LMFDB - Embedded newform 429.2.bb.a.25.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(25,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 5]))

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

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

chi := DirichletCharacter("429.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bb (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			25.9
Character	$\chi$	$=$	429.25
Dual form			429.2.bb.a.103.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.665766 + 0.916348i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.221584 - 0.681966i) q^{4} +(1.07016 - 1.47295i) q^{5} +(-0.665766 + 0.916348i) q^{6} +(1.70616 + 0.554365i) q^{7} +(2.92691 - 0.951009i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.665766 + 0.916348i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.221584 - 0.681966i) q^{4} +(1.07016 - 1.47295i) q^{5} +(-0.665766 + 0.916348i) q^{6} +(1.70616 + 0.554365i) q^{7} +(2.92691 - 0.951009i) q^{8} +(-0.809017 + 0.587785i) q^{9} +2.06221 q^{10} +(-2.11063 - 2.55837i) q^{11} +0.717061 q^{12} +(-1.43167 - 3.30913i) q^{13} +(0.627912 + 1.93251i) q^{14} +(1.73156 + 0.562617i) q^{15} +(1.65986 + 1.20596i) q^{16} +(5.15955 + 3.74863i) q^{17} +(-1.07723 - 0.350014i) q^{18} +(-0.0962874 + 0.0312857i) q^{19} +(-0.767371 - 1.05620i) q^{20} +1.79396i q^{21} +(0.939167 - 3.63735i) q^{22} -5.31768 q^{23} +(1.80893 + 2.48977i) q^{24} +(0.520746 + 1.60269i) q^{25} +(2.07916 - 3.51501i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.756116 - 1.04070i) q^{28} +(-2.94348 + 9.05909i) q^{29} +(0.637259 + 1.96128i) q^{30} +(0.688421 + 0.947531i) q^{31} -3.83116i q^{32} +(1.78093 - 2.79791i) q^{33} +7.22366i q^{34} +(2.64242 - 1.91983i) q^{35} +(0.221584 + 0.681966i) q^{36} +(4.88313 + 1.58662i) q^{37} +(-0.0927734 - 0.0674038i) q^{38} +(2.70476 - 2.38418i) q^{39} +(1.73147 - 5.32892i) q^{40} +(-10.8537 + 3.52658i) q^{41} +(-1.64390 + 1.19436i) q^{42} +7.15650 q^{43} +(-2.21240 + 0.872485i) q^{44} +1.82067i q^{45} +(-3.54033 - 4.87284i) q^{46} +(-2.79577 + 0.908401i) q^{47} +(-0.634010 + 1.95128i) q^{48} +(-3.05946 - 2.22282i) q^{49} +(-1.12193 + 1.54420i) q^{50} +(-1.97077 + 6.06541i) q^{51} +(-2.57395 + 0.243100i) q^{52} +(-8.04139 + 5.84241i) q^{53} -1.13267i q^{54} +(-6.02706 + 0.370993i) q^{55} +5.52098 q^{56} +(-0.0595089 - 0.0819069i) q^{57} +(-10.2609 + 3.33398i) q^{58} +(1.89051 + 0.614264i) q^{59} +(0.767371 - 1.05620i) q^{60} +(-5.91209 - 4.29539i) q^{61} +(-0.409941 + 1.26167i) q^{62} +(-1.70616 + 0.554365i) q^{63} +(6.83040 - 4.96258i) q^{64} +(-6.40630 - 1.43252i) q^{65} +(3.74954 - 0.230801i) q^{66} -1.12724i q^{67} +(3.69971 - 2.68800i) q^{68} +(-1.64325 - 5.05741i) q^{69} +(3.51847 + 1.14322i) q^{70} +(0.474976 - 0.653748i) q^{71} +(-1.80893 + 2.48977i) q^{72} +(-1.62240 - 0.527150i) q^{73} +(1.79712 + 5.53097i) q^{74} +(-1.36333 + 0.990518i) q^{75} +0.0725971i q^{76} +(-2.18281 - 5.53504i) q^{77} +(3.98547 + 0.891196i) q^{78} +(13.8005 - 10.0267i) q^{79} +(3.55264 - 1.15432i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-10.4576 - 7.59790i) q^{82} +(8.74667 - 12.0388i) q^{83} +(1.22342 + 0.397514i) q^{84} +(11.0431 - 3.58812i) q^{85} +(4.76456 + 6.55785i) q^{86} -9.52529 q^{87} +(-8.61065 - 5.48086i) q^{88} +16.0834i q^{89} +(-1.66837 + 1.21214i) q^{90} +(-0.608194 - 6.43957i) q^{91} +(-1.17831 + 3.62647i) q^{92} +(-0.688421 + 0.947531i) q^{93} +(-2.69374 - 1.95712i) q^{94} +(-0.0569608 + 0.175307i) q^{95} +(3.64365 - 1.18389i) q^{96} +(-5.57904 - 7.67890i) q^{97} -4.28341i q^{98} +(3.21131 + 0.829163i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9}+O(q^{10}) $ 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9	$ 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9} + 40 q^{10} - 52 q^{12} + 5 q^{13} - 6 q^{14} + 16 q^{16} - 14 q^{17} - 36 q^{22} + 28 q^{23} + 36 q^{25} + 6 q^{26} - 14 q^{27} + 34 q^{29} - 10 q^{30} + 18 q^{35} + 8 q^{36} - 18 q^{38} + 5 q^{39} + 40 q^{40} - 6 q^{42} + 48 q^{43} - 14 q^{48} - 14 q^{49} - 4 q^{51} + 11 q^{52} + 10 q^{53} + 8 q^{55} - 68 q^{56} + 10 q^{61} - 132 q^{62} - 52 q^{64} - 42 q^{65} + 14 q^{66} + 50 q^{68} - 2 q^{69} + 10 q^{74} + 6 q^{75} - 88 q^{77} + 26 q^{78} + 48 q^{79} - 14 q^{81} - 30 q^{82} - 36 q^{87} - 10 q^{88} - 10 q^{90} - 11 q^{91} - 126 q^{92} - 34 q^{94} + 36 q^{95}+O(q^{100}) $ 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9 + 40 * q^10 - 52 * q^12 + 5 * q^13 - 6 * q^14 + 16 * q^16 - 14 * q^17 - 36 * q^22 + 28 * q^23 + 36 * q^25 + 6 * q^26 - 14 * q^27 + 34 * q^29 - 10 * q^30 + 18 * q^35 + 8 * q^36 - 18 * q^38 + 5 * q^39 + 40 * q^40 - 6 * q^42 + 48 * q^43 - 14 * q^48 - 14 * q^49 - 4 * q^51 + 11 * q^52 + 10 * q^53 + 8 * q^55 - 68 * q^56 + 10 * q^61 - 132 * q^62 - 52 * q^64 - 42 * q^65 + 14 * q^66 + 50 * q^68 - 2 * q^69 + 10 * q^74 + 6 * q^75 - 88 * q^77 + 26 * q^78 + 48 * q^79 - 14 * q^81 - 30 * q^82 - 36 * q^87 - 10 * q^88 - 10 * q^90 - 11 * q^91 - 126 * q^92 - 34 * q^94 + 36 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.665766	+	0.916348i	0.470768	+	0.647956i	0.976698	−	0.214618i	$-0.0688507\pi$
$2$	0.665766	+	0.916348i	0.470768	+	0.647956i	−0.505930	+	0.862574i	$0.668851\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.221584	−	0.681966i	0.110792	−	0.340983i
$5$	1.07016	−	1.47295i	0.478591	−	0.658724i	−0.499643	−	0.866232i	$-0.666535\pi$
$5$	1.07016	−	1.47295i	0.478591	−	0.658724i	0.978233	+	0.207508i	$0.0665353\pi$
$6$	−0.665766	+	0.916348i	−0.271798	+	0.374098i
$7$	1.70616	+	0.554365i	0.644868	+	0.209530i	0.613150	−	0.789967i	$-0.289902\pi$
$7$	1.70616	+	0.554365i	0.644868	+	0.209530i	0.0317181	+	0.999497i	$0.489902\pi$
$8$	2.92691	−	0.951009i	1.03482	−	0.336233i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	2.06221			0.652129
$11$	−2.11063	−	2.55837i	−0.636379	−	0.771376i
$11$	−2.11063	−	2.55837i	−0.636379	−	0.771376i
$12$	0.717061			0.206998
$13$	−1.43167	−	3.30913i	−0.397074	−	0.917787i
$13$	−1.43167	−	3.30913i	−0.397074	−	0.917787i
$14$	0.627912	+	1.93251i	0.167817	+	0.516486i
$15$	1.73156	+	0.562617i	0.447086	+	0.145267i
$16$	1.65986	+	1.20596i	0.414965	+	0.301490i
$17$	5.15955	+	3.74863i	1.25137	+	0.909177i	0.998301	−	0.0582703i	$-0.0185585\pi$
$17$	5.15955	+	3.74863i	1.25137	+	0.909177i	0.253074	+	0.967447i	$0.418559\pi$
$18$	−1.07723	−	0.350014i	−0.253906	−	0.0824991i
$19$	−0.0962874	+	0.0312857i	−0.0220898	+	0.00717742i	−0.320041	−	0.947404i	$-0.603697\pi$
$19$	−0.0962874	+	0.0312857i	−0.0220898	+	0.00717742i	0.297951	+	0.954581i	$0.403697\pi$
$20$	−0.767371	−	1.05620i	−0.171589	−	0.236173i
$21$			1.79396i			0.391475i
$22$	0.939167	−	3.63735i	0.200231	−	0.775485i
$23$	−5.31768			−1.10881			−0.554406	−	0.832246i	$-0.687055\pi$
$23$	−5.31768			−1.10881			−0.554406	+	0.832246i	$0.687055\pi$
$24$	1.80893	+	2.48977i	0.369246	+	0.508223i
$25$	0.520746	+	1.60269i	0.104149	+	0.320538i
$26$	2.07916	−	3.51501i	0.407756	−	0.689351i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	0.756116	−	1.04070i	0.142893	−	0.196675i
$29$	−2.94348	+	9.05909i	−0.546590	+	1.68223i	0.170590	+	0.985342i	$0.445432\pi$
$29$	−2.94348	+	9.05909i	−0.546590	+	1.68223i	−0.717180	+	0.696888i	$0.754568\pi$
$30$	0.637259	+	1.96128i	0.116347	+	0.358079i
$31$	0.688421	+	0.947531i	0.123644	+	0.170182i	0.866352	−	0.499434i	$-0.166459\pi$
$31$	0.688421	+	0.947531i	0.123644	+	0.170182i	−0.742708	+	0.669616i	$0.766459\pi$
$32$		−	3.83116i		−	0.677260i
$33$	1.78093	−	2.79791i	0.310020	−	0.487053i
$34$			7.22366i			1.23885i
$35$	2.64242	−	1.91983i	0.446651	−	0.324511i
$36$	0.221584	+	0.681966i	0.0369307	+	0.113661i
$37$	4.88313	+	1.58662i	0.802781	+	0.260839i	0.681537	−	0.731783i	$-0.261312\pi$
$37$	4.88313	+	1.58662i	0.802781	+	0.260839i	0.121244	+	0.992623i	$0.461312\pi$
$38$	−0.0927734	−	0.0674038i	−0.0150498	−	0.0109343i
$39$	2.70476	−	2.38418i	0.433108	−	0.381774i
$40$	1.73147	−	5.32892i	0.273770	−	0.842577i
$41$	−10.8537	+	3.52658i	−1.69506	+	0.550760i	−0.987737	−	0.156127i	$-0.950099\pi$
$41$	−10.8537	+	3.52658i	−1.69506	+	0.550760i	−0.707327	+	0.706886i	$0.750099\pi$
$42$	−1.64390	+	1.19436i	−0.253659	+	0.184294i
$43$	7.15650			1.09136			0.545678	−	0.837995i	$-0.316272\pi$
$43$	7.15650			1.09136			0.545678	+	0.837995i	$0.316272\pi$
$44$	−2.21240	+	0.872485i	−0.333532	+	0.131532i
$45$			1.82067i			0.271409i
$46$	−3.54033	−	4.87284i	−0.521993	−	0.718462i
$47$	−2.79577	+	0.908401i	−0.407805	+	0.132504i	−0.505734	−	0.862690i	$-0.668778\pi$
$47$	−2.79577	+	0.908401i	−0.407805	+	0.132504i	0.0979288	+	0.995193i	$0.468778\pi$
$48$	−0.634010	+	1.95128i	−0.0915115	+	0.281643i
$49$	−3.05946	−	2.22282i	−0.437065	−	0.317546i
$50$	−1.12193	+	1.54420i	−0.158665	+	0.218383i
$51$	−1.97077	+	6.06541i	−0.275963	+	0.849328i
$52$	−2.57395	+	0.243100i	−0.356942	+	0.0337119i
$53$	−8.04139	+	5.84241i	−1.10457	+	0.802517i	−0.981800	−	0.189918i	$-0.939178\pi$
$53$	−8.04139	+	5.84241i	−1.10457	+	0.802517i	−0.122770	+	0.992435i	$0.539178\pi$
$54$		−	1.13267i		−	0.154137i
$55$	−6.02706	+	0.370993i	−0.812689	+	0.0500247i
$56$	5.52098			0.737772
$57$	−0.0595089	−	0.0819069i	−0.00788214	−	0.0108488i
$58$	−10.2609	+	3.33398i	−1.34733	+	0.437773i
$59$	1.89051	+	0.614264i	0.246124	+	0.0799704i	0.429481	−	0.903076i	$-0.358697\pi$
