LMFDB - Embedded newform 504.2.cc.b.293.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(293,504)]

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([0, 3, 5, 3]))

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

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

chi := DirichletCharacter("504.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cc (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:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			293.14
Character	$\chi$	$=$	504.293
Dual form			504.2.cc.b.461.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21983 - 0.715553i) q^{2} +(1.72909 - 0.101211i) q^{3} +(0.975968 + 1.74571i) q^{4} +(-2.82704 - 1.63219i) q^{5} +(-2.18162 - 1.11380i) q^{6} +(-2.15340 + 1.53716i) q^{7} +(0.0586299 - 2.82782i) q^{8} +(2.97951 - 0.350006i) q^{9} +O(q^{10})$	\(q+(-1.21983 - 0.715553i) q^{2} +(1.72909 - 0.101211i) q^{3} +(0.975968 + 1.74571i) q^{4} +(-2.82704 - 1.63219i) q^{5} +(-2.18162 - 1.11380i) q^{6} +(-2.15340 + 1.53716i) q^{7} +(0.0586299 - 2.82782i) q^{8} +(2.97951 - 0.350006i) q^{9} +(2.28058 + 4.01389i) q^{10} +(-0.686803 - 1.18958i) q^{11} +(1.86422 + 2.91970i) q^{12} +(2.68129 - 4.64414i) q^{13} +(3.72670 - 0.334194i) q^{14} +(-5.05340 - 2.53608i) q^{15} +(-2.09497 + 3.40750i) q^{16} -3.79810 q^{17} +(-3.88495 - 1.70505i) q^{18} -3.20217 q^{19} +(0.0902258 - 6.52814i) q^{20} +(-3.56786 + 2.87583i) q^{21} +(-0.0134232 + 1.94253i) q^{22} +(-4.84839 - 2.79922i) q^{23} +(-0.184830 - 4.89549i) q^{24} +(2.82809 + 4.89840i) q^{25} +(-6.59385 + 3.74645i) q^{26} +(5.11642 - 0.906751i) q^{27} +(-4.78508 - 2.25899i) q^{28} +(-2.33896 - 4.05120i) q^{29} +(4.34959 + 6.70956i) q^{30} +(-8.72073 - 5.03492i) q^{31} +(4.99376 - 2.65751i) q^{32} +(-1.30794 - 1.98738i) q^{33} +(4.63303 + 2.71774i) q^{34} +(8.59669 - 0.830833i) q^{35} +(3.51892 + 4.85976i) q^{36} +5.62919i q^{37} +(3.90610 + 2.29132i) q^{38} +(4.16616 - 8.30151i) q^{39} +(-4.78129 + 7.89866i) q^{40} +(0.912990 - 1.58135i) q^{41} +(6.40998 - 0.955035i) q^{42} +(3.05057 - 1.76125i) q^{43} +(1.40635 - 2.35995i) q^{44} +(-8.99447 - 3.87365i) q^{45} +(3.91122 + 6.88385i) q^{46} +(2.22135 + 3.84748i) q^{47} +(-3.27752 + 6.10392i) q^{48} +(2.27430 - 6.62024i) q^{49} +(0.0552738 - 7.99887i) q^{50} +(-6.56726 + 0.384409i) q^{51} +(10.7241 + 0.148219i) q^{52} +10.3327 q^{53} +(-6.88999 - 2.55499i) q^{54} +4.48398i q^{55} +(4.22055 + 6.17956i) q^{56} +(-5.53684 + 0.324094i) q^{57} +(-0.0457139 + 6.61543i) q^{58} +(-3.09566 - 1.78728i) q^{59} +(-0.504710 - 11.2969i) q^{60} +(-4.64085 - 8.03819i) q^{61} +(7.03506 + 12.3819i) q^{62} +(-5.87808 + 5.33368i) q^{63} +(-7.99313 - 0.331589i) q^{64} +(-15.1602 + 8.75276i) q^{65} +(0.173395 + 3.36016i) q^{66} +(-6.76364 - 3.90499i) q^{67} +(-3.70682 - 6.63036i) q^{68} +(-8.66662 - 4.34940i) q^{69} +(-11.0810 - 5.13791i) q^{70} +8.74884i q^{71} +(-0.815064 - 8.44604i) q^{72} +1.82906i q^{73} +(4.02798 - 6.86665i) q^{74} +(5.38581 + 8.18355i) q^{75} +(-3.12521 - 5.59004i) q^{76} +(3.30753 + 1.50592i) q^{77} +(-11.0222 + 7.14532i) q^{78} +(7.58602 + 13.1394i) q^{79} +(11.4843 - 6.21375i) q^{80} +(8.75499 - 2.08569i) q^{81} +(-2.24523 + 1.27568i) q^{82} +(1.91103 - 1.10333i) q^{83} +(-8.50247 - 3.42170i) q^{84} +(10.7374 + 6.19922i) q^{85} +(-4.98144 - 0.0344227i) q^{86} +(-4.45431 - 6.76817i) q^{87} +(-3.40418 + 1.87241i) q^{88} -5.81840 q^{89} +(8.19992 + 11.1612i) q^{90} +(1.36486 + 14.1223i) q^{91} +(0.154738 - 11.1958i) q^{92} +(-15.5885 - 7.82320i) q^{93} +(0.0434152 - 6.28277i) q^{94} +(9.05264 + 5.22655i) q^{95} +(8.36570 - 5.10050i) q^{96} +(14.4240 - 8.32773i) q^{97} +(-7.51139 + 6.44818i) q^{98} +(-2.46270 - 3.30398i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9	$ 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 4 q^{15} + 30 q^{16} - 2 q^{18} + 6 q^{22} - 84 q^{23} + 32 q^{25} + 4 q^{28} - 52 q^{30} + 24 q^{32} - 26 q^{36} + 44 q^{39} - 16 q^{46} + 54 q^{49} + 108 q^{50} - 24 q^{56} - 40 q^{57} + 6 q^{58} - 4 q^{60} - 86 q^{63} + 120 q^{64} + 60 q^{65} - 6 q^{70} + 52 q^{72} + 48 q^{74} - 184 q^{78} - 4 q^{79} - 104 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} - 90 q^{92} - 72 q^{95}+O(q^{100}) $ 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9 + 12 * q^14 - 4 * q^15 + 30 * q^16 - 2 * q^18 + 6 * q^22 - 84 * q^23 + 32 * q^25 + 4 * q^28 - 52 * q^30 + 24 * q^32 - 26 * q^36 + 44 * q^39 - 16 * q^46 + 54 * q^49 + 108 * q^50 - 24 * q^56 - 40 * q^57 + 6 * q^58 - 4 * q^60 - 86 * q^63 + 120 * q^64 + 60 * q^65 - 6 * q^70 + 52 * q^72 + 48 * q^74 - 184 * q^78 - 4 * q^79 - 104 * q^81 - 72 * q^84 - 144 * q^86 - 18 * q^88 - 90 * q^92 - 72 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.21983	−	0.715553i	−0.862550	−	0.505972i
$2$	−1.21983	−	0.715553i	−0.862550	−	0.505972i
$3$	1.72909	−	0.101211i	0.998291	−	0.0584341i
$3$	1.72909	−	0.101211i	0.998291	−	0.0584341i
$4$	0.975968	+	1.74571i	0.487984	+	0.872853i
$5$	−2.82704	−	1.63219i	−1.26429	−	0.729938i	−0.290388	−	0.956909i	$-0.593784\pi$
$5$	−2.82704	−	1.63219i	−1.26429	−	0.729938i	−0.973902	+	0.226971i	$0.927118\pi$
$6$	−2.18162	−	1.11380i	−0.890642	−	0.454705i
$7$	−2.15340	+	1.53716i	−0.813910	+	0.580991i
$7$	−2.15340	+	1.53716i	−0.813910	+	0.580991i
$8$	0.0586299	−	2.82782i	0.0207288	−	0.999785i
$9$	2.97951	−	0.350006i	0.993171	−	0.116669i
$10$	2.28058	+	4.01389i	0.721184	+	1.26930i
$11$	−0.686803	−	1.18958i	−0.207079	−	0.358671i	0.743714	−	0.668498i	$-0.233062\pi$
$11$	−0.686803	−	1.18958i	−0.207079	−	0.358671i	−0.950793	+	0.309826i	$0.899729\pi$
$12$	1.86422	+	2.91970i	0.538155	+	0.842846i
$13$	2.68129	−	4.64414i	0.743657	−	1.28805i	−0.207163	−	0.978306i	$-0.566423\pi$
$13$	2.68129	−	4.64414i	0.743657	−	1.28805i	0.950820	−	0.309745i	$-0.100244\pi$
$14$	3.72670	−	0.334194i	0.996003	−	0.0893172i
$15$	−5.05340	−	2.53608i	−1.30478	−	0.654813i
$16$	−2.09497	+	3.40750i	−0.523743	+	0.851876i
$17$	−3.79810			−0.921174			−0.460587	−	0.887614i	$-0.652361\pi$
$17$	−3.79810			−0.921174			−0.460587	+	0.887614i	$0.652361\pi$
$18$	−3.88495	−	1.70505i	−0.915690	−	0.401885i
$19$	−3.20217			−0.734627			−0.367314	−	0.930097i	$-0.619722\pi$
$19$	−3.20217			−0.734627			−0.367314	+	0.930097i	$0.619722\pi$
$20$	0.0902258	−	6.52814i	0.0201751	−	1.45974i
$21$	−3.56786	+	2.87583i	−0.778570	+	0.627558i
$22$	−0.0134232	+	1.94253i	−0.00286185	+	0.414148i
$23$	−4.84839	−	2.79922i	−1.01096	−	0.583678i	−0.0994868	−	0.995039i	$-0.531720\pi$
$23$	−4.84839	−	2.79922i	−1.01096	−	0.583678i	−0.911472	+	0.411361i	$0.865053\pi$
$24$	−0.184830	−	4.89549i	−0.0377282	−	0.999288i
$25$	2.82809	+	4.89840i	0.565619	+	0.979681i
$26$	−6.59385	+	3.74645i	−1.29316	+	0.734739i
$27$	5.11642	−	0.906751i	0.984656	−	0.174504i
$28$	−4.78508	−	2.25899i	−0.904294	−	0.426910i
$29$	−2.33896	−	4.05120i	−0.434335	−	0.752290i	0.562906	−	0.826521i	$-0.309683\pi$
$29$	−2.33896	−	4.05120i	−0.434335	−	0.752290i	−0.997241	+	0.0742310i	$0.976350\pi$
$30$	4.34959	+	6.70956i	0.794123	+	1.22499i
$31$	−8.72073	−	5.03492i	−1.56629	−	0.904298i	−0.996596	−	0.0824408i	$-0.973728\pi$
$31$	−8.72073	−	5.03492i	−1.56629	−	0.904298i	−0.569694	−	0.821857i	$-0.692938\pi$
$32$	4.99376	−	2.65751i	0.882780	−	0.469786i
$33$	−1.30794	−	1.98738i	−0.227684	−	0.345958i
$34$	4.63303	+	2.71774i	0.794559	+	0.466089i
$35$	8.59669	−	0.830833i	1.45311	−	0.140436i
$36$	3.51892	+	4.85976i	0.586486	+	0.809959i
$37$			5.62919i			0.925433i	0.886506	+	0.462716i	$0.153125\pi$
$37$			5.62919i			0.925433i	−0.886506	+	0.462716i	$0.846875\pi$
$38$	3.90610	+	2.29132i	0.633653	+	0.371701i
$39$	4.16616	−	8.30151i	0.667120	−	1.32931i
$40$	−4.78129	+	7.89866i	−0.755988	+	1.24889i
$41$	0.912990	−	1.58135i	0.142585	−	0.246965i	−0.785884	−	0.618374i	$-0.787792\pi$
$41$	0.912990	−	1.58135i	0.142585	−	0.246965i	0.928469	+	0.371409i	$0.121125\pi$
$42$	6.40998	−	0.955035i	0.989082	−	0.147365i
$43$	3.05057	−	1.76125i	0.465207	−	0.268588i	−0.249024	−	0.968497i	$-0.580110\pi$
$43$	3.05057	−	1.76125i	0.465207	−	0.268588i	0.714231	+	0.699910i	$0.246776\pi$
$44$	1.40635	−	2.35995i	0.212016	−	0.355775i
$45$	−8.99447	−	3.87365i	−1.34082	−	0.577450i
$46$	3.91122	+	6.88385i	0.576678	+	1.01497i
$47$	2.22135	+	3.84748i	0.324017	+	0.561213i	0.981313	−	0.192419i	$-0.0616333\pi$
$47$	2.22135	+	3.84748i	0.324017	+	0.561213i	−0.657296	+	0.753632i	$0.728300\pi$
$48$	−3.27752	+	6.10392i	−0.473070	+	0.881025i
$49$	2.27430	−	6.62024i	0.324900	−	0.945748i
$50$	0.0552738	−	7.99887i	0.00781689	−	1.13121i
$51$	−6.56726	+	0.384409i	−0.919600	+	0.0538280i
$52$	10.7241	+	0.148219i	1.48717	+	0.0205543i
$53$	10.3327			1.41930			0.709652	−	0.704552i	$-0.248852\pi$
$53$	10.3327			1.41930			0.709652	+	0.704552i	$0.248852\pi$
$54$	−6.88999	−	2.55499i	−0.937609	−	0.347690i
$55$			4.48398i			0.604619i
$56$	4.22055	+	6.17956i	0.563994	+	0.825779i
$57$	−5.53684	+	0.324094i	−0.733372	+	0.0429273i
$58$	−0.0457139	+	6.61543i	−0.00600253	+	0.868648i
$59$	−3.09566	−	1.78728i	−0.403021	−	0.232684i	0.284766	−	0.958597i	$-0.408084\pi$
$59$	−3.09566	−	1.78728i	−0.403021	−	0.232684i	−0.687787	+	0.725913i	$0.741417\pi$
$60$	−0.504710	−	11.2969i	−0.0651578	−	1.45842i
$61$	−4.64085	−	8.03819i	−0.594200	−	1.02918i	−0.993659	−	0.112434i	$-0.964135\pi$
$61$	−4.64085	−	8.03819i	−0.594200	−	1.02918i	0.399459	−	0.916751i	$-0.369198\pi$
$62$	7.03506	+	12.3819i	0.893453	+	1.57250i
