$	−1.47048e7			−0.738840			−0.369420	−	0.929263i	$-0.620444\pi$
$271$	−1.47048e7			−0.738840			−0.369420	+	0.929263i	$0.620444\pi$
$272$	−1.74334e6	+	1.00652e6i	−0.0866315	+	0.0500167i
$273$		0			0
$274$	−7.38262e6	+	1.27871e7i	−0.358888	+	0.621612i
$275$	5.45735e7	+	3.15080e7i	2.62412	+	1.51504i
$276$		0			0
$277$	5.46003e6	+	9.45705e6i	0.256895	+	0.444955i	0.965408	−	0.260742i	$-0.0839672\pi$
$277$	5.46003e6	+	9.45705e6i	0.256895	+	0.444955i	−0.708514	+	0.705697i	$0.750634\pi$
$278$		−	3.96727e6i		−	0.184653i
$279$		0			0
$280$	−158395.			−0.00721552
$281$	1.61727e7	−	9.33733e6i	0.728894	−	0.420827i	−0.0891235	−	0.996021i	$-0.528407\pi$
$281$	1.61727e7	−	9.33733e6i	0.728894	−	0.420827i	0.818017	+	0.575194i	$0.195073\pi$
$282$		0			0
$283$	7.31274e6	−	1.26660e7i	0.322642	−	0.558832i	−0.658390	−	0.752677i	$-0.728762\pi$
$283$	7.31274e6	−	1.26660e7i	0.322642	−	0.558832i	0.981032	+	0.193845i	$0.0620957\pi$
$284$	4.16629e6	+	2.40541e6i	0.181884	+	0.105011i
$285$		0			0
$286$	1.81697e7	+	3.14709e7i	0.776694	+	1.34527i
$287$		−	487743.i		−	0.0206322i
$288$		0			0
$289$	2.02730e7			0.839893
$290$	−3.79149e7	+	2.18902e7i	−1.55459	+	0.897543i
$291$		0			0
$292$	5.30704e6	−	9.19206e6i	0.213159	−	0.369202i
$293$	−4.14332e7	−	2.39215e7i	−1.64720	−	0.951010i	−0.978179	−	0.207763i	$-0.933382\pi$
$293$	−4.14332e7	−	2.39215e7i	−1.64720	−	0.951010i	−0.669018	−	0.743247i	$-0.733285\pi$
$294$		0			0
$295$	−1.59480e7	−	2.76228e7i	−0.621213	−	1.07597i
$296$			3.08036e6i			0.118775i
$297$		0			0
$298$	−2.67764e7			−1.01182
$299$	−4.11829e7	+	2.37769e7i	−1.54065	+	0.889493i
$300$		0			0
$301$	64333.0	−	111428.i	0.00235904	−	0.00408597i
$302$	−1.83089e7	−	1.05707e7i	−0.664725	−	0.383779i
$303$		0			0
$304$	144023.	+	249456.i	0.00512639	+	0.00887917i
$305$			3.36525e6i			0.118609i
$306$		0			0
$307$	4.24782e7			1.46808			0.734042	−	0.679104i	$-0.237631\pi$
$307$	4.24782e7			1.46808			0.734042	+	0.679104i	$0.237631\pi$
$308$	−263036.	+	151864.i	−0.00900250	+	0.00519760i
$309$		0			0
$310$	1.45732e7	−	2.52415e7i	0.489180	−	0.847285i
$311$	−2.68464e7	−	1.54998e7i	−0.892494	−	0.515282i	−0.0177365	−	0.999843i	$-0.505646\pi$
$311$	−2.68464e7	−	1.54998e7i	−0.892494	−	0.515282i	−0.874757	+	0.484561i	$0.838979\pi$
$312$		0			0
$313$	1.48914e7	+	2.57927e7i	0.485627	+	0.841131i	0.999864	−	0.0165178i	$-0.00525800\pi$
$313$	1.48914e7	+	2.57927e7i	0.485627	+	0.841131i	−0.514237	+	0.857648i	$0.671925\pi$
$314$			1.81394e7i			0.585913i
$315$		0			0
$316$	2.86756e7			0.908764
$317$	−1.88717e6	+	1.08956e6i	−0.0592424	+	0.0342036i	−0.529329	−	0.848417i	$-0.677556\pi$
$317$	−1.88717e6	+	1.08956e6i	−0.0592424	+	0.0342036i	0.470086	+	0.882620i	$0.344223\pi$
$318$		0			0
$319$	−4.19752e7	+	7.27031e7i	−1.29307	+	2.23966i
$320$	−5.91760e6	−	3.41653e6i	−0.180591	−	0.104264i
$321$		0			0
$322$	−198730.	−	344210.i	−0.00595244	−	0.0103099i
$323$			552987.i			0.0164099i
$324$		0			0
$325$	−7.91201e7			−2.30482
$326$	−4.72466e6	+	2.72779e6i	−0.136370	+	0.0787331i
$327$		0			0
$328$	1.05205e7	−	1.82220e7i	0.298135	−	0.516385i
$329$	−282239.	−	162951.i	−0.00792554	−	0.00457581i
$330$		0			0
$331$	−6.68355e6	−	1.15762e7i	−0.184299	−	0.319215i	0.759041	−	0.651043i	$-0.225668\pi$
$331$	−6.68355e6	−	1.15762e7i	−0.184299	−	0.319215i	−0.943340	+	0.331827i	$0.892335\pi$
$332$			3.02429e7i			0.826435i
$333$		0			0
$334$	−5.85480e6			−0.157135
$335$	8.57206e7	−	4.94908e7i	2.28008	−	1.31641i
$336$		0			0
$337$	−2.22744e7	+	3.85804e7i	−0.581991	+	1.00804i	0.413252	+	0.910617i	$0.364393\pi$
$337$	−2.22744e7	+	3.85804e7i	−0.581991	+	1.00804i	−0.995243	+	0.0974216i	$0.968940\pi$
$338$	−1.58670e7	−	9.16080e6i	−0.410907	−	0.237237i
$339$		0			0
$340$	−6.55900e6	−	1.13605e7i	−0.166879	−	0.289042i