$59$	1.89051	+	0.614264i	0.246124	+	0.0799704i	−0.183357	+	0.983046i	$0.558697\pi$
$60$	0.767371	−	1.05620i	0.0990672	−	0.136354i
$61$	−5.91209	−	4.29539i	−0.756966	−	0.549968i	0.141013	−	0.990008i	$-0.454964\pi$
$61$	−5.91209	−	4.29539i	−0.756966	−	0.549968i	−0.897978	+	0.440040i	$0.854964\pi$
$62$	−0.409941	+	1.26167i	−0.0520625	+	0.160232i
$63$	−1.70616	+	0.554365i	−0.214956	+	0.0698434i
$64$	6.83040	−	4.96258i	0.853800	−	0.620322i
$65$	−6.40630	−	1.43252i	−0.794604	−	0.177682i
$66$	3.74954	−	0.230801i	0.461537	−	0.0284096i
$67$		−	1.12724i		−	0.137714i	−0.997627	−	0.0688570i	$-0.978065\pi$
$67$		−	1.12724i		−	0.137714i	0.997627	−	0.0688570i	$-0.0219352\pi$
$68$	3.69971	−	2.68800i	0.448656	−	0.325968i
$69$	−1.64325	−	5.05741i	−0.197824	−	0.608841i
$70$	3.51847	+	1.14322i	0.420537	+	0.136641i
$71$	0.474976	−	0.653748i	0.0563693	−	0.0775856i	−0.779902	−	0.625902i	$-0.784731\pi$
$71$	0.474976	−	0.653748i	0.0563693	−	0.0775856i	0.836271	+	0.548316i	$0.184731\pi$
$72$	−1.80893	+	2.48977i	−0.213184	+	0.293423i
$73$	−1.62240	−	0.527150i	−0.189888	−	0.0616982i	0.212530	−	0.977155i	$-0.431830\pi$
$73$	−1.62240	−	0.527150i	−0.189888	−	0.0616982i	−0.402417	+	0.915456i	$0.631830\pi$
$74$	1.79712	+	5.53097i	0.208911	+	0.642962i
$75$	−1.36333	+	0.990518i	−0.157424	+	0.114375i
$76$			0.0725971i			0.00832746i
$77$	−2.18281	−	5.53504i	−0.248754	−	0.630777i
$78$	3.98547	+	0.891196i	0.451266	+	0.100908i
$79$	13.8005	−	10.0267i	1.55268	−	1.12809i	0.610975	−	0.791650i	$-0.290778\pi$
$79$	13.8005	−	10.0267i	1.55268	−	1.12809i	0.941706	−	0.336438i	$-0.109222\pi$
$80$	3.55264	−	1.15432i	0.397197	−	0.129057i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−10.4576	−	7.59790i	−1.15485	−	0.839047i
$83$	8.74667	−	12.0388i	0.960072	−	1.32143i	0.0131670	−	0.999913i	$-0.495809\pi$
$83$	8.74667	−	12.0388i	0.960072	−	1.32143i	0.946905	−	0.321513i	$-0.104191\pi$
$84$	1.22342	+	0.397514i	0.133486	+	0.0433723i
$85$	11.0431	−	3.58812i	1.19779	−	0.389186i
$86$	4.76456	+	6.55785i	0.513775	+	0.707151i
$87$	−9.52529			−1.02122
$88$	−8.61065	−	5.48086i	−0.917898	−	0.584262i
$89$			16.0834i			1.70483i	0.522864	+	0.852416i	$0.324864\pi$
$89$			16.0834i			1.70483i	−0.522864	+	0.852416i	$0.675136\pi$
$90$	−1.66837	+	1.21214i	−0.175861	+	0.127771i
$91$	−0.608194	−	6.43957i	−0.0637560	−	0.675050i
$92$	−1.17831	+	3.62647i	−0.122848	+	0.378086i
$93$	−0.688421	+	0.947531i	−0.0713860	+	0.0982544i
$94$	−2.69374	−	1.95712i	−0.277838	−	0.201861i
$95$	−0.0569608	+	0.175307i	−0.00584405	+	0.0179861i
$96$	3.64365	−	1.18389i	0.371879	−	0.120831i
$97$	−5.57904	−	7.67890i	−0.566466	−	0.779674i	0.425664	−	0.904881i	$-0.360040\pi$
$97$	−5.57904	−	7.67890i	−0.566466	−	0.779674i	−0.992131	+	0.125207i	$0.960040\pi$
$98$		−	4.28341i		−	0.432690i
$99$	3.21131	+	0.829163i	0.322748	+	0.0833340i
$100$	1.20837			0.120837
$101$	1.64015	−	1.19164i	0.163201	−	0.118573i	−0.503187	−	0.864178i	$-0.667839\pi$
$101$	1.64015	−	1.19164i	0.163201	−	0.118573i	0.666388	+	0.745605i	$0.267839\pi$
$102$	−6.87011	+	2.23223i	−0.680242	+	0.221024i
$103$	−4.15578	+	12.7902i	−0.409481	+	1.26025i	0.507614	+	0.861585i	$0.330528\pi$
$103$	−4.15578	+	12.7902i	−0.409481	+	1.26025i	−0.917095	+	0.398669i	$0.869472\pi$
$104$	−7.33737	−	8.32397i	−0.719489	−	0.816233i
$105$	2.64242	+	1.91983i	0.257874	+	0.187356i
$106$	−10.7074	−	3.47903i	−1.03999	−	0.337914i
$107$	−4.98892	−	15.3543i	−0.482297	−	1.48436i	−0.835857	−	0.548947i	$-0.815029\pi$
$107$	−4.98892	−	15.3543i	−0.482297	−	1.48436i	0.353560	−	0.935412i	$-0.384971\pi$
$108$	−0.580115	+	0.421478i	−0.0558216	+	0.0405567i
$109$		−	7.77290i		−	0.744509i	−0.928131	−	0.372255i	$-0.878585\pi$
$109$		−	7.77290i		−	0.744509i	0.928131	−	0.372255i	$-0.121415\pi$
$110$	−4.35257	−	5.27590i	−0.415002	−	0.503037i
$111$			5.13442i			0.487338i
$112$	2.16345	+	2.97773i	0.204427	+	0.281369i
$113$	−1.93719	−	5.96207i	−0.182236	−	0.560864i	0.817654	−	0.575710i	$-0.195274\pi$
$113$	−1.93719	−	5.96207i	−0.182236	−	0.560864i	−0.999890	+	0.0148457i	$0.995274\pi$
$114$	0.0354363	−	0.109062i	0.00331891	−	0.0102146i
$115$	−5.69077	+	7.83268i	−0.530667	+	0.730401i
$116$	5.52576	+	4.01470i	0.513054	+	0.372755i
$117$	3.10330	+	1.83563i	0.286900	+	0.169704i
$118$	0.695758	+	2.14132i	0.0640497	+	0.197125i
$119$	6.72491	+	9.25604i	0.616471	+	0.848500i
$120$	5.60316			0.511496
$121$	−2.09047	+	10.7995i	−0.190043	+	0.981776i
$122$		−	8.27726i		−	0.749388i
$123$	−6.70796	−	9.23271i	−0.604836	−	0.832486i
$124$	0.798727	−	0.259522i	0.0717278	−	0.0233058i
$125$	11.5758	+	3.76119i	1.03537	+	0.336411i
$126$	−1.64390	−	1.19436i	−0.146450	−	0.106402i
$127$	−4.21621	−	3.06326i	−0.374129	−	0.271820i	0.384792	−	0.923003i	$-0.374273\pi$
$127$	−4.21621	−	3.06326i	−0.374129	−	0.271820i	−0.758921	+	0.651183i	$0.774273\pi$
$128$	1.80759	+	0.587323i	0.159770	+	0.0519125i
$129$	2.21148	+	6.80624i	0.194710	+	0.599256i
$130$	−2.95241	−	6.82413i	−0.258943	−	0.598515i
$131$	−5.78566			−0.505495			−0.252748	−	0.967532i	$-0.581334\pi$
$131$	−5.78566			−0.505495			−0.252748	+	0.967532i	$0.581334\pi$
$132$	−1.51345	−	1.83450i	−0.131729	−	0.159673i
$133$	−0.181625			−0.0157489
$134$	1.03294	−	0.750476i	0.0892326	−	0.0648313i
$135$	−1.73156	+	0.562617i	−0.149029	+	0.0484224i
$136$	18.6665	+	6.06511i	1.60064	+	0.520079i
$137$	−6.78250	+	9.33531i	−0.579468	+	0.797569i	−0.993637	−	0.112631i	$-0.964072\pi$
$137$	−6.78250	+	9.33531i	−0.579468	+	0.797569i	0.414169	+	0.910200i	$0.364072\pi$
$138$	3.54033	−	4.87284i	0.301373	−	0.414804i
$139$	2.52618	−	7.77478i	0.214268	−	0.659449i	−0.784937	−	0.619576i	$-0.787305\pi$
$139$	2.52618	−	7.77478i	0.214268	−	0.659449i	0.999205	−	0.0398729i	$-0.0126953\pi$
$140$	−0.723740	−	2.22744i	−0.0611672	−	0.188253i
$141$	−1.72788	−	2.37822i	−0.145514	−	0.200283i
$142$	0.915284			0.0768089
$143$	−5.44423	+	10.6471i	−0.455269	+	0.890354i
$144$	−2.05170			−0.170975
$145$	10.1936	+	14.0303i	0.846532	+	1.16515i
$146$	−0.597086	−	1.83764i	−0.0494152	−	0.152084i
$147$	1.16861	−	3.59661i	0.0963852	−	0.296643i
$148$	2.16405	−	2.97855i	0.177884	−	0.244836i
$149$	−6.20878	+	8.54565i	−0.508643	+	0.700087i	−0.983690	−	0.179873i	$-0.942431\pi$
$149$	−6.20878	+	8.54565i	−0.508643	+	0.700087i	0.475047	+	0.879961i	$0.342431\pi$
$150$	−1.81532	−	0.589833i	−0.148220	−	0.0481596i
$151$	−13.3974	+	4.35309i	−1.09027	+	0.354250i	−0.798350	−	0.602194i	$-0.794293\pi$
$151$	−13.3974	+	4.35309i	−1.09027	+	0.354250i	−0.291918	+	0.956443i	$0.594293\pi$
$152$	−0.252071	+	0.183140i	−0.0204457	+	0.0148546i
$153$	−6.37755			−0.515595
$154$	3.61879	−	5.68526i	0.291610	−	0.458131i
$155$	2.13239			0.171278
$156$	−1.02659	−	2.37285i	−0.0821934	−	0.189980i
$157$	1.95591	+	6.01966i	0.156098	+	0.480421i	0.998271	−	0.0587873i	$-0.0187234\pi$
$157$	1.95591	+	6.01966i	0.156098	+	0.480421i	−0.842172	+	0.539209i	$0.818723\pi$
$158$	18.3758	+	5.97067i	1.46190	+	0.475001i
$159$	−8.04139	−	5.84241i	−0.637724	−	0.463333i
$160$	−5.64312	−	4.09996i	−0.446128	−	0.324131i
$161$	−9.07281	−	2.94793i	−0.715037	−	0.232330i
$162$	1.07723	−	0.350014i	0.0846353	−	0.0274997i
$163$	−0.702177	−	0.966464i	−0.0549988	−	0.0756993i	0.780632	−	0.624991i	$-0.214897\pi$
$163$	−0.702177	−	0.966464i	−0.0549988	−	0.0756993i	−0.835631	+	0.549292i	$0.814897\pi$
$164$			8.18329i			0.639008i
$165$	−2.21530	−	5.61744i	−0.172461	−	0.437317i
$166$	16.8549			1.30820
$167$	5.80038	+	7.98354i	0.448847	+	0.617785i	0.972149	−	0.234362i	$-0.0753002\pi$
$167$	5.80038	+	7.98354i	0.448847	+	0.617785i	−0.523302	+	0.852147i	$0.675300\pi$
$168$	1.70608	+	5.25076i	0.131627	+	0.405105i
$169$	−8.90064	+	9.47515i	−0.684665	+	0.728858i
$170$	10.6401	+	7.73048i	0.816058	+	0.592901i
$171$	0.0595089	−	0.0819069i	0.00455076	−	0.00626358i
$172$	1.58577	−	4.88049i	0.120914	−	0.372134i
$173$	6.93995	+	21.3590i	0.527635	+	1.62389i	0.759046	+	0.651037i	$0.225666\pi$
$173$	6.93995	+	21.3590i	0.527635	+	1.62389i	−0.231411	+	0.972856i	$0.574334\pi$
$174$	−6.34161	−	8.72848i	−0.480756	−	0.661704i
$175$			3.02313i			0.228527i
$176$	−0.418070	−	6.79187i	−0.0315132	−	0.511956i
$177$			1.98780i			0.149412i
$178$	−14.7380	+	10.7078i	−1.10466	+	0.802580i
$179$	−1.88176	−	5.79145i	−0.140649	−	0.432874i	0.855777	−	0.517345i	$-0.173080\pi$
$179$	−1.88176	−	5.79145i	−0.140649	−	0.432874i	−0.996426	+	0.0844718i	$0.973080\pi$
$180$	1.24163	+	0.403431i	0.0925459	+	0.0300700i
$181$	14.6274	+	10.6274i	1.08725	+	0.789932i	0.978932	−	0.204184i	$-0.0654542\pi$
$181$	14.6274	+	10.6274i	1.08725	+	0.789932i	0.108316	+	0.994117i	$0.465454\pi$
$182$	5.49597	−	4.84456i	0.407389	−	0.359103i
$183$	2.25822	−	6.95008i	0.166932	−	0.513765i
$184$	−15.5643	+	5.05716i	−1.14742	+	0.372819i
$185$	7.56275	−	5.49466i	0.556025	−	0.403976i
$186$	−1.32660			−0.0972707
$187$	−1.29954	−	21.1120i	−0.0950316	−	1.54386i
$188$			2.10791i			0.153735i
$189$	−1.05447	−	1.45135i	−0.0767011	−	0.105570i
$190$	−0.198565	+	0.0645177i	−0.0144054	+	0.00468061i
$191$	1.04074	−	3.20306i	0.0753050	−	0.231765i	−0.906318	−	0.422597i	$-0.861119\pi$
$191$	1.04074	−	3.20306i	0.0753050	−	0.231765i	0.981623	+	0.190832i	$0.0611186\pi$
$192$	6.83040	+	4.96258i	0.492942	+	0.358143i
$193$	−0.0825314	+	0.113595i	−0.00594074	+	0.00817673i	−0.811977	−	0.583689i	$-0.801609\pi$
$193$	−0.0825314	+	0.113595i	−0.00594074	+	0.00817673i	0.806036	+	0.591866i	$0.201609\pi$
$194$	3.32221	−	10.2247i	0.238520	−	0.734090i