$63$	−5.87808	+	5.33368i	−0.740569	+	0.671981i
$64$	−7.99313	−	0.331589i	−0.999141	−	0.0414487i
$65$	−15.1602	+	8.75276i	−1.88040	+	1.08565i
$66$	0.173395	+	3.36016i	0.0213434	+	0.413608i
$67$	−6.76364	−	3.90499i	−0.826310	−	0.477070i	0.0262775	−	0.999655i	$-0.491635\pi$
$67$	−6.76364	−	3.90499i	−0.826310	−	0.477070i	−0.852588	+	0.522584i	$0.824968\pi$
$68$	−3.70682	−	6.63036i	−0.449518	−	0.804049i
$69$	−8.66662	−	4.34940i	−1.04334	−	0.523606i
$70$	−11.0810	−	5.13791i	−1.32443	−	0.614098i
$71$			8.74884i			1.03830i	0.854684	+	0.519148i	$0.173751\pi$
$71$			8.74884i			1.03830i	−0.854684	+	0.519148i	$0.826249\pi$
$72$	−0.815064	−	8.44604i	−0.0960563	−	0.995376i
$73$			1.82906i			0.214075i	0.994255	+	0.107038i	$0.0341365\pi$
$73$			1.82906i			0.214075i	−0.994255	+	0.107038i	$0.965863\pi$
$74$	4.02798	−	6.86665i	0.468243	−	0.798232i
$75$	5.38581	+	8.18355i	0.621899	+	0.944955i
$76$	−3.12521	−	5.59004i	−0.358486	−	0.641221i
$77$	3.30753	+	1.50592i	0.376928	+	0.171615i
$78$	−11.0222	+	7.14532i	−1.24802	+	0.809048i
$79$	7.58602	+	13.1394i	0.853494	+	1.47829i	0.878035	+	0.478596i	$0.158854\pi$
$79$	7.58602	+	13.1394i	0.853494	+	1.47829i	−0.0245416	+	0.999699i	$0.507813\pi$
$80$	11.4843	−	6.21375i	1.28398	−	0.694718i
$81$	8.75499	−	2.08569i	0.972777	−	0.231744i
$82$	−2.24523	+	1.27568i	−0.247944	+	0.140875i
$83$	1.91103	−	1.10333i	0.209763	−	0.121106i	−0.391439	−	0.920204i	$-0.628022\pi$
$83$	1.91103	−	1.10333i	0.209763	−	0.121106i	0.601201	+	0.799098i	$0.294689\pi$
$84$	−8.50247	−	3.42170i	−0.927695	−	0.373338i
$85$	10.7374	+	6.19922i	1.16463	+	0.672400i
$86$	−4.98144	−	0.0344227i	−0.537162	−	0.00371190i
$87$	−4.45431	−	6.76817i	−0.477552	−	0.725624i
$88$	−3.40418	+	1.87241i	−0.362887	+	0.199600i
$89$	−5.81840			−0.616749			−0.308375	−	0.951265i	$-0.599785\pi$
$89$	−5.81840			−0.616749			−0.308375	+	0.951265i	$0.599785\pi$
$90$	8.19992	+	11.1612i	0.864347	+	1.17650i
$91$	1.36486	+	14.1223i	0.143076	+	1.48042i
$92$	0.154738	−	11.1958i	0.0161325	−	1.16724i
$93$	−15.5885	−	7.82320i	−1.61646	−	0.811228i
$94$	0.0434152	−	6.28277i	0.00447793	−	0.648018i
$95$	9.05264	+	5.22655i	0.928782	+	0.536232i
$96$	8.36570	−	5.10050i	0.853820	−	0.520568i
$97$	14.4240	−	8.32773i	1.46454	−	0.845553i	0.465324	−	0.885140i	$-0.345938\pi$
$97$	14.4240	−	8.32773i	1.46454	−	0.845553i	0.999216	+	0.0395876i	$0.0126044\pi$
$98$	−7.51139	+	6.44818i	−0.758765	+	0.651365i
$99$	−2.46270	−	3.30398i	−0.247510	−	0.332062i
$100$	−5.79104	+	9.71770i	−0.579104	+	0.971770i
$101$	−0.458979	+	0.264992i	−0.0456701	+	0.0263676i	−0.522661	−	0.852540i	$-0.675061\pi$
$101$	−0.458979	+	0.264992i	−0.0456701	+	0.0263676i	0.476991	+	0.878908i	$0.341727\pi$
$102$	8.28600	+	4.23031i	0.820437	+	0.418863i
$103$	14.7523	+	8.51727i	1.45359	+	0.839231i	0.998683	−	0.0513066i	$-0.0163386\pi$
$103$	14.7523	+	8.51727i	1.45359	+	0.839231i	0.454909	+	0.890538i	$0.349672\pi$
$104$	−12.9756	−	7.85450i	−1.27236	−	0.770197i
$105$	14.7804	−	2.30666i	1.44242	−	0.225107i
$106$	−12.6041	−	7.39359i	−1.22422	−	0.718128i
$107$	0.808964			0.0782055			0.0391028	−	0.999235i	$-0.487550\pi$
$107$	0.808964			0.0782055			0.0391028	+	0.999235i	$0.487550\pi$
$108$	6.57639	+	8.04681i	0.632813	+	0.774305i
$109$		−	16.2402i		−	1.55552i	−0.628558	−	0.777762i	$-0.716355\pi$
$109$		−	16.2402i		−	1.55552i	0.628558	−	0.777762i	$-0.283645\pi$
$110$	3.20852	−	5.46969i	0.305921	−	0.521514i
$111$	0.569735	+	9.73338i	0.0540769	+	0.923852i
$112$	−0.726545	−	10.5580i	−0.0686520	−	0.997641i
$113$	−0.101810	−	0.0587799i	−0.00957746	−	0.00552955i	0.495204	−	0.868777i	$-0.335093\pi$
$113$	−0.101810	−	0.0587799i	−0.00957746	−	0.00552955i	−0.504781	+	0.863247i	$0.668427\pi$
$114$	6.98590	+	3.56656i	0.654290	+	0.334039i
$115$	9.13772	+	15.8270i	0.852097	+	1.47588i
$116$	4.78945	−	8.03699i	0.444690	−	0.746215i
$117$	6.36347	−	14.7757i	0.588303	−	1.36602i
$118$	2.49728	+	4.39529i	0.229894	+	0.404619i
$119$	8.17884	−	5.83827i	0.749753	−	0.535194i
$120$	−7.46786	+	14.1414i	−0.681719	+	1.29093i
$121$	4.55660	−	7.89227i	0.414237	−	0.717479i
$122$	−0.0907032	+	13.1260i	−0.00821188	+	1.18837i
$123$	1.41859	−	2.82669i	0.127910	−	0.254874i
$124$	0.278325	−	20.1377i	0.0249943	−	1.80842i
$125$		−	2.14205i		−	0.191591i
$126$	10.9868	−	2.30010i	0.978781	−	0.204909i
$127$	2.61604			0.232136			0.116068	−	0.993241i	$-0.462971\pi$
$127$	2.61604			0.232136			0.116068	+	0.993241i	$0.462971\pi$
$128$	9.51298	+	6.12399i	0.840837	+	0.541289i
$129$	5.09645	−	3.35411i	0.448718	−	0.295313i
$130$	24.7560	+	0.171069i	2.17124	+	0.0150037i
$131$	8.31237	+	4.79915i	0.726255	+	0.419303i	0.817051	−	0.576566i	$-0.195608\pi$
$131$	8.31237	+	4.79915i	0.726255	+	0.419303i	−0.0907956	+	0.995870i	$0.528941\pi$
$132$	2.19286	−	4.22290i	0.190864	−	0.367556i
$133$	6.89556	−	4.92223i	0.597921	−	0.426812i
$134$	5.45626	+	9.60316i	0.471349	+	0.829587i
$135$	−15.9443	−	5.78756i	−1.37227	−	0.498114i
$136$	−0.222682	+	10.7403i	−0.0190948	+	0.920977i
$137$	−11.8679	+	6.85192i	−1.01394	+	0.585399i	−0.912343	−	0.409426i	$-0.865729\pi$
$137$	−11.8679	+	6.85192i	−1.01394	+	0.585399i	−0.101598	+	0.994826i	$0.532396\pi$
$138$	7.45958	+	11.5069i	0.635001	+	0.979536i
$139$	1.08802	−	1.88450i	0.0922844	−	0.159841i	−0.816188	−	0.577787i	$-0.803916\pi$
$139$	1.08802	−	1.88450i	0.0922844	−	0.159841i	0.908472	+	0.417946i	$0.137250\pi$
$140$	9.84048	+	14.1964i	0.831672	+	1.19982i
$141$	4.23032	+	6.42783i	0.356257	+	0.541321i
$142$	6.26026	−	10.6721i	0.525349	−	0.895582i
$143$	−7.36608			−0.615983
$144$	−5.04935	+	10.8860i	−0.420779	+	0.907163i
$145$			15.2705i			1.26815i
$146$	1.30879	−	2.23114i	0.108316	−	0.184650i
$147$	3.26243	−	11.6772i	0.269081	−	0.963118i
$148$	−9.82690	+	5.49391i	−0.807767	+	0.451596i
$149$	6.36891	−	11.0313i	0.521761	−	0.903717i	−0.477919	−	0.878404i	$-0.658609\pi$
$149$	6.36891	−	11.0313i	0.521761	−	0.903717i	0.999680	−	0.0253125i	$-0.00805807\pi$
$150$	−0.713999	−	13.8364i	−0.0582978	−	1.12973i
$151$	2.61458	+	4.52858i	0.212771	+	0.368531i	0.952581	−	0.304286i	$-0.0984177\pi$
$151$	2.61458	+	4.52858i	0.212771	+	0.368531i	−0.739809	+	0.672816i	$0.765084\pi$
$152$	−0.187743	+	9.05515i	−0.0152279	+	0.734470i
$153$	−11.3165	+	1.32936i	−0.914884	+	0.107472i
$154$	−2.95706	−	4.20368i	−0.238287	−	0.338742i
$155$	16.4359	+	28.4678i	1.32016	+	2.28659i
$156$	18.5580	−	0.829116i	1.48583	−	0.0663824i
$157$	−8.36599	+	14.4903i	−0.667679	+	1.15645i	0.310873	+	0.950452i	$0.399379\pi$
$157$	−8.36599	+	14.4903i	−0.667679	+	1.15645i	−0.978552	+	0.206002i	$0.933955\pi$
$158$	0.148265	−	21.4560i	0.0117953	−	1.70695i
$159$	17.8662	−	1.04578i	1.41688	−	0.0829358i
$160$	−18.4551	−	0.637886i	−1.45900	−	0.0504293i
$161$	14.7434	−	1.42488i	1.16194	−	0.112297i
$162$	−12.1720	−	3.72047i	−0.956324	−	0.292308i
$163$		−	11.5448i		−	0.904257i	−0.891953	−	0.452128i	$-0.850665\pi$
$163$		−	11.5448i		−	0.904257i	0.891953	−	0.452128i	$-0.149335\pi$
$164$	3.65161	+	0.0504691i	0.285143	+	0.00394098i
$165$	0.453827	+	7.75320i	0.0353304	+	0.603586i
$166$	−3.12062	−	0.0215641i	−0.242207	−	0.00167370i
$167$	2.14524	−	3.71567i	0.166004	−	0.287527i	−0.771007	−	0.636826i	$-0.780247\pi$
$167$	2.14524	−	3.71567i	0.166004	−	0.287527i	0.937011	+	0.349299i	$0.113580\pi$
$168$	7.92315	+	10.2579i	0.611284	+	0.791411i
$169$	−7.87867	−	13.6462i	−0.606051	−	1.04971i
$170$	−8.66189	−	15.2452i	−0.664337	−	1.16925i
$171$	−9.54090	+	1.12078i	−0.729611	+	0.0857079i
$172$	6.05187	+	3.60647i	0.461451	+	0.274991i
$173$	1.84020	−	1.06244i	0.139908	−	0.0807760i	−0.428412	−	0.903583i	$-0.640927\pi$
$173$	1.84020	−	1.06244i	0.139908	−	0.0807760i	0.568320	+	0.822807i	$0.307593\pi$
$174$	0.590510	+	11.4433i	0.0447664	+	0.867515i
$175$	−13.6196	−	6.20102i	−1.02955	−	0.468753i
$176$	5.49233	+	0.151849i	0.414000	+	0.0114460i
$177$	−5.53357	−	2.77706i	−0.415929	−	0.208736i
$178$	7.09746	+	4.16337i	0.531977	+	0.312058i
$179$	−21.0209			−1.57118			−0.785589	−	0.618749i	$-0.787640\pi$
$179$	−21.0209			−1.57118			−0.785589	+	0.618749i	$0.787640\pi$
$180$	−2.01606	−	19.4823i	−0.150268	−	1.45212i
$181$	3.02613			0.224931			0.112465	−	0.993656i	$-0.464125\pi$
$181$	3.02613			0.224931			0.112465	+	0.993656i	$0.464125\pi$
$182$	8.44034	−	18.2034i	0.625640	−	1.34932i
$183$	−8.83801	−	13.4291i	−0.653324	−	0.992704i
$184$	−8.19995	+	13.5463i	−0.604508	+	0.998643i
$185$	9.18791	−	15.9139i	0.675509	−	1.17002i
$186$	13.4174	+	20.6974i	0.983814	+	1.51761i
$187$	2.60855	+	4.51814i	0.190756	+	0.330399i
$188$	−4.54861	+	7.63284i	−0.331741	+	0.556682i
$189$	−9.62391	+	9.81735i	−0.700037	+	0.714107i
$190$	−7.30281	−	12.8531i	−0.529802	−	0.932465i
$191$	−2.10035	+	1.21264i	−0.151976	+	0.0877433i	−0.574059	−	0.818814i	$-0.694632\pi$
$191$	−2.10035	+	1.21264i	−0.151976	+	0.0877433i	0.422084	+	0.906557i	$0.361299\pi$
$192$	−13.8544	+	0.235643i	−0.999855	+	0.0170061i
$193$	5.62172	−	9.73710i	0.404660	−	0.700892i	−0.589622	−	0.807679i	$-0.700723\pi$
$193$	5.62172	−	9.73710i	0.404660	−	0.700892i	0.994282	+	0.106788i	$0.0340565\pi$
$194$	−23.5538	−	0.162762i	−1.69107	−	0.0116856i
$195$	−25.3276	+	16.6687i	−1.81374	+	1.19367i
$196$	13.7766	−	2.49089i	0.984045	−	0.177920i
$197$	−7.37332			−0.525328			−0.262664	−	0.964887i	$-0.584601\pi$
$197$	−7.37332			−0.525328			−0.262664	+	0.964887i	$0.584601\pi$
$198$	0.639901	+	5.79248i	0.0454758	+	0.411654i
