LMFDB - Embedded newform 231.2.u.a.20.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(20,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 6]))

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

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

chi := DirichletCharacter("231.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.u (of order $10$, degree $4$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			20.15
Character	$\chi$	$=$	231.20
Dual form			231.2.u.a.104.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.126891 + 0.0412293i) q^{2} +(-1.50633 - 0.854974i) q^{3} +(-1.60363 - 1.16511i) q^{4} +(0.887927 + 2.73276i) q^{5} +(-0.155889 - 0.170593i) q^{6} +(0.380318 + 2.61827i) q^{7} +(-0.312296 - 0.429838i) q^{8} +(1.53804 + 2.57574i) q^{9} +O(q^{10})$	\(q+(0.126891 + 0.0412293i) q^{2} +(-1.50633 - 0.854974i) q^{3} +(-1.60363 - 1.16511i) q^{4} +(0.887927 + 2.73276i) q^{5} +(-0.155889 - 0.170593i) q^{6} +(0.380318 + 2.61827i) q^{7} +(-0.312296 - 0.429838i) q^{8} +(1.53804 + 2.57574i) q^{9} +0.383371i q^{10} +(2.78405 - 1.80251i) q^{11} +(1.41946 + 3.12610i) q^{12} +(1.85148 + 0.601582i) q^{13} +(-0.0596909 + 0.347915i) q^{14} +(0.998930 - 4.87558i) q^{15} +(1.20316 + 3.70295i) q^{16} +(1.87135 + 5.75941i) q^{17} +(0.0889671 + 0.390250i) q^{18} +(-2.09302 - 2.88080i) q^{19} +(1.76005 - 5.41687i) q^{20} +(1.66567 - 4.26914i) q^{21} +(0.427587 - 0.113938i) q^{22} +5.52810i q^{23} +(0.102919 + 0.914481i) q^{24} +(-2.63447 + 1.91406i) q^{25} +(0.210133 + 0.152670i) q^{26} +(-0.114599 - 5.19489i) q^{27} +(2.44068 - 4.64186i) q^{28} +(-4.07967 + 5.61519i) q^{29} +(0.327772 - 0.577482i) q^{30} +(-3.17461 - 1.03149i) q^{31} +1.58209i q^{32} +(-5.73479 + 0.334884i) q^{33} +0.807972i q^{34} +(-6.81742 + 3.36415i) q^{35} +(0.534564 - 5.92252i) q^{36} +(-4.68486 - 3.40375i) q^{37} +(-0.146812 - 0.451842i) q^{38} +(-2.27459 - 2.48914i) q^{39} +(0.897348 - 1.23509i) q^{40} +(5.14995 - 3.74166i) q^{41} +(0.387372 - 0.473040i) q^{42} +2.30910 q^{43} +(-6.56472 - 0.353147i) q^{44} +(-5.67321 + 6.49016i) q^{45} +(-0.227920 + 0.701465i) q^{46} +(2.95837 - 2.14938i) q^{47} +(1.35357 - 6.60652i) q^{48} +(-6.71072 + 1.99155i) q^{49} +(-0.413206 + 0.134259i) q^{50} +(2.10529 - 10.2755i) q^{51} +(-2.26818 - 3.12189i) q^{52} +(1.75794 + 0.571189i) q^{53} +(0.199640 - 0.663909i) q^{54} +(7.39787 + 6.00764i) q^{55} +(1.00666 - 0.981150i) q^{56} +(0.689769 + 6.12891i) q^{57} +(-0.749184 + 0.544314i) q^{58} +(0.331949 + 0.241175i) q^{59} +(-7.28249 + 6.65478i) q^{60} +(6.76031 - 2.19656i) q^{61} +(-0.360301 - 0.261774i) q^{62} +(-6.15905 + 5.00661i) q^{63} +(2.34109 - 7.20514i) q^{64} +5.59381i q^{65} +(-0.741500 - 0.193948i) q^{66} +13.9386 q^{67} +(3.70938 - 11.4163i) q^{68} +(4.72638 - 8.32712i) q^{69} +(-1.00377 + 0.145803i) q^{70} +(-4.59930 + 1.49440i) q^{71} +(0.626828 - 1.46550i) q^{72} +(4.35552 - 5.99486i) q^{73} +(-0.454132 - 0.625059i) q^{74} +(5.60485 - 0.630789i) q^{75} +7.05835i q^{76} +(5.77830 + 6.60388i) q^{77} +(-0.185999 - 0.409630i) q^{78} +(1.05512 - 3.24734i) q^{79} +(-9.05095 + 6.57590i) q^{80} +(-4.26887 + 7.92318i) q^{81} +(0.807748 - 0.262453i) q^{82} +(-2.27384 - 6.99816i) q^{83} +(-7.64513 + 4.90544i) q^{84} +(-14.0775 + 10.2279i) q^{85} +(0.293004 + 0.0952027i) q^{86} +(10.9462 - 4.97029i) q^{87} +(-1.64424 - 0.633773i) q^{88} -11.8861 q^{89} +(-0.987464 + 0.589639i) q^{90} +(-0.870956 + 5.07647i) q^{91} +(6.44082 - 8.86503i) q^{92} +(3.90009 + 4.26797i) q^{93} +(0.464008 - 0.150765i) q^{94} +(6.01408 - 8.27768i) q^{95} +(1.35265 - 2.38315i) q^{96} +(-7.62887 - 2.47877i) q^{97} +(-0.933639 - 0.0239686i) q^{98} +(8.92479 + 4.39865i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) $ 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9	$ 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9} - 60 q^{16} + 2 q^{18} - 80 q^{22} - 36 q^{25} + 8 q^{28} + 24 q^{30} - 34 q^{36} + 4 q^{37} - 66 q^{39} - 30 q^{42} + 36 q^{46} + 26 q^{49} + 38 q^{51} - 86 q^{57} - 116 q^{58} + 88 q^{60} + 44 q^{63} - 32 q^{64} + 110 q^{70} + 86 q^{72} - 52 q^{78} - 156 q^{79} + 68 q^{81} - 30 q^{84} + 8 q^{85} - 112 q^{88} + 42 q^{91} + 56 q^{93} + 70 q^{99}+O(q^{100}) $ 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9 - 60 * q^16 + 2 * q^18 - 80 * q^22 - 36 * q^25 + 8 * q^28 + 24 * q^30 - 34 * q^36 + 4 * q^37 - 66 * q^39 - 30 * q^42 + 36 * q^46 + 26 * q^49 + 38 * q^51 - 86 * q^57 - 116 * q^58 + 88 * q^60 + 44 * q^63 - 32 * q^64 + 110 * q^70 + 86 * q^72 - 52 * q^78 - 156 * q^79 + 68 * q^81 - 30 * q^84 + 8 * q^85 - 112 * q^88 + 42 * q^91 + 56 * q^93 + 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.126891	+	0.0412293i	0.0897254	+	0.0291536i	0.353536	−	0.935421i	$-0.384979\pi$
$2$	0.126891	+	0.0412293i	0.0897254	+	0.0291536i	−0.263810	+	0.964575i	$0.584979\pi$
$3$	−1.50633	−	0.854974i	−0.869678	−	0.493619i
$3$	−1.50633	−	0.854974i	−0.869678	−	0.493619i
$4$	−1.60363	−	1.16511i	−0.801816	−	0.582554i
$5$	0.887927	+	2.73276i	0.397093	+	1.22213i	0.927319	+	0.374271i	$0.122107\pi$
$5$	0.887927	+	2.73276i	0.397093	+	1.22213i	−0.530226	+	0.847856i	$0.677893\pi$
$6$	−0.155889	−	0.170593i	−0.0636415	−	0.0696444i
$7$	0.380318	+	2.61827i	0.143747	+	0.989615i
$7$	0.380318	+	2.61827i	0.143747	+	0.989615i
$8$	−0.312296	−	0.429838i	−0.110413	−	0.151971i
$9$	1.53804	+	2.57574i	0.512680	+	0.858580i
$10$			0.383371i			0.121233i
$11$	2.78405	−	1.80251i	0.839423	−	0.543479i
$11$	2.78405	−	1.80251i	0.839423	−	0.543479i
$12$	1.41946	+	3.12610i	0.409762	+	0.902426i
$13$	1.85148	+	0.601582i	0.513508	+	0.166849i	0.554297	−	0.832319i	$-0.312987\pi$
$13$	1.85148	+	0.601582i	0.513508	+	0.166849i	−0.0407892	+	0.999168i	$0.512987\pi$
$14$	−0.0596909	+	0.347915i	−0.0159531	+	0.0929843i
$15$	0.998930	−	4.87558i	0.257923	−	1.25887i
$16$	1.20316	+	3.70295i	0.300790	+	0.925737i
$17$	1.87135	+	5.75941i	0.453868	+	1.39686i	0.872459	+	0.488688i	$0.162524\pi$
$17$	1.87135	+	5.75941i	0.453868	+	1.39686i	−0.418590	+	0.908175i	$0.637476\pi$
$18$	0.0889671	+	0.390250i	0.0209697	+	0.0919829i
$19$	−2.09302	−	2.88080i	−0.480173	−	0.660901i	0.498365	−	0.866967i	$-0.333934\pi$
$19$	−2.09302	−	2.88080i	−0.480173	−	0.660901i	−0.978538	+	0.206066i	$0.933934\pi$
$20$	1.76005	−	5.41687i	0.393559	−	1.21125i
$21$	1.66567	−	4.26914i	0.363480	−	0.931602i
$22$	0.427587	−	0.113938i	0.0911619	−	0.0242917i
$23$			5.52810i			1.15269i	0.817207	+	0.576344i	$0.195521\pi$
$23$			5.52810i			1.15269i	−0.817207	+	0.576344i	$0.804479\pi$
$24$	0.102919	+	0.914481i	0.0210082	+	0.186668i
$25$	−2.63447	+	1.91406i	−0.526895	+	0.382812i
$26$	0.210133	+	0.152670i	0.0412105	+	0.0299411i
$27$	−0.114599	−	5.19489i	−0.0220545	−	0.999757i
$28$	2.44068	−	4.64186i	0.461245	−	0.877229i
$29$	−4.07967	+	5.61519i	−0.757576	+	1.04271i	0.239836	+	0.970814i	$0.422906\pi$
$29$	−4.07967	+	5.61519i	−0.757576	+	1.04271i	−0.997412	+	0.0719007i	$0.977094\pi$
$30$	0.327772	−	0.577482i	0.0598427	−	0.105433i
$31$	−3.17461	−	1.03149i	−0.570176	−	0.185261i	0.00971880	−	0.999953i	$-0.496906\pi$
$31$	−3.17461	−	1.03149i	−0.570176	−	0.185261i	−0.579895	+	0.814691i	$0.696906\pi$
$32$			1.58209i			0.279677i
$33$	−5.73479	+	0.334884i	−0.998299	+	0.0582959i
$34$			0.807972i			0.138566i
$35$	−6.81742	+	3.36415i	−1.15235	+	0.568646i
$36$	0.534564	−	5.92252i	0.0890939	−	0.987087i
$37$	−4.68486	−	3.40375i	−0.770187	−	0.559573i	0.131831	−	0.991272i	$-0.457914\pi$
$37$	−4.68486	−	3.40375i	−0.770187	−	0.559573i	−0.902018	+	0.431699i	$0.857914\pi$
$38$	−0.146812	−	0.451842i	−0.0238161	−	0.0732984i
$39$	−2.27459	−	2.48914i	−0.364227	−	0.398582i
$40$	0.897348	−	1.23509i	0.141883	−	0.195285i
$41$	5.14995	−	3.74166i	0.804287	−	0.584349i	−0.107882	−	0.994164i	$-0.534407\pi$
$41$	5.14995	−	3.74166i	0.804287	−	0.584349i	0.912169	+	0.409815i	$0.134407\pi$
$42$	0.387372	−	0.473040i	0.0597729	−	0.0729917i
$43$	2.30910			0.352135			0.176067	−	0.984378i	$-0.443662\pi$
$43$	2.30910			0.352135			0.176067	+	0.984378i	$0.443662\pi$
$44$	−6.56472	−	0.353147i	−0.989668	−	0.0532389i
$45$	−5.67321	+	6.49016i	−0.845712	+	0.967496i
$46$	−0.227920	+	0.701465i	−0.0336049	+	0.103425i
$47$	2.95837	−	2.14938i	0.431522	−	0.313519i	−0.350735	−	0.936475i	$-0.614068\pi$
$47$	2.95837	−	2.14938i	0.431522	−	0.313519i	0.782257	+	0.622955i	$0.214068\pi$
$48$	1.35357	−	6.60652i	0.195371	−	0.953569i
$49$	−6.71072	+	1.99155i	−0.958674	+	0.284507i
$50$	−0.413206	+	0.134259i	−0.0584362	+	0.0189871i
$51$	2.10529	−	10.2755i	0.294799	−	1.43886i
$52$	−2.26818	−	3.12189i	−0.314540	−	0.432928i
$53$	1.75794	+	0.571189i	0.241471	+	0.0784588i	0.427253	−	0.904132i	$-0.359482\pi$
$53$	1.75794	+	0.571189i	0.241471	+	0.0784588i	−0.185781	+	0.982591i	$0.559482\pi$
$54$	0.199640	−	0.663909i	0.0271676	−	0.0903465i
$55$	7.39787	+	6.00764i	0.997529	+	0.810070i
$56$	1.00666	−	0.981150i	0.134521	−	0.131112i
$57$	0.689769	+	6.12891i	0.0913621	+	0.811794i
$58$	−0.749184	+	0.544314i	−0.0983727	+	0.0714719i
$59$	0.331949	+	0.241175i	0.0432161	+	0.0313984i	0.609184	−	0.793029i	$-0.291497\pi$
$59$	0.331949	+	0.241175i	0.0432161	+	0.0313984i	−0.565967	+	0.824428i	$0.691497\pi$
$60$	−7.28249	+	6.65478i	−0.940166	+	0.859129i
$61$	6.76031	−	2.19656i	0.865569	−	0.281241i	0.157617	−	0.987500i	$-0.449619\pi$
$61$	6.76031	−	2.19656i	0.865569	−	0.281241i	0.707953	+	0.706260i	$0.249619\pi$
$62$	−0.360301	−	0.261774i	−0.0457582	−	0.0332453i
$63$	−6.15905	+	5.00661i	−0.775967	+	0.630773i