$195$	−0.617247	−	6.53543i	−0.0442020	−	0.468012i
$196$	−2.19382	+	1.59390i	−0.156701	+	0.113850i
$197$		−	17.1425i		−	1.22135i	−0.791880	−	0.610677i	$-0.790898\pi$
$197$		−	17.1425i		−	1.22135i	0.791880	−	0.610677i	$-0.209102\pi$
$198$	1.37818	+	3.49470i	0.0979428	+	0.248358i
$199$	14.3006			1.01374			0.506871	−	0.862022i	$-0.330802\pi$
$199$	14.3006			1.01374			0.506871	+	0.862022i	$0.330802\pi$
$200$	3.04835	+	4.19569i	0.215551	+	0.296680i
$201$	1.07207	−	0.348335i	0.0756177	−	0.0245697i
$202$	2.18392	+	0.709598i	0.153660	+	0.0499271i
$203$	−10.0441	+	13.8245i	−0.704956	+	0.970289i
$204$	3.69971	+	2.68800i	0.259032	+	0.188198i
$205$	−6.42074	+	19.7610i	−0.448444	+	1.38017i
$206$	−14.4870	+	4.70712i	−1.00936	+	0.327961i
$207$	4.30209	−	3.12565i	0.299016	−	0.217248i
$208$	1.61430	−	7.21923i	0.111932	−	0.500563i
$209$	0.283267	+	0.180306i	0.0195940	+	0.0124720i
$210$			3.69954i			0.255292i
$211$	11.7744	−	8.55464i	0.810586	−	0.588925i	−0.103414	−	0.994638i	$-0.532977\pi$
$211$	11.7744	−	8.55464i	0.810586	−	0.588925i	0.914001	+	0.405713i	$0.132977\pi$
$212$	2.20248	+	6.77854i	0.151267	+	0.465552i
$213$	0.768527	+	0.249710i	0.0526586	+	0.0171098i
$214$	10.7485	−	14.7940i	0.734749	−	1.01130i
$215$	7.65861	−	10.5412i	0.522313	−	0.718902i
$216$	−2.92691	−	0.951009i	−0.199151	−	0.0647080i
$217$	0.649279	+	1.99828i	0.0440760	+	0.135652i
$218$	7.12269	−	5.17493i	0.482409	−	0.350491i
$219$		−	1.70589i		−	0.115273i
$220$	−1.08250	+	4.19246i	−0.0729819	+	0.282655i
$221$	5.01793	−	22.4404i	0.337542	−	1.50951i
$222$	−4.70492	+	3.41832i	−0.315774	+	0.229423i
$223$	−20.7753	+	6.75031i	−1.39122	+	0.452034i	−0.906341	−	0.422547i	$-0.861136\pi$
$223$	−20.7753	+	6.75031i	−1.39122	+	0.452034i	−0.484878	+	0.874582i	$0.661136\pi$
$224$	2.12386	−	6.53658i	0.141907	−	0.436744i
$225$	−1.36333	−	0.990518i	−0.0908887	−	0.0660345i
$226$	4.17362	−	5.74449i	0.277625	−	0.382118i
$227$	−5.27510	−	1.71398i	−0.350121	−	0.113761i	0.128677	−	0.991687i	$-0.458927\pi$
$227$	−5.27510	−	1.71398i	−0.350121	−	0.113761i	−0.478797	+	0.877926i	$0.658927\pi$
$228$	−0.0690439	+	0.0224337i	−0.00457255	+	0.00148571i
$229$	9.17577	+	12.6294i	0.606352	+	0.834572i	0.996271	−	0.0862772i	$-0.0274971\pi$
$229$	9.17577	+	12.6294i	0.606352	+	0.834572i	−0.389919	+	0.920849i	$0.627497\pi$
$230$	−10.9662			−0.723089
$231$	4.58961	−	3.78640i	0.301974	−	0.249127i
$232$			29.3144i			1.92458i
$233$	4.63293	−	3.36602i	0.303514	−	0.220516i	−0.425595	−	0.904914i	$-0.639935\pi$
$233$	4.63293	−	3.36602i	0.303514	−	0.220516i	0.729108	+	0.684398i	$0.239935\pi$
$234$	0.384000	+	4.06580i	0.0251029	+	0.265790i
$235$	−1.65390	+	5.09017i	−0.107888	+	0.332046i
$236$	0.837814	−	1.15315i	0.0545371	−	0.0750638i
$237$	13.8005	+	10.0267i	0.896440	+	0.651302i
$238$	−4.00454	+	12.3247i	−0.259576	+	0.798893i
$239$	−16.0730	+	5.22244i	−1.03968	+	0.337811i	−0.778609	−	0.627509i	$-0.784074\pi$
$239$	−16.0730	+	5.22244i	−1.03968	+	0.337811i	−0.261067	+	0.965321i	$0.584074\pi$
$240$	2.19565	+	3.02205i	0.141729	+	0.195073i
$241$		−	28.7987i		−	1.85509i	−0.373713	−	0.927544i	$-0.621916\pi$
$241$		−	28.7987i		−	1.85509i	0.373713	−	0.927544i	$-0.378084\pi$
$242$	−11.2879	+	5.27437i	−0.725614	+	0.339049i
$243$	1.00000			0.0641500
$244$	−4.23933	+	3.08005i	−0.271395	+	0.197180i
$245$	−6.54822	+	2.12765i	−0.418351	+	0.135930i
$246$	3.99445	−	12.2937i	0.254677	−	0.783815i
$247$	0.241380	+	0.273836i	0.0153586	+	0.0174238i
$248$	2.91606	+	2.11864i	0.185170	+	0.134534i
$249$	14.1524	+	4.59840i	0.896873	+	0.291412i
$250$	4.26018	+	13.1115i	0.269438	+	0.829244i
$251$	5.82796	−	4.23426i	0.367857	−	0.267264i	−0.388464	−	0.921464i	$-0.626994\pi$
$251$	5.82796	−	4.23426i	0.367857	−	0.267264i	0.756322	+	0.654200i	$0.226994\pi$
$252$			1.28638i			0.0810344i
$253$	11.2237	+	13.6046i	0.705625	+	0.855311i
$254$		−	5.90294i		−	0.370383i
$255$	6.82501	+	9.39382i	0.427399	+	0.588264i
$256$	−4.55272	−	14.0118i	−0.284545	−	0.875740i
$257$	5.65891	−	17.4163i	0.352993	−	1.08640i	−0.604171	−	0.796855i	$-0.706496\pi$
$257$	5.65891	−	17.4163i	0.352993	−	1.08640i	0.957164	−	0.289546i	$-0.0935044\pi$
$258$	−4.76456	+	6.55785i	−0.296628	+	0.408274i
$259$	7.45183	+	5.41407i	0.463034	+	0.336414i
$260$	−2.39646	+	4.05145i	−0.148622	+	0.251260i
$261$	−2.94348	−	9.05909i	−0.182197	−	0.560743i
$262$	−3.85190	−	5.30168i	−0.237971	−	0.327539i
$263$	9.09276			0.560684			0.280342	−	0.959900i	$-0.409552\pi$
$263$	9.09276			0.560684			0.280342	+	0.959900i	$0.409552\pi$
$264$	2.55177	−	9.88289i	0.157051	−	0.608250i
$265$			18.0969i			1.11168i
$266$	−0.120920	−	0.166432i	−0.00741408	−	0.0102046i
$267$	−15.2962	+	4.97003i	−0.936111	+	0.304161i
$268$	−0.768737	−	0.249778i	−0.0469581	−	0.0152576i
$269$	8.60800	+	6.25408i	0.524839	+	0.381318i	0.818424	−	0.574615i	$-0.194848\pi$
$269$	8.60800	+	6.25408i	0.524839	+	0.381318i	−0.293585	+	0.955933i	$0.594848\pi$
$270$	−1.66837	−	1.21214i	−0.101534	−	0.0737684i
$271$	28.5084	+	9.26292i	1.73176	+	0.562683i	0.993702	−	0.112056i	$-0.0357435\pi$
$271$	28.5084	+	9.26292i	1.73176	+	0.562683i	0.738057	+	0.674738i	$0.235744\pi$
$272$	4.04344	+	12.4444i	0.245169	+	0.754553i
$273$	5.93645	−	2.56836i	0.359290	−	0.155444i
$274$	−13.0700			−0.789585
$275$	3.00117	−	4.71495i	0.180977	−	0.284322i
$276$	−3.81310			−0.229522
$277$	−9.60123	+	6.97570i	−0.576882	+	0.419129i	−0.837599	−	0.546286i	$-0.816041\pi$
$277$	−9.60123	+	6.97570i	−0.576882	+	0.419129i	0.260717	+	0.965415i	$0.416041\pi$
$278$	8.80626	−	2.86133i	0.528164	−	0.171611i
$279$	−1.11389	−	0.361925i	−0.0666868	−	0.0216679i
$280$	5.90834	−	8.13213i	0.353091	−	0.485988i
$281$	10.9232	−	15.0345i	0.651624	−	0.896884i	−0.347544	−	0.937664i	$-0.612984\pi$
$281$	10.9232	−	15.0345i	0.651624	−	0.896884i	0.999168	+	0.0407800i	$0.0129843\pi$
$282$	1.02892	−	3.16668i	0.0612712	−	0.188573i
$283$	3.54651	+	10.9150i	0.210818	+	0.648832i	0.999424	+	0.0339329i	$0.0108033\pi$
$283$	3.54651	+	10.9150i	0.210818	+	0.648832i	−0.788606	+	0.614899i	$0.789197\pi$
$284$	−0.340587	−	0.468777i	−0.0202101	−	0.0278168i
$285$	−0.184329			−0.0109187
$286$	−13.3810	+	2.09966i	−0.791236	+	0.124155i
$287$	−20.4732			−1.20849
$288$	2.25190	+	3.09948i	0.132695	+	0.182638i
$289$	7.31542	+	22.5145i	0.430319	+	1.32438i
$290$	−6.07007	+	18.6818i	−0.356447	+	1.09703i
$291$	5.57904	−	7.67890i	0.327049	−	0.450145i
$292$	−0.718996	+	0.989613i	−0.0420761	+	0.0579127i
$293$	5.01370	+	1.62905i	0.292904	+	0.0951702i	0.451783	−	0.892128i	$-0.350788\pi$
$293$	5.01370	+	1.62905i	0.292904	+	0.0951702i	−0.158879	+	0.987298i	$0.550788\pi$
$294$	4.07376	−	1.32365i	0.237587	−	0.0771966i
$295$	2.92793	−	2.12727i	0.170471	−	0.123854i
$296$	15.8013			0.918434
$297$	0.203767	+	3.31036i	0.0118238	+	0.192087i
$298$	−11.9644			−0.693078
$299$	7.61316	+	17.5969i	0.440280	+	1.01765i
$300$	0.373407	+	1.14923i	0.0215586	+	0.0663507i
$301$	12.2101	+	3.96732i	0.703781	+	0.228672i
$302$	−12.9085	−	9.37858i	−0.742801	−	0.539677i
$303$	1.64015	+	1.19164i	0.0942244	+	0.0684580i
$304$	−0.197553	−	0.0641888i	−0.0113304	−	0.00368148i
$305$	−12.6538	+	4.11146i	−0.724554	+	0.235422i
$306$	−4.24596	−	5.84406i	−0.242725	−	0.334083i
$307$			8.88418i			0.507047i	0.967329	+	0.253523i	$0.0815895\pi$
$307$			8.88418i			0.507047i	−0.967329	+	0.253523i	$0.918411\pi$
$308$	−4.25839	+	0.262123i	−0.242644	+	0.0149358i
$309$	−13.4484			−0.765052
$310$	1.41967	+	1.95401i	0.0806320	+	0.110980i
$311$	−5.93694	−	18.2720i	−0.336653	−	1.03611i	−0.965902	−	0.258908i	$-0.916637\pi$
$311$	−5.93694	−	18.2720i	−0.336653	−	1.03611i	0.629249	−	0.777204i	$-0.283363\pi$
$312$	5.64919	−	9.55050i	0.319823	−	0.540691i
$313$	8.44989	+	6.13920i	0.477616	+	0.347008i	0.800402	−	0.599464i	$-0.204619\pi$
$313$	8.44989	+	6.13920i	0.477616	+	0.347008i	−0.322786	+	0.946472i	$0.604619\pi$
$314$	−4.21393	+	5.79998i	−0.237806	+	0.327312i
$315$	−1.00931	+	3.10635i	−0.0568684	+	0.175023i
$316$	−3.77987	−	11.6332i	−0.212634	−	0.654421i
$317$	−3.74404	−	5.15323i	−0.210286	−	0.289434i	0.690825	−	0.723022i	$-0.257247\pi$
$317$	−3.74404	−	5.15323i	−0.210286	−	0.289434i	−0.901111	+	0.433588i	$0.857247\pi$
$318$		−	11.2584i		−	0.631339i
$319$	29.3890	−	11.5899i	1.64547	−	0.648910i
$320$		−	15.3716i		−	0.859299i
$321$	13.0612	−	9.48949i	0.729003	−	0.529652i
$322$	−3.33903	−	10.2765i	−0.186077	−	0.572686i
$323$	−0.614078	−	0.199526i	−0.0341682	−	0.0111019i
$324$	−0.580115	−	0.421478i	−0.0322286	−	0.0234154i
$325$	4.55797	−	4.01774i	0.252831	−	0.222864i
$326$	0.418132	−	1.28688i	0.0231582	−	0.0712736i
$327$	7.39247	−	2.40196i	0.408804	−	0.132829i
$328$	−28.4140	+	20.6440i	−1.56890	+	1.13987i
$329$	−5.27362			−0.290744
$330$	3.67266	−	5.76988i	0.202173	−	0.317622i
$331$		−	21.7257i		−	1.19415i	−0.802184	−	0.597076i	$-0.796329\pi$
$331$		−	21.7257i		−	1.19415i	0.802184	−	0.597076i	$-0.203671\pi$
$332$	−6.27190	−	8.63253i	−0.344215	−	0.473772i
$333$	−4.88313	+	1.58662i	−0.267594	+	0.0869465i
$334$	−3.45401	+	10.6303i	−0.188995	+	0.581666i
$335$	−1.66037	−	1.20633i	−0.0907154	−	0.0659086i
$336$	−2.16345	+	2.97773i	−0.118026	+	0.162448i
$337$	5.34043	−	16.4362i	0.290912	−	0.895335i	−0.693652	−	0.720310i	$-0.744000\pi$
$337$	5.34043	−	16.4362i	0.290912	−	0.895335i	0.984564	−	0.175025i	$-0.0560005\pi$
$338$	−14.6083	−	1.84785i	−0.794586	−	0.100510i
$339$	5.07164	−	3.68476i	0.275454	−	0.200129i