$341$		−	5.58891e7i		−	1.40950i
$342$		0			0
$343$	−987272.			−0.0244655
$344$	4.80694e6	−	2.77529e6i	0.118085	−	0.0681761i
$345$		0			0
$346$	−1.83451e6	+	3.17746e6i	−0.0442885	+	0.0767100i
$347$	−1.80987e7	−	1.04493e7i	−0.433170	−	0.250091i	0.267526	−	0.963551i	$-0.413794\pi$
$347$	−1.80987e7	−	1.04493e7i	−0.433170	−	0.250091i	−0.700696	+	0.713460i	$0.747127\pi$
$348$		0			0
$349$	−3.22577e7	−	5.58720e7i	−0.758852	−	1.31437i	−0.943436	−	0.331554i	$-0.892427\pi$
$349$	−3.22577e7	−	5.58720e7i	−0.758852	−	1.31437i	0.184584	−	0.982817i	$-0.440906\pi$
$350$		−	661293.i		−	0.0154237i
$351$		0			0
$352$	−1.31026e7			−0.300421
$353$	3.64529e6	−	2.10461e6i	0.0828719	−	0.0478461i	−0.457991	−	0.888957i	$-0.651431\pi$
$353$	3.64529e6	−	2.10461e6i	0.0828719	−	0.0478461i	0.540863	+	0.841110i	$0.318098\pi$
$354$		0			0
$355$	−1.56749e7	+	2.71497e7i	−0.350364	+	0.606848i
$356$	−2.19015e7	−	1.26448e7i	−0.485427	−	0.280261i
$357$		0			0
$358$	−1.31575e7	−	2.27895e7i	−0.286764	−	0.496690i
$359$			5.61320e7i			1.21319i	0.795012	+	0.606593i	$0.207464\pi$
$359$			5.61320e7i			1.21319i	−0.795012	+	0.606593i	$0.792536\pi$
$360$		0			0
$361$	−4.69668e7			−0.998318
$362$	1.68388e7	−	9.72186e6i	0.354964	−	0.204939i
$363$		0			0
$364$	190674.	−	330256.i	0.00395354	−	0.00684774i
$365$	5.99002e7	+	3.45834e7i	1.23183	+	0.711195i
$366$		0			0
$367$	−1.67551e7	−	2.90207e7i	−0.338961	−	0.587097i	0.645277	−	0.763949i	$-0.276742\pi$
$367$	−1.67551e7	−	2.90207e7i	−0.338961	−	0.587097i	−0.984238	+	0.176852i	$0.943409\pi$
$368$		−	1.71461e7i		−	0.344051i
$369$		0			0
$370$	−2.00732e7			−0.396289
$371$	−503877.	+	290913.i	−0.00986740	+	0.00569695i
$372$		0			0
$373$	−1.11388e7	+	1.92931e7i	−0.214642	+	0.371770i	−0.953162	−	0.302461i	$-0.902192\pi$
$373$	−1.11388e7	+	1.92931e7i	−0.214642	+	0.371770i	0.738520	+	0.674231i	$0.235525\pi$
$374$	−2.17842e7	−	1.25771e7i	−0.416415	−	0.240417i
$375$		0			0
$376$	−7.02958e6	−	1.21756e7i	−0.132241	−	0.229048i
$377$		−	1.05404e8i		−	1.96714i
$378$		0			0
$379$	7.72205e7			1.41845			0.709226	−	0.704981i	$-0.249044\pi$
$379$	7.72205e7			1.41845			0.709226	+	0.704981i	$0.249044\pi$
$380$	−1.62558e6	+	938530.i	−0.0296250	+	0.0171040i
$381$		0			0
$382$	−3.32367e7	+	5.75676e7i	−0.596248	+	1.03273i
$383$	−2.88035e7	−	1.66297e7i	−0.512683	−	0.295998i	0.221253	−	0.975217i	$-0.428985\pi$
$383$	−2.88035e7	−	1.66297e7i	−0.512683	−	0.295998i	−0.733936	+	0.679219i	$0.762319\pi$
$384$		0			0
$385$	−989624.	−	1.71408e6i	−0.0173416	−	0.0300365i
$386$			3.93490e7i			0.684183i
$387$		0			0
$388$	−4.45656e7			−0.762965
$389$	1.30734e7	−	7.54793e6i	0.222096	−	0.128227i	−0.384825	−	0.922990i	$-0.625738\pi$
$389$	1.30734e7	−	7.54793e6i	0.222096	−	0.128227i	0.606920	+	0.794763i	$0.292405\pi$
$390$		0			0
$391$	1.64584e7	−	2.85069e7i	0.275333	−	0.476891i
$392$	−1.84408e7	−	1.06468e7i	−0.306140	−	0.176750i
$393$		0			0
$394$	−1.15865e6	−	2.00684e6i	−0.0189436	−	0.0328114i
$395$			1.86865e8i			3.03205i
$396$		0			0
$397$	−8.91350e7			−1.42455			−0.712273	−	0.701902i	$-0.752334\pi$
$397$	−8.91350e7			−1.42455			−0.712273	+	0.701902i	$0.752334\pi$
$398$	−1.59142e7	+	9.18807e6i	−0.252427	+	0.145739i
$399$		0			0
$400$	1.42639e7	−	2.47058e7i	0.222873	−	0.386027i
$401$	−9.70320e7	−	5.60214e7i	−1.50481	−	0.868803i	−0.999984	−	0.00558177i	$-0.998223\pi$
$401$	−9.70320e7	−	5.60214e7i	−1.50481	−	0.868803i	−0.504826	−	0.863221i	$-0.668443\pi$
$402$		0			0
$403$	3.50859e7	+	6.07706e7i	0.536065	+	0.928492i
$404$			4.20966e6i			0.0638414i
$405$		0			0
$406$	880978.			0.0131640
$407$	−3.33342e7	+	1.92455e7i	−0.494433	+	0.285461i
$408$		0			0
$409$	3.33970e7	−	5.78454e7i	0.488133	−	0.845471i	−0.511774	−	0.859120i	$-0.671011\pi$