$199$			8.19951i			0.581248i	0.956837	+	0.290624i	$0.0938629\pi$
$199$			8.19951i			0.581248i	−0.956837	+	0.290624i	$0.906137\pi$
$200$	14.0176	−	7.71015i	0.991195	−	0.545190i
$201$	−12.0902	−	6.06753i	−0.852775	−	0.427970i
$202$	0.749491	+	0.00517914i	0.0527340	+	0.000364403i
$203$	11.2641	+	5.12853i	0.790583	+	0.359952i
$204$	−7.08050	−	11.0893i	−0.495734	−	0.776408i
$205$	−5.16211	+	2.98035i	−0.360538	+	0.208157i
$206$	−11.9008	−	20.9457i	−0.829167	−	1.45936i
$207$	−15.4256	−	6.64335i	−1.07215	−	0.461744i
$208$	10.2077	+	18.8659i	0.707775	+	1.30811i
$209$	2.19926	+	3.80923i	0.152126	+	0.263490i
$210$	−19.6801	−	7.76240i	−1.35805	−	0.535656i
$211$	−13.4385	−	7.75871i	−0.925143	−	0.534132i	−0.0398710	−	0.999205i	$-0.512695\pi$
$211$	−13.4385	−	7.75871i	−0.925143	−	0.534132i	−0.885272	+	0.465073i	$0.846028\pi$
$212$	10.0844	+	18.0378i	0.692598	+	1.23884i
$213$	0.885478	+	15.1275i	0.0606719	+	1.03652i
$214$	−0.986798	−	0.578857i	−0.0674561	−	0.0395698i
$215$	−11.4988			−0.784209
$216$	−2.26415	−	14.5215i	−0.154056	−	0.988062i
$217$	26.5187	−	2.56292i	1.80021	−	0.173982i
$218$	−11.6207	+	19.8102i	−0.787052	+	1.34172i
$219$	0.185121	+	3.16261i	0.0125093	+	0.213709i
$220$	−7.82770	+	4.37622i	−0.527743	+	0.295045i
$221$	−10.1838	+	17.6389i	−0.685038	+	1.18652i
$222$	6.26977	−	12.2807i	0.420799	−	0.824229i
$223$	10.7965	−	6.23338i	0.722989	−	0.417418i	−0.0928628	−	0.995679i	$-0.529602\pi$
$223$	10.7965	−	6.23338i	0.722989	−	0.417418i	0.815852	+	0.578261i	$0.196268\pi$
$224$	−6.66857	+	13.3989i	−0.445563	+	0.895251i
$225$	10.1408	+	13.6050i	0.676054	+	0.907000i
$226$	0.0821305	+	0.144552i	0.00546324	+	0.00961544i
$227$	3.06928	−	1.77205i	0.203715	−	0.117615i	−0.394672	−	0.918822i	$-0.629142\pi$
$227$	3.06928	−	1.77205i	0.203715	−	0.117615i	0.598387	+	0.801207i	$0.295808\pi$
$228$	−5.96955	−	9.34938i	−0.395343	−	0.619178i
$229$	−5.08642	+	8.80994i	−0.336120	+	0.582177i	−0.983699	−	0.179821i	$-0.942448\pi$
$229$	−5.08642	+	8.80994i	−0.336120	+	0.582177i	0.647579	+	0.761998i	$0.275782\pi$
$230$	0.178592	−	25.8448i	0.0117760	−	1.70415i
$231$	5.87144	+	2.26911i	0.386313	+	0.149297i
$232$	−11.5932	+	6.37664i	−0.761131	+	0.418647i
$233$		−	3.72928i		−	0.244313i	−0.992511	−	0.122157i	$-0.961019\pi$
$233$		−	3.72928i		−	0.244313i	0.992511	−	0.122157i	$-0.0389810\pi$
$234$	−18.3352	+	13.4705i	−1.19861	+	0.880592i
$235$		−	14.5026i		−	0.946048i
$236$	0.0987990	−	7.14844i	0.00643127	−	0.465324i
$237$	14.4468	+	21.9514i	0.938418	+	1.42590i
$238$	−14.1544	+	1.26930i	−0.917493	+	0.0822767i
$239$	−3.54749	−	2.04815i	−0.229468	−	0.132484i	0.380858	−	0.924633i	$-0.375629\pi$
$239$	−3.54749	−	2.04815i	−0.229468	−	0.132484i	−0.610327	+	0.792150i	$0.708962\pi$
$240$	19.2284	−	11.9065i	1.24119	−	0.768559i
$241$	−3.88968	+	2.24571i	−0.250556	+	0.144659i	−0.620019	−	0.784587i	$-0.712875\pi$
$241$	−3.88968	+	2.24571i	−0.250556	+	0.144659i	0.369463	+	0.929246i	$0.379542\pi$
$242$	−11.2056	+	6.36673i	−0.720324	+	0.409269i
$243$	14.9271	−	4.49245i	0.957573	−	0.288191i
$244$	9.50299	−	15.9466i	0.608366	−	1.02087i
$245$	−17.2350	+	15.0036i	−1.10111	+	0.958543i
$246$	−3.75309	+	2.43301i	−0.239288	+	0.155123i
$247$	−8.58595	+	14.8713i	−0.546311	+	0.946238i
$248$	−14.7491	+	24.3655i	−0.936571	+	1.54721i
$249$	3.19267	−	2.10118i	0.202327	−	0.133157i
$250$	−1.53275	+	2.61294i	−0.0969397	+	0.165257i
$251$			16.3716i			1.03337i	0.856176	+	0.516685i	$0.172834\pi$
$251$			16.3716i			1.03337i	−0.856176	+	0.516685i	$0.827166\pi$
$252$	−15.0479	−	5.05589i	−0.947926	−	0.318491i
$253$			7.69005i			0.483469i
$254$	−3.19112	−	1.87191i	−0.200228	−	0.117454i
$255$	19.1933	+	9.63228i	1.20193	+	0.603197i
$256$	−7.22218	−	14.2773i	−0.451386	−	0.892329i
$257$	−1.65104	+	2.85969i	−0.102989	+	0.178383i	−0.912915	−	0.408150i	$-0.866174\pi$
$257$	−1.65104	+	2.85969i	−0.102989	+	0.178383i	0.809926	+	0.586533i	$0.199507\pi$
$258$	−8.61684	+	0.444656i	−0.536461	+	0.0276831i
$259$	−8.65295	−	12.1219i	−0.537668	−	0.753219i
$260$	−30.0756	−	17.9229i	−1.86521	−	1.11153i
$261$	−8.38692	−	11.2520i	−0.519137	−	0.696479i
$262$	−6.70563	−	11.8021i	−0.414275	−	0.729135i
$263$	20.0232	−	11.5604i	1.23468	−	0.712843i	0.266679	−	0.963786i	$-0.414074\pi$
$263$	20.0232	−	11.5604i	1.23468	−	0.712843i	0.968002	+	0.250942i	$0.0807404\pi$
$264$	−5.69663	+	3.58211i	−0.350603	+	0.220464i
$265$	−29.2109	−	16.8649i	−1.79441	−	1.03600i
$266$	−11.9335	+	1.07015i	−0.731691	+	0.0656148i
$267$	−10.0605	+	0.588885i	−0.615695	+	0.0360392i
$268$	0.215864	−	15.6185i	0.0131860	−	0.954050i
$269$		−	28.5660i		−	1.74170i	−0.491552	−	0.870848i	$-0.663570\pi$
$269$		−	28.5660i		−	1.74170i	0.491552	−	0.870848i	$-0.336430\pi$
$270$	15.3080	+	18.4688i	0.931618	+	1.12398i
$271$		−	24.0898i		−	1.46335i	−0.681653	−	0.731675i	$-0.738739\pi$
$271$		−	24.0898i		−	1.46335i	0.681653	−	0.731675i	$-0.261261\pi$
$272$	7.95692	−	12.9420i	0.482459	−	0.784727i
$273$	3.78929	+	24.2806i	0.229338	+	1.46953i
$274$	19.3797	+	0.133918i	1.17077	+	0.00809026i
$275$	3.88469	−	6.72848i	0.234256	−	0.405743i
$276$	−0.865582	−	19.3742i	−0.0521019	−	1.16619i
$277$	20.4819	−	11.8252i	1.23064	−	0.710510i	0.263476	−	0.964666i	$-0.415131\pi$
$277$	20.4819	−	11.8252i	1.23064	−	0.710510i	0.967163	+	0.254157i	$0.0817978\pi$
$278$	−2.67565	+	1.52024i	−0.160475	+	0.0911777i
$279$	−27.7458	−	11.9493i	−1.66110	−	0.715385i
$280$	−1.84542	−	24.3586i	−0.110285	−	1.45570i
$281$	−16.3653	+	9.44852i	−0.976273	+	0.563651i	−0.901143	−	0.433522i	$-0.857271\pi$
$281$	−16.3653	+	9.44852i	−0.976273	+	0.563651i	−0.0751300	+	0.997174i	$0.523937\pi$
$282$	−0.560815	−	10.8679i	−0.0333961	−	0.647172i
$283$	4.52882	−	7.84415i	0.269210	−	0.466286i	−0.699448	−	0.714684i	$-0.746571\pi$
$283$	4.52882	−	7.84415i	0.269210	−	0.466286i	0.968658	+	0.248398i	$0.0799040\pi$
$284$	−15.2729	+	8.53859i	−0.906279	+	0.506672i
$285$	16.1818	+	8.12095i	0.958529	+	0.481044i
$286$	8.98537	+	5.27082i	0.531316	+	0.311670i
$287$	0.464739	+	4.80868i	0.0274326	+	0.283848i
$288$	13.9488	−	9.66593i	0.821942	−	0.569570i
$289$	−2.57444			−0.151438
$290$	10.9269	−	18.6275i	0.641648	−	1.09384i
$291$	24.0976	−	15.8593i	1.41263	−	0.929687i
$292$	−3.19300	+	1.78510i	−0.186856	+	0.104465i
$293$	5.93608	+	3.42720i	0.346789	+	0.200219i	0.663270	−	0.748380i	$-0.269168\pi$
$293$	5.93608	+	3.42720i	0.346789	+	0.200219i	−0.316481	+	0.948599i	$0.602501\pi$
$294$	−12.3352	+	11.9097i	−0.719406	+	0.694589i
$295$	5.83437	+	10.1054i	0.339690	+	0.588360i
$296$	15.9183	+	0.330039i	0.925234	+	0.0191831i
$297$	−4.59263	−	5.46363i	−0.266491	−	0.317032i
$298$	−15.6624	+	8.89898i	−0.907300	+	0.515504i
$299$	−25.9999	+	15.0111i	−1.50361	+	0.868112i
$300$	−9.02970	+	17.3889i	−0.521330	+	1.00395i
$301$	−3.86179	+	8.48188i	−0.222590	+	0.488887i
$302$	0.0511007	−	7.39497i	0.00294052	−	0.425533i
$303$	−0.766796	+	0.504648i	−0.0440513	+	0.0289913i
$304$	6.70845	−	10.9114i	0.384756	−	0.625812i
$305$			30.2990i			1.73492i
$306$	14.7554	+	6.47596i	0.843511	+	0.370206i
$307$	−1.01107			−0.0577051			−0.0288525	−	0.999584i	$-0.509185\pi$
$307$	−1.01107			−0.0577051			−0.0288525	+	0.999584i	$0.509185\pi$
$308$	0.599157	+	7.24371i	0.0341401	+	0.412748i
$309$	26.3702	+	13.2340i	1.50015	+	0.752858i
$310$	0.321232	−	46.4866i	0.0182447	−	2.64026i
$311$	4.47545	−	7.75170i	0.253779	−	0.439559i	−0.710784	−	0.703410i	$-0.751660\pi$
$311$	4.47545	−	7.75170i	0.253779	−	0.439559i	0.964563	+	0.263852i	$0.0849930\pi$
$312$	−23.2309	−	12.2679i	−1.31519	−	0.694532i
$313$	6.22159	−	3.59204i	0.351665	−	0.203034i	−0.313753	−	0.949505i	$-0.601586\pi$
$313$	6.22159	−	3.59204i	0.351665	−	0.203034i	0.665418	+	0.746471i	$0.268253\pi$
$314$	20.5737	−	11.6894i	1.16104	−	0.659672i
$315$	25.3231	−	5.48437i	1.42680	−	0.309009i
$316$	−15.5338	+	26.0666i	−0.873842	+	1.46636i
$317$	−12.6556	−	21.9201i	−0.710808	−	1.23116i	−0.964554	−	0.263885i	$-0.914996\pi$
$317$	−12.6556	−	21.9201i	−0.710808	−	1.23116i	0.253746	−	0.967271i	$-0.418337\pi$
$318$	−22.5420	−	11.5085i	−1.26409	−	0.645365i
$319$	−3.21282	+	5.56476i	−0.179883	+	0.311567i
$320$	22.0556	+	13.9837i	1.23295	+	0.781714i
$321$	1.39877	−	0.0818760i	0.0780719	−	0.00456987i
$322$	−19.0040	−	8.81155i	−1.05905	−	0.491049i
$323$	12.1621			0.676720
$324$	12.1856	+	13.2481i	0.676978	+	0.736004i
$325$	30.3318			1.68251
$326$	−8.26090	+	14.0827i	−0.457529	+	0.779966i
$327$	−1.64368	−	28.0807i	−0.0908957	−	1.55287i
$328$	−4.41823	−	2.67448i	−0.243956	−	0.147674i
$329$	−10.6976	−	4.87063i	−0.589780	−	0.268527i
$330$	4.99424	−	9.78232i	0.274924	−	0.538499i
$331$	8.38896	−	4.84337i	0.461099	−	0.266216i	−0.251407	−	0.967881i	$-0.580893\pi$
$331$	8.38896	−	4.84337i	0.461099	−	0.266216i	0.712506	+	0.701666i	$0.247560\pi$
$332$	3.79119	+	2.25927i	0.208069	+	0.123994i
$333$	1.97025	+	16.7722i	0.107969	+	0.919113i
$334$	−5.27559	+	2.99745i	−0.288668	+	0.164013i
$335$	12.7474	+	22.0791i	0.696464	+	1.20631i
$336$	−2.32485	−	18.1823i	−0.126831	−	0.991924i
$337$	−3.71267	+	6.43053i	−0.202242	+	0.350293i	−0.949250	−	0.314521i	$-0.898156\pi$
$337$	−3.71267	+	6.43053i	−0.202242	+	0.350293i	0.747009	+	0.664814i	$0.231489\pi$
$338$	−0.153985	+	22.2837i	−0.00837567	+	1.21207i
$339$	−0.181988	−	0.0913316i	−0.00988421	−	0.00496045i
$340$	−0.342687	+	24.7945i	−0.0185848	+	1.34467i
$341$			13.8320i			0.749044i
$342$	12.4402	+	5.45986i	0.672691	+	0.295235i