$340$		−	8.32609i		−	0.451546i
$341$	0.971126	−	3.76112i	0.0525894	−	0.203676i
$342$	0.114674			0.00620087
$343$	−11.3689	−	15.6480i	−0.613864	−	0.844911i
$344$	20.9464	−	6.80590i	1.12935	−	0.366950i
$345$	−9.20786	−	2.99182i	−0.495735	−	0.161074i
$346$	−14.9519	+	20.5795i	−0.803818	+	1.10636i
$347$	−4.14278	−	3.00991i	−0.222396	−	0.161580i	0.471009	−	0.882129i	$-0.343890\pi$
$347$	−4.14278	−	3.00991i	−0.222396	−	0.161580i	−0.693405	+	0.720548i	$0.743890\pi$
$348$	−2.11065	+	6.49592i	−0.113143	+	0.348218i
$349$	9.46130	−	3.07416i	0.506452	−	0.164556i	−0.0446362	−	0.999003i	$-0.514213\pi$
$349$	9.46130	−	3.07416i	0.506452	−	0.164556i	0.551088	+	0.834447i	$0.314213\pi$
$350$	−2.77024	+	2.01270i	−0.148076	+	0.107583i
$351$	−0.786811	+	3.51865i	−0.0419969	+	0.187812i
$352$	−9.80152	+	8.08618i	−0.522423	+	0.430995i
$353$		−	12.4545i		−	0.662884i	−0.943476	−	0.331442i	$-0.892465\pi$
$353$		−	12.4545i		−	0.662884i	0.943476	−	0.331442i	$-0.107535\pi$
$354$	−1.82152	+	1.32341i	−0.0968126	+	0.0703385i
$355$	−0.454638	−	1.39923i	−0.0241297	−	0.0742635i
$356$	10.9683	+	3.56382i	0.581319	+	0.188882i
$357$	−6.72491	+	9.25604i	−0.355920	+	0.489882i
$358$	4.05418	−	5.58010i	0.214270	−	0.294917i
$359$	−19.6593	−	6.38769i	−1.03758	−	0.337130i	−0.259796	−	0.965664i	$-0.583655\pi$
$359$	−19.6593	−	6.38769i	−1.03758	−	0.337130i	−0.777782	+	0.628534i	$0.783655\pi$
$360$	1.73147	+	5.32892i	0.0912566	+	0.280859i
$361$	−15.3630	+	11.1619i	−0.808581	+	0.587468i
$362$			20.4792i			1.07636i
$363$	−10.9170	+	1.34909i	−0.572992	+	0.0708087i
$364$	−4.52633	−	1.01214i	−0.237244	−	0.0530505i
$365$	−2.51270	+	1.82558i	−0.131520	+	0.0955552i
$366$	7.87214	−	2.55781i	0.411483	−	0.133699i
$367$	5.59776	−	17.2281i	0.292201	−	0.899301i	−0.691947	−	0.721949i	$-0.743247\pi$
$367$	5.59776	−	17.2281i	0.292201	−	0.899301i	0.984147	−	0.177353i	$-0.0567533\pi$
$368$	−8.82660	−	6.41290i	−0.460118	−	0.334296i
$369$	6.70796	−	9.23271i	0.349202	−	0.480636i
$370$	10.0700	+	3.27196i	0.523517	+	0.170101i
$371$	−16.9587	+	5.51023i	−0.880453	+	0.286077i
$372$	0.493640	+	0.679438i	0.0255941	+	0.0352272i
$373$	8.17452			0.423261			0.211630	−	0.977350i	$-0.432123\pi$
$373$	8.17452			0.423261			0.211630	+	0.977350i	$0.432123\pi$
$374$	18.4808	−	15.2465i	0.955617	−	0.788377i
$375$			12.1715i			0.628532i
$376$	−7.31906	+	5.31761i	−0.377452	+	0.274235i
$377$	34.1917	−	3.22929i	1.76096	−	0.166317i
$378$	0.627912	−	1.93251i	0.0322963	−	0.0993978i
$379$	−21.1614	+	29.1262i	−1.08699	+	1.49611i	−0.235404	+	0.971898i	$0.575641\pi$
$379$	−21.1614	+	29.1262i	−1.08699	+	1.49611i	−0.851585	+	0.524216i	$0.824359\pi$
$380$	0.106932	+	0.0776906i	0.00548549	+	0.00398544i
$381$	1.61045	−	4.95646i	0.0825059	−	0.253927i
$382$	3.62800	−	1.17881i	0.185625	−	0.0603131i
$383$	3.05514	+	4.20504i	0.156110	+	0.214867i	0.879907	−	0.475146i	$-0.157605\pi$
$383$	3.05514	+	4.20504i	0.156110	+	0.214867i	−0.723797	+	0.690013i	$0.757605\pi$
$384$			1.90062i			0.0969904i
$385$	−10.4888	−	2.70822i	−0.534559	−	0.138024i
$386$	−0.159039			−0.00809487
$387$	−5.78973	+	4.20649i	−0.294309	+	0.213828i
$388$	−6.47297	+	2.10320i	−0.328615	+	0.106774i
$389$	10.8153	−	33.2861i	0.548358	−	1.68767i	−0.164512	−	0.986375i	$-0.552605\pi$
$389$	10.8153	−	33.2861i	0.548358	−	1.68767i	0.712870	−	0.701296i	$-0.247395\pi$
$390$	5.57779	−	4.91668i	0.282442	−	0.248966i
$391$	−27.4368	−	19.9340i	−1.38754	−	1.00811i
$392$	−11.0687	−	3.59643i	−0.559052	−	0.181647i
$393$	−1.78787	−	5.50249i	−0.0901860	−	0.277564i
$394$	15.7085	−	11.4129i	0.791383	−	0.574974i
$395$		−	31.0577i		−	1.56268i
$396$	1.27704	−	2.00627i	0.0641734	−	0.100819i
$397$			16.7498i			0.840646i	0.907375	+	0.420323i	$0.138083\pi$
$397$			16.7498i			0.840646i	−0.907375	+	0.420323i	$0.861917\pi$
$398$	9.52085	+	13.1043i	0.477237	+	0.656861i
$399$	−0.0561253	−	0.172736i	−0.00280978	−	0.00864762i
$400$	−1.06841	+	3.28824i	−0.0534207	+	0.164412i
$401$	−3.13884	+	4.32025i	−0.156746	+	0.215743i	−0.880166	−	0.474665i	$-0.842569\pi$
$401$	−3.13884	+	4.32025i	−0.156746	+	0.215743i	0.723420	+	0.690408i	$0.242569\pi$
$402$	1.03294	+	0.750476i	0.0515185	+	0.0374303i
$403$	2.14991	−	3.63463i	0.107095	−	0.181054i
$404$	−0.449227	−	1.38258i	−0.0223499	−	0.0687858i
$405$	−1.07016	−	1.47295i	−0.0531768	−	0.0731915i
$406$	−19.3551			−0.960576
$407$	−6.24732	−	15.8416i	−0.309668	−	0.785239i
$408$			19.6271i			0.971687i
$409$	4.63725	+	6.38262i	0.229297	+	0.315600i	0.908127	−	0.418695i	$-0.137513\pi$
$409$	4.63725	+	6.38262i	0.229297	+	0.315600i	−0.678830	+	0.734296i	$0.737513\pi$
$410$	−22.3827	+	7.27257i	−1.10540	+	0.359167i
$411$	−10.9743	−	3.56577i	−0.541323	−	0.175887i
$412$	7.80161	+	5.66820i	0.384358	+	0.279252i
$413$	2.88499	+	2.09607i	0.141961	+	0.103141i
$414$	5.72837	+	1.86126i	0.281534	+	0.0914760i
$415$	−8.37216	−	25.7668i	−0.410973	−	1.26484i
$416$	−12.6778	+	5.48496i	−0.621581	+	0.268922i
$417$	8.17489			0.400326
$418$	0.0233669	+	0.379613i	0.00114291	+	0.0185675i
$419$	−11.2993			−0.552007			−0.276003	−	0.961157i	$-0.589010\pi$
$419$	−11.2993			−0.552007			−0.276003	+	0.961157i	$0.589010\pi$
$420$	1.89478	−	1.37664i	0.0924557	−	0.0671730i
$421$	−16.0269	+	5.20745i	−0.781102	+	0.253795i	−0.672311	−	0.740269i	$-0.734698\pi$
$421$	−16.0269	+	5.20745i	−0.781102	+	0.253795i	−0.108791	+	0.994065i	$0.534698\pi$
$422$	15.6781	+	5.09411i	0.763196	+	0.247977i
$423$	1.72788	−	2.37822i	0.0840125	−	0.115633i
$424$	−17.9802	+	24.7476i	−0.873196	+	1.20185i
$425$	−3.32109	+	10.2212i	−0.161096	+	0.495803i
$426$	0.282838	+	0.870487i	0.0137036	+	0.0421752i
$427$	−7.70576	−	10.6061i	−0.372908	−	0.513264i
$428$	−11.5766			−0.559576
$429$	−11.8083	−	1.88764i	−0.570112	−	0.0911361i
$430$	14.7582			0.711705
$431$	20.6871	+	28.4733i	0.996463	+	1.37151i	0.927471	+	0.373896i	$0.121978\pi$
$431$	20.6871	+	28.4733i	0.996463	+	1.37151i	0.0689918	+	0.997617i	$0.478022\pi$
$432$	−0.634010	−	1.95128i	−0.0305038	−	0.0938812i
$433$	4.13546	−	12.7276i	0.198737	−	0.611651i	−0.801175	−	0.598430i	$-0.795792\pi$
$433$	4.13546	−	12.7276i	0.198737	−	0.611651i	0.999913	−	0.0132208i	$-0.00420844\pi$
$434$	−1.39885	+	1.92535i	−0.0671469	+	0.0924198i
$435$	−10.1936	+	14.0303i	−0.488745	+	0.672700i
$436$	−5.30085	−	1.72235i	−0.253865	−	0.0824857i
$437$	0.512025	−	0.166367i	0.0244935	−	0.00795841i
$438$	1.56319	−	1.13572i	0.0746922	−	0.0542670i
$439$	5.91208			0.282168			0.141084	−	0.989998i	$-0.454941\pi$
$439$	5.91208			0.282168			0.141084	+	0.989998i	$0.454941\pi$
$440$	−17.2878	+	6.81765i	−0.824165	+	0.325019i
$441$	3.78170			0.180081
$442$	23.9040	−	10.3419i	1.13700	−	0.491914i
$443$	9.24785	+	28.4620i	0.439379	+	1.35227i	0.888532	+	0.458814i	$0.151726\pi$
$443$	9.24785	+	28.4620i	0.439379	+	1.35227i	−0.449153	+	0.893455i	$0.648274\pi$
$444$	3.50150	+	1.13771i	0.166174	+	0.0539932i
$445$	23.6900	+	17.2118i	1.12301	+	0.815917i
$446$	−20.0171	−	14.5433i	−0.947839	−	0.688646i
$447$	−10.0460	−	3.26415i	−0.475160	−	0.154389i
$448$	14.4048	−	4.68042i	0.680565	−	0.221129i
$449$	−2.61087	−	3.59355i	−0.123215	−	0.169590i	0.742954	−	0.669343i	$-0.233424\pi$
$449$	−2.61087	−	3.59355i	−0.123215	−	0.169590i	−0.866168	+	0.499753i	$0.833424\pi$
$450$		−	1.90874i		−	0.0899788i
$451$	31.9305	+	20.3244i	1.50355	+	0.957040i
$452$	−4.49518			−0.211435
$453$	−8.28007	−	11.3965i	−0.389032	−	0.535456i
$454$	−1.94138	−	5.97494i	−0.0911133	−	0.280418i
$455$	−10.1360	−	5.99554i	−0.475185	−	0.281075i
$456$	−0.252071	−	0.183140i	−0.0118043	−	0.00857633i
$457$	−1.19353	+	1.64276i	−0.0558311	+	0.0768449i	−0.836020	−	0.548700i	$-0.815123\pi$
$457$	−1.19353	+	1.64276i	−0.0558311	+	0.0768449i	0.780189	+	0.625544i	$0.215123\pi$
$458$	−5.46398	+	16.8164i	−0.255315	+	0.785779i
$459$	−1.97077	−	6.06541i	−0.0919878	−	0.283109i
$460$	4.08063	+	5.61651i	0.190260	+	0.261871i
$461$		−	18.5651i		−	0.864664i	−0.901714	−	0.432332i	$-0.857691\pi$
$461$		−	18.5651i		−	0.864664i	0.901714	−	0.432332i	$-0.142309\pi$
$462$	6.52527	+	1.68483i	0.303583	+	0.0783854i
$463$		−	12.8238i		−	0.595971i	−0.954570	−	0.297986i	$-0.903685\pi$
$463$		−	12.8238i		−	0.595971i	0.954570	−	0.297986i	$-0.0963148\pi$
$464$	−15.8106	+	11.4871i	−0.733991	+	0.533276i
$465$	0.658944	+	2.02802i	0.0305578	+	0.0940473i
$466$	6.16890	+	2.00440i	0.285769	+	0.0928519i
$467$	5.62673	+	4.08806i	0.260374	+	0.189173i	0.710312	−	0.703887i	$-0.248554\pi$
$467$	5.62673	+	4.08806i	0.260374	+	0.189173i	−0.449938	+	0.893060i	$0.648554\pi$
$468$	1.93948	−	1.70960i	0.0896523	−	0.0790263i
$469$	0.624901	−	1.92325i	0.0288552	−	0.0888073i
$470$	−5.76548	+	1.87332i	−0.265942	+	0.0864097i
$471$	−5.12063	+	3.72036i	−0.235946	+	0.171425i
$472$	6.11752			0.281582
$473$	−15.1047	−	18.3089i	−0.694517	−	0.841846i
$474$			19.3215i			0.887466i
$475$	−0.100283	−	0.138027i	−0.00460128	−	0.00633312i
$476$	7.80244	−	2.53517i	0.357624	−	0.116199i
$477$	3.07154	−	9.45322i	0.140636	−	0.432833i
$478$	−15.4864	−	11.2515i	−0.708333	−	0.514634i
$479$	5.01692	−	6.90520i	0.229229	−	0.315507i	−0.678873	−	0.734256i	$-0.737531\pi$
$479$	5.01692	−	6.90520i	0.229229	−	0.315507i	0.908102	+	0.418749i	$0.137531\pi$
$480$	2.15548	−	6.63388i	0.0983837	−	0.302794i
$481$	−1.74068	−	18.4304i	−0.0793684	−	0.840354i
$482$	26.3897	−	19.1732i	1.20202	−	0.873316i
$483$		−	9.53972i		−	0.434072i
$484$	6.90170	+	3.81863i	0.313714	+	0.173574i
