LMFDB - Embedded newform 504.2.bm.c.107.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(107,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("504.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.14
Character	$\chi$	$=$	504.107
Dual form			504.2.bm.c.179.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.352402 - 1.36960i) q^{2} +(-1.75163 - 0.965301i) q^{4} +(-0.635051 + 1.09994i) q^{5} +(-2.64362 - 0.106220i) q^{7} +(-1.93936 + 2.05886i) q^{8} +O(q^{10})$	\(q+(0.352402 - 1.36960i) q^{2} +(-1.75163 - 0.965301i) q^{4} +(-0.635051 + 1.09994i) q^{5} +(-2.64362 - 0.106220i) q^{7} +(-1.93936 + 2.05886i) q^{8} +(1.28269 + 1.25739i) q^{10} +(-1.05060 + 0.606562i) q^{11} +3.91317i q^{13} +(-1.07710 + 3.58328i) q^{14} +(2.13639 + 3.38169i) q^{16} +(-5.05521 + 2.91863i) q^{17} +(3.80250 - 6.58612i) q^{19} +(2.17414 - 1.31367i) q^{20} +(0.460518 + 1.65265i) q^{22} +(-4.20712 + 7.28694i) q^{23} +(1.69342 + 2.93309i) q^{25} +(5.35949 + 1.37901i) q^{26} +(4.52810 + 2.73795i) q^{28} -6.09725 q^{29} +(2.14512 - 1.23849i) q^{31} +(5.38444 - 1.73429i) q^{32} +(2.21590 + 7.95217i) q^{34} +(1.79567 - 2.84037i) q^{35} +(-5.24618 - 3.02888i) q^{37} +(-7.68037 - 7.52888i) q^{38} +(-1.03303 - 3.44065i) q^{40} -1.01947i q^{41} -7.49728 q^{43} +(2.42577 - 0.0483285i) q^{44} +(8.49762 + 8.33001i) q^{46} +(0.704496 - 1.22022i) q^{47} +(6.97743 + 0.561612i) q^{49} +(4.61394 - 1.28569i) q^{50} +(3.77739 - 6.85441i) q^{52} +(1.74673 + 3.02543i) q^{53} -1.54079i q^{55} +(5.34561 - 5.23684i) q^{56} +(-2.14868 + 8.35082i) q^{58} +(4.86525 - 2.80895i) q^{59} +(-5.16681 - 2.98306i) q^{61} +(-0.940291 - 3.37441i) q^{62} +(-0.477804 - 7.98572i) q^{64} +(-4.30425 - 2.48506i) q^{65} +(-2.22382 - 3.85176i) q^{67} +(11.6722 - 0.232545i) q^{68} +(-3.25738 - 3.46030i) q^{70} -4.44191 q^{71} +(6.19070 + 10.7226i) q^{73} +(-5.99713 + 6.11780i) q^{74} +(-13.0181 + 7.86587i) q^{76} +(2.84181 - 1.49192i) q^{77} +(-0.204070 - 0.117820i) q^{79} +(-5.07637 + 0.202353i) q^{80} +(-1.39627 - 0.359263i) q^{82} -11.7359i q^{83} -7.41391i q^{85} +(-2.64205 + 10.2683i) q^{86} +(0.788654 - 3.33937i) q^{88} +(-8.38601 - 4.84167i) q^{89} +(0.415658 - 10.3449i) q^{91} +(14.4034 - 8.70286i) q^{92} +(-1.42296 - 1.39489i) q^{94} +(4.82956 + 8.36505i) q^{95} -8.07321 q^{97} +(3.22804 - 9.35840i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 8 q^{10} - 28 q^{16} - 32 q^{19} + 32 q^{22} + 4 q^{28} + 112 q^{34} - 36 q^{40} - 160 q^{43} + 40 q^{46} + 56 q^{49} - 36 q^{52} + 12 q^{58} - 24 q^{64} + 92 q^{70} + 16 q^{73} - 120 q^{76} + 20 q^{82} - 100 q^{88} - 32 q^{91} - 20 q^{94} + 240 q^{97}+O(q^{100}) $ 48 * q - 8 * q^10 - 28 * q^16 - 32 * q^19 + 32 * q^22 + 4 * q^28 + 112 * q^34 - 36 * q^40 - 160 * q^43 + 40 * q^46 + 56 * q^49 - 36 * q^52 + 12 * q^58 - 24 * q^64 + 92 * q^70 + 16 * q^73 - 120 * q^76 + 20 * q^82 - 100 * q^88 - 32 * q^91 - 20 * q^94 + 240 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.352402	−	1.36960i	0.249186	−	0.968456i
$2$	0.352402	−	1.36960i	0.249186	−	0.968456i
$3$		0			0
$3$		0			0
$4$	−1.75163	−	0.965301i	−0.875813	−	0.482650i
$5$	−0.635051	+	1.09994i	−0.284003	+	0.491908i	−0.972367	−	0.233458i	$-0.924996\pi$
$5$	−0.635051	+	1.09994i	−0.284003	+	0.491908i	0.688364	+	0.725366i	$0.258329\pi$
$6$		0			0
$7$	−2.64362	−	0.106220i	−0.999194	−	0.0401475i
$7$	−2.64362	−	0.106220i	−0.999194	−	0.0401475i
$8$	−1.93936	+	2.05886i	−0.685666	+	0.727917i
$9$		0			0
$10$	1.28269	+	1.25739i	0.405622	+	0.397621i
$11$	−1.05060	+	0.606562i	−0.316767	+	0.182885i	−0.649951	−	0.759977i	$-0.725210\pi$
$11$	−1.05060	+	0.606562i	−0.316767	+	0.182885i	0.333184	+	0.942862i	$0.391877\pi$
$12$		0			0
$13$			3.91317i			1.08532i	0.839953	+	0.542659i	$0.182582\pi$
$13$			3.91317i			1.08532i	−0.839953	+	0.542659i	$0.817418\pi$
$14$	−1.07710	+	3.58328i	−0.287866	+	0.957671i
$15$		0			0
$16$	2.13639	+	3.38169i	0.534097	+	0.845423i
$17$	−5.05521	+	2.91863i	−1.22607	+	0.707872i	−0.966205	−	0.257773i	$-0.917011\pi$
$17$	−5.05521	+	2.91863i	−1.22607	+	0.707872i	−0.259864	+	0.965645i	$0.583678\pi$
$18$		0			0
$19$	3.80250	−	6.58612i	0.872353	−	1.51096i	0.0127977	−	0.999918i	$-0.495926\pi$
$19$	3.80250	−	6.58612i	0.872353	−	1.51096i	0.859556	−	0.511042i	$-0.170740\pi$
$20$	2.17414	−	1.31367i	0.486154	−	0.293745i
$21$		0			0
$22$	0.460518	+	1.65265i	0.0981827	+	0.352347i
$23$	−4.20712	+	7.28694i	−0.877244	+	1.51943i	−0.0228916	+	0.999738i	$0.507287\pi$
$23$	−4.20712	+	7.28694i	−0.877244	+	1.51943i	−0.854353	+	0.519694i	$0.826046\pi$
$24$		0			0
$25$	1.69342	+	2.93309i	0.338684	+	0.586618i
$26$	5.35949	+	1.37901i	1.05108	+	0.270446i
$27$		0			0
$28$	4.52810	+	2.73795i	0.855730	+	0.517423i
$29$	−6.09725			−1.13223			−0.566116	−	0.824326i	$-0.691554\pi$
$29$	−6.09725			−1.13223			−0.566116	+	0.824326i	$0.691554\pi$
$30$		0			0
$31$	2.14512	−	1.23849i	0.385275	−	0.222439i	−0.294836	−	0.955548i	$-0.595265\pi$
$31$	2.14512	−	1.23849i	0.385275	−	0.222439i	0.680111	+	0.733109i	$0.261932\pi$
$32$	5.38444	−	1.73429i	0.951844	−	0.306582i
$33$		0			0
$34$	2.21590	+	7.95217i	0.380023	+	1.36379i
$35$	1.79567	−	2.84037i	0.303523	−	0.480110i
$36$		0			0
$37$	−5.24618	−	3.02888i	−0.862466	−	0.497945i	0.00237123	−	0.999997i	$-0.499245\pi$
$37$	−5.24618	−	3.02888i	−0.862466	−	0.497945i	−0.864837	+	0.502052i	$0.832579\pi$
$38$	−7.68037	−	7.52888i	−1.24592	−	1.22135i
$39$		0			0
$40$	−1.03303	−	3.44065i	−0.163337	−	0.544015i
$41$		−	1.01947i		−	0.159215i	−0.996826	−	0.0796073i	$-0.974633\pi$
$41$		−	1.01947i		−	0.159215i	0.996826	−	0.0796073i	$-0.0253666\pi$
$42$		0			0
$43$	−7.49728			−1.14333			−0.571663	−	0.820489i	$-0.693701\pi$
$43$	−7.49728			−1.14333			−0.571663	+	0.820489i	$0.693701\pi$
$44$	2.42577	−	0.0483285i	0.365698	−	0.00728580i
$45$		0			0
$46$	8.49762	+	8.33001i	1.25291	+	1.22819i
$47$	0.704496	−	1.22022i	0.102761	−	0.177988i	−0.810060	−	0.586347i	$-0.800566\pi$
$47$	0.704496	−	1.22022i	0.102761	−	0.177988i	0.912821	+	0.408359i	$0.133899\pi$
$48$		0			0
$49$	6.97743	+	0.561612i	0.996776	+	0.0802303i
$50$	4.61394	−	1.28569i	0.652509	−	0.181824i
$51$		0			0
$52$	3.77739	−	6.85441i	0.523829	−	0.950536i
$53$	1.74673	+	3.02543i	0.239932	+	0.415575i	0.960695	−	0.277608i	$-0.0895415\pi$
$53$	1.74673	+	3.02543i	0.239932	+	0.415575i	−0.720762	+	0.693182i	$0.756208\pi$
$54$		0			0
$55$		−	1.54079i		−	0.207760i
$56$	5.34561	−	5.23684i	0.714337	−	0.699802i
$57$		0			0
$58$	−2.14868	+	8.35082i	−0.282136	+	1.09652i
$59$	4.86525	−	2.80895i	0.633401	−	0.365694i	−0.148667	−	0.988887i	$-0.547498\pi$
$59$	4.86525	−	2.80895i	0.633401	−	0.365694i	0.782068	+	0.623193i	$0.214165\pi$
$60$		0			0
$61$	−5.16681	−	2.98306i	−0.661542	−	0.381941i	0.131322	−	0.991340i	$-0.458078\pi$
$61$	−5.16681	−	2.98306i	−0.661542	−	0.381941i	−0.792864	+	0.609398i	$0.791411\pi$
$62$	−0.940291	−	3.37441i	−0.119417	−	0.428550i
$63$		0			0
$64$	−0.477804	−	7.98572i	−0.0597255	−	0.998215i
$65$	−4.30425	−	2.48506i	−0.533877	−	0.308234i
$66$		0			0
$67$	−2.22382	−	3.85176i	−0.271682	−	0.470568i	0.697610	−	0.716477i	$-0.254247\pi$
$67$	−2.22382	−	3.85176i	−0.271682	−	0.470568i	−0.969293	+	0.245910i	$0.920913\pi$
$68$	11.6722	−	0.232545i	1.41546	−	0.0282002i
$69$		0			0
$70$	−3.25738	−	3.46030i	−0.389331	−	0.413585i
$71$	−4.44191			−0.527157			−0.263579	−	0.964638i	$-0.584903\pi$
$71$	−4.44191			−0.527157			−0.263579	+	0.964638i	$0.584903\pi$
$72$		0			0
$73$	6.19070	+	10.7226i	0.724567	+	1.25499i	0.959152	+	0.282891i	$0.0912936\pi$
$73$	6.19070	+	10.7226i	0.724567	+	1.25499i	−0.234585	+	0.972096i	$0.575373\pi$
