LMFDB - Embedded newform 504.2.cc.b.461.41

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			461.41
Character	$\chi$	$=$	504.461
Dual form			504.2.cc.b.293.41

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.00977226 - 1.41418i) q^{2} +(-1.72909 - 0.101211i) q^{3} +(-1.99981 - 0.0276395i) q^{4} +(2.82704 - 1.63219i) q^{5} +(-0.160028 + 2.44426i) q^{6} +(-2.15340 - 1.53716i) q^{7} +(-0.0586299 + 2.82782i) q^{8} +(2.97951 + 0.350006i) q^{9} +O(q^{10})$	\(q+(0.00977226 - 1.41418i) q^{2} +(-1.72909 - 0.101211i) q^{3} +(-1.99981 - 0.0276395i) q^{4} +(2.82704 - 1.63219i) q^{5} +(-0.160028 + 2.44426i) 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} +(3.45505 + 0.250194i) q^{12} +(-2.68129 - 4.64414i) q^{13} +(-2.19486 + 3.03028i) q^{14} +(-5.05340 + 2.53608i) q^{15} +(3.99847 + 0.110547i) q^{16} -3.79810 q^{17} +(0.524088 - 4.21015i) q^{18} +3.20217 q^{19} +(-5.69865 + 3.18593i) q^{20} +(3.56786 + 2.87583i) q^{21} +(-1.67557 - 0.982888i) q^{22} +(-4.84839 + 2.79922i) q^{23} +(0.387582 - 4.88362i) q^{24} +(2.82809 - 4.89840i) q^{25} +(-6.59385 + 3.74645i) q^{26} +(-5.11642 - 0.906751i) q^{27} +(4.26391 + 3.13354i) q^{28} +(2.33896 - 4.05120i) q^{29} +(3.53709 + 7.17120i) q^{30} +(-8.72073 + 5.03492i) q^{31} +(0.195408 - 5.65348i) q^{32} +(-1.30794 + 1.98738i) q^{33} +(-0.0371160 + 5.37120i) q^{34} +(-8.59669 - 0.830833i) q^{35} +(-5.94878 - 0.782297i) q^{36} +5.62919i q^{37} +(0.0312924 - 4.52844i) q^{38} +(4.16616 + 8.30151i) q^{39} +(4.44979 + 8.09005i) q^{40} +(0.912990 + 1.58135i) q^{41} +(4.10181 - 5.01749i) 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} +(-6.90253 - 0.595835i) q^{48} +(2.27430 + 6.62024i) q^{49} +(-6.89959 - 4.04730i) q^{50} +(6.56726 + 0.384409i) q^{51} +(5.23371 + 9.36149i) q^{52} -10.3327 q^{53} +(-1.33231 + 7.22668i) q^{54} -4.48398i q^{55} +(4.47305 - 5.99931i) q^{56} +(-5.53684 - 0.324094i) q^{57} +(-5.70627 - 3.34730i) q^{58} +(3.09566 - 1.78728i) q^{59} +(10.1759 - 4.93200i) 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} +(2.79773 + 1.86909i) q^{66} +(6.76364 - 3.90499i) q^{67} +(7.59547 + 0.104977i) q^{68} +(8.66662 - 4.34940i) q^{69} +(-1.25896 + 12.1491i) q^{70} -8.74884i q^{71} +(-1.16444 + 8.40500i) q^{72} -1.82906i q^{73} +(7.96069 + 0.0550099i) q^{74} +(-5.38581 + 8.18355i) q^{75} +(-6.40372 - 0.0885062i) q^{76} +(-3.30753 + 1.50592i) q^{77} +(11.7805 - 5.81058i) 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} +(-7.05554 - 5.84973i) q^{84} +(-10.7374 + 6.19922i) q^{85} +(-2.52053 + 4.29684i) q^{86} +(-4.45431 + 6.76817i) q^{87} +(3.32365 + 2.01190i) q^{88} -5.81840 q^{89} +(-5.39015 - 12.7577i) q^{90} +(-1.36486 + 14.1223i) q^{91} +(9.77322 - 5.46390i) q^{92} +(15.5885 - 7.82320i) q^{93} +(-5.41933 - 3.17898i) q^{94} +(9.05264 - 5.22655i) q^{95} +(-0.910072 + 9.75560i) q^{96} +(14.4240 + 8.32773i) q^{97} +(9.38443 - 3.15157i) 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 $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.00977226	−	1.41418i	0.00691003	−	0.999976i
$2$	0.00977226	−	1.41418i	0.00691003	−	0.999976i
$3$	−1.72909	−	0.101211i	−0.998291	−	0.0584341i
$3$	−1.72909	−	0.101211i	−0.998291	−	0.0584341i
$4$	−1.99981	−	0.0276395i	−0.999905	−	0.0138197i
$5$	2.82704	−	1.63219i	1.26429	−	0.729938i	0.290388	−	0.956909i	$-0.406216\pi$
$5$	2.82704	−	1.63219i	1.26429	−	0.729938i	0.973902	+	0.226971i	$0.0728822\pi$
$6$	−0.160028	+	2.44426i	−0.0653310	+	0.997864i
$7$	−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	$-0.766938\pi$
$11$	0.686803	−	1.18958i	0.207079	−	0.358671i	0.950793	+	0.309826i	$0.100271\pi$
$12$	3.45505	+	0.250194i	0.997388	+	0.0722247i
$13$	−2.68129	−	4.64414i	−0.743657	−	1.28805i	−0.950820	−	0.309745i	$-0.899756\pi$
$13$	−2.68129	−	4.64414i	−0.743657	−	1.28805i	0.207163	−	0.978306i	$-0.433577\pi$
$14$	−2.19486	+	3.03028i	−0.586601	+	0.809876i
$15$	−5.05340	+	2.53608i	−1.30478	+	0.654813i
$16$	3.99847	+	0.110547i	0.999618	+	0.0276368i
$17$	−3.79810			−0.921174			−0.460587	−	0.887614i	$-0.652361\pi$
$17$	−3.79810			−0.921174			−0.460587	+	0.887614i	$0.652361\pi$
$18$	0.524088	−	4.21015i	0.123529	−	0.992341i
$19$	3.20217			0.734627			0.367314	−	0.930097i	$-0.380278\pi$
$19$	3.20217			0.734627			0.367314	+	0.930097i	$0.380278\pi$
$20$	−5.69865	+	3.18593i	−1.27426	+	0.712396i
$21$	3.56786	+	2.87583i	0.778570	+	0.627558i
$22$	−1.67557	−	0.982888i	−0.357232	−	0.209552i
$23$	−4.84839	+	2.79922i	−1.01096	+	0.583678i	−0.911472	−	0.411361i	$-0.865053\pi$
$23$	−4.84839	+	2.79922i	−1.01096	+	0.583678i	−0.0994868	+	0.995039i	$0.531720\pi$
$24$	0.387582	−	4.88362i	0.0791149	−	0.996866i
$25$	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
$28$	4.26391	+	3.13354i	0.805803	+	0.592183i
$29$	2.33896	−	4.05120i	0.434335	−	0.752290i	−0.562906	−	0.826521i	$-0.690317\pi$
$29$	2.33896	−	4.05120i	0.434335	−	0.752290i	0.997241	+	0.0742310i	$0.0236502\pi$
$30$	3.53709	+	7.17120i	0.645781	+	1.30928i
$31$	−8.72073	+	5.03492i	−1.56629	+	0.904298i	−0.569694	+	0.821857i	$0.692938\pi$
$31$	−8.72073	+	5.03492i	−1.56629	+	0.904298i	−0.996596	+	0.0824408i	$0.973728\pi$
$32$	0.195408	−	5.65348i	0.0345436	−	0.999403i
$33$	−1.30794	+	1.98738i	−0.227684	+	0.345958i
$34$	−0.0371160	+	5.37120i	−0.00636535	+	0.921152i
$35$	−8.59669	−	0.830833i	−1.45311	−	0.140436i
$36$	−5.94878	−	0.782297i	−0.991464	−	0.130383i
$37$			5.62919i			0.925433i	0.886506	+	0.462716i	$0.153125\pi$
$37$			5.62919i			0.925433i	−0.886506	+	0.462716i	$0.846875\pi$
$38$	0.0312924	−	4.52844i	0.00507630	−	0.734610i
$39$	4.16616	+	8.30151i	0.667120	+	1.32931i
$40$	4.44979	+	8.09005i	0.703574	+	1.27915i
$41$	0.912990	+	1.58135i	0.142585	+	0.246965i	0.928469	−	0.371409i	$-0.121125\pi$
$41$	0.912990	+	1.58135i	0.142585	+	0.246965i	−0.785884	+	0.618374i	$0.787792\pi$
$42$	4.10181	−	5.01749i	0.632923	−	0.774215i
$43$	−3.05057	−	1.76125i	−0.465207	−	0.268588i	0.249024	−	0.968497i	$-0.419890\pi$
$43$	−3.05057	−	1.76125i	−0.465207	−	0.268588i	−0.714231	+	0.699910i	$0.753224\pi$
$44$	−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	−0.657296	−	0.753632i	$-0.728300\pi$
$47$	2.22135	−	3.84748i	0.324017	−	0.561213i	0.981313	+	0.192419i	$0.0616333\pi$
$48$	−6.90253	−	0.595835i	−0.996295	−	0.0860014i
$49$	2.27430	+	6.62024i	0.324900	+	0.945748i
$50$	−6.89959	−	4.04730i	−0.975749	−	0.572375i
$51$	6.56726	+	0.384409i	0.919600	+	0.0538280i
$52$	5.23371	+	9.36149i	0.725785	+	1.29821i
$53$	−10.3327			−1.41930			−0.709652	−	0.704552i	$-0.751148\pi$
$53$	−10.3327			−1.41930			−0.709652	+	0.704552i	$0.751148\pi$
$54$	−1.33231	+	7.22668i	−0.181304	+	0.983427i
$55$		−	4.48398i		−	0.604619i
$56$	4.47305	−	5.99931i	0.597737	−	0.801692i
$57$	−5.53684	−	0.324094i	−0.733372	−	0.0429273i
$58$	−5.70627	−	3.34730i	−0.749270	−	0.439523i
$59$	3.09566	−	1.78728i	0.403021	−	0.232684i	−0.284766	−	0.958597i	$-0.591916\pi$
$59$	3.09566	−	1.78728i	0.403021	−	0.232684i	0.687787	+	0.725913i	$0.258583\pi$
$60$	10.1759	−	4.93200i	1.31371	−	0.636719i
$61$	4.64085	−	8.03819i	0.594200	−	1.02918i	−0.399459	−	0.916751i	$-0.630802\pi$
$61$	4.64085	−	8.03819i	0.594200	−	1.02918i	0.993659	−	0.112434i	$-0.0358646\pi$
$62$	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
$66$	2.79773	+	1.86909i	0.344376	+	0.230069i
$67$	6.76364	−	3.90499i	0.826310	−	0.477070i	−0.0262775	−	0.999655i	$-0.508365\pi$
$67$	6.76364	−	3.90499i	0.826310	−	0.477070i	0.852588	+	0.522584i	$0.175032\pi$
$68$	7.59547	+	0.104977i	0.921086	+	0.0127304i
$69$	8.66662	−	4.34940i	1.04334	−	0.523606i
$70$	−1.25896	+	12.1491i	−0.150474	+	1.45210i
$71$		−	8.74884i		−	1.03830i	−0.854684	−	0.519148i	$-0.826249\pi$
$71$		−	8.74884i		−	1.03830i	0.854684	−	0.519148i	$-0.173751\pi$
$72$	−1.16444	+	8.40500i	−0.137231	+	0.990539i
$73$		−	1.82906i		−	0.214075i	−0.994255	−	0.107038i	$-0.965863\pi$
$73$		−	1.82906i		−	0.214075i	0.994255	−	0.107038i	$-0.0341365\pi$
$74$	7.96069	+	0.0550099i	0.925411	+	0.00639477i
$75$	−5.38581	+	8.18355i	−0.621899	+	0.944955i