$343$	5.27886	+	17.7520i	0.285032	+	0.958518i
$344$	−4.80163	−	8.72972i	−0.258887	−	0.470675i
$345$	17.4018	+	26.4415i	0.936882	+	1.42356i
$346$	−3.00497	−	0.0207649i	−0.161548	−	0.00111633i
$347$	−14.9417	+	25.8798i	−0.802114	+	1.38930i	0.116107	+	0.993237i	$0.462958\pi$
$347$	−14.9417	+	25.8798i	−0.802114	+	1.38930i	−0.918222	+	0.396066i	$0.870375\pi$
$348$	7.46797	−	14.3814i	0.400325	−	0.770925i
$349$	−3.74785	−	6.49147i	−0.200618	−	0.347481i	0.748110	−	0.663575i	$-0.230962\pi$
$349$	−3.74785	−	6.49147i	−0.200618	−	0.347481i	−0.948728	+	0.316094i	$0.897628\pi$
$350$	12.1765	+	17.3098i	0.650861	+	0.925246i
$351$	9.50756	−	26.1926i	0.507476	−	1.39806i
$352$	−6.59105	−	4.11528i	−0.351304	−	0.219345i
$353$	13.2046	+	22.8711i	0.702812	+	1.21731i	0.967475	+	0.252965i	$0.0814058\pi$
$353$	13.2046	+	22.8711i	0.702812	+	1.21731i	−0.264663	+	0.964341i	$0.585261\pi$
$354$	4.76288	+	7.34710i	0.253144	+	0.390494i
$355$	14.2798	−	24.7333i	0.757892	−	1.31271i
$356$	−5.67857	−	10.1572i	−0.300964	−	0.538331i
$357$	13.5511	−	10.9227i	0.717199	−	0.578090i
$358$	25.6420	+	15.0416i	1.35522	+	0.794973i
$359$			11.4797i			0.605875i	0.953010	+	0.302937i	$0.0979673\pi$
$359$			11.4797i			0.605875i	−0.953010	+	0.302937i	$0.902033\pi$
$360$	−11.4813	+	25.2076i	−0.605120	+	1.32856i
$361$	−8.74613			−0.460323
$362$	−3.69136	−	2.16536i	−0.194014	−	0.113809i
$363$	7.08000	−	14.1076i	0.371604	−	0.740458i
$364$	−23.3213	+	16.1655i	−1.22237	+	0.847303i
$365$	2.98537	−	5.17082i	0.156262	−	0.270653i
$366$	1.17166	+	22.7052i	0.0612436	+	1.18682i
$367$	−3.90010	+	2.25172i	−0.203583	+	0.117539i	−0.598326	−	0.801253i	$-0.704167\pi$
$367$	−3.90010	+	2.25172i	−0.203583	+	0.117539i	0.394742	+	0.918792i	$0.370834\pi$
$368$	19.6956	−	10.6566i	1.02670	−	0.555515i
$369$	2.16679	−	5.03119i	0.112798	−	0.261913i
$370$	−22.5949	+	12.8378i	−1.17466	+	0.667408i
$371$	−22.2505	+	15.8830i	−1.15519	+	0.824602i
$372$	−1.55691	−	34.8482i	−0.0807220	−	1.80679i
$373$	−26.3500	−	15.2132i	−1.36435	−	0.787707i	−0.374150	−	0.927368i	$-0.622065\pi$
$373$	−26.3500	−	15.2132i	−1.36435	−	0.787707i	−0.990199	+	0.139661i	$0.955399\pi$
$374$	0.0509828	−	7.37791i	0.00263626	−	0.381503i
$375$	−0.216799	−	3.70380i	−0.0111955	−	0.191264i
$376$	11.0102	−	6.05599i	0.567809	−	0.312314i
$377$	−25.0858			−1.29198
$378$	18.7644	−	5.08907i	0.965135	−	0.261754i
$379$		−	22.2755i		−	1.14421i	−0.820179	−	0.572107i	$-0.806126\pi$
$379$		−	22.2755i		−	1.14421i	0.820179	−	0.572107i	$-0.193874\pi$
$380$	−0.288918	+	20.9042i	−0.0148212	+	1.07236i
$381$	4.52336	−	0.264771i	0.231739	−	0.0135646i
$382$	3.42977	+	0.0237004i	0.175482	+	0.00121262i
$383$	−13.0931	+	22.6779i	−0.669025	+	1.15879i	0.309152	+	0.951013i	$0.399955\pi$
$383$	−13.0931	+	22.6779i	−0.669025	+	1.15879i	−0.978177	+	0.207773i	$0.933378\pi$
$384$	17.0686	+	9.62611i	0.871030	+	0.491231i
$385$	−6.89257	−	9.65581i	−0.351278	−	0.492106i
$386$	−13.8249	+	7.85496i	−0.703671	+	0.399807i
$387$	8.47276	−	6.31537i	0.430695	−	0.321028i
$388$	28.6152	+	17.0525i	1.45272	+	0.865712i
$389$	2.47747	+	4.29110i	0.125613	+	0.217567i	0.921972	−	0.387256i	$-0.126577\pi$
$389$	2.47747	+	4.29110i	0.125613	+	0.217567i	−0.796360	+	0.604823i	$0.793244\pi$
$390$	42.8226	−	2.20978i	2.16841	−	0.111897i
$391$	18.4147	+	10.6317i	0.931270	+	0.537669i
$392$	−18.5875	−	6.81945i	−0.938810	−	0.344434i
$393$	14.8586	+	7.45686i	0.749516	+	0.376149i
$394$	8.99420	+	5.27600i	0.453121	+	0.265801i
$395$		−	49.5273i		−	2.49199i
$396$	3.36426	−	7.52372i	0.169060	−	0.378081i
$397$	−20.5241			−1.03007			−0.515037	−	0.857168i	$-0.672222\pi$
$397$	−20.5241			−1.03007			−0.515037	+	0.857168i	$0.672222\pi$
$398$	5.86719	−	10.0020i	0.294095	−	0.501355i
$399$	11.4249	−	9.20889i	0.571959	−	0.461021i
$400$	−22.6161	−	0.625277i	−1.13081	−	0.0312638i
$401$	−12.6873	−	7.32503i	−0.633574	−	0.365794i	0.148561	−	0.988903i	$-0.452536\pi$
$401$	−12.6873	−	7.32503i	−0.633574	−	0.365794i	−0.782135	+	0.623109i	$0.785869\pi$
$402$	10.4063	+	16.0525i	0.519020	+	0.800627i
$403$	−46.7657	+	27.0002i	−2.32956	+	1.34497i
$404$	−0.910546	−	0.542618i	−0.0453013	−	0.0269963i
$405$	−28.1549	−	8.39349i	−1.39903	−	0.417076i
$406$	−10.0705	−	14.3160i	−0.499791	−	0.710489i
$407$	6.69636	−	3.86615i	0.331926	−	0.191638i
$408$	0.702002	+	18.5936i	0.0347543	+	0.920519i
$409$	8.24750	+	4.76170i	0.407813	+	0.235451i	0.689849	−	0.723953i	$-0.257677\pi$
$409$	8.24750	+	4.76170i	0.407813	+	0.235451i	−0.282037	+	0.959404i	$0.591010\pi$
$410$	8.42950	+	0.0582495i	0.416303	+	0.00287674i
$411$	−19.8272	+	13.0488i	−0.978001	+	0.643648i
$412$	−0.470826	+	34.0658i	−0.0231959	+	1.67830i
$413$	9.41354	−	0.909778i	0.463210	−	0.0447672i
$414$	14.0629	+	19.1416i	0.691155	+	0.940757i
$415$	−7.20340			−0.353601
$416$	1.04789	−	30.3173i	0.0513771	−	1.48643i
$417$	1.69055	−	3.36859i	0.0827865	−	0.164961i
$418$	0.0429835	−	6.22029i	0.00210239	−	0.304245i
$419$	7.96945	+	4.60117i	0.389333	+	0.224782i	0.681871	−	0.731472i	$-0.261166\pi$
$419$	7.96945	+	4.60117i	0.389333	+	0.224782i	−0.292538	+	0.956254i	$0.594500\pi$
$420$	18.4519	+	23.5509i	0.900362	+	1.14917i
$421$	−13.0114	+	7.51216i	−0.634139	+	0.366120i	−0.782353	−	0.622835i	$-0.785981\pi$
$421$	−13.0114	+	7.51216i	−0.634139	+	0.366120i	0.148214	+	0.988955i	$0.452648\pi$
$422$	10.8409	+	19.0802i	0.527726	+	0.928812i
$423$	7.96517	+	10.6861i	0.387280	+	0.519578i
$424$	0.605804	−	29.2190i	0.0294204	−	1.41900i
$425$	−10.7414	−	18.6046i	−0.521034	−	0.902457i
$426$	9.74442	−	19.0866i	0.472119	−	0.924750i
$427$	22.3496	+	10.1758i	1.08157	+	0.492439i
$428$	0.789523	+	1.41221i	0.0381630	+	0.0682619i
$429$	−12.7366	+	0.745528i	−0.614930	+	0.0359944i
$430$	14.0265	+	8.22797i	0.676419	+	0.396788i
$431$		−	28.6677i		−	1.38088i	−0.723392	−	0.690438i	$-0.757418\pi$
$431$		−	28.6677i		−	1.38088i	0.723392	−	0.690438i	$-0.242582\pi$
$432$	−7.62901	+	19.3339i	−0.367051	+	0.930201i
$433$			15.8290i			0.760695i	0.924844	+	0.380348i	$0.124196\pi$
$433$			15.8290i			0.760695i	−0.924844	+	0.380348i	$0.875804\pi$
$434$	−34.1822	−	15.8492i	−1.64080	−	0.760787i
$435$	1.54554	+	26.4042i	0.0741032	+	1.26598i
$436$	28.3505	−	15.8499i	1.35774	−	0.759071i
$437$	15.5254	+	8.96357i	0.742678	+	0.428786i
$438$	2.03720	−	3.99031i	0.0973411	−	0.190664i
$439$	−14.7960	+	8.54246i	−0.706173	+	0.407709i	−0.809642	−	0.586923i	$-0.800339\pi$
$439$	−14.7960	+	8.54246i	−0.706173	+	0.407709i	0.103469	+	0.994633i	$0.467006\pi$
$440$	12.6799	+	0.262895i	0.604489	+	0.0125330i
$441$	4.45918	−	20.5211i	0.212342	−	0.977195i
$442$	25.0441	−	14.2294i	1.19123	−	0.676822i
$443$	6.18223	+	10.7079i	0.293727	+	0.508749i	0.974688	−	0.223570i	$-0.0717711\pi$
$443$	6.18223	+	10.7079i	0.293727	+	0.508749i	−0.680961	+	0.732319i	$0.738438\pi$
$444$	−16.4356	+	10.4941i	−0.779998	+	0.498026i
$445$	16.4488	+	9.49674i	0.779750	+	0.450189i
$446$	−17.6302	−	0.121828i	−0.834816	−	0.00576874i
$447$	9.89593	−	19.7187i	0.468062	−	0.932661i
$448$	17.7221	−	11.5726i	0.837292	−	0.546756i
$449$		−	34.0650i		−	1.60763i	−0.594881	−	0.803814i	$-0.702801\pi$
$449$		−	34.0650i		−	1.60763i	0.594881	−	0.803814i	$-0.297199\pi$
$450$	−2.63496	−	23.8521i	−0.124213	−	1.12440i
$451$	−2.50818			−0.118106
$452$	0.00324929	−	0.235097i	0.000152834	−	0.0110580i
$453$	4.97919	+	7.56571i	0.233943	+	0.355468i
$454$	−5.01199	−	0.0346338i	−0.235224	−	0.00162545i
$455$	19.1917	−	42.1519i	0.899723	−	1.97611i
$456$	0.591856	+	15.6762i	0.0277162	+	0.734104i
$457$	−8.64764	−	14.9782i	−0.404520	−	0.700649i	0.589746	−	0.807589i	$-0.299228\pi$
$457$	−8.64764	−	14.9782i	−0.404520	−	0.700649i	−0.994265	+	0.106940i	$0.965895\pi$
$458$	12.5085	−	7.10702i	0.584486	−	0.332089i
$459$	−19.4327	+	3.44393i	−0.907040	+	0.160749i
$460$	−18.7111	+	31.3984i	−0.872412	+	1.46396i
$461$	15.3919	−	8.88652i	0.716872	−	0.413886i	−0.0967281	−	0.995311i	$-0.530838\pi$
$461$	15.3919	−	8.88652i	0.716872	−	0.413886i	0.813600	+	0.581424i	$0.197504\pi$
$462$	−5.53849	−	6.96926i	−0.257674	−	0.324239i
$463$	−7.85727	+	13.6092i	−0.365158	+	0.632473i	−0.988802	−	0.149236i	$-0.952319\pi$
$463$	−7.85727	+	13.6092i	−0.365158	+	0.632473i	0.623643	+	0.781709i	$0.285652\pi$
$464$	18.7046	+	0.517132i	0.868337	+	0.0240073i
$465$	31.3004	+	47.5599i	1.45152	+	2.20554i
$466$	−2.66850	+	4.54908i	−0.123616	+	0.210732i
$467$		−	29.8632i		−	1.38190i	−0.722901	−	0.690952i	$-0.757192\pi$
$467$		−	29.8632i		−	1.38190i	0.722901	−	0.690952i	$-0.242808\pi$
$468$	32.0046	−	3.31189i	1.47941	−	0.153092i
$469$	20.5674	−	1.98775i	0.949716	−	0.0917859i
$470$	−10.3774	+	17.6908i	−0.478674	+	0.816014i
$471$	−12.9990	+	25.9018i	−0.598962	+	1.19349i
$472$	−5.23561	+	8.64918i	−0.240988	+	0.398111i
$473$	−4.19028	−	2.41926i	−0.192669	−	0.111238i
$474$	−1.91522	−	37.1144i	−0.0879688	−	1.70472i
$475$	−9.05603	−	15.6855i	−0.415519	−	0.719700i
$476$	18.1742	+	8.57988i	0.833013	+	0.393258i
$477$	30.7864	−	3.61650i	1.40961	−	0.165588i
$478$	2.86178	+	5.03681i	0.130895	+	0.230378i
$479$	−13.1376	−	22.7550i	−0.600273	−	1.03970i	−0.992779	−	0.119954i	$-0.961725\pi$
$479$	−13.1376	−	22.7550i	−0.600273	−	1.03970i	0.392506	−	0.919749i	$-0.371608\pi$
$480$	−31.9751	+	0.764895i	−1.45946	+	0.0349125i
$481$	26.1427	+	15.0935i	1.19201	+	0.688205i
$482$	6.35167	+	0.0438913i	0.289310	+	0.00199919i
$483$	25.3484	−	3.95595i	1.15339	−	0.180002i
$484$	18.2247	+	0.251884i	0.828394	+	0.0114493i