$74$	−5.99713	+	6.11780i	−0.697152	+	0.711180i
$75$		0			0
$76$	−13.0181	+	7.86587i	−1.49328	+	0.902277i
$77$	2.84181	−	1.49192i	0.323854	−	0.170021i
$78$		0			0
$79$	−0.204070	−	0.117820i	−0.0229596	−	0.0132557i	0.488476	−	0.872577i	$-0.337553\pi$
$79$	−0.204070	−	0.117820i	−0.0229596	−	0.0132557i	−0.511436	+	0.859321i	$0.670886\pi$
$80$	−5.07637	+	0.202353i	−0.567556	+	0.0226238i
$81$		0			0
$82$	−1.39627	−	0.359263i	−0.154192	−	0.0396740i
$83$		−	11.7359i		−	1.28818i	−0.764950	−	0.644089i	$-0.777237\pi$
$83$		−	11.7359i		−	1.28818i	0.764950	−	0.644089i	$-0.222763\pi$
$84$		0			0
$85$		−	7.41391i		−	0.804152i
$86$	−2.64205	+	10.2683i	−0.284900	+	1.10726i
$87$		0			0
$88$	0.788654	−	3.33937i	0.0840708	−	0.355978i
$89$	−8.38601	−	4.84167i	−0.888916	−	0.513216i	−0.0153281	−	0.999883i	$-0.504879\pi$
$89$	−8.38601	−	4.84167i	−0.888916	−	0.513216i	−0.873588	+	0.486667i	$0.838213\pi$
$90$		0			0
$91$	0.415658	−	10.3449i	0.0435728	−	1.08444i
$92$	14.4034	−	8.70286i	1.50166	−	0.907336i
$93$		0			0
$94$	−1.42296	−	1.39489i	−0.146767	−	0.143872i
$95$	4.82956	+	8.36505i	0.495503	+	0.858236i
$96$		0			0
$97$	−8.07321			−0.819710			−0.409855	−	0.912151i	$-0.634421\pi$
$97$	−8.07321			−0.819710			−0.409855	+	0.912151i	$0.634421\pi$
$98$	3.22804	−	9.35840i	0.326082	−	0.945342i
$99$		0			0
$100$	−0.134925	−	6.77234i	−0.0134925	−	0.677234i
$101$	2.34225	+	4.05689i	0.233062	+	0.403676i	0.958708	−	0.284393i	$-0.0917920\pi$
$101$	2.34225	+	4.05689i	0.233062	+	0.403676i	−0.725645	+	0.688069i	$0.758459\pi$
$102$		0			0
$103$	1.56676	+	0.904571i	0.154378	+	0.0891300i	0.575199	−	0.818014i	$-0.304925\pi$
$103$	1.56676	+	0.904571i	0.154378	+	0.0891300i	−0.420821	+	0.907144i	$0.638258\pi$
$104$	−8.05667	−	7.58903i	−0.790021	−	0.744165i
$105$		0			0
$106$	4.75919	−	1.32616i	0.462253	−	0.128808i
$107$	9.89615	+	5.71355i	0.956697	+	0.552349i	0.895155	−	0.445755i	$-0.147065\pi$
$107$	9.89615	+	5.71355i	0.956697	+	0.552349i	0.0615423	+	0.998104i	$0.480398\pi$
$108$		0			0
$109$	0.945149	−	0.545682i	0.0905288	−	0.0522668i	−0.454052	−	0.890975i	$-0.650022\pi$
$109$	0.945149	−	0.545682i	0.0905288	−	0.0522668i	0.544581	+	0.838708i	$0.316689\pi$
$110$	−2.11027	−	0.542977i	−0.201207	−	0.0517709i
$111$		0			0
$112$	−5.28859	−	9.16683i	−0.499725	−	0.866184i
$113$			16.9348i			1.59309i	0.604577	+	0.796546i	$0.293342\pi$
$113$			16.9348i			1.59309i	−0.604577	+	0.796546i	$0.706658\pi$
$114$		0			0
$115$	−5.34346	−	9.25515i	−0.498281	−	0.863047i
$116$	10.6801	+	5.88568i	0.991623	+	0.546472i
$117$		0			0
$118$	−2.13263	−	7.65334i	−0.196324	−	0.704547i
$119$	13.6741	−	7.17878i	1.25350	−	0.658077i
$120$		0			0
$121$	−4.76416	+	8.25177i	−0.433106	+	0.750161i
$122$	−5.90640	+	6.02524i	−0.534740	+	0.545500i
$123$		0			0
$124$	−4.95296	+	0.0986778i	−0.444789	+	0.00886153i
$125$	−10.6521			−0.952756
$126$		0			0
$127$		−	4.46959i		−	0.396612i	−0.980140	−	0.198306i	$-0.936456\pi$
$127$		−	4.46959i		−	0.396612i	0.980140	−	0.198306i	$-0.0635440\pi$
$128$	−11.1056	−	2.15978i	−0.981610	−	0.190899i
$129$		0			0
$130$	−4.92037	+	5.01938i	−0.431545	+	0.440229i
$131$	−2.30451	−	1.33051i	−0.201346	−	0.116247i	0.395937	−	0.918278i	$-0.370420\pi$
$131$	−2.30451	−	1.33051i	−0.201346	−	0.116247i	−0.597283	+	0.802030i	$0.703753\pi$
$132$		0			0
$133$	−10.7519	+	17.0073i	−0.932311	+	1.47472i
$134$	−6.05907	+	1.68838i	−0.523424	+	0.145854i
$135$		0			0
$136$	3.79481	−	16.0682i	0.325402	−	1.37784i
$137$	−13.4169	+	7.74626i	−1.14628	+	0.661808i	−0.947979	−	0.318332i	$-0.896877\pi$
$137$	−13.4169	+	7.74626i	−1.14628	+	0.661808i	−0.198306	+	0.980140i	$0.563544\pi$
$138$		0			0
$139$	−9.02579			−0.765557			−0.382779	−	0.923840i	$-0.625033\pi$
$139$	−9.02579			−0.765557			−0.382779	+	0.923840i	$0.625033\pi$
$140$	−5.88715	+	3.24190i	−0.497555	+	0.273991i
$141$		0			0
$142$	−1.56533	+	6.08365i	−0.131360	+	0.510528i
$143$	−2.37358	−	4.11116i	−0.198489	−	0.343793i
$144$		0			0
$145$	3.87207	−	6.70661i	0.321558	−	0.556954i
$146$	16.8673	−	4.70014i	1.39595	−	0.388987i
$147$		0			0
$148$	6.26556	+	10.3696i	0.515026	+	0.852376i
$149$	−1.26130	+	2.18463i	−0.103329	+	0.178972i	−0.913054	−	0.407838i	$-0.866283\pi$
$149$	−1.26130	+	2.18463i	−0.103329	+	0.178972i	0.809725	+	0.586809i	$0.199616\pi$
$150$		0			0
$151$	18.0294	−	10.4093i	1.46721	−	0.847096i	0.467886	−	0.883789i	$-0.345016\pi$
$151$	18.0294	−	10.4093i	1.46721	−	0.847096i	0.999327	+	0.0366931i	$0.0116824\pi$
$152$	6.18550	+	20.6016i	0.501711	+	1.67101i
$153$		0			0
$154$	−1.04189	−	4.41790i	−0.0839577	−	0.356005i
$155$			3.14601i			0.252693i
$156$		0			0
$157$	19.1820	−	11.0748i	1.53089	−	0.883861i	0.531572	−	0.847013i	$-0.321602\pi$
$157$	19.1820	−	11.0748i	1.53089	−	0.883861i	0.999321	−	0.0368481i	$-0.0117318\pi$
$158$	−0.233281	+	0.237975i	−0.0185588	+	0.0189322i
$159$		0			0
$160$	−1.51178	+	7.02393i	−0.119517	+	0.555290i
$161$	11.8960	−	18.8170i	0.937538	−	1.48299i
$162$		0			0
$163$	−7.05908	+	12.2267i	−0.552910	+	0.957668i	0.445153	+	0.895455i	$0.353149\pi$
$163$	−7.05908	+	12.2267i	−0.552910	+	0.957668i	−0.998063	+	0.0622135i	$0.980184\pi$
$164$	−0.984096	+	1.78573i	−0.0768450	+	0.139442i
$165$		0			0
$166$	−16.0735	−	4.13574i	−1.24754	−	0.320995i
$167$	3.49745			0.270641			0.135320	−	0.990802i	$-0.456794\pi$
$167$	3.49745			0.270641			0.135320	+	0.990802i	$0.456794\pi$
$168$		0			0
$169$	−2.31290			−0.177915
$170$	−10.1541	−	2.61267i	−0.778785	−	0.200383i
$171$		0			0
$172$	13.1324	+	7.23713i	1.00134	+	0.551826i
$173$	12.8696	−	22.2908i	0.978459	−	1.69474i	0.310446	−	0.950591i	$-0.399522\pi$
$173$	12.8696	−	22.2908i	0.978459	−	1.69474i	0.668013	−	0.744150i	$-0.267145\pi$
$174$		0			0
$175$	−4.16520	−	7.93385i	−0.314860	−	0.599743i
$176$	−4.29569	−	2.25694i	−0.323800	−	0.170123i
$177$		0			0
$178$	−9.58641	+	9.77930i	−0.718532	+	0.732990i
$179$	−8.49726	+	4.90590i	−0.635115	+	0.366684i	−0.782730	−	0.622361i	$-0.786174\pi$
$179$	−8.49726	+	4.90590i	−0.635115	+	0.366684i	0.147615	+	0.989045i	$0.452840\pi$
$180$		0			0
$181$			15.0564i			1.11913i	0.828786	+	0.559566i	$0.189032\pi$
$181$			15.0564i			1.11913i	−0.828786	+	0.559566i	$0.810968\pi$
$182$	−14.0220	−	4.21486i	−1.03938	−	0.312426i
$183$		0			0
$184$	−6.84369	−	22.7938i	−0.504523	−	1.68038i
$185$	6.66318	−	3.84699i	0.489887	−	0.282836i
$186$		0			0
$187$	3.54066	−	6.13261i	0.258919	−	0.448461i
$188$	−2.41190	+	1.45732i	−0.175906	+	0.106286i
$189$		0			0
$190$	13.1587	−	3.66673i	0.954635	−	0.266012i
$191$	0.0845715	−	0.146482i	0.00611938	−	0.0105991i	−0.862949	−	0.505290i	$-0.831385\pi$
$191$	0.0845715	−	0.146482i	0.00611938	−	0.0105991i	0.869069	+	0.494691i	$0.164719\pi$
$192$		0			0
$193$	9.45090	+	16.3694i	0.680291	+	1.17830i	0.974892	+	0.222678i	$0.0714798\pi$
$193$	9.45090	+	16.3694i	0.680291	+	1.17830i	−0.294602	+	0.955620i	$0.595187\pi$
$194$	−2.84501	+	11.0571i	−0.204260	+	0.793853i
$195$		0			0
$196$	−11.6797	−	7.71906i	−0.834267	−	0.551361i
$197$	18.4417			1.31392			0.656959	−	0.753926i	$-0.271842\pi$
$197$	18.4417			1.31392			0.656959	+	0.753926i	$0.271842\pi$
$198$		0			0
$199$	−22.8428	+	13.1883i	−1.61929	+	0.934895i	−0.632181	+	0.774821i	$0.717840\pi$
$199$	−22.8428	+	13.1883i	−1.61929	+	0.934895i	−0.987105	+	0.160074i	$0.948827\pi$
$200$	−9.32297	−	2.20179i	−0.659233	−	0.155690i
$201$		0			0
$202$	6.38175	−	1.77830i	0.449018	−	0.125120i
$203$	16.1188	+	0.647652i	1.13132	+	0.0454563i
$204$		0			0
$205$	1.12136	+	0.647416i	0.0783189	+	0.0452175i
$206$	1.79103	−	1.82707i	0.124787	−	0.127298i
$207$		0			0
$208$	−13.2331	+	8.36005i	−0.917553	+	0.579665i