$409$	3.33970e7	−	5.78454e7i	0.488133	−	0.845471i	0.999907	+	0.0136491i	$0.00434478\pi$
$410$	1.18744e8	+	6.85567e7i	1.72290	+	0.994715i
$411$		0			0
$412$	3.09537e7	+	5.36135e7i	0.442610	+	0.766624i
$413$			641833.i			0.00911113i
$414$		0			0
$415$	−1.97078e8			−2.75736
$416$	1.42471e7	−	8.22554e6i	0.197900	−	0.114257i
$417$		0			0
$418$	−1.79966e6	+	3.11711e6i	−0.0246412	+	0.0426799i
$419$	4.10125e7	+	2.36786e7i	0.557537	+	0.321894i	0.752156	−	0.658985i	$-0.229014\pi$
$419$	4.10125e7	+	2.36786e7i	0.557537	+	0.321894i	−0.194619	+	0.980879i	$0.562347\pi$
$420$		0			0
$421$	−3.30784e7	−	5.72936e7i	−0.443301	−	0.767820i	0.554631	−	0.832096i	$-0.312859\pi$
$421$	−3.30784e7	−	5.72936e7i	−0.443301	−	0.767820i	−0.997932	+	0.0642763i	$0.979526\pi$
$422$		−	2.82552e7i		−	0.375977i
$423$		0			0
$424$	−2.50996e7			−0.329283
$425$	4.74297e7	−	2.73835e7i	0.617851	−	0.356716i
$426$		0			0
$427$	33859.0	−	58645.5i	0.000434901	−	0.000753270i
$428$	1.72350e7	+	9.95066e6i	0.219827	+	0.126917i
$429$		0			0
$430$	1.80852e7	+	3.13245e7i	0.227467	+	0.393984i
$431$			9.06666e7i			1.13244i	0.824254	+	0.566221i	$0.191595\pi$
$431$			9.06666e7i			1.13244i	−0.824254	+	0.566221i	$0.808405\pi$
$432$		0			0
$433$	−699414.			−0.00861530			−0.00430765	−	0.999991i	$-0.501371\pi$
$433$	−699414.			−0.00861530			−0.00430765	+	0.999991i	$0.501371\pi$
$434$	−507926.	+	293251.i	−0.00621342	+	0.00358732i
$435$		0			0
$436$	−2.15325e7	+	3.72953e7i	−0.259797	+	0.449982i
$437$	−4.07906e6	−	2.35505e6i	−0.0488782	−	0.0282199i
$438$		0			0
$439$	1.28648e7	+	2.22825e7i	0.152058	+	0.263372i	0.931984	−	0.362500i	$-0.118077\pi$
$439$	1.28648e7	+	2.22825e7i	0.152058	+	0.263372i	−0.779926	+	0.625872i	$0.784743\pi$
$440$		−	8.53835e7i		−	1.00234i
$441$		0			0
$442$	3.15825e7			0.365746
$443$	−143395.	+	82789.0i	−0.00164938	+	0.000952273i	−0.500824	−	0.865549i	$-0.666970\pi$
$443$	−143395.	+	82789.0i	−0.00164938	+	0.000952273i	0.499175	+	0.866501i	$0.333636\pi$
$444$		0			0
$445$	8.24003e7	−	1.42721e8i	0.935080	−	1.61961i
$446$	−2.78715e7	−	1.60916e7i	−0.314163	−	0.181382i
$447$		0			0
$448$	68749.8	+	119078.i	0.000764605	+	0.00132433i
$449$			4.30456e7i			0.475542i	0.971321	+	0.237771i	$0.0764169\pi$
$449$			4.30456e7i			0.475542i	−0.971321	+	0.237771i	$0.923583\pi$
$450$		0			0
$451$	2.62920e8			2.86611
$452$	3.43452e7	−	1.98292e7i	0.371921	−	0.214729i
$453$		0			0
$454$	−3.28278e7	+	5.68594e7i	−0.350812	+	0.607624i
$455$	2.15212e6	+	1.24253e6i	0.0228472	+	0.0131908i
$456$		0			0
$457$	6.77455e7	+	1.17339e8i	0.709793	+	1.22940i	0.964934	+	0.262493i	$0.0845448\pi$
$457$	6.77455e7	+	1.17339e8i	0.709793	+	1.22940i	−0.255141	+	0.966904i	$0.582122\pi$
$458$		−	1.95552e7i		−	0.203547i
$459$		0			0
$460$	1.11733e8			1.14791
$461$	−2.77431e7	+	1.60175e7i	−0.283173	+	0.163490i	−0.634859	−	0.772628i	$-0.718942\pi$
$461$	−2.77431e7	+	1.60175e7i	−0.283173	+	0.163490i	0.351686	+	0.936118i	$0.385608\pi$
$462$		0			0
$463$	−6.46664e7	+	1.12006e8i	−0.651532	+	1.12849i	0.331219	+	0.943554i	$0.392540\pi$
$463$	−6.46664e7	+	1.12006e8i	−0.651532	+	1.12849i	−0.982751	+	0.184933i	$0.940793\pi$
$464$	3.29132e7	+	1.90024e7i	0.329470	+	0.190220i
$465$		0			0
$466$	−3.61301e7	−	6.25791e7i	−0.357035	−	0.618403i
$467$		−	8.49294e7i		−	0.833887i	−0.908932	−	0.416944i	$-0.863101\pi$
$467$		−	8.49294e7i		−	0.833887i	0.908932	−	0.416944i	$-0.136899\pi$
$468$		0			0
$469$	−1.99178e6			−0.0193073
$470$	7.93424e7	−	4.58084e7i	0.764209	−	0.441216i
$471$		0			0
$472$	−1.38441e7	+	2.39788e7i	−0.131656	+	0.228035i
$473$	6.00657e7	+	3.46790e7i	0.567601	+	0.327705i
$474$		0			0
$475$	−3.91832e6	−	6.78673e6i	−0.0365611	−	0.0633257i
$476$			263969.i			0.00244755i
$477$		0			0
$478$	7.31043e7			0.669360