$485$	−54.3698			−2.46880
$486$	−21.4231	−	5.20109i	−0.971771	−	0.235926i
$487$	−26.5442			−1.20283			−0.601415	−	0.798937i	$-0.705396\pi$
$487$	−26.5442			−1.20283			−0.601415	+	0.798937i	$0.705396\pi$
$488$	−23.0026	+	12.6522i	−1.04128	+	0.572739i
$489$	−1.16846	−	19.9620i	−0.0528395	−	0.902712i
$490$	31.7596	−	5.96923i	1.43475	−	0.269662i
$491$	−3.19274	+	5.52998i	−0.144086	+	0.249565i	−0.929032	−	0.370000i	$-0.879358\pi$
$491$	−3.19274	+	5.52998i	−0.144086	+	0.249565i	0.784945	+	0.619565i	$0.212691\pi$
$492$	6.31908	−	0.282317i	0.284886	−	0.0127278i
$493$	8.88362	+	15.3869i	0.400098	+	0.692990i
$494$	21.1146	−	11.9967i	0.949990	−	0.539759i
$495$	1.56942	+	13.3601i	0.0705401	+	0.600490i
$496$	35.4262	−	19.1679i	1.59068	−	0.860665i
$497$	−13.4483	−	18.8398i	−0.603240	−	0.845080i
$498$	−5.39802	+	0.278554i	−0.241891	+	0.0124823i
$499$	−6.26715	−	3.61834i	−0.280556	−	0.161979i	0.353119	−	0.935578i	$-0.385121\pi$
$499$	−6.26715	−	3.61834i	−0.280556	−	0.161979i	−0.633675	+	0.773599i	$0.718454\pi$
$500$	3.73939	−	2.09057i	0.167231	−	0.0934933i
$501$	3.33326	−	6.64186i	0.148919	−	0.296736i
$502$	11.7148	−	19.9706i	0.522856	−	0.891332i
$503$	24.1526			1.07691			0.538456	−	0.842654i	$-0.319008\pi$
$503$	24.1526			1.07691			0.538456	+	0.842654i	$0.319008\pi$
$504$	14.7381	+	16.9349i	0.656485	+	0.754339i
$505$	1.73007			0.0769870
$506$	5.50264	−	9.38055i	0.244622	−	0.417016i
$507$	−15.0041	−	22.7982i	−0.666355	−	1.01250i
$508$	2.55317	+	4.56683i	0.113278	+	0.202620i
$509$	27.4850	+	15.8685i	1.21825	+	0.703357i	0.964543	−	0.263924i	$-0.0850169\pi$
$509$	27.4850	+	15.8685i	1.21825	+	0.703357i	0.253706	+	0.967281i	$0.418350\pi$
$510$	−16.5202	−	25.4836i	−0.731525	−	1.12843i
$511$	−2.81155	−	3.93870i	−0.124376	−	0.174238i
$512$	−1.40631	+	22.5837i	−0.0621507	+	0.998067i
$513$	−16.3836	+	2.90357i	−0.723356	+	0.128196i
$514$	4.06025	−	2.30693i	0.179090	−	0.101754i
$515$	−27.8036	−	48.1573i	−1.22517	−	2.12206i
$516$	10.8293	+	5.62340i	0.476731	+	0.247557i
$517$	3.05126	−	5.28493i	0.134194	−	0.232431i
$518$	1.88124	+	20.9783i	0.0826571	+	0.921734i
$519$	3.07435	−	2.02331i	0.134949	−	0.0888134i
$520$	23.8624	+	43.3836i	1.04644	+	1.90250i
$521$	−20.7010			−0.906926			−0.453463	−	0.891275i	$-0.649812\pi$
$521$	−20.7010			−0.906926			−0.453463	+	0.891275i	$0.649812\pi$
$522$	2.17923	+	19.7268i	0.0953824	+	0.863417i
$523$	−44.0553			−1.92641			−0.963203	−	0.268776i	$-0.913381\pi$
$523$	−44.0553			−1.92641			−0.963203	+	0.268776i	$0.913381\pi$
$524$	−0.265292	+	19.1948i	−0.0115893	+	0.838527i
$525$	−24.1772	−	9.34367i	−1.05518	−	0.407791i
$526$	−32.6969	−	0.225942i	−1.42565	−	0.00985154i
$527$	33.1222	+	19.1231i	1.44283	+	0.833016i
$528$	9.51210	−	0.293323i	0.413961	−	0.0127653i
$529$	4.17126	+	7.22483i	0.181359	+	0.314123i
$530$	23.5646	+	41.4743i	1.02358	+	1.80153i
$531$	−9.84912	−	4.24173i	−0.427415	−	0.184075i
$532$	15.3226	+	7.23367i	0.664319	+	0.313619i
$533$	−4.89599	−	8.48010i	−0.212069	−	0.367314i
$534$	12.6935	+	6.48051i	0.549303	+	0.280439i
$535$	−2.28697	−	1.32038i	−0.0988744	−	0.0570852i
$536$	−11.4392	+	18.8974i	−0.494096	+	0.816243i
$537$	−36.3471	+	2.12755i	−1.56849	+	0.0918104i
$538$	−20.4405	+	34.8456i	−0.881250	+	1.50230i
$539$	−9.43729	+	1.84135i	−0.406493	+	0.0793123i
$540$	−5.45776	−	33.4826i	−0.234865	−	1.44086i
$541$		−	8.01378i		−	0.344539i	−0.985050	−	0.172270i	$-0.944890\pi$
$541$		−	8.01378i		−	0.344539i	0.985050	−	0.172270i	$-0.0551100\pi$
$542$	−17.2375	+	29.3854i	−0.740415	+	1.26221i
$543$	5.23246	−	0.306277i	0.224546	−	0.0131436i
$544$	−18.9668	+	10.0935i	−0.813195	+	0.432755i
$545$	−26.5070	+	45.9115i	−1.13544	+	1.96663i
$546$	12.7517	−	32.3296i	0.545724	−	1.38358i
$547$	9.43514	−	5.44738i	0.403418	−	0.232913i	−0.284540	−	0.958664i	$-0.591841\pi$
$547$	9.43514	−	5.44738i	0.403418	−	0.232913i	0.687958	+	0.725751i	$0.258508\pi$
$548$	−23.5441	−	14.0306i	−1.00575	−	0.599356i
$549$	−16.6409	−	22.3256i	−0.710216	−	0.952832i
$550$	−9.55324	+	5.42790i	−0.407352	+	0.231446i
$551$	7.48975	+	12.9726i	0.319074	+	0.552653i
$552$	−12.8074	+	24.2526i	−0.545120	+	1.03226i
$553$	−36.5330	−	16.6335i	−1.55354	−	0.707327i
$554$	−33.4460	−	0.231119i	−1.42099	−	0.00981929i
$555$	14.2761	−	28.4466i	0.605986	−	1.20749i
$556$	4.35165	+	0.0601444i	0.184551	+	0.00255069i
$557$	42.5280			1.80197			0.900985	−	0.433851i	$-0.142845\pi$
$557$	42.5280			1.80197			0.900985	+	0.433851i	$0.142845\pi$
$558$	25.2948	+	34.4297i	1.07081	+	1.45752i
$559$		−	18.8897i		−	0.798948i
$560$	−15.1788	+	31.0338i	−0.641420	+	1.31142i
$561$	4.96770	+	7.54826i	0.209736	+	0.318688i
$562$	26.7238	+	0.184667i	1.12728	+	0.00778970i
$563$	−11.2415	−	6.49030i	−0.473774	−	0.273533i	0.244044	−	0.969764i	$-0.421526\pi$
$563$	−11.2415	−	6.49030i	−0.473774	−	0.273533i	−0.717818	+	0.696231i	$0.754859\pi$
$564$	−7.09244	+	13.6582i	−0.298645	+	0.575116i
$565$	0.191880	+	0.332346i	0.00807246	+	0.0139819i
$566$	−11.1373	+	6.32791i	−0.468135	+	0.265982i
$567$	−15.6470	+	17.9491i	−0.657112	+	0.753793i
$568$	24.7401	+	0.512943i	1.03807	+	0.0215226i
$569$	39.9276	−	23.0522i	1.67385	−	0.966399i	0.708404	−	0.705807i	$-0.249415\pi$
$569$	39.9276	−	23.0522i	1.67385	−	0.966399i	0.965449	−	0.260592i	$-0.0839179\pi$
$570$	−13.9281	−	21.4851i	−0.583384	−	0.899913i
$571$	−4.20640	−	2.42856i	−0.176032	−	0.101632i	0.409395	−	0.912357i	$-0.365740\pi$
$571$	−4.20640	−	2.42856i	−0.176032	−	0.101632i	−0.585427	+	0.810725i	$0.699073\pi$
$572$	−7.18906	−	12.8590i	−0.300590	−	0.537662i
$573$	−3.50896	+	2.30934i	−0.146589	+	0.0964739i
$574$	2.87397	−	6.19832i	0.119957	−	0.258713i
$575$		−	31.6658i		−	1.32056i
$576$	−23.9317	+	1.80966i	−0.997153	+	0.0754027i
$577$			8.61372i			0.358594i	0.983795	+	0.179297i	$0.0573823\pi$
$577$			8.61372i			0.358594i	−0.983795	+	0.179297i	$0.942618\pi$
$578$	3.14038	+	1.84215i	0.130623	+	0.0766233i
$579$	8.73496	−	17.4053i	0.363013	−	0.723340i
$580$	−26.6579	+	14.9036i	−1.10691	+	0.618837i
$581$	−2.41922	+	5.31347i	−0.100366	+	0.220440i
$582$	−40.7432	+	2.10247i	−1.68886	+	0.0871503i
$583$	−7.09652	−	12.2915i	−0.293908	−	0.509064i
$584$	5.17225	+	0.107237i	0.214029	+	0.00443752i
$585$	−42.1066	+	31.3851i	−1.74089	+	1.29762i
$586$	−4.78866	−	8.42817i	−0.197818	−	0.348165i
$587$	28.7257	−	16.5848i	1.18564	−	0.684528i	0.228326	−	0.973585i	$-0.426675\pi$
$587$	28.7257	−	16.5848i	1.18564	−	0.684528i	0.957312	+	0.289057i	$0.0933416\pi$
$588$	23.5689	−	5.70131i	0.971967	−	0.235118i
$589$	27.9252	+	16.1226i	1.15064	+	0.664322i
$590$	0.114030	−	16.5017i	0.00469454	−	0.679364i
$591$	−12.7492	+	0.746261i	−0.524430	+	0.0306971i
$592$	−19.1815	−	11.7930i	−0.788354	−	0.484689i
$593$	36.3837			1.49410			0.747050	−	0.664767i	$-0.231469\pi$
$593$	36.3837			1.49410			0.747050	+	0.664767i	$0.231469\pi$
$594$	1.69271	+	9.95096i	0.0694527	+	0.408293i
$595$	−32.6511	+	3.15559i	−1.33856	+	0.129366i
$596$	25.4732	+	0.352066i	1.04342	+	0.0144212i
$597$	0.829880	+	14.1777i	0.0339647	+	0.580255i
$598$	42.4567	+	0.293384i	1.73618	+	0.0119974i
$599$	−3.16383	−	1.82664i	−0.129271	−	0.0746345i	0.433970	−	0.900927i	$-0.357112\pi$
$599$	−3.16383	−	1.82664i	−0.129271	−	0.0746345i	−0.563241	+	0.826293i	$0.690446\pi$
$600$	23.4574	−	14.7503i	0.957643	−	0.602178i
$601$	34.9558	−	20.1818i	1.42588	−	0.823231i	0.429086	−	0.903264i	$-0.358836\pi$
$601$	34.9558	−	20.1818i	1.42588	−	0.823231i	0.996792	+	0.0800328i	$0.0255025\pi$
$602$	10.7800	−	7.58312i	0.439358	−	0.309065i
$603$	−21.5191	−	9.26765i	−0.876326	−	0.377408i
$604$	−5.35383	+	8.98404i	−0.217844	+	0.365555i
$605$	−25.7634	+	14.8745i	−1.04743	+	0.604734i
$606$	1.29646	−	0.0669015i	0.0526652	−	0.00271769i
$607$	−15.1967	−	8.77383i	−0.616816	−	0.356119i	0.158812	−	0.987309i	$-0.449234\pi$
$607$	−15.1967	−	8.77383i	−0.616816	−	0.356119i	−0.775628	+	0.631190i	$0.782567\pi$
$608$	−15.9908	+	8.50979i	−0.648515	+	0.345118i
$609$	19.9957	+	7.72764i	0.810265	+	0.313140i
$610$	21.6806	−	36.9596i	0.877820	−	1.49645i
$611$	23.8243			0.963829
$612$	−13.3652	−	18.4578i	−0.540256	−	0.746114i
$613$			33.1672i			1.33961i	0.742537	+	0.669805i	$0.233622\pi$
$613$			33.1672i			1.33961i	−0.742537	+	0.669805i	$0.766378\pi$
$614$	1.23334	+	0.723477i	0.0497735	+	0.0291972i
$615$	−8.62412	+	5.67576i	−0.347758	+	0.228869i
$616$	4.45239	−	9.26481i	0.179392	−	0.373290i
$617$	17.2437	+	9.95563i	0.694204	+	0.400799i	0.805185	−	0.593024i	$-0.202066\pi$
$617$	17.2437	+	9.95563i	0.694204	+	0.400799i	−0.110981	+	0.993823i	$0.535399\pi$
$618$	−22.6975	−	35.0125i	−0.913026	−	1.40841i
$619$	22.4708	+	38.9206i	0.903178	+	1.56435i	0.823344	+	0.567542i	$0.192106\pi$
$619$	22.4708	+	38.9206i	0.903178	+	1.56435i	0.0798336	+	0.996808i	$0.474561\pi$
$620$	−33.6555	+	56.4759i	−1.35164	+	2.26813i
$621$	−27.3446	−	9.92571i	−1.09730	−	0.398305i
$622$	−11.0060	+	6.25333i	−0.441302	+	0.250736i
$623$	12.5294	−	8.94379i	0.501979	−	0.358325i
$624$	19.5594	+	31.5877i	0.783004	+	1.26452i
$625$	10.6442	−	18.4364i	0.425769	−	0.737454i
$626$	−10.1596	−	0.0702047i	−0.406058	−	0.00280594i
$627$	4.18825	+	6.36391i	0.167263	+	0.254150i
$628$	−33.4608	−	0.462463i	−1.33523	−	0.0184543i
$629$		−	21.3802i		−	0.852485i
$630$	−34.8143	−	11.4301i	−1.38703	−	0.455384i
$631$	31.0143			1.23466			0.617329	−	0.786705i	$-0.288215\pi$
$631$	31.0143			1.23466			0.617329	+	0.786705i	$0.288215\pi$