$209$			9.22581i			0.638163i
$210$		0			0
$211$	7.23131			0.497824			0.248912	−	0.968526i	$-0.419927\pi$
$211$	7.23131			0.497824			0.248912	+	0.968526i	$0.419927\pi$
$212$	−0.139173	−	6.98554i	−0.00955843	−	0.479769i
$213$		0			0
$214$	11.3127	−	11.5403i	0.773321	−	0.788881i
$215$	4.76116	−	8.24656i	0.324708	−	0.562411i
$216$		0			0
$217$	−5.80243	+	3.04623i	−0.393895	+	0.206792i
$218$	−0.414296	−	1.48678i	−0.0280596	−	0.100697i
$219$		0			0
$220$	−1.48733	+	2.69889i	−0.100276	+	0.181959i
$221$	−11.4211	−	19.7819i	−0.768266	−	1.33068i
$222$		0			0
$223$			12.5905i			0.843126i	0.906799	+	0.421563i	$0.138518\pi$
$223$			12.5905i			0.843126i	−0.906799	+	0.421563i	$0.861482\pi$
$224$	−14.4186	+	4.01287i	−0.963385	+	0.268121i
$225$		0			0
$226$	23.1940	+	5.96785i	1.54284	+	0.396976i
$227$	17.2781	−	9.97551i	1.14679	−	0.662098i	0.198685	−	0.980063i	$-0.436333\pi$
$227$	17.2781	−	9.97551i	1.14679	−	0.662098i	0.948102	+	0.317965i	$0.103000\pi$
$228$		0			0
$229$	10.2200	+	5.90053i	0.675358	+	0.389918i	0.798104	−	0.602520i	$-0.205837\pi$
$229$	10.2200	+	5.90053i	0.675358	+	0.389918i	−0.122746	+	0.992438i	$0.539170\pi$
$230$	−14.5589	+	4.05690i	−0.959988	+	0.267504i
$231$		0			0
$232$	11.8247	−	12.5534i	0.776332	−	0.824170i
$233$	12.0552	+	6.96006i	0.789761	+	0.455969i	0.839878	−	0.542775i	$-0.182626\pi$
$233$	12.0552	+	6.96006i	0.789761	+	0.455969i	−0.0501176	+	0.998743i	$0.515960\pi$
$234$		0			0
$235$	0.894782	+	1.54981i	0.0583691	+	0.101098i
$236$	−11.2336	+	0.223806i	−0.731244	+	0.0145686i
$237$		0			0
$238$	−5.01331	−	21.2579i	−0.324965	−	1.37794i
$239$	−13.4160			−0.867812			−0.433906	−	0.900958i	$-0.642865\pi$
$239$	−13.4160			−0.867812			−0.433906	+	0.900958i	$0.642865\pi$
$240$		0			0
$241$	0.953994	+	1.65237i	0.0614521	+	0.106438i	0.895115	−	0.445836i	$-0.147094\pi$
$241$	0.953994	+	1.65237i	0.0614521	+	0.106438i	−0.833663	+	0.552274i	$0.813760\pi$
$242$	9.62276	+	9.43295i	0.618574	+	0.606373i
$243$		0			0
$244$	6.17077	+	10.2127i	0.395043	+	0.653803i
$245$	−5.04876	+	7.31811i	−0.322554	+	0.467537i
$246$		0			0
$247$	25.7726	+	14.8798i	1.63987	+	0.946781i
$248$	−1.61028	+	6.81837i	−0.102253	+	0.432967i
$249$		0			0
$250$	−3.75383	+	14.5892i	−0.237413	+	0.922702i
$251$			14.1032i			0.890185i	0.895485	+	0.445093i	$0.146829\pi$
$251$			14.1032i			0.890185i	−0.895485	+	0.445093i	$0.853171\pi$
$252$		0			0
$253$		−	10.2075i		−	0.641741i
$254$	−6.12156	−	1.57509i	−0.384101	−	0.0988300i
$255$		0			0
$256$	−6.87169	+	14.4492i	−0.429480	+	0.903076i
$257$	7.12724	+	4.11491i	0.444585	+	0.256681i	0.705540	−	0.708670i	$-0.250704\pi$
$257$	7.12724	+	4.11491i	0.444585	+	0.256681i	−0.260956	+	0.965351i	$0.584038\pi$
$258$		0			0
$259$	13.5472	+	8.56446i	0.841780	+	0.532169i
$260$	5.14061	+	8.50780i	0.318807	+	0.527631i
$261$		0			0
$262$	−2.63439	+	2.68739i	−0.162753	+	0.166028i
$263$	−7.68684	−	13.3140i	−0.473991	−	0.820977i	0.525566	−	0.850753i	$-0.323854\pi$
$263$	−7.68684	−	13.3140i	−0.473991	−	0.820977i	−0.999557	+	0.0297766i	$0.990520\pi$
$264$		0			0
$265$	−4.43705			−0.272566
$266$	19.5042	+	20.7193i	1.19588	+	1.27038i
$267$		0			0
$268$	0.177185	+	8.89350i	0.0108233	+	0.543257i
$269$	6.63449	+	11.4913i	0.404512	+	0.700635i	0.994265	−	0.106949i	$-0.0341081\pi$
$269$	6.63449	+	11.4913i	0.404512	+	0.700635i	−0.589753	+	0.807584i	$0.700775\pi$
$270$		0			0
$271$	11.0362	+	6.37176i	0.670402	+	0.387057i	0.796229	−	0.604996i	$-0.206825\pi$
$271$	11.0362	+	6.37176i	0.670402	+	0.387057i	−0.125827	+	0.992052i	$0.540158\pi$
$272$	−20.6698	−	10.8599i	−1.25329	−	0.658475i
$273$		0			0
$274$	5.88116	+	21.1057i	0.355294	+	1.27504i
$275$	−3.55820	−	2.05433i	−0.214568	−	0.123881i
$276$		0			0
$277$	−2.65013	+	1.53005i	−0.159231	+	0.0919320i	−0.577498	−	0.816392i	$-0.695971\pi$
$277$	−2.65013	+	1.53005i	−0.159231	+	0.0919320i	0.418267	+	0.908324i	$0.362638\pi$
$278$	−3.18070	+	12.3617i	−0.190766	+	0.741408i
$279$		0			0
$280$	2.36548	+	9.20551i	0.141364	+	0.550134i
$281$			10.2585i			0.611970i	0.952036	+	0.305985i	$0.0989857\pi$
$281$			10.2585i			0.611970i	−0.952036	+	0.305985i	$0.901014\pi$
$282$		0			0
$283$	15.2601	+	26.4312i	0.907118	+	1.57117i	0.818049	+	0.575149i	$0.195056\pi$
$283$	15.2601	+	26.4312i	0.907118	+	1.57117i	0.0890692	+	0.996025i	$0.471611\pi$
$284$	7.78056	+	4.28778i	0.461691	+	0.254433i
$285$		0			0
$286$	−6.46712	+	1.80208i	−0.382409	+	0.106559i
$287$	−0.108288	+	2.69509i	−0.00639207	+	0.159086i
$288$		0			0
$289$	8.53680	−	14.7862i	0.502165	−	0.869775i
$290$	−7.82088	−	7.66661i	−0.459258	−	0.450199i
$291$		0			0
$292$	−0.493251	−	24.7579i	−0.0288653	−	1.44885i
$293$	−10.9008			−0.636833			−0.318417	−	0.947951i	$-0.603151\pi$
$293$	−10.9008			−0.636833			−0.318417	+	0.947951i	$0.603151\pi$
$294$		0			0
$295$			7.13531i			0.415434i
$296$	16.4102	−	4.92706i	0.953826	−	0.286380i
$297$		0			0
$298$	2.54759	+	2.49734i	0.147578	+	0.144667i
$299$	−28.5150	−	16.4632i	−1.64907	−	0.952089i
$300$		0			0
$301$	19.8200	+	0.796364i	1.14240	+	0.0459016i
$302$	−7.90300	−	28.3614i	−0.454766	−	1.63201i
$303$		0			0
$304$	30.3959	−	1.21163i	1.74332	−	0.0694919i
$305$	6.56237	−	3.78879i	0.375760	−	0.216945i
$306$		0			0
$307$	−4.07544			−0.232598			−0.116299	−	0.993214i	$-0.537103\pi$
$307$	−4.07544			−0.232598			−0.116299	+	0.993214i	$0.537103\pi$
$308$	−6.41794	−	0.129904i	−0.365696	−	0.00740195i
$309$		0			0
$310$	4.30878	+	1.10866i	0.244722	+	0.0629675i
$311$	−0.838073	−	1.45158i	−0.0475227	−	0.0823118i	0.841286	−	0.540591i	$-0.181799\pi$
$311$	−0.838073	−	1.45158i	−0.0475227	−	0.0823118i	−0.888808	+	0.458279i	$0.848466\pi$
$312$		0			0
$313$	9.88667	−	17.1242i	0.558827	−	0.967917i	−0.438767	−	0.898601i	$-0.644585\pi$
$313$	9.88667	−	17.1242i	0.558827	−	0.967917i	0.997595	−	0.0693168i	$-0.0220819\pi$
$314$	−8.40824	−	30.1745i	−0.474504	−	1.70285i
$315$		0			0
$316$	0.243722	+	0.403364i	0.0137104	+	0.0226910i
$317$	11.5973	−	20.0871i	0.651369	−	1.12820i	−0.331422	−	0.943482i	$-0.607529\pi$
$317$	11.5973	−	20.0871i	0.651369	−	1.12820i	0.982791	−	0.184721i	$-0.0591381\pi$
$318$		0			0
$319$	6.40575	−	3.69836i	0.358653	−	0.207069i
$320$	9.08724	+	4.54578i	0.507992	+	0.254117i
$321$		0			0
$322$	−21.5796	−	22.9240i	−1.20259	−	1.27750i
$323$			44.3924i			2.47006i
$324$		0			0
$325$	−11.4777	+	6.62664i	−0.636667	+	0.367580i
$326$	14.2581	+	13.9768i	0.789682	+	0.774106i
$327$		0			0
$328$	2.09895	+	1.97712i	0.115895	+	0.109168i
$329$	−1.99203	+	3.15097i	−0.109824	+	0.173719i
$330$		0			0
$331$	−3.43672	+	5.95257i	−0.188899	+	0.327183i	−0.944883	−	0.327407i	$-0.893825\pi$
$331$	−3.43672	+	5.95257i	−0.188899	+	0.327183i	0.755984	+	0.654590i	$0.227159\pi$
$332$	−11.3286	+	20.5568i	−0.621740	+	1.12820i
$333$		0			0
$334$	1.23251	−	4.79012i	0.0674398	−	0.262104i
$335$	5.64895			0.308635
$336$		0			0
$337$	−9.78162			−0.532839			−0.266419	−	0.963857i	$-0.585841\pi$
$337$	−9.78162			−0.532839			−0.266419	+	0.963857i	$0.585841\pi$
$338$	−0.815068	+	3.16775i	−0.0443339	+	0.172303i
$339$		0			0
$340$	−7.15666	+	12.9864i	−0.388124	+	0.704287i
$341$	−1.50244	+	2.60230i	−0.0813616	+	0.140922i
$342$		0			0
$343$	−18.3860	−	2.22583i	−0.992752	−	0.120184i
$344$	14.5399	−	15.4359i	0.783939	−	0.832245i
$345$		0			0
$346$	−25.9943	−	25.4816i	−1.39746	−	1.36990i
$347$	−12.1813	+	7.03286i	−0.653925	+	0.377544i	−0.789958	−	0.613161i	$-0.789898\pi$
$347$	−12.1813	+	7.03286i	−0.653925	+	0.377544i	0.136033	+	0.990704i	$0.456565\pi$
$348$		0			0
$349$			10.9066i			0.583818i	0.956446	+	0.291909i	$0.0942904\pi$
$349$			10.9066i			0.583818i	−0.956446	+	0.291909i	$0.905710\pi$