$479$	−1.00215e8	+	5.78593e7i	−0.911858	+	0.526461i	−0.881028	−	0.473063i	$-0.843148\pi$
$479$	−1.00215e8	+	5.78593e7i	−0.911858	+	0.526461i	−0.0308294	+	0.999525i	$0.509815\pi$
$480$		0			0
$481$	2.41638e7	−	4.18530e7i	0.217135	−	0.376089i
$482$	−3.56661e7	−	2.05918e7i	−0.318504	−	0.183888i
$483$		0			0
$484$	−5.35179e7	−	9.26957e7i	−0.472023	−	0.817568i
$485$		−	2.90412e8i		−	2.54560i
$486$		0			0
$487$	4.52839e7			0.392064			0.196032	−	0.980597i	$-0.437194\pi$
$487$	4.52839e7			0.392064			0.196032	+	0.980597i	$0.437194\pi$
$488$	2.52993e6	−	1.46065e6i	0.0217695	−	0.0125686i
$489$		0			0
$490$	6.93799e7	−	1.20169e8i	0.589719	−	1.02142i
$491$	1.76939e8	+	1.02156e8i	1.49479	+	0.863017i	0.999982	−	0.00598645i	$-0.00190556\pi$
$491$	1.76939e8	+	1.02156e8i	1.49479	+	0.863017i	0.494807	+	0.869003i	$0.335239\pi$
$492$		0			0
$493$	3.64805e7	+	6.31861e7i	0.304453	+	0.527328i
$494$		−	4.51915e6i		−	0.0374866i
$495$		0			0
$496$	−2.53013e7			−0.207347
$497$	546324.	−	315420.i	0.00445022	−	0.00256933i
$498$		0			0
$499$	1.46495e7	−	2.53736e7i	0.117902	−	0.204212i	−0.801034	−	0.598619i	$-0.795717\pi$
$499$	1.46495e7	−	2.53736e7i	0.117902	−	0.204212i	0.918936	+	0.394407i	$0.129050\pi$
$500$	7.06999e7	+	4.08186e7i	0.565600	+	0.326549i
$501$		0			0
$502$	−4.86282e7	−	8.42265e7i	−0.384394	−	0.665790i
$503$			1.64834e8i			1.29522i	0.761973	+	0.647609i	$0.224231\pi$
$503$			1.64834e8i			1.29522i	−0.761973	+	0.647609i	$0.775769\pi$
$504$		0			0
$505$	−2.74323e7			−0.213004
$506$	1.85548e8	−	1.07126e8i	1.43220	−	0.826882i
$507$		0			0
$508$	−2.64475e7	+	4.58083e7i	−0.201740	+	0.349425i
$509$	−1.44920e8	−	8.36696e7i	−1.09894	−	0.634474i	−0.162999	−	0.986626i	$-0.552117\pi$
$509$	−1.44920e8	−	8.36696e7i	−1.09894	−	0.634474i	−0.935943	+	0.352152i	$0.885450\pi$
$510$		0			0
$511$	−695910.	−	1.20535e6i	−0.00521544	−	0.00903340i
$512$			5.93164e6i			0.0441942i
$513$		0			0
$514$	4.53177e7			0.333717
$515$	−3.49373e8	+	2.01711e8i	−2.55781	+	1.47675i
$516$		0			0
$517$	8.78391e7	−	1.52142e8i	0.635648	−	1.10097i
$518$	349811.	+	201963.i	0.00251677	+	0.00145306i
$519$		0			0
$520$	5.36019e7	+	9.28411e7i	0.381215	+	0.660283i
$521$			6.01419e7i			0.425270i	0.977132	+	0.212635i	$0.0682045\pi$
$521$			6.01419e7i			0.425270i	−0.977132	+	0.212635i	$0.931796\pi$
$522$		0			0
$523$	1.09251e8			0.763698			0.381849	−	0.924225i	$-0.375287\pi$
$523$	1.09251e8			0.763698			0.381849	+	0.924225i	$0.375287\pi$
$524$	−7.37509e7	+	4.25801e7i	−0.512594	+	0.295946i
$525$		0			0
$526$	4.75768e7	−	8.24054e7i	0.326917	−	0.566237i
$527$	−4.20655e7	−	2.42865e7i	−0.287405	−	0.165933i
$528$		0			0
$529$	6.61676e7	+	1.14606e8i	0.446970	+	0.774175i
$530$		−	1.63562e8i		−	1.09864i
$531$		0			0
$532$	37771.5			0.000250859
$533$	−2.85884e8	+	1.65055e8i	−1.88803	+	1.09005i
$534$		0			0
$535$	−6.48436e7	+	1.12312e8i	−0.423454	+	0.733443i
$536$	−7.44123e7	−	4.29620e7i	−0.483226	−	0.278991i
$537$		0			0
$538$	−9.43320e6	−	1.63388e7i	−0.0605776	−	0.104923i
$539$		−	2.66077e8i		−	1.69918i
$540$		0			0
$541$	4.52159e7			0.285561			0.142781	−	0.989754i	$-0.454396\pi$
$541$	4.52159e7			0.285561			0.142781	+	0.989754i	$0.454396\pi$
$542$	−7.20383e7	+	4.15914e7i	−0.452445	+	0.261219i
$543$		0			0
$544$	−5.69373e6	+	9.86183e6i	−0.0353672	+	0.0612577i
$545$	−2.43035e8	−	1.40317e8i	−1.50134	−	0.866801i
$546$		0			0
$547$	−2.55726e7	−	4.42930e7i	−0.156247	−	0.270628i	0.777265	−	0.629173i	$-0.216606\pi$
$547$	−2.55726e7	−	4.42930e7i	−0.156247	−	0.270628i	−0.933512	+	0.358545i	$0.883273\pi$
$548$			8.35248e7i			0.507544i
$549$		0			0
$550$	3.56473e8			2.14258
$551$	9.04133e6	−	5.22001e6i	0.0540477	−	0.0312045i
$552$		0			0
$553$	1.88011e6	−	3.25645e6i	0.0111175	−	0.0192561i