$64$	2.34109	−	7.20514i	0.292637	−	0.900643i
$65$			5.59381i			0.693826i
$66$	−0.741500	−	0.193948i	−0.0912723	−	0.0238733i
$67$	13.9386			1.70287			0.851433	−	0.524463i	$-0.175734\pi$
$67$	13.9386			1.70287			0.851433	+	0.524463i	$0.175734\pi$
$68$	3.70938	−	11.4163i	0.449829	−	1.38443i
$69$	4.72638	−	8.32712i	0.568989	−	1.00247i
$70$	−1.00377	+	0.145803i	−0.119973	+	0.0174268i
$71$	−4.59930	+	1.49440i	−0.545837	+	0.177353i	−0.568939	−	0.822380i	$-0.692646\pi$
$71$	−4.59930	+	1.49440i	−0.545837	+	0.177353i	0.0231019	+	0.999733i	$0.492646\pi$
$72$	0.626828	−	1.46550i	0.0738724	−	0.172711i
$73$	4.35552	−	5.99486i	0.509775	−	0.701646i	−0.474106	−	0.880468i	$-0.657229\pi$
$73$	4.35552	−	5.99486i	0.509775	−	0.701646i	0.983881	+	0.178822i	$0.0572287\pi$
$74$	−0.454132	−	0.625059i	−0.0527918	−	0.0726616i
$75$	5.60485	−	0.630789i	0.647192	−	0.0728372i
$76$			7.05835i			0.809648i
$77$	5.77830	+	6.60388i	0.658499	+	0.752582i
$78$	−0.185999	−	0.409630i	−0.0210603	−	0.0463814i
$79$	1.05512	−	3.24734i	0.118711	−	0.365354i	−0.873992	−	0.485940i	$-0.838477\pi$
$79$	1.05512	−	3.24734i	0.118711	−	0.365354i	0.992703	+	0.120586i	$0.0384773\pi$
$80$	−9.05095	+	6.57590i	−1.01193	+	0.735208i
$81$	−4.26887	+	7.92318i	−0.474319	+	0.880353i
$82$	0.807748	−	0.262453i	0.0892008	−	0.0289831i
$83$	−2.27384	−	6.99816i	−0.249586	−	0.768147i	−0.994848	−	0.101376i	$-0.967676\pi$
$83$	−2.27384	−	6.99816i	−0.249586	−	0.768147i	0.745262	−	0.666772i	$-0.232324\pi$
$84$	−7.64513	+	4.90544i	−0.834152	+	0.535227i
$85$	−14.0775	+	10.2279i	−1.52692	+	1.10937i
$86$	0.293004	+	0.0952027i	0.0315954	+	0.0102660i
$87$	10.9462	−	4.97029i	1.17355	−	0.532871i
$88$	−1.64424	−	0.633773i	−0.175276	−	0.0675605i
$89$	−11.8861			−1.25992			−0.629961	−	0.776627i	$-0.716929\pi$
$89$	−11.8861			−1.25992			−0.629961	+	0.776627i	$0.716929\pi$
$90$	−0.987464	+	0.589639i	−0.104088	+	0.0621535i
$91$	−0.870956	+	5.07647i	−0.0913010	+	0.532159i
$92$	6.44082	−	8.86503i	0.671502	−	0.924244i
$93$	3.90009	+	4.26797i	0.404421	+	0.442568i
$94$	0.464008	−	0.150765i	0.0478587	−	0.0155502i
$95$	6.01408	−	8.27768i	0.617032	−	0.849272i
$96$	1.35265	−	2.38315i	0.138054	−	0.243229i
$97$	−7.62887	−	2.47877i	−0.774594	−	0.251681i	−0.105064	−	0.994465i	$-0.533505\pi$
$97$	−7.62887	−	2.47877i	−0.774594	−	0.251681i	−0.669531	+	0.742784i	$0.733505\pi$
$98$	−0.933639	−	0.0239686i	−0.0943118	−	0.00242120i
$99$	8.92479	+	4.39865i	0.896975	+	0.442081i
$100$	6.45481			0.645481
$101$	−1.93250	+	5.94761i	−0.192291	+	0.591809i	0.807707	+	0.589584i	$0.200708\pi$
$101$	−1.93250	+	5.94761i	−0.192291	+	0.591809i	−0.999998	+	0.00222533i	$0.999292\pi$
$102$	0.690795	−	1.21707i	0.0683989	−	0.120508i
$103$	−0.965540	+	1.32895i	−0.0951375	+	0.130946i	−0.853932	−	0.520384i	$-0.825789\pi$
$103$	−0.965540	+	1.32895i	−0.0951375	+	0.130946i	0.758795	+	0.651330i	$0.225789\pi$
$104$	−0.319626	−	0.983707i	−0.0313419	−	0.0964604i
$105$	13.1455	+	0.761201i	1.28287	+	0.0742856i
$106$	0.199517	+	0.144957i	0.0193788	+	0.0140795i
$107$	−11.2375	−	15.4671i	−1.08637	−	1.49526i	−0.852307	−	0.523042i	$-0.824797\pi$
$107$	−11.2375	−	15.4671i	−1.08637	−	1.49526i	−0.234066	−	0.972221i	$-0.575203\pi$
$108$	−5.86883	+	8.46421i	−0.564728	+	0.814469i
$109$	−2.63945			−0.252814			−0.126407	−	0.991978i	$-0.540344\pi$
$109$	−2.63945			−0.252814			−0.126407	+	0.991978i	$0.540344\pi$
$110$	0.691032	+	1.06732i	0.0658873	+	0.101765i
$111$	4.14681	+	9.13260i	0.393598	+	0.866828i
$112$	−9.23775	+	4.55850i	−0.872885	+	0.430738i
$113$	9.22896	+	12.7026i	0.868188	+	1.19496i	0.979555	+	0.201178i	$0.0644771\pi$
$113$	9.22896	+	12.7026i	0.868188	+	1.19496i	−0.111367	+	0.993779i	$0.535523\pi$
$114$	−0.165166	+	0.806141i	−0.0154692	+	0.0755021i
$115$	−15.1070	+	4.90855i	−1.40873	+	0.457724i
$116$	13.0846	−	4.25144i	1.21487	−	0.394736i
$117$	1.29813	+	5.69418i	0.120012	+	0.526427i
$118$	0.0321779	+	0.0442890i	0.00296221	+	0.00407713i
$119$	−14.3680	+	7.09011i	−1.31711	+	0.649949i
$120$	−2.40767	+	1.09324i	−0.219789	+	0.0997991i
$121$	4.50188	−	10.0366i	0.409262	−	0.912417i
$122$	0.948385			0.0858627
$123$	−10.9565	+	1.23308i	−0.987917	+	0.111184i
$124$	3.88910	+	5.35289i	0.349252	+	0.480704i
$125$	4.05324	+	2.94485i	0.362533	+	0.263395i
$126$	−0.987946	+	0.381359i	−0.0880133	+	0.0339742i
$127$	−0.0468692	−	0.144249i	−0.00415897	−	0.0128000i	0.948955	−	0.315410i	$-0.102142\pi$
$127$	−0.0468692	−	0.144249i	−0.00415897	−	0.0128000i	−0.953114	+	0.302610i	$0.902142\pi$
$128$	2.45399	−	3.37763i	0.216904	−	0.298543i
$129$	−3.47826	−	1.97422i	−0.306244	−	0.173820i
$130$	−0.230629	+	0.709803i	−0.0202275	+	0.0622538i
$131$	5.61187			0.490312			0.245156	−	0.969484i	$-0.421161\pi$
$131$	5.61187			0.490312			0.245156	+	0.969484i	$0.421161\pi$
$132$	9.58668	+	6.14462i	0.834413	+	0.534820i
$133$	6.74671	−	6.57573i	0.585014	−	0.570188i
$134$	1.76868	+	0.574678i	0.152790	+	0.0496446i
$135$	14.0946	−	4.92585i	1.21307	−	0.423950i
$136$	1.89120	−	2.60301i	0.162169	−	0.223207i
$137$	16.0909	−	5.22826i	1.37474	−	0.446681i	0.473804	−	0.880630i	$-0.342880\pi$
$137$	16.0909	−	5.22826i	1.37474	−	0.446681i	0.900937	+	0.433950i	$0.142880\pi$
$138$	0.943056	−	0.861770i	0.0802782	−	0.0733587i
$139$	12.7305	−	17.5220i	1.07979	−	1.48620i	0.220033	−	0.975492i	$-0.429383\pi$
$139$	12.7305	−	17.5220i	1.07979	−	1.48620i	0.859754	−	0.510708i	$-0.170617\pi$
$140$	14.8522	+	2.54816i	1.25524	+	0.215359i
$141$	−6.29393	+	0.708341i	−0.530045	+	0.0596531i
$142$	−0.645223			−0.0541459
$143$	6.23897	−	1.66248i	0.521729	−	0.139024i
$144$	−7.68732	+	8.79431i	−0.640610	+	0.732859i
$145$	−18.9674	−	6.16289i	−1.57516	−	0.511800i
$146$	0.799840	−	0.581118i	0.0661953	−	0.0480937i
$147$	11.8113	+	2.73756i	0.974176	+	0.225790i
$148$	3.54706	+	10.9167i	0.291567	+	0.897350i
$149$	0.154577	−	0.0502252i	0.0126635	−	0.00411461i	−0.302678	−	0.953093i	$-0.597881\pi$
$149$	0.154577	−	0.0502252i	0.0126635	−	0.00411461i	0.315342	+	0.948978i	$0.397881\pi$
$150$	0.737211	+	0.151043i	0.0601930	+	0.0123326i
$151$	−2.98259	+	2.16698i	−0.242720	+	0.176346i	−0.702494	−	0.711689i	$-0.747930\pi$
$151$	−2.98259	+	2.16698i	−0.242720	+	0.176346i	0.459774	+	0.888036i	$0.347930\pi$
$152$	−0.584635	+	1.79932i	−0.0474202	+	0.145944i
$153$	−11.9565	+	13.6783i	−0.966630	+	1.10583i
$154$	0.460940	+	1.07621i	0.0371436	+	0.0867233i
$155$		−	9.59132i		−	0.770394i
$156$	0.747493	+	6.64182i	0.0598473	+	0.531771i
$157$	13.9560	+	19.2088i	1.11381	+	1.53303i	0.815681	+	0.578502i	$0.196363\pi$
$157$	13.9560	+	19.2088i	1.11381	+	1.53303i	0.298129	+	0.954526i	$0.403637\pi$
$158$	0.267771	−	0.368556i	0.0213028	−	0.0293207i
$159$	−2.15968	−	2.36339i	−0.171274	−	0.187429i
$160$	−4.32348	+	1.40478i	−0.341801	+	0.111058i
$161$	−14.4741	+	2.10243i	−1.14072	+	0.165695i
$162$	−0.868348	+	0.829376i	−0.0682239	+	0.0651619i
$163$	−4.33310	+	13.3359i	−0.339394	+	1.04455i	0.625122	+	0.780527i	$0.285049\pi$
$163$	−4.33310	+	13.3359i	−0.339394	+	1.04455i	−0.964517	+	0.264022i	$0.914951\pi$
$164$	−12.6181			−0.985305
$165$	−6.00724	−	15.3745i	−0.467663	−	1.19690i
$166$		−	0.981751i		−	0.0761987i
$167$	3.63417	−	11.1848i	0.281220	−	0.865507i	−0.706286	−	0.707927i	$-0.749631\pi$
$167$	3.63417	−	11.1848i	0.281220	−	0.865507i	0.987506	−	0.157580i	$-0.0503693\pi$
$168$	−2.35522	+	0.617263i	−0.181709	+	0.0476229i
$169$	−7.45115	−	5.41358i	−0.573165	−	0.416429i
$170$	−2.20799	+	0.717420i	−0.169345	+	0.0550236i
$171$	4.20104	−	9.82187i	0.321262	−	0.751097i
$172$	−3.70295	−	2.69035i	−0.282347	−	0.205137i
$173$	−5.88706	+	4.27720i	−0.447585	+	0.325189i	−0.788641	−	0.614853i	$-0.789215\pi$
$173$	−5.88706	+	4.27720i	−0.447585	+	0.325189i	0.341057	+	0.940043i	$0.389215\pi$
$174$	1.59389	−	0.179382i	0.120832	−	0.0135989i
$175$	−6.01346	−	6.16983i	−0.454575	−	0.466395i
$176$	10.0243	+	8.14048i	0.755608	+	0.613612i
$177$	−0.293826	−	0.647097i	−0.0220853	−	0.0486388i
$178$	−1.50824	−	0.490055i	−0.113047	−	0.0367312i
$179$	−5.18826	−	7.14102i	−0.387789	−	0.533745i	0.569838	−	0.821757i	$-0.307006\pi$
$179$	−5.18826	−	7.14102i	−0.387789	−	0.533745i	−0.957627	+	0.288012i	$0.907006\pi$
$180$	16.6595	−	3.79793i	1.24172	−	0.283081i
$181$	4.06669	−	1.32135i	0.302275	−	0.0982150i	−0.153953	−	0.988078i	$-0.549200\pi$
$181$	4.06669	−	1.32135i	0.302275	−	0.0982150i	0.456227	+	0.889863i	$0.349200\pi$
$182$	−0.319816	+	0.608249i	−0.0237063	+	0.0450864i
$183$	−12.0612	−	2.47116i	−0.891592	−	0.182673i
$184$	2.37618	−	1.72640i	0.175175	−	0.127272i
$185$	5.14182	−	15.8249i	0.378034	−	1.16347i
$186$	0.318921	+	0.702365i	0.0233844	+	0.0514999i
$187$	15.5914	+	12.6614i	1.14015	+	0.925891i
$188$	−7.24840			−0.528644
$189$	13.5581	−	2.27576i	0.986204	−	0.165537i
$190$	1.10442	−	0.802405i	0.0801227	−	0.0582126i
$191$	−10.9853	+	15.1200i	−0.794872	+	1.09405i	0.198613	+	0.980078i	$0.436356\pi$
$191$	−10.9853	+	15.1200i	−0.794872	+	1.09405i	−0.993484	+	0.113969i	$0.963644\pi$
$192$	−9.68666	+	8.85172i	−0.699074	+	0.638818i
$193$	−5.59689	−	17.2255i	−0.402873	−	1.23992i	−0.922658	−	0.385619i	$-0.873988\pi$
$193$	−5.59689	−	17.2255i	−0.402873	−	1.23992i	0.519785	−	0.854297i	$-0.326012\pi$
$194$	−0.865836	−	0.629067i	−0.0621634	−	0.0451644i
$195$	4.78256	−	8.42610i	0.342486	−	0.603405i
$196$	13.0819	+	4.62499i	0.934421	+	0.330356i
$197$		−	21.8141i		−	1.55419i	−0.629382	−	0.777096i	$-0.716692\pi$
$197$		−	21.8141i		−	1.55419i	0.629382	−	0.777096i	$-0.283308\pi$
$198$	0.951121	+	0.926112i	0.0675932	+	0.0658159i
$199$			15.7537i			1.11675i	0.829590	+	0.558373i	$0.188574\pi$
