LMFDB - Embedded newform 162.7.d.f.107.1

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			107.1
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	162.107
Dual form			162.7.d.f.53.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.89898 - 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-180.591 + 104.264i) q^{5} +(-2.09808 + 3.63397i) q^{7} -181.019i q^{8} +O(q^{10})$	\(q+(-4.89898 - 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-180.591 + 104.264i) q^{5} +(-2.09808 + 3.63397i) q^{7} -181.019i q^{8} +1179.62 q^{10} +(-1958.91 - 1130.98i) q^{11} +(-1420.00 - 2459.52i) q^{13} +(20.5569 - 11.8685i) q^{14} +(-512.000 + 886.810i) q^{16} -1965.86i q^{17} -281.295 q^{19} +(-5778.91 - 3336.46i) q^{20} +(6397.77 + 11081.3i) q^{22} +(-14501.0 + 8372.14i) q^{23} +(13929.6 - 24126.7i) q^{25} +16065.5i q^{26} -134.277 q^{28} +(32141.8 + 18557.1i) q^{29} +(12354.2 + 21398.0i) q^{31} +(5016.55 - 2896.31i) q^{32} +(-5560.29 + 9630.70i) q^{34} -875.017i q^{35} -17016.7 q^{37} +(1378.06 + 795.623i) q^{38} +(18873.8 + 32690.5i) q^{40} +(-100663. + 58117.9i) q^{41} +(15331.4 - 26554.8i) q^{43} -72382.5i q^{44} +94720.0 q^{46} +(-67261.3 - 38833.3i) q^{47} +(58815.7 + 101872. i) q^{49} +(-136481. + 78797.5i) q^{50} +(45440.1 - 78704.6i) q^{52} -138657. i q^{53} +471682. q^{55} +(657.820 + 379.792i) q^{56} +(-104975. - 181821. i) q^{58} +(132465. - 76478.8i) q^{59} +(8069.05 - 13976.0i) q^{61} -139771. i q^{62} -32768.0 q^{64} +(512880. + 296111. i) q^{65} +(237334. + 411074. i) q^{67} +(54479.4 - 31453.7i) q^{68} +(-2474.92 + 4286.69i) q^{70} +150338. i q^{71} +331690. q^{73} +(83364.7 + 48130.6i) q^{74} +(-4500.73 - 7795.49i) q^{76} +(8219.88 - 4745.75i) q^{77} +(448056. - 776056. i) q^{79} -213533. i q^{80} +657529. q^{82} +(818472. + 472545. i) q^{83} +(204969. + 355016. i) q^{85} +(-150217. + 86727.7i) q^{86} +(-204729. + 354600. i) q^{88} -790302. i q^{89} +11917.1 q^{91} +(-464031. - 267909. i) q^{92} +(219674. + 380487. i) q^{94} +(50799.4 - 29329.0i) q^{95} +(-696338. + 1.20609e6i) q^{97} -665424. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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	$-0.980687\pi$
$5$	−180.591	+	104.264i	−1.44473	+	0.834114i	−0.446568	+	0.894750i	$0.647354\pi$
$6$		0			0
$7$	−2.09808	+	3.63397i	−0.00611684	+	0.0105947i	−0.869068	−	0.494693i	$-0.835280\pi$
$7$	−2.09808	+	3.63397i	−0.00611684	+	0.0105947i	0.862951	+	0.505288i	$0.168614\pi$
$8$		−	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	$-0.656562\pi$
$11$	−1958.91	−	1130.98i	−1.47176	−	0.849719i	−0.999496	+	0.0317396i	$0.989895\pi$
$12$		0			0
$13$	−1420.00	−	2459.52i	−0.646338	−	1.11949i	−0.983991	−	0.178219i	$-0.942966\pi$
$13$	−1420.00	−	2459.52i	−0.646338	−	1.11949i	0.337653	−	0.941271i	$-0.390367\pi$
$14$	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	$-0.908223\pi$
$23$	−14501.0	+	8372.14i	−1.19183	+	0.688102i	−0.233107	+	0.972451i	$0.574889\pi$
$24$		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	$-0.0581019\pi$
$29$	32141.8	+	18557.1i	1.31788	+	0.760878i	0.334492	+	0.942399i	$0.391435\pi$
$30$		0			0
$31$	12354.2	+	21398.0i	0.414694	+	0.718272i	0.995396	−	0.0958444i	$-0.0305551\pi$
$31$	12354.2	+	21398.0i	0.414694	+	0.718272i	−0.580702	+	0.814116i	$0.697222\pi$
$32$	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	$-0.986029\pi$
$41$	−100663.	+	58117.9i	−1.46056	+	0.843253i	−0.461521	+	0.887129i	$0.652696\pi$
$42$		0			0
$43$	15331.4	−	26554.8i	0.192831	−	0.333993i	−0.753356	−	0.657613i	$-0.771566\pi$
$43$	15331.4	−	26554.8i	0.192831	−	0.333993i	0.946187	+	0.323619i	$0.104900\pi$
$44$		−	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	$-0.455359\pi$
$47$	−67261.3	−	38833.3i	−0.647846	−	0.374034i	−0.787630	+	0.616148i	$0.788692\pi$