$554$	5.34971e7	+	3.08866e7i	0.314631	+	0.181652i
$555$		0			0
$556$	−1.12211e7	−	1.94356e7i	−0.0652849	−	0.113077i
$557$			2.43306e7i			0.140795i	0.997519	+	0.0703974i	$0.0224267\pi$
$557$			2.43306e7i			0.140795i	−0.997519	+	0.0703974i	$0.977573\pi$
$558$		0			0
$559$	−8.70827e7			−0.498536
$560$	−775974.	+	448009.i	−0.00441858	+	0.00255107i
$561$		0			0
$562$	5.28199e7	−	9.14868e7i	0.297570	−	0.515406i
$563$	1.25053e8	+	7.21992e7i	0.700758	+	0.404583i	0.807630	−	0.589690i	$-0.200750\pi$
$563$	1.25053e8	+	7.21992e7i	0.700758	+	0.404583i	−0.106872	+	0.994273i	$0.534083\pi$
$564$		0			0
$565$	1.29217e8	+	2.23811e8i	0.716432	+	1.24090i
$566$		−	8.27342e7i		−	0.456284i
$567$		0			0
$568$	2.72141e7			0.148508
$569$	7.20146e7	−	4.15777e7i	0.390916	−	0.225696i	−0.291641	−	0.956528i	$-0.594201\pi$
$569$	7.20146e7	−	4.15777e7i	0.390916	−	0.225696i	0.682557	+	0.730832i	$0.260868\pi$
$570$		0			0
$571$	1.13040e8	−	1.95791e8i	0.607188	−	1.05168i	−0.384513	−	0.923119i	$-0.625631\pi$
$571$	1.13040e8	−	1.95791e8i	0.607188	−	1.05168i	0.991702	−	0.128561i	$-0.0410359\pi$
$572$	1.78026e8	+	1.02783e8i	0.951252	+	0.549205i
$573$		0			0
$574$	−1.37955e6	−	2.38944e6i	−0.00729458	−	0.0126346i
$575$			4.66481e8i			2.45375i
$576$		0			0
$577$	4.11006e7			0.213954			0.106977	−	0.994261i	$-0.465883\pi$
$577$	4.11006e7			0.213954			0.106977	+	0.994261i	$0.465883\pi$
$578$	9.93169e7	−	5.73406e7i	0.514327	−	0.296947i
$579$		0			0
$580$	−1.23830e8	+	2.14479e8i	−0.634659	+	1.09926i
$581$	3.43443e6	+	1.98287e6i	0.0175116	+	0.0101103i
$582$		0			0
$583$	−1.56818e8	−	2.71617e8i	−0.791390	−	1.37073i
$584$		−	6.00423e7i		−	0.301452i
$585$		0			0
$586$	−2.70640e8			−1.34493
$587$	9.93271e7	−	5.73465e7i	0.491081	−	0.283526i	−0.233942	−	0.972251i	$-0.575162\pi$
$587$	9.93271e7	−	5.73465e7i	0.491081	−	0.283526i	0.725023	+	0.688725i	$0.241829\pi$
$588$		0			0
$589$	−3.47517e6	+	6.01917e6i	−0.0170071	+	0.0294571i
$590$	−1.56258e8	−	9.02156e7i	−0.760827	−	0.439264i
$591$		0			0
$592$	8.71257e6	+	1.50906e7i	0.0419934	+	0.0727347i
$593$		−	2.90487e8i		−	1.39304i	−0.717539	−	0.696518i	$-0.754731\pi$
$593$		−	2.90487e8i		−	1.39304i	0.717539	−	0.696518i	$-0.245269\pi$
$594$		0			0
$595$	−1.72016e6			−0.00816616
$596$	−1.31177e8	+	7.57350e7i	−0.619610	+	0.357732i
$597$		0			0
$598$	−1.34503e8	+	2.32966e8i	−0.628966	+	1.08940i
$599$	3.09303e8	+	1.78576e8i	1.43914	+	0.830888i	0.997790	−	0.0664462i	$-0.0211661\pi$
$599$	3.09303e8	+	1.78576e8i	1.43914	+	0.830888i	0.441351	+	0.897335i	$0.354499\pi$
$600$		0			0
$601$	4.20047e7	+	7.27542e7i	0.193497	+	0.335147i	0.946407	−	0.322977i	$-0.104684\pi$
$601$	4.20047e7	+	7.27542e7i	0.193497	+	0.335147i	−0.752910	+	0.658124i	$0.771350\pi$
$602$		−	727845.i		−	0.00333618i
$603$		0			0
$604$	−1.19593e8			−0.542746
$605$	6.04053e8	−	3.48750e8i	2.72778	−	1.57488i
$606$		0			0
$607$	−2.58143e7	+	4.47117e7i	−0.115424	+	0.199920i	−0.917949	−	0.396698i	$-0.870156\pi$
$607$	−2.58143e7	+	4.47117e7i	−0.115424	+	0.199920i	0.802525	+	0.596618i	$0.203489\pi$
$608$	1.41113e6	+	814718.i	0.00627852	+	0.00362491i
$609$		0			0
$610$	9.51838e6	+	1.64863e7i	0.0419347	+	0.0726330i
$611$			2.20574e8i			0.967009i
$612$		0			0
$613$	4.44326e7			0.192895			0.0964473	−	0.995338i	$-0.469252\pi$
$613$	4.44326e7			0.192895			0.0964473	+	0.995338i	$0.469252\pi$
$614$	2.08100e8	−	1.20147e8i	0.899015	−	0.519046i
$615$		0			0
$616$	−859072.	+	1.48796e6i	−0.00367526	+	0.00636573i
$617$	−1.43248e8	−	8.27040e7i	−0.609862	−	0.352104i	0.163049	−	0.986618i	$-0.447867\pi$
$617$	−1.43248e8	−	8.27040e7i	−0.609862	−	0.352104i	−0.772911	+	0.634514i	$0.781200\pi$
$618$		0			0
$619$	−1.34081e8	−	2.32235e8i	−0.565320	−	0.979164i	−0.997020	−	0.0771460i	$-0.975419\pi$