$199$			15.7537i			1.11675i	−0.829590	+	0.558373i	$0.811426\pi$
$200$	1.64547	+	0.534645i	0.116352	+	0.0378051i
$201$	−20.9960	−	11.9171i	−1.48095	−	0.840568i
$202$	−0.490432	+	0.675022i	−0.0345067	+	0.0474944i
$203$	−16.2537	−	8.54615i	−1.14078	−	0.599822i
$204$	−15.3482	+	14.0253i	−1.07459	+	0.981964i
$205$	14.7978	+	10.7513i	1.03353	+	0.750900i
$206$	−0.177310	+	0.128823i	−0.0123538	+	0.00897554i
$207$	−14.2389	+	8.50243i	−0.989674	+	0.590959i
$208$			7.57973i			0.525560i
$209$	−11.0198	−	4.24759i	−0.762254	−	0.293812i
$210$	1.63666	+	0.638571i	0.112940	+	0.0440656i
$211$	7.73577	−	23.8083i	0.532552	−	1.63903i	−0.216326	−	0.976321i	$-0.569408\pi$
$211$	7.73577	−	23.8083i	0.532552	−	1.63903i	0.748879	−	0.662707i	$-0.230592\pi$
$212$	−2.15359	−	2.96416i	−0.147909	−	0.203580i
$213$	8.20573	+	1.68122i	0.562247	+	0.115196i
$214$	−0.788240	−	2.42595i	−0.0538830	−	0.165835i
$215$	2.05031	+	6.31022i	0.139830	+	0.430353i
$216$	−2.19717	+	1.67160i	−0.149499	+	0.113738i
$217$	1.49337	−	8.70428i	0.101377	−	0.590885i
$218$	−0.334922	−	0.108823i	−0.0226838	−	0.00737041i
$219$	−11.6863	+	5.30636i	−0.789686	+	0.358571i
$220$	−4.86393	−	18.2534i	−0.327926	−	1.23064i
$221$			11.7892i			0.793027i
$222$	0.149662	+	1.32981i	0.0100446	+	0.0892513i
$223$	−3.18652	−	4.38587i	−0.213385	−	0.293700i	0.688885	−	0.724871i	$-0.258101\pi$
$223$	−3.18652	−	4.38587i	−0.213385	−	0.293700i	−0.902270	+	0.431171i	$0.858101\pi$
$224$	−4.14235	+	0.601698i	−0.276773	+	0.0402027i
$225$	−8.98204	−	3.84182i	−0.598803	−	0.256122i
$226$	0.647352	+	1.99235i	0.0430612	+	0.132529i
$227$	10.4522	+	7.59399i	0.693739	+	0.504031i	0.877887	−	0.478867i	$-0.158953\pi$
$227$	10.4522	+	7.59399i	0.693739	+	0.504031i	−0.184148	+	0.982899i	$0.558953\pi$
$228$	6.03470	−	10.6322i	0.399658	−	0.704133i
$229$	1.37384	+	0.446389i	0.0907861	+	0.0294982i	0.354058	−	0.935224i	$-0.384802\pi$
$229$	1.37384	+	0.446389i	0.0907861	+	0.0294982i	−0.263272	+	0.964722i	$0.584802\pi$
$230$	−2.11931			−0.139743
$231$	−3.05786	−	14.8879i	−0.201193	−	0.979552i
$232$	3.68768			0.242108
$233$	−1.71006	−	0.555631i	−0.112030	−	0.0364006i	0.252466	−	0.967606i	$-0.418758\pi$
$233$	−1.71006	−	0.555631i	−0.112030	−	0.0364006i	−0.364495	+	0.931205i	$0.618758\pi$
$234$	−0.0700468	+	0.776061i	−0.00457911	+	0.0507327i
$235$	8.50056	+	6.17602i	0.554515	+	0.402879i
$236$	−0.251330	−	0.773513i	−0.0163602	−	0.0503514i
$237$	−4.36575	+	3.98945i	−0.283586	+	0.259143i
$238$	−2.11549	+	0.307286i	−0.137127	+	0.0199184i
$239$	−2.26968	−	3.12394i	−0.146813	−	0.202071i	0.729277	−	0.684219i	$-0.239857\pi$
$239$	−2.26968	−	3.12394i	−0.146813	−	0.202071i	−0.876090	+	0.482148i	$0.839857\pi$
$240$	19.2559	−	2.16713i	1.24296	−	0.139887i
$241$		−	21.0980i		−	1.35904i	−0.733657	−	0.679520i	$-0.762188\pi$
$241$		−	21.0980i		−	1.35904i	0.733657	−	0.679520i	$-0.237812\pi$
$242$	0.985050	−	1.08794i	0.0633214	−	0.0699355i
$243$	13.2044	−	8.28512i	0.847064	−	0.531491i
$244$	−13.4003	−	4.35402i	−0.857865	−	0.278737i
$245$	−11.4011	−	16.5704i	−0.728387	−	1.05865i
$246$	−1.44112	−	0.295263i	−0.0918826	−	0.0188253i
$247$	−2.14215	−	6.59287i	−0.136302	−	0.419494i
$248$	0.548041	+	1.68670i	0.0348006	+	0.107105i
$249$	−2.55810	+	12.4856i	−0.162113	+	0.791242i
$250$	0.392905	+	0.540787i	0.0248495	+	0.0342024i
$251$	−2.61399	+	8.04503i	−0.164994	+	0.507798i	−0.999036	−	0.0439027i	$-0.986021\pi$
$251$	−2.61399	+	8.04503i	−0.164994	+	0.507798i	0.834042	+	0.551701i	$0.186021\pi$
$252$	15.7101	−	0.852806i	0.989642	−	0.0537217i
$253$	9.96447	+	15.3905i	0.626461	+	0.967592i
$254$		−	0.0202362i		−	0.00126973i
$255$	29.9498	−	3.37066i	1.87553	−	0.211079i
$256$	−11.8075	+	8.57863i	−0.737967	+	0.536165i
$257$	−1.46483	−	1.06426i	−0.0913738	−	0.0663870i	0.541160	−	0.840919i	$-0.317985\pi$
$257$	−1.46483	−	1.06426i	−0.0913738	−	0.0663870i	−0.632534	+	0.774532i	$0.717985\pi$
$258$	−0.359964	−	0.393917i	−0.0224104	−	0.0245242i
$259$	7.13022	−	13.5608i	0.443050	−	0.842625i
$260$	6.51738	−	8.97041i	0.404191	−	0.556321i
$261$	−20.7380	−	1.87180i	−1.28365	−	0.115861i
$262$	0.712096	+	0.231374i	0.0439934	+	0.0142943i
$263$		−	1.39645i		−	0.0861089i	−0.999073	−	0.0430545i	$-0.986291\pi$
$263$		−	1.39645i		−	0.0861089i	0.999073	−	0.0430545i	$-0.0137089\pi$
$264$	1.93490	+	2.36045i	0.119085	+	0.145276i
$265$			5.31120i			0.326264i
$266$	1.12721	−	0.556238i	0.0691137	−	0.0341051i
$267$	17.9043	+	10.1623i	1.09573	+	0.621922i
$268$	−22.3523	−	16.2399i	−1.36539	−	0.992011i
$269$	−7.85053	−	24.1614i	−0.478655	−	1.47315i	−0.840964	−	0.541091i	$-0.818012\pi$
$269$	−7.85053	−	24.1614i	−0.478655	−	1.47315i	0.362309	−	0.932058i	$-0.381988\pi$
$270$	1.99157	−	0.0439337i	0.121203	−	0.00267372i
$271$	−10.1782	+	14.0091i	−0.618280	+	0.850990i	−0.997226	−	0.0744290i	$-0.976287\pi$
$271$	−10.1782	+	14.0091i	−0.618280	+	0.850990i	0.378946	+	0.925419i	$0.376287\pi$
$272$	−19.0753	+	13.8590i	−1.15661	+	0.840325i
$273$	5.65219	−	6.90218i	0.342086	−	0.417739i
$274$	2.25735			0.136372
$275$	−3.88439	+	10.0775i	−0.234238	+	0.607697i
$276$	−17.2814	+	7.84690i	−1.04022	+	0.472328i
$277$	−1.39162	+	4.28296i	−0.0836142	+	0.257338i	−0.984120	−	0.177507i	$-0.943197\pi$
$277$	−1.39162	+	4.28296i	−0.0836142	+	0.257338i	0.900505	+	0.434845i	$0.143197\pi$
$278$	2.33781	−	1.69852i	0.140212	−	0.101870i
$279$	−2.22581	−	9.76343i	−0.133256	−	0.584521i
$280$	3.57509	+	1.87977i	0.213652	+	0.112338i
$281$	−16.3034	+	5.29730i	−0.972580	+	0.316010i	−0.751857	−	0.659326i	$-0.770842\pi$
$281$	−16.3034	+	5.29730i	−0.972580	+	0.316010i	−0.220723	+	0.975337i	$0.570842\pi$
$282$	−0.827847	−	0.169613i	−0.0492976	−	0.0101003i
$283$	9.04299	+	12.4466i	0.537550	+	0.739874i	0.988258	−	0.152797i	$-0.0488282\pi$
$283$	9.04299	+	12.4466i	0.537550	+	0.739874i	−0.450707	+	0.892672i	$0.648828\pi$
$284$	9.11673	+	2.96221i	0.540978	+	0.175775i
$285$	−16.1364	+	7.32700i	−0.955836	+	0.434014i
$286$	0.860212	+	0.0462748i	0.0508654	+	0.00273629i
$287$	11.7553	+	12.0610i	0.693893	+	0.711936i
$288$	−4.07506	+	2.43332i	−0.240125	+	0.143385i
$289$	−15.9156	+	11.5634i	−0.936213	+	0.680199i
$290$	−2.15270	−	1.56403i	−0.126411	−	0.0918429i
$291$	9.37229	+	10.2563i	0.549413	+	0.601236i
$292$	−13.9693	+	4.53891i	−0.817492	+	0.265619i
$293$	18.3955	+	13.3651i	1.07468	+	0.780798i	0.976747	−	0.214395i	$-0.0687779\pi$
$293$	18.3955	+	13.3651i	1.07468	+	0.780798i	0.0979298	+	0.995193i	$0.468778\pi$
$294$	1.38587	+	0.834342i	0.0808257	+	0.0486598i
$295$	−0.364327	+	1.12128i	−0.0212120	+	0.0652837i
$296$			3.07671i			0.178830i
$297$	−9.68291	−	14.2563i	−0.561859	−	0.827233i
$298$	0.0216852			0.00125619
$299$	−3.32560	+	10.2351i	−0.192324	+	0.591914i
$300$	−9.72305	−	5.51870i	−0.561361	−	0.318622i
$301$	0.878192	+	6.04586i	0.0506181	+	0.348477i
$302$	−0.467807	+	0.152000i	−0.0269193	+	0.00874660i
$303$	7.99602	−	7.30681i	0.459360	−	0.419765i
$304$	8.14921	−	11.2164i	0.467389	−	0.643306i
$305$	12.0053	+	16.5239i	0.687423	+	0.946157i
$306$	−2.08112	+	1.24269i	−0.118970	+	0.0710400i
$307$		−	2.99825i		−	0.171119i	−0.996333	−	0.0855595i	$-0.972732\pi$
$307$		−	2.99825i		−	0.171119i	0.996333	−	0.0855595i	$-0.0272678\pi$
$308$	−1.57204	−	17.3225i	−0.0895755	−	0.987043i
$309$	2.59064	−	1.17632i	0.147376	−	0.0669187i
$310$	0.395444	−	1.21705i	0.0224597	−	0.0691239i
$311$	14.2545	−	10.3565i	0.808301	−	0.587265i	−0.105037	−	0.994468i	$-0.533496\pi$
$311$	14.2545	−	10.3565i	0.808301	−	0.587265i	0.913337	+	0.407203i	$0.133496\pi$
$312$	−0.359583	+	1.75506i	−0.0203574	+	0.0993604i
$313$	14.4783	−	4.70429i	0.818362	−	0.265902i	0.130227	−	0.991484i	$-0.458429\pi$
$313$	14.4783	−	4.70429i	0.818362	−	0.265902i	0.688136	+	0.725582i	$0.258429\pi$
$314$	0.978923	+	3.01282i	0.0552438	+	0.170023i
$315$	−19.1506	−	12.3857i	−1.07902	−	0.697855i
$316$	−5.47553	+	3.97821i	−0.308023	+	0.223792i
$317$	17.1221	+	5.56329i	0.961670	+	0.312466i	0.747449	−	0.664319i	$-0.231279\pi$
$317$	17.1221	+	5.56329i	0.961670	+	0.312466i	0.214222	+	0.976785i	$0.431279\pi$
$318$	−0.176602	−	0.388935i	−0.00990337	−	0.0218104i
$319$	−1.23656	+	22.9866i	−0.0692340	+	1.28700i
$320$	21.7686			1.21690
$321$	3.70339	+	32.9063i	0.206703	+	1.83665i
$322$	−1.92331	−	0.329977i	−0.107182	−	0.0183889i
$323$	12.6750	−	17.4456i	0.705253	−	0.970698i
$324$	16.0771	−	7.73217i	0.893170	−	0.429565i
$325$	−6.02913	+	1.95898i	−0.334436	+	0.108665i
$326$	−1.09966	+	1.51355i	−0.0609046	+	0.0838280i
$327$	3.97588	+	2.25666i	0.219866	+	0.124794i
$328$	−3.21661	−	1.04514i	−0.177608	−	0.0577082i
$329$	6.75279	+	6.92837i	0.372293	+	0.381974i
$330$	−0.128385	−	2.19855i	−0.00706736	−	0.121026i
$331$	−14.1713			−0.778926			−0.389463	−	0.921042i	$-0.627339\pi$
$331$	−14.1713			−0.778926			−0.389463	+	0.921042i	$0.627339\pi$
$332$	−4.50720	+	13.8717i	−0.247365	+	0.761311i
$333$	1.56168	−	17.3021i	0.0855794	−	0.948149i
$334$	0.922285	−	1.26942i	0.0504652	−	0.0694594i
$335$	12.3764	+	38.0907i	0.676197	+	2.08112i
$336$	17.8125	+	1.03144i	0.971750	+	0.0562698i
$337$	10.1350	+	7.36347i	0.552086	+	0.401114i	0.828554	−	0.559909i	$-0.189164\pi$
$337$	10.1350	+	7.36347i	0.552086	+	0.401114i	−0.276468	+	0.961023i	$0.589164\pi$
$338$	−0.722285	−	0.994140i	−0.0392871	−	0.0540741i
$339$	−3.04146	−	27.0247i	−0.165189	−	1.46778i
$340$	34.4917			1.87057
$341$	−10.6975	+	2.85055i	−0.579304	+	0.154366i
$342$	0.938023	−	1.07310i	0.0507225	−	0.0580266i
$343$	−7.76663	−	16.8131i	−0.419359	−	0.907821i
$344$	−0.721122	−	0.992539i	−0.0388803	−	0.0535141i