$48$		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	$-0.545209\pi$
$59$	132465.	−	76478.8i	0.644979	−	0.372379i	0.786530	+	0.617552i	$0.211876\pi$
$60$		0			0
$61$	8069.05	−	13976.0i	0.0355495	−	0.0615735i	−0.847703	−	0.530471i	$-0.822015\pi$
$61$	8069.05	−	13976.0i	0.0355495	−	0.0615735i	0.883253	+	0.468897i	$0.155349\pi$
$62$		−	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	0.926516	+	0.376255i	$0.122788\pi$
$67$	237334.	+	411074.i	0.789105	+	1.36677i	−0.137411	+	0.990514i	$0.543878\pi$
$68$	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	0.0929805	−	0.995668i	$-0.470361\pi$
$79$	448056.	−	776056.i	0.908764	−	1.57403i	0.815783	−	0.578357i	$-0.196306\pi$
$80$		−	213533.i		−	0.417057i
$81$		0			0
$82$	657529.			1.19254
$83$	818472.	+	472545.i	1.43143	+	0.826435i	0.997230	−	0.0743823i	$-0.0236985\pi$
$83$	818472.	+	472545.i	1.43143	+	0.826435i	0.434198	+	0.900817i	$0.357032\pi$
$84$		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	0.178351	+	0.983967i	$0.442924\pi$
$97$	−696338.	+	1.20609e6i	−0.762965	+	1.32149i	−0.941316	+	0.337527i	$0.890409\pi$
$98$		−	665424.i		−	0.707001i
$99$		0			0
$100$	891492.			0.891492
$101$	113927.	+	65775.9i	0.110577	+	0.0638414i	0.554268	−	0.832338i	$-0.312998\pi$
$101$	113927.	+	65775.9i	0.110577	+	0.0638414i	−0.443692	+	0.896179i	$0.646331\pi$
$102$		0			0
$103$	−967305.	−	1.67542e6i	−0.885221	−	1.53325i	−0.845460	−	0.534038i	$-0.820674\pi$
$103$	−967305.	−	1.67542e6i	−0.885221	−	1.53325i	−0.0397603	−	0.999209i	$-0.512659\pi$
$104$	−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	$-0.807962\pi$
$113$	−1.07329e6	+	619662.i	−0.743841	+	0.429457i	0.0796229	+	0.996825i	$0.474628\pi$
$114$		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	$-0.465048\pi$
$131$	2.30472e6	−	1.33063e6i	1.02519	−	0.591893i	0.915602	+	0.402085i	$0.131714\pi$
$132$		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	$-0.163887\pi$
$137$	2.26046e6	+	1.30508e6i	0.879092	+	0.507544i	0.00873327	+	0.999962i	$0.497220\pi$
$138$		0			0
$139$	350661.	+	607362.i	0.130570	+	0.226153i	0.923896	−	0.382643i	$-0.124986\pi$
$139$	350661.	+	607362.i	0.130570	+	0.226153i	−0.793327	+	0.608796i	$0.791653\pi$
$140$	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	$-0.412882\pi$
$149$	4.09928e6	−	2.36672e6i	1.23922	−	0.715464i	0.968935	+	0.247316i	$0.0795486\pi$
$150$		0			0
$151$	−1.86865e6	+	3.23659e6i	−0.542746	+	0.940063i	0.455999	+	0.889980i	$0.349282\pi$
$151$	−1.86865e6	+	3.23659e6i	−0.542746	+	0.940063i	−0.998745	+	0.0500829i	$0.984051\pi$
$152$			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	0.581052	−	0.813867i	$-0.302641\pi$
$157$	−1.60331e6	−	2.77701e6i	−0.414303	−	0.717594i	−0.995355	+	0.0962723i	$0.969308\pi$
$158$	−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	$-0.631226\pi$
$167$	896330.	−	517496.i	0.192450	−	0.111111i	0.593129	+	0.805107i	$0.297892\pi$
$168$		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	$-0.313383\pi$
$173$	561701.	+	324298.i	0.108484	+	0.0626334i	−0.444776	+	0.895642i	$0.646717\pi$
$174$		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	$-0.0139890\pi$
$191$	1.01766e7	+	5.87547e6i	1.46050	+	0.843222i	0.461470	+	0.887156i	$0.347322\pi$
$192$		0			0
$193$	−3.47800e6	−	6.02407e6i	−0.483790	−	0.837950i	0.516036	−	0.856567i	$-0.327407\pi$
$193$	−3.47800e6	−	6.02407e6i	−0.483790	−	0.837950i	−0.999827	+	0.0186172i	$0.994074\pi$
$194$	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	0.967788	−	0.251768i	$-0.0810121\pi$
$211$	2.49743e6	+	4.32568e6i	0.265856	+	0.460476i	−0.701932	+	0.712244i	$0.747679\pi$
$212$	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	−0.965305	−	0.261123i	$-0.915907\pi$
$223$	−2.84462e6	+	4.92703e6i	−0.256513	+	0.444294i	0.708792	+	0.705417i	$0.249240\pi$
$224$			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	$-0.168090\pi$