$619$	−1.34081e8	−	2.32235e8i	−0.565320	−	0.979164i	0.431699	−	0.902018i	$-0.357914\pi$
$620$		−	1.64876e8i		−	0.691805i
$621$		0			0
$622$	−1.75360e8			−0.728718
$623$	−2.87194e6	+	1.65811e6i	−0.0118771	+	0.00685726i
$624$		0			0
$625$	−4.83458e7	+	8.37373e7i	−0.198024	+	0.342988i
$626$	1.45905e8	+	8.42385e7i	0.594769	+	0.343390i
$627$		0			0
$628$	5.13059e7	+	8.88644e7i	0.207152	+	0.358797i
$629$			3.34525e7i			0.134424i
$630$		0			0
$631$	1.13998e8			0.453741			0.226871	−	0.973925i	$-0.427151\pi$
$631$	1.13998e8			0.453741			0.226871	+	0.973925i	$0.427151\pi$
$632$	1.40481e8	−	8.11068e7i	0.556502	−	0.321297i
$633$		0			0
$634$	−6.16346e6	+	1.06754e7i	−0.0241856	+	0.0418907i
$635$	−2.98511e8	−	1.72345e8i	−1.16584	−	0.673098i
$636$		0			0
$637$	1.67037e8	+	2.89317e8i	0.646241	+	1.11932i
$638$			4.74895e8i			1.82867i
$639$		0			0
$640$	−3.86536e7			−0.147452
$641$	−3.16652e7	+	1.82819e7i	−0.120229	+	0.0694142i	−0.558908	−	0.829229i	$-0.688780\pi$
$641$	−3.16652e7	+	1.82819e7i	−0.120229	+	0.0694142i	0.438680	+	0.898644i	$0.355446\pi$
$642$		0			0
$643$	1.41134e8	−	2.44452e8i	0.530883	−	0.919517i	−0.468467	−	0.883481i	$-0.655194\pi$
$643$	1.41134e8	−	2.44452e8i	0.530883	−	0.919517i	0.999350	−	0.0360362i	$-0.0114732\pi$
$644$	−1.94715e6	−	1.12419e6i	−0.00729022	−	0.00420901i
$645$		0			0
$646$	1.56408e6	+	2.70907e6i	0.00580179	+	0.0100490i
$647$		−	1.45187e8i		−	0.536062i	−0.963410	−	0.268031i	$-0.913627\pi$
$647$		−	1.45187e8i		−	0.536062i	0.963410	−	0.268031i	$-0.0863729\pi$
$648$		0			0
$649$	−3.45983e8			−1.26567
$650$	−3.87608e8	+	2.23786e8i	−1.41141	+	0.814877i
$651$		0			0
$652$	−1.54307e7	+	2.67267e7i	−0.0556727	+	0.0964280i
$653$	8.59015e7	+	4.95952e7i	0.308504	+	0.178115i	0.646257	−	0.763120i	$-0.276333\pi$
$653$	8.59015e7	+	4.95952e7i	0.308504	+	0.178115i	−0.337753	+	0.941235i	$0.609667\pi$
$654$		0			0
$655$	−2.77474e8	−	4.80599e8i	−0.987412	−	1.71025i
$656$		−	1.19025e8i		−	0.421627i
$657$		0			0
$658$	−1.84357e6			−0.00647117
$659$	−1.46859e8	+	8.47892e7i	−0.513150	+	0.296268i	−0.734128	−	0.679011i	$-0.762409\pi$
$659$	−1.46859e8	+	8.47892e7i	−0.513150	+	0.296268i	0.220977	+	0.975279i	$0.429075\pi$
$660$		0			0
$661$	−2.69025e8	+	4.65965e8i	−0.931511	+	1.61342i	−0.150771	+	0.988569i	$0.548176\pi$
$661$	−2.69025e8	+	4.65965e8i	−0.931511	+	1.61342i	−0.780740	+	0.624856i	$0.785158\pi$
$662$	−6.54851e7	−	3.78079e7i	−0.225719	−	0.130319i
$663$		0			0
$664$	8.55398e7	+	1.48159e8i	0.292189	+	0.506086i
$665$			246138.i			0.000836978i
$666$		0			0
$667$	−6.21449e8			−2.09425
$668$	−2.86825e7	+	1.65599e7i	−0.0962251	+	0.0555556i
$669$		0			0
$670$	2.79962e8	−	4.84909e8i	0.930840	−	1.61226i
$671$	3.16131e7	+	1.82518e7i	0.104640	+	0.0604141i
$672$		0			0
$673$	1.92682e7	+	3.33736e7i	0.0632116	+	0.109486i	0.895899	−	0.444257i	$-0.146532\pi$
$673$	1.92682e7	+	3.33736e7i	0.0632116	+	0.109486i	−0.832688	+	0.553743i	$0.813199\pi$
$674$			2.52006e8i			0.823060i
$675$		0			0
$676$	−1.03643e8			−0.335504
$677$	1.65239e8	−	9.54008e7i	0.532533	−	0.307458i	−0.209514	−	0.977806i	$-0.567188\pi$
$677$	1.65239e8	−	9.54008e7i	0.532533	−	0.307458i	0.742047	+	0.670347i	$0.233855\pi$
$678$		0			0
$679$	−2.92194e6	+	5.06095e6i	−0.00933387	+	0.0161667i
$680$	−6.42648e7	−	3.71033e7i	−0.204384	−	0.118001i
$681$		0			0
$682$	−1.58078e8	−	2.73799e8i	−0.498332	−	0.863136i
$683$			5.45896e8i			1.71336i	0.515850	+	0.856679i	$0.327476\pi$
$683$			5.45896e8i			1.71336i	−0.515850	+	0.856679i	$0.672524\pi$
$684$		0			0
$685$	−5.44291e8			−1.69340
$686$	−4.83663e6	+	2.79243e6i	−0.0149820	+	0.00864987i
$687$		0			0
$688$	1.56994e7	−	2.71921e7i	0.0482078	−	0.0834984i
$689$	3.41030e8	+	1.96894e8i	1.04264	+	0.601969i
$690$		0			0