$345$	26.9527	+	5.52218i	1.45108	+	0.297304i
$346$	−0.923360	+	0.300018i	−0.0496401	+	0.0161291i
$347$	14.4822	−	4.70555i	0.777445	−	0.252607i	0.106696	−	0.994292i	$-0.465973\pi$
$347$	14.4822	−	4.70555i	0.777445	−	0.252607i	0.670749	+	0.741685i	$0.265973\pi$
$348$	−23.3445	−	4.78293i	−1.25140	−	0.256392i
$349$	−2.57877	−	3.54937i	−0.138038	−	0.189993i	0.734401	−	0.678716i	$-0.237463\pi$
$349$	−2.57877	−	3.54937i	−0.138038	−	0.189993i	−0.872439	+	0.488722i	$0.837463\pi$
$350$	−0.508676	−	1.03083i	−0.0271899	−	0.0551000i
$351$	2.91297	−	9.68716i	0.155483	−	0.517063i
$352$	2.85175	+	4.40463i	0.151999	+	0.234768i
$353$	9.22440			0.490965			0.245483	−	0.969401i	$-0.421054\pi$
$353$	9.22440			0.490965			0.245483	+	0.969401i	$0.421054\pi$
$354$	−0.0106044	−	0.0942249i	−0.000563617	−	0.00500800i
$355$	−8.16769	−	11.2419i	−0.433496	−	0.596656i
$356$	19.0609	+	13.8486i	1.01023	+	0.733972i
$357$	27.7048	+	1.60426i	1.46629	+	0.0849067i
$358$	−0.363923	−	1.12004i	−0.0192339	−	0.0591959i
$359$	−2.62132	+	3.60793i	−0.138348	+	0.190419i	−0.872569	−	0.488491i	$-0.837548\pi$
$359$	−2.62132	+	3.60793i	−0.138348	+	0.190419i	0.734221	+	0.678910i	$0.237548\pi$
$360$	4.56144	+	0.411713i	0.240409	+	0.0216992i
$361$	1.95306	−	6.01089i	0.102793	−	0.316363i
$362$	0.570504			0.0299850
$363$	−15.3623	+	11.2694i	−0.806313	+	0.591489i
$364$	7.31132	−	7.12604i	0.383218	−	0.373506i
$365$	20.2499	+	6.57959i	1.05993	+	0.344392i
$366$	−1.42858	−	0.810844i	−0.0746729	−	0.0423835i
$367$	−14.8234	+	20.4027i	−0.773778	+	1.06501i	0.222164	+	0.975009i	$0.428688\pi$
$367$	−14.8234	+	20.4027i	−0.773778	+	1.06501i	−0.995941	+	0.0900042i	$0.971312\pi$
$368$	−20.4702	+	6.65119i	−1.06709	+	0.346717i
$369$	17.5584	+	7.51011i	0.914052	+	0.390961i
$370$	1.30490	−	1.79604i	0.0678385	−	0.0933717i
$371$	−0.826954	+	4.82000i	−0.0429333	+	0.250242i
$372$	−1.28168	−	11.3883i	−0.0664518	−	0.590455i
$373$	11.1033			0.574907			0.287454	−	0.957795i	$-0.407191\pi$
$373$	11.1033			0.574907			0.287454	+	0.957795i	$0.407191\pi$
$374$	1.45638	+	2.24943i	0.0753076	+	0.116315i
$375$	−3.58773	−	7.90132i	−0.185270	−	0.408022i
$376$	−1.84777	−	0.600377i	−0.0952915	−	0.0309621i
$377$	−10.9314	+	7.94214i	−0.562997	+	0.409041i
$378$	1.81422	+	0.270217i	0.0933135	+	0.0138985i
$379$	−3.22182	−	9.91574i	−0.165494	−	0.509337i	0.833579	−	0.552401i	$-0.186288\pi$
$379$	−3.22182	−	9.91574i	−0.165494	−	0.509337i	−0.999072	+	0.0430636i	$0.986288\pi$
$380$	−19.2888	+	6.26730i	−0.989493	+	0.321506i
$381$	−0.0527285	+	0.257357i	−0.00270136	+	0.0131848i
$382$	−2.01733	+	1.46568i	−0.103216	+	0.0749905i
$383$	−3.39011	+	10.4337i	−0.173227	+	0.533137i	−0.999548	−	0.0300620i	$-0.990430\pi$
$383$	−3.39011	+	10.4337i	−0.173227	+	0.533137i	0.826321	+	0.563199i	$0.190430\pi$
$384$	−6.58429	+	2.98971i	−0.336003	+	0.152568i
$385$	−12.9161	+	21.6545i	−0.658266	+	1.10361i
$386$		−	2.41651i		−	0.122997i
$387$	3.55149	+	5.94764i	0.180532	+	0.302336i
$388$	9.34587	+	12.8635i	0.474465	+	0.653045i
$389$	−2.76597	+	3.80704i	−0.140240	+	0.193024i	−0.873360	−	0.487076i	$-0.838064\pi$
$389$	−2.76597	+	3.80704i	−0.140240	+	0.193024i	0.733119	+	0.680100i	$0.238064\pi$
$390$	0.954266	−	0.872013i	0.0483211	−	0.0441561i
$391$	−31.8386	+	10.3450i	−1.61015	+	0.523168i
$392$	2.95177	+	2.26257i	0.149087	+	0.114277i
$393$	−8.45332	−	4.79801i	−0.426413	−	0.242027i
$394$	0.899382	−	2.76801i	0.0453102	−	0.139451i
$395$	9.81107			0.493649
$396$	−9.18718	−	17.4522i	−0.461673	−	0.877004i
$397$		−	28.0742i		−	1.40900i	−0.709703	−	0.704501i	$-0.751171\pi$
$397$		−	28.0742i		−	1.40900i	0.709703	−	0.704501i	$-0.248829\pi$
$398$	−0.649513	+	1.99900i	−0.0325571	+	0.100201i
$399$	−15.7848	+	4.13694i	−0.790230	+	0.207106i
$400$	−10.2574	−	7.45240i	−0.512868	−	0.372620i
$401$	0.0636777	−	0.0206901i	0.00317991	−	0.00103322i	−0.307427	−	0.951572i	$-0.599468\pi$
$401$	0.0636777	−	0.0206901i	0.00317991	−	0.00103322i	0.310607	+	0.950539i	$0.399468\pi$
$402$	−2.17287	−	2.37783i	−0.108373	−	0.118595i
$403$	−5.25719	−	3.81957i	−0.261879	−	0.190266i
$404$	10.0286	−	7.28622i	0.498942	−	0.362503i
$405$	−25.4426	−	4.63059i	−1.26425	−	0.230096i
$406$	−1.71009	−	1.75456i	−0.0848704	−	0.0870772i
$407$	−19.1782	−	1.03169i	−0.950629	−	0.0511388i
$408$	−5.07428	+	2.30406i	−0.251214	+	0.114068i
$409$	36.2146	+	11.7668i	1.79070	+	0.581833i	0.999556	−	0.0297988i	$-0.00948667\pi$
$409$	36.2146	+	11.7668i	1.79070	+	0.581833i	0.791142	+	0.611632i	$0.209487\pi$
$410$	1.43444	+	1.97434i	0.0708421	+	0.0975057i
$411$	−28.7082	−	5.88186i	−1.41607	−	0.290131i
$412$	3.09674	−	1.00619i	0.152566	−	0.0495716i
$413$	−0.505217	+	0.960858i	−0.0248601	+	0.0472807i
$414$	−2.15734	+	0.491818i	−0.106028	+	0.0241716i
$415$	17.1053	−	12.4277i	0.839665	−	0.610052i
$416$	−0.951759	+	2.92921i	−0.0466638	+	0.143616i
$417$	−34.1572	+	15.5097i	−1.67268	+	0.759511i
$418$	−1.22318	−	0.993319i	−0.0598279	−	0.0485848i
$419$	−35.7176			−1.74492			−0.872460	−	0.488685i	$-0.837477\pi$
$419$	−35.7176			−1.74492			−0.872460	+	0.488685i	$0.837477\pi$
$420$	−20.1937	−	16.5366i	−0.985352	−	0.806905i
$421$	7.11542	−	5.16965i	0.346784	−	0.251954i	−0.400734	−	0.916194i	$-0.631245\pi$
$421$	7.11542	−	5.16965i	0.346784	−	0.251954i	0.747519	+	0.664241i	$0.231245\pi$
$422$	1.96320	−	2.70211i	0.0955670	−	0.131537i
$423$	10.0863	+	4.31416i	0.490414	+	0.209761i
$424$	−0.303478	−	0.934008i	−0.0147382	−	0.0453595i
$425$	−15.9539	−	11.5912i	−0.773876	−	0.562254i
$426$	0.971916	+	0.551649i	0.0470895	+	0.0267275i
$427$	8.32226	+	16.8650i	0.402742	+	0.816153i
$428$			37.8965i			1.83180i
$429$	−10.8193	−	2.82992i	−0.522361	−	0.136630i
$430$			0.885242i			0.0426902i
$431$	1.05293	+	0.342119i	0.0507180	+	0.0164793i	0.334266	−	0.942479i	$-0.391512\pi$
$431$	1.05293	+	0.342119i	0.0507180	+	0.0164793i	−0.283548	+	0.958958i	$0.591512\pi$
$432$	19.0985	−	6.67464i	0.918878	−	0.321134i
$433$	−7.35809	+	10.1275i	−0.353607	+	0.486699i	−0.948354	−	0.317215i	$-0.897252\pi$
$433$	−7.35809	+	10.1275i	−0.353607	+	0.486699i	0.594746	+	0.803913i	$0.297252\pi$
$434$	0.548367	−	1.04292i	0.0263225	−	0.0500619i
$435$	23.3020	+	25.5000i	1.11725	+	1.22263i
$436$	4.23271	+	3.07524i	0.202710	+	0.147277i
$437$	15.9253	−	11.5704i	0.761813	−	0.553489i
$438$	−1.70166	+	0.191511i	−0.0813085	+	0.00915074i
$439$		−	14.8873i		−	0.710530i	−0.934766	−	0.355265i	$-0.884391\pi$
$439$		−	14.8873i		−	0.710530i	0.934766	−	0.355265i	$-0.115609\pi$
$440$	0.271988	−	5.05605i	0.0129665	−	0.241038i
$441$	−15.4511	−	14.2220i	−0.735765	−	0.677237i
$442$	−0.486061	+	1.49594i	−0.0231196	+	0.0711547i
$443$	4.17027	+	5.73989i	0.198136	+	0.272710i	0.896511	−	0.443021i	$-0.146093\pi$
$443$	4.17027	+	5.73989i	0.198136	+	0.272710i	−0.698376	+	0.715732i	$0.746093\pi$
$444$	3.99049	−	19.4768i	0.189380	−	0.924329i
$445$	−10.5540	−	32.4818i	−0.500306	−	1.53978i
$446$	−0.223514	−	0.687905i	−0.0105837	−	0.0325732i
$447$	−0.275785	−	0.0565040i	−0.0130442	−	0.00267255i
$448$	19.7554	+	3.38938i	0.933355	+	0.160133i
$449$	3.93556	+	1.27874i	0.185730	+	0.0603475i	0.400406	−	0.916338i	$-0.368869\pi$
$449$	3.93556	+	1.27874i	0.185730	+	0.0603475i	−0.214675	+	0.976686i	$0.568869\pi$
$450$	−0.981343	−	0.857816i	−0.0462609	−	0.0404378i
$451$	7.59333	−	19.6998i	0.357556	−	0.927629i
$452$		−	31.1230i		−	1.46390i
$453$	6.34547	−	0.714141i	0.298136	−	0.0335533i
$454$	1.01320	+	1.39455i	0.0475517	+	0.0654494i
$455$	−14.6461	+	2.12742i	−0.686620	+	0.0997352i
$456$	2.41903	−	2.21052i	0.113281	−	0.103517i
$457$	7.15347	+	22.0161i	0.334625	+	1.02987i	0.966906	+	0.255132i	$0.0821189\pi$
$457$	7.15347	+	22.0161i	0.334625	+	1.02987i	−0.632281	+	0.774739i	$0.717881\pi$
$458$	0.155924	+	0.113285i	0.00728585	+	0.00529348i
$459$	29.7051	−	10.3815i	1.38651	−	0.484565i
$460$	29.9450	+	9.72972i	1.39619	+	0.453650i
$461$	37.5827			1.75040			0.875202	−	0.483758i	$-0.160729\pi$
$461$	37.5827			1.75040			0.875202	+	0.483758i	$0.160729\pi$
$462$	0.225803	−	2.01521i	0.0105053	−	0.0937562i
$463$	−17.2455			−0.801466			−0.400733	−	0.916195i	$-0.631244\pi$
$463$	−17.2455			−0.801466			−0.400733	+	0.916195i	$0.631244\pi$
$464$	−25.7013	−	8.35084i	−1.19315	−	0.387678i
$465$	−8.20033	+	14.4477i	−0.380281	+	0.669994i
$466$	−0.194082	−	0.141009i	−0.00899069	−	0.00653212i
$467$	2.52908	+	7.78372i	0.117032	+	0.360187i	0.992365	−	0.123332i	$-0.0393581\pi$
$467$	2.52908	+	7.78372i	0.117032	+	0.360187i	−0.875333	+	0.483520i	$0.839358\pi$
$468$	4.55261	−	10.6438i	0.210445	−	0.492011i
$469$	5.30108	+	36.4950i	0.244781	+	1.68518i
$470$	0.824010	+	1.13415i	0.0380088	+	0.0523146i
$471$	−4.59928	−	40.8667i	−0.211924	−	1.88304i
$472$		−	0.218002i		−	0.0100344i
$473$	6.42865	−	4.16219i	0.295590	−	0.191378i
$474$	−0.718457	+	0.326228i	−0.0329998	+	0.0149841i
$475$	11.0280	+	3.58323i	0.506001	+	0.164410i
$476$	31.3018	+	5.37035i	1.43471	+	0.246150i
$477$	1.23254	+	5.40650i	0.0564343	+	0.247547i
$478$	−0.159203	−	0.489977i	−0.00728179	−	0.0224110i
$479$	−10.6434	−	32.7571i	−0.486311	−	1.49671i	−0.830074	−	0.557654i	$-0.811702\pi$
$479$	−10.6434	−	32.7571i	−0.486311	−	1.49671i	0.343763	−	0.939056i	$-0.388298\pi$
$480$	7.71363	+	1.58040i	0.352077	+	0.0721351i
$481$	−6.62629	−	9.12030i	−0.302133	−	0.415850i
$482$	0.869855	−	2.67714i	0.0396208	−	0.121940i
$483$	23.6002	+	9.20800i	1.07385	+	0.418979i
$484$	−18.9131	+	10.8498i	−0.859685	+	0.493174i
$485$		−	23.0488i		−	1.04659i
$486$	2.01711	−	0.506896i	0.0914980	−	0.0229933i