$76$	−6.40372	−	0.0885062i	−0.734557	−	0.0101524i
$77$	−3.30753	+	1.50592i	−0.376928	+	0.171615i
$78$	11.7805	−	5.81058i	1.33388	−	0.657919i
$79$	7.58602	−	13.1394i	0.853494	−	1.47829i	−0.0245416	−	0.999699i	$-0.507813\pi$
$79$	7.58602	−	13.1394i	0.853494	−	1.47829i	0.878035	−	0.478596i	$-0.158854\pi$
$80$	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	$-0.371978\pi$
$83$	−1.91103	−	1.10333i	−0.209763	−	0.121106i	−0.601201	+	0.799098i	$0.705311\pi$
$84$	−7.05554	−	5.84973i	−0.769823	−	0.638258i
$85$	−10.7374	+	6.19922i	−1.16463	+	0.672400i
$86$	−2.52053	+	4.29684i	−0.271796	+	0.463340i
$87$	−4.45431	+	6.76817i	−0.477552	+	0.725624i
$88$	3.32365	+	2.01190i	0.354302	+	0.214469i
$89$	−5.81840			−0.616749			−0.308375	−	0.951265i	$-0.599785\pi$
$89$	−5.81840			−0.616749			−0.308375	+	0.951265i	$0.599785\pi$
$90$	−5.39015	−	12.7577i	−0.568171	−	1.34477i
$91$	−1.36486	+	14.1223i	−0.143076	+	1.48042i
$92$	9.77322	−	5.46390i	1.01893	−	0.569651i
$93$	15.5885	−	7.82320i	1.61646	−	0.811228i
$94$	−5.41933	−	3.17898i	−0.558961	−	0.327887i
$95$	9.05264	−	5.22655i	0.928782	−	0.536232i
$96$	−0.910072	+	9.75560i	−0.0928838	+	0.995677i
$97$	14.4240	+	8.32773i	1.46454	+	0.845553i	0.999216	−	0.0395876i	$-0.0126044\pi$
$97$	14.4240	+	8.32773i	1.46454	+	0.845553i	0.465324	+	0.885140i	$0.345938\pi$
$98$	9.38443	−	3.15157i	0.947971	−	0.318357i
$99$	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	$-0.324939\pi$
$101$	0.458979	+	0.264992i	0.0456701	+	0.0263676i	−0.476991	+	0.878908i	$0.658273\pi$
$102$	0.607800	−	9.28353i	0.0601812	−	0.919206i
$103$	14.7523	−	8.51727i	1.45359	−	0.839231i	0.454909	−	0.890538i	$-0.349672\pi$
$103$	14.7523	−	8.51727i	1.45359	−	0.839231i	0.998683	+	0.0513066i	$0.0163386\pi$
$104$	13.2900	−	7.30993i	1.30319	−	0.716797i
$105$	14.7804	+	2.30666i	1.44242	+	0.225107i
$106$	−0.100974	+	14.6123i	−0.00980744	+	1.41927i
$107$	−0.808964			−0.0782055			−0.0391028	−	0.999235i	$-0.512450\pi$
$107$	−0.808964			−0.0782055			−0.0391028	+	0.999235i	$0.512450\pi$
$108$	10.2068	+	1.95474i	0.982151	+	0.188095i
$109$		−	16.2402i		−	1.55552i	−0.628558	−	0.777762i	$-0.716355\pi$
$109$		−	16.2402i		−	1.55552i	0.628558	−	0.777762i	$-0.283645\pi$
$110$	−6.34115	−	0.0438186i	−0.604605	−	0.00417794i
$111$	0.569735	−	9.73338i	0.0540769	−	0.923852i
$112$	−8.44040	−	6.38433i	−0.797543	−	0.603263i
$113$	−0.101810	+	0.0587799i	−0.00957746	+	0.00552955i	−0.504781	−	0.863247i	$-0.668427\pi$
$113$	−0.101810	+	0.0587799i	−0.00957746	+	0.00552955i	0.495204	+	0.868777i	$0.335093\pi$
$114$	−0.512435	+	7.82692i	−0.0479939	+	0.733058i
$115$	−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
$120$	−6.87530	−	14.4388i	−0.627626	−	1.31808i
$121$	4.55660	+	7.89227i	0.414237	+	0.717479i
$122$	−11.3221	−	6.64155i	−1.02505	−	0.601298i
$123$	−1.41859	−	2.82669i	−0.127910	−	0.254874i
$124$	17.5790	−	9.82784i	1.57864	−	0.882566i
$125$		−	2.14205i		−	0.191591i
$126$	−7.60023	+	8.26054i	−0.677082	+	0.735908i
$127$	2.61604			0.232136			0.116068	−	0.993241i	$-0.462971\pi$
$127$	2.61604			0.232136			0.116068	+	0.993241i	$0.462971\pi$
$128$	−0.547038	+	11.3005i	−0.0483518	+	0.998830i
$129$	5.09645	+	3.35411i	0.448718	+	0.295313i
$130$	−12.5261	+	21.3538i	−1.09861	+	1.87285i
$131$	−8.31237	+	4.79915i	−0.726255	+	0.419303i	−0.817051	−	0.576566i	$-0.804392\pi$
$131$	−8.31237	+	4.79915i	−0.726255	+	0.419303i	0.0907956	+	0.995870i	$0.471059\pi$
$132$	2.67057	−	3.93822i	0.232443	−	0.342778i
$133$	−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	−0.101598	−	0.994826i	$-0.532396\pi$
$137$	−11.8679	−	6.85192i	−1.01394	−	0.585399i	−0.912343	+	0.409426i	$0.865729\pi$
$138$	−6.06613	−	12.2987i	−0.516384	−	1.04693i
$139$	−1.08802	−	1.88450i	−0.0922844	−	0.159841i	0.816188	−	0.577787i	$-0.196084\pi$
$139$	−1.08802	−	1.88450i	−0.0922844	−	0.159841i	−0.908472	+	0.417946i	$0.862750\pi$
$140$	17.1688	+	1.89911i	1.45103	+	0.160504i
$141$	−4.23032	+	6.42783i	−0.356257	+	0.541321i
$142$	−12.3724	−	0.0854959i	−1.03827	−	0.00717466i
$143$	−7.36608			−0.615983
$144$	11.8748	+	1.72887i	0.989567	+	0.144072i
$145$		−	15.2705i		−	1.26815i
$146$	−2.58662	−	0.0178740i	−0.214070	−	0.00147927i
$147$	−3.26243	−	11.6772i	−0.269081	−	0.963118i
$148$	0.155588	−	11.2573i	0.0127892	−	0.925345i
$149$	−6.36891	−	11.0313i	−0.521761	−	0.903717i	−0.999680	−	0.0253125i	$-0.991942\pi$
$149$	−6.36891	−	11.0313i	−0.521761	−	0.903717i	0.477919	−	0.878404i	$-0.341391\pi$
$150$	11.5204	+	7.69647i	0.940635	+	0.628414i
$151$	2.61458	−	4.52858i	0.212771	−	0.368531i	−0.739809	−	0.672816i	$-0.765084\pi$
$151$	2.61458	−	4.52858i	0.212771	−	0.368531i	0.952581	+	0.304286i	$0.0984177\pi$
$152$	−0.187743	+	9.05515i	−0.0152279	+	0.734470i
$153$	−11.3165	−	1.32936i	−0.914884	−	0.107472i
$154$	2.09732	+	4.69216i	0.169007	+	0.378105i
$155$	−16.4359	+	28.4678i	−1.32016	+	2.28659i
$156$	−8.10208	−	16.7166i	−0.648686	−	1.33840i
$157$	8.36599	+	14.4903i	0.667679	+	1.15645i	0.978552	+	0.206002i	$0.0660454\pi$
$157$	8.36599	+	14.4903i	0.667679	+	1.15645i	−0.310873	+	0.950452i	$0.600621\pi$
$158$	−18.5073	−	10.8564i	−1.47236	−	0.863688i
$159$	17.8662	+	1.04578i	1.41688	+	0.0829358i
$160$	−8.67513	−	16.3015i	−0.685829	−	1.28875i
$161$	14.7434	+	1.42488i	1.16194	+	0.112297i
$162$	3.03510	−	12.3608i	0.238460	−	0.971152i
$163$		−	11.5448i		−	0.904257i	−0.891953	−	0.452128i	$-0.850665\pi$
$163$		−	11.5448i		−	0.904257i	0.891953	−	0.452128i	$-0.149335\pi$
$164$	−1.78210	−	3.18762i	−0.139158	−	0.248912i
$165$	−0.453827	+	7.75320i	−0.0353304	+	0.603586i
$166$	−1.57899	+	2.69175i	−0.122553	+	0.208921i
$167$	2.14524	+	3.71567i	0.166004	+	0.287527i	0.937011	−	0.349299i	$-0.113580\pi$
$167$	2.14524	+	3.71567i	0.166004	+	0.287527i	−0.771007	+	0.636826i	$0.780247\pi$
$168$	−8.34152	+	9.92064i	−0.643562	+	0.765394i
$169$	−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	$-0.359073\pi$
$173$	−1.84020	−	1.06244i	−0.139908	−	0.0807760i	−0.568320	+	0.822807i	$0.692407\pi$
$174$	9.52788	+	6.36533i	0.722307	+	0.482555i
$175$	−13.6196	+	6.20102i	−1.02955	+	0.468753i
$176$	2.87767	−	4.68057i	0.216912	−	0.352811i
$177$	−5.53357	+	2.77706i	−0.415929	+	0.208736i
$178$	−0.0568589	+	8.22826i	−0.00426176	+	0.616735i
$179$	21.0209			1.57118			0.785589	−	0.618749i	$-0.212360\pi$
$179$	21.0209			1.57118			0.785589	+	0.618749i	$0.212360\pi$
$180$	−18.0943	+	7.49797i	−1.34867	+	0.558865i
$181$	−3.02613			−0.224931			−0.112465	−	0.993656i	$-0.535875\pi$
$181$	−3.02613			−0.224931			−0.112465	+	0.993656i	$0.535875\pi$
$182$	19.9581	+	2.06816i	1.47939	+	0.153302i
$183$	−8.83801	+	13.4291i	−0.653324	+	0.992704i
$184$	−7.63143	−	13.8745i	−0.562596	−	1.02284i
$185$	9.18791	+	15.9139i	0.675509	+	1.17002i
$186$	−10.9111	−	22.1214i	−0.800039	−	1.62202i
$187$	−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	0.422084	−	0.906557i	$-0.361299\pi$
$191$	−2.10035	−	1.21264i	−0.151976	−	0.0877433i	−0.574059	+	0.818814i	$0.694632\pi$
$192$	13.7873	+	1.38234i	0.995011	+	0.0997617i
$193$	5.62172	+	9.73710i	0.404660	+	0.700892i	0.994282	−	0.106788i	$-0.0340565\pi$
$193$	5.62172	+	9.73710i	0.404660	+	0.700892i	−0.589622	+	0.807679i	$0.700723\pi$
$194$	11.9179	−	20.3168i	0.855653	−	1.45866i
$195$	25.3276	+	16.6687i	1.81374	+	1.19367i
$196$	−4.36518	−	13.3021i	−0.311799	−	0.950148i
$197$	7.37332			0.525328			0.262664	−	0.964887i	$-0.415399\pi$
$197$	7.37332			0.525328			0.262664	+	0.964887i	$0.415399\pi$
$198$	−4.64835	−	3.51499i	−0.330344	−	0.249799i
$199$		−	8.19951i		−	0.581248i	−0.956837	−	0.290624i	$-0.906137\pi$
$199$		−	8.19951i		−	0.581248i	0.956837	−	0.290624i	$-0.0938629\pi$
$200$	13.6860	+	8.28453i	0.967746	+	0.585805i
$201$	−12.0902	+	6.06753i	−0.852775	+	0.427970i
$202$	0.379231	−	0.646489i	0.0266826	−	0.0454868i
$203$	−11.2641	+	5.12853i	−0.790583	+	0.359952i
$204$	−13.1226	−	0.950260i	−0.918769	−	0.0665315i
$205$	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
$210$	3.40648	−	20.8796i	0.235069	−	1.44083i
$211$	13.4385	−	7.75871i	0.925143	−	0.534132i	0.0398710	−	0.999205i	$-0.487305\pi$