$632$	37.6005	−	20.6815i	1.49567	−	0.822667i
$633$	−24.0216	−	12.0554i	−0.954774	−	0.479159i
$634$	−0.247347	+	35.7945i	−0.00982342	+	1.42158i
$635$	−7.39563	−	4.26987i	−0.293487	−	0.169445i
$636$	19.2624	+	30.1684i	0.763805	+	1.19625i
$637$	−24.6472	−	28.3130i	−0.976559	−	1.12180i
$638$	7.90097	−	4.48912i	0.312802	−	0.177726i
$639$	3.06214	+	26.0673i	0.121136	+	1.03121i
$640$	−16.8980	−	32.8397i	−0.667954	−	1.29810i
$641$	−12.6860	+	7.32429i	−0.501068	+	0.289292i	−0.729155	−	0.684349i	$-0.760086\pi$
$641$	−12.6860	+	7.32429i	−0.501068	+	0.289292i	0.228086	+	0.973641i	$0.426753\pi$
$642$	−1.76485	−	0.901021i	−0.0696531	−	0.0355605i
$643$	−8.12747	+	14.0772i	−0.320516	+	0.555150i	−0.980595	−	0.196047i	$-0.937190\pi$
$643$	−8.12747	+	14.0772i	−0.320516	+	0.555150i	0.660079	+	0.751197i	$0.270523\pi$
$644$	16.8765	+	24.3470i	0.665027	+	0.959404i
$645$	−19.8824	+	1.16380i	−0.782869	+	0.0458246i
$646$	−14.8357	−	8.70266i	−0.583705	−	0.342402i
$647$	28.5250			1.12144			0.560718	−	0.828007i	$-0.310525\pi$
$647$	28.5250			1.12144			0.560718	+	0.828007i	$0.310525\pi$
$648$	−5.38466	−	24.8798i	−0.211529	−	0.977372i
$649$			4.91004i			0.192736i
$650$	−36.9996	−	21.7040i	−1.45124	−	0.851301i
$651$	45.5939	−	7.11550i	1.78697	−	0.278879i
$652$	20.1538	−	11.2673i	0.789283	−	0.441263i
$653$	4.64239	−	8.04086i	0.181671	−	0.314663i	−0.760779	−	0.649011i	$-0.775183\pi$
$653$	4.64239	−	8.04086i	0.181671	−	0.314663i	0.942450	+	0.334348i	$0.108516\pi$
$654$	−18.0882	+	35.4298i	−0.707306	+	1.38542i
$655$	−15.6663	−	27.1347i	−0.612131	−	1.06024i
$656$	3.47575	+	6.42389i	0.135705	+	0.250811i
$657$	0.640181	+	5.44970i	0.0249758	+	0.212613i
$658$	9.56410	+	13.5961i	0.372848	+	0.530030i
$659$	−6.55142	−	11.3474i	−0.255207	−	0.442031i	0.709745	−	0.704459i	$-0.248810\pi$
$659$	−6.55142	−	11.3474i	−0.255207	−	0.442031i	−0.964952	+	0.262428i	$0.915477\pi$
$660$	−13.0919	+	8.35913i	−0.509601	+	0.325379i
$661$	−10.9792	+	19.0166i	−0.427043	+	0.739660i	−0.996609	−	0.0822855i	$-0.973778\pi$
$661$	−10.9792	+	19.0166i	−0.427043	+	0.739660i	0.569566	+	0.821946i	$0.307111\pi$
$662$	−13.6988	−	0.0946614i	−0.532419	−	0.00367912i
$663$	−15.8235	+	31.5300i	−0.614534	+	1.22452i
$664$	−3.00798	−	5.46873i	−0.116732	−	0.212228i
$665$	−27.5280	+	2.66046i	−1.06749	+	0.103168i
$666$	9.59806	−	21.8691i	0.371917	−	0.847410i
$667$			26.1891i			1.01405i
$668$	8.58016	+	0.118587i	0.331976	+	0.00458826i
$669$	18.0373	−	11.8708i	0.697362	−	0.458952i
$670$	0.249141	−	36.0542i	0.00962517	−	1.39289i
$671$	−6.37470	+	11.0413i	−0.246093	+	0.426245i
$672$	−10.1745	+	23.8428i	−0.392488	+	0.919757i
$673$	−7.41541	−	12.8439i	−0.285843	−	0.495095i	0.686970	−	0.726686i	$-0.258940\pi$
$673$	−7.41541	−	12.8439i	−0.285843	−	0.495095i	−0.972813	+	0.231591i	$0.925607\pi$
$674$	9.13021	−	5.18754i	0.351682	−	0.199817i
$675$	18.9114	+	22.4979i	0.727899	+	0.865946i
$676$	16.1330	−	27.0721i	0.620500	−	1.04124i
$677$	−8.19779	+	4.73300i	−0.315067	+	0.181904i	−0.649191	−	0.760625i	$-0.724893\pi$
$677$	−8.19779	+	4.73300i	−0.315067	+	0.181904i	0.334125	+	0.942529i	$0.391559\pi$
$678$	0.156641	+	0.241631i	0.00601577	+	0.00927978i
$679$	−18.2598	+	40.1050i	−0.700746	+	1.53909i
$680$	18.1598	−	29.9999i	0.696397	−	1.15044i
$681$	5.12771	−	3.37468i	0.196494	−	0.129318i
$682$	9.89752	−	16.8727i	0.378996	−	0.646088i
$683$	21.1814			0.810484			0.405242	−	0.914210i	$-0.367187\pi$
$683$	21.1814			0.810484			0.405242	+	0.914210i	$0.367187\pi$
$684$	−11.2682	−	15.5617i	−0.430849	−	0.595018i
$685$	44.7346			1.70922
$686$	6.26319	−	25.4317i	0.239130	−	0.970988i
$687$	−7.90323	+	15.7480i	−0.301527	+	0.600823i
$688$	−0.389402	+	14.0846i	−0.0148458	+	0.536970i
$689$	27.7050	−	47.9864i	1.05548	−	1.82814i
$690$	−2.30697	−	44.7060i	−0.0878248	−	1.70193i
$691$	−1.94647	−	3.37139i	−0.0740473	−	0.128254i	0.826624	−	0.562754i	$-0.190258\pi$
$691$	−1.94647	−	3.37139i	−0.0740473	−	0.128254i	−0.900672	+	0.434500i	$0.856925\pi$
$692$	3.65069	+	2.17554i	0.138779	+	0.0827018i
$693$	10.3819	+	3.32925i	0.394376	+	0.126468i
$694$	36.7448	−	20.8774i	1.39481	−	0.792495i
$695$	−6.15173	+	3.55170i	−0.233348	+	0.134724i
$696$	−19.4003	+	12.1992i	−0.735367	+	0.462408i
$697$	−3.46763	+	6.00611i	−0.131346	+	0.227497i
$698$	−0.0732500	+	10.6003i	−0.00277255	+	0.401226i
$699$	−0.377444	−	6.44826i	−0.0142762	−	0.243896i
$700$	−2.46719	−	29.8279i	−0.0932509	−	1.12739i
$701$	−7.15162			−0.270113			−0.135056	−	0.990838i	$-0.543122\pi$
$701$	−7.15162			−0.270113			−0.135056	+	0.990838i	$0.543122\pi$
$702$	−30.3398	+	25.1474i	−1.14510	+	0.949127i
$703$		−	18.0256i		−	0.679848i
$704$	5.09525	+	9.73618i	0.192035	+	0.366946i
$705$	−1.46783	−	25.0764i	−0.0552815	−	0.944432i
$706$	0.258078	−	37.3475i	0.00971291	−	1.40559i
$707$	0.581033	−	1.27616i	0.0218520	−	0.0479948i
$708$	−0.552667	−	12.3703i	−0.0207705	−	0.464905i
$709$	12.2856	−	7.09308i	0.461394	−	0.266386i	−0.251236	−	0.967926i	$-0.580837\pi$
$709$	12.2856	−	7.09308i	0.461394	−	0.266386i	0.712630	+	0.701540i	$0.247504\pi$
$710$	−35.1169	+	19.9525i	−1.31791	+	0.748803i
$711$	27.2015	+	36.4938i	1.02014	+	1.36862i
$712$	−0.341132	+	16.4534i	−0.0127845	+	0.616617i
$713$	28.1877	+	48.8225i	1.05564	+	1.82842i
$714$	−24.3458	+	3.62732i	−0.911117	+	0.135749i
$715$	20.8242	+	12.0229i	0.778781	+	0.449629i
$716$	−20.5158	−	36.6963i	−0.766710	−	1.37141i
$717$	−6.34123	−	3.18239i	−0.236818	−	0.118848i
$718$	8.21433	−	14.0033i	0.306556	−	0.522597i
$719$	−49.3903			−1.84195			−0.920974	−	0.389623i	$-0.872605\pi$
$719$	−49.3903			−1.84195			−0.920974	+	0.389623i	$0.872605\pi$
$720$	32.0427	−	22.5335i	1.19416	−	0.839774i
$721$	−44.8601	+	4.33554i	−1.67068	+	0.161464i
$722$	10.6688	+	6.25832i	0.397051	+	0.232911i
$723$	−6.49832	+	4.27671i	−0.241675	+	0.159053i
$724$	2.95341	+	5.28273i	0.109763	+	0.196331i
$725$	13.2296	−	22.9144i	0.491336	−	0.851018i
$726$	−18.7311	+	12.1428i	−0.695178	+	0.450661i
$727$	2.38793	−	1.37867i	0.0885633	−	0.0511320i	−0.455064	−	0.890459i	$-0.650384\pi$
$727$	2.38793	−	1.37867i	0.0885633	−	0.0511320i	0.543628	+	0.839327i	$0.317050\pi$
$728$	40.0152	−	3.03158i	1.48306	−	0.112358i
$729$	25.3556	−	9.27865i	0.939097	−	0.343654i
$730$	−7.34164	+	4.17132i	−0.271726	+	0.154388i
$731$	−11.5864	+	6.68939i	−0.428537	+	0.247416i
$732$	14.8176	−	28.5349i	0.547673	−	1.05468i
$733$	6.51450	−	11.2834i	0.240619	−	0.416764i	−0.720272	−	0.693692i	$-0.755983\pi$
$733$	6.51450	−	11.2834i	0.240619	−	0.416764i	0.960891	+	0.276928i	$0.0893164\pi$
$734$	6.36868	+	0.0440088i	0.235072	+	0.00162440i
$735$	−28.2824	+	27.6869i	−1.04321	+	1.02125i
$736$	−31.6507	−	1.09398i	−1.16666	−	0.0403246i
$737$			10.7278i			0.395165i
$738$	−6.24319	+	4.58674i	−0.229815	+	0.168840i
$739$			17.7977i			0.654697i	0.944904	+	0.327349i	$0.106155\pi$
$739$			17.7977i			0.654697i	−0.944904	+	0.327349i	$0.893845\pi$
$740$	36.7481	+	0.507898i	1.35089	+	0.0186707i
$741$	−13.3407	+	26.5828i	−0.490085	+	0.976544i
$742$	38.5069	−	3.45313i	1.41363	−	0.126768i
$743$	34.5075	+	19.9229i	1.26596	+	0.730901i	0.974221	−	0.225597i	$-0.0724333\pi$
$743$	34.5075	+	19.9229i	1.26596	+	0.730901i	0.291738	+	0.956498i	$0.405767\pi$
$744$	−23.0365	+	43.6229i	−0.844561	+	1.59929i
$745$	−36.0103	+	20.7905i	−1.31931	+	0.761706i
$746$	21.2566	+	37.4122i	0.778261	+	1.36976i
$747$	5.30776	−	3.95626i	0.194201	−	0.144752i
$748$	−5.34148	+	8.96331i	−0.195304	+	0.327731i
$749$	−1.74203	+	1.24350i	−0.0636523	+	0.0454367i
$750$	−2.38581	+	4.67314i	−0.0871175	+	0.170639i
$751$	9.19443	−	15.9252i	0.335510	−	0.581120i	−0.648073	−	0.761578i	$-0.724425\pi$
$751$	9.19443	−	15.9252i	0.335510	−	0.581120i	0.983583	+	0.180459i	$0.0577582\pi$
$752$	−17.7640	−	0.491128i	−0.647786	−	0.0179096i
$753$	1.65699	+	28.3081i	0.0603840	+	1.03160i
$754$	30.6004	+	17.9502i	1.11440	+	0.653708i
$755$		−	17.0700i		−	0.621240i
$756$	−26.5308	−	7.21910i	−0.964917	−	0.262556i
$757$			38.9175i			1.41448i	0.706974	+	0.707240i	$0.250060\pi$
$757$			38.9175i			1.41448i	−0.706974	+	0.707240i	$0.749940\pi$
$758$	−15.9393	+	27.1723i	−0.578941	+	0.986942i
$759$	0.778317	+	13.2968i	0.0282511	+	0.482643i
$760$	15.3105	−	25.2928i	0.555370	−	0.917467i
$761$	15.4843	−	26.8196i	0.561305	−	0.972209i	−0.436078	−	0.899909i	$-0.643633\pi$
$761$	15.4843	−	26.8196i	0.561305	−	0.972209i	0.997383	−	0.0723002i	$-0.0230340\pi$
$762$	−5.70719	−	2.91373i	−0.206750	−	0.105553i
$763$	24.9637	+	34.9716i	0.903745	+	1.26606i
$764$	−4.16678	−	2.48309i	−0.150749	−	0.0898352i
$765$	34.1619	+	14.7125i	1.23513	+	0.531932i
$766$	32.1986	−	18.2944i	1.16338	−	0.661002i
$767$	−16.6007	+	9.58445i	−0.599418	+	0.346074i
$768$	−13.9328	−	23.9557i	−0.502757	−	0.864428i
$769$	11.7152	+	6.76375i	0.422459	+	0.243907i	0.696129	−	0.717917i	$-0.254904\pi$
$769$	11.7152	+	6.76375i	0.422459	+	0.243907i	−0.273670	+	0.961824i	$0.588237\pi$
$770$	1.49852	+	16.7104i	0.0540029	+	0.602203i
$771$	−2.56537	+	5.11177i	−0.0923897	+	0.184096i
$772$	22.4847	+	0.310763i	0.809243	+	0.0111846i
$773$		−	25.4343i		−	0.914808i	−0.889259	−	0.457404i	$-0.848779\pi$
$773$		−	25.4343i		−	0.914808i	0.889259	−	0.457404i	$-0.151221\pi$
$774$	−14.8543	+	1.64097i	−0.533927	+	0.0589834i
$775$		−	56.9569i		−	2.04595i
$776$	−22.7036	−	41.2769i	−0.815013	−	1.48175i
$777$	−16.1886	−	20.0841i	−0.580763	−	0.720514i
$778$	0.0484209	−	7.00717i	0.00173597	−	0.251219i
$779$	−2.92355	+	5.06373i	−0.104747	+	0.181427i