$487$	−14.1551	+	10.2843i	−0.641429	+	0.466025i	−0.860341	−	0.509719i	$-0.829749\pi$
$487$	−14.1551	+	10.2843i	−0.641429	+	0.466025i	0.218912	+	0.975745i	$0.429749\pi$
$488$	−3.05538	−	2.21986i	−0.138311	−	0.100488i
$489$	17.9289	−	16.3835i	0.810773	−	0.740889i
$490$	−0.763503	−	2.57269i	−0.0344916	−	0.116222i
$491$	−8.21813	+	11.3113i	−0.370879	+	0.510471i	−0.953140	−	0.302531i	$-0.902168\pi$
$491$	−8.21813	+	11.3113i	−0.370879	+	0.510471i	0.582260	+	0.813002i	$0.302168\pi$
$492$	19.0069	+	10.7881i	0.856898	+	0.486366i
$493$	−39.9747	−	12.9886i	−1.80037	−	0.584975i
$494$		−	0.924894i		−	0.0416130i
$495$	−4.09590	+	28.2950i	−0.184097	+	1.27176i
$496$		−	12.9965i		−	0.583558i
$497$	−5.66195	−	11.4739i	−0.253973	−	0.514674i
$498$	−0.839372	+	1.47884i	−0.0376131	+	0.0662683i
$499$	3.08110	+	2.23855i	0.137929	+	0.100211i	0.654610	−	0.755967i	$-0.272833\pi$
$499$	3.08110	+	2.23855i	0.137929	+	0.100211i	−0.516681	+	0.856178i	$0.672833\pi$
$500$	−3.06884	−	9.44492i	−0.137243	−	0.422390i
$501$	−15.0370	+	13.7409i	−0.671802	+	0.613897i
$502$	−0.663383	+	0.913068i	−0.0296082	+	0.0407522i
$503$	−16.9929	+	12.3461i	−0.757675	+	0.550483i	−0.898196	−	0.439594i	$-0.855122\pi$
$503$	−16.9929	+	12.3461i	−0.757675	+	0.550483i	0.140521	+	0.990078i	$0.455122\pi$
$504$	4.07547	+	1.08385i	0.181536	+	0.0482786i
$505$	−17.9693			−0.799624
$506$	0.629860	+	2.36374i	0.0280007	+	0.105081i
$507$	6.59540	+	14.5252i	0.292912	+	0.645085i
$508$	−0.0929041	+	0.285929i	−0.00412195	+	0.0126861i
$509$	−0.695649	+	0.505419i	−0.0308341	+	0.0224023i	−0.603096	−	0.797669i	$-0.706066\pi$
$509$	−0.695649	+	0.505419i	−0.0308341	+	0.0224023i	0.572261	+	0.820071i	$0.306066\pi$
$510$	3.93933	+	0.807107i	0.174437	+	0.0357393i
$511$	17.3527	+	9.12400i	0.767637	+	0.403622i
$512$	−9.79323	+	3.18201i	−0.432804	+	0.140626i
$513$	−14.7256	+	11.2032i	−0.650151	+	0.494632i
$514$	−0.141995	−	0.195440i	−0.00626314	−	0.00862047i
$515$	−4.48904	−	1.45858i	−0.197811	−	0.0642725i
$516$	3.27767	+	7.21847i	0.144291	+	0.317775i
$517$	4.36196	−	11.3165i	0.191839	−	0.497699i
$518$	1.46386	−	1.42676i	0.0643184	−	0.0626884i
$519$	12.5247	−	1.40958i	0.549774	−	0.0618735i
$520$	2.40443	−	1.74692i	0.105441	−	0.0766075i
$521$	−17.9749	−	13.0595i	−0.787495	−	0.572149i	0.119724	−	0.992807i	$-0.461799\pi$
$521$	−17.9749	−	13.0595i	−0.787495	−	0.572149i	−0.907219	+	0.420658i	$0.861799\pi$
$522$	−2.55429	−	1.09253i	−0.111798	−	0.0478186i
$523$	15.9355	−	5.17777i	0.696812	−	0.226408i	0.0608709	−	0.998146i	$-0.480612\pi$
$523$	15.9355	−	5.17777i	0.696812	−	0.226408i	0.635941	+	0.771738i	$0.280612\pi$
$524$	−8.99939	−	6.53844i	−0.393140	−	0.285633i
$525$	3.78320	+	14.4351i	0.165112	+	0.630001i
$526$	0.0575748	−	0.177197i	0.00251038	−	0.00772616i
$527$		−	20.2141i		−	0.880542i
$528$	−8.13994	−	20.8327i	−0.354245	−	0.906628i
$529$	−7.55983			−0.328688
$530$	−0.218977	+	0.673943i	−0.00951176	+	0.0292742i
$531$	−0.110654	+	1.22595i	−0.00480197	+	0.0532018i
$532$	−18.4807	+	2.68441i	−0.801239	+	0.116384i
$533$	11.7859	−	3.82948i	0.510505	−	0.165873i
$534$	1.85291	+	2.02769i	0.0801833	+	0.0877465i
$535$	32.2898	−	44.4431i	1.39601	−	1.92144i
$536$	−4.35295	−	5.99132i	−0.188019	−	0.258786i
$537$	1.70982	+	15.1925i	0.0737842	+	0.655606i
$538$		−	3.38954i		−	0.146133i
$539$	−15.0932	+	17.6407i	−0.650109	+	0.759841i
$540$	−28.3417	−	8.52249i	−1.21963	−	0.366750i
$541$	8.86302	−	27.2776i	0.381051	−	1.17276i	−0.558253	−	0.829671i	$-0.688528\pi$
$541$	8.86302	−	27.2776i	0.381051	−	1.17276i	0.939305	−	0.343084i	$-0.111472\pi$
$542$	−1.86910	+	1.35798i	−0.0802848	+	0.0583303i
$543$	−7.25548	−	1.48653i	−0.311362	−	0.0637932i
$544$	−9.11193	+	2.96065i	−0.390671	+	0.126937i
$545$	−2.34364	−	7.21299i	−0.100391	−	0.308970i
$546$	1.00178	−	0.642787i	0.0428724	−	0.0275087i
$547$	15.8751	−	11.5339i	0.678770	−	0.493155i	−0.194180	−	0.980966i	$-0.562204\pi$
$547$	15.8751	−	11.5339i	0.678770	−	0.493155i	0.872949	+	0.487811i	$0.162204\pi$
$548$	−31.8954	−	10.3635i	−1.36251	−	0.442705i
$549$	16.0554	+	14.0344i	0.685227	+	0.598974i
$550$	−0.908383	+	1.11859i	−0.0387336	+	0.0476970i
$551$	24.7151			1.05290
$552$	−5.05534	+	0.568945i	−0.215169	+	0.0242159i
$553$	8.90371	+	1.52758i	0.378624	+	0.0649595i
$554$	−0.353167	+	0.486093i	−0.0150046	+	0.0206521i
$555$	−21.2751	+	19.4413i	−0.903079	+	0.825238i
$556$	−40.8301	+	13.2665i	−1.73158	+	0.562625i
$557$	9.12422	−	12.5584i	0.386606	−	0.532117i	−0.570714	−	0.821149i	$-0.693333\pi$
$557$	9.12422	−	12.5584i	0.386606	−	0.532117i	0.957319	+	0.289032i	$0.0933334\pi$
$558$	0.120105	−	1.33066i	0.00508443	−	0.0563313i
$559$	4.27525	+	1.38911i	0.180824	+	0.0587532i
$560$	−20.6597	−	21.1969i	−0.873033	−	0.895734i
$561$	−12.6605	−	32.4024i	−0.534528	−	1.36803i
$562$	−2.28716			−0.0964779
$563$	−12.7011	+	39.0901i	−0.535290	+	1.64745i	0.207733	+	0.978186i	$0.433391\pi$
$563$	−12.7011	+	39.0901i	−0.535290	+	1.64745i	−0.743023	+	0.669266i	$0.766609\pi$
$564$	10.9185	+	6.19719i	0.459750	+	0.260949i
$565$	−26.5184	+	36.4995i	−1.11564	+	1.53555i
$566$	0.634308	+	1.95220i	0.0266619	+	0.0820570i
$567$	−22.3686	−	8.16375i	−0.939392	−	0.342845i
$568$	2.07869	+	1.51026i	0.0872200	+	0.0633690i
$569$	24.4307	+	33.6259i	1.02419	+	1.40967i	0.909226	+	0.416302i	$0.136674\pi$
$569$	24.4307	+	33.6259i	1.02419	+	1.40967i	0.114961	+	0.993370i	$0.463326\pi$
$570$	−2.34965	+	0.264437i	−0.0984158	+	0.0110761i
$571$	−1.86891			−0.0782114			−0.0391057	−	0.999235i	$-0.512451\pi$
$571$	−1.86891			−0.0782114			−0.0391057	+	0.999235i	$0.512451\pi$
$572$	−11.9420	−	4.60306i	−0.499320	−	0.192464i
$573$	29.4747	−	13.3835i	1.23133	−	0.559104i
$574$	0.994375	+	2.01509i	0.0415044	+	0.0841082i
$575$	−10.5811	−	14.5636i	−0.441262	−	0.607345i
$576$	22.1593	−	5.05175i	0.923303	−	0.210489i
$577$	11.1011	−	3.60698i	0.462147	−	0.150161i	−0.0686839	−	0.997638i	$-0.521880\pi$
$577$	11.1011	−	3.60698i	0.462147	−	0.150161i	0.530831	+	0.847478i	$0.321880\pi$
$578$	−2.49630	+	0.811096i	−0.103832	+	0.0337372i
$579$	−6.29658	+	30.7324i	−0.261677	+	1.27719i
$580$	23.2363	+	31.9821i	0.964836	+	1.32798i
$581$	17.4583	−	8.61506i	0.724293	−	0.357413i
$582$	0.766396	+	1.68785i	0.0317681	+	0.0699635i
$583$	5.92377	−	1.57849i	0.245337	−	0.0653744i
$584$	−3.93703			−0.162915
$585$	−14.4082	+	8.60349i	−0.595705	+	0.355711i
$586$	1.78319	+	2.45435i	0.0736628	+	0.101388i
$587$	−28.0616	−	20.3879i	−1.15822	−	0.841500i	−0.168672	−	0.985672i	$-0.553948\pi$
$587$	−28.0616	−	20.3879i	−1.15822	−	0.841500i	−0.989553	+	0.144173i	$0.953948\pi$
$588$	−15.7514	−	18.1514i	−0.649575	−	0.748552i
$589$	3.67301	+	11.3043i	0.151344	+	0.465788i
$590$	−0.0924596	+	0.127260i	−0.00380650	+	0.00523920i
$591$	−18.6505	+	32.8592i	−0.767180	+	1.35165i
$592$	6.96727	−	21.4431i	0.286353	−	0.881305i
$593$	−32.6467			−1.34064			−0.670319	−	0.742073i	$-0.733843\pi$
$593$	−32.6467			−1.34064			−0.670319	+	0.742073i	$0.733843\pi$
$594$	−0.640896	−	2.20821i	−0.0262963	−	0.0906040i
$595$	−32.1333	−	32.9688i	−1.31734	−	1.35159i
$596$	−0.306403	−	0.0995563i	−0.0125507	−	0.00407799i
$597$	13.4690	−	23.7301i	0.551248	−	0.971210i
$598$	−0.843977	+	1.16163i	−0.0345128	+	0.0475028i
$599$	12.5436	−	4.07566i	0.512518	−	0.166527i	−0.0413292	−	0.999146i	$-0.513159\pi$
$599$	12.5436	−	4.07566i	0.512518	−	0.166527i	0.553847	+	0.832618i	$0.313159\pi$
$600$	−2.02151	−	2.21218i	−0.0825276	−	0.0903120i
$601$	−3.80279	+	5.23409i	−0.155119	+	0.213503i	−0.879503	−	0.475894i	$-0.842125\pi$
$601$	−3.80279	+	5.23409i	−0.155119	+	0.213503i	0.724383	+	0.689397i	$0.242125\pi$
$602$	−0.137832	+	0.803371i	−0.00561762	+	0.0327430i
$603$	21.4381	+	35.9021i	0.873025	+	1.46205i
$604$	7.30775			0.297348
$605$	31.4249	+	3.39080i	1.27760	+	0.137856i
$606$	1.31588	−	0.597497i	0.0534539	−	0.0242717i
$607$	−25.1368	−	8.16743i	−1.02027	−	0.331506i	−0.249333	−	0.968418i	$-0.580211\pi$
$607$	−25.1368	−	8.16743i	−1.02027	−	0.331506i	−0.770936	+	0.636912i	$0.780211\pi$
$608$	4.55770	−	3.31136i	0.184839	−	0.134293i
$609$	17.1766	+	26.7698i	0.696031	+	1.08477i
$610$	0.842097	+	2.59171i	0.0340955	+	0.104935i
$611$	6.77038	−	2.19983i	0.273900	−	0.0889956i
$612$	35.1106	−	8.00432i	1.41926	−	0.323555i
$613$	−0.692534	+	0.503155i	−0.0279712	+	0.0203223i	−0.601683	−	0.798735i	$-0.705503\pi$
$613$	−0.692534	+	0.503155i	−0.0279712	+	0.0203223i	0.573712	+	0.819057i	$0.305503\pi$
$614$	0.123616	−	0.380450i	0.00498872	−	0.0153537i
$615$	−13.0983	−	28.8467i	−0.528175	−	1.16321i
$616$	1.03406	−	4.54609i	0.0416635	−	0.183167i
$617$			13.4949i			0.543285i	0.962398	+	0.271642i	$0.0875667\pi$
$617$			13.4949i			0.543285i	−0.962398	+	0.271642i	$0.912433\pi$
$618$	0.377227	−	0.0424545i	0.0151743	−	0.00170777i
$619$	−5.47566	−	7.53659i	−0.220085	−	0.302921i	0.684670	−	0.728853i	$-0.259946\pi$
$619$	−5.47566	−	7.53659i	−0.220085	−	0.302921i	−0.904755	+	0.425932i	$0.859946\pi$
$620$	−11.1749	+	15.3810i	−0.448796	+	0.617714i
$621$	28.7178	−	0.633512i	1.15241	−	0.0254219i
$622$	2.23576	−	0.726444i	0.0896460	−	0.0291277i
$623$	−4.52049	−	31.1210i	−0.181110	−	1.24684i
$624$	6.48047	−	11.4175i	0.259426	−	0.457068i
$625$	−9.47998	+	29.1764i	−0.379199	+	1.16706i
$626$	2.03112			0.0811799
$627$	12.9678	+	15.8199i	0.517884	+	0.631785i
$628$		−	47.0641i		−	1.87806i
$629$	10.8366	−	33.3517i	0.432084	−	1.32982i
$630$	−1.91939	−	2.36120i	−0.0764702	−	0.0940725i
$631$	20.7926	+	15.1067i	0.827739	+	0.601388i	0.918919	−	0.394447i	$-0.129064\pi$
$631$	20.7926	+	15.1067i	0.827739	+	0.601388i	−0.0911798	+	0.995834i	$0.529064\pi$