$211$	13.4385	−	7.75871i	0.925143	−	0.534132i	0.885272	+	0.465073i	$0.153972\pi$
$212$	20.6634	+	0.285590i	1.41917	+	0.0196144i
$213$	−0.885478	+	15.1275i	−0.0606719	+	1.03652i
$214$	−0.00790541	+	1.14402i	−0.000540403	+	0.0782036i
$215$	−11.4988			−0.784209
$216$	2.86410	−	14.4152i	0.194878	−	0.980828i
$217$	26.5187	+	2.56292i	1.80021	+	0.173982i
$218$	−22.9665	−	0.158703i	−1.55549	−	0.0107487i
$219$	−0.185121	+	3.16261i	−0.0125093	+	0.213709i
$220$	−0.123935	+	8.96710i	−0.00835568	+	0.604562i
$221$	10.1838	+	17.6389i	0.685038	+	1.18652i
$222$	−13.7592	−	0.900825i	−0.923456	−	0.0604594i
$223$	10.7965	+	6.23338i	0.722989	+	0.417418i	0.815852	−	0.578261i	$-0.196268\pi$
$223$	10.7965	+	6.23338i	0.722989	+	0.417418i	−0.0928628	+	0.995679i	$0.529602\pi$
$224$	−9.11107	+	11.8739i	−0.608759	+	0.793355i
$225$	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	$-0.370858\pi$
$227$	−3.06928	−	1.77205i	−0.203715	−	0.117615i	−0.598387	+	0.801207i	$0.704192\pi$
$228$	11.0637	+	0.801162i	0.732709	+	0.0530582i
$229$	5.08642	+	8.80994i	0.336120	+	0.582177i	0.983699	−	0.179821i	$-0.0575518\pi$
$229$	5.08642	+	8.80994i	0.336120	+	0.582177i	−0.647579	+	0.761998i	$0.724218\pi$
$230$	22.2929	+	13.0770i	1.46995	+	0.862275i
$231$	5.87144	−	2.26911i	0.386313	−	0.149297i
$232$	11.3189	+	6.85169i	0.743125	+	0.449835i
$233$			3.72928i			0.244313i	0.992511	+	0.122157i	$0.0389810\pi$
$233$			3.72928i			0.244313i	−0.992511	+	0.122157i	$0.961019\pi$
$234$	−20.9577	+	8.85470i	−1.37005	+	0.578850i
$235$		−	14.5026i		−	0.946048i
$236$	−6.24013	+	3.48866i	−0.406198	+	0.227092i
$237$	−14.4468	+	21.9514i	−0.938418	+	1.42590i
$238$	8.33629	−	11.5093i	0.540362	−	0.746037i
$239$	−3.54749	+	2.04815i	−0.229468	+	0.132484i	−0.610327	−	0.792150i	$-0.708962\pi$
$239$	−3.54749	+	2.04815i	−0.229468	+	0.132484i	0.380858	+	0.924633i	$0.375629\pi$
$240$	−20.4862	+	9.58181i	−1.32238	+	0.618503i
$241$	−3.88968	−	2.24571i	−0.250556	−	0.144659i	0.369463	−	0.929246i	$-0.379542\pi$
$241$	−3.88968	−	2.24571i	−0.250556	−	0.144659i	−0.620019	+	0.784587i	$0.712875\pi$
$242$	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
$246$	−4.01132	+	1.97852i	−0.255752	+	0.126146i
$247$	−8.58595	−	14.8713i	−0.546311	−	0.946238i
$248$	−13.7265	−	24.9559i	−0.871636	−	1.58470i
$249$	3.19267	+	2.10118i	0.202327	+	0.133157i
$250$	−3.02925	−	0.0209327i	−0.191586	−	0.00132390i
$251$			16.3716i			1.03337i	0.856176	+	0.516685i	$0.172834\pi$
$251$			16.3716i			1.03337i	−0.856176	+	0.516685i	$0.827166\pi$
$252$	11.6076	+	10.8288i	0.731211	+	0.682151i
$253$			7.69005i			0.483469i
$254$	0.0255646	−	3.69954i	0.00160406	−	0.232130i
$255$	19.1933	−	9.63228i	1.20193	−	0.603197i
$256$	15.9756	+	0.884041i	0.998472	+	0.0552526i
$257$	−1.65104	−	2.85969i	−0.102989	−	0.178383i	0.809926	−	0.586533i	$-0.199507\pi$
$257$	−1.65104	−	2.85969i	−0.102989	−	0.178383i	−0.912915	+	0.408150i	$0.866174\pi$
$258$	4.79311	−	7.17452i	0.298406	−	0.446666i
$259$	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	0.968002	−	0.250942i	$-0.0807404\pi$
$263$	20.0232	+	11.5604i	1.23468	+	0.712843i	0.266679	+	0.963786i	$0.414074\pi$
$264$	−5.54326	−	3.81515i	−0.341164	−	0.234806i
$265$	−29.2109	+	16.8649i	−1.79441	+	1.03600i
$266$	−7.02831	+	9.70346i	−0.430933	+	0.594957i
$267$	10.0605	+	0.588885i	0.615695	+	0.0360392i
$268$	−13.6339	+	7.62229i	−0.832824	+	0.465605i
$269$		−	28.5660i		−	1.74170i	−0.491552	−	0.870848i	$-0.663570\pi$
$269$		−	28.5660i		−	1.74170i	0.491552	−	0.870848i	$-0.336430\pi$
$270$	8.02884	+	22.6047i	0.488620	+	1.37568i
$271$			24.0898i			1.46335i	0.681653	+	0.731675i	$0.261261\pi$
$271$			24.0898i			1.46335i	−0.681653	+	0.731675i	$0.738739\pi$
$272$	−15.1866	−	0.419870i	−0.920823	−	0.0254583i
$273$	3.78929	−	24.2806i	0.229338	−	1.46953i
$274$	−9.80583	+	16.7164i	−0.592392	+	1.00987i
$275$	−3.88469	−	6.72848i	−0.234256	−	0.405743i
$276$	−17.4518	+	8.45842i	−1.05047	+	0.509137i
$277$	−20.4819	−	11.8252i	−1.23064	−	0.710510i	−0.263476	−	0.964666i	$-0.584869\pi$
$277$	−20.4819	−	11.8252i	−1.23064	−	0.710510i	−0.967163	+	0.254157i	$0.918202\pi$
$278$	−2.67565	+	1.52024i	−0.160475	+	0.0911777i
$279$	−27.7458	+	11.9493i	−1.66110	+	0.715385i
$280$	2.85347	−	24.2612i	0.170527	−	1.44988i
$281$	−16.3653	−	9.44852i	−0.976273	−	0.563651i	−0.0751300	−	0.997174i	$-0.523937\pi$
$281$	−16.3653	−	9.44852i	−0.976273	−	0.563651i	−0.901143	+	0.433522i	$0.857271\pi$
$282$	9.04876	+	6.04524i	0.538846	+	0.359989i
$283$	−4.52882	−	7.84415i	−0.269210	−	0.466286i	0.699448	−	0.714684i	$-0.253429\pi$
$283$	−4.52882	−	7.84415i	−0.269210	−	0.466286i	−0.968658	+	0.248398i	$0.920096\pi$
$284$	−0.241813	+	17.4960i	−0.0143490	+	1.03820i
$285$	−16.1818	+	8.12095i	−0.958529	+	0.481044i
$286$	−0.0719833	+	10.4170i	−0.00425646	+	0.615968i
$287$	0.464739	−	4.80868i	0.0274326	−	0.283848i
$288$	2.56097	−	16.7762i	0.150907	−	0.988548i
$289$	−2.57444			−0.151438
$290$	−21.5953	−	0.149228i	−1.26812	−	0.00876296i
$291$	−24.0976	−	15.8593i	−1.41263	−	0.929687i
$292$	−0.0505542	+	3.65777i	−0.00295846	+	0.214055i
$293$	−5.93608	+	3.42720i	−0.346789	+	0.200219i	−0.663270	−	0.748380i	$-0.730832\pi$
$293$	−5.93608	+	3.42720i	−0.346789	+	0.200219i	0.316481	+	0.948599i	$0.397499\pi$
$294$	−16.5455	+	4.49955i	−0.964954	+	0.262419i
$295$	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
$300$	10.9968	−	16.2167i	0.634899	−	0.936271i
$301$	3.86179	+	8.48188i	0.222590	+	0.488887i
$302$	−6.37868	−	3.74174i	−0.367052	−	0.215313i
$303$	−0.766796	−	0.504648i	−0.0440513	−	0.0289913i
$304$	12.8038	+	0.353991i	0.734347	+	0.0203028i
$305$		−	30.2990i		−	1.73492i
$306$	−1.99054	+	15.9906i	−0.113791	+	0.914119i
$307$	1.01107			0.0577051			0.0288525	−	0.999584i	$-0.490815\pi$
$307$	1.01107			0.0577051			0.0288525	+	0.999584i	$0.490815\pi$
$308$	6.65606	−	2.92013i	0.379264	−	0.166390i
$309$	−26.3702	+	13.2340i	−1.50015	+	0.752858i
$310$	40.0980	+	23.5215i	2.27741	+	1.33593i
$311$	4.47545	+	7.75170i	0.253779	+	0.439559i	0.964563	−	0.263852i	$-0.0849930\pi$
$311$	4.47545	+	7.75170i	0.253779	+	0.439559i	−0.710784	+	0.703410i	$0.751660\pi$
$312$	−23.7194	+	11.2944i	−1.34285	+	0.639422i
$313$	6.22159	+	3.59204i	0.351665	+	0.203034i	0.665418	−	0.746471i	$-0.268253\pi$
$313$	6.22159	+	3.59204i	0.351665	+	0.203034i	−0.313753	+	0.949505i	$0.601586\pi$
$314$	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	−0.253746	−	0.967271i	$-0.581663\pi$
$317$	12.6556	−	21.9201i	0.710808	−	1.23116i	0.964554	−	0.263885i	$-0.0850040\pi$
$318$	1.65351	−	25.2557i	0.0927245	−	1.41627i
$319$	−3.21282	−	5.56476i	−0.179883	−	0.311567i
$320$	−23.1381	+	12.1089i	−1.29346	+	0.676908i
$321$	1.39877	+	0.0818760i	0.0780719	+	0.00456987i
$322$	2.15912	−	20.8359i	0.120323	−	1.16114i
$323$	−12.1621			−0.676720
$324$	−17.4507	−	4.41297i	−0.969481	−	0.245165i
$325$	−30.3318			−1.68251
$326$	−16.3264	−	0.112819i	−0.904235	−	0.00624844i
$327$	−1.64368	+	28.0807i	−0.0908957	+	1.55287i
$328$	−4.52529	+	2.48906i	−0.249867	+	0.137435i
$329$	−10.6976	+	4.87063i	−0.589780	+	0.268527i
$330$	10.9600	+	0.717560i	0.603328	+	0.0395004i
$331$	−8.38896	−	4.84337i	−0.461099	−	0.266216i	0.251407	−	0.967881i	$-0.419107\pi$
$331$	−8.38896	−	4.84337i	−0.461099	−	0.266216i	−0.712506	+	0.701666i	$0.752440\pi$
$332$	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
$336$	13.9481	+	11.8934i	0.760929	+	0.648835i
$337$	−3.71267	−	6.43053i	−0.202242	−	0.350293i	0.747009	−	0.664814i	$-0.231489\pi$
$337$	−3.71267	−	6.43053i	−0.202242	−	0.350293i	−0.949250	+	0.314521i	$0.898156\pi$
$338$	19.2213	+	11.2752i	1.04550	+	0.613290i
$339$	0.181988	−	0.0913316i	0.00988421	−	0.00496045i
$340$	21.6440	−	12.1005i	1.17381	−	0.656241i
$341$			13.8320i			0.749044i
$342$	1.67822	−	13.4816i	0.0907475	−	0.729001i
$343$	5.27886	−	17.7520i	0.285032	−	0.958518i
$344$	5.15934	−	8.52319i	0.278173	−	0.459540i
$345$	17.4018	−	26.4415i	0.936882	−	1.42356i
$346$	−1.52047	+	2.59200i	−0.0817409	+	0.139347i