$227$	1.00514e7	+	5.80319e6i	0.859310	+	0.496123i	−0.00447105	+	0.999990i	$0.501423\pi$
$228$		0			0
$229$	1.72845e6	+	2.99376e6i	0.143930	+	0.249294i	0.928973	−	0.370147i	$-0.120693\pi$
$229$	1.72845e6	+	2.99376e6i	0.143930	+	0.249294i	−0.785043	+	0.619441i	$0.787359\pi$
$230$	−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	$-0.823607\pi$
$239$	−1.11918e7	+	6.46157e6i	−0.819795	+	0.473309i	0.0305510	+	0.999533i	$0.490274\pi$
$240$		0			0
$241$	−3.64016e6	+	6.30494e6i	−0.260057	+	0.450433i	−0.966257	−	0.257580i	$-0.917075\pi$
$241$	−3.64016e6	+	6.30494e6i	−0.260057	+	0.450433i	0.706200	+	0.708013i	$0.250408\pi$
$242$		−	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	$-0.742495\pi$
$257$	−6.93783e6	+	4.00556e6i	−0.408718	+	0.235974i	0.281521	+	0.959555i	$0.409161\pi$
$258$		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	$-0.486320\pi$
$263$	−1.45674e7	−	8.41046e6i	−0.800780	−	0.462331i	−0.843744	+	0.536746i	$0.819653\pi$
$264$		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	−0.708514	−	0.705697i	$-0.750634\pi$
$277$	5.46003e6	−	9.45705e6i	0.256895	−	0.444955i	0.965408	+	0.260742i	$0.0839672\pi$
$278$		−	3.96727e6i		−	0.184653i
$279$		0			0
$280$	−158395.			−0.00721552
$281$	−1.61727e7	−	9.33733e6i	−0.728894	−	0.420827i	0.0891235	−	0.996021i	$-0.471593\pi$
$281$	−1.61727e7	−	9.33733e6i	−0.728894	−	0.420827i	−0.818017	+	0.575194i	$0.804927\pi$
$282$		0			0
$283$	7.31274e6	+	1.26660e7i	0.322642	+	0.558832i	0.981032	−	0.193845i	$-0.0620957\pi$
$283$	7.31274e6	+	1.26660e7i	0.322642	+	0.558832i	−0.658390	+	0.752677i	$0.728762\pi$
$284$	−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	0.669018	−	0.743247i	$-0.266715\pi$
$293$	4.14332e7	−	2.39215e7i	1.64720	−	0.951010i	0.978179	−	0.207763i	$-0.0666183\pi$
$294$		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	$-0.494354\pi$
$311$	2.68464e7	−	1.54998e7i	0.892494	−	0.515282i	0.874757	+	0.484561i	$0.161021\pi$
$312$		0			0
$313$	1.48914e7	−	2.57927e7i	0.485627	−	0.841131i	−0.514237	−	0.857648i	$-0.671925\pi$
$313$	1.48914e7	−	2.57927e7i	0.485627	−	0.841131i	0.999864	+	0.0165178i	$0.00525800\pi$
$314$			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	$-0.322444\pi$
$317$	1.88717e6	+	1.08956e6i	0.0592424	+	0.0342036i	−0.470086	+	0.882620i	$0.655777\pi$
$318$		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	−0.943340	−	0.331827i	$-0.892335\pi$
$331$	−6.68355e6	+	1.15762e7i	−0.184299	+	0.319215i	0.759041	+	0.651043i	$0.225668\pi$
$332$			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	−0.995243	−	0.0974216i	$-0.968940\pi$
$337$	−2.22744e7	−	3.85804e7i	−0.581991	−	1.00804i	0.413252	−	0.910617i	$-0.364393\pi$
$338$	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	$-0.586206\pi$
$347$	1.80987e7	−	1.04493e7i	0.433170	−	0.250091i	0.700696	+	0.713460i	$0.252873\pi$
$348$		0			0
$349$	−3.22577e7	+	5.58720e7i	−0.758852	+	1.31437i	0.184584	+	0.982817i	$0.440906\pi$
$349$	−3.22577e7	+	5.58720e7i	−0.758852	+	1.31437i	−0.943436	+	0.331554i	$0.892427\pi$
$350$		−	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	$-0.348569\pi$
$353$	−3.64529e6	−	2.10461e6i	−0.0828719	−	0.0478461i	−0.540863	+	0.841110i	$0.681902\pi$
$354$		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	−0.984238	−	0.176852i	$-0.943409\pi$
$367$	−1.67551e7	+	2.90207e7i	−0.338961	+	0.587097i	0.645277	+	0.763949i	$0.276742\pi$
$368$		−	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	0.738520	−	0.674231i	$-0.235525\pi$
$373$	−1.11388e7	−	1.92931e7i	−0.214642	−	0.371770i	−0.953162	+	0.302461i	$0.902192\pi$
$374$	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	$-0.571015\pi$
$383$	2.88035e7	−	1.66297e7i	0.512683	−	0.295998i	0.733936	+	0.679219i	$0.237681\pi$