$632$	−1.72534	+	0.560597i	−0.0686304	+	0.0222994i
$633$	−32.0080	+	29.2491i	−1.27221	+	1.16255i
$634$	1.94326	+	1.41186i	0.0771768	+	0.0560722i
$635$	0.352580	−	0.256165i	0.0139917	−	0.0101656i
$636$	0.709729	+	6.30626i	0.0281426	+	0.250060i
$637$	−13.6228	−	0.349729i	−0.539756	−	0.0138568i
$638$	−1.10463	+	2.86581i	−0.0437328	+	0.113459i
$639$	−10.9231	−	9.54815i	−0.432111	−	0.377719i
$640$	11.4092	+	3.70708i	0.450988	+	0.146535i
$641$	2.81318	+	3.87201i	0.111114	+	0.152935i	0.860952	−	0.508686i	$-0.169869\pi$
$641$	2.81318	+	3.87201i	0.111114	+	0.152935i	−0.749838	+	0.661621i	$0.769869\pi$
$642$	−0.886780	+	4.32820i	−0.0349984	+	0.170820i
$643$	−14.2181	+	4.61973i	−0.560706	+	0.182184i	−0.575639	−	0.817704i	$-0.695247\pi$
$643$	−14.2181	+	4.61973i	−0.560706	+	0.182184i	0.0149329	+	0.999888i	$0.495247\pi$
$644$	25.6606	+	13.4923i	1.01117	+	0.531672i
$645$	2.30663	−	11.2582i	0.0908234	−	0.443292i
$646$	2.32761	−	1.69110i	0.0915784	−	0.0665356i
$647$	−3.04442	+	9.36976i	−0.119688	+	0.368363i	−0.992896	−	0.118985i	$-0.962036\pi$
$647$	−3.04442	+	9.36976i	−0.119688	+	0.368363i	0.873208	+	0.487349i	$0.162036\pi$
$648$	4.73883	−	0.639450i	0.186159	−	0.0251200i
$649$	1.35889	+	0.0731009i	0.0533410	+	0.00286946i
$650$	−0.845810			−0.0331754
$651$	−9.69144	+	11.8347i	−0.379837	+	0.463838i
$652$	22.4864	−	16.3374i	0.880637	−	0.639820i
$653$	14.6781	−	20.2026i	0.574397	−	0.790590i	−0.418670	−	0.908139i	$-0.637503\pi$
$653$	14.6781	−	20.2026i	0.574397	−	0.790590i	0.993067	+	0.117548i	$0.0375035\pi$
$654$	0.411462	+	0.450273i	0.0160894	+	0.0176071i
$655$	4.98294	+	15.3359i	0.194699	+	0.599223i
$656$	20.0514	+	14.5682i	0.782875	+	0.568792i
$657$	22.1402	+	1.99836i	0.863770	+	0.0779635i
$658$	0.571215	+	1.15756i	0.0222683	+	0.0451264i
$659$			0.563519i			0.0219516i	0.999940	+	0.0109758i	$0.00349377\pi$
$659$			0.563519i			0.0219516i	−0.999940	+	0.0109758i	$0.996506\pi$
$660$	−8.27949	+	31.6541i	−0.322279	+	1.23213i
$661$			27.4669i			1.06834i	0.845377	+	0.534170i	$0.179376\pi$
$661$			27.4669i			1.06834i	−0.845377	+	0.534170i	$0.820624\pi$
$662$	−1.79821	−	0.584274i	−0.0698895	−	0.0227085i
$663$	10.0795	−	17.7584i	0.391454	−	0.689678i
$664$	−2.29796	+	3.16287i	−0.0891783	+	0.122743i
$665$	23.9605	+	12.5984i	0.929148	+	0.488544i
$666$	0.911517	−	2.13109i	0.0353206	−	0.0825781i
$667$	−31.0413	−	22.5528i	−1.20192	−	0.873249i
$668$	−18.8594	+	13.7021i	−0.729691	+	0.530152i
$669$	1.05014	+	9.33094i	0.0406006	+	0.360755i
$670$			5.34364i			0.206443i
$671$	14.8617	−	18.3009i	0.573731	−	0.706498i
$672$	6.75417	+	2.63525i	0.260548	+	0.101657i
$673$	−4.23025	+	13.0194i	−0.163064	+	0.501860i	−0.998888	−	0.0471372i	$-0.984990\pi$
$673$	−4.23025	+	13.0194i	−0.163064	+	0.501860i	0.835824	+	0.548997i	$0.184990\pi$
$674$	0.982442	+	1.35222i	0.0378422	+	0.0520854i
$675$	10.2452	+	13.4665i	0.394339	+	0.518324i
$676$	5.64151	+	17.3628i	0.216981	+	0.667799i
$677$	1.31022	+	4.03244i	0.0503558	+	0.154979i	0.973072	−	0.230500i	$-0.0740362\pi$
$677$	1.31022	+	4.03244i	0.0503558	+	0.154979i	−0.922717	+	0.385479i	$0.874036\pi$
$678$	0.728279	−	3.55459i	0.0279694	−	0.136513i
$679$	3.58870	−	20.9172i	0.137722	−	0.802728i
$680$	8.79266	+	2.85691i	0.337183	+	0.109557i
$681$	−9.25181	−	20.3754i	−0.354530	−	0.780788i
$682$	−1.47495	−	0.0793443i	−0.0564786	−	0.00303825i
$683$			23.0921i			0.883595i	0.897115	+	0.441798i	$0.145659\pi$
$683$			23.0921i			0.883595i	−0.897115	+	0.441798i	$0.854341\pi$
$684$	−18.1805	+	10.8560i	−0.695147	+	0.415090i
$685$	28.5752	+	39.3303i	1.09180	+	1.50274i
$686$	−0.292323	−	2.45364i	−0.0111609	−	0.0936804i
$687$	−1.68781	−	1.84701i	−0.0643938	−	0.0704677i
$688$	2.77822	+	8.55048i	0.105919	+	0.325984i
$689$	2.91117	+	2.11509i	0.110907	+	0.0805784i
$690$	3.19237	+	1.81196i	0.121532	+	0.0689800i
$691$	32.2057	+	10.4643i	1.22516	+	0.398079i	0.848959	−	0.528458i	$-0.177230\pi$
$691$	32.2057	+	10.4643i	1.22516	+	0.398079i	0.376203	+	0.926537i	$0.377230\pi$
$692$	14.4241			0.548321
$693$	−8.12262	+	25.0404i	−0.308553	+	0.951207i
$694$	2.03166			0.0771209
$695$	59.1873	+	19.2311i	2.24510	+	0.729478i
$696$	−5.55486	−	3.15287i	−0.210556	−	0.119509i
$697$	31.1871	+	22.6588i	1.18130	+	0.858261i
$698$	−0.180884	−	0.556704i	−0.00684656	−	0.0210715i
$699$	2.10085	+	2.29902i	0.0794616	+	0.0869568i
$700$	2.45488	+	16.9005i	0.0927857	+	0.638777i
$701$	−19.1700	−	26.3853i	−0.724042	−	0.996558i	−0.999380	−	0.0352108i	$-0.988790\pi$
$701$	−19.1700	−	26.3853i	−0.724042	−	0.996558i	0.275338	−	0.961348i	$-0.411210\pi$
$702$	0.769025	−	1.10911i	0.0290250	−	0.0418608i
$703$			20.6203i			0.777709i
$704$	−6.46965	−	24.2793i	−0.243834	−	0.915062i
$705$	−7.52428	−	16.5709i	−0.283381	−	0.624094i
$706$	1.17049	+	0.380316i	0.0440521	+	0.0143134i
$707$	−16.3074	−	2.79782i	−0.613304	−	0.105223i
$708$	−0.282749	+	1.38004i	−0.0106264	+	0.0518652i
$709$	−12.9200	−	39.7637i	−0.485221	−	1.49336i	−0.831660	−	0.555285i	$-0.812609\pi$
$709$	−12.9200	−	39.7637i	−0.485221	−	1.49336i	0.346439	−	0.938072i	$-0.387391\pi$
$710$	−0.572911	−	1.76324i	−0.0215010	−	0.0661732i
$711$	9.98713	−	2.27681i	0.374547	−	0.0853870i
$712$	3.71197	+	5.10909i	0.139112	+	0.191471i
$713$	5.70219	−	17.5495i	0.213549	−	0.657235i
$714$	3.44934	+	1.34582i	0.129088	+	0.0503659i
$715$	10.0829	+	15.5734i	0.377080	+	0.582414i
$716$			17.4965i			0.653873i
$717$	0.747985	+	6.64619i	0.0279340	+	0.248207i
$718$	−0.481374	+	0.349739i	−0.0179647	+	0.0130521i
$719$	21.5408	+	15.6503i	0.803337	+	0.583659i	0.911891	−	0.410432i	$-0.134622\pi$
$719$	21.5408	+	15.6503i	0.803337	+	0.583659i	−0.108554	+	0.994091i	$0.534622\pi$
$720$	−30.8585	−	13.1989i	−1.15003	−	0.491894i
$721$	−3.84677	−	2.02262i	−0.143261	−	0.0753265i
$722$	0.495651	−	0.682204i	0.0184462	−	0.0253890i
$723$	−18.0382	+	31.7804i	−0.670848	+	1.18193i
$724$	−8.06099	−	2.61917i	−0.299584	−	0.0973408i
$725$		−	22.6018i		−	0.839410i
$726$	−2.41397	+	0.796604i	−0.0895908	+	0.0295647i
$727$			2.38919i			0.0886100i	0.999018	+	0.0443050i	$0.0141073\pi$
$727$			2.38919i			0.0886100i	−0.999018	+	0.0443050i	$0.985893\pi$
$728$	2.45405	−	1.21099i	0.0909533	−	0.0448822i
$729$	−26.9737	+	1.19065i	−0.999027	+	0.0440983i
$730$	2.29826	+	1.66978i	0.0850623	+	0.0618014i
$731$	4.32113	+	13.2991i	0.159823	+	0.491884i
$732$	16.4626	+	18.0155i	0.608476	+	0.665871i
$733$	−14.1156	+	19.4284i	−0.521371	+	0.717606i	−0.985785	−	0.168013i	$-0.946265\pi$
$733$	−14.1156	+	19.4284i	−0.521371	+	0.717606i	0.464414	+	0.885618i	$0.346265\pi$
$734$	−2.72215	+	1.97776i	−0.100476	+	0.0730004i
$735$	3.00644	+	34.7081i	0.110894	+	1.28023i
$736$	−8.74596			−0.322380
$737$	38.8057	−	25.1245i	1.42943	−	0.925472i
$738$	1.91836	+	1.67688i	0.0706158	+	0.0617270i
$739$	9.56903	−	29.4504i	0.352002	−	1.08335i	−0.605725	−	0.795674i	$-0.707117\pi$
$739$	9.56903	−	29.4504i	0.352002	−	1.08335i	0.957727	−	0.287678i	$-0.0928832\pi$
$740$	−26.6833	+	19.3865i	−0.980897	+	0.712663i
$741$	−2.40995	+	11.7625i	−0.0885317	+	0.432106i
$742$	−0.303658	+	0.577519i	−0.0111476	+	0.0212014i
$743$	17.7205	−	5.75775i	0.650103	−	0.211231i	0.0346434	−	0.999400i	$-0.488970\pi$
$743$	17.7205	−	5.75775i	0.650103	−	0.211231i	0.615460	+	0.788168i	$0.288970\pi$
$744$	0.616553	−	3.00928i	0.0226039	−	0.110325i
$745$	0.274507	+	0.377826i	0.0100571	+	0.0138425i
$746$	1.40891	+	0.457782i	0.0515838	+	0.0167606i
$747$	14.5282	−	16.6203i	0.531558	−	0.608103i
$748$	−10.2509	−	38.4698i	−0.374812	−	1.40659i
$749$	36.2233	−	35.3053i	1.32357	−	1.29003i
$750$	−0.129484	−	1.15053i	−0.00472809	−	0.0420112i
$751$	−30.9278	+	22.4703i	−1.12857	+	0.819954i	−0.985486	−	0.169757i	$-0.945702\pi$
$751$	−30.9278	+	22.4703i	−1.12857	+	0.819954i	−0.143084	+	0.989711i	$0.545702\pi$
$752$	11.5184	+	8.36864i	0.420034	+	0.305173i
$753$	10.8158	−	9.88355i	0.394150	−	0.360177i
$754$	−1.71455	+	0.557090i	−0.0624401	+	0.0202880i
$755$	−8.57016	−	6.22659i	−0.311900	−	0.226609i
$756$	−24.3936	−	12.1471i	−0.887188	−	0.441786i
$757$	9.77388	−	30.0809i	0.355238	−	1.09331i	−0.600634	−	0.799524i	$-0.705085\pi$
$757$	9.77388	−	30.0809i	0.355238	−	1.09331i	0.955872	−	0.293785i	$-0.0949149\pi$
$758$		−	1.39105i		−	0.0505252i
$759$	−1.85127	−	31.7025i	−0.0671969	−	1.15073i
$760$	−5.43623			−0.197193
$761$	12.7956	−	39.3807i	0.463838	−	1.42755i	−0.396599	−	0.917992i	$-0.629810\pi$
$761$	12.7956	−	39.3807i	0.463838	−	1.42755i	0.860437	−	0.509556i	$-0.170190\pi$
$762$	−0.0173014	+	0.0304824i	−0.000626765	+	0.00110426i
$763$	−1.00383	−	6.91081i	−0.0363411	−	0.250188i
$764$	35.2329	−	11.4479i	1.27468	−	0.414169i
$765$	−47.9961	−	20.5290i	−1.73530	−	0.742228i
$766$	−0.860349	+	1.18417i	−0.0310857	+	0.0427858i
$767$	0.469510	+	0.646226i	0.0169530	+	0.0233339i
$768$	25.1204	−	2.82714i	0.906455	−	0.102016i
$769$		−	6.07959i		−	0.219235i	−0.993974	−	0.109618i	$-0.965037\pi$
$769$		−	6.07959i		−	0.219235i	0.993974	−	0.109618i	$-0.0349627\pi$
$770$	−2.53174	+	2.21523i	−0.0912374	+	0.0798314i
$771$	1.29660	+	2.85552i	0.0466959	+	0.102839i
$772$	−11.0942	+	34.1443i	−0.399287	+	1.22888i
$773$	−22.2293	+	16.1506i	−0.799533	+	0.580895i	−0.910777	−	0.412898i	$-0.864517\pi$
$773$	−22.2293	+	16.1506i	−0.799533	+	0.580895i	0.111244	+	0.993793i	$0.464517\pi$
$774$	0.205434	+	0.901127i	0.00738417	+	0.0323903i
$775$	10.3378	−	3.35894i	0.371343	−	0.120657i
$776$	1.31699	+	4.05329i	0.0472773	+	0.145504i
$777$	−22.3345	+	14.3308i	−0.801247	+	0.514114i
$778$	−0.507938	+	0.369039i	−0.0182105	+	0.0132307i