$350$	−12.3341	+	2.90878i	−0.659283	+	0.155481i
$351$		0			0
$352$	−4.60492	+	5.08804i	−0.245443	+	0.271193i
$353$	11.8554	−	6.84471i	0.630999	−	0.364307i	−0.150140	−	0.988665i	$-0.547972\pi$
$353$	11.8554	−	6.84471i	0.630999	−	0.364307i	0.781139	+	0.624357i	$0.214639\pi$
$354$		0			0
$355$	2.82084	−	4.88583i	0.149714	−	0.259313i
$356$	10.0155	+	16.5758i	0.530820	+	0.878517i
$357$		0			0
$358$	3.72468	+	13.3667i	0.196856	+	0.706453i
$359$	−12.0519	+	20.8744i	−0.636072	+	1.10171i	0.350214	+	0.936670i	$0.386109\pi$
$359$	−12.0519	+	20.8744i	−0.636072	+	1.10171i	−0.986287	+	0.165040i	$0.947225\pi$
$360$		0			0
$361$	−19.4180	−	33.6330i	−1.02200	−	1.77016i
$362$	20.6213	+	5.30589i	1.08383	+	0.278871i
$363$		0			0
$364$	−10.7140	+	17.7192i	−0.561568	+	0.928739i
$365$	−15.7256			−0.823118
$366$		0			0
$367$	−27.1353	+	15.6666i	−1.41645	+	0.817789i	−0.995985	−	0.0895193i	$-0.971467\pi$
$367$	−27.1353	+	15.6666i	−1.41645	+	0.817789i	−0.420467	+	0.907308i	$0.638134\pi$
$368$	−33.6302	+	1.34056i	−1.75310	+	0.0698815i
$369$		0			0
$370$	−2.92073	−	10.4816i	−0.151842	−	0.544912i
$371$	−4.29633	−	8.18362i	−0.223054	−	0.424872i
$372$		0			0
$373$	−25.4358	−	14.6853i	−1.31701	−	0.760378i	−0.333767	−	0.942656i	$-0.608320\pi$
$373$	−25.4358	−	14.6853i	−1.31701	−	0.760378i	−0.983247	+	0.182277i	$0.941653\pi$
$374$	−7.15150	−	7.01044i	−0.369795	−	0.362501i
$375$		0			0
$376$	1.14600	+	3.81690i	0.0591004	+	0.196842i
$377$		−	23.8596i		−	1.22883i
$378$		0			0
$379$	−14.6945			−0.754804			−0.377402	−	0.926049i	$-0.623183\pi$
$379$	−14.6945			−0.754804			−0.377402	+	0.926049i	$0.623183\pi$
$380$	−0.384801	−	19.3144i	−0.0197399	−	0.990808i
$381$		0			0
$382$	−0.170819	−	0.167450i	−0.00873988	−	0.00856749i
$383$	15.0406	−	26.0510i	0.768536	−	1.33114i	−0.169820	−	0.985475i	$-0.554319\pi$
$383$	15.0406	−	26.0510i	0.768536	−	1.33114i	0.938357	−	0.345669i	$-0.112348\pi$
$384$		0			0
$385$	−0.163663	+	4.07326i	−0.00834106	+	0.207593i
$386$	25.7501	−	7.17537i	1.31065	−	0.365217i
$387$		0			0
$388$	14.1412	+	7.79307i	0.717913	+	0.395633i
$389$	14.0945	+	24.4124i	0.714620	+	1.23776i	0.963106	+	0.269122i	$0.0867336\pi$
$389$	14.0945	+	24.4124i	0.714620	+	1.23776i	−0.248486	+	0.968635i	$0.579933\pi$
$390$		0			0
$391$		−	49.1160i		−	2.48391i
$392$	−14.6880	+	13.2764i	−0.741856	+	0.670559i
$393$		0			0
$394$	6.49889	−	25.2578i	0.327409	−	1.27247i
$395$	0.259189	−	0.149643i	0.0130412	−	0.00752935i
$396$		0			0
$397$	−1.04460	−	0.603098i	−0.0524267	−	0.0302686i	0.473558	−	0.880763i	$-0.342970\pi$
$397$	−1.04460	−	0.603098i	−0.0524267	−	0.0302686i	−0.525984	+	0.850494i	$0.676303\pi$
$398$	10.0129	+	35.9332i	0.501902	+	1.80117i
$399$		0			0
$400$	−6.30101	+	11.9929i	−0.315050	+	0.599643i
$401$	−5.28952	−	3.05391i	−0.264146	−	0.152505i	0.362078	−	0.932148i	$-0.382067\pi$
$401$	−5.28952	−	3.05391i	−0.264146	−	0.152505i	−0.626224	+	0.779643i	$0.715401\pi$
$402$		0			0
$403$	4.84641	+	8.39422i	0.241417	+	0.418146i
$404$	−0.186621	−	9.36714i	−0.00928475	−	0.466032i
$405$		0			0
$406$	6.56732	−	21.8481i	0.325931	−	1.08430i
$407$	7.34882			0.364268
$408$		0			0
$409$	−1.01855	−	1.76419i	−0.0503642	−	0.0872333i	0.839744	−	0.542982i	$-0.182705\pi$
$409$	−1.01855	−	1.76419i	−0.0503642	−	0.0872333i	−0.890108	+	0.455749i	$0.849372\pi$
$410$	1.28187	−	1.30766i	0.0633071	−	0.0645809i
$411$		0			0
$412$	−1.87120	−	3.09687i	−0.0921874	−	0.152572i
$413$	−13.1602	+	6.90901i	−0.647572	+	0.339970i
$414$		0			0
$415$	12.9087	+	7.45287i	0.633666	+	0.365847i
$416$	6.78657	+	21.0702i	0.332739	+	1.03305i
$417$		0			0
$418$	12.6357	+	3.25119i	0.618032	+	0.159021i
$419$			7.37216i			0.360153i	0.983653	+	0.180077i	$0.0576346\pi$
$419$			7.37216i			0.360153i	−0.983653	+	0.180077i	$0.942365\pi$
$420$		0			0
$421$		−	22.6066i		−	1.10178i	−0.834578	−	0.550889i	$-0.814289\pi$
$421$		−	22.6066i		−	1.10178i	0.834578	−	0.550889i	$-0.185711\pi$
$422$	2.54833	−	9.90403i	0.124051	−	0.482121i
$423$		0			0
$424$	−9.61647	−	2.27111i	−0.467017	−	0.110295i
$425$	−17.1212	−	9.88494i	−0.830501	−	0.479490i
$426$		0			0
$427$	13.3422	+	8.43489i	0.645675	+	0.408193i
$428$	−11.8191	−	19.5608i	−0.571296	−	0.945505i
$429$		0			0
$430$	−9.61668	−	9.42700i	−0.463758	−	0.454610i
$431$	5.66321	+	9.80896i	0.272787	+	0.472481i	0.969574	−	0.244797i	$-0.0787212\pi$
$431$	5.66321	+	9.80896i	0.272787	+	0.472481i	−0.696787	+	0.717278i	$0.745388\pi$
$432$		0			0
$433$	−34.2887			−1.64781			−0.823904	−	0.566730i	$-0.808208\pi$
$433$	−34.2887			−1.64781			−0.823904	+	0.566730i	$0.808208\pi$
$434$	2.12734	+	9.02053i	0.102116	+	0.432999i
$435$		0			0
$436$	−2.18229	+	0.0434778i	−0.104513	+	0.00208221i
$437$	31.9951	+	55.4172i	1.53053	+	2.65096i
$438$		0			0
$439$	−8.62539	−	4.97987i	−0.411667	−	0.237676i	0.279839	−	0.960047i	$-0.409719\pi$
$439$	−8.62539	−	4.97987i	−0.411667	−	0.237676i	−0.691506	+	0.722371i	$0.743052\pi$
$440$	3.17227	+	2.98814i	0.151232	+	0.142454i
$441$		0			0
$442$	−31.1182	+	8.67119i	−1.48014	+	0.412446i
$443$	−25.4344	−	14.6846i	−1.20842	−	0.697684i	−0.246010	−	0.969267i	$-0.579120\pi$
$443$	−25.4344	−	14.6846i	−1.20842	−	0.697684i	−0.962415	+	0.271583i	$0.912453\pi$
$444$		0			0
$445$	10.6511	−	6.14941i	0.504910	−	0.291510i
$446$	17.2441	+	4.43693i	0.816530	+	0.210095i
$447$		0			0
$448$	0.414885	+	21.1619i	0.0196015	+	0.999808i
$449$		−	14.2598i		−	0.672960i	−0.941691	−	0.336480i	$-0.890764\pi$
$449$		−	14.2598i		−	0.672960i	0.941691	−	0.336480i	$-0.109236\pi$
$450$		0			0
$451$	0.618372	+	1.07105i	0.0291180	+	0.0504339i
$452$	16.3472	−	29.6635i	0.768907	−	1.39525i
$453$		0			0
$454$	−7.57367	−	27.1795i	−0.355450	−	1.27560i
$455$	11.1148	+	7.02675i	0.521072	+	0.329419i
$456$		0			0
$457$	0.586623	−	1.01606i	0.0274411	−	0.0475293i	−0.851979	−	0.523576i	$-0.824597\pi$
$457$	0.586623	−	1.01606i	0.0274411	−	0.0475293i	0.879420	+	0.476047i	$0.157931\pi$
$458$	11.6829	−	11.9180i	0.545908	−	0.556892i
$459$		0			0
$460$	0.425746	+	21.3696i	0.0198505	+	0.996364i
$461$	−34.1274			−1.58947			−0.794735	−	0.606957i	$-0.792390\pi$
$461$	−34.1274			−1.58947			−0.794735	+	0.606957i	$0.792390\pi$
$462$		0			0
$463$			7.37095i			0.342557i	0.985223	+	0.171279i	$0.0547898\pi$
$463$			7.37095i			0.342557i	−0.985223	+	0.171279i	$0.945210\pi$
$464$	−13.0261	−	20.6190i	−0.604722	−	0.957215i
$465$		0			0
$466$	13.7808	−	14.0581i	0.638382	−	0.651227i
$467$	0.195691	+	0.112982i	0.00905551	+	0.00522820i	0.504521	−	0.863399i	$-0.331669\pi$
$467$	0.195691	+	0.112982i	0.00905551	+	0.00522820i	−0.495465	+	0.868628i	$0.665002\pi$
$468$		0			0
$469$	5.46979	+	10.4188i	0.252571	+	0.481096i
$470$	2.43794	−	0.679341i	0.112454	−	0.0313357i
$471$		0			0
$472$	−3.65221	+	15.4644i	−0.168106	+	0.711808i
$473$	7.87662	−	4.54757i	0.362167	−	0.209097i
$474$		0			0
$475$	25.7569			1.18181
$476$	−30.8815	−	0.625064i	−1.41545	−	0.0286498i
$477$		0			0
$478$	−4.72784	+	18.3747i	−0.216246	+	0.840437i
$479$	−9.61683	−	16.6568i	−0.439404	−	0.761070i	0.558239	−	0.829680i	$-0.311477\pi$
$479$	−9.61683	−	16.6568i	−0.439404	−	0.761070i	−0.997644	+	0.0686096i	$0.978144\pi$
$480$		0			0
$481$	11.8525	−	20.5292i	0.540429	−	0.936050i
$482$	2.59927	−	0.724297i	0.118394	−	0.0329908i
$483$		0			0
$484$	16.3105	−	9.85517i	0.741385	−	0.447962i
$485$	5.12690	−	8.88005i	0.232800	−	0.403222i
$486$		0			0
$487$	−15.0342	+	8.68002i	−0.681266	+	0.393329i	−0.800332	−	0.599557i	$-0.795343\pi$
$487$	−15.0342	+	8.68002i	−0.681266	+	0.393329i	0.119066	+	0.992886i	$0.462010\pi$
$488$	16.1620	−	4.85252i	0.731618	−	0.219663i
$489$		0			0