$691$	8.52235e7	+	1.47611e8i	0.258301	+	0.447390i	0.965787	−	0.259337i	$-0.0835042\pi$
$691$	8.52235e7	+	1.47611e8i	0.258301	+	0.447390i	−0.707486	+	0.706727i	$0.750171\pi$
$692$			2.07551e7i			0.0626334i
$693$		0			0
$694$	−1.18220e8			−0.353682
$695$	1.26652e8	−	7.31227e7i	0.377275	−	0.217820i
$696$		0			0
$697$	1.14251e8	−	1.97889e8i	0.337414	−	0.584419i
$698$	−3.16060e8	−	1.82477e8i	−0.929400	−	0.536589i
$699$		0			0
$700$	−1.87042e6	−	3.23966e6i	−0.00545311	−	0.00944507i
$701$			8.02305e7i			0.232909i	0.993196	+	0.116454i	$0.0371529\pi$
$701$			8.02305e7i			0.232909i	−0.993196	+	0.116454i	$0.962847\pi$
$702$		0			0
$703$	4.78673e6			0.0137776
$704$	−6.41895e7	+	3.70598e7i	−0.183970	+	0.106215i
$705$		0			0
$706$	1.19055e7	−	2.06209e7i	0.0338323	−	0.0585993i
$707$	478056.	+	276006.i	0.00135276	+	0.000781015i
$708$		0			0
$709$	−2.00566e8	−	3.47390e8i	−0.562754	−	0.974718i	−0.997255	−	0.0740465i	$-0.976409\pi$
$709$	−2.00566e8	−	3.47390e8i	−0.562754	−	0.974718i	0.434501	−	0.900671i	$-0.356925\pi$
$710$			1.77341e8i			0.495489i
$711$		0			0
$712$	−1.43060e8			−0.396349
$713$	3.58295e8	−	2.06862e8i	0.988489	−	0.570705i
$714$		0			0
$715$	−6.69790e8	+	1.16011e9i	−1.83240	+	3.17381i
$716$	−1.28917e8	−	7.44302e7i	−0.351213	−	0.202773i
$717$		0			0
$718$	1.58765e8	+	2.74990e8i	0.428926	+	0.742922i
$719$			1.02302e8i			0.275232i	0.990486	+	0.137616i	$0.0439439\pi$
$719$			1.02302e8i			0.275232i	−0.990486	+	0.137616i	$0.956056\pi$
$720$		0			0
$721$	8.11792e6			0.0216590
$722$	−2.30089e8	+	1.32842e8i	−0.611342	+	0.352959i
$723$		0			0
$724$	5.49951e7	−	9.52544e7i	0.144913	−	0.250997i
$725$	−8.95441e8	−	5.16983e8i	−2.34976	−	1.35663i
$726$		0			0
$727$	2.93837e8	+	5.08941e8i	0.764722	+	1.32454i	0.940393	+	0.340089i	$0.110457\pi$
$727$	2.93837e8	+	5.08941e8i	0.764722	+	1.32454i	−0.175671	+	0.984449i	$0.556209\pi$
$728$		−	2.15723e6i		−	0.00559115i
$729$		0			0
$730$	3.91266e8			1.00578
$731$	5.22030e7	−	3.01394e7i	0.133642	−	0.0771583i
$732$		0			0
$733$	5.60077e7	−	9.70083e7i	0.142212	−	0.246318i	−0.786117	−	0.618077i	$-0.787912\pi$
$733$	5.60077e7	−	9.70083e7i	0.142212	−	0.246318i	0.928329	+	0.371759i	$0.121245\pi$
$734$	−1.64166e8	−	9.47813e7i	−0.415141	−	0.239682i
$735$		0			0
$736$	−4.84966e7	−	8.39986e7i	−0.121640	−	0.210687i
$737$		−	1.07367e9i		−	2.68207i
$738$		0			0
$739$	6.86968e8			1.70217			0.851086	−	0.525027i	$-0.175945\pi$
$739$	6.86968e8			1.70217			0.851086	+	0.525027i	$0.175945\pi$
$740$	−9.83382e7	+	5.67756e7i	−0.242676	+	0.140109i
$741$		0			0
$742$	−1.64565e6	+	2.85036e6i	−0.00402835	+	0.00697730i
$743$	4.82909e8	+	2.78808e8i	1.17733	+	0.679732i	0.955396	−	0.295329i	$-0.0954292\pi$
$743$	4.82909e8	+	2.78808e8i	1.17733	+	0.679732i	0.221936	+	0.975061i	$0.428763\pi$
$744$		0			0
$745$	−4.93528e8	−	8.54816e8i	−1.19356	−	2.06730i
$746$			1.26022e8i			0.303549i
$747$		0			0
$748$	−1.42294e8			−0.340001
$749$	2.26003e6	−	1.30483e6i	0.00537859	−	0.00310533i
$750$		0			0
$751$	−2.02498e8	+	3.50737e8i	−0.478080	+	0.828059i	−0.999684	−	0.0251288i	$-0.992000\pi$
$751$	−2.02498e8	+	3.50737e8i	−0.478080	+	0.828059i	0.521604	+	0.853188i	$0.325334\pi$
$752$	−6.88756e7	−	3.97653e7i	−0.161961	−	0.0935085i
$753$		0			0
$754$	−2.98128e8	−	5.16374e8i	−0.695488	−	1.20462i
$755$		−	7.79332e8i		−	1.81085i
$756$		0			0
$757$	6.51769e8			1.50247			0.751235	−	0.660035i	$-0.229458\pi$
$757$	6.51769e8			1.50247			0.751235	+	0.660035i	$0.229458\pi$
$758$	3.78301e8	−	2.18412e8i	0.868621	−	0.501499i
$759$		0			0
$760$	−5.30912e6	+	9.19567e6i	−0.0120943	+	0.0209480i
$761$	2.69514e8	+	1.55604e8i	0.611543	+	0.353074i	0.773569	−	0.633712i	$-0.218470\pi$
$761$	2.69514e8	+	1.55604e8i	0.611543	+	0.353074i	−0.162026	+	0.986786i	$0.551803\pi$
$762$		0			0