$779$	−21.5579	−	7.00460i	−0.772394	−	0.250966i
$780$	−17.4868	+	7.94017i	−0.626127	+	0.284304i
$781$	−10.1110	+	12.4508i	−0.361800	+	0.445525i
$782$	−4.46654			−0.159723
$783$	29.6378	+	20.5500i	1.05917	+	0.734395i
$784$	−15.4487	−	22.4533i	−0.551739	−	0.801903i
$785$	−40.1011	+	55.1944i	−1.43127	+	1.96997i
$786$	−0.874830	−	0.957348i	−0.0312042	−	0.0341475i
$787$	−37.1972	+	12.0861i	−1.32594	+	0.430823i	−0.884530	−	0.466483i	$-0.845521\pi$
$787$	−37.1972	+	12.0861i	−1.32594	+	0.430823i	−0.441408	+	0.897307i	$0.645521\pi$
$788$	−25.4158	+	34.9818i	−0.905400	+	1.24618i
$789$	−1.19393	+	2.10351i	−0.0425051	+	0.0748871i
$790$	1.24494	+	0.404504i	0.0442928	+	0.0143916i
$791$	−29.7489	+	28.9950i	−1.05775	+	1.03094i
$792$	−0.896463	−	5.20989i	−0.0318544	−	0.185125i
$793$	13.8380			0.491401
$794$	1.15748	−	3.56236i	0.0410774	−	0.126423i
$795$	4.54094	−	8.00040i	0.161050	−	0.283745i
$796$	18.3547	−	25.2631i	0.650565	−	0.895426i
$797$	−8.23094	−	25.3322i	−0.291555	−	0.897313i	−0.984357	−	0.176186i	$-0.943624\pi$
$797$	−8.23094	−	25.3322i	−0.291555	−	0.897313i	0.692802	−	0.721128i	$-0.256376\pi$
$798$	−2.17351	−	0.125859i	−0.0769416	−	0.00445536i
$799$	17.9153	+	13.0162i	0.633798	+	0.460481i
$800$	−3.02822	−	4.16798i	−0.107064	−	0.147361i
$801$	−18.2813	−	30.6155i	−0.645936	−	1.08174i
$802$	0.00893316			0.000315441
$803$	1.32017	−	24.5409i	0.0465878	−	0.866029i
$804$	19.7852	+	43.5733i	0.697770	+	1.53671i
$805$	−18.5974	−	37.6873i	−0.655471	−	1.32830i
$806$	−0.509611	−	0.701419i	−0.0179503	−	0.0247064i
$807$	−8.83194	+	43.1070i	−0.310899	+	1.51744i
$808$	3.16002	−	1.02675i	0.111169	−	0.0361210i
$809$	−39.2594	+	12.7562i	−1.38029	+	0.448483i	−0.902764	−	0.430136i	$-0.858466\pi$
$809$	−39.2594	+	12.7562i	−1.38029	+	0.448483i	−0.477524	+	0.878619i	$0.658466\pi$
$810$	−3.03752	−	1.63656i	−0.106727	−	0.0575029i
$811$	−15.0446	−	20.7071i	−0.528286	−	0.727123i	0.458582	−	0.888652i	$-0.348357\pi$
$811$	−15.0446	−	20.7071i	−0.528286	−	0.727123i	−0.986868	+	0.161529i	$0.948357\pi$
$812$	16.1077	+	32.6421i	0.565271	+	1.14551i
$813$	27.3090	−	12.4001i	0.957770	−	0.434892i
$814$	−2.39100	−	0.921617i	−0.0838047	−	0.0323026i
$815$	−40.2913			−1.41134
$816$	40.5827	−	4.56731i	1.42068	−	0.159888i
$817$	−4.83300	−	6.65206i	−0.169085	−	0.232726i
$818$	4.11017	+	2.98621i	0.143709	+	0.104410i
$819$	−14.4152	+	5.56445i	−0.503709	+	0.194438i
$820$	−11.2039	−	34.4821i	−0.391258	−	1.20417i
$821$	−18.6638	+	25.6885i	−0.651370	+	0.896534i	−0.999158	−	0.0410397i	$-0.986933\pi$
$821$	−18.6638	+	25.6885i	−0.651370	+	0.896534i	0.347788	+	0.937573i	$0.386933\pi$
$822$	−3.40031	−	1.92998i	−0.118599	−	0.0673156i
$823$	1.05090	−	3.23433i	0.0366320	−	0.112742i	−0.931068	−	0.364845i	$-0.881122\pi$
$823$	1.05090	−	3.23433i	0.0366320	−	0.112742i	0.967700	+	0.252103i	$0.0811221\pi$
$824$	0.872768			0.0304043
$825$	14.4672	−	11.8590i	0.503682	−	0.412876i
$826$	−0.103723	+	0.101094i	−0.00360898	+	0.00351752i
$827$	−49.3876	−	16.0470i	−1.71738	−	0.558009i	−0.725843	−	0.687861i	$-0.758550\pi$
$827$	−49.3876	−	16.0470i	−1.71738	−	0.558009i	−0.991533	+	0.129852i	$0.958550\pi$
$828$	32.7403	+	2.95512i	1.13780	+	0.102697i
$829$	15.0632	−	20.7326i	0.523165	−	0.720075i	−0.462905	−	0.886408i	$-0.653193\pi$
$829$	15.0632	−	20.7326i	0.523165	−	0.720075i	0.986070	+	0.166333i	$0.0531928\pi$
$830$	2.68289	−	0.871724i	0.0931245	−	0.0302580i
$831$	5.75805	−	5.26173i	0.199744	−	0.182528i
$832$	8.66897	−	11.9318i	0.300542	−	0.413661i
$833$	−24.0283	−	34.9229i	−0.832530	−	1.21001i
$834$	−4.97369	+	0.559756i	−0.172225	+	0.0193828i
$835$	33.7923			1.16943
$836$	12.7228	+	19.6508i	0.440026	+	0.679637i
$837$	−4.99468	+	16.6099i	−0.172641	+	0.574123i
$838$	−4.53224	−	1.47261i	−0.156564	−	0.0508706i
$839$	3.24231	−	2.35568i	0.111937	−	0.0813270i	−0.530408	−	0.847742i	$-0.677961\pi$
$839$	3.24231	−	2.35568i	0.111937	−	0.0813270i	0.642346	+	0.766415i	$0.277961\pi$
$840$	−3.77809	−	5.88816i	−0.130357	−	0.203161i
$841$	−5.92511	−	18.2356i	−0.204314	−	0.628815i
$842$	1.11602	−	0.362618i	0.0384607	−	0.0124966i
$843$	29.0873	+	5.95953i	1.00182	+	0.205257i
$844$	−40.1445	+	29.1667i	−1.38183	+	1.00396i
$845$	8.17792	−	25.1691i	0.281329	−	0.865842i
$846$	1.10199	+	0.963280i	0.0378873	+	0.0331183i
$847$	27.9907	+	7.97007i	0.961771	+	0.273855i
$848$			7.19679i			0.247139i
$849$	−2.98017	−	26.4802i	−0.102279	−	0.908798i
$850$	−1.54650	−	2.12858i	−0.0530447	−	0.0730097i
$851$	18.8163	−	25.8984i	0.645013	−	0.887785i
$852$	−11.2002	−	12.2566i	−0.383711	−	0.419905i
$853$	34.4436	−	11.1914i	1.17932	−	0.383186i	0.347209	−	0.937788i	$-0.387129\pi$
$853$	34.4436	−	11.1914i	1.17932	−	0.383186i	0.832116	+	0.554602i	$0.187129\pi$
$854$	0.360688	+	2.48313i	0.0123425	+	0.0849710i
$855$	30.5710	+	2.75933i	1.04551	+	0.0943670i
$856$	−3.13893	+	9.66063i	−0.107286	+	0.330193i
$857$	−38.9293			−1.32980			−0.664900	−	0.746933i	$-0.731526\pi$
$857$	−38.9293			−1.32980			−0.664900	+	0.746933i	$0.731526\pi$
$858$	−1.25620	−	0.805163i	−0.0428858	−	0.0274878i
$859$			19.8219i			0.676315i	0.941090	+	0.338158i	$0.109804\pi$
$859$			19.8219i			0.676315i	−0.941090	+	0.338158i	$0.890196\pi$
$860$	4.06413	−	12.5081i	0.138586	−	0.426523i
$861$	−7.39552	−	28.2182i	−0.252038	−	0.961674i
$862$	0.119502	+	0.0868235i	0.00407026	+	0.00295722i
$863$	7.67761	−	2.49461i	0.261349	−	0.0849174i	−0.175412	−	0.984495i	$-0.556126\pi$
$863$	7.67761	−	2.49461i	0.261349	−	0.0849174i	0.436761	+	0.899578i	$0.356126\pi$
$864$	8.21880	−	0.181306i	0.279609	−	0.00616814i
$865$	−16.9158	−	12.2901i	−0.575155	−	0.417875i
$866$	−1.35123	+	0.981724i	−0.0459166	+	0.0333603i
$867$	33.8605	−	3.81078i	1.14996	−	0.129421i
$868$	−12.5362	+	12.2185i	−0.425508	+	0.414724i
$869$	−2.91586	−	10.9426i	−0.0989137	−	0.371204i
$870$	1.90547	+	4.19644i	0.0646013	+	0.142273i
$871$	25.8070	+	8.38519i	0.874435	+	0.284121i
$872$	0.824289	+	1.13454i	0.0279139	+	0.0384202i
$873$	−5.34883	−	23.4624i	−0.181031	−	0.794083i
$874$	2.49782	−	0.811592i	0.0844901	−	0.0274525i
$875$	−6.16891	+	11.7325i	−0.208547	+	0.396630i
$876$	24.9230	+	5.10633i	0.842070	+	0.172527i
$877$	−5.89489	+	4.28289i	−0.199056	+	0.144623i	−0.682848	−	0.730560i	$-0.739259\pi$
$877$	−5.89489	+	4.28289i	−0.199056	+	0.144623i	0.483792	+	0.875183i	$0.339259\pi$
$878$	0.613792	−	1.88906i	0.0207145	−	0.0637526i
$879$	−16.2828	−	35.8599i	−0.549206	−	1.20952i
$880$	−13.3451	+	34.6221i	−0.449865	+	1.16711i
$881$	14.7701			0.497619			0.248809	−	0.968552i	$-0.419961\pi$
$881$	14.7701			0.497619			0.248809	+	0.968552i	$0.419961\pi$
$882$	−1.37424	−	2.44168i	−0.0462730	−	0.0822155i
$883$	−31.8443	+	23.1362i	−1.07165	+	0.778597i	−0.976207	−	0.216838i	$-0.930426\pi$
$883$	−31.8443	+	23.1362i	−1.07165	+	0.778597i	−0.0954391	+	0.995435i	$0.530426\pi$
$884$	13.7357	−	18.9055i	0.461981	−	0.635862i
$885$	1.50746	−	1.37753i	0.0506729	−	0.0463052i
$886$	0.292518	+	0.900277i	0.00982732	+	0.0302454i
$887$	−38.8857	−	28.2521i	−1.30565	−	0.948614i	−0.305661	−	0.952140i	$-0.598877\pi$
$887$	−38.8857	−	28.2521i	−1.30565	−	0.948614i	−0.999994	+	0.00352687i	$0.998877\pi$
$888$	2.63051	−	4.63453i	0.0882740	−	0.155525i
$889$	0.359857	−	0.177577i	0.0120692	−	0.00595573i
$890$		−	4.55678i		−	0.152744i
$891$	2.39689	+	29.7532i	0.0802987	+	0.996771i
$892$			10.7460i			0.359801i
$893$	−12.3839	−	4.02377i	−0.414411	−	0.134650i
$894$	−0.0326650	−	0.0185403i	−0.00109248	−	0.000620080i
$895$	14.9079	−	20.5190i	0.498316	−	0.685873i
$896$	9.77685	+	5.14064i	0.326622	+	0.171737i
$897$	13.7602	−	12.5742i	0.459441	−	0.419839i
$898$	0.446665	+	0.324521i	0.0149054	+	0.0108294i
$899$	18.7434	−	13.6179i	0.625127	−	0.454181i
$900$	9.92775	+	16.6259i	0.330925	+	0.554197i
$901$			11.1936i			0.372913i
$902$	1.77574	−	2.18666i	0.0591255	−	0.0728078i
$903$	3.84621	−	9.85787i	0.127994	−	0.328049i
$904$	2.57789	−	7.93391i	0.0857392	−	0.263878i
$905$	7.22185	+	9.94002i	0.240062	+	0.330418i
$906$	0.834626	+	0.171002i	0.0277286	+	0.00568115i
$907$	−4.11868	−	12.6760i	−0.136759	−	0.420900i	0.859101	−	0.511806i	$-0.171024\pi$
$907$	−4.11868	−	12.6760i	−0.136759	−	0.420900i	−0.995859	+	0.0909066i	$0.971024\pi$
$908$	−7.91373	−	24.3560i	−0.262626	−	0.808281i
$909$	−18.2918	+	4.17005i	−0.606699	+	0.138312i
$910$	−1.94617	−	0.333899i	−0.0645149	−	0.0110686i
$911$	−0.692287	−	0.224938i	−0.0229365	−	0.00745251i	0.297526	−	0.954714i	$-0.403838\pi$
$911$	−0.692287	−	0.224938i	−0.0229365	−	0.00745251i	−0.320463	+	0.947261i	$0.603838\pi$
$912$	−21.8651	+	9.92824i	−0.724027	+	0.328757i
$913$	−18.9448	−	15.3846i	−0.626980	−	0.509156i
$914$			3.08858i			0.102161i
$915$	−3.95643	−	35.1547i	−0.130795	−	1.16218i
$916$	−1.68305	−	2.31652i	−0.0556095	−	0.0765399i
$917$	2.13430	+	14.6934i	0.0704807	+	0.485220i
$918$	4.19732	−	0.0925924i	0.138532	−	0.00305600i
$919$	7.76703	+	23.9045i	0.256211	+	0.788535i	0.993589	+	0.113055i	$0.0360637\pi$
$919$	7.76703	+	23.9045i	0.256211	+	0.788535i	−0.737378	+	0.675480i	$0.763936\pi$
$920$	6.82771	+	4.96062i	0.225103	+	0.163547i
$921$	−2.56342	+	4.51634i	−0.0844676	+	0.148818i
$922$	4.76891	+	1.54951i	0.157056	+	0.0510305i
$923$	−9.41451			−0.309882
$924$	−12.4423	+	27.4375i	−0.409322	+	0.902626i
$925$	18.8571			0.620019
$926$	−2.18830	−	0.711020i	−0.0719118	−	0.0233656i
$927$	−4.90807	−	0.443000i	−0.161202	−	0.0145500i
$928$	−8.88375	−	6.45442i	−0.291623	−	0.211877i
$929$	5.57190	+	17.1486i	0.182808	+	0.562626i	0.999904	−	0.0138765i	$-0.00441717\pi$