$347$	14.9417	+	25.8798i	0.802114	+	1.38930i	0.918222	+	0.396066i	$0.129625\pi$
$347$	14.9417	+	25.8798i	0.802114	+	1.38930i	−0.116107	+	0.993237i	$0.537042\pi$
$348$	9.09483	−	13.4119i	0.487534	−	0.718955i
$349$	3.74785	−	6.49147i	0.200618	−	0.347481i	−0.748110	−	0.663575i	$-0.769038\pi$
$349$	3.74785	−	6.49147i	0.200618	−	0.347481i	0.948728	+	0.316094i	$0.102372\pi$
$350$	8.63626	+	19.3212i	0.461628	+	1.03276i
$351$	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	−0.264663	−	0.964341i	$-0.585261\pi$
$353$	13.2046	−	22.8711i	0.702812	−	1.21731i	0.967475	−	0.252965i	$-0.0814058\pi$
$354$	3.87318	+	7.85260i	0.205857	+	0.417361i
$355$	−14.2798	−	24.7333i	−0.757892	−	1.31271i
$356$	11.6357	+	0.160818i	0.616690	+	0.00852331i
$357$	−13.5511	−	10.9227i	−0.717199	−	0.578090i
$358$	0.205422	−	29.7274i	0.0108569	−	1.57114i
$359$		−	11.4797i		−	0.605875i	−0.953010	−	0.302937i	$-0.902033\pi$
$359$		−	11.4797i		−	0.605875i	0.953010	−	0.302937i	$-0.0979673\pi$
$360$	10.4267	+	25.6619i	0.549533	+	1.35250i
$361$	−8.74613			−0.460323
$362$	−0.0295722	+	4.27949i	−0.00155428	+	0.224925i
$363$	−7.08000	−	14.1076i	−0.371604	−	0.740458i
$364$	3.11978	−	28.2041i	0.163521	−	1.47830i
$365$	−2.98537	−	5.17082i	−0.156262	−	0.270653i
$366$	18.9047	+	12.6298i	0.988166	+	0.660168i
$367$	−3.90010	−	2.25172i	−0.203583	−	0.117539i	0.394742	−	0.918792i	$-0.370834\pi$
$367$	−3.90010	−	2.25172i	−0.203583	−	0.117539i	−0.598326	+	0.801253i	$0.704167\pi$
$368$	−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
$372$	−31.3903	+	15.2140i	−1.62751	+	0.788811i
$373$	26.3500	−	15.2132i	1.36435	−	0.787707i	0.374150	−	0.927368i	$-0.377935\pi$
$373$	26.3500	−	15.2132i	1.36435	−	0.787707i	0.990199	+	0.139661i	$0.0446013\pi$
$374$	6.36397	+	3.73311i	0.329073	+	0.193034i
$375$	−0.216799	+	3.70380i	−0.0111955	+	0.191264i
$376$	10.7498	+	6.50714i	0.554376	+	0.335580i
$377$	−25.0858			−1.29198
$378$	13.9775	−	13.5140i	0.718927	−	0.695085i
$379$		−	22.2755i		−	1.14421i	−0.820179	−	0.572107i	$-0.806126\pi$
$379$		−	22.2755i		−	1.14421i	0.820179	−	0.572107i	$-0.193874\pi$
$380$	−18.2480	+	10.2019i	−0.936104	+	0.523346i
$381$	−4.52336	−	0.264771i	−0.231739	−	0.0135646i
$382$	−1.73541	+	2.95842i	−0.0887913	+	0.151366i
$383$	−13.0931	−	22.6779i	−0.669025	−	1.15879i	−0.978177	−	0.207773i	$-0.933378\pi$
$383$	−13.0931	−	22.6779i	−0.669025	−	1.15879i	0.309152	−	0.951013i	$-0.399955\pi$
$384$	2.08961	−	19.4842i	0.106635	−	0.994298i
$385$	−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	$-0.873423\pi$
$389$	−2.47747	+	4.29110i	−0.125613	+	0.217567i	0.796360	+	0.604823i	$0.206756\pi$
$390$	23.8201	−	35.6548i	1.20618	−	1.80545i
$391$	18.4147	−	10.6317i	0.931270	−	0.537669i
$392$	−18.8542	+	6.04316i	−0.952280	+	0.305226i
$393$	14.8586	−	7.45686i	0.749516	−	0.376149i
$394$	0.0720541	−	10.4272i	0.00363003	−	0.525315i
$395$		−	49.5273i		−	2.49199i
$396$	−5.01625	+	6.53926i	−0.252076	+	0.328610i
$397$	20.5241			1.03007			0.515037	−	0.857168i	$-0.327778\pi$
$397$	20.5241			1.03007			0.515037	+	0.857168i	$0.327778\pi$
$398$	−11.5956	−	0.0801278i	−0.581234	−	0.00401644i
$399$	11.4249	+	9.20889i	0.571959	+	0.461021i
$400$	11.8496	−	19.2735i	0.592478	−	0.963675i
$401$	−12.6873	+	7.32503i	−0.633574	+	0.365794i	−0.782135	−	0.623109i	$-0.785869\pi$
$401$	−12.6873	+	7.32503i	−0.633574	+	0.365794i	0.148561	+	0.988903i	$0.452536\pi$
$402$	8.46243	+	17.1570i	0.422068	+	0.855712i
$403$	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
$406$	7.14258	+	15.9795i	0.354480	+	0.793051i
$407$	6.69636	+	3.86615i	0.331926	+	0.191638i
$408$	−1.47208	+	18.5485i	−0.0728787	+	0.918287i
$409$	8.24750	−	4.76170i	0.407813	−	0.235451i	−0.282037	−	0.959404i	$-0.591010\pi$
$409$	8.24750	−	4.76170i	0.407813	−	0.235451i	0.689849	+	0.723953i	$0.257677\pi$
$410$	4.26519	−	7.27103i	0.210643	−	0.359091i
$411$	19.8272	+	13.0488i	0.978001	+	0.643648i
$412$	−29.7373	+	16.6252i	−1.46505	+	0.819063i
$413$	−9.41354	−	0.909778i	−0.463210	−	0.0447672i
$414$	9.24414	+	21.8795i	0.454325	+	1.07532i
$415$	−7.20340			−0.353601
$416$	−26.7795	+	14.2511i	−1.31297	+	0.698719i
$417$	1.69055	+	3.36859i	0.0827865	+	0.164961i
$418$	−5.36544	−	3.14737i	−0.262432	−	0.153943i
$419$	−7.96945	+	4.60117i	−0.389333	+	0.224782i	−0.681871	−	0.731472i	$-0.738834\pi$
$419$	−7.96945	+	4.60117i	−0.389333	+	0.224782i	0.292538	+	0.956254i	$0.405500\pi$
$420$	−29.4942	−	5.02141i	−1.43917	−	0.245020i
$421$	13.0114	+	7.51216i	0.634139	+	0.366120i	0.782353	−	0.622835i	$-0.214019\pi$
$421$	13.0114	+	7.51216i	0.634139	+	0.366120i	−0.148214	+	0.988955i	$0.547352\pi$
$422$	−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
$426$	21.3844	+	1.40005i	1.03608	+	0.0678329i
$427$	−22.3496	+	10.1758i	−1.08157	+	0.492439i
$428$	1.61777	+	0.0223593i	0.0781980	+	0.00108078i
$429$	12.7366	+	0.745528i	0.614930	+	0.0359944i
$430$	−0.112369	+	16.2613i	−0.00541891	+	0.784190i
$431$			28.6677i			1.38088i	0.723392	+	0.690438i	$0.242582\pi$
$431$			28.6677i			1.38088i	−0.723392	+	0.690438i	$0.757418\pi$
$432$	−20.3576	−	4.19123i	−0.979458	−	0.201650i
$433$		−	15.8290i		−	0.760695i	−0.924844	−	0.380348i	$-0.875804\pi$
$433$		−	15.8290i		−	0.760695i	0.924844	−	0.380348i	$-0.124196\pi$
$434$	3.88358	−	37.4772i	0.186418	−	1.79896i
$435$	−1.54554	+	26.4042i	−0.0741032	+	1.26598i
$436$	−0.448869	+	32.4772i	−0.0214969	+	1.55538i
$437$	−15.5254	+	8.96357i	−0.742678	+	0.428786i
$438$	4.47069	+	0.292700i	0.213618	+	0.0139857i
$439$	−14.7960	−	8.54246i	−0.706173	−	0.407709i	0.103469	−	0.994633i	$-0.467006\pi$
$439$	−14.7960	−	8.54246i	−0.706173	−	0.407709i	−0.809642	+	0.586923i	$0.800339\pi$
$440$	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	$-0.928229\pi$
$443$	−6.18223	+	10.7079i	−0.293727	+	0.508749i	0.680961	+	0.732319i	$0.261562\pi$
$444$	−1.40839	+	19.4492i	−0.0668391	+	0.923016i
$445$	−16.4488	+	9.49674i	−0.779750	+	0.450189i
$446$	8.92062	−	15.2073i	0.422404	−	0.720087i
$447$	9.89593	+	19.7187i	0.468062	+	0.932661i
$448$	16.7027	+	13.0007i	0.789130	+	0.614227i
$449$			34.0650i			1.60763i	0.594881	+	0.803814i	$0.297199\pi$
$449$			34.0650i			1.60763i	−0.594881	+	0.803814i	$0.702801\pi$
$450$	−19.1408	−	14.4739i	−0.902307	−	0.682305i
$451$	2.50818			0.118106
$452$	0.205225	−	0.114735i	0.00965297	−	0.00539667i
$453$	−4.97919	+	7.56571i	−0.233943	+	0.355468i
$454$	−2.53599	+	4.32319i	−0.119020	+	0.202897i
$455$	19.1917	+	42.1519i	0.899723	+	1.97611i
$456$	1.24110	−	15.6382i	0.0581200	−	0.732325i
$457$	−8.64764	+	14.9782i	−0.404520	+	0.700649i	−0.994265	−	0.106940i	$-0.965895\pi$
$457$	−8.64764	+	14.9782i	−0.404520	+	0.700649i	0.589746	+	0.807589i	$0.299228\pi$
$458$	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	$-0.469162\pi$
$461$	−15.3919	−	8.88652i	−0.716872	−	0.413886i	−0.813600	+	0.581424i	$0.802496\pi$
$462$	−3.15156	−	8.32545i	−0.146624	−	0.387335i
$463$	−7.85727	−	13.6092i	−0.365158	−	0.632473i	0.623643	−	0.781709i	$-0.285652\pi$
$463$	−7.85727	−	13.6092i	−0.365158	−	0.632473i	−0.988802	+	0.149236i	$0.952319\pi$
$464$	9.80013	−	15.9401i	0.454960	−	0.739999i
$465$	31.3004	−	47.5599i	1.45152	−	2.20554i
$466$	5.27387	+	0.0364435i	0.244307	+	0.00168821i
$467$		−	29.8632i		−	1.38190i	−0.722901	−	0.690952i	$-0.757192\pi$
$467$		−	29.8632i		−	1.38190i	0.722901	−	0.690952i	$-0.242808\pi$
$468$	12.3173	+	29.7245i	0.569369	+	1.37402i
$469$	−20.5674	−	1.98775i	−0.949716	−	0.0917859i
$470$	−20.5093	−	0.141724i	−0.946026	−	0.00653723i
$471$	−12.9990	−	25.9018i	−0.598962	−	1.19349i
$472$	4.87261	+	8.85876i	0.224280	+	0.407757i
$473$	−4.19028	+	2.41926i	−0.192669	+	0.111238i
$474$	30.9020	+	20.6448i	1.41938	+	0.948249i
$475$	9.05603	−	15.6855i	0.415519	−	0.719700i
$476$	−16.1948	−	11.9015i	−0.742286	−	0.545504i
$477$	−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	0.392506	+	0.919749i	$0.371608\pi$
$479$	−13.1376	+	22.7550i	−0.600273	+	1.03970i	−0.992779	+	0.119954i	$0.961725\pi$
$480$	13.3502	+	29.0649i	0.609350	+	1.32662i
$481$	26.1427	−	15.0935i	1.19201	−	0.688205i