$490$	8.24371	+	9.49372i	0.372413	+	0.428882i
$491$		−	39.5740i		−	1.78595i	−0.450108	−	0.892974i	$-0.648615\pi$
$491$		−	39.5740i		−	1.78595i	0.450108	−	0.892974i	$-0.351385\pi$
$492$		0			0
$493$	30.8229	−	17.7956i	1.38819	−	0.801475i
$494$	29.4618	−	30.0546i	1.32555	−	1.35222i
$495$		0			0
$496$	8.77099	+	4.60825i	0.393829	+	0.206917i
$497$	11.7427	+	0.471821i	0.526732	+	0.0211640i
$498$		0			0
$499$	−10.8738	+	18.8339i	−0.486777	+	0.843122i	−0.999884	−	0.0152020i	$-0.995161\pi$
$499$	−10.8738	+	18.8339i	−0.486777	+	0.843122i	0.513108	+	0.858324i	$0.328494\pi$
$500$	18.6586	+	10.2825i	0.834437	+	0.459848i
$501$		0			0
$502$	19.3158	+	4.96999i	0.862105	+	0.221821i
$503$	−4.00460			−0.178556			−0.0892782	−	0.996007i	$-0.528456\pi$
$503$	−4.00460			−0.178556			−0.0892782	+	0.996007i	$0.528456\pi$
$504$		0			0
$505$	−5.94979			−0.264762
$506$	−13.9802	−	3.59714i	−0.621497	−	0.159913i
$507$		0			0
$508$	−4.31450	+	7.82905i	−0.191425	+	0.347358i
$509$	5.14346	−	8.90873i	0.227980	−	0.394872i	−0.729230	−	0.684269i	$-0.760121\pi$
$509$	5.14346	−	8.90873i	0.227980	−	0.394872i	0.957209	+	0.289397i	$0.0934547\pi$
$510$		0			0
$511$	−15.2269	−	29.0041i	−0.673598	−	1.28306i
$512$	17.3681	+	14.5034i	0.767569	+	0.640966i
$513$		0			0
$514$	8.14745	−	8.31138i	0.359368	−	0.366599i
$515$	−1.98995	+	1.14890i	−0.0876876	+	0.0506265i
$516$		0			0
$517$			1.70928i			0.0751742i
$518$	16.5039	−	15.5361i	0.725142	−	0.682617i
$519$		0			0
$520$	13.4639	−	4.04243i	0.590430	−	0.177272i
$521$	19.5567	−	11.2911i	0.856795	−	0.494671i	−0.00614293	−	0.999981i	$-0.501955\pi$
$521$	19.5567	−	11.2911i	0.856795	−	0.494671i	0.862938	+	0.505311i	$0.168622\pi$
$522$		0			0
$523$	2.71693	−	4.70585i	0.118803	−	0.205773i	−0.800491	−	0.599345i	$-0.795428\pi$
$523$	2.71693	−	4.70585i	0.118803	−	0.205773i	0.919294	+	0.393573i	$0.128761\pi$
$524$	2.75230	+	4.55511i	0.120235	+	0.198991i
$525$		0			0
$526$	−20.9438	+	5.83605i	−0.913191	+	0.254464i
$527$	−7.22937	+	12.5216i	−0.314916	+	0.545451i
$528$		0			0
$529$	−23.8996	−	41.3954i	−1.03912	−	1.79980i
$530$	−1.56363	+	6.07700i	−0.0679195	+	0.263968i
$531$		0			0
$532$	35.2505	−	19.4116i	1.52830	−	0.841598i
$533$	3.98936			0.172798
$534$		0			0
$535$	−12.5691	+	7.25678i	−0.543410	+	0.313738i
$536$	12.2430	+	2.89141i	0.528818	+	0.124890i
$537$		0			0
$538$	18.0765	−	5.03707i	0.779333	−	0.217164i
$539$	−7.67112	+	3.64222i	−0.330419	+	0.156882i
$540$		0			0
$541$	−11.8933	−	6.86658i	−0.511331	−	0.295217i	0.222049	−	0.975035i	$-0.428725\pi$
$541$	−11.8933	−	6.86658i	−0.511331	−	0.295217i	−0.733381	+	0.679818i	$0.762059\pi$
$542$	12.6160	−	12.8698i	0.541902	−	0.552806i
$543$		0			0
$544$	−22.1578	+	24.4824i	−0.950006	+	1.04967i
$545$			1.38614i			0.0593758i
$546$		0			0
$547$	−16.1414			−0.690157			−0.345079	−	0.938574i	$-0.612148\pi$
$547$	−16.1414			−0.690157			−0.345079	+	0.938574i	$0.612148\pi$
$548$	30.9789	−	0.617192i	1.32335	−	0.0263651i
$549$		0			0
$550$	−4.06754	+	4.14938i	−0.173440	+	0.176930i
$551$	−23.1848	+	40.1573i	−0.987706	+	1.71076i
$552$		0			0
$553$	0.526967	+	0.333146i	0.0224089	+	0.0141668i
$554$	1.16166	+	4.16882i	0.0493541	+	0.177116i
$555$		0			0
$556$	15.8098	+	8.71260i	0.670485	+	0.369497i
$557$	−19.8445	−	34.3717i	−0.840839	−	1.45638i	−0.889186	−	0.457545i	$-0.848729\pi$
$557$	−19.8445	−	34.3717i	−0.840839	−	1.45638i	0.0483472	−	0.998831i	$-0.484605\pi$
$558$		0			0
$559$		−	29.3381i		−	1.24087i
$560$	13.4415	+	0.00426906i	0.568007	+	0.000180401i
$561$		0			0
$562$	14.0501	+	3.61511i	0.592666	+	0.152494i
$563$	−21.5339	+	12.4326i	−0.907544	+	0.523971i	−0.879640	−	0.475640i	$-0.842217\pi$
$563$	−21.5339	+	12.4326i	−0.907544	+	0.523971i	−0.0279041	+	0.999611i	$0.508883\pi$
$564$		0			0
$565$	−18.6273	−	10.7545i	−0.783655	−	0.452444i
$566$	41.5780	−	11.5858i	1.74765	−	0.486990i
$567$		0			0
$568$	8.61443	−	9.14526i	0.361454	−	0.383727i
$569$	35.6653	+	20.5914i	1.49517	+	0.863235i	0.999985	−	0.00555444i	$-0.00176804\pi$
$569$	35.6653	+	20.5914i	1.49517	+	0.863235i	0.495182	+	0.868789i	$0.335101\pi$
$570$		0			0
$571$	6.91820	+	11.9827i	0.289518	+	0.501459i	0.973695	−	0.227857i	$-0.0731718\pi$
$571$	6.91820	+	11.9827i	0.289518	+	0.501459i	−0.684177	+	0.729316i	$0.739838\pi$
$572$	0.189118	+	9.49244i	0.00790741	+	0.396899i
$573$		0			0
$574$	3.65304	+	1.09807i	0.152475	+	0.0458324i
$575$	−28.4977			−1.18844
$576$		0			0
$577$	9.48931	+	16.4360i	0.395045	+	0.684238i	0.993107	−	0.117212i	$-0.0373956\pi$
$577$	9.48931	+	16.4360i	0.395045	+	0.684238i	−0.598062	+	0.801450i	$0.704062\pi$
$578$	−17.2428	−	16.9027i	−0.717206	−	0.703059i
$579$		0			0
$580$	−13.2563	+	8.00977i	−0.550438	+	0.332588i
$581$	−1.24659	+	31.0251i	−0.0517171	+	1.28714i
$582$		0			0
$583$	−3.67022	−	2.11900i	−0.152005	−	0.0877602i
$584$	−34.0823	−	8.04917i	−1.41034	−	0.333077i
$585$		0			0
$586$	−3.84147	+	14.9298i	−0.158690	+	0.616745i
$587$			22.8616i			0.943601i	0.881705	+	0.471800i	$0.156396\pi$
$587$			22.8616i			0.943601i	−0.881705	+	0.471800i	$0.843604\pi$
$588$		0			0
$589$		−	18.8374i		−	0.776181i
$590$	9.77254	+	2.51449i	0.402329	+	0.103520i
$591$		0			0
$592$	−0.965126	−	24.2118i	−0.0396665	−	0.995100i
$593$	−36.1224	−	20.8553i	−1.48337	−	0.856424i	−0.483548	−	0.875318i	$-0.660652\pi$
$593$	−36.1224	−	20.8553i	−1.48337	−	0.856424i	−0.999821	+	0.0188942i	$0.993985\pi$
$594$		0			0
$595$	−0.787508	+	19.5996i	−0.0322847	+	0.803503i
$596$	4.31814	−	2.60912i	0.176878	−	0.106874i
$597$		0			0
$598$	−32.5967	+	33.2526i	−1.33298	+	1.35980i
$599$	−5.34683	−	9.26097i	−0.218465	−	0.378393i	0.735874	−	0.677119i	$-0.236772\pi$
$599$	−5.34683	−	9.26097i	−0.218465	−	0.378393i	−0.954339	+	0.298726i	$0.903438\pi$
$600$		0			0
$601$	34.4348			1.40463			0.702313	−	0.711868i	$-0.252151\pi$
$601$	34.4348			1.40463			0.702313	+	0.711868i	$0.252151\pi$
$602$	8.07529	−	26.8648i	0.329124	−	1.09493i
$603$		0			0
$604$	−41.6289	+	0.829371i	−1.69386	+	0.0337466i
$605$	−6.05097	−	10.4806i	−0.246007	−	0.426097i
$606$		0			0
$607$	27.1137	+	15.6541i	1.10051	+	0.635381i	0.936356	−	0.351053i	$-0.114176\pi$
$607$	27.1137	+	15.6541i	1.10051	+	0.635381i	0.164157	+	0.986434i	$0.447510\pi$
$608$	9.05209	−	42.0573i	0.367111	−	1.70565i
$609$		0			0
$610$	−2.87654	−	10.3230i	−0.116468	−	0.417967i
$611$	4.77494	+	2.75681i	0.193173	+	0.111529i
$612$		0			0
$613$	−34.6449	+	20.0022i	−1.39929	+	0.807883i	−0.994319	−	0.106444i	$-0.966053\pi$
$613$	−34.6449	+	20.0022i	−1.39929	+	0.807883i	−0.404976	+	0.914327i	$0.632720\pi$
$614$	−1.43619	+	5.58173i	−0.0579599	+	0.225260i
$615$		0			0
$616$	−2.43961	+	8.74425i	−0.0982946	+	0.352316i
$617$			5.35937i			0.215760i	0.994164	+	0.107880i	$0.0344063\pi$
$617$			5.35937i			0.215760i	−0.994164	+	0.107880i	$0.965594\pi$
$618$		0			0
$619$	−6.16807	−	10.6834i	−0.247916	−	0.429403i	0.715032	−	0.699092i	$-0.246412\pi$
$619$	−6.16807	−	10.6834i	−0.247916	−	0.429403i	−0.962947	+	0.269689i	$0.913079\pi$
$620$	3.03684	−	5.51063i	0.121963	−	0.221312i
$621$		0			0
$622$	−2.28343	+	0.636286i	−0.0915573	+	0.0255128i
$623$	21.6551	+	13.6903i	0.867595	+	0.548490i
$624$		0			0
$625$	−1.70245	+	2.94874i	−0.0680982	+	0.117949i
$626$	−19.9693	−	19.5754i	−0.798134	−	0.782391i
$627$		0			0
$628$	−44.2902	+	0.882393i	−1.76737	+	0.0352113i
$629$	35.3607			1.40992
$630$		0			0
$631$			23.2173i			0.924266i	0.886811	+	0.462133i	$0.152916\pi$
$631$			23.2173i			0.924266i	−0.886811	+	0.462133i	$0.847084\pi$
$632$	0.638337	−	0.191656i	0.0253917	−	0.00762368i
$633$		0			0
$634$	−23.4244	−	22.9624i	−0.930303	−	0.911954i
$635$	4.91628	+	2.83842i	0.195097	+	0.112639i