$485$	−17.2811			−0.784695
$486$	0.665766	+	0.916348i	0.0301998	+	0.0415664i
$487$	−12.3288	+	4.00588i	−0.558672	+	0.181524i	−0.574724	−	0.818348i	$-0.694890\pi$
$487$	−12.3288	+	4.00588i	−0.558672	+	0.181524i	0.0160515	+	0.999871i	$0.494890\pi$
$488$	−21.3891	−	6.94973i	−0.968238	−	0.314600i
$489$	0.702177	−	0.966464i	0.0317536	−	0.0437050i
$490$	−6.30925	−	4.58394i	−0.285023	−	0.207081i
$491$	13.4206	−	41.3043i	0.605662	−	1.86404i	0.113491	−	0.993539i	$-0.463797\pi$
$491$	13.4206	−	41.3043i	0.605662	−	1.86404i	0.492171	−	0.870498i	$-0.336203\pi$
$492$	−7.78277	+	2.52878i	−0.350874	+	0.114006i
$493$	−49.1462	+	35.7068i	−2.21343	+	1.60815i
$494$	−0.0902269	+	0.403499i	−0.00405950	+	0.0181543i
$495$	4.65793	−	3.84276i	0.209359	−	0.172719i
$496$			2.40298i			0.107897i
$497$	1.17280	−	0.852089i	0.0526073	−	0.0382214i
$498$	5.20846	+	16.0300i	0.233397	+	0.718322i
$499$	−11.5891	−	3.76552i	−0.518799	−	0.168568i	0.0379013	−	0.999281i	$-0.487933\pi$
$499$	−11.5891	−	3.76552i	−0.518799	−	0.168568i	−0.556700	+	0.830714i	$0.687933\pi$
$500$	5.13001	−	7.06085i	0.229421	−	0.315771i
$501$	−5.80038	+	7.98354i	−0.259142	+	0.356678i
$502$	7.76011	+	2.52141i	0.346351	+	0.112536i
$503$	−4.74232	−	14.5954i	−0.211449	−	0.650775i	−0.999387	−	0.0350189i	$-0.988851\pi$
$503$	−4.74232	−	14.5954i	−0.211449	−	0.650775i	0.787937	−	0.615756i	$-0.211149\pi$
$504$	−4.46656	+	3.24515i	−0.198957	+	0.144550i
$505$		−	3.69112i		−	0.164252i
$506$	−4.99419	+	19.3422i	−0.222019	+	0.859867i
$507$	−11.7619	−	5.53703i	−0.522362	−	0.245908i
$508$	−3.02328	+	2.19654i	−0.134137	+	0.0974559i
$509$	5.27277	−	1.71323i	0.233711	−	0.0759374i	−0.189820	−	0.981819i	$-0.560790\pi$
$509$	5.27277	−	1.71323i	0.233711	−	0.0759374i	0.423531	+	0.905882i	$0.360790\pi$
$510$	−4.06415	+	12.5082i	−0.179964	+	0.553871i
$511$	−2.47584	−	1.79880i	−0.109525	−	0.0795744i
$512$	12.0430	−	16.5757i	0.532230	−	0.732551i
$513$	0.0962874	+	0.0312857i	0.00425119	+	0.00138130i
$514$	19.7269	−	6.40967i	0.870118	−	0.282719i
$515$	14.3919	+	19.8088i	0.634185	+	0.872881i
$516$	5.13165			0.225908
$517$	8.22486	+	5.23530i	0.361729	+	0.230248i
$518$			10.4330i			0.458399i
$519$	−18.1690	+	13.2006i	−0.797532	+	0.579441i
$520$	−20.1130	+	1.89960i	−0.882012	+	0.0833029i
$521$	−1.40575	+	4.32646i	−0.0615871	+	0.189545i	−0.977116	−	0.212706i	$-0.931772\pi$
$521$	−1.40575	+	4.32646i	−0.0615871	+	0.189545i	0.915529	+	0.402252i	$0.131772\pi$
$522$	6.34161	−	8.72848i	0.277565	−	0.382035i
$523$	−19.8906	−	14.4514i	−0.869755	−	0.631914i	0.0607658	−	0.998152i	$-0.480646\pi$
$523$	−19.8906	−	14.4514i	−0.869755	−	0.631914i	−0.930521	+	0.366238i	$0.880646\pi$
$524$	−1.28201	+	3.94562i	−0.0560049	+	0.172365i
$525$	−2.87517	+	0.934199i	−0.125483	+	0.0407718i
$526$	6.05365	+	8.33214i	0.263952	+	0.363299i
$527$			7.46947i			0.325375i
$528$	6.33026	−	2.49641i	0.275489	−	0.108642i
$529$	5.27768			0.229464
$530$	−16.5831	+	12.0483i	−0.720322	+	0.523345i
$531$	−1.89051	+	0.614264i	−0.0820412	+	0.0266568i
$532$	−0.0402453	+	0.123862i	−0.00174485	+	0.00537011i
$533$	27.2088	+	30.8674i	1.17855	+	1.33702i
$534$	−14.7380	−	10.7078i	−0.637774	−	0.463370i
$535$	−27.9551	−	9.08317i	−1.20861	−	0.392700i
$536$	−1.07201	−	3.29932i	−0.0463039	−	0.142509i
$537$	4.92650	−	3.57932i	0.212594	−	0.154459i
$538$			12.0517i			0.519585i
$539$	0.770586	+	12.5188i	0.0331915	+	0.539222i
$540$			1.30553i			0.0561811i
$541$	−22.0670	−	30.3726i	−0.948733	−	1.30582i	−0.952088	−	0.305824i	$-0.901068\pi$
$541$	−22.0670	−	30.3726i	−0.948733	−	1.30582i	0.00335544	−	0.999994i	$-0.498932\pi$
$542$	10.4918	+	32.2905i	0.450663	+	1.38700i
$543$	−5.58718	+	17.1956i	−0.239769	+	0.737933i
$544$	14.3616	−	19.7671i	0.615749	−	0.847506i
$545$	−11.4491	−	8.31826i	−0.490426	−	0.356315i
$546$	6.30580	+	3.72993i	0.269863	+	0.159626i
$547$	−1.69392	−	5.21335i	−0.0724268	−	0.222907i	0.908290	−	0.418341i	$-0.137388\pi$
$547$	−1.69392	−	5.21335i	−0.0724268	−	0.222907i	−0.980717	+	0.195434i	$0.937388\pi$
$548$	4.86347	+	6.69399i	0.207757	+	0.285953i
$549$	7.30775			0.311887
$550$	6.31861	−	0.388939i	0.269426	−	0.0165844i
$551$		−	0.964364i		−	0.0410833i
$552$	−9.61929	−	13.2398i	−0.409424	−	0.563524i
$553$	29.1043	−	9.45657i	1.23764	−	0.402134i
$554$	−12.7844	−	4.15389i	−0.543155	−	0.176482i
$555$	7.56275	+	5.49466i	0.321021	+	0.233235i
$556$	−4.74237	−	3.44554i	−0.201121	−	0.146123i
$557$	4.13353	+	1.34307i	0.175143	+	0.0569075i	0.395276	−	0.918562i	$-0.370649\pi$
$557$	4.13353	+	1.34307i	0.175143	+	0.0569075i	−0.220133	+	0.975470i	$0.570649\pi$
$558$	−0.409941	−	1.26167i	−0.0173542	−	0.0534107i
$559$	−10.2457	−	23.6818i	−0.433349	−	1.00163i
$560$	6.70129			0.283181
$561$	19.6771	−	7.75990i	0.830769	−	0.327623i
$562$	21.0492			0.887905
$563$	−1.31241	+	0.953520i	−0.0553114	+	0.0401861i	−0.615097	−	0.788451i	$-0.710883\pi$
$563$	−1.31241	+	0.953520i	−0.0553114	+	0.0401861i	0.559786	+	0.828637i	$0.310883\pi$
$564$	−2.00474	+	0.651379i	−0.0844147	+	0.0274280i
$565$	−10.8549	−	3.52699i	−0.456671	−	0.148381i
$566$	−7.64084	+	10.5167i	−0.321168	+	0.442050i
$567$	1.05447	−	1.45135i	0.0442834	−	0.0609508i
$568$	0.768489	−	2.36517i	0.0322451	−	0.0992402i
$569$	13.0622	+	40.2014i	0.547597	+	1.68533i	0.714733	+	0.699398i	$0.246548\pi$
$569$	13.0622	+	40.2014i	0.547597	+	1.68533i	−0.167135	+	0.985934i	$0.553452\pi$
$570$	−0.122720	−	0.168910i	−0.00514017	−	0.00707484i
$571$	35.9652			1.50510			0.752549	−	0.658537i	$-0.228824\pi$
$571$	35.9652			1.50510			0.752549	+	0.658537i	$0.228824\pi$
$572$	6.05459	+	6.07200i	0.253155	+	0.253883i
$573$	3.36789			0.140696
$574$	−13.6303	−	18.7606i	−0.568920	−	0.783051i
$575$	−2.76916	−	8.52259i	−0.115482	−	0.355417i
$576$	−2.60898	+	8.02962i	−0.108708	+	0.334567i
$577$	5.97374	−	8.22215i	0.248690	−	0.342293i	−0.666362	−	0.745629i	$-0.732149\pi$
$577$	5.97374	−	8.22215i	0.248690	−	0.342293i	0.915052	+	0.403336i	$0.132149\pi$
$578$	−15.7608	+	21.6929i	−0.655563	+	0.902305i
$579$	−0.133539	−	0.0433893i	−0.00554968	−	0.00180320i
$580$	11.8269	−	3.84280i	0.491086	−	0.159563i
$581$	21.5971	−	15.6912i	0.895999	−	0.650981i
$582$	10.7509			0.445638
$583$	31.9194	+	8.24163i	1.32197	+	0.341334i
$584$	−5.24993			−0.217244
$585$	6.02482	−	2.60660i	0.249096	−	0.107769i
$586$	1.84518	+	5.67887i	0.0762235	+	0.234592i
$587$	36.7409	+	11.9378i	1.51646	+	0.492727i	0.944768	−	0.327741i	$-0.106287\pi$
$587$	36.7409	+	11.9378i	1.51646	+	0.492727i	0.571692	+	0.820469i	$0.306287\pi$
$588$	−2.19382	−	1.59390i	−0.0904715	−	0.0657314i
$589$	−0.0959304	−	0.0696975i	−0.00395274	−	0.00287184i
$590$	3.89864	+	1.26674i	0.160504	+	0.0521510i
$591$	16.3035	−	5.29733i	0.670636	−	0.217903i
$592$	6.19191	+	8.52243i	0.254486	+	0.350270i
$593$			35.8312i			1.47141i	0.677302	+	0.735705i	$0.263149\pi$
$593$			35.8312i			1.47141i	−0.677302	+	0.735705i	$0.736851\pi$
$594$	−2.89778	+	2.39065i	−0.118897	+	0.0980894i
$595$	20.8304			0.853965
$596$	4.45208	+	6.12776i	0.182364	+	0.251003i
$597$	4.41913	+	13.6007i	0.180863	+	0.556639i
$598$	−11.0563	+	18.6917i	−0.452125	+	0.764360i
$599$	−28.1118	−	20.4244i	−1.14862	−	0.834519i	−0.160321	−	0.987065i	$-0.551253\pi$
$599$	−28.1118	−	20.4244i	−1.14862	−	0.834519i	−0.988296	+	0.152546i	$0.951253\pi$
$600$	−3.04835	+	4.19569i	−0.124448	+	0.171288i
$601$	9.42534	−	29.0082i	0.384468	−	1.18327i	−0.552398	−	0.833580i	$-0.686287\pi$
$601$	9.42534	−	29.0082i	0.384468	−	1.18327i	0.936866	−	0.349689i	$-0.113713\pi$
$602$	4.49365	+	13.8300i	0.183148	+	0.563671i
$603$	0.662573	+	0.911954i	0.0269821	+	0.0371376i
$604$			10.1012i			0.411011i
$605$	13.6700	+	14.6364i	0.555766	+	0.595054i
$606$			2.29631i			0.0932811i
$607$	−6.71341	+	4.87758i	−0.272489	+	0.197975i	−0.715635	−	0.698475i	$-0.753862\pi$
$607$	−6.71341	+	4.87758i	−0.272489	+	0.197975i	0.443146	+	0.896450i	$0.353862\pi$
$608$	0.119860	+	0.368893i	0.00486099	+	0.0149606i
$609$	−16.2517	−	5.28049i	−0.658551	−	0.213976i
$610$	−12.1920	−	8.85800i	−0.493639	−	0.358650i
$611$	7.00864	+	7.95103i	0.283539	+	0.321664i
$612$	−1.41316	+	4.34927i	−0.0571238	+	0.175809i
$613$	−30.0990	+	9.77977i	−1.21569	+	0.395001i	−0.845510	−	0.533959i	$-0.820703\pi$
$613$	−30.0990	+	9.77977i	−1.21569	+	0.395001i	−0.370179	+	0.928961i	$0.620703\pi$
$614$	−8.14100	+	5.91478i	−0.328544	+	0.238701i
$615$	−20.7779			−0.837847
$616$	−11.6527	−	14.1247i	−0.469503	−	0.569099i
$617$		−	12.5858i		−	0.506686i	−0.967377	−	0.253343i	$-0.918470\pi$
$617$		−	12.5858i		−	0.506686i	0.967377	−	0.253343i	$-0.0815301\pi$
$618$	−8.95348	−	12.3234i	−0.360162	−	0.495720i
$619$	25.1392	−	8.16821i	1.01043	−	0.328308i	0.243403	−	0.969925i	$-0.421736\pi$
$619$	25.1392	−	8.16821i	1.01043	−	0.328308i	0.767025	+	0.641617i	$0.221736\pi$
$620$	0.472503	−	1.45422i	0.0189762	−	0.0584027i
$621$	4.30209	+	3.12565i	0.172637	+	0.125428i
$622$	12.7909	−	17.6052i	0.512869	−	0.705904i
$623$	−8.91605	+	27.4408i	−0.357214	+	1.09939i
$624$	7.36474	−	0.695573i	0.294825	−	0.0278452i
$625$	11.1113	−	8.07285i	0.444453	−	0.322914i
$626$			11.8303i			0.472835i
$627$	−0.0839466	+	0.325121i	−0.00335250	+	0.0129841i
$628$	4.53860			0.181110
$629$	19.2471	+	26.4913i	0.767431	+	1.05628i
$630$	−3.51847	+	1.14322i	−0.140179	+	0.0455469i
$631$	11.3205	+	3.67826i	0.450663	+	0.146429i	0.525550	−	0.850763i	$-0.323860\pi$