$482$	−3.21384	+	5.47876i	−0.146387	+	0.249551i
$483$	−25.3484	−	3.95595i	−1.15339	−	0.180002i
$484$	−8.89420	−	15.9090i	−0.404282	−	0.723135i
$485$	54.3698			2.46880
$486$	−6.49901	+	21.0657i	−0.294801	+	0.955559i
$487$	−26.5442			−1.20283			−0.601415	−	0.798937i	$-0.705396\pi$
$487$	−26.5442			−1.20283			−0.601415	+	0.798937i	$0.705396\pi$
$488$	22.4585	+	13.5948i	1.01665	+	0.615406i
$489$	−1.16846	+	19.9620i	−0.0528395	+	0.902712i
$490$	21.3862	−	24.2268i	0.966129	−	1.09446i
$491$	3.19274	+	5.52998i	0.144086	+	0.249565i	0.929032	−	0.370000i	$-0.120642\pi$
$491$	3.19274	+	5.52998i	0.144086	+	0.249565i	−0.784945	+	0.619565i	$0.787309\pi$
$492$	2.75879	+	5.69206i	0.124376	+	0.256618i
$493$	−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
$498$	3.00264	−	4.49448i	0.134552	−	0.201402i
$499$	6.26715	−	3.61834i	0.280556	−	0.161979i	−0.353119	−	0.935578i	$-0.614879\pi$
$499$	6.26715	−	3.61834i	0.280556	−	0.161979i	0.633675	+	0.773599i	$0.281546\pi$
$500$	−0.0592052	+	4.28370i	−0.00264774	+	0.191573i
$501$	−3.33326	−	6.64186i	−0.148919	−	0.296736i
$502$	23.1524	+	0.159988i	1.03334	+	0.00714062i
$503$	24.1526			1.07691			0.538456	−	0.842654i	$-0.319008\pi$
$503$	24.1526			1.07691			0.538456	+	0.842654i	$0.319008\pi$
$504$	15.4273	−	16.3094i	0.687187	−	0.726480i
$505$	1.73007			0.0769870
$506$	10.8751	+	0.0751492i	0.483458	+	0.00334079i
$507$	15.0041	−	22.7982i	0.666355	−	1.01250i
$508$	−5.23157	−	0.0723058i	−0.232113	−	0.00320805i
$509$	−27.4850	+	15.8685i	−1.21825	+	0.703357i	−0.964543	−	0.263924i	$-0.914983\pi$
$509$	−27.4850	+	15.8685i	−1.21825	+	0.703357i	−0.253706	+	0.967281i	$0.581650\pi$
$510$	−13.4342	−	27.2369i	−0.594877	−	1.20607i
$511$	−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
$516$	−10.0992	−	6.84843i	−0.444594	−	0.301486i
$517$	−3.05126	−	5.28493i	−0.134194	−	0.232431i
$518$	−17.0580	−	12.3553i	−0.749486	−	0.542860i
$519$	3.07435	+	2.02331i	0.134949	+	0.0888134i
$520$	25.6401	−	42.3572i	1.12439	−	1.85749i
$521$	−20.7010			−0.906926			−0.453463	−	0.891275i	$-0.649812\pi$
$521$	−20.7010			−0.906926			−0.453463	+	0.891275i	$0.649812\pi$
$522$	−15.8303	−	11.9706i	−0.692875	−	0.523937i
$523$	44.0553			1.92641			0.963203	−	0.268776i	$-0.0866191\pi$
$523$	44.0553			1.92641			0.963203	+	0.268776i	$0.0866191\pi$
$524$	16.7558	−	9.36763i	0.731980	−	0.409227i
$525$	24.1772	−	9.34367i	1.05518	−	0.407791i
$526$	16.5441	−	28.2034i	0.721358	−	1.22973i
$527$	33.1222	−	19.1231i	1.44283	−	0.833016i
$528$	−5.44948	+	7.80188i	−0.237158	+	0.339533i
$529$	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
$532$	13.6538	+	10.0341i	0.591965	+	0.435034i
$533$	4.89599	−	8.48010i	0.212069	−	0.367314i
$534$	0.931104	−	14.2217i	0.0402928	−	0.615432i
$535$	−2.28697	+	1.32038i	−0.0988744	+	0.0570852i
$536$	10.6461	+	19.3553i	0.459839	+	0.836022i
$537$	−36.3471	−	2.12755i	−1.56849	−	0.0918104i
$538$	−40.3974	−	0.279154i	−1.74166	−	0.0120352i
$539$	9.43729	+	1.84135i	0.406493	+	0.0793123i
$540$	32.0456	−	11.1333i	1.37902	−	0.479102i
$541$		−	8.01378i		−	0.344539i	−0.985050	−	0.172270i	$-0.944890\pi$
$541$		−	8.01378i		−	0.344539i	0.985050	−	0.172270i	$-0.0551100\pi$
$542$	34.0673	+	0.235412i	1.46332	+	0.0101118i
$543$	5.23246	+	0.306277i	0.224546	+	0.0131436i
$544$	−0.742179	+	21.4725i	−0.0318207	+	0.920625i
$545$	−26.5070	−	45.9115i	−1.13544	−	1.96663i
$546$	−34.3000	−	5.59601i	−1.46791	−	0.239487i
$547$	−9.43514	−	5.44738i	−0.403418	−	0.232913i	0.284540	−	0.958664i	$-0.408159\pi$
$547$	−9.43514	−	5.44738i	−0.403418	−	0.232913i	−0.687958	+	0.725751i	$0.741492\pi$
$548$	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
$552$	11.7912	+	24.7626i	0.501866	+	1.05397i
$553$	−36.5330	+	16.6335i	−1.55354	+	0.707327i
$554$	−16.9232	+	28.8495i	−0.718996	+	1.22570i
$555$	−14.2761	−	28.4466i	−0.605986	−	1.20749i
$556$	2.12374	+	3.79871i	0.0900666	+	0.161101i
$557$	−42.5280			−1.80197			−0.900985	−	0.433851i	$-0.857155\pi$
$557$	−42.5280			−1.80197			−0.900985	+	0.433851i	$0.857155\pi$
$558$	16.6273	+	39.3543i	0.703890	+	1.66600i
$559$			18.8897i			0.798948i
$560$	−34.2818	−	4.27240i	−1.44867	−	0.180542i
$561$	4.96770	−	7.54826i	0.209736	−	0.318688i
$562$	−13.5218	+	23.0512i	−0.570384	+	0.972355i
$563$	11.2415	−	6.49030i	0.473774	−	0.273533i	−0.244044	−	0.969764i	$-0.578474\pi$
$563$	11.2415	−	6.49030i	0.473774	−	0.273533i	0.717818	+	0.696231i	$0.245141\pi$
$564$	8.63749	−	12.7375i	0.363704	−	0.536346i
$565$	−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	0.965449	+	0.260592i	$0.0839179\pi$
$569$	39.9276	+	23.0522i	1.67385	+	0.966399i	0.708404	+	0.705807i	$0.249415\pi$
$570$	11.3264	+	22.9634i	0.474409	+	0.961830i
$571$	4.20640	−	2.42856i	0.176032	−	0.101632i	−0.409395	−	0.912357i	$-0.634260\pi$
$571$	4.20640	−	2.42856i	0.176032	−	0.101632i	0.585427	+	0.810725i	$0.300927\pi$
$572$	14.7308	+	0.203595i	0.615924	+	0.00851272i
$573$	3.50896	+	2.30934i	0.146589	+	0.0964739i
$574$	−6.79580	−	0.704216i	−0.283651	−	0.0293934i
$575$			31.6658i			1.32056i
$576$	−23.6996	−	3.78561i	−0.987482	−	0.157734i
$577$		−	8.61372i		−	0.358594i	−0.983795	−	0.179297i	$-0.942618\pi$
$577$		−	8.61372i		−	0.358594i	0.983795	−	0.179297i	$-0.0573823\pi$
$578$	−0.0251581	+	3.64072i	−0.00104644	+	0.151434i
$579$	−8.73496	−	17.4053i	−0.363013	−	0.723340i
$580$	−0.422070	+	30.5382i	−0.0175255	+	1.26803i
$581$	2.41922	+	5.31347i	0.100366	+	0.220440i
$582$	−22.6634	+	33.9234i	−0.939426	+	1.40617i
$583$	−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	$-0.573325\pi$
$587$	−28.7257	−	16.5848i	−1.18564	−	0.684528i	−0.957312	+	0.289057i	$0.906658\pi$
$588$	6.20149	+	23.4423i	0.255745	+	0.966744i
$589$	−27.9252	+	16.1226i	−1.15064	+	0.664322i
$590$	−14.2339	−	8.34960i	−0.585999	−	0.343747i
$591$	−12.7492	−	0.746261i	−0.524430	−	0.0306971i
$592$	−0.622292	+	22.5082i	−0.0255760	+	0.925080i
$593$	36.3837			1.49410			0.747050	−	0.664767i	$-0.231469\pi$
$593$	36.3837			1.49410			0.747050	+	0.664767i	$0.231469\pi$
$594$	7.68167	+	6.54819i	0.315183	+	0.268676i
$595$	32.6511	+	3.15559i	1.33856	+	0.129366i
$596$	12.4317	+	22.2365i	0.509222	+	0.910841i
$597$	−0.829880	+	14.1777i	−0.0339647	+	0.580255i
$598$	21.4824	−	36.6219i	0.878481	−	1.49758i
$599$	−3.16383	+	1.82664i	−0.129271	+	0.0746345i	−0.563241	−	0.826293i	$-0.690446\pi$
$599$	−3.16383	+	1.82664i	−0.129271	+	0.0746345i	0.433970	+	0.900927i	$0.357112\pi$
$600$	−22.8258	−	15.7099i	−0.931861	−	0.641353i
$601$	34.9558	+	20.1818i	1.42588	+	0.823231i	0.996792	−	0.0800328i	$-0.0255025\pi$
$601$	34.9558	+	20.1818i	1.42588	+	0.823231i	0.429086	+	0.903264i	$0.358836\pi$
$602$	12.0326	−	5.37838i	0.490414	−	0.219207i
$603$	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
$606$	−0.721157	+	1.07946i	−0.0292950	+	0.0438499i
$607$	−15.1967	+	8.77383i	−0.616816	+	0.356119i	−0.775628	−	0.631190i	$-0.782567\pi$
$607$	−15.1967	+	8.77383i	−0.616816	+	0.356119i	0.158812	+	0.987309i	$0.449234\pi$
$608$	0.625729	−	18.1034i	0.0253767	−	0.734189i
$609$	19.9957	−	7.72764i	0.810265	−	0.313140i
$610$	−42.8483	−	0.296090i	−1.73488	−	0.0119883i
$611$	−23.8243			−0.963829
$612$	22.5941	+	2.97124i	0.913311	+	0.120105i
$613$			33.1672i			1.33961i	0.742537	+	0.669805i	$0.233622\pi$
$613$			33.1672i			1.33961i	−0.742537	+	0.669805i	$0.766378\pi$
$614$	0.00988049	−	1.42984i	0.000398744	−	0.0577037i
$615$	−8.62412	−	5.67576i	−0.347758	−	0.228869i
$616$	−4.06455	−	9.44140i	−0.163765	−	0.380405i
$617$	17.2437	−	9.95563i	0.694204	−	0.400799i	−0.110981	−	0.993823i	$-0.535399\pi$
$617$	17.2437	−	9.95563i	0.694204	−	0.400799i	0.805185	+	0.593024i	$0.202066\pi$
$618$	18.4576	+	37.4215i	0.742474	+	1.50531i
$619$	−22.4708	+	38.9206i	−0.903178	+	1.56435i	−0.0798336	+	0.996808i	$0.525439\pi$
$619$	−22.4708	+	38.9206i	−0.903178	+	1.56435i	−0.823344	+	0.567542i	$0.807894\pi$
$620$	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
$624$	15.7406	+	33.6539i	0.630127	+	1.34723i
$625$	10.6442	+	18.4364i	0.425769	+	0.737454i
$626$	5.14059	−	8.76335i	0.205459	−	0.350254i