$384$		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	$-0.374262\pi$
$389$	−1.30734e7	−	7.54793e6i	−0.222096	−	0.128227i	−0.606920	+	0.794763i	$0.707595\pi$
$390$		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	0.504826	−	0.863221i	$-0.331557\pi$
$401$	9.70320e7	−	5.60214e7i	1.50481	−	0.868803i	0.999984	−	0.00558177i	$-0.00177674\pi$
$402$		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	0.999907	−	0.0136491i	$-0.00434478\pi$
$409$	3.33970e7	+	5.78454e7i	0.488133	+	0.845471i	−0.511774	+	0.859120i	$0.671011\pi$
$410$	−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	$-0.770986\pi$
$419$	−4.10125e7	+	2.36786e7i	−0.557537	+	0.321894i	0.194619	+	0.980879i	$0.437653\pi$
$420$		0			0
$421$	−3.30784e7	+	5.72936e7i	−0.443301	+	0.767820i	−0.997932	−	0.0642763i	$-0.979526\pi$
$421$	−3.30784e7	+	5.72936e7i	−0.443301	+	0.767820i	0.554631	+	0.832096i	$0.312859\pi$
$422$		−	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	−0.779926	−	0.625872i	$-0.784743\pi$
$439$	1.28648e7	−	2.22825e7i	0.152058	−	0.263372i	0.931984	+	0.362500i	$0.118077\pi$
$440$		−	8.53835e7i		−	1.00234i
$441$		0			0
$442$	3.15825e7			0.365746
$443$	143395.	+	82789.0i	0.00164938	+	0.000952273i	0.500824	−	0.865549i	$-0.333030\pi$
$443$	143395.	+	82789.0i	0.00164938	+	0.000952273i	−0.499175	+	0.866501i	$0.666364\pi$
$444$		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	−0.255141	−	0.966904i	$-0.582122\pi$
$457$	6.77455e7	−	1.17339e8i	0.709793	−	1.22940i	0.964934	−	0.262493i	$-0.0845448\pi$
$458$		−	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	$-0.281058\pi$
$461$	2.77431e7	+	1.60175e7i	0.283173	+	0.163490i	−0.351686	+	0.936118i	$0.614392\pi$
$462$		0			0
$463$	−6.46664e7	−	1.12006e8i	−0.651532	−	1.12849i	−0.982751	−	0.184933i	$-0.940793\pi$
$463$	−6.46664e7	−	1.12006e8i	−0.651532	−	1.12849i	0.331219	−	0.943554i	$-0.392540\pi$
$464$	−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	$-0.156852\pi$
$479$	1.00215e8	+	5.78593e7i	0.911858	+	0.526461i	0.0308294	+	0.999525i	$0.490185\pi$
$480$		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	$-0.998094\pi$
$491$	−1.76939e8	+	1.02156e8i	−1.49479	+	0.863017i	−0.494807	+	0.869003i	$0.664761\pi$
$492$		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	0.918936	−	0.394407i	$-0.129050\pi$
$499$	1.46495e7	+	2.53736e7i	0.117902	+	0.204212i	−0.801034	+	0.598619i	$0.795717\pi$
$500$	−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	$-0.447883\pi$
$509$	1.44920e8	−	8.36696e7i	1.09894	−	0.634474i	0.935943	+	0.352152i	$0.114550\pi$
$510$		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	−0.933512	−	0.358545i	$-0.883273\pi$
$547$	−2.55726e7	+	4.42930e7i	−0.156247	+	0.270628i	0.777265	+	0.629173i	$0.216606\pi$
$548$			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	$-0.799250\pi$
$563$	−1.25053e8	+	7.21992e7i	−0.700758	+	0.404583i	0.106872	+	0.994273i	$0.465917\pi$
$564$		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	$-0.405799\pi$
$569$	−7.20146e7	−	4.15777e7i	−0.390916	−	0.225696i	−0.682557	+	0.730832i	$0.739132\pi$
$570$		0			0
$571$	1.13040e8	+	1.95791e8i	0.607188	+	1.05168i	0.991702	+	0.128561i	$0.0410359\pi$
$571$	1.13040e8	+	1.95791e8i	0.607188	+	1.05168i	−0.384513	+	0.923119i	$0.625631\pi$
$572$	−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	$-0.424838\pi$
$587$	−9.93271e7	−	5.73465e7i	−0.491081	−	0.283526i	−0.725023	+	0.688725i	$0.758171\pi$
$588$		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	$-0.978834\pi$
$599$	−3.09303e8	+	1.78576e8i	−1.43914	+	0.830888i	−0.441351	+	0.897335i	$0.645501\pi$
$600$		0			0
$601$	4.20047e7	−	7.27542e7i	0.193497	−	0.335147i	−0.752910	−	0.658124i	$-0.771350\pi$
$601$	4.20047e7	−	7.27542e7i	0.193497	−	0.335147i	0.946407	+	0.322977i	$0.104684\pi$
$602$		−	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	0.802525	−	0.596618i	$-0.203489\pi$