$631$	11.3205	+	3.67826i	0.450663	+	0.146429i	−0.0748872	+	0.997192i	$0.523860\pi$
$632$	30.8574	−	42.4715i	1.22744	−	1.68943i
$633$	11.7744	+	8.55464i	0.467992	+	0.340016i
$634$	2.22950	−	6.86169i	0.0885447	−	0.272513i
$635$	−9.02406	+	2.93210i	−0.358109	+	0.116357i
$636$	−5.76617	+	4.18937i	−0.228643	+	0.166119i
$637$	−2.97548	+	13.3065i	−0.117893	+	0.527222i
$638$	30.1866	+	19.2144i	1.19510	+	0.760707i
$639$			0.808077i			0.0319670i
$640$	2.79951	−	2.03397i	0.110661	−	0.0803996i
$641$	−1.14275	−	3.51702i	−0.0451358	−	0.138914i	0.925949	−	0.377649i	$-0.123267\pi$
$641$	−1.14275	−	3.51702i	−0.0451358	−	0.138914i	−0.971085	+	0.238735i	$0.923267\pi$
$642$	17.3914	+	5.65080i	0.686382	+	0.223019i
$643$	19.6503	−	27.0463i	0.774931	−	1.06660i	−0.220892	−	0.975298i	$-0.570897\pi$
$643$	19.6503	−	27.0463i	0.774931	−	1.06660i	0.995823	−	0.0913026i	$-0.0291031\pi$
$644$	−4.02078	+	5.53413i	−0.158441	+	0.218075i
$645$	12.3919	+	4.02637i	0.487930	+	0.158538i
$646$	−0.225997	−	0.695547i	−0.00889173	−	0.0273659i
$647$	−15.2421	+	11.0740i	−0.599228	+	0.435365i	−0.845605	−	0.533809i	$-0.820760\pi$
$647$	−15.2421	+	11.0740i	−0.599228	+	0.435365i	0.246377	+	0.969174i	$0.420760\pi$
$648$		−	3.07753i		−	0.120897i
$649$	−2.41866	−	6.13310i	−0.0949407	−	0.240745i
$650$	6.71619	+	1.50182i	0.263431	+	0.0589061i
$651$	−1.69984	+	1.23500i	−0.0666218	+	0.0484036i
$652$	−0.814687	+	0.264708i	−0.0319056	+	0.0103668i
$653$	−7.46817	+	22.9847i	−0.292252	+	0.899459i	0.691879	+	0.722014i	$0.256783\pi$
$653$	−7.46817	+	22.9847i	−0.292252	+	0.899459i	−0.984131	+	0.177445i	$0.943217\pi$
$654$	7.12269	+	5.17493i	0.278519	+	0.202356i
$655$	−6.19159	+	8.52199i	−0.241925	+	0.332982i
$656$	−22.2686	−	7.23549i	−0.869441	−	0.282499i
$657$	1.62240	−	0.527150i	0.0632958	−	0.0205661i
$658$	−3.51100	−	4.83247i	−0.136873	−	0.188389i
$659$	9.40677			0.366436			0.183218	−	0.983072i	$-0.441349\pi$
$659$	9.40677			0.366436			0.183218	+	0.983072i	$0.441349\pi$
$660$	−4.32177	+	0.266025i	−0.168225	+	0.0103550i
$661$			9.50340i			0.369640i	0.982772	+	0.184820i	$0.0591701\pi$
$661$			9.50340i			0.369640i	−0.982772	+	0.184820i	$0.940830\pi$
$662$	19.9083	−	14.4642i	0.773759	−	0.562169i
$663$	22.8927	−	2.16213i	0.889080	−	0.0839703i
$664$	14.1517	−	43.5545i	0.549193	−	1.69024i
$665$	−0.194369	+	0.267525i	−0.00753729	+	0.0103742i
$666$	−4.70492	−	3.41832i	−0.182312	−	0.132457i
$667$	15.6524	−	48.1733i	0.606065	−	1.86528i
$668$	6.72977	−	2.18664i	0.260383	−	0.0846035i
$669$	−12.8399	−	17.6725i	−0.496418	−	0.683260i
$670$		−	2.32460i		−	0.0898073i
$671$	1.48908	+	24.1913i	0.0574853	+	0.933893i
$672$	6.87297			0.265130
$673$	−4.94541	+	3.59305i	−0.190631	+	0.138502i	−0.679007	−	0.734132i	$-0.737590\pi$
$673$	−4.94541	+	3.59305i	−0.190631	+	0.138502i	0.488376	+	0.872633i	$0.337590\pi$
$674$	18.6167	−	6.04894i	0.717089	−	0.232996i
$675$	0.520746	−	1.60269i	0.0200435	−	0.0616876i
$676$	4.48949	+	8.16948i	0.172673	+	0.314211i
$677$	9.68693	+	7.03797i	0.372299	+	0.270491i	0.758164	−	0.652064i	$-0.226097\pi$
$677$	9.68693	+	7.03797i	0.372299	+	0.270491i	−0.385865	+	0.922555i	$0.626097\pi$
$678$	6.75305	+	2.19420i	0.259349	+	0.0842677i
$679$	−5.26183	−	16.1943i	−0.201931	−	0.621479i
$680$	28.9098	−	21.0042i	1.10864	−	0.805474i
$681$		−	5.54657i		−	0.212545i
$682$	4.09304	−	1.61414i	0.156731	−	0.0618085i
$683$		−	28.5937i		−	1.09411i	−0.837098	−	0.547053i	$-0.815750\pi$
$683$		−	28.5937i		−	1.09411i	0.837098	−	0.547053i	$-0.184250\pi$
$684$	−0.0426715	−	0.0587323i	−0.00163159	−	0.00224568i
$685$	6.49208	+	19.9806i	0.248050	+	0.763419i
$686$	6.76996	−	20.8358i	0.258478	−	0.795514i
$687$	−9.17577	+	12.6294i	−0.350077	+	0.481840i
$688$	11.8788	+	8.63045i	0.452875	+	0.329033i
$689$	30.8459	+	18.2456i	1.17514	+	0.695101i
$690$	−3.38874	−	10.4295i	−0.129007	−	0.397043i
$691$	12.1682	+	16.7481i	0.462900	+	0.637127i	0.975107	−	0.221735i	$-0.0711721\pi$
$691$	12.1682	+	16.7481i	0.462900	+	0.637127i	−0.512207	+	0.858862i	$0.671172\pi$
$692$	16.1039			0.612177
$693$	5.01935	+	3.19492i	0.190669	+	0.121365i
$694$		−	5.80012i		−	0.220170i
$695$	−8.74845	−	12.0412i	−0.331848	−	0.456749i
$696$	−27.8796	+	9.05864i	−1.05677	+	0.343367i
$697$	−69.2201	−	22.4910i	−2.62190	−	0.851906i
$698$	9.11602	+	6.62317i	0.345046	+	0.250691i
$699$	4.63293	+	3.36602i	0.175234	+	0.127315i
$700$	2.06167	+	0.669878i	0.0779239	+	0.0253190i
$701$	−7.30878	−	22.4941i	−0.276049	−	0.849591i	−0.988940	−	0.148316i	$-0.952615\pi$
$701$	−7.30878	−	22.4941i	−0.276049	−	0.849591i	0.712891	−	0.701275i	$-0.247385\pi$
$702$	−3.74815	+	1.62161i	−0.141465	+	0.0612036i
$703$	−0.519822			−0.0196055
$704$	−27.1126	−	7.00049i	−1.02184	−	0.263841i
$705$	−5.35212			−0.201573
$706$	11.4126	−	8.29176i	0.429520	−	0.312065i
$707$	3.45897	−	1.12389i	0.130088	−	0.0422681i
$708$	1.35561	+	0.440465i	0.0509470	+	0.0165537i
$709$	−5.36059	+	7.37822i	−0.201321	+	0.277095i	−0.897726	−	0.440554i	$-0.854782\pi$
$709$	−5.36059	+	7.37822i	−0.201321	+	0.277095i	0.696405	+	0.717649i	$0.254782\pi$
$710$	0.979502	−	1.34817i	0.0367600	−	0.0505959i
$711$	−5.27133	+	16.2235i	−0.197690	+	0.608428i
$712$	15.2954	+	47.0745i	0.573220	+	1.76419i
$713$	−3.66080	−	5.03866i	−0.137098	−	0.188699i
$714$	−12.9590			−0.484977
$715$	9.85643	+	19.4132i	0.368610	+	0.726012i
$716$	−4.36654			−0.163185
$717$	−9.93366	−	13.6725i	−0.370979	−	0.510609i
$718$	−7.23514	−	22.2675i	−0.270013	−	0.831015i
$719$	−8.33300	+	25.6463i	−0.310768	+	0.956447i	0.666693	+	0.745333i	$0.267709\pi$
$719$	−8.33300	+	25.6463i	−0.310768	+	0.956447i	−0.977461	+	0.211114i	$0.932291\pi$
$720$	−2.19565	+	3.02205i	−0.0818271	+	0.112625i
$721$	−14.1809	+	19.5183i	−0.528123	+	0.726898i
$722$	−20.4564	−	6.64668i	−0.761307	−	0.247364i
$723$	27.3892	−	8.89929i	1.01862	−	0.330968i
$724$	10.4888	−	7.62053i	0.389812	−	0.283215i
$725$	−16.0517			−0.596146
$726$	−8.50437	−	9.10556i	−0.315627	−	0.337939i
$727$	−42.5893			−1.57955			−0.789776	−	0.613396i	$-0.789803\pi$
$727$	−42.5893			−1.57955			−0.789776	+	0.613396i	$0.789803\pi$
$728$	−7.90422	−	18.2696i	−0.292950	−	0.677117i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−3.34573	−	1.08710i	−0.123831	−	0.0402352i
$731$	36.9243	+	26.8271i	1.36570	+	0.992236i
$732$	−4.23933	−	3.08005i	−0.156690	−	0.113842i
$733$	23.2305	+	7.54805i	0.858038	+	0.278794i	0.704809	−	0.709397i	$-0.251033\pi$
$733$	23.2305	+	7.54805i	0.858038	+	0.278794i	0.153229	+	0.988191i	$0.451033\pi$
$734$	19.5138	−	6.34041i	0.720266	−	0.234029i
$735$	−4.04703	−	5.57025i	−0.149277	−	0.205462i
$736$			20.3729i			0.750955i
$737$	−2.88388	+	2.37918i	−0.106229	+	0.0876383i
$738$	12.9263			0.475824
$739$	6.55266	+	9.01897i	0.241044	+	0.331768i	0.912349	−	0.409412i	$-0.134266\pi$
$739$	6.55266	+	9.01897i	0.241044	+	0.331768i	−0.671306	+	0.741180i	$0.734266\pi$
$740$	−2.07139	−	6.37507i	−0.0761456	−	0.234352i
$741$	−0.185843	+	0.314186i	−0.00682713	+	0.0115419i
$742$	−16.3398	−	11.8716i	−0.599854	−	0.435820i
$743$	20.7227	−	28.5224i	0.760244	−	1.04639i	−0.236950	−	0.971522i	$-0.576148\pi$
$743$	20.7227	−	28.5224i	0.760244	−	1.04639i	0.997194	−	0.0748639i	$-0.0238522\pi$
$744$	−1.11383	+	3.42803i	−0.0408351	+	0.125678i
$745$	5.94293	+	18.2905i	0.217732	+	0.670111i
$746$	5.44232	+	7.49071i	0.199257	+	0.274254i
$747$			14.8807i			0.544457i
$748$	−14.6856	−	3.79184i	−0.536959	−	0.138643i
$749$		−	28.9626i		−	1.05827i
$750$	−11.1533	+	8.10335i	−0.407261	+	0.295893i
$751$	1.59474	+	4.90811i	0.0581929	+	0.179099i	0.975928	−	0.218094i	$-0.0699841\pi$
$751$	1.59474	+	4.90811i	0.0581929	+	0.179099i	−0.917735	+	0.397194i	$0.869984\pi$
$752$	−5.73609	−	1.86377i	−0.209174	−	0.0679646i
$753$	5.82796	+	4.23426i	0.212383	+	0.154305i
$754$	25.7229	+	29.1816i	0.936771	+	1.06273i
$755$	−7.92553	+	24.3923i	−0.288440	+	0.887726i
$756$	−1.22342	+	0.397514i	−0.0444954	+	0.0144574i
$757$	10.1795	−	7.39583i	0.369980	−	0.268806i	−0.387223	−	0.921986i	$-0.626566\pi$
$757$	10.1795	−	7.39583i	0.369980	−	0.268806i	0.757203	+	0.653180i	$0.226566\pi$
$758$	−40.7783			−1.48114
$759$	−9.47040	+	14.8784i	−0.343754	+	0.540051i
$760$			0.567278i			0.0205773i
$761$	18.2652	+	25.1399i	0.662114	+	0.911322i	0.999549	−	0.0300271i	$-0.00955936\pi$
$761$	18.2652	+	25.1399i	0.662114	+	0.911322i	−0.337435	+	0.941349i	$0.609559\pi$
$762$	5.61403	−	1.82411i	0.203375	−	0.0660804i
$763$	4.30903	−	13.2618i	0.155997	−	0.480110i
$764$	−1.95376	−	1.41949i	−0.0706847	−	0.0513554i
$765$	−6.82501	+	9.39382i	−0.246759	+	0.339634i
$766$	−1.81927	+	5.59914i	−0.0657330	+	0.202305i
$767$	−0.673909	−	7.13536i	−0.0243334	−	0.257643i
$768$	11.9192	−	8.65979i	0.430096	−	0.312483i
$769$		−	23.8874i		−	0.861401i	−0.902495	−	0.430700i	$-0.858267\pi$
$769$		−	23.8874i		−	0.861401i	0.902495	−	0.430700i	$-0.141733\pi$
$770$	−4.50142	−	11.4144i	−0.162220	−	0.411348i
$771$	18.3126			0.659513
$772$	0.0591801	+	0.0814544i	0.00212994	+	0.00293161i
$773$	−17.5526	+	5.70317i	−0.631321	+	0.205129i	−0.607160	−	0.794579i	$-0.707691\pi$
$773$	−17.5526	+	5.70317i	−0.631321	+	0.205129i	−0.0241610	+	0.999708i	$0.507691\pi$
$774$	−7.70921	−	2.50488i	−0.277102	−	0.0900359i
$775$	−1.16011	+	1.59675i	−0.0416723	+	0.0573570i
$776$	−23.6320	−	17.1697i	−0.848341	−	0.616356i
$777$	−2.84635	+	8.76015i	−0.102112	+	0.314269i
$778$	37.7021	−	12.2502i	1.35169	−	0.439189i
$779$	0.934743	−	0.679131i	0.0334907	−	0.0243324i