$636$		0			0
$637$	−2.19768	+	27.3039i	−0.0870753	+	1.08182i
$638$	−2.80789	−	10.0767i	−0.111166	−	0.398938i
$639$		0			0
$640$	9.42828	−	10.8440i	0.372685	−	0.428646i
$641$	−11.2629	+	6.50261i	−0.444856	+	0.256838i	−0.705655	−	0.708555i	$-0.749347\pi$
$641$	−11.2629	+	6.50261i	−0.444856	+	0.256838i	0.260799	+	0.965393i	$0.416014\pi$
$642$		0			0
$643$	21.4094			0.844304			0.422152	−	0.906525i	$-0.361275\pi$
$643$	21.4094			0.844304			0.422152	+	0.906525i	$0.361275\pi$
$644$	−39.0015	+	21.4771i	−1.53687	+	0.846317i
$645$		0			0
$646$	60.7999	+	15.6439i	2.39214	+	0.615503i
$647$	−3.84524	−	6.66015i	−0.151172	−	0.261837i	0.780487	−	0.625172i	$-0.214971\pi$
$647$	−3.84524	−	6.66015i	−0.151172	−	0.261837i	−0.931659	+	0.363335i	$0.881638\pi$
$648$		0			0
$649$	−3.40761	+	5.90215i	−0.133760	+	0.231680i
$650$	5.03112	+	18.0551i	0.197337	+	0.708180i
$651$		0			0
$652$	24.1673	−	14.6024i	0.946465	−	0.571876i
$653$	1.42337	−	2.46535i	0.0557007	−	0.0964765i	−0.836831	−	0.547462i	$-0.815594\pi$
$653$	1.42337	−	2.46535i	0.0557007	−	0.0964765i	0.892531	+	0.450985i	$0.148927\pi$
$654$		0			0
$655$	2.92697	−	1.68988i	0.114366	−	0.0660293i
$656$	3.44754	−	2.17799i	0.134604	−	0.0850360i
$657$		0			0
$658$	3.61359	+	3.83870i	0.140872	+	0.149648i
$659$		−	15.3684i		−	0.598666i	−0.954149	−	0.299333i	$-0.903236\pi$
$659$		−	15.3684i		−	0.598666i	0.954149	−	0.299333i	$-0.0967641\pi$
$660$		0			0
$661$	18.3456	−	10.5919i	0.713562	−	0.411975i	−0.0988162	−	0.995106i	$-0.531506\pi$
$661$	18.3456	−	10.5919i	0.713562	−	0.411975i	0.812379	+	0.583130i	$0.198172\pi$
$662$	6.94155	+	6.80464i	0.269791	+	0.264470i
$663$		0			0
$664$	24.1625	+	22.7600i	0.937687	+	0.883260i
$665$	−11.8790	−	22.6270i	−0.460647	−	0.877437i
$666$		0			0
$667$	25.6518	−	44.4303i	0.993244	−	1.72035i
$668$	−6.12623	−	3.37609i	−0.237031	−	0.130625i
$669$		0			0
$670$	1.99070	−	7.73682i	0.0769074	−	0.298899i
$671$	7.23764			0.279406
$672$		0			0
$673$	−3.62837			−0.139863			−0.0699316	−	0.997552i	$-0.522278\pi$
$673$	−3.62837			−0.139863			−0.0699316	+	0.997552i	$0.522278\pi$
$674$	−3.44706	+	13.3969i	−0.132776	+	0.516031i
$675$		0			0
$676$	4.05133	+	2.23264i	0.155820	+	0.0858708i
$677$	−10.7200	+	18.5676i	−0.412004	+	0.713612i	−0.995109	−	0.0987849i	$-0.968504\pi$
$677$	−10.7200	+	18.5676i	−0.412004	+	0.713612i	0.583105	+	0.812397i	$0.301838\pi$
$678$		0			0
$679$	21.3425	+	0.857539i	0.819049	+	0.0329093i
$680$	15.2642	+	14.3782i	0.585355	+	0.551379i
$681$		0			0
$682$	3.03466	+	2.97480i	0.116203	+	0.113911i
$683$	−14.9757	+	8.64621i	−0.573028	+	0.330838i	−0.758358	−	0.651838i	$-0.773998\pi$
$683$	−14.9757	+	8.64621i	−0.573028	+	0.330838i	0.185330	+	0.982676i	$0.440665\pi$
$684$		0			0
$685$		−	19.6771i		−	0.751823i
$686$	−9.52777	+	24.3972i	−0.363772	+	0.931488i
$687$		0			0
$688$	−16.0171	−	25.3535i	−0.610647	−	0.966593i
$689$	−11.8390	+	6.83526i	−0.451031	+	0.260403i
$690$		0			0
$691$	−9.38118	+	16.2487i	−0.356877	+	0.618129i	−0.987437	−	0.158011i	$-0.949492\pi$
$691$	−9.38118	+	16.2487i	−0.356877	+	0.618129i	0.630560	+	0.776140i	$0.282825\pi$
$692$	−44.0601	+	26.6222i	−1.67491	+	1.01202i
$693$		0			0
$694$	5.33953	+	19.1619i	0.202686	+	0.727376i
$695$	5.73183	−	9.92783i	0.217421	−	0.376584i
$696$		0			0
$697$	2.97546	+	5.15364i	0.112703	+	0.195208i
$698$	14.9377	+	3.84351i	0.565402	+	0.145479i
$699$		0			0
$700$	−0.362669	+	17.9178i	−0.0137076	+	0.677230i
$701$	5.96308			0.225222			0.112611	−	0.993639i	$-0.464079\pi$
$701$	5.96308			0.225222			0.112611	+	0.993639i	$0.464079\pi$
$702$		0			0
$703$	−39.8972	+	23.0346i	−1.50475	+	0.868768i
$704$	5.34581	+	8.09995i	0.201478	+	0.305278i
$705$		0			0
$706$	−5.19668	−	18.6493i	−0.195580	−	0.701875i
$707$	−5.76109	−	10.9737i	−0.216668	−	0.412707i
$708$		0			0
$709$	−24.2059	−	13.9753i	−0.909070	−	0.524852i	−0.0289381	−	0.999581i	$-0.509213\pi$
$709$	−24.2059	−	13.9753i	−0.909070	−	0.524852i	−0.880132	+	0.474729i	$0.842546\pi$
$710$	−5.69758	−	5.58520i	−0.213826	−	0.209609i
$711$		0			0
$712$	26.2318	−	7.87591i	0.983077	−	0.295162i
$713$			20.8418i			0.780532i
$714$		0			0
$715$	6.02938			0.225486
$716$	19.6197	−	0.390883i	0.733222	−	0.0146080i
$717$		0			0
$718$	24.3426	+	23.8624i	0.908457	+	0.890538i
$719$	−13.1386	+	22.7567i	−0.489988	+	0.848683i	−0.999934	−	0.0115231i	$-0.996332\pi$
$719$	−13.1386	+	22.7567i	−0.489988	+	0.848683i	0.509946	+	0.860206i	$0.329665\pi$
$720$		0			0
$721$	−4.04584	−	2.55776i	−0.150675	−	0.0952561i
$722$	−52.9068	+	14.7427i	−1.96899	+	0.548665i
$723$		0			0
$724$	14.5339	−	26.3731i	0.540149	−	0.980150i
$725$	−10.3252	−	17.8838i	−0.383469	−	0.664188i
$726$		0			0
$727$			15.8172i			0.586626i	0.956016	+	0.293313i	$0.0947578\pi$
$727$			15.8172i			0.586626i	−0.956016	+	0.293313i	$0.905242\pi$
$728$	20.4926	+	20.9183i	0.759508	+	0.775283i
$729$		0			0
$730$	−5.54174	+	21.5379i	−0.205109	+	0.797153i
$731$	37.9004	−	21.8818i	1.40180	−	0.809327i
$732$		0			0
$733$	33.2558	+	19.2002i	1.22833	+	0.709176i	0.966680	−	0.255987i	$-0.0824003\pi$
$733$	33.2558	+	19.2002i	1.22833	+	0.709176i	0.261649	+	0.965163i	$0.415734\pi$
$734$	11.8945	+	42.6855i	0.439033	+	1.57555i
$735$		0			0
$736$	−10.0153	+	46.5325i	−0.369169	+	1.71521i
$737$	4.67267	+	2.69777i	0.172120	+	0.0993735i
$738$		0			0
$739$	0.820090	+	1.42044i	0.0301675	+	0.0522516i	0.880715	−	0.473647i	$-0.157063\pi$
$739$	0.820090	+	1.42044i	0.0301675	+	0.0522516i	−0.850547	+	0.525898i	$0.823729\pi$
$740$	−15.3849	+	0.306513i	−0.565560	+	0.0112676i
$741$		0			0
$742$	−12.7223	+	3.00035i	−0.467052	+	0.110146i
$743$	−20.4688			−0.750926			−0.375463	−	0.926837i	$-0.622516\pi$
$743$	−20.4688			−0.750926			−0.375463	+	0.926837i	$0.622516\pi$
$744$		0			0
$745$	−1.60197	−	2.77470i	−0.0586917	−	0.101657i
$746$	−29.0767	+	29.6618i	−1.06457	+	1.08599i
$747$		0			0
$748$	−12.1217	+	7.32423i	−0.443214	+	0.267800i
$749$	−25.5548	−	16.1556i	−0.933750	−	0.590313i
$750$		0			0
$751$	−10.3261	−	5.96179i	−0.376806	−	0.217549i	0.299622	−	0.954058i	$-0.403140\pi$
$751$	−10.3261	−	5.96179i	−0.376806	−	0.217549i	−0.676428	+	0.736509i	$0.736473\pi$
$752$	5.63150	−	0.224482i	0.205360	−	0.00818600i
$753$		0			0
$754$	−32.6782	−	8.40816i	−1.19007	−	0.306207i
$755$			26.4417i			0.962312i
$756$		0			0
$757$			45.2958i			1.64630i	0.567820	+	0.823152i	$0.307787\pi$
$757$			45.2958i			1.64630i	−0.567820	+	0.823152i	$0.692213\pi$
$758$	−5.17836	+	20.1256i	−0.188086	+	0.730995i
$759$		0			0
$760$	−26.5887	−	6.27941i	−0.964473	−	0.227778i
$761$	22.3749	+	12.9182i	0.811091	+	0.468283i	0.847334	−	0.531060i	$-0.178206\pi$
$761$	22.3749	+	12.9182i	0.811091	+	0.468283i	−0.0362439	+	0.999343i	$0.511539\pi$
$762$		0			0
$763$	−2.55657	+	1.34218i	−0.0925542	+	0.0485902i
$764$	−0.289537	+	0.174945i	−0.0104751	+	0.00632929i
$765$		0			0
$766$	−30.3792	−	29.7800i	−1.09765	−	1.07600i
$767$	10.9919	+	19.0385i	0.396895	+	0.687442i
$768$		0			0
$769$	34.0125			1.22652			0.613261	−	0.789880i	$-0.289857\pi$
$769$	34.0125			1.22652			0.613261	+	0.789880i	$0.289857\pi$
$770$	5.52108	+	1.65958i	0.198966	+	0.0598071i
$771$		0			0
$772$	−0.753011	−	37.7961i	−0.0271015	−	1.36031i
$773$	7.80535	+	13.5193i	0.280739	+	0.486254i	0.971567	−	0.236765i	$-0.0760872\pi$
$773$	7.80535	+	13.5193i	0.280739	+	0.486254i	−0.690828	+	0.723019i	$0.742754\pi$
$774$		0			0
$775$	7.26519	+	4.19456i	0.260973	+	0.150673i
$776$	15.6568	−	16.6216i	0.562047	−	0.596681i
$777$		0			0
$778$	38.4022	−	10.7009i	1.37679	−	0.383646i
$779$	−6.71436	−	3.87654i	−0.240567	−	0.138891i
$780$		0			0