$627$	−4.18825	+	6.36391i	−0.167263	+	0.254150i
$628$	−16.3299	−	29.2091i	−0.651633	−	1.16557i
$629$		−	21.3802i		−	0.852485i
$630$	−8.00334	+	35.7579i	−0.318861	+	1.42463i
$631$	31.0143			1.23466			0.617329	−	0.786705i	$-0.288215\pi$
$631$	31.0143			1.23466			0.617329	+	0.786705i	$0.288215\pi$
$632$	36.7110	+	22.2222i	1.46029	+	0.883954i
$633$	−24.0216	+	12.0554i	−0.954774	+	0.479159i
$634$	−30.8753	−	18.1115i	−1.22621	−	0.719299i
$635$	7.39563	−	4.26987i	0.293487	−	0.169445i
$636$	−35.7000	−	2.58517i	−1.41560	−	0.102509i
$637$	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	0.228086	−	0.973641i	$-0.426753\pi$
$641$	−12.6860	−	7.32429i	−0.501068	−	0.289292i	−0.729155	+	0.684349i	$0.760086\pi$
$642$	0.129457	−	1.97732i	0.00510924	−	0.0780384i
$643$	8.12747	+	14.0772i	0.320516	+	0.555150i	0.980595	−	0.196047i	$-0.0628104\pi$
$643$	8.12747	+	14.0772i	0.320516	+	0.555150i	−0.660079	+	0.751197i	$0.729477\pi$
$644$	−29.4446	−	3.25700i	−1.16028	−	0.128344i
$645$	19.8824	+	1.16380i	0.782869	+	0.0458246i
$646$	−0.118852	+	17.1995i	−0.00467616	+	0.676704i
$647$	28.5250			1.12144			0.560718	−	0.828007i	$-0.310525\pi$
$647$	28.5250			1.12144			0.560718	+	0.828007i	$0.310525\pi$
$648$	−6.41127	+	24.6353i	−0.251858	+	0.967764i
$649$		−	4.91004i		−	0.192736i
$650$	−0.296410	+	42.8946i	−0.0116262	+	1.68247i
$651$	−45.5939	−	7.11550i	−1.78697	−	0.278879i
$652$	−0.319092	+	23.0873i	−0.0124966	+	0.904170i
$653$	−4.64239	−	8.04086i	−0.181671	−	0.314663i	0.760779	−	0.649011i	$-0.224817\pi$
$653$	−4.64239	−	8.04086i	−0.181671	−	0.314663i	−0.942450	+	0.334348i	$0.891484\pi$
$654$	39.6951	+	2.59887i	1.55220	+	0.101624i
$655$	−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
$658$	6.78341	+	15.1760i	0.264445	+	0.591622i
$659$	6.55142	−	11.3474i	0.255207	−	0.442031i	−0.709745	−	0.704459i	$-0.751190\pi$
$659$	6.55142	−	11.3474i	0.255207	−	0.442031i	0.964952	+	0.262428i	$0.0845231\pi$
$660$	1.12186	−	15.4924i	0.0436684	−	0.603040i
$661$	10.9792	+	19.0166i	0.427043	+	0.739660i	0.996609	−	0.0822855i	$-0.0262219\pi$
$661$	10.9792	+	19.0166i	0.427043	+	0.739660i	−0.569566	+	0.821946i	$0.692889\pi$
$662$	−6.93138	+	11.8162i	−0.269396	+	0.459249i
$663$	−15.8235	−	31.5300i	−0.614534	−	1.22452i
$664$	3.23207	−	5.33935i	0.125429	−	0.207207i
$665$	−27.5280	−	2.66046i	−1.06749	−	0.103168i
$666$	23.6997	+	2.95019i	0.918345	+	0.114317i
$667$			26.1891i			1.01405i
$668$	−4.18738	−	7.48993i	−0.162015	−	0.289794i
$669$	−18.0373	−	11.8708i	−0.697362	−	0.458952i
$670$	−31.0993	−	18.2428i	−1.20147	−	0.704783i
$671$	−6.37470	−	11.0413i	−0.246093	−	0.426245i
$672$	16.9556	−	19.6088i	0.654078	−	0.756427i
$673$	−7.41541	+	12.8439i	−0.285843	+	0.495095i	−0.972813	−	0.231591i	$-0.925607\pi$
$673$	−7.41541	+	12.8439i	−0.285843	+	0.495095i	0.686970	+	0.726686i	$0.258940\pi$
$674$	−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	$-0.275107\pi$
$677$	8.19779	+	4.73300i	0.315067	+	0.181904i	−0.334125	+	0.942529i	$0.608441\pi$
$678$	−0.127381	−	0.258256i	−0.00489203	−	0.00991825i
$679$	−18.2598	−	40.1050i	−0.700746	−	1.53909i
$680$	−16.9008	−	30.7268i	−0.648114	−	1.17832i
$681$	5.12771	+	3.37468i	0.196494	+	0.129318i
$682$	19.5609	+	0.135170i	0.749026	+	0.00517592i
$683$	−21.1814			−0.810484			−0.405242	−	0.914210i	$-0.632813\pi$
$683$	−21.1814			−0.810484			−0.405242	+	0.914210i	$0.632813\pi$
$684$	−19.0490	−	2.50504i	−0.728356	−	0.0957828i
$685$	−44.7346			−1.70922
$686$	−25.0529	−	7.63873i	−0.956526	−	0.291648i
$687$	−7.90323	−	15.7480i	−0.301527	−	0.600823i
$688$	−12.0029	−	7.37953i	−0.457607	−	0.281342i
$689$	27.7050	+	47.9864i	1.05548	+	1.82814i
$690$	−37.2230	−	24.8677i	−1.41705	−	0.946697i
$691$	1.94647	−	3.37139i	0.0740473	−	0.128254i	−0.826624	−	0.562754i	$-0.809742\pi$
$691$	1.94647	−	3.37139i	0.0740473	−	0.128254i	0.900672	+	0.434500i	$0.143075\pi$
$692$	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
$696$	−18.8780	−	12.9928i	−0.715569	−	0.492491i
$697$	−3.46763	−	6.00611i	−0.131346	−	0.227497i
$698$	−9.14348	−	5.36358i	−0.346086	−	0.203014i
$699$	0.377444	−	6.44826i	0.0142762	−	0.243896i
$700$	27.4081	−	12.0244i	1.03593	−	0.454480i
$701$	7.15162			0.270113			0.135056	−	0.990838i	$-0.456878\pi$
$701$	7.15162			0.270113			0.135056	+	0.990838i	$0.456878\pi$
$702$	37.1340	−	13.1894i	1.40153	−	0.497803i
$703$			18.0256i			0.679848i
$704$	−5.88416	+	9.28071i	−0.221767	+	0.349780i
$705$	−1.46783	+	25.0764i	−0.0552815	+	0.944432i
$706$	−32.2148	−	18.8972i	−1.21242	−	0.711207i
$707$	−0.581033	−	1.27616i	−0.0218520	−	0.0479948i
$708$	11.1428	−	5.40064i	0.418774	−	0.202968i
$709$	−12.2856	−	7.09308i	−0.461394	−	0.266386i	0.251236	−	0.967926i	$-0.419163\pi$
$709$	−12.2856	−	7.09308i	−0.461394	−	0.266386i	−0.712630	+	0.701540i	$0.752496\pi$
$710$	−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
$714$	−15.5791	+	19.0569i	−0.583032	+	0.713187i
$715$	−20.8242	+	12.0229i	−0.778781	+	0.449629i
$716$	−42.0378	−	0.581008i	−1.57103	−	0.0217133i
$717$	6.34123	−	3.18239i	0.236818	−	0.118848i
$718$	−16.2343	−	0.112183i	−0.605860	−	0.00418662i
$719$	−49.3903			−1.84195			−0.920974	−	0.389623i	$-0.872605\pi$
$719$	−49.3903			−1.84195			−0.920974	+	0.389623i	$0.872605\pi$
$720$	36.3924	−	14.4944i	1.35626	−	0.540174i
$721$	−44.8601	−	4.33554i	−1.67068	−	0.161464i
$722$	−0.0854695	+	12.3686i	−0.00318085	+	0.460312i
$723$	6.49832	+	4.27671i	0.241675	+	0.159053i
$724$	6.05168	+	0.0836407i	0.224909	+	0.00310848i
$725$	−13.2296	−	22.9144i	−0.491336	−	0.851018i
$726$	−20.0199	+	9.87453i	−0.743008	+	0.366478i
$727$	2.38793	+	1.37867i	0.0885633	+	0.0511320i	0.543628	−	0.839327i	$-0.317050\pi$
$727$	2.38793	+	1.37867i	0.0885633	+	0.0511320i	−0.455064	+	0.890459i	$0.650384\pi$
$728$	−39.8552	−	4.68755i	−1.47713	−	0.173732i
$729$	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
$732$	18.0455	−	26.6113i	0.666981	−	0.983581i
$733$	−6.51450	−	11.2834i	−0.240619	−	0.416764i	0.720272	−	0.693692i	$-0.244017\pi$
$733$	−6.51450	−	11.2834i	−0.240619	−	0.416764i	−0.960891	+	0.276928i	$0.910684\pi$
$734$	−3.22245	+	5.49343i	−0.118943	+	0.202766i
$735$	−28.2824	−	27.6869i	−1.04321	−	1.02125i
$736$	14.8779	+	27.9573i	0.548407	+	1.03052i
$737$		−	10.7278i		−	0.395165i
$738$	7.13618	−	3.01506i	0.262686	−	0.110986i
$739$			17.7977i			0.654697i	0.944904	+	0.327349i	$0.106155\pi$
$739$			17.7977i			0.654697i	−0.944904	+	0.327349i	$0.893845\pi$
$740$	−17.9342	−	32.0788i	−0.659275	−	1.17924i
$741$	13.3407	+	26.5828i	0.490085	+	0.976544i
$742$	22.6788	−	31.3109i	0.832565	−	1.14946i
$743$	34.5075	−	19.9229i	1.26596	−	0.730901i	0.291738	−	0.956498i	$-0.405767\pi$
$743$	34.5075	−	19.9229i	1.26596	−	0.730901i	0.974221	+	0.225597i	$0.0724333\pi$
$744$	21.2086	+	44.5402i	0.777546	+	1.63292i
$745$	−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
$750$	5.23573	+	0.342787i	0.191182	+	0.0125168i
$751$	9.19443	+	15.9252i	0.335510	+	0.581120i	0.983583	−	0.180459i	$-0.0577582\pi$
$751$	9.19443	+	15.9252i	0.335510	+	0.581120i	−0.648073	+	0.761578i	$0.724425\pi$
$752$	9.30732	−	15.1385i	0.339403	−	0.552044i
$753$	1.65699	−	28.3081i	0.0603840	−	1.03160i
$754$	−0.245145	+	35.4758i	−0.00892765	+	1.29195i
$755$		−	17.0700i		−	0.621240i
$756$	−18.9746	−	19.8988i	−0.690101	−	0.723713i
$757$			38.9175i			1.41448i	0.706974	+	0.707240i	$0.250060\pi$
$757$			38.9175i			1.41448i	−0.706974	+	0.707240i	$0.749940\pi$
$758$	−31.5015	−	0.217682i	−1.14419	−	0.00790656i
$759$	0.778317	−	13.2968i	0.0282511	−	0.482643i
$760$	14.2490	+	25.9057i	0.516865	+	0.939698i
$761$	15.4843	+	26.8196i	0.561305	+	0.972209i	0.997383	+	0.0723002i	$0.0230340\pi$
$761$	15.4843	+	26.8196i	0.561305	+	0.972209i	−0.436078	+	0.899909i	$0.643633\pi$
$762$	−0.418638	+	6.39426i	−0.0151656	+	0.231640i
$763$	−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
$768$	−27.5337	−	3.14549i	−0.993538	−	0.113503i
$769$	11.7152	−	6.76375i	0.422459	−	0.243907i	−0.273670	−	0.961824i	$-0.588237\pi$
$769$	11.7152	−	6.76375i	0.422459	−	0.243907i	0.696129	+	0.717917i	$0.254904\pi$