$780$	−4.59371	−	1.02721i	−0.164481	−	0.0367798i
$781$	−2.67503	+	0.164660i	−0.0957200	+	0.00589199i
$782$		−	38.4131i		−	1.37365i
$783$	7.70612	−	5.59882i	0.275394	−	0.200086i
$784$	−2.39763	−	7.37916i	−0.0856298	−	0.263541i
$785$	10.9598	+	3.56106i	0.391172	+	0.127100i
$786$	3.85190	−	5.30168i	0.137393	−	0.189105i
$787$	−4.50803	+	6.20478i	−0.160694	+	0.221176i	−0.881770	−	0.471680i	$-0.843648\pi$
$787$	−4.50803	+	6.20478i	−0.160694	+	0.221176i	0.721076	+	0.692856i	$0.243648\pi$
$788$	−11.6906	−	3.79851i	−0.416461	−	0.135316i
$789$	2.80982	+	8.64773i	0.100032	+	0.307867i
$790$	28.4596	−	20.6771i	1.01255	−	0.735659i
$791$		−	11.2462i		−	0.399867i
$792$	10.1877	−	0.627101i	0.362005	−	0.0222830i
$793$	−5.74981	+	25.7134i	−0.204182	+	0.913111i
$794$	−15.3486	+	11.1514i	−0.544702	+	0.395749i
$795$	−17.2112	+	5.59225i	−0.610417	+	0.198337i
$796$	3.16879	−	9.75252i	0.112315	−	0.345669i
$797$	−33.6108	−	24.4197i	−1.19056	−	0.864990i	−0.197233	−	0.980357i	$-0.563196\pi$
$797$	−33.6108	−	24.4197i	−1.19056	−	0.864990i	−0.993323	+	0.115367i	$0.963196\pi$
$798$	0.120920	−	0.166432i	0.00428052	−	0.00589163i
$799$	−17.8302	−	5.79338i	−0.630786	−	0.204955i
$800$	6.14017	−	1.99506i	0.217088	−	0.0705361i
$801$	−9.45356	−	13.0117i	−0.334025	−	0.459746i
$802$	−6.04858			−0.213583
$803$	2.07565	+	5.26331i	0.0732480	+	0.185738i
$804$		−	0.808298i		−	0.0285065i
$805$	−14.0515	+	10.2090i	−0.495252	+	0.359821i
$806$	4.76192	−	0.449746i	0.167731	−	0.0158416i
$807$	−3.28796	+	10.1193i	−0.115742	+	0.356217i
$808$	3.66731	−	5.04762i	0.129016	−	0.177575i
$809$	26.0733	+	18.9434i	0.916688	+	0.666013i	0.942697	−	0.333649i	$-0.108280\pi$
$809$	26.0733	+	18.9434i	0.916688	+	0.666013i	−0.0260092	+	0.999662i	$0.508280\pi$
$810$	0.637259	−	1.96128i	0.0223910	−	0.0689124i
$811$	−19.6866	+	6.39655i	−0.691289	+	0.224613i	−0.633531	−	0.773717i	$-0.718395\pi$
$811$	−19.6866	+	6.39655i	−0.691289	+	0.224613i	−0.0577578	+	0.998331i	$0.518395\pi$
$812$	7.20222	+	9.91301i	0.252748	+	0.347878i
$813$			29.9755i			1.05129i
$814$	10.3572	−	16.2715i	0.363019	−	0.570316i
$815$	−2.17500			−0.0761869
$816$	−10.5859	+	7.69107i	−0.370579	+	0.269241i
$817$	−0.689081	+	0.223896i	−0.0241079	+	0.00783313i
$818$	−2.76138	+	8.49867i	−0.0965496	+	0.297149i
$819$	4.27712	+	4.85223i	0.149455	+	0.169551i
$820$	12.0536	+	8.75744i	0.420930	+	0.305823i
$821$	8.99272	+	2.92191i	0.313848	+	0.101975i	0.461705	−	0.887033i	$-0.347238\pi$
$821$	8.99272	+	2.92191i	0.313848	+	0.101975i	−0.147857	+	0.989009i	$0.547238\pi$
$822$	−4.03884	−	12.4303i	−0.140871	−	0.433555i
$823$	−11.9524	+	8.68396i	−0.416636	+	0.302704i	−0.776283	−	0.630385i	$-0.782897\pi$
$823$	−11.9524	+	8.68396i	−0.416636	+	0.302704i	0.359647	+	0.933088i	$0.382897\pi$
$824$			41.3878i			1.44181i
$825$	5.41159	+	1.39728i	0.188408	+	0.0486470i
$826$			4.03914i			0.140540i
$827$	−2.55662	−	3.51889i	−0.0889024	−	0.122364i	0.762249	−	0.647284i	$-0.224095\pi$
$827$	−2.55662	−	3.51889i	−0.0889024	−	0.122364i	−0.851151	+	0.524920i	$0.824095\pi$
$828$	−1.17831	−	3.62647i	−0.0409492	−	0.126029i
$829$	−4.96738	+	15.2880i	−0.172524	+	0.530976i	−0.999512	−	0.0312450i	$-0.990053\pi$
$829$	−4.96738	+	15.2880i	−0.172524	+	0.530976i	0.826987	+	0.562221i	$0.190053\pi$
$830$	18.0375	−	24.8265i	0.626091	−	0.861741i
$831$	−9.60123	−	6.97570i	−0.333063	−	0.241985i
$832$	−26.2007	−	15.4979i	−0.908345	−	0.537293i
$833$	−7.45286	−	22.9375i	−0.258226	−	0.794739i
$834$	5.44257	+	7.49105i	0.188461	+	0.259394i
$835$	17.9667			0.621764
$836$	0.185730	−	0.153226i	0.00642360	−	0.00529942i
$837$		−	1.17121i		−	0.0404830i
$838$	−7.52269	−	10.3541i	−0.259867	−	0.357676i
$839$	−8.52167	+	2.76886i	−0.294201	+	0.0955916i	−0.452399	−	0.891816i	$-0.649432\pi$
$839$	−8.52167	+	2.76886i	−0.294201	+	0.0955916i	0.158198	+	0.987407i	$0.449432\pi$
$840$	9.55989	+	3.10620i	0.329848	+	0.107174i
$841$	−49.9415	−	36.2846i	−1.72212	−	1.25119i
$842$	−15.4420	−	11.2193i	−0.532166	−	0.386641i
$843$	17.6741	+	5.74267i	0.608729	+	0.197788i
$844$	−3.22494	−	9.92534i	−0.111007	−	0.341644i
$845$	4.43131	+	23.2502i	0.152442	+	0.799830i
$846$	3.32965			0.114476
$847$	−9.55356	+	17.2669i	−0.328264	+	0.593296i
$848$	−20.3933			−0.700309
$849$	−9.28489	+	6.74587i	−0.318657	+	0.231518i
$850$	−11.5773	+	3.76169i	−0.397098	+	0.129025i
$851$	−25.9669	−	8.43715i	−0.890133	−	0.289222i
$852$	0.340587	−	0.468777i	0.0116683	−	0.0160601i
$853$	−20.3324	+	27.9851i	−0.696168	+	0.958193i	0.303817	+	0.952730i	$0.401739\pi$
$853$	−20.3324	+	27.9851i	−0.696168	+	0.958193i	−0.999985	+	0.00546283i	$0.998261\pi$
$854$	4.58862	−	14.1223i	0.157019	−	0.483256i
$855$	−0.0569608	−	0.175307i	−0.00194802	−	0.00599538i
$856$	−29.2042	−	40.1961i	−0.998179	−	1.37388i
$857$	41.3458			1.41235			0.706174	−	0.708039i	$-0.250420\pi$
$857$	41.3458			1.41235			0.706174	+	0.708039i	$0.250420\pi$
$858$	−6.13185	−	12.0773i	−0.209338	−	0.412311i
$859$	6.17660			0.210743			0.105371	−	0.994433i	$-0.466397\pi$
$859$	6.17660			0.210743			0.105371	+	0.994433i	$0.466397\pi$
$860$	−5.49169	−	7.55867i	−0.187265	−	0.257748i
$861$	−6.32656	−	19.4712i	−0.215609	−	0.663575i
$862$	−12.3187	+	37.9132i	−0.419578	+	1.29133i
$863$	−25.9115	+	35.6641i	−0.882037	+	1.21402i	0.0938159	+	0.995590i	$0.470093\pi$
$863$	−25.9115	+	35.6641i	−0.882037	+	1.21402i	−0.975853	+	0.218430i	$0.929907\pi$
$864$	−2.25190	+	3.09948i	−0.0766112	+	0.105446i
$865$	38.8876	+	12.6353i	1.32222	+	0.429615i
$866$	14.4162	−	4.68410i	0.489882	−	0.159172i
$867$	−19.1520	+	13.9147i	−0.650436	+	0.472570i
$868$	1.50663			0.0511382
$869$	−54.7797	−	14.1442i	−1.85827	−	0.479808i
$870$	−19.6432			−0.665966
$871$	−3.73017	+	1.61383i	−0.126392	+	0.0546826i
$872$	−7.39210	−	22.7506i	−0.250328	−	0.770431i
$873$	9.02708	+	2.93308i	0.305520	+	0.0992696i
$874$	0.493339	+	0.358432i	0.0166874	+	0.0121241i
$875$	17.6650	+	12.8344i	0.597187	+	0.433882i
$876$	−1.16336	−	0.377999i	−0.0393063	−	0.0127714i
$877$	3.18927	−	1.03626i	0.107694	−	0.0349919i	−0.254674	−	0.967027i	$-0.581968\pi$
$877$	3.18927	−	1.03626i	0.107694	−	0.0349919i	0.362368	+	0.932035i	$0.381968\pi$
$878$	3.93606	+	5.41753i	0.132836	+	0.182833i
$879$			5.27172i			0.177811i
$880$	−10.4515	−	6.65260i	−0.352320	−	0.224259i
$881$	15.3727			0.517920			0.258960	−	0.965888i	$-0.416620\pi$
$881$	15.3727			0.517920			0.258960	+	0.965888i	$0.416620\pi$
$882$	2.51772	+	3.46535i	0.0847762	+	0.116684i
$883$	−11.9897	−	36.9004i	−0.403484	−	1.24180i	−0.922154	−	0.386822i	$-0.873573\pi$
$883$	−11.9897	−	36.9004i	−0.403484	−	1.24180i	0.518670	−	0.854974i	$-0.326427\pi$
$884$	−14.1917	−	8.39449i	−0.477318	−	0.282337i
$885$	2.92793	+	2.12727i	0.0984214	+	0.0715073i
$886$	−19.9242	+	27.4233i	−0.669366	+	0.921303i
$887$	−0.00161885	+	0.00498232i	−5.43557e−5	+	0.000167290i	−0.951084	−	0.308933i	$-0.900028\pi$
$887$	−0.00161885	+	0.00498232i	−5.43557e−5	+	0.000167290i	0.951029	+	0.309101i	$0.100028\pi$
$888$	4.88288	+	15.0280i	0.163859	+	0.504306i
$889$	−5.49538	−	7.56373i	−0.184309	−	0.253680i
$890$			33.1673i			1.11177i
$891$	−3.08537	+	1.21675i	−0.103364	+	0.0407627i
$892$			15.6638i			0.524464i
$893$	0.240778	−	0.174935i	0.00805731	−	0.00585398i
$894$	−3.69720	−	11.3788i	−0.123653	−	0.380564i
$895$	−10.5443	−	3.42605i	−0.352457	−	0.114520i
$896$	2.75845	+	2.00413i	0.0921535	+	0.0669534i
$897$	−14.3830	+	12.6783i	−0.480235	+	0.423315i
$898$	1.55472	−	4.78493i	0.0518816	−	0.159675i
$899$	−10.6101	+	3.44744i	−0.353867	+	0.114978i
$900$	−0.977591	+	0.710262i	−0.0325864	+	0.0236754i
$901$	−63.3910			−2.11186
$902$	2.63396	+	42.7907i	0.0877013	+	1.42478i
$903$			12.8385i			0.427239i
$904$	−11.3400	−	15.6081i	−0.377162	−	0.519119i
$905$	31.3074	−	10.1724i	1.04069	−	0.338142i
$906$	4.93061	−	15.1749i	0.163809	−	0.504151i
$907$	0.388457	+	0.282231i	0.0128985	+	0.00937132i	0.594216	−	0.804306i	$-0.297462\pi$
$907$	0.388457	+	0.282231i	0.0128985	+	0.00937132i	−0.581317	+	0.813677i	$0.697462\pi$
$908$	−2.33776	+	3.21764i	−0.0775812	+	0.106781i
$909$	−0.626483	+	1.92812i	−0.0207791	+	0.0639516i
$910$	−1.25423	−	13.2798i	−0.0415772	−	0.440220i
$911$	−31.3534	+	22.7796i	−1.03878	+	0.754720i	−0.970048	−	0.242914i	$-0.921897\pi$
$911$	−31.3534	+	22.7796i	−1.03878	+	0.754720i	−0.0687359	+	0.997635i	$0.521897\pi$
$912$		−	0.207719i		−	0.00687828i
$913$	−49.2606	+	3.03221i	−1.63029	+	0.100351i
$914$	−2.29995			−0.0760756
$915$	−7.82047	−	10.7640i	−0.258537	−	0.355845i
$916$	10.6460	−	3.45909i	0.351754	−	0.114292i
$917$	−9.87126	−	3.20737i	−0.325978	−	0.105917i
$918$	4.24596	−	5.84406i	0.140138	−	0.192883i
$919$	37.0385	+	26.9101i	1.22179	+	0.887681i	0.996247	−	0.0865527i	$-0.0275851\pi$
$919$	37.0385	+	26.9101i	1.22179	+	0.887681i	0.225541	+	0.974234i	$0.427585\pi$
$920$	−9.20741	+	28.3375i	−0.303559	+	0.934259i
$921$	−8.44936	+	2.74536i	−0.278416	+	0.0904628i
$922$	17.0121	−	12.3600i	0.560264	−	0.407056i
$923$	−2.84334	−	0.635804i	−0.0935898	−	0.0209277i
$924$	−1.56521	−	3.96896i	−0.0514915	−	0.130569i
$925$			8.65237i			0.284488i
$926$	11.7510	−	8.53763i	0.386163	−	0.280564i
$927$	−4.15578	−	12.7902i	−0.136494	−	0.420084i
$928$	34.7068	+	11.2769i	1.13931	+	0.370184i
$929$	−15.4737	+	21.2977i	−0.507674	+	0.698754i	−0.983525	−	0.180772i	$-0.942140\pi$
$929$	−15.4737	+	21.2977i	−0.507674	+	0.698754i	0.475851	+	0.879526i	$0.342140\pi$