$607$	−2.58143e7	−	4.47117e7i	−0.115424	−	0.199920i	−0.917949	+	0.396698i	$0.870156\pi$
$608$	−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	$-0.552133\pi$
$617$	1.43248e8	−	8.27040e7i	0.609862	−	0.352104i	0.772911	+	0.634514i	$0.218800\pi$
$618$		0			0
$619$	−1.34081e8	+	2.32235e8i	−0.565320	+	0.979164i	0.431699	+	0.902018i	$0.357914\pi$
$619$	−1.34081e8	+	2.32235e8i	−0.565320	+	0.979164i	−0.997020	+	0.0771460i	$0.975419\pi$
$620$		−	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	$-0.311220\pi$
$641$	3.16652e7	+	1.82819e7i	0.120229	+	0.0694142i	−0.438680	+	0.898644i	$0.644554\pi$
$642$		0			0
$643$	1.41134e8	+	2.44452e8i	0.530883	+	0.919517i	0.999350	+	0.0360362i	$0.0114732\pi$
$643$	1.41134e8	+	2.44452e8i	0.530883	+	0.919517i	−0.468467	+	0.883481i	$0.655194\pi$
$644$	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	$-0.723667\pi$
$653$	−8.59015e7	+	4.95952e7i	−0.308504	+	0.178115i	0.337753	+	0.941235i	$0.390333\pi$
$654$		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	$-0.237591\pi$
$659$	1.46859e8	+	8.47892e7i	0.513150	+	0.296268i	−0.220977	+	0.975279i	$0.570925\pi$
$660$		0			0
$661$	−2.69025e8	−	4.65965e8i	−0.931511	−	1.61342i	−0.780740	−	0.624856i	$-0.785158\pi$
$661$	−2.69025e8	−	4.65965e8i	−0.931511	−	1.61342i	−0.150771	−	0.988569i	$-0.548176\pi$
$662$	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	−0.832688	−	0.553743i	$-0.813199\pi$
$673$	1.92682e7	−	3.33736e7i	0.0632116	−	0.109486i	0.895899	+	0.444257i	$0.146532\pi$
$674$			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	$-0.432812\pi$
$677$	−1.65239e8	−	9.54008e7i	−0.532533	−	0.307458i	−0.742047	+	0.670347i	$0.766145\pi$
$678$		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	−0.707486	−	0.706727i	$-0.750171\pi$
$691$	8.52235e7	−	1.47611e8i	0.258301	−	0.447390i	0.965787	+	0.259337i	$0.0835042\pi$
$692$			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	0.434501	+	0.900671i	$0.356925\pi$
$709$	−2.00566e8	+	3.47390e8i	−0.562754	+	0.974718i	−0.997255	+	0.0740465i	$0.976409\pi$
$710$			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	−0.175671	−	0.984449i	$-0.556209\pi$
$727$	2.93837e8	−	5.08941e8i	0.764722	−	1.32454i	0.940393	−	0.340089i	$-0.110457\pi$
$728$		−	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	0.928329	−	0.371759i	$-0.121245\pi$
$733$	5.60077e7	+	9.70083e7i	0.142212	+	0.246318i	−0.786117	+	0.618077i	$0.787912\pi$
$734$	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	$-0.904571\pi$
$743$	−4.82909e8	+	2.78808e8i	−1.17733	+	0.679732i	−0.221936	+	0.975061i	$0.571237\pi$
$744$		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	0.521604	−	0.853188i	$-0.325334\pi$
$751$	−2.02498e8	−	3.50737e8i	−0.478080	−	0.828059i	−0.999684	+	0.0251288i	$0.992000\pi$
$752$	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	$-0.781530\pi$
$761$	−2.69514e8	+	1.55604e8i	−0.611543	+	0.353074i	0.162026	+	0.986786i	$0.448197\pi$
$762$		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	0.999755	−	0.0221345i	$-0.00704620\pi$
$769$	2.18605e8	+	3.78636e8i	0.480708	+	0.832612i	−0.519047	+	0.854746i	$0.673713\pi$
$770$	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	+	0.0586619i	$0.981317\pi$
$774$		0			0
$775$	6.88352e8			1.47879
$776$	2.18326e8	+	1.26051e8i	0.467219	+	0.269749i
$777$		0			0
$778$	4.26976e7	+	7.39543e7i	0.0906701	+	0.157045i
$779$	2.83161e7	−	1.63483e7i	0.0598991	−	0.0345828i
$780$		0			0
$781$	1.70029e8	−	2.94498e8i	0.356918	−	0.618201i
$782$		−	1.86206e8i		−	0.389380i
$783$		0			0
$784$	−1.20455e8			−0.249963
$785$	5.79086e8	+	3.34336e8i	1.19711	+	0.691152i
$786$		0			0
$787$	2.01160e7	+	3.48419e7i	0.0412684	+	0.0714789i	0.885922	−	0.463835i	$-0.153527\pi$
$787$	2.01160e7	+	3.48419e7i	0.0412684	+	0.0714789i	−0.844653	+	0.535314i	$0.820193\pi$