$770$	13.5877	+	9.84170i	0.489667	+	0.354670i
$771$	2.56537	+	5.11177i	0.0923897	+	0.184096i
$772$	−10.9732	−	19.6277i	−0.394935	−	0.706417i
$773$		−	25.4343i		−	0.914808i	−0.889259	−	0.457404i	$-0.848779\pi$
$773$		−	25.4343i		−	0.914808i	0.889259	−	0.457404i	$-0.151221\pi$
$774$	−9.01387	+	11.9203i	−0.323997	+	0.428466i
$775$			56.9569i			2.04595i
$776$	−24.3950	+	40.3004i	−0.875729	+	1.44670i
$777$	−16.1886	+	20.0841i	−0.580763	+	0.720514i
$778$	6.04418	+	3.54552i	0.216694	+	0.127113i
$779$	2.92355	+	5.06373i	0.104747	+	0.181427i
$780$	−50.1896	−	34.0343i	−1.79707	−	1.21862i
$781$	−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
$784$	8.36187	+	26.7223i	0.298638	+	0.954366i
$785$	47.3020	+	27.3098i	1.68828	+	0.974728i
$786$	−10.4001	−	21.0856i	−0.370961	−	0.752097i
$787$	−11.0828	−	19.1959i	−0.395058	−	0.684261i	0.598050	−	0.801459i	$-0.295942\pi$
$787$	−11.0828	−	19.1959i	−0.395058	−	0.684261i	−0.993109	+	0.117198i	$0.962609\pi$
$788$	−14.7452	−	0.203795i	−0.525277	−	0.00725989i
$789$	−33.4518	−	22.0155i	−1.19092	−	0.783773i
$790$	−70.0405	−	0.483994i	−2.49193	−	0.0172197i
$791$	0.309592	+	0.0299207i	0.0110078	+	0.00106386i
$792$	9.19867	+	7.15778i	0.326860	+	0.254341i
$793$	−49.7739			−1.76752
$794$	0.200567	−	29.0248i	0.00711785	−	1.03005i
$795$	52.2152	−	26.2045i	1.85188	−	0.929379i
$796$	−0.226630	+	16.3975i	−0.00803270	+	0.581193i
$797$	−19.7595	+	11.4082i	−0.699918	+	0.404098i	−0.807317	−	0.590118i	$-0.799081\pi$
$797$	−19.7595	+	11.4082i	−0.699918	+	0.404098i	0.107399	+	0.994216i	$0.465748\pi$
$798$	13.1347	−	16.0668i	0.464962	−	0.568759i
$799$	−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
$804$	24.3457	−	11.7997i	0.858608	−	0.416144i
$805$	44.0058	−	20.0358i	1.55100	−	0.706170i
$806$	38.6401	−	65.8712i	1.36104	−	2.32021i
$807$	−2.89119	+	49.3931i	−0.101775	+	1.73872i
$808$	−0.776258	+	1.28237i	−0.0273087	+	0.0451137i
$809$			28.8273i			1.01351i	0.862089	+	0.506757i	$0.169156\pi$
$809$			28.8273i			1.01351i	−0.862089	+	0.506757i	$0.830844\pi$
$810$	−11.5948	−	39.8982i	−0.407398	−	1.40188i
$811$	10.8394			0.380621			0.190311	−	0.981724i	$-0.439051\pi$
$811$	10.8394			0.380621			0.190311	+	0.981724i	$0.439051\pi$
$812$	22.6677	−	9.94474i	0.795482	−	0.348992i
$813$	2.43815	−	41.6534i	0.0855096	−	1.46085i
$814$	5.53286	−	9.43208i	0.193927	−	0.330594i
$815$	−18.8433	−	32.6375i	−0.660051	−	1.14324i
$816$	26.2165	+	2.26304i	0.917761	+	0.0792223i
$817$	−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	$-0.936687\pi$
$821$	−9.14093	+	15.8326i	−0.319021	+	0.552560i	0.661263	+	0.750154i	$0.270021\pi$
$822$	18.6470	−	27.9116i	0.650390	−	0.973530i
$823$	14.2450	+	24.6730i	0.496549	+	0.860048i	0.999992	−	0.00398013i	$-0.00126692\pi$
$823$	14.2450	+	24.6730i	0.496549	+	0.860048i	−0.503443	+	0.864028i	$0.667934\pi$
$824$	23.2204	+	42.2163i	0.808920	+	1.47068i
$825$	6.03599	+	12.0273i	0.210146	+	0.418738i
$826$	−1.37858	+	13.3035i	−0.0479670	+	0.462890i
$827$	23.8157			0.828153			0.414077	−	0.910242i	$-0.364105\pi$
$827$	23.8157			0.828153			0.414077	+	0.910242i	$0.364105\pi$
$828$	31.0318	−	12.8591i	1.07843	−	0.446883i
$829$	−14.1272			−0.490659			−0.245329	−	0.969440i	$-0.578896\pi$
$829$	−14.1272			−0.490659			−0.245329	+	0.969440i	$0.578896\pi$
$830$	−0.0703935	+	10.1869i	−0.00244339	+	0.353592i
$831$	34.2182	+	22.5199i	1.18702	+	0.781207i
$832$	19.8920	+	38.0102i	0.689630	+	1.31777i
$833$	−8.63801	−	25.1443i	−0.299289	−	0.871199i
$834$	4.78031	−	2.35782i	0.165529	−	0.0816446i
$835$	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	−0.910484	−	0.413545i	$-0.864290\pi$
$839$	−2.81259	+	4.87155i	−0.0971015	+	0.168185i	0.813382	+	0.581730i	$0.197624\pi$
$840$	−7.38940	+	41.6610i	−0.254959	+	1.43744i
$841$	3.55850	+	6.16350i	0.122707	+	0.212535i
$842$	10.7507	−	18.3271i	0.370494	−	0.631594i
$843$	27.3408	+	17.9937i	0.941668	+	0.619736i
$844$	−27.0888	+	15.1445i	−0.932436	+	0.521295i
$845$			51.4379i			1.76952i
$846$	−15.0343	−	11.3686i	−0.516890	−	0.390861i
$847$	2.31944	−	23.9995i	0.0796970	−	0.824631i
$848$	−41.3150	−	1.14225i	−1.41876	−	0.0392251i
$849$	7.03683	+	14.0216i	0.241503	+	0.481220i
$850$	26.2053	+	15.3721i	0.898835	+	0.527257i
$851$	−15.7573	−	27.2925i	−0.540154	−	0.935575i
$852$	2.18890	−	30.2277i	0.0749906	−	1.03558i
$853$	27.3976	−	47.4541i	0.938076	−	1.62480i	0.169022	−	0.985612i	$-0.445939\pi$
$853$	27.3976	−	47.4541i	0.938076	−	1.62480i	0.769054	−	0.639183i	$-0.220728\pi$
$854$	14.1719	+	31.7058i	0.484954	+	1.08495i
$855$	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	0.205960	+	0.978560i	$0.433968\pi$
$857$	−21.7943	+	37.7488i	−0.744478	+	1.28947i	−0.950438	+	0.310914i	$0.899365\pi$
$858$	1.17878	−	18.0046i	0.0402428	−	0.614667i
$859$	−12.9118	−	22.3639i	−0.440545	−	0.763046i	0.557185	−	0.830388i	$-0.311881\pi$
$859$	−12.9118	−	22.3639i	−0.440545	−	0.763046i	−0.997730	+	0.0673423i	$0.978548\pi$
$860$	22.9953	+	0.317820i	0.784134	+	0.0108376i
$861$	−1.29027	+	8.26762i	−0.0439722	+	0.281760i
$862$	40.5413	+	0.280148i	1.38084	+	0.00954190i
$863$			5.30974i			0.180746i	0.995908	+	0.0903728i	$0.0288059\pi$
$863$			5.30974i			0.180746i	−0.995908	+	0.0903728i	$0.971194\pi$
$864$	−6.12609	+	28.7484i	−0.208414	+	0.978041i
$865$	−6.93644			−0.235846
$866$	−22.3851	−	0.154686i	−0.760677	−	0.00525643i
$867$	4.45144	+	0.260561i	0.151179	+	0.00884913i
$868$	−52.9615	−	5.85831i	−1.79763	−	0.198844i
$869$	−10.4202	−	18.0483i	−0.353481	−	0.612248i
$870$	37.3251	+	2.44371i	1.26544	+	0.0828494i
$871$	−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
$876$	0.457619	−	6.31950i	0.0154615	−	0.213516i
$877$	−12.7473	+	7.35967i	−0.430446	+	0.248518i	−0.699537	−	0.714597i	$-0.746610\pi$
$877$	−12.7473	+	7.35967i	−0.430446	+	0.248518i	0.269090	+	0.963115i	$0.413277\pi$
$878$	−12.2252	+	20.8407i	−0.412579	+	0.703339i
$879$	10.6109	−	5.32514i	0.357896	−	0.179612i
$880$	0.495692	−	17.9291i	0.0167098	−	0.604388i
$881$	0.816537			0.0275098			0.0137549	−	0.999905i	$-0.495622\pi$
$881$	0.816537			0.0275098			0.0137549	+	0.999905i	$0.495622\pi$
$882$	29.0641	−	6.10555i	0.978639	−	0.205584i
$883$			35.1168i			1.18177i	0.806755	+	0.590886i	$0.201222\pi$
$883$			35.1168i			1.18177i	−0.806755	+	0.590886i	$0.798778\pi$
$884$	−19.8782	−	35.5559i	−0.668575	−	1.19587i
$885$	−11.1109	+	16.8827i	−0.373490	+	0.567505i
$886$	15.0825	+	8.84743i	0.506708	+	0.297235i
$887$	3.86884	+	6.70103i	0.129903	+	0.224999i	0.923639	−	0.383264i	$-0.125200\pi$
$887$	3.86884	+	6.70103i	0.129903	+	0.224999i	−0.793736	+	0.608263i	$0.791867\pi$
$888$	27.4908	+	2.18177i	0.922532	+	0.0732156i
$889$	−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
$894$	27.9825	−	13.8019i	0.935873	−	0.461606i
$895$	59.4270	−	34.3102i	1.98642	−	1.14686i
$896$	18.5486	−	23.4936i	0.619665	−	0.784866i
$897$	−43.4369	−	28.5870i	−1.45032	−	0.954491i
$898$	48.1741	+	0.332892i	1.60759	+	0.0111088i
$899$			47.1059i			1.57107i
$900$	−20.6557	+	26.9271i	−0.688524	+	0.897571i
$901$	39.2446			1.30743
$902$	0.0245106	−	3.54702i	0.000816113	−	0.118103i
$903$	−5.81894	−	15.0568i	−0.193642	−	0.501059i
$904$	−0.160250	−	0.291346i	−0.00532983	−	0.00969003i
$905$	−8.55499	+	4.93922i	−0.284377	+	0.164185i
$906$	10.6506	+	7.11540i	0.353843	+	0.236393i
$907$	−14.2113	−	8.20487i	−0.471877	−	0.272438i	0.245148	−	0.969486i	$-0.421163\pi$
$907$	−14.2113	−	8.20487i	−0.471877	−	0.272438i	−0.717025	+	0.697047i	$0.754497\pi$
$908$	6.08899	+	3.62859i	0.202070	+	0.120419i
$909$	1.27478	+	0.950191i	0.0422819	+	0.0315158i
$910$	59.7979	−	26.7287i	1.98228	−	0.886046i
$911$	−24.6180	−	14.2132i	−0.815630	−	0.470904i	0.0332774	−	0.999446i	$-0.489406\pi$
$911$	−24.6180	−	14.2132i	−0.815630	−	0.470904i	−0.848907	+	0.528542i	$0.822739\pi$
$912$	−22.1031	−	1.90796i	−0.731906	−	0.0631790i
$913$	−2.62500	+	1.51554i	−0.0868748	+	0.0501572i
$914$	21.0973	+	12.3757i	0.697837	+	0.409351i
$915$	−3.06659	+	52.3898i	−0.101378	+	1.73195i
$916$	−9.92837	−	17.7588i	−0.328043	−	0.586767i