$929$	5.57190	+	17.1486i	0.182808	+	0.562626i	−0.817095	+	0.576502i	$0.804417\pi$
$930$	−1.63622	+	1.49518i	−0.0536536	+	0.0490290i
$931$	19.7830	+	15.1639i	0.648360	+	0.496976i
$932$	2.09493	+	2.88343i	0.0686218	+	0.0944499i
$933$	−30.3266	+	3.41305i	−0.992847	+	0.111738i
$934$			1.09196i			0.0357299i
$935$	−20.7565	+	53.8498i	−0.678810	+	1.76108i
$936$	2.04218	−	2.33625i	0.0667506	−	0.0763628i
$937$	11.4713	+	3.72724i	0.374750	+	0.121764i	0.490335	−	0.871534i	$-0.336874\pi$
$937$	11.4713	+	3.72724i	0.374750	+	0.121764i	−0.115585	+	0.993298i	$0.536874\pi$
$938$	−0.832005	+	4.84944i	−0.0271659	+	0.158340i
$939$	−25.8311	−	5.29238i	−0.842966	−	0.172710i
$940$	−6.43605	−	19.8081i	−0.209921	−	0.646070i
$941$	2.28182	+	7.02273i	0.0743853	+	0.228934i	0.981336	−	0.192303i	$-0.0615958\pi$
$941$	2.28182	+	7.02273i	0.0743853	+	0.228934i	−0.906950	+	0.421238i	$0.861596\pi$
$942$	1.10130	−	5.37524i	0.0358823	−	0.175135i
$943$	20.6842	+	28.4694i	0.673571	+	0.927092i
$944$	−0.493671	+	1.51936i	−0.0160676	+	0.0494511i
$945$	18.2577	+	35.0302i	0.593922	+	1.13953i
$946$	0.987342	−	0.263094i	0.0321013	−	0.00855394i
$947$		−	5.86546i		−	0.190602i	−0.995449	−	0.0953009i	$-0.969619\pi$
$947$		−	5.86546i		−	0.190602i	0.995449	−	0.0953009i	$-0.0303813\pi$
$948$	11.6492	−	1.31104i	0.378349	−	0.0425806i
$949$	11.6706	−	8.47916i	0.378842	−	0.275245i
$950$	1.25162	+	0.909358i	0.0406080	+	0.0295035i
$951$	−21.0349	−	23.0190i	−0.682104	−	0.746444i
$952$	7.53466	+	3.96171i	0.244200	+	0.128400i
$953$	19.5556	−	26.9160i	0.633468	−	0.871894i	−0.364778	−	0.931095i	$-0.618855\pi$
$953$	19.5556	−	26.9160i	0.633468	−	0.871894i	0.998246	+	0.0592002i	$0.0188550\pi$
$954$	−0.0665080	+	0.736853i	−0.00215328	+	0.0238565i
$955$	−51.0736	−	16.5948i	−1.65270	−	0.536996i
$956$			7.65407i			0.247550i
$957$	21.5156	−	33.5682i	0.695502	−	1.08510i
$958$		−	4.59540i		−	0.148471i
$959$	19.8087	+	40.1421i	0.639656	+	1.29626i
$960$	−32.7907	−	18.6116i	−1.05831	−	0.600688i
$961$	−16.0654	−	11.6722i	−0.518238	−	0.376522i
$962$	−0.464791	−	1.43048i	−0.0149855	−	0.0461205i
$963$	22.5555	−	52.7340i	0.726842	−	1.69933i
$964$	−24.5814	+	33.8334i	−0.791713	+	1.08970i
$965$	42.1034	−	30.5899i	1.35536	−	0.984725i
$966$	2.61501	+	2.14143i	0.0841366	+	0.0688994i
$967$	−46.5230			−1.49608			−0.748040	−	0.663654i	$-0.769005\pi$
$967$	−46.5230			−1.49608			−0.748040	+	0.663654i	$0.769005\pi$
$968$	−5.72002	+	1.19930i	−0.183848	+	0.0385470i
$969$	−34.0081	+	15.4420i	−1.09250	+	0.496068i
$970$	0.950288	−	2.92469i	0.0305119	−	0.0939060i
$971$	22.2116	−	16.1377i	0.712803	−	0.517882i	−0.171273	−	0.985224i	$-0.554788\pi$
$971$	22.2116	−	16.1377i	0.712803	−	0.517882i	0.884077	+	0.467342i	$0.154788\pi$
$972$	−30.8281	−	2.09829i	−0.988812	−	0.0673026i
$973$	50.7191	+	26.6680i	1.62598	+	0.854937i
$974$	−2.22017	+	0.721376i	−0.0711387	+	0.0231144i
$975$	10.7567	+	2.20388i	0.344491	+	0.0705807i
$976$	16.2675	+	22.3903i	0.520710	+	0.716695i
$977$	−53.1546	−	17.2710i	−1.70057	−	0.552548i	−0.711848	−	0.702333i	$-0.752142\pi$
$977$	−53.1546	−	17.2710i	−1.70057	−	0.552548i	−0.988719	+	0.149786i	$0.952142\pi$
$978$	2.95050	−	1.33972i	0.0943465	−	0.0428397i
$979$	−33.0915	+	21.4248i	−1.05761	+	0.684741i
$980$	−1.02320	+	39.8563i	−0.0326850	+	1.27316i
$981$	−4.05958	−	6.79854i	−0.129612	−	0.217061i
$982$	−1.50916	+	1.09647i	−0.0481593	+	0.0349898i
$983$	21.6483	+	15.7284i	0.690474	+	0.501659i	0.876816	−	0.480826i	$-0.159663\pi$
$983$	21.6483	+	15.7284i	0.690474	+	0.501659i	−0.186342	+	0.982485i	$0.559663\pi$
$984$	3.95170	+	4.32444i	0.125976	+	0.137858i
$985$	59.6128	−	19.3694i	1.89942	−	0.617159i
$986$	−4.53691	−	3.29626i	−0.144485	−	0.104974i
$987$	−4.24833	−	16.2098i	−0.135226	−	0.515965i
$988$	−4.24617	+	13.0684i	−0.135089	+	0.415760i
$989$			12.7649i			0.405901i
$990$	−1.68632	+	3.42150i	−0.0535946	+	0.108743i
$991$	20.9093			0.664206			0.332103	−	0.943243i	$-0.392242\pi$
$991$	20.9093			0.664206			0.332103	+	0.943243i	$0.392242\pi$
$992$	1.63192	−	5.02252i	0.0518134	−	0.159465i
$993$	21.3466	+	12.1161i	0.677415	+	0.384493i
$994$	−0.245390	−	1.68937i	−0.00778329	−	0.0535836i
$995$	−43.0509	+	13.9881i	−1.36481	+	0.443453i
$996$	18.6493	−	17.0418i	0.590925	−	0.539991i
$997$	36.0637	−	49.6374i	1.14215	−	1.57203i	0.379538	−	0.925176i	$-0.376083\pi$
$997$	36.0637	−	49.6374i	1.14215	−	1.57203i	0.762611	−	0.646857i	$-0.223917\pi$
$998$	0.298670	+	0.411084i	0.00945423	+	0.0130126i
$999$	−17.1452	+	24.7274i	−0.542451	+	0.782341i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.u.a.20.15	yes	112
3.2	odd	2	inner	231.2.u.a.20.13	✓	112
7.6	odd	2	inner	231.2.u.a.20.16	yes	112
11.5	even	5	inner	231.2.u.a.104.14	yes	112
21.20	even	2	inner	231.2.u.a.20.14	yes	112
33.5	odd	10	inner	231.2.u.a.104.16	yes	112
77.27	odd	10	inner	231.2.u.a.104.13	yes	112
231.104	even	10	inner	231.2.u.a.104.15	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.u.a.20.13	✓	112	3.2	odd	2	inner
231.2.u.a.20.14	yes	112	21.20	even	2	inner
231.2.u.a.20.15	yes	112	1.1	even	1	trivial
231.2.u.a.20.16	yes	112	7.6	odd	2	inner
231.2.u.a.104.13	yes	112	77.27	odd	10	inner
231.2.u.a.104.14	yes	112	11.5	even	5	inner
231.2.u.a.104.15	yes	112	231.104	even	10	inner
231.2.u.a.104.16	yes	112	33.5	odd	10	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.126891 + 0.0412293i) q^{2} +(-1.50633 - 0.854974i) q^{3} +(-1.60363 - 1.16511i) q^{4} +(0.887927 + 2.73276i) q^{5} +(-0.155889 - 0.170593i) q^{6} +(0.380318 + 2.61827i) q^{7} +(-0.312296 - 0.429838i) q^{8} +(1.53804 + 2.57574i) q^{9} +O(q^{10})\)	\(q+(0.126891 + 0.0412293i) q^{2} +(-1.50633 - 0.854974i) q^{3} +(-1.60363 - 1.16511i) q^{4} +(0.887927 + 2.73276i) q^{5} +(-0.155889 - 0.170593i) q^{6} +(0.380318 + 2.61827i) q^{7} +(-0.312296 - 0.429838i) q^{8} +(1.53804 + 2.57574i) q^{9} +0.383371i q^{10} +(2.78405 - 1.80251i) q^{11} +(1.41946 + 3.12610i) q^{12} +(1.85148 + 0.601582i) q^{13} +(-0.0596909 + 0.347915i) q^{14} +(0.998930 - 4.87558i) q^{15} +(1.20316 + 3.70295i) q^{16} +(1.87135 + 5.75941i) q^{17} +(0.0889671 + 0.390250i) q^{18} +(-2.09302 - 2.88080i) q^{19} +(1.76005 - 5.41687i) q^{20} +(1.66567 - 4.26914i) q^{21} +(0.427587 - 0.113938i) q^{22} +5.52810i q^{23} +(0.102919 + 0.914481i) q^{24} +(-2.63447 + 1.91406i) q^{25} +(0.210133 + 0.152670i) q^{26} +(-0.114599 - 5.19489i) q^{27} +(2.44068 - 4.64186i) q^{28} +(-4.07967 + 5.61519i) q^{29} +(0.327772 - 0.577482i) q^{30} +(-3.17461 - 1.03149i) q^{31} +1.58209i q^{32} +(-5.73479 + 0.334884i) q^{33} +0.807972i q^{34} +(-6.81742 + 3.36415i) q^{35} +(0.534564 - 5.92252i) q^{36} +(-4.68486 - 3.40375i) q^{37} +(-0.146812 - 0.451842i) q^{38} +(-2.27459 - 2.48914i) q^{39} +(0.897348 - 1.23509i) q^{40} +(5.14995 - 3.74166i) q^{41} +(0.387372 - 0.473040i) q^{42} +2.30910 q^{43} +(-6.56472 - 0.353147i) q^{44} +(-5.67321 + 6.49016i) q^{45} +(-0.227920 + 0.701465i) q^{46} +(2.95837 - 2.14938i) q^{47} +(1.35357 - 6.60652i) q^{48} +(-6.71072 + 1.99155i) q^{49} +(-0.413206 + 0.134259i) q^{50} +(2.10529 - 10.2755i) q^{51} +(-2.26818 - 3.12189i) q^{52} +(1.75794 + 0.571189i) q^{53} +(0.199640 - 0.663909i) q^{54} +(7.39787 + 6.00764i) q^{55} +(1.00666 - 0.981150i) q^{56} +(0.689769 + 6.12891i) q^{57} +(-0.749184 + 0.544314i) q^{58} +(0.331949 + 0.241175i) q^{59} +(-7.28249 + 6.65478i) q^{60} +(6.76031 - 2.19656i) q^{61} +(-0.360301 - 0.261774i) q^{62} +(-6.15905 + 5.00661i) q^{63} +(2.34109 - 7.20514i) q^{64} +5.59381i q^{65} +(-0.741500 - 0.193948i) q^{66} +13.9386 q^{67} +(3.70938 - 11.4163i) q^{68} +(4.72638 - 8.32712i) q^{69} +(-1.00377 + 0.145803i) q^{70} +(-4.59930 + 1.49440i) q^{71} +(0.626828 - 1.46550i) q^{72} +(4.35552 - 5.99486i) q^{73} +(-0.454132 - 0.625059i) q^{74} +(5.60485 - 0.630789i) q^{75} +7.05835i q^{76} +(5.77830 + 6.60388i) q^{77} +(-0.185999 - 0.409630i) q^{78} +(1.05512 - 3.24734i) q^{79} +(-9.05095 + 6.57590i) q^{80} +(-4.26887 + 7.92318i) q^{81} +(0.807748 - 0.262453i) q^{82} +(-2.27384 - 6.99816i) q^{83} +(-7.64513 + 4.90544i) q^{84} +(-14.0775 + 10.2279i) q^{85} +(0.293004 + 0.0952027i) q^{86} +(10.9462 - 4.97029i) q^{87} +(-1.64424 - 0.633773i) q^{88} -11.8861 q^{89} +(-0.987464 + 0.589639i) q^{90} +(-0.870956 + 5.07647i) q^{91} +(6.44082 - 8.86503i) q^{92} +(3.90009 + 4.26797i) q^{93} +(0.464008 - 0.150765i) q^{94} +(6.01408 - 8.27768i) q^{95} +(1.35265 - 2.38315i) q^{96} +(-7.62887 - 2.47877i) q^{97} +(-0.933639 - 0.0239686i) q^{98} +(8.92479 + 4.39865i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) \) 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9	\( 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9} - 60 q^{16} + 2 q^{18} - 80 q^{22} - 36 q^{25} + 8 q^{28} + 24 q^{30} - 34 q^{36} + 4 q^{37} - 66 q^{39} - 30 q^{42} + 36 q^{46} + 26 q^{49} + 38 q^{51} - 86 q^{57} - 116 q^{58} + 88 q^{60} + 44 q^{63} - 32 q^{64} + 110 q^{70} + 86 q^{72} - 52 q^{78} - 156 q^{79} + 68 q^{81} - 30 q^{84} + 8 q^{85} - 112 q^{88} + 42 q^{91} + 56 q^{93} + 70 q^{99}+O(q^{100}) \) 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9 - 60 * q^16 + 2 * q^18 - 80 * q^22 - 36 * q^25 + 8 * q^28 + 24 * q^30 - 34 * q^36 + 4 * q^37 - 66 * q^39 - 30 * q^42 + 36 * q^46 + 26 * q^49 + 38 * q^51 - 86 * q^57 - 116 * q^58 + 88 * q^60 + 44 * q^63 - 32 * q^64 + 110 * q^70 + 86 * q^72 - 52 * q^78 - 156 * q^79 + 68 * q^81 - 30 * q^84 + 8 * q^85 - 112 * q^88 + 42 * q^91 + 56 * q^93 + 70 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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