$781$	4.66665	−	2.69429i	0.166986	−	0.0964094i
$782$	−67.2695	−	17.3086i	−2.40555	−	0.618953i
$783$		0			0
$784$	13.0073	+	24.7954i	0.464547	+	0.885549i
$785$			28.1321i			1.00408i
$786$		0			0
$787$	−20.2567	−	35.0856i	−0.722072	−	1.25067i	−0.960168	−	0.279424i	$-0.909857\pi$
$787$	−20.2567	−	35.0856i	−0.722072	−	1.25067i	0.238096	−	0.971242i	$-0.423477\pi$
$788$	−32.3030	−	17.8018i	−1.15075	−	0.634163i
$789$		0			0
$790$	−0.113613	−	0.407721i	−0.00404216	−	0.0145060i
$791$	1.79882	−	44.7692i	0.0639587	−	1.59181i
$792$		0			0
$793$	11.6732	−	20.2186i	0.414528	−	0.717983i
$794$	−1.19412	+	1.21815i	−0.0423778	+	0.0432305i
$795$		0			0
$796$	52.7428	−	1.05079i	1.86942	−	0.0372444i
$797$	17.8936			0.633824			0.316912	−	0.948455i	$-0.397354\pi$
$797$	17.8936			0.633824			0.316912	+	0.948455i	$0.397354\pi$
$798$		0			0
$799$			8.22465i			0.290967i
$800$	14.2050	+	12.8562i	0.502221	+	0.454535i
$801$		0			0
$802$	−6.04668	+	6.16835i	−0.213516	+	0.217812i
$803$	−13.0079	−	7.51010i	−0.459038	−	0.265026i
$804$		0			0
$805$	13.1430	+	25.0347i	0.463230	+	0.882356i
$806$	13.2046	−	3.67952i	0.465113	−	0.129605i
$807$		0			0
$808$	−12.8950	−	3.04540i	−0.453645	−	0.107137i
$809$	21.6303	−	12.4883i	0.760482	−	0.439064i	−0.0689870	−	0.997618i	$-0.521977\pi$
$809$	21.6303	−	12.4883i	0.760482	−	0.439064i	0.829469	+	0.558553i	$0.188643\pi$
$810$		0			0
$811$	−14.6502			−0.514437			−0.257219	−	0.966353i	$-0.582806\pi$
$811$	−14.6502			−0.514437			−0.257219	+	0.966353i	$0.582806\pi$
$812$	−27.6089	−	16.6939i	−0.968884	−	0.585843i
$813$		0			0
$814$	2.58974	−	10.0650i	0.0907702	−	0.352777i
$815$	−8.96575	−	15.5291i	−0.314057	−	0.543962i
$816$		0			0
$817$	−28.5084	+	49.3780i	−0.997383	+	1.72752i
$818$	−2.77517	+	0.773312i	−0.0970317	+	0.0270382i
$819$		0			0
$820$	−1.33925	−	2.21648i	−0.0467685	−	0.0774027i
$821$	−12.4265	+	21.5233i	−0.433687	+	0.751168i	−0.997187	−	0.0749478i	$-0.976121\pi$
$821$	−12.4265	+	21.5233i	−0.433687	+	0.751168i	0.563500	+	0.826116i	$0.309454\pi$
$822$		0			0
$823$	11.4375	−	6.60344i	0.398686	−	0.230181i	−0.287231	−	0.957861i	$-0.592735\pi$
$823$	11.4375	−	6.60344i	0.398686	−	0.230181i	0.685917	+	0.727680i	$0.259401\pi$
$824$	−4.90089	+	1.47146i	−0.170731	+	0.0512607i
$825$		0			0
$826$	4.82492	+	20.4590i	0.167880	+	0.711861i
$827$			52.0801i			1.81100i	0.424342	+	0.905502i	$0.360506\pi$
$827$			52.0801i			1.81100i	−0.424342	+	0.905502i	$0.639494\pi$
$828$		0			0
$829$	31.0576	−	17.9311i	1.07867	−	0.622773i	0.148136	−	0.988967i	$-0.452673\pi$
$829$	31.0576	−	17.9311i	1.07867	−	0.622773i	0.930538	+	0.366194i	$0.119339\pi$
$830$	14.7565	−	15.0535i	0.512207	−	0.522513i
$831$		0			0
$832$	31.2495	−	1.86973i	1.08338	−	0.0648211i
$833$	−36.9116	+	17.5255i	−1.27891	+	0.607222i
$834$		0			0
$835$	−2.22106	+	3.84699i	−0.0768629	+	0.133130i
$836$	8.90568	−	16.1602i	0.308010	−	0.558911i
$837$		0			0
$838$	10.0969	+	2.59796i	0.348793	+	0.0897450i
$839$	53.2325			1.83779			0.918894	−	0.394504i	$-0.129083\pi$
$839$	53.2325			1.83779			0.918894	+	0.394504i	$0.129083\pi$
$840$		0			0
$841$	8.17649			0.281948
$842$	−30.9621	−	7.96660i	−1.06702	−	0.274547i
$843$		0			0
$844$	−12.6666	−	6.98039i	−0.436001	−	0.240275i
$845$	1.46881	−	2.54405i	0.0505285	−	0.0875179i
$846$		0			0
$847$	13.4711	−	21.3085i	0.462874	−	0.732168i
$848$	−6.49937	+	12.3704i	−0.223189	+	0.424801i
$849$		0			0
$850$	−19.5720	+	19.9658i	−0.671314	+	0.684821i
$851$	44.1425	−	25.4857i	1.51319	−	0.873639i
$852$		0			0
$853$			46.2200i			1.58254i	0.611464	+	0.791272i	$0.290581\pi$
$853$			46.2200i			1.58254i	−0.611464	+	0.791272i	$0.709419\pi$
$854$	16.2543	−	15.3011i	0.556209	−	0.523592i
$855$		0			0
$856$	−30.9555	+	9.29419i	−1.05804	+	0.317669i
$857$	−38.1633	+	22.0336i	−1.30363	+	0.752652i	−0.981025	−	0.193881i	$-0.937893\pi$
$857$	−38.1633	+	22.0336i	−1.30363	+	0.752652i	−0.322607	+	0.946533i	$0.604559\pi$
$858$		0			0
$859$	−17.4008	+	30.1391i	−0.593707	+	1.02833i	0.400021	+	0.916506i	$0.369003\pi$
$859$	−17.4008	+	30.1391i	−0.593707	+	1.02833i	−0.993728	+	0.111825i	$0.964330\pi$
$860$	−16.3002	+	9.84895i	−0.555832	+	0.335846i
$861$		0			0
$862$	15.4301	−	4.29965i	0.525552	−	0.146447i
$863$	3.41590	−	5.91652i	0.116279	−	0.201401i	−0.802011	−	0.597309i	$-0.796237\pi$
$863$	3.41590	−	5.91652i	0.116279	−	0.201401i	0.918290	+	0.395908i	$0.129570\pi$
$864$		0			0
$865$	16.3457	+	28.3116i	0.555771	+	0.962624i
$866$	−12.0834	+	46.9619i	−0.410610	+	1.59583i
$867$		0			0
$868$	13.1042	+	0.265239i	0.444786	+	0.00900279i
$869$	0.285860			0.00969713
$870$		0			0
$871$	15.0726	−	8.70217i	0.510716	−	0.294862i
$872$	−0.709497	+	3.00420i	−0.0240266	+	0.101735i
$873$		0			0
$874$	87.1747	−	24.2915i	2.94873	−	0.821673i
$875$	28.1602	+	1.13147i	0.951988	+	0.0382508i
$876$		0			0
$877$	−26.3245	−	15.1985i	−0.888916	−	0.513216i	−0.0153285	−	0.999883i	$-0.504879\pi$
$877$	−26.3245	−	15.1985i	−0.888916	−	0.513216i	−0.873588	+	0.486666i	$0.838213\pi$
$878$	−9.86005	+	10.0584i	−0.332761	+	0.339456i
$879$		0			0
$880$	5.21048	−	3.29173i	0.175645	−	0.110964i
$881$		−	25.9266i		−	0.873489i	−0.899586	−	0.436745i	$-0.856131\pi$
$881$		−	25.9266i		−	0.873489i	0.899586	−	0.436745i	$-0.143869\pi$
$882$		0			0
$883$	−8.26902			−0.278275			−0.139137	−	0.990273i	$-0.544433\pi$
$883$	−8.26902			−0.278275			−0.139137	+	0.990273i	$0.544433\pi$
$884$	0.909988	+	45.6753i	0.0306062	+	1.53623i
$885$		0			0
$886$	−29.0751	+	29.6602i	−0.976799	+	0.996453i
$887$	21.4124	−	37.0873i	0.718957	−	1.24527i	−0.242457	−	0.970162i	$-0.577953\pi$
$887$	21.4124	−	37.0873i	0.718957	−	1.24527i	0.961414	−	0.275107i	$-0.0887134\pi$
$888$		0			0
$889$	−0.474761	+	11.8159i	−0.0159230	+	0.396292i
$890$	−4.66879	−	16.7548i	−0.156498	−	0.561623i
$891$		0			0
$892$	12.1537	−	22.0539i	0.406935	−	0.738420i
$893$	−5.35769	−	9.27980i	−0.179288	−	0.310537i
$894$		0			0
$895$		−	12.4620i		−	0.416558i
$896$	29.1297	+	6.88928i	0.973154	+	0.230155i
$897$		0			0
$898$	−19.5302	−	5.02516i	−0.651732	−	0.167692i
$899$	−13.0793	+	7.55136i	−0.436221	+	0.251852i
$900$		0			0
$901$	−17.6602	−	10.1961i	−0.588347	−	0.339682i
$902$	1.68483	−	0.469484i	0.0560988	−	0.0156321i
$903$		0			0
$904$	−34.8664	−	32.8426i	−1.15964	−	1.09233i
$905$	−16.5611	−	9.56156i	−0.550510	−	0.317837i
$906$		0			0
$907$	−23.3139	−	40.3809i	−0.774127	−	1.34083i	−0.935284	−	0.353898i	$-0.884856\pi$
$907$	−23.3139	−	40.3809i	−0.774127	−	1.34083i	0.161157	−	0.986929i	$-0.448477\pi$
$908$	−39.8941	+	0.794810i	−1.32393	+	0.0263767i
$909$		0			0
$910$	13.5407	−	12.7467i	0.448871	−	0.422548i
$911$	−21.5385			−0.713603			−0.356802	−	0.934180i	$-0.616133\pi$
$911$	−21.5385			−0.713603			−0.356802	+	0.934180i	$0.616133\pi$
$912$		0			0
$913$	7.11853	+	12.3297i	0.235589	+	0.408052i
$914$	−1.18487	−	1.16150i	−0.0391921	−	0.0384191i
$915$		0			0
$916$	−12.2059	−	20.2009i	−0.403293	−	0.667457i
$917$	5.95093	+	3.76215i	0.196517	+	0.124237i
$918$		0			0
$919$	38.9789	+	22.5045i	1.28580	+	0.742355i	0.977902	−	0.209066i	$-0.0670422\pi$
$919$	38.9789	+	22.5045i	1.28580	+	0.742355i	0.307895	+	0.951420i	$0.400376\pi$
$920$	29.4179	+	6.94758i	0.969880	+	0.229055i
$921$		0			0
$922$	−12.0265	+	46.7409i	−0.396073	+	1.53933i
$923$		−	17.3819i		−	0.572133i
$924$		0			0
$925$		−	20.5167i		−	0.674584i
$926$	10.0953	+	2.59753i	0.331751	+	0.0853603i
$927$		0			0
$928$	−32.8303	+	10.5744i	−1.07771	+	0.347122i
$929$	26.4883	+	15.2930i	0.869052	+	0.501747i	0.867033	−	0.498251i	$-0.166024\pi$
$929$	26.4883	+	15.2930i	0.869052	+	0.501747i	0.00201867	+	0.999998i	$0.499357\pi$
$930$		0			0
$931$	30.2305	−	43.8187i	0.990766	−	1.43610i