$917$	25.2769	+	2.44291i	0.834718	+	0.0806719i
$918$	5.06024	−	27.4477i	0.167013	−	0.905908i
$919$	−44.9942			−1.48422			−0.742110	−	0.670278i	$-0.766175\pi$
$919$	−44.9942			−1.48422			−0.742110	+	0.670278i	$0.766175\pi$
$920$	−44.2201	−	26.7678i	−1.45790	−	0.882507i
$921$	−1.74824	−	0.102332i	−0.0576065	−	0.00337195i
$922$	−12.7175	+	21.6801i	−0.418830	+	0.713995i
$923$	−40.6308	+	23.4582i	−1.33738	+	0.772136i
$924$	−11.8045	+	4.37551i	−0.388339	+	0.143944i
$925$	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	−0.366527	−	0.930407i	$-0.619453\pi$
$929$	18.9733	−	32.8627i	0.622493	−	1.07819i	0.989020	−	0.147782i	$-0.0472134\pi$
$930$	−66.9524	−	44.7292i	−2.19546	−	1.46673i
$931$	7.28268	+	21.1991i	0.238680	+	0.694773i
$932$	0.103075	−	7.45785i	0.00337634	−	0.244290i
$933$	−6.95390	−	13.8564i	−0.227660	−	0.453637i
$934$	−42.2319	−	0.291831i	−1.38187	−	0.00954900i
$935$			17.0306i			0.556960i
$936$	42.1562	−	17.1285i	1.37792	−	0.559861i
$937$			37.8218i			1.23559i	0.786341	+	0.617793i	$0.211973\pi$
$937$			37.8218i			1.23559i	−0.786341	+	0.617793i	$0.788027\pi$
$938$	−3.01203	+	29.0666i	−0.0983463	+	0.949059i
$939$	−10.3941	−	6.84065i	−0.339200	−	0.223236i
$940$	−0.400845	+	29.0025i	−0.0130741	+	0.945958i
$941$	22.5442	−	13.0159i	0.734921	−	0.424307i	−0.0852987	−	0.996355i	$-0.527184\pi$
$941$	22.5442	−	13.0159i	0.734921	−	0.424307i	0.820220	+	0.572049i	$0.193851\pi$
$942$	−36.7569	+	18.1298i	−1.19760	+	0.590700i
$943$	−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	$-0.929720\pi$
$947$	−9.17669	+	15.8945i	−0.298202	+	0.516502i	0.677522	+	0.735502i	$0.263054\pi$
$948$	29.4975	−	43.4993i	0.958034	−	1.41279i
$949$	−8.49440	+	4.90424i	−0.275740	+	0.159198i
$950$	−22.0936	−	12.9601i	−0.716812	−	0.420482i
$951$	−24.1012	+	36.6210i	−0.781535	+	1.18752i
$952$	−16.9891	+	22.7860i	−0.550620	+	0.738498i
$953$		−	47.0368i		−	1.52367i	−0.647770	−	0.761836i	$-0.724298\pi$
$953$		−	47.0368i		−	1.52367i	0.647770	−	0.761836i	$-0.275702\pi$
$954$	−5.41523	+	43.5021i	−0.175325	+	1.40843i
$955$	−7.91701			−0.256189
$956$	7.15092	−	3.99785i	0.231277	−	0.129300i
$957$	4.99204	+	9.94715i	0.161370	+	0.321546i
$958$	32.0513	+	18.8013i	1.03553	+	0.607443i
$959$	15.0239	+	32.9977i	0.485146	+	1.06555i
$960$	41.2334	−	18.5956i	1.33080	−	0.600169i
$961$	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
$966$	−5.84213	+	35.8086i	−0.187967	+	1.15212i
$967$	22.0735	+	38.2325i	0.709837	+	1.22947i	0.964917	+	0.262554i	$0.0845648\pi$
$967$	22.0735	+	38.2325i	0.709837	+	1.22947i	−0.255080	+	0.966920i	$0.582102\pi$
$968$	−22.5851	+	12.4225i	−0.725911	+	0.399275i
$969$	21.0295	+	1.23094i	0.675564	+	0.0395435i
$970$	0.531316	−	76.8886i	0.0170595	−	2.46875i
$971$			25.9425i			0.832535i	0.909242	+	0.416267i	$0.136662\pi$
$971$			25.9425i			0.832535i	−0.909242	+	0.416267i	$0.863338\pi$
$972$	29.7271	+	9.39663i	0.953499	+	0.301397i
$973$	−0.553832	+	5.73054i	−0.0177550	+	0.183713i
$974$	−0.259396	+	37.5382i	−0.00831160	+	1.20280i
$975$	52.4465	+	3.06991i	1.67963	+	0.0983158i
$976$	19.4449	−	31.6274i	0.622416	−	1.01237i
$977$	−7.80914	+	4.50861i	−0.249836	+	0.144243i	−0.619689	−	0.784847i	$-0.712741\pi$
$977$	−7.80914	+	4.50861i	−0.249836	+	0.144243i	0.369853	+	0.929090i	$0.379408\pi$
$978$	28.2184	+	1.84748i	0.902325	+	0.0590760i
$979$	−3.99610	+	6.92144i	−0.127716	+	0.221210i
$980$	−34.0521	−	30.4806i	−1.08775	−	0.973669i
$981$	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	−0.992686	−	0.120724i	$-0.961478\pi$
$983$	−12.2838	+	21.2762i	−0.391793	+	0.678605i	0.600893	+	0.799329i	$0.294812\pi$
$984$	8.07655	−	3.84580i	0.257471	−	0.122600i
$985$	20.8447	−	12.0347i	0.664166	−	0.383457i
$986$	21.6730	+	12.7134i	0.690209	+	0.404877i
$987$	18.9902	−	7.33905i	0.604463	−	0.233605i
$988$	16.7592	+	29.9771i	0.533182	+	0.953697i
$989$	19.7205			0.627074
$990$	−18.8782	−	2.35000i	−0.599989	−	0.0746878i
$991$	15.8161			0.502414			0.251207	−	0.967933i	$-0.419172\pi$
$991$	15.8161			0.502414			0.251207	+	0.967933i	$0.419172\pi$
$992$	26.7607	+	50.2863i	0.849653	+	1.59659i
$993$	14.0151	+	9.22368i	0.444755	+	0.292705i
$994$	26.5114	+	19.2025i	0.840891	+	0.609065i
$995$	−13.3832	−	23.1803i	−0.424275	−	0.734866i
$996$	−6.32666	−	4.29020i	−0.200468	−	0.135940i
$997$	−1.75501	+	3.03976i	−0.0555816	+	0.0962702i	−0.892477	−	0.451092i	$-0.851035\pi$
$997$	−1.75501	+	3.03976i	−0.0555816	+	0.0962702i	0.836896	+	0.547362i	$0.184368\pi$
$998$	−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.461.41	yes	168
7.6	odd	2	inner	504.2.cc.b.461.42	yes	168
8.5	even	2	inner	504.2.cc.b.461.14	yes	168
9.5	odd	6	inner	504.2.cc.b.293.13	✓	168
56.13	odd	2	inner	504.2.cc.b.461.13	yes	168
63.41	even	6	inner	504.2.cc.b.293.14	yes	168
72.5	odd	6	inner	504.2.cc.b.293.42	yes	168
504.293	even	6	inner	504.2.cc.b.293.41	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cc.b.293.13	✓	168	9.5	odd	6	inner
504.2.cc.b.293.14	yes	168	63.41	even	6	inner
504.2.cc.b.293.41	yes	168	504.293	even	6	inner
504.2.cc.b.293.42	yes	168	72.5	odd	6	inner
504.2.cc.b.461.13	yes	168	56.13	odd	2	inner
504.2.cc.b.461.14	yes	168	8.5	even	2	inner
504.2.cc.b.461.41	yes	168	1.1	even	1	trivial
504.2.cc.b.461.42	yes	168	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.00977226 - 1.41418i) q^{2} +(-1.72909 - 0.101211i) q^{3} +(-1.99981 - 0.0276395i) q^{4} +(2.82704 - 1.63219i) q^{5} +(-0.160028 + 2.44426i) q^{6} +(-2.15340 - 1.53716i) q^{7} +(-0.0586299 + 2.82782i) q^{8} +(2.97951 + 0.350006i) q^{9} +O(q^{10})\)	\(q+(0.00977226 - 1.41418i) q^{2} +(-1.72909 - 0.101211i) q^{3} +(-1.99981 - 0.0276395i) q^{4} +(2.82704 - 1.63219i) q^{5} +(-0.160028 + 2.44426i) 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} +(3.45505 + 0.250194i) q^{12} +(-2.68129 - 4.64414i) q^{13} +(-2.19486 + 3.03028i) q^{14} +(-5.05340 + 2.53608i) q^{15} +(3.99847 + 0.110547i) q^{16} -3.79810 q^{17} +(0.524088 - 4.21015i) q^{18} +3.20217 q^{19} +(-5.69865 + 3.18593i) q^{20} +(3.56786 + 2.87583i) q^{21} +(-1.67557 - 0.982888i) q^{22} +(-4.84839 + 2.79922i) q^{23} +(0.387582 - 4.88362i) q^{24} +(2.82809 - 4.89840i) q^{25} +(-6.59385 + 3.74645i) q^{26} +(-5.11642 - 0.906751i) q^{27} +(4.26391 + 3.13354i) q^{28} +(2.33896 - 4.05120i) q^{29} +(3.53709 + 7.17120i) q^{30} +(-8.72073 + 5.03492i) q^{31} +(0.195408 - 5.65348i) q^{32} +(-1.30794 + 1.98738i) q^{33} +(-0.0371160 + 5.37120i) q^{34} +(-8.59669 - 0.830833i) q^{35} +(-5.94878 - 0.782297i) q^{36} +5.62919i q^{37} +(0.0312924 - 4.52844i) q^{38} +(4.16616 + 8.30151i) q^{39} +(4.44979 + 8.09005i) q^{40} +(0.912990 + 1.58135i) q^{41} +(4.10181 - 5.01749i) 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} +(-6.90253 - 0.595835i) q^{48} +(2.27430 + 6.62024i) q^{49} +(-6.89959 - 4.04730i) q^{50} +(6.56726 + 0.384409i) q^{51} +(5.23371 + 9.36149i) q^{52} -10.3327 q^{53} +(-1.33231 + 7.22668i) q^{54} -4.48398i q^{55} +(4.47305 - 5.99931i) q^{56} +(-5.53684 - 0.324094i) q^{57} +(-5.70627 - 3.34730i) q^{58} +(3.09566 - 1.78728i) q^{59} +(10.1759 - 4.93200i) 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} +(2.79773 + 1.86909i) q^{66} +(6.76364 - 3.90499i) q^{67} +(7.59547 + 0.104977i) q^{68} +(8.66662 - 4.34940i) q^{69} +(-1.25896 + 12.1491i) q^{70} -8.74884i q^{71} +(-1.16444 + 8.40500i) q^{72} -1.82906i q^{73} +(7.96069 + 0.0550099i) q^{74} +(-5.38581 + 8.18355i) q^{75} +(-6.40372 - 0.0885062i) q^{76} +(-3.30753 + 1.50592i) q^{77} +(11.7805 - 5.81058i) 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} +(-7.05554 - 5.84973i) q^{84} +(-10.7374 + 6.19922i) q^{85} +(-2.52053 + 4.29684i) q^{86} +(-4.45431 + 6.76817i) q^{87} +(3.32365 + 2.01190i) q^{88} -5.81840 q^{89} +(-5.39015 - 12.7577i) q^{90} +(-1.36486 + 14.1223i) q^{91} +(9.77322 - 5.46390i) q^{92} +(15.5885 - 7.82320i) q^{93} +(-5.41933 - 3.17898i) q^{94} +(9.05264 - 5.22655i) q^{95} +(-0.910072 + 9.75560i) q^{96} +(14.4240 + 8.32773i) q^{97} +(9.38443 - 3.15157i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more