$780$	−53.8175	−	27.9463i	−1.92698	−	1.00064i
$781$	10.4074	−	6.00873i	0.372407	−	0.215009i
$782$	−14.8552	−	26.1455i	−0.531221	−	0.934963i
$783$	−15.6406	−	18.6068i	−0.558948	−	0.664954i
$784$	17.7939	+	21.6189i	0.635496	+	0.772104i
$785$	47.3020	−	27.3098i	1.68828	−	0.974728i
$786$	−12.7891	−	19.7282i	−0.456174	−	0.703681i
$787$	11.0828	−	19.1959i	0.395058	−	0.684261i	−0.598050	−	0.801459i	$-0.704058\pi$
$787$	11.0828	−	19.1959i	0.395058	−	0.684261i	0.993109	+	0.117198i	$0.0373911\pi$
$788$	−7.19613	−	12.8717i	−0.256351	−	0.458534i
$789$	33.4518	−	22.0155i	1.19092	−	0.783773i
$790$	−35.4394	+	60.4149i	−1.26088	+	2.14947i
$791$	0.309592	−	0.0299207i	0.0110078	−	0.00106386i
$792$	−9.48744	+	6.77035i	−0.337122	+	0.240574i
$793$	−49.7739			−1.76752
$794$	25.0359	+	14.6861i	0.888491	+	0.521189i
$795$	−52.2152	−	26.2045i	−1.85188	−	0.929379i
$796$	−14.3139	+	8.00246i	−0.507344	+	0.283640i
$797$	19.7595	+	11.4082i	0.699918	+	0.404098i	0.807317	−	0.590118i	$-0.200919\pi$
$797$	19.7595	+	11.4082i	0.699918	+	0.404098i	−0.107399	+	0.994216i	$0.534252\pi$
$798$	−20.5258	+	3.05818i	−0.726607	+	0.108258i
$799$	−8.43689	−	14.6131i	−0.298476	−	0.516975i
$800$	27.1404	+	16.9458i	0.959558	+	0.599123i
$801$	−17.3360	+	2.03647i	−0.612537	+	0.0719552i
$802$	10.2349	+	18.0137i	0.361408	+	0.636087i
$803$	2.17581	−	1.25620i	0.0767826	−	0.0443305i
$804$	−1.20751	−	27.0276i	−0.0425856	−	0.953190i
$805$	−44.0058	−	20.0358i	−1.55100	−	0.706170i
$806$	76.3662	+	0.527706i	2.68989	+	0.0185876i
$807$	−2.89119	−	49.3931i	−0.101775	−	1.73872i
$808$	0.722438	+	1.31345i	0.0254153	+	0.0462069i
$809$		−	28.8273i		−	1.01351i	−0.862089	−	0.506757i	$-0.830844\pi$
$809$		−	28.8273i		−	1.01351i	0.862089	−	0.506757i	$-0.169156\pi$
$810$	28.3382	+	30.3850i	0.995704	+	1.06762i
$811$	−10.8394			−0.380621			−0.190311	−	0.981724i	$-0.560949\pi$
$811$	−10.8394			−0.380621			−0.190311	+	0.981724i	$0.560949\pi$
$812$	2.04048	+	24.6690i	0.0716067	+	0.865713i
$813$	−2.43815	−	41.6534i	−0.0855096	−	1.46085i
$814$	−10.9349	−	0.0755620i	−0.383266	−	0.00264845i
$815$	−18.8433	+	32.6375i	−0.660051	+	1.14324i
$816$	12.4484	−	23.1833i	0.435780	−	0.811578i
$817$	−9.76843	+	5.63980i	−0.341754	+	0.197312i
$818$	−6.65330	−	11.7100i	−0.232627	−	0.409430i
$819$	9.00948	+	41.5998i	0.314817	+	1.45361i
$820$	−10.2409	−	6.10281i	−0.357627	−	0.213119i
$821$	9.14093	+	15.8326i	0.319021	+	0.552560i	0.980284	−	0.197594i	$-0.0633127\pi$
$821$	9.14093	+	15.8326i	0.319021	+	0.552560i	−0.661263	+	0.750154i	$0.729979\pi$
$822$	33.5228	−	1.72988i	1.16924	−	0.0603365i
$823$	14.2450	−	24.6730i	0.496549	−	0.860048i	−0.503443	−	0.864028i	$-0.667934\pi$
$823$	14.2450	−	24.6730i	0.496549	−	0.860048i	0.999992	+	0.00398013i	$0.00126692\pi$
$824$	24.9502	−	41.2176i	0.869182	−	1.43588i
$825$	6.03599	−	12.0273i	0.210146	−	0.418738i
$826$	−12.1339	−	5.62611i	−0.422193	−	0.195757i
$827$	−23.8157			−0.828153			−0.414077	−	0.910242i	$-0.635895\pi$
$827$	−23.8157			−0.828153			−0.414077	+	0.910242i	$0.635895\pi$
$828$	−3.45755	−	33.4122i	−0.120158	−	1.16115i
$829$	14.1272			0.490659			0.245329	−	0.969440i	$-0.421104\pi$
$829$	14.1272			0.490659			0.245329	+	0.969440i	$0.421104\pi$
$830$	8.78691	+	5.15441i	0.304998	+	0.178912i
$831$	34.2182	−	22.5199i	1.18702	−	0.781207i
$832$	−22.9719	+	36.2321i	−0.796406	+	1.25612i
$833$	−8.63801	+	25.1443i	−0.299289	+	0.871199i
$834$	−4.47259	+	2.89943i	−0.154873	+	0.100399i
$835$	−12.1294	+	7.00290i	−0.419754	+	0.242345i
$836$	−4.50338	+	7.55694i	−0.155753	+	0.261362i
$837$	−49.1844	−	17.8532i	−1.70006	−	0.617098i
$838$	−6.42900	−	11.3152i	−0.222086	−	0.390877i
$839$	−2.81259	−	4.87155i	−0.0971015	−	0.168185i	0.813382	−	0.581730i	$-0.197624\pi$
$839$	−2.81259	−	4.87155i	−0.0971015	−	0.168185i	−0.910484	+	0.413545i	$0.864290\pi$
$840$	−5.65626	−	41.9315i	−0.195159	−	1.44677i
$841$	3.55850	−	6.16350i	0.122707	−	0.212535i
$842$	21.2471	+	0.146822i	0.732223	+	0.00505981i
$843$	−27.3408	+	17.9937i	−0.941668	+	0.619736i
$844$	0.428893	−	31.0319i	0.0147631	−	1.06816i
$845$			51.4379i			1.76952i
$846$	−2.06965	−	18.7348i	−0.0711559	−	0.644115i
$847$	2.31944	+	23.9995i	0.0796970	+	0.824631i
$848$	−21.6467	+	35.2087i	−0.743351	+	1.20907i
$849$	7.03683	−	14.0216i	0.241503	−	0.481220i
$850$	−0.209935	+	30.3805i	−0.00720072	+	1.04204i
$851$	15.7573	−	27.2925i	0.540154	−	0.935575i
$852$	−25.5440	+	16.3098i	−0.875124	+	0.558764i
$853$	−27.3976	−	47.4541i	−0.938076	−	1.62480i	−0.769054	−	0.639183i	$-0.779272\pi$
$853$	−27.3976	−	47.4541i	−0.938076	−	1.62480i	−0.169022	−	0.985612i	$-0.554061\pi$
$854$	−19.9814	−	28.4050i	−0.683749	−	0.971999i
$855$	28.8018	+	12.4041i	0.985001	+	0.424211i
$856$	0.0474294	−	2.28760i	0.00162110	−	0.0781887i
$857$	−21.7943	−	37.7488i	−0.744478	−	1.28947i	−0.950438	−	0.310914i	$-0.899365\pi$
$857$	−21.7943	−	37.7488i	−0.744478	−	1.28947i	0.205960	−	0.978560i	$-0.433968\pi$
$858$	16.0700	+	8.20432i	0.548620	+	0.280091i
$859$	12.9118	−	22.3639i	0.440545	−	0.763046i	−0.557185	−	0.830388i	$-0.688119\pi$
$859$	12.9118	−	22.3639i	0.440545	−	0.763046i	0.997730	+	0.0673423i	$0.0214519\pi$
$860$	−11.2224	−	20.0734i	−0.382681	−	0.684499i
$861$	1.29027	+	8.26762i	0.0439722	+	0.281760i
$862$	−20.5133	+	34.9697i	−0.698685	+	1.19107i
$863$		−	5.30974i		−	0.180746i	−0.995908	−	0.0903728i	$-0.971194\pi$
$863$		−	5.30974i		−	0.180746i	0.995908	−	0.0903728i	$-0.0288059\pi$
$864$	23.1405	−	18.1251i	0.787256	−	0.616627i
$865$	−6.93644			−0.235846
$866$	11.3265	−	19.3087i	0.384891	−	0.656138i
$867$	−4.45144	+	0.260561i	−0.151179	+	0.00884913i
$868$	30.3555	+	43.7925i	1.03033	+	1.48642i
$869$	10.4202	−	18.0483i	0.353481	−	0.612248i
$870$	17.0083	−	33.3145i	0.576634	−	1.12947i
$871$	−36.2706	+	20.9408i	−1.22898	+	0.709553i
$872$	−45.9242	−	0.952158i	−1.55519	−	0.0322441i
$873$	40.0619	−	29.8611i	1.35589	−	1.01064i
$874$	−12.5244	−	22.0432i	−0.423643	−	0.745623i
$875$	3.29267	+	4.61271i	0.111313	+	0.155938i
$876$	−5.34031	+	3.40977i	−0.180432	+	0.115206i
$877$	12.7473	+	7.35967i	0.430446	+	0.248518i	0.699537	−	0.714597i	$-0.253390\pi$
$877$	12.7473	+	7.35967i	0.430446	+	0.248518i	−0.269090	+	0.963115i	$0.586723\pi$
$878$	24.1611	+	0.166958i	0.815399	+	0.00563457i
$879$	10.6109	+	5.32514i	0.357896	+	0.179612i
$880$	−15.2792	−	9.39381i	−0.515061	−	0.316665i
$881$	0.816537			0.0275098			0.0137549	−	0.999905i	$-0.495622\pi$
$881$	0.816537			0.0275098			0.0137549	+	0.999905i	$0.495622\pi$
$882$	−20.1234	+	21.8415i	−0.677589	+	0.735440i
$883$			35.1168i			1.18177i	0.806755	+	0.590886i	$0.201222\pi$
$883$			35.1168i			1.18177i	−0.806755	+	0.590886i	$0.798778\pi$
$884$	−40.7314	−	0.562951i	−1.36994	−	0.0189341i
$885$	11.1109	+	16.8827i	0.373490	+	0.567505i
$886$	0.120829	−	17.4856i	0.00405932	−	0.587439i
$887$	3.86884	−	6.70103i	0.129903	−	0.224999i	−0.793736	−	0.608263i	$-0.791867\pi$
$887$	3.86884	−	6.70103i	0.129903	−	0.224999i	0.923639	+	0.383264i	$0.125200\pi$
$888$	27.5576	−	1.04044i	0.924774	−	0.0349149i
$889$	−5.63338	+	4.02126i	−0.188938	+	0.134869i
$890$	−13.2694	−	23.3544i	−0.444790	−	0.782842i
$891$	−8.49405	−	8.98229i	−0.284561	−	0.300918i
$892$	21.4187	+	12.7640i	0.717151	+	0.427370i
$893$	−7.11312	−	12.3203i	−0.238031	−	0.412283i
$894$	−26.1811	+	16.9724i	−0.875627	+	0.567640i
$895$	59.4270	+	34.3102i	1.98642	+	1.14686i
$896$	−29.8988	+	1.43552i	−0.998849	+	0.0479574i
$897$	−43.4369	+	28.5870i	−1.45032	+	0.954491i
$898$	−24.3753	+	41.5535i	−0.813415	+	1.38666i
$899$			47.1059i			1.57107i
$900$	−13.8532	+	30.9809i	−0.461774	+	1.03270i
$901$	−39.2446			−1.30743
$902$	3.05955	+	1.79473i	0.101872	+	0.0597581i
$903$	−5.81894	+	15.0568i	−0.193642	+	0.501059i
$904$	−0.172188	+	0.284454i	−0.00572689	+	0.00946079i
$905$	−8.55499	−	4.93922i	−0.284377	−	0.164185i
$906$	−0.660094	−	12.7918i	−0.0219301	−	0.424977i
$907$	14.2113	−	8.20487i	0.471877	−	0.272438i	−0.245148	−	0.969486i	$-0.578837\pi$
$907$	14.2113	−	8.20487i	0.471877	−	0.272438i	0.717025	+	0.697047i	$0.245503\pi$
$908$	6.08899	+	3.62859i	0.202070	+	0.120419i
$909$	−1.27478	+	0.950191i	−0.0422819	+	0.0315158i
$910$	−53.5726	+	37.6854i	−1.77591	+	1.24926i
$911$	−24.6180	+	14.2132i	−0.815630	+	0.470904i	−0.848907	−	0.528542i	$-0.822739\pi$
$911$	−24.6180	+	14.2132i	−0.815630	+	0.470904i	0.0332774	+	0.999446i	$0.489406\pi$
$912$	10.4952	−	19.5458i	0.347530	−	0.647225i
$913$	−2.62500	−	1.51554i	−0.0868748	−	0.0501572i
$914$	−0.169014	+	24.4586i	−0.00559049	+	0.809020i
$915$	3.06659	+	52.3898i	0.101378	+	1.73195i
$916$	−20.3437	−	0.281172i	−0.672176	−	0.00929019i
$917$	−25.2769	+	2.44291i	−0.834718	+	0.0806719i
$918$	26.1689	+	9.70411i	0.863702	+	0.320283i
$919$	−44.9942			−1.48422			−0.742110	−	0.670278i	$-0.766175\pi$
$919$	−44.9942			−1.48422			−0.742110	+	0.670278i	$0.766175\pi$
$920$	45.2916	−	24.9119i	1.49322	−	0.821321i
$921$	−1.74824	+	0.102332i	−0.0576065	+	0.00337195i
$922$	−25.1343	−	0.173683i	−0.827753	−	0.00571994i
$923$	40.6308	+	23.4582i	1.33738	+	0.772136i
$924$	1.76914	+	12.4644i	0.0582004	+	0.410048i
$925$	−27.5740	+	15.9199i	−0.906629	+	0.523442i
$926$	19.3226	−	10.9786i	0.634981	−	0.360779i
$927$	46.9359	+	20.2139i	1.54158	+	0.663912i
$928$	−22.4463	−	14.0149i	−0.736837	−	0.460062i
$929$	18.9733	+	32.8627i	0.622493	+	1.07819i	0.989020	+	0.147782i	$0.0472134\pi$