$932$	−14.3976	−	23.8283i	−0.471609	−	0.780521i
$933$		0			0
$934$	0.223703	−	0.228204i	0.00731978	−	0.00746707i
$935$	4.49700	+	7.78903i	0.147068	+	0.254729i
$936$		0			0
$937$	−11.8473			−0.387034			−0.193517	−	0.981097i	$-0.561989\pi$
$937$	−11.8473			−0.387034			−0.193517	+	0.981097i	$0.561989\pi$
$938$	16.1972	−	3.81983i	0.528857	−	0.124722i
$939$		0			0
$940$	−0.0712927	−	3.57842i	−0.00232531	−	0.116715i
$941$	−29.9904	−	51.9449i	−0.977659	−	1.69336i	−0.670865	−	0.741579i	$-0.734077\pi$
$941$	−29.9904	−	51.9449i	−0.977659	−	1.69336i	−0.306794	−	0.951776i	$-0.599256\pi$
$942$		0			0
$943$	7.42882	+	4.28903i	0.241916	+	0.139670i
$944$	19.8931	+	10.4518i	0.647464	+	0.340176i
$945$		0			0
$946$	−3.45263	−	12.3904i	−0.112255	−	0.402847i
$947$	49.7619	+	28.7300i	1.61704	+	0.933600i	0.987680	+	0.156490i	$0.0500178\pi$
$947$	49.7619	+	28.7300i	1.61704	+	0.933600i	0.629364	+	0.777111i	$0.283316\pi$
$948$		0			0
$949$	−41.9594	+	24.2253i	−1.36206	+	0.786386i
$950$	9.07679	−	35.2768i	0.294490	−	1.14453i
$951$		0			0
$952$	−11.7388	+	42.0752i	−0.380457	+	1.36366i
$953$		−	23.3735i		−	0.757141i	−0.925572	−	0.378570i	$-0.876416\pi$
$953$		−	23.3735i		−	0.757141i	0.925572	−	0.378570i	$-0.123584\pi$
$954$		0			0
$955$	0.107414	+	0.186047i	0.00347585	+	0.00602035i
$956$	23.4999	+	12.9505i	0.760041	+	0.418850i
$957$		0			0
$958$	−26.2022	+	7.30134i	−0.846556	+	0.235896i
$959$	36.2920	−	19.0530i	1.17193	−	0.615254i
$960$		0			0
$961$	−12.4323	+	21.5334i	−0.401042	+	0.694625i
$962$	−23.9400	−	23.4678i	−0.771856	−	0.756631i
$963$		0			0
$964$	−0.0760105	−	3.81522i	−0.00244813	−	0.122880i
$965$	−24.0072			−0.772819
$966$		0			0
$967$		−	2.81834i		−	0.0906317i	−0.998973	−	0.0453158i	$-0.985571\pi$
$967$		−	2.81834i		−	0.0906317i	0.998973	−	0.0453158i	$-0.0144294\pi$
$968$	−7.74984	−	25.8119i	−0.249089	−	0.829625i
$969$		0			0
$970$	−10.3554	−	10.1512i	−0.332492	−	0.325934i
$971$	6.81576	+	3.93508i	0.218728	+	0.126283i	0.605361	−	0.795951i	$-0.293029\pi$
$971$	6.81576	+	3.93508i	0.218728	+	0.126283i	−0.386633	+	0.922234i	$0.626362\pi$
$972$		0			0
$973$	23.8607	+	0.958722i	0.764940	+	0.0307352i
$974$	6.59009	+	23.6498i	0.211160	+	0.757788i
$975$		0			0
$976$	−0.950525	−	23.8455i	−0.0304256	−	0.763277i
$977$	−4.31905	+	2.49361i	−0.138179	+	0.0797775i	−0.567496	−	0.823376i	$-0.692088\pi$
$977$	−4.31905	+	2.49361i	−0.138179	+	0.0797775i	0.429317	+	0.903154i	$0.358754\pi$
$978$		0			0
$979$	11.7471			0.375439
$980$	15.9077	−	7.94501i	0.508154	−	0.253794i
$981$		0			0
$982$	−54.2006	−	13.9459i	−1.72961	−	0.445033i
$983$	−15.1135	−	26.1774i	−0.482047	−	0.834929i	0.517741	−	0.855537i	$-0.326773\pi$
$983$	−15.1135	−	26.1774i	−0.482047	−	0.834929i	−0.999788	+	0.0206082i	$0.993440\pi$
$984$		0			0
$985$	−11.7114	+	20.2848i	−0.373157	+	0.646327i
$986$	−13.5109	−	48.4864i	−0.430275	−	1.54412i
$987$		0			0
$988$	−30.7805	−	50.9422i	−0.979258	−	1.62069i
$989$	31.5419	−	54.6322i	1.00298	−	1.73720i
$990$		0			0
$991$	19.3601	−	11.1776i	0.614994	−	0.355067i	−0.159923	−	0.987129i	$-0.551125\pi$
$991$	19.3601	−	11.1776i	0.614994	−	0.355067i	0.774917	+	0.632062i	$0.217791\pi$
$992$	9.40239	−	10.3888i	0.298526	−	0.329845i
$993$		0			0
$994$	4.78435	−	15.9166i	0.151751	−	0.504843i
$995$		−	33.5010i		−	1.06205i
$996$		0			0
$997$	20.7935	−	12.0052i	0.658538	−	0.380207i	−0.133182	−	0.991092i	$-0.542519\pi$
$997$	20.7935	−	12.0052i	0.658538	−	0.380207i	0.791720	+	0.610885i	$0.209186\pi$
$998$	21.9631	+	21.5299i	0.695229	+	0.681516i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bm.c.107.14	yes	48
3.2	odd	2	inner	504.2.bm.c.107.11	yes	48
4.3	odd	2		2016.2.bu.c.1871.7		48
7.4	even	3	inner	504.2.bm.c.179.18	yes	48
8.3	odd	2	inner	504.2.bm.c.107.7	✓	48
8.5	even	2		2016.2.bu.c.1871.17		48
12.11	even	2		2016.2.bu.c.1871.18		48
21.11	odd	6	inner	504.2.bm.c.179.7	yes	48
24.5	odd	2		2016.2.bu.c.1871.8		48
24.11	even	2	inner	504.2.bm.c.107.18	yes	48
28.11	odd	6		2016.2.bu.c.431.8		48
56.11	odd	6	inner	504.2.bm.c.179.11	yes	48
56.53	even	6		2016.2.bu.c.431.18		48
84.11	even	6		2016.2.bu.c.431.17		48
168.11	even	6	inner	504.2.bm.c.179.14	yes	48
168.53	odd	6		2016.2.bu.c.431.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bm.c.107.7	✓	48	8.3	odd	2	inner
504.2.bm.c.107.11	yes	48	3.2	odd	2	inner
504.2.bm.c.107.14	yes	48	1.1	even	1	trivial
504.2.bm.c.107.18	yes	48	24.11	even	2	inner
504.2.bm.c.179.7	yes	48	21.11	odd	6	inner
504.2.bm.c.179.11	yes	48	56.11	odd	6	inner
504.2.bm.c.179.14	yes	48	168.11	even	6	inner
504.2.bm.c.179.18	yes	48	7.4	even	3	inner
2016.2.bu.c.431.7		48	168.53	odd	6
2016.2.bu.c.431.8		48	28.11	odd	6
2016.2.bu.c.431.17		48	84.11	even	6
2016.2.bu.c.431.18		48	56.53	even	6
2016.2.bu.c.1871.7		48	4.3	odd	2
2016.2.bu.c.1871.8		48	24.5	odd	2
2016.2.bu.c.1871.17		48	8.5	even	2
2016.2.bu.c.1871.18		48	12.11	even	2

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.352402 - 1.36960i) q^{2} +(-1.75163 - 0.965301i) q^{4} +(-0.635051 + 1.09994i) q^{5} +(-2.64362 - 0.106220i) q^{7} +(-1.93936 + 2.05886i) q^{8} +O(q^{10})\)	\(q+(0.352402 - 1.36960i) q^{2} +(-1.75163 - 0.965301i) q^{4} +(-0.635051 + 1.09994i) q^{5} +(-2.64362 - 0.106220i) q^{7} +(-1.93936 + 2.05886i) q^{8} +(1.28269 + 1.25739i) q^{10} +(-1.05060 + 0.606562i) q^{11} +3.91317i q^{13} +(-1.07710 + 3.58328i) q^{14} +(2.13639 + 3.38169i) q^{16} +(-5.05521 + 2.91863i) q^{17} +(3.80250 - 6.58612i) q^{19} +(2.17414 - 1.31367i) q^{20} +(0.460518 + 1.65265i) q^{22} +(-4.20712 + 7.28694i) q^{23} +(1.69342 + 2.93309i) q^{25} +(5.35949 + 1.37901i) q^{26} +(4.52810 + 2.73795i) q^{28} -6.09725 q^{29} +(2.14512 - 1.23849i) q^{31} +(5.38444 - 1.73429i) q^{32} +(2.21590 + 7.95217i) q^{34} +(1.79567 - 2.84037i) q^{35} +(-5.24618 - 3.02888i) q^{37} +(-7.68037 - 7.52888i) q^{38} +(-1.03303 - 3.44065i) q^{40} -1.01947i q^{41} -7.49728 q^{43} +(2.42577 - 0.0483285i) q^{44} +(8.49762 + 8.33001i) q^{46} +(0.704496 - 1.22022i) q^{47} +(6.97743 + 0.561612i) q^{49} +(4.61394 - 1.28569i) q^{50} +(3.77739 - 6.85441i) q^{52} +(1.74673 + 3.02543i) q^{53} -1.54079i q^{55} +(5.34561 - 5.23684i) q^{56} +(-2.14868 + 8.35082i) q^{58} +(4.86525 - 2.80895i) q^{59} +(-5.16681 - 2.98306i) q^{61} +(-0.940291 - 3.37441i) q^{62} +(-0.477804 - 7.98572i) q^{64} +(-4.30425 - 2.48506i) q^{65} +(-2.22382 - 3.85176i) q^{67} +(11.6722 - 0.232545i) q^{68} +(-3.25738 - 3.46030i) q^{70} -4.44191 q^{71} +(6.19070 + 10.7226i) q^{73} +(-5.99713 + 6.11780i) q^{74} +(-13.0181 + 7.86587i) q^{76} +(2.84181 - 1.49192i) q^{77} +(-0.204070 - 0.117820i) q^{79} +(-5.07637 + 0.202353i) q^{80} +(-1.39627 - 0.359263i) q^{82} -11.7359i q^{83} -7.41391i q^{85} +(-2.64205 + 10.2683i) q^{86} +(0.788654 - 3.33937i) q^{88} +(-8.38601 - 4.84167i) q^{89} +(0.415658 - 10.3449i) q^{91} +(14.4034 - 8.70286i) q^{92} +(-1.42296 - 1.39489i) q^{94} +(4.82956 + 8.36505i) q^{95} -8.07321 q^{97} +(3.22804 - 9.35840i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 8 q^{10} - 28 q^{16} - 32 q^{19} + 32 q^{22} + 4 q^{28} + 112 q^{34} - 36 q^{40} - 160 q^{43} + 40 q^{46} + 56 q^{49} - 36 q^{52} + 12 q^{58} - 24 q^{64} + 92 q^{70} + 16 q^{73} - 120 q^{76} + 20 q^{82} - 100 q^{88} - 32 q^{91} - 20 q^{94} + 240 q^{97}+O(q^{100}) \) 48 * q - 8 * q^10 - 28 * q^16 - 32 * q^19 + 32 * q^22 + 4 * q^28 + 112 * q^34 - 36 * q^40 - 160 * q^43 + 40 * q^46 + 56 * q^49 - 36 * q^52 + 12 * q^58 - 24 * q^64 + 92 * q^70 + 16 * q^73 - 120 * q^76 + 20 * q^82 - 100 * q^88 - 32 * q^91 - 20 * q^94 + 240 * q^97

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