$763$	2.82355e6	+	4.89053e6i	0.00635655	+	0.0110099i
$764$			3.76030e8i			0.843222i
$765$		0			0
$766$	−1.88144e8			−0.418604
$767$	3.76202e8	−	2.17200e8i	0.833749	−	0.481365i
$768$		0			0
$769$	2.18605e8	−	3.78636e8i	0.480708	−	0.832612i	−0.519047	−	0.854746i	$-0.673713\pi$
$769$	2.18605e8	−	3.78636e8i	0.480708	−	0.832612i	0.999755	+	0.0221345i	$0.00704620\pi$
$770$	−9.69629e6	−	5.59816e6i	−0.0212390	−	0.0122623i
$771$		0			0
$772$	1.11296e8	+	1.92770e8i	0.241895	+	0.418975i
$773$			5.41906e7i			0.117324i	0.998278	+	0.0586619i	$0.0186834\pi$
$773$			5.41906e7i			0.117324i	−0.998278	+

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	162.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.89898 - 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(180.591 + 104.264i) q^{5} +(-2.09808 - 3.63397i) q^{7} -181.019i q^{8} +O(q^{10})\)	\(q+(4.89898 - 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(180.591 + 104.264i) q^{5} +(-2.09808 - 3.63397i) q^{7} -181.019i q^{8} +1179.62 q^{10} +(1958.91 - 1130.98i) q^{11} +(-1420.00 + 2459.52i) q^{13} +(-20.5569 - 11.8685i) q^{14} +(-512.000 - 886.810i) q^{16} -1965.86i q^{17} -281.295 q^{19} +(5778.91 - 3336.46i) q^{20} +(6397.77 - 11081.3i) q^{22} +(14501.0 + 8372.14i) q^{23} +(13929.6 + 24126.7i) q^{25} +16065.5i q^{26} -134.277 q^{28} +(-32141.8 + 18557.1i) q^{29} +(12354.2 - 21398.0i) q^{31} +(-5016.55 - 2896.31i) q^{32} +(-5560.29 - 9630.70i) q^{34} -875.017i q^{35} -17016.7 q^{37} +(-1378.06 + 795.623i) q^{38} +(18873.8 - 32690.5i) q^{40} +(100663. + 58117.9i) q^{41} +(15331.4 + 26554.8i) q^{43} -72382.5i q^{44} +94720.0 q^{46} +(67261.3 - 38833.3i) q^{47} +(58815.7 - 101872. i) q^{49} +(136481. + 78797.5i) q^{50} +(45440.1 + 78704.6i) q^{52} -138657. i q^{53} +471682. q^{55} +(-657.820 + 379.792i) q^{56} +(-104975. + 181821. i) q^{58} +(-132465. - 76478.8i) q^{59} +(8069.05 + 13976.0i) q^{61} -139771. i q^{62} -32768.0 q^{64} +(-512880. + 296111. i) q^{65} +(237334. - 411074. i) q^{67} +(-54479.4 - 31453.7i) q^{68} +(-2474.92 - 4286.69i) q^{70} +150338. i q^{71} +331690. q^{73} +(-83364.7 + 48130.6i) q^{74} +(-4500.73 + 7795.49i) q^{76} +(-8219.88 - 4745.75i) q^{77} +(448056. + 776056. i) q^{79} -213533. i q^{80} +657529. q^{82} +(-818472. + 472545. i) q^{83} +(204969. - 355016. i) q^{85} +(150217. + 86727.7i) q^{86} +(-204729. - 354600. i) q^{88} -790302. i q^{89} +11917.1 q^{91} +(464031. - 267909. i) q^{92} +(219674. - 380487. i) q^{94} +(-50799.4 - 29329.0i) q^{95} +(-696338. - 1.20609e6i) q^{97} -665424. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 128 q^{4} + 4 q^{7}+O(q^{10}) \) 8 * q + 128 * q^4 + 4 * q^7	\( 8 q + 128 q^{4} + 4 q^{7} + 5280 q^{10} - 3836 q^{13} - 4096 q^{16} + 20488 q^{19} + 27072 q^{22} + 25700 q^{25} + 256 q^{28} + 40096 q^{31} - 60528 q^{34} - 40400 q^{37} + 84480 q^{40} - 184940 q^{43} + 325440 q^{46} + 470484 q^{49} + 122752 q^{52} + 1899720 q^{55} - 24624 q^{58} - 609056 q^{61} - 262144 q^{64} + 2008972 q^{67} - 8160 q^{70} + 1051648 q^{73} + 327808 q^{76} + 848716 q^{79} + 1411584 q^{82} + 987840 q^{85} - 866304 q^{88} + 70520 q^{91} + 1965408 q^{94} - 3621728 q^{97}+O(q^{100}) \) 8 * q + 128 * q^4 + 4 * q^7 + 5280 * q^10 - 3836 * q^13 - 4096 * q^16 + 20488 * q^19 + 27072 * q^22 + 25700 * q^25 + 256 * q^28 + 40096 * q^31 - 60528 * q^34 - 40400 * q^37 + 84480 * q^40 - 184940 * q^43 + 325440 * q^46 + 470484 * q^49 + 122752 * q^52 + 1899720 * q^55 - 24624 * q^58 - 609056 * q^61 - 262144 * q^64 + 2008972 * q^67 - 8160 * q^70 + 1051648 * q^73 + 327808 * q^76 + 848716 * q^79 + 1411584 * q^82 + 987840 * q^85 - 866304 * q^88 + 70520 * q^91 + 1965408 * q^94 - 3621728 * q^97

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