$788$	1.13524e7	−	6.55431e6i	0.0232011	−	0.0133952i
$789$		0			0
$790$	5.28534e8	−	9.15447e8i	1.07199	−	1.85674i
$791$		−	5.20039e6i		−	0.0105077i
$792$		0			0
$793$	−4.58323e7			−0.0919078
$794$	4.36670e8	+	2.52112e8i	0.872353	+	0.503653i
$795$		0			0
$796$	−5.19756e7	−	9.00244e7i	−0.103053	−	0.178493i
$797$	−7.74252e7	+	4.47015e7i	−0.152935	+	0.0882972i	−0.574515	−	0.818494i	$-0.694809\pi$
$797$	−7.74252e7	+	4.47015e7i	−0.152935	+	0.0882972i	0.421579	+	0.906791i	$0.361476\pi$
$798$		0			0
$799$	−7.63408e7	+	1.32226e8i	−0.149664	+	0.259225i
$800$		−	1.61377e8i		−	0.315190i
$801$		0			0
$802$	−6.33810e8			−1.22867
$803$	−6.49750e8	−	3.75133e8i	−1.25487	−	0.724501i
$804$		0			0
$805$	7.32577e6	+	1.26886e7i	0.0140432	+	0.0243235i
$806$	−3.43770e8	+	1.98476e8i	−0.656543	+	0.379055i
$807$		0			0
$808$	1.19067e7	−	2.06230e7i	0.0225713	−	0.0390947i
$809$			7.82985e8i			1.47879i	0.673270	+	0.739397i	$0.264889\pi$
$809$			7.82985e8i			1.47879i	−0.673270	+	0.739397i	$0.735111\pi$
$810$		0			0
$811$	−6.76238e6			−0.0126776			−0.00633880	−	0.999980i	$-0.502018\pi$
$811$	−6.76238e6			−0.0126776			−0.00633880	+	0.999980i	$0.502018\pi$
$812$	−4.31590e6	−	2.49178e6i	−0.00806126	−	0.00465417i
$813$		0			0
$814$	−1.08869e8	−	1.88567e8i	−0.201851	−	0.349617i
$815$	1.74165e8	−	1.00554e8i	0.321728	−	0.185750i
$816$		0			0
$817$	−4.31266e6	+	7.46975e6i	−0.00790823	+	0.0136974i
$818$		−	3.77844e8i		−	0.690324i
$819$		0			0
$820$	7.75631e8			1.40674
$821$	2.54001e7	+	1.46648e7i	0.0458993	+	0.0265000i	0.522774	−	0.852471i	$-0.324897\pi$
$821$	2.54001e7	+	1.46648e7i	0.0458993	+	0.0265000i	−0.476875	+	0.878971i	$0.658230\pi$
$822$		0			0
$823$	4.45476e8	+	7.71587e8i	0.799144	+	1.38416i	0.920174	+	0.391509i	$0.128047\pi$
$823$	4.45476e8	+	7.71587e8i	0.799144	+	1.38416i	−0.121031	+	0.992649i	$0.538620\pi$
$824$	−3.03284e8	+	1.75101e8i	−0.542085	+	0.312973i
$825$		0			0
$826$	1.81538e6	−	3.14433e6i	0.00322127	−	0.00557940i
$827$			4.36886e8i			0.772417i	0.922411	+	0.386209i	$0.126216\pi$
$827$			4.36886e8i			0.772417i	−0.922411	+	0.386209i	$0.873784\pi$
$828$		0			0
$829$	2.08489e8			0.365948			0.182974	−	0.983118i	$-0.441428\pi$
$829$	2.08489e8			0.365948			0.182974	+	0.983118i	$0.441428\pi$
$830$	9.65482e8	+	5.57421e8i	1.68853	+	0.974876i
$831$		0			0
$832$	4.65307e7	+	8.05935e7i	0.0807922	+	0.139936i
$833$	2.00265e8	−	1.15623e8i	0.346474	−	0.200037i
$834$		0			0
$835$	−1.07913e8	+	1.86910e8i	−0.185359	+	0.321051i
$836$			2.03609e7i			0.0348480i
$837$		0			0
$838$	2.67892e8			0.455227
$839$	9.64994e8	+	5.57140e8i	1.63395	+	0.943361i	0.982858	+	0.184362i	$0.0590219\pi$
$839$	9.64994e8	+	5.57140e8i	1.63395	+	0.943361i	0.651091	+	0.758999i	$0.274311\pi$
$840$		0			0
$841$	3.91317e8	+	6.77781e8i	0.657871	+	1.13947i
$842$	3.24101e8	−	1.87120e8i	0.542931	−	0.313461i
$843$		0			0
$844$	−7.99178e7	+	1.38422e8i	−0.132928	+	0.230238i
$845$		−	6.75389e8i		−	1.11940i
$846$		0			0
$847$	−1.40356e7			−0.0230983
$848$	1.22963e8	+	7.09925e7i	0.201644	+	0.116419i
$849$		0			0
$850$	1.54905e8	+	2.68303e8i	0.252236	+	0.436886i
$851$	2.46759e8	−	1.42467e8i	0.400392	−	0.231166i
$852$		0			0
$853$	3.51904e7	−	6.09516e7i	0.0566993	−	0.0982060i	−0.836283	−	0.548299i	$-0.815276\pi$
$853$	3.51904e7	−	6.09516e7i	0.0566993	−	0.0982060i	0.892982	+	0.450093i	$0.148609\pi$
$854$		−	383071.i		−	0.000615043i
$855$		0			0
$856$	1.12579e8			0.179488
$857$	1.37625e8	+	7.94581e7i	0.218653	+	0.126240i	0.605327	−	0.795977i	$-0.293043\pi$
$857$	1.37625e8	+	7.94581e7i	0.218653	+	0.126240i	−0.386673	+	0.922217i	$0.626376\pi$
$858$		0			0
$859$	−1.57121e8	−	2.72141e8i	−0.247887	−	0.429353i	0.715052	−	0.699071i	$-0.246403\pi$
$859$	−1.57121e8	−	2.72141e8i	−0.247887	−	0.429353i	−0.962939	+	0.269718i	$0.913069\pi$