$929$	18.9733	+	32.8627i	0.622493	+	1.07819i	−0.366527	+	0.930407i	$0.619453\pi$
$930$	−4.14951	−	80.4121i	−0.136068	−	2.63682i
$931$	−7.28268	+	21.1991i	−0.238680	+	0.694773i
$932$	6.51022	−	3.63966i	0.213249	−	0.119221i
$933$	6.95390	−	13.8564i	0.227660	−	0.453637i
$934$	−21.3687	+	36.4280i	−0.699205	+	1.19196i
$935$		−	17.0306i		−	0.556960i
$936$	−41.4100	−	18.8611i	−1.35353	−	0.616493i
$937$		−	37.8218i		−	1.23559i	−0.786341	−	0.617793i	$-0.788027\pi$
$937$		−	37.8218i		−	1.23559i	0.786341	−	0.617793i	$-0.211973\pi$
$938$	−26.5111	−	12.2924i	−0.865618	−	0.401360i
$939$	10.3941	−	6.84065i	0.339200	−	0.223236i
$940$	25.3173	−	14.1541i	0.825761	−	0.461656i
$941$	−22.5442	−	13.0159i	−0.734921	−	0.424307i	0.0852987	−	0.996355i	$-0.472816\pi$
$941$	−22.5442	−	13.0159i	−0.734921	−	0.424307i	−0.820220	+	0.572049i	$0.806149\pi$
$942$	34.3907	−	22.2943i	1.12051	−	0.726389i
$943$	−8.85306	+	5.11132i	−0.288295	+	0.166447i
$944$	12.5755	−	6.80418i	0.409297	−	0.221457i
$945$	43.2309	−	12.0459i	1.40630	−	0.391855i
$946$	3.38032	+	5.94945i	0.109904	+	0.193433i
$947$	9.17669	+	15.8945i	0.298202	+	0.516502i	0.975725	−	0.219000i	$-0.0702796\pi$
$947$	9.17669	+	15.8945i	0.298202	+	0.516502i	−0.677522	+	0.735502i	$0.736946\pi$
$948$	−24.2211	+	46.6436i	−0.786663	+	1.51491i
$949$	8.49440	+	4.90424i	0.275740	+	0.159198i
$950$	−0.176996	+	25.6137i	−0.00574250	+	0.831018i
$951$	−24.1012	−	36.6210i	−0.781535	−	1.18752i
$952$	−16.0301	−	23.4706i	−0.519537	−	0.760686i
$953$			47.0368i			1.52367i	0.647770	+	0.761836i	$0.275702\pi$
$953$			47.0368i			1.52367i	−0.647770	+	0.761836i	$0.724298\pi$
$954$	−40.1419	−	17.6178i	−1.29964	−	0.570396i
$955$	7.91701			0.256189
$956$	0.113219	−	8.19180i	0.00366178	−	0.264942i
$957$	−4.99204	+	9.94715i	−0.161370	+	0.321546i
$958$	−0.256769	+	37.1579i	−0.00829582	+	1.20052i
$959$	15.0239	−	32.9977i	0.485146	−	1.06555i
$960$	39.5515	+	21.9469i	1.27652	+	0.708332i
$961$	35.2008	+	60.9695i	1.13551	+	1.96676i
$962$	−21.0895	−	37.1180i	−0.679951	−	1.19673i
$963$	2.41032	−	0.283142i	0.0776714	−	0.00912412i
$964$	−7.71654	−	4.59849i	−0.248533	−	0.148107i
$965$	−31.7856	+	18.3514i	−1.02321	+	0.590753i
$966$	−33.7515	−	13.3126i	−1.08594	−	0.428325i
$967$	22.0735	−	38.2325i	0.709837	−	1.22947i	−0.255080	−	0.966920i	$-0.582102\pi$
$967$	22.0735	−	38.2325i	0.709837	−	1.22947i	0.964917	−	0.262554i	$-0.0845648\pi$
$968$	−22.0508	−	13.3480i	−0.708738	−	0.429020i
$969$	21.0295	−	1.23094i	0.675564	−	0.0395435i
$970$	66.3219	+	38.9045i	2.12947	+	1.24915i
$971$			25.9425i			0.832535i	0.909242	+	0.416267i	$0.136662\pi$
$971$			25.9425i			0.832535i	−0.909242	+	0.416267i	$0.863338\pi$
$972$	22.4109	+	21.6738i	0.718829	+	0.695187i
$973$	0.553832	+	5.73054i	0.0177550	+	0.183713i
$974$	32.3793	+	18.9937i	1.03750	+	0.608599i
$975$	52.4465	−	3.06991i	1.67963	−	0.0983158i
$976$	37.1126	+	1.02607i	1.18795	+	0.0328436i
$977$	−7.80914	−	4.50861i	−0.249836	−	0.144243i	0.369853	−	0.929090i	$-0.379408\pi$
$977$	−7.80914	−	4.50861i	−0.249836	−	0.144243i	−0.619689	+	0.784847i	$0.712741\pi$
$978$	−12.8585	+	25.1863i	−0.411170	+	0.805369i
$979$	3.99610	+	6.92144i	0.127716	+	0.221210i
$980$	−43.0126	−	15.4443i	−1.37399	−	0.493349i
$981$	−5.68415	−	48.3877i	−0.181481	−	1.54490i
$982$	7.85159	−	4.46107i	0.250554	−	0.142358i
$983$	−12.2838	−	21.2762i	−0.391793	−	0.678605i	0.600893	−	0.799329i	$-0.294812\pi$
$983$	−12.2838	−	21.2762i	−0.391793	−	0.678605i	−0.992686	+	0.120724i	$0.961478\pi$
$984$	−7.91021	−	4.17726i	−0.252168	−	0.133166i
$985$	20.8447	+	12.0347i	0.664166	+	0.383457i
$986$	0.173626	−	25.1261i	0.00552938	−	0.800177i
$987$	−18.9902	−	7.33905i	−0.604463	−	0.233605i
$988$	−34.3405	−	0.474622i	−1.09252	−	0.0150997i
$989$	−19.7205			−0.627074
$990$	7.64541	−	17.4200i	0.242987	−	0.553644i
$991$	15.8161			0.502414			0.251207	−	0.967933i	$-0.419172\pi$
$991$	15.8161			0.502414			0.251207	+	0.967933i	$0.419172\pi$
$992$	−56.9296	−	1.96773i	−1.80752	−	0.0624754i
$993$	14.0151	−	9.22368i	0.444755	−	0.292705i
$994$	2.92381	+	32.6043i	0.0927377	+	1.03415i
$995$	13.3832	−	23.1803i	0.424275	−	0.734866i
$996$	6.78398	+	3.52278i	0.214959	+	0.111624i
$997$	1.75501	+	3.03976i	0.0555816	+	0.0962702i	0.892477	−	0.451092i	$-0.148965\pi$
$997$	1.75501	+	3.03976i	0.0555816	+	0.0962702i	−0.836896	+	0.547362i	$0.815632\pi$
$998$	5.05574	+	8.89824i	0.160037	+	0.281669i
$999$	5.10427	+	28.8013i	0.161492	+	0.911234i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cc.b.293.14	yes	168
7.6	odd	2	inner	504.2.cc.b.293.13	✓	168
8.5	even	2	inner	504.2.cc.b.293.41	yes	168
9.2	odd	6	inner	504.2.cc.b.461.42	yes	168
56.13	odd	2	inner	504.2.cc.b.293.42	yes	168
63.20	even	6	inner	504.2.cc.b.461.41	yes	168
72.29	odd	6	inner	504.2.cc.b.461.13	yes	168
504.461	even	6	inner	504.2.cc.b.461.14	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cc.b.293.13	✓	168	7.6	odd	2	inner
504.2.cc.b.293.14	yes	168	1.1	even	1	trivial
504.2.cc.b.293.41	yes	168	8.5	even	2	inner
504.2.cc.b.293.42	yes	168	56.13	odd	2	inner
504.2.cc.b.461.13	yes	168	72.29	odd	6	inner
504.2.cc.b.461.14	yes	168	504.461	even	6	inner
504.2.cc.b.461.41	yes	168	63.20	even	6	inner
504.2.cc.b.461.42	yes	168	9.2	odd	6	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21983 - 0.715553i) q^{2} +(1.72909 - 0.101211i) q^{3} +(0.975968 + 1.74571i) q^{4} +(-2.82704 - 1.63219i) q^{5} +(-2.18162 - 1.11380i) q^{6} +(-2.15340 + 1.53716i) q^{7} +(0.0586299 - 2.82782i) q^{8} +(2.97951 - 0.350006i) q^{9} +O(q^{10})\)	\(q+(-1.21983 - 0.715553i) q^{2} +(1.72909 - 0.101211i) q^{3} +(0.975968 + 1.74571i) q^{4} +(-2.82704 - 1.63219i) q^{5} +(-2.18162 - 1.11380i) q^{6} +(-2.15340 + 1.53716i) q^{7} +(0.0586299 - 2.82782i) q^{8} +(2.97951 - 0.350006i) q^{9} +(2.28058 + 4.01389i) q^{10} +(-0.686803 - 1.18958i) q^{11} +(1.86422 + 2.91970i) q^{12} +(2.68129 - 4.64414i) q^{13} +(3.72670 - 0.334194i) q^{14} +(-5.05340 - 2.53608i) q^{15} +(-2.09497 + 3.40750i) q^{16} -3.79810 q^{17} +(-3.88495 - 1.70505i) q^{18} -3.20217 q^{19} +(0.0902258 - 6.52814i) q^{20} +(-3.56786 + 2.87583i) q^{21} +(-0.0134232 + 1.94253i) q^{22} +(-4.84839 - 2.79922i) q^{23} +(-0.184830 - 4.89549i) q^{24} +(2.82809 + 4.89840i) q^{25} +(-6.59385 + 3.74645i) q^{26} +(5.11642 - 0.906751i) q^{27} +(-4.78508 - 2.25899i) q^{28} +(-2.33896 - 4.05120i) q^{29} +(4.34959 + 6.70956i) q^{30} +(-8.72073 - 5.03492i) q^{31} +(4.99376 - 2.65751i) q^{32} +(-1.30794 - 1.98738i) q^{33} +(4.63303 + 2.71774i) q^{34} +(8.59669 - 0.830833i) q^{35} +(3.51892 + 4.85976i) q^{36} +5.62919i q^{37} +(3.90610 + 2.29132i) q^{38} +(4.16616 - 8.30151i) q^{39} +(-4.78129 + 7.89866i) q^{40} +(0.912990 - 1.58135i) q^{41} +(6.40998 - 0.955035i) q^{42} +(3.05057 - 1.76125i) q^{43} +(1.40635 - 2.35995i) q^{44} +(-8.99447 - 3.87365i) q^{45} +(3.91122 + 6.88385i) q^{46} +(2.22135 + 3.84748i) q^{47} +(-3.27752 + 6.10392i) q^{48} +(2.27430 - 6.62024i) q^{49} +(0.0552738 - 7.99887i) q^{50} +(-6.56726 + 0.384409i) q^{51} +(10.7241 + 0.148219i) q^{52} +10.3327 q^{53} +(-6.88999 - 2.55499i) q^{54} +4.48398i q^{55} +(4.22055 + 6.17956i) q^{56} +(-5.53684 + 0.324094i) q^{57} +(-0.0457139 + 6.61543i) q^{58} +(-3.09566 - 1.78728i) q^{59} +(-0.504710 - 11.2969i) q^{60} +(-4.64085 - 8.03819i) q^{61} +(7.03506 + 12.3819i) q^{62} +(-5.87808 + 5.33368i) q^{63} +(-7.99313 - 0.331589i) q^{64} +(-15.1602 + 8.75276i) q^{65} +(0.173395 + 3.36016i) q^{66} +(-6.76364 - 3.90499i) q^{67} +(-3.70682 - 6.63036i) q^{68} +(-8.66662 - 4.34940i) q^{69} +(-11.0810 - 5.13791i) q^{70} +8.74884i q^{71} +(-0.815064 - 8.44604i) q^{72} +1.82906i q^{73} +(4.02798 - 6.86665i) q^{74} +(5.38581 + 8.18355i) q^{75} +(-3.12521 - 5.59004i) q^{76} +(3.30753 + 1.50592i) q^{77} +(-11.0222 + 7.14532i) q^{78} +(7.58602 + 13.1394i) q^{79} +(11.4843 - 6.21375i) q^{80} +(8.75499 - 2.08569i) q^{81} +(-2.24523 + 1.27568i) q^{82} +(1.91103 - 1.10333i) q^{83} +(-8.50247 - 3.42170i) q^{84} +(10.7374 + 6.19922i) q^{85} +(-4.98144 - 0.0344227i) q^{86} +(-4.45431 - 6.76817i) q^{87} +(-3.40418 + 1.87241i) q^{88} -5.81840 q^{89} +(8.19992 + 11.1612i) q^{90} +(1.36486 + 14.1223i) q^{91} +(0.154738 - 11.1958i) q^{92} +(-15.5885 - 7.82320i) q^{93} +(0.0434152 - 6.28277i) q^{94} +(9.05264 + 5.22655i) q^{95} +(8.36570 - 5.10050i) q^{96} +(14.4240 - 8.32773i) q^{97} +(-7.51139 + 6.44818i) q^{98} +(-2.46270 - 3.30398i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9	\( 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 4 q^{15} + 30 q^{16} - 2 q^{18} + 6 q^{22} - 84 q^{23} + 32 q^{25} + 4 q^{28} - 52 q^{30} + 24 q^{32} - 26 q^{36} + 44 q^{39} - 16 q^{46} + 54 q^{49} + 108 q^{50} - 24 q^{56} - 40 q^{57} + 6 q^{58} - 4 q^{60} - 86 q^{63} + 120 q^{64} + 60 q^{65} - 6 q^{70} + 52 q^{72} + 48 q^{74} - 184 q^{78} - 4 q^{79} - 104 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} - 90 q^{92} - 72 q^{95}+O(q^{100}) \) 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9 + 12 * q^14 - 4 * q^15 + 30 * q^16 - 2 * q^18 + 6 * q^22 - 84 * q^23 + 32 * q^25 + 4 * q^28 - 52 * q^30 + 24 * q^32 - 26 * q^36 + 44 * q^39 - 16 * q^46 + 54 * q^49 + 108 * q^50 - 24 * q^56 - 40 * q^57 + 6 * q^58 - 4 * q^60 - 86 * q^63 + 120 * q^64 + 60 * q^65 - 6 * q^70 + 52 * q^72 + 48 * q^74 - 184 * q^78 - 4 * q^79 - 104 * q^81 - 72 * q^84 - 144 * q^86 - 18 * q^88 - 90 * q^92 - 72 * q^95

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