$930$	−1.41967	+	1.95401i	−0.0465529	+	0.0640745i
$931$	0.364130	+	0.118313i	0.0119339	+	0.00387755i
$932$	−1.26893	−	3.90536i	−0.0415651	−	0.127924i
$933$	15.5431	−	11.2927i	0.508859	−	0.369707i
$934$			7.87774i			0.257767i
$935$	−32.4876	−	20.6791i	−1.06246	−	0.676279i
$936$	10.8288	+	2.42143i	0.353949	+	0.0791471i
$937$	−25.0177	+	18.1765i	−0.817294	+	0.593799i	−0.915936	−	0.401324i	$-0.868550\pi$
$937$	−25.0177	+	18.1765i	−0.817294	+	0.593799i	0.0986422	+	0.995123i	$0.468550\pi$
$938$	2.17840	−	0.707806i	0.0711274	−	0.0231107i
$939$	−3.22757	+	9.93344i	−0.105328	+	0.324166i
$940$	3.10484	+	2.25580i	0.101269	+	0.0735761i
$941$	5.74800	−	7.91144i	0.187379	−	0.257906i	−0.704984	−	0.709223i	$-0.749046\pi$
$941$	5.74800	−	7.91144i	0.187379	−	0.257906i	0.892363	+	0.451318i	$0.149046\pi$
$942$	−6.81829	−	2.21540i	−0.222152	−	0.0721815i
$943$	57.7165	−	18.7532i	1.87951	−	0.610689i
$944$	2.39721	+	3.29947i	0.0780224	+	0.107389i
$945$	−3.26621			−0.106250
$946$	6.72115	−	26.0307i	0.218523	−	0.846330i
$947$		−	57.1340i		−	1.85661i	−0.371824	−	0.928303i	$-0.621268\pi$
$947$		−	57.1340i		−	1.85661i	0.371824	−	0.928303i	$-0.378732\pi$
$948$	9.89582	−	7.18973i	0.321401	−	0.233512i
$949$	0.578336	+	6.12343i	0.0187736	+	0.198775i
$950$	0.0597162	−	0.183787i	0.00193745	−	0.00596285i
$951$	3.74404	−	5.15323i	0.121409	−	0.167105i
$952$	28.4858	+	20.6961i	0.923229	+	0.670765i
$953$	2.41887	−	7.44451i	0.0783548	−	0.241151i	−0.904205	−	0.427099i	$-0.859536\pi$
$953$	2.41887	−	7.44451i	0.0783548	−	0.241151i	0.982560	+	0.185948i	$0.0595355\pi$
$954$	10.7074	−	3.47903i	0.346664	−	0.112638i
$955$	−3.60419	−	4.96074i	−0.116629	−	0.160526i
$956$			12.1184i			0.391939i
$957$	20.1044	+	24.3692i	0.649882	+	0.787743i
$958$	9.66767			0.312348
$959$	−16.7472	+	12.1676i	−0.540795	+	0.392911i
$960$	14.6193	−	4.75009i	0.471835	−	0.153308i
$961$	9.15564	−	28.1782i	0.295343	−	0.908973i
$962$	15.7298	−	13.8654i	0.507149	−	0.447039i
$963$	13.0612	+	9.48949i	0.420890	+	0.305795i
$964$	−19.6397	−	6.38134i	−0.632553	−	0.205529i
$965$	0.0789975	+	0.243129i	0.00254302	+	0.00782661i
$966$	8.74170	−	6.35122i	0.281260	−	0.204347i
$967$			22.3889i			0.719977i	0.932957	+	0.359989i	$0.117219\pi$
$967$			22.3889i			0.719977i	−0.932957	+	0.359989i	$0.882781\pi$
$968$	4.15186	+	33.5973i	0.133446	+	1.07986i
$969$		−	0.645680i		−	0.0207422i
$970$	−11.5052	−	15.8355i	−0.369409	−	0.508448i
$971$	−3.11643	−	9.59139i	−0.100011	−	0.307802i	0.888516	−	0.458845i	$-0.151737\pi$
$971$	−3.11643	−	9.59139i	−0.100011	−	0.307802i	−0.988527	+	0.151043i	$0.951737\pi$
$972$	0.221584	−	0.681966i	0.00710731	−	0.0218741i
$973$	8.62014	−	11.8646i	0.276349	−	0.380362i
$974$	−11.8789	−	8.63052i	−0.380624	−	0.276540i
$975$	5.22959	+	3.09334i	0.167481	+	0.0990662i
$976$	−4.63319	−	14.2595i	−0.148305	−	0.456435i
$977$	−1.14871	−	1.58106i	−0.0367505	−	0.0505827i	0.790246	−	0.612789i	$-0.209953\pi$
$977$	−1.14871	−	1.58106i	−0.0367505	−	0.0505827i	−0.826997	+	0.562207i	$0.809953\pi$
$978$	1.35310			0.0432675
$979$	41.1471	−	33.9460i	1.31507	−	1.08492i
$980$			4.93712i			0.157710i
$981$	4.56880	+	6.28841i	0.145870	+	0.200773i
$982$	46.7841	−	15.2011i	1.49294	−	0.485086i
$983$	−28.4100	−	9.23098i	−0.906139	−	0.294422i	−0.181371	−	0.983415i	$-0.558053\pi$
$983$	−28.4100	−	9.23098i	−0.906139	−	0.294422i	−0.724769	+	0.688992i	$0.758053\pi$
$984$	−28.4140	−	20.6440i	−0.905804	−	0.658105i
$985$	−25.2501	−	18.3453i	−0.804535	−	0.584529i
$986$	−65.4397	−	21.2627i	−2.08403	−	0.677141i
$987$	−1.62964	−	5.01551i	−0.0518720	−	0.159645i
$988$	0.240233	−	0.103935i	0.00764283	−	0.00330662i
$989$	−38.0560			−1.21011
$990$	6.62240	+	1.70991i	0.210474	+	0.0543445i
$991$	−40.0562			−1.27243			−0.636214	−	0.771513i	$-0.719500\pi$
$991$	−40.0562			−1.27243			−0.636214	+	0.771513i	$0.719500\pi$
$992$	3.63015	−	2.63746i	0.115257	−	0.0837393i
$993$	20.6624	−	6.71361i	0.655701	−	0.213050i
$994$	1.56162	+	0.507402i	0.0495316	+	0.0160938i
$995$	15.3040	−	21.0641i	0.485168	−	0.667776i
$996$	6.27190	−	8.63253i	0.198733	−	0.273532i
$997$	−3.15309	+	9.70422i	−0.0998595	+	0.307336i	−0.988490	−	0.151289i	$-0.951658\pi$
$997$	−3.15309	+	9.70422i	−0.0998595	+	0.307336i	0.888630	+	0.458625i	$0.151658\pi$
$998$	−4.26509	−	13.1266i	−0.135009	−	0.415515i
$999$	−3.01794	−	4.15384i	−0.0954833	−	0.131422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bb.a.25.9	yes	56
11.4	even	5	inner	429.2.bb.a.103.6	yes	56
13.12	even	2	inner	429.2.bb.a.25.6	✓	56
143.103	even	10	inner	429.2.bb.a.103.9	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bb.a.25.6	✓	56	13.12	even	2	inner
429.2.bb.a.25.9	yes	56	1.1	even	1	trivial
429.2.bb.a.103.6	yes	56	11.4	even	5	inner
429.2.bb.a.103.9	yes	56	143.103	even	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.665766 + 0.916348i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.221584 - 0.681966i) q^{4} +(1.07016 - 1.47295i) q^{5} +(-0.665766 + 0.916348i) q^{6} +(1.70616 + 0.554365i) q^{7} +(2.92691 - 0.951009i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.665766 + 0.916348i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.221584 - 0.681966i) q^{4} +(1.07016 - 1.47295i) q^{5} +(-0.665766 + 0.916348i) q^{6} +(1.70616 + 0.554365i) q^{7} +(2.92691 - 0.951009i) q^{8} +(-0.809017 + 0.587785i) q^{9} +2.06221 q^{10} +(-2.11063 - 2.55837i) q^{11} +0.717061 q^{12} +(-1.43167 - 3.30913i) q^{13} +(0.627912 + 1.93251i) q^{14} +(1.73156 + 0.562617i) q^{15} +(1.65986 + 1.20596i) q^{16} +(5.15955 + 3.74863i) q^{17} +(-1.07723 - 0.350014i) q^{18} +(-0.0962874 + 0.0312857i) q^{19} +(-0.767371 - 1.05620i) q^{20} +1.79396i q^{21} +(0.939167 - 3.63735i) q^{22} -5.31768 q^{23} +(1.80893 + 2.48977i) q^{24} +(0.520746 + 1.60269i) q^{25} +(2.07916 - 3.51501i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.756116 - 1.04070i) q^{28} +(-2.94348 + 9.05909i) q^{29} +(0.637259 + 1.96128i) q^{30} +(0.688421 + 0.947531i) q^{31} -3.83116i q^{32} +(1.78093 - 2.79791i) q^{33} +7.22366i q^{34} +(2.64242 - 1.91983i) q^{35} +(0.221584 + 0.681966i) q^{36} +(4.88313 + 1.58662i) q^{37} +(-0.0927734 - 0.0674038i) q^{38} +(2.70476 - 2.38418i) q^{39} +(1.73147 - 5.32892i) q^{40} +(-10.8537 + 3.52658i) q^{41} +(-1.64390 + 1.19436i) q^{42} +7.15650 q^{43} +(-2.21240 + 0.872485i) q^{44} +1.82067i q^{45} +(-3.54033 - 4.87284i) q^{46} +(-2.79577 + 0.908401i) q^{47} +(-0.634010 + 1.95128i) q^{48} +(-3.05946 - 2.22282i) q^{49} +(-1.12193 + 1.54420i) q^{50} +(-1.97077 + 6.06541i) q^{51} +(-2.57395 + 0.243100i) q^{52} +(-8.04139 + 5.84241i) q^{53} -1.13267i q^{54} +(-6.02706 + 0.370993i) q^{55} +5.52098 q^{56} +(-0.0595089 - 0.0819069i) q^{57} +(-10.2609 + 3.33398i) q^{58} +(1.89051 + 0.614264i) q^{59} +(0.767371 - 1.05620i) q^{60} +(-5.91209 - 4.29539i) q^{61} +(-0.409941 + 1.26167i) q^{62} +(-1.70616 + 0.554365i) q^{63} +(6.83040 - 4.96258i) q^{64} +(-6.40630 - 1.43252i) q^{65} +(3.74954 - 0.230801i) q^{66} -1.12724i q^{67} +(3.69971 - 2.68800i) q^{68} +(-1.64325 - 5.05741i) q^{69} +(3.51847 + 1.14322i) q^{70} +(0.474976 - 0.653748i) q^{71} +(-1.80893 + 2.48977i) q^{72} +(-1.62240 - 0.527150i) q^{73} +(1.79712 + 5.53097i) q^{74} +(-1.36333 + 0.990518i) q^{75} +0.0725971i q^{76} +(-2.18281 - 5.53504i) q^{77} +(3.98547 + 0.891196i) q^{78} +(13.8005 - 10.0267i) q^{79} +(3.55264 - 1.15432i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-10.4576 - 7.59790i) q^{82} +(8.74667 - 12.0388i) q^{83} +(1.22342 + 0.397514i) q^{84} +(11.0431 - 3.58812i) q^{85} +(4.76456 + 6.55785i) q^{86} -9.52529 q^{87} +(-8.61065 - 5.48086i) q^{88} +16.0834i q^{89} +(-1.66837 + 1.21214i) q^{90} +(-0.608194 - 6.43957i) q^{91} +(-1.17831 + 3.62647i) q^{92} +(-0.688421 + 0.947531i) q^{93} +(-2.69374 - 1.95712i) q^{94} +(-0.0569608 + 0.175307i) q^{95} +(3.64365 - 1.18389i) q^{96} +(-5.57904 - 7.67890i) q^{97} -4.28341i q^{98} +(3.21131 + 0.829163i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9}+O(q^{10}) \) 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9	\( 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9} + 40 q^{10} - 52 q^{12} + 5 q^{13} - 6 q^{14} + 16 q^{16} - 14 q^{17} - 36 q^{22} + 28 q^{23} + 36 q^{25} + 6 q^{26} - 14 q^{27} + 34 q^{29} - 10 q^{30} + 18 q^{35} + 8 q^{36} - 18 q^{38} + 5 q^{39} + 40 q^{40} - 6 q^{42} + 48 q^{43} - 14 q^{48} - 14 q^{49} - 4 q^{51} + 11 q^{52} + 10 q^{53} + 8 q^{55} - 68 q^{56} + 10 q^{61} - 132 q^{62} - 52 q^{64} - 42 q^{65} + 14 q^{66} + 50 q^{68} - 2 q^{69} + 10 q^{74} + 6 q^{75} - 88 q^{77} + 26 q^{78} + 48 q^{79} - 14 q^{81} - 30 q^{82} - 36 q^{87} - 10 q^{88} - 10 q^{90} - 11 q^{91} - 126 q^{92} - 34 q^{94} + 36 q^{95}+O(q^{100}) \) 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9 + 40 * q^10 - 52 * q^12 + 5 * q^13 - 6 * q^14 + 16 * q^16 - 14 * q^17 - 36 * q^22 + 28 * q^23 + 36 * q^25 + 6 * q^26 - 14 * q^27 + 34 * q^29 - 10 * q^30 + 18 * q^35 + 8 * q^36 - 18 * q^38 + 5 * q^39 + 40 * q^40 - 6 * q^42 + 48 * q^43 - 14 * q^48 - 14 * q^49 - 4 * q^51 + 11 * q^52 + 10 * q^53 + 8 * q^55 - 68 * q^56 + 10 * q^61 - 132 * q^62 - 52 * q^64 - 42 * q^65 + 14 * q^66 + 50 * q^68 - 2 * q^69 + 10 * q^74 + 6 * q^75 - 88 * q^77 + 26 * q^78 + 48 * q^79 - 14 * q^81 - 30 * q^82 - 36 * q^87 - 10 * q^88 - 10 * q^90 - 11 * q^91 - 126 * q^92 - 34 * q^94 + 36 * q^95

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