$860$	−1.77198e8	+	1.02305e8i	−0.278589	+	0.160843i
$861$		0			0
$862$	2.56444e8	−	4.44174e8i	0.400378	−	0.693476i
$863$		−	3.90351e8i		−	0.607328i	−0.952779	−	0.303664i	$-0.901790\pi$
$863$		−	3.90351e8i		−	0.607328i	0.952779	−	0.303664i	$-0.0982101\pi$
$864$		0			0
$865$	−1.35251e8			−0.208974
$866$	3.42641e6	+	1.97824e6i	0.00527577	+	0.00304597i
$867$		0			0
$868$	−1.65888e6	−	2.87326e6i	−0.00253662	−	0.00439355i
$869$	−1.75540e9	+	1.01348e9i	−2.67496	+	1.54439i
$870$		0			0
$871$	6.74029e8	−	1.16745e9i	1.02006	−	1.76679i
$872$			2.43612e8i			0.367408i
$873$		0			0
$874$	−2.66443e7			−0.0399089
$875$	−9.27087e6	−	5.35254e6i	−0.0138387	−	0.00798979i
$876$		0			0
$877$	5.77897e8	+	1.00095e9i	0.856745	+	1.48393i	0.875017	+	0.484092i	$0.160850\pi$
$877$	5.77897e8	+	1.00095e9i	0.856745	+	1.48393i	−0.0182723	+	0.999833i	$0.505817\pi$
$878$	−1.26049e8	+	7.27743e7i	−0.186232	+	0.107521i
$879$		0			0
$880$	−2.41501e8	+	4.18292e8i	−0.354381	+	0.613806i
$881$		−	7.82859e8i		−	1.14487i	−0.819951	−	0.572434i	$-0.805999\pi$
$881$		−	7.82859e8i		−	1.14487i	0.819951	−	0.572434i	$-0.194001\pi$
$882$		0			0
$883$	1.01047e9			1.46772			0.733860	−	0.679300i	$-0.237717\pi$
$883$	1.01047e9			1.46772			0.733860	+	0.679300i	$0.237717\pi$
$884$	−1.54722e8	−	8.93288e7i	−0.223973	−	0.129311i
$885$		0			0
$886$	−468325.	−	811163.i	−0.000673358	−	0.00116629i
$887$	−2.84354e8	+	1.64172e8i	−0.407463	+	0.235249i	−0.689699	−	0.724096i	$-0.742257\pi$
$887$	−2.84354e8	+	1.64172e8i	−0.407463	+	0.235249i	0.282236	+	0.959345i	$0.408924\pi$
$888$		0			0
$889$	3.46805e6	−	6.00684e6i	0.00493605	−	0.00854950i
$890$		−	9.32253e8i		−	1.32240i
$891$		0			0
$892$	−1.82056e8			−0.256513
$893$	1.89203e7	+	1.09236e7i	0.0265689	+	0.0153396i
$894$		0			0
$895$	4.85026e8	+	8.40089e8i	0.676543	+	1.17181i
$896$	−673607.	+	388907.i	−0.000936446	+	0.000540657i
$897$		0			0
$898$	1.21751e8	−	2.10879e8i	0.168130	−	0.291209i
$899$			9.17028e8i			1.26213i
$900$		0			0
$901$	−2.72580e8			−0.372666
$902$	−1.28804e9	−	7.43649e8i	−1.75513	−	1.01332i
$903$		0			0
$904$	1.12171e8	+	1.94286e8i	0.151836	+	0.262988i
$905$	−6.20727e8	+	3.58377e8i	−0.837442	+	0.483497i
$906$		0			0
$907$	−1.07719e8	+	1.86575e8i	−0.144368	+	0.250053i	−0.929137	−	0.369736i	$-0.879448\pi$
$907$	−1.07719e8	+	1.86575e8i	−0.144368	+	0.250053i	0.784769	+	0.619789i	$0.212782\pi$
$908$			3.71404e8i			0.496123i
$909$		0			0
$910$	1.40576e7			0.0186546
$911$	−6.51453e8	−	3.76117e8i	−0.861645	−	0.497471i	0.00291806	−	0.999996i	$-0.499071\pi$
$911$	−6.51453e8	−	3.76117e8i	−0.861645	−	0.497471i	−0.864563	+	0.502525i	$0.832404\pi$
$912$		0			0
$913$	−1.06887e9	−	1.85134e9i	−1.40448	−	2.43262i
$914$	−6.63767e8	+	3.83226e8i	−0.869315	+	0.501899i
$915$		0			0
$916$	−5.53104e7	+	9.58004e7i	−0.0719649	+	0.124647i
$917$			1.11670e7i			0.0144820i
$918$		0			0
$919$	6.81968e8			0.878653			0.439327	−	0.898327i	$-0.355217\pi$
$919$	6.81968e8			0.878653			0.439327	+	0.898327i	$0.355217\pi$
$920$	−5.47378e8	−	3.16029e8i	−0.702950	−	0.405848i
$921$		0			0
$922$	−9.06085e7	−	1.56938e8i	−0.115605	−	0.200233i
$923$	3.69759e8	−	2.13480e8i	0.470234	−	0.271489i
$924$		0			0
$925$	−2.37036e8	+	4.10558e8i	−0.299494	+	0.518739i
$926$			7.31617e8i			0.921406i
$927$		0			0
$928$	2.14988e8			0.269011
$929$	−9.66823e7	−	5.58196e7i	−0.120587	−	0.0696208i	0.438493	−	0.898734i	$-0.355512\pi$
$929$	−9.66823e7	−	5.58196e7i	−0.120587	−	0.0696208i	−0.559080	+	0.829114i	$0.688846\pi$
$930$		0			0
$931$	−1.65446e7	−	2.86561e7i	−0.0205025	−	0.0355114i
$932$	3.54001e8	−	2.04383e8i	0.437277	−	0.252462i
$933$		0			0
$934$	−2.40217e8	+	4.16067e8i	−0.294824	+	0.510649i
$935$		−	9.27259e8i		−	1.13440i
$936$		0			0
$937$	7.66443e8			0.931668			0.465834	−	0.884872i	$-0.345754\pi$
$937$	7.66443e8			0.931668			0.465834	+	0.884872i	$0.345754\pi$
$938$	9.75767e6	+	5.63359e6i	0.0118233	+	0.00682617i
$939$		0			0
$940$	2.59131e8	+	4.48829e8i	0.311987	+	0.540377i
$941$	4.61588e8	−	2.66498e8i	0.553969	−	0.319834i	−0.196752	−	0.980453i	$-0.563039\pi$
$941$	4.61588e8	−	2.66498e8i	0.553969	−	0.319834i	0.750721	+	0.660619i	$0.229706\pi$
$942$		0			0
$943$	9.73142e8	−	1.68553e9i	1.16049	−	2.01003i
$944$			1.56629e8i			0.186189i
$945$		0			0
$946$	3.92348e8			0.463445
$947$	−2.71610e7	−	1.56814e7i	−0.0319812	−	0.0184644i	0.483924	−	0.875110i	$-0.339211\pi$
$947$	−2.71610e7	−	1.56814e7i	−0.0319812	−	0.0184644i	−0.515905	+	0.856646i	$0.672544\pi$
$948$		0			0
$949$	−4.71001e8	−	8.15797e8i	−0.551090	−	0.954517i
$950$	3.83916e7	−	2.21654e7i	0.0447780	−	0.0258526i
$951$		0			0
$952$	746618.	−	1.29318e6i	0.000865341	−	0.00149882i
$953$			6.21244e8i			0.717767i	0.933382	+	0.358883i	$0.116842\pi$
$953$			6.21244e8i			0.717767i	−0.933382	+	0.358883i	$0.883158\pi$
$954$		0			0
$955$	−2.45040e9			−2.81337
$956$	−3.58137e8	−	2.06770e8i	−0.409897	−	0.236654i
$957$		0			0
$958$	−3.27302e8	−	5.66903e8i	−0.372264	−	0.644781i
$959$	−9.48522e6	+	5.47629e6i	−0.0107545	+	0.00620913i
$960$		0			0
$961$	1.38501e8	−	2.39891e8i	0.156057	−	0.270299i
$962$		−	2.73383e8i		−	0.307076i
$963$		0			0
$964$	−2.32970e8			−0.260057
$965$	1.25619e9	+	7.25261e8i	1.39789	+	0.807073i
$966$		0			0
$967$	3.14992e8	+	5.45583e8i	0.348354	+	0.603366i	0.985957	−	0.166998i	$-0.0534075\pi$
$967$	3.14992e8	+	5.45583e8i	0.348354	+	0.603366i	−0.637603	+	0.770365i	$0.720074\pi$
$968$	5.24366e8	−	3.02743e8i	0.578108	−	0.333771i
$969$		0			0
$970$	−8.21410e8	+	1.42272e9i	−0.900005	+	1.55885i
$971$			1.38333e8i			0.151101i	0.997142	+	0.0755507i	$0.0240715\pi$
$971$			1.38333e8i			0.151101i	−0.997142	+	0.0755507i	$0.975929\pi$
$972$		0			0
$973$	−2.94285e6			−0.00319470
$974$	−2.21845e8	−	1.28082e8i	−0.240089	−	0.138616i
$975$		0			0
$976$	8.26271e6	+	1.43114e7i	0.00888736	+	0.0153934i
$977$	7.13583e8	−	4.11988e8i	0.765175	−	0.441774i	−0.0659754	−	0.997821i	$-0.521016\pi$
$977$	7.13583e8	−	4.11988e8i	0.765175	−	0.441774i	0.831151	+	0.556047i	$0.187683\pi$
$978$		0			0
$979$	−8.93813e8	+	1.54813e9i	−0.952574	+	1.64991i
$980$		−	7.84944e8i		−	0.833989i
$981$		0			0
$982$	1.15576e9			1.22049
$983$	1.11372e9	+	6.43006e8i	1.17251	+	0.676947i	0.954269	−	0.298949i	$-0.0966360\pi$
$983$	1.11372e9	+	6.43006e8i	1.17251	+	0.676947i	0.218237	+	0.975896i	$0.429969\pi$
$984$		0			0
$985$	4.27113e7	+	7.39781e7i	0.0446924	+	0.0774096i
$986$	−3.57435e8	+	2.06365e8i	−0.372877	+	0.215281i
$987$		0			0
$988$	−1.27821e7	+	2.21392e7i	−0.0132535	+	0.0229558i
$989$			5.13428e8i			0.530751i
$990$		0			0
$991$	−1.70244e8			−0.174924			−0.0874621	−	0.996168i	$-0.527876\pi$
$991$	−1.70244e8			−0.174924			−0.0874621	+	0.996168i	$0.527876\pi$
$992$	1.23951e8	+	7.15630e7i	0.126974	+	0.0733083i
$993$		0			0
$994$	1.78429e6	+	3.09048e6i	0.00181679	+	0.00314678i
$995$	5.86645e8	−	3.38700e8i	0.595534	−	0.343831i
$996$		0			0
$997$	3.50539e8	−	6.07152e8i	0.353713	−	0.612649i	−0.633184	−	0.774001i	$-0.718252\pi$
$997$	3.50539e8	−	6.07152e8i	0.353713	−	0.612649i	0.986897	+	0.161353i	$0.0515856\pi$
$998$		−	1.65740e8i		−	0.166738i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.7.d.f.107.1		8
3.2	odd	2	inner	162.7.d.f.107.4		8
9.2	odd	6		162.7.b.a.161.2	✓	4
9.4	even	3	inner	162.7.d.f.53.4		8
9.5	odd	6	inner	162.7.d.f.53.1		8
9.7	even	3		162.7.b.a.161.3	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.7.b.a.161.2	✓	4	9.2	odd	6
162.7.b.a.161.3	yes	4	9.7	even	3
162.7.d.f.53.1		8	9.5	odd	6	inner
162.7.d.f.53.4		8	9.4	even	3	inner
162.7.d.f.107.1		8	1.1	even	1	trivial
162.7.d.f.107.4		8	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
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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